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Full text of "Elements of surveying and navigation : with a description of the instruments and the necessary tables"

LIBRARY 



^NSSACfft;^^^ 




1895 



ELEMENTS 



OF 



SURVEYING, 



NAVIGATION; 

WITH A DESCRIPTION OF THE INSTRIFMENTS AND 
THE NECESSARY TABLES. 



BY CHARf.ES DAVIES, LL.D. 

AOTUOROF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRACTICAL 
GEOMETRY, ELEMENTS OF SURVEYING, ELEMENTS OF DESCRIPTIVB 
GEOMETRY, SHADES SHADOWS AND PERSPECTIVE, ANA- 
LYTICAL GEOMETRY, DIFFERENTIAL AND 
INTEGRAL CALCULUS. 



REVISED EDITION 



NEW YORK: 

PUBLISHED BY A. S. BARNES &. CO. 
No. 51 JOHN STREET. 

1847. 



DAVIES' 

COURSE OF MATHEMATICS. 



DAVIES' FIRST LESSONS IN ARITHMETIC— For Beginners. 

DAVIES' ARITHMETIC— Designed for the use of Academies and Schools. 

KEY TO DAVIES' ARITHMETIC. 

DAVIES' UNIVERSITY ARITHMETIC— Embracing the Science of Num- 
bers and their numerous Applications. 

KEY TO DAVIES' UNIVERSITY ARITHMETIC. 

DAVIES' ELEMENTARY ALGEBRA— Being an introduction to the Sci- 
ence, and forming a connecting luik between Arithmetic and Algebra. 

KEY TO DAVIES' ELEMENTARY ALGEBRA. 

DAVIES' ELEMENTARY GEOMETRY.— This work embraces the ele- 
mentaiy principles of Geometiy. The reasoning is plain and concise, but at the 
same time strictly rigorous. 

DAVIES' ELEMENTS OF DRAWING AND MENSURATION — Ap- 
plied to the Mechanic Arts. 

DAVIES' BOURDON'S ALGEBRA— Including Sturm's Theorem— Being 
an abridgment of the Work of M. Bourdon, with the addition of practical examples. 

DAVIES' LEGENDRE'S GEOMETRY and TRIGONOMETRY— Being 

an abridgment of the work of M. Legendre, with the addition of a Treatise on Men- 
suration OF Planes and Solids, and a Table of Logarithms and Logarithmic 
Sines. 

DAVIES' SURVEYING— With a description and plates of the Theodolite, 
Compass, Plane-Table. and Level; also, Maps of the Topographical Signs 
adopted by the Engineer Department — an explanation of the method of sui-veying 
the Public Lands, and an Elementary Treatise on Navigation. 

DAVIES' ANALYTICAL GEOMETRY — Embracing the Equations of 
THE Point and Straight Line — of the Conic Sections — of the Line and Plane 
IN Space ; also, the discussion of the General Equation of the second degree, and 
of Surfaces of the second order. 

DAVIES' DESCRIPTIVE GEOMETRY— With its application to Spher- 
ical Projections. 

DAVIES' SHADOWS and LINEAR PERSPECTIVE. 

DAVIES' DIFFERENTIAL and INTEGRAL CALCULUS. 



Entered, according to Act of Congress, in the year 1835, by Charles Davies, in the Clerk's 
Office of the District Court of the United States, in and for the Southern District of 
New York. 



28652 






PREFACE 



The Elements of Surveying-, published by the author in 
1830, was designed especially as a text-book for the Military 
Academy, and in its preparation little regard was had to the 
supposed wants of other Institutions. 

It was not the aim of the author to make it so elementary 
as to admit of its introduction into academies and schools, and 
he did not, therefore, anticipate for it an extensive circulation. 

It has been received, however, with more favor than was 
anticipated, and this circumstance has induced the author to 
re-write the entire work. In doing so, he has endeavored to 
make it both plain and practical. 

It has been the intention to begin with the very elements 
of the subject, and to combine those elements in the simplest 
manner, so as to render the higher branches of plane-survey- 
ing comparatively easy. 

All the instruments needed for plotting have been carefully 
described ; and the uses of those required for the measurement 
of angles are fully explained. 

The conventional signs adopted by the Topographical Beau- 
reau, and which are now used by the United States Engineers 
in all their charts and maps, are given in plates 5 and 6. 

Should these signs be generally adopted in the country, it 
would give entire uniformity to all maps and delineations of 
ground, and would establish a kind of language by which 
all the peculiarities of soil and surface could be accurately 
represented. 

An account is also given of the manner of surveying the 
public lands; and although the method is simple, it has, 
nevertheless, been productive of great results, by defining, 
with mathematical precision, the boundaries of lands in the 
new States, and thus settling their titles on an indisputable 
basis. 



MITI i EHPA 



4 PREFACE. 

The method was originated by Col. Jared Mansfield, whose 
great acquirements in science introduced him to the notice 
of President Jefferson, by whom he was appointed surveyor- 
general of the North-Western Territory. 

May it be permitted to one of his pupils, and a graduate of 
the Military Academy, further to add, that at the organization 
of the institution in 1812, he was appointed Professor of Nat- 
ural and Experimental Philosophy. This situation he filled 
for sixteen years, when he withdrew from the academy to 
spend the evening of his life in retirement and study. His 
pupils, who had listened to his instructions with delight, who 
honored his learning and wisdom, and had been brought near 
to him by his kind and simple manners, have placed his por- 
trait in the public library, that the institution might possess 
an enduring memorial of one of its brightest ornaments and 
distinguished benefactors. 

At the solicitation of several distinguished teachers here is 
added, in the present edition, an article on Plane Sailing, most 
of which has been taken, by permission of the author, from an 
excellent work on Trigonometry and its applications by Pro- 
^*~^or Charles Hackley. 

Hartford, 

March, 1841. 



CONTENTS. 



INTRODUCTION 





CHAPTER L 




Of Logarithms, 
Table of Logarithms, 





Page. 
9 


Multiplication by Logarithms, 
Division by Logarithms, 
Arithmetical Complement, 




14 
15 
16 



CHAPTER H. 

Geometrical Definitions, 17 

CHAPTER in. 

Description of Instruments, 21 

Of the Dividers, " . .22 

Ruler and Triangle, 22 

Scale of Equal Parts, . . . . • 23 

Diagonal Scale of Equal Parts, 24 

Scale of Chords : : 25 

Semicircular Protractor, : . . . . 26 

Sectoral Scale of Equal Parts, 27 

Gunter's Scale, 28 

Solution of Problems, 29 

CHAPTER IV. 

Plane Trigonometry, .......... 34 

Table of Logarithmic Sines, 37 

Solution of Right Angled Triangles, .49 



ELEMENTS OF SURVEYING 



CHAPTER L 
Definitions and Introductory Remarks, 



51 



CHAPTER II. 

Of the Measurement and Calculation of Lines and Angles, .... 53 

To Measure a Horizontal Line, 54 

Of the Theodolite, 55 

Heights and Distances, .... ..... 66 

Of Measurements with the Tape or Chain, , . . . . 74 

Surveying Cross, 76 



CONTENTS. 



CHAPTER III 



Of the Content of Ground, 

Of Laying Out and Dividing Land, 



Page. 
79 
89 



CHAPTER IV. 

Surveying with the Compass, 91 

Of the Compass, 92 

Field Notes 96 

Traverse Table, 98 

Of Balancing the Work, 100 

Of the Double Meridian Distances of the Courses, 102 

Of the Area, 104 

First Method of Plotting, 107 

Second Method of Plotting, 107 

Method of Finding the Content of Land by Means of the Table of Natural 

Sines, 120 

Method of Surveying the Public Lands, . . • 126 

Variation of the Needle, 127 

Of the Plain Table, . 133 

CHAPTER V. 

Of Levelling, 137 

Of the Level 140 

Of the Level Staves, 143 

CHAPTER VI. 

Of the Contour of Ground, 148 



CHAPTER VI. 

Of Surveying Harbours, .159 

To fix the Principal Points, . # 159 

Manner of Using the Compass, 163 

Of the Circular Protractor, ......... 165 

First Method of Plotting, 166 

Second Method of Plotting, 167 

Surveying a Harbour for the Purpose of Determining the Depth of Water, &c., 168 



CHAPTER VII. 



Of Navigation, 
Of Plane Sailing, . 
Of Traverse Sailing, 
Parallel Sailing, 
Middle Latitude Sailing, 
Mercator's Sailing, . 
Mercator's Chart, . 



171 
174 
176 
179 
181 
184 
187 



INTRODUCTION. 



CHAPTER I. 

Of Logarithms. 

1. The nature and properties of the logarithms in common 
use, will be readily vuiderstood, by considering attentively the 
different powers of the nmiiber lo. They are, 

10'' = i 
10' = 10 
10* = 100 
10^=1000 
10^ = 10000 
10^ = 100000 

&c. &c. 
It is plain, that the indices or exponents 0, l, 2, 3, 4, 5, &c. 
form an arithmetical series of which the common difference is 
1 ; and that the numbers 1, 10, 100, 1000, 10000, 1 00000, &c. 
form a geometrical series of which the common ratio is 10, 
The number 1 0, is called the base of the system of logarithms ; 
and the indices, 0, 1, 2, 3, 4, 5, &c., are the logarithms of the 
numbers which are produced by raising 10 to the powers de- 
noted by those indices. 

2. Let a denote the base of the system of logarithms, m any 
exponent, and M the corresponding number : we shall then 
have, a'^=M 

in which m is the logarithm of M. 

If we take a second exponent n, and let JST denote the cor- 
responding number, we shall have, 

in which n is the logarithm of JV. 

If now, we multiply .the first of these equations by the 
second, member by member, we have 



8 INTRODUCTION. 

but since a is the base of the system, m+n is the log-arithm 
Mx»N*; hence, 

The sum of the loganthms of any two numbers is equal to the 
logarithm of their product. 

Therefore, the addition of logarithms corresponds to the mul- 
tiplication of their numbers, 

3. If we divide the equations by each other, member by 
member, we have, 

but since a is the base of the system, m—n is the logarithm 
of — hence : 

jsr 

If one number be divided by another, the logarithm of the quo- 
dent will be equal to the logarithm of the dividend diminished by 
that of the divisor. 

Therefore, the subtraction of logarithms corresponds to the di- 
vision of their numbers. 

4. Let us examine further the equations 

10^ = 10 
10« = 100 

io'=iooo 
&c. &c. 
It is plain that the logarithm of 1 is 0, and that the loga- 
rithms of all the numbers between 1 and 10, are greater than 
and less than 1. They are generally expressed by decimal 
fractions : thus, 

log 2=0.301030. 

The logarithms of all numbers greater than 10 and less 
than 100, are greater than 1 and less than 2, and are gen- 
erally expressed by 1 and a decimal fraction : thus, 
log 50 = 1.698970. 

The logarithms of numbers greater than 100 and less than 
1000, are greater than 2 and less than 3, and are generally 
expressed by uniting 2 Avith a decimal fraction ; thus, 
log 126=2.100371. 

The part of the logarithm which stands on the left of the 
decimal point, is called the cluiracterislic of the logarithm. 



OF LOGARITHMS. 9 

The characteristic is always one less than the places of integer 
figures in the number whose logarithm is taken. 

Thus, ill the first case, for numbers between i and 10, 
there is but one place of figures, and the characteristic is 0. 
For numbers between 10 and 100, there are two places of 
figures, and the characteristic is 1 ; and similarly for other 
numbers. 

TABLE OF LOGARITHMS. 

5. A table of logarithms, is a table in which are written 
the logarithms of all numbers between 1 and some other given 
number. The logarithms of all numbers between l and 
10,000 are written in the annexed table. 

6. The first column on the left of each page of the table, 
IS the column of numbers, and is designated by the letter JV; 
the logarithms of these numbers are placed directly opposite 
them, and on the same horizontal line. 

To find, from the table, the logarithm of any number. 

7. If the number is less than 100, look on the first page of 
the table, along the column of numbers under JV, until the 
number is found : the number directly opposite, in the column 
designated log, is the logarithm sought. Thus, 

log 9=0.954243. 

When the number is greater than 100, and less than 10,000. 

8. Since the characteristic of every logarithm is less by 
unity than the places of integer figures in its corresponding 
number (Art. 4), its value is known by a simple inspection 
of the number whose logarithm is sought. Hence, it has not 
been deemed necessary to write the characteristics in the table. 

To obtain the decimal part of the logarithm, find, in the 
column of numbers, the first three figures of the given number. 
Then, pass across the page, along a horizontal line, into the 
columns marked 0, 1, 2, 3, 4, 5, &c., until you come to the 
column which is designated by the fourth figure of the given 
number: at this place there are four figures of the required 
logarithm. To the four figures so found, two figures taken 
from the column marked 0, are to be prefixed. If the four 
figures thus found, stand opposite to a row of six figures in the 
column marked 0, the two figures from this column, which 
are to be prefixed, are the first two on the left hand : but if 



10 INTRODUCTION. 

the four figures found are opposite a line of only four figures, 
you are then to ascend the column till you come to tlie line 
of six figures ; the two figures, at the left hand, are to be 
prefixed, and then the decimal part of the logarithm is ob- 
tained ; to which prefix the characteristic, and you have the 
entire logarithm sought. For example, 

log 1122 = 3.049993 

log 8979===3. 953228 
In several of the columns, designated 0, 1,2, 3, 4, &c., small 
dots are found. When the logarithm falls at such places, 
a cipher must be written for each of the dots, and the two 
figures, from the column 0, which are to be prefixed, are then 
found in the horizontal line directly below. 

Thus, .... 'log 2188 = 3.340047 
the two dots being changed into two ciphers, and the 34 to 
be taken from the column 0, is found in the horizontal line 
directly below. 

The two figures from the column 0, must also be taken from 
the horizontal line below, if any dots shall have been passed 
over, in passing along the horizontal line : thus, 

log 3098 = 3.491081 
the 49 from the column 0, being taken from the line 310. 

When the number exceeds 10,000, or is expressed by Jive or 
more figures. 

9. Consider all the figures, after the fourth from the left 
hand, as ciphers. Find from the table the logarithm of the 
first four figures, and to it prefix a characteristic less by unity 
than all the places of figures in the given number. Take 
from the last column on the right of the page, marked D, the 
number on the same horizontal line with the logarithm, and 
multiply this number by the figures that have been considered 
as ciphers : then cut oflf from the right hand as many places 
for decimals as there are figures in the multiplier, and add the 
product so obtained to the first logarithm, and the sum will be 
the logarithm sought. 

Let it be required, for example, to find the logarithm of 
672887. 

log 672800 = 5.827886 
the characteristic being 5, since there are six places of figures. 
The corresponding number, in the column J9 is 65, which 



OF LOGARITHMS. Jl 

being multiplied by 87, the figures regarded as ciphers, gives 
for a product 5655 ; then pointing off two decimal places, we 
obtain 56.55 for the number to be added. 

Hence . . log 672800 = 5.827880 
Adding .... +56.55 

gives . log 672887=5.827943. 

In adding the proportional number, we omit the decimal 
part ; but when the decimal part exceeds 5 tenths, as in the 
case above, its value is nearer unity than ; in which case, 
we augment by one, the figure on the left of the decimal 
point. 

10. This method of findmg the logarithms of numbers 
which exceed four places of figures, does not give the exact 
logarithm ; for, it supposes that the logarithms are propor- 
tional to their corresponding numbers, which is not rigorously 
true. 

To explain the reason of the above method, let us take the 
logarithm of 672900, a number greater than 672800 by 100. 
We then have, 

log 672900 = 5.827951 
log 672800 = 5.827886 
Difference of numbers 100 6 5 =difrerence of loga- 

rithms. 
Then, 100 : 65 :: 87 : 56.55 

In this proportion the first term 100 is the difference be- 
tween two numbers, one of which is greater and the other 
less than the given number; and the second term 65 is the 
difference of their logarithms, or tabular difference. 

The third term 87 is the difference betAveen the given num- 
ber and the less number 672800; and hence the fourth term 
56.55 is the difference of their logarithms. This difference 
therefore, added to the logarithm of the less nimiber, will give 
that of the greater, nearly. 

Had there been three figures of the given number treated 
as ciphers, the first term would have been 1000 ; had there 
been four, it would have been 10000, &c. Therefore, the 
reason of the rule, for the use of the column of differences, is 
manifest. 

To find the logarithm of a decimal number. 

11. If the given number is composed of a Avhole number 



GMT U^^^'"-^ 



12 iNtnODUCTIOW. 

and a decimal, such as 36.78, it may be put under the form 
»_e_7_8. But since a fraction is equal to the quotient obtained 
by dividing the numerator by the denominator, its logarithm 
will be equal to the logarithm of the numerator minus the 
logarithm of the denominator. Therefore, 

log 3_6_7_«3=log 3678 — log 100 = 3.565612 — 2 = 1.565612 
from which we see, that a mixed number may be treated 
as though it were entire, except in fixing the value of the 
characteristic, which is always one less than the number of the 
integer figures. 

12. The logarithm of a decimal fraction is also readily 
found. For, 

log 0.8=log j\=\og 8 — l = -l+log 8. But, 
log 8=0.903090 
which is positive and less than 1. Therefore, 

log 0.8 = -l+0. 903090 = — 1.903090 
in which, however, the minus sign belongs only to the charade^ 
ristic. Hence it appears, that the logarithm of tenths is the 
same as the logarithm of the corresponding whole number, 
excepting, that the characteristic instead of being 0, is— 1. 

If the fraction were of the form 0.06 it might be written yVo J 
taking the logarithms, we have, 

log -0/-=log 06— 2 = -2+log 06 = — 2.778151 
in which the minus sign, as before, belongs only to the char- 
acteristic. If the decimal were 0.006 its logarithm would be 
the same as before, excepting the characteristic, which would 
be — 3. It is, indeed, evident, that the negative characteristic 
will always be one greater than the number of ciphers be- 
tween the decimal point and the first significant figure. 
Therefore, the logarithm of a decimal fraction is found, by 
considering it as a whole number, and then prefixing to the deci- 
mal part of its logarithm a negative characteristic greater by 
unity than the number of ciphers between the decimal point ana 
Ihe first significant figure. 

That we may not, for a moment, suppose the negative sign 
to belong to the whole logarithm, when in fact it belongs only 
to the characteristic, we place the sign above the characte- 
ristic, thus, 

log 8=1.903090, and log 0.00=2.778151. 







OP 


LOGARITHMS. 










EXAMPLES 


• 






log 2756 . 






is 






. 3.440270 


log 3270 






is 






. 3.514548 


log 287.965 






is 






. 2.459340 


log 1.004 . 






is 






. 0.001734 


log 0.002 . 






is 






. 3.301030 


log 0.000678 






is 






. 4.831230 



13 



To find in the table, the number answering to a given logarithm. 

13. Search in the columns of logarithms for the decimal 
part of the given logarithm, and if it can be exactly found, 
set down the corresponding number. Then, if the character- 
istic of the given logarithm is positive, point off from the left 
of the number found, one more place for whole numbers than 
there are units in the characteristic of the given logarithm, 
and treat the figures to the right as decimals. 

If the characteristic of the given logarithm is 0, there will 
be one place of whole numbers ; if it is — 1, the number will 
be entirely decimal; if it is— 2, there will be one cipher 
between the decimal point and the first significant figure ; 
if it is — 3, there will be two, &c 

The number whose logarithm is 1.492481, is found at page 
5, and is 31.08. 

But when the decimal part of the logarithm cannot be 
exactly found in the table, take the number answering to the 
nearest less logarithm; take also from the table the corres- 
ponding difference in the column D, Then, subtract this 
less logarithm from the given logarithm, and having annexed 
any number of ciphers to the remainder, divide it by the dif- 
ference taken from the column 2?, and annex the quotient to 
the number answering to the less logarithm : this gives the 
required number, nearly. This rule, like that for finding 
the logarithm of a number when the places of figures ex- 
ceed four, supposes the numbers to be proportional to their 
corresponding logarithms. 

1. Find the number answering to the logarithm 1.532708. 
Given logarithm is . . 1.532708 

Next less tabular logarithm is 1.532627 

Their difference is . . 81 



14 INTRODUCTION. 

The number corresponding to the tabular logarithm is 34.09 
And the tabular difference is . • . . 128 : 

and, 128)81.00(63 

The 63 being annexed to the tabular number 34.09 gives 

34.0963 for the number answering to the logarithm 1.532708. 

2. Required the number answering to the logarithm 
3.233568. 

The given logarithm is . . 3.233568 

Next less tabular logarithm of 1712 is 3.233504 
Their difference is ... . 64 

Tabular difference . 253)64.00(25 
Hence the number sought, is 1712.25, marking four places 
for integers since the characteristic is 3. 

MULTIPLICATION BY LOGARITHMS. 

14. When it is required to multiply numbers by means of 
their logarithms, we first find from the table the logarithms 
of the numbers to be multiplied ; we next add these loga- 
rithms together, and their sum is the logarithm of the pro- 
duct of the numbers (Art. 2). 

The term sum is to be understood in its algebraic sense ; 
therefore, if any of the logarithms have negative charac- 
teristics, the difference between their sum and that of the 
positive characteristics, is to be taken, and the sign of the 
greater prefixed. 

EXAMPLES. 

1. Multiply 23.14 by 5.062. 

log 23.14 = 1.364363 
log 5.062=0.704322. 
Product 117.1347 . . . . 2.068685 

2. Multiply 3.902, 597.16 and 0.0314728 together. 

log 3.902 = 0.591287 

log 597.16=2.776091 

log 0.0314728 = 2.497936 

Product 73.3354 .... 1.865314 

Here the 2 cancels the + 2, and the 1 carried from the 
decimal part is set down. 



OF LOGARITHMS. 15 

3. Multiply 3.586, S.1046, 0.8372, and 0.029 4, together. 

log 3.586=0.554610 
log 2.1046 = 0.323170 
log 0.8372 = 1.922829 
log 0.0294 = 2.468347 
Product 0.1857615 . . 1.268956. 
In this example the 2, carried from the decimal part, can- 
cels 2, and there remains T to be set down. 

DIVISION OF NUMBERS BY LOGARITHMS. 

15. When it is required to divide numbers by means of 
their logarithms, we have only to recollect, that the subtrac- 
tion of logarithms corresponds to the division of their num- 
bers (Art. 3). Hence, if we find the logarithm of the divi- 
dend, and from it subtract the logarithm of the divisor, the 
remainder will be the logarithm of the quotient. 

This additional caution may be added. The difference of 
the logarithms, as here used, means the algebraic difference ; 
so that, if the logarithm of the divisor have a negative 
characteristic its sign must be changed to positive, after 
diminishing it by the unit, if any, carried in the subtraction 
from the decimal part of the logarithm. Or, if the charac- 
teristic of the logarithm of the dividend is negative, it must 
be treated as a negative number. 

EXAMPLES. 

1. To divide 24163 by 4567. 

log 24163=4.383151 

log 4567 = 3.659631 

Quotient 5.29078 . . 0.723520. 

2. To divide .0631*4 by .007241 

log 0.06314=2.800305 
log 0.007241=3.859799 
Quotient . . 8.7198 . . 0.940506 
Here, 1 carried from the decimal part to the 3 changes it to 
2, which being taken from §, leaves for the characteristic. 

3. To divide 37.149 by 523.76 

log 37.149 = 1.569947 

log 523.76=2.719133 

Quotient . 0.07092T4 . 2.8508l~4 



I(? INTRODUCTION. 

4. To divide 0.7438 by 12.9476 

log 7438 = 1.871456 

log 12.9476 = 1.112189 
Quotient 0.057447 . . 2.759267 
Here, the l taken from f, gives 2 for a result, as set down. 

ARITHMETICAL COMPLEMENT. 

16. The Arithmetical complement of a logarithm is the num- 
ber which remains after subtracting this logarithm from 10. 
Thus . . 10—9.274687 = 0.725313. 

Hence, 0.725313 is the arithmetical complement 

of 9.274687. 

17 We will now show that, the difference between two logo- 
rithms is truly found, by adding to the first logarithm tfie arith- 
metkal complement of the logarithm to be subtracted^ and then 
diminishing the sum by 10. 

Let a=the first logarithm 

b=the logarithm to be subtracted 
and c = io — 6=the arithmetical complement of b, 

P^ow the difference between the two logarithms will be 
expressed by a—b. 

But, from the equation c = lO — b, we have 
c~10 = — 6 
hence, if we place for— 6 its value, we shall have 

a— b=a-\-c— 10 
which agrees with the enunciation. 

When we wish the arithmetical complement of a logarithm, 
we may write it directly from the table, by subtracting the left 
hand figure from 9, then proceeding to the rights subtract each 
figure from 9 till we reach the last significant figure, which must 
be taken from 10 : this will be the same as taking the logarithm 
from 10. 

EXAMPLES. 

I. From 3.274107 take 2.104729. 
By common method. By arith. comp, 

3.274107 3.274107 

2.1 04729 its ar. comp. 7.895271 

Diff. 1.169378 Sum 1.169378 after 

subtracting 10« 



DEFIMTlONb. 



17 



Hence, to perform division by means of the arithmetical 
complement we have the follov^ring 



RULE. 



To the logarithm of the dividend add the arithmetical comple- 
ment of the logarithm of the divisor: the sum, after subtracting 
10, will be the logarithm of the quotient 



EXAMPLES. 



1. Divide 327.5 by 22.07. 
log 327.5 
log 22.07 ar. comp. 

Quotient . . 14.839 . . 



2.515211 
8.656198 

1.171409 



1.871456 

8.887811 

2.759267 



2. Divide 0.7438 by 12.9476. 

log 0.7438 

log 12.9476 ar. comp. 

Quotient . . 0.057447 . . 

In this example, the sum of the characteristics is 8, 
from which, taking lo, the remainder is 2. 

3. Divide 37.149 by 523.76. 

log 37.149 . . 1.569947 

log 523.76 ar. comp. 7.2808G7 

Quotient . . 0.0709273 . . . 2.850814 



CHAPTER H. 

Definitions. 

1. Geometry is the science which has for its object the 
measurement of extension. 

Extension has three dimensions, length, breadth, height, 
or thickness. 

2. A line is length without breadth, or thickness. 

The extremities of a line are called points : a point, there- 
fore, has neither length, breadth, nor thickness, but position 
oiily. 

2 



18 



INTRODUCTION. 




3. A straight line is the shortest distance from one point to 
another. 

4. Every line which is not straight, or composed of straight 
lines, is a curved line. 

Thus, AB is a straight line ; ACDB is 
a broken line, or one composed of straight A. 
lines ; and AEB is a curved line. 

The Avord line, when used alone, will designate a straight 
line ; and the word curve, a curved line. 

5. A surface is that which has length and breadth, without 
height or thickness. 

6. A plane is a surface, in which, if two points be assumed 
at pleasure, and connected by a straight line, that line will lie 
wholly in the surface. 

7. Every surface, which is not a plane surface, or composed 
of plane surfaces, is a curved surface. 

8. A solid or body is that which has length, breadth, and 
thickness; and therefore combines the three dimensions of 
extension. 

9. When two straight hnes, AB,AC, 
meet each other, their inclination or open- 
ing is called an angle, which is greater or 
less as the lines are more or less inclined 
or opened. The point of intersection A is 
the vertex of the angle, and the lines AB, 
AC, are its sides. 

The angle is sometimes designed simply by the letter at 
the vertex A; sometimes by the three letters BAG, or CAB, 
the letter at the vertex being always placed in the middle. 

Angles, like all other quantities, are susceptible of addition, 
subtraction, multiplication, and division. 

Thus tlie angle DCE is the sum 
of the two angles DCB, BCE ; and 
the angle DCB is the difference of the a 
two angles DCE, BCE. 





DEFINITIONS. 



n 




-!• 



10 When a straight line AB meets 
another straight line CD, so as to make 
the adjacent angles BAG, BAD, equal to 
each other, each of these angles is called a 
right angle; and the line AB is said to be 
perpendicular to CD. 

11. Every angle BAC, less than 
a right angle, is an acute angle; and 
every angle DEF, greater than a 
right angle, is an obtuse angle. 

12. Two lines are said to be parallel, 
when being situated in the same plane, they 
cannot meet, how far soever, either way, — 
both of them be produced 

13. A plane figure is a plane terminated on 
all sides by lines, either straight or curved. 

If the lines are straight, the space they en- 
close is called a rectilineal figure, or polygon, and 
the lines themselves, taken together, form the 
contour, or perimeter of the polygon. 

14. The polygon of three sides, the simplest of all, is called 
a triangle; that of four sides, a quadrilateral ; that of five, 
n pentagon ; that of six, a hexagon ; that of seven, a heptagon; 
that of eight, an octagon; that of nine a nonagon ; that of 
ten, a decagon ; that of twelve, a dodecagon. 







15. An equilateral triangle is one which has its three sides 
equal ; an isosceles triangle, one which has two of its sides 
equal; a scalene triangle, one which has its three sides unequal. 

16. A right-angled triangle is one which 
has a right angle. The side opposite the 
right angle is called the hypothenuse. Thus, 
in the triangle ABC, right-angled at A, 
the side BC is the hypothenuse. 




20 INTRODUCTION. 

17. Among the quadrilaterals, we distinguish : 

The square, which has its sides equal, and 
its angles right angles. 

The rectangle, which has its angles right 
angles, without having its sides equal. 




The parallelogram, or rhomboid, which 
has its opposite sides parallel. 




The rhombus, or lozenge, which has its sides equal, 
o^ithout having its angles right angles. 



And lastly, the trapezoid, only two of whose 
sides are parallel. 



18. A diagonal is a line which joins the 
vertices of two angles not adjacent to each 
other. Thus, AF, AE, AD, AC, are diagonals. 



19. An axiom is a self-evident proposition. 

20. A theorem is a truth, which becomes evident by means 
of a train of reasoning called a demonstration. 

21. A problem is a question proposed, which requires 
a solution. 

22. A lemma is a subsidiary truth, employed for the de- 
monstration of a theorem, or the solution of a problem. 

23. The common name, proposition, is applied indifferently, 
to theorems, problems, and lemmas. 

24. A corollary is an obvious consequence, deduced from 
one or several propositions. 

25. A scholium is a remark on one or several preceding 
propositions, which tends to point out their connexion, their 
use, their restriction, or their extension. 

26. A hypothesis is a supposition, made either in the eniin- 
ciation of a proposition, or in the course of a demonstration. 



DESCRIPTION OF INSTRUMENTS. 21 

Axioms. 

I. Things which are equal to the same thing, are equal 
to each other. 

2 If equals be added to equals, the wholes will be equal. 

3. If equals be taken from equals, the remainders will be 
equal. 

4. If equals be added to unequals, the wholes will be 
unequal. 

5. If equals be taken from unequals, the remainders will 
be unequal. 

6. Things which are double of the same thing, are equal 
to each other. 

7. Things which are halves of the same thing, are equal 
to each other. 

8. The whole is greater than any of its parts. 

9. The whole is equal to the sum of all its parts. 

10. All right angles are equal to each other. 

II. From one point to another, only one straight line can 
be drawn. 

12. Through the same point, only one straight line can 
be drawn which shall be parallel to a given line. 

13. Magnitudes, whict being applied to each other, coin- 
cide throughout their whole extent, are equal. 



CHAPTER III. 

Description of the Instruments used for Delineating or Drawing 
Lines and Angles on paper. Construction of Problems. 

18. Drawings, or delineations on paper, are the copies of 
things which they are intended to represent. 

In order that these copies may be exact, their different parts 
must bear the same proportion to each other that exists 
between the corresponding parts of the things themselves. 

To enable us to delineate lines and angles correctly, upon 
paper, certain instruments are necessary ; these we will now 
describe. 



22 



INTRODUCTION. 



DIVIDERS. 




19. The dividers is the most simple and useful of the in- 
struments used for drawing. It consists of two legs 6a, be, 
which may be easily turned around a joint at b. 

One of the principal uses of this instrument is to lay off on 
a line, a distance equal to a given line. 

For example, to lay off on CD a dis- ^ ^ 

tance equal to AB. ' "* 

For this purpose, place the forefinger C ^ n 

on the joint of the dividers, and set one 

foot at A : then extend, with the thumb and other fingers, 
the other leg of the dividers, until its foot reaches the point 
B. Then raise the dividers, place one foot at C, and mark 
with the other the distance CE : this will evidently be 
equal to AB. 



RULER AND TRIANGLE. 




20. A Ruler of a convenient size, is about twenty inches 
in length, two inches wide, and a fifth of an inch in thick- 
ness. It should be made of a hard material, perfectly straight 
and smooth. 

The hypothenuse of the right-angled triangle, which is 
used in connexion with it, should be about ten inches in 



DESCRIPTION OF INSTRUMENTS. 23 

length, and it is most convenient to have one of the sides 
considerably longer than the other. We can solve, with the 
ruler and triangle, the two following problems. 

I. To draw through a given point a line which shall be parallel 
to a given line. 

Let C be the given point, and AB the 
given line. 1 

Place the hypothenuse of the triangle ^ ^ 

against the edge of the ruler, and then "" 

place the ruler and triangle on the paper, so that one of the 
sides of the triangle shall coincide exactly with AB : the 
triangle being below the line. 

Then placing the thumb and fingers of the left hand firmly 
on the ruler, slide the triangle with the other hand along the 
ruler until the side which coincided with AB reaches the 
point C Leaving the thumb of the left hand an the ruler, 
extend the fingers upon the triangle and hold it firmly, and 
with the right hand, mark with a pen or pencil, a line through 
C: this line will be parallel to AB. 

n. To draw through a given point a line which shall be per- 
pendicular to a given line. 

Let AB be the given line, and D the ip 

given point. 

Place the hypothenuse of the triangle . 
against the edge of the ruler, as before. 
Then place the ruler and triangle so that one of the sides of 
the triangle shall coincide exactly with the line AB. Then 
slide the triangle along the ruler until the other side reaches 
the point D: draw through D a right line, and it will be per« 
pendicular to AB. 

SCALE OF EQUAL PARTS. 

, ; I .7 .g ..t.A.g .a .7 .8 jfip 

I ' I I I 1 I { I I I I I - 

21. A scale of equal parts is formed by dividing a line of a 
given length into equal portions. 

If, for example, the line ab of a given length, say one inch, be 
divided into any number of equal parts, as 10, the scale thus 
formed, is called a scale of ten parts to the inch. The line 



24 



rNTRODUCTION. 



I 1 -z ..1.A.5 .a .7 .a .970 



a6, which is divided, is called the i*m^ o/i/ie scale. This unit 
is laid off several times on the left of the divided line, ani 
the points marked, 1, 2, 3, &c. 

The unit of scales of equal parts, is, in general, either an 
mch, or an exact part of an inch. If, for example, ab the 
unit of the scale, were half an inch, the scale would be one 
of 10 parts to half an inch, or of 20 parts to the inch. 

If it were required to take from the scale a line equal to 
two inches and six-tenths, place one foot of the dividers at 2 
on the left, and extend the other to .6, which marks the sixth 
of the small divisions : the dividers will then embrace the 
required distance. 

DIAGONAL SCALE OF EQUAL PARTS. 



r/^ 







i / f / / / / 1 1 






oa 


1 / M / 1 M / 






08 


ll 1 1191 n I 






07 


1 li u n i I 






06 


n I I 1 I ll I 






05 


I icj 1 1 n 






04 


I ////// 






03 


i III I I 






02 


n n 1 I I 






0.1 


n n I i i 



a .1 .3.3.4.5.6.7.8 .9 b 



22. This scale is thus constructed. Take ah for the unit 
of the scale, which may be one inch, i, i or | of an inch, 
in length. On ah describe the square ahcd. Divide the sides 
ah and dc each into ten equal parts. Draw aj and the other 
nine parallels as in the figure. 

Produce ha to the left, and lay off the unit of the scale any 
convenient number of times, and mark the point 1, 2, 3, &c. 
Then, divide the line ad into ten equal parts, and through the 
points of division draw parallels to ah as in the figure. 

Now, the small divisions of the line ah are each one-tenth 
(.1) of ah; they are therefore .1 of ad., or .1 of ««• or gh. 

If we consider the triangle adj., the base df is one-tenth 
of ad the unit of the scale. Since the distance from a to the 
first horizontal line above a6, is one tenth of the distance arf, 
11 follows that the distance measured on that Ime between ad 



DESCRIPTION OF INSTRUMENTS. 



26 



And af is one-tenth of dj : but since one-tenth of a tenth is a 
hundredth, it follows that this distance is one hundredth (.01) 
of the unit of the scale. A like distance measured on the 
second line will be two hundredths (.02) of the unit of the 
scale ; on the third, .03 ; on the fourth, .04, &c. 

If it were required to take, in tlie dividers, the unit of the 
scale, and any number of tenths, place one foot of the dividers 
at 1, and extend the other to that figure betv/een a and h 
which designates the tenths. If two or more units, are re- 
quired, the dividers must be placed on a point of division 
farther to the left. 

When units, tenths, and hundredths, are required, place one 
foot of the dividers where the vertical hue through the point 
which designates the units, intersects the line which desig- 
nates the hundredths : then, extend the dividers to that Hne 
between ad and be which designates the tenths : the dis- 
tance so determined will be the one required. 

For example, to take off the distance 2.34, we place one 
foot of the dividers at /, and extend the other to e ; and to 
take off the distance 2.58, we place one fool of the dividers 
at p and extend the other to q. 

Remark I. If a line is so long that the whole of it can- 
not be taken from the scale, it must be divided, and the parts 
of it taken from the scale in succession. 

Remark II. If a line be given upon the paper, its length can 
be found by taking it ia the dividers and applying it to the scale. 

SCALE OF CHORDS, 



D^? 




S\0 S\0 fiO 



23. If, with any radius, as AC, we describe the quadrant 
CD, and then divide it into 90 equal parts, each part is called 
9 '\egree 



26 INTRODUCTION. 

Through C, and each point of division, let a chord be 
drawn, and let the lengths of these chords be accurately laid 
off on a scale : 3uch a scale is called a scale of chords. In 
the figure, the chords are drawn for every ten degrees. 

The scale of chords being once constructed, the radius of 
the circle from which the chords were obtained, is known ; 
for, the chord marked 60 is always equal to the radius of the 
circle. A scale of chords is generally laid down on the scales 
which belong to cases of mathematical instruinents, and is 
marked ciio. 

To lay off, at a given point of a line, with the scale of chords, 
an angle equal to a given angle. 

Let AB be the line, and Jl the given 
point. 

Take from the scale the chord of 6 de- ^^ 

grees, and with this radius and the point ^^^2_^ \ 

.^ as a centre, describe the arc BC. Then -^ ^ 

take from the scale the chord of the given angle, say 30 
degrees, and with this line as a radius, and 5 as a centre, 
describe an arc cutting BC in C. Through Jl and C draw 
the line AC, and BAC will be the required angle. 



Cx- 



SEMICIRCULAR PROTRACTOR. 




24. This instrument is used to lay down, or protract angles. 
It may also be used to measure angles included between lines 
already drawn upon paper. 



DESCRIPTION OF INSTRUMENTS. 



27 



It consists of a brass semicircle ABC divided to half de- 
grees. The degrees are numbered from to 180, both ways ; 
that is, from A to B and from B to A. The divisions, in the 
figure, are only made to degrees. There is a small notch at 
the middle of the diameter AB, which indicates the centre of 
the protractor. 

To lay off an angle with a Protractor. 

Place the diameter AB on the line, so that the centre shall 
fall on the angular point. Then count the degrees contained 
in the given angle from A towards B, or from B towards A 
and mark the extremity of the arc with a pin. Remove the 
protractor, and draw a line through the point so marked and 
the angular point : this line will make with the given line the 
required angle. 

SECTORAL SCALE OP EQUAL PARTS. 




25. The sector is an instrument generally made of ivory or 
brass. It consists of two arms, or sides, which open by turn- 
ing round a joint at their common extremity. 

There are several scales laid down on the sector : those, 
however, which are chiefly used in drawing lines and angles, 
are, the scale of chords already described, and the scale of 
equal parts now to be explained. 

On each arm of the sector, there is a diagonal line that 
passes through the point about which the arms turn: these 
diagonal lines are divided into equal parts. 

On the sectors which belong to the cases of English in- 
struments, the diagonal lines are designated by the letter Z», 
and numbered from the centre of the sector, 1, 2, 3, 4, 5, 6, 7, 
8, 9, 10, to the two extremities. On the sectors which belong 



28 INTRODUCTION. 

to cases of French instruments, they are desi^ated, " Les 
parties egales," and numbered, 10, 20, 30, 40, &c. to 200. 
On the English sectors there are 20 equal divisions between 
either two of the hues nurnbered 1, 2, 3, &c., so that, there are 
200 equal parts on the scale. 

The advantage of the sectoral scale of equal parts, is this — 
When it is proposed to draw a line upon paper, on such a 
scale that any number of parts of the line, 40 for example, 
shall be represented by one inch on the paper, or by any part 
of an inch, take the inch, or part of the inch from the scale 
of inches on the sector: then, placing one foot of the dividers 
at 40 on one arm of the sector, open the sector until the other 
foot reaches to the corresponding number on the other arm : 
then lay the sector on the table without varying the angle. 

Now, if we regard the lines on the sector as the sides of a 
triangle, of which the line 40 measured across, is the base, it 
is plain, that if any other line be likewise measured across the 
angle of the sector, the bases of the triangles, so formed, will 
be proportional to their sides. Therefore, if we extend the 
dividers from 50 to 50, this distance will represent a line of 50, 
to tbe given scale : and similarly for other lines. 

Let it now be required to lay down a line of sixty-seven feet, 
to a scale of twenty feet to the inch. 

Take one inch from the scale of inches : then place one 
foot of the dividers at the twentieth division, and open the 
sector until the dividers will just reach the twentieth division 
on the other arm : the sector is then set to the proper angle ; 
after which the required distance to be laid down on the paper, 
is found, by extending the dividers from the sixty-seventh 
division on one arm, to the sixty-seventh division on the 
other. 

GUNTERS' SCALE. 

26. This is a scale of two feet in length, on the faces of 
which a variety of scales are marked. The face on which the 
divisions of inches are made, contains, however, all the scales 
necessary for laying down lines and angles. These are, the 
scale of equal parts, the diagonal scale of equal parts, and the 
scale of chords, all of which have been described. 



SOLUTION OF PROBLEMS* 29 

SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN- 
STRUMENTS THAT HAVE BEEN DESCRIBED. 

PROBLEM I. 

*Bt a given point in a given straight line, to erect a perpendicu- 
lar to the line, 

27. Let .^ be the given point, and BC the given line. 

From A lay off any two distances AB 
and AC equal to each other. Then, from \a^ 

the points B and C, as centres, with a 
radius greater than BA, describe tw^o 
arcs intersecting each other in D : ^ '^ 

draw AD, and it will be the perpendicular required. 

PROBLEM II. 

From a given point without a straight line, to let fall a perpen^ 
dicular on the line. 

23. Let A be the given point and BD 
the given line. 

From the point .^ as a centre, with a 
radius sufficiently great, describe an arc 
cutting the line BD in tlie two points B 
and D : then mark a point E, equally 
distant from the points B and D, and 
draw AE : AE will be the perpendicular required. 

PROBLEM III. 

At a point, in a given line, to make an angle equal to a given 

angle, 
29. Let A be the given point, AE 
the given line, and IKL the given 




D 




From the vertex K, as a centre, K I J 



w^ith any radius, describe the arc IL, terminating in the two 
sides of the angle. From the point A us a centre, with a dis- 
tance AE equal to KI, describe the arc ED ; then take the 
chord LI, with which, from the point £J as a centre, describe 
an arc cutting the indefinite arc DE, in D; draw AD, and 
the angle EAD will be equal to the given angle K. 




nf 




E^ 


\ 


,,' 


-'•"A 


i 


,■'''' 


I 



30 INTRODUCTION. 

PROBLEM IV. 

To divide a given angle, or a given arc, into two equal parts, 

30. Let C be the given angle, and ^EB 
the arc which measures it. 

From the points A and B as centres, de- A\^ 
scribe with the same radius two arcs cutting 
each other in D : through D and the centre 
C draw CD: the angle ^CE will be equal 
to the angle ECB, and the arc AE to the arc EB. 

PROBLEM V. 

Through a given point to draw a parallel to a given line, 

31. Let A be the given point, and 
BC the given line. 

From .^ as a centre, with a radius 
greater than the shortest distance from 
e^ to BC, describe the indefinite arc ED : from the point E as 
a centre, with the same radius, describe the arc AF ; make 
ED=AF, and draw JID : then will AD be the parallel 
required. 

PROBLEM VI. 

Tim angles of a triangle being given, to find the third. 

32 Draw the indefinite line 
DEF. At the point E, make 
the angle DEC equal to one of 
the given angles, and the angle "^ W 

CEH equal to the other : the remaining angle HEF will be 
the third angle required. 

PROBLEM VII. 

To lay down, on paper, a line of a given length, so that any 
number of its parts shall correspond to the unit of the scale. 

33. Suppose that the given line were 75 feet in length, and 
it were required to draw it on paper, on a scale of 25 feet to 
the inch. 




SOLUTION OF PROBLEMS. 31 

The length of the hne 75 feet, being divided by 25, will -give 
3, the number of inches which will represent the line on 
paper 

Therefore, draw the indefinite line .S.B, on which lay of! a 



distance AC equal to 3 inches: AC will represent the given 
line of 75 feet draw^n to the required scale. 

Remark I. This problem explains the manner of laying 
dow^n a line upon paper, in such a manner that a given num- 
ber of parts shall correspond to the unit of the scale, whether 
that unit be an inch or any part of an inch. 

When the length of the line to be laid down is given, and it 
has been determined how many parts of it are to be repre- 
sented on the paper by a distance equal to the unit of the 
scale, we find the length which is to be taken frv ^vi the scale 
by the following 

RULE. 

Divide the length of the line by the number of parts which is to 
be represented by the unit of the scale : the quotient will show the 
number of parts which is to be taken from the scale. 

EXAMPLES. 

1. If a line of 640 feet in length is to be laid down on 
paper, on a scale of 40 feet to the inch ; what length must 
be taken from the scale ? 

40)640(16 inches. 

2. If a line of 357 feet is to be laid down on a scale of 6S 
feet to the unit of the scale, (which we will suppose half an 
inch), how many parts are to be taken? 



Ans. \ ^•^^' P^'^f' ^' 
I 2.62 5 inches. 



Remark II. When the length of a hne is given on the 
paper, and it is required to find the true length of the line 
which it represents, take the line in the dividers and apply it 
to the scale, and note the number of units, and parts of an 



32 



INTRODUCTION. 



unit to which it is equal. Then multiply this number by the 
mmiber of parts which the imit of the scale represents, and 
the product will be the length of the line. 

For example, suppose the length of a line drawn on the 
paper was found to be 3. 50 inches, the scale being 40 feet to 
the inch : then, 

3.56 X 40=142 feet, the length of the line. 



PROBLEM VIII. 



Having given two sides and the included angle of a triangle, to 



describe the triangle. 



34. Let the line ji5 = 150 feet, and 
C= 120 feet, be the given sides ; and 
^ = 30 degrees, the given angle: to 
describe the triangle on a scale of 200 
feet to the inch. 

Draw the indefinite line DG, and 
Jit the point D, make the angle GDH equal to 30 degrees; 
then lay off DGf equal to 150, equal to three quarters of an 
inch, and D// equal to 120, equal to six tenths of an inch, 
and draw Gil: DG/f will be the required triangle. 




PROBLEM IX. 




Tlie three sides of a triangle being given, to describe the 
triangle, 

35. Let ^, B and C, be the sides. 
Draw DE equal to the side A, From 
the point J9 as a centre, with a radius 
equal to the second side B, describe an 
arc : from ^ as a centre, with a radius 
equal to the third side C, describe 
another arc intersecting the former in 

F ; draw DF and EF, and DEF will be the triangle 
required. 



AV 



SOLUTION OP PROBLEMS. 33 



PROBLEM X. 

Having given two sides of a triangle and an angle opposite one 
of them, to describe the triangle. 

36. Let A and B be the given 

sides, and C the given angle which ^"^ 

we will suppose is opposite the side 




B. Draw the indefinite line DF and 

make the angle FDH equal to the 

angle C: take DH=A, from the 

point H, as a centre, with a radius equal to the other given 

side B, describe an arc cutting DF m F; draw HF: then 

will DHF be the required triangle. 

If the angle C is acute, and ^' ' ^^^^ 

the side 5 less than A. then the ^' ' 

E 
arc described from the centre F ^^^^-^^^'^ 

with the radius FF — B will cut ^.^^y^ ^v 

the side BF in two points, F and -O jyC /QT 

Gy lying on the same side of D : ''" - ' 

hence there will be two triangles, DEF, and DEG, either of 

which will satisfy all the conditions of the problem. 



PROBLEM XI. 

The adjacent sides of a parallelogram, with the angle which 
they contain, being given, to describe the parallelogram. 

37. Let Jl and B be the given sides, /?y -^G 

and C the given angle. / r * 

Draw the line 1)^=.^; at the point j^L IE 

D, make the angle EDF= C ; take A\ 1 / 

DF=B : describe two arcs, the one ^' ' 



from F, as a centre, with a radius FG=DE, the other from E, 
as a centre, with a radius EG=DF ; through the point G, 
where these arcs intersect each other, draw FG, EG; DEGF 
will be the parallelogram required. 



34 INTRODUCTION. 

PROBLEM XII. 

To find the centre of a given circle or arc. 

38. Take three points, A, B, C, any- 
where in the circumference, or in the 
arc : draw AB, BC ; bisect these two 
lines by the perpendiculars, DE, FG : 
the point O where these perpendiculars 
meet will be the centre sought. 

The same construction serves for 
making a circumference pass through 
three given points Jl, B, C, and also for yff^ 

describing a circumference, about a given triangle. 




CHAPTER III. 

Plane Trigonometry* 

39. In every plane triangle there are six parts : three sides 
and three angles. These parts are so related to each other, 
that if a certain number of them are known or given, the re- 
maining ones can be determined. 

40. Plane Trigonometry explains the methods of finding, by 
calculation, the unknown parts of a triangle when a sufficient 
number of the six parts is given^ 

It has already been shown, in the problems, that triangles 
may be constructed when three parts are known. But these 
constructions, which are called graphic methods, though per- 
fectly correct in theory, would give only a moderate approxi- 
mation in practice, on account of the imperfection of the in 
struments required in constructing them. 

Trigonometrical methods, on the contrary, being inde- 
pendent of mechanical operations, give solutions with the 
utmost accuracy. 

41. For the purposes of trigonometrical calculations, the cir- 
cumference of the circle is divided into 360 equal parts, called 
degrees; each degree into 60 equal parts, called minutes; 
and each minute into 6 equal parts, called seconds. 



PLANE TRIGONOMETRY. 



35 




As the circumference of a circle may be regarded as a pro- 
per measure of angles, having their vertices at the centre, the 
four right angles which can be formed about the same point, 
are measured by 360 degrees ; two right angles by 180 de 
grees, one right angle by 90 degrees, and an angle less 
than a right angle, by an arc less than 90 degrees. 

Degrees, minutes, and seconds, are usually designated by 
the respective characters, ° ' ". Thus, 16" 12' 15" is read, 
16 degrees, 12 minutes, and 15 seconds. 

42. The complement of an arc is -^ 
what remains after subtracting the 
arc from 90°. Thus, the arc EB is 
the complement of AB. The sum of 
an arc and its complement is equal 
to 90°. 

43. The supplement of an arc is 
what remains after subtracting the 
arc from 180°. Thus, Gl^ is the sup- q 
plement of the arc AEF. The sum of an arc and its sup- 
plement is equal to 180°. 

44. The sine of an arc is the perpendicular let fall from one 
extremity of the arc on the diameter which passes through 
the other extremity. Thus, BD is the sine of the arc t^B. 

45. The cosine of an arc is the part of the diameter inter- 
cepted between the foot of ths sine and centre. Thus, OD is 
the cosine of the arc AB. 

46. The tangent of an arc is the line which touches it at 
one extremity, and is limited by a line drawn through the 
other extremity and the centre of the circle. Thus, AC is the 
tangent of the arc AB. 

47. The secant of an arc is the line drawn from the centre 
of the circle through one extremity of the arc, and limited by 
the tangent passing through the other extremity. Thus, OC 
is the secant of the arc AB. 

48. The four lines, BD, OD, AC, OC, depend for their 
values on the arc AB and the radius OA ; they are thus 
designated : 



sin AB 
cos JIB 

ianAB 
sec AB 



for 
for 
for 
for 



INTRODUCTION. 

BD 

OD 

AC 

OC. 




49. If ABE be equal to a quad- 
rant, or 90°, then EB Avill be the 
complement of AB. Let the lines 
ET and IB be drawn perpendicular 
to OE. Then, 

ET, the tangent of EB, is called the cotangent of AB; 

IB, the sine of EB, is equal to the cosine of AB ; 

OT, the secant of EB, is called the cosecant of AB, 

In general, if A is any arc or angle, we have, 

cos A=s\n {900 — A) 

cot .^=tan (900 — ^) 

cosec*^=sec (900 — ^3) 

50. If we take an arc ABEF, greater than 90°, its sine 
will be FH ; OH will be its cosine ; ^Q its tangent, and 0(2 
its secant. But FH is the sine of the arc GF, which is the 
supplement of AF, and OH is its cosine : hence, the sine of 
an arc is equal to the sine of its supplement ; and the cosine of 
an arc is equal to the cosine of its supplement."^ 

Furthermore, AQ^ is the tangent of the arc AF, and OQ, is 
its secant : GL is the tangent, and OL the secant, of the sup- 
plemental arc GF. But since AQ is equal to GL, and OQ, to 
OL, it follows that, the tangent of an arc is equal to the tan- 
gent of its supplement ; and the secant of an arc is equal to the 
secant of its supplement.^ 

Let us suppose, that in a circle of a given radius, th.e lengths 
of the sine, cosine, tangent, and cotangent, have been calcu- 
lated for every minute or second of the quadrant, and arranged 
in a table ; such a table is called a table of sines and tangents. 
If the radius of the circle is 1, the table is called a table of 
natural sines. A table of natural sines, therefore, sliows the 



+ These relations are between the vdues of the trigonometrical lines; the 
algebraic signs, wliich they have in the different quadrants, are not considered. 



PLANE TRIGONOiMETRY. 



37 



values of the sines, cosines, tangents and cotangents of all 
the arcs of a quadrant, divided to minutes or seconds. 

If the sines, cosines, tangents and secants are known for 
arcs less than 90°, those for arcs which are greater can be 
found from them. For if an arc is less than 90°, its supple- 
ment will be greater than 90°, and the values of these lines 
are the same for an arc and its supplement. Thus, if we know 
the sine of 20°, we also know the sine of its supplement 160°; 
for the two are equal to each other. 

TABLE OF LOGARITHMIC SINES. 

51. In this table are arranged the logarithms of the nu- 
merical values of the sines, cosines, tangents and cotan- 
gents of all the arcs of a quadrant, calculated to a radius 
of 10,000,000,000. The logarithm of this radius is 10. In 
the first and last horizontal lines of each page, are written the 
degrees whose sines, cosines, &c. are expressed on the page. 
The vertical columns on the left and right, are columns of 
minutes. 

CASE I. 

To Jind, in the table, the logarithmic sine, cosine, tangent, or 
cotangent of any given arc or angle. 

52. If the angle is less than 45°, look for the degrees in the 
first horizontal line of the different pages : then descend along 
the column of minutes, on the left of the page, till you reach 
the number showing the minutes : then pass along the hori- 
zontal line till you come into the column designated, sine, 
cosine, tangent, or cotangent, as the case may be : the number 
so indicated is the logarithm sought. Thus, on page 37, for 
19" 55' we find, 

sin 19° 55' . . 9.532312 

cos 19° 55' . . 9.973215 

tan 19° 55' . . 9.559097 

cot 19° 55' . . 10.440903 

53. If the angle is greater than 45°, search for the degrees 
along the bottom line of the different pages : then, ascend 
along the column of mmutes on the right hand side of the 
page, till you reach the number expressing the minutes : then 
pass along the horizontal hne into the columns designated 



S8 INTRODUCTION. 

tang, cot, sine, or cosine, as the case may be ; the number so 
pointed out is the logarithm required. 

54. The column designated sine, at the top of the page, is 
designated cosine at the bottom ; the one designated tang, by 
cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of the 
page and the minutes from the first vertical column on the 
left, is the complement of the angle found by taking the cor- 
responding degrees at the bottom of the page, and the minutes 
traced up in the right hand column to the same horizontal 
line. Therefore, sine, at the top of the page, should correspond 
with cosine, at the bottom ; cosine with sine, tang with cotang, 
and cotang with tang, as in the tables (Art. 49). 

If the angle is greater than 90°, we have only to subtract it 
from 180°, and take the sine, cosine, tangent or cotangent of 
the remainder. 

The column of the table next to the column of sines, and 
on the right of it, is designated by the letter D, This column 
is calculated in the following manner. 

Opening the table at any page, as 42, the sine of 24° is 
found to be 9.609313 ; that of 24° 01', 9.609597: their dif- 
ference is 284 ; this being divided by 60, the number of seconds 
in a minute, gives 4.73, which is entered in the column Z^, 
omitting the decimal point. 

Now, supposing the increase of the logarithmic sine to be 
proportional to the increase of the arc, and it is nearly so for 
60", it follows, that 473 (the last two places being regarded as 
decimals), is the increase of the sine for l". Similarly, if the 
arc were 24° 20' the increase of the sine for l", would be 465, 
the last two places being decimals 

The same remarks are equally applicable in respect of the 
column D, after tlie column cosine, and of the column D, be- 
tween the tangents and cotangents. The column D, between 
the columns tangents and cotangents, answers to both of these 
columns. 

Now, if it were required to find the logarithmic sine of an 
arc expressed in degrees, minutes, and seconds, we have only 
to find the degrees and minutes as before ; then, multiply the 
corresponding tabular number by the seconds, cut off two 
places to the right hand for decimals, and then add the pro- 
duct to the number first found, for the sine of the given arc. 



PLANE TRIGONOMETRY. 39 

Thus, if we wish the sine of 40° 26' 28". 

The sine 40° 26' .... 9.811952 

Tabular difference .247 

Number of seconds .28 . . 

Product . . 69 16 to be added 69.16 

Gives for the sine of 40« 36' 28" 9.812021. 

The decimal figures at the right are generally omitted 
in the last result ; but when they exceed five-tenths, the 
figure on the left of the decimal point is increased by i ; this 
gives the result to the nearest unit. 

The tangent of an arc, in which there are seconds, is found 
in a manner entirely similar. In regard to the cosine and 
cotangent, it must be remembered, that they increase while 
the arcs decrease, and decrease as the arcs are increased ; con- 
sequently, the proportional numbers found for the seconds, 
must be subtracted, not added. 

EXAMPLLS. 

1. To find the cosine of 3° 40' 40" 

The cosine of 3° 40' . . 9.999110 

Tabular difference .13 

Number of seconds 40 . . 

Product . 5.20 to be subtracted 5.20 

Gives for the cosine of 3° 40' 40" . . 9.999105 

2. Find the tangent of 37° 28' 31" 



3. Find the cotangent of 87" 57' 59" 



Alls. 9.884592. 
Ans. 8.550356. 



CASE II. 



To find the degrees, minutes and seconds, answering to any 
given logarithmic sine, cosine, tangent or cotangent. 

56. Search in the table, and in the proper column, until the 
number is found : the degrees will be shown either at the top 
or bottom of the page, and the minutes in the side columns, 
either at the left or right. 

But, if the number cannot be exactly found in the table, 
take from the table the degrees and minutes answering to the 
nearest less logarithm, the logarithm itself, and also the cor- 
responding tabular difference. Subtract the logarithm taken 



40 



INTRODUCTION. 



from the table from the given logarithm, annex two ciphers to 
the remainder, and then divide "the remainder by the tabular 
difference : the quotient will be seconds, and is to be connected 
with the degrees and minutes before found ; to be added for 
the sine and tangent, and subtracted for the cosine and 
cotangent. 



EXAMPLES. 



1. Find the arc answering to the sine 
Sine 49" 20', next less in the table 
Tabular difference 



9.880054 
9.879963 



181)9100(50" 

Hence, the arc 49° 20' 50" corresponds to the given sine 
9.880054. 

2. Find the arc whose cotangent is . 10.008688 
cot 44° 26', next less in the table . . 10.008591 

Tabular difference . . 421)9700(23" 

Hence, 44° 26' — 23" = 44° 25' 37" is the arc answering to 
the given cotangent 10.008688. 

3. Find the arc answering to tangent 9.979110 

Ans. 43° 37' 21" 

4. Find the arc answering to cosine 9.944599 

Ans. 28° 19' 45". 
We shall now demonstrate the principal theorems of Plane 
Trigonometry. 



THEOREM I. 

The sides of a plane triangle are 'proportional to Vie sines of 
their opposite angles. 

67. Let ABC be a triangle ; then will 
CB : CA :: sin A : sin B. 

For, with .^ as a centre, and AD 
equal to the less side BC, as a radius, 
describe the arc DI : and with B as 
a centre and the equal radius BC, . 
describe the arc CL : now DE is the 
sine of the angle A, and CF is the sine of B, to the same 
radius AD or BC. But by similar triangles, 
AD : DE :: AC : CR 




El L 




PLANE TRIGONOMETRY. 41 

But AD being equal to BC, we have 

BC : s'mA:: AC : sm B, or 
BC : AC ::smA : sin J5. 
By comparing the sides AB, AC, in a similar manner, we 
should find, AB : AC :: sin C : sin B, 

THEOREM II. 

In any triangle, the sum of the two sides containing either 
angle, is to their difference, as the tangent of half the sum of 
the two other angles, to the tangent of half their difference, 

58. Let ACB be a triangle : then will 

AB-]-AC: AB-AC: : tan i(C+^) : tan i(C-jB). 

With ,^ as a centre, and a radius 
AC the less of the two given sides, ,\" 
let the semicircle IFCE be de- < \ 
scribed, meeting AB in /, and BA \ 
produced, in E. Then, BE will \ 
be the sum of the sides, and Bl ^. pr-rr 

their difference. Draw C/ and .^7^. 

Since CAE is an outward angle of the triangle ACB, it is 
equal to the sum of the inward angles C and B (Bk. I, Prop. 
XXV, Cor. 6). But the angle CIE being at the circumfe- 
rence, is half the angle CAE at the centre (Bk. Ill, Prop. 
XVIII) ; that is, half the sum of the angles C and B, or 
equal to i(C+J5). 

The angle AFC=ACB, is also equal to ABC+BAF ; 
therefore, BAF=ACB-ABC. 

But, ICF={{BAF)=\{ACB-ABC), or \{C-B). 

With / and C as centres, and the common radius IC, let 
the arcs CD and IG be described, and draw the lines CE and 
IH perpendicular to IC. The perpendicular CE will pass 
through E, the extremity of the diameter IE, since the right 
angle ICE must be inscribed in a semicircle. 

But CE is the tangent of CIE = \{C+B) ; and IH \s the 
tangent of ICB = \{C--B), to the common radius CI. 

But since the lines CE and IH are parallel, the triangles 
BHI and BCE are similar, and give the proportion, 

BE : BI :: CE : IH, or 
by placing for BE and BI, CE and IH, their values, we have 

AB+AC : AB-AC : : tan i(C+B) • tan 1{C-B). 




42 INTRODUCTION. 

THEOREM III. 

In any plane triangle, if a line he drawn from the vertical 
angle perpendicular to the base, dividing it into two segments : 
then, the whole base, or sum of the segments, is to the sum of the 
other two sides, as the difference of those sides to the difference 
of the segments. 

59. Let BAC be a triangle, and AD perpendicular to the 
base ; then will 

BC: CA+AB:: CA-AB : CD-^DB 

For, AB'=BD'+AD^ 

(Bk. IV, Prop. XI) ; 
and AC^=DC^+AD^ 

by subtraction AC^^AB^=CD^— 
BD\ 

But since the difference of the squares ^ 
of two lines is equal to the rectangle 

contained by their sum and difference (Bk. IV, Prop X), we 
have, 

AC^--AB' = (AC+AB). (AC-AB) 
and CD'-DB^ = {CD+DB). (CD-DB) 

therefore, {CD+DB).{CD-DB) = (AC+AB).{AC^AB) 
hence, CD+DB : AC+AB : : AC-AB : CD-DB. 

THEOREM IV. 

In any right-angled plane triangle, radius is to the tangent 
of either of the acute angles, as the side adjacent to the side 
opposite. 

60. Let CAB be the proposed triangle, 
and denote the radius by R : then will 

R. i^nC : AC : AB. 
For, with any radius as CD describe 
the arc DH, and draw the tangent jDCr. ^ D ^ 

From the similar triangles CDG and CAB we shall have, 
CD : DG:: CA: AB; hence, * 

R : tan C : : CA : AB. 
By describing an arc with 5 as a centre, we could show in 
the same manner that, 

R : idiu B :: AB : AC. 




PLANE TRIGONOMETRY. 4S 

THEOREM V. 

In every right-angled plane triangle, radius is to the cosine oj 
either of the acute angles, as the hypothenuse to the side adjacent. 

61. Let ABC be a triangle, right 
angled at B then will 

R : cos A : AC : AB. 
For, from the point .^ as a centre, and 
any radius as AD, describe the arc DF, ^^ 

which will measure the angle A, and draw jDiJ perpendicular 
io AB : then will AE be the cosine of A. 

The triangles ADE and ACB, being similar, we have 
AD : AE : : AC : AB : thatis, 
jR : cos ^ ; : AC: AB. 

62. Remark. The relations between the sides and angles 
of plane triangles, demonstrated in these five theorems, are suf- 
ficient to solve all the cases of Plane Trigonometry. Of the 
six parts which make up a plane triangle, at least three must 
be given, and one of these a side, before the others can be de- 
termined. 

If the three angles are given, it is plain, that an indefi- 
nite number of similar triangles may be constructed, the 
angles of which shall be respectively equal to the angles 
that are given, and therefore, the sides could not be de- 
termined. 

Assuming, with this restriction, any three parts of a triangle 
as given, one of the four following cases will always be pre- 
sented. 

I. When two angles and a side are given. 

II. When two sides and an opposite angle are given. 

III. When two sides and the included angle are given. 

IV. When the three sides are given. 

CASE I. 

When two angles and a side are given. 

63. Add the given angles together and subtract their sum 
from 180 degrees. The remaining parts of the triangle can 
then be found by Theorem I. 



44 



INTRODUCTION, 



EXAMPLES. 



1. In 

are given 



a plane triangle ABC, there 
the angle .^ = 58° 07', the 
angle ^=22° 37', and the side AB = 
408 yards. Required the other parts. 




INSTRUMENTALLY. 

Draw an indefinite straight line AB, and from the scale of 
equal parts lay off AB equal to 408. Then at A lay off an 
angle equal to 58° 07', and at B an angle equal to 22" 37', and 
draw the lines AC and BC : then will ABC be the triangle 
required. 

The angle C may be measured either with the protractor or 
the scale of chords (Arts. 23 and 24), and will be found equal 
to 99° 16'. The sides AC and BC may be measured by re- 
ferring them to the scale of equal parts (Art. 22). We shall 
find .^0 = 158.9 and BC=S5l yards. 



BY 


LOGARITHMS. 




To the angle 


. ^-58° 07' 




Add the angle . 


. B = 22»37' 




Their sum 


. =80° 44' 




taken from . 


180° 00' 




leaves C 


99° 16' which, 


exceeding 90* 


we use its supplement 


80° 44'. 




To find the side BC. 




As sin C . 99° 16' 


ar. comp. . 


0.005705 


: sin A , 580 07' 


. • • • 


. 9.928972 


: : AB . 408 


. 


. 2.610660 


: BC . 351.024 


(after rejecting 1 0) 


. . 2.545337 



Remark. The logarithm of the fourth term of a proportion 
IS obtained by adding the logarithm of the second term to that 
of the third, and subtracting from their sum the logarithm of 
the first term. But to subtract the first term is the same as 
to add its arithmetical complement and reject 1 from the sinn 
(Art. 17) : hence, the arithmetical complement of the first 
term added to the logarithms of the second and third terms, 
will give the logarithm of the fourth term. 



PLANE TRIGONOMETRY. 46 





To find side AC, 




As sin C 
: sin B 
: : ^B 


990 16' 
22° 37' 
408 
158.976 


ar. comp. . 


. 0.005705 
. 9.58496S 
. 2.610660 


: AC 


. 2.201333 



2. In a triangle ABC, there are given .^ = 38° 25', 
B = bl^ 42', and .^5 = 400 : required the remaining parts. 
Ans. C = 83» 53', ^C = 249.974, .^C = 340.04. 

CASE II. 

When two sides and an opposite angle are given 

64. In a plane triangle ABC, there c 

are given .^C=216, CJ5=117, 
angle .^=22° 37', to find the 
parts. 

INSTRUMENTALLY. 

Draw an indefinite right line ABB' : from any point as 
A, draw AC making BAC = 22^ 37', and make ^C=216. 
With C as a centre, and a radius equal to 117, the other given 
side, describe the arc B'B; draw B'C and BC: then will 
either of the triangles ABC or AB'C, Sinswev all the condi- 
tions of the question. 






BY LOGARITHMS. 






To find the angle B. 




As BC 


. 117 . ar. comp. 


. 7.931814 


: AC 


. 216 ... . 


. 2.334454 


: : sin .^ 


. 22° 37' .... 


. 9.584968 


: sin B' 


45° 13' 55", or ABC 134° 46' 05" 


9.851236 



The ambiguity in this, and similar examples, arises in conse- 
quence of the first proportion being true for either of the angles 
ABC, or AB'C, which are supplements of each other, and 
therefore have the same sine (Art. 43). As long as the two tri- 
angles exist, the ambiguity will continue. But if the side CB, 
opposite the given angle, is greater than AC, the arc BB' will 
cut the line ABB', on the same side of the point A, in but one 



46 INTRODUCTION. 

point, and then there will be only one triangle answering the 
conditions. 

If the side CB is equal to the perpendicular Cd, the 
arc BB' will be tangent to ABB', and in this case also there will 
be but one triangle. When CB is less than the perpendicular 
Cd, the arc BB' will not intersect the base ABB', and in that 
case, no triangle can be formed, or it will be impossible to fuU 
fil the conditions of the problem. 

2. Given two sides of a triangle 50 and 40 respectively, and 
the angle opposite the latter equal to 32" : required the remain- 
ing parts of the triangle. 

Ans, If the angle opposite the side 50 is acute, it is equal 
to 41028' 59"; the third angle is then equal to 1060 31'01", 
and the third side to 72.368. If the angle opposite the side 
50 is obtuse, it is equal to 138° 31' 01", the third angle to 
9" 28' 59", and the remaining side to 12.436. 

CASE III. 

When the two sides and their included angle are given. 

65. Let ABC be a triangle ; AB, j^ 

EC, the given sides, and B the given 
angle. 

Since B is known, we can find the 
sum of the two other angles : for 

A+C=180'--B and 
i{A+C) =1(180' -B) 
We next find half the difference of the angles A and C by 
Theorem II. Viz. 

BC+BA : BC-BA : : tan i{A+C) : tan K«^-Q- 
in which we consider BC greater than BA, and therefore A 
is greater than C ; since the greater angle must be opposite 
the greater side. 

Having found half the difference of A and C, by adding il 
to the half sum \{A-{-C), we obtain the greater angle, and by 
subtractmg it from half the sum, we obtain the less. That is 
^{A-{- C)+\{A - C) =A, and 




PLANE TRIGONOMETRY. 47 

Having found the angles A and C, the third side AC may 
be found by the proportion. 

sin.^: sinJ5 :: BC: AC. 

EXAMPLES. 

1. In the triangle .^^C,let ^C=540, .^5=450, and the 
included angle ^ = 80° : required the remaining parts. 

INSTRUMENTALLY. 

Draw an indefinite right line BC and from any point, 
as B, lay off a distance 5C = 540. At B make the angle 
CB A = 80°: draw BA and make the distance BA = ^50; 
draw AC ; then will ABC be the required triangle. 

BY LOGARITHMS. 

J9C+ 5.^ = 540+450=990; and BC-BA = 5i0-450=Q0. 
.y3+C=180°— S = 180°— 80°=100°, and therefore, 
i(.^+C) =1(100°) =500 

To find ^(A-C), 
As BC+BA . 990 . ar. comp. . 7.004365 

BC-BA .90 . . . . 1.954243 

:tani(.^+C) . 50° . . . . 10.076187 

tanl(.^— C) . 6M1' . . . . 9.034795 

Hence, 50°+6° ll' = 56* 11'=.^?; and 50»-6» ll'=430 49' = C. 

To find the third side AC. 

As sin C . 43° 49' . ar. comp. . 0.159672 

sin J5 . 80° 9.993351 

: AB .450 2.653213 

AC . 640.082 .... 2.806236 

2. Given two sides of a plane triangle, 1686 and 960, and 
their included angle 128° 04' : required the other parts. 

Ans. Angles, 33° 34' 39"; 18'»2l'21"; side 2400. 

CASE IV. 

Having given the three sides of a plane triangle, to find the 

angles. 

66. Let fall a perpendicular from the angle opposite the 



48 



INTRODUCTION. 



greater side, dividing the given triangle into two right-angled 
triangles : then find the difference of the segments of the 
base by Theorem III. Half this difference being added to 
half the base, gives the greater segment; and, being sub- 
tracted from half the base, gives the less segment. Then, 
since, the greater segment belongs to the right-angled triangle 
having the greatest hypothenuse, we have the sides and right 
angle of two right-angled triangles, to find the acute an- 
gles. 

EXAMPLES. 



1. The sides of a plane trian- 
gle being given; viz. BC = 40^ AC 
= 34 and AB=25 : required the 
angles. 




INSTRUMENTALLY. 



With the three given lines as sides construct a triangle as 
m Problem IX. Then measure the angles of the triangle, 
either with the protractor or scale of chords. 



BY LOGARITHMS. 



As BC: dC+AB:: AC-AB: CD-ED 

That is, 40 : 59 : : 9 : 5l2i^=:i3.275 



40 



Then, iHllMl!.=26.6375 = CD 
2 



And 



40-13.275 



= 13.3625=52). 



In the triangle DAC, to find the angle DAC. 

As AC . 34 . . ar. comp. . 8.468521 

: DC . 26.6375 .... 1.425493 

:: sinD . 90° lo.oooooo 

• sin D.^C 51° 34' 40" . . . 9.894014 



PLANE TRIGONOMETRY. 



49 



In the triangle BAD, to find the angle BAD. 
As AB . . 25 . . ar. comp. . . . 8.602060 

BD . . 13.3625 1.125887 

: sin Z) . . 90<^ 10,000000 

sin BAD . . 32^ 18' 35" 9.727947 

Hence 900-l}^C = 90°— 51° 34' 40" = 380 25' 20"=C 
and 90^-BAD'=90^-Z2'' 18' 35"^57° 41' 25" = 5 
and BAD-\-DAC = bl'' 34' 40"+320 jg' 35"^83° 53' 15"=cy3. 

2. In a triangle, in which the sides are 4, 5 and 6, what 
are the angles. 1 

Ans. 41° 24' 35"; 55^46' 16"; and 820 49' 09"'. 

SOLUTION OF RIGHT-ANGLED TRIANGLES. 

67. The unknown parts of a right-angled triangle may be 
found by either of the four last cases : or, if two of the sides 
are given, by means of the property that the square of the 
hypothenuse is equal to the sum of the squares of the other 
t vvo sides. Or the parts may be found by Theorem V. 

EXAMPLES. 

1. In a right-angled triangle BAC, 
there are given the hypothenuse BC 
= 250, and the base .^C=240 : re- C-^ 
quired the other parts. 

To find the angle B. 

As BC . . 250 . . ar. comp. . . 7.602060 

AC . . 240 2.380211 

: sin ^ . . 900 10.000000 

sin B . . 73° 44' 23" 9.982271 

But C = 90« — 5 = 900 — 73° 44' 23" = 16° 15' 37" : 

Or C might be found from the proportion. 
As CB . . 250 . . ar. comp. . . 7.602060 

AC . . 240 2.380211 

R 10.000000 

cos C . . 16" 15' 37" 9.982271 

4 




50 





INTRODUCTION. 


B 






fl.-^^"'^^ I 


A 






To find side AB by Theorem IV. 




4s sin A 


90** ar. comp. 


0.000000 


: tan C 


. 16° 15' 37" 


9.464889 


:: AC 


.240 . . . 


2.380211 


: AB 


70.0003 


• 


1.845100 



2. In a right-angled triangle BAG, there are given AC- 
384, and J5=53'' 08' : required the remaining parts. 

Ans. AB = 28'7,96; 50 = 479.979; C = 36« 52'. 



ELEMENTS OF SURVEYING. 



CHAPTER 1. 

Definitions and Introductory Remarks, 

68. Surveying, in its most extensive signification, com- 
prises all the operations necessary .for finding, 

1st. The area or content of any portion of the surface of 
the earth ; 

2d. The lengths and directions of the bounding lines; 
and 

3d. The accurate delineation of the whole on paper. 

69. The earth being spherical, its surface is curved, and 
every line traced on its surface is also curved. 

If large portions of the surface are to be measured, such 
as states and territories, the curvature must be taken into 
account ; and very material errors will arise if it be neglected. 
When the curvature is considered, the method of measure- 
ment and computation is called Geodesic Surveying. 

The radius of the earth, however, being large, the curva- 
ture of its surface is small, and when the measurement is 
limited to small portions of the surface, the error becomes 
insensible, if we consider the surface a plane. This method 
of measurement and computation, is called Plane Surveying, 
and is the only kind that will be treated of in these Elements. 

70. If at any point of the surface of the earth, a plane be 
drawn perpendicular to the radius passing through this point, 
such plane is tangent to the surface, and is called a horizontal 
plane. All planes parallel to such a plane, are also called 
horizontal planes. 

71. A plane which is perpendicular to a horizontal plane 
is called a vertical plane. 




52 ELEMENTS OF SURVEYING. 

72. All lines of a horizontal plane, and all lines which are 
parallel to it, are called horizontal lines. 

73. Lines which are perpendicular to a horizontal plane, 
are called vertical lines ; and all lines which are inclined to it, 
are called oblique lines. 

Thus, *^B and DC are hori- j)^ _^^ 

zontal lines ; BC and JID are ver- 
tical lines ; and AC and BD are 
oblique lines. 

74. The horizontal distance be- -,,«^^^^^=^^ 
tween two points, is the horizontal line intercepted between 
the two vertical lines passing through those points. Thus, 
DC or AB is the horizontal distance between the two points 
A and C, or the points B and D. 

75. A horizontal angle is one whose sides are horizontal ; its 
plane is also horizontal. 

A horizontal angle may also be defined to be, the angle 
included between two vertical planes passing through the angular 
point, and the two objects which subtend the angle. 

76. A vertical angle is one, the plane of whose sides is 
vertical. 

77. An angle of elevation, is a vertical angle having one of 
its sides horizontal, and the inclined side above the horizontal 
side. 

Thus, in the last figure, BAC is the angle of elevation 
from A to C 

78. An angle of depression, is a vertical angle having one 
of its sides horizontal, and the inclined side under the hori- 
zontal side. Thus, DCA is the angle of depression from 
C to A. 

79. An oblique angle is one, the plane of whose sides is 
oblique t6 the horizontal plane. 

80. All lines, which can be the object of measurement, 
must belong to one of the classes above named, viz. : 

1st. Horizontal lines : 

2d. Vertical lines : 

3d. Oblique lines. 

All the angles may also be divided into three classes, viz. : 

1st. Horizontal angles : 



MEASUREMENT OF LINES. 



'?d. Vertical angles ; which may be again divided into 
angles of elevation and angles of depression : and 
3d. Oblique angles. 



CHAPTER II. 

Of the measurement and calculation of Lanes and Angles. 

81. It has been shown (Art. 62), that at least one side and 
two of the other parts of a plane triangle must be given or 
known, before the remaining parts can be found by calculation. 

When, therefore, distances are to be found, by trigonomet- 
rical calculations, two things are necessary. 

1st. To measure certain lines on the ground; and also, as 
many angles as may be necessary to render at least three 
parts of every triangle known : and 

2d. To calculate, by trigonometry, the other sides and 
angles that may be required. Our attention, then, is di- 
rected, 

1st. To the measurement of lines ; 

2d. To the measurement of angles ; and 

3d. To the calculations for the unknown and required 
parts. 

82. Any tape, rod, or chain, on which equal parts are 
marked, may be used as a measure ; and one of the equal 
parts into which the measure is divided, is called the unit of 
the measure. The unit of a measure may be a foot, a yard, 
a rod, or any other ascertained distance. 

83. The measure in general use, is a chain of four rods or 
sixty-six feet in length ; it is called Gunter's chain, from the 
name of the inventor. This chain is composed of 100 links. 
Every tenth link from either end, is marked by a small 
attached brass plate, which is notched, to designate its num- 
ber from the end. The division of the chain into lOo equal 
parts, is a very convenient one, since the divisions or links, 
are decimals of the whole chain, and in the calculations may 
be treated as such. 



54 ELEMENTS OF SURVEYING. 

TABLE. 

1 chain = 4 rods = 66 feet = 792 inches= 100 links 
Hence, l link is equal to 7.92 inches. 
80 chains = 320 rods = l mile. 
40 chains = I mile. 
20 chains = i mile. 

84. Besides the chain, there are wanted for measuring, ten 
marking pins, which should be of iron, about ten inches in 
length and an eighth of an inch in thickness. These pins 
should be strung upon an iron ring, and this ring should be 
attached to a belt, to be passed over the right shoulder, 
suspending the pins at the left side. Two staves are also 
required. They should be about six feet in length, and have 
a spike in the lower end to aid in holding them firmly, and a 
horizontal strip of iron to prevent the chain from slipping off; 
these staves are to be passed through the rings at the ends of 
the chain. 

TO MEASURE A HORIZONTAL LINE. 

85. At the point where the measurement is to be begun, 
place in a vertical position, a signal staff, having a small flag 
attached to its upper extremity ; and place another at the 
point where the measurement is to be terminated. These two 
points are generally called stations. 

Having passed the staves through the rings of the chain, 
let the ten marking pins and one end of the chain be taken by 
the person who is to go forward, and who is called the leader, 
and let him plant the staff as nearly as possible in the direc- 
tion of the stations. Then, taking the staflT in his right hand, 
let him stand off at arm's length, so that the person at the 
other end of the chain can align it exactly with the stations : 
when the alignment is made, let the chain be stretched and a 
marking pin placed ; then measvire a second chain in the 
same manner, and so on, until all the marking pins shall have 
been placed. When the marking pins are exhausted, a note 
should be made, that ten chains have been measured ; alter 
which, the marking pins are to be returned to the leader, and 
the measurement continued as before, until the whole distance 
is passed over 



OF THE THEODOLITE. 



55 



Great, care must be taken to keep the chain horizontal, and 
if the acclivity or decUvity of the ground be too great to 
admit of measuring a whole chain at a time, a part of a 
chain only should be measured : the sum of all the horizon- 
tal lines so measured, is evidently the horizontal distance 
between the stations. 

For example, in measuring the 
horizontal distance between A 
and C, we first place a staff at Jl 
and another at 6, in the direction 
towards C. Then slide up the 
chain on the staff at A until it 
becomes horizontal, and note the 
distance ah. Then remove the 
staves and place them at h and d : 
make the chain horizontal, and note the distance cd. Mea- 
sure in the same manner the line fC ; and the sum of the 
horizontal lines ah, cd and /C, will be equal to AB, the 
horizontal distance between Jl and C. 

86. We come now to the measurement of angles, and for 
this purpose several instruments are used. The one, however, 
which affords the most accurate results, and which indeed can 
alone be relied on for nice or extensive operations, is called a 
Theodolite. This instrument only will be described at present ; 
others will be subsequently explained. 




OF THE THEODOLITE. 



PL 1. The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a 
tripod ABC, which enters by means of a screw the lower 
horizontal plate DE, and becomes firmly attached to the body 
of the instrument. Through the horizontal plate DE, four 
small hollow cylinders are inserted, which receive four screws 
with milled heads, that work against a second horizontal 
plate, FG. The upper side of the plate DE terminates in a 
curved surface, which encompasses a ball, that is nearly a 
semi-sphere, with the plane of its base horizontal. This ball, 
which is hollow, is firmly connected with the smaller base of 
a hollow conic frustrum, that passes through the curved part 



5G ELEMENTS OF SURVEYING, 

of the plate DE, and screws firmly into the curved part of tVie 
second horizontal plate FG. 

A hollow conic spindle passes through the middle of the 
ball, and the hollow frustrum with which it is connected. To 
this spindle, a third horizontal and circular plate HI, caUed 
the limb of the instrument, is permanently attached. Within 
this spindle, and concentric with it, there is a second spindle, 
called the inner, or solid spindle, To this latter, is united a 
thin circular plate, called the vernier plate, which rests on the 
limb of the instrument, and supports the upper frame-work. 
The two spindles terminate at the base of the spherical ball, 
where a small screw enters the inner one, and presses a 
washer against the other, and the base of the ball. On the 
upper surface of the plate FG, rests a clamp which goes round 
the outer spindle, and which being compressed by the clamp- 
screw K, is made fast to it. This clamp is thus connected with 
the plate FG. A small cylinder a, is fastened to the plate FG: 
through this cylinder a thumb-screw L passes, and works 
into a small cylinder b, connected with the clamp. The 
cylinders b and a, admit of a motion round their axes, to 
relieve the screw L of the pressure which would otherwise be 
occasioned by working it. 

Directly above the clamp, is the lower telescope MJST 
This telescope is connected with a hollow cylinder, which is 
worked freely round the outer spindle, by the thumb-screw P 
having a pinion working into a concealed cog-wheel, that is 
permanently fastened to the limb of the instrument. By 
means of a clamp-screw Q, the telescope is made fast to the 
limb, when it will have a common motion with the limb and 
outer spindle. 

The circular edge of the limb is chamfered, and is generally 
made of silver, and on this circle the graduation for horizontal 
angles is made. In the instrument described, the circle is cut 
into degrees and half degrees ; the degre\es are numbered from 
to 360. 

On the circular edge of the vernier plate, is a small space 
of silver, called a vernier ; this space is divided into 30 equal 
parts, and numbered from the line marked to the left. 

There are two levels attached to the vernier plate, at right 
angles to each other, by small adjusting screws; one of them 
is seen in the figure. The vernier plate turns freely around 



OF THE THEODOLITE. 57 

with the inner spindle. It is made fast to the limb of the 
instrument by the damp-screw S ; after which the smaller 
motions are made by the tangent-screw T. 

There is a compass on the vernier plate, that is concentric 
with it, the use of which will be explained under the head 
compass. 

The frame-work which supports the horizontal axis of the 
vertical semicircle UV and the upper telescope, with its 
attached level, rests on the vernier plate, to which it is made 
fast by three adjusting screws, placed at the angular points of 
an equilateral triangle. The vertical semicircle UV, is called 
the vertical limb ; its motions are governed by the thumb-screw 
Z, which has a pinion, that works with the teeth of the ver- 
tical limb. On the face of the vertical limb, opposite the 
thumb-screw Z, the limb is divided into degrees and half 
degrees : the degrees are numbered both ways from the line 
marked 0. There is a small plate resting against the gradu- 
ated face of the vertical limb, called the vernier ; it is divided 
into 30 equal parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges of 
divisions, commencing at the point, and extending each way 
45". The one shows the vertical distance of any object to 
which the upper telescope is directed, above or below the 
place of the instrument, in lOOth parts of the horizontal 
distance : the other, the difference between the hj'^pothenusal 
and base lines : the hypothenuse being supposed to be divided 
into one hundred equal. parts: therefore, by mere inspection, 
we can ascertain the number of links, which must be sub- 
tracted from every chain of an oblique line, to reduce it to 
a true horizontal distance. 

The supports of the upper telescope are called the wyes, 
and designated Y^s. Two loops, turning on hinges, pass over 
the telescope, and are made fast by the pins c and d; these 
loops confine the telescope in the Y^s. By withdrawing the 
pins, and turning the loops on their hinges, the telescope may 
be removed for the purpose of being reversed in position ; and 
in both situations, the telescope can be revolved in the F's 
about its axis. 

In the telescopes attached to the theodolite, are two prin- 
cipal lenses, one a,t each end. The one at the end Avhere 



58 ELEMENTS OF SURVEYING. 

llic eye is placed, is called the eyeglass, the other the object 
glass. 

In order that the axis of the telescope may be directed to 
an object with precision, two spider's lines, or small hairs, are 
fixed at right angles to each other, and placed within the 
barrel of the telescope, and at the focus of the eyeglass. 
The vertical hair is moved by two small horizontal screws, 
one of which, /, is seen in the figure ; and the horizontal 
hair, by two vertical screws, g and h. 

Before using the theodolite, it must be properly adjusted. 
The adjustment consists in bringing the different parts to their 
proper places. 

The line of collimation, is the axis of the telescope. With 
this axis, the line drawn through the centre of the eyeglass, 
and the intersection of the spider's hues, ought to coincide. 

First adjustment. The first adjustment regards the line 
of coUimation: it is, to fix the intersection of the spider^s lines m 
the axis of the telescope. 

Having screwed the tripod to the instrument, extend the 
legs, and place them firmly. Then loosen the clamp-screw *S 
of the vernier plate, and direct the telescope to a small, well- 
defined, and distant object. By means of a small pin i, on 
the under side of the telescope, slide the eyeglass till the 
spider's lines are seen distinctly ; then with the thumb-screw 
X, which forces out and draws in, the object glass, adjust this 
glass to its proper focus, when the object, as well as the 
spider's lines, will be distinctly seen: after which, by the 
tangent-screw T and the thumb-screw Z, bring the inter- 
section of the spider's lines exactly upon a well-defined point 
of the object. 

Having done this, revolve the telescope in the Y^s, half round, 
when the attached level mn, will come to the upper side. 
See, in this position, if the horizontal hair appears above oi 
below the point, and in either case, loosen one, and tighten 
the other, of the two screws that work the horizontal hair, 
till the horizontal hair has been carried over half the space 
between its last position and the observed point. Carry the 
telescope back to its place ; direct again the intersection of the 
spider's lines, to the point, and repeat the operation till the 
horizontal hair neither ascends nor descends, while the tele- 



OF THE THEODOLITE. 59 

scope is revolved. A siHiilar process will arrange the vertical 
hair, and the line of colliniation is then adjusted. 

Second adjustment. — To make the axis of the attached 
level of the upper telescope, parallel to the line of collimation. 

Turn the vernier plate, till the telescope comes directly over 
two of the levelling screws, between the plates DE and FG. 
Turn these screws contrary ways, keeping them firm against 
the plate FG, till the bubble of the level mn, stands at the 
middle of the tube. Then, open the loops, and reverse the 
telescope. If the bubble still stands in the middle of the 
tube, the axis of the tube is horizontal ; but if not, it is in- 
clined, the bubble being at the elevated end. In that case, 
by means of the small vertical screws m and n, at the ends 
of the level, raise the depressed end, or depress the elevated 
one, half the inclination ; and then, with the levelling screws, 
bring the level into a horizontal position. Reverse the tele- 
scope in the F's, and make the same correction again ; and so 
on, until the bubble stands in the middle of the tube, in both 
positions of the telescope : the axis of the level is then hori- 
zontal. Let the telescope be now revolved in the Y^s. If the 
bubble continue in the middle of the tube, the axis of the 
level is not only horizontal, but also parallel to rh • tine of 
collimation. If, however, the bubble recede from its centre, 
the axis of the level is inclined to the line of collimation, and 
must be made parallel to it by means of two small screws, 
(one of which is seen at p,) which work horizontally. By 
loosening one of them, and tightening the other, the level is 
soon brought parallel to the line of collimation, and tiien, if the 
telescope be revolved in the F'5, the bubble will continue in 
the middle of the tube. 

It is difficult to make the first part of this' adjustment, while 
the axis of the level is considerably inclined to the liiic of 
collimation ; for, if the level were truly horizontal in one 
position of the telescope, when the telescope is reversed, the 
bubble would not stand in the middle of the tube, except 
in one position of the level. This suggests the necessity of 
making the first part of the adjustment with tolerable accu- 
racy; then, having made the second with care, let the first 
be again examined, and proceed thus till the adjustment is 
completed 



60 ELEMENTS OF SURVEYING. 

Third adjustment. — To make the limb of the instrument 
horizontal, or, to make the common axis of the limb and vernier 
plate truly vertical. 

This adjustment is effected, partly by the levelling screws, 
and partly by the thumb-screw Z. Turn the vernier plate, 
until the upper telescope comes directly over two of the level- 
ling screws, then turn them contrary ways, till the upper tel- 
escope is horizontal ; after which, turn the vernier plate 180°, 
and if the bubble of the level remains in the middle of the 
tube, one line of the limb is horizontal. But if the bubble 
recede from the centre of the level, raise the lower, or depress 
the upper end, one-half by the levelling screws, the other by 
the thumb-screw Z, till it is brought into a horizontal posi- 
tion. Turn the vernier plate again 180°, and if the level 
be not then horizontal, make it so, by dividing the error as 
before, and repeat the operation until the line of the limb 
is truly horizontal. Then turn the vernier plate 90", and 
level as before. The limb ought now to be truly horizontal ; 
but lest the first horizontal line may have been changed, in 
obtaining the second, it is well to bring the telescope and 
level two or three times over the levelling screws, until an 
entire revolution can be made without displacing the bubble 
from the middle of the tube. As this can only be the case 
when tlie level revolves around a vertical line, it follows that 
the limb will then be horizontal, and the axis of the instru- 
ment vertical. 

This adjustment being completed, the levels of the vernier 
plate are readily made parallel with it, by means of the small 
screws at their extremities. The three levels being then hori- 
zontal, and perpendicular in direction to the axis of the theo- 
dolite, the bubbles will retain the middle places in tlie tubes, 
during an entire revolution of the vernier plate, or of the 
limb and vernier plate together. 

But the levels of the vernier plate may be made parallel 
with the limb, and the limb made truly horizontal, without 
the aid of the upper level. 

Let the upper telescope be placed directly over two of the 
levelling screws. One of the levels of the vernier plate will 
then be parallel to the line of these two screws, and the other 
level will be at right angles to this line, or parallel to the line 
of the other two levelling screws. In thi-s situation, let the 



OF THE THEODOLITE. 61 

levels be made horizontal, by means of the levelling screws. 
Then turn the vernier plate 180°, and if they both continue 
horizontal, the limb is truly level. But if both, or either of 
them, be changed from a horizontal position, let the error 
be divided between the level and the limb ; and repeat the 
operation until the levels will continue horizontal during au 
entire revolution : the limb is then horizontal, and the axis 
of the instrument truly vertical. 

Fourth adjustment. — To make the axis of the vertical 
limb truly horizontal, or perpendicular to the axis of the instru- 
ment. 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb line, or any well-defined vertical 
object, and move the telescope with the thumb-screw Z : if 
the intersection of the spider's lines continue on the vertical 
line, the axis is horizontal. 

Or, the adjustment may be effected thus: Direct the inter- 
section of the spider's lines to a well-defined point that is 
considerably elevated : then turn the vertical limb, until the 
axis of the telescope rests on some other well-defined point, 
upon or near the ground : reverse the telescope, and turn the 
vernier plate 180°; now, if in elevating and depressing the 
telescope, the line of collimation passes through the two 
points before noted, the axis is horizontal. If it be found, by 
either of the above methods, that the axis is not horizontal, it 
must be made so by the screws which fasten the frame-work 
to the vernier plate. 

There are two important lines of the theodolite, the positions 
of which are determined with great care by the maker, and 
fixed permanently. First, the axis of the instrument is placed 
exactly at right angles with the limb and vernier plate ; and 
unless it have this position, the vernier plate will not revolve 
at right angles to the axis, as explained in the third adjust- 
ment. Secondly, the line of collimation of the upper telescope, 
is fixed at right angles to the horizontal axis of the vertical 
limb. We can ascertain whether these last lines are truly at 
right angles, by directing the intersection of the spider's lines 
to a well-defined point ; then removing the caps which con- 
fine the horizontal axis in its supports, and reversing the 
axis : if the intersection of the spider's lines can be made to 



bZ ELEMENTS OF SURVEYING. 

cover exactly the same point, without moving the vernier 
plate, the line of collimation is at right angles to the axis. 

If the theodolite be so constructed that either of the Y^s 
admits of being moved laterally, so as to vary the angle be- 
tween the horizontal axis and the line of collimation, these 
lines may be adjusted at right angles to each other, if they 
have not been so placed by the maker. 

The lower telescope being used merely as a guard, requires 
no adjustment, although it is better to make the axis, about 
which its vertical motions are performed, horizontal, or per- 
pendicular to the axis of the instrument ; and this is easily 
effected by means of the two small screws k and /, which 
work into the slide A', that is connected with the horizontal 
axis. 

The theodolite being properly adjusted, the particular uses 
of its several parts, and the manner of measuring angles, are 
now to be explained. 

There are two verniers on the vernier plate, and the points 
of them marked 0, are at the opposite extremities of a diam- 
eter ; which diameter is the intersection of a vertical plane 
passed through the line of collimation, with the vernier plate. 
It is important to ascertain the exact arc intercepted on the 
limb, between its point, (this being the point from which the 
degrees are numbered), and this diameter, for any position 
which it may assume. The limb being divided to half degrees, 
if we had only the line marked on the vernier, to guide 
us, the place of the extremity of the diameter could only be 
ascertained with certainty to half degrees, as there would be 
no means of determining its exact position, when it falls 
between the lines of division on the limb. But the vernier 
affords results much more accurate. As most instruments 
for the measurement of angles have verniers, it will perhaps 
be best to explain their use generally. 

First. — Count carefully the number of spaces into which 
the vernier is divided : this number is one less than the num- 
ber of lines which limit them. 

Secondly. — Turn the vernier till the line at one extremity 
coincides with a line of the graduated limb,, when the line 
at the other extremity will also coincide with a line of the 
graduated limb ; for the sum of the spaces on the vernier ia 



OF THE THEODOLITE. 63 

always exactly equal to a given number of spaces on the 
limb ; then count the number of spaces on the limb which 
the vernier covers. 

Thirdly. — Examine the limb of the instrument, and ascer 
tain into what parts of a degree it is divided, and express one 
of those equal parts in minutes. 

Let X represent the value of one of the equal spaces of the 
vernier, and n their number; then nx will be equal to the 
space covered by the vernier. Let a represent the smallest 
equal space into which the limb is divided, and m the number 
of such spaces covered by the vernier ; then ma will be equal 
to the space on the limb covered by the vernier, which is also 
equal to nx. 

The equation nx=ma is called the equation of the instru- 
ment. In this equation, 

ma 
x=— ; 
n 

m, a, and n, being known, x can be found, as also the differ- 
ence between a and x, which we shall show presently, to be 
the smallest certain count of the instrument. 

In the theodolite, m = 29, a==30' andn=30 hence ; 

x = 'l^^ = 20'; 
30 

and a—x = 30' — 29' = l', 

the excess of a space on the limb over a space on the vernier. 

Fig. 2. Let AB be a portion of the limb of the instru- 
ment, and CED the vernier in one of its positions, its 
point coinciding with the line marked 10 on the limb. Now, 
since each space of the vernier is less by l' than each space 
of the limb, the first line on the left of 0, will be l' to ihe 
right of the first line on the left of the 1 on the limb ; and if 
the vernier plate be moved l' towards the left, these lines will 
coincide, and the second line from will then be 1' to the right 
of the second line from 10 ; if the vernier be moved another 
minute, these last lines will coincide. The vernier would then 
show 100 2'. 

If the vernier plate be turned still farther, till the thirrl, 
fourth, fifth, &c. lines coincide, it is plain, that the point of 
the vernier will have passed the line 10 on the limb, by as 
many minutes as there are lines of the vernier which shall 
have coincided with Imes of the limb. When the last Ime 



64 ELEMENTS OF SURVEYING. 

of the vernier coincides with a line of the limb, the vernier 
will have been moved 30', or half a degree; and the point 
will at the same time coincide with a line of the limb, and 
show 10° 30'. 

The general rule for reading the angle for any position of 
the vernier may now be stated. 

When the line of the vernier coincides with a line of the 
limb, the arc is easily read from the limb ; but when it falls 
between two lines, note the degrees and half degrees up to 
the line on the right ; then pass along the vernier till a line is 
found coinciding with a line of the limb : the number of this 
line from the point, indicates the minutes which are to be 
added to the degrees and half degrees, for the entire angle. 

To measure a horizontal angle with the theodolite. 

Place the axis of the instrument directly over the point at 
which the angle is to be measured. This is effected by means 
of a plumb, suspended from the plate which forms the upper 
end of the tripod. 

Having made the limb truly level, place the of the ver- 
nier at or 3600 of the Umb, and fasten the clamp-screw S 
of the vernier plate. Then, facing in the direction between 
the lines which subtend the angle to be measured, turn the 
limb with the outer spindle, until the telescope points to the 
object on the left, very nearly. Clamp the limb with the 
ciamp-screw K, and by means of the tangent screws L and 
Z, bring the intersection of the spider's lines to coincide 
exactly with the object. 

Having loosened the clamp-screw Q of the lower telescope 
MJ^, direct it with the thumb-screw P to the same object at 
which the upper telescope is directed ; then tighten the clamp- 
screw Q. This being done, loosen the clamp-screw /S of the 
vei niei plate, and direct the telescope to the other object : the 
arc imssed over by the point of the vernier, is the measure 
of the angle sought. 

The lower telescope having been made fast to the limb, 
will indicate any change of its position, should any have taken 
place ; and, as the accuracy of the measurements depends on 
the fixedness of the limb, the lower telescope ought to be 
often examined, and if its position has been altered, the limb 
must be brought back to its place by the tangent-screw L. 



OP THE THEODOLITE. 65 

It is not necessary to place the point of the vernier at the 
point of the limb, previously to commencing the measure- 
ment of the angle, but convenient merely ; for, whatever be 
the position of this point on the limb, it is evident that the arc 
which it passes over is the true measure of the horizontal 
angle. If, therefore, its place be carefully noted for the first 
direction, and also for the second, the difference of these two 
readings will be the true angle, unless the vernier shall have 
passed the point of the limb, in which case the greater read- 
ing must be subtracted from 360", and the remainder added 
to the less. 

To measure a vertical angle. 

In Fig. 3, AB represents a view of the vertical limb oppo- 
site the thumb-screw Z, and ED is the vernier. The 
point of this vernier is at tlie middle division line, and fifteen 
spaces lie on each side of it. The relation which exists be- 
tween the spaces on the limb and those of the vernier, is the 
same as that between the divisions of the horizontal limb and 
its vernier, and the degrees and half degrees are read in the 
same manner : the angles of elevation being read from the 
of the limb towards the right, and those of depression in the 
contrary direction. For the minutes, we pass along the ver- 
nier in tlie direction in which the degrees are counted, and if 
we reach the extreme line, which is the fifteenth, without 
finding a coincidence, we must then pass to the other extre- 
mity of the vernier, and look along towards the point till 
two lines are found to coincide : the number of the line on the 
vernier will show the minutes. The lines of the vernier are 
numbered both ways from the point, and marked 5, 10, 1 5, 
to one extremity, and correspondingly from the other extre 
mity 15, 20 and 25, to the point again. The upper range 
shows the minutes for angles of elevation, and the lower 
range for those of depression. The vernier in Fig. 3 stands 
at 2" 15' of depression. Had the 15th line at the left, 
passed the short line with which it now coincides, we should 
pass to the line 15, on the lower range to the right, and then 
count towards the to the left. 

The first thing to be done, is to ascertain the point of the 
vertical limb at which the point of the vernier stands, when 
the line of collimation of the upper telescope, together with 



66 ELEMENTS OF SURVEYING. 

its attached level, is truly horizontal. This is called the true 
of the limb. 

If the instrument be accurately constructed, and the parts 
have not been disarranged, this point is the point of the 
hmb. This, however, is easily ascertained by turning the limb 
till the O's correspond, and then examining if the upper level 
be truly horizontal. If not, direct the telescope to a distant 
and elevated object, and read the degrees on the vertical 
limb. Turn the vernier plate 180", reverse the telescope, 
direct it a second time to the same point, and read the arc on 
the vertical limb. The half difference of these two readings, 
counted from the point of the limb, in the direction of the 
greater arc read, gives the true point of the vertical limb ; 
that is, the point at which the of the vernier stands when 
the line of collimation is horizontal. 

Suppose for example, that we had directed the telescope to 
a point and found the of the vernier to stand at 10° of ele- 
vation. If we now reverse the telescope, it ought to incline 
at an equal angle of depression. If then we turn the whole 
180°, and then raise the depressed end of the telescope with 
the thumb-screw Z", until it is directed to the same point as 
before, the ought to stand at 10°. If it shows a less arc, 
the true is between the of the limb and the first arc read ; 
if a greater, it is on the other side, and the difference divided 
by two will indicate the exact point. The half difference 
thus found is called the correction. When the true o falls 
between the marked and the eyeglass, the correction is to 
be subtracted from the arc read, for angles of elevation, and 
added, for angles of depression ; and the reverse when it falls 
on the other side. The eyeglass is supposed to be over the 
thumb-screw Z, as in the plate. 

These preparatory steps being taken, let the axis of the 
telescope be directed to any point either above or below the 
plane of the limb, and read the arc indicated by the of the 
vernier. To the arc so read apply the proper correction, if 
any, and the result will be the true angle of elevation or de- 
pression. 

87. Having explained the preliminary principles, it only 
remains to apply them to the measurement of Heights and 
Distances. 



HEIGHTS AND DISTANCES. 



67 



PROBLEM I. 

To determine the horizontal distance to a 'point which is inacces' 
sible by reason of an intervening river. 

88. Let C be the point. Measure 
along- the bank of the river a hori- 
zontal base line t^B, and select the 
stations ^ and B, in such a manner 
that each can be seen from the other, 
and the point C from both of them. 
Then measure the horizontal angles 
CAB and CBA. 

Let us suppose that we have found .^5 = 600 yards, CAB 
57035' and CjBcy2 = 640 5l'. 

The angle 0=180° - (^+jB) = 570 34'. 

To find the distance BC. 




As sin C 


. 57" 34' . ar. comp. 


. 0.073649 


: sin A 


. 570 35' . 


. 9.926431 


:: AB 


. 600 ... . 

. 600.11 yards. 


. 2.778151 


: BC 


. 2.778231 


% 


To find the distance AC. 




As sin C 


57° 34' ar. comp. 


. 0.073649 


: sin B 


64051'. 


. 9.956744 


:: AB 


600 ... . 
643.94 yards 

PROBLEM II. 


. 2.778151 


: AC 


2.808544 







To determine the altitude of an inaccessible object above a giveu 
horizontal plane. 



FIRST METHOD. 

89. Suppose D to be the inacces- 
sible object, and BC the horizontal 
plane from which the altitude is to 
be estimated : then, if we suppose 
DC to be a vertical line, it will re- 
present the required distance. 




C3 ELEMENTS OF SURVEYING. 



Measure any horizontal base line, as B*B. ; and at the ex- 
tremities B and A, measure the horizontal angles CBA and 
CAB. Measure also, the angle of elevation DBC. 

Then in the triangle CBA there will be known, two angles 
and the side AB ; the side BC can therefore be determined. 
Having found BC, we shall have, in the right-angled triangle 
DBC, the base BC and the angle at the base, to find the 
perpendicular DC, which measures the altitude of the point 
D above the horizontal plane BC. 

Let us suppose that we have found 

BA = 1S0 yards, the horizontal angle CBA = ilo2i', 
the horizontal angle CAB — de>° 28', and the angle of elevation 
DBC=10<^43'. 

In the triangle BAC, to find the horizontal distance BC 

The angle 5C^ = 180°— (41° 24'+96° 28') =42''08' = C. 



As sin C . .42° 08' ar. comp. 


. 


. 0.173369 


: sin.^ . . 960 28' . 


• 


. 9.997228 


:: AB . . ISO 


to 


. 2.892095 


: BC . . 1155.29 


. 3.062G92 


In the right-angled triangle DBC, 


find DC. 


As R . . ar. comp. . 




0.000000 


: tan DBC . . 10° 43' . 




9.277043 


BC . . 1155.29 . 




3.062692 


: DC . . 218.64 . 




2.339735 



Remark I. It might, at first, appear that the solution which 
we have given, requires that the points B and A should be in 
the same horizontal plane, but it is entirely independent of 
such a supposition. 



HEIGHTS AND DISTANCES. 69 

For, the horizontal distance, which is represented by BA, 
is the same, whether the station Jl is on the same level with 
J5, above it, or below it (Art. 74). The horizontal angles 
CAB and CBA are also the same, so long as the point C is in 
the vertical line DC (Art. 75). Therefore, if the horizontal hne 
through A should cut the vertical line DC, at any point as E, 
above or below C, AB would still be the horizontal distance 
between B and A, and .^JE which is equal to AC, would be 
the horizontal distance between A and C. 

If at A, we measure the angle of elevation of the point D, 
we shall know in the right angled DAE, the base AE, and 
the angle at the base ; from which the perpendicular DE can 
be determined. 

Let us suppose that we had measured the angle of elevation 
DAE, and found it equal to 20° 15'. 

First: In the triangle BAC, to find AC or its equal AE, 



As sin C . . 42° 08' ar. comp. . 


. 0.173369 


: sin B . . 41°24' 


. 9.820406 


: : AB . . 780 ... 


. 2.892095 


: AC . . 768.9 


. 2.885870 


In the right-angled triangle DAE, to 


find DE, 


As iJ . . • ar. comp. 


. 0.000000 


: tan .^ . . 20« 15' 


. 9.566932 


: : AE . . 768.9 


. 2.885870 


: DE . . 283.66 


. 2.452802 



Now, since DC is less than DE, it follows that the station 
B is above the station A. That is, 

JDE-i)C = 283.66 -2 18.64= 65.02 =J5:C, 

which expresses the vertical distance that the station B is 
above the station A. 

Remark II. It should be remembered, that the vertical 
distance which is obtained by the calculation, is estimated from 
a horizontal hne passing through the eye at the time of 
observation. Hence, the height of the instrument is to be 
added, in order to obtain the true result. 



70 ELEMENTS OF SURVEYING. 



SECOND METHOD. 




90. When the nature 
of the ground will ad- 
mit of it, measure a base 
line AB in the direction 
of the object D. To 

do this, it will be well to A ^^^^w^^v^^^^^-jy - 

place the theodolite at Jl^ and range the chain staves by means 
of the upper telescope. Having measured the base, measure 
with the instrument the angles of elevation at A and B. 

Then, since the outward angle DBC is equal to the sum 
of the angles A and ADB, it follows, that the angle ADB 
is equal to the difference of the angles of elevation at A and 
B. Hence, we can find all the parts of the triangle ADB. 
Having found DB, and knowing the angle DBC, we can find 
the altitude DC. 

This method supposes that the stations .^ and 5 are on 
the same horizontal plane ; and therefore can only be used 
when the line AB is nearly horizontal. 

Let us suppose that we have measured the base line, and 
the two angles of elevation, and 

CAB = Q15 yards 
found ?^ = 15° 36' 

(2)50 = 270 29'; 
required the altitude DC. 

First: ADB=DBC-A=2i' 29' -15' 36' = ii» 53'. 





In tlie triangle ADB, to find BD. 




As sin D 


11° 53' . ar. comp. 


, 


0.686302 


: sin A 


. 15° 36' . 


. 


9.429623 


: : AB 


975 . . 
. 1273.3 . 


• 


2.989005 


: DB 


3.104930 




In the triangle DBC, to find 


DC. 




As R 


ar. comp. 


, 


0.000000 


: sin 5 


27° 29' . . . 


. 


9.664163 


:: DB 


. 1273.3 


. 


3.104930 


: DC 


. 587.61 


. 


2.769093 




HEIGHTS AND DISTANCES. 71 

PROBLEM III. 

To determine the perpendicular distance of an object below a given 
horizontal plane, 

91. Suppose C to be directly 
over the given object, and A the 
point through which the horizontal 
plane is supposed to pass. 

Measure a horizontal base line 
AB, and at the stations A and B 
conceive the two horizontal lines . , 
.^C, BC, to be drawn. The oblique ^'^ ' ^"^^4^ 

lines from A and B to the object will be the hypothenuse? 
of two right-angled triangles, of which AC, BC, are the 
bases. The perpendiculars of these triangles will be the 
distances from the horizontal lines AC, BC, to the object. 
If we turn the triangles about their bases AC, BC, until 
they become horizontal, the object, in the first case, will fall 
at C, and in the second at C". 

Measure the horizontal angles CAB, CBA, and also the 
angles of depression C'AC, C"BC. 

Let us suppose that we have 

\AB = Q12 yards 

found <^ ABC = 39' 20' 
CV3C = 27° 49' 

C"BC = 19' 10' 
First: In the triangle ABC, the horizontal angle 
ACB = lS0'—{A+B) = l80'-lll' 49'=6S° 11'. 

To find the horizontal distance AC. 

As sin C . 68° 11' . ar. comp. . 0.032275 

sin 5 . 39° 20' . . . • 9.801973 

AB .672 . . . . 2.827369 

AC . 458.79 . . . . 2.661617 

To find the horizontal distance BC. 
As sin C . 68° u' . ar. comp. . 0.032275 

9.979380 
2.827369 
2.839024 



sin A 


72° 29' 


AB . 


672 


BC . 


690.28 



7t 



ELEMEiNTS OF SURVEYING. 



In the triangle CJlC, to find CC\ 



As 



R 

tan C'^C 

AC 

CO 



ar. comp 



. 27" 49' 
. 458.79 
. 242.06 



In the triangle CBC'\ to find CC". 
ar. comp. 



As R . 


. 


: tan C'BC 


. 19° 10' 


:: BC 


. 690.28 


: CC" 


. 239.93 



0.000000 
9.722315 
2.061017 
2.383932 



0.000000 
9.541061 
2.839024 
2.380085 



Hence also, CC — CC"=:242. 06 — 239.93 = 2.13 yards; 
which is the height of the station A above station B. 

Remark. In measuring a base line, if great accuracy is 
required, the theodolite should be placed at one extremity, 
and the telescope directed to the other, and the alignment of 
the staves made by means of the intersection of the spider's 
lines. If the highest degree of accuracy is necessary, the 
base line should be measured with rods, which admit of being 
adjusted to a horizontal position by means of a spirit level. 

APPLICATIONS. 

1. Wanting to know the distance between two inaccessible 
objects, which lie in a direct line from the bottom of a tower 
of 120 feet in height, the angles of depression are measured, 
and are found to be, of the nearest 57°, of the most remote 
2 5° 30' : required the distance between them. 

Jlns. 17 3.656 feet. 



2. In order to find the distance between 
two trees A and B, which could not be 
directly measured because of a pool which 
occupied the intermediate space, the dis- 
tances of a third point C from each of 
them were measured, and also the included 
angle ACB : it was found that 




HEIGHTS AND DISTANCES. 



73 



CB = Q12 yards 
Cd = 588 yards 



required the distance AB. 



55° 40'; 



Ans. 592.967 yards. 



3. Being on a horizontal plane, and wanting to ascertain 
the height of a tower, standing on the top of an inaccessible 
hill, there were measured, the angle of elevation of the top 
of the hill 40°, and of the top of the tower 51°; then mea- 
suring in a direct line 180 feet farther from the hill, the angle 
of elevation of the top of the tower was 33° 45' ; required the 
height of the tower. ^^^^ g3_^g3 ^^^^^ 

4. Wanting to know the horizon- 
tal distance between two inaccessi- 
ble objects E and W, the following ^^r 
measurements were made, 

AB = 5ZG yards 
BAW=40' 16' 

viz. { WAE=5i' 40' 

.^^^=42° 22' 
EBW=1\' 07' 
required the distance EW. 

5. Wanting to know the hor- 
izontal distance between two 
inaccessible objects A and B,S^ 
and not finding any station from 
which both of them could be 
seen, two points C and D, were 
chosen, at a distance from each 
other, equal to 200 yards ; from the former of these points A 
could be seen, and from the latter Bf and at each of the points 
C and D a staff was set up. From C a distance CF was 
measured, not in the direction DC, equal to 2 00 yards, and 
from D a distance DE equal to 200 yards, and the following 
angles taken, 

r^FC = 83° 00' J52)E = 54° 30' 
viz. <.4CZ)=.53° 30' i?DC=156°25' 
(ACF-.^5^o 31' BEn=88' 30' 

Ans, .^^=345.467 yards. 




74 



ELEiMKxNTS OF SURVEYING. 



6. From a station P there can be 
seen three objects A, B and C, whose 
distances from each other are known : 
viz. AB = SOO, JlC = eoo, and BC 
==400 yards. Now, there are mea- 
sured the liorizontal angles 

.5PC = 33o 45' and BPC=22° 30' : 
it is required to find the three distances 
PA, PC, and PB. 




r P^ = 710.193 yards. 
Ans. ^PC= 1042. 522 
r P^ = 934.291 



OF MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 

92. It often happens that instrmnents for the measurement 
of angles cannot be easily obtained ; we must then rely 
entirely on the tape or chain. 

We now propose to explain the best methods of determining 
distances, without the aid of instruments for the measurement 
of horizontal or vertical angles. 

PROBLEM I. 

To trace, on the ground, the direction of a right line, that shall be 
perpendicular at a given point, to a given right line. 



£> 



FIRST METHOD. 

93. Let BC be the given right line, and 
A the given point. Measure frj*m A, on 
the line BC, two equal distances AB, AC, 
one on each side of the point A. Take a b A C 

portion of the chain or tape, greater than ^^B, and place one 
extremity at B, and with the other trace the arc of a circle on 
the ground. Then remove the end which was at B, to C, 
and trace a second arc intersecting the former at D. The 
straight line drawn through D and A will be perpendicular 
to jBC at A. 



PRACTICAL PROBLEMS. 



75 



f SECOND METHOD. 

94. Having made AB=AC, take 
any portion of the tape or chain, con- 
siderably greater than the distance _^ 
between B and C. Mark the middle 
point of it, and fasten its two extremi- 
ties, the one at B and the other at JJ 
C, Then, taking the chain by the middle point, stretch it 
tightly on either side of BC, and place a staff at D or £ : 
then will DJlE be the perpendicular required. 




f 



THIRD METHOD. 

95. Let JIB be the given line, and 
C the point at which the perpendicular 
is to be drawn. From the point C 
measure a distance CA equal to 8. 
With C as a centre, and a radius equal 
to 6, describe an arc on either side of 
»^B : then, with .^ as a centre, and a 
radius equal to 1 0, describe a second arc 
intersecting the one before described at E: then draw the 
line EC, and it will be perpendicular to AB at C, 



Ar 



k 



Remark. Any three lines, having the ratio of 6, 8 and 10, 
form a right-angled triangle, of which the side corresponding 
to 10 is the hypothenuse 



FOURTH METHOD. 




96. Let AD be the given right 
hne, and D the point at which 
the perpendicular is to be drawn. 
Take any distance on the tape or 
chain, and place one extremity at 
D, and fasten the other at some 

point as E, between the two lines ***- --'" 

which are to form the right angle. Place a staff at E. 
Then, having stationed a person at D, remove the extremity 
of the chain and carry it round until it ranges on the line 
DA at A. Place a staff at A : then remove the end of the 



76 ELEMENTS OF SURVEYING. 

chain at Jl^ and carry it round until it falls on the line AE 
at F. Then place a staff at F, and JIDF will be a right 
angle, being an angle in a semi-circle. 

97. There is a very siinple instrument, used exclusively 
in laying off right angles on the ground, which is called the 

SURVEYING CROSS. 

PI. 2. Fig. 1. This instrument consists of two bars, JIB 
and CD, permanently fixed at right angles to each other, 
and firmly attached at ^ to a pointed staff, Avhich serves as 
a support. Four sights are screwed firmly to the bars, by 
means of the screws a, 6, c, and d. 

As the only use of this instrument is to lay off right angles, 
it is of the first importance that the lines of sight be truly 
at right angles. To ascertain if they are so, let the bar AB 
be turned until its sights mark some distinct object ; then 
look through the other sights and place a staff on the line 
which they indicate : let the cross be then turned until the 
sights of the bar AB come to the same line : if the other 
sights are directed to the first object, the lines of sight are 
exactly at right angles. 

The sights being at right angles, if one of them be turned 
in the direction of a given line, the other will mark the direc- 
tion of a line perpendicular to it, at the point where the 
instrument is placed. 

PROBLEM II. 

From a given point without a straight line, to let fall a perpen- 
dicular on the line. 

98. Let C be the given point, 
and AB the given line. 

From C measure a line, as CA, 

to any point of the line AB. From ^Ir-'"^ \ n 

A, measure on AB any distance ^ Jb' D 

as AF, and at F erect FF perpendicular to AB. 

Having stationed a person at A, measure along the perpen- 
dicular FF until the forward staff is aligned on the line AC : 
then measure the distance AE. Now, by similar triangles, 
we have 

AE : AF :: AC : AD 




HEIGHTS AND DISTANCES. 77 

in which all the terms are known except AD, which may, 
therefore, be considered as foimd. The distance AD being 
laid off from A, the pomt D, at which the perpendicular 
CD meets AB, becomes known. If we wish the length of 
the perpendicular, we use the proportion 

AE : EF : : AC : CD, 
in which all the terms are known, excepting CD : there- 
fore, CD is determined. 

PROBLEM III. 

To determine the horizontal distance from a given point to an 
inaccessible object. 

99. Let A be an inaccessible ob- 
ject, and E the point from which I 
the distance is to be measured. 

At E lay off the right angle AED, --^^ 

and measure in the direction ED, U 

any convenient distance to D, and » ^f-r 
place a staff at D. Then measure ^..x" ; 
from E, directly towards the object D F ■ ''' 

A, a distance EB of a convenient length, and at B lay off 
a line BC perpendicular to EA. Measure along the line 
BC, until a person at D shall range the forward staff on the 
line DA. Now, DF is known, being equal to the difference 
between the two measured lines DE and CB. Hence, by 
similar triangles, 

DF : FC : : DE : EA, 
in which proportion all the terms are known, except the 
fourth, which may, therefore, be regarded as found : hence, 
EA is determined. 

SECOND METHOD. 

100. At the point E lay off 
EB perpendicular to the line 
EA, and measure along it any 
convenient distance, as EB. 

At B lay off the right angle 
EBD, and measure any distance 
in the direction BD. Let a per- 
son at D align a staff on DA, 




78 



ELEMENTS OF SURVEYING. 



while a second person at B aligns it on BE : the staff will 
thus be fixed at C. Then measure the distance BC. 
The two triangles BCD and CAE being similar, we have, 

BC : BD : : CE : EA, 

m which all the terms are known, except the fourth, which 
may, therefore, be regarded as found. 



THIRD METHOD. 

101. Let B be the given point, 
and A the inaccessible object, it 
is required to find BA. 

Measure any horizontal base 
line, as BC. Then, having placed 
staves at B and C, measure any 
convenient distances BD and CE, 
such that the points D, B and A, 
shall be in the same right line, 
as also, the points E, C and A ; 
then rrieasure the diagonal lines DC and EB. 

Now, in the triangle BEC, the three sides are known, 
therefore, the angle ECB can be found. In the triangle 
CDB, the three sides are also known, therefore the angle 
CBD can be determined. These angles being respectively 
subtracted from 180°, the two angles ACB and ABC be- 
come known ; and hence, in the triangle ABC, we have 
two angles and the included side, to find the side BA. 




PROBLEM IV. 



To find the altitude of an object, when the distance to the 
vertical line passing through the top of it is known. 



102. Let CD be the alti- 
tude required, and AC the 
known distance. 

From A, measure on the 



line AC, any convenient ^i ,.'■ 




B 



distance AB, and place a 

staff vertically af, B. Then placing the eye at A, sight to 



CONTENT OF GROUND. 79 

the object D, and let the point, at which the line AD cuts 
the staff BE, be marked. Measure the distance BE on the 
gtaff; then say, 

As . AB : BE : : AC : CD, 
then, CD becomes known. 

If the line AC cannot be measured, on account of inter- 
vening objects, it may be determined by calculation, as in 
the last problem, and then, having found the horizontal dis- 
tance, the vertical line is readily determined, as before. 



CHAPTER III. 

Of the area or content of ground. — Of laying out and 
dividing land. 

103. We come next to the determination of the area or 
content of ground. 

The surface of the ground being, in general, broken and 
uneven, it is impossible, without great trouble and expense, 
to ascertain its exact area or content. To avoid this incon- 
venience, it has been agreed to refer every surface to a 
horizontal plane : that is, to regard all its bounding lines as 
horizontal, and its area as measured by that portion of the 
horizontal plane which the boundary lines enclose. 

For example, if ABCD were a 
piece of ground having an uneven 
surface, we should refer the whole to 
a horizontal plane, and take for the 
measure of the area that part of the 
plane which is included between the 
bounding lines AB, BC, CD, DA. 

In estimating land in this manner, the sum of the areas 
of all the parts into which a tract may be divided, is equal 
to the area estimating it as an entire piece : but this would 
not be the case if the areas of the parts had reference to 
the actual surface, and the area of the whole were calcu- 
lated from its bounding lines. 




80 



ELEMENTS OF SURVEYING. 



104. The unit of a quantity is one of the equal parts of 
which the quantity is composed {Arilh. In. VI). Thus, a 
Jine of three feet in length is made up of' three single feet, 
and of this line, 1 foot is the unit. The unit of a line may 
be 1 foot, 1 yard, 1 rod, 1 chain, or any other known distance. 

If, on the unit of length, a square be described, it will 
form the unit for computing areas. 



1 foot. 



Thus, is 1 square foot, 



1 square yard, or 9 square feet. 



1 yard=3 foet. 





















I square chain, or 16 square rods. . 



1 chain: 


=4 rn 


ds. 



































Thus it is seen that there are two kinds of quantity to be 
considered, viz. lines, and areas or surfaces ; and each kind 
has its own unit of measure. 

When, therefore, the linear measures of ground are feet, 
yards, rods, or chains, the superficial measures will be square 
feet, square yards, square rods, or square chains ; and the 
number expressing the area will be nothing else than the 
number of times which the unit of superficial measure is 
contained in the land measured. 

It has been already observed (Art. 83), that Gunter's chain 
of four rods or 66 feet in length, and which is divided into 
100 links, is the chain in general use among surveyors. We 
shall, therefore, take the length of this chain for the unit 
of linear measure. 



CONTENT OP GROUND. 



81 



105. An acre is a surface equal in extent to 10 square 
chains ; that is, equal to a rectangle of which one side is 
ten chains, and the other side one chain. 

One-quarter of an acre, is called a rood. 

Since the chain is 4 rods in length, 1 square chain con- 
tains 16 square rods; and therefore, an acre, which is 10 
square chains, contains 160 square rods, ar i a rood contains 
40 square rods. The square rods are called perches. 

106. Land is generally computed in acres, roods, and perches, 
which are respectively designated by the letters A. R. P. 

When the linear dimensions of a survey are chains or links, 
the area will be expressed in square chains or square links, 
and it is necessary to form a rule for reducing this area to 
acres, roods, and perches. For this purpose, let us form the 
following 

TABLE. 

1 square chain = 10000 square links. 
1 acre = 10 square chains = 100000 square links. 

1 acre = 4 roods = 160 perches. 
1 square mile = 6400 square chains = 640 acres. 

Now, when the linear dimensions are links, the area will 
be expressed in square links, and may be reduced to acres 
by dividing by 100000, the number of square links in an 
acre : that is, by pointing off five decimal places from the 
right hand. 

If the decimal part be then multiplied by 4, and five places 
of decimals pointed off from the right hand, the figures to 
the left will express the roods. 

If the decimal part of this result be now multiplied by 40, 
and five places for decimals pointed off, as before, the figures 
to the left will express the perches. 

If one of the dimensions be in links, and the other in 
chains, the chains may be reduced to links by annexing two 
ciphers : or, the multiplication may be made without annex- 
ing the ciphers, and the product reduced to acres and deci- 
mals of an acre, by pointing off three decimal places at the 
right hand. 

When both the dimensions are in chains, the product is 
reduced to acres by dividing by 10, or pointing off one deci- 
mal place. ' ^ 



82 ELEMENTS OF SURVEYING. 

From v/hich we conclude ; that, 

1st. If links be multipUed by links^ the product is reduced 
to acres by pointing off five decimal places from the right hand. 

'2d. If chains be multiplied by links, the product is reduced 
to acres by pointing off three decimal places from the right hand. 

3d. If chains be multiplied by chains, the product is reduced 
to acres by pointing off one decimal place from the right hand. 

107. Since there are 16.5 feet in a rod, a square rod is 
equal to . 16.5 x 16.5=272.25 square feet. 

If the last number Irr multiphed by 160, we shall have 

272.25 X 160 = 43560 =the square feet in an acre. 
Since there are 9 square feet in a square yard, if the las* 
iiumber be divided by 9, we obtain 

4840= the number of square yards in an acre. 

PROBLEM I. 

108. To find the area of a square or rectangular piece 
of ground. 

Multiply the two sides together, and the product will express 
the area (Geom. Bk. IV, Prop. IV). 

1. To find the area of the rectangular jy f^ 

field ABCD. 

Measure the two sides AB, EC : let us 
suppose that we have found AB = 14 chains 
27 links, and 5C=9 chains 75 links. Then, 
JIB =1^-21 links, 
BC=^ 975 links, 
d35x J5C=1391325 square links, 
= 13.91325 acres. 
4 



3.65300 roods, 
40 



26.12000 perches. 

Ms. izA 3R 26P. 

3. What is the area of a square field, of which the sides 
are each 33 ch sH 

Ans. 109.1 IR 29P. 




CONTENT OF GROUND. 83 

3. What is the content of a rectangular field, of which 
the longest side is 49 ch 27 1, and the shorter 38 ch 7 1? 

As. 187^ 2R llP. 

PROBLEM II. 

109. To find the content of a piece of land in the form 
of a triangle. 

FIRST METHOD. 

Measure either side of the triangle 
as BC, and from the opposite angle 
A let fall a perpendicular AD, and 
measure this perpendicular ; then, mul- 
tiply the base and perpendicular to- 
gether, and divide the product by 2, 
the result will express the area of the triangle. Or, the area 
is equal to the base multiplied by half the perpendicular, or 
to the perpendicular multiplied by half the base (Georn. Bk. 
IV, Prop. 11). 

1. What is the content of a triangle whose base is 25 ch 
1 1, and perpendicular 1 8 ch 14 1? 

Ans. 22A 2R 29P. 

2. What is the content of a triangle whose base is 15.48 
chains, and altitude 9.67 chains 1 

Ans. lA \R 38P 

SECOND METHOD. 

Measure two sides and their included angle. Then, add 
together the logarithms of the two sides and the logarithmic 
sine of their ificluded angle ; from iliis sum subtract the loga- 
rithm of the radius, which is 10, and the remainder will he 
the logarithm of double the area of the triangle. Find, from 
the table, the number answering to this logarithm, and divide 
it by 2 ; the quotient will be the required area (Geom. Mens. 
Prob. II). 

1. In a triangle ABC, suppose that we have found AB = 
57.65 ch, w3C=125.81 ch, and the included angle CAB — 

57° 25' : required the area. 



2.099715 
9.925626 

10 

3.786140 



84 ELEMENTS OF SURVEYING. 

Let the required area be designated by Q • then 

(+\og AB 57.65 . . 1.760799 

+ log^C 125.81 
+ logsin^57«'25 
-log R 
2Q . . 6111.4 

And . Q . . 3055.7 square chains. 

Ans. 305.^ 2R ilP. 

Remark. In this example, the links are treated as deci- 
mal parts of the chain ; the result, therefore, is in square 
chains and decimal parts of a square chain. 

2. What is the area of a triangle whose sides are 30 and 
40 chains, and their included angle 28° 57' 1 

Ms. 29.^ OR 7P. 

THIRD METHOD. 

Measure the three sides of the triangle. Then, add them to- 
gether and take half their sum. From this half sum subtract 
each side separately. Then, multiply the half sum and the three 
remainders together, and extract the square root of the product : 
the result icill be the area (Geom. Mens. Prob. II). 

Or, after having obtained the three remainders, add together 
the logarithm of the half sum and the logarithms of the respective 
remainders, and divide their sum by 2 : the quotient will be the 
logarithm of the area. 

1. Find the area of a triangular piece of ground whose 
sides are 20, 30, and 40 chains. 







FIRST METHOD. 








20 




45 


45 




f 


45 


30 




— 20 


-30 






-40 


40 




2 5 1st rem. 


15 


2d 


rem. 


5 








___ 






— 


2)90 














45 = 


=half 


sum. Then, 











5 3d rem. 



45X25X 15x5 = 84375 : and V84375=290.4737=the area. 

Ans. 29A OR 8P. 

2. What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 



CONTENT OF GROUND. 85 





SECOND METHOD 


• 


2669 


6252 6252 


6252 


4900 


— 2569 —4900 


-5035 


5035 
)12504 


3683 1st rem. 1352 


2d rem. 1217 3d rem. 


62 52 = 


:half sum. 




Then, 


'log 6252 

J log 3683 

\ log 1352 

log 1217 


3.796019 
3.566202 
3.130977 
3.085291 
2)13.578489 


Area in 


square links, 6155225 

PROBLEM III. 


6.789244 
Ms. 61 A 2R SP. 



LLl 



110. To find the area of a piece of land in the form of 
a trapezoid. 

Measure the two parallel sides, and also the perpendicular 
distance between them. Add the two parallel sides together, 
and take half the sum ; then multiply the half sum by the per- 
pendicular, and the product will be the area (Geom. Bk. IV. 
Prop. VII). 

1. What is the area of a trapezoid, of 
which the parallel sides are 30 and 49 
chains, and the perpendicular distance be- 
tween them 16 ch 60 1, or 16.60 chains 1 

30 + 49=79 ; dividing by 2, gives . 39.5 

multiply by 16.60 

gives for the area in square chains, . 655.700 

Ans, 65A 2R 11 P. 

2. Required the content, when the parallel sides are 20 
And 32 ch, and the perpendicular distance between them 

^^'^^' Ms. GlA 2R 16P. 

PROBLEM IV. 

111. To find the area of a piece of land in the form of a 
quadrilateral. 

Measure the four sides of the quadrilateral, and also one 
of the diagonals: the quadrilateral will thus be divided into 



86 



ELEMENTS OF SURVEYING. 




two triangles, in both of which all the sides will be known. 
Then, find the areas of the triangles separately, and their sum 
will be the area of the quadrilateral. 

1. Suppose that we have measured 
the sides and diagonal AC, of the 
quadrilateral ABCD, and found 

.^J5 = 40.05 ch, Ci> = 29.87 ch, 

5C = 26.27 ch, AD = Z1.01 ch, 
and AC =55 ch : 

required the area of the quadrilateral. 

Ans. 101 A iR 15P. 

Remark. Instead of measuring the four sides of the 
quadrilateral, we may let fall the perpendiculars Bb, Dg, 
on the diagonal AC. The area of the triangle may then 
be determined by measuring these perpendiculars and the 
diagonal AC. The perpendiculars are 1)^ = 18.95 ch, and 
J56 = 17.92 ch. 

PROBLEM V. 

112. To find the content of a field having any number 
of sides. 

Measure the sides of the field and also the diagonals : the 
three sides of each of the triangles into which the field will be 
thus divided will then be known, and the areas of the triangles 
may then be calculated by the preceding rules. Or, measure 
the diagonals, and from the angular points of the field draw 
perpendiculars to the diagonals and measure their lengths : the 
base and perpendicular of each of the triangles will then be 
known. 

1. Let it be required to determine the content of the 
field ABCDE, having five sides. 

Let us suppose that we have mea- 
sured the diagonals and perpendicu- 
lars, and found 

^0 = 36.21 ch, EC = 39.11 ch, 

Bb = 4.08 ch, Dd = 1.26 ch, Aa = 
4.19ch; also JE:a = 4.00 ch, E£/= 13.60 ch, ^6=20.30ch; 
required the area of the field. 




CONTENT OP GROUND. 87 

Area of triangle ABC= 73.8684 square chains 
area of " Ci)E = 141.9693 " " 

area of " J1CE= 81.7399 " " 

area of ABCDE= 291.511Q " " 

Ans, 29A 3R 12P 

PROBLEM VI. 

113. To find the content of a long and irregular figure, 
bounded on one side by a straight line. 

Suppose the ground, of which the content is required, to be 
of tiie form ABEeda, bounded on one side by the right line 
AE, and on the other by the curve edca. 
At A and E, the extremities of the 
right line AE, erect the two perpen- 
diculars Aa. jEe, and on each of them : i '• J- 4. 

measure the breadth of the land. Then ^ ^ 

divide the base into any convenient number of equal parts 

and measure the breadth of the land at each point of 

division. 

Add together the intermediate breadths and half the sum of 
the two extreme ones : then multiply this sum by one of the equal 
parts of the base line, and the product will be the required area 
very nearly (Mens. Prob. VI). 

1. The breadths of an irregular figure, at five equidis- 
tant places, being 8.20 ch, 7.40 ch, 9.20 ch, 10.20 ch, and 
8.60 chains, and the whole length 40 chains, required the 
area. 

8.20 4)^ 

8.60 10 one of the equal parts. 

2)16.80 

8.40 mean of the extremes 35.20 sum 

7.40 10 

9.20 area 352.00 square ch. 

10.20 



35.20 sura 

Ans. S5A 2R. 

2. The length of an irregular piece of land being 21 ch, 
and the breadths, at six equidistant points, being 4.35 ch, 




88 ELEMENTS OF SURVEYING. 

5.15 ch, 3.55 ch, 4.12 ch, 5.02 ch, and 6.10 chains : required 
the area. 

Ms. 9J1 2R 3oP. 

Remark. If it is not convenient to erect the perpendic- 
ulars at equal distances from each other, the areas of the 
trapezoids, into which the whole figure is divided, must be 
computed separately : their sum will be the required area. 

PROBLEM VII, 

114. To find the area of a piece of ground in the form 
of a circle. 

Measure the radius AC: then multiply the 

square of the radius by 3.1416 (Mens. Prob. /i[ ^- 

X). 

1. To find the area of a circular piece of land, of which 
the diameter is 25 ch. 

Ans. 49.^ OR 14P. 

PROBLEM VIH. 

115. To find the content of a piece of ground in the 
form of an ellipsis. 

c 

Measure the semi-axes AE, CE. Then 
multiply them together, and their product ^f ^ 
by 3.1416. 

1. To find the area of an elliptical piece of ground, of 
which the transverse axis is 16.08 ch, and the conjugate 
axis 9.72 ch. 

Ms. 12.^ iR 4P. 

Remark I. The following is the manner of tracing an 
eUipse on the ground, when the two axes are know^n. 

From C, one of the extremities of the conjugate axis 
as a centre, and AE half the transverse axis as a radius, 
describe the arc of a circle cutting AB in the two points 
F and G : these points are called the foci of the ellipse. 




CONTENT OF GROUND. 89 

Then, take a tape, the length of which is equal to AB, 
and fasten the two ends, one at the focus jP, the other at 
the focus G. Place a pin against the tape and move it 
around, keeping the tape tightly stretched : the extremity 
of the pin will trace the curve of the ellipse. 

Remark II. In determining the content of ground, in 
the examples which have been given, the linear dimen- 
sions have been taken in chains and decimals of a chain 

If the linear dimensions were taken in terms of any other 
unit, they may be readily reduced to chains. For, a chain 
is equal to 4 rods, equal to 22 yards, equal to 66 feet 
Hence, 

1st. Rods may he reduced to chains and the decimal of a 
chain, by dividing by 4. 

2d. Yards may be reduced to chains and the decimal of a 
chain, by dividing by 22. 

3d. Feet may be reduced to chains and the decimal of a 
chain, by dividing by Q6. 

Remark III. If it is thought best to calculate the area, 
without reducing the linear dimensions to chains, the re- 
sult can be reduced to acres. 

1st. By dividing it by 160 when it is in square rods (Art. 
107). 

2d. By dividing it by 4840 lohen it is in square yards 
(Art. 107). 

2d. By dividing it by 43560 when it is in square feet 
(Art. 107). 

OF LAYING OUT AND DIVIDING LAND. 

116. The surveyor is often required to lay off a given 
quantity of land, in such a way that its bounding lines shall 
form a particular figure, viz., a square, a rectangle, a tri- 
angle, &c. He is also often called upon to divide given 
pieces of land into parts containing given areks, or bearing 
certain relations with each other. 

The manner of making such divisions must always de- 
pend on a judicious application of the principles of g:eom- 
etry to the particular case. 



90 ELEMENTS OF SURVEYING. 

If, for example, it were required to lay out an acre of 
ground in a square form, it would first be necessary to 
find, by calculation, the side of such a square, and then to 
trace, on the ground, four equal lines at right angles to each 
other. 

PROBLEM I. 

117. To lay out a given quantity of land in a square form. 

Reduce the given area to square chains , or square rods 
then extract the square root, and the result will be the side oj 
the required square. This square being described on the groundy 
will be the figure required. 

1. To trace a square which shall contain 15.^ oR 12P 
First, . 15A = 60 R=2i00 P 

Add . . . 12 P; hence, 

15*4 OR 12 P=2412 P; the square root of 
which is 49.11. 

Therefore, if a square be traced on the ground, of which 
the side is 49.11 rods, it will be the required figure. 

2. To trace a square which shall contain 176^ iR 24P. 
First, . 176.^=1760 square chains, 

1R= 2.5 " " 

24 P= 1.5 " " ; hence, 
176.^ iR 24P=1764 square chains: the square 
root of which is 42. Hence, if a square be traced on the 
ground, of which the side is 42 ch, it will be the required 
figure. 

PROBLEM II. 

118. To lay out a given quantity of land in a rectangular 
form, having one of its sides given. 

Divide the given area, reduced to square chains or square 
rods, by the given side of the required rectangle, and the quo- 
tient will be the other side. Then trace the rectangle on the 
ground. 

1. To lay oflf 240 acres in a rectangular form, one of the 
sides being given, and equal to 80 rods. 

First, 240.^ = 2400 square chains = 38400 square rods. 

Then, 80)38400(480 rods ; which is the required side 
of the rectangle. 



OF THE COMPASS. 91 

119. A great number of similar problems might be pro- 
posed. The solution of them does not, however, properly 
belong to surveying. The laying out of the ground, and 
the tracing of lines, after the figure and area have been 
determined, are the only parts which appertain to a practical 
treatise. The manner of tracing lines having been already 
explained, it seems unnecessary to add the numerous ex- 
amples often given under this head of the subject. 



. CHAPTER IV. 

Of the Surveying Compass. — Of Surveying with the Compass. — 
Of the Plane-Tahle. 

120. Before considering the principles involved in the 
method of surveying now to be explained, it will be neces- 
sary to describe the instrument principally used in the field, 
and which is called 

THE CIRCUMFERENTER, OR SURVEYOR'S COMPASS. 

PL 2, Fig. 2. This instrument consists of a compass-box 
DCE, a magnetic needle, a brass plate AB, from twelve 
to fourteen inches long, two plain sights, AF and J5G, one 
of which is more fully shown in Fig. 3 ; and a stand, which 
is sometimes a tripod, and sometimes a single staff pointed 
with iron at the lower end, so that it may be placed firmly 
in the ground. 

The open sights, AF and BG, are placed at right angles 
to the plate AB, and fastened to it firmly by the screws 
a and 6. In each sight there is a large and small aperture 
or slit ; the larger aperture being above the smaller in one 
of the sights, and below it in the other. A hair or thread 
of silk is drawn vertically through the middle of the large 
aperture, as shown in Fig. 3. 

The compass-box DCE is circular, and generally about 
six inches in diameter. At the centre is a small pin, on 
which the magnetic needle is poised. This needle, if allowed 



92 ELEMENTS OF SURVEYING. 

to turn freely around the point of support, will settle to a 
state of rest : the direction which it then indicates, is called 
the magnetic meridian. 

Jn the interior of the compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees : the 
degrees are numbered from the extremities of the diameter 
JS*S, both ways to 90". 

The length of the magnetic needle is a little less than 
the diameter of the graduated circle, so that the needle can 
move freely around its centre, within the circle, and its posi- 
tions be noted on the graduated arc. 

The compass-box is turned about its centre, without moving 
the plate AB, by means of the milled screw L: it is fast- 
ened to the plate AB, by the screw P. 

In using the compass, it is important to ascertain the 
exact angle which may be included between the magnetic 
meridian and the direction that may be given to the line 
drawn through the eye and the sights AF and BG. 

To effect this, a small arc HI is described on the bar 
ABi having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts 
of a degree. A vernier is also used, which is permanently 
attached to the compass-box. 

When the point of this vernier coincides with the 
point of the graduated arc HI, the line of the compass-box 
marked J^'S, has the same horizontal direction as the line 
along which the sights are directed. 

Now, supposing the of the vernier to coincide with the 
of the arc HI, if the end of the needle does not stand 
at one of the lines of division of the graduated circle, let 
the whole degrees be read. Then, turn the compass-box 
by means of the screw L, until the needle points exactly to 
the line which marked the whole degrees: the space passed 
over by the of the vernier, shows the minutes that are to 
be added. 

OP SURVEYING WITH THE COMPASS. 

121. The line about which the earth revolves is called its 
axis; and the two points in which the axis meets the surface 
of the earth are called the poles. 



WITH THE COMPASS. 93 

122. A meridian is a line traced on the surface of the 
earth, which would, if sufficiently produced in both direc- 
tions, pass through the poles. Hence, all the meridian lines 
intersect each other at the two poles. 

Tlie poles, however, are so distant from each other, that 
no sensible error will arise in supposing the meridians to be 
parallel ; and since, in all the surveys made with the compass, 
the surface of the ground is regarded as a horizontal plane, 
the n^pridians are represented by horizontal and parallel lines. 

123. When the compass is placed on its stand,' and the 
needle is allowed to settle to a state of rest, the direction it 
assumes has been named the magnetic meridian. Although 
this line is different from the true meridian, yet in the sur 
veys irade with the compass, Ave shall take for the meridian 
that line which is determined by the direction of the mag- 
netic needle. 

124. If the right hand be turned towards the point where 
the sun rises, the direction pointed by the farthest end of the 
needle is called north; the direction shown by the nearest 
end is called south, and the line thus indicated is called a 
north and south line, as well as a meridian. 

125. A line perpendicular to the meridian is called an east 
and west line : the east point being on the right hand, and 
the west on the left. 

126. A line traced or measured on the ground, is called a 
course ; and the angle which this line makes with the meri- 
dian passing through the point of 
beginning, is called the hearing. 

Thus, if we start from the point 
A, and measure in the direction 
AB, the line AB is the course, 
and the angle J>CAB is the bear- 
ing. 

s 

When the course, like AB, falls between the north and 
east points, the bearing is read, north 46® east, and is writ- 
ten, N 46° E 




94 



ELEMENTS OF SURVEYING. 




Wlien the course, like j2C, falls between the north and 
west points, the bearing is read, north 30" west, and is 
written, N 30° W. 

When the course, like SF, 
falls between the south and east 
points, the bearing is read, south 
70" east, and is written, S 70° E. 

When the course, like AD, 
falls between the south and west 
points, the bearing is read, south 
70° west, and is written, S 70° 
W. 

A course which runs due north, or due south, is desig 
nated by the letter N or S : and one which runs due east, 
or due west, by the letter E or W. 

127. If, after having passed over a course, the bearing 
oe taken to the back station, this bearing is called the back 
sight, or reverse bearing. 

128. The perpendicular distance between the east and west 
lines, drawn through the extremities of a course, is called the 
northing or southing, according as the course is run towards 
the north or south. This distance is also called the difference 
of latitude, or simply the latitude, because it shows the dis- 
tance which one of the points is north or south of the other. 



Thus, in running the course from A 
to B, JIC is the difference of latitude, 
north. 



c 



W- 



A 



H 



■y'F 



^E 



129. The perpendicular distance be- 
tween the meridians passing through the 
extremities of a course, is called the de- 
parture of that course, and is east or west, ^ 
according as the course lies on the east or west side of the 
meridian passing through the point of beginning. 

Thus, in running the course AB, CB is the departure, east. 

130. It will be found convenient, in explaining the rules 
for surveying with the compass, to attribute to the latitudes 
and departures the algebraic signs, -\- and — ; which are 
read plus and minus. 

We shall, therefore, consider every northing as affected 



WITH THE COMPASS. 



95 



with the sign -f-j ^^^ every southing as affected with the 

sign — . We shall also consider every easting as affected 

with the sign +, and every westing as affected with the 
sign — . 

131. The meridian distance of a point is the perpendicular 
let fall on the meridian, from which the distance is estimated. 
This meridian is called the assumed meridian. Thus, if the 
distance be estimated from NS, BC will be the meridian 
distance of the point B. 

132. The meridian distance of a Hue, is the distance of the 
middle point of that line from an assumed meridian : and is 
east or west, according as this point lies on the east or west 
side of the assumed meridian. Thus, FG drawn through 
the middle point of AB, is the meridian distance of the 
line AB. 

The sign + will always be given to the meridian distance 
of a point or line, when it lies on the east of the assumed 
meridian, and the sign — , when it lies on the w^est. 

1 33. When a piece of ground is to be surveyed, we begin 
at some prominent corner of the field, and go entirely around 
the land, measuring the lengths of the bounding lines with 
the chain, and taking their bearings with the compass. It 
is not material whether the ground be kept on the right hand 
or on the left, and all the rules deduced for one of the cases, 
are equally applicable to the other. To preserve, however, 
an uniformity in the language of the rules, we shall suppose 
the land to be always kept on the right hand of the sur- 
veyor. 



Let ABCD be a piece of ground 
to be surveyed, A the point w^here 
the w^ork is to be begun, and NS a 
meridian. 

On a sheet of paper, rule three 
columns, as in next page, and head 
them stations, bearings, distances. 




96 



ELEMENTS OF SURVEYING. 



FIELD NOTES. 



Stations. 


Bearings. 


Distances. 


1 


N 3ii° W 


10. 


2 


N 62f E 


9.25 


3 


S 36° E 


7.60 


4 


S 451" W 


10.40 



Place the compass at A and take 
the bearing to B^ which is PAB : 
suppose this angle has been found 
to be 3li°. The bearing from A to 
B is then N 3li° W. Enter this B 
bearing in the field notes opposite xat 
station 1. Then measure the dis- 
tance from A to B^ which we will 
suppose to be 10 ch, and insert that 
distance opposite station 1, in the H 
column of distances. 




We next take the bearing from B to C^ N 62 f° E, and then 
measure the distance J?C = 9 ch 25 1, both of which we insert 
in the notes opposite station 2. 

At station C we take the bearing to Z), S 36° E, and then 
measure the distance CD = 1 ch 60 1, and place them in the 
notes opposite station 3. 

At D we take the bearmg to .^, S 451® W, and then mea- 
sure the distance DA = io ch 40 1. We have thus made all 
the measurements on the field which are necessary to deter- 
mine the content of the ground. 

134. Remark I. The reverse bearing, or back sight, from 
B to A, is the angle ABH ; and since the meridians NS and 
HG are parallel, this angle is equal to the bearing ^AB. 
The reverse bearing is, therefore, S 31^° E. 

The reverse bearing from C, is S 62i'' W: that is, it is the 
angle ICB=:GBC. 



WITH THE COMPASS. 97 

And generally, a reverse hearing, or hack sight, is always 
equal to the forward hearing, and differs from it in hoth of the 
letters by which it is designated. 

135. Remark II. In taking the bearings with the com- 
pass, there are two sources of error. 1st. The inaccuracy of 
the observations : 2d. Local attractions, or the derangement 
which the needle experiences when brought into the vicinity 
of iron-ore beds, or any ferruginous substances. 

To guard against these sources of error, the reverse bearing 
should be taken at every station : if this and the forward 
bearing are of the sartie value, the work is probably right ; 
but if they differ considerably, they should both be taken 
again. 

136. Remark III. In passing over the course AB, the 
northing is found to be HB, and the departure, which is west, 
is represented by AH. Of the course BC, the northing is 
expressed by BG, and the departure, which is east, by GC. 
Of the course CD, the southing is expressed by CI, and the 
departure, which is east, by CF. Of the course DA, the 
southing is expressed by KA, and the departure, which is west, 
by DK. It is seen from the figure, that the sum of the 
northings is equal to HB-{-BG = IIG ; and that the sum of 
the southings is equal to CI-\-KA = PA = HG : hence, the sum 
of the northings is equal to the sum of the southings. 

If we consider the departures, it is apparent that the sum 
of the eastings is equal to GC-\-CF=GF ; and that the sum 
of the westings is equal to AH-\-DK= GF : hence also, the 
sum of the eastings is equal to the sum of the westings. We 
therefore conclude, that when any survey is correctly made, 
the sum of the northings will he equal to the sum of the southings, 
and the sum of the eastings to the sum of the westings. 

It would indeed appear plain, even without a rigorous de- 
monstration, that after having gone entirely round a piece of 
land, the distance passed over in the direction due north, must 
be equal to that passed over in the direction due south ; and 
the distance passed over in the direction due east, equal to 
that passed over in the direction due west. 

Having now explained the necessary operations on the 
field, we shall proceed to show the manner of computing the 
content of the ground. We shall first explain 



c 


-f;;^ 


G 

r 




A 


\L 



98 ELEMENTS OF SURVEYING, 



THE TRAVERSE TABLE. 

137. This table shows the difference of latitude, and the 
departure, corresponding to any bearing, aftd for courses less 
than 100. 

Let JIB denote any course, NS the t^ 

meridian, and N.^jB the bearing of AB. 
Then will AC h& the difference of lati- 
tude, and BC the departure. vAv: 

It is evident that the course, the cKffer- 
ence of latitude, and the departure, are 
respectively, the hypothenuse, tlie base, 
and the perpendicular of a right-angled ^ 

triangle, of which the bearing is the angle at the base. 

If there he two hearings, which are complements of each other, 
or of which the sum is 90°, the difference of latitude correspond- 
ing to the one, will he the departure of the other, and reciprocally. 
For, if BC were a meridian, CBA which is the complement 
of CAB, would be the bearing of BA ; CB would be the 
difference of latitude, and CA would be the departure. 

In the traverse table, the figures at the top and bottom 
of each page, show the bearings to degrees and parts of a 
degree ; and the columns on the left and right, the distances 
to which the latitudes and departures correspond. 

If the bearing is less than 45°, the angle will be found at 
tlie top of the page ; if greater, at the bottom. Then, if the 
distance is less than 50, it will be found in the column "dis- 
tance," on the left hand page ; if greater than 50, in the 
corresponding column of the right hand page. The table is 
calculated only to quarter degrees, for the bearings cannot 
be relied on to smaller parts of a degree. 

The latitudes or departures of courses of different lengths, 
but which have the same bearing, will be proportional to the 
lengths of the courses. Thus, in the last figure, the lati- 
tudes AG, AC, or the departures GF, CB, are to each other 
as the courses AF, AB. 

Therefore, when the distance is greater than 100, it may 
be divided by any number w^hich will give an exact quo- 
tient, less than 100: then the latitude and departure being 



WITH THE COMPASS. 90 

found and multiplied by the divisor, the products will be the 
latitude and departure of the whole course. It is also plain, 
that the latitude or departure of two or more courses, hav- 
ing the same bearing", is equal to the sum of the latitudes 
or departures of the courses taken separately. 

Hence, if we have any number greater than lOO, as 614, 
we have only to regard the last figure as a cipher, and recol- 
lect that, 610-}-4 = 614 ; and also, that the latitude and de- 
parture of 610, are ten times greater, respectively, than the 
latitude and departure of 61 : that is, equal to the latitude 
and departure of 61 multiplied by 10, or with the decimal 
point removed one place to the right. 

I. To find the latitude and departure for the bearing 29i", 
and the course 614. 



Latitude for 610 . . 530.90 
Latitude for 4 ... 3.48 



Latitude for 614 . . 534.38 



Departure for 610 . . 300.40 
Departure for 4 . . 1.97 
Departure for 614 . . 302.37 



In this example, the latitude and departure answering to 
the bearing 29|°, and to the distance 61, are first taken from 
the table, and the decimal point removed one place to the 
right : this gives the latitude and departure for the distance 
610; the latitude and departure answering to the same bear- 
ing and the distance 4, are then taken from the table and 
added. 

2. To find the latitude and departure for the bearing 62^*, 
and the course 7855 chains. 



Latitude for 7800 . 3602.00 
Latitude for 55 . . 25.40 
Latitude for 7855 . 3627.40 



Departure for 7800 . 6919.00 
Departure for 55 . . 48.79 
Departure for 7855 . 6967.79 



Remark. When the distances are expressed in whole 
numbers and decimals, the manner of finding the latitudes 
and departures is still the same, except in pointing oflf the 
places for decimals : but this is not diflScult, when it is re- 
membered that the column of distances in the table, may be 
regarded as decimals, by removing the decimal point to the 
left in the other columns. 



100 ELEMENTS OF SURVEYING. 

3. To find the latitude and departure for the bearing 47f •', 
and the course 37.67. 
Latitude for 37.00 . . 24.88 
Latitude for 57 . . . 38 



Latitude for 37.57 . . 2 5.26 



Departure for 37.00 . . 27.39 
Departure for 57 . . 42 

Departure for 37.57 . . 27.81 



Of Balancing the work. 

138. The use of the traverse table being explained, we 
can proceed to compute the area of the ground. 

The field notes having been completed, rule a new table, 
as below, with four additional columns, two for latitude, and 
two for departure. 

Then find, from the traverse table, the latitude and de- 
parture of each course, and enter them in the proper columns 
opposite the station. 

Then add up the column of northings, and also the column 
of southings : the two sums should be equal to each other. 
If they are not, subtract the less from the greater, and the 
remainder is called the error in latitude. This error takes the 
name of that column which is the least. For example, if 
the sum of the northings is less than the sum of the south- 
ings, the error is called, error in northing : but if the sum of 
the southings is less than the sum of the northings, the error 
is called, error in southing. We find the error for eacli par- 
ticular course by the following proportion. 
As the sum of the courses 
Is to the error of latitude, 
So is each particular course 
To its correction. 

The error of each course, thus found, may be entered in 
a separate column; after which, add it to the latitude of the 
course, when the error and latitude are of the same name, but 
subtract it, when they are of different names. This will make 
the sum of the northings equal to the sum of the southings, 
and is called balancing the work. The northings and south- 
ings, thus corrected, are entered in columns on the right, 
under the head, balanced. Having done this, balance the 
eastings and westings in the very same manner. The dif- 
ference between their sums, is called the error in departure. 



WITH THE COMPASS. 



101 



For an example, we will resume the same example that 
has already been considered. 






' 


Dislan- 


LATITUDE. 


DEPARTURE. 






BALANCED. ] 


1 


Bearings. 


N. 


S. 


E. 

+ 


W. 


Cor. 
Lau 


Cor. 
Dep. 


N. 
+ 


S. 


E. 
+ 


W. 


N3U0W 


10. 


8.53 




5.22 


+0.18 


+0.02 


8.71 






6.24 


2 

3 


N 62^0 E 


9.25 


4.23 


6.15 

7.29 

13.44 
12.76 


8.22 


7.41 


+0.17 


-0.01 


4.40 




8.21 


SSS^'E 


7.60 




4.47 


-0.14 


-00.1 




6.01 


4.46 


7.43 
12.67 


4 


S 45i« W 


10.40 




-0.19 


+0.02 




7.10 


Sum ol' courses, 37.23 


12.76 


12.69 
12.63 


12.63 




13.11 


12.67 


Error in Northing, . 


. . 


0.68 


0.06 Error in Westing. 











As 37.25 : 0.68 
As 37.25 : 0.68 
As 37.25 : 0.68 
As 37.25 : 0.68 



10 : 0.18 error in lat. of 1st course. 

9.25 : 0.17 error in lat. of 2d course. 

7.60 : 0.14* error in lat. of 3d course, 
10.40 : 0.19 error in lat. of 4th course. 



As 37.25 : 0.06 : : 10 : 0.02* error in dep. of 1st course. 

A.S 37.25 : 0.06 : : 9.25 : 0.01 error in dep. of 2d course. 

A.S 37.25 : 0.06 : : 7.60 : O.Ol error in dep. of 3d course. 

As 37.25 : 0.06 : : 10.40 : 0.02 error in dep. of 4th course. 

139. Remark I. In finding the error in latitude or de- 
parture, for a particular course, the last figure is sometimes 
doubtful ; in which case it is best to mark it, as in the third 
proportion for error in latitude, and the first for error in depar- 
ture ; and then, if the figures taken do not balance the work, 
let each be increased or diminished by 1. 

140. Remark II. It has already been observed (Art. 136), 
that if the measurements on the field are correctly made, the 
sums of the northings and southings will be equal to each 
other, as also those of the eastings and westings. It is the 
opinion of some surveyors, that when the error in latitude or 
departure exceeds one link for every five chains of the courses, 
the field notes ought not to be relied on. This, perhaps, is a 
higher degree of accuracy than can be attained. The error, 
however, should always be made considerably less than one 
link to a chain. 



102 ELEMENTS OF SURVEYING. 

Of the double meridian distances of the courses. 

141. After the work has been balanced, the next thing 
to be done is to calculate the double meridian distance of 
each course. 

For this purpose, a meridian line is assumed, lying either 
wholly without the land, or passing through any point within 
it. It is, however, most convenient to take that meridian 
which passes through the most easterly or westerly station of 
the survey ; and these two stations are readily determined by 
inspecting the field notes. 

Having chosen the meridian, let the station through which 
it passes, be called the principal station^ and the course which 
begins at this point, the first course. Care, however, must be 
taken, not to confound this with the course which begins at station 
1, and which is the first course that is entered in the field notes. 

It has already been remarked (Art. 132), that all depar- 
tures in the direction east, are considered as plus, and all 
departures in the direction west, as minus : then, through 
whatever station of the survey the assumed meridian be taken, 
we shall have for the calculation of the double meridian dis- 
tances, the following 

RULE. 

I. The double meridian distance of the first course is equal 
to its departure. 

II. The double meridian distance of the next course is equal 
to the double meridian distance of the first course, plus its de- 
parture, plus the departure of the second course. 

III. The double meridian distance of the third course is equal 
to the double meridian distance of the second, plus its departure, 
plus the departure of the third course. 

IV. ^nd, the double meridian distance of any course is equal 
to the double meridian distance of the preceding course, plus its 
departure, plus the departure of the course itself 

Remark. It should be recollected that plus is here used 
in its algebraic sense, and that when double the meridian 
distance of a course and the departure which is to be added 
to it, are of different names, that is, one east and the other 
west, they will have contrary algebraic signs ; hence, their 
algebraic sum will be expressed by their difference, with the 
sign of the greater prefixed to it. 



WITH THE COMPASS. 



103 




Demonstration of the Rule. 

Let the figure JIB CD, which we i^ 
have aheady surveyed with the com- 
pass, be resumed. By inspecting 
the field notes, it will be seen that 
B, or station 2, is the most westerly 
station. Through this point let the 
assumed meridian NS be supposed 
to pass. Then, B will be the princi- 
pal station, and BC the first course. 
By what has been already said, every 
departure towards the east is to be 
considered as plus, and every departure towards the west, as 
minus. 

Now, since p. A:, d and a, are the middle points of the 
courses BC^ CD, DA and AB, we have, by similar triangles, 
2 qp=2 sx=sC =ihe first departure. 
2 Cr=2 hk = Cy = ih.e second departure. 
2fg=2 gA=Af=i[ie third departure. 
2 At=2 ab= Ac =ihe fourth departure. 
We also have, 

2 qp=sC=douh. mer. dis. of BC, 
2 qp+2 xC-{-2 Cr = 2 A:n=doub. mer. dis. of CD. ' 
2 kn-{-2 kh-2 gf=2 c?e=doub. mer. dis. of DA. 
2 de — 2 gA — 2 At =2 a6 = doub. mer. dis. of AB. 
The departure of the courses BC, CD, are east, and there- 
fore positive ; while the departures of the courses DA, AB, 
are west, and consequently negative. 

Since the course of reasoning just pursued is applicable to 
all figures, we may regard the rule as demonstrated for every 
case which can occur. 

Remark. The double meridian distance of the last course 
should be equal to the departure of that course. A verifi- 
cation of the work is, therefore, obtained by comparing this 
double meridian distance with the departure of the course. 

142. To apply the above rule to the particular example 
already considered, rule a new table, as below, in which are 
entered the balanced northings and southings, and the bal- 
anced eastings and westings. 



104 



ELEMENTS OF SURVEYING. 



In this table there is but a single column for the diflerence 
of latitude, and a single column for the departures. The 
-|- sign shows when the difference of latitude is north, and 
the — sign, when it is south. The -j- sign also shows when 
the departure is east, and the — sign, when it is west. 



Station*. 


Bearings. 


Distoncefc 


Dif. Lat. 


Uep. 


D. M. D. 


1 


N3110W 


10. 


+8.71 


—5.24 


+ 17.91 
Z7.43 
-5.24 


+5.24 


2* 


N 62|o E 


9.25 


+4.40 


+8.21 


8.21 

1 


3 


S36°E 


7.60 


—6.01 


+4.46 


+8.21 
+8.21 

+4.46 


+20.88 


4 


S45ioW 


10.40 


—7.10 


—7.43 


3 7.43 


+17.91 



We see, from inspecting the notes, that 2 is the most 
westerly, and 4 the most easterly station. Either of them 
may, therefore, be taken for the principal station. Let us 
assume 2 for the principal station, and distinguish it by a 
star, thus *. 

Having done so, we enter the departure 8.21 in the column 
of double meridian distances, which gives the double meridian 
distance of the first course. The double meridian distances 
of the other courses are calculated according to the rule ; and 
as the last, opposite to station 1, is equal to the departure of 
the course, the work is known to be right. 

Of the Area. 

143. Having calculated the double meridian distance of 
each course, the next and last operation for finding the content 
of the ground, is explained in the following 

RULE. 

I. Multiply the double meridian distance of each course by 
its northing or southing, observing that like signs in the multi- 
plicand and multiplier give plus in the product, and that unlike 
signs give minus in the product. 

II. Place all the products which have a plus sign in one 
column, and all the products which have a minus sign in another. 

III. *Bdd up each of the columns separately and take their 
difference : this difference will be double the area of the land. 



WITH THE COMPASS. 



105 



Demonf^tration of the Rule. 

N 

S 

Let us agaia resume the example ^ 



considering, 



B 



which we have been 
and write the difference of latitude ^n 
and the double meridian distances W 
of the courses, in the following table. 




stations. 


Dif. of Latitude. 


D. M. D. 


Area. 
+ 


Area. 


1 


~{-cB 


+25a 


2cAB 




2* 


-^Bs 


+ 27P 


2BsC 




3 


-yD 


+ 2n/i 




2ms CD 


4 


-Df 


-f2ec/ 




2cmDJ 



It is now evident, that cB multiplied by 2ba = cA, wil 
give double the area of the triangle cAB. But cB and ba 
are both plus ; hence, the product will be plus, and must be 
put in the column of plus areas. Double the area of the 
triangle BsC, is equal to Bs multiplied by 2qpf which pro- 
duct is also plus. 

The area of the trapezoid msCD is equal to yD=ms multi- 
plied by nh (Geom. Bk. IV, Prop. VII) ; hence, double the 
area is equal to yD into 2nh. But since yD is minus, and 
2nh plus, it follows that the product will be negative ; hence, 
it must be placed in the column of negative areas. 

Double the area of the trapezoid cJlDm, is equal to Df=mc 
multiplied by 2de : but, since Df is negative and 2de posi- 
tive, the product will be negative. 

It is now evident that the difference between the two 
columns is equal to twice the content of the figure ABCD * 



106 



ELEMENTS OF SURVEYING. 



and as the same may "be shown for any figure whatever, 
we may regard the rule as demonstrated for all cases. 

We will now make the calculations in numbers. Having 
balanced the work, we can place it in the following table. 



1 
Sta. 


Bear. 


Dist. 


Dif.Lat. 


Dep. 


D.M.D. 


Area. 

+ 


Area. 


' 1 


N31i°W 


1 
10. 


+8.71 


-5.24 


+5.24 


45.6404 




1 

2* 


N 62f E 


9.25 


+4.40 


+8.21 


+S.21 


36.1240 




3 


S 36" E 


7.60 


—6.01 


+4.46 


+20.88 




125.4888 


4 


S45inV 


10.40 


—7.10 


—7.43 


+17.91 




127.1610 



81.7644 I 252.6498 
81.7644 



Area in square chains, 
Dividing by 10, 



d3rw. 8.^ 2R 7P. 



2 )170.8854 
85.4427 
8.54427 
4 



2.177( 



40 



7.08320 



Observing in the field notes that station 2 is the most 
westerly point of the land, we assume the meridian which 
passes through this point, as the one from which the me- 
ridian distances are calculated. We mark the principal sta- 
tion with a star. 

Opposite station 2, we enter, in the column of double me- 
ridian distances, headed D. M. D., the departure of the course 
from 2 to 3, which is the double meridian distance of that 
course, and plus. To this we add the departure of the 
course, and also the departure of the next course : their sum 
is the double meridian distance of the course from 3 to 4. 

To the last sum add the departure opposite station 3, and 
the minus departure opposite station 4 : their algebraic sum is 
the double meridian distance from 4 to 1. 

To the last sum add tne last departure, which is minus, 
also the next departure which is likewise minus : this will 
give the double meridian distance of the course from l to 2, 
which is also equal to its departure. 

Then forming the products, adding them together, taking 
their difTerence, and dividing it by 2, according to the rule, we 
obtain the content of the ground. 



WITH THE COMPASS. 



107 



144. It only remains to make a 
plot of the ground. 

For this purpose, draw any line, 
as NS, to represent the meridian 
passing through the principal sta- 
tion, on which take any point, as 
Bt to represent that station. 



FIRST METHOD OF PLOTTING. 




Having fixed upon the scale on which the plot is to be 
made, lay off from B on the meridian, a distance Bs equal to 
the difference of latitude of the first course, and at s erect a 
perpendicular to the meridian, and make it equal to the de- 
parture of the first course : then draw BC, which will be the 
first course. 

Through C draw a meridian, and make Cf equal to the 
difference of latitude of the second course, and through / 
draw a perpendicular /D, and make it equal to the depar- 
ture of the second course : draw CD, and it will be the 
second course. 

Lay down, in the same manner, the courses DA and AB, 
and the entire plot will be completed. 

SECOND METHOD OF PLOTTING. 

The work may be plotted in another manner, thus. At 
the principal station B, lay off an angle equal to the bearing 
from B to C, which will give the direction of BC. Then, 
firom the scale of equal parts, make BC equal to the first 
course : this will give the station C. 

Through C draw a meridian, and lay off an angle equal to 
the bearing from C to D, and then lay off the course CD. 
Do the same for the bearing at D and the course DA; also, 
for the bearing at A and the course AB, and a complete plot 
of the ground will thus be obtained. If the work is all right, 
the last line AB will exactly close the figure. This plot is 
made on a scale of 40 chains to an inch. 



108 



ELEMENTS OF SURVEYING. 



2. It is required to determine the content and plot of a piece 
of land, of which the following are the field notes, viz. 



stations. 1 Bearing | DUtancea. 


1 1 N46i«W 1 20 ch. 


2 1 NSll^'E 1 13.80 


3 1 E 1 21.25 


4 1 S560E 1 27.60 


5 1 S 33iO W 1 18.80 


6 1 N 741° W 1 30.95 



CALCULATION. 



sta- 
tions 


Bearing.. 


Dist 


Dif. 


Lat. 


Dep. 


BALANCED. 


D.M.D. 

+ 


AREA. 
+ 


AREA. 


N 
+ 


S 


E 

4- 


W 


Lat 


Dep. 


1 


N461«W 


20 ch 


13.77 






14.51 


+13.88 


—14.56 


14.56 


202.0928 




2* 


N51|° E 


13.80 


8.54 




10.84 




+8.61 


+10.81 


10.81 


93.0741 




3 


E 


21.25 






21.25 






+21.20 


42.82 


.... 




4 


S 56° E 


27.60 




15.44 


22.88 




-15.29 


+22.82 


86.84 




1327.7836 


5 


S 33|0 W 


18.80 




15.72 


10.31 


—15.63 


- 10.36 


99.30 




1552.0590 


6 


N74i«W 


30.95 


8.27 






29.83 


+8.43 


-29.91 


59.03 


497.6229 



loTcoor*.. . 132.40130.68131.16.54.97154.65 
30.5854.65 



792.7898I2879.842S 
792.7898 



Error in Nerthing. . . 0.6810.32 Error in Weeting 2 )2087.0528 

Ans. 104A liJ 16P 1043.6264 



Plot of the above example. 




Remark. Wlien a bearing is due east or west, the error 
in latitude is nothing, and the course must be subtracted from 



WITH THE COMPASS. 



109 



the sum of the courses, before balancing the columns of lati- 
tude. In the last example, the 3d bearing is due east, and 
the first term of the several proportions for error in latitude, 
was 132.40-21.25 = 111.15. 

In like manner, if a bearing is due north or south, the error 
in. departure is nothing ; and the sum of the courses must be 
diminished by this course, before balancing the columns of 
departure. 

3. Required the content and plot of a piece of land, of 
which the following are the field notes. 



Stations 


Bearings. 


Distances. 


1 


S 34" W 


3.95 ch. 


2 


s 


4.60 


3 


S 361° E 


8.14 


4 


N59i°E 


3.72 


5 


N25<'E 


6.24 


6 


N 16° W 


3.50 


7 


NG5»W 


8.20 



Ms. 10^ OR 6P. 



4. Required the content and plot of a piece of land, from 



the following field notes. 



stations. 


Bearing. 


Distances. 


1 


S40°W 


70 rods 


2 


N45MV 


89 


3 


N 36»E 


125 


4 


N 


54 


5 


S 8i»E 


186 


6 


S 8MV 


137 


7 


W 


130 



Ms. 207^ ZR 33P- 



no 



ELEMENTS OF SURVEYING. 



6. Required the content and plot of a piece of land, from 
the following field notes. 



stations. 


Bearings. 


Distances. 


1 


S 40i»E 


31.80 ch. 


2 


N 54»E 


2.08 


3 


N 2910 E 


2.21 


4 


N 28|o E 


35.35 


5 


N57°W 


21.10 


6 


S47«>W 


31.30 1 



dns. 92.^ 3R 32P. 

6. Required the area of a survey of which the following 
are the field notes. 



Stations. 


Bearings. 


Distances. 


2 


East. 


4.00 ch. 


3 


N9oE 


4.00 


4 


S690E 


5.56 


6 


S360E 


7.00 


6 


S420W 


4.00 


7 


S75oW 


10.00 


8 


N 39« W 


7.50 


1 


N420E 


5.00 




If, in this example, we assume 1 as the principal station, 
the double meridian distances will all be plus, and the positive 
area will exceed the negative. 

In balancing we shall find the area in southing to be 
.28 ch. and in westing .22 ch. The area is ISA OR IIP. 
It should however be remarked, that in all the examples the 
answers may be slightly varied by distributing the corrections. 



WITH THE COMPASS. 



Ill 



7. What is the area of a survey of which the following are 
the field notes. 



Stations. 


Bearings. 


Distances. 


1 


N 75" 00^ E 


54.8 rods. 


2 


N 20" 30' E 


41.2 


3 


East. 


64.8 


4 


S 33" 30^ W 


141.2 


5 


S 76° 00^ W 


64.0 


6 


North. 


36.0 


7 


S 84° 00^ W 


46.4 


8 


Nss' 15' W 


46.4 


9 


N36°45'E 


70.8 


10 


N 22° 30' E 


56.0 


11 


S 76° 45' E 


48.0 


12 


S 15°00' W 


43.4 


13 


S 16°45'W 


40.5 



In this survey 4 is the most easterly and 9 the most we^i- 
erly station. The area is equal to 110^ 2R 23P. It may 
vary a little, on account of the way in which the balancing is 
done. 



112 



ELEMENTS OF SURVEYING. 



8. What is the content of a piece of land of which the fol- 
lowing are the field notes. 



Stations. 


Bearings. 


Distances. 


1 


S75»W 


13.70 ch. 


2 


S 201° W 


10.30 


3 


West. 


16.20 


4 


N 331° E 


35.30 


5 


N 76» E 


16.00 


C 


South. 


9.00 


7 


N84°E 


11.60 


8 


S 53J»E 


11.60 


9 


S 36J° W 


19.20 


10 


S22l«W 


14.00 


11 


N 76^ W 


12.00 


12 


N 15»E 


10.85 


13 


N 1GJ»E 


10.12 



In lliis survey 4 is the most westerly station and 9 the most 
easterly. The area is 1 10.^2 2R 23P. The result may, iiow- 
ever, as in the other examples, be slightly varied by the 
balancing. 



WITH THE COMPASS. 



113 



0. What is the area of a survey of which the following 
are the notes 1 



I Stations. 


Bearings. 


Distances. 


1 


S 46^0 E 


80 rods. 


2 


S 5lf W 


34.16 


3 


West. 


85 


4 


N 560 W 


110.40 


5 


N 3310 E 


75.20 


6 


S 7410 E 


123.80 



Jlns. 104.5 iR 16P. 



PROBLEM. 

To determine the content and boundary of a piece of land, hi/ 
means of offsets from the principal lines. 

145. An offset is a line drawn perpendicular to a course, 
and may lie either on the right or left of it. 

146. Let ABODE be a piece of 
ground to be surveyed. Let us sup- 
pose it to be bounded on the west 
and north by a fence and road, and 
on the east and south by a creek or 
river. 

Place stations at the principal 
points, as A, B, C, D and E, Take, 
with the compass, the bearings from 
A to J5, from B to C, from C to D, 
from D to E, and from E to A ; and 
measure the distances AB, BC, CD, 
DE, and EA. 

At convenient points of the course AB, as a, c and /, make 
the offsets ab, cd, fg. Then, having measured these lines, 
as also the distances Aa, ac, cf and fB, enough will be 
known to determine the area which lies without the station 

8 




114 



ELEMENTS OF SURVEYING. 



line JIB. The points 6, d, and g^ of the fence which runs 
from A to B, are also determined. 

Erect, in a similar manner, offsets to the other courses, 
and determine the areas which lie without the station lines. 
Tliese several areas being added to the area within the sta- 
tion lines, will give the entire area of the ground. 

If the offsets fall within the station lines, the corresponding 
area must be subtracted from the area which is bounded by 
the station lines. 



PROBLEM. 

To determine the bearing and distance from one point to another^ 
when the points are so situated that one cannot be seen from the 
other. 



147. Let AB be a meridian, and 
*^ and C the two points. From 
either of them, as A, measure a 
course .^2, of a convenient length 
in the direction towards C, and take 
the bearing with the compass. At 
2, take the bearing of a second 
course, and measure the distance 
to 3. At 3, take a third bearing and 
measure to 4. At 4, take the bear- 
ing to C, and measure the distance 
from 4 to C. 

Then, the difference between the 
sum of the northings and the sum of the southings will be 
represented by AB, and the difference between the sum of 
the eastings and the sum of the westings by BC. The base 
AB, and the perpendicular BC of the right-angled triangle 
ABC, are then known. The angle at the base, BAC, is the 
bearing from A to C; or the equal alternate angle at C is 
the bearing from C to A, and the hypothenuse AC is the 
distance. 

Having measured the bearings and courses on the field, 
form a table, and find the base and perpendicular of the right- 
angled triangle, in numbers. 




WITH THE COMPASS. 



115 



Remark. Had any of the courses 
run south, AB would have been 
equal to the sum of the northings, 
minus the sum of the southings. 

To find the angle BAG, or the 
bearing from A to C. 

As radius : tan A : : AB : jBC, 

ox AB \ BC : \ R : inn A X 

that is, 



As AB 87.77 
BC 35.29 

R 
tan A 21054' 12". 



ar. comp. 



SUUon. 


Bearings. 


Distances. 


1 - 


- 


- 


w. 1 


1 


N61MV 


40 ch. 


1 19.39 




1 34.98 1 


2 


N42''W 


41. 


1 30.47 




1 27.43 


3 


N 12« E 


16.10 


1 15.75 




3.35 1 


4 


N47°E 


32.50 


1 22.16 




2.3.77 1 








AB==87.77 




27.12 


62.41 



27.12 



C£=35.29 ch. 
Cs B 




8.056654 
1.547659 

10. 
9.604306 



To find the distance AC. 

As sin ^21054' 12" ar. comp. . 0.428242 
R 10. 

BC 35.29 .... 1.547052 

AC 94.6 . . . . 1.975894 

Hence, the bearing and distance are both found. 

Of supplying omissions in the field notes. 

148. The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey, 
when the bearings and lengths of all the others are knowiL 
It may be necessary to use this method when there are obsta- 
cles which prevent the measuring of a course, or when the 



116 



ELEMENTS OF SURVEYING. 



bearing cannot be taken. Indeed, any two omissions may 
always be supplied by calculation. It is far better, however, 
if possible, to take all the notes on the field. For, when any 
of them are supplied by calculation, there are no test by 
which the accuracy of the work can be ascertained, and all 
the errors of the notes affect also the parts which are supplied. 
1. In a survey we have the following notes. 



i 

Stations. 


Bearings. 


Distances. 


1 


N3ii°W 


10 ch. 


2 


N eafE 


9.25 


3 


Lost. 


Lost. 


4 


S45i''W 


10.40 



What is the bearing and distance from station 3 to 4. 

^^- 1 Distance, 6. 98. ch, 
2. In a survey we have the following notes : 



Stations. 


Bearings. 


Distances. 


1 


S 40i» E 


31.80 ch. 


2 


N 54° E 


2.08 


3 


Lost. 


Lost. 


4 


N 28f°E 


35.35 


5 


N57° W 


21.10 


I " 


S 47° W 


31.30 

1 



What is the bearing and distance from 3 to 4 ? 



. CBearing.N340 4r E. 
^^^'7 Distance, 2.19. ch. 



WITH THE COMPASS. 117 



To determine the angle included between any two courses, when 

N 



their bearings are knoicn. 




149. Let NS be a meridian 
passing through *^. 

Let ^B, AC, AD and AH be 
four courses running from A. 
We readily deduce the following 

RULES. 

c^C is N 260 W ^ When the meridional letters arc 

AH is N 65" W > alike, and those of departure also 

CAH=39'' ^ alike, the difference of the bearings 

will be the angle between the courses. 

AB is N 46* E ^ When the meridional letters are 

w3C is N 26° W > alike, and those of departure unhke, 

CAB = 12^ ^ the sum of the bearings will be the 

angle between the courses. 

When the meridional letters are 

.^C is N 26° W J unhke, and those of departure alike, 

AD is S 66° W \ the angle between the courses will be 

CAD— 180'^ — Q2° = 88° 5 equal to 180° minus the sum of the 

bearings. 

When the meridional letters are 

.y^C is N 26° W ^ unlike, and those of departure also 

AF is S 66° E > unlike, the angle between the courses 

Cj2F=180° — 40°=140o ^ will be equal to the difference of the 

bearings taken from 180°. 
Remark. The above rules are determined, under the sup- 
position that the two courses are both run from the angular 
point. Hence, if it be required to apply the rules to two 
courses run in the ordinary way, as we go around the field, 
the bearing of one of them must be reversed before the calcu- 
lation for the angle is made. 

1. The bearings of two courses, from the same point, are 
N 37° E, and S 85° W : what is the angle included between 
them ] 

Ans. 132\ 



118 



ELEMENTS OF SURVEYING. 



2. The bearings of two adjacent courses, in going round a 
piece of land, are N 39° W, and S 48° W : what is the angle 
included between them ] 

^ns. 87". 

3. The bearings of two adjacent courses, in going round a 
piece of land, are S 85° W, and N 69° W : what is the angle 
included between them 1 

Ans. 154°. 

4. The bearings of two adjacent courses, in going round a 
piece of land, are N 55° 30^ E, and S 69° 20^ E : what is the 
angle included between them 1 

Ms. 124° 50^ 

PROBLEM. 

To run a line from a given point in the boundary of a piece 
of land, so as to cut off on either side of it a given portion 
of the field. 

150. Make a complete survey of the field, by the rules 
already given. Let us take, as an example, the field whose 
area is computed at page 106. That field contains I04w3 
ijR 16P, and the following is a plot of it. 

N 




Let it now be required to run a line from station A, jq 
such a manner as to cut off on the left any part of the field ; 



say, 



26^ 2R ZIP. 



It is seen, by examining the field, that the division line 
will probably terminate on the course CD. Therefore, draw 
a line from A to C, which we will call the first closing line. 

The bearings and lengths of the courses JIB, BC, are 
always known ; and in the present example are found in the 



WITH THE COMPASS. 119 

table on page 106 : hence, the bearing and distance from C 
to ./?, can be calculated by the last problem : they are in this 
example, 

Bear. S 9° 28' E : Course 22.8 ch. 

Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts off: 
that area, in the present case, is 

13^ 3R SP. 

It is now evident that the division line must fall on the 
right of the closing line AC, and must cut off an area ACH, 
equal to the difference between that already cut off, and the 
given area : that is, an area equal 

26 A 2R 31 P given area. 
13^5 SR 3P area already cut off. 
to . . . 12.^2 3R 28P. 

Since the bearing of the next course CD, and the bearing 
of the closing line AC are known, the angle ACD which 
they form with each other, can be calculated, and is in this 
example 80° 32°. Hence, knowing the hypothenuse AC, and 
the angle ACG at the base, the length AG of the perpen- 
dicular let fall on the course CD, can be found, and is 
22.49 chains. 

Since the area of a triangle is equal to its base multiplied 
by half its altitude, it follows, that the base is equal to the 
area divided by half the altitude. Therefore, if the area 

12 A 3R 28P 

be reduced to square chains, and divided by 11.24^ chains, 
which is half the perpendicular AG, the quotient, which is 
1 1.58 chains, will be the base CH. Hence, if we lay off from 
C, on CD, a distance CH, equal to 11.5 chains, and then run 
the line AH, it will cut off from the land the required area. 

Remark I. If the part cut off by the first closing line, 
should exceed the given area, the division line will fall on 
the left of AC. 

Remark II. If the difference between the given area and 
the first area cut off, divided by half the perpendicular AG, 
gives a quotient larger than the course CD ; then, draw a 



120 ELEMENTS OP SURVEYING. 

line from ^5 to D, and consider it as the first closing line, and 
let fall a perpendicular on DE. 

Remark III. When the point from which the division 
line is to be drawn, falls between the extremities of a course, 
dividing the course into two parts, consider one of the parts 
as an entire course, and the otlier as forming a new course, 
having the same bearing. Tlie manner of making the cal- 
culation will then be the same as before. 

Method of determining the area of a Survey by means of the 
Table of J^atural Sines and Cosines. 

If, in a circle of which the radius is 1, we calculate the 
sine and cosine for every minute of the quadrant, they form 
what is called a Table of Natural Sines and Cosines. The 
natural sine is the perpendicular, and the natural cosine the 
base of a right angled triangle of which the hypothenuse, 
or radius of the circle, is 1. 

Since either leg of a right angled triangle is less than the 
hypothenuse, it follows that the natural sine or cosine of every 
arc of the quadrant is less than 1. These sines and cosines 
are expressed in decimals of the radius 1, and although the 
decimal point is not written in the table, yet it must always 
be prefixed to the number before using it. 

Thus in page 67, the sine of 5° 30' is .09585. 

The cosine of 5° 30' „ .99540. 

Sine of 40° 25' (page 71) „ .64834. 

Cosine of 40° 25' „ .76135. 

When the angle exceeds 45°, the degrees are found at the 
bottom of the page, and the minutes are counted upwards in 
the right hand column of the page, as in the table of loga- 
rithmic sines. 

Thus, sine of 84° 20' (page 64) 

The cosine of 84° 20' 

(page 65) 



Sine of 


79° 37' 


Cosine of 


79° 37' 


Sine of 


69° 25' 


Cosine of 


69° 25' 


Sine of 


57° 59' 


Cosine of 


57° 59' 



is 




.99511. 


j» 


- 


.09874. 


j> 




.98362. 


j> 




.18023. 


jj 




.93016. 


99 




.35157. 


» 




.84789. 


»> 




.53017 



WITH THE COMPASS. 



121 



If the Surveying Compass has a vernier which enables you 
to read the bearings to smaller parts of a degree than 15', 
greater accuracy may be attained by using the table of 
natural sines, instead of the Traverse Table, for computing 
the area. 

We shall now show the method of calculating the latitude 
and departure of any course, from the table of natural sines. 



Let JID, for example be any course, 
DAE the bearing, and AC=l the 
radius of the table of natural sines. 



Having formed the right angled ^ B 

triangles ACB, JlDE, we have DAE = hesLnng, 
AE=di{. of latitude and jEZ) = departure, 

.^5 = cosine of bearing and ^C= sine of bearing. 
From similar triangles, we have, 

AB \\ AD : AE ; that is, 




AC 



1 : cosine of bear. : : course : dif. of lat. ; hence, 
dif. of latitude = course X cosine of bearing ; that is ; 
The difference of latitude is equal to the length of the course 
multiplied by the cosine of the bearing. 
Again, 

AC : CB :: AD : DE; that is, 

1 : sine of bearing : : course : departure ; hence, 
departure = course x sine of bearing, that is. 
The departure is equal to the length of the course multiplied by 
the sine of the bearing. 

Ex. 1. Find, from the Table of natural sines, the latitude 
and departure of the course 49 yards and bearing 35® 18' 
Natural cosine of 35" 18' - - - .81614 

Length of the course - - - - 49 

Product, which is the dif. of latitude 



Natural sine of 35M8' 
Length of the course 

Product, which is the departure 



39.99086. 

.57786 
49 

28.31514. 



122 



ELEMENTS OF SURVEYING. 



.41231 

69.41 
28.618437T 

.91104 
69.41 



2. The bearing is 65° 39', the course 69.41 chains: what 
is the latitude, and what the departure? 

Natural cosine of 65° 39' 

Length of the course - - - 

Product, which is the Dif. of Latitude 

Natural sine of 65° 39' 

Length of the course 

Product, which is the Departure - 63.2352864. 

3. The bearing is 75° 47', the course 89.75 chains : what 
rs the latitude, and what the departure ? 

Natural cosine of 75° 47' - - - .24559 

Length of course - . - - 89.76 

Product, which is the Dif. of Latitude 22.0417025. 

Natural sine of 75° 47' - - - I .96937 

Length of course ----- 89.75 

Product, which is the Departure - 87.0009575. 



4. Find the area of a piece of land from the following 
notes. 



stations. 


Bearings. 


Distances. 


1 


N 45° 55' W 


53 ch. 


2 


N 4° 50' E 


74.40 


3 


N 89° 05' E 


125.50 


4 


S 1° 50' W 


71.80 


5 


S7°40'E 


31.20 


6 


1 N89°25'W 


35.50 


7 


S 84° 35' W 


40. 


8 


S 74° 35' W 


21. 



WITH THE COMPASS. 



123 



Calculating the latitude and departure of each course by 
the rules already given, we have 



^ta. 


Bearings. 


Dist. 


Dif. of Latitude. 


Departure. 


Balanced. 1 


N. I 


S. 


E. 1 W. 


N. 


S. 


E. 


W. 


1 


N45«'55'V4^ 


53 ch. 


36.87210 j 


1 38.07149 


36.65908 






38.07149 


2 


N 4°50'E 


74.40 


74.135131 


6.26894 1 


73.72813 




6.26S94 




3 


N 89^^ 05' E 


125.50 


2.00800 1 


125.48368 




1.96126 




125.49228 




4 


S 1°50'W 


71.80 


1 


71.76338 




2.29688 




72.17110 




2.29688 


5 


S 7''40'E 


31.20 


j 30.92107 


4.16239 






31.12138 


4.16239 




N89"25'V^^ 


35.50 


0.36139| 




35.49822 


0.36139 






35.49822 


7 


S 84° 35' W 


40. 


1 3.77600 




39.82120 




3.80352 




39.81260 


8 


S 74° 35' V^ 


21. 


1 5.58264 




20.24442 




5.61385 




20.24442 








113.376621112.04309 
112.043091 


135.91501 


135.93221 
135.91501 


112.70986I112.709851135.923611135.923C1 



Error in Southing 
«alf Error 



1.33353 
0.6667fi 



0.01720 Error in Easting. 
0.00860 Half Error. 



Instead of balancing by the method explained m Art. 138, 
we divide each error by two. Now if we subtract half the 
error in southing from the column of northings and at the 
same time add it to the column of southings, these two 
columns will exactly balance. In like manner, if we subtract 
half the error in easting from the column of westings and at 
the same time add it to the column of eastings, these cohimns 
will also balance. 

The errors should be distributed in proportion to the lengths 
of the courses, but this may be done with sufficient accuracy 
without making the proportions. If any of the courses have 
been run over rough ground, the probability is that the errors 
belong to these courses and they should be distributed among 
them. 

In this example we separate the half error in southing into 
the three parts .40700, .21302 and .04674, and subtract them 
respectively from the northings of courses 2, 1 and 3, and then 
place the northings in the balanced columns. For the south- 
ings, we separate the error into the four parts .40772, .2 0031, 
.03121, and .02752, and add them respectively to the south- 
ings of the courses 4, 5, 8 and 7. We then enter the southings 
in the balanced columns. As the error in easting is so small 
we add half of it to the easting of course 3, and subtract half 
from the westing of course 7. 



24 



ELEMENTS OF SURVEYING. 



Forming a new table and entering the balanced latitudes 
and departures with their proper signs, we have, 



Sta. 


Beaoing. 


Dist. 


Lat. 


Dep. 


D. M. D. 


Area. 

+ 


Area. 


1 


N 45« 55' W 


53 ch. 


+36.65908 


— 38.07149 


+ 38.07149 


1395.66579 




2* 


N 4°50'E 


74.40 


+73.72813 


+ 6.26894 


+ 6.26894 


462.19722 




3 


N 89" 05' E 


125.50 


+■ 1.96126 


+125.49228 


+138.03016 


270.71303 




4 


S PSO'W 


71.80 


—72.17110 


— 2.29688 


+261.22556 




18854.24214 


5 
6 


S TMO'W 


31.20 


-31.12138 


+ 4.16239 


+263.09107 




8187.75716 


N 89° 25' W 


35.50 


+ 0.36139 


— 35.49822 


+231.75524 


83.75402 




7 


S 84" 35' W 


40. 


— 3.80352 


— 39.81260 


+156.44442 




595.03948 


8 


S 74° 35' W 


21. 


— 5.61385 


— 20.24442 


+ 96.38740 




541.10440 


An. 1298^2. iR. fiP. 


|2212.33006|28178. 14318 
1 2212.33006 


2)25965.81312 
12982.90656 



Having entered the balanced latitudes and departures we 
seek for the most easterly or westerly station. We see at 
once that station 2 is the most westerly. 

Assuming this for the principal station (see Art. 14 1), the 
double meridian distances will all be east, and consequently 
will be plus. 

We then enter the departure of course 2 in the column of 
double meridian distances, and then calculate the double 
meridian distance of each course, according to the rule given 
in Art. 141. 

Having done this we multiply each departure by the double 
meridian distance of its course and place the product in the 
column of plus or minus areas, according as the signs of the 
factors are like or unlike. We enter but five decimal places 
in the columns of areas. This will give the result with suffi- 
cient accuracy. We then add up the columns of area, take 
the difference of the two sums, divide it by two and reduce 
the quotient to acres, roods and perches. 

We thus find the area to be 1298 acres, 1 rood and 6 perches. 



WITH THE COMPASS. 



125 



Ex, 5. Find the area of a piece of land of whicli the 
following are the field notes. 



stations. 


Bearings. 


Distances. 


1 


N52°36'W 


20 ch. 


2 


N 45° 39^ E 


13.80 


3 


N83° 54^ E 


21.25 


4 


S 62» 06' E 


27.60 


5 


S27°09^W 


18.80 


6 


N 80° 36' W 


30.95 



In this example station 2 is the most westerly and station 5 
the most easterly point of the land. 

6. Find the content of a piece of land from the following 
field notes. 



stations. 


Bearings. 


Distances. 


1 


w. 


35.25 ch. 


2 


S88°15'W 


45.65 


3 


N 30' W 


32.55 


4 


N88°45'E 


20.25 


5 


N 1°15'W 


25.40 


6 


N 88° 30' E 


60.00 


7 


S 1° 00' E 


25.50 


8 


S 1° 45' E 


33.10 



In this example station 1 is the most easterly and station 4 
the most westerly point of the land. If the meridian dis- 
tances of the courses be calculated from the meridian passing 
through station I they will all be west : if from the meridian 
passing through 4, they will all be east. 



126 



ELEMENTS OF SURVEYING. 



Method of Surveying the Public Lands. 

151. Soon after the organization of the present government, 
several of the states ceded to the United States large tracts of 
wild land, and these together with the lands since acquired 
by treaty and purchase, constitute what is called the public 
lands or public domain. Previous to the year 1802 these 
lands were parcelled out without reference to any general 
plan, in consequence of which the titles often conflicted with 
each other, and in many cases, several grants covered the 
same premises. 

In the year 1802, the following method of surveying the 
public lands, was adopted by Colonel Jared Mansfield, then 
surveyor-general of the North-Western Territory. 

152. The country to be surveyed is first divided by par- 
allel meridians, six miles distant .from each other ; and then 
again, by a system of east and west lines, also six miles from 
each other. The whole country is thus divided into equal 
squares, which are called townships. Hence, each township 
is a square, six miles on a side, and contains 36 square miles. 

The townships which lie along the same meridian, are 
called a range, and are numbered, to distinguish them from 
each other. 

Each township is divided into equal squares, by meridians 
one mile apart, and by east and west lines at the same dis- 
tance from each other. Hence, each township is divided into 
36 square miles, each one of which is called a section. The 
sections of a township are numbered from 1 to 36, and each 
contains 640 acres. 

Tlie diagram exhibits the 36 sections of a township. 



i ( 1 i 



WITH THE COMPASS. 127 

To describe a section accurately, we saj?^, section number 
5, in township number 4, in range 3d, west of a known me- 
ridian, the one, for example, drawn through the mouth of the 
Great Miami river. This description fixes precisely the place 
of the section. Go to the 3d range of townships, west of the 
known meridian, find township number 4 in this range, and 
lastly, section number 5 of that township. Tiie corners of 
the sections should be marked by permanent corner-posts, or 
by lines blazed on trees. 

The sections are divided into half sections, quarter sections, 
and even into eighths of sections. The following table shows 
the content of a township, and its subdivisions. 

1 township = 36 sections = 23040 acres. 

1 section = 6 40 acres. 

I section = 320 acres. 

^ section = 160 acres. 

■1 section = 80 acres. 
The principal meridians, and the principal east and west 
hues, have been established by astronomical observation, and 
the lines of subdivision run with the compass.. 

VARIATION OF THE NEEDLE. 

153. The line indicated by the magnetic needle, when 
allowed to move freely about the point of support, and settle 
to a state of rest, has been called the magnetic meridian. 
This, in general, is a different line from the true meridian, 
which always passes through the poles of the earth, when 
sufliciently produced in both directions. 

154. The angle which the magnetic meridian makes with 
the true meridian, at any place on the surface of the earth, is 
called the variation of the needle at that place, and is east or 
west, according as the north end of the needle lies on the 
east or west side of the true meridian. 

155. The variation is diflerent at different places, and even 
at the same place it does not remain constant for any length 
of time. The variation is ascertained by comparing the mag- 
netic, with the true meridian. 

156. The best practical method of determining the true 
meridian of a place, is by observing the north star. If this 
star were precisely at the point in which the axis of the earth, 



128 



ELEMENTS OP SURVEYING. 



produced, pierces the heavens, then, the interh^eclion of the 
vertical plane passing through it and the place, with the sur- 
face of the earth, would be the true meridian. But, the star 
being at a distance from the pole, equal to 1° 34' nearly, it 
performs a revolution about the pole in a circle, the polar dis- 
tance of which is 1° 34' : the time of revolution is 2 3 h. and 
56 min. 

To the eye of an observer, this star is continually in motion, 
and is due north but twice in 23 h. 56 min. ; and is then said 
to be on the meridian. Now, when it departs from the me« 
ridian, it apparently moves east or west, for 5 h. and 59 min., 
and then returns to the meridian again. When at its greatest 
distance from the meridian, east or west, it is said to be at its 
greatest eastern or western elongation. 

The following tables show the times of its greatest eastern 
and western elongations. 

Eastern Elongations. 



Days 


April 


May 


June 


July 


August 


Sept 




H. M. 


n. M. 


H. M. 


H. M. 


H. M. 


H. M. 


1 


18 18 


16 26 


14 24 


12 20 


10 16 


8 20 


7 


17 56 


16 03 


14 00 


11 55 


9 53 


7 58 


13 


17 34 


15 40 


13 35 


11 31 


9 30 


7 36 


19 


17 12 


15 17 


13 10 


11 07 


9 08 


7 15 


25 

• 


16 49 


14 53 


12 45 


10 43 


8 45 


6 53 



Western Elongations. 



Days 


Oct. 


Nov. 


Dec. 


Jan. 


Feb. 


March 

1 




H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


1 


18 18 


16 22 


14 19 


12 02 


9 50 


8 01 


7 


17 56 


15 59 


13 53 


11 36 


9 26 


7 38 


13 


17 34 


15 35 


13 27 


11 10 


9 02 


7 16 


1 19 


17 12 


15 10 


13 00 


10 44 


8 39 


6 54 


' 25 


16 49 


14 45 


12 34 


10 18 


8 16 


6 33 



The eastern elongations are put down from the first of 
April to the first of October ; and the western, from the first 
of October to the first of April ; the time is computed from 
12 at noon. The western elongations in the first case, and 
the eastern in the second, occurring in the daytime, cannot 



VARIATION OP THE NEEDLE. 



129 



be used. Some of those put down are also invisible, occur- 
ring- in the evening, before it is dark, or after daylight in the 
morning. In such case, if it be necessary to determine the 
meridian at that particular season of the year, let 5 h. and 
59 min. be added to, or subtracted from, the time of greatest 
eastern or western elongation, and the observation be made at 
night, when the star is on the meridian. 

The following table exhibits the angle which the meridian 
plane makes with the vertical plane passing through the pole- 
star, when at its greatest eastern or western elongation : such 
angle is called the azimuth. The mean angle only is put 
down, being calculated for the first of July of each year 

AZIMUTH TABLE. 



Years 


Lat. 32« 
Azimutli 


Lat. 34° 

Azimuth 


Lat. 36« 
Azimuth 


Lat. 3S» 
Azimuth 


Lat. 40O 
Azimuth 


Lat. 42« 
Azimuth 


Lat. 440 1 
Azimuth 


1836 


IO5O' 


1° 521' 


10 56' 


10 581' 


20 21' 


20 


6' 


20 


101' 


1837 


1° 501' 


lO 521' 


IO55I' 


10 581' 


20 2' 


20 


H' 


20 


10' 


1838 


1050' 


10 521' 


1055' 


10 58' 


20 11' 


20 


5' 


20 


91' 


1839 


10 491' 


IO52' 


IO54I' 


IO57I' 


20 1' 


2" 


H' 


2.« 


9' 


1840 


1» 49' 


1°511' 


1»54' 


1»571' 


2« 01' 


2° 


4' 


2° 


81' 


1841 


l°48l' 


1°51' 


l''53l' 


l''57l' 


2° 0' 


20 


31' 


20 


8' 


1842 


10 48' 


10 501' 


1053' 


IO56I' 


IO59I' 


20 


3' 


20 


H' 


1843 


IO47I' 


IO5O' 


lO 521' 


lO 56' 


IO59' 


2° 


21' 


2° 


7' 


1844 


lUl' 


l°49i' 


l'»52' 


l''55l' 


|l°58l' 


2° 


2' 


2" 


61' 


1845 


1"461' 


1»49' 


1°511' 


1»55' 


1»58' 


2° 


11' 2" 


6' 


; 1846 


1°46' 


l''48V 


1" 51' 


1° 541' 


1° 571' 


2° 


1' 2° 


H' 



The use of the above tables, in finding the true meridian, 
will soon appear. 

To find the true meridian with the theodolite. 
157. Take a board, of about one foot, square, paste white 
paper upon it, and perforate it through the centre ; the diam- 
eter of the hole being somewhat larger than the diameter of 
tlie telescope of the theodolite. Let this board be so fixed 



130 ELEMENTS OF SURVEYING. 

to a vertical staff, as to slide up and down freely : aiivl lot a 
small piece of board, about three inches square, be nailed to 
the lower edge of it, for the purpose of holding a candle. 

About twenty-five minutes before the time of the great esf 
eastern or western elongation of the pole-star, as shown b\ 
the tables of elongations, let the theodolite be placed at a con* 
venient point and levelled. Let the board be placed about 
one foot in front of the theodolite, a lamp or candle placed on 
the shelf at its lower edge ; and let the board be slipped up or 
down, until the pole-star can be seen through the hole. The 
light reflected from the paper will show the cross hairs in the 
telescope of the theodolite. 

Then, let the vertical spider's line be brought exactly upon 
the pole-star, and, if it is an eastern elongation that is to be 
observed, and the star has not yet reached the most easterly 
point, it will move from the line towards the east, and the 
reverse when the elongation is west. 

At the time the star attains its greatest elongation, it will 
appear to coincide with the vertical spider's line for some time, 
and then leave it, in the direction contrary to its fovmer 
motion. 

As the star moves towards the point of greatest elongation, 
the telescope must be continually directed to it, by means of 
the tangent-screw of the vernier plate ; and when the star 
has attained its greatest elongation, great care should be 
taken that the instrument be not afterwards moved. 

Now, if it be not convenient to leave the instrument in its 
place until daylight, let a staff, with a candle or small lamp 
upon its upper extremity, be arranged at thirty or forty yards 
from the theodolite, and in the same vertical plane with the 
axis of the telescope. This is easily effected, by revolving 
the vertical limb about its horizontal axis without moving 
the vernier plate, and aligning the staff to coincide with the 
vertical hair. Then mark the point directly under the theodo- 
lite ; the line passing through this point and the staff, makes 
an angle with the true meridian equal to the azimuth of the 
pole-star. 

From the table of azimuths, take the azimuth correspond- 
ing to the year and nearest latitude. If the observed elonga- 
tion were east, the true meridian lies on the west of the lirio 
which has been found, and makes with it an angle equal to 



VARIATION OF THE NEEDLE. 131 

die azimuth. If the elongation were west, the true meridian 
lies on the east of the line : and, in either case, laying off the 
azimuth angle with the theodolite, gives the true meridian. 

To find the true meridian with the compass. 

158. 1. Drive two posts firmly into the ground, in a line 
nearly east and west ; the uppermost ends, Avhen driven 
firml}', heing about three feet above the surface, and the posts 
about four feet apart : then lay a plank, or piece of timber 
three or four inches in width, and smooth on the upper side, 
upon the posts, and let it be pinned or nailed, to hold it firmly. 

2. Prepare a piece of board four or five inches square, and 
smooth on the under side. Let one of the compass-sights be 
placed at right angles to the upper surface of the board, and 
let a nail be driven through the board, so that it can be tacked 
to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the direc- 
tion of the pole-star, let a plumb be suspended from the top 
of an inclined stake or pole. The top of the pole should be 
of such a height that the pole-star will appear about six 
inches below it ; and the plumb should be swung in a vessel 
of water to prevent it from vibrating. 

This being done, about twenty minutes before the time of 
elongation, place the board, to which the compass-sight is 
fastened, on the horizontal plank, and slide it east or west, 
until the aperture of the compass-sight, the plumb line, and 
the star, are brought into the same range. Then if the star 
depart from the plumb-line, move the compass-sight, east 
or west, along the timber, as the case may be, until the star 
shall attain its greatest elongation, when it will continue 
behind the plumb-line for several minutes ; and will then 
recede from it in the direction contrary to its motion before it 
became stationary. Let the compass-sight be now fastened 
to the horizontal plank. During this observation it will be 
necessary to have the plumb-line lighted : this may be done 
by an assistant holding a candle near it. 

Let now a staff, with a candle or lamp upon it, be placed 
at a distance of thirty or forty yards from the plumb-line, and 
in the same direction with it and the compass-sight. The 
line so determined, makes, with the true meridian, an ojsi^le 



132 ELEMENTS OP SURVEYING. 

equal to the azimuth of the pole-star; and, from this line, 
the variation of the needle is readily determined, even witliout 
tracing the true meridian on the ground. 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. 
Now, if the elongation, at the time of observation, were west, 
and the north end of the needle on the west side of the line, 
the azimuth, plus the angle shown by the needle, is tlie true 
variation. But should the north end of the needle be found 
on the east side of the line, the elongation being west, the 
difference between the azimuth and the angle would show the 
variation : and the reverse when the elongation is east. 

1. Elongation west, azimuth 
North end of the needle on the west, angle 

Variation 

2. Elongation west, azimuth 
North end of the needle on the east, angle 

Variation 

3. Elongation east, azimuth 
North end of the needle on the west, angle 

Variation 

4,. Elongation east, azimuth 
North end of the needle on the east, angle 

Variation 

Remark I. The variation at West Point, in September, 
1835, was 6° 32' west. 

Remark II. The variation of the needle should always 
be noted on every survey made Avith the compass, and then 
if the land be surveyed at a future time, the old lines can 
always be re-run. 

159. It has been found by observation, that heat and cold 
sensibly affect the magnetic needle, and that the same needle 
will, at the same place, indicate different lines at different 
hours of the day. 

If the magnetic meridian be observed early in the morning, 
and again at different hours of the day, it will be found that 
the needle will continue to recede from the meridian as the 
day advances, until about the time of the highest tempera- 



20 04' 




40 06' 




6° 10' 


west. 


P 59' 




4» 50' 




2" 51' 


east* 


2" 05' 




8° 30' 




6" 25' 


west. 


1« 57' 




8» 40' 




10° 37' 


east. 



WITH THE PLAIN-TABLE. 133 

ture, when it will begin to return, and at evening will make 
the same line as in the morning. This change is called the 
diurnal variation, and varies, during the summer season, from 
one-fourth to one-fifth of a degree. 

OF THE PLAIN-TABLE. 

160. PL 3, Fig. 1. The plain-table consists of two parts; 
a rectangular board CDBA, and a tripod EHG, to which it 
is firmly secured. 

Directly under the rectangular board are four milled screws 
which pass through sockets inserted in a horizontal brass 
plate : these screws are worked against a second horizontal 
plate, for the purpose of levelling the table ; the table having 
a ball and socket motion, similar to the limb of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the centre, 
and also over two of the levelling screws, the screws are turned 
contrary ways until the level is horizontal ; after which, it is 
placed over the other two screws, and made horizontal in the 
same manner. 

Between the upper horizontal plate and the table, there is 
a clamp-screw, similar to the clamp-screw of the theodolite, 
which being loosened, the table can be turned freely about 
its axis. There is, also, a small tangent-screw, by which the 
smaller motions of the table are regulated, after the clamp- 
screw is made fast. Neither of these screws can be seen in 
the figure. 

The upper side of the table is bordered by four brass plates, 
about one inch in width, and the centre of the table is marked 
by a small pin, F. About this centre, and tangent to the 
sides of the table, conceive a circle to be described. Suppose 
the circumference of the circle to be divided into degrees and 
parts of a degree, and radii to be drawn through the centre 
and the points of division. The points in which these radii 
intersect the outer edge of the brass border, are marked by 
lines on the brass plates, and the degrees are numbered in the 
direction from left to right, from the point L to the point /, 
180°, and from the point / to the point L, 180°. In some 
plain-tables, however, they are numbered from to 360". 

There are, generally, diagonal scales of equal parts cut on 



134 ELEMENTS OF SURVEYING. 

the plates DLC and AIB^ the use of which will be explained 
hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass DB and CJi are 
fitted, and these plates are drawn to their places by means of 
milled screws which pass through the table from the under 
side, and screw firmly into the plates. The heads of two of 
the screws, Q and S, are seen in the figure, as also one of the 
plates and its two screws in Fig. 3. The object of these 
plates is to confine a sheet of paper on the table. By loosen- 
ing the screws, and pressing them upwards, the plates are 
raised above the surface of the table ; the edges of the paper 
can then be placed under them : then, by turning the screws 
back again, the plates are drawn down and the paper held 
tightly. Fig. 1 represents the table with the paper partly put 
upon it : one edge of the paper has been placed under the 
plate DB, and the screws >S and Q, tightened. The paper, 
before being put on, should be moistened, in order to expand 
it; and then, after it has been dried, it will fit closely to the 
table. 

A ruler, JIB (Fig. 2), with open vertical sights, is used 
with the plain-table. This ruler has a fiducial edge, which 
is in the same vertical plane with the hairs of the sights. 
A ruler with a telescope, and a vertical limb, similar to the 
vertical limb of the theodolite, is sometimes used with the 
plain-table. A compass, also, is often attached to the table, 
to show the bearings of the lines. 

The plain-table is used for two distinct objects. 

1st. For the measurement of horizontal angles. 

2dly. For the determination of the shorter lines of a sur- 
vey, both in extent and position. 

To measure a horizontal angle. 

161. Place, by means of a plumb, the centre of the table 
directly over the angular point : then level the table ; after 
which, place the fiducial edge of the ruler against the small 
pin at the centre : direct the sights to one of the objects, and 
note the degrees on the brass plate ; then turn the ruler and 
sights to the other object, and note the degrees as before. 
If the ruler has not passed over the point, the difference of 
the readings is the angle sought ; but, if it has, the larger 



WITH THE PLAIN-TABLE. 135 

taken from 180*, and the remainder added to the smaller, 
gives the required angle. 

Of the determination of lines in extent and position. 

162. Having placed a paper on the table, examine the ob- 
jects and lines which are to be determined, and measure a 
base line in such a direction, if possible, that all the objects 
can be seen from its extremities. Then place the plain-table 
with its centre, nearly, though not accurately, over one ex- 
tremity of the base ; make it truly horizontal, and turn it 
until the larger part of the paper lies on the same side of the 
base with the objects. 

Then, tighten the clamp-screw, and mark with a pin the 
point of the paper directly over the station, which point is de- 
termined most accurately by suspending a plumb from the 
lower side of the table. Press the pin /irmly on this point, 
bring the fiducial edge of the ruler against it, and sight to the 
other extremity of the base line, and mark with the pin or 
pencil, the direction of the line on the paper. Sight in like 
manner to every other object, and draw on the paper the cor- 
responding lines, numbering them from the base line, 1, 2, 3, 
4, &c. 

Then, with a pair of dividers, take from the scale a certain 
number of equal parts to represent the base, and lay off the 
distance on the base line from the place of the pin. Take 
up the table, carry it to the other extremity of the base, and 
place the point of the paper corresponding to that extremity, 
directly over it. Place the fiducial edge of the ruler on the 
base line, and turn the table, by means of the tangent-screw, 
until the sights are directed to the first station. If, however, 
in bringing the table to this position, the corresponding point 
of the paper has been moved from over the extremity of the 
base line, move the legs of the tripod until it is brought back 
to its place. Let the table be then levelled, after which, 
place the ruler again on the base line, and bring the table to 
its proper position by the tangent-screw, and continue the ad- 
justment until the extremity of the base line on the paper is 
directly over the station, and in the same vertical plane with 
the base line on the ground. Then direct the sights to all 
the objects sighted to from the other station, and mark the 
lines 1, 2, 3, 4, &c. from the base line, as before. The inter- 



136 



ELEMENTS OF SURVEYING. 




sections of the corresponding lines 1,1, 2,2, 3,3, 4,4, &c*, 
determine, on the paper, the positions of the several objects; 
and a reference of these lines to the scale of equal parts, 
determines the true distances. 

1 63. Let it be required, for ex- 
ample, to determine, by means 
of the plain-table, the relative 
position of several houses. 

Measure the base line JiB, 
which we will suppose equal 
to 300 yards. Place the plain- 
table at A, and sight to the 
corners of the houses, and mark the lines 1, 2, 3, 4, &c. Then 
remove the table to B, and sight to the same corners as 
before, and draw the lines as in the figure. The points at 
which they intersect the corresponding lines before drawn, 
determine the corners of the houses. The front lines of the 
houses may then be drawn on the paper. Draw lines at riglil 
angles to the front lines, and on them lay off the depths of 
the houses, with the same scale as that used for the base line. 

To find the length of any line drawn on the paper, as the 
line 1, drawn through A, for example, place the dividers at 
A and extend them to the other extremity of the line, and 
then apply the line to the scale. The length of the line 1 is 
equal to 198 yards. 

164. In this example, we de- 
termine from the base line CD, 
the positions of the points B, F, 
E, and H. 

Of changing the Paper. 

165. When one paper is filled, and there is yet more work 
to be done, let the paper be removed, and a second paper put 
on the table ; after which, the table may be used as before. 

Now, in order that the two papers may be put together and 
form one entire plan, it is necessary that two points deter- 
mined on the first paper, be also determined on the second ; 
and then, by placing the lines joining these points upon each 
other, all the lines on the two papers will have the same 




OF LEVELLING. 137 

relative position as the corresponding lines on the ground ; 
and the same for as many papers as it may be necessary to 
use. If -different scales are used, the corresponding points 
will not join, and then the work must be reduced to the same 
scale, before the papers can be put together. 

In the first example, the position of the point F was deter- 
mined, in order to unite the first paper with the second. 

In the second example, we sighted from C and D, the 
extremities of the base line, to the points B and F; we thus 
determined the hue BF on the second paper. Placing the 
line BF of the one paper on BF of the other, we have the 
following plan. 




In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in the same 
manner. 

The plain-table is used to great advantage when only a 
plot of the ground is wanted. It ought not to be used for 
the determination of long lines, nor can it be relied on in 
determining extended areas. 



CHAPTER V. 

Of Levelling. 

166. If all the points of the earth's surface were equidistant 
from the centre, it would be perfectly even, and present to 
the eye an unbroken level. 

Intersected, however, as it is, by valleys and ridges of 
mountains, it becomes an important problem to ascertain the 
difference between the distances of given points from the 
centre of the earth ; such difference is called the difference 



138 ELEMENTS OF SURVEYING. 

of level ; and a line, all the points of which are equally dis- 
tant from the centre, is called the line of true level* 

167. One point is said to be above another, when it is 
farther from the centre of the earth ; and below it, when it is 
nearer. 

168. Let C (PL 4, Fig. 1), represent the centre of the 
earth. A a point of its surface, and JIEF the line of true 
level. If, at the point Jl, a tangent line JlBD be drawn to 
the surface, such line is called the line of apparent level. 

169. Now, if an instrument were placed at Ay and brought 
into a horizontal position so as to indicate a horizontal line, 
this line would be tangent to the earth at A, and would be 
the line ABD of apparent level. 

170. When, therefore, we have ascertained the direction of 
a tangent, or horizontal line, we have found the line of appa- 
rent level only ; the line of true level is yet to be determined. 

If at the points E and jP, vertical staves be placed, the 
line of apparent level passing through A will cut them at 
B and D, while the line of true level cuts them at E and F. 
Therefore, BE and DF are, respectively, the differences be- 
tween the apparent levels of the points E and F, as deter- 
mined by the horizontal line passing through A^ and the true 
levels of those points. 

But AB' = BE {BE+^EC), and AD^=DF (DF+sFC) 
(Geom. Bk. IV, Prop. XXX). In the common operations of 
levelling, the arcs AE, AF, are small ; and since the differ- 
ence between small arcs and their tangents is very incon- 
siderable, the arcs AE, AF may be substituted for the tan- 
gents AB, AD. And since the external parts of the secants 
BE and DF are very small in comparison with the diameter 
of the earth, they may be neglected without sensible error : 
the expressions above will then become, 

AE'=BEx2EC, and AF^=DFx2FC, 

J.J. AE^ . j.j^ AF^ 

or, BE= ; and DF= ; 

2EC 2FC 

and since the diameter of the earth is constant, BE and DF 
are proportional to AE^ and AF^. 

* The spheroidal form of the earth is not considered, as it affects the results 
too inconsiderably to be regarded in the common operations of levelUng. 



OF LEVELLING. 



139 



But BE and DF are respectively the differences between 
the true levels of the points E and F, and their apparent 
levels, as determined from the point A : hence, the difference 
between the apparent and true level of any point, is equal to 
the square of the distance of that point from the place where the 
apparent level was made, divided by the diameter of the earth; 
or, the diameter being constant, the rise of the apparent above 
the true level, is proportional to the square of the distance. 

171. The mean diameter of the earth being about 7919 
miles, if AE be taken equal to 1 mile, then the excess 

ft 7^2 1 

BE=—T— becomes equal to = 8.001 inches. 

2dC 7919 

If the excess FD, for any other distance AF, were required, 

AE"" : AF^ : : BE : FD ; 

and by similar proportions the following table is calculated. 

Table showing the differences in inches between the true and appa 
rent level, for distances between 1 and 100 chains. 



Chains. 


Inches. 


Cfains. 


Inches. 


Chains. 


Inles. 


1 
Chains. 


1 

Inches. 


1 


.001 


-26 


.845 


51 


3.255 


76 


7.221 


2 


.005 


27 


.911 


52 


3.380 


77 


7.412 


3 


.011 


28 


.981 


53 


3.511 


78 


7.605 


4 


.020 


29 


1.051 


54 


3.645 


79 


7.802 


5 


.031 


30 


1.125 


55 


3.781 


80 


8.001 


6 


.045 


31 


1.201 


56 


3.925 


81 


8.202 


7 


.061 


32 


1.280 


57 


4.061 


82 


8.406 


8 


.080 


33 


1.360 


58 


4.205 


83 


8.612 


9 


.101 


34 


1.446 


59 


4.351 


84 


8.832 


10 


.125 


35 


1.531 


60 


4.500 


85 


9.042 


11 


.151 


36 


1.620 


61 


4.654 


86 


9.246 


12 


.180 


37 


1.711 


62 


4.805 


87 


9.462 


13 


.211 


38 


1.805 


63 


4.968 


88 


9.681 


14 


.245 


39 


1.901 


64 


5.120 


89 


9.902 


15 


.281 


40 


2.003 


65 


5.281 


90 


10.126 


16 


.320 


41 


2.101 


66 


5.443 


91 


10.351 


17 


.361 


42 


2.208 


67 


5.612 


92 


10.587 


18 


.405 


43 


2.311 


68 


5.787 


93 


10.812 


19 


.451 


44 


2.420 


69 


5.955 


94 


11.046 


20 


.500 


45 


2.531 


70 


6.125 


95 


11.233 


21 


.552 


46 


2.646 


71 


6.302 


96 


11.521 


22 


.605 


47 


2.761 


72 


6.480 


97 


11.763 1 


23 


.661 


48 


2.880 


73 


6.662 


98 


12.017 1 


24 


.720 


49 


3.004 


74 


6.846 


99 


12.246 


25 


.781 


J2^ 


3.125 • 


75 


7.032 


100 


12.502 



140 ELEMENTS OF SURVEYING. 

We cnnnot proceed farther in the discussion of the principles 
of levelling, until we have described the instruments which 
are to be used, and explained the particular objects which 
they are to answer. 

OF THE LEVEL. 

172. The level is an instrument used to determine hori- 
zontal lines, and the difference of level of any points on the 
surface of the earth. 

The part of the instrument shown in PI. 4, Fig. 2, rests on 
a tripod to which it is permanently attached at Z. IIH is a 
horizontal brass plate, through which four levelling screws 
with milled heads are passed, and worked against a second 
horizontal plate GG. Two of these screws, K and /, are 
seen in the figure. *S is a clamp-screw, which, being loosened, 
allows the upper part of the instrument to turn freely around 
its axis. Q is a tangent-screw, by means of which the upper 
part of the instrument is moved gently, after the clamp-screw 
S has been made fast. EE is a horizontal bar, perpendicular 
to which are the wyes, designated F's,that support the tele- 
scope LB. This telescope is confined in the F's by the loops 
r, r, which arc fastened by the pins p and p. The object- 
glass J5, is adjustedxto its focus by the screw X ; the eye- 
glass L slides out and hi freely. The screws /, /, Avork the 
slide which carries the ^horizontal hair ; and two horizontal 
screws, only one of which, «, is seen, work the slide that 
carries the vertical hair. CD is an attached spirit level. The 
screw JV elevates and depresses the F, nearest the eye-glass. 
In some instruments this Y is elevated and depressed, by 
means of two screws at M and R. 

Before using the level, it must be adjusted. The adjustment 
consists in bringing the different parts to their proper places. 

The line of collimation is the axis of the telescope. With 
this axis, the Hne drawn through the centre of the eye-glass, 
and the intersection of the spider's lines, within the barrel of 
the telescope, ought to coincide. 

First adjustment.* To fix the intersection of the spider's 
lines in the axis of the telescope. 

Having screwed the tripod to the instrument, extend the 

* This, and some of the following adjustments, are so similar to those of the 
theodolite, that they would not be repeated, but that some may use the level without 
wishing to study a more complicated instrument 



OF LEVELLING. 141 

legs, and place them firmly. Then loosen the clamp-sciew S, 
and direct the telescope to a small, well-defined,, and distant 
object. Then slide the eye-glass till the spider's lines are 
seen distinctly ; after which, with the screw X, adjust the 
object-glass to its proper focus, when the object and the 
Fpider's lines will be distinctly seen. Note now the precise 
point covered by the intersection of the spider's lines. 

Having done this, revolve the telescope in the F's, half 
round, when the attached level CD will come to the upper 
side. See if, in this position, the horizontal hair appears 
above or below the point, and in either case, loosen the one, 
and tighten, the other, of the two screws which work the hori- 
zontal hair, until it has been carried over half the space 
between its last position and the observed point. Carry the 
telescope back to its place ; direct again, by the screws at 
JH and R, the intersection of the spider's lines to the point, 
and repeat the operation, till the horizontal hair neither 
ascends nor descends while the telescope is revolved. A 
similar process will arrange the vertical hair, and the line 
of collimation is then adjusted. 

Second adjustment. To make the axis of the attached 
level CD parallel to the line of collimation. 

Turn the screw JV, or the screws M and R, until the bub- 
ble of the level DC stands at the middle of the tube. Then 
open the loops, and reverse the telescope. If the bubble still 
stands at the middle of the tube, the axis of the level is hori- 
zontal ; but if not, it is inclined, the bubble being at the ele- 
vated end. In such case, raise the depressed, or depress the 
elevated end, by means of the screw h, half the inclination ; 
and then with the screw JV, bring the level to a horizontal 
position. Reverse the telescope in the F's, and make the 
same correction again ; and proceed thus, until the bubble 
stands in the middle of the tube, in both positions of the tele- 
scope ; the axis of the level is then horizontal. 

Let the telescope be now revolved in the F's. If the bub- 
ble continue in the middle of the tube, the axis of the level 
is not only horizontal, but also parallel to the line of collima- 
tion. If, however, the bubble recedes from the centre, the 
axis of the level is inclined to the line of collimation, and 



142 ELEMENTS OF SURVEYING. 

must be made parallel to it, by means of two small screws, 
which work horizontally ; one of these screws is seen at q. 
By loosening one of them, and tightening the other, the level 
is soon brought parallel to the line of collimation ; and then, 
if the telescope be revolved in the F's, the bubble will con 
tinuc at the middle point of the tube. It is, however, difficult 
to make the first part of this adjustment, while the axis of 
the level is considerably inclined to the line of collimation : 
for, allowing the level to be truly horizontal in one position 
of the telescope, after it is reversed, there will be but one cor- 
responding position in which the bubble will stand at the 
middle of the tube. This suggests the necessity of making 
the first part of the adjustment with tolerable accuracy ; then, 
having made the second with care, re-examine the first, and 
proceed thus till the adjustment is completed. 

Third adjustment. To make the level CD and the line of 
collimation perpendicular to the axis of the instrument, or parallel 
to the horizontal bar EE. 

Loosen the clamp-screw S, and turn the bar EE, until the 
level DC comes directly over two of the levelling screws. By 
means of these screws, make the level CD truly horizontal. 
Then, turn the level quite round ; if, during the revolution, 
it continue horizontal, it must be at right angles to the axis 
of the instrument about which it has been revolved. But if, 
after the revolution, the level CD be not horizontal, rectify 
half the error with the screw^s at M and jR, and half with the 
levelling screws. Then place the bar EE over the other two 
levelling screws, and make the same examinations and correc- 
tions as before ; and proceed thus, until the level can be turned 
entirely around without displacing the bubble at the centre. 
When this can be done, it is obvious that the level DC and 
the line of coUimation, are at right angles to the axis of the 
instrument about which they revolve ; and since the axis is 
carefully adjusted by the maker, at right angles to the bar 
EE, it follows, that the line of collimation, the level DC, 
and the bar EE, are parallel to each other. 

The level is now adjusted. When used, however, it is 
best to re-examine it every day or two, as the work will be 
erroneous unless the adjustments are accurate. 



OF LEVELLING. 143 

Of Levelling Staves. 

173. The levelling staves are used to determine the points 
at which a given horizontal line intersects lines that are per- 
pendicular to the surface of the earth, and to show the dis- 
tance of such points of intersection from the ground. 

They are thus constructed. AB (PL 4, Fig. 3) is a rec- 
tangular piece of wood, in the middle of which is a groove 
abed. Into this groove a slide Inst enters, and is moved freely 
along the groove. At the upper end of the slide is a rectan- 
gular board fhow, called a vane, six inches, in the direction 
hi. The vane is divided into four equal parts, by the lines 
fg, hi : the two rectangles //i, ig, are usually painted black, 
and the other two, if, hg, white ; so that the lines /^ and hi 
may be distinguished with great accuracy. The slide from 
fg to In, is of the same length with the body of the staff 
AB : hence, when the line fg coincides with be, the lower 
end of the slide In, will coincide with ad. The pins p and q, 
which work in grooves, and are largest at the ends p and q, 
are pressed in to hold the slide in any position at which it 
may be placed. The length of the staff is generally six feet, 
and it is usually divided into eighths or tenths of an inch. 
The slide is divided in the same way. The longer lines show 
the feet, the shorter, the inches. The object to be attained by 
these divisions, is, to ascertain the distance of the line fg from 
the ground. 

When the line fg is brought to the top of the staff, to 
coincide with be, the lower line wio of the vane, coincides 
with the line marked 6, on the left of the staff: which shows, 
the staff standing upright, that the line fg is six feet above 
the ground. From the line marked 6, to the lower end of 
the staff, is, indeed, but 5 feet 9 inches ; but the line fg is 
three inches above the line wio, so that fg is six feet from the 
ground. 

If, from the last position, the slide be run up until the line 
wio coincides with the division marked 1, on the left of the 
staff, the line fg will be six feet and one inch from the ground : 
if, till it coincides with 6c, it will be six feet and three inches, 
the inches being marked on the staff. If the slide be still run 
up, until 7 on the slide coincides with be, the hne fg will be 
seven feet from the ground. In the j&gure, the line fg is 



144 ELEMENTS OF SURVEYING. 

seven feet from the bottom of the staff. The count above 6 
feet 3 inches is always made on the slide. The manner of 
counting off, for the parts of an inch, is too plain to require 
particular explanation. 

Having run down the slide till the upper line h, of the 
vane, coincides with be, place bB on the ground, and the 
staff vertical. It is now plain, that the line fg is three inches 
above the ground. These three inches are marked on the 
right of the staff. If the slide be run up till the lower line h 
coincides with 1, on the right of the staff, the line fg will be 
one foot from the ground, and similarly, until six feet be 
shown at the other end of the staff. 

The feet are marked 1, 2, 3, &c., from the upper end, and 
are reversed in the present position of the staff; but are up- 
right when the staff is placed for use. In the last position of 
the staff, the count is made at the lower line of the vane. 

174. There is a method of testing the adjustments of the 
level, which ought not to be neglected, since all the results de- 
pend on the accuracy of the instrument. The method is this: 

Tlie level being adjusted, place it at any convenient point, 
as G (Fig. 4). At equal distances of about 100 yards, on 
either side, and in the same line with the level, place the 
levelling staves CE, BF. Make the level horizontal with 
the levelling screws. Then, turn it towards either staff, as 
BF, and run the vane up or down, as required, until the 
intersection of the hairs strikes the centre : then make the 
slide fast, and note carefully the neight of the vane. Turn 
the level half round, and do the same in respect of the staff 
CE. Let the telescope be now reversed in the F's. Sight 
again to the staff BF, and note the exact height of the vane. 
Let the telescope be now turned half round, and the same be 
done for the staff CE. If the two heiglits last observed, are 
equal to those first noted, each to each, the line of collimation 
will be perpendicular to the axis of the instrument, and if the 
bubble has, at the same time, preserved its place at the middle 
point of the tube, the instrument is truly adjusted. 

For, had the line of collimation been inclined to the axis 
of the level, it would, in the first instance, have taken the 
direction JlF or £d ; and when turned half round, it would 
have taken the direction Ab or AE. The telescope being 



OF LEVELLING. 



145 



reversed in the F's, and again directed to the staff BF, the 
line of colhmation would take the direction Ad or AF, and 
when turned to the staff CE, it would take the direction AE 
or Ab : and the two distances BF, Bd, or Cb, CE, can only 
be equal to each other when the line of coUimation falls on 
the horizontal line gf. 

175. Having described the instruments used in levelling, 
we will explain the practical operations on the field. 

When it is proposed to find the difference of level of anj 
two objects, or stations, all levels made in the direction of the 
station at which the work is begun, are, for the sake of dis- 
tinction merely, called back-sights ; and levels taken in the 
direction of the other station, fore-sights. 

Before going on the field with the level, rule three columns, 
as below, and head them, stations, back-sights, fore-sights. 



stations. 


Back-Sights. 


1 
Fore-Sights. 


1 


10 


3 


2 


11-6 





r 

3 


6-8 


4-9 


4 


3-9 


8-3 


Sums . . . . 31-11 

16-00 

Dif. of level ... 15-11 


10-0 



PROBLEM. 

176. To find the difference of level between any two points, 
as A and G (PI. 4, Fig. 5). 

The level being adjusted, place it at any point as B, as 
nearly in the line joining A and G as may be convenient. 
Place a levelling staff at A, and another at JV, a point lying 
as near as may be in the direction of G. Make the level 
horizontal, by means of the levelling screws ; turn the tele- 
scope to the staff at A, and direct the person at the staff (o 
slide up the vane until the horizontal line ab cuts its centre ;. 
then note the distance Ab (equal to 10 feet in the present 
example), and enter it in the column of back-sights, opposite 
station l. Sight also to the staff at JV, and enter the distance 

10 



146 ELEMENTS OF SURVEYING. 

JVa, equal to 3 feet, in tlie column of fore-sights, opposite 
station 1. 

Take up 'the level, and place it at some other convenient 
station, as C, and remove the staff at Jl, to M. Having 
levelled the instrument, sight to the staff at JV, and enter the 
distance J^d, 1 1 feet G inches, in the column of hack-sights, 
opposite station 2 : sight also to the staff at M, and enter the 
distance J\IJ^ equal 0, in the column of fore-sights, opposite 
station 2. 

Let the level he now removed to any other station, as Z>, 
and the staff at A*, to some other point, as P. Let the dis- 
tance J\Ig, equal to 6 feet 8 inches, be entered in the column 
of hack-sights, opposite station 3, and the distance PJi, equal 
to 4 feet 9 inches, in the column of fore-sights. Let the 
instrument be now placed at E, and the distance Pm, equal 
to 3 feet 9 inches, and Gn, equal to 8 feet 3 inches, be entered 
opposite station 4, in their proper columns. 

By adding up the columns, we find, that the sum of the 
l)ack-sights is equal to 31 feet 11 inches, and the sum of the 
fore-sights, IC feet; the difference, 15 feet and 11 inches, is 
the difference of level of the points Jl and G. 

DEMONSTRATION. 

Let the back-sights he called plus, and the fore-sights, 
minus. 

Then, having let fall the perpendiculars J^F, Mil, PI, and 
GL, on the horizontal line AL, it remains to be proved, that 
the difference of level, 

GL=^6 + JV^+Jl% + P>n-JVa-0-/iP-na 

Now, Jlb-\-.m-J^a=M-\-ad = Fd; 
Therefore, GL = Fd+Mg-{- Pm --liP-nG. 
But Fd-\.Mg = IIg, and -f Pm-/iP= -/jm, 
Therefore, GL = IIg-hm-nG = hI-{hm+nG) = GL. 

As the same mj\y be shown in every example, we conclude 
(hat, the difference between the sum of the fore-sights and the sum 
of the back-sights is, in all cases, equal to the difference of level. 

It is also evident that^ when the sum of the hack-sights 
exceeds tlie sum of the fore-sights, the last station is more 
elevated than the first ; and, conversely, if the sum of the 



OF LEVELLING. 



147 



back-sights is less than the sum of tlie fore-sights, the second 
station is lower than the first. 

177. In tliis example, we have not regarded the difTerence 
between the true and apparent level. If it be nece3sary to 
ascertain the result with extreme accuracy, this difTerence must 
be considered: and then, the horizontal distances between the 
level, at each of its positions, and the staves, must be mea- 
sured, and the apparent levels diminished by the differences 
of level ; which differences can be found from the table. 

The following is such an Example. 



Stat. 


Bark-sfs. 


Disfanres. 


Fore-st. 


Distances. \ Cor. back-sights. 


Cor. fore-sts. 


1 


9-8 


20 ch. 


1-0 


32 ch. 


9-7.500 


1-4.720 


2 


8-7 


25 ch. 


2-4 


28 ch. 


8-6.219 


2-3.019 


3 


5-2 


18 ch. 


3-1 


10 ch. 


5-1.595 


3-0.080 


4 


10-3 


29 ch. 


1-9 


87 ch. 


10-1.949 


0-11.538 


5 


11-0 


45 ch. 


2-5 


72 ch. 


10-9.409 


1-10.520 












44-2.732 


9-6.477 



In this example, the first column shows the stations ; the 
second, the back-sights ; the third, the distances from the 
level in each of its positions to the bflck staff; the fourth, the 
fore-sights ; the fifth, the distances from the level to the 
forward staff; the sixth and seventh, are the columns of back 
and fore sights, corrected by the difference of level. The cor- 
rections are thus made : — The difference of level in the table 
corresponding to 20 chains, is 5 tenths of an inch, which be- 
ing subtracted from 9 feet 8 inches, leaves 9 feet 7.5 inches for 
the corrected back-sight ; this is entered opposite station 1 in 
the sixth column. The difference of level corresponding, to 
32 chains, is 1.280 inches, which being subtracted from the 
apparent level, 1 foot inches, leaves 1 foot 4.720 inciies for 
the true fore-sight from station 1. The other corrections are 
made in the same manner. 

The sum of the back-sights being 44 feet 2.732 inr!ies, 
and the sum of the fore-sights 9 feet 0.477 inches, it follows, 



148 ELEMENTS OF SURVEYING. 

that the difference, 34 feet 8.255 inches, is the true difference 
of level. 

178. In finding the true from the apparent level, we have 
not regarded the effect caused by refraction on the apparent 
elevation of objects, as well because the refraction is different 
in different states of the atmosphere, as because the correc 
tions are inconsiderable in themselves. 

179. The small errors that would arise from regarding the 
apparent as the true level, may be avoided by placing the 
levelling staves at equal distances from the level. In such case, 
it is plain, 1st, that equal corrections must be made in the 
fore and back sights ; and, sdly, that when the fore and back 
sights are diminished equally, the result, which is always the 
difference of their sums, will not be affected. 

This method should always be followed, if practicable, as it 
avoids the trouble of making corrections for the difference of 
true and apparent level. 

The differences between the true and apparent level, being 
very inconsiderable for short distances, if only ordinary accu- 
racy be required, it will be unnecessary to make measure- 
ments at all. Care, however, ought to be taken, in placing 
the levelling staves, to have them as nearly at equal distances 
from the level as can be determined by the eye ; and if the 
distances are unequal, let the next distances also be made 
unequal ; that is, if the back-sight was the longest in the first 
case, let it be made proportionably shorter in the second, and 
the reverse. 



CHAPTER VL 

Of the methods of showing the contour and accidents of ground. 

180. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is fre- 
quently necessary to make minute and careful examinations 
for the purpose of ascertaining the form and accidents of the 
ground, and to make such a plan as will distinguish the 



CONTOUR OF GROUND. 149 

swelling hill from the sunken valley, and the course of the 
rivulet from the unbroken plain. 

181. This branch of surveying is called Topography. In 
surveys made with a view to the location of extensive w^orks, 
the determination of the slopes and irregularities of the ground 
is of the first importance : indeed, the examinations would 
otherwise be useless. 

182. The manner of ascertaining these irregularities is, to 
intersect the surface of the ground by a system of horizontal 
planes at equal distances from each other ; the curves deter- 
mined by these secant planes, being lines of the surface, will 
indicate its form at the places of section, and, as the curves 
are more or less numerous, the form of the surface will be 
more or less accuratelj?^ ascertained. 

If such a system of curves be determined, and then pro- 
jected or let fall on a horizontal plane, it is obvious that the 
curves on such plane will be nearer together or farther apart, 
as the ascent of the hill is steep or gentle. 

If, therefore, such intersections be made, and the curves so 
determined be accurately delineated on paper, the map will 
present such a representation of the ground as will show its 
form, its inequalities, and its striking characteristics. 

183. The subject divides itself, naturally, into two parts. 
First, To make the necessary examinations and measure- 
ments on the field. 

And, 2dly, to make the delineations on paper. 

For the former of these objects, the theodolite is the best 
instrument ; the common level, however, will answer all the 
purposes, though it is less convenient. 

Before going on the field, it is necessary to provide a num- 
ber of wooden stakes, about two feet in length, with heads. 
These stakes are used to designate particular points, and are 
to be driven to the surface of the ground. A nail should 
then be driven into the head of each of them, to mark its 
centre. 

184. We shall, perhaps, be best understood, by giving an 
example or two, and then adding such general remarks as 
will extend the particular cases to all others that can occur. 

Let A (PI. 4, Fig. 6), be the summit of a hill, the contour of 



150 ELExMENTS OF SURVEYING. 

which it is required to represent. At Jl^ let a stake he driven, 
and let the axis of the theodolite, or level, he placed directly 
over (he nail which marks its centre. From ./?, measure any 
line down the hill, as AB^ nsing the telescope of the theodo- 
lite or level to arrange all its points in the same vertical plane. 
Great care must be taken to keep the measuring chain hori- 
zontal, for it is the horizontal distances that are required. At 
diflerent points of this line, as a, h, c, d, &c., let stakes be 
driven, and let the horizontal distances Jla, ab, be, and cd, be 
carefully measured. In placing the stakes, reference must 
be had to the abruptness of the declivity, and the accuracy 
with which the surface is to be delineated : their differences 
of level ought not to exceed once and a half, or twice, the 
distance between the horizontal planes of section. 

Having placed stakes, and measured all the distances along 
the line ^B, run another line down the hill, as JlC, placing 
stakes at the points e, /, g, and //, and measuring the hori- 
zontal distances *Me, ef, fg, and gh. Run also the line *^D, 
placing stakes at i, /, m, and «, and measuring the horizontal 
distances Jli, il, hi, and mn. 

Each line, ^B, AC, AD, running down the hill from A^ 
may be regarded as the intersection of the hill by a vertical 
plane ; and these secant planes an; to be continued over all 
the ground which is to be surveyt'd. If the work is done 
with a theodolite, or with a level having a compass, the angles 
DAB and BAC, contained by the vertical secant planes, can 
be measured ; if it is done with a level, having no needle, let 
any of the distances ae, bf, ai, bl, «Sic. be measured with the 
chain, and there will then be known the three sides of the 
triangles Aae, Abf, Aai, Abl, Slc. 

Let now, the difference of level of the several points marked 
in each of the lines AB, AD, AC, be determined. 

Tn the present example the results of the measurements 
and levelling, are — 

Line AB. 
Distances. Difference of Level. 

A above a 12 feet 



Aa = 40 feet 
ab =50 « 
be =30 " 



a above 6 8" 
b above c 9 " 



cd =4G " c above d 11 *' 



CONTOUR OP GROUND. 



151 



Distances. 

•^e = 28 feet 
cf =45 ** 
fg=55 « 
gh =49 " 



Distances. 
Ai=2 5 feet 
U =55 " 
Im =38 " 
nin =48 " 

Angle CAB = 25% 



Line AC. 

Difleience of Level 

A above ell feet 
e above / 9 " 
/ above ^12 " 
g above /i 14 " 

Line AD. 

Difference of Level. 
A above i 9 feet 
i above Z 13 " 
Z above m 7 " 
m above fi 14 " 
Ande DAB = 30'. 



These data are sufficient, not only to find the intersections 
of horizontal planes with the surface of the hill, but also for 
delineating such curves of section on paper. 

Having drawn on the paper the line AB, lay off the angle 
BAC = 2 5% and the angle BAD = 30°. Then, from a con- 
venient scale of equal parts, lay off the distances Aa, ah, be, 
cd, Ae, ef, fg, gh, Ai, il, Im, and mn. 

Let it be required that the horizontal planes be at a dis- 
tance of eight feet from each other. Since A is the highest 
point of the hill, and the difference of level of the points A 
and a, is 12 feet, the first plane, reckoning downwards, will 
intersect the line traced on the ground from A to B, between 
A and a. Regarding the descent as uniform, which we may 
do for small distances without sensible error, we have this 
proportion ; as the difference of level of the points A and a, 
is to the horizontal distance Aa, so is 8 feet, to the horizontal 
distance from A to where the first horizontal plane will cut 
the line from A to B. This distance being thus found, and 
laid off from A to o, gives o, a point of the curve in which 
the first plane intersects the ground. The points at which it 
cuts the line from A to C, and the line from A to D, are de- 
termined similarly, and three points in the first curve are thus 
found. 

By the aid of the sector, the graphic operations are greatly 
facilitated. Let it be borne in mind, that the descent from A 
to a, is 12 feet, and that it is required, upon the supposition 



152 ELEMENTS OF SURVEYING. 

of the descent being uniform, to find that part of the distance 
corresponding to a descent of 8 feet. Take the distance from 
Ji to a, in the dividers, and open the arms of the sector until 
the dividers will reach from 12 on the line of equal parts, on 
one side, to 12 on the line of equal parts, on the other. Then, 
without changing the angle, extend the dividers from 8 on 
one side, to 8 on the other ; this will give the proportional 
distance to be laid off from Jl to o. Or, if the dividers be 
extended from 4 to 4, the proportional distance may be laid 
off from a to 0. 

If the distances to be taken from the sector fall too near 
the joint, let multiples of them be used ; as for instance, on 
the French sectors, let the arms be extended until the dividers 
reach from 120 on the one, to 120 on the other, then 80 or 
40 will be the proportional numbers. Other multiples may 
be used, though it is generally more convenient to multiply 
by 10. 

The second plane is to pass 8 feet below the first, that is, 
16 feet below A, or 4 feet below a, a being 12 feet below A. 
Take the distance ah in the dividers, and extend the sector, 
so that the dividers will reach from 8 to (the descent from a 
to b being 8 feet) 8, or from 80 to 80; then, the distance from 
4 to 4, or from 40 to 40, being laid off from a to p, gives p, a 
point of the second curve. 

The difference of level between a and h being 8 feet, and 
the difference of level between a and p being 4 feet, the dif- 
ference of level between p and h must also be 4 feet : hence, 
the third plane will pass 4 feet below 6, and q, determined as 
above, is a point of the third curve. 

The difference of level between h and c being 9 feet, and 
consequently between q and c, 5 feet, the fourth plane will 
pass 3 feet below c, and r is a point of the fourth curve. 

The difference of level between c and d being 11 feet, the 
difference of level between r and </ is 8 feet ; so that the fifth 
plane will pass through c?, which is consequently a point of 
the fifth curve. 

The points at which the horizontal planes cut the lines 
drawn from A to C, and from A to D, are determined in a 
manner entirely similar. Having thus made as many diverg- 
ing sections from the point A as may be necessary, and found 
the points in which they are cut by horizontal planes, the 



CONTOUR OF GROUND. 153 

horizontal curves of section can be described through the 
several corresponding points. These curves being represented 
on paper, their curvature shows the form of the surface of the 
hill in the direction of a horizontal line traced around it ; and 
the distances between them, the abruptness or gentleness of 
the declivity. The numbers (8), (16), &c. show the vertical 
distances of the respective planes below the point A. 

Having drawn the horizontal curves, the next thing to be 
done is so to shade the drawing that it may represent accu- 
rately the surface of the ground. This is done by drawing a 
system of small broken lines, as in the figure, perpendicular 
in direction to the horizontal curves already described. In 
all topographical representations of undulating ground, the 
lines of shading are drawn perpendicular to the horizontal 
curves. 

, 185. If it be required to show a profile of the ground, let 
the vertical plane passing through Jl and B be revolved about 
its intersection with a horizontal plane passing through d. 
Erect perpendiculars at r, c, q^ b, p, a, o, and A, to the line 
BA, and make them equal to the respective distances of these 
points above the horizontal plane passing through d, viz. at r, 
8 feet, at c, 11, at q, 16, at b, 20, at p, 24, at a, 28, at o, 32, 
and at A, 40 ; and through the extremities of the perpen- 
diculars so determined, let a curve be traced : this curve will 
be the curve of the hill from d to A. 



186. This method of finding the form of the surface of a 
hill, is perhaps the best, when the hill slopes gradually from 
its summit, and the declivity is sufficiently gentle to measure 
down it. If the surface were that of an undulating plain, 
the following method is preferable. 

Measure a horizontal line, as AB (PL 4, Fig. 7), running 
along one side of the ground to be surveyed. At the ex- 
tremities A and B, erect the perpendiculars AD and BC, and 
produce them until all the land to be surveyed shall be in- 



154 



ELEMENTS OF SURVEYING. 



eluded within the rectangle ABCD. On the line JIB, mea- 
sure the horizontal distances JiE, EF, FG, and GB ; and on 
the line DC, the distances !>//, ///, IL, and LC, respeciivehj 
equal to the distances on JIB: that is, DH—JIE, HI -EF, 
&c. The distances AE, EF, &c. are regulated by the ine- 
qualities of the ground, being less if the changes in the sur- 
face are considerable, and greater if the changes are nearly 
uniform. In the present example, they are 100 feet each, 
which, upon ordinary ground, would render the work tole- 
rably accurate. 

Let stakes be driven at ./?, E, F, G, B, C, L, /, //, and D. 
Measme now the line »^D, and place stakes at convenient 
distances, as a, b, c, and d : place stakes also along the other 
lines EH, FI, GL, and BC, at suitable points, and measure 
the respective distances Ef, fg, &c. It is best to use the tel- 
escope of the theodolite or level, in order to run the lines 
and place the stakes truly. In placing the stakes, it should 
be borne in mind, that the dilTerence of level of either two 
that follow each other, ought not to be very great ; and also, 
that they ought not to be on the same horizontal plane. 

After the stakes are all placed, and the distances measured, 
let the differences of level of all the points so designated be 
found. In the present example, the results of the measure- 
ments are — 



Fl 


Ft 


FL 


Ft 


PL 


Jla =80 


AE=ioo 


EF=ioo 


FG = ioo 


GB--=ioo 


ab =60 


Ef =105 


Fi = 74 


Gm= 96 


Bq = 76 


be =90 


fg = 85 


ik =115 


mn =76 


qs = 85 


cd =55 


gk = 71 


kl = 60 


np = 76 


St =127 


dD=50 


hH= 74 


// = 86 


pL = 87 


tC = 47 


Of the Levelling. 


Line AD. Line EH. Line FI. Line GL. Line BC. 


Fl . Ft 


Ft. . FL . Ft 


A above a 5 


E below A 3 


F below E 2 


G below F 1 


B below G 2 


a "66 


E above / 9 


F above i 3 


G above m 2 


B above q 3 


b « c 7 


f '' g^ 


i " fc 5 


m '' n 1 


9 " S 2 


C below d 2 


g "hi 


/c " Z 2 


n " j9 2 


5 "is 


d above D 4 


h below // 3 


I below / 3 


p below L 4 


t below C 5 



The heights of the points are here compared with each 
other, two and two. Before, however, we can conceive 
clearly their relative heights, we must assume some one point. 



CONTOUR OF GROUND. 



155 



and compare all the others with it. Let the point A be taken. 



Tlie height of 










Ft 


Ft Pt PL 


A above a 5 


A above / 12 


A above fc 1 3 


A above p ll 


A. " 6 11 


A " 


g- 15 


^ " Z 15 


A '' L 1 


^ " C 18 


A « 


/i 16 


.5 « / 12 


A " B 8 


A " d 16 


A " 


//13 


A '' G G 


A " 9 11 


A " D20 


A " 


F 5 


A " m 8 


.^ " 5 13 


A '' E 2 


c^ " 


i 8 


A " n 9 


A « t 16 



And of A above C, 1 1 feet. 

This being done, a mere inspection shows us the highest 
and lowest points, as also the relative heights of the others, 
reckoning upwards or downwards. Let them be now written 
in the order of their heights above the lowest point, which is 
D. The difference of level between A and D being 20 feet, 
if the difference of level of each of the points below A, be 
taken from 20 feet, the remainder will be the height above 
D. Arranging them in their order, we have 



c above 


Ft. 

D 2 


H above D 7 


d " 


D 4 


k 


* D 7 


h " 


D 4 


s 


' Dl 


t " 


D 4 


f 


' 7)8 


g. u 


D 5 


I 


« D% 


I " 


D 5 


b 


" D 9 



p above Z) 9 


B 


above D 


12 


7 " 


D 9 


L 


(C 


D 


13 


C « 


D 9 


G 


u 


D 


14 


n " 


/) 11 


a 


cc 


D 


15 


i " 


D 12 


F 


c< 


D 


15 


m " 


D 12 


E 


a 


D 


17 



A above D, 20 feet. 

Let the surface be now intersected by a system of hori- 
zontal planes at 3 feet from each other, — the first plane being 
3 feet above the point D. The point h being 9 feet above D, 
and the point c, 2 feet, the first plane will intersect the line 
AD between h and c : let the proportional distance be found, 
as in ihe last example, and one point u, of the first cune, 
will be known. The point // being 7 feet above D, the plane 
will cut the line DC between // and J), and finding the 
proportional distance as before, a second point, v, of the first 
curve, is determined. Now, in drawing this curve, it will be 
borne in mind, that the point h is but 4 feet above D, and 
consequently but 1 foot above the first curve, so that the curve 
muet run from u towards h, and then turn around to the 
poini V. The curve is maked (3), which is the number of 
feet that it is above the lowest point, and similarly for the 



156 ELEMENTS OP SURVEYING. 

Other curves of the figure ; their number showmg their dis- 
tance in feet above D. Around the point d, there is a small 
curve, also marked (3). By inspecting the table, it will be 
seen that cZ is 4 feet above D, and that the ground descends 
from d towards D and c : d \s therefore a small knowl, the 
top of which is cut off by the first plane. To show that the 
ground descends from d, even below the first curve (3), a 
plane is passed 1 foot below the first plane, or 2 feet above 
D ; the curve of section is marked (2). 

The second of the system of curves, or the one marked (6), 
must cut the line JID between h and c, the line EH between 
/ and g, the line FI between k and /, and also between I 
and /; it also cuts EH again between h and H, and the line 
DC between fZ" and D. 

The third curve, or the one passing 9 feet above D, passes 
through 6, cuts the line EH between E and /, the line Fl 
between i and k; thence it passes to p, and thence to the 
line DC, crossing it between / and L. There is also another 
curve determined by this plane, since it passes through the 
points C and q, leaving the points t and s below it. This 
curve runs from C to p, and from p to q, as drawn in the 
figure. 

The fourth curve, marked (12), intersects the line AD 
between a and h, EH between E and /, FI at i, GL at m, 
and BC at B. There is also another curve lying around 
the point L : for the plane cuts GL between p and L, the 
line DC between C and L, and again between / and L. 

The fifth curve, marked (15), cuts AD at a, EH between 
E and /, and AB at F. The sixth curve, marked (18), cuts 
AD between A and a, and AB between A and E. The 
proportional distances in all these cases are found as in the 
first example. 

In looking on the little map that has been made, it is 
clearly indicated by the curves and shading, that the ground 
slopes from A to c, thence rises to d, and then slopes to D. 
It also slopes from A along the line AB ; from E in the 
directions / and i, from F in the directions i and m, from G 
in the directions m and J5, and from B in the direction Bqs. 
The ground also slopes from L to p, thence to I and /i, and 
along to curve (2), and the point D : and on the other side 
10 t and s. 



CONTOUR OF GROUND. 157 

187. Thus far, we have said nothmg of a plane of reference, 
which is any horizontal plane to which the levels of all the points 
are referred. In the first example, the plane of reference was 
assumed through the point A (PI. 4, Fig. 6), and tangent to 
the surface of the hill : in the second example, it was taken 
through D, the lowest point of the work. 

188. After having compared all the levels with any one 
point, the highest and the lowest points are at once discovered, 
and the plane of reference may be assumed through either 
of them. As, however, in comparing the heights of objects, 
the mind most readily refers the higher to the lower, it is con- 
sidered preferable to take the plane of reference through the 
lowest point. We say, for example, that the summit of a 
hill is 200 feet above a given plain, and not that the plain 
is 200 feet below the summit of the hill ; so we say that a 
plain is at a given distance above a river, and not that the 
river is below the plain. This habit of the mind of referring 
the higher to the lower objects, suggests the propriety of 
taking the plane of reference through the lowest point, where 
there is no other circumstance to influence its selection. If, 
however, there are fixed and permanent objects, to which, as 
points of comparison, the mind readily refers all others, sucli 
as the court-house or church of a village, the market-house 
of a town, or any public building or monument, it is best to 
assume the plane of reference through some such point ; 
for, it must be kept in mind, that the ends proposed in the 
construction of maps, are, to present an accurate view of the 
ground, its form, its accidents, and the relative position of 
objects upon it. 

189. When the plane of reference is so chosen that the 
points of the work fall on different sides of it, all the refer- 
ences on one side are called positive, and those on the other, 
negative. The curves having a negative reference are dis- 
tinguished by placing the minus sign before the number ; 
thus — ( ). 

190. In topographical surveys, great care should be taken 
to leave some permanent marks, with their levels written on 
them in a durable manner. For example, if there are any 
rocks, let one or more of them be smoothed, and the vertical 
distance from the plane of reference marked thereon : or let 



158 ELEMENTS OF SURVEYING. 

the vertical distance of a point on some prominent building, 
be ascertained and marked permanenily on the building. 
Such points shoukl also be noted on the maj), so lliat a pei^son, 
ahhough unacquainted with the ground, could by means of 
the map, go upon it, and trace out all the points, t( gether 
with their difTerences of level. 

191. The manner of sliading the map, so as to indicate 
\he hills and slopes, consists in drawing the lines of shading 
perpendicular to the horizontal curves, as already explained. 

192. In making topograpliical surve^^s, the great point is, 
to determine the curves which result from the intersection 
of llie surface by iiorizontal planes. 

Besides the methods of diverging and parallel sections, we 
may assume a point on the surface of a hill, place the level 
tliere, and run a line of level round the hill, measuring the 
angles at every turn or cliange of direction : such a line wi'l 
be a horizontal curve. Then, levelling up or down the hill, a 
distance equal to the vertical distance between the horizontal 
curves, let a second curve be traced; and shnilarly for as 
many curves as may be necessary. 

This method, however, is not as good as the methods before 
explained. 

193. Besides representing the contour of the ground, it is 
often necessary to make a map which shall indicate the 
cultivated field, the woodland, the marsh, and the winding 
river. For this, certain characters, or conventional signs, 
have been agreed upon, as the representatives of things, and 
when these are once fixed in the mind, they readily suggest 
the objects for v;hich they stand. Those which are given in 
Plates 5 and G, have been ado[.ted by the Engineer Depart- 
ment, and are used in all plans .'vnd maps made by the United 
States Engineers. 

It is very desirable that a uniform method of delineation 
should be adopted, and none would seem to be of higher au- 
thority than that establisiied by the Topographical Beaureau. 
It is, therefore, recommende(i^ that the convention;d signs 
given ill Plates 5 and C, be carefully studied and closely fol- 
lowed. 



OP SURVEYING HARBOURS. 159 

CHAPTER VII. 

Of Surveying Harbours. 

194 There are two objects to be attained m the survey 
of a harbour. 

1st. To survey the shore along higli or low water mark, 
to trace its windings, to note the points and inlets, and to 
ascertain and fix the places at which rivers and creeks dis- 
charge tlieniselves. And, 

2dly. To discover tlie channels, their direction, depth, and 
width ; the position of shoals, the depth of water upon them, 
the nature of the bottom, and in short, whatever may contri- 
bute to easy and safe navigation. 

To determine the principal jwints and trace the shore. 

195. Having provided a boat and crew, row once or twice 
around the harbour, mark tiie more important and prominent 
points ; at which, let station-slaves with flags upon them be 
erected. 

Then, measure a base line, and form a series of triangles, 
having their angles at the stations already chosen. Let the 
angles of ihese triangles be measured with the tlieodolite, 
and their sides calculated; afler whicli, the high or low water 
mark may be traced along the shore with the compass, as 
hereafter explained. 

Let us suppose that Plate G is a map of a harbour to be sur- 
veyed. 

We see, by inspecting it, that the upper end of the lake at 
t/?, the termination of the harbour at 2>, tlie rocks at C, the 
point at D, the fisheries at iJ, and tlie two bays at F and G, 
are all prominent points. At these points, therefore, let sta- 
tion-flags be placed. Then, measure the distance from A to 
B, for a base line, and let the work be begun at J2. 

Remove the stafTat ,;-7, and place, by means of a plumb-line, 
the axis of the theodolite over the station. Then, having 
levelled the instrument, bring the of the eyeglass vernier to 
coincide with the of the linjl), and tighten the clamp-screw 
of the vernier plate. Loosen the lower clanip-scrcw, and luru 



160 ELEMENTS OP SURVEYING. 

the body of the instrument until the telescope comes nearly on 
the base line AB : then tighten the clamp-screw K, and by 
means of the lower tangent-screw L, and the thumb-screw Z, 
bring the intersection of the spider's lines to coincide with 
the bottom of the staff at B. Then, direct the lower tele- 
scope to the same point, without moving the limb. 

Having thus placed the instrument, examine the opposite 
vernier, and if it stands exactly at 180^, enter the direction 
from A to B^ 00, as in the j5eld notes below. 

But if the reading of the opposite vernier exceeds 180^, 
enter half the excess for the direction. If the reading is less 
than 180^, take half of what it falls short, from 360^, and 
enter the remainder for the direction from A to B. 

The two verniers are used to avoid any error which might 
arise from a defective graduation of the limb, or from an im- 
perfect centring. A false centring, is when the centre of the 
limb or vernier plate is out of the axis of the instrument, and 
w^hen this is the case, it is a fruitful source of error. 

Both verniers should be read at every observation, and a 
mean between the readings taken for the true direction. 

Having thus placed the instrument, loosen the clamp-screw 
of the vernier plate, and direct the telescope to station E. 
Note the degrees, and take a mean between the readings of 
the two verniers for the minutes, and enter the result opposite 
direction AE, as in the field notes. Do the same for the 
station 6r, and then enter in a column to the right, the angle 
formed by the lines which join the stations. The angle will 
either be the difference of the readings, or the difference be- 
tween 360® and the larger reading, plus the smaller reading. 

Station A, 



Direction AB 


. 00 




Direction AE 


. 730 25' 


BAE = 13'^ 2 5' 


\ Direction AG . 


. 138° 35' 


EAG = 65' 10' 



Having sighted to all the stations which can be seen from 
A, remove the instrument and replace the station staff. 

Tal^e the theodolite to B, the otiier extremity of the base 
line. It is now required to place the instrument in such a 
manner that the horizontal limb shall have the same relative 
position with the base line AB, as it had at the station A 



OF SURVEYING HARBOURS. 161 

For this purpose, after having levelled the instrurnetit, add 
180^ to the direction from A to B, and place the of the eye- 
glass vernier at the point so found. Then clamp the vernier 
plate, after which direct both the telescopes to station A. It 
is now plain that the line of the limb drawn through and 
180'' will coincide with the base line JIB, the o being towards 
»4, as before ; hence the theodolite is like placed. 

Having clamped the limb, loosen the clamp-screw of the 
vernier plate, and sight to stations E and C, and enter the 
dhections as below. 

Station B, 



Direction BA . 


. 1800 00' 




Direction BE , 


. 1390 40' 


ABE=iO^ 20' 


Direction BC . 


. 570 12' 


EBC = 82' 28' 



Having sighted to all the stations which can be seen from 
B, replace the station-staff and remove the instrument to 
station C. To the direction BC = 5l^ 12' add 180°, and the 
sum is 237'^ 12'. Having levelled the instrument, place the 
of the eyeglass vernier at 237® 12', and then sight to station 
B. The limb of the theodolite will then have the same 
relative position as at the stations A and B, Then sight to 
E and Z), and enter the directions as below. 

Station C. 



Direction CB . 


. 237° 12' 




Direction CE . 


. 180° 27' 1 


BCE = 5G' 45' 


Direction CD . 


. 150° 27' 1 


ECD = 30^ 00' 



Remove the instrument to E. To the direction C^= 180 27', 
add 180®, and the sum will be 360° 27'. Then place the of 
the vernier at 27', and direct the telescope to C. Or, the 
theodohte may be placed at E by adding 180° to the direction 
AE, as taken from A, or to the direction BE, as taken from 
B, and then directing the telescope to A or B. 

By placing the instrument in a similar manner at every 
station, the line of the limb passing through and 180®, con- 
tinues parallel to the base AB, the being constantlv in the 
direction towards A. The instrument is thus placed at all 
the stations, and the following are the results of the measure- 
ments of the angles. 

^ 11 



162 



ELEMENTS OF SURVEYING. 



Station E. 



Direction EC . 


. . 0° 27' 




Direction EB . 


. 319° 40' 


CEB = iO^ 47' 


Direction EA . 


. 253° 25' 


BEA = 66' 15 


Direction EG . 


. 199" 15' 


J1EG = 5A' 10' 


Direction EF . 


. 164° 10' 


GEF=35^ 05' 


Direction ED . 


. 94° 10' 


FEI)=io^ 00' 



Station D, 



Direction DC . 


. 330" 27' 




Direction DE . 


. 274° 10' 


CDE = 5Q^ 17' 


Direction DF . 


. 2250 50' 


EDF=48^ 20' 



Station F, 



Direction FD . 


. . 45° 50' 




Direction FE . 


. 344° 10' 


DFE=6i' 40' 


Direction FG . 


. 2470 10' 


EFG=9i' 00' 



Station G. 



Direction GF . . 


. 67° 10' 




Direction GE . . 


. 19° 15' 


FGE = 41' 55' 


Direction GJl . . 


318° 35' 


EGA = 6i^ 40' 



The measurements which have been made, enable us to 
calculate the lengths of the lines joining the several stations. 
For, commencing vi^ith the triangle AEB, we know all the 
angles and the base line AB ; we can, therefore, find the 
sides EB, EA. We shall then know one side and all the 
angles of the triangle CEB, and by pursuing the calculation, 
the sides of all the triangles can be readily found. 

Smce the third angle of a triangle can always be found 
when two of the angles are known, it may seem unnecessary 
lo measure all the angles. But when the three angles are 
measured and their sum found equal to 180°, the work is 
proved to be right, and this verification should never be 
omitted. 

[t is not probable that the sum of the three measured an- 
gles will be exactly equal to 180°. But they ought not to 
difTer much from it. If each of them be measured several 



OF SURVEYING HARBOURS. t 

times, and a mean of the measurements be taken, the errors 
of observation and of the instrument will be much dimhiished. 

196 The method of determining points by a series of con- 
secutive triangles, is called the method by triangulation. It 
may be extended to any number of triangles, and if the three 
angles of every triangle be measured, and the work carefully 
verified at each step, there is little danger of error. We have 
applied the method only in the survey of a harbour, but it 
may be used with equal advantage in all surveys in which 
long lines are to be determined, and is, indeed, the only one 
that can be relied on, where great accuracy is required. 

Of the Manner of using the Compass. 

197. The compass is often used in connection with the 
theodolite, and although a rude instrument, may yet be relied 
on for the shorter lines and smaller parts of a survey. The 
following is the manner of keeping the field notes. 

Divide a paper into two equal parts, by two parallel lines 
near to each other, and consider each part as a separate leal 
or page. Each leaf is divided into three spaces, and the 
middle one is generally smaller than either of the others, 
which are equal. 

The notes begin at the bottom of the first page, and run 
up the page to the top. They then commence again at the 
bottom of the next page, and run up to the top ; thence to 
the bottom of the third page, and thus, for as many pages as 
the work may require. 

When the compass is used in the way we are about to 
explain, the distances to objects which lie on the rioht or left 
of the courses, are determined by means of offsets. 

The beginning of every course is designated in the middle 
column b}^ o, and the bearing is entered directly above. The 
other figures of the middle column, express the distances from 
the beginning of each course to the oflfsets, and those in the 
side columns indicate the lengths of the oflfsets, or the dis- 
tances to objects on the right or left of fhe compass lines. 

The stations, at which the compass is placed, are designated 
by in the middle column, and the bearing of each course is 
entered directlv above. 



164 



ELEMENTS OF SURVEYING. 



To explain more definitel}^ the manner of using the com 
pass on the field, let us suppose that we have determined, 
with the theodolite, the prominent parts of the harbour. Place 
the compass at .^ (Plate 6), and take the bearing of the line 
^E, which is S 12° W. 




Enter this bearing at A. Then measure along the line 
AE any distance, as Aa equal to 130 yards, and make an 
ofi'set to the lake, which we measure and find to be 50 yards. 
Enter the 130 in the middle column, and as the lake lies on 
the right (in going from A to E), we insert the 50 in the 
right hand column. 

We then measure along the line AE to b, 350 yards from 
A. Here we make a second oflTset to the lake, and find it to 
be equal to 100 yards. Having entered the distances in the 
notes, we measure to q, the point where the line AE crosses 
the creek, and w^e enter the distance from A, Alb yards. 

At rf, we lay off an offset on the left, to the pond, 70 yards : 
at e, an offset to the mouth of the creek, 150 yards : and at 
E, where the course terminates, an offset to the lake, of 160 
yards. The entire distance from .^ to E is 800 yards. 

At E, w^e take the bearing to H, which is N 50® E. Hav» 
ing measured along this line to/, 315 yards, we make an 
offset to the pond, on the left, of 50 yards, and to the shore, 
on the right, of 90 yards. Having entered these distances, 



OF SURVEYING HARBOURS. 165 

we recommence the notes at 315 below, which we suppose U) 
be at the bottom of the second page. Having reached H^ 
the extremity of the course, we enter the entire distance from 
jG, 680 yards. We next take the bearing to /, S 52*^ E. Wc 
then measure the distances to m, n, p, and /, and enter them, 
together with the offsets, as in the notes. 

198. It is also well to make, in the columns on the right 
and left, such sketches of the ground, fields, houses, creeks 
and rivers, as will afford the means of making an accurate 
delineation on paper. 

199. In making the plan of the harbour, it might be found 
convenient to use the plain-table in connexion with the theod- 
olite and compass. For example, we might place the plain- 
table at G, and having fixed stations at the principal points 
of the sliore, between G and F, we would sight to each of 
them : then remove the table to F, and do the same for that 
station : we should thus determine the points between F and 
G, with reference to the line GF, 

Of Plotting, 

200. The lines of the triangles determined with the theodo- 
lite, can be plotted in the manner already explained. It would 
be better, however, to use the instrument which we are about 
to describe, and which is called 

THE CIRCULAR PROTRACTOR. 

201. This instrument consists of a brass circular limb (PI, 
2, Fig. 4), of about six inches in diameter, with a moveable 
index AB, having a vernier at one extremity A, and a milled 
screw at the other extremity B, with a concealed cog-wheel 
that works with the cogs of the limb, and thus moves the 
index JIB about the centre of the protractor. At the centre 
of the protractor is a small circular glass plate, on which two 
lines are cut ; the point of their intersection, is the exact 
centre of the instrument. The limb is generally divided to 
half degrees ; the degrees are numbered from to 360. 

At the point, and at the opposite extremity of the diameter 
passing through that point, are small lines on the inner edge 
of the limb; the two extremities of the diameter, perpendicular 
to this latter, are also designated in the same way. 



166 ELEMENTS OF SURVEYING. 

Two angular pieces of brass, each having a small and 
sharp steel pin at its extremity, are fastened to the index, 
and revolve freely around the lines ab and cd. The small 
screws, a, b, c, and d, move them in the directions of the lines 
abf cd, for the purpose of bringing the steel pins exactly into 
the line which passes through the of the index and the 
centre of the protractor. 

To adjust them to their places, place the centre of the pro- 
tractor over a marked point, and the of the index to the 
of the limb. Then mark the place of the index by the pins : 
after which, turn the index 180°, and see if the pins will mark 
the same points as before. If they do, the index is adjusted ; 
if they do not, correct the error with the screws a, b, c, and d. 

To lay off an angle with the Protractor. 

202. Let its centre be placed over the angular point, and 
the diameter passing through and 180°, on the given line. 
Turn the screw that works the index, until the of the ver- 
nier coincides with the division corresponding to the given 
angle ; then let the angular brass pieces be turned down ; 
the points dotted by the steel pins will show the direction of 
the required line. 

If this line does not pass through the angular point, the 
pins are out of place, and must be adjusted. 

First Method of Plotting. 

203. Suppose it were required to make the plan of the 
harbour on a scale of 450 yards to an inch. 

Divide the length of the base line ^B, which we will sup- 
pose equal to 1140 yards, by 450, and the quotient 2.53 will 
express the length which is to represent the base line on the 
paper (Art. 33). 

Draw an indefinite line ^B, to represent the base, and 
having chosen any point, as .^, for the first station, lay off 
2.53 inches to B. The other extremity of the base line will 
thus be determined. 

Then, place the circular protractor at A, and lay off the 
angle BAE, and then the angle EAG. Next, place the 
protractor at B, and lay off the angles ABE and EBC. 
The intersection of the lines AE and BE will determine 



OF SURVEYING HARBOURS. 167 

the station E. Let the protractor be then placed at this 
point, and all the angles of station E, laid down. 

The point G, where EG intersects AG, and the point C, 
where EC intersects BC, will then be found. 

By placing the protractor at C and G, we can determine 
the points D and F, when the place, on the paper, of all the 
stations will be known. 

To vuiite the work done with the compass, spread the com- 
pass-notes before you, and draw through A a line to represent 
the meridian. This line makes an angle of 12^ with the 
course JlE. 

Then, lay off from the scale the distances Aa, Ab, Aq, Ac, 
Ad, Ae, and at the several points erect perpendiculars to AE. 
Lay off on these perpendiculars the lengths of the offsets, and 
the curve traced through the points so determined, will be 
the margin of the lake. 

At E, draw a parallel to the meridian through A, and lay 
down the course EH, which makes an angle of 50° with the 
meridian. Then, lay down the several distances to the off- 
sets, and draw the offsets and lay off their lengths. Do the 
same for the course HI, and all the compass-work will be 
plotted. 

Had there been work done with the plain-table, it could 
easily be united to that done with the theodolite. 

Second Method of Plotting. 

204. Place the centre of the protractor near the centre of 
the paper, and draw a line through the points and 180^. 
This line will have the same position with the circular pro- 
tractor that the base line AB had with the limb of the 
theodolite. 

Lay off then from the point an arc equal to the direction 
from A to E, also an arc equal to the direction AG, and 
through the centre point, and the points so determined, draw 
lines. Lay off in succession, in a similar manner, the direc- 
tions taken at all the stations ; and through the centre point, 
and the points so determined, draw lines, and designate each 
by the letters of the direction to which it corresponds. 

Now, since all the lines drawn on the paper have the same 
position with the circular protractor, as the corresponding 



168 ELEMENTS OF SURVEYING. 

lines on the ground have with the limb of the tlieodolite, it 
follows that each direction will be parallel to its corresponding 
line upon the ground. 

Hence, any line may be drawn parallel to that passing 
through and 180°, to represent the base line AB. Having 
drawn such a line, and marked a point for the station Jl, lay 
off the length of the base, and the extremity will be the 
station B. 

Through A and B^ so determined, draw parallels respec- 
tively to the lines corresponding to the directions JIE and 
BE, and the point of intersection will determine station E. 
Through B and E draw parallels to the lines which corre- 
spond to the directions BC, CE, and their point of intersection 
will determine station C. Through C and E draw lines 
parallel to the lines corresponding to the directions CE and 
ED, and the point of intersection will determine D. In a 
similar manner we may determine the stations F and G. 

Of surveying a harbour for the purpose of determining the depth 
of loater, <^c. 

205. When a harbour is surveyed for the second object, viz., 
for the purpose of ascertaining the channels, their depth and 
width, the positions of shoals, and the depth of water thereon, 
other means must be used, and other examinations made in 
addition to those already referred to. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel, and using any of the lines already 
determined as a base, let the angles subtended by lines drawn 
from its extremities, to the buoys respectively, be measured 
with the theodolite. Then, there will be known in each 
triangle the base and angles at the base, from which the dis- 
tances to the buoys are easily found ; and hence, their posi- 
tions become known. 

Having made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of the 
harbour are established, at which the precise depth of the water 
is known ; and by increasing the number of the buoys, the 
depth of the water can be found at as many points as may be 
deemed necessary. 

206. If a person with a theodolite, or with any other in- 
strument adapted to the measurement of horizontal angles, be 



OF SURVEYING HARBOURS. 169 

stationed at each extremity of the base Hne, it will not be 
necessary to establish buoys. A boat, provided with an an- 
chor, a sounding line, and a signal flag, has only to throw iis 
anclior, hoist its signal flag, and make the sounding, while 
the persons at the extremities of the base line measure the 
angles ; — from these data, the precise place of the boat can 
be determined. 

207. There is also another method of determining the 
places at which the soundings are made, that admits of great 
despatch, and which, if the observations be made with care, 
affords results sufficiently accurate. 

Having established, trigonometrically, three points which 
can be seen from all parts of the harbour, and having provided 
a sextant, let the sounding be made at any place in the har- 
bour, and at the same time the three angles subtended by lines 
drawn to the three fixed points, measured with the sextant. 

The problem, to find from these data the place of the boat 
at the time of the sounding, is the same as example 6, page 74. 

It is only necessary to measure two of the angles, but it is 
safest to measure the third also, as it affords a verification 
of the work. 

The great rapidity with which angles can be measured with 
the sextant, by one skilled in its use, renders this a most ex- 
peditions method of sounding and surveying a harbour. 

The sextant is not described, nor are its uses explained in 
these Elements, because its construction combines many phi- 
losophical principles, with which the surveyor cannot be sup- 
posed conversant. 

208. There is yet another method of finding the soundings, 
which, although not as accurate as those already explained, 
will, nevertheless, afford results approximating nearly to the 
truth. It is this : — Let a boat be rowed uniform.ly across the 
harbour, from one extremity to the other of any of the lines 
determined trigonometrically. Let soundings be made con- 
tinually, and let the precise time of making each be care- 
fully noted. Then, knowing the length of the entire line, 
the tPme spent in passing over it, as also the time of making 
each of the soundings, we can easily find the points of the 
line at which the several soundings were made ; and hence, 
the depth of water at those points becomes known. Sound- 



170 ELEMENTS OF SURVEYING. 

ings may thus be made along any number of known lines, 
and a comparison of the depths found on different lines, at or 
near their points of intersection, will show with what degree 
of accuracy the work has been done. 

209. If the soundings are made in tide-waters, the time of 
high tide must be carefully noted, as also the precise time 
of making the sounding, so that the exact depth at high or 
low water may be known. It is considered preferable to re- 
duce the soundings to high-water mark, and the number of 
feet which the tide rises and falls should be noted on the map. 

210. Having plotted the work done with the theodolite, as 
also the outline of the harbour traced with the compass, it re- 
mains to delineate the bottom of the harbour ; and this is done 
by means of horizontal curves (Chap. VI), which have already 
been used to represent broken or undulating ground. 

Let the plane of reference be taken through high-water 
mark, or to coincide with the surface of the water at high 
tide. The accuracy with which the bottom of the harbour is 
to be delineated, will guide us in fixing the distance between 
the horizontal planes of section. 

The first horizontal plane should be passed at a distance 
below the shallowest point that has been sounded, equal to 
the number of feet fixed upon for the distance between the 
planes of section ; and the curve, in which it intersects the 
bottom of the harbour determined as in Chapter VI. And 
similarly, for the other horizontal planes of section. 

Having thus delineated the bottom of the harbour, and noted 
on the map the distance of each intersecting plane below the 
plane of reference, let such lines be drawn as will indicate the 
channels, shoals, sunken rocks, and direction of the current. 

In the example given in plate 6, soundings have been made 
in three directions from the sand-bar in the harbour, and also 
from the rocky shore across to the light-house. 



PRINCIPLES OF NAVIGATION. 171 

CHAPTER VIII. 

Of Navigation. 

1. We have given, in the preceeding chapters of this work, 
various apphcations of Trigonometry. We propose, in the fol- 
lowing chapter to explain the best methods of determining the 
place of a ship at sea. This application constitutes the science 
of Navigation. 

There are two methods of determining the place of a ship at 
sea. 

1st. When a ship departs on her voyage, if we note her 
courses and the distance sailed, we may, at any time, by means 
of Plane Trigonometry, determine her place very nearly. 

2nd. By means of observations on the heavenly bodies and 
the aid of Spherical Trigonometry, we may determine with great 
accuracy, the exact place of the ship. This method is called 
Nautical Astronomy. 

The first part of Navigation, viz. the cases which can be 
solved without the aid of observations on the heavenly bodies, 
will be alone treated of in this chapter. 

2. The earth is nearly spherical. For the purposes of Navi- 
gation it may be considered as perfectly so. It revolves round 
one of its diameters, called the aocis, in about twenty-four hours. 

3. The great circle, whose poles are the extremities of the 
axis, is called the equator'. The poles of the equator are called 
the poles of the earth — the one is called the north pole, and the 
other the south pole. 

4. Every great circle which passes through the poles cuts the 
equator at right angles, and is called a ineindian circle. Every 
place on the surface of the earth has its own meridian ; but for 
the purposes of Geography and Navigation, all these meridians 
are reckoned from a particular meridian, which is called \hQji7'st 
meridian. The English have fixed on the meridian of Green- 
wich Observatory for the first meridian. 

5. The longitude of any place is the arc of the equator inter- 
cepted between the meridian of that place and the first meridian, 
and is east or west, according as the place hes east or west of 
the first meridian. 

6. The difference of longitude of two places is the arc of the 
equator included between their meridians ; this arc is equal to 
the difference of longitudes when they are of the same name, 
and to their sum, when they are of different names. 

7. The latitude of a place is its distance from the equator 



172 



ELEMENTS OF SURVEYING. 



measured on the meridian of the place, and is north or south ac- 
cording as the place lies north or south of the equator. 

8. 'I'he small circles drawn parallel to the equator, are called 
parallels of latitude. The arc of any meridian intercepted be- 
tween the parallels passing through any two places, measures 
the difference of latitude of those places; this difference is found 
by subtracting their latitudes wdien they are of the same name, 
and by adding them when they are of different names. 

9. The sensible horizon of any place is an imaginary plane, 
supposed to touch the earth at that place, and to be extended to 
the heavens. A plane passing through the centre of the earth, 
and parallel to the sensible horizon, is called the rational hori- 
zon. The north and south line, is the intersection of the plane 
of the meridian circle with the sensible horizon, and the line 
which is drawn perpendicular to this, is called the east and west 
line. 

10. The course of a ship, at any point, is the angle which her 
track makes with the meridian. So long as the course is un- 
changed, the ship w^ould sail in a straight line, provided the 
meridians were truly parallel ; but as the meridians bend con- 
stantly toward the pole, the direction of her path is continually 
changing, and she moves in a curve called the i^humh line. The 
course of a ship is indicated by the mariner's compass. 

11. The marine7'^s 
compass consists of a 
circular card, whose 
circumference is di- 
vided into thirty-two 
equal parts called 
pom^5; each point be- 
ing subdivided into 
four equal parts call- 
ed quarter points. 

To the under side 
of this card a slender 
bar of magnetized 
steel, called a needle, 
is permanently at- 
tached. The direc- 
tion of the needle 
corresponds to the 
diameter NS. The 
diameter EW, at right angles to NS, is intended to indicate the 
east and west points. The points of the compass are thus read: 
beginning at the north pohit, and going east, we say, north and 




PHINCIPLES OF NAVIGATION, 173 

by eastj north north east, north east and by north, north east; 
and so on, round the compass, as indicated by the letters. 

The card being permitted to turn freely on the pin, on which 
it is poised as a centre, the line NS will always indicate the 
true magnetic meridian, but this, as we have seen it Art. 153, 
page 127, is not the true meridian, and hence, the variation must 
always be allowed for. 

On the interior of the compass box, in which the card swings, 
are two marks, a and b, which lie in a line passing through the 
centre of the card, and the compass box is so placed that this 
line shall be parallel to the keel of the ship. Consequently, if a 
be placed towards the bow of the vessel, the point which it 
marks on the card will show the compass course, for the line 
NS is always north and south, and EW east and west. The 
course is generally read to quarter points, and as a quadrant con- 
tains eight points, each point will be equal to 60° --8= 11° 15'; 
and a quarter point ==11° 15' ^4 = 2° 48' 45". The table oi 
Rhumbs, after the Traverse Table, shows the degrees of each 
course to quarter points. 

1 2. A ship's rate of sailing is determined by means of an in- 
struments, called the log, and an attached line called the log line. 
The log is a piece of wood in the form of a sector of a circle, 
the rim of which is loaded with lead, so that when it is heaved 
into the sea it assumes a vertical position. The log line is so 
attached as to draw the log square against the water, that it may 
not be drawn along after the ship as the line unwinds from the 
reel, by the ship's forward motion. 

The time in which the log line unwinds from the reel, is 
noted by a sand-glass, through which the sand passes in half a 
minute; that is, in the one hundred and twentieth part of an 
hour. 

For convenience, the log line is divided into equal parts, 
marked by knots, and each part is equal to the one hundred and 
twentieth part of a nautical or geographical mile.* 

Now, since half a minute is the one hundred and twentieth 
part of an hour, and each knot measures the one hundred and 
twcnticlli part of a mile, it follows that the number of knots 
reeled off while the half minute glass runs out, will indicate how 
fast the ship sails per hour. 



* A geogra):)hical mile is one minute, or one-sixtieth of a degree, measured on the 
equator. Taking the diameter at 7916 English miles, the geographical mile will 
be about C079 feet ; that is, about oi.e-sixth greater than the English mile, which is 
6280 feet. 



174 



ELEMENTS OF SURVEYING. 



Of Plane Sailing* 




13. Let the diagram 
EPQ represent a por- 
tion of the earth's sur- 
face, P the pole, and 
EQ the equator. Let 
AB be any rhumb hne, 
or track described by a 
ship in saiUng from A 
to B, 

Conceive the path of 
the ship to be divided 
into very small parts, and through the points of division draw 
meridians, and also the parallels of latitude b'b, c'c, d'd, e'e, and 
B'B: a series of triangles will thus be formed, but so small that 
each may be considered as a plane triangle. 

In these triangles, the sum of the bases 

Ab' + be + cd! 4- de' + e/= AB\ 

which is equal to the diiference of latitude between the points 
A and B. Also, 

b'b-{-cc-\-d'd-\-eeA-fB' = BB\ 
which is equal to the distance that the ship has departed from 
the meridian AB'P, and is called the departure in sailing from 
A to B. 

Therefore, the distance sailed, the 
difference of latitude made, and the 
departure, are correctly represented by 
the hypothenuse and sides of a right 
angled triangle, of which the angle op- 
posite the departure is the course. 

When any two of the four things 
above named are given, the other two 
can be determined. This method of 
determining the place of a ship reduces 
all the elements to the parts of a plane 
triangle, and hence is called plane 
sailing. 




EXAMPLES. 



LA ship from latitude 47° 30' N. has sailed S. W. by S. 98 
miles. What latitude is she in, and what departure has she 
made? 



PRINCIPLES OF NAVIGATION. 



.75 



Let C be the place sailed from, CB the 
meridian, and BCA the course, which we 
find from the table of rhumbs to be equal to 
33° 45'; then AC will be the distance 
sailed, equal to 98 miles. Also, AB will 
be the departure, and CB the difference of 
latitude. 

Then by the formulas for the solution of 
right angled triangles. 




As radius 
AC 98 
: COS. C 33° 45' 
CB 81.48 

Latitude left 



10.000000 
1.991226 
9.919846 



1.911072 



As radius 
CA 98 

; sin. C 33° 45' 
AB 54.45 



10.000000 
1.991226 
9.744739 



1.735965 



47° 30' N. 
Dif. Iat.=:z81.48 miles==81.48 minutes^ 1° 22' S. 

In latitude 46° 08'. 

Departure 54.45 miles. 

2. A ship sails 24 hours on a direct course, from latitude 
38° 32' N. till she arrives at latitude 36° 56' N. The course is 
between S. and E. and the rate 5| miles an hour. Required 
the course, distance, and departure. 

Lat. left 38° 32' N. 24 x5|=r 132 miles = distance. 

In lat. 36° 56' 

Diff. 1° 36'-96 miles. 



As dist. 
: radius 
: : diff. lat. 



132 



96 



2.120574 

10.000000 

1.982271 



cos. course 43° 20' 9.801697 



As radius 10.000000 

dist. 132 2.120574 

: sin. course 43° 20' 9.836477 
dep. 



90.58 1.957051 



Hence, the course is S. 43° 20' E., and the departure 90.58 
miles east. 

3. A ship sails from latitude 3° 52' S. to latitude 4° 30' N., 
the course being N . W. by W. |-W : required the distance and 
departure. Arts. Dist. 1065 miles ; dep. 938.9 miles W. 

4. Two points are under the same meridian, one in latitude 
52° 30' N., the other in latitude 47° 10' N. A ship from the 
southern place sails due east, at the rate of 9 miles an hour, and 
two days after meets a sloop that had sailed from the other : re- 
quired the sloops direct course, and distance run. 

Arts. Course S. 53° 28' E.; dist. 537.6 miles. 

5. If a ship from latitude 48° 27' S., sail S. W. by W. 7 
miles an hour, in what time will she reach the parallel of 50° 
south? Ans. 23.914 hours. 



176 



ELEMENTS OF SURVEYING. 



Of Traverse Sailing, 

14. When a ship, in going. from one place to another, sails on 
different courses, it is called Traverse Sailing. The determi- 
nation of the distance and course, from the place of departure to 
the place of termination, is called compounding or working the 
traverse. This is done by the aid of the " Traverse Table," 
which has already been explained, and the method is in all 
respects similar to that adopted in the Prob. of Art. 147, p. 115. 



EXAMPLES. 



1. A ship from Cape 
Clear, in lat. 51° 25' N., 
sails, 1st, S. S. E. \ E. 16 
miles; 2nd, E. S. E. 23 
miles ; 3rd, S. W. by W. \ 
W. 36 miles; 4th, W. f N. 
12 miles ; 5th, S. E-. by E. 
A E. 41 miles: required 
the distance run, the direct 
course, and the latitude. 

We first form the table 
below, in which w^e enter 
the courses, from the table 
of rhumbs, omitting the sec- 
onds, and then enter the lat- 
itudes and departures, taken 
from the traverse table, to 
the nearest quarter degree. 
Thus, in taking the latitude 
and departure for 25° 18' 
we take for 25i°. The dif- 
ference of latitudes gives the 
line A G, and the difference 
of departures the line GF. 








Traverse 


Table. 








Courses. [Dist's. 1 


Diff. of Latitude. 


Departure. 


No.l 


Angle. 




N. 


S. 


E. 


[ W. 


2 
3 
4 
5 


S. S. E. i E. . . 

E. S. E 

S. W. by W. i W. 

w. 1 N. . . : . . 

S. E. by E. 1 E. 


25° 18' 
67° 30' 
61° 52' 
8P33 
5<J° 3' 


16 
23 
36 
12 
41 


1.77 


14.47 

8.80 

17.04 

21.12 


6.83 
21.25 

35.14 


31.71 
11.87 




1.77 


61.43 
1.77 


63.22 
43.58 


43.58 










Diff. 


59.66 


19.64 





PRINCIPLES OF NAVIGATION. 177 

Latitude left 51° 25' N. 

Difference of latitude 59.66 miles = 1° 00' S. 



In latitude 50° 25' N. 

Then, by formulas for the solution of right angled triangles, 



we 



have 



As A G, diff. lat. 59.66 1 .775683 
: radius, 10.000000 

: : departure 19.64 1.293141 



tangt. course 18° 13 9.517458 



As sin. course 18° 13' 9.495005 
: departure 19.64 1.293141 

: : radius 10.000000 

: distance 62.83 T.798136 



Therefore the direct course is S. 18° 13' E., and the distance 
62.83 miles. 

Of Plotting, 

15. There is yet another method of finding the direct course 
and distance, much practiced by seamen, although it does not 
afford a high degree of accuracy. It is a method by plotting, 
which requires the use of a mariner's scale and a pair of dividers 

One of the scales marked on the mariner's scale, is a scale of 
chords, commonly called a scale of rhumbs, being divided to every 
quarter point of the compass ; and there is also a second scale 
of chords divided to degrees. Both of these scales are con 
structed in reference to the same common radius, so that the 
chords on the scale of rhumbs correspond to those on the scale of 
marked chords. The manner of using the scales will appear in 
plotting the last example. 

To construct this traverse, describe a circle with a radius 
equal to the chord of 60° and draw the meridian NS. Then 
take from the line of rhumbs the chord of the first course 2^ 
points, and apply it from »S* to 1, to the right of A^^S*. since the 
course is southeasterly, and draw >S'l ; take, in like manner, the 
chord of the second course, 6 points, from *S to 2, and lay it off 
also to the right of the meridian line. Apply the chord of the 
third course, 5| points, from 8 to 3, to the left of the meridian; 
the fourth course, 7} points from N to 4, to the left of NS, this 
course being northwesterly; and, lastly, apply the chord of the 
fifth course, 5| points, from S to 5, to the right of NS, and join 
all the lines as in the figure. 

In the direction .41, lay off the distance ^17/— 16 miles from 
a scale of equal parts, and through the extremity H, draw HC 
parallel to A2, and lay off HC — 2S miles. Draw CD parallel 
to .43, and lay off CD = 36 miles; then draw DE parallel to .44,- 
and lay off 12 miles; and lastly draw EF parallel to A5, and 
lay off 41 miles, and F will be the place of the ship. Hence, 
we conclude that AF will be the distance made good, and GAF 
will be the course. -.q 



ITS ELEMENTS OF SURVEYING. 

Applying, then, tlie distance AF to the scale of equal parts, 
we ftnd it equal to 62| miles ; and applying the chord Sa to the 
scale of chords we find the course GAF=l'^l°. 

2. A ship sails from a place in latitude 24° 32^ N., and runs 
the following courses and distances, viz. 1st, S. W. by W. dist. 
45 miles ; 2nd, E. S. E. dist. 50 miles; 3rd, S. W. dist. 30 miles , 
4th, S. E. by E. dist. 60 miles; 5th, S. W. by S. j W. dist. 
63 miles : required her latitude, and the direct course and dis- 
tance from the place left to the place arrived at, and the con- 
struction of the traverse. 

. 5 Lat. 22° 3' N., course S. 
^^^' ( Dist. 149.2 miles. 

3. A ship from lat. 28° 32^ N. has run the following courses, 
viz. 1st, N. W. by N. 20 miles; 2nd, S. W. 40 miles; 3rd, N. 
E. by E. 60 miles; 4th, S. E. 55 miles; 5th, W. by S. 41 
miles ; 6th, E. N. E. 66 miles : required her latitude, the dis- 
tance made good, and the direct course, also the construction of 
the traverse. Ans. Dist. 70.2 miles, course E. 

4. A ship from lat. 41° 12^ N. sails S. W. by W. 21 miles; 
S. W. i S. 31 miles; W. S. W. i S. 16 miles; S. | E. 18 
miles; S. W. i W. 14 miles; then W. | N. 30 miles: required 
the latitude, the direct course, and the distance. 

Lat. 40° 05', course S. 52* 49' W. 



^^^- '^ Dist. 111.7 miles. 

5. A ship runs the following courses, viz. 

1st, S. E. 40 miles ; 2d, N. E. 28 miles ; 3d, S. W. by W. 
52 miles ; 4th, N. W. by W. 30 miles ; 5th, S. S. E. 36 miles; 
6th, S. E. by E. 58 miles : required the direct course, and dis- 
tance made good. 

J Direct course S. 25° 59^ E., or S. S. E. k E., nearly. 
'^^^' i Distance 95.87 miles. 

6. A ship sails, 1st, N. W. by W. i W. 40 miles; 2nd, N. 
W. by ^ N., 41 miles; 3rd, N. by E. 16.1 miles; and 4th, 
N. E. i E. 32.5 miles : required the distance made, and the 
direct course. 

Ans. Course 21° 54' West of North. Dist. 94.6 miles. 

These examples will, perhaps, suffice to illustrate the princ» 
pies of plane sailing. 

The longitude, made on any course, cannot be determined by 
these methods, for this being the arc of the equator intercepted 
between two meridians, cannot be found under the supposition 
that the meridians are parallel. 

The most simple case of finding the difiference of longitude is 
when the ship sails due east or due west : this is called Parallel 
Sailing. 



PRINCIPLES OF NAVIGATION. 



179 




Parallel Sailinsc. 

16. The entire theory of parallel sailing is comprehended in 
the following proposition, viz. 

The cosine of the latitude of the parallel, is to the distance 
rurif as radius to the difference of longitude. 

Let JQ/f represent the equa- 
tor, and FDN any parallel of 
latitude : then, CI will be the 
radius of the equator, and EF 
the radius of the parallel. 

Suppose FD to be the dis- 
tance sailed, then the difference 
of longitude will be measured 
by /Q, the arc intercepted on 
the equator. Then, since sim- 
ilar arcs are to each other as 
their radii (Bk. V. Prop. xi. 
Cor.), we have, 

EF : CI :: dist. FD : diff. long. IQ. 

But EF is the sine of PF, or cosine of FI, the latitude, and 
CI is the radius of the sphere : hence, 

COS. lat. : R : : distance . diff. longitude. 

Corollary. If we denote by D the distance between any two 
meridians, measured on the parallel whose latitude is L ; and 
by D^ the distance between the same meridians measured on the 
parallel whose latitude is U, the arcs will be similar, and W€ 
shall have (Bk. V. Prop. xi. Cor.), 

COS. L : D : : cos. L' : D\ 
that is, COS. L : cos. L' : : D : D'. 

Hence, when the longitude made on different parallels is the 
same, the distances sailed are proportional to the cosines of the 
parallels of latitude. 

By referring to Th. V. page 43, we see that in any right an- 
gled triangle 

R : COS. angle at base : : hyp. : base, 
or cos E : R :: EG : EC; 

and by comparing this with the proportion, 

cos. lat. : R : : dist. ■ diff. long. 

We see, that if one leg of a right angled tri- 
angle represent the distance run on any paral- 
lel, and the adjacent acute angle be made equal 




E 



180 ELEMENTS OF SURVEYING. 

to the degrees of latitude of that parallel, then the hypothenuse 
will represent the difference of longitude. It follows therefore, 
that any problem in parallel sailing, may be solved as a simple 
case of plane sailing. For, if we regard the latitude as the 
course, the distance run as the base, the difference of longitude 
will be the hypothenuse of the corresponding right angled 
triangle. 

EXAMPLES. 

1. A ship from latitude 53° 56^ N., longitude 10° 18^ E., has 
sailed due west, 236 miles : required her present longitude. 

By the rule 

As COS. lat. 53° 56' - - • - 9.769913 

: radius 10.000000 

: : distance 236 ... - 2.372912 

: diff. long. 400.8 - - - 2.602999 

Long, left - - 10° 18' E. 

Diff. long. =— degrees = 6° 40' W. 

Long, in - - 3° 38' E. 

2. If a ship sails E. 126 miles, from the North Cape, in lat. 
71° 10' N., and then due N., till she reaches lat. 73° 26' N.; 
how far must she sail W. to reach the meridian of the North 
Cape? 

Here the ship sails on two parallels of latitude, first on the 
parallel of ,71^ 10', and then on the parallel of 73° 26', and 
makes the same difference of longitude on each parallel. 
Hence, by the corollary. 

As cos. lat. 71° 10' arith comp. 0.491044 
: distance 126 - - 2.100371 

: : cos. lat. 73 26 - - 9.45504 4 

: distance 111.3 - - 2.046459 

3. A ship in latitude 32° N. sails due E. till her difference of 
longitude is 384 miles : required the distance run. 

Ans. 325.6 miles. 

4. If two ships in latitude 44° 30' N., distant from each other 
216 miles, should both sail directly S. till their distance is 256 
miles, what latitude would they arrive at ? 

Ans. 320 irN. 

5. Two ships in the parallel of 47° 54' N., have 9° 35' dif- 
ference of longitude, and they both sail directly S., a distance of 
836 miles : required their distance from each other at the parallel 
left, and at that reached. j^^s. 385.5 miles, and 479.9 miles. 



PRINCIPLES OF NAVIGATION. 181 

Middle Latitude Sailing. 

1 7. Having seen how the longitude which a ship makes when 
sailing on a parallel of latitude may be determined, we come 
now to examine the more general problem, viz. to find the lon- 
gitude which a ship makes when sailing upon any oblique rhumb. 

There are two methods of solving this problem, the one by 
what is called middle latitude sailing, and the other by Merca- 
tor^s sailing. The first of these methods is confined in its ap- 
plication, and is moreover somewhat inaccurate even where 
applicable ; the second is perfectly general, and rigorously true ; 
but still there are cases in which it is advisable to employ the 
method of middle latitude sailing, in preference to that of Mer- 
cator's sailing. It is, therefore, proper that middle latitude sail- 
ing should be explained, especially since, by means of a correc- 
tion to be hereafter noticed, the usual inaccuracy of this method 
may be rectified. 

Middle latitude sail- 
ing proceeds on the 
supposition that the de- 
parture or sum of all 
the meridional distan- 
ces, h^h, &c, d^df &c. 
from O to T, is equal 
to the distance M'M of 
the meridians of O and 
T, measured on the 
middle parallel of lati- 
tude between O and T. 

The middle latitude is half the sum of the two extreme lati- 
tudes, if they are both of the same name, and to half their dif- 
ference if they are of contrary names. 

This supposition becomes very inaccurate when the course is 
small, and the distance run great ; for it is plain that the middle 
latitude distance will receive a much greater accession than the 
departure, if the track OT cuts the successive meridians at a 
very small angle. 

The principal approaches nearer to accuracy as the angle O 
of the course increases, because then as but little advance is 
made in latitude, the several component departures lie more in 
the immediate vicinity of the middle parallel M'M. But still, in 
very high latitudes, a small advance in latitude makes a con- 
siderable difference in meridional distance ; hence, this principle 
is not to be used in such latitudes, if much accuracy is required. 

By means, however, of a small table of corrections, con- 
stnicted by Mr. Workman, the imperfections of the middle lat- 




182 



ELEMENTS OF SURVEYING. 




itude method may be removed, and the results of it rendered in 
all cases accurate. This table w^e have given at the end of this 
work. 

The rules for middle latitude sailing may be thus deduced. 

We have seen, in the first case of plane sail- 
ing, that if a ship sails on an oblique rhumb 
from O to T, that the hypothenuse OT will 
represent the distance ; O [P the difference of 
latitude, and T'T, the departure. Now, by 
the present hypothesis, the departure T'T is 
equal to the middle parallel of latitude between 
the meridians of the places sailed from and ar- 
rived at : so that the difference of longitude of 
these two places is the same as if the ship had 
sailed the distance T'T on the middle parallel 
of latitude. The determination of the differ- 
ence of longitude is, therefore, reduced to the case of parallel 
sailing: for, T'-'T now representing the distance on the parallel, 
if the angle T^TO" be made equal to the latitude of that parallel, 
we shall have, by the last case, the difference of longitude rep- 
resented by the hypothenuse (yT. We therefore have the 
following theorem : 

I. In the triangle C/TT ^ 

COS. a TV : TT :: R : TO'; 
that is, 

COS. mid. lat. : departure : : R : diff. longitude. 

II. In the triangle C/TO 

sin. O' : OT :: sin O : O'T ; 
that is, since sin. O^rcos. CTT 

COS. mid. lat. : distance : : sin. course : diff. longitude. 

III. In the triangle OTT^, we have 

R : tangent O : : OT : TT ; 
comparing this with the first proportion, and observing that the 
extremes of this are the means of that, we have 



O'T 



COS. O'TT : tangt. 0; 



OT 
that is, 

diff. lat. : diff. long. : : cos. mid. lat. : tangt. course. 

These three propositions comprise the theory of middle lati- 
tude sailing ; and when to the middle latitude sailing, the proper 
correction, taken from Mr. Workman's table, is applied, these 
theorems will be rendered accurate. 

In the table of pages 93 and 94, the middle latitude is to be 
found in the first column to the left. Then, along in the hori- 
zontal line, and under the given difference of latitude, is inserted 



PRINCIPLES OF NAVIGATION. 183 

the proper correction to be added to the middle latitude to obtain 
the latitude in which the meridian distance is accurately equal to 
the departure. Thus, if the middle latitude be 37°, and the dif- 
ference of latitude 18°, the correction will be found on page 94, 
and is equal to 0° 40^. 

EXAMPLES. 

1. A ship, in latitude 51° 18' N., longitude 22° 6' W., is 
Dound to a place in the S. E. quarter, 1024 miles distant, and 
in lat. 37° N. : what is her direct course and distance, as also 
the difference of longitude between the two places ? 

T *\ o^o f\ AT* ( Sum of latitudes - - - 88° 18' 
Lat. to 37__0 N. S jjy_ i^j_ 44° 9' 



Diff. lat. 14M8 =858 miles. 



As distance 1024 
radius .... 
: diff. lat. 858 . 
COS. course 33° 5^ 



3.010300 

10 000000 

2.933487 

9.923187 



Cos. mid. lat. 44° 9^ ar. comp. 0.144167 
: tang, course 33'' 5 . . . 9.813899 
: : diff. lat. 858 ... . 2.933487 
: diff long. 779 ... . 2.891552 



In this operation the middle latitude has not been corrected, 
so that the difference of longitude here determined is not without 
error. To find the proper correction, look for the given middle 
latitude, viz. 44° 9', in the table of corrections, the nearest to 
which we find to be 45° ; against this and under 14° diff. of lat. 
we find 27', and also under 15° we find 31', the difference be- 
tween the two being 4'; hence, corresponding to 14° 18' the 
correction will be about 28', Hence, the corrected middle lati- 
tude is 44° 37', therefore, 

Cos. corrected mid. lat. 44° 37' ar. comp. 0.147629 
: tangt. course 33 5 - - - l^-. 8 13899 

: : diff. lat. 858 - - - - 3.933487 

: diff. long. 785.3 - - - - 2.895015 

therefore, the error in the former result is about 6 j miles. 

2. A ship sails in the N. W. quarter, 248 miles, till her de- 
parture is 135 miles, and her difference of longitude 310 miles 
required her course, the latitude left, and the latitude come to. 

. 5 Course N. 32° 59' W ; 
"^''•^- I Lat. left 62° 27' N. ; lat. in 65° 55' N. 

3. A ship, from latitude 37° N., longitude 9° 2' W., having 
sailed between the N. and W., 1027 miles, reckons that she has 
made 564 miles of departure : what was her direct course, and 
the latitude and longitude reached ? 



. 5 Course N. 33° 19' W., or N. W. nearly; 
^"'^- } Lat. 51° 18' N. ; long. 22° 8' W 



184 ELEMENTS OF SURVEYING. 

4. Required the course and distance from the east point of 
St. Michael's, lat. 37° 48^ N., long. 25° 13^ W., to the Start 
Point, lat. 50° 13^ N., long. 3° S& W. ; the middle latitude be- 
ing corrected by Workman's tables. 

Ans. Course N. 57° 11' E ; dist. 1189 miles. 

Mercator's Sailing. 

18. It has already been observed, that when a ship sails on an 
oblique rhumb, the departure, the difference of latitude, and the 
distance run, are truly represented by the sides of a right angled 
triangle. 

Thus, if a ship sails from A to i?, the 
departure B^B w^ill represent the sum oi 
all the very small meridian distances, or 
elementary departures, b% p'p, &c. ; the 
difference of latitude AB^ vi^ill represent, 
in like manner, the small differences of 
latitude Ab'^ b'p', &c ; and the hypothe- 
nuse AB, will express the sum of the 
distances corresponding to these several 
differences of latitude and departure. 
Each of these elements is supposed to 
be taken so small, as to form on the sur- 
face of the sphere a series of triangles, differing insensibly from 
plane triangles. 

Let Ab^b represent one of these elementary triangles ; b^b will 
then be one of the elements of departure ; and Ab' the corres- 
ponding difference of latitude. Now, as b^b is a small arc of a 
parallel of latitude, it will be to a portion of the equator or of a 
meridian containing an equal number of degrees, as the cosine 
of its latitude is to radius (Art. 16). This similar portion of 
the equator, or of the meridian, will be the difference of longi- 
tude between 6^ and b. 

Let us now suppose Ab to be prolonged until the perpendicular 
p^p shall become equal to the difference of longitude between b" 
and b: then, 
bb^ will be to p^p, as the cosine of the latitude of b% to radius. 

But, b'b : p'p : : Ab' : Ap' : 

hence, Ab' : Ap' : : cos. lat. of b'b : radius ; 

that is, if the latitude be so increased that p'p shall become the 
true difference of longitude^ then, 

true diff. lat. Ab' : increased lat. Ap' : : cos. lat. : radius. 

The increased latitude Ap' is called the meridional difference 
of latitude. Denoting, therefore, the true difference of latitude 




PRINCIPLES OF NAVIGATION. 185 

by d^ the increased or meridional difference of latitude by D, the 
latitude of h'h by Z, and the radius by 1, which is, indeed, the 
radius of the tables of natural sines, and we shall have 

d ' D : : cos. I : 1, 
which gives 

D=d secant /, since L=sec. l. 

COS. / 

If then, we know the latitude I of the beginning of a course, 
and the true difference of latitude d of the extremity of the 
course, we can easily find the meridional latitude D correspond- 
ing to that course. 

Conceiving each elementary distance to be increased in this 
manner, giving the meridional differences of latitude on the line 
AC^, the sum of all the corresponding elements will be the entire 
meridional departure during the course. 

To represent, therefore, the difference of longitude due to any 
departure, as B B, and to its corresponding difference of latitude 
AB^, we must produce AB' lill AC is equal to the meridional 
difference of latitude ; the perpendicular C^C will then be the 
difference of longitude actually made in sailing from A to B. 

The determination of AC requires the determination of all its 
elementary parts. If d be taken equal to V, we shall have from 
the equation above 

D=y sec I. or D — sec. Z, 

it being understood that I expresses minutes or geographical miles. 

From ibis equation, the value of D, corresponding to every 
minute of /, from the equator to the pole, may be calculated ; 
and from the continued addition of these there may be obtained, 
in succession, the meridional parts corresponding to V, 2^, 3^, 4^ 
&c. of true latitude, and when registered in a table, they form a 
table of meridional parts, given in all books on Navigation. 

The following may serve as a specimen of the manner in 
which such a table may be constructed, and, indeed, of the man 
ner in which the first table of meridional parts was actually 
formed by Mr. Wright, the proposer of this valuable method. 

Mer. pts. of l^=:nat. sec. V. 

Mer. pts. of 2^=:nat. sec. T+nat. sec. 2\ 

Mer. pts. of 3^==nat. sec. T + nat. sec. 2^ + nat. sec. 3^ 

Mer. pts. of 4^=:nat. sec. T + nat. sec. 2''+nat. sec. 3^ +&c. 

Hence, by means of a table of natural secants we have 

Nat. Sees. Mer. Pts. 

Mer. pts. of V= 1.000000 =1.0000000 

Mer. pts. of 2^=1.0000000+1.0000000 = 2.0000002 
Mer. pts. of 3^=2.00000024-1.0000004 = 3.0000006 
Mer. pts. of 4"= 3.0000006+ 1.0000007=4.0000013 &c. 



186 



ELEMENTS OF SURVEYING. 



There are other methods of construction, but this is the most 
simple and obvious. The meridional parts thus determined, are 
all expressed in geographical miles, because in the general ex- 
pression 

D=l' sec. I. 
r is a geographical mile. 

Having thus formed the table of meridional parts, if we enter 
it, and find the meridional parts corresponding to the latitudes of 
the place left and the place arrived at, their difference will be 
the meridional difference of latitude, or the line AC^ in the dia 
gram. The difference of longitude CC may then be found by 
the following proportion. 

I. As radius is to the tangent of the course, so is the meridional 
difference of latitude to the difference of longitude. 

But if the departure be given instead of the course, then, 

II. As the true difference of latitude, is to the departure, so is the 
meridional difference of latitude to the tangent of the course. 

Other proportions may also be deduced from the diagram. 



EXAMPLES. 



As an example of Mercator's or rather Wright's, sailing, let us 
take the following: 

1. Required the course and distance from the east point of 
St. Michael's to the Start point : the latitudes being 37° 48' N., 
and 50° 13' N., and the longitudes 25° 13' W., and 3° 38' W. 

Start Point, lat. 50° 13' N. Mer. pts. 3495 
St. Michael's, lat. 37° 48' N. 



True difference of lat. 12° 25' 
60 

Diff. in miles 745 



Mer. pts. 2453 
Mer. diff. 1042 

Diff. oflongT~2l° 35' 
60 
Diff. in miles 1 295 



Now, let us suppose that we have sailed 
from Ato B: we shall then know A5' equal 
true diff. lat. = 745 miles; J. C^ = merid- 
ional diff. of lat.=rl042; and C'C= the 
difference of longitude equal to 1295 
miles. It is required to find the course 
B^ABy and the distance AB. 




PRINCIPLES OF NAVIGATION. 187 

For the Course. > For the Distance. 



As AC 1042 . . 3.017868 

radius 10.000000 

; C'C 1295 . . 3.112270 



^ 510 11' E. 10.094402 



As COS. A. 51° 11' 9.797150 
: AB' 745 . . 2.872156 

: : radius .... 10.000000 



AB 1189 . 3.075006 

2. A ship sails from latitude 37° N. longitude 22° 56' W., on 
the course N: 33° 19' E: till she arrives at 51° 18' N.: required 
the distance sailed, and the longitude arrived at. 

Ans. Dis. 1027 miles; long. 9° 45' W. 



Mercator's Chart. 



Mercator's Chart is a Map constructed for the use of Navi- 
gators. In this chart all the meridians are represented by straight 
lines drawn parallel to each other, and the parallels of latitude 
are also represented by parallel straight lines drav^^n at right 
angles to the meridians. 

The chart may be thus constructed. Draw on the lower part 
of the paper a horizontal line to represent the parallel of latitude 
which is to bound the southern portion of the chart. From a 
scale of equal parts, corresponding in size to the extent of the 
map to be made, lay off, on this line, any number of equal dis- 
tances and throiigh the points draw a series of parallels to rep- 
resent the meridians. 

Then draw a line on the side of the map, and for the second 
parallel of latitude, find from the table of meridional parts the 
meridional difference of latitude corresponding to the degrees 
between the first and second parallel, and lay off this distance 
for the interval between the two parallels. Then find the meri- 
dional difference between the second and third, and lay it off in 
the same way for the third parallel, and so on, for the fourth, 
fifth, &c. 

A place whose latitude and longitude is known, may be laid 
down in the same manner; for it will always be determined by 
the intersection of the meridian and parallel of latitude. 

If the chart is constructed on a small scale the divisions on 
the graduated lines, may be degrees instead of minutes ; and 
the meridians and parallels may be drawn only for every fifth 
or tenth degree. 

We have already seen (Art. 18.), that the meridional difference 
of latitude bears a constant ratio to the difference of longitude, 
so long as the course remains unchanged : and hence we see 
that on Mercator's chart, every rhumb will be represented by a 
straight line. 



*®° ELEMENTS OF SURVEYING. 

Line of Meridional Parts on Gunter's Scale. 

This scale corresponds exactly with the table of meridional 
parts, excepting, that in the table the circle is divided to minutes, 
while the scale is divided only to degrees. A scale of equal parts 
is placed directly beneath the scale of meridional parts ; if the 
former corresponds to divisions of longitude, the latter will rep- 
resent those of latitude. Hence, a chart may be constructed 
trom these scales by using the scale of equal parts for the lines 
01 longitude, and the scale of meridional parts for those of 



THE END. 



A TABLE 

OF 

LOGARITHMS OF NUMBERS 

FROM 1 TO 10,000. 



?L 


Log. 
0.000000 


N. 
26 


Log. 


N. 
51 


Lo?. 
1.707570 


N. 
76 


Lo?. 
1.880814 


1.414973 


2 


0.301030 


27 


1.431364 


52 


1.716003 


77 


1.886491 


3 


0.477121 


28 


1.447158 


53 


1.724276 


78 


1.892095 


4 


0.602060 


29 


1.462398 


54 


1.732394 


79 


1.897627 


5 


0.698970 


30 


1.477121 


55 


1.740363 


80 


1.903090 


6 


0.778151 


31 


1.491362 


56 


1.748188 


81 


1.908485 


7 


0.845098 


32 


1.505150 


57 


1.755875 


82 


1.913814 


8 


0.903090 


33 


1.518514 


58 


1.763428 


83 


1.919078 


9 


0.954243 


34 


1.531479 


59 


1.770852 


84 


1.924279 


10 


1.000000 


35 


1.544068 


60 


1.778151 


85 


1.929419 


li 


1.041393 


36 


1.556303 


61 


1.785330 


86 


1.934498 


12 


1.079181 


37 


1.568202 


62 


1.792392 


87 


1.939519 


13 


1.113943 


38 


1.579784 


63 


1.799341 


88 


1.944483 


14 


1.146128 


39 


1.691065 


64 


1.806180 


89 


1.949390 


15 


1.176091 


40 


1.602060 


65 


1.812913 


90 


i. 954243 


16 


1.204120 


41 


1.612784 


66 


1.819544 


91 


1.959041 


17 


1.230449 


42 


1.623249 


67 


1.826075 


92 


1.963788 


18 


1.255273 


43 


1.633468 


68 


1.832509 


93 


1.968483 


19 


1.278754 


44 


1.643453 


69 


1.838849 


94 


1.973128 


20 


1.301030 


45 


1.653213 


70 


1.845098 


95 


1.977724 


21 


1.322219 


46 


1.662758 


71 


1.851258 


96 


1.982271 


22 


1.342423 


47 


1.672098 


72 


1.857333 


97 


1.986772 


23 


1.361728 


48 


1.681241 


73 


1.863323 


98 


1.991226 


24 


1.380211 


49 


1.690196 


74 


1.869232 


99 


1.995635 


UL 


1.397940 


50 


1 1.698970 


75 


1.875061 


100 


2.000000 



N. B. In the following table, in the last nine columns of 
each page, where the first or leading figures change from 9's 
to O's, points or dots are introduced instead of the O's through 
the rest of the line, to catch the eye, and to indicate that from 
thence the annexed first two figures of the Logarithm in the 
second column stand in the next lower line. 



A Table of logarithms from 1 to 10,000. 



N. 1 |x|2,u|4i5i6|7i8|9 


_D. > 


100 


000000 


U434 


0868 


i30l 


1734 2166 


2598 


3029 


3461 


3S91 


"432" 


101 


4321 


4751 


5181 


.5609 


6038 


6466 


6894 


7321 


7748 


8174 


428 


102 


8600 


9026 


945 J 


9876 


.300 


.724 


1147 


1570 


1993 


2415 


424 


103 


012837 


3259 
7451 


3680 


4100 


4521 


4940 


5360 


5779 


6197 


6616 


419 


104 


7033 


7868 


8284 


8700 


9116 


9532 


9947 


.361 


.775 


416 


105 


021189 


1603 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 


412 


106 


5306 


5715 


6125 


6.533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


107 


9384 


9789 


.195 


.600 


1004 


1408 


1812 


2216 


2619 


3021 


404 


108 


033424 


3826 


4227 


4628 


.5029 


5430 


5830 


6230 


6629 


7028 


400 


109 
110 


7426 


7825 


8223 
2182 


8620 
2576 


90171 9414 


9811 
3755 


.207 
4148 


.602 


.998 


396 
393 


041393 


1787 


2969 


3362 


4540' 


4932 


111 


5323 


5714 


6105 


6495 


6885 


7275 


7664 


8053 


8442 


8830 


389 


112 


9218 


9606 


9993 


.380 


.766 


1153 


1538 


1924 


2309 


2694 


386 


113 


053078 


3463 


3846 


4230 


4613 


4996 


,5378 


5760 


6142 


6524 


382 


114 


6905 


7286 


7666 


8046 


8426 


8805 


9185 


9563 


9942 


.320 


379 


115 


000698 


1075 


1452 


1829 


2206 


2582 


29.58 


3333 


3709 


4083 


376 


116 


4458 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


7815 


372 


117 


8186 


8557 


8928 


9298 


9668 


...38 


.407 


.776 


1145 


1514 


369 


118 


071882 


2250 


2617 


2985 


3352 


3718 


4085 


4451 


4816 


5182 


366 


119 
120 


5547 


5912 
9543 


6276 
9904 


6640 
.266 


7004 
.626 


7368 
.987 


7731 
1347 


8094 
1707 


8457 


8819 


363 
360 


079181 


2067 


2426 


121 


082785 


3144 


3503 


3861 


4219 


4576 


4934 


5291 


5647 


6004 


357 


122 


6360 


6716 


7071 


7426 


7781 


8136 


8490 


8845 


9198 


9552 


355 


123 


9905 


.258 


.611 


.963 


1315 


1667 


2018 


2370 


2721 


3071 


351 


124 


093422 


3772 


4122 


4471 


4820 


5169 


.5518 


5866 


6215 


6562 


349 


125 


6910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


..26 


3^6 


126 


100371 


0715 


1059 


1403 


1747 


2091 


2434 


2777 


3119 


3462 


343 


127 


3804 


4146 


4487 


4828 


5169 


5510 


5851 


6191 


6.531 


6871 


340 


128 


7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


.2.53 


338 


129 
130 


110590 


0926 
4277 


1263 
4611 


1.599 
4944 


1934 

5278 


2270 
5611 


2605 
5943 


2940 
6276 


3275 


3609 
6940 


335 
333 


113943 


6608 


131 


7271 


7603 


7934 


8265 


8595 


8926 


9256 


9586 


9915 


.245 


330 


132 


120574 


0903 


1231 


1.560 


1888 


2216 


2544 


2871 


3198 


3525 


328 


133 


3852 


4178 


4504 


4830 


5156 


.5481 


5806 


6131 


6456 


6781 


325 


134 


7105 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


..12 


323 


135 


130334 


0655 


0977 


1298 


1619 


1939 


2260 


2580 


2900 


3219 


321 


136 


3539 


3858 


4177 


4-196 


4814 


5133 


5451 


5769 


6086 


6403 


318 


137 


6721 


7037 


7354 


7671 


7987 


8303 


8618 


8934 


9249 


9564 


315 


138 


9879 


.194 


.508 


.822 


1136 


1450 


1763 


2076 


2389 


2702 


314 


139 
140 


143015 


3327 
6438 


3639 
6748 


3951 

7058 


4263 


4574 
7676 


4885 
7985 


5196 


.5507 
8603 


.5818 
8911 


311 
309 


146128 


7367 


8294 


141 


9219 


9527 


9835 


.142 


.449 


.756 


1063 


1370 


1676 


1982 


307 


142 


152288 


2594 


2900 


3205 


3510 


3815 


4120 


4424 


4728 


5032 


305 


143 


5336 


5640 


5943 


6246 


6.549 


6852 


71.54 


7457 


7759 


8061 


303 


144 


8362 


8664 


8965 


9266 


9567 


9868 


.168 


.469 


.769 


1068 


301 


145 


161368 


1667 


1967 


2266 


2564 


2863 


3161 


3460 


3758 


4055 


299 


146 


4353 


4650 


4947 


5244 


5541 


5838 


6134 


6430 


6726 


7022 


297 


147 


7317 


7613 


7908 


8203 


8497 


8792 


9086 


9380 


9674 


9968 


295 


148 


170262 


0555 


0848 


1141 


1434 


1726 


2019 


2311 


2603 


2895 


293 


149 
150 


3186 


3478 
6381 


3769 
6670 


4060 
6959 


4351 


4641 


4932 


5222 
8113 


.5512 
8401 


5802 
8689 


291 

289 


176091 


7248 


7536 


7825 


151 


8977 


9264 


9552 


9839 


.126 


.413 


.699 


.985 


1272 


1,5,58 


287 


152 


181844 


2129 


2415 


2700 


2985 


3270 


3555 


.3839 


4123 


4407 


285 


153 


4691 


4975 


5259 


5542 


5825 


6108 


6391 


6674 


6956 


7239 


283 


154 


7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


..51 


281 


155 


190332 


0612 


0892 


1171 


1451 


1730 


2010 


2289 


2567 


2846 


279 


156 


3125 


3403 


3681 


3959 


4237 


4514 


4792 


5069 


5346 


5623 


278 


157 


5899 


6176 


6453 


6729 


7005 


7281 


7556 


7832 


8107 


8382 


276 


153 


8657 


8932 


9206 


9481 


9755 


..29 


.303 


.577 


,850 


1124 


1274 


159 


201397 


1670 


1943 


2216 


2488 


2761 


3033 


3305 


3577 


33481272 1 


N. 1 |l|2|3|4|5|6|7|8|9|D. 1 





A 


FABLE OF LOGARrrllSi 


S FROM 1 TO 10,000 




3 


N. I 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 I r». 1 


IfiO 


204120 43911 


4663 


4934 


5204 


5475 


5740 


0010 


6236 


0556 


271 


161 


6826 


7096 


7365 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


102 


9515 


9783 


..51 


.319 


.586 


.853 


1121 


1388 


1654 


1921 


20? 


163 


212188 


2454 


2720 


2986 


3252 


3518 


3783 


4049 


4314 


4579 


266 


104 


4844 


5109 


5373 


5638 


5902 


6166 


0430 


0694 


6957 


7221 


264 


165 


7484 


7747 


8010 


8273 


8536 


8798 


9000 


9323 


9585 


9840 


262 


166 


220108 


0370 


0631 


0892 


1153 


1414 


1075 


1936 


2196 


2450 


261 


107 


2716 


2976 


3236 


3496 


3755 


4015 


4274 


4533 


4792 


5051 


259 


168 


5309 


5568 


5826 


6084 


0342 


6600 


0858 


7115 


7372 7630 


258 


169 
170 


7887 


8144 
0704 


8400 
0960 


8657 
1215 


8913 
1470 


9170 

1724 


9420 
1979 


9682 
2234 


9938 

2488 


.193 

2742 


256 

254 


230449 


171 


2996 


3250 


3504 


3757 


4011 


4264 


4517 


4770 


6023 


5270 


253 


172 


5528 


5781 


6033 


6285 


6537 


6789 


7041 


7292 


75-14 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


95.50 


9800 


..50 


.300 


250 


174 


240549 


0799 


1048 


1297 


1546 


1795 


2044 


2293 


2541 


2790 


249 


175 


3038 


3286 


3534 


3782 


4030 


4277 


4525 


4772 


.5019 


.5206 


248 


176 


5513 


5759 


6006 


6252 


6499 


6745 


0991 


7237 


7482 


7728 


246 


177 


7973 


8219 


8464 


8709 


8954 


9198 


9443 


9087 


9932 


.176 


245 


178 


250420 


0664 


0908 


1151 


1395 


1638 


1881 


2125 


2368 


2010 


243 


179 

180 


2853 


3096 
5514 


3338 i 3580 


3822 
6237 


4064 
0477 


4300 
0718 


4548 
0958 


4790 
7198 


5031 
7439 


242 

241 


255273 


5755 


.5996 


181 


7679 


7918 


8158 


8398 


8637 


8877 


9110 


9355 


9594 


9833 


239 


182 


260071 


0310 


0548 


0787 


1025 


1203 


1501 


1739 


1976 


2214 


238 


183 


2451 


2688 


2925 


3162 


3399 


3636 


3873 


4109 


4346 


4.582 


237 


184 


4818 


5054 


5290 


5525 


5761 


5996 


0232 


6467 


6702 


6937 


235 


185 


7172 


7406 


7641 


7875 


8110 


8344 


8578 


8812 


9040 


9279 2341 


186 


9513 


9746 


9980 


.213 


.446 


.679 


.912 


1144 


1377 


1609 


233 


187 


271842 


2074 


2306 


2538 


2770 


3001 


3233 


3464 


3090 


3927 


232 


188 


4158 


4389 


4620 


4850 


5081 


5311 


5542 


5772 


6002 


6232 


230 


189 
190 


6462 


6692 

8982 


6921 
92 if 


7151 
9439 


7380 
9667 


7009 
9895 


7838 
.123 


8007 
.351 


8290 
.578 


8525 
.806 


229 

228 


278754 


191 


281033 


1261 


1488 


1715 


1942 


2169 


2390 


2622 


2849 


3075 


227 


192 


3301 


3527 


3753 


3979 


4205 


4431 


4056 


4882 


5107 


5332 


226 


193 


5557 


5782 


6007 


6232 


6456 


6681 


6905 


7130 


7354 


7578 


225 


194 


7802 


8026 


8249 


8473 


8696 


8920 


9143 


9366 


958y 


9812 


223 


195 


290035 


0257 


0480 


0702 


0925 


1147 


1369 


1591 


1813 


2034 


222 


196 


2256 


2478 


269^ 


2920 


3141 


3303 


3584 


3804 


4025 


4246 


221 


197 


4466 


4687 


4907 


5127 


5347 


5507 


5787 


6007 


6226 


6446 


220 


198 


6065 


6884 


7104 


7323 


7542 


7701 


7979 


8198 


8416 


8635 


219 


199 
200 


8853 


9071 
1247 


9289 
1464 


9507 
1681 


9725 
1898 


9943 
2114 


.161 
2331 


.378 

2547 


.595 

2764 


.813 
2980 


218 
217 


301030 


201 


3196 


3412 


3628 


3844 


4059 


4275 


4491 


4706 


4921 


5136 


216 


202 


5351 


5566 


5781 


.5996 


6211 


0425 


6639 


6854 


7068 


7282 


215 


203 


7496 


7710 


7924 


8137 


8351 


8504 


8778 


8991 


9204 


9417 


213 


204 


9630 


9843 


..56 


.268 


.481 


.693 


.906 


1118 


1330 


1542 


212 


205 


311754 


1966 


2177 


2389 


2600 


2812 


3023 


3234 


3445 


3656 


211 


206 


3867 


4078 


4289 


4499 


4710 


4920 


5130 


5340 


5.551 


5760 


210 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7430 


7646 


7854 


209 


208 


8063 


8272 


8481 


8689 


8898 


9100 


9314 


9522 


9730 


9938 


208 


209 
210 


320146 


0354 
2426 


0562 
2633 


0769 
2839 


0977 
3046 


1184 
.3252 


1391 
3458 


1598 
3005 


1805 
3871 


2012 
4077 


207 
206 


322219 


211 


4282 


4488 


4694 


4899 


5105 


5310 


5516 


5721 


5926 


6131 


205 


212 


6336 


6541 


6745 


6950 


7155 


7359 


7503 


7767 


7972 


8176 


204 


213 


8380 


8583 


8787 


8991 


9194 


9398 


9001 


9805 


...8 


.211 


203 


214 


330414 


0617 


0819 


1022 


1225 


1427 


1630 


1832 


2034 


2236 


202 


215 


2438 


2640 


2842 


3044 


3246 


3447 


3049 


3850 


4051 


4253 


202 


216 


4454 


4655 


4856 


5057 


5257 


5458 


5058 


5859 


0059 


6260 


201 


217 


6460 


06601 6860 


7060 


7260 


7459 


7059 


7858 


8058 


8257 


200 


218 


8456; 86561 885>5 


9054 


9253 


9451 


9650 


9849 


..47 


.246 


199 


219 


340444 


' 0642 


'0841 


1039 


1237 


' 1435 


1032 


1830 


2028 


2225 


198 



__L I 2 I 3 I 4 I 5 I 6 



Dj 



A TABLE OF LOGARITHMS PROJl 1 TO 10,000. 



N. 1 1 1 f 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 i D. 1 


220 


342423, 2620 


2817 


3014 


.3212 


3409 


3606 3802 


1 3999:41961 1971 


221 


4392 


4589 


4785 


4981 


5178 


5374 


5570 


15766 


5962 


' 6167 


196 


222 


6353 


16549 


6744 


6939 


7135 


7330 


7525 


7720 


7915 


8110 


195 


223 


8305 


: 8500 


8694 


8889 


9083 


9278 


9472 


1 9666 


9860 


...64 


194 


224 


350248 


04-12 


0636 


0829 


\ 1023 


1216 


1410 


1 1603 


1796 


1989 


193 


225 


2183 


1 2375 


2568 


2761 


! 2954 


3147 


3339 


3532 


3724 


3916 


193 


226 


4108 


4301 


4493 


4685 


i4876 


5068 


5260 


; .5452 


5643 


5834 


192 


227 


6026 


6217 


6408 


6599 


6790 


6981 


7172 


1 7363 


7554 


7744 


19] 


228 


7935 


8125 


8316 


8506 


8096 


8886 


9076 


9266 


9456 


9646 


190 


229 
230 


9835 


..25 

1917 


.215 
2105 


.404 
2294 


.593 

2482 


.783 
2671 


.972 
2859 


I 1161 
3048 


1350 
3236 


1539 
3424 


189 

188 


361728 


231 


3612 


3800 


3988 


4176 


4363 


4551 


4739 


4926 


5113 


5301 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


6796 


6983 


7169 


187 


233 


7356 


7542 


7729 


7915 


8101 


8287 


8473 


8659 


8845 


9030 


186 


234 


9216 


9401 


9587 


9772 


9958 


.143 


.328 


.513 


.698 


.883 


185 


235 


371068 


1253 


1437 


1622 


1806 


1991 


2175 


2360 


2544 


2728 


184 


236 


2912 


3096 


3280 


3464 


3047 


3831 


4015 


4198 


4382 


45G5 


184 


237 


4748 


4932 


5115 


5293 


5481 


5664 


5846 


6029 


6212 


6394 


183 


238 


6577 


6759 


6942 


7124 


7306 


7488 


7670 


7852 


8034 


8216 


182 


239 
240 


8398 


8580 
0392 


8761 
0573 


8943 
0754 


9124 
0934 


9306 
1115 


9487 
1296 


9668 
1476 


9849 
1656 


..30 

1837 


181 
181 


380211 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


3815 


3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


5606 


5785 


5964 


6142 


6321 


6499 


6677 


6856 


7034 


7212 


178 


244 


7390 


7568 


7746 


7923 


8101 


8279 


8456 


8634 


8811 


8989 


178 


245 


9166 


9343 


9520 


9698 


9875 


..51 


.228 


.405 


.582 


.759 


177 


246 


390935 


1112 


1288 


1464 


1641 


1817 


1993 


2160 


2345 


2.521 


176 


247 


2697 


2873 


3048 


3224 


3400 


3575 


3751 


3926 


4101 


4277 


176 


248 


4452 


4627 


4802 


4977 


5152 


5326 


6501 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7766 


174 


250 


397940 


8114 


8287 


8461 


8634 


8808 


8981 


91.54 


9328 


9501 


173 


251 


9674 


9847 


..20 


.192 


.365 


.538 


.711 


.883 


1056 


1228 


173 


252 


401401 


1573 


1745 


1917 


2089 


2261 


2433 


2605 


2777 


2949 


172 


253 


3121 


3292 


3464 


3635 


3807 


3978 


4149 


4320 


4492 


4663 


171 


254 


4834 


5005 


5176 


5346 


55.7 


5688 


5858 


6029 


6199 


6370 


171 


255 


6540 


6710 


6881 


7051 


7221 


7391 


7561 


7731 


7901 


8070 


170 


256 


8240 


8410 


8579 


8749 


8918 


9087 


9257 


9426 


9595 


9764 


169 


257 


9933 


.102 


.271 


.440 


.609 


.777 


.946 


1114 


1283 


1451 


169 


258 


411620 


1788 


1956 


2124 


2293 


2461 


2629 


2796 


2964 


3132 


168 


259 


3300 


3467 


3635 


3803 


3970 


4137 


4305 


4472 


4639 


4306 


167 


260 


414973 


5140 


5307 


5474 


5641 


6808 


5974 


6141 


6303 


6474 


167 


261 


6641 


6807 


6973 


7139 


7306 


7472 


7633 


7804 


7970 


81.35 


166 


262 


8301 


8467 


8633 


8798 


8964 


9129 


9295 


9460 


9625 


9791 


165 


263 


9956 


.121 


.286 


.451 


.616 


.781 


.945 


1110 


1275 


1439 


165 


264 


421604 


1788 


1933 


2097 


2261 


2426 


2590 


2754 


2918 


3082 


164 


265 


3246 


3410 


3574 


3737 


3901 


4065 


4228 


4392 


4555 


4718 


164 


266 


4882 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6186 


6349 


163 


267 


6511 


6674 


6S36 


6999 


716] 


7324 


7486 


7648 


7811 


7973 


162 


268 


8135 


8297 


8459 


8821 


8783 


8944 


9108 


9268 


9429 


9591 


162 


269 


9752 


9914 


..75 


.236 


.398 


.559 


.720 


.881 


1042 


1203 


161 


270 


431364 


1525 


1685 


1846 


2007 


2167 


2328 


2488 


2049 


2809 


161 


271 


2969 


3130 


3290 


3450 


3610 


3770 


3930 


4090 


4249 


4409 


160 


272 


4569 


4729 


4888 


5048 


5207 


5367 


5526 


5685. 


5344 


6004 


159 


273 


6163 


6322 


6481 


6640 


6798 


6957 


7116,7275' 


7433 


7592 


159 


274 


7751 


7909 


8067 


8226 


8384! 


8542 


8701 88591 


90 J 7 


9175 


158 


275 


9333 


94911 


9648 


9806 


99641 


.1221 


.279j .4371 


..594 


.752 


158 


276 


440909 


lOfiO 


1224 


1381. 


1538' 


1695' 


18.52 2009! 


2106 


2323 


157 


277 


24S0 


?637 


2793 


2950 


3106; 


3263 


3119135761 


3732' 


3889 


157 


278 


4045 


4201 


43571 


4513 


4669 4825 


4981 51371 


5293 


5449 


156 


279 


6604 


5760 59151 


6071' 62261 6382 6537 6692 6848' 


7003 155 1 


N. 1 1 1 1 2 i 3 1 4 1 5 1 6 1 7 1 8 i 9 : D. 1 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


} |l|2|3i4|5|6|7!8|9lD. 1 


tso" 


447158 


7313 


7468 


7623 


7778 


7933 


8088 


8242i 8397i 8552| 155 I 


281 


8706 


8861 


9015 


9170 


9324 


9478 


9633 


9787 


9941 ; ..95 


154 


282 


450249 


0403 


0557 


0711 


0865 


1018 


1172 


1326 


1479 


1633 


154 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2700 


2859 


3012 


3165 


153 


284 


3318 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 


4692 


153 


285 


4845 


4997 


5150 


5302 


5454 


5606 


5758 


5910 


6062 


6214 


152 


286 


6366 


6518 


6670 


6821 


6973 


7125 


7276 


7428 


7579 


7731 


152 


287 


7882 


8033 


8184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


151 


288 


9392 


9543 


9694 


9845 


9995 


.146 


.296 


.447 


.597 


.748 


151 


289 


460898 


1048 


1198 


1348 


1499 


1649 


1799 


1948 


2098 


2248 


150 


290 


462398 


2548 


2697 


2847 


2997 


3146 


3296 


3445 


3594 


3744 


150 


291 


3893 


4042 


4191 


4340 


4490 


4639 


4788 


4936 


5085 


5234 


149 


292 


5383 


5532 


5680 


5829 


5977 


6126 


6274 


6423 


6571 


6719 


149 


293 


6868 


7016 


7164 


7312 


7460 


7608 


7756 


7904 


8052 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9085 


9233 


9380 


9527 


9675 


148 


295 


9822 


9969 


.116 


.263 


.410 


.55/ 


.704 


.851 


.998 


1145 


147 


296 


471292 


1438 


1585 


1732 


1878 


2025 


2171 


2318 


2464 


2610 


146 


297 


2756 


2903 


3049 


3195 


3341 


3487 


3633 


3779 


3925 


4071 


146 


298 


4216 


4362 


4508 


4653 


4799 


4944 


5090 


5235 


5381 


5526 


146 


299 
300 


5671 


6816 


5962 
7411 


6107 
7555 


6252 
7700 


6397 

7844 


6542 
7989 


6687 
8133 


6832 

8278 


6976 

8422 


145 
145 


477121 


7266 


301 


8566 


8711 


8855 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


302 


480007 


0151 


0294 


0438 


0582 


0725 


0869 


1012 


1156 


1299 


144 


303 


1443 


1586 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


2731 


143 


304 


2874 


3016 


3159 


3302 


3445 


3587 


3730 


3872 


4015 


4157 


143 


305 


4300 


4442 


4585 


4727 


4869 


5011 


5153 


5295 


5437 


5579 


■42 


306 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


.42 


307 


7138 


7280 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


141 


308 


8551 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9818 


141 


309 
310 


9958 
491362 


..99 
1502 


.239 
1642 


.380 


.520 
1922 


.661 
2062 


.801 
2201 


.941 
2341 


1081 
2481 


1222 
2621 


140 
140 


1782 


311 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


.3876 


4015 


139 


312 


4155 


4294 


4433 


4572 


4711 


4850 


4989 


5128 


5267 


5406 


139 


313 


5544 


5683 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


6791 


139 


314 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


315 


8311 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


138 


316 


9687 


9824 


9962 


..99 


.236 


..3,4 


.511 


.648 


.785 


.922 


137 


317 


501059 


1196 


1333 


1470 


1607 


1744 


1880 


2017 


2154 


2291 


137 


318 


2427 


2564 


2700 


L»337 


2973 


3109 


3246 


3382 


3518 


3655 


1.36 


319 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


505150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


321 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


7586 


7721 


135 


322 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


323 


9203 


9337 


9471 


9606 


9740 


9874 


...9 


.143 


.277 


.411 


134 


324 


510545 


0679 


0813 


0947 


1081 


1215 


1349 


1482 


1616 


1750 


134 


325 


1883 


2017 


2151 


2284 


2418 


2551 


2684 


2818 


2951 


3084 


133 


326 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4414 


133 


327 


4548 


4681 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


328 


5874 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


13a 


329 


7196 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330, 


■518514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


331 


9828 


9959 


..90 


.221 


.353 


.484 


.615 


745 


.876 


1007 


131 


332 


521138 


1269 


1400 


1530 


1661 


1792 


1922 


2053 


2183 


2314 


131 


333 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


334 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4056 


4785 


4915 


130 


335 


5045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 


6081 


6210 


129 


336 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7X'13 


7372 


7501 


129 


337 


7630 


7759 


7888 


8016 


'8145 


8274 


8402 


8531 


8660 


8788 


129 


338 


8917 


9045 


9174 


9302 


9430 


9559 


9687 


9315 


9943 


..72| 128 


339 


530200 0328 


0456 


05,94 


0712 


0840 


0968' 1096 


1223 


13511 128 





1 ] 


1 2 


3 


4 i 5 1 6 1 7 I 8 1 9 1 V. \ 



G 


A 


TABLE OF LGGARlTjrfMS FKOM 1 


10 10,000 


. 




N- 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 1). 1 


340 


531479 


160/ 


1734 


1862 


1990 


2117 


2245 


2372 


2500 


2627 


128 


341 


2754 


2882 


3009 


3136 


3264 


3391 


.3518 


3645 


3772 


3899 


127 


342 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


.5041 


5167 


127 


343 


5294 


5421 


5547 


5674 


5800 


5927 


60.53 


6180 


6306 


6432 


126 


344 


6558 


6685 


6811 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


346 


7819 


7945 


8071 


8197 


8322 


8448 


8574 


8699 


8825 


8951 


126 


346 


9076 


9202 


9327 


9452 


9578 


9703 


9829 


9954 


..79 


.204 


125 


34 V 


5'i0329 


0455 


0580 


0705 


0830 


0955 


1080 


1205 


1.3.30 


14.541 125 


348 


1579 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


270l! 125 


349 

350 


2825 


2950 
4192 


3074 
4316 


3199 
4440 


3323 
4564 


3447 
4688 


3571 
4812 


3696 
4936 


3820 
5060 


394-4 
5183 


124 
124 


544068 


351 


5307 


5431 


5555 


5678 


5802 


5925 


6049 


6172 


6296 


6419 


124 


3o2 


6543 


6666 


6789 


6913 


7036 


7159 


7282 


7405 


7529 


76,52 


123 


3o3 


7775 


7898 


8021 


8144 


8267 


8389 


8512 


8635 


87.58 


8881 


123 


354 


9003 


9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


.106 


123 


355 


550228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


1328 


122 


356 


1450 


1572 


1694 


1816 


1938 


2060 


2181 


2.303 


2425 


2.547 


122 


1 357 


2C68 


2790 


2911 


3033 


31.55 


3276 


3398 


.3519 


3640 


3762 


121 


■358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4852 


4973 


121 


1 359 
360 


5094 


5215 
6423 


5336 
6544 


5457 
6664 


5578 
6785 


5699 
6905 


5820 


5940 


6061 
7267 


6182 
7.387 


121 
120 


556303 


7026 


7146 


361 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8.349 


8469 


8.589 


120 


362 


8709 


8829 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


363 


9907 


..26 


.146 


.265 


.385 


..504 


.624 


.743 


.863 


.982 


119 


364 


561101 


1221 


1340 


1459 


1578 


1698 


1817 


1936 


2055 


2174 


119 


365 


2293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


119 


m6 


3481 


3600 


3718 


3837 


3955 


4074 


4192 


4311 


4429 


4548 


119 


367 


4666 


4784 


4903 


5021 


51.39 


5257 


5376 


5494 


5612 


5730 


lis 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6.555 


6673 


6791 


6909 


118 


369 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


568202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


371 


9374 


9491 


9608 


9725 


9842 


99.59 


..76 


.19.3 


.309 


.426 


117 


372 


570543 


0660 


0776 


0893 


1010 


1126 


1243 


13.59 


1476 


1.592 


117 


373 


1709 


1825 


1942 


2058 


2174 


2291 


2407 


2.523 


26.39 


2755 


116 


3V4 


2872 


2988 


3104 


3220 


3336 


3452 


3568 


3684 


3800 


.3915 


116 


375 


4031 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5188 


5303 


5419 


5534 


5650 


5765 


.5880 


5996 


6111 


6226 


115 


377 


6341 


6457 


6572 


6687 


6802 


6917 


7032 


7147 


7262 


7377 


115 


378 


7492 


7607 


7722 


7836 


7951 


8066 


8181 


8295 


8410 


8525 


115 


379 

380 


8639 


8754 
9898 


8868 
..12 


8983 
.126 


9097 
.241 


9212 
.35.5 


9326 
.469 


9441 


9555 


9669 
.811 


114 

114 


579784 


..583 


.697 


381 


580925 


1039 


1153 


1267 


1.381 


1495 


1608 


1722 


1836 


19,50 


114 


382 


2063 


2177 


2-291 


2404 


2518 


2631 


2745 


2858 


2972 


3085 


114 


383 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 


113 


384 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


113 


385 


5461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 


113 


386 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


7486 


7599 


112 


387 


7711 


7823 


7935 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


.388 


8832 


8944 


9056 


9167 


9279 


9391 


9503 


9615 


9726 


9838 


112 


3^9 
390 


9950 


..61 
1176 


.173 
1287 


.284 
1399 


.396 
1510 


..507 
1021 


.619 
17,32 


.730 
1843 


.842 
1955 


.953 
2066 


112 
HI 


591065 


391 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


29.54 


3064 


3175 


111 


392 


3286 


3397 


3508 


3618 


3729 


3840 


39.50 


4061 


4171 


4282 


111 


393 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 


110 


394 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


626. 


6377 


6487 


110 


395 


6597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


7586 


110 


396 


7695 


7805 


7914 


8024 


8134 


8243 


8353 


8462 


8572 


8681 


110 


397 


8791 


8900 


9009 


9119 


9228 


9337 


9446 


95.56 


9665 ^774 


109 


398 


9883 


9992 


.101 


.210 


.319 


.428 


.537 


.646 


.7.551 864 


109 


399 


600973 


1082 


1191 


1299 


1408 


1517 


1625 


1734 


18431 19i>i 1091 


N. 1 1 1 1 2 1 3 i 4 1 5 i 6 1 7 1 8 i 9 


n 





A TABLE OF LOGARITHMS FROM 1 TO 10,000. 




7 


nr 


1 |i|2|3|4|5|6|7!8|9|d| 


:400 


1 602060 


2169 


2277 


2386 


2494 


2603 


2711 


2819 


2928 


3036' 108 1 


401 


1 3144 


3253 


3361 


3469 


3577 


3686 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


6197 


108 


403 


5305 


5413 


5.521 


5628 


5736 


5844 


.5951 


6059 


6166 


6274 


108 


404 


6381 


6489 


6596 


6704 


6811 


6919 


7026 


7133 


7241 


7348 


107 


405 


7455 


7562 


7669 


7777 


r884 


7991 


8098 i 8205 


8312 


8419 


107 


406 


8526 


8633 


8740 


8847 


89.54 


906 1 


9167 


9274 


9381 


9488 


107 


407 


9594 


i 9701 


9808 


9914 


..21 


.128 


.2.34 


.341 


.447 


.,554 


107 


408 


610660 


0767 


0873 


0979 


1086 


1192 


1298 


1405 


1511 


1617 


106 


409 
410 


1723 


1829 
2890 


1936 
2996 


2042 
3102 


2148 
3207 


2254 
3313 


2360 
3419 


2466 
3525 


2572 
3630 


2678 
3736 


106 
106 


612784 


411 


3842 


3947 


1 4053 


4159 


4264 


4370 


4475 


4.581 


4686 


4792 


106 


412 


4897 


5003 


5108 


.5213 


5319 


5424 


5529 


5634 


5740 


5845 


105 


413 


5950 


6055 


6160 


6265 


6370 


6476 


6581 


6686 


6790 


6895 


105 


414 


7000 


7105 


7210 


7315 


7420 


7626 


7629 


7734 


7839 


7943 


105 


415 


8048 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


416 


9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


..32 


104 


417 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


1072 


101 


418 


1176 


1280 


1384 


1488 


1592 


1696 


1799 


1903 


2007 


2110 


104 


419 

420 


2214 
623249 


2318 
3353 


2421 
3456 


2525 
3559 


2628 
3663 


2732 
37'56 


2835 


29.39 
3973 


3042 
4076 


3146 
4179 


104 
.03 


3809 


421 


4282 


4385 


4488 


4591 


4695 


4798. 


4901 


5004 


6107 


.5210 


103 


422 


5312 


5415 


6518 


5621 


6724 


5827 


5929 


6032 


61.35 


6238 


103 


423 


6340 


6443 


6546 


664S 


6751 


68S3 


6956 


7058 


7161 


7263 


103 


424 


7366 


7468 


7571 


7673 


7775 


7378 


7980 


8082 


8185 


8287 


102 


425 


8389 


8491 


8593 


8695 


8797 


8900 


9002 9104 


9206 


9308 


102 


426 


9410 


9512 


9613 


9715 


9817 


9919 


..211 .123 


.224 


.326 


102 


427 


630428 


0530 


0631 


0733 


0836 


0936 


1038 


1139 


1241 


1342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2163 


2255 


2350 


101 


429 

430 


2457 
633468 


2559 
^569 


2660 
3670 


2761 
3771 


2862 
3872 


2963 
3973 


3064 


3165 

4175 


3266 
4276 


3367 
4376 


101 
100 


4074 


431 


4477 


4578 


4679 


4779 


4880 


4981 


5081 


5182 


5283 


5383 


100 


132 


5484 


5584 


5685 


6785 


5886 


5986 


6087 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


7390 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


8389 


99 


435 


8489 


8589 


8689 


8789 


88S8 


8988 


9088 


9188 


9287 


9387 


99 


436 


9486 


9586 


9686 


9785 


9885 


9984 


..84 


.183 


.283 


.382 


99 


437 


640481 


0581 


0680 


07it) 


0879 


0978 


1077 


1177 


1276 


1375 


99 


438 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 


99 


439 
440 


2465 


2503 
3551 


2662 
3650 


2761 
3749 


2860 
3847 


2959 
3946 


3058 


3156 

4143 


3255 

4242 


3354 
4340 


99 
98 


643453 


4044 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 


98 


442 


6422 


5521 


5619 


5717 


5815 


5913 


6011 


6110 


6208 


6306 


98 


443 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


444 


7383 


7481 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 


98 


445 


8360 


8458 


8.5.551 


86.53 


8750 


8848 


8945 


9043 


9140 


9237 


97 


446 


9335 


9452 


9530! 


9627 


9724 


9821 


9919 


..16 


.113 


.210 


97 


447 


650308 


0405 


0502! 


0599 


0696 


0793 


0890 


0987 


1084 


1181 


97 


448 


1278 


1375 


14721 


1569 


1666 


1762 


18.59 


1956 


2053 


2150 


97 


4:49 

450 


2246 


2343 
3309 


24401 

340.5 


2536 
3502 


2633 


2730 


2826 
3791 


2923 

3888 


3019 
3984 


3116 
4080 


97 
96 


653213 


3.5981 3695 


451 


4177 


4273 


4369' 


4465 


45621 4658 


4754 


4850 


4946 


5042 


96 


452 


5138 


5235 


.5331 


.5427 


.5.5231 5619 


5715 


5810 


5906 


6002: 96 I 


453 


6098 


6194 


6290 


6386 


64821 6577 


6673 


6769 


6864 


6960 


96 


454 


7050 


7152 


7247 


7343 


7438 7534 


7629 


7725 


7820 


7916 


96 


455 


8011 


8107 


8202 


8298 


8393 


8488 


8684 


8679 


8774 


8870 


95 


456 


8965 


9060 


91.55 


9250 


9346 


94-11 


9536 


9631 


9726 


9821 


95 


457 


9916 


..11 


.106 


.201 


.296 


..391 


.486 


..581 


.676 


.771 


95 


458 


660>!65 


0960 


1055 


1150 


1245 


1.339 


1434 


1529 


1623 


1718 


95 


459 


18131 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 


95 


XI 


<• 1 1 1 2 i 3 1 4 1 5 i 6 1 7 1 8 1- 9 1 


D. 



u 



A TAHLE OF LOOARITIIMS FROM I TO 10.000. 



N. 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 D. i 


460 


6627581 2852 1 2947 1 


3041 3135, 3230, 


3324, 3418| 


3512 3607, 941 


461 


3701 


3795 


3889 


3983 4078 


4172 


4266 


4360 


4454 


4.548! 94 


162 


4642 


4736 


4S30 


4924 5018 


5112 


5206 


5299 


5393 


54871 94 


463 


5581 


5675 


5769! 


5862 5956 


6050 


6143 


6237 


6331 


6424 


94 


464 


6518 


6612 


67051 


6799 6892 


6986 


7079 


7173 


7266 


7360 


94 


465 


7453 


7546 


7640| 


7733 7826 


7920 


8013 


8106 


8199 


8293 


93 


406 


8386 


8479 


8572 


»665 87591 


8S52I 


8945 


9038 


9131 


9224 93 1 


467 


9317 


9410 


9503 


9596 9689 i 97821 


9875 


99671 


..60 


.1.53 931 


468 


670246 


0339 


0431 


0524 0617107101 


0802 


0895 


0988 


1080 


93 


469 


1173 


1265 


135S 


1451 


1543 1636 


1728 


1821 


1913 


2005 


93 


470 


672098 


2100 


2283 


2375 


2467 2560 


2852 


2744 


2836 


2929! 92 


471 


:.021 


3113 


3205; 


3297 


3390 


3482 


3574 


3666 


3758 


3850; 92 


472 


•1942 


4034 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 92 


473 


4861 


4953 


5045 


5137 


5228 


5320 


5412 


5503 


5595 


5687 92 


474 


5778 


5870 


5962 


6053 


0145 


6236 


6328 


6419 


6511 


6602! 92 


475 


6694 


6785 


6876 


6968 


7059 


7151 


7242 


7333 


7424 


7516 91 


476 


7607 


7698 


7789 


7881 


7972 


8063 


8154 


S245 


8336 


8427 


91 


477 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 


478 


9428 


9519 


9610 


9700 


9791 


GS82 


9973 


..63 


.154 


.245 


91 


479 

480 


680336 


0426 
1332 


0517 
1422 


0607 
1513 


0698 
1603 


0789 
1693 


0879 

1784 


0970 

1874 


1060 
1964 


1151 
2055 


91 
90 


681241 


481 


2145 


223o 


2326 


2416 


2506 


2596 


2680 


2777 


2867 


2957 


90 


482 


3047 


3137 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 


483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 


484 


4845 


4935 


5025 


5114 


5204 


5294 


5383 


5473 


5563 


5652 


90 


485 


5742 


5831 


5921 


6010 


6100 


6189 


6279 


6368 


6458 


6547 


89 


486 


6636 


6726 


6815 


6904 


6994 


7083 


7172 


7261 


7351 


7440 


89 


487 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


8153 


8242 


8331 


su 


488 


8420 


8509 


8598 


8687 


8776 


8865 


8953 


9042 


9131 


9220 


89 


489 
490 


9309 
690196 


9398 
0285 


9486 
0373 


9575 
0462 


9664 
0550 


9753 
0639 


9841 


9930 


..19 
0905 


.107 
0993 


89 
89 


0728 


0816 


491 


1081 


1170 


1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 


88 


492 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 


2671 


2759 


88 


493 


2847 


2935 


3023 


3111 


3199 


3287 


3375 


3463 


3551 


3639 


88 


494 


3727 


3815 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 


88 


495 


4605 


4093 


4781 


4868 


4956 


5044 


5131 


5219 


5307 


5394 


88 


496 


5482 


5569 


5657 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 


497 


6356 


6444 


6531 


6618 


6706 


6793 


6880 


6968 


7055 


7142 


87 


498 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 


7926 


8014 


87 


499 


8101 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


500 


698970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


9751 


87 


501 


9838 


9924 


..11 


..98 


.184 


.271 


.358 


.444 


.531 


.617 


87 


502 


700704 


0790 


0877 


0963 


1050 


11.36 


1222 


1309 


1395 


1482 


80 


503 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


504 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 


86 


505 


3291 


3377 


3463 


3549 


3635 


3721 


3807 


3895 


3979 


4065 


86 


506 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


8(5 


507 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


508 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 


6632 


85 


509 


6718 


6803 


0888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 


85 


510 


707570 


7655 


7740 


7826 


7911 


7996 


8081 


8160 


8251 


8336 


'S5 


611 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


512 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 


..33 


85 


513 


710117 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0879 


85 


514 


0963 


1048 


1132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 


84 


515 


1807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


84 


516 


2650 


2734 


2818 


2902 


2986 


3070 


3154 


3238 


3323 


3407 


84 


517 


3491 


3575 


3650 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


518 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


84 


519 1 5167 


5251 


5335 


5418 


5502 


558C 


5669 


5753' 583b 


f 5920 


84 


N. 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 ! 9 1 D.1 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 |l|2|3|4|5|6|7|8|9iD. 1 


■520 


7160031 6087 


0170 


62.54 


6337 


6421 


6504 


6588 


6671 


6754 


83 


521 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


7421 


7504 


7687 


83 


522 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


523 


8502 


8585 


8668 


8751 


8834 


8917 


9000 


9083 


9165 


9248 


83 


524 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


9911 


9994 


..77 


83 


525 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0903 


83 


52G 


0986 


1068 


1151 


1233 


1316 


1398 


1481 


1563 


1646 


1728 


82 


527 


1811 


189.? 


1975 


20.58 


2140 


2222 


2305 


2387 


2469 


2652 


82 


528 


2634 


2716 2798 


2881 


2963 


3045 


3127 


3209 


3291 


,'">374 


82 


529 


345G 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


530 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


6013 


82 


531 


5095 


5176 


5258 


6340 


6422 


6603 


5585 


5667 


5748 


5830 


82 


532 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6664 


6640 


82 


533 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


7460 


81 


634 


7541 


7623. 


7704 


7785 


7866 


7948 


8029 


8110 


8191 


8273 


81 


535 


8354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


81 


536 


9165 


9246 


9327 


9408 


9489 


9570 


9651 


9732 


9813 


9893 


81 


537 


9974 


..55 


.136 


.217 


.298 


.378 


.459 


•540 


.621 


.702 


81 


538 


730782 


0863 


09 14 


1024 


1105 


1186 


1266 


1347 


1428 


1608 


81 


539 


1589 


1669 


1750 


1830 


1911 


1991 


2072 


2152 


2233 


2313 


81 


540 


732394 


2474 


2555 


263.^ 


2715 


2796 


2876 


2956 


3037 


3117 


80 


541 


3197 


3278 


3368 


34" j> 


3518 


3598 


3679 


3769 


3839 


3919 


80 


542 


3999 


4079 


4160 


4.i0 


4320 


4400 


4480 


4660 


4640 


4720 


80 


543 


4800 


4880 


4960 


6040 


6120 


5200 


6279 


5359 


5439 


5519 


80 


544 


5599 


5679 


5759 


6838 


5918 


6998 


6078 


6157 


6237 


6317 


80 


545 


6397 


6476 


6666 


6636 


6715 


6795 


6874 


6954 


7034 


7113 


80 


546 


7193 


7272 


7352 


7431 


7511 


7690 


7670 


7749 


7829 


7908 


79 


547 1 


7987 


8067 


8146 


8225 


8305 


8384 


8463 


8543 


8622 


8701 


79 


548 


87S1 


8860 


8939 


9018 


9097 


9177 


9256 


9336 


9414 


9493 


79 


549 


9572 


9651 


9731 


9810 


9889 


9968 


..47 


.126 


.205 


.284 


79 


550 


740363 


0442 


0521 


0600 


0678 


0767 


0836 


0915 


0994 


1073 


79 


551 


1152 


1230 


1309 


1388 


1467 


1646 


1624 


1703 


1782 


1860 


79 


552 


1939 


2018 


2096 


2176 


2254 


2332 


2411 


2489 


2668 


2646 


79 


553 


2725 


2804 


2882 


2961 


3039 


3118 


3196 


3275 


3353 


3431 


78 


554 


3510 


3588 


3667 


3745 


.3823 


3902 


3980 


4058 


4136 


4215 


78 


555 


4293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5153 


5231 


5309 


6387 


6465 


6543 


5621 


5G99 


6777 


78 


557 


5855 


6933 


6011 


6089 


6167 


6245 


6323 


6401 


6479 


6666 


78 


558 


6G34 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7955 


8033 


8110 


78 


560 


748188 


8266 


8343 


8421 


8498 


8576 


8663 


8731 


8808 


8886 


77 


561 


8963 


9040 


9118 


9195 


9272 


9350 


9427 


9604 


9682 


9669 


77 


562 


9736 


9814 


9891 


9968 


..46 


.123 


.200 


.277 


.354 


.431 


77 


563 


750508 


0586 


0663 


0740 


0817 


0894 


0971 


1048 


1126 


1202 


77 


564 


1279 


1356 


1433 


1510 


1587 


1664 


1741 


1818 


1896 


1972 


77 


565 


2048 


2125 


2202 


2279 


2366 


2433 


2509 


2586 


2663 


2740 


77 


566 


2816 


2893 


2970 


3047 


3123 


3200 


3277 


3353 


3430 


3606 


77 


567 


3583 


3660 


3736 


3813 


3889 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


4501 


4578 


4654 


4730 


4807 


4883 


4960 


6036 


76 


569 
570 


5112 


6189 
5951 


5265 
6027 


5341 
6103 


6417 
6180 


5494 
6256 


5570 
6332 


5646 
6408 


5722 
6484 


6799 
6660 


76 
76 


755875 


571 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7648 


7624 


7700 


7775 


7851 


7927 


8003 


8079 


76 


573 


8155 


8230 


8306 


8382 


8458 


8533 


8«09 


8685 


8761 


8836 


76 


574 


8912 


8988 


9063 


9139 


9214 


9290 


9366 


9441 


9517 


9592 


76 


575 


9668 


9743 


9819 


9894 


9970 


..46 


.121 


.196 


.272 


.347 


75 


576 


760422 


0498 


0573 


0649 


0724 


0799 


0875 


0950 


1025 


1101 


75 


577 


1176 


1251 


1326 


1402 


1477 


1.552 


1627 


1702 


1778 


18.53 


75 


578 


1928 


2003 


2078 


2163 


2228 


2303 


2378 


2463 


2529 


2604 


75 


579 


2679 


275412829 


2904 2978 


3O53I 3128 


3203 


3278 


3363 


75 


nTJ 


1 1 1 2 1 3 1 4 i 5 1 6 1 7 1 8 1 y 1 i). 1 



10 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 |lf2|3i4|5|6|7|8l9|D. 1 


580 


76342): 


i 3503|357t 


i 3653, 3727 


3802; 3877, 395x 


4027 


|4101 


75 


581 


4176 


425 


4326 


) 440C 


447.= 


455C 


) 462^3 


I 469S 


4774 


4848 


75 


582 


492C 


499t 


507S 


. 5147 


5221 


5296 


> 5370 5445 


5520 


5594 


75 


583 


566!J 


574L 


581^ 


5892 


5966 


0041 


! 6115 619^ 


6264 


6338 


74 


584 


6413 


1 6487 


6562 


6636 


6716 


678f 


j 6S5i 


> 6933 


7007 


7082 


74 


585 


7156 


i 7230 


7304 


7379 


7453 


7527 


7601 


7675 


7749 


7«23 


74 


586 


7898 


17972 


8046 


8120 


8194 


8268 


i 834S 


8416 


8490 


8564 


74 


587 


8638 


8712 


8786 


8860 


8934 


900^i 


1 908-^ 


9156 


9230 


9303 


74 


588 


9377 


9451 


9525 


9599 


9673 


9746 


1 982C 


9894 


9968 


..42 


74 


589 


770115 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 


0778 


1 74 


590 


770852 


0926 


0999 


1073 


1146 


1220 


1293 


1367 


1440 


1514 


li 


591 


1587 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


21 75 


2248 


73 


592 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2835 


2908 


2981 


73 


593 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4S98 


4371 


4444 


73 


595 


4517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


6100 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


5610 


5683 


! 5756 


5829 


6902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


6411 


16483 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


599 
600 


7427 


7499 

8224 


7572 
8296 


7644 


7717 


7789 
8513 


7862 
8585 


7934 

8658 


8006 
8730 


8079 

8802 


72 
72 


778151 


8368 1 8441 


601 


8874 


8947 


9019 


9091! 9163 


9236 


9308 


9380 


9452 


9524 


72 


602 


9596 


9669 


9741 


9813 


9885 


9957 


..29 


.101 


.173 


.245 


72 


603 


780317 


0389 


0461 


0533 


0605 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 


1684 


72 


605 


1755 


1827 


1899 


197] 


2042 


2114 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3117 


72 


607 


3189 


3260 


3332 


3403 


3475 


3546 


3618 


3689 


3761 


3832 


71 


608 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


4403 


4475 


4546 


71 


609 


4617 


4689 


4760 


4831 


4902 


4974 


5045 


5116 


5187 


.5259 


71 


610 


785330 


5401 


5472 


6543 


5615 


6686 


5757 


6828 


5899 


5970 


71 


611 


6041 


6112 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


612 


6751 


6822 


6893 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


71 


613 


7460 


7531 


7602 


7673 


7744 


7815 


7885 


7956 


8027 


8098 


71 


614 


8168 


8239 


8310 


8381 


8451 


8622 


8693 


8663 


8734 


8804 


71 


615 


8875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


9510 


71 


616 


9581 


9651 


9722 


9792 


9863 


9933 


...4 


..74 


.144 


.215 


70 


617 


790285 


0356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 


0988 


1059 


1129 


1199 


1269 


1340 


1410 


1480 


1550 


1620 


70 


619 


1691 


1761 
2462 


1831 
2532 


1901 
2602 


1971 

2673 


2041 

2742 


2111 
2812 


2181 

2882 


2252 
2952 


2322 
3022 


70 
70 


620 


792392 


621 


3092 


3162 


3231 


3301 


3371 


3441 


3511 


3581 


3651 


3721 


70 


622 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


6115 


70 


624 


5185 


5254 


5324 


5393 


5463 


6532 


5602 


5672 


6741 


5811 


70 


625 


5880 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 


68 


626 


6574! 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


71291 


7198 


69 


627 


7268! 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 


7890 


69 


628 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 


69 


629 


8651 


8720! 


8789 


8858 8927 


89961 


9066 


9134 


9203 


9272 


69 


630 


799341 


9409 


9478 


9547 9616 


9685! 


9754 


9823 


9892 


9961 


69 


631 


800029' 


00981 


0187 


0236! 0305! 


0373 


0442 


0511 


0580 


0648! 


69 


632 


0717 


0786 


0854 


0923 0992 


1061 


1129 


1198 


1266 


1335 


69 


633 


1404 


1472 


1541 


1609 I678i 


1747 


1815 


I884I 


1952 


2021 


69 


634 


2089! 


2158! 


2226 


22951 2363! 


2432 


2500 


25681 


2637! 


2705 


69 


635 


2774! 


2842' 


2910 


29791 3047 


3116i 


3184 


32.521 


33211 


3389 


68 


636 


34571 


35251 


3594 


3662! 3730 


37981 


38071 


3935 i 


4003! 


40711 


68 ( 


637 


4139i 


4208' 


4276 


4344: 4412 4480- 


4548! 


4616| 


4685 


47.53! 


68 


638 


48211 


4889 


4957 


5025 5093 5161 


5229. 


5297. 5365! 


.543.?: 68 1 


639 


55011 


5509 5637 i 


5705 5773' 584 1' 5908i 


.0976' 6044' 


6112' 68 


N. I 


I 1 2 I 3 ! 4 ! 5 1 6 1 7 1 8 1 9 ; D. } 



A TABLE or LOGARITHMS PROM I TO 10,000. 



N. 


1 


1 1 1 2 1 3 1 4 1 6 


I 6 1 7 1 8 1 9 1 D. 1 


640 


806180 


6248 


63161 63«4 


6451 


6519 


6587 


6655 


6723 


6790 


68 


641 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 


68 


643 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


9492 


67 


645 


9560! 9627 


9094 


9762 


9829 


9896 


9964 


..31 


..98 


.165 


67 


646 


810233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 


67 


647 


0904 


0971 


1039 


1106 


1173 


1240 


1307 


1374 


1441 


1508 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 


67 


619 
650 


2245 


2312 
2980 


2379 
3047 


2445 
3114 


2512 
3181 


2579 
3247 


2646 
3314 


2713 
3381 


2780 
3448 


2847 
3514 


67 

67 


812913 


651 


3581 


3648 


3714 


3781 


3S4S 


3914 


3981 


4048 


4114 


4181 


67 


652 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 


67 


653 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 


66 


654 


5578 


56-44 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


624] 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 


66 


656 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 66 1 


657 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


659 
660 


8885 


8951 
9610 


9017 
9676 


9083 
9741 


9149 

9807 


9215 

9873 


9281 
9939 


9346 

...4 


9412 
..70 


9478 
.136 


66 
66 


819544 


661 


820201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 


66 


662 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 


66 


663 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 


65 


665 


2822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 


65 


666 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 


65 


668 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


G69 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 


65 


670 


826075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


72401 7305 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 


65 


073 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


9304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


..11 


..75 


.139 


.204 


.268 


..332 


•396 


.460 


.525 


64 


677 


830589 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1166! 64 


678 


1230 


1294 


1358 


1422 


1486 


1550 


1614 


1078 


1742 


1806! 64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 


64 


680 


832509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 


64 


681 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


372 1 j 64 1 


632 


3784 


3848 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357| 64 1 


683 


4421 


4484 


4548 


4611 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 


63 


685 


5691 


5754 


5817 


5881 


5944 


6007 


6071 


6134 


6197 


6261 


63 


686 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6830 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525! 63 


688 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156! 63 


689 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


87^6! 63 


690 


838849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415! 63 


691 


9478 


9541 


9604 


9667 


9729 


9792 


9855 


9918 


9981 


..43 63 


692 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608: 007 1; 63 


693 


0733 


0796 


0859 


0921 


098 i 


1046 


1109 


1172 


12341 12971 63 


694 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


1860, 1922: 63 


695 


1985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484! 2547: 62 


696 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


310813170. 62 


697 


3-233 


3295 


3357 


3420 


34 S 2 


3544 


3606 


3669 


373113793. 62 


698 


3855 


3918 


3980 


4042 


i 1 04 


41 (56 


4229 


429 1 


4353144151 62 


699 


4477 


4539 


460; 


4>>r, 1 


4726 


47.^8 


4S50 


4912 4974; n()3G 62 | 


N. 


1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 t 9 ! n. 1 



12 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 D. 1 


700 


845098 


5160' 5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


02 


701 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 


62 


703 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7't49 


7511 


65. 


704 


7572 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 


67. 


705 


8189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 


6>"{ 


706 


8805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 


ei 


707 


9419 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


9911 


9972 


61 


70S 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0.585 


61 


709 
710 


0646 


0707 
1320 


0769 
1381 


0830 
1442 


0891 
1503 


09.52 
1564 


1014 
1625 


1075 
1686 


1136 
1747 


1197 
1809 


61 
61 


851258 


711 


1870 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2480 


254 i 


2602 


2663 


2724 


2785 


2846 


2907 


2908 


302ii 


61 


713 


3090 


3150 


3211 


3272 


3333 


3.'^94 


3455 


3516 


3577 


3037 


6] 


714 


3898 


3759 


3820 


3881 


3941 


4002 


4063 


4124 


4185 


4245 


61 


715 


4306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4H52 


61 


716 


4913 


4974 


5034 


5095 


5150 


.5216 


5277 


.5337 


5398 


5459 


61 


717 


5519 


5580 


5640 


5701 


5761 


5822 


5882 


5943 


6003 


6064 


61 


718 


6124 


6185 


6245 


6306 


6360 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


6789 


6850 


6910 


0970 


7031 


7091 


7152 


7212 


7272 


60 


720 


857332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


7815 


7875 


60 


721 


7935 


7995 


8056 


8116 


8170 


8236 


8297 


8357 


8417 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


8833 


8898 


8958 


9018 


9078 


60 


723 


9138 


9198 


9258 


9318 


9379 


9439 


9499 


9559 


9619 


9679 


60 


724 


9739 


9799 


9859 


9918 


9978 


..38 


..98 


.158 


.218 


.278 


60 


725 


860338 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


1056 


1116 


1176 


1236 


1295 


1355 


1415 


1475 


60 


727 


1534 


1594 


1654 


1714 


1773 


1833 


1893 


1952 


2012 


2072 


60 


728 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2.549 


2608 


266S 


60 


729 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 


60 


730 


883323 


3382 3442 i 


3501 


3561 


3620 


3080 


3739 


3799 


:^58 


59 


731 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 


59 


732 


4511 


4570 


4630 


4689 


4748 


4808 


4867 


4926 


4985 


5045 


59 


733 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


.5519 


5578 


5037 


59 


734 


5696 


5755 


5814 


5874 


5933 


5992 


6051 


6110 


6169 


0228 


59 


735 


6287 


6346 


6405 


6465 


6524 


6583 


6642 


6701 


6760 


0819 


59 


73b 


6878 


6937 


6996 


7055 


7114 


7173 


7232 


7291 


7350 


7409 


59 


737 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


7939 


7998 


59 


73S 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8.586 


59 


739 
740 


8644| 


8703 
9290 


8762 
9349 


8821 
9408 


8879 
9466 


8938 
9525' 


8997 
9584 


9056 
9642 


9114 
9701 


9173 
9700 


59 
59 


869232 


741 


9818 


9877 


9935 


9994 


..53 


.111 


.170 


.228 


.287 


.345 


59 


742 


870404 


0462 


0521 


0579 


0638 


0696 


0755 


0813 


0872 


0930 


58 


743 


0989 


1047 


1106 


1164 


1223 


1281 


1339 


1398 


14.56 


1515 


58 


744 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


1981 


2040 


2098 


58 


745 


2156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 


58 


746 


2739 


2797 


2855 


2913 


2972 


3030 


3088 


3146 


3204 


3262 


58 


747 


3321 


3379 


3437 


3495 


3553 


3611 


3669 


3727 


3785 


3844 


58 


748 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 


4366 


4424 


58 


749 
750 


4482 


4540 
5119 


4598 


4656 
5235 


4714 
5293 


4772 
,5351 


4830 
5409 


4888 
5466 


4945 
5524 


5003 
5582 


58 

58 


87506 1 


5177 


751 


5640 


5098 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


0100 


58 


752 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


0737 


58 


753 


6795 


6853 


6910 


6968 


7020 


7083 


7141 


7199 


7256 


73 1 4 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 


755 


7947 


8004 


8002 


S119 


8177 


8234 


8292 


8349 


8407 


8404 


57 


756 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 


57 


757 


9096 


9153! 9211 


9268 


9325 


9383 


9440 


9497 


95.55 


9012 


57 


■r5« 


9669 


97261 9784 


9841 


9898 


9956 


..13 


..70 


.127 


.185 


57 


759 


880242, 


02991 0356 


0413 


0471 


0528 


0585 


0642 


0699 


0756 


57 


, N. 1 


1 1 i 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 ; D. 1 



.V TAlU.r Oi LOGAItlTIIMS FKOM I TO 10,000. 



13 



N. 1 


|l!2|3|4l5|6|7l8|9lD. 1 


7fi0 


880814 


0871 0928, 


0985 


1042 


1099 


1156 


1213 


1271' 1328 


57 


761 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


18411 l'^98 


57 


762 


1955 


2012 


2069 


2126 


2183 


2240 


2297 


2354 


24111 2468 


57 


763 


2525 


2581 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


30371 


57 


764 


3093 


3150 


3207 


3264 


3321 


3377 


3434 


3491 


3548 


3605 


57 


765 


3661 


3718 


3775 


3832 


3888 


3945 


4002 


4059 


4115 


4172 


57 


766 


4229 


4285 


4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 


4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


57 


768 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


57 


769 

770 


5926 


5983 
6547 


6039 
6604 


6096 
6660 


6152 
6716 


6209 
6773 


6265 
6829 


6321 

6885 


6378 

6942; 


6434 
6998 


56 
56 


886491 


771 


7054 


7111 


7167 


72231 


7280 


7336 


7392 


7449 


7505! 


7561 


56 


772 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


8011 


8067| 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629| 


8685 


56 


774 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190! 


9246 


56 


775 


9302 


9358 


9414 


9470 


9526 


9582 


9638 


9694 


97501 


9806 


56 


776 


9862 


9918 


9974 


..30 


..86 


.141 


.197 


.253 


.3091 


.365 


56 


777 


890421 


0477 


0533 


0589 


0645 


0700 


0756 


0812 


0868 


0924 


56 


778 


0980 


1035 


1091 


1147 


1203 


1269 


1314 


1370 


1426 


1482 


56 


779 

780 


1537 


1593 

2150 


1649 
2206 


1705 
2262 


1760 
2317 


1816 
2373 


1872 
2429 


1928 

2484 


1983 
2540 


2039 
2595 


56 
56 


892095 


781 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 


56 


782 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 


55 


784 


4316 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 


55 


785 


4870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5804 


5920 


55 


787 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 


55 


788 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


55 


789 
790 


7077 


7132 

7682 


7187 
7737 


7242 
7792 


7297 

7847 


7352 
7992 


7407 
7957 


7462 
8012 


7517 
8067 


7572 
8122 


55 
55 


897627 


791 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


55 


794 


9821 


9875 


9930 


9985 


..39 


..94 


.149 


.203 


.258 


.312 


55 


795 


900367 


0422 


0470 


0531 


0586 


0640 


0695 


0749 


0804 


0859 


55 


79G 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 


55 


797 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 


799 
800 


2547 


2601 
3144 


2655 
3199 


2710 
3253 


2764 
.3307 


2818 
3361 


2873 
3416 


2927 
3470 


2981 
3524 


3036 
3578 


54 

54 


903090 


301 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 


54 


803 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


804 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


54 


805 


5796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 


54 


807 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 


54 


80d 


7411 


74G5 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 


54 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 


54 


812 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


..37 


53 


813 


910091 


0144 


0197 


0251 


0304 


0358 


0411 


0464 


0518 


0571 


53 


814 


0624 


0678 


0731 


0784 


0838 


0891 


0944 


0998 


1051 


1104 


53 


815 


1158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 


53 


816 


1690 


1743 


1797 


1850 


1903 


1956 


200S 


2063 


2116 


216S 


53 


817 


2222 


2275 


2328 


2381 


2435 


248g 


|2541 


2594 


- 2647 


270C 


53 


818 


2753 


2806 


2859 


2913 


2966 


30 IS 


307S 


312^ 


317)^ 


3231 


53 


819 


•S2H4 


. 3337 


339C 


3443 


3496 


354S 


13605 


, 365f 


370S 


3761 


63 


JL 


1 U |ll2l3l4l5l6l7|8!9|Dl 



14 


A TABLI 


: OP LOGARITHMS FROM I TO 10, 


000. 






"n!" 


1 |l!2|3|4|6|6|7|8|9|D. 1 


"82(r 


913814,3867 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


42901 53 1 


821 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


5505 


5558 


5611 


5664 


5716 


5769 


.5822 


5875 


53 


824 


5927 


, 5980 


0033 


6085 


61.38 


6191 


6243 


6296 


6349 


640] 


53 


825 


6454 


6507 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


G927 


53 


826 


6980 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 


53 


827 


7506 


7558 


7611 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8030 


8083 


8135 


8188 


8240 


8293 


8345 


8397 


8450 


8502 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


830 


019078 


9130 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


831 


9001 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


..19 


..71 


52 


832 


920123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 


0541 


0593 


52 


833 


0645 


0697 


0749 


0801 


0853 


0900 


0958 


1010 


1062 


1114 


52 


834 


1166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 


52 


835 


1686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 


52 


836 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 


52 


837 


2725 


2777 


2829 


2881 


2933 


2985 


3037 


3089 


3140 


3192 


52 


838 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 


52 


839 

840 


3762 
924279 


3814 
4331 


3865 
4383 


3917 
4434 


3969 
4486 


4021 
4538 


4072 


4124 
4641 


4176 
4693 


4228 
4744 


52 
52 


4589 


841 


4796 


4848 


4899 


4951 


5003 


5054 


5106 


5157 


5209 


526] 


52 


842 


5312 


5364 


5415 


5467 


5518 


5570 


5621 


5673 


5725 


5776 


52 


843 


5828 


5879 


5931 


5982 


6034 


6085 


6137 


6188 


6240 


6291 


51 


844 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 


51 


845 


6857 


6908 


6959 


7011 


7062 


7114 


7165 


7216 


7268 


7319 


51 


846 


7370 


7422 


7473 


7524 


7576 


7627 


7678 


7730 


7781 


7832 


51 


847 


7883 


7935 


7986 


8037 


8088 


8140 


8191 


8242 


8293 


8345 


51 


848 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


8805 


8857 


51 


849 

850 


8908 


8959 
9470 


9010 
9521 


9061 
9572 


9112 
9623 


9163 
9674 


9215 
9725 


9266 
9776 


9317 

9827 


9368 


51 


929419 


9879] 51 


851 


9930 


9981 


..32 


..83 


.134 


.185 


.236 


.287 


.338 


.389, 51 


852 


930440 


0491 


0542 


0592 


0643 


0694 


0745 


0796 


0847 


08981 51 


853 


0949 


1000 


1051 


1102 


1153 


1204 


1254 


1305 


1356 


1407; 51 


854 


1458 


1509 


1560 


1610 


1661 


1712 


1763 


1814 


1865 


1915 51 


855 


1966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


51 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


51 


857 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 


51 


858 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 


51 


859 
860 


3993 
934498 


4044 
4549 


4094 


4145 
4650 


4195 
4700 


4246 
4751 


4296 
4801 


4347 

4852 


4397 


4448 
4953 


51 

50 


4599 


4902 


861 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 


50 


862 


5507 


5558 


5608 


5658 


5709 


5759' 5809 


5860 


5910 


5960 


50 


863 


6011 


6061 


6111 


6162 


6212 


6262' 6313 


6363 


6413 


6463 


50 


864 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 


50 


865 


7016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


50 


866 


7518 


7566 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


867 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


50 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


50 


870 


939519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


50 


871 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 


50 


872 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 


50 


87b 


1014 


1064 


1114 


1163 


1213 


1263 


1313 


1362 


1412 


1462 


50 


874 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 


50 


875 


2008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 


50 


876 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 


50 


877 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


3593 


3643 


3692 
4186 


3742 


3791 


3841 


3890 


2939 49 1 


879 


3989 


4038 


4088 


4137 


42361 4285 


4335 


4384' 4433 49 | 


N. 


il|2|3|4|5'6l7|8l9|n! 





A TABLE Of LOGARITHMS FROM I TO 10,000. 




15 


nn 


1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 i D. 1 


880 


944483 


4532 


4581 46311 


4680] 


4729 


4779 


48281 


4877 


4927! 49 


881 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419' 49 


882 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912; 49 


883 


5961 


6010 


6059 


6108 


6157 


6207 


6256 


6305 


6354 


6403 49 


884 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 49 


885 


6943 


6992 


7041 


7090 


7140 


7189 


7238 


7287 


7336 


73851 49 


886 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 49 


887 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


83641 49 


888 


8413 


8462 


8511 


8560 


8609 


8657 


8706 


8755 


8804 


8853| 49 


889 
890 


8902 


8951 


8999 


9048 
9536 


9097 
9585 


9146 
9634 


9195 
9683 


9244 
9731 


9292 

9780 


9341 49 
9829| 49 


949390 


9439 ^488 


891 


9878 


9926 9975 


..24 


..73 


.121 


.170 


.219 


.267 


.316 49 


892 


950365 


0414 0462 


0511 


0560 


0608 


0657 


0706 


0754 


08031 49 


893 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289! 49 


894 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


17751 49 


895 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260i 48 


396 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744! 48 


897 


2792 


2841 


2889 


2938 


2986 


3034 


3083 


3131 


3180 


3229 48 


898 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


37ir 48 


899 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194' 48 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


46771 48 


901 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


5110 


5158! 48 


902 


5207 


5255 


5303 


5351 


5399 


5't47 


5495 


5543 


5592 


5640, 48 


903 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 48 


904 


6168 


6216 


6265 


6313 


6361 


6409 


6457 


6505 


6553 


6601 48 


905 


6649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080; 48 


906 


71 28 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559: 48 


907 


7607 


7655 


7703 


7751 


7799 


7847 


7894 


7942 


7990 


8038: 48 


908 


8086 


8134 


8181 


S229 


8277 


83251 8373 


8421 


8468 


8516 48 


909 
910 


8564 


8612 
9089 


8659 
9137 


8707 
9185 


8755 
9232 


8803 8850 
9280 9328 


8898 8946 


8994; 48 


959041 


9375 9423' 9471 48 | 


911 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 9900 


9947 


4S 


912 


9995 


..42 


..90 


.138 


.185 


.233 


.280 


.328 .376 


.423 


48 


913 


960471 


0518 


0566 


0613 


0661 


0709 


0756 


0804' 0851 


0899 


48 


914 


0946 


0994 


1041 


1089 


1136 


1184 


1231 


1279 


1326 


1374 


47 


915 


1421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


2511 


2559 


2606 


2653 


2701 


274« 


2795 


47 


918 


2843 


2890 


2937 


2985 


3032 


3079 


3126 


3174 


3221 


3268 


47 


919 
920 


3316 


3363 
3835 


3410 

3882 


3457 
3929 


3504 
3977 


1 3552 

4024 


3599 
4071 


3646 

4118 


3693 
4165 


3741 
^212 


47 
47 


963788 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4584 


47 


922 


4731 


4778 


4825 


4S72 


4919 


i 4966 


5013 


5061 


5108 


1 5155 


47 


923 


5202 


5249 


5296 


5343 


5390 


: 5437 


5484 


5531 


5578 


5625 


47 


924 


5672 


5719 


5766 


5813 


; 5860 


5907 


5954 


6001 


6048 


6095 


47 


925 


6142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 


47 


926 


6611 


6658 


16705 


6752 


j 6799 


6845 


6892 


6939 


6'i80 


7033 


47 


927 


7080 


7127 


7173 


7220 


1 7267 


! 7314 


7361 


7408 


7454 


7501 


47 


928 


7548 


7595 


7642 


7688 


7735 


! 7782 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8156 


1 8203 


1 8249 


8296 


8343 


8390 


8436 


47 


930 


968483 


1 8530 


;8576 


8623 


] 8670 


i 371t 


8763 


8810 


8856 


8903; 47 


931 


8950 


8996 


'9043 


909C 


913C 


: 918S 


9229 


9276 


9323 


9369; 47 


932 


9416 


9463 


19509 


9556 


9602 


1 964f 


9695 


9742 


9789 


9835 47 


933 


9882 


9928 


9975 


..21 


1 ..08 


! .114 


t .101 


.207 


.254 


.3001 47 


934 


970347 


039.g 


044C 


048fc 


i 053S 


"i 05791 062C 


0672 


071S 


0765i 46 


935 


0815 


085b 


090^ 


[ 095 


!0997 


! 1044! 10901 1137 


118;] 


1229! 46 


936 


1276 


) 132S 


136[ 


)\ U\l 


)! 1461 


■ 1508'i lo54i 1601 


1647 


1693' 40 


937 


174( 


) 178e 


) 1835 


>1 187t 


) 192f 


)! 19711 20181206^ 


[ 211C 


) 2157: 46 


938 


220: 


^ 224f 


)|229. 


jl 2345 


I' 238? 


? 12434: 24811252' 


f 257[ 


{ 2619 46 


939 


266 


i 2715 


2' 2 75 J 


^i 280^ 


I 2Hr> 


'289 


r 294r 


r298f 


) 303^ 


) 3082 


46 



.1 I 



I 6 i 7 I 8 I 9 I D. 



16 



A TABLE OF LOGARITHMS FROM 1 TO 10,000- 



JL- 


|l|2|3|4|5|6|7|8l9|D. 1 


940 


973128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4005 


46 


942 


4051 


4097 


4143 


4189 


4235 


4281 


4327 


4374 


4420 


4466 


46 


943 


4512 


4558 


4604 


4650 


4696 


4742 


4788 


4834 


4880 


4926 


46 


944 


4972 


5018 


5064 


5110 


5156 


5202 


5248 


5294 


5340 


5386 


46 


945 


5432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 


46 


946 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 


40 


947 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 
950 


7266 


7312 
7769 


7358 

7815 


7403 
7861 


7M9 
7906 


7495 

7952 


7541 
7998 


7586 
8043 


7632 

8089 


7678 
8135 


46 
46 


977724 


951 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 


46 


952 


8637 


8683 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 


46 


953 


9093 


9138 


9184 


9230 


9275 


9321 


9366 


9412 


9457 


9503 


46 


954 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 


46 


955 


9S0003 


0049 


0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 


45 


956 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 45 


957 


0912 


0957 


1003 


1048 


1093 


1139 


1184 


1229 


1275 


1320 45 


958 


1366 


1411 


1450 


1501 


1547 


1592 


1637 


1683 


1728 


1773 45 


959 
960 


1819 


1864 
2316 


1909 
2362 


1954 

2407 


2000 
2452 


2045 
2497 


2090 
2543 


2135 

2588 


2181 
2633 


2226 45 
2678 45 


9S2271 


961 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 45 


962 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


358 1| 45 


963 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


.3942 


.3987 


4032 


45 


961 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4-182 


45 


965 


4527 


4572 


4617 


4062 


4707 


4752 


4797 


4842 


4887 


4932 


45 


966 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


.5830 


45 


968 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


0279| 45 


969 
970 


6324 
986772 


6369 

6817 


6413 
6861 


6458 


6503 
6951 


6548 
6996 


6593 


6637 

7085 


6682 
7130 


6727 45 
7175J 45 


6906 


7040 


971 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 45 


972 


7666 


7711 


7756 


78 00 


7845 


7890 


7934 


7979 


8024 


8068! 45 


973 


8113 


8157 


8202 


8247 


8291 


8336 


8381 


8425 


8470 


8514J 45 


974 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


89G0| 45 


975 


9005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 


1 45 


976 


9450 


9494 


9539 


9583 


9628 


9672 


9717 


9701 


9806 


9850 


44 


977 


9395 


9939 


9983 


..28 


..72 


.117 


.161 


.206 


.2.50 


.294 


U 


978 


990339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 


U 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1182 


44 


980 


991226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 


44 


981 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509[ U 


983 


2554 


2598 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 1 44 


984 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392' 44 


985 


3436 


3480 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


38331 44 


9S6 


3877 


3921 


3965 


4009 


4053 


4097 


4141 


4185 


4^29 


4273 44 


987 


4317 


4361 


4405 


4449 


4493 


4537 


4581 


4625 


4669 


4713 44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


51521 44 


989 
990 


5196 


5240 
5679 


5284 


5338 
5767 


5372 

.5811 


5416 

5854 


5460 

.5898 


5504 
5942 


5547 

5986 


6591 44 
6"!)30l 44 


995635 


5723 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6408' 44 
69061 44 


992 


6512 


6555 


6599 


6643 


0687 


6731 


6774 


6818 


6862 


993 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 


44 


^94 


7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 


44 


095 


7823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 


44 


996 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 


44 


997 


8695 


8739 


8782 


8826 


8869 


8913 


89.56 


9000 


9043 


9087 


44 


998 


9131 


9174 


9218 


92-81 


9305 


9348 


9392 


9435 


9479 


9522 


44 


999 


9565; J609 


96521 9996 


9739 


9783 


9826 


9870 


9913 


9957 


43 


In. 


1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 D. 1 



A TABLE 

OF 

LOGARITHMIC 
SINES AND TANGENTS 

FOR ETERT 

DEGREE AND MINUTE 

OF THE QUADRANT. 



N. B The minutes in the left-hand column of each pagC; 
increasing downwards, belong to the degrees at the top ; and 
those increasing upwards, in the right-hand column, belong ti 
the degrees below. 



18 


(0 Degree.) a table op logarithmic 




M. 


1 Sine 1 D. 


1 Cosine | D. 


1 Tang. 


1 D. 


1 Cotang. 1 ] 


"^ 


O.OUUOUO 




10.000000 




O.OOOOOOl 


liiiiiiue. 


60 


1 


6.463726 


501717 


000000 


00 


6.4637261501717 


13.. 5.36274 


59 


2 


764756 


293485 


000000 


00 


764756 


293483 


235244 


58 


3 


940847 


208231 


000000 


00 


940847 


208231 


059153 


57 


4 


7.065786 


161517 


000000 


00 


7.065786 


161517 


12.934214 


56 


5 


162696 


131968 


000000 


00 


162696 


131969 


837304 


55 


6 


241877 


111575 


9.999999 


01 


241878 


111578 


7.58122 


54 


7 


308824 


96653 


999999 


01 


308825 


996.53 


691175 


53 


8 


366816 


85254 


999999 


01 


366817 


85254 


633183 


52 


9 


417968 


76263 


999999 


01 


417970 


76263 


582030 


51 


10 
11 


463725 
7.505118 


68988 


999998 


01 
01 


463727 


68988 


536273 


50 
49 


62981 


9.999998 


7.505120 


62981 


12.494880 


12 


.542906 


57936 


999997 


01 


542909 


57933 


457091 


48 


13 


577668 


53041 


999997 


01 


577672 


53642 


422328 


47 


14 


609853 


49938 


999996 


01 


609857 


49939 


390143 


46 


15 


639816 


46714 


999996 


01 


639820 


46715 


360180 


45 


16 


667845 


43881 


999995 


01 


667849 


43882 


332151 


44 


17 


694173 


41372 


999995 


01 


694179 


41373 


305821 


43 


18 


718997 


39135 


999994 


01 


719003 


39136 


280997 


42 


19 


742477 


37127 


999993 


01 


742484 


37128 


257516 


41 


20 

21 


764754 
7.785943 


35315 


999993 


01 
01 


764761 


35136 


235239 
12.214049 


40 
39 


.33672 


9.999992 


7.785951 


33673 


22 


806146 


32175 


999991 


01 


806155 


32176 


193845 


38 


23 


825451 


30805 


999990 


01 


825460 


30806 


174540 


37 


24 


843934 


29547 


999989 


02 


843944 


29549 


156056 


36 


25 


861662 


28388 


999988 


02 


861674 


28390 


138326 


35 


26 


878695 


27317 


999988 


02 


878708 


27318 


121292 


34 


27 


895085 


26323 


999987 


02 


89.5099 


26325 


104901 


33 


28 


910879 


25399 


999986 


02 


910894 


25401 


089106 


32 


29 


926119 


24538 


999985 


02 


926134 


24540 


073866 


31 


30 
31 


940842 


23733 


999983 


02 
02 


940858 


23735 


059142 


30 
29 


7.955082 


22980 


9.999982 


7.955100 


22981 


12.044900 


32 


968870 


22273 


999981 


02 


968889 


22275 


031111 


28 


33 


982233 


21608 


999980 


02 


9822.53 


21610 


017747 


27 


34 


995198 


20981 


999979 


02 


995219 


2'I:jS3 


004781 


•26 


35 


8.007787 


203901 


999977 


02 


8.007809 


2:!:^J2 


11.992191 


25 


30 


020021 


19831 


999976 


02 


020045 


l;)s:^:3 


979955 


24 


37 


031919 


19302 


999975 


02 


031945 


19305 


968055 


23 


38 


043501 


18801 


999973 


02 


043527 


18803 


956473 


Of> 


39 


054781 


18325 


999972 


02 


054809 


18327 


945191 


21 


40 
41 


065776 


17872 


999971 


02 
02 


065806 
8.076.531 


17874 
17444 


9.34194 


20 
19 


8.076.500 


17441 


9.999969 


11.923469 


42 


086965 


17031 


999968 


02 


086997 


17034 


913003 


18 


43 


097183 


16639 


999966 


02 


097217 


16642 


902783 


17 


44 


107J67 


16265 


999964 


03 


107202 


16268 


892797 


16 


45 


116926 


15908 


999963 


03 


116963 


15910 


883037 


15 


46 


126471 


15566 


999961 


03 


126510 


15568 


873490 


14 


47 


135810 


15238 


9999.59 


03 


135851 


15241 


864149 


13 


48 


144953 


14924 


999958 


03 


144996 


14927 


85.5004 


12 


49 


153907 


14622 


9999.56 


03 


1.53952 


14627 


846048 


11 


oOJ 
51 


162681 
8.171280 


14333 


999954 


03 
03 


162727 


14336 


837273 
11 828672 


10 
9 


14054 


9.999952 


8.171328 


14057 


52 


179713 


13786 


9999,50 


03 


179763 


13790 


820237 


8 


53 


187985 


13529 


999948 


03 


188036 


13532 


811964 


- 


54 


196102 


13280 


999946 


03 


196156 


13284 


803844 


6 


55 


204070 


13041 


999944 


3 


204126 


13044 


795874 


5 


56 


211895 


12810 


999942 


4 


211953 


12814 


788047 


4 


57 


219581 


12587 


999940 


04 


219641 


12590 


780359 


3 


58 


227134 


12372 


9999.38 


04 


227195 


12376 


772805 


2 


59! 


234557 


12164 


999936 


04 


234621 


12168 


765379 


1 


60! 


241855 


11963 


999934 


04 


241921 


11967 


758079 





J. 


Cosine | 


Sine ! 1 


Cotang. 


.. 1 


Tang. i M. | 



8y Dogrees. 





SINES AND TANGENTS. (I Degree. J 




10 


M. 


Sine 


D. 


Cosine | D. 


Tang. 


D 


Cotnns. I 1 


~0^ 


8.241855 


11963 


9.999934 


04 


8.241921 


11967 


11.7580791 


60 


1 


249033 


11768 


999932 


04 


249102 


11772 


750898' 


59 


2 


256094 


11.^80 


999929 


04 


256165 


11584 


743835 


58 


3 


263042 


11398 


999927 


04 


263115 


11402 


736885 


57 


4 


269881 


11221 


999925 


04 


269956 


11225 


730044 


56 


5 


276614 


11050 


999922 


04 


276691 


11054 


723309 


55 


6 


283243 


10883 


999920 


04 


283323 


10887 


716677 


54 


7 


289773 


10721 


999918 


04 


289856 


10726 


710144 


53 


8 


296207 


10565 


999915 


04 


296292 


10570 


703708 


52 


9 


302546 


10413 


999913 


04 


302634 


10418 


697366 


51 


10 

11 


308794 
8.314954 


10266 


999910 
9.999907 


04 
04 


308884 


10270 


691116 


50 
49 


10122 


8.315046 


10126 


11.684954 


12 


321027 


9982 


999905 


04 


321122 


9987 


678878 


48 


13 


327016 


9847 


999902 


04 


327114 


9851 


672886 


47 


14 


332924 


9714 


999899 


05 


333025 


9719 


666975 


46 


15 


338753 


9586 


999897 


05 


338S56 


9590 


661 M4 


45 


16 


3^14504 


9460 


999894 


05 


344610 


9465 


655390 


44 


17 


350181 


9338 


999891 


05 


350289 


9343 


649711 


43 


18 


355783 


9219 


999888 


05 


3.55895 


9224 


644105 


42 


19 


361315 


9103 


999835 


05 


361430 


9108 


638570 


41 


20 
21 


366777 


8990 
8880 


999882 


05 
05 


366895 


8995 


633105 
11.627708 


40 
39 


8.372171 


9.999879 


8.372292 


8885 


22 


377499 


8772 


999876 


05 


377622 


8777 


622378 


38 


23 


382762 


8667 


999873 


05 


382889 


8672 


617111 


37 


24 


387962 


8564 


999870 


05 


388092 


8570 


611908 


36 


25 


393101 


8464 


999867 


05 


393234 


8470 


606766 


35 


26 


398179 


8366 


999864 


05 


398315 


8371 


601685 


34 


27 


403199 


8271 


999861 


05 


403338 


8276 


596662 


33 


28 


408161 


8177 


999858 


05 


408304 


8182 


591606 


32 


29 


413068 


8086 


999854 


05 


413213 


8091 


586787 


31 


30 
31 


417919 
8.422717 


7996 


999851 


06 
06 


418068 


8002 


581932 
11.577131 


30 
29 


7909 


9.999848 


8.422869 


7914 


32 


427462 


7823 


999844 


06 


427618 


7830 


572332 


28 


33 


432156 


7740 


999841 


06 


432315 


7745 


.5676sr) 


27 


34 


436800 


7657 


999838 


06 


436962 


7663 


563038 


26 


35 


441394 


7577 


999834 


06 


441560 


7583 


558410 


25 


36 


445941 


7499 


999831 


06 


446110 


7505 


553890 


24 


37 


450440 


7422 


999827 


06 


450613 


7428 


5493 87 


23 


38 


454893 


7346 


999823 


06 


455070 


7352 


544930 


22 


39 


459301 


7273 


999820 


06 


459481 


7279 


540519 


21 


40 
41 


463665 


7200 


999816 
9.999812 


06 
06 


463849 
8.468172 


7206 


536151 
11.531828 


20 
19 


8.467985 


7129 


7135 


42 


472263 


7060 


999809 


06 


472454 


7066 


527546 


18 


43 


476498 


6991 


999805 


06 


476693 


6998 


523307 


17 


44 


480693 


6924 


999801 


06 


480892 


6931 


519108 


16 


45 


484848 


6859 


999797 


07 


485050 


6865 


514950 


15 


46 


488963 


6794 


999793 


07 


489170 


6801 


510830 


14 


47 


493040 


6731 


999790 


07 


493250 


6738 


506750 


13 


48 


497078 


6669 


999788 


07 


497293 


6676 


502707 


12 


49 


501080 


6608 


999782 


07 


501298 


6615 


498702 


11 


50 


505045 


6548 


999778 


07 


505267 


6555 


494733 


10 


51 


8.508974 


6489 


9.999774 


07 


8.509200 


6496 


11.490800 


9 


52 


512867 


6431 


999769 


07 


513098 


6439 


486902 


8 


53 


516726 


6375 


999765 


07 


516961 


6382 


483039 


7 


54 


520551 


6319 


999761 


07 


520790 


6326 


479210 


6 


55 


524343 


6264 


999757 


07 


524586 


6272 


475414 


5 


56 


528102 


6211 


999753 


07 


528349 


6218 


471651 


4 


57 


531828 


6158 


999748 


07 


532080 


6165 


467920 


3 


58 


535523 


6106 


999744 


07 


535779 


6113 


464221 


2 


59 


5.39186 


6055 


999740 


07 


539447 


6062 


460553 


I 


60 


.542819 


6004 


999735 


07 


543084 


6012 


456916 





Zi 


Cosine 




1 Sine 1 


Cotang. 


1 


Tan? |M. 1 



88 Degrees. 



20 


(2 Degrees.) a 


TABLE OF LOGARITHMIC 




"m" 


1 Sine 


D. 


»;osiiie 1 D. 


1 T;in?. 


1 D. 


Oiiansr. | 1 


^ 


8.M2819 


6004 


9.999735 


07 


8.543084 


6012 


ll 1.456916 


00 


1 


546422 


5955 


999731 


07 


546691 


5962 


453309 


59 


2 


549995 


5906 


999726 


07 


550268 


5914 


449732 


58 


3 


553539 


5858 


999722 


08 


553817 


6866 


446183 


57 


4 


557054 


5811 


999717 


08 


657336 


6819 


442664 


66 


5 


560540 


5765 


999713 


08 


560828 


5773 


439172 


65 


6 


563999 


5719 


999708 


08 


564291 


5727 


435709 


54 


7 


567431 


5674 


999704 


08 


567727 


6682 


432273 


53 


8 


570836 


5630 


999699 


08 


671137 


66.38 


428863 


62 


9 


574214 


5587 


999694 


08 


574520 


5595 


426480 


51 


10 
11 


577566 
8.580892 


5544 


999689 


08 
08 


577877 


6552 


422123 


50 
49 


5502 


9.999685 


8.581208 


6510 


11.418792 


12 


584193 


5460 


999680 


08 


584514 


5468 


416486 


48 


13 


587469 


5419 


999675 


08 


587795 


6427 


412205 


47 


14 


590721 


5379 


999670 


08 


591051 


6387 


408949 


46 


15 


593948 


5339 


999665 


08 


594283 


6347 


405717 


46 


16 


597152 


5300 


999660 


08 


697492 


6308 


402508 


44 


17 


600332 


5261 


999655 


08 


600677 


5270 


399323 


43 


18 


603489 


5223 


999650 


08 


603839 


5232 


396161 


42 


19 


606623 


5186 


999645 


09 


606978 


5194 


393022 


41 


20 

21 


609734 
8.612823 


5149 


999640 
9.999035 


09 
09 


610094 
8.613189 


5158 


389906 


40 
39 


5112 


5121 


11.386811 


22 


615891 


5076 


999629 


09 


616262 


5085 


383738 


38 


23 


618937 


5041 


999624 


09 


619313 


5050 


380687 


37 


24 


621962 


5006 


999619 


09 


622343 


5016 


377657 


36 


25 


624965 


4972 


999G14 


09 


625352 


4981 


374648 


36 


26 


627948 


4938 


999608 


09 


628340 


4947 


371660 


34 


27 


630911 


4904 


999603 


09 


631308 


4913 


368692 


33 


28 


633854 


4871 


999597 


09 


634256 


4880 


365744 


32 


29 


636776 


4839 


999592 


09 


637184 


4848 


362816 


31 


30 
31 


639080 
8.642563 


4806 


999586 


09 

09 


640093 


4816 


359907 
11.357018 


30 

29 


4775 


9.999581 


8.642982 


4784 


32 


645428 


4743 


999575 


09 


645853 


4753 


354147 


28 


33 


648274 


4712 


999570 


09 


648704 


4722 


351290 


27 


34 


601102 


4682 


999564 


09 


6515.37 


4691 


348463 


26 


35 


653911 


4652 


999558 


10 


654352 


4661 


345648 


25 


36 


656702 


4622 


999553 


10 


657149 


4631 


34285] 


24 


37 


659475 


4592 


999547 


10 


659928 


4602 


340072 


23 


38 


662230 


4563 


999541 


10 


662689 


4573 


337311 


22 


39 


664968 


4535 


999535 


10 


665433 


4544 


334567 


21 


40 


667689 


4506 


999529 


10 


668160 


4626 


331840 


20 


41 


8.670393 


4479 


9.999524 


10 


a. 670870 


4488 


11.329130 


19 


42 


673080 


4451 


999518 


10 


673563 


4461 


326437 


18 


43 


675751 


4424 


999512 


10 


676239 


4434 


323761 


17 


44 


678405 


4397 


999506 


10 


678900 


4417 


321100 


16 


45 


681043 


4370 


999500 


10 


681544 


4380 


318456 


15 


46 


683665 


4344 


9>99493 


10 


684172 


4354 


315828 


14 


47 


686272 


4318 


999487 


10 


686784 


4328 


313216 


13 


48 


688863 


4292 


999481 


10 


689381 


4303 


310619 


12 


49 


691438 


4267 


999475 


10 


691963 


4277 


308037 


11 


50 
51 


693998 
8.696543 


4242 


999469 
9.999463 


10 
11 


694529 
8.697081 


4252 


305471 


10 
9 


4217 


4228 


11.302919 


52 


699073 


4192 


999456 


11 


699617 


4203 


300383 


8 


63 


701589 


4168 


999450 


11 


702139 


4179 


297861 


7 


54 


704090 


4144 


999443 


11 


704646 


4156 


295354 


6 


55 


706577 


4121 


999437 


11 


707140 


4132 


292860 


5 


56 


709049 


4097 


999431 


11 


709618 


4108 


290382 


4 


57 


711507 


4074 


999424 


11 


712083 


4085 


287917 


3 


58 


713952 


4051 


999418 


11 


714534 


4062 


285465 


2 


59 


716383 


4029 


999411 


11 


716972 


4040 


283028 


1 


60 


718800 


4006 


999404 


11 


719396 


4017 


280ri04 





n 


(Josiiie *^ 


1 


Sme 1 


CotaiiL'. 1 


1 


Tang. |M. | 



87 Degrees 





SINES A]:^D TANGENTS. ^^3 Degrees.^ 




21 


JI. 


.^ine 1 D. 1 


Cosine | D. | 


Tane. 1 


D. 1 CoiaML'. 1 •' 


~o 


8.718800 


4006 


9.999404 


11 


8.719396 


4017 


11.2806041 60 




721204 


3984 


999398 


11 


721806 


3995 


278194 59 


2 


723595 


3962 


999391 


11 


724204 


3974 


275796, 


58 


3 


725972 


3941 


999384 


11 


726588 


3952 


273412 


.57 


4 


72S337 


3919 


999373 


11 


728959 


3930 


271041 


56 


5 


730688 


3898 


999371 


11 


731317 


3909 


268683 


55 


6 


733027 


3877 


999364 


12 


733663 


38S9 


266337 


54 


7 


735354 


3857 


999357 


12 


735996 


3868 


264004 


53 


8 


737667 


3836 


999350 


12 


738317 


3848 


261683 


52 


9 


739969 


3816 


999343 


12 


740626 


3827 


259374 


51 


10 
11 


742259 
8 . 744536 


3796 


999336 
9.999329 


12 
12 


742922 


3807 

3787 


257078 


50 
49 


3776 


8.745207 


11.254793 


12 


746802 


3756 


999322 


12 


747479 


3768 


2.52521 


48 


13 


749055 


3737 


999315 


12 


749740 


3749 


250260 


47 


14 


751297 


3717 


999308 


12 


751989 


3729 


248011 


40 


15 


7.53528 


3698 


999301 


12 


754227 


3710 


245773 


45 


16 


755747 


3679 


999294 


12 


756453 


3692 


243547 


44 


17 


757955 


3661 


999286 


12 


758668 


3673 


241332 


43 


18 


760151 


3642 


999279 


12 


760872 


3655 


239128 


42 


19 


762337 


3624 


999272 


12 


763065 


3636 


236935 


41 


20 
21 


764511 
8.766675 


3606 


999265 
9.999257 


12 
12 


765246 


3618 


234754 


40 
39 


3588 


8.767417 


3600 


11.232583 


22 


768828 


3570 


999250 


13 


769578 


3583 


230422 


38 


,,«> 


770970 


3553 


999242 


13 


771727 


3565 


228273 


37 


-<,4: 


773101 


3535 


999235 


13 


773866 


3548 


2261.34 


36 


2^ 


775223 


3518 


999227 


13 


77.5995 


3531 


224005 


35 


/O 


777333 


3501 


999220 


13 


778114 


3514 


221886 


34 


27 


779434 


3484 


999212 


13 


780222 


3497 


219778 


33 


28 


781524 


3467 


999205 


13 


782320 


3480 


217680 


32 


29 


783605 


3451 


999197 


13 


784408 


3464 


215592 


31 


30 
31 


785675 


3431 
3418 


999189 
9.999181 


13 
13 


786486 

8.788554 


3447 


213514 


30 

29 


8.787736 


3431 


11.211446 


32 


789787 


3402 


999174 


13 


790613 


3414 


209387 


28 


33 


791828 


3386 


999166 


13 


792662 


3399 


207338 


27 


34 


793859 


3370 


999 L5S 


13 


794701 


.3383 


205299 


26 


35 


795881 


3354 


999150 


13 


796731 


3368 


203269 


25 


36 


797894 


3339 


999142 


13 


798752 


3352 


201248 


24 


37 


■7[)9897 


3323 


999134 


13 


S00763 


3337 


199237 


23 


38 


S01S92 


3308 


999126 


13 


802765 


3322 


197235 


22 


39 


803876 


3293 


999118 


13 


804758 


3307 


195242 


21 


40 
41 


805852 
8.807819 


3278 


999110 


13 
13 


806742 
8.808717 


3292 
3278 


193258 


20 
19 


3263 


9.999102 


11.191283 


42 


809777 


3249 


999094 


14 


810683 


3262 


189317 


18 


43 


811726 


3234 


999086 


14 


812641 


3248 


187359 


17 


44 


81 3667 


3219 


999077 


14 


814589 


3233 


185411 


16 


45 


815599 


3205 


999069 


14 


816529 


3219 


183471 


15 


46 


817522 


3191 


999061 


14 


818461 


3205 


181539 


14 


47 


819436 


3177 


999053 


14 


820384 


3191 


179616 


13 


48 


821343 


3163 


999044 


14 


822298 


3177 


177702 


12 


49 


823240 


3149 


999036 


14 


824205 


3163 


175795 


11 


50 
51 


825130 
8.827011 


3135 


999027 
9.999019 


14 


826103 


3150 
3136 


173897 


10 
9 


3122 


14 


8.827992 


1 1.172008 


52 


828884 


3108 


999010 


14 


829374 


3123 


170126 


8 


53 


830749 


3095 


999002 


14 


831748 


3110 


168252 


7 


54 


832607 


3082 


998993 


14 


833613 


3096 


166387 


6 


55 


834456 


3069 


998984 


14 


835471 


3083 


1 64529 


5 


56 


836297 


3056 


998976 


14 


837321 


3070 


162679 


4 


57 


838130 


1 3043 


998967 


15 


839163 


3057 


160837 


3 


58 


839956 


3030 


998958 


15 


840998 


3045 


159002 


2 


59 


841774 


3017 


998950 


15 


842825 


3032 


1W175 


1 


60 


843585 


3000 


998941 


15 


844644 


3019 


155356 







Cmuti 1 


Sine j 


Cotang. 




Ta.)8. ( M. 1 



86 liPKrees 

14 



22 


r 


4 Degrees.) a 


TABLE OF LOGARITUMIC 




"m" 


Sine 


1 D. 


Cosine | D. 


Tang. 1 


D 1 


Cotang. \ \ 





8.843585 


3005 


9.998941 


15 


8.844644 


3019 


11.155356 


■60~ 


I 


845387 


2992 


998932 


15 


846455 


3007 


153545 


50 


2 


847183 


2980 


998923 


15 


848260 


2905 


161740 


58 


3 


848971 


2967 


998914 


15 


850057 


2982 


149943 


57 


4 


85075 1 


2955 


998905 


15 


851846 


2970 


1481.54 


56 


5 


852525 


2943 


998896 


15 


853628 


2958 


146372 


55 


n 


854291 


2931 


998887 


15 


855403 


2946 


144597 


54 


7 


856049 


2919 


998878 


15 


857171 


2935 


142829 


53 


8 


857801 


2907 


998809 


15 


8.58932 


2923 


141068 


52 


9 


859546 


2896 


998860 


15 


860686 


2911 


139314 


51 


10 
11 


86 1283 
8.863014 


288 i 


998851 


15 


862433 


2900 

2888 


137567 
11.135827 


50 
49 


2878 


9.998841 


15 


8.864173 


12 


86473S 


2861 


998832 


15 


865906 


2877 


134094 


48 


13 


866455 


2850 


998823 


16 


867632 


2866 


132368 


47 


14 


868165 


2839 


998813 


16 


869351 


2854 


] 30649 


46 


15 


S69868 


2828 


998804 


16 


871064 


2843 


12893G 


45 


Ifi 


871565 


2817 


998795 


16 


872770 


2832 


127230 


44 


17 


873255 


2806 


998785 


16 


874469 


2821 


125531 


43 


18 


874938 


2795 


998776 


16 


876162 


2811 


123838 


42 


19 


876615 


2786 


998766 


16 


877849 


2800 


1221 ->1 


41 


20 
21 


878285 


2773 


998757 
9.998747 


16 
16 


879529 


2789 


120471 


40 
39 


8.879949 


2763 


8.881202 


2779 


11.118798 


22 


881607 


2752 


998738 


16 


882869 


2768 


117131 


38 


23 


883258 


2742 


998728 


16 


884530 


2758 


115470 


37 


24 


884903 


2731 


998718 


16 


886185 


2747 


113815 


36 


25 


886542 


2721 


998708 


16 


887833 


2737 


112167 


35 


26 


388174 


2711 


998699 


16 


889476 


2727 


110.524 


34 


27 j 


889801 


2700 


998689 


16 


891112 


2717 


108888 


33 


28 i 


891421 


2690 


998679 


16 


892742 


2707 


107258 


32 


29 


S93035 


2680 


998669 


17 


894366 


2097 


105634 


31 


30 
31 


894643 


2670 
2660 


998659 


17 

17 


895984 


2687 


104016 


30 
29 


8.896246 


9.998649 


8.897590 


2677 


11.103404 


32 


897842 


2651 


99S639 


17 


899203 


2667 


100797 


28 


33 


899432 


2641 


998629 


17 


900803 


2658 


099197 


27 


34 


901017 


2631 


998619 


17 


902398 


2648 


097602 


26 


35 


902596 


2622 


998609 


17 


903987 


2638 


096013 


25 


36 


904169 


2612 


998599 


17 


90.5570 


2629 


094430 


24 


37 


905730 


2603 


998.589 


17 


907147 


2620 


092853 


23 


38 


907297 


2593 


998578 


17 


908719 


2610 


091281 


22 


39 


908853 


2584 


998568 


17 


910285 


2601 


089715 


21 


40 

41 


910404 


2575 


998558 
9.998.548 


17 
17 


911846 


2592 


088154 


20 
19 


8.911949 


2566 


8.913401 


2583 


11.086.599 


42 


913488 


255G 


998.537 


17 


914951 


2574 


C85049 


18 


43 


9150--i2 


2547 


998527 


17 


916495 


2565 


083505 


17 


44 


916.550 


2538 


998516 


18 


918034 


2556 


081966 


16 


45 


918073 


2529 


998506 


18 


919568 


2547 


080432 


15 


46 


919591 


2520 


998495 


18 


921096 


2538 


078904 


14 


47 


921103 


2512 


998485 


18 


922619 


2530 


077381 


13 


48 


922610 
924112 


2503 


998474 


18 


924136 


2.521 


075S64 


12 


49 


2494 


998464 


18 


925649 


2512 


074351 


11 


50 
51 


925609 
8.927100 


2486 
i 2477 


998453 
9.998442 


18 
18 


927156 


2503 


072844 


10 
9 


8.928658 


2495 


11.071342 


62 


N 928587 


1 2469 


998431 


18 


930155 


2486 


069845 


8 


53 


93006S 


; 2460 


998421 


18 


931647 


2478 


068353 


7 


54 


931544 


: 2452 


998410 


18 


933134 


2470 


066866 


6 


55 


933015 


2443 


998399 


18 


934616 


2461 


065384 


5 


56 


934481 


2435 


998388 


18 


936093 


2453 


063907 


4 


57 


935942 


2427 


998377 


18 


937565 


2445 


062435 


3 


58 


937398 


2419 


998366 


18 


939032 


2437 


060968 


2 


59 


938850 


2411 


998355 


18 


940494 


2430 


059506 


1 


60 


940296 


1 2403 


998344 


18 


941952 


2421 


058048 


_o^ 




Cosine 


1 


1 ^'"^ 1 


1 Cotang. 




1 Tang. 1 M. 1 



S.5 D'-tsroes 







SINES AND TANGEN-bs. (5 Degrees. 


) 


23 


M 


1 Sine 1 D. 


1 Cosine | D. 


i Tang. 


1 D. 


\ Cotii.ia. j 1 


"o" 


8 . 940296 


24 J3 


9.998344 


19 


8.941952 


2421 


11.058048 


60 


1 


94173S 


2394 


998333 


19 


943401 


2413 


056596 


69 


2 


943174 


2387 


998322 


19 


944852 


2405 


055148 


58 


3 


944606 


2379 


998311 


19 


946295 


2397 


053705 


57 


4 


946034 


2371 


998300 


19 


947734 


2390 


052266 


56 


fi 


947456 


2363 


998289 


19 


949168 


2382 


0.50832 


55 


r. 


948874 


2355 


998277 


19 


950597 


2374 


049403 


54 


V 


950287 


2348 


998260 


19 


952021 


2366 


047979 


53 


^ 


951696 


2340 


998255 


19 


953441 


2360 


046559 


52 


c 


953100 


2332 


998243 


19 


954856 


2.351 


045144 


51 


10 
ll" 


954499 
8.955894 


2325 


998232 
9.998220 


19 
19 


956267 
8.957674 


2344 


043733 


50 
49 


2317 


2337 


11.042326 


12 


957284 


2310 


998209 


19 


959075 


2329 


040925 


48 


k; 


958670 


2302 


998197 


19 


960473 


2323 


039527 


47 


14 


960052 


2295 


998186 


19 


961866 


2314 


038134 


46 


15 


961429 


2288 


998174 


19 


963255 


2307 


036745 


45 


16 


962801 


2280 


998163 


19 


964639 


2300 


035361 


44 


17 


964170 


2273 


998151 


19 


966019 


2293 


033981 


43 


18 


965534 


2266 


998139 


20 


967394 


2286 


032606 


42 


10 


966893 


2259 


998128 


20 


968766 


2279 


031234 


41 


20 

21 


968249 


2252 


998116 
9.998104 


20 

20 


970133 


2271 


029867 


40 
39 


8.969600 


2244 


8.971496 


2265 


11.028504 


22 


970947 


2238 


998092 


20 


972855 


2257 


027145 


38 


23 


972289 


2231 


998080 


20 


974209 


2251 


025791 


37 


24 


973628 


2224 


998068 


20 


975560 


2244 


024440 


36 


25 


974962 


2217 


998056 


20 


976906 


2237 


023094 


35 


26 


976293 


2210 


998044 


20 


978248 


2230 


021752 


34 


27 


977819 


2203 


993032 


20 


979586 


2223 


020414 


33 


28 


978941 


2197 


998020 


20 


980921 


2217 


019079 


32 


29 


930259 


2190 


998008 


20 


982251 


2210 


017749 


31 


30 
31 


98 1573 
8 . 982883 


2183 


997996 
9.997984 


20 
20 


983577 


2204 


016423 


30 
29 


2177 


8.984899 


2197 


11.015101 


32 


984189 


2170 


997972 


20 


986217 


2191 


013783 


28 


33 


985491 


2163 


997959 


20 


987532 


2184 


012468 


27 


J 34 


986789 


21.57 


997947 


20 


988842 


2178 


0111.58 


26 


35 


988083 


2150 


997935 


21 


990149 


2171 


009851 


25 


3ri 


989374 


2144 


997922 


21 


991451 


2165 


008549 


24 


37 


990660 


21.38 


997910 


21 


992750 


21.58 


007250 


23 


33 


991943 


2131 


997897 


21 


994045 


2152 


005955 


22 


»39 


993222 


2125 


997885 


21 


995337 


2146 


004663 


21 


40 
41 


934497 

8.995768 


2119 


997872 


21 
21 


996024 


2140 


003376 


20 
19 


2112 


9.997860 


8.997908 


2134 


11.002092 


42 


997036 


2106 


997847 


21 


999188 


2127 


000812 


18 


43 

44 


998299 


2100 


997835 


21 


9.000465 


2121 


10.999535 


17 


999560 


2094 


997822 


21 


001738 


2115 


998262 


16 


45 


9.000816 


2087 


997809 


21 


003007 


2109 


996993 


15 


46 


002069 


2082 


997797 


21 


004272 


2103 


995728 


14 


47 


003318 


2078 


997784 21 i 


005534 


2097 


994466 


13 


48 


004563 


2070 


9977711 


21 


006792 


2091 


993208 


12 


49 


005805 


2064 


997758 


21 


008047 


2085 


9919.53 


11 


50 

51 


007044 
9.008278 


2053 


997745I 


21 

21 


009298 
9.010546 


2080 


990702 


10 
9 


2052 


9.997732 


2074 


10.989454J 


52 


0095101 


2046 


997719 


21 


011790 


2068 


9882101 


8 


53 


010737 


2040 


997706 


21 


013031 


2062 


986969; 


7 


54 


0119621 


2034 


997693' 22 ' 


014268 


2056 


985732 


6 


55 


013182! 


2029 


997680| 22 


015502 


2051 


934498' 


5 


56 


0144001 


2023 


997667| 22 


016732 


2045 


983268 


^ 


57 


015613! 


2017 


997654! 22 


017959 


2040 


982041 


3 


58 


016824 


2012 


997641 i 22 


019183 


2033 


980817 


2 


59 


018031 


2006 


997628; 22 


020403 


2028 


979597! 


1 


no 


019235 


2000 


997614 til 


021620 


2023 


9783801 





_i 


Cisine 1 1 


Sine 1 1 


Cotang. 


1 


Tang. jM | 



b4Uegrees. 



24 



[6 DeL^rcos.) a table of logarithmic 



il 


Sine 


D. 


Cosine ! L). 


Tang. 1 


D. 


Cotang. 1 1 


"o" 


9.019235 


2000 


9.997614 


22 


9.021620 


2023 


10.978.380 


60 


1 


0204;35 


1995 


997601 


22 1 


022834 


2017 


977166 


59 


2 


021632 


1989 


997588 


22 1 


024044 


2011 


975956 


58 


3 


022825 


1984 


997574 


22 


025251 


2006 


974749 


57 
56 


4 


024016 


1978 


997561 


22 


026455 


2000 


973545 


r-i 


025203 


1973 


997547 


22 


027655 


1995 


972345 


55 ! 


f) 


026386 


1967 


9975.34 


23 


028852 


1990 


971148 


54 • 


7 


027567 


1962 


997520 


23 


030046 


1985 


9699.54 


53 ) 


8 


028744 


1957 


997507 


23 


():^i2'i'- 


1979 


968763 


52 


y 


029918 


1951 


997493 


23 


032425 


1974 


967575 


51 


10 


OSrjHb 
M.v'i'^x57 


1947 
194] 


9<74S0 
0.997466 


n 


033609 
9.034791 


1959 


966391 
10.965209 


50 
49 


ill 


1964 


|12 


033421 


1936 


997452 


^3 


035969 


1958 


964031 


48 


-^ 


034582 


1930 


997439 


23 


0.37144 


1953 


962856 


47 


14 


035741 


1925 


997425 


23 


038316 


1948 


961684 


46 


15 


036896 


1920 


997411 


23 ; 


039485 


1943 


960515 


45 


16 


038048 


1915 


997397 


23 


040651 


1938 


959349 


44 


17 


039197 


1910 


997383 


23 


041813 


1933 


958187 


43 


18 


040342 


1905 


997369 


23 


042973 


1928 


957027 


42 


19 


041485 


1899 


997355 


23 


044130 


1923 


955870 


41 


20 


042625 


1894 


997341 


23 


045284 


1918 


9o47l6 


40 


21 


9.043762 


.389 


9.997327 


24 


9.046434 


1913 


10.953566 


39 


22 


044895 


1884 


997313 


24 


047582 


1908 


952418 


38 


23 


046026 


1879 


997299 


24 


048727 


1903 


951273 


37 


24 


047154 


1875 


997285 


24 


049869 


1898 


950131 


36 


25 


048279 


1870 


997271 


24 


051008 


1893 


948992 


35 


26 


049400 


1865 


997257 


24 


052144 


1889 


947856 


34 


27 


050519 


1860 


997242 


24 


053277 


1884 


946723 


3:1 


28 


051635 


1855 


997228 


24 


054407 


1879 


945593 


:v^ 


29 


052749 


1850 


997214 


24 


055535 


1874 


944465 


31 


30 
31 


053859 


1845 


997199 
9.997185 


24 
24 


056659 
9.0.57781 


1870 


943341 


30 
29 


054966 


1841 


1865 


10.942219 


32 


056071 


1836 


997170 


24 


058900 


1869 


941100 


28 


33 


057172 


1831 


997156 


24 


060016 


1855 


939984 


27 


34 


058271 


1827 


997141 


24 


061130 


1851 


938870 


26 


35 


059367 


1822 


997127 


24 


062240 


1846 


937760 


25 


36 


060460 


1817 


997112 


24 


063348 


1842 


936652 


24 


37 


061551 


1813 


997098 


24 


064453 


1837 


935547 


23 


38 


062639 


1808 


997083 


25 


065556 


1833 


934444 


22 


39 


063724 


1804 


997068 


25 


066655 


1828 


933345 


21 


40 
41 


064806 
9.065885 


1799 


997053 


25 
25 


067752 


1824 


932248 


20 
19 


1794 


9.997039 


9.068846 


1819 


10.931154 


42 


066962 


1790 


997024 


25 


069938 


1815 


930062 


18 


43 


068036 


1786 


997009 


25 


071027 


1810 


928973 


17 


44 


069107 


1781 


996994 


25 


072il3 


1806 


927887 


16 


45 


070176 


1777 


996979 


25 


073197 


1802 


926803 


15 


46 


071242 


1772 


996964 


25 


074278 


1797 


925722 


14 


47 


072306 


1768 


996949 


25 


075356 


1793 


924644 


13 


48 


073366 


1763 


996934 


25 


076432 


1789 


923568 


12 


49 


074424 


1759 


996919 


25 


077505 


1784 


922495 


11 


50 
51 


075480 
9.076533 


1755 


996904 


25 
25 


078576 


1780 


921424 


10 
9 


1750 


9.996889 


9.079644 


1776 


10.920356 


52 


077583 


1746 


996874 


25 


080710 


1772 


919290 


8 


53 


078031 


1742 


996858 


25 


081773 


1767 


918227 


7 


54 


079676 


1738 


996843 


25 


082833 


1763 


917167 


6 


65 


080719 


1733 


996828 


25 


083891 


1759 


916109 


5 


56 


081759 


1729 


996812 


26 


084947 


1755 


915053 


4 


57 


08279/ 


1725 


996797 


26 


086000 


1751 


914000 


3 


58 


083832 


1721 


996782 


26 


087050 


1747 


912950 


2 


69 


084864 


1717 


996766 


26 


088098 


1743 


911902 


1 


60 


085894 


1713 


996751 


26 


089144 


1738 


9108.56 





_J 


Cosine 1 




Sine 1 


Cotaiii.'. 




Tang 1 M. | 





SINES AND TANGENTS 


. (7 Degree;;.) 




25 


nn 


Sine 1 


n. 1 


Cosine | D. | 


Tang. 1 


D. 1 


Cotang. j j 





9.085894 


1713 


9.9967511 


26 


9.089144 


1738 


10.910850 


-60 


1 


086922 


1709 


9967351 


26 


090187 


1734 


909813 


59 


2 


087947 


1704 


996720 


26 


091228 


1730 


908772 


58 


3 


088970 


1700 


996704 


26 


092266 


1727 


907734 


57 


4 


089990 


1696 


996688 


26 


093302 


1722 


906698 


56 


5 


091008 


1692 


996673 


26 


094336 


1719 


905664 


bt 


6 


092024 


1688 


996657 


26 


095367 


1715 


904633 


54 


7 


093037 


1684 


996641 


26 


096395 


1711 


9036051 


53 


8 


094047 


1680 


9966251 


26 


097422 


1707 


902578 


52 


9 


095056 


1676 1 


996610 


26 


098446 


1703 


901554 


51 


10 
ll 


096062 
9.097065 


167.*^ 1 
1668 


996594 
9.996578 


26 

27 


099468 
9.100487 


1699 


900532 
10.899513 


50 
49 


1695 


J2 


098066 


1665 


9965C2 


27 


101504 


1691 


898496 


48 


13 


099065 


1661 


996546 


27 


102519 


1687 


897481 


47 


14 


100062 


1657 


996530 


27 


103532 


1684 


896468 


46 


-5 


101056 


1653 


996514 


27 


104542 


1680 


895458 


45 


16 


102048 


1649 


996498 


27 


105550 


1676 


894450 


44 


17 


103037 


1645 


996482 


27 


106556 


1672 


893444 


43 


18 


104025 


1641 


996465 


27 


107559 


1669 


892441 


42 


19 


105010 


1638 


996449 


27 


108560 


1665 


891440 


41 


20 

21 


105992 


1634 
1630 


996433 


27 
27 


109559 


1661 

1658 


890441 


40 
39 


9.106973 


9.996417 


9.110556 


10.889444 


22 


107951 


1627 


996400 


27 


111551 


1654 


888449 


38 


23 


108927 


1623 


996384 


27 


112543 


1650 


887457 


37 


24 


109901 


1619 


996368 


27 


113533 


1646 


886467 


36 


25 


110873 


1616 


996351 


27 


114521 


1643 


885479 


35 


26 


111842 


1612 


996335 


27 


115507 


1639 


884493 


34 


27 


112809 


1608 


996318 


27 


116491 


1636 


883509 


33 


28 


113774 


1605 


996302 


28 


117472 


1632 


882528 


32 


29 


114737 


1601 


996285 


28 


118452 


1629 


881548 


31 


30 
31 


11.5698 


1597 
1594 


996269 
9.996252 


28 
28 


119429 


1625 
1622 


880571 


30 

29 


9.116656 


9.120404 


10.879596 


32 


117613 


1.590 


996235 


28 


121377 


1618 


878623 


28 


33 


118567 


1587 


996219 


28 


122348 


1615 


877652 


27 


34 


119519 


1583 


996202 


28 


123317 


1611 


876683 


26 


35 


120469 


1.580 


996185 


28 


124284 


1607 


875716 


25 


36 


121417 


1.576 


996168 


28 


125249 


1604 


874751 


24 


37 


122362 


1573 


996151 


28 


126211 


1601 


873789 


23 


38 


123306 


1569 


996134 


28 


127172 


1597 


872828 


22 


39 


124248 


1566 


996117 


28 


128130 


1594 


871870 


21 


40 
41 


125187 


1562 


996100 


28 
29 


129087 
9.130041 


1591 
1587 


870913 
10.869959 


20 
19 


9.126125 


1559 


9.996083 


42 


127060 


1556 


996066 


29 


130994 


1584 


869006 


18 


43 


127993 


1552 


996049 


29 


131944 


1581 


868056 


17 


44 


128925 


1549 


996032 


29 


132893 


1577 


867107 


16 


45 


129854 


1545 


996015 


29 


133839 


1574 


866161 


15 


46 


130781 


1542 


995998 


29 


134784 


1571 


8r,5216 


14 


47 


131706 


1539 


995980 


29 


135726 


1.567 


864274 


13 


48 


132630 


1535 


995963 


29 


136667 


1564 


863333 


12 


49 


133551 


1532 


995946 


29 


137605 


1561 


862395 


11 


50 
51 


134470 
9.135387 


1529 
1525 


995928 


29 
29 


138542 


1558 
1555 


861458 


10 


9.995911 


9.139476 


10.860524 


9 


52 


136303 


1522 


995894 


29 


140409 


1551 


859591 


8 


53 


137216 


1519 


995876 


29 


141340 


1548 


858060 


7 


54 


138128 


1516 


995859 


29 


142269 


1545 


857731 


6 


55 


139037 


1512 


995841 


29 


143196 


1542 


856804 


5 


56 


139944 


1509 


995823 


29 


144121 


1539 


85.5879 


4 


57 


140850 


1506 


995806 


29 


145044 


1 1535 


854956 


3 


58 


141754 


1503 


995788 


29 


145966 


' 1532 


854034 


2 


59 


142655 


1 1500 


995771 


29 


146885 


I 1529 


853115 


1 


60 


143555 


1 1496 


995753 


29 


147803 


' 1.526 


852197 






I Cosine j 



j Cotang. 



Tang. 



82 Degrees. 



2(^ 


(6 


Degrees.; a • 


rABLE OF LOi 


>AR1TJ! 


MIC 




M. 


1 Sine 


1 D. 


Cosine | D. 


Tai,^. 


D. 


Col^hi:. 1 


^ 


I 9.143555 


1496 


9.995753 


30 


9.147803 


1526 


10. 8521971 60 


1 


1 144453 


1493 


995735 


30 


148718 


1523 


851282 59 


9 


145349 


1490 


995717 


30 


149632 


1520 


850368 58 


3 


146243 


1487 


995699 


30 


1.50544 


1517 


849456 


57 


4 


147136 


1484 


995681 


30 


151454 


1514 


848546 


56 


5 


148026 


1481 


995664 


30 


152363 


1511 


847637 


55 


C 


, 148915 


1478 


995646 


30 


153269 


1508 


846731 


54 


7 


149802 


1475 


995628 


30 


154174 


1505 


845826 


53 


8 


150686 


1472 


995610 


30 


1. 55077 


1502 


844923 


52 


9 


151569 


1469 


995591 


30 


155978 


1499 


844022 


21 


10 


152451 


1466 


995573 


30 


156877 


1496 


843123 


50 


11 


9 153330 


1463 


9.9955.55 


30 


9.157775 


1493 


10.842225 


49 


12 


154208 


1460 


995.537 


30 


158671 


1490 


841329 


48 


13 


155083 


1457 


995519 


30 


159565 


1487 


840435 


47 


14 


155957 


1454 


995501 


31 


160457 


1484 


839543 


46 


15 


156830 


1451 


995482 


31 


161347 


1481 


838653 


45 


16 


157700 


1448 


995464 


31 


162236 


1479 


837764 


44 


17 


158569 


1445 


99.5446 


31 


163123 


1476 


836877 


43 


18 


159435 


1442 


995427 


31 


164008 


1473 


835992 


42 


19 


160301 


1439 


99.5409 


31 


164892 


1470 


835108 


41 


20 

21 


161164 
9.162025 


1436 
1433 


995390 


31 
31 


165774 
9.166654 


1467 


834226 


40 
39 


9.995372 


1464 


10.833346 


22 


162885 


1430 


• 995353 


31 


167532 


1461 


832468 


38 


23 


163743 


1427 


99.5334 


31 


168409 


1458 


831591 


37 


24 


164600 


1424 


995316 


31 


1692S4 


1455 


830716 


36 


25 


165454 


1422 


99.5297 


31 


170157 


1453 


829843 


35 


26 


166307 


1419 


995278 


31 


171029 


1450 


828971 


34 


27 


167159 


1416 


995260 


31 


171899 


1447 


828101 


33 


28 


168008 


1413 


995241 


32 


172767 


1444 


S27233 


32 


29 


168856 


1410 


995222 


32 


173634 


1442 


826306 


31 


30 


169702 


1407 


995203 


32 


174499 


i439 


825501 


30 


31 


9.170547 


1405 


9.995184 


32 


9.175362 


1436 


10.824638 


29 


32 


171389 


1402 


995165 


32 


176224 


1433 


823770 


28 


33 


172230 


1399 


995146 


32 


177084 


1431 


822916 


27 


34 


173070 


1396 


995127 


32 


177942 


1428 


822058 


26 


35 


173908 


1394 


995108 


32 


178799 


1425 


821201 


25 


36 


174744 


1391 


995089 


32 


1796.55 


1423 


820345 


24 


37 


17.5578 


1388 


995070 


32 


180508 


1420 


819492 


23 


38 


176411 


1386 


99.5051 


32 


181360 


1417 


818640 


22 


39 


177242 


1383 


995032 


32 


182211 


1415 


817789 


21 


40 
41 


178072 


1380 
1377 


995013 
9.994993 


32 
32 


1830.59 


1412 


816941 


20 
19 


9.178900 


9.183907 


1409 


10.816093 


42 


179726 


1374 


994974 


32 


184752 


1407 


815248 


18 


43 


180,551 


1372 


994955 


32 


185597 


1404 


814^103 


17 


44 


181374 


1369 


994935 


32 


186439 


1402 


813561 


16 


45 


182196 


1366 


994916 


33 


187280 


1399 


812720 


15 


46 


183016 


1364 


994896 


33 


188120 


1396 


811880 


14 


47 


183834 


1361 


994877 


33 


188958 


1393 


811042 


13 


48 


184651 


1359 


994857 


33 


189794 


1391 


810206 


12 


49 


185466 


1356 


994838 


33 


190629 


1389 


809371 


11 


50 
51 


186280 


1353 
1351 


994818 


33 
33 


191462 
9.192294 


1386 
1.384 


808538 
10.807706 


10 
9 


9.187092 


9.994798 


52 


187903 


1348 


994779 


33 


193124 


1381 


80C876 


8 


53 


188712 


1346 


994759 


33 


1939.53 


1379 


806047 


7 


54 


189519 


1343 


994739 


33 


194780 


1376 


805220 


6 


55 


190325 


1341 


994719 


33 


195606 


1374 


804394 


5 


56 


191130 


1338 


994700 


33 


1964.30 


1371 


803570 


4 


57 


191933 


1336 


994680 


33 


197253 


1369 


802747 


3 


58 


192734 


1333 


994660 


33 


198074 


1366 


801926 


2 


59 


193534 


1330 


994640 


33 


198894 


1364 


801106 


1 


60 


194332 


1328 


994620 


33 


199713 


1361 


800287 


__0 




Cosine 




Sin. j 


Cninwj 




Tang. 1 M. 



^1 Degrees. 





SINES AIND TAA'GF.NTS. (^9 Degret.-:. 


; 


27 


M. 


Sine 


D. 


Cosine | D 


'J'iiiig. 


T). _ 


Coiaiig. 1 


~o" 


19.194332 


1328 


9.994620 


33 


9.199713 


1361 


10.800287.60 


1 


195129 


1326 


994600 


33 


200529 


1359 


799471 


59 


2 


195925 


1323 


994580 


33 


201345 


1356 


798655 


5S 


3 


196719 


1321 


994560 


34 


202159 


1354 


797841 


57 


4 


197511 


1318 


994540 


34 


202971 


1352 


797029 


56 


5 


198302 


1316 


994519 


34 


203782 


1349 


798218 


55 


6 


199091 


1313 


99M99 


34 


204592 


1347 


795408 


54 


7 


I99S79 


1311 


994479 


34 


205400 


1345 


794600 


53 


8 


200666 


1308 


994459 


34 


206207 


1342 


793793 


52 


9 


201451 


1306 


994-138 


34 


207013 


1340 


792987 


51 


10 

11 


202234 


1304 
1301 


994418 
9.994397 


34 
34 


207817 


1338 


792183 


50 

49 


9.203017 


9.208619 


1335 


10.791381 


12 


203797 


1299 


994377 


34 


209420 


1333 


790580 


48 


13 


204577 


1296 


994357 


34 


210220 


1331 


789780 


47 


14 


205354 


1294 


994336 


34 


211018 


1328 


788982 


46 


15 


206131 


1292 


994316 


34 


211815 


1326 


788185 


45 


16 


206906 


1289 


994295 


34 


212611 


1324 


7S73S9 


44 


17 


207679 


1287 


994274 


35 


213405 


1321 


786595 


43 


18 


208452 


1285 


994254 


35 


214198 


1319 


785802 


42 


19 


209222 


1282 


994233 


35 


214989 


1317 


785011 


41 


20 
21 


209992 
9.210760 


1280 


994212 


35 
35 


215780 
9.216568 


1315 


784220 


40 
39 


1278 


9.994191 


1312 


10.783432 


22 


211526 


1275 


994171 


35 


217356 


1310 


782644 


38 


23 


212291 


1273 


994150 


35 


218142 


1308 


7818.58 


37 


24 


213055 


1271 


994129 


35 


218926 


1305 


781074 


36 


25 


213818 


1268 


994108 


35 


219710 


1303 


780290 


35 


26 


214579 


1288 


994087 


35 


220492 


1301 


779.508 


34 


27 


215338 


1264 


994066 


35 


221272 


1299 


778728 


33 


28 


216097 


1261 


994045 


35 


222052 


1297 


777948 


32 


29 


2168.54 


1259 


994024 


35 


222830 


1294 


777170 


31 


30 
31 


217609 


1257 


994003 


35 
35 


22.3606 


1292 


776394 


30 

29 


9.218363 


1255 


9.993981 


9.224382 


1290 


10. 7756 IS 


32 


219116 


1253 


993960 


35 


225156 


1288 


774844 


28 


33 


219868 


1250 


993939 


35 


225929 


1286 


774071 


27 


34 


220618 


1248 


993918 


35 


226700 


1284 


773300 


26 


35 


221367 


1246 


993896 


36 


227471 


1281 


772529 


25 


36 


222115 


1244 


993875 


36 


228239 


1279 


771761 


24 


37 


222861 


1242 


993854 


36 


229007 


1277 


770993 


23 


38 


223006 


1239 


993832 


36 


229773 


1275 


770227 


22 


39 


224349 


1237 


993811 


36 


230539 


1273 


769481 


21 


40 
41 


225092 
9 . 225833 


1235 
12.33 


993789 
9 . 993768 


36 
36 


231302 


1271 


768698 


20 
19 


9.232065 


1209 


10.767935 


42 


226573 


1231 


993746 


36 


232826 


1267 


767174 


18 


43 


227311 


1228 


993725 


36 


233586 


1265 


706414 


17 


44 


228048 


1220 


993703 


36 


234345 


1262 


765855 


16 


45 


228784 


1224 


993681 


36 


235103 


1260 


764897 


15 


46 


229518 


1222 


993660 


36 


235859 


1258 


764141 


•t 


47 


230252 


1220 


993638 


36 


236614 


1256 


763386 


.3 


48 


230984 


1218 


993616 


36 


237368 


1254 


762632 


12 


49 


231714 


1216 


993594 


37 


238120 


1252 


761880 


11 


50 
51 


232441 


1214 
1212 


993572 


37 
37 


238872 
9.239622 


1250 


761128 
10.760378 


10 
9 


9.233172 


9.993550 


1248 


52 


233899 


1209 


993528 


37 


240371 


1246 


75982.0 


8 


53 


234625 


1207 


993508 


37 


241118 


12'14 


7.58882 


7 


54 


235349 


1205 


993484 


37 


24 1865 


1242 


758 1 35 


6 


55 


236073 


1203 


993462 


37 


242610 


1240 


757390 


5 


56 


236795 


1201 


993440 


37 


243354 


1238 


756646 


4 


57 


237515 


1199 


993418 


37 


244097 


1236 


755903 


3 


58 


238235 


1197 


993396 


37 


244839 


1234 


755181 


2 


59 


238953 


1195 


9933T4 


37 


245579 


1232 


7,54421 


1 


60 


239670 


1193 


993351 


37 


246319 


1230 


753681 





,Ii 


Cosine 




Sine j 


Cotai'ii. 




Tang. |M. 1 



SO Degrees 



28 


(10 D-r 


:c..) A 


■JAHLK or LOGAIJITIIMIC 




M. 


Siiiu 


D. ] Cosine 1 D. 


1 TaiiR. 


1 D. 


1 Cotang. 1 1 





9.239670 


1193 


9.993351 


37 


9.246319 


1230 


10.753681 


60 


1 


240386 


1191 


993329 


37 


247057 


1228 


752943 


59 


2 


241101 


1189 


993307 


37 


247794 


1226 


752206 


58 


3 


241814 


1187 


993285 


37 


248530 


1224 


751470 


57 


4 


242526 


1185 


993262 


37 


249264 


1222 


750736 


56 


5 


243237 


1183 


993240 


37 


249998 


1220 


750002 


55 


6 


243947 


1181 


993217 


38 


2507.30 


1218 


749270 


54 


7 


244656 


1179 


993195 


38 


251461 


1217 


748539 


53 


8 


245363 


1177 


993172 


38 


252191 


1215 


747809 


52 


9 


246069 


1175 


993149 


38 


2.52920 


1213 


747080 


51 


10 
11 


246775 
9.247478 


1173 
1171 


993127 


38 

38 


253648 


1211 


746352 


50 
49 


9.993104 


9.2.54374 


1209 


10.745626 


12 


248181 


1169 


993081 


38 


255100 


1207 


744900 


48 


13 


248883 


1167 


993059 


38 


255824 


1205 


744176 


47 


14 


249583 


1165 


993036 


38 


256.547 


1203 


743453 


46 


15 


250282 


1163 


993013 


38 


257269 


1201 


742731 


45 


16 


250980 


1161 


992990 


38 


257990 


1200 


742010 


44 


17 


251677 


1159 


992967 


38 


258710 


1198 


741290 


43 


18 


252373 


11.58 


992944 


38 


259429 


1196 


740571 


42 


19 


253007 


1156 


992921 


38 


260146 


1194 


7398.54 


41 


20 

21 


25376 1 
9.254453 


1154 
1152 


992898 
9.992875 


38 
38 


260863 


1192 
1190 


739137 


40 
39 


9.261578 


10.738422 


22 


255144 


1150 


992852 


38 


262292 


1189 


737708 


38 


23 


255834 


1148 


992829 


39 


263005 


1187 


736995 


37 


24 


256523 


1146 


992806 


39 


263717 


1185 


736283 


36 


25 


257211 


1144 


992783 


39 


264428 


1183 


735572 


35 


26 


257898 


1142 


992759 


39 


265138 


1181 


734862 


34 


27 


258583 


1141 


992736 


39 


265847 


1179 


7341.53 


33 


28 


25926S 


1139 


992713 


39 


'^66555 


1178 


733445 


32 


29 


2.59951 


1137 


992690 


39 


267261 


1176 


732739 


31 


30 


260633 


11.35 


992666 


39 


267967 


1174 


732033 


30 


31 


9.261314 


1133 


9.992643 


39 


9.268671 


1172 


10.731329 


29 


32 


201994 


1131 


992619 


39 


269375 


1170 


730625 


28 


33 


262673 


1130 


992596 


39 


270077 


1169 


729923 


27 


34 


263351 


1128 


992572 


39 


270779 


1167 


729221 


26 


35 


264027 


1126 


992549 


39 


271479 


1165 


728521 


25 


36 


264703 


1124 


992525 


39 


272178 


1164 


727822 


24 


37 


265377 


1122 


992501 


39 


272876 


1162 


727124 


23 


38 


26605 1 


1120 


992478 


40 


273573 


1160 


726427 


22 


39 


266723 


1119 


992454 


40 


274269 


1158 


725731 


21 


40 
41 


267395 
9.268065 


1117 


992430 
9.992406 


40 
40 


274964 
9.275658 


1157 


725036 


20 
19 


1115 


1155 


10.724342 


42 


268734 


1113 


992382 


40 


276351 


1153 


723649 


18 


13 


269402 


1111 


992359 


40 


277043 


1151 


722957 


17 


■1 , 


270069 


1110 


992335 


40 


277734 


1150 


722266 


]S 


Id 


270735 


1108 


992311 


40 


278424 


1148 


721576 


15 


46 


271400 


1106 


992287 


40 


279113 


1147 


720887 


14 


47 


272064 


1105 


992263 


40 


279801 


1145 


720199 


13 


48 


272726 


1103 


992239 


40 


280488 


1143 


719512 


12 


49 


273388 


1101 


992214 


40 


281174 


1141 


718826 


11 


50 
51 


274049 
9.274708 


1099 
1098 


992190 


40 
40 


281858 


1140 


718142 


JO 
9 


9.992166 


9.282542 


1138 


10.717458 


52 


275367 


1098 


992142 


40 


283225 


1136 


716775 


8 


53 


276024 


1094 


992117 


41 


283907 


1135 


716093 


7 


54 


276681 


1092 


992093 


41 


284588 


1133 


715412 


6 


55 


277337 


1091 


992069 '41 


285268 


1131 


7147.32 


5 


56 


277991 


1089 


992044 


41 


285947 


1130 


714053 


4 


57 


278644 


1087 


992020 


41 


286624 


1128 


713376 


3 


58 


279297 


1086 


991996 


41 


287301 


1126 


712699 


2 


59 


279948 


1084 


991971 


41 


287977 


1125 


712023 


1 


60 


280599 


1082 


991947 


41 


288652 


1123 


711348 







Cosine i 


] Sine 1 


Clang, 1 




Tang. 1 M. [ 



97 Degreei 



SINES AND TANGENTS. ( 1 1 Degrees. ) 



29 



M. 


1 Sine 


1 r>. 


1 Cnsiire | D. 


1 Tang. 


D. 


Co-ran?. 1 ) 


"o" 


9.280599 


1082 


9.991947 


41 


9.288652 


1123 


10.711348 


60 


1 


2812't8 


1081 


991922 


41 


289326 


1122 


710674 


59 


2 


281897 


1079 


991897 


41 


289999 


1120 


710001 


58 


3 


282544 


1077 


991873 


41 


290671 


1118 


709329 


67 


4 


283190 


1076 


991848 


41 


391342 


1117 


708658 


56 


5 


283836 


1074 


991823 


41 


292013 


1115 


707987 


55 


6 


284480 


1072 


991799 


41 


292682 


1114 


707318 


54 


7 


285124 


1071 


991774 


42 


293350 


1112 


706650 


53 


8 


285766 


1069 


991749 


42 


294017 


nil 


705983 


52 


9 


286408 


1067 


991724 


42 


294684 


1109 


705316 


51 


10 
11 


287048 
9.287687 


1066 


991699 
9.991674 


42 
42 


295349 


1107 


704651 


50 
49 


1064 


9.296013 


1106 


10.703987 


12 


288326 


1063 


991649 


42 


296677 


1104 


703323 


48 


13 


288964 


1061 


991624 


42 


297339 


1103 


702661 


47 


14 


289600 


1059 


991599 


42 


298001 


1101 


701999 


46 


15 


290236 


1058 


991574 


42 


298662 


1100 


701338 


45 


16 


290870 


1056 


991549 


42 


299322 


1098 


700678 


44 


17 


291504 


1054 


991524 


42 


299980 


1096 


700020 


43 


18 


292137 


1053 


991498 


42 


300638 


1095 


699362 


42 


19 


292768 


1051 


991473 


42 


301295 


1093 


698705 


41 


20 
21 


293399 
9.294029 


1050 


991448 
y. 99 1422 


42 
42 


301951 
9.302607 


1092 
1090 


698049 


40 
39 


1048 


10.697393 


22 


294658 


1046 


991397 


42 


303261 


1089 


696739 


38 


23 


295280 


1045 


991372 


43 


303914 


1087 


696086 


37 


24 


295913 


1043 


991346 


43 


304567 


1086 


695433 


36 


25 


296539 


1042 


991.321 


43 


305218 


1084 


694782 


35 


26 


297164 


1040 


991295 


43 


305869 


1083 


694131 


34 


27 


297788 


1039 


991270 


43 


306519 


1081 


693481 


33 


28 


298412 


1037 


991244 


43 


307168 


1080 


692832 


32 


2iJ 


299034 


1036 


991218 


43 


307815 


1078 


692185 


31 


30 

31 


299655 
9.300276 


1034 
1032 


991193 
9.991167 


43 
43 


308463 
9.309109 


1077 


691537 


30 

29 


1075 


10.690891 


32 


300895 


1031 


991141 


43 


309754 


1074 


690246 


28 


33 


301514 


1029 


991115 


43 


310398 


1073 


689602 


27 


34 


302132 


1028 


991090 


43 


811042 


1071 


688958 


26 


35 


302748 


1026 


991064 


43 


311685 


1070 


688315 


25 


36 


303364 


1025 


991038 


43 


312327 


1068 


687673 


24 


37 


303979 


1023 


991012 


43 


312967 


1067 


687033 


23 


38 


304593 


1022 


990986 


43 


313608 


1005 


686392 


22 


39 


305207 


1020 


990960 


43 


314247 


1064 


685753 


21 


40 
41 


305819 
9 . 306430 


1019 


990934 
9.990908 


44 
44 


314885 
9.315523 


1062 


685115 


20 
19 


1017 


1061 


10.684477 


42 


307041 


1016 


990882 


44 


316159 


1060 


683841 


18 


43 


307650 


1014 


990855 


44 


316795 


1058 


683205 


17 


44 


308259 


1013 


990829 


44 


317430 


1057 


682570 


16 


45 


308867 


1011 


990803 


44 


318064 


1055 


681936 


15 


46 


309474 


1010 


990777 


44 


318697 


1054 


681.303 


14 


47 


310080 


1008 


990750 


44 


319329 


1053 


680671 


13 


48 


310685 


1007 


990724 


44 


319961 


1051 


680039 


12 


49 


311289 


1005 


990697 


44 


320592 


10.50 


679408 


11 


50 
51 


311893 
9.312495 


1004 


990671 
9.990644 


44 
44 


321222 
9.321851 


1048 


678778 


10 
9 


1003 


1047 


10.678149 


52 


313097 


1001 


990618 


4-4 


322479 


1045 


677521 


8 


53 


313698 


1000 


990591 


44 


323106 


1044 


676894 


7 


54 


314297 


998 


990565 44 


323733 


1043 


676267 


6 


55 


314897 


997 


990538 44 


324358 


1041 


675642 


5 


56 


315495 


996 


990511 45 


324983 


1040 


' 675017 


4 


57 


316092 


994 


c)90485 45 


325607 


1039 


1 674393 


3 


58 


316689 


993 


990458 45 


326231 


1037 


I 673769 


2 


59 


1 317284 


991 


990431 45 


326853 


1036 


! 673147 


1 


60 


1 317879 


990 


990404 45 


327475 


1035 


' 672525 




1 Cosine 




' Sine 1 


1 Cotaiii;. 




1 Tang. 1 



78 Degrees 



30 


(12 X)egrees.) a 


TABLE OP LOGARITHMIC 




M. 


Sine 


! i>- 


1 Cosine 1 D. 


1 Tang. 


1 D. 


1 Cotaiig. i 1 


~o" 


9.317879 


990 


9.990404 


45 


9.327474 


1035 


10 672526 


60 


1 


318473 


988 


990378 


45 


328095 


1033 


671905 


69 


2 


319066 


987 


990351 


45 


328715 


1032 


671285 


58 


3 

4 


319658 


986 


990.324 


45 


329334 


1030 


670666 


57 


320249 


984 


990297 


45 


329953 


1029 


670047 


66 


* 5 


320840 


983 


990270 


45 


330570 


1028 


669430 


55 


6 


321430 


982 


990243 


45 


331187 


1026 


668813 


54 


7 


322019 


980 


990215 


45 


331803 


1025 


668197 


53 


8 


322C07 


979 


990188 


45 


332418 


1024 


667582 


62 


9 
10 

ll 


323194 


977 


990161 


45 


3330.33 


1023 


666967 


61 


323780 


976 


990134 
9.990107 


45 

46 


333646 


1021 


666354 


50 
49 


9.324366 


975 


9.334259 


1020 


10.665741 


12 


324950 


973 


990079 


46 


3.34871 


1019 


665129 


48 


13 


325534 


972 


990052 


46 


335482 


1017 


664618 


47 


14 


326117 


970 


990025 


46 


336093 


1016 


663907 


46 


15 


326700 


969 


989997 


46 


336702 


1015 


663298 


46 


J6 


327281 


968 


989970 


46 


337311 


1013 


662689 


44 


17 


327862 


966 


989942 


46 


337919 


1012 


662081 


43 


18 


328442 


965 


989915 


46 


338527 


1011 


661473 


42 


19 


329021 


964 


989887 


46 


339133 


1010 


660867 


41 


20 

21 


329599 


962 


989860 


46 
46 


339739 
9.340344 


1008 
1007 


660261 


40 
39 


9.330176 


961 


9.989832 


10.6.59656 


22 


330753 


960 


989804 


46 


340948 


1006 


659052 


38 


23 


331329 


958 


989777 


46 


341552 


1004 


658448 


37 


24 


331903 


957 


989749 


47 


342155 


1003 


667845 


36 


25 


332478 


956 


989721 


47 


342757 


1002 


657243 


36 


26 


333051 


954 


989693 


47 


343358 


1000 


656642 


34 


27 


333624 


953 


989605 


47 


343958 


999 


656042 


33 


28 


334195 


952 


989637 


47 


344558 


998 


655442 


32 


29 


334766 


950 


989609 


47 


345157 


997 


654843 


31 


30 
31 


335337 


949 


989582 
9.989553 


47 
47 


345755 
9.346353 


996 
994 


654245 


30 


9.335906 


948 


10.653647 


29 


32 


336475 


946 


989525 


47 


346949 


993 


653051 


28 


33 


337043 


945 


989497 


47 


347545 


992 


652455 


27 


34 


337610 


944 


989469 


47 


.348141 


991 


651859 


26 


35 


338176 


943 


989441 


47 


348735 


990 


651265 


25 


36 


338742 


941 


989413 


47 


349329 


988 


650671 


24 


37 


339306 


940 


989384 


47 


349922 


987 


650078 


23 


38 


339871 


939 


989356 


47 


350514 


986 


649480 


22 


39 


340434 


937 


989328 


47 


351106 


985 


648894 


21 


40 
41 


340996 


936 


989300 
9.989271 


47 
47 


351697 


983 

982 


648303 


20 
19 


9.341558 


935 


9.352287 


10.647713 


42 


342119 


934 


989243 


47 


352876 


981 


647124 


18 


43 


342679 


932 


989214 


47 


353465 


980 


646535 


17 


44 


343239 


931 


989186 


47 


354053 


979 


645947 


16 


45 


343797 


930 


989157 


47 


354640 


977 


645360 


15 


46 


34-t355 


929 


989128 


48 


355227 


976 


644773 


14 


47 


344912 


927 


989100 


48 


355813 


975 


644187 


13 


48 


345469 


926 


989071 


48 


356398 


974 


643602 


12 


49 


346024 


925 


989042 


48 


356982 


973 


643018 


11 


50 


346579 


924 


989014 


48 


357566 


971 


642434 


10 


31 


9.347134 


922 


9.988985 


48 


9.358149 


970 


10.641851 


9 


52 


347687 


921 


988956 


48 


358731 


969 


641269 


S 


53 


348240 


920 


988927 


48 


359313 


968 


640687 


7 


54 


348792 


919 


988898 


48 


359893 


967 


640107 


6 


55 


349343 


917 


988869 


48 


360474 


966 


639526 


5 


66 


349893 


916 


988840 


48 


361053 


965 


638947 


4 


57 


350443 


915 


988811 


49 


361632 


963 


638368 


3 


58 


350992 


914 


988782 


49 


362210 


962 


637790 


2 


59 


351540 


913 


988753' 49 1 


362787 


961 


637213 


T 


60 


352088 


911 


9887241 49 ' 


363364 


960 


636636 





|l 


CO:^illC 




Sine 1 


Colaiig. 1 


1 


Tang 1 M. j 



77 Degrees. 



SIXES AND TANGENTS. (^13 Df^gieOS.) 



M. 


Su.e 1 


D. 1 


Cosine 1 D. 1 


Tan,. 


D. 1 


Cora;i^. | 


~0~ 


9 . 3520S8 


911 


9.988724 


49 


9.363364 


960 


10.6366361 60 


1 


352635 


910 


988695 


49 


363940 


959 


636060 59 


2 


353181 


909 


988666 


49 


364515 


958 


635485 .^8 


3 


353726 


908 


988636 


49 


365090 


957 


634910 5? 


4 


354271 


907 


988607 


49 


305664 


9.55 


634336 56 


5 


354815 


905 


983578 


49 


366237 


954 


033763 55 


6 


35535S 


904 


988548 


49 


366810 


953 


633190 


54 


7 


355901 


903 


988519 


49 


367382 


952 


632618 


53 


8 


356443 


902 


988489 


49 


367953 


951 


632047 


52 


9 


350934 


901 


988460 


49 


368524 


950 


631476 


51 


10 
11 


357524 


899 


988430 
9.988401 


49 

49 


369091 


949 


630906 


50 


9.358064 


898 


9.369663 


948 


10.630337 


49 


12 


358603 


897 


988371 


49 


370232 


946 


629768 


48 


13 


359141 


896 


988342 


49 


370799 


945 


62920 1 


47 


14 


359678 


895 


988312 


50 


371367 


944 


628633 


46 


15 


360215 


893 


988282 


50 


371933 


943 


628067 


45 


16 


360752 


892 


988252 


50 


372499 


942 


627501 


44 


17 


361287 


891 


988223 


50 


373064 


941 


626936 


43 


18 


361822 


890 


988193 


50 


373629 


940 


626371 




19 


362356 


889 


988163 


50 


374193 


939 


625807 


41 


20 


362889 


888 


988133 


50 


374756 


938 


625244 


40 


21 


9.3;i3422 


887 


9.988103 


50 


9.375319 


937 


10.624681 


39 


22 


363954 


885 


988073 


50 


375881 


935 


624119 


33 


23 


364485 


834 


988043 


50 


376442 


9,34 


623558 


37 


24 


365016 


883 


988013 


50 


377003 


933 


622997 


36 


25 


365546 


882 


987983 


50 


377563 


932 


622437 


35 


26 


366075 


881 


987953 


50 


378122 


031 


621873 


34 


27 


366604 


880 


987922 


50 


378881 


930 


621319 


33 


28 


367131 


879 


987892 


50 


379239 


929 


620761 


32 


29 


367659 


877 


987862 


50 


379797 


928 


6202v)3 


31 


30 
31 


368185 


876 


987832 
9.987801 


51 
51 


380351 


927 


6196 V6 


30 


9. 3687 11 


875 


9.380910 


926 


lO.oiouyo, 29 


32 


369236 


874 


987771 


51 


381466 


925 


6185341 28 


33 


369761 


873 


987740 


51 


382020 


924 


617930J 27 


3i 


370285 


872 


987710 


51 


382575 


923 


617425 26 


35 


370808 


871 


987679 


51 


383129 


922 


6168711 25 


3ri 


371330 


870 


987649 


51 


383682 


921 


616318 24 


37 


371852 


889 


987618 


51 


384234 


920 


615766 23 


:?.^ 


372373 


857 


987588 


51 


384786 


919 


6152 Ml 22 


■M) 


372894 


866 


987557 


51 


385337 


918 


6146631 21 


40 


373414 


865 


987526 
9.987496 


51 
51 


385888 


917 


6141121 20 


41 


9.373933 


864 


9.336438 


915 


10.613562J 19 


42 


374452 


863 


987465 


51 


.386987 


914 


613013; 13 


43 


374970 


862 


987434 


51 


337536 


913 


612464 17 


44 


375487 


861 


987403 


52 


388084 


912 


611916 16 


45 


376003 


860 


987372 


52 


338631 


911 


6113691 15 


46 


376519 


859 


987341 


52 


389178 


910 


610822! 14 


47 


377035 


858 


997310 


52 


389724 


909 


610276 13 


49 


377549 


857 


987279 


52 


390270 


908 


609730 12 


49 


378003 


856 


987248 


52 


390815 


907 


609185! 11 


50 
51 


378577 


854 


987217 

S. 987186 


52 

52 


391360 


906 


608640, !0 


9.379089 


853 


9.391903 


905 


roT603097| '') 


52 


379601 


852 


987155 


52 


392447 


904 


607553! 8 


53 


380113 


851 


987124 


52 


392989 


903 


6070 11 j 7 


54 


380624 


850 


987092 


52 


393531 


902 


606469 6 


55 


381134 


849 


987061 


52 


394073 


901 


605927 5 


56 


381643 


848 


987030 


52 


394614 


900 


605336! 4 


57 


382152 


847 


986998 


52 


395154 


899 


6048461 3 


68 


3S2661 


846 


986967 


52 


395694 


898 


604306! 2 


59 


383168 


845 


986936 


62 


396233 


897 


6037671 1 


60 


38367.5 


844 


986904 


52 


396771 


896 


603229' 




<■..-:... 




1 Si;,e 1 


Cor-iiii: 


1 


1 .. aiif. 1 .M. 



:t; DRgreea. 



32 


(1^ 


[ Degrees.; a 


TABLE OF LOGARITHMIC 




nn 


Sill.,' 1 


D. 


Cosine | D. 


Tang. 1 


D. 1 


Cotang. 1 j 


(' 


9.383675 


844 1 


9.986904 


52 


9.3967711 


896 


10.603229 


60 


I 


384182 


843 1 


986873 


53 


397309 


896 


602691 


59 


o 


384687 


842 


93684! 


53 


397846 


895 


602154 


58 


3 


385192 


841 


986809 


53 


398383 


894 


601617 


57 


4 


385697 


840 


986778 


53 


398919 


893 


601081 


56 


5 


386201 


'»39 


986746 


53 


399455 


892 


600545 


55 


6 


386704 


838 


986714 


53 


399990 


891 


600010 


54 


7 


387207 


837 


986683 


53 


400524 


890 


599476 


53 


8 


387709 


836 


986651 


53 


401058 


889 


598942 


52 


9 


388210 


835 


986619 


53 


401591 


888 


598409 


51 


10 
11 


388711 


834 


986587 


53 
53 


402124 


887 


597876 
10.597344 


50 
49 


9.389211 


833 


9 . 986555 


9.402656 


886 


12 


389711 


832 


986523 


53 


403187 


885 


.596813 


48 


13 


390210 


831 


986491 


53 


403718 


884 


596282 


47 


14 


390708 


830 


986459 


53 


404249 


883 


595751 


46 


15 


391206 


828 


986427 


53 


404778 


882 


595222 


45 


16 


391703 


827 


986396 


53 


405308 


881 


594692 


44 


17 


392199 


826 


986363 


54 


405836 


880 


594164 


43 


18 


392695 


825 


986331 


54 


406364 


879 


593636 


42 


19 


393191 


824 


986299 


54 


406892 


878 


5931 OS 


41 


20 

21 


393685 
9.394179 


823 
822 


986260 
9.986234 


54 
54 


407419 


877 


592.581 


40 
39 


9.407945 


876 


10.592055 


2-^ 


394673 


821 


986202 


54 


408471 


875 


591529 


38 


23 


395166 


820 


986169 


54 


408997 


874 


591003 


37 


2i 


395658 


819 


986137 


54 


409521 


874 


590479 


36 


2.T 


.390150 


818 


986104 


54 


410045 


873 


589955 


35 


26 


396641 


817 


986072 


54 


410.569 


872 


589431 


34 


27 


397132 


817 


986039 


54 


411092 


871 


588908 


33 


28 


397621 


816 


986007 


54 


411615 


870 


5883S5 


32 


29 


398 1 1 1 


815 


985974 


54 


412137 


869 


587863 


31 


30 
31 


398600 


814 


985942 
9.985909 


54 
55 


412658 


868 


587342 
10.586821 


30 

29 


9.399088 


813 


9.413179 


867 


32 


399575 


812 


985876 


55 


413699 


866 


586301 


28 


33 


400062 


811 


985843 


55 


414219 


865 


58578 1 


27 


31 


400549 


810 


985811 


55 


414738 


864 


585262 


26 


35 


401035 


809 


985778 


55 


41.5257 


864 


584743 


25 


36 


401.520 


808 


985745 


55 


415775 


863 


.584225 


24 


37 


402005 


807 


985712 


55 


416293 


862 


583707 


23 


38 


402489 


806 


98567S 


55 


416810 


861 


583190 


22 


33 


402972 


805 


985646 


55 


417326 


860 


582674 


21 


40 
41 


403455 


804 


985013 


55 
55 


417842 


8.59 


.582158 


20 
19 


9.403938 


803 


9.985580 


9.418358 


858 


10.. 58 1642 


■i-z 


404420 


802 


985.547 


55 


418873 


857 


.581127 


IS 


43 


404901 


801 


985514 


55 


419387 


858 


580613 


17 


44 


405382 


800 


985480 


55 


419901 


855 


580099 


16 


45 


405862 


799 


985447 


55 


420415 


855 


579585 


15 


46 


406341 


798 


985414 


56 


420927 


854 


579073 


14 


47 


406820 


797 


985380 


56 


421440 


8.53 


578560 


13 


48 


407299 


796 


985347 


56 


421952 


852 


578048 


12 


49 


407777 


795 


985314 


56 


422463 


851 


577537 


11 


50 
51 


408254 


794 


985280 
9.985247 


56 
56 


422974 


850 


577026 
10.576510 


10 
9 


9.408731 


794 


9.423484 


849 


52 


409207 


793 


98.5213 


56 


423993 


848 


576007 


8 


53 


409682 


792 


985180 


56 


424503 


848 


575497 


7 


54 


410157 


791 


985146 


56 


42.5011 


847 


574989 


6 


55 


410632 


790 


985113 


56 


425519 


846 


574481 


5 


56 


411106 


789 


985079 


56 


426027 


845 


573973 


4 


57 


411.579 


788 


985045 


56 


426534 


844 


573466 


3 


58 


412052 


787 


985011 


56 


427041 


843 


572959 


2 


59 


412524 


786 


984978 


56 


427547 


843 


572453 


1 


_60_ 


412996 


785 


984944 


56 


428052 


842 


571948 





"~ 


Cosine 




Sine 1 


1 Cdtaiig. 




1 Tang 1 M. | 



75 Degrees. 





SINES AND TAl^GENTS. (16 


Degrees.) 


HH 


M. 


1 Sine 


1 D. 


1 Cosine | D. 


1 Taiiu. 


1 D. 


! Culilii::. 1 


^ 


9.412996 


785 


9.984944 


,57 


9.428052 


842 


10.571948 1 GO 


1 


413467 


784 


984910 


57 


428557 


841 


571443 o9 


2 


413938 


783 


984876 


57 


429062 


840 


570938 53 


3 


414408 


783 


984842 


57 


429566 


839 


570434 hi 


4 


414878 


782 


984808 


57 


430070 


838 


569930 56 


5 


415347 


781 


984774 


67 


430573 


838 


569427 


55 


6 


416815 


780 


984740 


57 


431075 


837 


568925 


54 


7 


416283 


779 


9S4706 


67 


431577 


836 


568423 


53 


8 


416751 


778 


984672 


67 


432079 


835 


567921 


52 


9 


417217 


777 


984637 


57 


432580 


8.34 


567420 


61 


10 
11 


417684 
9.418150 


770 
775 


984603 


57 
57 


433080 
9.433.580 


833 


566920 
10., 566420 


50 
49 


9.984.569 


832 


12 


418615 


774 


984535 


57 


434080 


832 


565920 


48 


13 


419079 


773 


984500 


57 


434579 


831 


56.5421 


47 


14 


419544 


773 


984466 


57 


435078 


830 


564922 


46 


15 


420007 


772 


984432 


58 


435576 


829 


564424 


45 


16 


420470 


771 


984397 


58 


436073 


828 


563927 


44 


17 


420933 


770 


984363 


58 


436570 


828 


563430 


43 


18 


421395 


769 


984328 


68 


437067 


827 


562933 


42 


19 


421857 


768 


984294 


58 


437563 


826 


562437 


41 


20 
21 


422318 
9 422778 


767 
767 


984259 


58 
58 


4.38059 
9.438.554 


825 
824 


561941 
10.561446 


40 
39" 


9 . 984224 


22 


423238 


766 


984190 


58 


439048 


823 


560952 


38 


23 


423697 


765 


9841.55 


68 


439543 


823 


560457 


37 


24 


42-1 ! hC 


764 


984120 


58 


440036 


822 


569964 


36 


26 


424615 


763 


984085 


58 


440529 


821 


559471 


35 


26 


425073 


762 


984050 


58 


441022 


820 


5.58978 


34 


27 


425530 


761 


984015 


58 


441614 


819 


.558486 


33 


28 


425987 


760 


983981 


58 


442006 


819 


557994 


32 


29 


426443 


760 


983946 


58 


442497 


818 


557503 


31 


30 
31 


426899 


759 


983911 

9 . 983875 


68 
58 


442988 


817 


557012 


30 

29 


9.4273.54 


758 


9.4^13479 


816 


10.566521 


32 


427809 


757 


983840 


69 


443968 


816 


556032 


28 


33 


428263 


756 


983805 


59 


444458 


815 


555.542 


27 


34 


428717 


756 


983770 


69 


444947 


814 


5.56053 


26 


35 


429170 


764 


983735 


59 


445435 


813 


554565 


25 


36 


429623 


753 


983700 


59 


445923 


812 


6.54077 


24 


37 


430075 


762 


983664 


59 


446411 


812 


663589 


23 


38 


4.30527 


762 


983629 


59 


446898 


811 


6.53102 


22 


39 


430978 


751 


983594 


59 


447384 


810 


552616 


21 


40 
41 


431429 


750 


983558 
9.983523 


69 
59 


447870 


809 


552130 


20 
19 


9.431879 


749 


9.448356 


800 


10.551644 


42 


432329 


749 


983487 


59 


448841 


808 


.5511.59 


18 


43 


432778 


748 


98.3462 


59 


449326 


807 


5.50674 


17 


44 


433226 


747 


983416 


59 


449810 


806 


550190 


16 


45 


4.33675 


746 


983381 


69 


450294 


806 


549706 


15 


46 


434122 


745 


983345 


69 


450777 


805 


549223 


14 


47 


434569 


744 


983309 


59 


451260 


804 


548 740 


13 


48 


43,5016 


744 


983273 


60 


451743 


803 


548257 


12 


49 


435462 


743 


983238 


60 


462225 


802 


547775 


11 


50 
51 


435908 


742 


983202 


60 
60 


452706 


802 


547294 
10.546813 


10 
9 


9.4363,53 


741 


9.983166 


9.453187 


801 


52 


436798' 


740 


983130 


60 


453668 


800 


546332 


8 


53 


437242 


740 


983094 


60 


454148 


799 


.545852 


7 


54 


437686; 


739 


9830.58 


60 


454628 


799 


545372 


6 


55 


438129 


738 


983022 


60 


455107 


798 


644893 


5 


56 


438572 


737 


982986 


60 


455586 


797 


644414 


4 


57 


439014 


736 


982950 


60 


456064 


796 


543936 


3 


58 


439456 


736 


982914 


no 


456.542 


796 


543458 


2 


69 


439897 


735 


982878 


60 


457019 


796 


642981 


1 


60 


440338 


734 


982842 


60 


457496 


794 


542504 





1™ 


Cdsiue 1 




s... 1 


Cdlaii;;. 




1 Tang. |M.J 



74 Degrees. 



34 


(16 Degrees.) a 


TABLE OF LOGARITHMIC 




M. 


Sine 


I). 


Cosine 


D. 


Tanp. 


D. 


Cotai:g 1 J 


"IT 


9.440338 


734 


9.982842 


"60" 


9.457496 


7"94 


10.542504 


60 


1 


440778 


733 


982805 


60 


457973 


793 


542027 


59 


2 


441218 


732 


982769 


61 


458449 


793 


541551 


58 


3 


441658 


731 


982733 


61 


458925 


792 


541075 


57 


4 


442096 


731 


982696 


61 


459400 


791 


540600 


56 


f) 


442535 


730 


982660 


61 


459875 


790 


540125 


55 


6 


442973 


729 


982624 


61 


460349 


790 


539651 


54 


7 


443410 


728 


982587 


61 


460323 


789 


539177 


53 


8 


443847 


727 


982551 


61 


461297 


788 


538703 


52 


9 


444284 


727 


982514 


61 


461770 


788 


538230 


51 


10 
11 


444720 


726 


982477 
9.982441 


61 
61 


462242 


787 


537758 
10.537286 


50 

49" 


9.445155 


T25 


9.462714 


786 


12 


445590 


724 


982404 


61 


463186 


785 


530814 


48 


V3 


446025 


723 


982367 


61 


463658 


785 


536342 


47 


14 


446459 


723 


982331 


61 


464129 


784 


.535871 


46 


15 


446893 


722 


982294 


01 


464599 


783 


, 535401 


45 


16 


447326 


721 


982257 


61 


465069 


783 


534931 


44 


17 


447759 


720 


982220 


62 


465539 


782 


534461 


43 


18 


448191 


720 


982183 


62 


466008 


781 


533992 


42 


19 


448623 


719 


982146 


62 


466476 


780 


533524 


41 


20 

21 


449054 


718 


982109 


62 
62 


466945 


780 


633055 
10.532587 


40 
39 


9.449485 


717 


9.982072 


9.467413 


779 


22 


449915 


716 


982035 


62 


467880 


778 


532120 


38 


23 


450345 


716 


981998 


62 


468347 


778 


531653 


37 


24 


450775 


715 


981961 


62 


468814 


777 


631186 


36 


25 


451204 


714 


981924 


62 


469280 


776 


530720 


P 


26 


451632 


713 


981886 


62 


469746 


775 


630254 


O-x 


27 


452060 


713 


981849 


62 


470211 


775 


529789 


33 


28 


452488 


712 


981812 


62 


470676 


774 


629324 


32 


29 


452915 


711 


981774 


62 


471141 


773 


528859 


31 


30 


453342 


710 


981737 


62 


471605 


773 


528395 


30 


31" 


9.453768 


710 


9.981699 


63 


9.472068 


772 


10.527932 


2y 


32 


454194 


709 


981662 


63 


472532 


771 


527468 


28 


33 


454619 


708 


981625 


63 


472995 


771 


527005 


27 


34 


455044 


707 


981587 


63 


473457 


770 


526543 


26 


35 


455469 


707 


981549 


63 


473919 


769 


.526081 


25 


36 


455893 


706 


981512 


63 


474381 


769 


525619 


24 


37 


456316 


705 


981474 


63 


474842 


768 


525158 


23 


38 


456739 


704 


981436 


63 


475303 


767 


524697 


22 


39 


457162 


704 


981399 


63 


475763 


767 


524237 


21 


40 
41 


457584 


703 


981361 
9.981323 


63 
63 


476223 
9.476683 


766 
765 


523777 
10.523317 


20 
19 


9.458006 


702 


42 


458427 


701 


981285 


63 


477142 


765 


522858 


18 


43 


458848 


701 


981247 


63 


477601 


764 


522399 


17 


44 


459268 


700 


981209 


63 


478059 


763 


521941 


16 


45 


459688 


699 


981171 


63 


478517 


763 


521483 


15 


46 


460108 


698 


981133 


64 


478975 


762 


521025 


14 


47 


460527 


698 


981095 


64 


479432 


761 


620568 


13 


48 


460946 


697 


981057 


64 


479889 


761 


520111 


12 


49 


461364 


696 


981019 


64 


480345 


760 


519655 


11 


50 

51 


461782 


695 


980981 

9.980942 


64 
64 


480801 


759 


519199 
10.518743 


10 
9 


9.462199 


695 


9.481257 


759 


52 


462616 


694 


980904 


64 


481712 


758 


518288 


8 


53 


463032 


693 


980866 


64 


482167 


757 


6178.33 


7 


54 


463448 


693 


980827 


64 


482621 


757 


617379 


6 


55 


463864 


692 


980789 


64 


483075 


756 


616925 


5 


56 


464279 


691 


9S0750 


64 


483529 


755 


516471 


4 


57 


464694 


690 


980712 


64 


483982 


755 


516018 


3 


58 


465108 


690 


980673 


64 


484435 


754 


516565 


2 


59 


465522 


689 


980635! 64 


484887 


753 


515i)3 


1 


60 


465935 


688 


980596 64 


485339 


753 


514nRi 







Cosine 




1 Sine 1 


1 Colang. 




j Tang. 1 M. 



73 DoK'-ees. 





SINES AM) TANGENTS. 


(17 D 


egrees 


) 


35 


M. 


Sine 


I' 


Cosine 1 D. 


Tang. i 


D. 1 


Cotang. 1 1 


{) 


9.465935 


688 


9.980596 


64 


9.485339 


755 


10.514661 1 


60 


1 


466348 


688 


980558 


64 


485791 


752 


614209 


59 




466761 


687 


980519 


65 


486242 


751 


513758 


58 


3 


467173 


686 


980480 


65 


486693 


751 


513307 


57 


4 


467585 


685 


980442 


65 


487143 


750 


512857 


56 


5 


467996 


685 


980403 


65 


487593 


749 


512407 


55 


6 


468407 


684 


980364 


65 


488043 


749 


511957 


54 


7 


468817 


683 


980325 


65 


488492 


748 


511.508 


53 


8 


469227 


683 


980286 


65 


488941 


747 


511059 


52 


^ 


469637 


682 


980247 


65 


489390 


747 


510610 


51 


10 
11 


470046 


681 


980208 
9.980169 


65 
65 


489838 


746 


510162 
10 509714 


50 
49 


9.470455 


680 


9.490285 


746 


12 


470863 


680 


980130 


65 


490733 


745 


.509267 


48 


13 


471271 


679 


980091 


65 


491180 


744 


508820 


47 


14 


471679 


678 


980052 


65 


491627 


744 


508373 


46 


15 


472086 


678 


980012 


65 


492073 


743 


.507927 


45 


16 


472492 


677 


979973 


65 


492519 


743 


.507481 


44 


17 


472S98 


076 


9799.34 


66 


492965 


742 


507035 


43 


18 


473304 


676 


979895 


66 


493410 


741 


506590 


42 


19 


473710 


675 


979855 


66 


493854 


740 


506143 


41 


20 
21 


474115 


674 


979816 
9.979776 


66 
66 


494299 


740 


505701 
10.50.5257 


40 
39 


9.474519 


674 


9.494743 


740 


22 


474923 


673 


979737 


66 


495186 


739 


504814 


38 


23 


475327 


672 


979697 


66 


495G30 


738 


504370 1 37 \ 


24 


475730 


672 


979658 


66 


496073 


737 


.503927 


36 


25 


476133 


671 


979618 


66 


490515 


737 


503485 


35 


2G 


476536 


670 


979579 


66 


496957 


736 


503043 


34 


27 


476938 


669 


979539 


66 


497399 


736 


502601 


33 


28 


477340 


669 


979499 


66 


497841 


735 


502159 1 32 


29 


177741 


668 


979459 


66 


498282 


734 


501718 1 31 


30 
31 


478142 


667 


979420 
9.979380 


66 
66 


498722 


734 


.501278 


30 


9.478542 


667 


9.499163 


733 


10.500837 


29 


32 


478942 


666 


979340 


66 


499603 


733 


500397 j 28 


33 


479342 


665 


979300 


67 


500042 


732 


499958 1 27 


34 


479741 


665 


979260 


67 


500481 


731 


499519 26 


35 


480140 


664 


979220 


67 


.500920 


731 


499080 ! 25 


36 


480539 


663 


979180 


67 


.5013.59 


730 


498641 1 24 


37 


480937 


663 


979140 


67 


501797 


730 


498203 S3 


38 


481334 


662 


979100 


67 


502235 


729 


497765 ! 22 


39 


481731 


661 


979059 


G7 


502672 


728 


49732S j 21 


40 
4] 


482128 


661 


979019 
9.978979 


67 
67' 


503109 
9.503546 


728 
727 


496891 I 20 i 


9.482525 


6G0 


10.496454 


19 


42 


482921 


659 


978939 


67 


503982 


727 


496018 


18 


43 


483316 


659 


978898 


67 


504418 


726 


495582 


17 


44 


483712 


6.58 


978858 


67 


504854 


725 


495146 


16 


45 


484107 


657 


978817 


67 


,505289 


725 


494711 


15 


46 


484.501 


657 


978777 


67 


505724 


724 


494276 


14 


47 


484895 


656 


978736 


67 


506159 


724 


493841 


13 


48 


485289 


655 


978696 


68 


506593 


723 


493407 


12 


49 


485682 


655 


978655 


68 


507027 


722 


492973 


11 


50 
51 


486075 


654 


978615 


68 
68 


507460 
9.507893 


722 
721 


492540 


10 
9 


9.486467 


653 


9.978574 


10.492107 


52 


486860 


653 


978533 


68 


508326 


721 


491674 


8 


53 


487251 


652 


978493 


68 


508759 


720 


491241 


7 


54 


487643 


651 


978452 


68 


509191 


719 


490809 


6 


55 


488034 


651 


978411 


68 


509622 


719 


490378 


5 


56 


488424 


650 


978370 


68 


510054 


718 


489946 


4 


57 


488814 


650 


978329 


68 


510485 


718 


489515 


3 


58 


489204 


649 


978288 


68 


510916 


717 


489084 


2 


59 


489593 


648 


978247 


68 


511346 


716 


488654' 1 


60 


489982 


648 


978206 


68 


511776 


716 


488224 1 


~ 


Cosine 




Sine j 


Cotang. 




1 Tang. |M. 



71 Degrees. 



88 


(' 


8 Degi 


ees.) A 


TABI.I1 OF LOGARITir?.TIC 




M. 


Sine 


1 i>- 


1 Cosine 1 J). 


1 Tang. 


1 n. 


[ Cotans. j 





9.489982 


648 


9.978206; 68 


9.5117761 716 


10.488224 


60 


1 


490371 


648 


978165 


68 


512206 


1 716 


487794 


59 


2 


490759 


647 


978124 


68 


512635 


' 715 


487365 


68 


3 


491147 


' 646 


978083 


69 


613064 


■ 714 


486936 


67 


4 


491535 


646 


978042 


69 


513493 


714 


486507 


56 


5 


491922 


646 


978001 


69 


513921 


713 


486079 


55 


6 


492308 


644 


977959 


69 


614349 


713 


485651 


54 


7 


492695 


644 


977918 


69 


514777 


712 


485223 


53 


8 


493081 


643 


977877 


69 


615204 


712 


484796 


52 


9 


493466 


642 


977835 


69 


516631 


711 


484369 


51 


10 
11 


493851 


642 


977794 

9.977752 


69 
69 


616057 
9.516484 


710 


483943 
10.483516 


50 
49 


9.494236 


641 


710 


12 


494621 


641 


977711 


69 


616910 


709 


483090 


48 


13 


495005 


640 


977669 


69 


517335 


709 


482605 


47 


14 


495388 


639 


977628 


69 


617761 


708 


482239 


46 


15 


495772 


639 


977.586 


69 


618185 


708 


481815 


45 


16 


496154 


638 


977544 


70 


518610 


707 


481390 


44 


17 


496537 


637 


977503 


70 


619034 


706 


480966 


43 


18 


496919 


637 


977461 


70 


519458 


706 


480542 


42 


19 


497301 


636 


977419 


70 


519882 


705 


480118 


41 


20 
21 


497682 


636 


977377 


70 
70 


520305 


705 


479695 
10.479272 


40 
39 


9.498064 


635 


9.977335 


9.520728 


704 


22 


498444 


634 


977293 


70 


521151 


703 


478849 


38 


23 


498825 


634 


977251 


70 


621.573 


703 


478427 


37 


24 


499204 


633 


977209 


70 


621996 


703 


478005 


36 


25 


499584 


632 


977167 


70 


522417 


702 


477583 


35 


26 


499963 


632 


977125 


70 


522838 


702 


477162 


34 


27 


500342 


631 


977083 


70 


523259 


701 


476741 


33 


28 


.500721 


631 


977041 


70 


623680 


701 


476320 


32 


29 


501099 


630 


976999 


70 


524100 


700 


475900 


31 


30 
31 


.501476 


629 


976957 


70 
70 


524520 


699 


475480 


30 

29 


9.5018.54 


629 


9.976914 


9.524939 


699 


10.47.5061 


32 


602231 


628 


976872 


71 


525359 


698 


474641 


28 


33 


502607 


628 


9768.30 


71 


526778 


698 


474222 


27 


34 


502984 


627 


976787 


71 


526197 


697 


473803 


26 


35 


503360 


626 


976745 


71 


626616 


697 


473385 


25 


36 


503735 


626 


976702 


71 


527033 


696 


472967 


24 


37 


504110 


625 


976660 


71 


527451 


696 


472.549 


23 


38 


504485 


625 


976617 


71 


527868 


695 


4721.32 


22 


39 


504860 


624 


976574 


71 


528285 


695 


471715 


21 


40 
41 


505234 


623 


976532 
9.976489 


71 
71 


528702 


694 


471298 
0.470881 


20 
19 


9.505608 


623 


9.529119 


693 


42 


505981 


622 


976446 


71 


529535 


693 


470465 


18 


43 


506354 


622 


976404 


71 


529950 


693 


470050 


17 


44 


.506727 


621 


976361 


71 


530366 


692 


469634 


16 


45 


507099 


620 


976318 


71 


530781 


691 


409219 


15 


46 


507471 


620 


976275 


71 


531196 


691 


468804 


14 


47 


507843 


619 


976232 


72 


531611 


690 


468389 


13 


48 


508214 


619 


976189 


72 


632025 


690 


467975 


12 


49 


508585 


618 


976146 


72 


53243^ 


689 


467561 


11 


50 

51 


508956 
9.509326 


618 


976103 
9.976060 


72 

72 


532863 


689 


467147 
10.466734 


10 
9 


617 


9.633266 


688 


52 


509696 


636 


976017 


72 


533679 


688 


466321 


8 


53 


510065 


616 


975974 


72 


534092 


687 


465908 


7 


54 


510434 


615 


975930 


72 


534504 


687 


465496 


6 


55 


510803 


615 


975887 


72 


634916 


686 


465084 


5 


56 


511172 


014 


975844 


72 


635328 


686 


464672 


4 


57 


611540 


613 


975800 


72 


535739 


685 


464261 


3 


58 


511907 


613 


975757 


72 


536150 


685 


463850 


2 


59 


612275 


612 


975714 


72 


536561 


684 


463439 


1 


60 


612642 


612 


975670 


72 


530972 


684 


463028 





J 


Cosine 


1 


Sine 1 


Cotaiij;. 


.... 


Tanp. ! M. 



71 Decrees. 



SINES AND TANGENTS. ''^0 DeiTrees.) 



;;7 



M. 


Sine 


D. 


Cosine 


D. 


1 Tang. 


1). 


1 Cotariir. j | 


"IT 


9.512642 


612 


9.975670 


73 


9.536972 


684 


10.463028 


60 


1 


513009 


611 


975627 


73 


537382 


683 


462618 


59 


2 


513375 


611 


975583 


73 


537792 


683 


462208 


58 


3 


513741 


610 


9r5539 


73 


538202 


682 


461798 


57 


4 


514107 


609 


975496 


73 


538611 


682 


461389 


56 


5 


514-472 


609 


975452 


73 


539020 


681 


460980 


55 


6 


514837 


608 


975408 


73 


539429 


681 


460571 


54 


7 


515202 


608 


975365 


73 


539837 


680 


460163 


53 


8 


515566 


607 


975321 


73 


540245 


680 


459755 


52 


9 


515930 


607 


975277 


73 


540653 


679 


459347 


51 


10 


516294 


606 


975233 
9.975189 


73 
73 


541061 


679 


458939 
10.458532- 


50 
49 


9.516657 


605 


9.541468 


678 


12 


517020 


605 


975145 


73 


541875 


678 


458125 


48 


13 


517382 


604 


975101 


73 


542281 


677 


457719 


47 


14 


517745 


604 


975057 


73 


542688 


677 


457312 


46 


15 


518107 


603 


975013 


73 


543094 


676 


456906 


45 


16 


518468 


603 


974969 


74 


543499 


676 


456501 


44 


17 


518829 


602 


974925 


74 


543905 


675 


456095 


43 


18 


519190 


601 


974880 


74 


544310 


675 


455690 


42 


19 


519551 


601 


974836 


74 


544715 


674 


455285 


41 


20 

21 


519911 


600 


974792 


74 
74 


545119 


674 


454881 
10.454476 


40 
39 


9.520271 


600 


9.974748 


9.545524 


673 


22 


520631 


599 


974703 


74 


545928 


673 


454072 


38 


23 


520990 


599 


974659 


74 


546331 


672 


453669 


37 


24 


521349 


598 


974614 


74 


546735 


672 


453265 


36 


25 


521707 


598 


974570 


74 


547138 


671 


452862 


35 


26 


522066 


597 


974525 


74 


547540 


671 


452460 


34 


27 


522424 


596 


974481 


74 


547943 


670 


452057 


33 


28 


522781 


596 


974436 


74 


548345 


670 


451655 


32 


29 


5231.38 


595 


974391 


74 


548747 


669 


451253 


31 


30 
31 


523495 


595 


974347 
9.974.302 


75 
75 


549149 


669 


4.50851 
10.450450 


30 
29 


9.523852 


594 


9.549550 


668 


32 


524208 


594 


974257 


75 


549951 


668 


4500^9 


28 


33 


524564 


593 


974212 


75 


550352 


667 


443648 


27 


34 


524920 


593 


974167 


75 


550752 


667 


^49248 


26 


35 


525275 


592 


974122 


75 


551152 


666 


448848 


25 


36 


525630 


591 


974077 


75 


551552 


666 


448448 


24 


37 


525984 


591 


974032 


75 


551952 


665 


448048 


23 


38 


526339 


590 


973987 


75 


552351 


665 


447649 


22 


39 


526693 


590 


973942 


75 


552750 


665 


447250 


^\ 


40 
41 


527046 


589 


973897 


75 

75 


553149 


664 


446851 


20 
19 


9.527400 


589 


9.973852 


9.553548 


664 


10.446452 


42 


527753 


588 


973807 


75 


553946 


6-63 


446054 


18 


43 


528105 


588 


973761 


75 


554344 


663 


445656 


17 


44 


528458 


687 


973716 


76 


554741 


662 


445259 


16 


45 


528810 


587 


973671 


76 


5551S9 


662 


444861 


15 


46 


529161 


586 


973625 


76 


555^36 


661 


444464 


14 


47 


529513 


586 


973580 


76 


555933 


661 


444067 


13 


48 


529864 


585 


973535 


76 


556329 


660 


443671 


12 


49 


530215 


585 


973489 


76 


556725 


660 


443275 


11 


50 
51 


530565 
9.530915 


584 


973444 
9.973398 


76 

76 


557121 


659 


442879 
10.442483 


10 
9 


584 


9.557517 


659 


52 


531265 


583 


973352 


re 


557913 


659 


442087 


8 


53 


531614 


582 


973307] 


76 


558308 


658 


441692 


7 


54 


531963 


582 


9732^1 


76 


558702 


658 


441298 


6 


55 


532312 


581 


973S15 


76 


559097 


657 


440903 


5 


56 


532661 


581 


973169 


76 


559491 


657 


440509 


4 


57 


533009 


58^ 


P73124 


76 


559885 


656 


440115 


3 


58 


533357 


580 


973078 


76 


560279 


656 


439721 


2 


59 


533704 


579 


97J032 


77 


560673 


655 


439327 


1 


60_ 


534052 


. •'^78 


P72986 


77 


561066 


655 


438934 





1 Cosine 




Sine 1 


Cotang. 




Taiis. 1 AL j 



70 DfL'i- 

15 



38 


C-' 


Degrees.^ a 


TABLE at lo.;arh 


U3I1C 




M. 


1 Sine 


1 D. 


1 Cosine | D. 


1 Tane. 


1 D. 


1 C.tans. 1 j 


~w 


9.5340521 578 


9.972986 


i77 


9.561066 


655 


10.438934 


-60* 


1 


534399 


577 


972940 


77 


661459 


654 


438541 


69 


2 


534745 


577 


972894 


77 


661861 


654 


438149 


58 


3 


535092 


677 


972848 


77 


562244 


653 


437756 


o7 


4 


53543S 


576 


972802 


77 


562636 


663 


437364 


56 


6 


535783 


576 


972765 


77 


563028 


6.53 


436972 


56 


6 


536129 


675 


972709 


77 


56.3419 


652 


436581 


64 


7 


536474 


574 


972663 


77 


563811 


652 


436189 


53 


8 


536818 


574 


972617 


77 


564202 


661 


435798 


52 


9 


537163 


573 


972570 


77 


664592 


651 


435408 


61 


10 

11 


537607 
9.537851 


573 


972524 
9.972478 


77 
77 


564983 


650 


435017 


50 
49 


572 


9.56537S 


650 


10.434627 


12 


538194 


672 


972431 


78 


565763 


649 


434237 


48 


13 


588638 


571 


972385 


78 


666153 


649 


433847 


47 


14 


538880 


571 


972338 


78 


566642 


649 


433458 


46 


15 


539223 


570 


972291 


78 


566932 


648 


433068 


45 


16 


539565 


570 


972245 


78 


567320 


648 


432680 


44 


17 


539907 


669 


972198 


78 


667709 


647 


432291 


43 


18 


540249 


569 


972151 


78 


568098 


647 


431902 


42 


19 


.540590 


568 


972105 


79 


568486 


646 


431514 


41 


20 

21 


.540931 


568 


972058 


78 
78 


568873 


646 


431127 
10.430739 


40 
39 


9.541272 


567 


9.972011 


9.669261 


645 


22 


.541613 


567 


971964 


78 


669648 


645 


430352 


38 


23 


541963 


666 1 


971917 


78 


570035 


645 


429965 


37 


24 


542293 


566 i 


971870 


78 


570422 


644 


429578 


36 


25 


.542632 


665 i 


971823 


78 


570809 


644 


429191 


35 


26 


542971 


566 ; 


971776 


78 


671195 


643 


428805 


34 


27 


543310 


664 i 


971729 


79 


571581 


643 


428419 


33 


28 


543649 


664 ; 


971682 


79 


571967 


642 


428033 


32 


29 


543987 


563 


971635 


79 


572362 


642 


427648 


31 


31 


54i326 


663 1 


971588 


79 

79 


572738 
9.573123 


642 


427262 
10.426877 


30 

29 


9.544663 


662 1 


9.971540 


641 


32 


545000 


562 j 


971493 


79 


673607 


641 


426493 


28 


33 


54533S 


561 1 


971446 


79 


573892 


640 


426108 


27 


34 


645P,74 


561 i 


971398 


79 


574276 


640 


425724 


26 


35 


546011 


560 


971351 


79 


574660 


639 


425340 


26 


36 


546347 


560 ; 


971303 


79 


575044 


639 


424956 


24 


37 


546683 


&59 ! 


971256 


79 


675427 


639 


424573 


23 


38 


547019 


559 ' 


971208 


79 


67.5810 


638 


424190 


22 


39 


547354 


558 1 


971161 


79 


676193 


638 


423807 


21 


40 
41 


547089 


558 ! 


971113 
9.971066 


79 
80 


676576 


637 


423424 


20 
19 


9.548024 


557 


9.676958 


637 


10.423041 


42 


548359 


557 > 


971018 


80 


677341 


636 


422659 


18 


43 


548693 


556 


970970 


80 


577723 


636 


422277 


n 


44 


549027 


556 


970922 


80 


578104 


636 


421896 


16 


45 


549360 


655 


S70874 


80 


578486 


635 


421514 


15 


46 


649693 


555 


970827 


80 


578867 


635 


421133 


14 


47 


650026 


554 


970779 


80 


579248 


634 


420752 


13 


48 


550359 


654 


970731 


80 


579629 


634 


420371 


12 


49 


550692 


6.53 


970683 


80 


580009 


634 


419991 


11 


50 
51 


551024 


653 


970635 


fiO 
80 


580389 
9.580769 


633 


419611 
10.419231 


10 
9 


9.551356 


552 


9.970586 


633 


52 


551687 


552 


970538 


80 


581149 


632 


418851 


8 


53 


5.52018 


652 


970490 


80 


581528 


632 


418472 


7 


54 


552349 


551 


970442 


80 


5S1907 


632 


418093 


6 


56 


552680 


551 


970394 


80 


682286 


631 


417714 


6 


56 


553010 


550 


970345 


81 


582&65 


631 


417335 


4 


57 


553341 


550 


970297 


81 


583043 


630 


416957 


3 


58 


553670 


649 


970249 


81 


583422 


630 


416578 


2 


59 


654000 


549 


970200 


81 


583800 


629 


416200 


1 


60 


554329 


548 


9701,52 


81 


584177 


629 


. 415823 







Cof^iiJf 




1 S>n. 1 


Cotang. 




Tang. [ 


W 



Degrt-fcs, 





SINES AND TANOENTs. (21 Degrees 


•; 


39 


_M_| 


Sine 1 


D. 1 


Cosine | D. | 


Tang. 1 


D. 1 


Cntang. | | 


U 


9.554329 


548 


9.970152 


81 


9.584177 


629 


10.415823 


60 


1 


554658 


548 


970103 


81 


584555 


629 


415445 


59 


2 


554987 


547 


970055 


81 


684932 


628 


415068 


58 


3 


555315 


547 


970006 


81 


585309 


628 


414691 


57 


4 


556643 


546 


969957 


81 


585686 


627 


414314 


56 


6 


555971 


546 


969909 


81 


586062 


627 


413938 


65 


8 


556299 


545 


969860 


81 


586439 


627 


413561 


54 


7 


556626 


545 


969811 


81 


586815 


626 


4131&5 


53 


8 


556953 


544 


969762 


81 


587190 


626 


412810 


52 


9 


557280 


544 1 


969714 


81 


587566 


625 


412434 


51 


10 
11 


557606 


543 


969665 
9.969616 


81 

82 


587941 


625 

625 


412059 
10.411684 


50 
49 


9.557932 


543 


9.588316 


12 


558258 


643 


969567 


82 


588691 


624 


411309 


48 


13 


558583 


542 


969518 


82 


589066 


624 


410934 


47 


14 


558909 


542 


969469 


82 


589440 


623 


410560 


46 


15 


659234 


541 


969420 


82 


589814 


623 


410186 


45 


16 


559558 


541 


969370 


82 


590188 


623 


409812 


44 


17 


659883 


540 


969321 


82 


590562 


622 


409438 


43 


18 


560207 


540 


969272 


82 


690935 


622 


409065 


42 


19 


560531 


539 


969223 


82 


.'^91308 


622 


408692 


41 


20 
21 


560855 


539 


969173 


82 
82 


591681 
9.592054 


621 


408319 


40 
39 


9.561178 


538 


9.969124 


621 


10.407946 


22 


561501 


538 


969075 


82 


692426 


620 


407674 


38 


23 


561824 


537 


969025 


82 


592798 


620 


407202 


37 


24 


562146 


.537 


968976 


82 


593170 


619 


406829 


36 


25 


562468 


536 


968926 


83 


593542 


619 


406468 


35 


26 


562790 


6.36 


968877 


83 


593914 


618 


406086 


34 


27 


563112 


536 


968827 


83 


594285 


618 


405715 


33 


28 


563433 


535 


968777 


83 


594656 


618 


405344 


32 


29 


563755 


536 


968728 


83 


595027 


617 


404973 


31 


30 

31" 


564075 


534 


968678 
9.968628 


83 

83 


595398 
9.. 595768 


617 
617 


404602 
10.404232 


30 

29 


9.. 564396 


534 


32 


564716 


.533 


968578 


83 


596138 


616 


403862 


28 


33 


565036 


533 


968528 


83 


696508 


616 


403492 


27 


34 


565356 


532 


968479 


83 


596878 


616 


403122 


26 


*.J5 


565076 


532 


968429 


83 


597247 


615 


402763 


25 


36 


565995 


631 


968379 


83 


597616 


616 


402384 


24 


37 


566314 


.531 


968329 


83 


597986 


616 


402015 


23 


38 


566632 


531 


968278 


83 


598354 


614 


401646 


22 


39 


566951 


530 


968228 


84 


598722 


614 


401278 


21 


40 
41 


567269 


630 


968178 
9.968128 


84 
84 


599091 


613 


400909 
10.400541 


20 
19 


9.567587 


529 


9.599459 


613 


42 


567904 


529 


968078 


84 


599827 


613 


400173 


18 


43 


668222 


528 


968027 


84 


600194 


612 


399806 


17 


44 


568539 


528 


967977 


84 


600562 


612 


399438 


16 


45 


668856 


.528 


967927 


84 


600929 


611 


399071 


15 


46 


569172 


527 


967876 


84 


601296 


611 


398704 


14 


!7 


569488 


527 


967826 


84 


601602 


611 


398338 


13 


if=^ 


569804 


526 


967775 


84 


602029 


610 


397971 


12 


A\i 


570120 


526 


967726 


84 


602395 


610 


397605 


11 


50 
M 


570435 


525 


967674 
9.967624 


84 
84 


602761 


610 


397239 
10.396873 


10 
9 


9.570751 


526 


9.603127 


609 


62 


571066 


524 


967573 


84 


603493 


609 


396507 


8 


53 


571380 


524 


967522 


85 


603858 


609 


396142 


7 


54 


571695 


523 


967471 


85 


604223 


608 


396777 


6 


55 


672009 


523 


967421 


85 


604588 


608 


395412 


5 


56 


572323 


523 


967370 


85 


604953 


607 


395047 


4 


57 


573636 


522 


967319 


85 


605317 


607 


394683 


3 


58 


57295C 


522 


967268 


85 


605682 


607 


394318 


2 


59 


573262 


521 


967217 


86 


606046 


606 


393954 


1 


60 


57357£ 


521 


967166 


85 


606410 


606 


393590 







1 Conine 


j 


1 Sine 1 


1 C.l;u>g. 


I 


1 Tantr. \M.\ 



iiS Uegi 



40 



(22 Degrees.; a tab/.js of LOGARtxnMic 



M. I 



I p. I Cosine | D. | Tanz. | D. 



Cotiinc j 



8 

9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
&7 
58 
59 
60 



9. n73575' 


521 i 


9.967166 


573888 


.520 


967115 


574200 


520 


907064 


574512 


519 


967013 


574824 


519 


966961 


575136 


519 


966910 


575447 


518 


966859 


575758 


518 


966808 


570069 


517 


966756 


576379 


517 


966705 


576689 


516 


966663 
9.966602 


9.576999 


516 


577309 


516 


966550 


577618 


515 


966499 


577927 


515 


966447 


578236 


514 


966395 


678545 


514 


966344 


578853 


513 


966292 


579162 


513 


966240 


579470 


513 


966188 


579777 


612 


966136 
9 966085 


9.. 580085 


bl2 


580392 


511 


966033 


5S0699 


511 


96.5981 


581005 


511 


965928 


581312 


510 


965876 


581618 


510 


965824 


581924 


509 


965772 


682229 


509 


905720 


582535 


509 


965668 


582840 


508 


965615 


9.583145 


508 


9.965563 


583449 


507 


965611 


683754 


607 


96.5468 


5840.58 


506 


96.5406 


684361 


506 


965353 


684665 


-^06 


965301 


584968 


505 


965248 


585272 


505 


965195 


585574 


504 


965143 


585877 


504 


965090 
9.965037 


9.586179 


503 


586482 


503 


964984 


686783 


503 


964931 


587085 


502 


964879 


587386 


502 


964826 


587688 


501 


964773 


587989 


501 


964719 


588289 


501 


964666 


588590 


500 


964613 


688890 


600 


964560 


9.589190 


499 


9.964607 


589489 


499 


964454 


589789 


499 


964400 


690088 


498 


964347 


590387 


498 


964294 


690686 


497 


964240 


690984 


497 


964187 


591282 


497 


964133 


691580 


496 


964080 


591878 


496 


964026 



,606410 
606773 
607137 
607500 
607863 
608225 
608588 
608950 
609312 
609674 
610036 



9.610397 
610759 
611120 
611480 
611841 
612201 
612561 
612921 
613281 
613641 



9.614000 
614359 
614718 
616077 
615435 
615793 
616161 
616509 
616867 
617224 



9 617582 
617939 
618296 
618652 
619008 
619364 
619721 
620076 
620432 
620787 



9.621142 
621497 
621852 
622207 
622561 
622915 
623269 
623623 
623976 
624330 



9.624683 
625036 
625388 
625741 
626093 
626445 
626797 
627149 
627501 
627852 



600 
606 
605 
605 
604 
604 
604 
603 
603 
603 
602 



602 
602 
601 
601 
601 
600 
600 
600 
699 
599 



598 
698 
598 
597 
597 
697 
596 
596 
596 
595 



.596 
695 
594 
694 
694 
693 
593 
693 
592 
592 



10.393590 
393227 
892863 
392500 
392137 
391775 
391412 
391050 
390688 
390326 

389964 

10.389603 
389241 
388880 
388520 
388159 
.387799 
387439 
387079 
386719 
386359 



10, 



10. 



692 
691 
691 
690 
690 
690 
689 
689 
589 
588 



588 
588 
687 
687 
687 
586 
686 
.586 
585 
585 



386000 
385641 
38.5282 
384923 
384565 
384207 
383849 
383491 
383133 
382776 
383418 
382061 
381705 
381348 
380992 
380636 
380279 
379924 
379668 
379213 



10.378868 
378503 
378148 
377793 
377439 
377085 
376731 
376377 
376024 
375670 



10.375317 
374964 
374612 
374259 
373907 
373.555 
373203 
372851 
372499 
372148 



60 

59 

58 

67 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

3: 

32 

31 

30 

29 

28 

27 

56 

25 

24 

23 

22 

21 

20 

19 
18 
17 
16 
15 
14 
13 
12 
11 

9 



I 1 



Cotaii". 



I ''-''^- I 



67 DeKrp/^s 





^ 


ixrs AND TANGENTS. (23 Degrccs.j 


4i 


M. 


1 Sine 


I «• 


Cosine i D. 


Tang 


D. 


CotaT.g. 1 1 


'^ 


9.591878 


496 


9.964026 


89 


9.627852 


585 


10.372148 


"60' 


1 


592176 


495 


963972 


89 


628203 


585 


371797 


59 


2 


592473 


495 


963919 


89 


628554 


585 


371446 


58 


3 


592770 


495 


963865 


90 


628905 


584 


371095 


57 


4 


593067 


494 


963811 


90 


629255 


584 


370745 


56 


5 


593363 


494 


963757 


90 


629606 


583 


370394 


55 


6 


593659 


493 


963704 


90 


629956 


583 


370044 


54 


7 


593955 


493 


963650 


90 


630306 


583 


369694 


53 


8 


594251 


493 


963596 


90 


630656 


583 


369344 


52 


9 


594547 


492 


963542 


90 


631005 


582 


368995 


51 


10 
11 


594842 


492 


963488 


90 
90 


631355 


582 


368645 


50 
49 


9.595137 


491 


9.963434 


9.631704 


582 


10.368296 


12 


595432 


491 


963379 


90 


632053 


581 


367947 


48 


13 


595727 


491 


963325 


90 


632401 


581 


367599 


47 


14 


596021 


490 


963271 


90 


632750 


581 


367250 


46 


lo 


596315 


490 


963217 


90 


633098 


580 


366902 


45 


16 


596609 


489 


963163 


90 


633447 


580 


366553 


44 


17 


596903 


489 


963108 


91 


633795 


580 


366205 


43 


18 


597196 


489 


963054 


91 


634143 


579 


365857 


42 


19 


597490 


488 


962999 


91 


634490 


579 


365510 


41 


20 

21 


597783 


488 


962945 


91 
91 


634838 


579 


365162 
10.364815 


40 
39 


9.598075 


487 


9.962890 


9.635185 


578 


22 


598368 


487 


962836 


91 


635532 


578 


364468 


38 


23 


598660 


487 


962781 


91 


63.5879 


578 


364121 


37 


24 


598952 


486 


962727 


91 


638226 


577 


363774 


36 


i.o 


599244 


486 


962672 


91 


636572 


577 


363428 


35 


26 


599536 


485 


962617 


91 


636919 


577 


363081 


34 


27 


599827 


485 


962562 


91 


637265 


577 


362735 


33 


28 


600118 


485 


962508 


91 


637611 


576 


362389 


32 


29 


600409 


484 


962453 


91 


637956 


576 


362044 


31 


30 
31 


600700 


484 


962398 


92 
92 


638302 


576 


361698 
10.361353 


30 
29 


9.600990 


484 


9.962343 


9.638647 


575 


32 


601280 


483 


962288 


92 


638992 


575 


361008 


28 


33 


601570 


483 


962233 


92 


639337 


575 


360663 


27 


34 


601860 


482 


962178 


92 


639682 


574 


360318 


26 


35 


602150 


482 


962123 


92 


640027 


574 


359973 


25 


36 


602439 


482 


962067 


92 


640371 


574 


359629 


24 


37 


602728 


481 


962012 


92 


640716 


573 


359284 


23 


38 


603017 


481 


961957 


92 


641060 


573 


358940 


22 


39 


603305 


481 


961902 


92 


641404 


573 


358596 


21 


40 
41 


603594 


480 


961846 


92 
92 


641747 


572 


358253 


20 
19 


9.603882 


480 


9.961791 


9.642091 


l?l 


10.357909 


42 


604170 


479 


961735 


92 


642434 


357566 


18 


43 


604457 


479 


961680 


92 


642777 


572 


357223 


17 


44 


604745 


479 


961624 


93 


643120 


571 


356880 


16 


45 


60.5032 


478 


961569 


93 


64.St63 


571 


356537 


15 


46 


605319 


478 


961513 


93 


643806 


571 


356194 


14 


47 


605606 


478 


961458 


93 


644148 


570 


355852 


13 


48 


605892 


477 


961402 


93 


644490 


570 


355510 


12 


49 


606179 


477 


961346 


93 


644832 


570 


355168 


11 


50 
51 


606465 


476 


961290 
9.961235 


93 
93 


645174 


569 


354826 
10.354484 


10 
9 


9 606751 


476 


9.645516 


569 


52 


607036 


476 


961179 


93 


645857 


569 


354143 


8 


53 


607322 


475 


961123 


93 


646199 


569 


353801 


7 


54 


607607 


475 


961067 


93 


646540 


568 


353460 


6 


55 


607892 


474 


961011 


93 


646881 


568 


353119 


5 


56 


608177 


474 


960955 


93 


647222 


568 


352778 


4 


57 


608461 


474 


960899 


93 


647562 


567 


352438 


3 


5;^ 


608745 


473 


960843 


94 


647903 


567 


352097 


2 


59 


609029 


473 


960786 


94 


648243 


567 


351757 


1 


60 


609313 


473 


960730 


94 


6485S3 


566 


351417 





^ 


Cosine 




Sine 1 


Coiane. 




TanfT. , M | 



^ Degrees. 



42 


(24 DegreesO a 


TABLE OP LOGARITHMIC 




IP 


Sine 


D. 


1 Cosine 1 D. 


'i'ang. 


D. 


Cotang. 1 1 


"o 


9.609313 


473 


9.960730 


94 


9.648.583 


566 


10.351417 


60 


1 


609597 


472 


960674 


94 


648923 


566 


351077 


59 


2 


6098S0 


472 


960618 


94 


649263 


566 


650737 


58 


3 


610164 


472 


960561 


94 


649602 


566 


350398 


57 


4 


610447 


471 


960505 


94 


649942 


565 


350058 


56 


5 


610729 


471 


960448 


94 


6.50281 


565 


349719 


55 


6 


611012 


470 


960392 


94 


650020 


565 


349380 


54 


7 


611294 


470 


960335 


94 


650959 


564 


3490il 


53 


8 


. 611576 


470 


960279 


94 


651297 


564 


348703 


52 


y 


611858 


469 


96-0222 


94 


651636 


564 


348364 


61 


10 

11 


612140 


469 


960165 


94 
95 


651974 


563 


348026 
10.347688 


60 

49 


9.612421 


469 


9.960109 


9.652312 


563 


12 


612702 


468 


960052 


95 


652650 


563 


347350 


48 


13 


612983 


468 


959995 


95 


652988 


563 


347012 


47 


14 


613264 


467 


959938 


95 


653326 


662 


346674 


46 


15 


613545 


467 


959882 


95 


653663 


562 


346337 


45 


Ifi 


613825 


467 


959825 


95 


654000 


562 


346000 


44 


17 


614105 


466 


959768 


95 


654337 


561 


345663 


43 


18 


614385 


466 


959711 


95 


654674 


561 


345326 


42 


19 


614665 


466 


959654 


95 


655011 


561 


344989 


41 


20 
21 


614944 


465 


959596 


95 
95 


655348 


561 


344652 
10.344316 


40 
39 


9.615223 


465 


9.959539 


9.655684 


560 


22 


615502 


465 


959482 


95 


656020 


560 


343980 


38 


23 


615781 


464 


959425 


95 


656356 


560 


343644 


37 


24 


616060 


464 


959368 


95 


656692 


559 


343308 


36 


25 


616338 


464 


959310 


96 


657028 


559 


342972 


36 


26 


616616 


463 


959253 


96 


657364 


559 


342636 


34 


27 


616894 


463 


959195 


96 


657699 


559 


342301 


33 


28 


617172 


462 


959138 


96 


6580,S4 


558 


341966 


32 


29 


617450 


462 


959081 


96 


658369 


558 


341631 


31 


30 

31 


617727 


462 


959023 


96 
96 


658704 


558 


341296 


30 

29 


9.618004 


461 


9.958965 


9.6.59039 


558 


10.340961 


32 


618281 


461 


958908 


96 


6.59373 


557 


340027 


28 


33 


618558 


461 


958850 


96 


659708 


.557 


340292 


27 


34 


618834 


460 


958792 


96 


660042 


557 


339958 


26 


35 


619110 


460 


958734 


96 


660376 


557 


339624 


25 


36 


619386 


460 


958677 


96 


660710 


556 


339290 


24 


37 


619662 


459 


958619 


96 


661043 


556 


338957 


23 


38 


619938 


459 


958561 


96 


661377 


556 


338623 


22 


39 


620213 


459 


958503 


97 


661710 


555 


338290 


21 


40 
41 


620488 


458 


958445 
9.9.58387 


97 
97 


662043 


555 


337957 
10.337624 


20 
19 


9.620763 


458 


9 662376 


555 


42 


621038 


457 


958329 


97 


662709 


554 


337291 


18 


43 


621313 


457 


958271 


97 


663042 


554 


336958 


17 


4-1 


621587 


457 


958213 


97 


663375 


654 


336625 


16 


45 


621861 


456 


y.581.54 


97 


663707 


554 


336293 


15 


46 


622135 


456 


958096 


97 


664039 


653 


335961 


14 


47 


622409 


456 


958038 


97 


664371 


663 


335629 


13 


48 


622682 


455 


957979 


97 


664703 


6.53 


335297 


12 


49 


622956 


455 


957921 


97 


665035 


663 


834965 


11 


50 
51 


623229 


455 


957863 
9.9.57804 


97 

97 


665366 


562 


334634 


10 
9 


9.623502 


454 


9.665697 


652 


10.334303 


52 


623774 


454 


957746 


98 


666029 


552 


333971 


8 


53 


624047 


454 


9.57687 


98 


666360 


651 


333640 


7 


54 


624319 


453 


957628 98 


666691 


551 


.333309 


6 


55 


624591 


453 


957570 98 


667021 


551 


332979 


5 


56 


624863 


453 


957511 98 


6673.52 


551 


332648 


4 


57 


625135 


452 


957452 


98 


667682 


550 


332318 


3 


58 


625406 


452 


957393 


98 


668013 


550 


331987 


2 


69 


625677 


452 


957.335 


98 


668343 


550 


331657 


1 


60 


625918 


451 


9572761 98 


668672 


550 


331328 







1 Cosine 




1 Sine 1 


Colang. 


1 


1 I'ang. 1 M. 1 



65 Dc-grees. 



SINKS A XT) TA^'al:^'TS. (25 Degrees.) 



43 



M. 


Sine 


I). 


Cosine | D. 


1 Tang. 


D. 


Cotang. j 1 





9.625948 


451 , 


9.957276 


98 


9.668673 


550 


10. 3313271 


60 


1 


626219 


451 


957217 


98 


669002 


549 


330998 


59 


2 


626490 


451 


957158 


98 


669332 


549 


33066« 


58 


3 


626760 


450 


957099 


98 


669661 


549 


330339 


57 


4 


627030 


450 


957040 


98 


669991 


548 


3:'0009 


66 


5 


627300 


450 


956981 


98 


670320 


548 


329680 


55 


6 


627570 


449 


956921 


99 


670649 


548 


329351 


54 


7 


627840 


449 


956862 


99 


670977 


548 


329023 


53 


8 


628109 


449 


956803 


99 


671306 


547 


328894 


52 


9 


628378 


448 


956744 


99 


671634 


547 


328366 


51 


10 
11 


628647 
9.628916 


448 
447 


956684 


99 
99 


671963 


547 


328037 
10.327709 


50 
49 


9.956625 


9.672291 


547 


12 


629185 


447 


956566 


99 


672619 


546 


327381 


48 


13 


629453 


447 


956506 


99 


672947 


546 


327053 


47 


14 


629721 


446 


956447 


99 


673274 


546 


326726 


46 


16 


629989 


446 


956387 


99 


673602 


546 


326398 


45 


16 


630257 


446 


956327 


99 


673929 


545 


326071 


44 


17 


630524 


446 


956268 


99 


674257 


545 


326743 


43 


18 


630792 


445 


956208 


100 


674584 


545 


325416 


42 


19 


631059 


445 


956148 


100 


674910 


544 


325090 


41 


20 
21 


631326 


445 


956089 


100 
100 


675237 
9.675564 


544 
544 


324763 


40 
39 


9.631593 


444 


9.956029 


10.324436 


22 


631859 


444 


955969 


100 


675890 


544 


324110 


38 


23 


632125 


444 


955909 


100 


676216 


543 


323784 


37 


24 


632392 


443 


955849 


100 


676543 


543 


323457 


36 


25 


632658 


443 


955789 


100 


676869 


543 


323131 


35 


26 


632923 


443 


955729 


100 


677194 


543 


322806 


34 


27 


633189 


442 


955669 


100 


677520 


542 


322480 


33 


28 


633454 


442 


955609 


100 


677846 


542 


322154 


32 


29 


633719 


442 


955548 


100 


678171 


642 


321829 


31 


30 
31 


633984 


441 


955488 
9.955428 


100 
101 


678496 
9.678821 


542 
641 


321604 
10.321179 


30 
29 


9.634249 


441 


32 


634514 


440 


955368 


101 


679146 


541 


320864 


28 


33 


634778 


440 


955307 


101 


679471 


541 


320529 


27 


34 


635042 


MO 


955247 


101 


679795 


541 


320206 


20 


35 


635306 


439 


955186 


101 


680120 


640 


319880 


26 


36 


635570 


439 


955126 


101 


680444 


640 


319556 


24 


37 


635834 


439 


955065 


101 


680768 


540 


319232 


23 


38 


636097 


438 


955005 


101 


681092 


540 


318908 


22 


39 


636360 


438 


954944 


101 


681416 


539 


318584 


21 


40 
41 


636623 


438 


954883 
9 954823 


101 
101 


681740 


539 


318260 


20 
19 


9.636886 


43/ 


9.682063 


539 


10.317937 


42 


637148 


437 


954762 


101 


682387 


639 


317013 


18 


43 


637411 


437 


954701 


101 


682710 


538 


317290 


17 


44 


637673 


437 


954640 


101 


683033 


538 


316967 


16 


45 


637935 


436 


954579 


101 


683356 


638 


31 6644 


16 


46 


638197 


436 


954518 


102 


683679 


538 


316321 


14 


47 


638458 


436 


954457 


102 


684001 


537 


315999 


13 


48 


638720 


435 


954396 


102 


684324 


537 


315676 


12 


49 


638981 


435 


954335 


102 


684646 


537 


316354 


11 


50 


639242 


435 


954274 


102 


684968 


637 


315032 


10 


51 


9.639503 


434 


9.954213 


102 


9.685290 


636 


10.314710 


9 


52 


639764 


434 


954152 


102 


685612 


536 


314388 


8 


53 


640024 


434 


954090 


102 


685934 


536 


314066 


7 


54 


640284 


433 


954029 


102 


686255 


636 


313745 


6 


55 


640544 


433 


953968 


102 


686577 


535 


313423 


5 


56 


640804 


433 


953906 


102 


686898 


535 


313102 


4 


57 


641064 


432 


963845 


102 


687219 


535 


312781 


3 


58 


641324 


432 


953783 


102 


687640 


536 


312460 


2 


59 


641584 


432 


953722 


103 


687861 


534 


312139 


1 


60 


641842 


431 


953660 


103 


688182 


534 


3118IS 







Co:^ine 




1 Sine 1 


Colang. 




Tan,. 


fu. 



64 Degrees. 



44 



(26 Degrees.) a table of logarithmic 



M. 


Sine 


D. 


Cosine 1 D. 


T... 


D 


1 Clang. ) j 





9.641842 


431 


9,9.53660 


103 


9.688182 


534 


10.311818 


60 


] 


642101 


431 


953599 


103 


688502 


534 


311498 


59 


2 


642360 


431 


053537 


103 


688823 


534 


311177 


58 


3 


642618 


430 


953475 


103 


689143 


533 


310857 


57 


4 


642877 


430 


953413 


103 


689463 


533 


310.537 


56 


5 


643135 


430 


953352 


103 


689783 


533 


310217 


55 


6 


643393 


430 


953290 


103 


690103 


533 


309897 


54 


7 


643650 


429 


953228 


103 


690423 


533 


309577 


53 


8 


643908 


429 


953166 


103 


690742 


532 


309258 


52 


9 


644165 


429 


953104 


103 


691062 


532 


308938 


51 


10 

11 


644423 


428 


953042 


103 
104 


691381 


532 


308619 
10.308300 


50 
49 


9.644680 


428 


9.9.529S0 


9.691700 


531 


12 


644936 


428 


952918 


104 


692019 


531 


307981 


48 


13 


645193 


427 


952855 


104 


692338 


531 


307662 


47 


14 


645450 


427 


952793 


104 


692856 


531 


307344 


46 


15 


645706 


427 


952731 


104 


692975 


531 


307025 


45 


16 


645962 


426 


952669 


104 


693293 


530 


306707 


44 


17 


646218 


426 


952606 


104 


693612 


530 


306388 


43 


18 


646474 


426 


952544 


104 


693930 


530 


306070 


42 


19 


646729 


425 


952481 


104 


694248 


530 


305752 


41 


20 


6469841 


425 


952419 
9.9523.56 


104 
104 


694566 


529 


305434 


40 
39 


9.647240; 


425 


9.694883 


529 


10.305117 


•>■■> 


647494 


424 


952294 


104 


695201 


529 


304799 


38 


•73 


647749' 


424 


952231 


104 


695518 


529 


304482 


37 


2-1 


648004 


424 


952168 


105 


695836 


529 


304164 


36 


'/5 


648258 


424 


952106 


105 


696153 


528 


303847 


35 


2'J 


648512 


423 


952043 


105 


696470 


528 


303530 


34 


27 


648766 


423 


951980 


105 


696787 


528 


303213 


33 


28 


649020 


423 


951917 


105 


697103 


528 


302897 


32 


29 


649274 


422 


951854 


105 


697420 


527 


302580 


31 


30 
31 


649527 


422 


951791 


105 
105 


697736 


527 


302264 


30 
29 


9.649781 


422 


9.951728 


9.698053 


527 


10.301947 


32 


650034 


422 


951665 


105 


698369 


527 


301631 


28 


3.3 


650287 


421 


951602 


105 


698685 


526 


301315 


27 


34 


650.539 


421 


951.5.39 


105 


699001 


526 


300999 


26 


35 


650792' 


421 


951476 


105 


699316 


526 


300684 


25 


36 


651044 


420 


951412 


105 


699632 


526 


300368 


24 


37 


651297 


420 


951349 


106 


699947 


526 


300053 


23 


38 


051.549 


420 


951286 


106 


700263 


525 


299737 


22 


39 


651800 


419 


951222 


106 


700578 


525 


299422 


21 


40 
4\ 


652052 


419 


951159 


106 
106 


700893 


525 


299107 
10.298792 


20 
19 


9.652304 


419 


9.951096 


9.701208 


524 


42 


652555 


418 


951032 


106 


701523 


524 


298477 


18 


43 


652806 


418 


950968 


106 


7018.37 


524 


298163 


17 


44 


653057 


418 


9.50905 


106 


702152 


524 


297848 


16 


45 


653308 


418 


950841 


106 


702466 


524 


297534 


15 


46 


653558 


417 


950778 


106 


702780 


523 


297220 


14 


47 


653808 


417 


950714 


106 


703095 


523 


296905 


13 


48 


654059 


417 


9506.50 


106 


703409 


523 


296591 


12 


49 


654309 


416 


950586 


106 


703723 


.523 


296277 


11 


50 
51 


6.54558 


416 


950522 
9.950458 


107 
107 


704036 


522 


295964 
10.295650 


10 
9 


9.654808 


416 


9.7043.50 


522 


52 


655058 


416 


950394 


107 


704663 


522 


295337 


8 


53 


655307 


415 


950330 


107 


704977 


522 


295023 


7 


54 


655556 


415 


950266 


107 


705290 


522 


294710 


6 


55 


655805 


415 


950202 


107 


705603 


521 


294397 


5 


56 


656054 


414 


950138 


107 


705916 


.521 


294084 


4 


57 


656302 


414 


950074 


107 


706228 


521 


293772 


3 


58 


656551 


414 


950010 


10-^ 


706541 


521 


293459 


2 


59 


656799 


413 


949945 


107 


706854 


521 


293146 


1 


60 


657047 


413 


949881 


107 


707166 


520 


292834 







CoLiiiie 




1 ^i..e 1 


Cntani|. 


1 


j Tang. j M. | 



fi3 Degrees. 





sixNEs AND TA.NGENTS. (27 Pegrcei 





45 


M_ 


Sine 1 


D 


Cosine i D. 


Tang. 


D. 


Cotang. , 1 


"o" 


P. 657047 


413 


9.949881 


107 


9.707166 


520 


10.292834 


60 


1 


657295 


413 


949816 


107 


707478 


520 


292522 


5Q 


2 


657542 


412 


949752 


107 


707790 


520 


292210 


f^ 


3 


657790 


412 


949688 


108 


708102 


520 


291898 


57 


4 


0JSO37 


412 


949623 


108 


708414 


519 


291586 


56 


5 


658284 


412 


949558 


108 


708726 


519 


291274 


55 


6 


658531 


411 


949494 


108 


709037 


519 


290903 


54 


7 


658778 


411 


949429 


108 


709349 


519 


290651 


53 


8 


659025 


411 


949364 


108 


709660 


519 


290340 


52 


9 


659271 


410 


949300 


108 


709971 


518 


290029 


51 


10 
11 


659517 


410 


949235 
9.949170 


108 
108 


710282 


518 


289718 


50 
49 


9.659763 


410 


9.710593 


518 


10.289407 


12 


660009 


409 


949105 


108 


710904 


518 


289096 


48 


13 


660255 


409 


949040 


108 


711215 


518 


288785 


47 


14 


660501 


409 


948975 


108 


711.525 


5.17 


288475 


46 


15 


660746 


409 


948910 


108 


711836 


517 


288164 


45 


16 


660991 


408 


948845 


108 


712146 


517 


287854 


44 


17 


661236 


408 


948780 


109 


712456 


517 


287544 


43 


18 


661481 


408 


948715 


109 


712766 


516 


287234 


42 


19 


661726 


407 


948650 


109 


713076 


516 


286924 


41 


20 
21 


661970 
9.662214 


407 
407 


948584 


109 
109 


713386 


516 


286614 
10.286304 


40 
39 


9.948519 


9.713696 


516 


22 


662459 


407 


948454 


109 


714005 


516 


285995 


38 


23 


662703 


406 


948388 


109 


714314 


515 


285686 


37 


24 


662946 


406 


948323 


109 


714624 


^:5 


285376 


36 


25 


663190 


406 


948257 


109 


714933 


51b 


285067 


35 


26 


663433 


405 


948192 


109 


715242 


515 


284758 


34 


27 


663677 


405 


948126 


109 


715551 


514 


284449 


33 


28 


663920 


405 


948060 


109 


715860 


514 


284140 


32 


29 


664163 


405 


947995 


110 


716168 


514 


283832 


31 


30 


664406 


404 


947929 


110 


716477 


514 


283523 


30 


31 


9 . 664648 


404 


9.947863 


110 


9.716785 


514 


10.283215 


29 


32 


664891 


404 


947797 


110 


717093 


513 


282907 


28 


33 


665133 


403 


947731 


110 


717401 


513 


282599 


27 


34 


665375 


403 


947665 


110 


717709 


513 


282291 


26 


36 


665617 


403 


947600 


110 


718017 


513 


281983 


25 


36 


665859 


402 


947533 


110 


718325 


518 


281670 


24 


37 


666100 


402 


947467 


110 


718633 


512 


281367 


23 


38 


666342 


402 


947401 


110 


718940 


512 


281060 


22 


39 


666583 


402 


947335 


110 


719248 


512 


280752 


21 


40 
41 


666824 


401 


947269 
9.947203 


110 
110 


719555 


512 


280445 


20 
19 


9.667065 


401 


9.719862 


512 


10.280138 


42 


667305 


401 


947136 


111 


720169 


511 


279831 


18 


43 


667546 


401 


947070 


111 


720476 


511 


279524 


17 


44 


667786 


400 


947004 


111 


720783 


511 


279217 


16 


45 


668027 


400 


946937 


111 


721089 


511 


278911 


15 


46 


668267 


400 


946871 


111 


721396 


511 


278604 


14 


47 


668506 


399 


946804 


111 


721702 


510 


278298 


13 


48 


668746 


399 


946738 


111 


722009 


510 


277991 


12 


49 


668986 


399 


946671 


111 


722315 


510 


277685 


11 


50 
51 


669225 


399 


946604 


111 
111 


722621 


510 


277379 


10 
9 


9.669464 


398 


9.946538 


9.722927 


510 


10.277073 


52 


669703 


398 


946471 


111 


723232 


509 


276768 


8 


53 


669942 


398 


946404 


111 


723538 


509 


276462 


7 


54 


670181 


397 


946337 


111 


723844 


509 


276156 


6 


55 


670419 


397 


946270 


112 


724149 


509 


275851 


5 


56 


670658 


397 


946203 


112 


724454 


509 


275546 


4 


57 


670896 


1 897 


946136 


112 


724759 


508 


275241 


3 


58 


671134 


396 


946069 


112 


725065 


508 


274935 


2 


59 


671372 


396 


946002 


112 


725369 


508 


274631 


1 


= 


671609 


396 


945935 


112 


725674 


508 


274326 





, 


Ci>suie 


) 


Sine 1 


Cotang. 




1 Tang. |M. 1 



62 Degrees. 



46 



(28 Degrees. j a table of logarithmic 



M 


. 1 Sine 


1 !>• 


I Cosine | D 


1 Taut-. 


1 n. 


1 Cotaui. j 


1 


9.67160 


^ 396 


9.94593. 


31 1121 9.7256741 508 


10.27432' 


J|60 


1 


67184 


7 395 


94.5868 112 725979 508 


27402 


I 59 


2 


67208 


i 395 


945800 112 726284 507 


273716 58 


3 


67232 


I 395 


945733 112 726588 507 


273412 57 


4 


67255f 


i 395 


94566f 


112| 7268921 507 


2731 OS 


) 56 


5 


67279. 


3 394 


94559.^ 


lis 


I 727] 971 507 


27280C 


J 55 


6 


67303$ 


I 394 


945.531 


lis 


72750] 


507 


272499 


54 


7 


67326^ 


i 3G4 


945464 


iia 


72780£ 


506 


272 19S 


53 


8 


67350^ 


) 394 


945396 


113 


728 lOS 


506 


27^891 


52 


9 


67374] 


393 


945328 


113 


728412 


506 


271588 


51 


10 
11 


67397'- 
9.67421S 


^ 393 


945261 
9.945193 


113 
113 


728716 


506 


271284 


50 
49 


I 393 


9.729020 


506 


10.270980 


12 


67444S 


392 


945125 


113 


729323 


505 


270677 


48 


13 


674684 


392 


945058 


113 


729626 


505 


270374 


47 


14 


674919 


392 


944990 


1 113 


729929 


505 


270071 


46 


15 


6751.55 


392 


944922 


113 


730233 


505 


269767 


45 


16 


675390 


391 


944854 


113 


730535 


505 


269465 


44 


17 


675624 


391 


944786 


113 


730838 


504 


269162 


43 


18 


67.5859 


391 


944718 


113 


731141 


504 


268859 


42 


19 


676094 


391 


944650 


113 


731444 


504 


268556 


41 


20 


676328 
9.676562 


390 


944582 


114 
114 


731746 
9.732048 


504 
504 


268254 


40 
39 


21 


390 


9.944514 


10.267952 


22 


676796 


390 


944446 


114 


7.32351 


503 


267649 


38 


23 


677030 


390 


944377 


114 


732653 


503 


267347 


37 


24 


677264 


389 


944309 


114 


732955 


503 


267045 


36 


25 


677498 


389 


944241 


114 


733257 


503 


266743 


35 


26 


677731 


389 


944] 72 


114 


733558 


503 


266442 


34 


27 


677964 


388 


944104 


114 


733860 


502 


266140 


33 


28 


678197 


388 


944036 


114 


734162 


502 


2658.38 


32 


29 


678430 


388 


943967 


114 


734463 


502 


265537 


31 


30 
31 


678683 


388 


943899 
9.943830 


114 
114 


734764 


502 


265236 
10. 26493 i 


30 

29 


9 678895 


387 


9.7.35066 


502 


32 


679128 


387 


943761 


114 


735367 


502 


264633 


28 


33 


679360 


387 


943693 


115 


735668 


501 


264332 


27 


34 


679592 


387 


943624 


115 


735969 


501 


264031 


26 


35 


679824 


386 


943555 


115 


736269 


501 


263731 


25 


36 


680056 


386 


943486 


115 


736570 


501 


263430 24 1 


37 


680288 


386 


943417 


115 


736871 


501 


263129 


23 


38 


680519 


385 


943348 


115 


737171 


500 


262829 


22 


39 


680750 


385 


943279 


115 


737471 


500 


262529 


21 


40 


680982 


385 
385 


943210 


115 
115 


737771 
9.738071 


500 

500 


262229 


20 
19 


41 


9.681213 


9.943141 


10.261929 


42 


681443 


384 


943072 


115 


738371 


500 


261629 


18 


43 


681674 


384 


943003 


115 


738671 


499 


261329 


17 


44 


681905 


384 


942934 


115 


738971 


499 


261029 


16 


45 


682135 


384 


942864 


115 


739271 


499 


260729 


15 


46 


682365 


383 


9427951 


116 


739570 


499 


260430 


14 


47 


682595 


383 


942726 


116 


739870 


499 


260130 


13 


48 


682825 


383 


942656 


116 


740169 


499 


259831 


12 


49 


683055 


383 


942587 


116 


740468 


498 


259532 


11 


50 
51 


683284 
9.683514 


382 


942517 
9.942448 


116 
116 


740767 
9.741066 


498 
498 


259233 


10 
9 


382 


10.258934 


32 


683743 


382 


942378 


116 


741365 


498 


258635 


8 


53 


683972 


382 


942308 


116 


741664 


498 


258336 


7 


54 


684201 


381 


942239 


116 


741962 


49? 


258038 


6 


55 


684430 


381 


942169 


116 


742261 


497 


257739 


5 


56 


684658 


381 


9420991 


116 


742559 


497 


257441 


4 


57 


684887 


380 


942029 


116 


742858 


497 


2.57142 


3 


58 


685115 


380 


941959 


116 


743156 


497 


256844 


2 


59 


685343 


380 


9418891 


117 


743454 


497 


256546 


1 


60 


685571 


380 


9418191 


117 


743752 


496 1 


256248 





u. 


Cosine 1 


...J 


Si no 1 j 


Cotang. 


1 


Tang. 1 M. | 





SINES AND TANCxENTS. 


(29 Degrees 


.; 


47 


J>L_ 


Sine 


D. 


Cosine | D. | Taii^. | 


D. 1 


Cotang. 1 1 





9.685571 


380 


9.941819 


117 


9.743752 


496 


10.256218 


60 


1 


685799 


379 


941749 


117 


744050 


496 


255950 


59 


2 


686027 


379 


941679 


117 


744348 


496 


255652 


58 


3 


68C254 


379 


941609 


117 


744645 


496 


25.5355 


57 


4 


686482 


379 


941539 


117 


744943 


496 


255057 


56 


5 


686709 


378 


941469 


117 


745240 


496 


254730 


55 


6 


086936 


378 


941398 


117 


745538 


495 


2544G2 


54 


7 


687163 


378 


941328 


117 


745835 


495 


254165 


53 


8 


6^7389 


878 


941258 


117 


746132 


495 


2538G8 


52 


9 


687616 


377 


941187 


117 


746429 


495 


253571 


51 


10 
11 


687843 
9.688069 


377 
377 


941117 
9.941046 


117 
118 


746726 


495 


253274 
10.252977 


50 
49 


9.747023 


494 


12 


688295 


377 


940975 


118 


747319 


494 


252681 


48 


13 


688581 


376 


940905 


118 


747616 


494 


252384 


47 


14 


688747 


376 


940834 


118 


747913 


494 


252087 


4C 


15 


688972 


376 


940763 


118 


748209 


494 


251791 


45 


16 


689198 


376 


940693 


118 


748505 


493 


251495 


4^1 


17 


689423 


375 


940622 


118 


748801 


493 


251199 


43 


18 


689648 


375 


940551 


118 


749097 


493 


250903 


42 


19 


689873 


375 


940480 


118 


749393 


493 


250607 


41 


20 
21 


690098 
9 . 690323 


375 

374 


940409 


118 
118 


749689 


493 


250311 
10.250015 


40 
39 


9.940338 


9.749985 


493 


22 


690548 


374 


940267 


118 


750281 


492 


249719 


38 


23 


690772 


374 


940196 


118 


750576 


492 


249424 


37 


24 


690996 


374 


940125 


119 


750872 


492 


249128 


36 


25 


691220 


373 


940054 


119 


751167 


492 


248833 


35 


26 


691444 


373 


939982 


119 


751462 


492 


248538 


34 


27 


691668 


373 


939911 


119 


7517.57 


492 


248243 


33 


28 


691892 


373 


939840 


119 


7520.'>2 


491 


247948 


32 


29 


692115 


372 


939768 


119 


752347 


491 


247653 


31 


30 


692339 


372 


989697 


113 


752642 


491 


247358 


30 


31 


9 . 692562 


372 


9.939625 


119 


9 . 752937 


491 


10.247063 


29 


32 


692785 


371 


939554 


119 


753231 


491 


2467()9 


28 


33 


693008 


371 


939482 


119 


753526 


491 


246474 


27 


34 


693231 


371 


939410 


119 


753820 


490 


246180 


26 


35 


693453 


371 


939339 


119 


7.54115 


490 


245885 


25 


36 


693676 


370 


939267 


120 


7.54409 


490 


245591 


24 


37 


693898 


370 


939195 


120 


754703 


490 


245297 


23 


38 


694120 


370 


9.39123 


120 


7.54997 


490 


245003 


22 


39 


694342 


370 


939052 


120 


755291 


490 


244709 


2] 


40 


694564 


369 


93S9S0 


120 


755585 


489 


244415 


20 


41 


9.694786 


369 


9.938908 


120 


9.755878 


489 


10.244122 


19 


42 


695007 


369 


938836 


120 


756172 


489 


243828 


18 


43 


695229 


360 


938763 


120 


756465 


489 


243535 


17 


44 


695450 


I 368 


938691 


120 


756759 


489 


243241 


16 


45 


695671 


368 


938619 


120 


757052 


489 


242948 


15 


46 


695892 


i .368 


938547 


120 


757345 


488 


242655 


14 


47 


696113 


; 368 


938475 


120 


757638 


488 


242362 


13 


48 


696334 


j .367 


938402 


121 


757931 


488 


242069 


12 


49 


6965.54 


' 367 


938330 


121 


758224 


488 


241776 


11 


50 
51 


696775 


\ 367 


938258 


121 

1 121 


7.58517 


488 


241483 
10.24119C 


10 



9.696995 


; 367 


9.938185 


9.758810 


488 


52 


697215 


1 366 


9.38113 


121 


759102 


487 


24089S 


8 


53 


697435 


366 


93804(1 


i 121 


759395 


487 


240605 


7 


54 


69765^ 


[\ 366 


937967 


121 


759687 


487 


240311 


6 


55 


69787^ 


[\ 366 


937895 


121 


759979 


487 


240021 


5 


56 


69809^ 


H 365 


937825 


J 121 


760272 


487 


23972S 


4 


57 


6983K 


J 365 


93774c 


) 121 


760564 


487 


239436 


3 


58 


698535 


I 365 


93767f 


) 121 


760856 


486 


23914^ 


2 


59 


• 69875 


I 365 


93760^ 


[' 121 


761148 


486 


238855 


' i 


60 


69897 


3 364 


1 93753] 


1 121 


76143J: 


486 


238.561 


J_o 




] Cosine 


1 


Sine 1 1 Coiaiig. 


1 


1 Tang. 


']"m7 








ft 


Def; 


reea. 







48 


(30 Dcgr 


ees.) A 


TABLE OF LOGAniUlMlr 




~ 


Sine 1 


n. 1 


("ot;ine D. | 


Tani;. | 


D. 1 


Cot .nit:. 1 





9.608970 


364 


9.937531 


121 


9.761439 


486 


10.2385611 60 


1 


699189 


364 


9374.58 


122 


761731 


486 


238269 


59 


2 


699407 


364 


937385 


122 


762023 


486 


237977 


58 


3 


699626 


364 


937312 


122 


762314 


486 


237686 


57 


4 


699844 


363 


937238 


122 


762606 


485 


237394 


56 


5 


700062 


363 


937165 


122 


762897 


485 


237103 


55 


6 


70;)280 


363 


937092 


122 


763188 


485 


236812 


54 


7 


700498 


363 


937019 


122 


763479 


485 


23652] 


53 


8 


700716 


363 


936946 


122 


763770 


485 


236230 


52 


9 


700933 


362 


936872 


122 


764061 


485 


235939 


51 


10 
11 


701151 


362 


936799 
9.936725 


122 

122 


764352 


484 


235648 
10.235357 


50 
49 


9.701368 


362 


9.764643 


484 


12 


701. 585 


362 


936652 


123 


764933 


484 


235067 


48 


13 


701802 


361 


936578 


123 


765224 


484 


. 234776 


47 


14 


702019 


361 


936505 


123 


765514 


484 


234486 


46 


15 


702236 


361 


936431 


123 


765805 


484 


234195 


45 


16 


702452 


361 


936357 


123 


766095 


484 


233905 


44 


17 


702669 


360 


936284 


123 


766385 


483 


233615 


43 


18 


702885 


360 


936210 


123 


766675 


483 


233325 


42 


19 


703101 


360 


936136 


123 


766965 


483 


233035 


41 


20 
21 


703317 
9.703533 


360 
359 


936062 
9.935988 


123 
123 


767255 


483 


232745 


40 
39 


9.767545 


483 


10.232455 


22 


703749 


359 


935914 


123 


767834 


483 


232166 


38 


23 


703964 


359 


935840 


123 


768124 


482 


231876 


37 


24 


704179 


359 


935766 


124 


768413 


482 


231587 


36 


25 


704395 


359 


935692 


124 


768703 


482 


231297 


35 


26 


704610 


358 


935618 


124 


768992 


482 


231008 


34 


27 


704825 


358 


935543 


124 


769281 


482 


230719 


33 


28 


705040 


358 


935469 


124 


769570 


482 


230430 


32 


29 


705254 


358 


93.5395 


124 


769860 


481 


230140 


31 


30 
31 


705469 


3.57 


935320 
9.935246 


124 
124 


770148 


481 


229852 


30 

29 


9 705683 


357 


9.770437 


481 


10.229.563 


32 


705898 


357 


935171 


124 


770726 


481 


229274 


28 


33 


706112 


357 


935097 


124 


771015 


481 


228985 


27 


34 


706326 


356 


935022 


124 


771303 


481 


228697 


26 


35 


706539 


356 


934948 


124 


771592 


481 


228408 


25 


36 


700753 


356 


934873 


124 


771880 


480 


228120 


24 


37 


706967 


356 


934798 


125 


772168 


480 


227832 


23 


38 


707180 


355 


934723 


125 


772457 


480 


227543 


22 


39 


707393 


355 


934649 


125 


772745 


480 


227255 


21 


40 
41 


707606 


355 


934574 
9.934499 


125 
125 


773033 


480 


226967 
10.226679 


20 
19 


9.707819 


355 


9.773321 


480 


42 


708032 


354 


934424 


125 


773608 


479 


226392 


18 


43 


708245 


3.54 


934349 


125 


773896 


479 


226104 


17 


44 


708458 


354 


934274 


125 


774184 


479 


225816 


16 


45 


708670 


354 


934199 


125 


774471 


479 


225,529 


15 


46 


708882 


353 


934123 


125 


774759 


479 


225241 


14 


47 


709094 


353 


934048 


125 


775040 


479 


224954 


13 


48 


709306 


353 


933973 


125 


775333 


479 


224667 


12 


49 


709518 


353 


933898 


126 


775621 


478 


224379 


11 


50 
51 


709730 


353 


933822 
9.933747 


126 
126 


775908 


478 


224092 


10 
9 


9 709941 


352 


9.776195 


478 


10.223805 


52 


710153 


352 


933671 


126 


776482 


478 


223518 


8 


53 


710364 


352 


933596 


126 


776769 


478 


223231 


7 


54 


710575 


352 


933520 


126 


777055 


478 


222945 


6 


55 


710786 


351 


933445 


126 


777342 


478 


222658 


5 


56 


710997 


351 


933369 


126 


777628 


477 


222372 


4 


57 


711208 


351 


933293 


126 


777915 


477 


22208.'= 


3 


58 


711419 


351 


933217 


126 


778201 


477 


22179S 


2 


59 


711629 


350 


933141 


126 


778487 


477 


221512 


., 1 


k60 


711839 


350 


933066 


12C 


778774 


477 


221226 


J 



I I 



59 l^egiecs 





S1?JES AND TaNGE^!T.S. 


(31 D 


egrrees 


J 


49 


M. i 


Sine 


D. 1 


Cosine { D. | 


Taim. 1 


D.- 1 


Cutang. I 





9 711839 


350 


9.933066 


126 


9.778774 


477 


10.221226 60 


1 


/I 2050 


350 


932990 


127 


779060 


477 


220940 59 


2 


712260 


350 


932914 


127 


779346 


476 


220654 58 


3 


712469 


349 


932838 


127 


779632 


476 


220368 


57 


4 


712679 


349 


932762 


127 


779918 


476 


220082 


56 


5 


712889 


349 1 


932685 


127 


780203 


476 


219797 


55 


6 


713098 


349 1 


932609 


127 


780489 


476 


219511 


54 


7 


713308 


349 


932533 


127 


780775 


476 


219225 


53 


8 


713517 


348 


932457 


127 


781060 


476 


218940 


52 


9 


713726 


348 


932380 


127 


781346 


475 


218654 


51 


10 
11 


713935 


348 


932304 
9.932228 


3 27 
127 


781631 


475 


218369 


50 
49 


9.714144 


348 1 


9.7819161 


475 


10.218084 


12 


714352 


.347 


932151 


127 


782201 


475 


217799 


48 


13 


714561 


347 


932075 


128 


782486 


475 


217514 


47 


14 


714769 


347 


931998 


128 


782771 


475 


217229 


46 


15 


714978 


347 


931921 


128 


783056 


475 


216944 


45 


16 


715186 


347 


931845 


128 


783341 


475 


216659 


44 


17 


715394 


346 


931768 


128 


783626 


474 


216374 


43 


18 


715602 


346 


931691 


128 


783910 


474 


216090 


42 


19 


715809 


346 


931614 


128 


784195 


474 


215805 


41 


20 

2i 


716017 


346 


931537 


128 
128 


784479 


474 


21.5521 


40 
39 


9.716224 


345 


9.931460 


9.784764 


474 


10.215236 


22 


716432 


345 


931383 


128 


785048 


474 


214952 


3S 


23 


716639 


345 


931306 


128 


785332 


473 


214668 


37 


24 


716846 


345 


931229 


129 


785616 


473 


214384 


36 


25 


717053 


345 


931152 


129 


785900 


473 


214100 


35 


26 


717259 


344 


931075 


129 


786184 


473 


213816 


34 


27 


717466 


344 


930998 


129 


786468 


473 


213532 


33 


28 


717673 


344 


930921 


129 


786752 


473 


213248 


32 


29 


717879 


344 


930843 


129 


787036 


473 


212964 


31 


30 

31 


718085 


343 


930766 


129 
129 


787319 


472 


212681 


30 

29 


9.718291 


343 


9.930688 


9.787603 


472 


10.212397 


32 


718497 


343 


930611 


129 


787886 


472 


212114 


28 


33 


718703 


343 


930533 


129 


788170 


472 


211830 


27 


34 


718909 


343 


930456 


129 


788453 


472 


211547 


26 


35 


719114 


342 


930378 


129 


788736 


472 


211264 


25 


36 


719.320 


342 


930300 


130 


789019 


472 


210981 


24 


37 


719525 


342 


930223 


130 


789302 


471 


210698 


23 


38 


719730 


342 


930145 


130 


789585 


471 


210415 


22 


39 


719935 


341 


930067 


130 


789868 


471 


210132 


21 


40 
41 


720140 


341 


929989 
9.929911 


130 
130 


790151 


471 


209849 


20 
19 


9.720345 


341 


9.790433 


471 


10.209567 


42 


720549 


341 


929833 


130 


790716 


471 


209284 


18 


43 


720754 


340 


929755 


130 


790999 


471 


209001 


17 


44 


720958 


340 


929677 


130 


791281 


471 


208719 


16 


45 


721162 


340 


929599 


130 


791563 


470 


208437 


15 


40 


721366 


340 


929521 


130 


791846 


470 


208154 


14 


47 


721570 


340 


929442 


130 


792128 


470 


207872 


13 


48 


721774 


339 


929364 


131 


792410 


470 


207590 


12 


49 


721978 


339 


929286 


131 


792692 


470 


207308 


11 


50 
51 


722181 
9.722385 


339 
339 


929207 


131 
131 


792974 


470 


207026 


10 
9 


9.929129 


9.793256 


470 


10.206744 


52 


722588 


339 


929050 


131 


793538 


469 


206462 


8 


53 


722791 


338 


928972 


131 


793819 


1 469 


206181 


7 


51 


72299^ 


338 


928893 


131 


794101 


1 469 


205899 


6 


55 


723197 


338 


928815 


131 


794383 


i 469 


205617 


5 


56 


723400 


338 


928736 


131 


794664 


i 469 


205336 


4 


57 


723603 


1 337 


928657 


131 


794945 


469 


205055 


3 


58 


723805 


! 337 


928578 


131 


795227 


469 


204773 


2 


59 


724007 


1 337 


928499 


131 


795508 


468 


204492 


1 


60 


72421C 


1 337 


928420 


131 


i 795789 


1 468 


2042 li 







Ciisiiie 


1 


1 Sine 1 


1 Coiaiii;. 


1 . 


Tang. j M. 1 



58 Degrees 



*., 



M) 


(3 


2 Degrees.) a 


TABLE OF I^OGAEITII.MIC 




nr 


1 Sii.c 


D. 


1 Cosine | D. 


1 Tung. 


f D. 


I Coiang. 1 1 





9.724210 


337 


9 . 928420 


132 


9.795789 


468 


10.204211 


.60 


1 


724412 


337 


928342 


132 


796070 


468 


203930 


59 


2 


724614 


336 


928263 


132 


796351 


468 


203649 


58 


3 


724816 


336 


928183 


132 


796632 


468 


203368 


57 


4 


725017 


335 


928104 


132 


796913 


468 


203087 


56 


6 


725219 


336 


928025 


132 


797194 


468 


202806 


55 


6 


725420 


335 


927946 


132 


797475 


468 


202525 


54 


7 


725622 


335 


927867 


132 


797755 


468 


202245 


53 


8 


725823 


335 


927787 


132 


798036 


467 


201964 


52 


9 


726024 


335 


927708 


132 


798316 


467 


201684 


51 


10 
11 


726225 


335 


927629 


132 
132 


798596 


467 


201404 
10.201123 


50 
49 


9.726426 


334 


9.927.549 


9.798877 


467 


12 


726626 


334 


927470 


133 


799157 


467 


200843 


48 


13 


726827 


334 


927390 


1.33 


799437 


467 


200563 


47 


14 


727027 


334 


927310 


133 


799717 


467 


200283 


46 


15 


727228 


334 


927231 


133 


799997 


466 


200003 


45 


16 


727428 


333 


92T151 


133 


800277 


466 


199r23 


44 


17 


727628 


333 


927071 


133 


800557 


466 


199443 


43 


18 


727828 


333 


926991 


133 


800836 


466 


199164 


42 


19 


728027 


333 


926911 


133 


801116 


466 


198884 


41 


20 

21 


728227 


333 


926831 


133 
133 


801396 


466 


198604 


40 
39 


9.728427 


332 


9.92675] 


9.801675 


466 


10.198325 


22 


728626 


332 


926671 


133 


8019.55 


466 


198045 


38 


23 


728825 


332 


926591 


133 


802234 


465 


197766 


37 


24 


729024 


332 


926511 


134 


802513 


465 


197487 


36 


25 


729223 


331 


926431 


134 


802792 


465 


197208 


35 


26 


729422 


,331 


926351 


134 


803072 


465 


196928 


3t 


27 


729621 


331 


926270 


134 


803351 


465 


196649 


33 


28 


729820 


331 


926190 


134 


803630 


465 


196370 


32 


29 


7.30018 


330 


926110 


134 


803908 


465 


196092 


31 


30 


730216 


330 


926029 


134 


804187 


465 


195813 


30 


31 


9.730415 


330 


9.92.5949 


134 


9.804466 


464 


10.195534 


29 


32 


730613 


3.30 


925868 


134 


804745 


464 


1952.55 


28 


33 


730811 


330 


925788 


134 


80,5023 


464 


194977 


27 


34 


731009 


329 


925707 


134 


805302 


464 


194698 


26 


35 


731206 


329 


925626 


134 


805580 


464 


194420 


25 


36 


731404 


329 


925545 


135 


80.5859 


464 


194141 


24 


37 


731602 


329 


925465 


135 


806137 


464 


193863 


23 


38 


731799 


329 


925384 


135 


806415 


463 


193585 


22 


39 


731996 


328 


92.5303 


135 


806693 


463 


193307 


21 


40 
41 


732193 


328 


925222 
9.925141 


135 
135 


806971 


463 


193029 


20 
19 


9.732390 


328 


9.807249 


463 


10.192751 


42 


732587 


328 


925060 


135 


807527 


463 


192473 


18 


43 


732784 


328 


924979 


135 


807805 


463 


192195 


17 


44 


732980 


327 


924897 


135 


808083 


463 


191917 


16 


45 


733177 


327 


924816 


135 


808361 


463 


191639 


15 


46 


733373 


327 


924735 


136 


808638 


462 


191362 


14 


47 


733569 


327 


924654 


136 


808916 


462 


191084 


I -3 


48 


733765 


327 


924572 


136 


809193 


462 


190807 


12 


49 


733961 


326 


924491 


136 


809471 


462 


190529 


11 


50 
51 


734157 


326 


924409 


136 
136 


809748 


462 


190252 


10 
9 


9.734353 


326 


9.924328 


9.810025 


462 


10.1899751 


52 


734549 


326 


924246 


136 


810302 


462 


189698] 


8 


53 


734744 


325 


924164 


136 


810580 


462 


1894201 


7 


54 


734939 


325 


924083 


136 


810857 


462 


189143 


6 


55 


735135 


325 


924001 


136 


811134 


461 


188866 


5 


56 


735330 


325 


923919 


136 


811410 


461 


188590 


4 


67 


735525 


325 


923837 


136 


811687 


461 


188313 


3 


58 


735719 


324 


923755 


137 


811964 


461 


188036 


2 


59 


735914 


324 


923673 


137 


812241 


461 


187759 


1 


60 


736 1 09 


324 


923591 


137 


812517 


461 


187483 





n; 


Cosine 


1 


Sine 1 i 


Cotang. 1 




Tang. |M.| 



57 Degree^. 





s 


I ,;S ASD TA.^aE^-TS 


. <^o3 Degrees 


) 


6] 


T" 


Sir.d 


D. 


Cosine 1 D. 


Tang i 


D. 1 


Cotang. \ 1 


U 


9.7361091 
736303 


324 


9.923591 


137 


9.812517 


461 


10.187482 60'1 


1 


324 


923509 


137 


812794 


461 


187206 


59 

581 


2 


736498 


324 


923427 


137 


31.3070 


461 


186930 


3 


736692 


323 


923.345 


137 


813347 


460 


186653 


57 


4 


736880 


323 


923263 


137 


813623 


460 


186.377 


56 


ft 


737080 


323 


923181 


137 


813899 


460 


186101 


55 


6 


737274 


.323 


923098 


137 


814175 


460 


185825 


54 


7 


737467 


323 


923016 


137 


814452 


460 


185548 


53 


8 


737661 


322 


922933 


137 


814728 


460 


185272 


52 


9 


737855 


322 


922851 


137 


815004 


460 


184996 


51 


10: 
11 


738048 


322 


922768} 
9.922686 


138 
138 


815279 
9.815555 


460 
459 


184721 


50 


:> 738241 


322 


10.184445 


49 


12 


738434 


322 


922603 


138 


815831 


459 


134169 


48 


i3: 


738627 


321 


922520 


138 


816107 


459 


183893 


47 


14 j 


738820 


321 


922438 


138 


816382 


459 


183618 


46 


15 


739013 


321 


922355 


138 


816658 


459 


183342 


45 


16| 


739206 


321 


922272 


138 


816933 


459 


183067 


44 


17 t 


739398 


321 


922189 


138 


817209 


459 


182791 


43 


18 


739590 


320 


922106 


138 


817484 


459 


182516 


42 


19 


739783 


320 


922023 


138 


817759 


459 


182241 


41 


20 
21 


739975 


320 


921940 


138 
139 


818035 


458 


181965 


40 
39 


9.740167 


320 


9.9218.57 


9.818310 


458 


iO. 181690 


22 


740359 


320 


921774 


139 


818585 


458 


181415 


38 


2:3 


740550 


319 


921691 


139 


818860 


458 


181140 


37 


24 


740742 


319 


921607 


1.39 


819135 


458 


180865 


36 


25 


740934 


319 


921524 


139 


819410 


458 


180590 


35 


2fi 


741125 


319 


921441 


139 


819684 


458 


180316 


34 


27 


741316 


319 


921357 


139 


819959 


458 


180041 


33 


2S 


741508 


318 


921274 


139 


820234 


458 


179766 


32 


29 


741699 


318 


921190 


139 


820508 


457 


179492 


31 


30 


741889 


318 


921107 


1,39 
139 


820783 


457 


179217 


30 
29 


9 . 742080 


318 


9.921023 


9.821057 


457 


10.178943 


;32 


742271 


318 


920939 


140 


821332 


457 


178668 


28 


;{:} 


742462 


317 


920856 


140 


821606 


457 


178394 


27 


31 


742652 


317 


920772 


140 


821880 


457 


178120 


26 


35 


742842 


317 


920688 


140 


822154 


457 


177846 


25 


36 


743033 


317 


920604 


140 


822429 


457 


177571 


24 


37 


743223 


317 


920520 


140 


82270.^ 


457 


177297 


23 


38 


743413 


316 


920436 


140 


822977 


456 


177023 


22 


39 


743802 


316 


920352 


140 


823250 


456 


176750 


21 


40 
4l' 


743792 


316 


920268 
9.920184 


140 
140 


823524 

9.823798 


456 
456 


176476 


20 
19 


9.743982 


316 


10.176202 


42 


744171 


316 


920099 


140 


824072 


456 


175928 


18 


43 


7443G1 


315 


920015 


140 


824345 


456 


1756.55 


17 


44 


744550 


315 


919931 


141 


824619 


456 


175381 


16 


45 


744739 


315 


919846 


141 


824893 


456 


175107 


15 


4(5 


744928 


315 


919762 


141 


825166 


456 


174834 


14 


17 


745117 


315 


919677 


141 


825439 


455 


174561 


13 


18 


745306 


314 


919.593 


141 


825713 


455 


174287 


12 


49 


745494 


314 


919508 


141 


82.5986 


455 


174014 


11 


50 


745683 


314 


919424 


141 


826259 


455 


173741 


10 


51 


9.745871 


314 


9.9L9339 


141 


9.826532 


455 


10.173468 


9 


52 


746059 


314 


919254 


141 


826805 


455 


173195 


8 


53 


746248 


313 


919169 


141 


827078 


455 


172922 


7 


54 


746436 


313 


919085 


141 


827351 


455 


172649 


6 


55 


746624 


313 


919000 


141 


827624 


455 


172376 


5 


56 


746812 


313 


918915 


142 


827897 


454 


172103 


4 


57 


746999 


313 


918830 


142 


828170 


454 


171830 


3 


58 


747187 


312 


918745 


142 


828442 


454 


171558 


2 


59 


747374 


312 


918659 


142 


828715 


454 


17128.'i 


1 


60 


747562 


1 312 


918574 


142 


828987 


454 


171013 






I Cos 



I I Colaiig. I 

56 D'>jv(.'es. 



|M 



52 


(34 Degrees.) a 


TABLE OF LOGARITHMIC 




M. 


1 Sine 


1 D. 


Cosine 1 D. 


Tang. 


n 


Coian?. j 1 





9.747562 


312 


9.918574 


142 


9.828987 


45i 


10.171013 


60 


1 


747749 


312 


918489 


142 


829260 


454 


170740 


59 


2 


747936 


312 


9184U4 


142 


829532 


454 


170468 


58 


3 


748123 


311 


918318 


142 


829805 


454 


170195 


57 


4 


748310 


311 


918233 


142 


830077 


454 


169923 


56 


5 


748497 


311 


918147 


142 


830349 


453 


169651 


55 


6 


748683 


311 


918062 


142 


830621 


453 


169379 


54 


7 


748870 


311 


917976 


143 


830893 


453 


169107 


53 


8 


749056 


310 


917891 


143 


831165 


453 


168835 


52 


9 


749243 


310 


917805 


143 


831437 


453 


168563 


51 


10 


749429 


310 


917719 


143 


831709 


453 


168291 


50 


11 


9.749615 


310 


9.917634 


143 


9.831981 


453 


10.168019 


49 


12 


749801 


310 


917548 


143 


832253 


453 


167747 


48 


13 


749987 


309 


917462 


143 


832525 


453 


167475 


47 


14 


750172 


309 


917376 


143 


832796 


453 


167204 


46 


15 


750358 


309 


917290 


143 


833068 


452 


166932 


45 


16 


750543 


309 


917204 


143 


833339 


452 


166661 


44 


17 


750729 


309 


917118 


144 


833611 


452 


166389 


43 


18 


750914 


308 


917032 


144 


833882 


452 


166118 


42 


19 


751099 


308 


916946 


144 


834154 


452 


165846 


41 


20 
21 


751284 


308 


916859 


144 
144 


834425 


452 


16.5575 


40 
39 


9.751469 


308 


9.916773 


9.834696 


452 


10.165304 


22 


751654 


308 


916687 


144 


834967 


452 


165033 


38 


23 


751839 


308 


916600 


144 


835238 


452 


164762 


37 


24 


752023 


307 


916514 


144 


835509 


452 


164491 


36 


25 


752208 


307 


916427 


144 


835780 


451 


164220 


35 


26 


752392 


307 


916341 


144 


836051 


451 


163949 


34 


27 


752576 


307 


916254 


144 


836322 


451 


163678 


33 


28 


752760 


307 


916167 


145 


836593 


451 


163407 


32 


29 


752944 


306 


916081 


145 


836864 


451 


163130 


31 


30 
31 


753128 


306 


915994 


145 
145 


837134 


451 


162806 


30 

29 


9 753312 


306 


9.915907 


9.837405 


451 


10.162595 


32 


753495 


306 


915820 


145 


837675 


451 


162325 


28 


33 


753679 


306 


915733 


145 


837946 


451 


162054 


27 


34 


753862 


305 


915646 


145 


838216 


451 


161784 


26 


35 


754046 


305 


915559 


145 


838487 


450 


161513 


25 


36 


754229 


305 


915472 


145 


838757 


450 


161243 


24 


37 


754412 


305 


915385 


145 


839027 


450 


160973 


23 


38 


754595 


305 


915297 


145 


839297 


450 


160703 


22 


39 


754778 


304 


915210 


145 


839568 


450 


160432 


21 


40 
41 


754960 
9.755143 


304 


915123 
9.915035 


146 
146 


839838 


450 


160162 


20 
19 


304 


9.840108 


450 


10.159892 


42 


755326 


304 


914948 


146 


840378 


450 


159622 


18 


43 


755508 


304 


914860 


146 


840647 


450 


159353 


17 


44 


755690 


304 


914773 


146 


840917 


449 


159083 


16 


45 


755872 


303 


914685 


146 


841187 


449 


15S813 


15 


46 


756054 


303 


914598 


146 


841457 


449 


158543 


14 


47 


756236 


303 


914510 


146 


841726 


449 


158274 


13 


48 


756418 


303 


914422 


146 


841996 


449 


158004 


12 


49 


756600 


303 


914334 


146 


842266 


449 


157734 


11 


50 
51 


756782 


302 


914246 
9.914158 


147 
147 


842535 
9.842805 


449 
449 


157465 


10 
9 


9.756963 


302 


10.157195 


52 


757144 


302 


914070 


147 


843074 


449 


156926 


8 


53 


757326 


302 


913982 


147 


843343 


449 


156657 


7 


54 


757507 


302 


913894 


147 


843612 


449 


156388 


6 


55 


757688 


301 


913806 


147 


843882 


448 


156118 


5 


56 


757869 


301 


913718 


147 


844151 


448 


155849 


4 


57 


758050 


301 


913630 


147 


8444^0 


448 


155580 


3 


58 


758230 


301 


913541 


147 


844689 


448 


15.5311 


2 


59 


758411 


301 


913453 


147 


844958 


448 


155042 


1 


60 


75S591 


301 


913365 


147 


845227 


448 


154773 







1 Ci)*ine 




Sine j 


Colang. 




Tsns. i M 1 



55 Degrees. 



SINES AND TANGENTS. (35 Degrees.) 



53 



M. 


Sine 


1). 1 Cosine 1 D. 


Tansz. 


D. 


ColmiL'. 




~T 


9.758591 


.301 


9.913365 


147 


9.845227 


448 


10. J 54773 


60 


1 


758772 


300 


913276 


147 


845496 


448 


154504 


5.9 


2 


758952 


300 


913187 


148 


845764 


448 


154236 


58 


3 


759132 


300 


913099 


148 


846033 


448 


153967 


57 


4 


759312 


300 


Q 1 30 10 


148 


846302 


448 


153698 


56 


5 


759492 


300 


912922 


148 


846570 


447 


153430 


56 


6 


759672 


299 


912833 


148 


846839 


447 


153161 


54 


7 


759852 


299 


912744 


148 


847107 


447 


152893 


53 


8 


760031 


299 


912655 


148 


847376 


447 


152624 


52 


9 


760211 


299 


912566 


148 


847644 


447 


152356 


51 


10 
11 


760390 


299 


912477 
0.912388 


148 
148 


847913 


447 


162087 


50 
49 


9.760569 


298 


9.848181 


447 


10.151819 


12 


760748 


298 


912299 


149 


848449 


447 


151551 


48 


13 


760927 


298 


912210 


149 


848717 


447 


151283 


47 


14 


761106 


298 


912121 


149 


848986 


447 


151014 


46 


1.5 


761285 


298 


912031 


149 


849254 


447 


150746 


45 


16 


761464 


298 


911942 


149 


849522 


447 


150478 


44 


17 


761642 


297 


911853 


149 


849790 


446 


150210 


43 


18 


761821 


297 


911763 


149 


850058 


446 


149942 


42 


19 


761999 


297 


911674 


149 


850325 


446 


149675 


41 


20 

21 


762177 


297 


911584 
!>. 911495 


149 
149 


850693 


446 


149407 


40 
39 


9.7i;2ii56 


297 


9.850861 


446 


10.149139 


22 


762534 


296 


911405 


149 


851129 


446 


148871 


38 


23 


762712 


296 


911315 


150 


851396 


446 


148604 


37 


24 


762889 


296 


911226 


150 


851664 


446 


148336 


36 


25 


763067 


296 


911136 


150 


851931 


446 


148069 


35 


26 


763245 


296 


911046 


160 


852199 


446 


147801 


34 


27 


763422 


296 


910956 


150 


852466 


446 


147534 


33 


28 


763600 


295 


910866 


150 


852733 


445 


147267 


32 


29 


763777 


295 


910776 


150 


853001 


446 


146999 


31 


30 
31 


7639.54 


295 


910686 


150 
150 


853268 


446 


146732 


30 

29 


9.764131 


295 


9.910596 


9.853536 


445 


10.146465 


32 


764308 


295 


910506 


150 


853802 


445 


146198 


28 


33 


704485 


294 


910415 


150 


854069 


445 


145931 


27 


34 


764662 


294 


910325 


151 


854336 


445 


145664 


26 


35 


764838 


294 


910235 


151 


854603 


445 


145397 


25 


36 


765015 


294 


910144 


151 


854870 


446 


145130 


24 


37 


765191 


294 


910054 


151 


855137 


445 


144863 


23 


38 


765387 


294 


909963 


151 


855404 


445 


144596 


22 


39 


765544 


293 


909873 


151 


855671 


444 


144329 


21 


40 
4! 


765720 


293 


909782 
9.909691 


151 
151 


855938 


444 


144062 


20 
19 


9 . 765896 


293 


9.856204 


444 


10.143796 


42 


766072 


293 


909601 


161 


8.56471 


444 


143529 


18 


43 


766247 


293 


909510 


151 


856737 


444 


143263 


17 


44 


766423 


293 


909419 


161 


857004 


444 


142996 


16 


46 


766{j98 


292 


909328 


152 


857270 


444 


142730 


15 


46 


766774 


292 


909237 


152 


857537 


444 


142463 


14 


47 


766949 


292 


909146 


152 


857803 


444 


142197 


13 


48 


767124 


292 


909055 


152 


858069 


444 


141931 


12 


49 


767300 


292 


908964 


152 


858336 


444 


141664 


11 


50 
51 


767475 


291 


908873 
9.908781 


152 
152 


858602 


443 


141398 


10 
'9 


9.767649 


291 


9.858868 


4-13 


10.141132 


52 


767824 


291 


908690 


152 


859134 


443 


140866 


8 


53 


767999 


291 


908699 


1.52 


859400 


443 


140600 


7 


54 


768173 


291 


908507 


152 


859666 


443 


140334 


6 


55 


768348 


290 


908416 


153 


859932 


443 


140068 


6 


56 


768522 


290 


908324 


153 


860198 


443 


139802 


4 


57 


768697 


290 


908233 


153 


860464 


443 


139536 


3 


58 


768871 


290 


908141 


153 


860730 


443 


139270 


2 


59 


769045 


290 


90S049 


153 


860995 


443 


139005 


1 


60 


769219 


' 290 


907958 


153 


861261 


443 


138739 







1 C.)>i.ie 


: 1 ^''"^ 1 


1 C'dtano. 




f Tang. 1 M. | 



54 Degrees. 

16 



51 


[- 


'! i)(;;,'ieC3.) A 


TVULK OF LOGAlilTlfMlC 




~ 


1 Fine 


D. 


Cosine 1 D. 


1 '/"nnsr. 


D. 


1 Cntan-.'. ' 


~o" 


9.7692] 9 


290 


9.9079.58 


153 


9.861261 


443 


10.1.38739,60 


1 


769393 


289 


907866 


1.53 


861.527 


443 


138473 


59 


2 


769566 


289 


907774 


1.53 


861792 


442 


138208 


58 


3 


769740 


289 


907682 


1.53 


862058 


442 


137942 


57 


4 


769913 


289 


907590 


153 


862323 


442 


137677 


56 


5 


770087 


289 


907498 


1.53 


862.589 


442 


137411 


55 


6 


770260 


288 


907406 


153 


862854 


442 


137146 


54 


7 


770433 


288 


907314 


154 


863119 


442 


136881 


53 


8 


770606 


288 


907222 


154 


863385 


442 


136615 


52 


9 


770779 


288 


907129 


1.54 


863650 


442 


136350 


51 


10 
11 


770952 


288 


907037 


154 
154 


863915 


442 


136085 
10.1.35820 


50 

49 


9.771125 


288 


9 906945 


9.864180 


442 


12 


771298 


287 


906852 


154 


864445 


442 


135555 


48 


13 


771470 


287 


906760 


1,54 


864710 


442 


135290 


47 


14 


771643 


287 


906667 


154 


864975 


441 


135025 


46 


15 


771815 


287 


906575 


154 


865240 


441 


134760 


45 


16 


771987 


287 


906482 


154 


805505 


441 


134495 


44 


17 


772159 


287 


906389 


1.55 


865770 


441 


134230 


43 


18 


772331 


286 


900296 


155 


866035 


441 


133965 


42 


19 


772503 


286 


906204 


155 


866300 


441 


133700 


41 


20 
21 


772675 


286 


906111 
9.906018 


155 
155 


866564 


441 


133436 
10.133171 


40 
39 


9.772847 


286 


9.866829 


441 


22 


773018 


286 


905925 


155 


867094 


441 


1,32906 


38 


23 


773190 


286 


905S32 


155 


867358 


441 


132642 


37 


24 


773361 


285 


305739 


155 


867623 


441 


132377 


36 


2.5 


773533 


285 


905645 


155 


867887 


441 


132113 


35 


26 


773704 


285 


905.552 


155 


868152 


440 


131848 


34 


27 


773875 


285 


905459 


155 


868416 


440 


131.584 


33 


28 


774046 


285 


905366 


1.56 


868680 


440 


131320 


32 


29 


774217 


285 


905272 


156 


868945 


440 


1310,55 


31 


30 

31 


774388 
9.774558 


284 
284 


905179 


156 

156 


869209 


440 


130791 
10.13052'7 


30 

29 


9.905085 


9.889473 


440 


32 


774729 


284 


904992 


156 


869737 


440 


130263 


28 


33 


774899 


284 


904898 


156 


870001 


440 


129999 


27 


34 


775070 


284 


904804 


156 


870265 


440 


129735 


26 


35 


775240 


284 


904711 


156 


870529 


440 


129471 


25 


36 


775410 


283 


904617 


156 


870793 


440 


129207 


24 


37 


775580 


283 


904523 


156 


871057 


440 


128943 


23 


33 


775750 


283 


904429 


157 


871321 


440 


128679 


22 


39 


775920 


2-83 


904335 


157 


871.585 


440 


128415 


21 


40 
41 


776090 


283 


904241 


157 
1.57 


871849 


439 


12S151 
10.127888 


20 
19 


9.776259 


283 


9.904147 


9.872112 


439 


42 


776429 


282 


904053 


157 


872376 


439 


127624 


18 


43 


776598 


282 


903959 


157 


872640 


439 


127360 


17 


44 


776768 


282 


903864 


157 


872903 


439 


127097 


16 


45 


776937 


282 


903770 


157 


873167 


439 


126833 


15 


46 


7 77106 


282 


903676 


157 


873430 


439 


126570 


14 


47 


777275 


281 


903.581 


157 


873694 


439 


126306 


13 


48 


777444 


281 


903487 


157 


873957 


439 


126043 


12 


49 


777613 


281 


903392 


158 


874220 


439 


125780 


11 


50 
51 


777781 


281 


903298 
9.903203 


1.58 
1.58 


874484 


439 


125516 
10.12.5253 


10 
9 


9.777950 


281 


9.874747 


439 


52 


778119 


2S1 


903108 


1.58 


875010 


439 


124990 


8 


53 


778287 


280 


903014 


158 


875273 


438 


124727 


7 


54 


778455 


280 


902919 


1.58 


875536 


438 


124^164 


6 


55 


778624 


280 


902824 


158 


875800 


438 


124200 


5 


66 


778792 


280 


902729 


1.58 


876063 


438 


12.3937 


4 


67 


778960 


280 


9026.34 


1.58 


876326 


438 


123674 


3 


58 


779128 


280 


902539 


1.59 


876589 


438 


123411 


2 


59 


779295 


270 


902444 


159 


876851 


438 


123149 


1 


60 


779463 


279 


902349 


159 


877114 


438 


122888 





_J 


Cosine 




t Sine 1 


Coliintr. 




1 Taii!2. 1 M. 1 



53 n.^greH'.. 







^TNFS AND TANGENTS. \^37 DcgreCS 




55 


.VI. 


.Slue 


l>. 1 Cosine | D. | 


Tu.ig. 1 


D. 


Cotuns;. i 


IT 


9 . 779463 


279 


y. 902349 


1.59 


9.877114 


438 


10.122836, 60 


1 


779631 


279 


902253 


159 


877377 


438 


122623! 59 


2 


779798 


279 


902158 


159 


877640 


438 


122360 


58 


3 


779966 


279 


902063 


159 


877903 


438 


122097 


57 


4 


780133 


279 


901967 


159 


878165 


438 


121835 


56 


5 


780300 


278 


901872 


159 


878128 


438 


121572 


55 


6 


780467 


278 


901776 


1.59 


878691 


438 


121309 


54 


7 


780634 


278 


901681 


159 


878953 


437 


121047 


53 


8 


780801 


278 


901585 


159 


879216 


437 


120784 


52 


9 


780968 


278 


901490 


159 


879478 


437 


120522 


51 


10 


781134 


278 


901394 


160 


879741 


437 


120259 


50 


11 


9.781301 


277 


9.901298 


160 


9,880003 


437 


10.119997 


49 


12 


781468 


277 


901202 


160 


880265 


437 


119735 


48 


13 


781634 


277 


901106 


160 


830528 


437 


119472 


47 


14 


781800 


277 


901010 


160 


880790 


437 


119210 


46 


15 


781966 


277 


900914 


100 


881052 


437 


118948 


45 


16 


782132 


277 


900S18 


160 


881314 


437 


118686 


44 


17 


782298 


276 


900722 


160 


881576 


437 


118424 


43 


18 


782464 


276 


900626 


160 


881839 


437 


118161 


42 


19 


782630 


276 


900529 


160 


882101 


437 


117899 


41 


20 


782796 


276 


900433 


161 


882363 


436 


117637 


40 


21 


9.782961 


276 


9.900337 


161 


9.882625 


436 


10.117375 


39 


22 


783127 


276 


900240 


161 


882887 


436 


117113 


38 


23 


733292 


275 


900144 


161 


883148 


436 


116852 


37 


24 


783458 


275 


900047 


161 


883410 


436 


116590 


36 


25 


783623 


275 


899951 


161 


883672 


436 


116328 


35 


26 


7S3788 


275 


899854 


161 


883934 


436 


116066 


34 


27 


733953 


275 


899757 


161 


884196 


436 


11, 5804 


33 


28 


784118 


275 


899660 


161 


884457 


436 


115543 


32 


29 


784282 


274 


899564 


161 


884719 


436 


115281 


31 


30 
31 


784447 


274 


899457 
9.899370 


162 
162 


884980 


436 


11.5020 


30 

29 


9.784612 


274 


9.885242 


436 


10.114753 


32 


784776 


274 


899273 


162 


8S5503 


436 


ll'W97 


28 


33 


784941 


274 


899176 


162 


885765 


436 


1 14235 


27 


34 


735105 


274 


899073 


162 


8S6026 


436 


113974 


26 


35 


785269 


273 


893931 


162 


886288 


436 


113712 


25 


3B 


785433 


273 


898884 


162 


886549 


435 


113451 


24 


37 


785597 


273 


898787 


162 


886810 


435 


113190 


23 


38 


785761 


273 


898689 


162 


887072 


435 


112928 


22 


39 


785925 


273 


898592 


162 


887333 


435 


112667 


21 


40 
41 


786089 


273 


898494 
9.898397 


163 
163 


837594 


435 


112400 


20 
19 


9.786252 


272 


9.8873.55 


435 


10.112145 


42 


78 'MI 6 


272 


898299 


163 


888116 


435 


111884 


18 


43 


786579 


272 


898202 


163 


888377 


435 


111623 


17 


44 


786742 


272 


898104 


163 


888639 


435 


111361 


16 


45 


786906 


272 


898006 


163 


888900 


435 


1 11 100 


15 


46 


787069 


272 


897908 


163 


889160 


435 


110840 


14 


47 


787232 


271 


897810 


163 


889421 


435 


110579 


13 


48 


787395 


271 


897712 


163 


889682 


435 


110318 


12 


49 


787557 


271 


897814 


163 


889943 


435 


110057 


11 


50 
51 


787720 


271 


897516 
9.897418 


163 
164 


890204 


434 


109796 


10 
9 


9.787833 


271 


9.890465 


434 


10.109535 


52 


788045 


271 


897320 


164 


890725 


434 


109275 


8 


53 


788208 


271 


897222 


164 


890986 


434 


109014 


7 


54 


788370 


\ 270 


897123 


164 


891247 


434 


108753 


6 


55 


788532 


1 ii70 


897025 


164 


891.507 


434 


108493 


5 


56 


i 788694 


270 


896926 


164 


891768 


434 


108232 


4 


57 


788856 


270 


896828 


164 


892028 


434 


107972 


3 


58 


789018 


270 


890729 


164 


892289 


434 


107711 


2 


59 


789180 


i 270 


896631 


164 


892549 


434 


107451 


1 


60 


789342 


I 269 


! 896532 


164 


892810 


434 


107190 







Coiiiie 


1 1 Si«e 1 


Colaiig. 




1 Tang. 





z 



52 Degrees 



5f5 



(,1B f?0::rors.; a rABLE of LOOAIIITltMIC 



w 


1 s,... 


"■ 


r.,sn,.. 1 1). 


T.-.ML'. 


I). 


rotans;. | 


() 


9.7S!.342 


269 


9.89i;5:5-,' 


164 


9.892810 


434 


10.107190 tiO^ 


1 


789504 


269 


896433 


165 


893070 


434 


I06y30 


59 


2 


789665 


269 


896335 


165 


89333 1 


434 


106669 


58 


3 


739827 


269 


896236 


.1.65 


893591 


4.34 


106409 


57 


4 


789988 


269 


896137 


165 


893S5 I 


4.34 


106149 


56 


5 


790149 


269 


89603S 


1 65 


89411! 


434 


10.5839 


55 


n 


790310 


268 


895939 


165 


S94371 


434 


105629 


54 


7 


790471 


268 


895840 


165 


894632 


433 


10.5368 


53 


8 


790632 


26S 


895741 


165 


894892 


433 


105108 


52 


9 


700793 


268 


89564 1 


165 


89^., 52 


433 


104848 


51 


10 


790954 
9.7911)5 


268 


895542 
9.895443 


165 
166 


895412 
9.895072 


433 
433 


104588 50 i 
10 104328 49 | 


11 


268 


12 


791275 


267 


895343 


166 


895932 


433 


104068 


48 : 


13 


791436 


26r 


895244 


166 


896192 


433 


103808 


47 j 


14 


791596 


267 


895145 


166 


896452 


433 


103.548 


46 f 


15 


791757 


267 


895045 


166 


896712 


433 


103288 


45! 


16 


791917 


267 


894945 


166 


896971 


433 


103029 


44 1 


17 


792077 


267 


894846 


166 


897231 


433 


102769 


43 


18 


792237 


266 


894746 


166 


897491 


433 


102509 


42 


19 


792397 


266 


894646 


166 


897751 


433 


102249 


41 


20 

21 


792557 
9.792716 


266 
266 


894546 
9.894446 


166 
167 


898010 


433 


101990 


40 
39 


9.898270 


433 


10.101730 


22 


792876 


266 


894346 


167 


898530 


433 


101470 


38 


23 


793035 


266 


894246 


167 


898789 


433 


101211 


37 


24 


793195 


265 


894146 


167 


899049 


432 


100951 


36 


26 


793354 


265 


894046 


167 


899308 


432 


100692 


35 


26 


793514 


265 


893946 


167 


899568 


432 


100432 


34 


27 


793673 


265 


893846 


167 


899827 


432 


100173 


:i) 


28 


793832 


265 


893745 


167 


900086 


432 


099914 


32 
31 


29 


793991 


265 


893645 


167 


900346 


432 


099654 


30 


794150 


264 


893544 


167 


900605 


432 


099395 


30 


31 


9.794308 


264 


9.893444 


168 


9.900864 


432 


10.099136 


29 


32 


794467 


204 


893343 


168 


901124 


432 


098376 


28 


33 


794626 


264 


893243 


168 


901383 


432 


093617 


U 


34 


794784 


264 


893142 


168 


901642 


432 


098358 


35 


794942 


264 


893041 


168 


901901 


432 


098099 


25 


36 


795101 


264 


8G2940 


168 


902160 


432 


097840 


2 4 


37 


795259 


263 


892839 


168 


902419 


432 


097581 


23 


38 


795417 


263 


892739 


168 


902679 


432 


097321 


22 


39 


795575 


203 


892638 


168 


902938 


432 


097062 


21 


40 


795733 


263 


S92536 


168 


903197 


431 


096803 


20 


41 


9.795891 


263 


9.892435 


169 


9 . 903455 


431 


10.096545 


'19 


42 


796049 


263 


892334 


169 


903714 


431 


096286 


18 


43 


796206 


263 


892233 


169 


903973 


431 


096027 


17 


44 


796364 


262 


892132 


169 


904232 


431 


095768 


16 


45 


796521 


262 


892030 


169 


904491 


431 


095509 


15 


46 


796679 


262 


891929 


169 


904750 


43] 


095250 


14 


47 


796836 


262 


891827 


169 


90.5008 


431 


094992 


13 


48 


796993 


262 


891726 


169 


905267 


431 


094733 


12 


49 


797150 


261 


891624 


169 


905.526 


431 


094474 


11 


50 
51 


797307 


261 


891523 
9.891421 


rro 

170 


905784 
9.906043 


431 

431 


094216 


10 
9 


9.797464 


261 


i 0.093957 


52 


797621 


261 


891319 


170 


906302 


431 


093698 


8 


53 


797777 


261 


891217 


170 


906560 


431 


093440 


7 


54 


797934 


261 


891115 


170 


906819 


431 


093181 


6 


55 


798091 


261 


891013 


170 


907077 


431 


092923 


5 


56 


798247 


261 


890911 


170 


907336 


431 


092664 


4 


57 


798403 


260 


890809 


170 


907594 


431 


092406 


3 


58 


798560 


260 


890707 


170 


907852 


431 


092148 


2 


59 


793716 


260 


890605 


170 


908111 


430 


091889 


I 


60 


79SS72 


260 


890503 


170 


908369 


430 


091631 







Cosine 




Sine 1 


Cotaiig. 




i Tai.g. 1 M. 1 



51 DegiGo< 



SINES AND TANGENTS. (39 Degrees.) 



M. 


1 i^nu.. 


1 r.. 


Cosir.e 1 I). 


'i'^m. 1 


D. 


Cotaii}?. j 





9.798S72 


260 


9.890503 


170 


9.908369' 


430 


10.0916311 60 


1 


799028 


260 


890400 


171 


9086281 


430 


0913721 59 


2 


799184 


260 


890298 


171 


908886 


430 


091114 58 


3 


799339 


259 


890195 


171 


909144! 


430 


090856 


57 


4 


799495 


259 


890098 


171 


909402! 


430 


090598 


56 


5 


799651 


259 


889990 


171 


909660 


430 


090340 


55 


6 


799806 


259 


889888 


171 


909918 


430 


090082 


54 


• 7 


799962 


259 


889785 


171 


9101771 


430 


089823 


53 


8 


800117 


259 


889682 


171 


910435' 


430 


089565 


52 


9 


800272 


258 


889579 


171 


910693 


430 


089307 


51 


10 

11 


800427 


258 


889477 
9.889374 


171 
172 


9109511 
9.911209; 


430 
430 


089049 


50 
49 


9.800582 


258 


10.088791 


12 


800737 


258 


8892/1 


172 


9114671 


430 


088533 


48 


13 


800892 


258 


8S9168 


172 


911724 


430 


088276 


47 


14 


801047 


258 


889064 


172 


911982; 


430 


088018 


46 


15 


801201 


258 


888961 


172 


9122401 


430 


087760 


45 


16 


801356 


257 ' 


888858 


172 


9124981 


430 


087502 


44 


17 


801511 


257 


888755 


172 


9127561 


430 


087244 


43 


18 


801665 


257 , 


888651 


172 


913014: 


429 


080986 


42 


19 


801819 


257 


888548 


172 


91.3271 


429 


086729 


41 


20 
21 


801973 
9,802128 


257 1 
257 ' 


888444 
9.888341 


173 
173 


913.529, 


429 


086471 
10.086213 


40 
39 


9.913787| 


429 


22 


802282 


256 


888237 


173 


914044: 


429 


08.5956 


38 


23 


802436 


256 


888134 


173 


914302. 


429 


085698 


37 


24 


802.589 


256 


888030 


173 


914560: 


429 


085440 


36 


25 


802743 


2.56 


887926 


173 


914817; 


429 


085183 


35 


26 


802897 


256 


887822 


173 


91.5075^ 


429 


084925 


34 


27 


80.3050 


2.56 


887718 


173 


91.5332' 


429 


084668 


33 


28 


80.3204 


256 


887614 


173 


91,5590! 


429 


084410 


32 


29 


803357 


255 


887510 


173 


915847; 


429 


084153 


31 


30 

31 


80.3511 


255 


887406 
9.887302 


174 

174 


916104! 


429 


083896 


30 
29 


9.803664 


255 


9.916362; 


429 


10.0836.38 


32 


803817 


255 


887198 


174 


916619; 


429 


083381 


28 


33 


803970 


255 


887093 


174 


916877; 


429 


083123 


27 


34 


804123 


255 


886989 


174 


917134 


429 


082866 


26 


35 


804276 


254 


886885 


174 


917391 


429 


082609 


25 


36 


804428 


254 


886780 


174 


917648 


429 


082352 


24 


H7 


804581 


254 


886676 


174 


917905! 


429 


082095 


23 


38 


804734 


254 


886.57 1 


174 


918163 


428 


081837 


22 


39 


804886 


254 


886466 


174 


918420 


428 


081580 


21 


40 

41 


805039 


254 


886362 
9.886257 


175 
175 


918677 


428 


081323 
10.081066 


20 
19 


9.805191 


2.54 


9.918934 


428 


42 


805343 


253 


886152 


175 


919191 


428 


080809 


18 


43 


805495 


2,53 


886047 


175 


919448 


428 


080552 


17 


44 


805647 


253 


885942 


175 


919705 


428 


080295 


16 


45 


805799 


253 


88.5837 


175 


919962 


428 


080038 


15 


46 


805951 


253 


885732 


175 


920219 


428 


079781 


14 


47 


806103 


2.53 


885627 


175 


920476 


428 


079524 


13 


48 


806254 


253 


885522 


175 


9207,33 


428 


079267 


12 


49 


806406 


252 


885410 


175 


920990 


428 


079010 


11 


50 
51 


806557 


252 


88.5311 


176 
176 


921247 
9.921503 


428 
428 


078753 


10 
9 


9.806709 


252 


9.88.5205 


; 10.078497 


52 


806860 


252 


885100 


176 


921760 


428 


078240 


8 


53 


807011 


252 


884994 


176 


922017 


428 


077983 


7 


54 


807163 


252 


884889 


176 


922274 


428 


; 077726 


6 


55 


807314 


I 252 


884783 


176 


922530 


428 


! 077470 


5 


56 


807465 


251 


884677 


176 


922787 


428 


; 077213 


4 


57 


807615 


251 


884572 


176 


923044 


428 


07695r 


3 


58 


807766 


251 


884466 


176 


923300 


428 


076700 


2 


59 


807917 


! 251 


884360 


176 


923.557 


427 


076443 


1 


60 


808067 


' 251 


884254 


177 


923S13 


427 


1 076187 







Codne 


1 


1 S.ne 1 


1 Cotaiifr. 


1 


1 T.,,. |M.| 



23* 



50 Deafces. 



58 



(40 Dei^ecs.) a taulk jf logaiiithmtc 



M. 


1 Su.e 1 


I). 


i Cosine 1 I) 


Tiihc. 


._JL_ 


Coianp. 1 \ 





9. S 080 67 


251 


9.884254 


177 


t>. 9238 13 


427 


t0.076i87 


"60 


1 


8032 1 8 


251 


884148 


177 


924070 


427 


07593U 


59 


2 


808368 


251 


884042 


177 


924327 


427 


075673 


58 


3 


8085 19j 


250 


883936 


177 


924583 


427 


075417 


57 


4 


8086691 


250 


883829 


177 


924840 


427 


075160 


56 


5 


8088 19! 


250 


883723 


177 


925096 


427 


074904 


55 


6 


8081>69j 


250 


883617 


177 


925352 


427 


074648 


54 


7 


809119 


250 


883510 


177 


925609 


427 


074391 


53 


8 


809269: 


250 


883104 


177 


925865 


427 


074135 


52 


9 


8094 1 91 


249 


883297 


178 


926122 


427 


073878 


51 


10 


8095691 


249 


883191 


178 


926378 


427 


073622 


50 


11 


9.809718] 


249 


D. 883084 


178 


9.926634 


427 


10.073366 


49 


12 


809S68 


249 


SS2977 


178 


92e«>i>9i"> 


427 


073110 


48 


13 


810017; 


249 


882871 


178 


927147 


427 


072853 


47 


14 


8101671 


249 


882764 


178 


927403 


427 


072597 


46 


15 


8103I6I 


248 


882657 


178 


927659 


427 


072341 


45 


16 


8101651 


248 


882550 


178 


927915 


427 


072085 


44 


17 


8106141 


248 


882443 


178 


92S171 


427 


071829 


43 


18 


810763| 


248 


882336 


179 


928427 


427 


071573 


42 


19 


8109121 


248 


882229 


179 


928683 


427 


071317 


41 


20 


8H06l| 


248 


882121 


179 


928940 


427 


071060! 401 


21 


9.811210; 


248 


9.882014 


179 


9.929196 


427 


10.070804! 391 


22 


811358! 


247 


881907 


179 


929452 


427 


070548 


38 


23 


811507! 


247 


881799 


179 


929708 


427 


070292 


37 


24 


8116551 


247 


881692 


179 


929964 


426 


070036 


36 


25 


8118041 


247 


881584 


179 


930220 


426 


069780 


35 


26 


811952! 


247 


881477 


179 


930475 


426 


069525 


34 


27 


812100 


247 


8813G9 


179 


930731 


426 


069269 


33 


28 


81 2248 i 


247 


881261 


180 


930987 


426 


069013 


32 


29 


812396' 


246 


881153 


180 


931243 


426 


068757 


31 


30 


812544 


246 


881046 


180 


931499 


426 


068501 


30 


3i 


9.812692 


246 


9.880938 


180 


9.931755 


426 


UK 068245 


29 


32 


812840; 


246 


880830 


180 


932010 


426 


067990 


28 


33 


812988 


246 


880722 


180 


932265 


426 


067734 


27 


34 


813135 


246 


880613 


180 


932522 


426 


067478 


26 


35 


813283 


246 


880505 


ISO 


932778 


426 


067222 


25 


36 


813430 


245 


880397 


180 


933033 


426 


066967 


24 


37 


813578 


245 


880289 


181 


933289 


426 


066711 


23 


38 


813725 


245 


880180 


181 


933545 


426 


066455 


22 


39 


813872 


245 


880072 


181 


933800 


420 


066200 


21 


40 


814019. 


245 


879963 


181 


93405S 


426 


065944 


20 


41 


9.814166 


245 


9.879855 


181 


9.934311 


426 


10.065689 


19 


42 


814313 


245 


879746 


i81 


934567 


426 


065433 


18 


43 


814460 


244 


879637 


181 


934S23 


426 


065 1 77 


17 


44 


814607 


244 


879529 


181 


935078 


426 


064922 


16 


45 


814753 


244 


879420 


181 


935333 


426 


064667 


15 


46 


814900 


244 


879311 


181 


935589 


426 


064411 


14 


47 


815046 


244 


879202 


182 


935844 


426 


064156 


13 


48 


815193 


244 


879093 


182 


938100 


426 


063900 


12 


49 


815339 


244 


878984 


182 


936355 


426 


003645 


11 


50 

51 


815485 


243 


878875 
9.878766 


182 
182 


936610 


426 


063390 
10.063134 


10 
i) 


9.815631 


243 


9.9.36866 


425 


52 


815778 


243 


878656 


182 


937121 


425 


062S79 


8 


53 


815924 


243 


878547 


182 


937376 


425 


062624 


7 


54 


816069 


243 


878438 


182 


937632 


425 


062368 


6 


55 


816215 


243 


878328 182 


937887 


425 


062113 


r 


56 


816361 


243 


878219 183 


938142 


425 


001858 


4 


57 


816507 


242 


878109 183 


938398 


425 


061602 


3 


58 


816652; 


242 


877999 183 


938653 


425 


001347 


2 


59 


816798 


242 


877890 183 


93-^9()S 


42.5 


061092 


1 


60 


8l6943i 


242 


877780 183 


939 i 63 


425 


060S37 


Al 


1 


(J„Mno j 




Si:.. 1 


<■..;;.,„.. 




'.•:.,.«. |M.[ 



49 Uesjti^s 





SI^IES AND TANGENTS 


. i41 D 


cgiees 


•) 


59 


nr 


1 Si,.. 


1 D. 


Cosine j D. 


Tnnu. 


D. 


Cotaii". 1 j 





9.816943 


242 


9.877780 


183 


9.939163 


425 


10.060837 


60 


1 


817088 


242 


877670 


183 


939418 


425 


060582 


59 


2 


817233 


242 


877560 


183 


939673 


425 


060327 


58 


3 


817379 


242 


877450 


183 


939928 


425 


060072 


57 


4 


817524 


24] 


877340 


183 


940183 


425 


059817 


56 


5 


817668 


241 


877230 


184 


940438 


425 


059562 


55 


6 


817813 


241 


877120 


184 


940G94 


425 


059306 


54 


7 


817958 


241 


877010 


184 


340949 


425 


059051 


63 


8 


818103 


241 


876899 


184 


941204 


425 


058796 


52 


9 


818247 


241 


876789 


184 


941458 


425 


058542 


51 


10 
11 


818392 


241 


876678 


184 
184 


941714 


425 


058286 


50 
49 


9.818536 


240 


9.876568 


9.941968 


425 


10.058032 


12 


81868] 


240 


876457 


184 


942223 


425 


057777 


48 


13 


818825 


240 


876347 


184 


942478 


425 


057522 


47 


14 


818969 


240 


876236 


185 


942733 


425 


057267 


46 


15 


819113 


240 


876125 


185 


942988 


425 


057012 


45 


16 


819257 


240 


876014 


185 


943243 


425 


0567.57 


44 


17 


819401 


240 


875904 


185 


943498 


425 


056502 


43 


18 


819545 


239 


875793 


185 


943752 


425 


056248 


42 


19 


819089 


239 


875682 


1S5 


944007 


425 


055993 


41 


20 

21 


819832 


239 


875571 
9.875459 


185 

185 


944262 


425 


055738 
10.05.5483 


40 
39 


0.819976 


239 


9.944517 


425 


22 


820120 


239 


875348 


185 


944771 


424 


055229 


38 


23 


820263 


239 


875237 


185 


945026 


424 


0.54974 


37 


24 


820406 


239 


875126 


186 


94.5281 


424 


054719 


36 


25 


820550 


238 


875014 


186 


945535 


424 


054465 


35 


26 


8206S3 


238 


874903 


186 


945790 


424 


0,54210 


34 


27 


820836 


238 


874791 


186 


946045 


424 


053955 


33 


28 


820979 


238 


874680 


186 


946299 


424 


053701 


32 


29 


821122 


238 


874568 


186 


9465.54 


424 


053446 


31 


30 
31 


821265 


238 


874456 
9.874344 


180 

186 


946808 


424 


0.53192 
10.052937 


30 
29 


9.821407 


238 


9.947063 


424 


32 


821550 


238 


874232 


187 


947318 


424 


052682 


28 


33 


821693 


237 


874121 


187 


947572 


424 


052428 


27 


34 


821835 


237 


874009 


187 


947826 


424 


0.52)74 


20 


35 


821977 


237 


873896 


187 


948081 


424 


051919 


25 


36 


822120 


237 


873784 


187 


948336 


424 


051664 


24 


37 


822262 


237 


873ti72 


187 


948590 


424 


051410 


23 


38 


822404 


237 


873560 


187 


948844 


424 


051156 


22 


39 


822546 


237 


873148 


187 


949099 


424 


050901 


21 


40 
41 


822688 
9.822830 


236 
236 


873335 
9.873kJ23 


187 
]87 


949353 


424 


050647 


20 
19 


9.949607 


424 


10.050.393 


42 


822972 


236 


873110 


188 


949862 


424 


0.50 13S 


18 


43 


823114 


236 


872998 


188 


950116 


424 


049884 


17 


44 


823255 


236 


872885 


188 


950370 


424 


049630 


16 


45 


823397 


236 


872772 


188 


950625 


424 


049375 


15 


46 


823539 


236 


872659 


188 


950879 


424 


049121 


14 


47 


823680 


235 


872.547 


188 


951133 


424 


048867 


13 


48 


823821 


235 


872434 


188 


951388 


424 


048012 


12 


49 


823963 


235 


872321 


188 


951642 


424 


048358 


11 


50' 


824104 


235 


872208 


188 


951896 


424 


048104 


10 


51 


9.824245 


235 


9.872095 


189 


9.952150 


424 


10.047850 


9 


52 


824386 


235 


871981 


189 


952405 


424 


047595 


8 


53 


824527 


235 


871868 


189 


952659 


424 


047341 


7 


54 


824668 


234 


8717.55 


189 


952913 


424 


047087 


6 


55 


824808 


234 


871641 


189 


953167 


423 


046833 


5 


56 


824949 


234 


871528 


189 


953421 


423 


046579 


4 


57 


825090 


. 234 


871414 


189 


953675 


423 


046325 


3 


58 


825230 


{ 234 


871301 


189 


9.53929 


423 


046071 


3 


59 


825371 


234 


871187 


189 


954183 


423 


045817 


] 


GO 


82551] 


1 234 


871073 


190 


954437 


423 


0455631 




1 Cosine 




Sine 1 


(;(i:uiir 




Tanii. 1 M. 



60 


(42 Degrees.) a 


TABLE OF LOUAEITHMIC 




M. 


Sine 


I). 


Cnsinc; 1 D. 


Tar.L'. 


D. 


Coiiinc. 1 1 





9.825511 


234 


9.871073 


190 


9.954437 


423 


10.045563 


60 


1 


825651 


233 


870960 


190 


9.54691 


423 


045309 


59 


2 


825791 


233 


870846 


190 


954945 


423 


045055 


58 


3 


825931 


233 


870732 


190 


95.5200 


423 


044800 


57 


4 


826071 


233 


870618 


l&O 


955454 


423 


044546 


56 


5 


826211 


233 


870504 


190 


955707 


423 


044293 


55 


6 


826351 


233 


870390 


190 


955961 


423 


044039 


54 


7 


826491 


233 


870276 


190 


956215 


423 


043785 


53 


8 


826631 


233 


870161 


190 


956469 


423 


043531 


52 


9 


826770 


232 


870047 


191 


956723 


423 


043277 


51 


10 
11 


826910 


232 


869933 
9.809818 


191 

Toi 


956977 


423 


043023 
10.042769 


50 
49 


9.827049 


232 


9.957231 


423 


12 


827189 


232 


869704 


191 


957485 


423 


042515 


48 


13 


827328 


232 


869589 


191 


957739 


423 


042261 


47 


14 


827467 


232 


869474 


191 


957993 


423 


042007 


46 


15 


827606 


232 


869360 


191 


958246 


423 


041754 


45 


16 


827745 


232 


869245 


191 


958500 


423 


041500 


44 


17 


827884 


231 


869130 


191 


9587.54 


423 


041246 


43 


18 


828023 


231 


869015 


192 


959008 


423 


040992 


42 


19 


828162 


231 


868900 


192 


959262 


423 


040738 


41 


20 


828301 


231 


868785 


192 


959516 


423 


040484 


40 


21 


9.828439 


231 


9.868670 


192 


9.959769 


423 


10.040231 


39 


22 


828578 


231 


8685.55 


192 


960023 


423 


039977 


38 


23 


828716 


231 


868440 


192 


960277 


423 


039723 


37 


24 


828855 


230 


868324 


192 


960531 


423 


039469 


36 


25 


828993 


230 


868209 


192 


960784 


423 


039216 


35 


26 


829131 


230 


868093 


192 


961038 


423 


038962 


34 


27 


829269 


230 


867978 


193 


961291 


423 


038709 


33 


28 


829407 


230 


867862 


193 


961.545 


423 


038455 


32 


29 


829545 


2.30 


867747 


193 


961799 


423 


038201 


31 


30 
31 


829683 


230 


867631 
9.867515 


193 
193 


962052 


423 


037948 
10.037694 


30 

29 


9.829821 


229 


9.962306 


423 


32 


829959 


229 


867399 


193 


962560 


423 


037440 


28 


33 


830097 


229 


867283 


193 


962813 


423 


037187 


27 


34 


830234 


229 


867167 


193 


963067 


423 


036933 


26 


35 


830372 


229 


867051 


193 


963320 


423 


036680 


25 


36 


830509 


229 


866935 


194 


963574 


423 


036426 


24 


37 


830646 


229 


866819 


194 


963827 


423 


036173 


23 


38 


830784 


229 


866703 


194 


964081 


423 


035919 


22 


39 


830921 


228 


866586 


194 


964335 


423 


035665 


21 


40 
4 ! 


831058 


228 


866470 
9.866353 


194 
194 


964588 


422 


035412 
10.035158 


20 
19 


9.831195 


228 


9.964842 


422 


42 


831332 


228 


866237 


194 


965095 


422 


0.34905 


18 


43 


831469 


228 


866120 


194 


965.349 


422 


0.34651 


17 


44 


831606 


228 


866004 


195 


965602 


422 


034398 


16 


45 


831742 


228 


865887 


195 


965855 


422 


034145 


15 


46 


831879 


228 


865770 


195 


966109 


422 


0.33S91 


14 


47 


832015 


20-7 


865653 


195 


966362 


422 


033638 


13 


48 


832152 


227 


865536 


195 


966616 


422 


033384 


12 


49 


832288 


227 


865419 


195 


966869 


422 


033131 


11 


50 

51 


832425 


227 


865302 
9.865185 


195 

195 


967123 


422 


032877 


10 
9 


0.832561 


227 


9.967376 


422 


10.032624 


62 


832697 


227 


865068 


195 


967629 


422 


032371 


8 


53 


832833 


227 


864950 


195 


067883 


422 


032117 


7 


54 


832909 


226 


864833 


196 


968136 


422 


031864 


6 


56 


833105 


226 


864716 


196 


968389 


422 


031611 


5 


50 


833241 


226 


864598 


196 


968643 


422 


031357 


4 


57 


833377 


226 


864481 


196 


968896 


422 


031104 


3 


58 


833512 


226 


864363 


196 


969149 


422 


030851 


2 


59 


833648 


226 


864245 


196 


969403 


422 


030597 


1 


60 


833783 


' 226 


864127 


196 


969656 


422 


030344 







1 C...-iiie 




1 8.,,.. 1 


Cnu.n.. 




1 'J'.-tni;. 1 -M. 1 



47 Degrees. 





S1.\KS AND TANGENTS 


(43 Decrrces 


') 


61 


M 


Sine 


D. 


Csilie 1 D. 


Tans. 


I D. 


Co:..,.. 


~l 





9.833783 


226 


9.864127 


196 


9.969656 


422 


10.030344 60 1 


i 


83391!) 


225 


864010 


196 


969909 


422 


030091 


59 


2 


834054 


225 


863892 


197 


970162 


422 


029838 


58 


3 


834189 


225 


863774 


197 


970416 


422 


029584 


57 


4 


834325 


225 


863656 


197 


970669 


422 


029331 


50 


5 


834160 


225 


863538 


197 


970922 


422 


029078 


55 


6 


834595 


225 


863419 


197 


971175 


422 


028825 


54 


7 


834730 


225 


863301 


197 


971429 


422 


028571 


53 


8 


834865 


225 


863183 


197 


971682 


422 


028318 


52 


9 


834999 


224 


863064 


197 


971935 


422 


028065 


51 


10 
11 


835134 


224 


862946 


198 
198 


972188 


422 


027812 


50 
49 


9.835269 


224 


9.862827 


9.972441 


422 


10.027559 


12 


835403 


224 


862709 


198 


972694 


422 


027306 


48 


13 


835538 


224 


862590 


198 


972948 


422 


027052 


47 


14 


835672 


224 


862471 


198 


973201 


422 


026799 


46 


15 


835807 


224 


862353 


198 


973454 


422 


026546 


45 


16 


83594 I 


224 


862234 


198 


973707 


422 


026293 


44 


17 


836075 


223 


862115 


198 


973960 


422 


026040 


43 


18 


836209 


223 


861996 


198 


974213 


422 


025787 


42 


19 


836343 


223 


861877 


198 


974466 


422 


025534 


41 


20 
21 


836477 
9.836611 


223 

223 


861758 


199 
199 


974719 


422 


025281 


40 
39 


9.861638 


9.974973 


422 


10.025027 


22 


836745 


223 


861519 


199 


975226 


422 


024774 


38 


23 


836878 


223 


861400 


199 


975479 


422 


024.521 


37 


24 


837012 


222 


861280 199 


975732 


422 


024268 


36 


25 


837146 


222 


861161 


199 


975985 


422 


024015 


35 


26 


837279 


222 


861041 


199 


976238 


422 


023762 


34 


27 


837412 


222 


860922 


199 


976491 


422 


023509 


33 


28 


837546 


222 


800802 


199 


976744 


422 


023256 


32 


29 


837679, 


222 


860682 


200 


976997 


422 


023003 


31 


30 
31 


837812 
9.837945 


222 
222 


860.562 
9.860442 


200 
200 


977250 


422 


022750 


30 
29 


9.977503 


422 


10.022497 


32 


638078 


221 


860322 


200 


977756 


422 


022244 


28 


33 


838211 


221 


860202 


200 


978009 


422 


021991 


27 


34 


83834^1 


221 


860082 


200 


978262 


422 


0217.38 


26 


35 


838477 


221 


859962 


200 


978515 


422 


021485 


25 


36 


838610 


221 


859842 


200 


978768 


422 


021232 


24 


37 


838742 


221 


869721 


201 


979021 


422 


020979 


23 


38 


83S875 


221 


859801 


201 


979274 


422 


020726 


22 


39 


839007 


221 


859480 


201 


979527 


422 


020473 


21 


40 
U 


839140 


220 


859360 
9.859239 


201 
201 


979780 


422 


020220 
10.019967 


20 
19 


9.839272 


220 


9.980033 


422 


42 


839404 


220 


859119 


201 


980286 


422 


019714 


18 


43 


839536 


220 


858998 


201 


9805.38 


422 


019462 


17 


44 


839668 


220 


858877 


201 


980791 


421 


019209 


10 


45 


839800 


220 


858756 


202 


981044 


421 


018956 


15 


46 


839932 


220 


8.58635 


202 


981297 


421 


018703 


14 


47 


840064 


219 


858514 


202 


981550 


421 


018450 


13 


48 


840196 


219 


858393 


202 


981803 


421 


018197 


12 


49 


84032S 


219 


858272 


202 


982056 


421 


017944 


11 


50 


840459 


219 


858151 


202 


982309 


421 


017691 


10 


51 


0.840591 


219 


9.858029 


202 


0.982562 


421 


10.017438 


9 


52 


840722 


219 


857908 


202 


982814 


421 


017186 


8 


53 


84085^ 


219 


857786 


202 


983067 


421 


016933 


7 


54 


840985 


219 


857665 


203 


983320 


421 


016680 


6 


55 


841116 


218 


857543 


203 


983573 


421 


016427 


5 


56 


841247 


218 


857422 


203 


983826 


421 


016174 


4 


57 


841378 


218 


857300 


203 


984079 


421 


015921 


3 


58 


841509 


218 


857178 


203 


9S4331 


421 


015669 


2 


59 


841640 


218 


857056 


203 


984584 


421 


015416 


1 


60 


841771 


218 


856934 


203 


984837 


421 


015163 




Co.-ine 


1 


giiie 1 


Coiaiig. 


1 


1 Tang. 1 M. 



46 Detjri'cs. 



62 


(44 Degrees.) a 


TABLE OF LOGARITHxMlC 




M.l 


Sine 


1). 1 


(•..>i,.e ; ... ; 


Tail!,'. ! D. 


CotaI^i,^ | ^ 





9.841771 


218 


9.856034 


203 


9.934837 421 


10.015163 


6U 


1 


841902 


218 


856812 


203 


985090 421 


014910 


59 


2 


842033 


218 


85G690 


204 


9S5343 421 


014657 


58 


3 


842 1G3 


217 


856568 


204 


985S96 


421 


014404 


57 


4 


842294 


217 


856446 


204 


985848 


421 


0141.52 


56 


5 


842424 


217 


856323 


204 


986101 


421 


013899 


55 


6 


842555 


217 


85820 1 


204 


986354 


421 


013646 


54 


7 


842685 


217 


856078 


204 


986607 


421 


013393 


53 


8 


842815 


217 


855956 


204 


986860 


421 


013140 


52 


9 


842946 


217i 


855833 


204 


987112 


421 


012888 


51 


10 


843076 


217 


855711 


205 


937305 


421 


012635 


50 


ll 


9.843206 


2l6 


9.855588 


205 


9.987618 


421 


10.012382 


49 


12 


843336 


216 


855465 


205 


987871 


421 


012129 


48 


13 


843466 


216 


855342 


205 


988123 


421 


011877 


47 


14 


843595 


216 


855219 


205 


988376 


421 


011624 


46 


15 


843725 


216 


855096 


205 


988629 


421 


011371 


45 


16 


843855 


216 


. 854973 


205 


988882 


421 


011118 


44 


17 


8439S4 


216 


854850 


205 


989134 


421 


010866 


43 


18 


844114 


215 


854727 


200 


989387 


421 


010613 


42 


19 


844243 


215 


854603 


206 


939640 


421 


010360 


41 


20 
21 


844372 


215 


854480 
9.854356 


206 

206 


989893 


421 


010107 


40 
39 


9.344502 


2i5 


9.990145 


421 


10.009855 


22 


844631 


215 


854233 


206 


990398 


421 


009602 


38 


23 


844760 


215 


854109 


20-6 


990651 


421 


009349 


37 


24 


844889 


215 


853986 


206 


990903 


421 


009097 


36 


25 


845018 


215 


853S62 


206 


991156 


421 


008844 


35 


26 


845147 


215 


853738 


206 


991409 


421 


008591 


34 


27 


845276 


214 


853614 


207 


991662 


421 


008338 


33 


28 


845405 


214 


853490 


207 


991914 


421 


008086 


32 


23 


845533 


214 


853366 


207 


992167 


421 


007833 


31 


30 
31 


845662 


214 


853342 

9.853118 


207 

207 


992420 


421 


007580 


30 

29 


9.845790 


214 


9.992672 


421 


10 007323 


32 


845919 


214 


852994 


207 


992925 


421 


007075 


28 


33 


846047 


214 


852869 


207 


993178 


421 


006822 


27 


34 


846175 


214 


852745 


207 


993430 


421 


006570 


26 


35 


846304 


214 


852620 


207 


993883 


421 


006317 


25 


36 


846432 


213 


852496 


208 


993936 


421 


006064 


24 


37 


846560 


213 


852371 


203 


994189 


421 


005811 


23 


38 


846688 


213 


852247 


20S 


994441 


42i 


005559 


22 


39 


840816 


213 


852122 


208 


994694 


421 


005306 


21 


40 
41 


846944 
9.847071 


213 


851997 
9.851872 


208 
208 


994947 1 421 


005053 


20 
19 


213 


0.995199 


421 


10.004801 


42 


847199 


213 


851747 


208 


995452 


421 


004548 


18 


43 


847327 


213 


851622 


208 


995705 


421 


004295 


17 


44 


847454 


212 


851497 


209 


995957 


421 


004043 


16 


45 


847582 


212 


851372 


209 


996210 


421 


003790 


15 


46 


847709 


212 


851246 


209 


996463 


421 


003537 


14 


47 


847836 


212 


851121 


209 


996715 


421 


003285 


13 


48 


847964 


212 


850996 


209 


996968 


421 


003032 


12 


49 


848091 


212 


850870 


209 


997221 


421 


002779 


11 


50 


848218 


212 


850745 


209 


997473 


421 


002527 


10 


51 


9.848345 


212 


9.850619 


209 


9.997726 


421 


10. »92274 


9 


52 


848472 


211 


850493 


210 


997979 


421 


/0202 1 


8 


53 


84S599 


211 


850368 


210 


998231 


421 


001769 


7 


54 


848726 


211 


850242 


210 


998484 


421 


001516 


6 


55 


848852 


211 


850116 


210 


998737 


421 


001263 


5 


56 


848979 


211 


849990 


210 


998989 421 


001011 


4 


57 


840106 


211 


! 849 S 64 


210 


999242 421 


000758 


3 


58 


843232 


211 


84973a 


210 


!)99495 421 


000505 


3 


59 


849359 


211 


849611 


210 


999748 ; 421 


000253 


1 


60 


849485 


211 


849485 


210 


10.000000 421 


000000 





~ 


Cosine 




1 ^="« 1 


1 Coia,.,'. 1 


1 Ta,.g. (M.| 



45 DcFrefis. 



A TABLE OF JVATURAL SlIVJES. 



Deir. 



iNat. 
Sine 



OUOOO 
00029 
00058 
00087 
00116 
00145 
00175 
00204 
00233 
00262 
00291 
00320 
00349 
00378 
00407 
15';G0436 



Unit. 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
99999 
99999 
99999 
99999 
99999 



16 00465 
17100495 
18100524 
19!00553]999.)3 
20 00582'99998 
2]i006n!99998 
99993 
99993 
24|00698 99998 
25'00727 99997 
26100756 99997 
27100785 99997 
28100814 99997 
29 00844I9999G 
30lO0S73|99996 



1 Deg._ 

Nai. iN. Co- 
sine j Sine 

01745 1 99985 

01774 90984 

01803199984 

01832J99983 

01862 

01891 

,01920 

01949 

01978 

02007 

02036 

02065 

02094 

02123 

;02152 

[ 02181 



01600 
01629 
01658 
01687 
01716 



\l N. ('o- Nai 
Sine Sine 



022 1 1 
02240 
02269 
:02298 
!02327 
02356 
02385 
02414 
,02443 
102472 
J02501 
1 02530 
02560 
02589 
02618 
02647 
02676 
02705 
02734 
02763 

)2792 
02821 

(2350 
02879 
02908 
02938 
02967 
02996 
03025 
03054 



89 Dpst. 



2 Ueg. 



iNut. N. Co- 
Snie Sine 



03490 
03519 
03548 
03577 
03606 
03635 
03864 
03693 
03723 
03752 
03781 
03810 
03839 
03868 
03897 
03926 



03083 
03113 
03141 
031 70 
03199 
03228 
03257 
03286 
03316 
03345 
03374 
03403 
03452 
03461 
N. Co- 
Sine 



99976| 
99975 
99974 
99974 
99973: 
99972; 
99972' 
999711 
99970; 
99969 
99969; 
99968 
99967, 
999o6 
99GG6; 
99965 
99964 
99963 
99963 
99962 
99961 
99960 
99959 
99959 
99958 
99957 
99956 
99955 
99954 
9 9953 
99952'04827 
99952104856 
9995 111 04885 
99950 ; 049 14 
99949 : 04943; 
99948 04972' 
99947 050011 
99946 05030 
99945:05059 
99944! 05088 
99943' 05117 
99942:05146 
99941 '05175 
99940 05205 
Nat. ''{N. t'.)- 
' Sine 11 Siiid 



03955 
03984 
04013 
01042 
04071 
04100 
04129 
04159 
04188 
04217 
04246 
04275 
04304 
04333 
04362 
04391 
04420 
'04149 
; 04478 
04507 
104536 
04565 
: 04594 
04623 
04653 
04682 
J04711 
04740 
;04769 
04798 



3 Ueg. 

Nat. iNTCo^ 
Sine I Sine 

05234i 99863 
05263:99861 
05292i 99860 
105321199858 
05350 99857 



4 Deg. 



Nat. N. Co- 
Sine Sine 



05379 
05408 
05437 
05466 
05495 
05524 
05553 
05582 
05611 
05640 
05669 



99855 
99854 
99852 
9985 1 
99849 
99847 
99846 
99844 
99842 
99841 
99839 



06976 
07005 
07034 
[07063 
107092 
07121 
'07150 
07179 
07203 
07237 
07266 
07295 
07324 
07353 
07382 
07411 



059S9 99821 



06018 
00047 
00076 
06105 



06134 
06163 
06192 
06221 
06250 
06279 
06308 
06337 
06366 
06395 
06424 
06453 
06482 
06511 
06540 



99319 
99817 
99815 
99813 



07440 
07469 
0749S 
07527 
07556 
07585 
07614 
0764;" 
07672 
07701 
07730 
07759 
0778^ 
07817 
07846 



99812 
99810 
99808 
99806 
99804 
99803 
99801 
99799 
99797 
99795 
99793 
99792 
99790 
99788 
99786 



99756 
99754 
99752 
99750 
99748 
99746 
99744 
99Y42 
99740 
99738 
99730 
99734 
99731 
99729 
99727 
9 9725 

99723 

99721 

99719 

99716 

99714 

99712 

99710 

99708 

99705 

99703 

99701 

99699. :"!3 

99696 

99694 

99692 



Nat. 
Sine 



06569 
06598 
06627 
06656 
06685 
06714 
06743 
,06773 
06802 
0033 1 
06860 
06889 
06918 
06947 
N. Co- Nat. 
Sine Sine 



88 Deir. 



87 [)er 



99784 
99782 
99780 
99778 
99776 
99774 
99772 
99770 
99768 
99766 
99764 
99762 
99760 
99758 



86 D. 



08310 

08339 
083681 
08397: 
03426 
08455 
08484 
08513 
08542 
08571 
08600 
086291 
08658 
98687 



99654 
99652 
99649 
99647 
99644 
99642 
99639 
99837 
99635, 
99632' 
99630 
99627 
99625 
99622 



Sine 



Nat. 
Sine 



85 Peg. 



64 



A TABLE OF NATURAL SINES. 



6 i-)eg. 

N. s7]n. cs. 



09()14 
0964-2 
)967] 
09700 
09720 
09758 
09787 
09816 
09S45 
09874 
09903 
0993'^^ 
09981 
09990 
10019 



99578 
99575 
99572 
99570 
99567 
99564 
99562 
99559 
99556 
99553 
99551 
99548 
99545 
99542 
99540 



S. N.CS. N.S. N.CS. ■ N.S, 



10453 
10482 
10511 
10540 
10569 
10597 
10626 
10655 
10684 
10713 
10742 
10771 
10800 
10829 
10858 
10887 



10916 
10945 
10973 
11002 
11031 
11060 
11089 
11118 
11147 
11176 
11205 
11234 
11263 
11291 
11320 



99452 
99449 
99446 
99443 
99440 
99437 
99434 
9943 1 
9942.^ 
99424 
99421 
99418 
99415 
99412 
99409 
99406 
99402 
99399 
99396 
99393 
99390 
99386 
99383 
99380 
99377 
99374 
99370 
99367 
99364 
99360 
99357 



7 Ueg. 



99494 
99491 
99488 
99485 
99482 
99479 
99476 
99473 
99470 
99467 
99464 
99461 
99458 
99455 
NTCS. I N. S. 



84 Desr. 



11783 
11812 
11840 
11869 
11898 
11927 
11956 
11985 
12014 
12043 
12071 
12100 
12129 
12158 



12187 
12216 
12245 
12274 
12302 
12331 
12360 
12389 



99255 
99251 
99248 
99244 
99240 
99237 
99233 
99230 



8Deg. 



124 18,99226 
124471 99222 
1247b 99219 



12504 
12533 
12562 
12591 
12620 



99215 
99211 
99208 
99204 
99200 



12649 
12678 
12706 
12735 
12764 
12793 
12821. 
12851 
12880 
12908 
12937 
12966 
12995 
13024 
13053 



13081 
13110 
13139 
13168 
13197 
13226 
13254 
13283 
1331 



i 



99303 
99300 
992'97 
99293 
99290 
99286 
99283 
99279 
99276 
99272 
99269 
99265 
99262 
99258 



99197 
991931 
99189: 
99186 
99182 
99178 
99175 
99171 
99167 
99163 
99160 
99156 
99152 
99148 
99144 



13917 

i 13946 

13975 

44004 

I 14033 

14061 

:|14090 

14119 

1 14148 

1114177 

114205 

i 14234 

•14263! 

114292 

114320 

14349 

114378 

,14407 

14436 

[14464 

14493 

14522 

114551 

14580 

14608 

14637 

14666 

14695 



N.cs. :| 

990271 
99023,1 
99019 
9901 5:| 

99011;! 

99006 
99002 
98998 
98994 
98990 
98986 
98982 
98978, 
98973 
98969 
98965 



98961 
98957 
98953 
98948 
98944 
98940 
98936 
98931 
98927 
98923 
98919 
98914 
14723j989l0 
14752198906 
14781 98902 



98723 
98718 
98714 48 
98709 47 
98704 
98700 



99141 

99137 

99133 

99129, 

99125 

991221 

99118 

99114 

99110 

99106 

99102 

99098 

99094 

99091 

99087 



13514 
13543 
13572 
13600 
13629 
13658 
13687 
13716 
13744 
13773 
13802 



99083 
99079 
99075 
99071 
99067 
99063 
99059 
99055 
99051 
99047 
99043 



13831199039 
13860 99035 
13889 99031 



N.CS. N. S. iN. CS. N'.S. i N. CS. N.S 



83 Deff. 



m Dejr. 



14810198897 
14838 98893 
1486798889 
14896 98884 
1492598880 
14954198876 
14982198871 
150ll|98867 
15040198863 
15069 98858 
15097198854 
1512619884. 
15155' 98845 
15184198841 
; 15212 1 98836 
15241 
;15270 
115292 
15327 
15356 
1 15385 
15414 
45442 
il5471 
15500 
1.5529 
15.557 
15586 
15615 



9 Deg. 

N.S. i nTc^v 

15643198769 
15672198764 
15701 98760 
15730; 98755 
15758 1 98751 
16787198746 
15816 98741 
15845 198737 
15873198732 
15902 98728 
15931 
15959 
15988 
16017 
16046 
1C074 
16103 98695 
16132 
|16160 
Il6189 
116218 

|16246|98671 
16275 98667 
16304 9866 
16333 98657 
163t)l 198652 
16390198648 
16419198643 
16447198638 
I6476i98633 
1650 51 98629 
16533 1 98624 
16562 98619 
16591198614 



98690 
98686 
98681 
98676 



98832 
98827 
98823 
98818 
98814 
98809 
98805 
98800 
98796 
98791 
98787 
98782 
98778 
98773 



81 Deg. 



16620 
16648 
16677 
16706 
16734 



9S609 
98604 
98600 
98595 
98590 



16763 98585 
16792 98580 
16820198575 
16849! 98570 
16878|9S565 
16906 98561 
16935 98556 



44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 

28 

27 

26 

25 1 

24 

23 

22 

21 

20 

19 



N.CS. I N. 



80 i:>eg. 



A TABLE OP NATUBAL SINES. 



65 



10 Ueg. 



17365 
17393 

17422 
17451 
17479 
17508 
17537 



17651 
17680 



98430 
98425 

17708 98420 

17737 

17766 

17 794 



17823 
17852 
17880 
17909 
17937 
17966 
17995 
18023 
18052 
18081 
18109 
18138 
18166 
18195 
18224 



18252 
18281 
18309 
18338 
18367 
18395 
18424 
18452 
18481 
18509 
18538 
18567 
18595 
18624 
18652 



1'8681 
18710 
18738 
18767 
18795 
18824 
18852 
18881 
18910 



98399 
98394 
98389 
98383 
98378 
98373 
98388 
98362 
98357 
98352 
98347 
98341 
98336 
98331 
98325 



11 Deer. 



M N. S. I N. CS. I N. S. N. CS. N. S. N. CS. 

97815 
97809 
97803 
97797 
97791 
97784 
97778 
97772 
97766 
97760 
97754 
97748 
97742 
97735 
97729 
97723 
97717 
97711 
97705 
97698' 
97692' 
976861 
976801 
97673 
97667 
97661 
97655 
97648 
97642 
97636 
97630 



19081 
19109 
19138 
19167 
19195 
19224 
19252 
19281 
19309 
19338 
19366 
19395 
19423 
19452 
19481 
19509 



19533 
19566 
19595 
1 9623 
19652 
19680 
19709 
19737 
19766 
19794 
19823 
19851 
19880 
19908 
19937 



98240 20393 



20507 
20535 
20563 
20592 
20620 
20649 
20677 
18995J98179 120706 



18938 98190 

18967|98185 



97987 
97981 
97975 
97969 
97983 
97958 
97952 
97946 
97940 
97934 
97928 
97022 
97916 
97910 
97905 



12 L>eg. 



21246 
21275 
21303 
21331 
21360 
21388 
21417 
21445 
21474 
21502 
21530 
21559 
21587 
21616 
21644 



19024 98174 
19052!98168 



N. CS. I N. 8. 



79 Deg. 



20734 
20763 



97899 
97893 
97887 
97881 
97875 
97869 
97863 
97857 
97851 
97845 
97839 
97833 
97827 
97821 



N. (.'S. 



22098 
22126 
22155 
22183 
22212 
22240 
22268 
22297 
22325 
22353 
22382 
22410 
22438 
22467 



14 Dtg. 



13 P eg. 
N.S . "nTcS. N.S. |N. CS. M 
22495 
22523 
22552 
22580 
22608 
22637 
22665 
22693 
22722 
22750 
22778 
22807 
22835 
22863 
22892 
22920 



97623 
97617 
97611 
97604 
97598 
97592 
97585 
97579 
97573 
97566 
97560 
97553 
97547 
97541 
97534 



22948 
22977 
23005 
23033 
23062 
23090 
23118 
23146J 
23175 
232031 
2323 1 i 
23260 
23288 
23316! 
1 23345 1 
2337397230 



97331 
97325 
97318 
97311 
97304 
97298 
97291 
97284, 
97278 
97271 
97264 
97257 
97251 
97244 
97237 



23401 97223 
23429 19721 7 
!23458!97210 
:23480i97203 
23514 97196 
23542 97189 
123571 197182 
23599197176 
23627i97169 
97162 
97155 
97148 
97141 
97134 



N. 



97528 
97521 
97515 
97508 
97502 
97496 
97489 
97483 
97476 
97470 
97463 
97457 
97450 

97444 

N. CS. ! N. S. 



1 78 Deg. il 77 Dt 



123656 
23684 
,23712 
,23740 
123769 



23797 
23825 
23853 
123882 
|23910 
123938 
'23966 
23995 
i24023 
[24051 
124079 
:24108 
24136 
24164 



i N. C8. 

i 76 1)^ 



N.S. 



24192 97030 

24220197023 

24249 97015 

24277 97008 

24305^97001 

[24333190994 

24362 96987 

24390196980 

24418,96973 

24446,96966 

2447496959 

2450396952 

24531 96945 

24559 96937 

24587 96930 

24615 96923 

2464496916 

24672 96909 

24700 [96902 

24728 

24756 

24784 

24813 

24841 

24869 

24897 

24925 

24953 

24982 

25010 

25038 



125066 
25094 
125122 
[25151 
25179 
!25207 
25235 
125263 
25291 
25320 
25348 
25376 
25404 
25432 
25460 



25488 
25516 
25545 
25573 
25601 
25629 
25657 
25685 
25713 
25741 
25769 
25798 
25826 
25854 



96807 
96800 
96793 
96786 
96778 
96771 
96764 
96756 
96749 
96742 
96734 
96727 
96719 
96712 
98705 



N. CS. 



96697 
96690 
96682 
96675 
196667 
[96660 
96653 
,96645 
96638 
196630 
196623 
[96615 
(96608 
'96600 
I N.S 



1 75 Deg. 



66 



A TABLE OF NATURAL SINES. 



33 



15 De^r. 



N.« 



258 Sr2 

1 25910 
25938 
25966 
25994 
26022 
26050 

;6U79 
26107 
26135 
26163 
26191 
19 
26247 
26275 
26303 
26331 
26359 
26337 



N. CSi. 



96585 
96578 
96570 
96562 
96555 
96547 
96540 
96532 
96524 
96517 
96509 
96502 
96494 
96486 
96479 
9647] 
96463 
98456 



26415 9844 
26443 96440 
26471 '98433 
26500' 96425 
26528 96417 
26556196410 



16 Deg. 



26584 
26612 
26640 

28 26668 

29 26696 

30 26724 



9640 

96394 

96386 

96379 

96371 

96363 



31 26752 

32 26780 
26803 



26836 
26864 
26892 
26920 
26948 
26976 
27004 
27032 
27060 
27088 
27116 
451 27144 
46 27172 
4727200 
48 27228 
49127256 
50127284 
51 27312 
52127340 
53127368 
54127396 
55 27424 
56 '27452 
57127480 
58 1 27508 
59 27536 



96355 
96347 
95340 
96332 
96324 
96316 
96308 
96301 
96293 
96285 
96277 
96269 
96261 
96253 
96246 



96238 
96230 
96222" 
96214 
96206 
96198 
96190 
96182 
96174 
96166 
96158 
96150 
96142 
96134 



I N. CS . 

96593! 27564 96126 
2759296118 
27620 96110 
27648 96102 
27676 96094 
27704 96086 
27731 96078 
27759 96070 
27787 96062 
27S 15 96054 
27843 96046 
27871 96037 
27899 96029 
27927 96021 
27955 96013 
27983 9^0^ 
280 1 1 35997 
28039 95989 
28067 9598 
28095 95972 
28123 95964 
28150 95956 
28178 95948 
28206 95940 
28234 95931 
28262 95923 
28290 95915 
28318 95907 
28346 95898 
28374 95890 
28402 95882 



17 Ueg. 



N.s. 



29237 
29265 
29293 
29321 
29348 
29376 
29404 
29432 
29460 
29487 
29515 
29543 
29571 
29599 
29626 
29654 



29682 

29710 

9737 



N. CS. 



95630 
95622 
95613 
95605 
95596 
95588 
95579 
95571 
95562 
95554 
95545 
95536 
95528 
95519 
95511 
95502 



18 P eg. || 

N. CS. li 



N.S. 
[30902 
30929 
30957 
30985 
31012 
31040 
31068 
31095 
31123 
31151 
31178 
31206 
31233 
31261 
31289 
31316 



95493 
95485 
95476 



29765 95467 
:9793|95459 



29821 
29849 
29S76 
29904 
29932 
29960 
29987 
30015 
30043 
30071 



28429 95874 
28457 95865 

;8485 95S57 
28513 95849 
28541 95841 
28569 95S32 

8597 95824 
28625 95816 
28652 95807 
28680 95799 
28708 95791 



95450 
95441 
5433 
95424 
95415 
95407 
95398 
95339 
95330 
95372 



30098 
30120 
30154 
30182 
30209 
30237 
;0265 
30292 
30320 
30348 
30376 



31344 
31372 
31399 
31427 



J1510 
31537 
31565 
31593 
31620 
31648 
31675 
31703 
31730 



28736 95782 '30403 



28764 95774 
28792 95766 
28820 95757 



30431 
30459 
30486 



95106 
95097 
95088 
95079 
95070 
95061 
95052 
95043 
95033 
95024 
95015 
95006 
94997 
94988 
949791 
94970 



19 Peg. [ 
N CS [M 
94552 60 



N.S, 



94961 
94952 
94943 
94933 



U454 94924 
31482 94915 



94906 
94897 
94888 
94878 
94869 
94860 
94851 
94842 
94832 



N. CS 



N.S. 



74 Peer. 



8847 95749 
JS875|95740 
28903 95732 



95724 
95715 
95707 
95698 
95690 
95681 
95673 



28931 

28959 

28987 

29015 

29042 

29070 

29098 

29126|95664 

29154 95656 

29182,95647 

29209 95639 

N. CS. I N 8. 



"3 Peg. 




30514 

30542 

30570 

30597 

30625 

30653 

30680 

30708 

130736 

i30763 

30791 

30819 

30846195124 

30874 95115 

N.CS. I N.S. 



32557 
32.1S4 
32612 
32639 
32667 
32694 
32722 
32749 
32777 
32804 
32832 
32859 
32887 
32914 
32942 
32969 



94542 
94533 
94523 
94514 
94504 
94495 
94485 
94476 
94466 
94457 
94447 
94438 
94428 
94418 
94409 



32997 
33024 
33051 
33079 
33106 
33134 
33161 
33189 
33216 
33244 
33271 
33298 
33326 
33353 
33381 



94399 
94390 
94380 
94370 
94361 
94351 
94342 
94332 
94322 
94313 
94303 
9429.3 
94284 
94274 
94264 



iPeg. 



33408 
33436 
33463 
33490 
33518 
33545 
33573 
33600 
33627 
33655 
33632 
33710 
33737 
33764 



94254 
94245 
94235 
94225 
94215 
94206 
94196 
94186 
94176 
94167 
94157 
94147 
94137 
94127 
33792 94^1J_8 
33819 94108 
33846194098 
33874194088 
33901194078 
33929 94068 
33956 94058 
33983 94049 
34011 94039 
34038 94029 
34065 94019 
34093 94009 
34120,93999 
34147193989 
34175,9 3979 _ 
■N.CS.! "N.S. Im 
-1 



27 
26 
25 

24 
23 
22 
21 
20 
19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 



70 Peg. 



A TABLE OF NATURAL SINES. 



67 



20 Ueg. 



N. S. 



21 Peg. 

~N. S. x\. CS. 



34202 
34229 
34257 
34284 
34311] 
34339! 
343061 
34393 
34421' 
34448 
34475: 
34503 
345:30 
34557 
34584 



93829 



15 34612 93319 
:j4639 93809 i 
34666l93799| 
34694193789 
3472 1193779 1 

20 347481 9376C; 

21 34775193759: 
34803 193748 1 
348301937381 
34857193728; 
34884! 93718! 
34912193708! 
34939l93698i 



93358 
93348 
93337 
93327 
93316 
93306 
93295 
3285 
93274 
93264 
93253 
93243 
93232 
93222 
93211 
93201 



34966 
34993 
35021 



31 35048 

32 35075 
33 1 35102 
34135130 
35|35157 
36 [35 1 83 
37:35211 
38,35239 
"" 35266 

35293 
35320 
35347 
35375 
35402 
35429 
35456 
35484 
35511 
35538, 
35565' 
35592 
35619 
35647 
35674 
35701 
35728 
35755 
35782 
59 35810 



93688 
93677i 
9366 7 
93657 
93647 
93637 
93626 
93616 
93606 
93596 
93585 
93575 
93565 
93555 
93544 
93534 
93524 
93514 



36271 
36298 
36325 
36352 
36379 
36406 
36434 
36461 
36488 
36515 
38542 
36569 
36596 
36623 
36650 

36677 

36704 

36731 

36758 

36785 

36812 

36839 

36867 

' 36894 

36921 

36948 

36975 

37002 

' 37029 

37056 

I 37083 

37110 

I 37137 

137164 

!i37191 

37218 

37245 

l'37272 

j 37299 

|37326 

37353 

37380 

37407 

37434 



M' N.CS .I N. S. 
1 69 Deg. 



93190 
93180 
93169 
93159 
93148 
93137 
93127 
93116 
93106 
93095 
93084 
93074 
93063 
93052 
93042 
930311 
J3020 
93010 
92999 
92988 
92978 
92967 
92956 
92945 
92935 
92924 
92913 
92902 
92892 
92881 



iii Dejr. 



N. S. 



23 Peg. 

N. CS. 



N. S, 



39073 
39100 
39127 
39153 
;39180 
39207 
39234 
39260 
39287 
39314 
39341 
39367 
39394 
39421 
39448 
39474 
39501 
39528 
39555 
39581 



92050 
92039 
92028 
92010 
92005 
91994 
91982 
91971 
91959 
91948 
91936 
91925 
91914 
91902 
91891 
91879 



24 Peg. 



N. S. I N. CS. i M 



40674 913 
40700 913 
40727 913 
407531913 
40780|913 
40806:91295155 
40833i91283 
40860191272 
40886 91260 
40913191248 
40939 1 9 1236 
40966 91224 
40992 91212 
41019|91200 
1188 
1176 



41098 

!41125 

141151 

41178 

41204 

;41231 

41257 

141284 

,41310 

;41337 

41363'91044|34 

41390 1 9 1032 1 33 

;41416 91020 32 

;4 1443 91008 31 

414G9 90990 30 



38698 
138725 
! 38752 
(38778 
138805 
,38832 
38859 
38886 
38912 
38939 
38966 
,38993 
39020 
39046 



N. CS. I N.& 



68 Peg. i 



N. CS. 



39902 91694 
39928;916S3 
39955191671 
39982 91660 
40008191648 
40035.91636 
40062191625 
400S8J91613 
40115:91601 
40141 91590 
,;40168'91578 
1 40195191566 
; 40221:91555 
140248 91543 
140275 91631 



92209140301 
92198 1'40328 
921 861 40355 
92175140381 
92164140408 
92152140434 
92141 j 40461 
92130 140488 
92119140514 
92107 40541 
92096140567 
92085 i:40594 
92073 i40621 
92062 40647 



N.S. N. CS, 



67 Peg. 



41496 90984 
41522 90972 
41549 90960 27 
41575 90948 '26 
;41602 90936i25 
41628190924124 
141655 9091i|23 
41681 190899122 
!!4i707:90S87 21 
j'4 1734 1 90875 20 
141760190863 19 
r41787|9085!!l8 
141813,908391 17 
,41840 90836 16 
41866 90814 15 



91519 
91508 
91496 
91484 
91472 
91461 
91449 
91437 
91425 
91414 
91402 
91390 
91378 
91366 



N. S. 



60 Peg. 



'41892 90802 
[41919 90790 
4 1945; 90778 
41972190766 
41998 90753 
',4202490741 
42051 190729 
42077j90717 
42 104' 90704 
42130 190692 
42156 90680 
42183190668 
42209 90655 
42235 ' 90643 
N. CS.l N.S. 



65 Deg. 



68 



A TABLE OP NATURAL SINES. 



25 Deg. ^26 Ueg. i 



N.S . 
4226 
42288 
4231;-) 
1234 1 
42307 
423<J4 
42420 
4244 G 
42473 
42499 
42525 
42552 
42578 
42604 
42631 
42657 





1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
II 
12 
13 
14 
15 

16|42683 
1742709 
1842736 
19 42762 
20 
21 

22 42841 
42867 
42894 
4292( 
42946 
4297 
42999 



9'06:31 
90618 
90606 
90594 
90582 
90569 
90557 
90545 
90532 
90520 
90507 
90495 
90483 
90470 
90458 
90446 



90433 
90421 
90408 
90396 
42788190383 
12815 90371 
90358 
90346 
90334 
90321 
90309 
90296 
90284 
43025 90271 
43051 90259 



43077 
43104 
43130 
43156 
43182 
43209 
43235 
43261 



90246 
90233 
90221 
90208 
90196 
90183 
90171 
90158 



43287'90146 
43313I90133 



90120 
90108 
90095 



43340 

43366 
43143392 
44 43418190082 
■^ 43445 1 90070 

43471 90057 

43497 90045 



48 43523 
49143549 
50|43575 
51143602 
52143628 
53143654 
5443680 
55 43706 
56|43733 
57,43759 
58 43785 
59143811 



90032 
90019 
90007 
•S9994 
89981 
89968 
89956 
89943 
89930 
89918 
89905 
89892 



MJN.CS. N.S 
I 64 Deg. 



N. CS. 



14255 
44281 
44307 
44333 
44359 
44385 
14411 
44437 
14464 
14490 
14516 
14542 
4456S 
44594 
14620 



89879; 

89867, 

89854! 

S9841I 

89S28I 

898 16| 

89803; 

S9790; 

89777 

897641 

89752 

89739 

89726 

89713 

89700 

89687 

89674 

89662 

89649 

89636 

89623 

89610 

89597 

89584 

89571 

89558 

S9545 

89532 

89519 

89506 

8 9 '193 

S9480 

894671 

89454 



Deg. 



N. S. 



45399 
45425 
45451 
45477 
45503 
45529 
45554 
45580 
45606 
45632 
45658 
45684 
45710 
45736 
15762 
45787 



N. US. 



45813 
45839 
45865 
45S91 
45917 
15942 



89101 
89087 
89074 
89061 
89048 
89035 
89021 
89008 
88995 
88981 
88968 
88955 
88942 
88928 
88915 
88902 



^l>eg^_j| 29 Deg. I 
xTsT 7.V. CS. ij N. s. Tn. cs. m 



146947,88295 
46973 88281 
46999 88267 
47024.88254 
47050 88240 



88888 
88875 
88862 
88848 
8S835 
S8822 



4598888808 
4599488795 
4602088782 



46046 
46072 
46097 
46123 
46149 
46175 



89441 



llifi 



89428 j 
89415!! 
894021! 
89389 ! 
89376: 
893631; 
S93oO|; 
89337! 
89324 1 
893 11 1! 
8929S! 



46201 
46228 
46252 
46278 
46304 
46330 
46355 
46331 
46407 
40433 
46458 
46484 
46510 
146536 
!; 46561 
l!46587 
'46613 
46639 



88485 

88472 

88458 

|46664 88445 

'46690 88431 

!46716 88417 

,46742 88404 

46767 88390 

146793 88377 

468l9'S8363 

i46844'8S349 

4687088336 

46896j88322 

!46921 88308 



88768 
88755 
88741 
88728 
88715 
88701 



63 Deg. i 



N.CS. i N.g 
62 Deg. 



,47741 
47767 
47793 
47818 
47844 
47869 
47895 
47920 
47946 
47971 
47997 
48022 
48048 
48073 
48099 



48124 

48150 

48175 

48201 

48226 

48252 

48277 

48303 

48328187546 

483.54 87532 

48379 



87868 
87854 
87840 
87826 
87812 
87798 
87784 
87770 
87756 
S7743 
87729 
87715 
87701 
87687 
8 7673 
876.59 
87645 
87631 
87617 
87603 
87.539 
87575 
87561 



48405 
48430 



S 7.504 
87490 



18456 J87476 



61 De<r. 



4848l!S7462;G0 
48.506 S7448!59 
48532(87434158 
48557 !87420i57 
48583'87406!56 
48608 87391 !55 



48634 
48659 
48684 
48710 
48735 
48761 
48786 
48811 
48837 
48862 



48888 
48913 
48938 
48964 
48989 
49014 
49040 
49065 
49090 
49110 
49141 
49166 
49192 
49217 
49242 



8737754 

87363153 

8734 9! 52 

87335!51 

87321 i50 

87.306 49 

87292148 

87278|47 

87264146 

87250 !45 

87235144 

8722143 

8720742 

87193 41 

87178 40 

8716439 

87150 38 

87136 37 

87121 

87107 

87093 

87079 



87064 
87050 
870^6 
87021 
87007 
86993 
36978 
86964 
86949 
86935 
86921 
86906 
86892 
86878 
86863 
86849 
86834 
86820 



49268 
49293 
49318 
49344 
49369 
49394 
49419 
49445 
49470 
49495 
49521 
49546 
495? 1 
19596 
49622 
49647 
49672 
49697 
49723 
49748 
49773 
49798 
49824 
49849 
49874 
49899 
49924 
49950 

19975 

N. CS. I N.S. M 



,86805 
86791 
186777 
! 86762 
18 6748 
\S6733 
86719 
86704 
86690 
86675 
86661 
,86646 
86632 
'866171 



60 DeiT. 



A TABLE OF NATUKAL SINES. 



5000086603 
50025^86588 
50050l86573| 
50076 
5010] 
50126 
0151 
50176 
50201 

50227 

50252 86457 



5027 

50302 

50327 

50352 

50377 



30 Ueg. 



31 Ueg. 



N. S. |N. CS. |i_N^S^ 
51504 
51529 
51554 
51579 
51004 
51628 
51653 
51 678 
51703 
51728 
51753 
51778 
51803 
51828 
51852 
51877 



86442 
86427 
86413 
88398 
86384 



86369 
86354 
86340 
86325 
86310 
86295 
86281 
86266 
86251 
86237 
8G222 
86207 
80192 
86178 
86163 



50403 
50428 
0453 
50478 
50503 
50528 
50553 
505781 
50603 
506281 
50654J 
50679| 
50704] 
50729 

50754 

50779 8C 148 
50804 86133 
50829186119 
50854186104 
50879 86089 
50904186074 
50929186059 
50954 86045 



51104 85956 
51129 85941 



52646 
52671 
52696 
52720 
52745 
52770 
52794 
52819 
52844 
52869 
52893 
52918 
52943 
52967 



N. CS. I N. S. 
59 Deg. 



N. C8. N. S, 



N. CS. 



85020 
85005 
84989 
84974 
84959 
84943 
84928 
84913 
84897 
84882 
84866 
84851 
84836 
84820 



32 Ueg. 



N.S. IN. CS. 



Si P eg. 

JSfTcs." 



N.S, 



52992 84805 154464 

53017 84789 i5448S 

53041 84774 154513 

53066 84759-54537 

53091 84743 154561 

53115 84728 

53140 84712 

53164 

53189 

53214 

53238 

53263 



53288 
53312 
53337 
53361 



53386 
53411 
53435 



84619 



84557 
84542 
84526 



53460i£4511| 

53484184495 



53509 



84480 



84324 
84308 
84292 
84277 
84261 
84245 
84230 
84214 
84198 
84182 
84167 
84151 
84135 
84120 
84104 



58 Deg. 



57 Peg. 

17 



55218 



N. CS. N. S, 



83867 
83851 
83835 
83819 



34 Deg. 

nTsT I N. CS. 



55919 82904 
55943 82887 
55968 82871 

55992 82855 



83804 56016182839 

83788 56040 82822 
83772 56064 82806 



83756 
83740 
83724 
83708 
83692 
82676 
83660; 
83645 
83629 



56 Des. 



56088182790 
50112 82773 



56305 
56329 
56353 
56377 
56401 
56425 



82643 
82626 
82610 
82593 
82577 
82561 



56449 82544 



56473 
56497 
56521 
56545 
56569 
56593 
56617 
56641 



82528 
82511 
82495 
82478 
82462 
82446 
82429 
82413 
56665 82390 
56689182380 



56713 
56736 
56760 
56784 
56808 
56832 



82363 
82347 
82330 

82314 
82297 
8228 



56856 82264 



56880 
56904 
56928 
56952 
56976 



57000 82165 

57024 

57047 

57071 

57095 



82248 
82231 
82214 
82198 
82181 



82 148 
82132 
82115 
82098 
57119182082 
5714382065 
..7167182048 
57191 182032 
57215 820 15 
57238 81999 
57262181982 
57236 81965 
57310|81949 
57334 81932 
N. CS. I N. S. 



55 Deff. 



70 



A TABLE OP NATURAL SINES. 



35 i)ejr. 



57 

57381 
57405 

3 57429 

4 57453 
57177 
57501 
57524 
57548 
57572 
57596 
57(519 
57643 
57687 
57691 
57715 



:358'8r9l5h' 



6 

7 

8 

9 
10 
11 
12 
13 
14 
15 

16 5773S 

17 57762 

18 57786 

19 57S10 

20 57833 
57857 
57881 
57904 
57928 
57952 
57976 
57999 
58023 
5804 



81899 

81882 

81865 

81848 

81832 

8181 

81798 

81782 

81765 

81748 

81731 

81714 

81698 

8168 

81664 



30|58070 

31 

32 

83 

34 

35 

36 

37 



81647 
81631 
81614 
81597 
81580 
81563 
81546 
81530 
81513 
81496 
81479 
81462 
81445 
81428 
81412 



58094 
581 18i 
58141 
58165 
58189 
58212 
58236 
38|t/82C0 
39158283 
40|58307 

41 58330 

42 58354 

43 58378 

44 58401 

45 58425 
46 
47 
48 
49 
50 
51 
52 
53 
54 



81395 
81378 
81361 
SI 344 
81327 
81310 
81293 
81276 
81259 
81242 
81225 
81208 
81191 
81174 
81157 



58449 
58472 
58496 
58519 
58543 
58567 
53590 
58614 
58637 
58661 
58684 
58708 
58731 
58755 



81140 
81123 
81106 
81089 
81072 
81055 
81038 
81021 
81004 
80987 
80970 
80953 
80930 
80919 
N . Ce>. N. S.' 
54 Deg. 



36 Deg^. I 37 Peg. 
i\. (js. i 'nTs~"n.Ts. 



N. S. 
58779 
58802 
58826 
58849 
58873 
58896 
58920 
58943 
5896 
58990 
59014 
59037 
59061 
59084 
59108 
59131 



60182 
00205 
6022S 
00251 
60274 
60298 
60321 
60344 
60367 
60390 
60414 
GO 437 
60460 
60483 
60506 
60529 



S0368i 
80351 j 
80334 
30316 
80299 160991 



60553 
60570 
60599 
60622 
60645 
60668 
60691 
60714 
60738 
60761 
60784 
60807 
60830 
60853 
00^8^ 

60899 
60922 
60945 
60968 



80282 
S0264 
80247 
80230 
80212 
30195 
30178 



61015 
61038 
161061 
{61084 
61107 
161130 
161153 



80160 16117 
80143 61199 

80125 61222 



80108 
800911 
80073 
800561 
80038! 
59972!8002l| 
599951800031 
60019 79986 
60042179968 
60065 I79G51 
60089179934 
601 12 '799 16 
G0l35i79899l 
60 1 58 1 79881 ! 
N.CSri N. S. I 
53 Deg. ' 



79864 
79846 
79829 
7t:8 1 1 
79793 
79776 
79758 
79741 
79723 
79706 
79688 
79671 
79653 
79635 
79618 
79600 
79583 
79565 
79547 
79530 
79512 
79494 
79477 
79459 
79441 
79424 
79406 
79338 
79371 
79353 
79335 
7~93r8 
79300 
79282 
79264 
79247 
79229 
'(9211 
79193 
79176 
79158 
79140 
79122 
79105 
79087 
79069 



62932 77715 
62955 77696 
6297777678 
63000 177660 
63022177641 
63045177623 



3li Peg. I 39 Peg. 

N. CS. N. S. 1 N. CS. M 
60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 



61566 
61589 
61612 
61635 
61658 
61681 
61704 
61726 
61749 
61772 
61795 
61818 
61841 
61864 
61887 
61909 



78801 
78783 
78765 
78747 
78729 
78711 
78694 
78676 
78658 
78640 
78622 
78604 
78586 
78568 
78550 
7853_2 
61932 785~14 
61955 78496 



61978 
62001 
62024 
62046 
62069 
62092 
62115 
62138 
62160 
62183 
62206 
62229 
62251 



79051 
79033 
79015 
7899S 
78980 
78962 
78944 
78926 
78908 
78891 
78873 
61497,78855 
61520 78837 
61543 78819 
N. CS . I N. S. I 
52 Deg. 



62274 
62297 
62320 
62342 
62365 
62388 
82411 
62433 
62456 
62479 
62502 
62524 
62547 
62570 
62592 



78478 
78460 
78442 
78424 
78405 
78337 
78369 
78351 
78333 
78315 
78297 
78279 
78261 



782431 
782251 
78206 
78188 
78170 
78152 
78134 
78116 
78098 
78079 
78061 
78043 
78025 
78007 
77988 



62796177824 
628l9i77806 
62842 77788 
«i2864i 77769 
62887 77751 
62909 1 77733 

r 51 Deff. 



63068 
63090 
63113 
63135 
63158 
63180 
63203 
63225 
63248 
6327^1 
63293 
63316 
33338 
63361 
63333 
63406 
B428 
63451 
63473 
6349G 
63518 
63540 
63563 
63585 
63608 



63630 
63653 
63675 
63898 
63720 
63742 
63765 
63787 
63810 
63832 
63854 
63877 
83899 
63922 
63944 



77605 
775S6 
77568 
77550 
77531 
77513 
77494 
77476 
77458 
77439 



77421 
77402 
77384 
77366 
77347 
77329 
77310 
77292 
77273 
77255 
77236 
77218 
77199 
77181 
77162 



63966 
63989 
64011 
64033 



77144 
77125 
77107 
77088 
77070 
7705 1 
77033 
77014 
76996 
76977 
78959 
76940 
76921 
76903 
76884 



76866 
76847 
76828 
76810 



64056176791 
64078176772 
64100 76754 
64123 76735 
64145 76717 
64167 76698 
64190 76679 
64212,76661 
64234178642 
64256 :76623 
N.CS.i N.S. 
50 itesT 



J 



A TABLE OF NATURAL SINES. 



71 



10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

HO 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 
46 
47 
48 
49 
50 
61 
62 
53 
54 
55 
56 
57 
58 
59 
60 
M 



40 Deg. 



N.S . 

64279 
64301 
64323 



IN.CS. 
70604 
76586 
76567 



64346 7654S 
64368 76530 
64390 76511 
644 1'2 76492 
64435 76473 



64457 
64479 
64501 
64524 
64546 
G4568 
64590 
64612 



64635 
64657 
64679 
64701 
64723 
64746 
64768 
64790 
64812 
64834 
64856 
64878 
64901 
64923 
64945 
64967 
64989 
65011 
65033 
65055 
65077 
65099 
65122 
65144 
65166 
65188 
65210 
65232 
65254 
65276 



76455 
76436 
76417 
76398 
76380 
76361 
6342 
76323 



76304 
76286 
76267 
76248 
76229 
76210 
76192 
76173 
76154 
76135 
76116 
76097 
76078 
76059 
6041 
76022 
76003 
75984 
75965 
75946 
75927 
75908 
75889 
75870 
75851 
75832 
75813 
75794 
75775 
75756 



41 Deg. 



N.S . 
65606 
6562S 
65650 
65672 
65694 
65716 
6573S 
65759 
65781 
65803 
65825 
65847 
65869 
165891 
65913 
65935 



N. CS. 



75471 



66913 



75452 166936 



65298175738 
6532075719 



65956 
65978 
66000 
66022 
66044 
66066 
66088 
66109 

66ir;i 

66153 
66175 
66197 
66218 
66240 
6626 2 
66284 
66306 
66327 
66349 
66371 
66393 
66414 
66436 
66458 
66480 
66.50 
66523 
166545 
i66566 
66588 
166610 
16663 



75165 
75146 
75126 
75107 
75088 
75069 
75050 
75030 
75011 
74992 



75433 
75414 
75395 
75375 
75356 
75337 
75318 
75299 
76280 
75261 
75241 
76222 
75203 
76184 



66956 
66978 
66999 
67021 
67043 
67064 
67086 
67107 
67129 
67151 
67172 
67194 
67215 
67237 



67258 
67280 
6730] 
67323 
67344 
67366 
67387 
67409 
67430 
67452 



N.CS . 
74314 
74295 
74276 
74256 
74237 
74217 
74198 
74178 
74159 
74139 
74120 
74100 
74080 
740G1 
74041 
74022 



43 Deg. 44 Deg. 

N.S. "nTcsT "nTI 



749731 67473 

49531167495 

4934167516 

74915 67538 

74896 67559 



74876 67580 

4867167602 

74838I67G23 

74818 67645 



74799 
74780 
74760 
74741 
747221 
74703! 
74683 
74664 
74644 
74625 
74606 



67666 
676S8 



74002 
73983 
73963 
73944 
73924 
73904 
73885 
73865 
73846 
73826 
73806 
73787 
73707 
73747 
73728 



68200 
68221 
68242 
68264 
08285 
68306 
68327 
68349 
68370 
168391 
68412 
:68433 
;68456 
68476 
68497 
'68518 
;68539 
68561 
168582 
68603 
68624 
68645 
68666 
68688 
68709 
68730 
68751 



69466 
69487 
69508 
69529 
69549 
69570 
69591 
69612 
69633 
69654 
69675 
69696 
69717 
69737 
69758 
69779 



72817 
72797 
72777 
72757 
72737 
72717 
72697 
72677 
72667 
72637 
72617 
6S772I72597 
687931 72577 
688 14^2557 
68835 72537 



737081 
730881 
736691 
73649 
73629 
73610 
87709 j 735901 
67730' 735701 
67752IV3551 



65342 
65364 
65386 
65408 
65430 
65452 
65474 
65496 
66518 
65540 
66662 
65584 



75699 
75680 
75661 
75642 
75623 
75604 
75585 
75566 
75647 
76528 
75509 
75490 



74586 
74567 
; 666531 74548 
! 66676 74528 



656061 75471 

N. CS. ' N. S. 



66697 
66718 
66740 
66762 
66783 
66805 
166827 
66848 
66870 
66891 



I 49 Deg. I 



74509 
74489 
4470 
74451 
74431 
74412 
74392 
74373 
74353 
74334 



67773 
67795 
67816 
67837 
67859 
67880 



73531 
73511 
73491 
73472 
73452 
73432 



67901 
67923 
67944 
67965 
67987 
68008 
68029 
68051 
68072 
68093 
68115 
68136 



48 Deg. I 



73412 
73393 
73373 
73353 
73333 
73314 
73294 
73274 
73254 
73234 
73215 
73195 



68857172517 
6887872497 
68899:72477 
68920172457 
6894 ij 72437 
68962 72417 
68983172397 
69004:72377 
69025172357 
69046:72337 
69067J723I7 
69088 72297 
69109172277 
69130172257 
69151172236 
69172 72216 



69800 
69821 
69842 
69862 
69883 
69904 
69925 
69946 
69966 
69987 
70008 
70029 
70049 
70070 
70091 



6815773176 
6817973165 
6820073135 
N.CS. I N.S. 



47 Deg. 



69193 72196 

69214 

69235 

69256 

69277 

69298 

69319 72075 

69340 

69361 

69382 

69403 

69424 

69445 

69466 



N.CS. 



N.S. 



46 Deg. 



70112 
70132 
70153 
70174 

70195171223 
70215 
70236 
70257 
70277171141 
70298] 7 112 i 
70319 71100 
70339 71080 
0360 71059 
70381 71039 
70401 71019 
70422170998 
70443170978 
70463170957 
70484170937 
70505170916 
70525 170896 
70546 70875 
70567|70856 
70587 70834 
70608170813 
70628170793 
70649 70772 
70670 70752 
70690 1707 J I 
70711 1 70711 
N.S 



N.CS. 
i 45 Deg/ 



A TRAVERSE TABLE, 

SHOWINS THK DirfEBXjm OF 

LATITUDE AND DEPARTURE 

FOR DISTANCES BETWEEN 1 AND 100, AND FOR ANOl It 
TO QUARTER DEGREES BETWEEN 1° AND 90* 



TRAVERSE TABLE. 



1' 

s 
c 
9 

1 


iDeg. 


iDeg. 


IDeg. 


1 

1 


Lat. 


Dep. 
0.00 


Lat. 


Dep. 


Lat. 


Dep. 1 
0.01 


1.00 


1.00 


0.01 


1.00 


/b 


2.00 


0.01 


2.00 


0.02 


2.00 


0.03 


2 


3 


3.00 


0.01 


3.00 


0.03 


3.00 


0.04 


3 


4 


4.00 


0.02 


4.00 


0.03 


4.00 


0.05 


4 


5 


5.00 


0.02 


5.00 


0.04 


5.00 


0.07 


6 


6 


6.00 


0.03 


6.00 


0.05 


6.00 


0.08 


6 


7 


7.00 


0.03 1 


7.00 


0.06 


7.00 


0.09 


7 


8 


N.OO 


0.03 1 


8.00 


0.07 


8.00 


0.10 


8 


9 


9.00 


0.04 


9.00 


0.08 


9.00 


0.12 1 


9 


10 


iO.OO 


0.04 


10.00 


0.09 


10.00 


0.13 


10 


11 


11.00 


0.05 


li.OO 


0.10 


11.00 


0.14 1 


if 


12 


12.00 


0.05 


12.00 


0.10 


12.00 


0.16 j 


12 


13 


13.00 


0.06 1 
0.06 


13.00 


0.11 


13.00 


0.17 


13 


14 


14.00 


14.00 


0.12 


14.00 


0.18 i 


14 


15 


15.00 


0.07 


15.00 


0.13 


15.00 


0.20 


15 


16 


16.00 


0.07 


16.00 


0.14 


16.00 


0.21 


16 


17 


17.00 


0.07 1 


17.00 j 


0.15 


17.00 


0.22 


17 


18 


18.00 


08 j 


18 :)0 


0.16 


18.00 


0.24 


18 


19 


19.00 


0.08 1 


19.00 


0.17 


19.00 


0.25 


19 


2-0 


20.00 


0.09 ! 


20.00 


0.17 


20.00 


0.26 


20 


21 


21.00 


0.09 i 


21.00 


0.18 


21.00 


0.27 


21 


22 


22.00 


0.10 
0.10 


22.00 


0.19 


22.00 


0.29 


22 


23 


23.00 


23.00 


0.20 


23.00 


0..30 


23 


24 1 


24.00 


0.10 


24.00 


0.21 


24.00 


0.31 


24 


25 


25.00 


O.ll 


25.00 


0.22 


25.00 


0.33 


25 


20 


26.00 


0.11 


26.00 


0.23 


26.00 


0.34 


26 


27 


27.00 


0.12 


27.00 


0.24 


27.00 


0.35 


27 


28 


28.00 


0.12 


28.00 


0.24 


28.00 


0.37 


28 


29 


29.00 


0.13 


29.00 


0.25 


29.00 


0.38 


29 


30 


30.00 


0.13 


30.00 


0.26 


ao.oo 


0.39 


30 


' 31 


31.00 


0.14 


31.00 


0.27 


31.00 


0.41 


31 


32 


32.00 


0.14 


32.00 


0.28 


32.00 


0,42 


32 


33 


33 . 00 


0.14 


83.00 


0-29 


33.00 


0.43 


33 


34 


34.00 


0.15 


34.00 


0.30 


34.00 


0.45 


34 


35 


35.00 


0.15 


35.00 


0.31 


35.00 


0.46 


35 


36 


36.00 


0.16 


36.00 


0.31 


'' 36.00 


0.47 


36 


37 


37.00 


0.16 


37.00 


0.32 


37.00 


0.48 


37 


38 


38.00 


0.17 


38.00 


0.33 


! 38.00 


0.50 


38 


39 


39.00 


0.17 


39.00 


0.34 


1 39.00 


0.51 


39 


40 


40.00 


0.17 


40.00 


0.35 


i 40.00 


0.52 


40 


41 


41.00 


0.18 


41.00 


0.36 


i 41.00 


0..54 


41 


42 


42.00 


0.18 


42.00 


0.37 


42.00 


0.55 


42 


43 


43.00 


0.19 


43.00 


0.38 


1 43.00 
44.00 


0.56 


43 


44 


44.00 


0.19 


44.00 


0.38 


0.58 


44 


45 


45.00 


0.20 


45.00 


0.39 


45.00 


0.59 


45 


46 


46.00 


0.20 


46.00 


0.40 


1 46.00 


0.60 


46 


47 


47.00 


0.21 


47.00 


0.41 


47.00 


0.62 


47 


48 


48.00 


0.21 


48.00 


0.42 


I 48.00 


0.63 


48 


49 


49.00 


0.21 


49.00 


0.43 


j 49.00 


0.64 


49 


60 


50.00 


0.22 


50.00 


0.44 


jl 50.00 


0.65 


50 


J 


Dep. 


Lat. 


Dep. 


Lat. 


j Dep. 

i "'' 


Lat. 
Deg. 


"5 

Q 


891 Deg. 


89-^ 


Deg. 



travep.sk tahle. 



5 

i" 

r. 


iDeg. 


1 


Dcg. 


11 i Deg. 


C 

i ^ 
P 


Lat. 


' Dop. 


|| Lai. 


; Dep. 


La,, 

1 


Dep. 


TI 


51.00 


! 0.22 


i 51.00 


' 0.45 


1 51.00 


■ 0.67 


~6T 


;V2 


52.00 


0.23 


[I 52.00 


((.45 


j 52.00 


; (J. 68 


52 


53 


53.00 


0.23 


i 53.00 


0.46 


! 53.00 


i 0.69 


, 53 


i'?4 


54.00 


0.24 


54.00 


0.47 


54.00 


0.71 


54 


5.'! 


55.00 


0.24 


55.00 


0.48 


1 56.00 


0.72 


■ 65 


r)G 


50.00 


0.24 


56.00 


0.49 


j 56.00 


0.73 


' 56 


57 


57.00 


0.25 


1 57.00 


0..50 


57.00 


0.75 


57 


58 


58.00 


0.25 


I 68.00 


0.51 


67.99 


0.76 


58 


o'J 


59.00 


0.26 


i 59.00 


0.51 


58.99 


0.77 


59 


60 


60.00 


0.26 


1 60.00 


0.52 


59.99 


0.79 


60 


6"i 


ei7(7ii 


0.27 


1 61.00 


0..53 


60.99 


0.80 


~t\ ! 


(i-^ 


62.00 


0.27 


62.00 


0.54 


61.99 


0.81 


62 i 


0:> 


63.00 


0.27 


1 63.00 


0.55 


62.99 


0.82 


63 


(il 


64.00 


0.28 


[ 64.00 


0.56 


1 63.99 


0.84 


64 


r,5 


65.00 


0.28 


65.00 


o..5r 


i 64.99 


0.85 


65 


6G 


6.'>.00 


0.29 


' 66.00 


0.58 


1 65.99 


0.86 


66 


67 


67.00 


0.29 


67.00 


0.68 


! 66.99 


0.88 


67 


PS 


68.00 


0.30 


68.00 


0.59 


i 67.99 


0.89 


68 


no 


69.00 


0.30 


69.00 


0.60 


1 6^.99 


0.90 


69 


70 


70.00 


0.31 


70.00 


0.61 


1 69.99 


0.92 


70 


7T 


71.00 


0.31 


71.00 


0.62 


70.99 


0.93 


71 j 


72 


72.00 


0.31 


72.00 


0.63 


71.99 


0.94 


72 


7:{ 


73.00 


0.32 . 


73.00 


0.64 


-2.99 


0.96 


73 


74 


74.00 


0.32 


74.00 


0.65 


73.99 


0.97 


74 


7 5 


75.00 


0.33 


75.00 


. 65 


74.99 


0.98 


75 


76 


76 . 00 


0.33 


76.00 


0.66 


75.99 


0.99 


76 


77 


77.00 


0..34 


77.00 


0.67 


1 76.99 


1.01 


77 


78 


78.00 


0.34 


78.00 


0.68 


77.99 


1.02 


78 


79 


79.00 


0.34 


79.00 


0.69 


78.99 


1.03 


79 


.SO 


80.00 


0.35 


80.00 


0.70 


79.99 


1.05 


80 


81 


81.00 


0.35 


81.00 


0.71 


80.99 


1.06 


81 


82 


82.00 


0.36 


82.00 


0.72 


81.99 


1.07 


82 


h3 


83.00 


0.36 


83.00 


0.72 


82.99 


1.09 


83 


84 


vS4.00 


0.37 


8-1.00 


0.73 


83.99 


1. 10 


84 


85 


85.00 


0.37 


85.00 


0.74 


84.99 


1.11 


85 


86 


86.00 


0.38 


86.00 


0.75 


85.99 


1.13 


86 


87 


87.00 


0.38 


87.00 


0.76 


86.99 


1.14 


87 


88 


88.00 


0..38 


88.00 


0.77 


87.99 


1.15 


88 


89 


89.00 


0.39 


89.00 


0.78 


88.99 


1.16 


89 


90 


90.00 


0.39 


90.00 


0.79 


89.99 


1.18 


90 


'91 


'91.00 


0.40 


91.00 


0.79 


90.99 


1.19 


91 


92 


92.00 


0.40 


92.00 


0.80 


91.99 


1.20 


92 


93 


93.00 


0.41 


93.00 


0.81 


92.99 


1.22 


93 


94 


94.00 


0.41 


94.00 


0.82 


93.99 


1.23 


94 


95 


95.00 


0.41 


95.00 1 


0.83 


94.99 


1.24 1 


95 


96 


96.00 


0.42 


96.00 


0.84 


95.99 1 


1.26 


96 


97 


97.00 


0.42 


97.00 ! 


0.85 


96.99 


1.27 


97 


98 


98.00 


0.43 


98.00 1 


0.86 


97.99 


1.28 


98 


99 


99.00 


0.43 


99.00 1 


0.86 


98.99 


1.30 


99 


100 


100.00 


0.44 


100.00 ; 


0.87 


99.99 j 


1.31 


100 


6 
c 


Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. 1 
89U 


Lat. 
)eg. 


5 


8P, 1 


89^1 


)eg. 

1 



TRAVFRSE TABLE. 



D 
55' 

3 
O 


- 

1 Dog. 


UD^g. 


1 2 Deg. 


U Deg. 


C 
55' 

3 
O 
p 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1.00 


0.02 


1.00 


0.02 


1.00 


0.03 


1.00 


0.03 


2 


2.00 


0.03 


2.00 


0.04 


2.00 


0.05 


2.00 


0.06 


o 


3 


3.00 


0.05 


3.00 


0.07 1 3.00 


0.08 


3.00 


0.09 


3 


4 


4.00 


0.07 


4.00 


0.09 


4.00 


0.10 


4.00 


0.12 


4 


6 


5.00 


0.09 


5.00 


0.11 


5.00 


0.13 


5.00 


0.15 


5 


6 


6.00 


0.10 


6.00 


0.13 


6.00 


0.16 


6.00 


0.18 


6 


7 


7.00 


0.12 


7.00 


0.15 


7.00 


0.18 


7.00 


0.21 


7 


8 


8.00 


0.14 


8.00 


0.17 


8.00 


0.21 


8.00 


0.25 


8 


9 


9.00 


0.16 


9.00 


0.20 


9.00 


0.24 


9.00 


0.28 


9 


10 
11 


10.00 
11.00 


0.17 
0.19 


10.00 


0.22 


10.00 


0.26 
0.28 


10.00 


0.31 


10 


11.00 


0.24 


11.00 


10.99 


0..34 


11 


12 


12.00 


0.21 


12.00 


0.26 


12.00 


0.31 


11.99 


0.37 


12 


13 


13.00 


0.23 


13.00 


0.28 


13.00 


0.34 


12.99 


0.40 


13 


14 


14.00 


0.24 


14.00 


0.31 


14.00 


0.37 


13.99 


0.43 


14 


15 


15.00 


0.26 


15.00 


0.33 


14.99 


0.39 


14.99 


0.46 


i5 


16 


16.00 


0.28 


16.00 


0.35 


15.99 


0.42 


15.99 


0.49 


16 


17 


17.00 


0.30 


17.00 


0.37 


16.99 


0.45 


16.99 


0..52 


17 


18 


18.00 


0.31 


18.00 


0.39 


17.99 


0.47 


17.99 


0..55 


18 


19 


19.00 


0.33 


19.00 


0.41 


18.99 


0..50 


18.99 


0.,58 


19 


20 


20.00 


0.35 


20.00 


0.44 


19.99 


0..52 


19.99 


0.61 


20 


21 


21.0!) 


0.37 


21.00 


0.46 


20.99 


O.fSi 


20.99 


0.64 


21 


22 


22.00 


0.38 


21.99 


0.48 


21.99 


0..58 


21.99 


0.67 


22 


23 


23.00 


0.40 


22.99 


0.50 


22.99 


0.60 


22.99 


0.70 


23 


24 


24.00 


0.42 


23.99 


0..52 


23.99 


0.63 
0.G5J 


23.99 


0.73 


24 


2,'i 


25.00 


0.44 


24.99 


0.55 


24.99 


24.99 


0.76 


25 


26 


20.00 


0.45 


25.99 


0.57 


25.99 


0.68 


25.99 


0.79 


26 


27 


27.00 0.47 1 


26.99 


59 


26.99 


0.71 


26.99 


0.83 


27 


28 


2S.00 


0.49 


27.99 


0.61 


27.99 


0.73 


27.99 


0.86 


28 


29 


29.00 


0.51 


28.99 


0.63 


28.99 


0.76 


28.99 


0.89 


29 


30 


30.00 


0.52 


29.99 


0.65 


29.99 


0.79 


29.99 


0.92 


30 


31 


31.00 


0..'i4 


30.99 


0.68 


30.99 


0.81 


30.99 


0.95 


31 


32 


32.00 


0.56 


31.99 


0.70 


31.99 


0.84 


31.99 


0.98 


32 


33 


32.99 


0..58 


32.99 


0.72 


32.99 


0.86 


32.98 


i.Ol .33 


34 


33.99 


0.59 


33.99 


0.74 


33.99 


0.89 


33.98 


1.04 .34 


35 


34.99 


0.61 


34.99 


0.76 


34.99 


0.92 


34.98 


1.07 35 


36 


35.99 


0.63 


35.99 


0.79 


35.99 


0.94 


35.98 


l.iO 36 


37 


.36.99 


0.65 


36.99 


0.81 


36.99 


0.97 


36.98 


1.13 1 37 


38 


37.99 0.66 


37.99 


0.83 


37.99 


0.99 


! 37.98 


1.16 


38 


39 


38.99 


0.68 


38.99 


0.85 


38.99 


1.02 


38.98 


1.19 


39 


40 


39.99 


0.70 


39.99 


0.87 


39.99 


1.05 


39.98 


1.22 


40 


41 


40.99 


0.72 


40.99 


0.89 


40.99 


1.07 


40.98 


1 25r41 


42 


41.99 


0.73 


41.99 


0.92 


41.99 


I.IO 


41.98 


1 2« i 42 


43 


42.99 


0.75 


42.99 


0.94 


42.99 


1.13 


42.98 


1.3f 43 


44 


43.99 


0.77 


43.99 


0.96 


43.99 


1.15 


143.98 


1.34 44 


45 


44.99 


0.79 


44.99 


0.98 


44.99 


1.18 


44.98 


1.37 45 


46 


45.99 1 0.80 


45.99 


1.00 


45.99 


1.20 


45.98 


1.40 46 


47 


46.99 


0.W2 


46.99 


1.03 


46.99 


1.23 


46.98 


1.44 47 


48 


47.99 


0.84 


47.99 


1.05 


47.98 


1.26 


47.98 


1.47 1 49 


49 


48.99 


0.88 


48.99 


1.07 


48.98 


1.28 


48.98 


1..50 


49 


50 


49.99 


0.87 


49.99 


1.09 


49.98 


1.31 


49.98 


1..53 


50 

c 
Q 


T 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


LaU 


Dep. 


Lai. 


09 Deg. 


881 Deg. 


88J 


Deg. 


m 


Deg. 



TRAVEBSE TABLE. 



o 

E 
^ 


iDeg. 


U Deg. 


H 


Deg. 


U l^<3g. 


c 

nr. 


o 
9 
51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




50.99 


0.89 


50.99 


1.11 


50.98 


1.34 


.50.98 


1.56 


~51 


52 


51.99 


0.91 


51.99 


1.13 


51.98 


1.36 


51.98 


1.59 


52 


53 


52.99 


0.92 


52.99 


1.16 


52.98 


1.39 


52.98 


1.62 


53 


54 


53 99 


0.94 


53.99 


1.18 


53.98 


1.41 


53.97 


1.65 


54 


55 


54 99 


0.96 


54.99 


1.20 


54.98 


1.44 


54.97 


1.68 


55 


56 


55.99 


0.98 


55.99 


1.22 


55.98 


1.47 


55.97 


1.71 


56 


57 


50.99 


0.99 


56.99 


1.24 


.56.98 


1.49 


56.97 


1.74 


57 


58 


57.99 


1. 01 


57.99 


1.27 


.57.98 


l.,52 


57.97 


1.77 


58 


59 


58.99 


1.03 


.58.99 


1.29 


58.98 


1.54 


58.97 


1.80 


59 


60 
61 


59.99 


1.05 


59.99 


1.31 


59.98 
60.98 


1..57 
1.60 


.59.97 


1.83 


60 


60.99 


1.06 


60.99 


1.33 


60.97 


1.86 


61 


62 


61.99 


1.08 


61.99 


1..35 


61.98 


1.G2 


61.97 


1.89 


62 


63 


62.99 


1.10 


62.99 


1.37 


62.98 


1.65 


62.97 


1.92 


63 


64 


63.99 


1.12 


63.98 


1.40 


63.98 


1.68 


63.97 


1.95 


64 


65 


64.99 


1.13 


64.98 


1.42 


64.98 


1.70 


64.97 


1.99 


65 


66 


65.99 


1.15 


65.98 


1.44 


85.98 


1.73 


65.97 


2.02 


66 


67 


66.99 


1.17 


66.98 


1.46 


66.98 


1.75 


66.97 


2.05 


67 


68 


67.99 


1.19 


67.98 


1.48 


67.98 


1.78 


67.97 


2.08 


68 


69 


68.99 


1.20 


68.98 


1.51 


68.98 


1.81 


68.97 


2.11 


69 


70 
71 


69.99 
70.99 


1.22 
1.24 


69.98 


1..53 


69.98 


1.83 
1.86 


69.97 


2.14 


70 


70.98 


1.55 


70.98 


70.97 


2.17 


71 


72 


71.99 


1.26 


71.98 


1.57 


71.98 


1.88 


71.97 


2.20 


72 


73 


72.99 


1.27 


72.98 


1.59 


72.97 


1.91 


'"2.97 


2.23 


73 


74 


73.99 


1.29 


73.98 


1.61 


73.97 


1.94! 


73.97 


2.26 


74 


75 


74.99 


1.31 


74.98 


1.64 


74.97 


1.96 i 


74.97 


2.29 


75 


76 


75.99 


1..33 


75.98 


1.66 


75.97 


1.99 


75 . 96 


2.32 


76 


77 


76.99 


1.34 


76.98 


1.68 


76.97 


2.02 


76.96 


2.35 


77 


78 


77.99 


1.36 


77.98 


1.70 


77.97 


2.04 


77.96 


2.38 


78 


79 


78.99 1 


1..38 


78.98 


1.72 


78.97 


2.07 


78.96 


2.41 


79 


80 
81 


79.99 i 
80.99 1 


1.40 
1.41 


79.98 
80.98 


1.75 
1.77 


79.97 


2.09 
" 2.12 


79.96 
80.96 


2.44 
2.47 


80 


80.97 


"81 


82 1 8i.r?n 1 


1.43 


81.98 


1.79 


81.97 


2.15 


81.96 


2.. 50 


82 


83 


82.99 ' 


i.45 


82.98 


1.81 


82.97 


2.17 


82.96 


2.. 53 


83 


84 


83.99 , 


1.47 


83.98 


1.83 


83.97 


2.20 


83. 9G 


2.57 


84 


85 


84.99 ' 


1.48 


84.98 


1.85 


84.97 


2.23 


84.96 


2.60 


85 


86 


85.90 


1.50 


85.98 


1.88 


85.97 


2.25 


85.96 


2.63 


86 


87 


86.99 


1.52 


86.98 


1.90 


86.97 


2.28 


86.96 


2.66 


87 


88 


87.99 '■ 


1.54 


87.98 


1.92 


87.97 


2.30 


87.96 


2.69 


88 


89 


88.99 ; 


1..55 


88.98 


1.94 


88.97 


2.33 


88.96 


2.72 


89 


90 


89.99 : 
90.99 1 


1..57 
1.59 


89.98 


1.96 


89.97 


2.36 


89.96 
90.9b 


2.75 
2.78 


90 


91 


'90.98 


i.99 


90.97 


2.38 


91 


92 


91.99 i 


1.61 


91.98 


2.01 


91.97 


2.41 


91.96 


2.81 


92 


93 92.99 ' 


1.62 


92.98 


2.03 


92.97 


2.43 


92.96 


2.84 


93 


94 93.99 1 


1.64 


93.98 


2.05 


93.97 


2.46 


93.96 


2.87 


94 


95. 94. 99 


1.66 


94.98 


2.07 


94.97 


2.49 


94.96 


2.90 95 


96 


95.99 


1.68 


95.98 


2.09 


95.97 


2.51 


95.96 


2.94 j 96 


97 


96.99 


1.69 


96.98 


2.12 


96.97 


2.54 


96.95 


2.96 , 97 


98 


97.99 


1.71 


97.98 


2.14 


97.97 


2.. 57 


97.95 


2.99 


98 


99 


98.98 


1.73 


98.98 


2.16 


98.97 


2.59 


98.95 


3.02 


99 


100 

o 
§ 

5 


99.98 


1.75 


99.98 


2.18 


99.97 


2.62 


99.95 
Dep. 


3.05 
Lat. 


100 


Dep. 


Lat. 


Dep. 


1 

Lat. 


Dep. 


Lat. 


1 


80 T 


^c^. 


1 
881 Dejr. 


881 


Deg. 


88^ Deg. 


1 



TRAVERSE TABLE. 



1 

1 


2 Deg. 


2i Deg. 


H Deg. 


2| Deg. j 

1 


? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


3 
o 
9 


1.00 


0.03 


1.00 


0.04 


1.00 i 


0.04 


1.00 


0.05 


1 


2 


2.00 


0.07 


2.00 


0.08 


2.00 


0.09 


2.00 


0.10 


2 


2 


3.00 


0.10 


3.00 


0.12 


3.00 


0.13 


3.00 


0.14 


3 


4 


4.00 


0.14 


4.00 


0.16 


4.00 


0.77 


4.00 


0.19 


4 


5 


5.00 


0.17 


5.00 


0.20 


5 . 00 


0.22 


4.99 


0.24 


5 


6 


6.00 


0.21 


6.00 


0.24 


5.99 


0.26 


5.99 


0.29 


6 


7 


7.00 


0.24 


6.99 


0.27 


6.99 


0.31 


6.99 


0.34 


7 


S 7.99 


0.28 


7.99 


0.31 


7.99! 


0.35 


7.99 


0.38 


8 


9 8.99 


0.31 


8.99 


0.35 


8.99 i 


0.39 


8.99 


0.43 


9 


10 


9.99 


0.35 


9.99 


0.39 


9.99 


0.44 


9.99 


0.48 


10 
11 


n 


10.99 


0.38 


10.99 


0.43 


10.99 


0.48 


10.99 


0.53 


12 


11.99 


0.42 


11.99 


0.47 1 


11.99 


0.52 


11.99 


0.58 


12 


13 


12.99 


0.45 


12.99 


0.51 1 


12.99 


0.57 


12.99 


0.62 


13 


14 


13.99 


0.49 


13.99 


0.55 


13.99 


0.61 


13.98 


0.67 


14 


15 


14.99 


0..52 


14.99 


0.59 


14.99 


0.65 


14.98 


0.72 


15 


16 ! 15.99 


0..56 


15.99 


0.63 


15.99 


0.70 


15.98 


0.77 


16 


17 1 16.99 


0.59 


16.99 


0.67 


16.98 


0.74 


16.98 


0.82 


17 


18 i 17.99 


0.63 


17.99 


0.71 


17.98 


0.79 


17.98 


0.86 


18 


19 ! 18.99 


0.66 


18.99 


0.75 


18.98 


0.83 


18.98 


0.91 


19 


20 


19.99 


0.70 


19.98 


0.79 


19.98 


0.87 


19.98 


0.96 


20 


'21 


20.99 


0.73 


20.98 


0.82 


20.98 


0.92 


20.98 


1.01 


21 


22 121.99 


0.77 


21.98 


0.86 


21.98 


0.96 


21.97 


1.06 


22 


23 i 22 . 99 


0.80 


22.98 


0.90 


22.98 


1.00 


22.97 


1.10 


23 


24! 23.99 


0.84 


23.98 


0.94 


23.98 


1.05 


',23.97 


1.15 


24 


2o 24.98 


0.87 


24.98 


0.98 


24.98 


1.09 


24.97 


1.20 


25 


26 1 25.98 


0.91 


25.98 


1.02 


25.98 


1.13 


1 25.97 


1.25 


26 


27 26.98 


0.94 


26.98 


1.06 


26.97 


1.18 


126.97 


1.30 


27 


28 127.98 


0.98 


27.98 


1.10 


27.97 


1.22 


27.97 


1.34 


28 


29 128.98 


1.01 


28.98 


1.14 


28.97 


1.26 


128.97 


1.39 


29 


30 129.98 


1.05 


29.98 
30.98 


1.18 
1.22 


29.97 


1.31 


1 29.97 


!.44 


30 

31 


31 i 30.98 


1.08 


30.97 


1.35 


130.96 


1.49 


32 31.98 


1.12 


31.98 


1.26 


31.97 


1.40 


31.96 


1..54 


32 


33 I 32.98 


1.15 


32.97 


1.30 


32.97 


1.44 


132.96 


1.58 


33 


34 i 33.98 


1.19 


33.97 


1.33 


33.97 


1.48 


33.96 


1.63 


34 


35 ! 34.98 


1.22 


34.97 


1.37 


34.97 


1.53 


34.96 


1.68 


35 


36 1 35.98 


1.26 


35.97 


1.41 


.35.97 


1.57 


35.96 


1.73 


36 


37 136.98 


1.29 


36.97 


1.45 


36.96 


1.61 


.36.96 


1.78 


37 


38 i 37.98 


1.33 


37.97 


1.49 


37.96 


1.66 


37.96 


1.82 


38 


39 138.98 


1.36 


38 . 97 


1.53 


38.96 


1.70 


38.96 


1.87 


39 


40 
41 


39.98 

40.98 


1.40 

■"'r.43 


39.97 


1.57 


39.96 
40.96 


1.75 

1.77 


39.95 


1.92 


40 

' 41 


40.97 


1.61 


40.95 


1.97 


42 


41.97 


1.47 


41.97 


1.65 


41.96 


1.83 


41.95 


2.02 


42 


43 


42.97 


1.50 


42.97 


1.69 


42.96 


1.88 


42.95 


2.06 


43 


44 


43.97 


1..54 


43.97 


1 . 73 


43.96 


1.92 


43.95 


2.11 


44 


45 


44.97 


1.57 


44.97 


1.77 


44.96 


1.96 


44.95 


2.16 


45 


40 


45.97 


1.61 


45.96 


1.81 


45.96 


2.01 


45.95 


2.21 


46 


47 146.97 


! 1.64 


46.96 


1.85 


46 . 96 


2.05 


46.95 


2.25 


47 


48 47.97 


i 1.68 


47.96 


1.88 


47.95 


2.09 


47.95 


2.30 


48 


49 148.97 


1.71 


48.96 


1.92 


48.95 


2.14 


48.94 


2.35 


49 


fiOJ 49.97 


1 1.74 


49.96 


1.^ 


49.95 


2.18 


49.94 


2.40 


50 


u 

c 


i Dcp. 


1 Lat. 


Dep. 


Lat. 
De^. 


Dep. 


Lat. 


Dep. 


j I.a.. 


5 


5 


1 

1 C3 Deg 


m 


Deg. 


87i 


Deg. 



TRAVEKSE TABLE. 





1 2 Deg. 


! n Deg. 


^ 


Deg. 


21 Deg. 




a 

8 


1 f.at. 


Dep. 

1.78 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


61 


150.97 


60.93 
151.96 


2.00 150.95 


2.22 


50.94 


2.45 


52 


161.97 


1.81 


2.04 ' 51.95 


2.27 


61.94 


2.. 50 


i 52 


53 


152.97 


1.85 


i 52.96 


2.08 J. 52. 95 


2.31 


52.94 


2.. 54 


1 53 


54 


53.97 


1.83 


; 53.96 


2.12 j 53.95 


2.36 


53.94 


2.59 


i 54 


55 


154.97 


1.92 


1 54.96 


2.16 j.54.95 


2.40 


, 54.94 

1 55.94 


2.64 


i 55 


5S 


155.97 


1.95 


'55.96 


2.20 I 55.95 


2.44 


2.69 


i 56 


57 


150.97 


1.99 56.96 


2.24; 56.95 


2.49 


56.93 
\ 57.93 


2.73 


i 57 


53 


157.96 


2.02: 57.96 


2.23 i! 57.94 


2.53 


2.73 


i 58 


69 


: 58.98 


2.08 


158.95 


2.32 i 58.94 


2.57 


58.93 


2.83 


. 59 


60 
61 


1 59 . 96 
' 60.96 


2.09 
2.13 


1 59.95 


1 2.36 


1.59.94 
160.94 


2.62 

2.66 


59.93 


2.83 


60 

61 


60,95 2.39 


60.93 


2.93" 


62 


! 61.96 


2.16 


161.95 2.43 1161.94 


2.70 


i6l.93 


e2.97 


62 


63 


:62.9o 


2.20 


62.95 2.47 i 62.94 


2.75 


62.93 


3.02 


63 


64 


63.96 


2.23 


63.95 1 2.51 63.94 


2.79 


63.93 


3.07 


64 


65 


64.96 


2.27 


64.95 1 2.. 55; 64.94 


2.84 


64.93 


3.12 


65 


66 


6;k96 


2 . 30 


65.95 2.,59 1,65.94 


2.88 


65.92 


3.17 


66 


67 


66.96 


2.34 


66.95 2.63 166.94 


2.92 


66.92 


3.21 


67 


6S 


67.95 


2.37, 


87.95 2.67 


67.94 


2.97 


67.92 


3.26 


68 


69 


68.96 


2.41 


68.95 2.71 


68.93 


3.01 


68.92 


3.31 


69 


70 


69.96 


2.44 


69.95; 2.75 


69.93 


3.05 


69.92 


3.36 


70 


71 


70.96 


2.48 i 


70.95 1 2.79 


70.93 


3.10 


70.92 


3'. 41 


71 


72 


71.96 


2.51 


71.94 1 2.83 


71.93 


3.14 


71.92 


3.45 


72 


73 


72.96 


2. .55 1 


72.94 i 2.87 


72.93 


3.18 


72. r 2 


3.. 50 


73 


74 


73.95 


2.. 53 


73.94 1 2.91 


73.93 


3.23 


73.91 


3.. 55 


74 


75 


74.95 


2.62 


74.941 2.94 


74.93 


3.27 


74.91 


3.60 


75 


76 ' 75.9o 


2.65 


75.94 2.98 


75.93 


3.31 


1 75.91 


3.65 


76 


77 


76.95 


2.69! 


76.94 


3.02 


76.93 


3.36 


176.91 


3.70 


77 


78 


77.95 


2.72 i 77.94 


3.06 


77.93 


3.40 


77. 9J 


3.74 


78 


79 


78.95 


2.76 1 73.94 


3.10 


78.92 


3.45 


78.91 


3.79 


79 


80 
81 


79.95 


2.79 


79.94 


3.14 


79.92 
80.92 


3.49 1 
3.53 


79.91 


3.84 


80 
81 


80.95 


2.83 1 


80.94 


3.18 


80.91 


3.89 


82 


81.95 


2.86 


81,94 


3.22 


81.92 


3.58 


81.91 


3.93 


82 


83 


82.95 


2.90 


82.94 


3.26 


82.92 


3.62 


82.90 


3.98 


83 


84 


83.95 


2.93 


83.94 


3.30 


83.92 


3.66 


83.90 


4.03 


84 


85 


84.95 


2.97 


84.93 


3.34 


84.92 


3.71 1 


84.90 


4.08 


85 


86 


85 . 95 


3.00 


85.93 


3,. 38 


85.92 


3.751 


85.90 


4.13 


86 


87 


86.95! 


3.04 


86.93 


3.42 


86.92 


3.79 


86.90 


4.17 


87 


88 


87.95 


3.07 


87.93 


3.45 


87.92 


3.84 


87.90 


4.22 


88 


89 


88 . 95 


3.11 


88.93 


3.49 


88.92 


3.88 


88.90 


4.27 


89 


90 
91 


89 . 95 


3.14! 


89.93 


3.53 


89.91 


3.93 1 


89.90 


4.32 


90 
91 


90.95 


3.18| 


90.93 


3.-57 


90.91 


3.97 


90.90 


4.37 


92 


91.94 


3.21 


91.93 


3.61 


91.91 


4.01 


91.89 


4.41 


92 


93 


92.94 


3.25 


92.93 


3.65 


92.91 


4.06 


92.89 


4.46 


93 


94 


93.94 


3.28 


93.93 


3.69 


93.91 


4.10 


93.89 


4.51 


94 


95 


94.94 


3.32 


94 . 93 


3.73 


94.91 


4.14 


94.89 


4.56 


95 


96 


95.94 


3.35 


95.93 


3.77 


95.91 


4.19 


95.89 


4.61 


96 


97 


96.94 


3.39 


96.93 


3.81 


96.91 


4.23 


96.89 


4.85 


97 


98 


97.94 


3.42 


97.92 


3.85 


97.91 


4.27 


97.89 


4.70 


98 


99 


93.94 


3.46 


98.92 


3.89 


98.91 


4.32 


98.89 


4.75 i 


99 


100 

d 
o 

a 

Q 


99.94 


3.49 


99.92 


3.93 


99.91 


4.36 


99.88 


4.80 


100 

a 


C 

Q 


Dep. 
88 E 


Lac. 

)eg. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


L^t. 


871 Deg. 


8711 


3eg. 


87^ 


1 
)eg. 

1 



TRAVERSE TABLE. 



1" 


SDeg. 


3i Deg. 


n ^og- 


3f Deg. 




3 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1.00 


0.05 


1. 00 


0.06 


"TTob" 


0.06 


1.00 


0.06 


~1 


2 


2.00 


0.10 


2.00 


0.11 


2.00 


0.12 


2.00 


0.13 2 


3 


3.00 


0.16 


3.00 


0.17 


2.99 


0.18 


2.99 


0.20 3 


4 


3.99 


0.21 


3.99 


0.23 


3.99 


0.24 


3.99 


0.26 4 


5 


4.99 


0.36 


4.99 


0.28 


4.99 


0.31 


4.99 


0.33 5 


6 


5.99 


0.31 


5.99 


0.34 


5 . 99 


0.37 


5.99 


0.39 


6 


7 


6.99 


0.37 


6.99 


0.40 


6.99 


0.43 


6.99 


0.46 


7 


8 


7.99 


0.42 


7.99 


0.45 


7.99 


0.49 


7.98 


0.52 


8 


9 


8.99 


0.47 


8.99 


0.51 


8.98 


0..55 


8.98 


0.59 


9 


10 
' 11 


9.99 


0.52 


9.98 


0.57 


9.98 


0.61 


9.98 


0.65 


10 
11 


10.98 


0.58 


10.98 


0.62 


10.98 


0.67 


10.98 


0.72 


12 


11.9^ 
12.9^ 


0.63 


11.98 


0.68 


11.98 


0.73 


11.97 


0.78 


12 


13 


0.68 


12.98 


0.73 


12.98 


0.79 


12.97 


0.85 


13 


14 


13. 9S 


0.73 


13.98 


0.79 


13.97 


0.85 


13.97 


0.92 


14 


15 


14.98 


0.79 


14.98 


0.85 


14.97 


0.92 


14.97 


0.98 


15 


16 


15.98 


0.84 


15.97 


0.91 


15.97 


0.98 


15.97 


1.05 


16 


17 


16.98 


0.89 


16.97 


0.90 


16.97 


1.04 


16.96 


1.11 


17 


18 


17.98 


0.94 


17.97 


1.02 


17.97 


1.10 


17.96 


1.18 


18 


19 


18.98 


0.99 


18.97 


1.08 


18.96 


1.16 


18.90 


1.24 


19 


20 
21 


19.97 


1.05 


19.97 


1.13 


19.96 


1.22 


19.96 


1.31 


20 
21 


20.97 


1.10 


20.97 


1.19 


20.96 


1.28 


20.96 


1.37 


22 


21.97 


1.15 


21.96 


1.25 


21.96 


1.34 


21.95 


1.44 


22 


23 


22.97 


1.20 


22.96 


1.30 


22.96 


1.40 


22.95 


1.5i> 


23 


24 


23.97 


1.26 


23.96 


1.36 


23.96 


1.47 


23.95 


1..57 


24 


25 


24.97 


1.31 


24.96 


1.42 


24.95 


1.53 


24.95 


1.64 


25 


26 


25.96 


1.36 


25.96 


1.47 


25.95 


1..59 


25.94 


1.70 


26 


27 


26.96 


1.41 


26.96 


1.53 


26.95 


1.65 


26.94 


1.77 


27 


28 


27.96 


1.47 


27.95 


1.59 


27.95 


1.71 


27.94 


1.83 


28 


29 


28.96 


1..52 


28.95 


1.64 


28.95 


1.77 


28.94 


1.90 


29 


30 
31 


29.96 


1.57 


29.95 


1.70 


29.94 


1.S3 


29.94 


1.96 
2.03 


30 
31 


30.96 


1.62 


30.95 


1.76 


30.94 


1.89 


30.03 


32 


31.96 


1.67 


31.95 


1.81 


31.94 


1.95 


31.93 


2.09 


32 


33 


32.95 


1.73 


32.95 


1.87 


32.94 


2.01 


32.93 


2.16 


33 


34 


33.95 


1.78 


33.95 


1.93 


33.94 


2.08 


33.93 


2.22 


34 


35 


34.95 


1.83 


34.94 


1.98 


34.93 


2.U 


34.92 


2.29 


35 


36 


35.95 


1.88 


35.94 


2.04 


35.93 


2.20 


35.92 


2.35 


36 


37 


36.95 


1.94 


36.94 


2.10 


38.93 


2.26 


36.92 


2.42 


37 


38 


37.95 


1.99 


37.94 


2.15 


37.93 


2.32 


37.92 


2.49 


38 


39 


38.95 


2.04 


38.94 


2.21 


38.93 


2.38 


38.92 


2.55 


39 


40 
41 


39.95 


2.09 


39.94 


2.27 


39.93 


2.44 


39.91 


2.62 


40 
41 


40.94 


2.15 


40.93 


2.32 


40.92 


2.. 50 


40.91 


2.68 


42 


41.94 


2.20 


41.93 


2.38 


41.92 


2.56 


41.91 


2.75 


42 


43 


42.94 


2.25 


42.93 


2.44 


42.92 


2.63 


42.91 


2.81 


43 


44 


43.94 


2.30 


43.93 


2.49 


43.92 


2.69 


43.91 


2.88 


44 


45 


44.94 


2.36 


44.93 


2.55 


44.92 


2.75 


44.90 


2.94 


45 


46 


45.94 


2.41 


45.93 


2.61 


45.91 


2.81 


45.90 


3.01 


46 


47 


46.94 


2.46 


46.92 


2.66 


46.91 


2.87 


46.90 


3.07 


47 


48 


47.93 


2.51 


47.92 


2.72 


47.91 


2.93 


47.90 


3.14 


48 


49 


48.93 


2.56 


48.92 


2.78 


48.91 


2.99 


48.90 


3.20 


49 


_50 

V 

o 

a 
a 

Q 


49.93 


2.62 


49.92 


2.83 


49.91 


3.05 


49.89 


3.27 


_50 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


87 Deg. 


86i Deg. 


86^ 


Deg. 


86^ Deg. 

1 



TRAVERSE TABLE. 



5- 


3 Deg. 


3i Deg. 


3^ Deg. 


CI Deg. 


D 

i 

51 


B 
o 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

1 


Dep. 


Lat. 


Dep. 


61 


50.93 


2.67 


50.92 
01.92 


2.89 


;.-".3o 


~W A 


50.89 


3.34 


52 


51.93 


2.72 


".35 


51.90 


0.17 


51.89 


3.40 


52 


53 


52.93 


2.77 


0x5.91 


3.00 


152.90 


3.24 


52.89 


3.47 


53 


54 


53.93 


2.83 


53.91 


3.06 


153.90 


3.30 


53.88 


3.53 


54 


55 


54.92 


2.88 


54.91 


3.12 


[54.90 


3.36 


54.88 


3.60 


55 


56 


55.92 


2.93 


55.91 


3.17 


i 55.90 


3.42 


55.88 


3.66 


56 


57 


56.92 


2.98 


56.91 


3.23 


1 56.89 


3.48 


56.88 


3 73 


57 


58 


57.92 


3.04 


57.91 


3.29 


L57.89 


3.54 


57.88 


3.79 


58 


59 


58.92 


3.09 


58.91 


3.34 


: 58.89 


3.60 


58.87 


3.86 


59 


60 


59.92 


3.14 


59.90 
60.90 


3.40 
3.46 


; 59.89 


3.66 


59.87 
60.87 


3,92 
3.99 


60 
61 


61 


60.92 


3.19 


60.89 


3.72 


62 


61.92 


3.24 


61.90 


3.51 


i 61.88 


3.79 


61.87 


4.05 


62 


63 


62.91 


3.30 


62.90 


3.57 


1 62.88 


3.85 


62.87 


4.12 


63 


64 


63.91 


3.35 


63.90 


3.63 


1 63. PQ 


3.91 


63.86 


4.19 


64 


65 


64.91 


3.40 


64.90 


3.69 


64.88. 3.97 


64.86 


4.25 


65 


60 


65.91 


3.45 


65.89 


3.74 


65.88 


. 03 


65.86 


4.32 


66 


07 


66.91 


3.51 


66.89 


3.80 


66.88 


4 .^ 


66.86 


4.38 


67 


68 


67.91 


3.56 


67.89 


3.86 


167.87 


4. 15 ,,67.85 


4.45 


68 


69 


68.91 


3.61 


68.89 


3.91 


i 68.87 


4.21 


68.85 


4.51 


69 


70 

71 


69.90 
70.90 


3.06 


69.89 


3.97 


169.87 


4.27 


69.85 


4.58 


70 

71 


3.72 


70.89 


4.03 


1 70.87. 4.33 


70.85 


4.64 


72 


71.90 


3.77 


71.88 


4.08 


71.87 4.40 


71.85 


4.71 


72 


73 


72.90 


3.82 


72.88 


4.14 


172.86 


4.46 


72.84 


4.77 


73 


74 


73.90 


3.87, 
3.93 


73.88 


4.20 


73.86 


4.52 


73.84 


4.84 


74 


75 


74.90 


74.88 


4.25 


74.86 


4.58 


74.84 


4.91 


75 


76 


75.90 


3.98 


75.88 


4.31 


75 86 


4.64 


75.84 


4.97 


76 


77 


76.89 


4.03 


76.88 


4.37 


76.86 


4.70 


76.84 


5.04 


77 


78 


77.89 


4.08 


77.87 


4.42 


77.85 


4.76 


77.83 


5.10 


78 


79 


78.89 


4.13 


78.87 


4.48 


78.85 


4.82 


i 78.83 


5.17 


79 


80 
81 


79.89 
80.89 


4.19 
4.24 


79.87 


4.54 


79.85 


4.88 


179.83 


5.23 


80 
81 


80.87 


4.59 


80.85 


4.94 


80.83 


5.30 


82 


81.89 


4.29 


81.87 


4.65 


81.85 


5.01 


^81.82 


5.36 


82 


83 


82.89 


4.34 


82.87 


4.71 


82.85 


5.07 


i 82.82 


5.43 


83 


84 


83.88 


4.40 


83.86 


4.76 


83.84 


5.13 


83.82 


5.49 


84 


85 


84.88 


4.45 


84.86 


4.82 


84.84 


5.19 


84.82 


5.56 


85 


86 


85.88 


4.. 50 


85.86 


4.88 


85.84 


5.25 


85.82 


5.62 


86 


87 


86.88 


4.55 


86.86 


4.93 


86.84 


5.31 


86.81 


6.69 


87 


88 


87.88 


4.61 


87.86 


4.99 


87.84 


5.37 


1 87.81 


5.76 


88 


89 


88.88 


4.66 


88.86 


5.05 


88.83 


5.43 


188.81 


5.82 


89 


90 
91 


89.88 


4.71 


89.86 


5.10 
5.16 


89.83 
90.83 


5.49 


j 89.81 


5.89 


90 
91 


90.88 


4.76 


90.85 


5.56 


[90.81 


5.95 


92 


91.87 


4.81 


91.85 


5.22 


91.83 


5.62 


91.80 


6.02 


92 


93 


92.87 


4.87 


92.85 


5.27 


92.83 


5.68 


92.80 


6.08 


93 


94 


93.87 


4.92 


93.85 


5.33 


93.82 


5.74 


93.80 


6.15 


94 


95 


94.87 


4.97 


94.85 


5.39 


94.82 


5.80 


94.80 


6.21 


95 


96 


95.87 


5.02 


95.85 


5.44 


95.82 


5.86 


95.79 


6.28 


96 


97 


96.87 


5.08 


96.84 


5.50 


96.82 


5.92 


96.79 


6.34 


97 


98 


97.87 


5.13 


97.84 


5,^.& 


97.82 


5.98 


97.79 


6.41 


98 


99 


98.86 


5.18 


98.84 


5.61 


98.82 


6.04 


98.79 


6.47 


99 


100 

o 

c 

p 


99.86 
Dep. 


5.23 


99.84 


5.67 


99.81 


6.10 


99.79 


6.54 


100 

1 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


87 E 


>eg. 


861 Deg. 


1 
80^ Deg. 


86i Deg. 



iO 



TRAVERSE TABLE. 



1 


4Deg. 


4i Deg. 


^ Deg. 


4| Deg. 





■~ 


Lat. 

1.00 


Dep. 
0.07 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 


Dep. 


3 

a 

~1. 


1.00 


0.07 


1.00 


0.08 


1.00 


0.08 


2 2.001 


0.14 


1.99 


0.15 


1.99 


0.16 


1.99 


0.17 


2 


3^ 2.99 


0.21 


2.99 


0.22 


2.99 


0.24 


2.99 


0.25 


3 


4; 3.99 


0.28 


3.99 


0.30 1 


3.99 


0.3] 


3.98 


0.33 


4 


5 4.99 


0.35 


4.99 


0.37 


4.98 


0.39 


4.98 


0.41 


5 


6 5.99, 


0.42 


5.98 


0.44 


5.98 


0.47 


5.98 


0..50 


6 


7 1 


6.98 


0.49 


6.98 


0.52 


6.98 


0..55 


6.97 


0.58 


7 


8 


7.98 


0.56 


7.98 


0..59 


7.98 


0.63 


7.97 


0.66 


8 


9: 


8.98! 


0.63 


8.98 


0.67 


8.97 


0.7J 


8.97 


0.75 


9 


10 

"11 


9.98 1 


0.70 


9.97 


0.74 


9.97 


0.78 
0.86 


9.97 


0.83 


10 
11 


10.97' 


"0.77 


10.97 


0.82 


10.97 


10.96 


0.91 


12 


11.97! 


0.84 


11.97 


0.89 


11.96 


0.94 


11.96 


0.99 


12 


13 


12.97 


0.91 j 


12.96 


0.96 


12.96 


1.02 


12.96 


1.08 


13 


14 


13.97, 


0.98 1 


13.96 


1.G4 


13.96 


1.10 


13.95 


l.lB 


14 


15 


14.961 


1.05 


14.96 


1.11 


14.95 


1.18 


14.95 


1.24 


15 


16 


15.96 


1.12 


15.96 


1.19 


15.95 


1.26 


15.95 


1.32 


16 


17 


16.96 


1.19 


16.95 


1.26 


16.95 


1.33 


16.94 


1.41 


17 


18 


17.96 


1.26 


17.95 


1.33 


17.94 


1.41 


17.94 


1.49 


18 


19 


18.95 


1..33 


18.95 


1.40 


18.94 


1.49 


18.93 


1.57 


19 


20 
21 


19.95 


1.40 i 


19.95 


1.48 


19.94 
20.94 


1.57 
1.65 


19.93 


1 . 66 


20 
"21 


20.95 


1.46 


20.94 


1.56 


20.93 


1.74 


22 


21.95 


1.53 1 


21.94 


1.63 


21.93 


1.73 


21.92 


1.82 


22 


23 


22.94 


1.60 


22.94 


1.70 


22.93 


1.80 


22.92 


1.90 


23 


24 


23.94 


1.67' 


23.93 


1.78 


23.93 


1.88 


23.92 


1.99 


24 


25 


24.94 


1.74 


24.93 


1.85 


24.92 


1.96 


24.91 


2.07 


25 


26 


25.94 


1.81 


25.93 


1.93 


25.92 


2.04 


25.91 


2.15 


26 


27 


26.93 


1.88 


26.93 


2.00 


26.92 


2.12 


26.91 


2.24 


27 


28 


27.93 


1.95 


27.92 


2.08 


27.91 


2.20 


27.90 


2.32 


2S 


29 


28.93 


2.02 


28.92 


2.15 


28.91 


2.28 


28.90 


2.40 


29 


30 
31 


29.93 


2.09 


29.92 


2.22 


29.91 


2.35 


29.90 


2.48 


31 


30.92 


2.16 


30.91 


2.30 


30.90 


2.43 


30.89 


2.57 


32 


31.92 


2.23 


31.91 


2.37 


31.90 


2.51 


31.89 


2.65 


32 


33 


32.92 


2. SO 


32.91 


2.45 


32.90 


2.59 


32.89 


2.73 


33 


34 


33.92 


2.37 


33.91 


2.52 


33.90 


2.67 


33.88 


2.82 


34 


35 


34.91 


2.44 


34.90 


2.59 


34.89 


2.75 


34.88 


2.90 


35 


36 


35.91 


2.51 


35.90 


2.67 


35.89 


2.82 


35.88 


2.98 


36 


3.7 


36.91 


2.58 


36.90 


2.74 


.36.89 


2.90 


36.87 


3.06 


37 


38 


37.91 


2.65 


37.90 


2.82 


37.88 


2.98 


.37.87 


3.15 


38 


39 


38.90 


2.72 


38.89 


2.89 


.38.88 


3.06 


38.87 


3.23 


39 


40 
41 


39.90 


2.79 


39.89 


2.96 


39.88 


3.14 


39.86 


3.31 


40 

41 


40.90 


1 2.86 


40.89 


3.04 


40.87 


3.22 


40.86 


3.40 


42 


41.90 


i 2.93 


41.88 


3.11 


41.87 


3.30 


41.86 


3.48 


42 


43 


42.90 


! 3.00 


42.88 


3.19 


42.87 


3.37 


42.85 


3.56 


43 


44 


43.89 


i 3.07 


43.88 


3.26 


43.86 


3.45 


43.85 


3.64 


44 


45 


44.89 


1 3.14 


44.88 


3.33 


44.86 


3.63 


44.85 


3.73 


45 


46 


45.89 


i 3.21 


45.87 


3.41 


45.86 


3.61 


45.84 


3.81 


46 


47 


46.89 


3.28 


46.87 


3.48 


46.86 


3.69 


46.84 


3.89 


47 


48 


47.88 


3.35 


47.87 


3.. 56 


47.8.') 


3.77 


47.84 


3.97 


48 


49 


48.88 


3.42 


48.87 


3.63 


48.85 


3.84 


48.83 


4.06 


49 


_60 

g 

1 

"to 


49.88 


1 3.49 


49.86 


3.71 


_49_.85 


3.92 


49.83 


4.14 


50 


Dep. 


1 Lat. 


Dep. 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

Q 


86 


Deg. 


85| Deg. 


85-» 


Deg. 


m Deg. 



TltA VERSE TABLE. 



11 



o 

3 
? 

51 


4 Deg. 


4k Deg. 


4^ Deg. 


4| Deg. 


3 
? 

51 


Lat. 


Dep. j 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50.88 


3.56 


50.86 


3.78 


"50."84r 


4.00 


50.82 


4.22 


52 


51.87 


3.63 


51.86 


3.85 


51.84 


4.08 


51.82 


4.31 


52 


53 


52.87 


3.70 


52.85 


3.93 


52.84 


4.16 


52.82 


4.39 


53 


54 


53.87 


3.77 


.53.85 


4.00 


53.83 


4.24 


53.81 


4.47 


54 


55 


54.87 


3.84 


54.85 


4.08 


54.83 


4.32 


54.81 


4-55 


55 


56 


55.86 


3.91 


55.85 


4.15 


55.83 


4.39 


55.81 


4.64 


56 


57 


56.86 


3.98 


56.84 


4.22 


56.82 


4.47 


56.80 


4.72 


57 


58 


57.86! 4.05 


57.84 


4.30 


57.82 


4.55 


57.80 


4.80 


58 


59 


58.86 1 4.12 


58.84 


4.37 


58.82 


4.63 


58.80 


4.89 


59 


60 
"61 


59.85 1 4.19 


59.84 


4.45 


59.82 


4.71 


59.79 


4.97 
5.05 


60 
61 


60.85 4.26 


60.83 


4.52 


60.81 


4.79 


60.79 


02 


61.85 4.32 


61.83 


4.59 


61.81 


4.86 


61.70 


5.13 


62 


63 


62.85! 4.39 


H2.83 


4.67 


62.81 


4.94 


62.78 


5.22 


63 


64 


63.84! 4.46 


63.82 


4.74 


63.80 


5.02 


63 . 78 


5.. 30 


64 


65 


64.84 1 4.53 


64.82 


4.82 


64.80 


5.10 


04.78 


5.38 


65 


66 


65.84 1 4.60 


65.82 


4.89 


65.80 


5.18 


65.77 


5.47 


66 


67 


6f>.84' 4.67 


66.82 


4.97 


66.79 


5.26 


66.77 


5.. 55 


67 


68 


67.83! 4.74 


67.81 


5.04 


67.79 


5.34 


67.77 


5.63 


68 


6y 


68.83 j 4.81 


68.81 


5.11 


68.79 


5 . 4 1 


68.76 


5.71 


69 


70 
71 


69.83; 4.88 


69.81 


5.19 


69.78 


5.49 
5.. 57 


69.76 
70 . 76' 


5.80 


70 

71 


70.83 1 4.95 


70.80 


5.26 


70.78 


5.88 


72 


71.82 1 5.02 


71.80 


5.34 


71.78 


5.65 


71.75 


5.96 


72 


73 


72.82 ! 5.09 


72.80 


5.41 


72.77 


5.73 


72 . 75 


6.04 


73 


74 


73.82 


5.16 


73.80 


5.48 


73.77 


5.81 


73.75 


6.13 


74 


75 


74.82 


5.23 


74.79 


5.56 


74.77 


5.88 


74.74 


6.21 


75 


76 


75.81 


5.30 


75 79 


5.63 


75.77 


5.96 


75.74 


6.29 


76 


77 


76.81 


5.37 


76.79 


5.71 


76.76 


6.04 


76.74 


6.38 


77 


78 


77.81 I 5.44 


177.79 


5.78 


77.76 


6.12 


77.73 


6.46 


78 


79 


78.81 


5.51 


78.78 


5.85 


78.76 


6.20 


78.73 


6.. 54 


79 


80 
81 


79.81 


5.58 


79.78 


5.93 


79.75 

80.75 


6.28 
6.36 


79 . 73 


6.62 


80 
81 


80.80 


5.65 


80.78 


6.00 


80.72 


6.71 


82 


81.80 


5.72 


181.78 


6.08 


81.75 


6.43 


81.72 


6.79 


82 


83 


82.80 


5.79 


82.77 


6.15 


82.74 


6.51 


82.71 


6.87 


83 


84 


83.80 


5.86 


83.77 


6.23 


83.74 


6.59 


83.71 


6.96 


84 


85 


84.79 


5.93 


84.77 


6.30 


84.74 


6.67 


84.71 


7.04 


85 


86 


85.79 


6.00 


85.76 


6.37 


85.73 


6.75 


85.70 


7.12 


85 


87 


86 . 79 


6.07 


86.76 


6.45 


86.73 


6.83 


96.70 


7.20 


87 


88 


87.79 


6.14 


87.76 


6.. 52 


87.73 


6.90 


87.70 


7.29 


8S 


89 


88.78 1 6.21 


88.78 


6.60 


88.73 


6.98 


88 . 70 


7.37 


89 


90 
91 


89. 7S 


6.28 


89.75 


6.67 
6.74 


89.72 


7.06 


89.69 
90.69 


7.45 
7.54 


90 
91 


90.78 


6.35 


90.75 


90.72 


7.14 


92 


91.78 


6.42 


91.75 


6.82 


91.72 


7.22 


91.68 


7.62 


92 


93 


92.77 


6.49 


92.74 1 6.89 


92.71 


7.30 


92.68 


7.70 


93 


94 


93.77 


6.56 


93.74 


6.97 


93.71 


7.38 


93.68 


7.78 


94 


95 


94.77 


6.63 


94.74 


7.04 


94.71 


7.45 


94.67 


7.87 


95 


96 


95.77 


6.70 


95.74 


7.11 


95.70 


7.53 


195.67 


7.95 


96 


97 


96.76 


6.77 


96.73 


7.19 


96.70 


7.61 


96.67 


8.03 


97 


98 


97.76 


6.84 


97.73 


7.26 


97.70 


7.69 


197.66 


8.12 


98 


99 


98.76 


6.91 


98.73 


7.34 


98.69 


7.77 


198.66 


8.20 


99 


100 

6 
o 

c 

Q 


99.76 


6.98 


99.73 


7.41 


99.69 


7.85 


199.66 


8.28 


100 

6 

o 

B 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
851 


Lat. 


Dep. 


Lat. 


86 Deg. 


1 


Dejr. 


Deg. 


85.1 Deg. 



12 



TRAVKRSE TABLE. 



D 

09 

3 
o 


3 Deg. 


5k Deg. 


5-i- Deg. 


5.1 Deg. 


1 
9 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

1 


Lat. 


Dep. 


T 


1.00 


0.09 


1.00 


0.09 


1.00 


0.10 


0.99 


0.10 


1 


2 


1.99 


0.17 


1.99 


0.18 


1.99 


0.19 


1.99 


0.20 


2 


3 


2.99 


0.26 


2.99 


0.27 


2.99 


0.29 


2.98 


0.30 


3 


4 


3.98 


0.35 


3.98 


0.37 


3.98 


0.38 


3.98 


0.40 


4 


5 


4.98 


0.44 


4.98 


0.46 


4 . 98 


0.48 


4.97 


0.50 


5 


6 


5.98 


0.52 


5.97 


0.55 


5 . 97 


0.58 


5.97 


0.60 


6 


7 


6.97 


0.61 


6 . 97 


0.64 


6.97 


0.67 


6.96 


0.70 


7 


8 


7.97 


0.70 1 7.97 


0.73 


7.96 


0.76 


7.96 


0.80 


8 


9 


8.97 


0.78 8.96 


0.82 


8 96 


0.86 


8.95 


0.90 


i>' 


10 


9.96 


0.87: 9.96 


0.92 


9 . 95 


0.96 


9.95 


1.00 


10: 


11 


10. 9G" 


0.96 ! 10.95 


"■ 1. 01 


10.95 


1.05 


10.94 


1. 10 


11 i 


12 


11.95 


1.05 


1 1 . 95 


1.10 


11.94 


1.15 1 


11.94 


1.20 


12 1 


13 


12.95 


1.13 


12.95 


1.19 


12.94 


1.25 


12.93 


1.30 


13 


14 


13.95 


1.22 


13.94 


1.28 


13.94 


1.34 1 


13.93 


1.40 


14 i 


15 


14.91 


1.31 


14.94 


1.37 


14.93 


1.44 


14.92 


1.50 


1^ 
16? 


16 15.94 


1.39 


15.93 


1.46 


15.93 


1.53 


15.92 


1.60 


17 


16.94 


1.48 


16.93 


1.56 


16.92 


1.63 


16.91 


1.70 


17 


18 


17.93 


1.5? i 


17.92 


1.65 


17.92 


1.73 


17.91 


1.80 


18 


i9 


18.93 


1.66; 


18.92 


1.74 


18.91 


1.82 1 


18.90 


1.90 


19 


20 
21 


19.92 

20.92' 


1.74 

1.83 


19.92 


1.83 


19.91 


1.92 


19.90 


2.00 


20 

21 


20.91 


1.92 


20.90 


■ 2.01 1 


20.89 


2.10 


22 


21.92 


1.92 


21.91 


2.01 


21.90 


2.11 


21.89 


2.20 


22 


23 


22.91 


2.00 1 22.90 


2.10 


22.89 


2.20 


22.88 


2.30 


23 


24 


23.91 


2.09 1,23.90 


2.20 


23.89 


2.30 


23.88 


2.40 


24 


25 


24.90 


2.18 


24.90 


2.29 


24.88 


2.40 1 


24.87 


2.50 


25 


2() 


25.90 


2.27 


25.89 


2.38 


25.88 


2.49 i 


25.87 


2.60 


26 
27 

28 


27 


26.90 


2.35 


26.89 


2.47 


26.88 


2.59 


26.86 


2.71 


2S 


27.89 


2.44 


27.88 


2.56 


27.87 


2.88 


27.86 


2.81 


29 


28.89 


2.53 


28.88 2.65 


28.87 


2.78 


28.85 


2.91 


29 


30 
3i 


29.89 


2.61 


29.87 2.75 


29.86 


2.88 


29.85 


3.01 


-§ 


30.88 


2.70 


30.87 


2.84 


30.86 


2.97 


.30.84 


3.11 


32 


31. 8S 


2.79 


31.87 


2.93 


31.85 


3.07 


31.84 


3.21 


32 


33 


32.87 


2.88 


32.86 


3.02 


32.85 


3.16 


32.83 


3.31 


33 


34 


33.87 


2.96 


33.86 


3.11 


33.84 


3.26 


33.83 


3.41 


34 


35 


34.87 


3.05 


34.85 


3.20 


34.84 


3.35 


34.82 


3.51 


35 


36 


35.86 


3.14 


35.85 


3.29 


35.83 


3.45 


35.82 


3.61 


36 


37 


36.86 


3.22 


36.84 


3.39 


36.83 


3.55 


36.81 


3.71 


37 


38 


37.86 


3.31 


37.84 


3.48 


37.83 


3.64 


37.81 


3.81 


38 


39 


38.85 


3.40 


38.84 


3.57 


38.82 


3.74 


38.80 


3.91 


39 


40 

4i 


39.85 
40.84 


3.57 


39.83 


3.66 


39.82 


3.83 


39.80 


4.01 


40 
41 


40.83 


3.75 


40.81 


3.93 


40.79 


4.11 


42 


41.84 


3.66 


41.82 


3.84 


41.81 


4.03 


41.79 


4.21 


42 


43 


42.84 


3.75 


42.82 


3.93 


42.80 


4.12 


42.78 


4.:^! 


43 


44 


43.83 


3.83 


43.82 


4.03 


43.80 


4.22 


43.78 


4.41 


44 


45 


44.83 


3.92 


44.81 


4.12 


44.79 


4!31 


44.77 


4.51 


45 


46 


45.82 


4.01 


45.81 


4.21 


45.79 


4.41 


45.77 


4.61 


40 


47 


46.82 


4.10 


46.80 


4.30 


46.78 


4.50 


46.76 


4.71 


47 


48 


47.82 


4.18 


47.80 


4.39 


47.78 


4.60 


47.76 


4.81 


48 


49 


48.81 


4.27 


48,79 


4.48 


48.77 


4.70 


48.75 


4.91 


49 


50 


49.81 


4.36 


49.79 


4.58 


49.77 


4.79 


49.75 


5.01 


50 


.2 

Q 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

o 

c 

.2 


85 


Deg. 


84| Deg. 


841 Deg. 


84i 


Deg. 



TKAVEliSK TABL:-. 



o 

p 
n 

9 

IT 


5Deg. 


5i Deg. 


H l^eg. 


■^i 


Deg. 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


..i 


50.81 


4.44 


50.79 


4.67 


50.77 


4.89 


50.74 


5.11 


51 


52 


51.80 


4.53 


51.78 


4.76 


51.76 


4.98 


51.74 


6.21 ! 62 1 


53 


52.80 


4.62 


52.78 


4.85 


52.76 


5.08 


52.73 


6.31 ' 5Ci 


54 


53.79 


4.71 


53.77 


4.94 


53.75 


5.18 


53.73 


6.41 


54 


55 


rvl.79 


4.79 


54.77 


5.03 


54.75 


6.27 


54.72 


5.51 


65 


66 


55.79 


4.88 


55.77 


6.12 


.56.74 


5.37 


55.72 


6.61 


66 


57 


56.78 


4.97 


56.76 


5.22 


56.74 


5.46 


66.71 


5.71 


57 


58 


57.78 


5.06 


57.76 


6.31 


57.73 


5.56 


67.71 


5. 81 


58 


59 


58.78 


5.14 


.58.75 


5.40 


58.73 


5.66 


68.70 


6.91 


59 


60 
61 


59.77 


5.23 


59.76 
60.74 


6.49 


69.72 


5.75 


59.70 


6.01 ; 601 


60.77 


5.32 


5.68 


60.72 


5.86 


60.69 


6.11 ! 6ll 


62 


61.76 


5.40 


61.74 


5.67 


61.71 


6.94 


61.69 


0.21 


62 


63 


62.76 


5.49 


62.74 


6.76 


62.71 


6.04 


62.68 


6.31 


63 


64 


63.76 


5.58 


63.73 


5.86 


63.71 


6.13 


63.68 


6.41 


64 


65 


64.75 


5.67 


64.73 


5.95 


64.70 


6.23 


64.67 


6.61 


65 


66 


65.75 


5.75 


65.72 


6.04 


66.70 


6.33 


66.67 


6.61 


66 


67 


66.75 


5.84 


66.72 


6.13 


66.69 


6.42 


66.66 


6.71 


6? 


68 


67.74 


5.93 


67.71 


6.22 


67.69 


6.62 


67.66 


6.81 


68 


69 


68.74 


6.01 


68.71 


6.31 


68.68 


6.61 


68.65 


6.91 


69 


70 

71 


69.73 


6.10 


69.71 


6.41 


69.68 


6.71 


69.65 


7,01 


70 
71 


70.73 


6.19 


70.70 


6.50 


70.67 


6.81 


70.64 


7.11 


72 


71.73 


6.28 


71.70 


6.59 


71.67 


6.90 


71.64 


7.21 


72 


73 


72.72 


6.36 


72.69 


6.68 


72.66 


7.00 


72.63 


7.31 


78 


74 


73.72 


6.45 


73.69 


6.77 


73.66 


7.09 


73.63 


7.41 


74 


75 


74.71 


6.54 


74.69 


6.86 


74.65 


7.19 


74.62 


7.61 


75 


76 


75.71 


6.62 


75.68 


6.96 


76.65 


7.28 


76.62 


7.61 


76 


77 


76.71 


6.71 


76.68 


7.05 


76.65 


7.38 


76.61 


7.71 


77 


78 


77.70 


6.80 


77.67 


7.14 


77.64 


7.48 


77.61 


7.81 


78 


79 


78.70 


6.89 


78.67 


7.23 


78.64 


7.57 


78.60 


7.91 


79 


80 
81 


79.70 
80.69 


6.97 


79.66 


7.32 


79.63 


7.67 


79.60 


8.02 


80 


7.06 


80.66 


7.41 


80.63 


7.76 


80.59 


8.12 


81 


82 


81.69 


7.15 


81.66 


7.50 


81.62 


7.86 


81.69 


8.22 


82 


83 


82.68 


7.23 


82.65 


7.69 


82.62 


7.96 


82.. 58 


8.32 


83 


84 


83.68 


7.32 


83.65 


7.69 


83.61 


8.05 


83.68 


8.42 


84 


85 


84.68 


7.41 


84.64 


7.78 


84.61 


8.15 


84.57 


8.52 


85 


86 


85.67 


7.50 


85.64 


7.87 


85.60 


8.24 


86.57 


8.62 


86 


87 


86.67 


7.58 


86.64 


7.96 


86.60 


8.34 


86.66 


8.72 


87 


88 


87.67 


7.67 


87.63 


8.05 


87.59 


8.43 


87.66 


8.82 


88 


89 


88.66 


7.76 


88.63 


8.14 


88.69 


8.53 


88.55 


8.92 


89 


90 
91 


89.66 


7.84 


89.62 


8.24 


89.. 59 


8.63 


89.56 


9.02 


90 


90.65 


7.93 


90.62 


8.33 


90.58 


8.72 


90.64 


9.12 


91 


92 


91.65 


8.02 


91.61 


8.42 


91.68 


8.82 


91.54 


9.22 


93 


93 


92.65 


8.11 


92.61 


8.51 


92.57 


8.91 


92.63 


9.32 


93 


94 


93.64 


8.19 


93.61 


8.60 


93.57 


9.01 


93.63 


9.42 


94 


95 


94.64 


8.28 


94.60 


8.69 


94.56 


9.11 


94.52 


9.52 


95 


96 


95.63 


8.37 


95.60 


8.78 


95.56 


9.20 


95.52 


9.62 


96 


97 


96.63 


8.45 


96.59 


8.88 


96.65 


9.30 


96.51 


9.72 


97 


98 


97.63 


8.54 


97.59 


8.97 


97.55 


9.39 


97.51 


9.82 


98 


99 


98.62 


8.63 


98.59 


9.06 


98.64 


9.49 


9S.50 


9.92 


99 


100 

6 
o 

5 


99.62 


8.72 


99.58 


9.16 


99.54 


9.68 


99.50 


10.02 


100 

— :- 

s 

a 
S 

to 

s 


Dep. 


Lat. 


Dep. 


Lat.| 


Dep. 


Lat. 


Dep. 


Lat. 


85 1 


)eg. 


841 Deg. 1 


84A Deg. \ 


844 Deg. 



18 



14 



TRAVERSE TABLE. 



1 

tn' 

3 
P 


6 Deg. 


64 Deg. 


6i Deg. 


1 
6l Deg. 


5 
P 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.99 


0.10 


0.99 


0.11 i 


0.99 


0.11 


0.99 


0.12 


1 


2 


1.99 


0.21 


1.99 


0.22 


1.99 


0.23 


1.99 


0.24 


2 


3 


2.98 


0.31 


2.98 


0.33 


2.98 


0.34 


2.98 


0.35 


3 


4 


3.98 


0.41 


3.98 


0.44 


3.97 


0.45 


3.97 


0.47 


4 


5 


4.97 


0.52 


4.97 


0.64 


4.97 


0.57 


4.97 


0.59 


5 


6 


5.97 


0.63 


5.96 


0.65 


5.96 


0.68 


5.96 


0.71 


6 


7 


6.96 


0.73 


6.96 


0.76 


6.96 


0.79 


6.95 


0.82 


7 


8 


7.96 


0.84 


7.95 


0.87 


7.95 


0.91 


7.94 


0.94 


8 


9 


8.95 


0.94 


8.95 


0.98 


8.94 


1.02 


8.94 


1.00 


9 


10 
11 


9.95 


1.05 


9.94 


1.09 


9.94 


1.13 


9.93 


1.18 


10 


10.94 


1.15 


10.93 


1.20 


10.93 


1.25 


10.92 


1.29 


11 


12 


11.93 


1.25 


11.93 


1.31 


11.92 


1.36 


11.92 


1.41 


12 


13 


12.93 


1.36 


12.92 


1.42 


12.92 


1.47 


12.91 


1.53 


13 


14 


13.92 


1.46 


13.92 


1.52 


13.91 


1.59 


13.90 


1.65 


14 


15 


14.92 


1.57 


14.91 


1.63 


14.90 


1.70 


14.90 


1.76 


15 


16 


15.91 


1.67 


15.90 


1.74 


15.90 


1.81 


15.89 


1.88 


16 


17 


16.91 


1.78 


16.90 


1.85 


16.89 


1.92 


16.88 


2 00 


17 


18 


17.90 


1.88 


17.89 


1.96 


17.88 


2.04 


17.88 


2.12 


18 


19 


18.90 


1.99 


18.89 


2.07 


18.88 


2.15 


18.87 


2.23 


19 


20 
21 


19.89 


2.09 


19.88 
20.88 


2.18 
2.29 


19.87 


2.26 


19.86 


2.35 


20 


20.88 


2.20 


20.87 


2.38 


20.85 


2.47 


21 


22 


21.88 


2.30 


21.87 


2.40 


21.86 


2.49 


21.85 


2.59 


22 


23 


22.87 


2.40 


22.86 


2.50 


22.85 


2.60 


22.84 


2.70 


23 


24 


23.87 


2.51 


23.86 


2.61 


23.85 


2.72 


23.83 


2.82 


24 


25 


24.86 


2.61 


24.85 


2.72 


24.84 


2.83 


24.83 


2.94 


25 


26 


25.86 


2.72 


25.85 


2.83 


25.83 


2.94 


25.82 


3.06 


26 


27 


26.85 


2.82 


26.84 


2.94 


26.83 


3.06 


26.81 


3.17 


27 


28 


27.85 


2.93 


27.83 


3.05 


27.82 


3.17 


27.81 


3.29 


28 


29 


28.84 


3.03 


28.83 


3.16 


28. SI 


3.28 


28.80 


3.41 


29 


30 


29.84 


3.14 


29.82 


3.27 


29.81 


3.40 


29.79 


3.53 


30 


'31 


30.83 


3.24 


30.82 


3.37 


30.80 


3.51 


30.79 


3.64 


31 


32 


31 82 


3.34 


31.81 


3.48 


31.79 


3.62 


31.78 


3.76 


32 


33 


32.82 


3.45 


32.80 


3.59 


32.79 


3.74 


32.77 


3.88 


33 


34 


.33.81 


3.55 


33.80 


3.70 


33.78 


3.85 


33.76 


4.00 


34 


35 


34.81 


3.66 


34.79 


3.81 


34.78 


3.96 


34.76 


4.11 


35 


36 


35.80 


3.76 


35.79 


3.92 


35.77 


4.08 


35.75 


4.23 


36 


37 


36.80 


3.87 


36.78 


4.03 


36.76 


4.19 


36.75 


4.35 


37 


38 


37.79 


3.97 


37.77 


4.14 


37.76 


4.30 


37.74 


4.47 


38 


39 


38.79 


4.08 


38.77 


4.25 


38.75 


4.41 


38.73 


4.58 


39 


40 


39.78 


4.18 


39.76 


4.35 


39.74 


4.. 53 


39.72 


4.70 


40 


'41 


40.78 


4.29 


40.76 


4.46 


40.74 


4.64 


40.72 


4.82 


41 


42 


41.77 


4.39 


41.73 


4.57 


41.73 


4.76 


41.71 


4.94 


42 


43 


42.76 


4.49 


42.74 


4.68 


42.72 


4.87 


42.70 


5.05 


43 


44 


43.76 


4.60 


43.74 


4.79 


43.72 


4.98 


43.70 


5.17 


44 


45 


44.75 


4.70 


44.73 


4.90 


44.71 


5.09 


44.69 


5.29 


45 


46 


45.75 


4.81 


45.73 


5.01 


45.70 


5.21 


45.68 


5.41 


46 


47 


46.74 


4.91 


46.72 


5.12 


46.70 


5.32 


46.67 


5.52 


47 


48 


47.74 


5.02 


47.71 


5.23 


47.69 


5.43 


47.67 


6.64 


48 


49 


48.73 


, 5.12 


48.71 


5.34 


48.69 


5.55 


48.66 


5.76 


49 


50 


49.73 


5.23 


49.70 


5.44 


49.68 


5.66 


49.65 


5.88 


50 


i 


Dop. 


Lat. 


Dep. 

83} 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

5 
1 




I 84 


Deg 


B3.i 


Deg. 


83\ 


Deg. 



TRAVERSE TABLE. 



!5 



5 

"61 


6 Deg. 


64 Deg. 


6^ Deg J 
Lat. Dep. 


6| Deg. 


1 
P 
51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50.72 


5.33 


50.70 


5.55 


50.67 


5.77 


50.65 


5.99 


52 


51.72 


5.44 


51.69 


5.66 


51.67 


5.89 


51.64 


6.11 


52 


53 


52.71 


5.. 54 


52.68 


5.77 


.52.66 


6.00 


52.63 


6.23 


53 


54 53.70 1 


5.64 


53.68 


5.88 


53.65 


6.11 


53.63 


6.35 


54 


55 ; 


54.70 


5.75 


54.67 


5.99 


54.65 


6.23 


54.62 


6.46 1 


55 


56 


55.69 


5.85 


55.67 


6.10 


55.64 


6.. 34 


55.61 


6.. 58 


56 


57 


56.69 


5.96 


56.66 


6.21 


56.63 


6.45! 


56.60 


6.70 


57 


58 


57.68 


6.06 


57.66 


6.31 


.57.63 


6.57; 


57.60 


6.82 


58 


59 


58.68 


6.17 


58.65 


6.42 


,58.62 


6.68 


58.59 


6.93 


59 


60 
61 


59.67 


6.27 


59.64 


6.53 


59.61 


6.79! 


59.58 
60.58 


7.05 


60 

61 


60.67 


6.. 38 


60.64 


6.64 


60.61 


6.91 


7.17 1 


62 


61.66 


6.48 


61.63 


6.75 


61.60 


7.02 


61.57 


7.29 


62 


63 


62.65 


6. .59 


62.63 


6.86 


62.60 


7.13! 


62.56 


7.40 


63 


64 


63.65 


6.69 i 


63.62 


6.97 


63.59 


7.25 


63.56 


7.52 


64 


65 


64.64 


6.79! 


64.61 


7.08 


64.58 


7.36 1 


64.55 


7.64 


65 


66 


65.64 


6.90 


65.61 


7.19 


65.58 


7.47 


65.54 


7.76, 


66 


67 


66.63 


7.00 


66.60 


7.29 


66.57 


7 58 


66.54 


7.88 1 


67 


68 


67.63 


7.11 


67.60 


7.40 


67.56 


7.70 


67.53 


7.99 1 


68 


69 


68.62 


7.21 


68.59 


7.51 


68.56 


7.81 


68.52 


8.11 ! 


69 


70 
71 


69.62 


7.32 


69.58 


7.62 


69.55 


7.92 


69.51 


8.23! 


70 
71 


70.61 


7.42 


70.58 


7.73 


70.54 


8.04 


70.51 


8.35 


72 


71.61 


7.53 


71.. 57 


7.84 


71.54 


8.15 


71.50 


8.46 ! 


72 


73 


72.60 


7.63 


72.57 


7.95 


72.53 


8.26 


72.49 


8.58 


73 


74 


73.. 59 


7.74 


73.56 


8.06 


73.52 


8.. 38 


73.49 


8.70 


74 


75 


74.. 59 


7.84 


74.55 


8.17 


74.52 


8.49 


74.48 


8.82 


75 


76 


75.58 


7.94 


75.55 


8.27 


75.51 


8.60 


75.47 


8.93 


76 


77 


76.58 


8.05 


76.54 


8.38 


76.51 


8.72 


76.47 


9.05 


77 


78 


77.57 


8.15 


77.54 


8.49 


77.50 


8.83 


77.46 


9.17 


78 


79 


78.. 57 


8.26 


78.53 


8.60 


78.49 


8.94 


78.45 


9.29 


79 


80 

81 


79.56 


8.36 


79.53 


8.71 


79.49 


9.06 
9.17 


79.45 


9.40 


80 

81 


80.56 


8.47 


80.52 


8.82 


80.48 


80.44 


9.52 


82 


81.55 


8.57 


81.51 


8.93 


81.47 


9.28 


! 81.43 


9.64 


82 


83 


82.55 


8.68 


82.51 


9.04 


82.47 


9.40 


82.42 


9.76 


83 


84 


83.. 54 


8.78 


83.50 


9.14 


83.46 


9.51 


83.42 


9.87 


84 


85 


84.53 


8.88 


84.50 


9.25 


84.45 


9.62 


,84.41 


9.99 


85 


86 


85.53 


8.99 


85.49 


9.36 


85.45 


9.74 


85.40 


10.11 


86 


87 


86.52 


9.09 


86.48 


9.47 


86.44 


9.85 


(86.40 


10.23 


87 


88 


87.52 


9.20 


87.48 


9.58 


87.43 


9.96 


; 87.39 


10.34 


88 


89 


88.51 


9.30 


88.47 


9.69 


88.43 


10.08 


188.38 


10.46 


89 


90 


89.51 


9.41 


89.47 


9.80 


89.42 


10.19 


! 89.38 


10.58 


90 
91 


91 


90.50 


9.51 


90.46 


9.91 


90.42 


10.30 


90.37 


10.70 


92 


91.50 


9.62 


91.45 


10.02 


91.41 


10.41 


91.30 


10.81 


92 


93 


92.49 


9.72 


92.45 


10.12 


92.40 


10.53 


92.36 


10.93 


93 


94 


93.49 


9.83 


93.44 


10.23 


93.40 


10.64 


93.35 


11.05 


94 


95 


94.48 


9.93 


94.44 


10.34 


94.39 


10.75 


94.34 


11.17 


95 


96 


95.47 


10.03 


95.43 


10.45 


95.38 


10.87 


95.33 


11.28 


96 


97 


96.47 


10.14 


96.42 


10.56 


96.38 


10.98 


96.33 


11.40 


97 


98 


97.46 


10.24 


97.42 


10.67 


97.. 37 


11.09 


97.32 


11.52 


98 


99 


98.46 


10.35 


98.41 


10.78 


98.36 


11.21 


98.31 


11.64 


99 


100 

1 

.2 
Q 


99.45 


10.45 


99.41 


10.89 


99.36 


11.32 


99.31 


11.75 


100 

6 

B 

X 

1 " 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


84 Deg. 


83| Deg. 


8^ 


Deg. 


83i Deg. 



16 



I'ravkkse table. 



3 
O 

9 


7Deg. 


1\ Deg. 


7^ Deg 


71 Deg. 


53 
§ 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


0.99 


0.12 


0.99 


0.13 


0.99 


0.13 


0.99 


0.13 


1 


2 


1.99 


0.24 


1.98 


0.25 


1.98 


0.20 


1.98 


0.27 


2 


3 


2.98 


0.37 


2.98 


0.38 


2.97 


0.39 


2.97 


0.40 


3 


4 


3.97 


0.49 


3.97 


0.50 


3.97 


0.52 


3.96 


0.64 


4 


5 


4.96 


0.61 


4.96 


0.63 


4.96 


0.65 


4.95 


0.67 


6 


6 


6.96 


0.73 


5.95 


0.76 


6.95 


0.78 


5.96 


0.81 


6 


7 


6.95 


0.85 


0.94 


0.88 


6.94 


0.91 


6.94 


0.94 


7 


8 


7.94 


0.97 


7.94 


1. 01 


7.93 


1.04 


7.93 


1.08 


8 


9 


8.93 


1.10 


8.93 


1.14 


8.92 


1.17 


8.92 


1.21 


9 


10 


9.93 


1.22 


9.92 


1.26 


9.91 


1.31 


9.91 


1.36 


10 
11 


n 


10.92 


1.34 


10.91 


1.39 


10.91 


1.44 


10.90 


1.48 


12 


11.91 


1.46 


11.90 


1.51 


11.90 


1.67 


11.89 


1.62 


12 


13 


12.90 


1.58 


12.90 


1.64 


12.89 


1.70 


12.88 


1.75 


13 


14 


13.90 


1.71 


13.89 


1.77 


13.88 


1.83 


13.87 


1.89 


14 


15 


14.89 


1.83 


14.88 


1.89 


14.87 


1.96 


14.86 


2.02 


16 


16 


15.88 


1.95 


15.87 


2.02 


15.86 


2.09 


16.85 


2.16 161 


17 


16.87 


2.07 


16.86 


2.15 


16.85 


2.22 


16.84 


2.29 


17 


18 


17.87 


2.19 


17.86 


2.27 


17.86 


2.36 


17.84 


2.43 


18 


19 


18.86 


2.32 


18.85 


2.40 


18.84 


2.48 


18.83 


2.56 


19 


20 


19.85 


2.44 


19.84 


2.52 


19.83 


2.61 


19.82 


2.70 


20 


21 


20.84 


2.56 


20.83 


2.65 


20.82 


2.74 


20.81 


2.83 


21 


22 


21.84 


2.68 


21.82 


2.78 


21.81 


2.87 


21.80 


2.97 


22 


23 


22:83 


2.80 


22.82 


2.90 


22.80 


3.00 


22.79 


3.10 


23 


24 


23.82 


2.92 


23.81 


3.03 


23.79 


3.13 


23.78 


3.24 


24 


25 


24.81 


3.05 


24.80 


3.15 


24.79 


3.26 


24.77 


3.37 


25 


26 


25.81 


3.17 


25.79 


3.28 


25.78 


3.39 


25.76 


3.51 


26 


27 


26.80 


3.29 


26.78 


3.41 


26.77 


3.62 


26.75 


3.64 


27 


28 


27.79 


3.41 


27.78 


3.53 


27.76 


3.66 


27.74 


3.78 


28 


29 


28.78 


8.53 


28.77 


3.66 


28.76 


3.79 


28.74 


3.91 


29 


80 


29.78 


3.66 


29.76 


3.79 


29.74 


3.92 


29.73 


4.06 


30 


31 


30.77 


3.78 


30.75 


3.91 


30.73 


4.05 


30.72 


4.18 


31 


32 


31.76 


3.90 


31.74 


4.04 


31.73 


4.18 


31.71 


4.32 


32 


33 


32.75 


4.02 


32.74 


4.16 


32.72 


4.31 


32.70 


4.45 


33 


34 


33.75 


4.14 


33.73 


4.2-9 


33.71 


4.44 


33.69 


4.58 


34 


35 


34.74 


4.27 


34.72 


4.42 


34.70 


4.67 


34.68 


4.72 


36 


36 


35.73 


4.39 


35.71 


4.54 


36.69 


4.70 


36.67 


4.85 


»6 


37 


36.72 


4.51 


36.70 


4.67 


36.68 


4.83 


36.66 


4.99 


37 


38 


37.72 


4.63 


37.70 


4.80 


37.67 


4.96 


37.65 


5.12 


38 


39 


38.71 


4.75 


38.69 


4.92 


38.67 


5.09 


38.64 


5.26 


39 


40 

41 


39.70 


4.87 


39.68 


5.05 


39.66 


5.22 


39.63 


6.39 


40 
41 


40.70 


5.00 


40.67 


5.17 


40.66 


6.35 


40.63 


5.53 


42 


41.69 


5.12 


41.66 


5.30 


41.64 


6.48 


41.62 


6.66 


42 


43 


42.68 


5.24 


42.66 


5.43 


42.63 


5.61 


42.61 


6.80 


43 


44 


43.67 


5.36 


43.65 


5.55 


43.62 


5.74 


43.60 


5.93 


44 


45 


44.67 


5.48 


44.64 


5.68 


44.62 


5.87 


44.59 


6.07 


45 


46 


45.66 


5.61 


45.63 


5.81 


46.61 


6.00 


45.58 


6.20 


46 


47 


46.65 


5.73 


46.62 


5.93 


46.60 


6.13 


46.57 


6.34 


47 


48 


47.64 


5.85 


47.62 


6.06 


47.69 


6.27 


47. ?6 


6.47 


48 


49 


48.63 


5.97 


48.61 


6.18 


48.58 


6.40 


48.65 


6.61 


49 


50 


49.63 


6.00 


49.60 


6.31 


49.67 


6.53 


49.54 


6.74 


50 


9 
U 

a 
S 
.2 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 


83 


Deg. 


82^ 


Deg. 


821 

i, 


Deg. 


m Deg. 



TRAVEIt^J; TA]?LE. 



17 



9. 

I 


7Deg. 


1i Deg. 


H Deg. 


7| Deg. 

i 


C 

m' 

i" 

9 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. 


51 


50.62 


6.22 


50.59 


6.44 


.50.56 6.66 1 
51.56 6.79 


50.53 


6. 88 


51 


52 


51.61 


6.34 


51.58 


6.56 


51.53 


7.01 i 


52 


53 


52.60 


6.46 


52.58 


6.69 


.52.55 6.92 1 


52.52 


7.15 


63 


54 


53.60 


6.58 


53.57 


6.81 


.53.54 7.05 


53.51 


7.28 1 


54 


55 


54.59 1 


6.70 


54.56 


6.94 


54.53 7.18 


54. 5U 


7.42 1 


55 


56 


55.58 1 


6.82 


55.55 


7.07 


55.52 7.31 


55.49 


7.55 


56 


57 


.56.58 


6.95'; 


56.54 


7.19 


56.51 7.441 


56.48 


7.69 


57 


58 


57.57 


7.07 


57.54 


7.32 


57.50 


7.57 


.57.47 


7.82 1 


58 


59 


58.56 


7.19 


58.53 


7.45 


58.50 


7.70 


58.46 


7.96 


59 


60 
61 


59 . 55 


7.31 


59.52 


7.57 


59.49 


7.83 


59.45 


8.09 ! 


60 
61 


60.55 


7.43 


60.51 


7.70 


60.48 


7.96 


60.44 


8.23 1 


63 


61.54 


7.56 


61.50 


7.82 


61.47 


8.09 


61.43 


8.36 


62 


63 


62.53 


7.68 


62.50 


7.95 


62.46 


8.22 


62.42 


8.50 


63 


64 


63.52 


7.80 


63.49 


8.08 


63.45 


8.35 


63.42 


8.63 


64 


65 


64.52 


7.92 


64.48 


8.20 


64.44 


8.48 


64.41 


8.77 


65 


66 


65.51 


8.04 


65.47 


8.33 


65.44 


8.G1 


65.40 


8.90 


66 


67 


63 50 


8.17 


66.46 


8.46 


66.43 


8.75 


66.39 


9.04 


67 


G8 


67.49 


8.29 


67.46 


8.58 


67.42 


8.88 


67.38 


9.17 


6S 


69 


68.49 


8.41 


68.45 


8.71 


68.41 


9.01 


68.37 


9.30 


69 


70 
71 


69.48 


8.63 


69.44 


8.83 


69.40 


9.14 


69.36 


9.44 


70 
71 


70.47 


8.65 


70.43 8.96 


70.39 


9.27 


70.35 


9.57 


72 


71.46 


8.77 


71.42 9.09 


71.38 


9.40 


71.34 


9.71 


72 


73 


72.46 


8.90 


72.42 9.21 


72 38 


9.53 


72.33 


9.84 


73 


74 


73.45 


9.02 


73.41 9.34 


73.37 


9.661 


73.32 


9.98 


74 


75 


74.44 


9.14 


74.40 9.46 


74.36 


9.79 


74.31 


10.11 


75 


76 


75.43 


9.26 


75.39 9.59 


75.35 


9.92 


75.31 


10.25 


76 


77 


76.43 


9.38 


176.38 1 9.72 


76.34 


10.05 


76.30 


10.38 


77 


78 


77.42 


9,51 


1 77.38 1 9.84 


77.33 


10.18 i 77.29 


10., 52 


78 


79 


73.41 


9.63 


178.37! 9.97 


78.32 


10.31 !i 78.28 


10.65 


79 


80 
81 


79.40 


9.75 


79.36 


10.10 


79.32 

"80.31 


10.44 ll 79.27 


10.79 


80 
81 


80.40 


9.87 


180.35 


10.22 


10.57 


1 80.26 1 10.92 


82 


81.39 


9.99 


81.34 


10.35 


81.30 


10.70 


181.25 


11.06 


82 


83 


82.38 


10.12 


82.34 


10.47 


82.29 


10.83 


82.24 


11.19 


83 


84 


83.37 


10.24 


83.33 


10.60 


83.28 


10.96 


83.23 


11.33 


84 


85 


84.37 


10.36 


84.32 


10.73 


84.27 


11.09 


84.22 


11.46 


85 


86 


85.36 


10.48 


85.31 


10.85 


85.26 


11.23 


85.21 


11.60 


1 86 


87 


86.35 


10.60 


86.30 


10.98 


86.26 


11.36 


86.21 


11.73 


87 


88 


87.34 


10.72 


87.30 


11.11 


87.25 


11.49 


87.20 


11.87 


88 


89 


88.34 


10.85 


88.29 


11.23 


88.24 


11.62 


88.19 


12.00 


89 


90 
91 


89.33 


10 97 


89.28 


11.36 


89.23 


11.75 


89.18 


12.14 


90 
91 


90.32 


11.09 


90.27 


11.48 


90.22 


11.88 


90.17 


12.27 


92 


91.31 


11.21 


91.26 


11.61 


91.21 


12.01 


91.16 


12.41 


92 


93 


92.31 


11.33 


92.26 


11.74 


92.20 


12.14 


92.15 


12.54 


93 


94 


93.30 


11.46 


93.25 


11.86 


93.20 


12.27 


93.14 


12.68 


94 


95 


94.29 


11.58 


94.24 


11.99 


94.19 


12.40 


94.13 


12.81 


95 


96 


95.28 


11.70 


95.23 


12.12 


95.18 


12.53 


95.12 


12.95 


96 


97 


96.28 


11.82 


96.22 


12.24 


96.17 


12.66 


96.11 


13.08 


97 


98 


97.27 


11.94 


97.22 


12.37 


97.16 


12.79 


97.10 


13.22 


98 


99 


98.26 


12.07 


98.21 


12.49 


98.15 


12.92 


98.10 


13.35 


99 


100 

(3 


99.25 


12.19 


99.20 


12.62 


99.14 


13.05 


99.09 


13.49 


100 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dc-p. 


Lat. 


Dep. 


Lat. 


83] 


Deg. 


82| Deg. 


82i Deg. 


82i Deg. 



18 



TRAVERSE TARLE. 



w i 8 Deg. 


8i Deg. 


8| Dog. 


8! Deg. 


3 


1 


















P 


i 

CO 


Lai. 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 1 0.99 


0.14 


0.99 


0.141 


0.99 


0.15 


0.99 


0.15 


1 


2| 1.98 


0.28 


1.98 


0.29 


1.98 


0.30 


1.98 


0..30 


2 


3l 2.97 


0.42 


2.97 


0.43 


2.97 


0.44 


2.97 


0.46 


3 


4i 3.9G 


0..56 


3.96 


0.57 


3. 90 


0.59 


3.95 


0.61 


4 


5! 4.95 


0.70; 

0.84 


4.95 


0.72 


4.95 


0.74 


4.94 


0.76 5 1 


6 I 5.94 


5.94 


0.86 


5.93 


0.89 


5.93 


0.91 6| 


7i 6.93 


0.97 1 6.93 


1.00 


6.92 


1.03 


fi.92 


1.06 


7 


8! 7.92 


l.Il !! 7.92 


1.15 


7.91 


1.18 


7.91 


1.22 


8 


9 1 S.91 


1.25 ii 8.91 


1.29 


8.90 


1.33 


8.90 


1.37 


9 


10 


9.90 


1.39 1! 9.90 


1.43 


9.89 


1.48 


9.88 


1.52 


10 


U 


10.89 


1.53 


10.89 


1.58! 


10.88 


1.63! 


10.87 


1.07 


11 


12 i 11.88 


1.67 


11.88 


1.72 1 


11.87 


1.77 


11.86 


1.83 


12 


13! 12.87 


1.81 


12.87 


1.87 1 


12.86 


1.92 


12.85 


1.98 


13 


14 1 13.86 


1.95 


13.80 


2.01 


13.85 


2.07 


13.84 


2.13 


14 


15 : 14.85 


2.09 


14.85 


2.15 


14.84 


2.22 


14.83 


2.28 


15 


16 


15.84 


2.23 


15.84 


2.30 1 


15.82 


2.36 


15.81 


2.43 


16 


17 


10.83 


2.37 


10.83 


2.44 


16.81 


2.51 


16.80 


2.59 17 


IS 


17.82 


2.51 


17.81 


2.. 58 


17.80 


2.66 


17.79 


2.74 1 18 


19 


18.82 


2.64 


18.80 


2.73 1 


18.79 


2.81 


18.78 


2.89 19 


20 


19.81 


2.78 


19.79 


2.87! 


19.78 


2.96 


19.77 


3.04 20 


21 


20.80 


2.92 


20 . 78 


3.01 1 


20.77 


3.10 


20.76 


3.19 1 21 


22 


21.79 


3.06 


21.77 


3.16 


21.76 


3.25 


21.74 


3.35 22 


23 


22.78 


3.20 


22.76 


3.30 


22.75 


3.40 


22.73 


3.50 23 


24 


23.77 


3.34 


23.75 


3.44 


23.74 


3.55 ';' 23.72 


3.65 24 


25^24.76 


3.48 


24.74 


3.59 


24.73 


3.70 i 24.71 


3.80 25 


26 125.75 


3.62 


25 . 73 


3.73 


25.71 


3.84 


125.70 


3.96 26 


27 126.74 


3.76 


26.72 


3.87 


26.70 


3.99 


;26.69 


4.11 1 27 


28 127.73 


3.90 1 


27.71 


4.02 


27.69 


4.14 


1 27.67 


4.26 


28 


29:28.72 


4.04 


28.70 


4.16 


28.68 


4.29 


,28.66 


4.41 


29 


30 129.71 


4.18' 


29.69 


4.30 


29.67 


4.43 


29.65 


4.56 


30 


31 ! 30.70 


4.31 


30.68 


4.45 


30.66 


4.58 


! 30.64 


4.72 


31 


32 131.69 


4.45 


31.67 


4.59 


31.65 


4.73 


31.63 


4.87 


32 


33! 32.68 


4.59 


32.66 


4.74 


32.64 


4.83 


32.62 


5.02 


33 


34 1 33.67 


4.73 


33.65 


4.88 


33.63 


5.03 


33.60 


5.17 


34 


35 134.66 


4.87 


34.64 


5.02 


34.62 


5.17 


34.59 


5.32 


35 


36 135.65 


5.01 


35.63 


5.17 


35.60 


5.. 32 


35.58 


5.48 


36 


37 136.64 


5.15 


36.62 


5.31 


36.59 


5.47 


36.57 


5.63 


37 


38 37.63 


5.29 


37.61 


5.45 


37.58 


5.62 


37.56 


5.78 


38 


39 38.62 


5.43 


38.60 


5.60 


38.57 


5.76 


38.55 


5.93 


39 


40 139.61 


5.. 57 


39.59 


5.74 


39.56 


5.91 


39.53 
40.52 


6.08 


40 


41 ! 40.60 


5.71 


40.58 


5.88 


40.55 


6.06 


6.24 


41 


42 


41.59 


5.85 


41.57 


6.03 


41.54 


6.21 


41.51 


6.39 


42 


43 


42.. 58 


5.98 


42.56 


6.17 


42.53 


6.36 


42.50 


6.54 


43 


44 


43.57 


6.12 


43., 54 


6.31 


43.52 


6.50 


43.49 


6.69 


44 


45 


44.56 


6.26 


44.53 


6.46 


44.51 


6.65 


! 44.43 


6.85 


45 


46 


45.55 


6.40 


45.52 


6.60 


45.49 


6.80 


'45.46 


7.00 


46 


47 


46.54 


6.54 


46.51 


6.74 


46.48 


6.95 


46.45 


7.15! 47 1 


48 


47.53 


6.68 


47.50 


6.89 


47.47 


7.09 


147.44 


7.30 


48 


49 


48.52 


6.82 


48.49 


7.03 


48.46 


7.24 


48.43 


7.45 


49 


50 

i 

5 


49.51 


6.96 


49.48 


7.17 


49.45 


7.39 


49.42 


7.61 


50 


Dep. 


L.at. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




82 


Deg. 


nil 


Deg. 


s\k 


Deg. 


8U 


Deg. 



TRAVERSE TABLE. 



19 



? 

61 


8Deg. 


«i Deg. 


H Deg. 


81 Deg. 


B 

o 

? 

~5l 


Lat. 
50750 


Dep. 


Lat. 
50.47 


Dep. 
7.32 


Lat. Dep. 

1 


Lat. 


Dep. 


7.10 


50.44 


7.54 


50.41 


7.76 


52 


51.49 


7.24 


51.46 


7.46 


51.43 


7.89 


61.. 39 


7.91 


62 


53 


62.48 


7.38 


52.45 


7.61 


52.42 


7.83 


62.38 


8.06 


63 


54 


53.47 


7.52 


53.44 7.75 


53.41 


7.98 


53.37 


8.21 


54 


55 


54.46 


7.85 


54.43 7.89 


54.40 


8.13 


54.36 


8.37 


55 


56 


55.48 


7.79 


55.42 


8.04 


55.38 


8.28 


55.36 


8.62 


68 


57 


56.45 


7.93 


56.41 


8.18 


58.37 


8.43 


56.34 


8.67 


67 


58 


57.44 


8.07 


67.40 


8.32 


57.38 


8.57 


57.32 


8.82 


58 


59 


58.43 


8.21 


58.39 


8.47 


68.35 


8.72 


68.31 


8.98 


59 


60 


59.42 


8.35 


59-38 


8.61 


59.34 


8.87 


69.30 


9.13 


60 


61 


60.41 


8.49 


60.37 


8.75 


60.33 


9.02 


80.29 


9.28 


81 


62 


61.40 


8.83 


61.36 


8.90 


61.32 


9.16 


61.28 


9.43 


62 


63 


62.39 


8.77 


62.35 


9.04 


82.31 


9.31 


62.27 


9.58 


63 


64 


63.38 


8.91 


63.34 


9.18 


63.30 


9.46 


63.20 


9.74 


64 


65 


64.37 


9.05 


64.33 


9.33 


64.29 


9.81 


64.24 


.9.89 


65 


60 


65.38 


9.19 


85.32 


9.47 


65.28 


9.76 


65.23 


10.04 


66 


67 


66.35 


9.32 


66.31 


9.61 


86.26 


9.90 


86.22 


10.19 


87 


68 


67.34 


9.46 


67.30 


9.76 


67.25 


10.05 


87.21 


10.34 


68 


69 


68.33 


9.60 


68.29 


9.90 


68.24 


10.20 


68.20 


10.50 


69 


70 
71 


69.32 


9.74 


69.28 


10.04 


69.23 


10.35 


69.19 


10.65 


70 

71 


70.31 


9.88 


70.27 


10.19 


70.22 


10.49 


70.17 


10.80 


72 


71.30 


10.02 


71.25 


10.33 


71.21 


10.64 


71.16 


10.95 


72 


73 


72.29 


10.16 


72.24 


10.47 


72.20 


10.79 


72.15 


11.10 


73 


74 


73.28 


10.30 


73.23 


10.62 


73.19 


10.94 


73.14 


11.26 


74 


75 


74.27 


10.44 


74.22 


10.76 


74.18 


11.09 


74.13 


11.41 


75 


78 


75.28 


10.58 


75.21 


10.91 


75.17 


11.23 


75.12 


11.66 


76 


77 


78.25 


10.72 


76.20 


11.05 


78.15 


11.38 


76.10 


11.71 


77 


78 


77.24 


10.86 


77.19 


11.19 


77.14 


11.63 


77.09 


11.87 


78 


79 


78.23 


10.99 


78.18 


11.34 


78.13 


11.68 


78.08 


12.02 


79 


80 
81 


79.22 


11.13 


79.17 


11.48 


79.12 


11.82 


79.07 


12.17 


80 
81 


80.21 


11.27 


80.16 


11.62 


80.11 


11.97 


80.08 


12.32 


82 


81.20 


11.41 


81.15 


11.77 


81.10 


12.13 


81.05 


12.47 


82 


83 


82.19 


11.55 


82.14 


11.91 


82.09 


12.27 


82.03 


12.63 


83 


84 


83.18 


11.69 


83.13 


12.05 


83.08 


12.42 


83.02 


12.78 


84 


85 


84.17 


11.83 


84.12 


12.20 


84.07 


12.66 


84.01 


12.93 


85 


86 


85.16 


11.97 


85.11 


12.34 


85.08 


12.71 


85.00 


13.08 


88 


87 


86.15 


12.11 


88.10 


12.48 


86.04 


12.86 


86.99 


13.23 


87 


88 


87.14 


12.25 


87.09 


12.63 


87.03 


13.01 


86.98 


13.39 


88 


89 


88.13 


12.39 


88.08 


12.77 


88.02 


13.18 


87.98 


13.64 


89 


90 
31 


89.12 


12.53 


89.07 
90.06 


12.91 


89.01 


13.30 


88.96 


13.69 


90 
91 


90.11 


12.66 


13.08 


90.00 


13.45 


89.94 


13.84 


92 


91.10 


12.80 


91.05 


13.20 


90.99 


13.60 


90.93 


14.00 


92 


93 


92.09 


12.94 


•92.04 


13.34 


91.98 


13.76 


91.92 


14.15 


93 


94 


93.09 


13.08 


93.03 


13.49 


92.97 


13.89 


92.91 


14.30 


94 


95 


94.08 


13.22 


94.02 


13.63 


93.98 


14.04 


93.89 


14.45 


96 


96 


95.07 


13.38 


95.01 


13.78 


94.95 


14.19 


94.88 


14.60 


96 


97 


96.06 


13.50 


96.00 


13.92 


95.93 


14.34 


95.87 


14.76 


97 


98 


97.05 


13.64 


96.99 


14.06 


96.92 


14.49 


96.86 


14.91 


98 


99 


98.04 


13.78 


97.98 


14.21 


97.91 


14.63 


97.85 


15.06 


99 


100 

i 

Ir. 

o 


99.03 


13.92 


98.97 


14.35 


98.90 


14.78 


98.84 


15.21 


100 


Dep. 


1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


.2 


82 


Dcg. 


1 Kl| Dej:. 

1^ 


81^ Deg. 


1 OU Deg. 

'1 



20 



TRAVIKSE TAIJLK. 





1 

9 Deg. 


9i Deg. 


9-^ 


Deg. 


91 


Deg 


55' 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 


Dep. 


1 1 0.99 


0.16 


0.99 


0.16 


0.99 


0.17 


0.99 


0.17 


1 


2 


1.98 


0.31 


1 .97 


0.32 


1.97 


0.33 


1.97 


0.34 


2 


3 


2.96 


0.47 


2.96 


0.48 


2.96 


0..50 


2.96 


0.51 


3 


4 


3.95 


0.63 


3.95 


0.64 


3.95 


0.66 


3.94 


0.68 


4 


5 


4.94 


0.78 


4.93 


0.80 


4.93 


0.83 


4.93 


0.85 


5 


6 


5.93 


0.94 


5.92 


0.96 


5.92 


0.99 


5.91 


1.02 


6 


7 


6.91 


1.10 


0.91 


1.13 


6.90 


1.16 


6.90 


1.19 


7 


8 


7.90 


1.25 


7.90 


1.29 


7.89 


1.32 


7.88 


1.35 


8 


9 


8.89 


1.41 


8.88 


1.45 


8.88 


1.49 


8.87 


1.52 


9 


10 
11 


9.88 


1.56 


9.87 


1.61 


9.86 


1.65 


9.86 


1.69 


10 


10.86 


1.72 


10.86 


1.77 


10.85 


1.82 


10.84 


1.86 


11 


12 


11.85 


1.88' 


11.84 


1.93 


11.84 


1.98 


11.83 


2.03 


12 


13 


12.84 


2.03] 


12.83 


2.09 


12.82 


2.15 


12.81 


2.20 


13 


14 


13.83 


2.191 


13.82 


2.25 


13.81 


2.31 


13.80 


2.37 


14 


15 


14.82 


2.35 


14.80 


2.41 


14.79 


2.48 


14.78 


2.54 


15 


16 


15.80 


2.50 


15.79 


2.57 


15.78 


2.64 


15.77 


2.71 


16 


17 


16.79 


2.661 


16.78 


2.73 


16.77 


2.81 


16.75 


2.88 


17 


IS 


17.78 


2.82 1 


17.77 


2.89 


17.75 


2.97 


17.74 


3.05 


18 


19 


18.77 


2.97i 


18.75 


3.05 


18.74 


3.14 


18.73 


3.22 


19 


20 
21 


19.75 


3.13 1 


19.74 


3.21 


19.73 


3.30 


19.71 


3.39 


20 


20.74 


3.29 j 


20.73 


3.38 


20.71 


3.47 


20.70 


3.. 56 


21 


22 


21.73 


3.44 


21.71 


3.. 54 


21.70 


3.63 


21.68 


3.73 


22 


23 


22.72 


3.60l 


22.70 


3.70 


22.68 


3.80 


22.67 


3.90 


23 


24 


23.70 


3.75 1 


23.69 


3.86 


23.67 


3.96 


23.65 


4.06 


24 


25 


24.69 


3.91 


24.67 


4.02 


24.68 


4.13 i 


24.64 


4.23 


25 


2fi 


25.68 


4.07 


25.66 


4.18 


25.64 


4.29 


25.62 


4.40 


26 


27 


28.67 


4.22 


26.65 


4.34 


26.63 


4.46 


26.61 


4.. 57 


27 


28 27.66 


4.38 


27.64 


4.50 


27.02 


4.62 


27.60 


4.74 


28 


29 28,64 


4.54 


28.62 


4.66 


28.60 


4.79 


28.58 


4.91 


29 


30 
31 


29.63 


4.69 


29.61 


4.82 


29.59 


4.95 


29.57 


5.08 


30 
31 


30.62 


4.85 


30.-30 


4.98 


30.57 


5.12 


30.55 


5.25 


32 


31.61 


5.01 


31.58 


5.14 


31.. 56 


5.28 


31.54 


5.42 


32 


33 


32.59 


5.16 


32.57 


5.30 


32.55 


5.45 


32.52 


5.59 


33 


34 


33.58 


5.32 


33.. 56 


5.47 


33.53 


5.61 


33.51 


5.76 


34 


35 


34.57 


5.48 


34.54 


5.63 


34.52 


5.78 


34.49 


5.93 


35 


36 


35.56 


5.63 


35.53 


5.79 


35.51 


5.94 


35.48 


6.10 


36 


37 


36.54 


5.79 


36.52 


5.95 


36.49 


6.11 


36.47 


6.27 


37 


38 


37.53 


5.94 


37.51 


6.11 


37.48 


6.27 


37.45 


6.44 


38 


39 


38.52 


6.10 


38.49 


6.27 


38.47 


6.44 


38.44 


6.60 


39 


40 
41 


39.51 


6.26 


39.48 


6.43 


39.45 


6.60 


39.42 


6.77 


40 
41 


40.50 


6.41 


40.47 


6.59 


40.44 


6.77 


40.41 


6.94 


42 


41.48 


6.57 


41.45 


6.75 


41.42 


6.92 


41.39 


7.11 


42 


43 


42.47 


6.73 


42.44 


6.91 


42.41 


7.10 


42.38 


7.28 


43 


44 


43.46 


6.88 


43.43 


7.07 


43.40 


7.26 


43.36 


7,45 


44 


45 


44.45 


7.04 


44.41 


7.23 


44.. 38 


7.43 


44.35 


7.62 


45 


46 


45.43 


7.20 


45.40 


7.39 


45.37 


7.59 


45.34 


7.79 


46 


47 


46.42 


7.35 


46.39 


7.55 


46.36 


7.76 


46.32 


7.96 


47 


48 


47.41 


7.51 


47.38 


7.72 


47.34 


7.92 


47.31 


8.13 


48 


49 


48.40 


7.67 


48.36 


7.88 


48.33 


8.09 


48.29 


8.30 


49 


50 


49.38 


7.82 


49.35 


8.04 


49.32 
Dep. 


8.25 


49.28 


8.47 


50 

" i 

a 

ft 


i 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


Dep. 


Lat. 


81] 


Oeg. 


80| Deg. 


801 


Deg. 


80i Deg. 



T 11 A V E KS K T A BL F. 



21 



1 

51 


9 Beg. 1 


1 
9i Deg. 


H Deg. 


n Deg. 


"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


60.37 


7.98 


50.34 


8.20 


50.30 


8.42 


50.26 


8.64 


52 


51.36 


8.13 


51.32 


8.36 


51.29 


8.58 


51.25 


8.81 


52 


53 


52.35 


8.29 


52.31 


8.52 


52.27 


8.75 


52.23 


8.98 


53 


54 


.53.34 


8.45 


53.30 


8.68 


53.26 


8.91 


53.22 


9.14 


54 


55 


54.32 


8.60 


54.28 


8.84 


54.25 


9.08 


54.21 


9.31 


55 


56 


55.31 


8.76 


55.27 


9.00 


55.23 


9.24 


55.19 


9.48 


56 


67 


56.30 1 8.92 


56.26 


9.16 


56.22 


9.41 


56.18 


9.65 


57 


58 


57.29 1 9.07 


57.25 9.32 


57.20 


9.57 


57.16 


9.82 


58 


69 


58.27 9.23 


58.23 9.48 


58.19 


9.74 


58.15 


9.99 


59 


60 
61 


59.26 9.39 


59.22 


9.64 
9.81 


59.18 


9.90 


59.13 


10.16 


60 
6] 


60.25 9. .54 


60.21 


60.16 


10.07 


60.12 


10.33 


62 


61.24 9.70 


61.19 


9.97 


61.15 


10.23 


61.10 


10.50 


62 


63 


62.22 9.86 


62.18 


10.13 


62.14 


10.40 


62.09 


10.67 


63 


64 


63.21 


10.01 


63.17 


10.29 


63.12 


10.56 


63.08 


10.84 


64 


65 


64.20 


10.17 


64.15 


10.45 


64.11 


10.73 


64.06 


11.01 


65 


66 


65.19 


10.32 


65.14 


10.61 


65.09 


10.89 


65.05 


11.18 


66 


67 


66.18 


10.48 


66.13 


10.77 


66.08 


11.06 


66.03 


11.35 


67 


68 


67.16 


10.64 


67.12 


10.93 


67.97 


11.22 


67.02 


11.52 


68 


69 


68.15 


10.79 


68.10 


11.09 


68.05 


11.39 


68.00 


11.69 


69 


70 
71 


69.14 


10.95 


69.09 


11.25 


69.04 


11.55 


68.99 
69.97 


11.85 
12.02 


70 

71 


70.13 


11.11 


70.08 


11.41 


70.03 


11.72 


72 


71.11 


11.26 


71.06 


11.57 


71.01 


11.88 


70.96 


12.19 


72 


73 


72.10 


11.42 


72.05 


11.73 


72.00 


12.05 


71.95 


12.36 


73 


74 


73.09 


11.58 


73.04 


11.89 


72.99 


12.21 


72.93 


12.53 


74 


75 


74.08 


11.73 


74.02 


12.06 


73.97 


12.38 


73.92 


12.70 


75 


76 


75.06 


11.89 


75.01 


12.22 


74.96 


12.54 


74.90 


12.87 


76 


77 


76.05 


12.05 


76.00 


12.38 


75.94 


12.71 


75.89 


13.04 


77 


78 


77.04 


12.20 


76.99 


12.54 


76.93 


12.87 


76.87 


13.21 


78 


79 


78.03 


12.36 


77.97 


12.70 


77.92 


13.04 


77.86 


13.38 


79 


80 
81 


79.02 


12.51 


78.96 


12.86 


78.90 


13.20 


178.84 
179.83 


13.55 


80 
81 


80.00 


12.67 


79.95 


13.02 


79.89 


13.37 


13.72 


82 


80.99 


12.83 


80.93 


13.18 


80.88 


13.53 


80.82 


13.89 


82 


83 


81.98 


12.98 


81.92 


13.34 


81.86 


13.70 


181.80 


14.06 


83 


84 


82.97 


13.14 


82.91 


13.50 


82.85 


13.86 


82.79 


14.23 


84 


85 


83.95 


13.30 


83.89 


13.66 


83.83 


14.03 


83.77 


14.39 


85 


86 


84.94 


13.45 


84.88 


13.82 


84.82 


14.19 


84.76 


14.. 56 


86 


87 


85.93 


13.61 


85.87 


13.98 


85.81 


14.36 


185.74 


14.73 


87 


88 


86.92 


13.77 


86.86 


14.15 


86.79 


14.. 52 


j 86.73 


14.90 


88 


89 


87.90 


13.92 


87.84 


14.31 


87.78 


14.69 


87.71 


15.07 


89 


90 
91 


88.89 


14.08 


88.83 


14.47 


88.77 


14.85 


88.70 


15.24 


90 
91 


89.88 


14.24 


89.82 


14.63 


89.75 


15.02 


89.69 


15.41 


92 


90.87 


14.39 


90.80 


14.79 


90.74 


15.18 


90.67 


15.58 


92 


93 


91.86 


14.55 


91.79 


14.95 


91.72 


15.35 


91.66 


15.75 


93 


94 


92.84 


14.70 


92.78 


15.11 


92.71 


15.51 


92.64 


15.92 


94 


95 


93.83 


14.86 


93.76 


15.27 


93.70 


15.68 


93.63 


16.09 


95 


96 


94.82 


15.02 


94.75 


15.43 


94.68 


15.84 


94.61 


16.26 


96 


97 


95.81 


15.17 


95.74 


15.59 


95.67 


16.01 


95.60 


16.43 


97 


98 


96.79 


15.33 


96.73 


15.75 


96.66 


16.17 


96.58 


16.60 


98 


99 


97.78 


15.49 


97.71 


15.91 


97.64 


16.34 


97.57 


16.77 


99 


100 

8 

B 
d 

Q 


98.77 


15.64 


98.70 


16.07 


98.63 


16.50 


98.56 


16.93 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


81 Deg. 


80J Deg. 


80^ Deg. 


80i Deg. 



22 



TRAVERSE TABLE. 



ft 


10 Deg. 


104 Deg. 


\0i 


Deg. 


m Deg. 




a 
J. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.98 


0.17 


0.98 


0.18 


0.98 


0.18 


0.98 


0.19 


2 


1.97 


0.35 


1.97 


0.30 


1.97 


0.36 


1.96 


0.37 


2 


3 


2.95 


0.52 


2.95 


0.53 


2.96 


0.55 


2.95 


56 


3 


4 


3.94 


0.69 


3.94 


0.71 


3.93 


0.73 


3.93 


0.75 


4 


5 


4.92 


0.87 


4.92 


0.89 


4.92 


0.91 


4.91 


0.93 


5 


6 


5.91 


1.04 


5.90 


1.07 


5.90 


1.09 


5.89 


],12 


6 


7 


6.89 


1.22 


6.89 


1.25 


6.88 


1.28 


6.88 


1.31 


7 


8 


7.88 


1.39 


7.87 


1.42 


7.87 


1.46 


7.86 


1.49 


8 


9 


8.86 


1.56 


8.86 


1.60 


8.85 


1.64 


8.84 


1.68 


9 


10 
11 


9.85 


1.74 


9.84 


1.78 


9.83 


1.82 


9.82 


1.87 


10 
11 


10.83 


1.91 


10.82 


1.96 


10.82 


2.00 


10.81 


2.05 


12 


11.82 


2.08 


11.81 


2.14 


11.80 


2.19 


11.79 


2.24 


12 


13 


12.80 


2.26 


12.79 


2.31 


12.78 


2.37 


12.77 


2.42 


13 


14 


13.79 


2.43 


13.78 


2.49 


13.77 


2.55 


13.75 


2.61 


14 


15 


14.77 


2.60 


14.76 


2.67 


14.75 


2.73 


14.74 


2.80 


15 


16 


15.76 


2.78 


15.74 


2.85 


15.73 


2.92 


15.72 


2.98 


16 


17 


16.74 


2.95 


16.73 


3.03 


16.72 


3.10 


16.70 


3.)7 


17 


18 


17.73 


3.13 


l'7.71 


3.20 


17.70 


3.28 


17.68 


3.36 


18 


19 


18.71 


3.30 


18.70 


3.38 


18.68 


3.46 


18.67 


3.54 


19 


20 
21 


19.70 


3.47 


19.68 


3.56 


19.67 


3.64 


19.65 


3.73 


20 
21 


20.68 


3.65 


20.66 


3.74 


20.65 


3.83 


20.63 


3.92 


22 


21.67 


3.82 


21.65 


3.91 


21.63 


4.01 


21.61 


4.10 


22 


23 


22.65 


3.99 


22.63 


4.09 


22.61 


4.19 


22.60 


4.29 


23 


24 


23.64 


4.17 


23.62 


4.27 


23.60 


4.37 


23.58 


4.48 


24 


25 


24.62 


4.34 


24.60 


4.45 


24.58 


4.56 


24.56 


4.66 


25 


26 


25.61 


4.51 


25.59 


4.63 


25.56 


4.74 


25.. 54 


4.85 


26 


27 


26.59 


4.69 


26.57 


4.80 


26.55 


4.92 


26.53 


5.04 


27 


28 


27.57 


4.86 


27.55 


4.98 


27.53 


5.10 


27.51 


5.22 


28 


29 


28.56 


5.04 


28.54 


5.16 


28.51 


5.28 


28.49 


5.41 


29 


30 
31 


29.54 


5.21 


29.52 


5.34 


29.50 


5.47 


29.47 


5.60 


30 
31 


30.53 


5.38 


30.51 


5.52) 


30.48 


5.65 


30.46 


5.78 


32 


31.51 


5.56 


31.49 


5.69 


31.46 


5.83 


31.44 


5.97 


32 


33 


32.50 


5.73 


32.47 


5.87 


32.45 


6.01 


32.42 


6.16 


33 


34 


33.48 


5.90 


33.46 


6.05 


33.43 


6.20 


33.40 


6.34 


34 


35 


34.47 


6.08 


34.44 


6.23 


34.41 


6.38 


34.39 


6.53 


35 


36 


35.45 


6.25 


35.43 


6.41 


35.40 


6.56 


35.37 


6.71 


36 


37 


36.44 


6.42 


36.41 


6.58 


36.38 


6.74 


36.35 


6.90 


37 


38 


37.42 


6.60 


37.39 


6.76 


37.36 


6.92 


37.33 


7.09 


38 


39 


38.41 


6.77 


38.38 


6.94 


38.35 


7.11 


38.32 


7.27 


39 


40 
41 


39.39 


6.95 


39.36 


7.12 


39.33 


7.29 


39.30 


7.46 


40 

41 


40.38 


7.12 


40.35 


7.30 


40.31 


7.47 


40.28 


7.65 


42 


41.36 


7.29 


41.33 


7.47 


41.30 


7.65 


41.26 


7.83 


42 


43 


42.35 


7.47 


42.31 


7.65 


42.28 


7.84 


42.25 


8.02 


43 


44 


43.33 


7.64 


43.30 


7.83 


43.26 


8.02 


43.23 


8.21 


44 


45 


44.32 


7.81 


44.28 


8.01 


44.25 


8.20 


44.21 


8.39 


45 


46 


45.30 


7.99 


45.27 


8.19 


45.23 


8.38 


45.19 


8.58 


46 


47 


46.29 


8.16 


46.25 


8.36 


46.21 


8.57 


46.18 


8.77 


47 


48 


47.27 


8.34 


47.23 


8.54 


47.20 


8.75 


47.16 


8.95 


48 


49 


48.26 


8.51 


48.22 


8.72 


48.18 


8.93 


48.14 


9.14 


49 


50 

8 
1 

.2 


49.24 


8.68 


49.20 


8.90 


49.16 


9.11 


49.12 


9.33 


50 

"co 

Q 


Dep. 


T.at. 


Dep. 

79! 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


80 Deg. 


791 


Deg. 


794 Deg. 



TKAVEKSE TARLE. 



23 



51 


10 Deg. 


lOi Deg. 


10^ Deg. 


101 Deg. 




O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


3 
O 

o 
~5l 


50.23 


8.86 


50.19 


9.08 


50.15 


9.29 


.50.10 


9.51 


52 


51.21 


9.03 


51.17 


9.25 


51.13 


9.48 


51.09 


9.70 


52 


53 


52.19 


9.20 


52.15 


9.43 


.52.11 


9.66 


52.07 


9.89 


53 


54 


53.18 


9.38 


53.14 


9.61 


53.10 


9.84 


53.05 


10.07 


54 


55 


54.16 


9.55 


54.12 


9.79 


54.08 


10.02 


54.03 


10.26 


55 


56 


55.15 


9.72 


55.11 


9.96 


55.06 


10.21 


55.02 


10.45 


56 


57 


56.13 


9.90 


56.09 


10.14 


56.05 


10.39 


56.00 


10.63 


57 


58 


57.12 


10.07 


57.07 


10.32 


57.03 


10.57 


56.98 


10.82 


58 


59 


58.10 


10.25 


58.06 


10.50 


58.01 


10.75 


57.96 


11.00 


59 


60 
61 


59.09 


10.42 


59.04 


10.68 


59.00 


10.93 


58.95 


11.19 


60 
61 


60.07 


10.59 


60.03 


10.85 


59.98 


11.12 


59.93 


11.38 


62 


61.06 


10.77 


61.01 


11.03 


60.96 


11.30 


60.91 


11.56 


62 


63 


62.04 


10.94 


61.99 


11.21 


61.95 


11.48 


61.89 


11.75 


63 


64 


63.03 


11.11 


62.98 


11.39 


62.93 


11.66 


62.88 


11.94 


64 


65 


64.01 


11.29 


63.96 


11.57 


63.91 


11.85 


63.86 


12.12 


65 


66 


65.00 


11.46 


64.95 


11.74 


64.89 


12.03 


64.84 


12.31 


66 


67 


65.98 


11.63 


65.93 


11.92 


65.88 


12.21 


65.82 


12.50 


67 


68 


66.97 


11.81 


66.91 


12.10 


66.86 


12.39 


66.81 


12.68 


68 


69 


67.95 


11.98 


67.90 


12.28 


67.84 


12.57 


67.79 


12.87 


69 


70 
71 


68.94 


12.16 


68.88 


12.46 


68.83 


12.76 


68.77 


13.06 


70 

71 


69.92 


12.33 


69.87 


12.63 


69.81 


12.94 


69.75 


13.24 


72 


70.91 


12.50 


70.85 


12.81 


70.79 


13.12 


70.74 


13.43 


72 


73 


71.89 


12.68 


71.83 


12.99 


71.78 


13.30 


71.72 


13.62 


73 


74 


72.88 


12.85 


72.82 


13.17 


72.76 


13.49 


72.70 


13.80 


74 


75 


73.86 


13.02 


73.80 


13.35 


73.74 


13.67 


73.68 


13.99 


75 


76 


74.85 


13.20 


74.79 


13.52 


74.73 


13.85 


74.67 


14.18 


76 


77 


75.83 


13.37 


75.77 


13.70 


75.71 


14.03 


75.65 


14.36 


77 


78 


76.82 


13.54 


76.76 


13.88 


76.69 


14.21 


76.63 


14.55 


78 


79 


77.80 


13.72 


77.74 


14.06 


77.68 


14.40 


77.61 


14.74 


^? 


80 
81 


78.78 


13.89 


78.72 


14.24 


78.66 


14.. 58 


78.60 


14.92 


80 
81 


79.77 


14.07 


79.71 


14.41 


79.64 


14.76 


79.58 


15.11 


82 


80.75 


14.24 


80.69 


14.59 


80.63 


14.94 


80.50 


15.29 


82 


83 


81.74 


14.41 


81.68 


14.77 


81.61 


15.13 


81.54 


15.48 


83 


84 


82.72 


14.59 


82.66 


14.95 


82.59 


15.31 


82.53 


15.67 


84 


85 


83.71 


14.76 


83.64 


15.13 


83.58 


15.49 


83.51 


15.85 


85 


86 


84.69 


14.93 


84.63 


15.30 


84.56 


15.67 


84.49 


16.04 


86 


87 


85.68 


15.11 


85.61 


15.48 


85.54 


15.85 


85.47 


16.23 


87 


88 


86.66 


15.28 


86.60 


15.66 


86.53 


16.04 


83.46 


16.41 


88 


89 


87.65 


15.45 


87.58 


15.84 


87.51 


16.22 


87.44 


16.60 


89 


90 


88.63 


15.63 


88.56 


16.01 


88.49 


16.40 


88.42 


16.79 


90 


91 


89.62 


15.80 


89.55 


16.19 


89.48 


16.58 


89.40 


16.97 


92 


90.60 


15.98 


90.53 


16.37 


90.46 


16.77 


90.39 


17-16 


92 


93 


91.59 


16.15 


91.52 


16.55 


91.44 


16.95 


91.37 


17.35 


93 


94 


92.57 


16.32 


92.50 


16.73 


92.43 


17.13 


92.35 


17.53 


94 


95 


93.56- 


16.50 


93.48 


16.90 


93.41 


17.31 


93.33 


17.72 


95 


96 


94.54 16.67 


94,47 


17.08 


94.39 


17.49 


94.32 


17.91 


96 


97 


95.53 16.84 


95.45 


17.26 


95.38 


17.68 


95.30 


18.09 


97 


98 


96.51 17.02 


96.44 


17.44 


96.36 


17.86 


96.28 


18.28 


98 


99 


97.50 17.19 


97.42 


17.62 


97.34 


18.04 


97.26 


18.47 


99 


100 

•S 


98.48 17.36 


98.40 


17.79 


98.33 


18.22 


98.25 


18.65 


100 

s 

p 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


80 Deg. 


791 Deg. 


791 Deg. 


79i Deg. 



24 



TRAVERSK TABLE. 



o 

5' 

a 
P 


11 Deg. 


lU Deg. 


Ui 


Deg. 


Ill Deg. 


K 

p 


Lat. 


Dep. 
0.19 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.98 


0.98 


0.20 


0.98 


0.20 


0.98 


0.20 


1 


2 


1.96 


0..38 


1.96 


0.39 


1.90 


0.40 


1.96 


0.41 


2 


3 


2.94 


0.57 


2.94 


0.59 


2.94 


0.60 


2.94 


0.61 


3 


4 


3.93 


0.76 


3.92 


0.78 


3.92 


0.80 


3.92 


9.82 


4 


5 4.91 


0.95 


4.90 


0.98 


4.90 


1.00 


4.90 


1.02 


5 


6 


5.89 


1.14 


5.88 


1.17 


5.88 


1.20 


5.87 


1.22 


6 


7 


6.87 


1.34 


6.87 


1.37 


6.86 


1.40 


6.85 


1.43 


7 


8 


7.85 


1.53 


7.85 


1.56 


7.84 


1.59 


7.83 


1.63 


8 


9 


8.83 


1.72 


8.83 


1.76 


8.82 


1.79 


8.81 


1.83 


9 


10 


9.82 


1.91 


9.81 


1.95 


9.80 


1.99 


9.79 


2.04 


10 


11 


10.80 


2.10 


10.79 


2.15 


10.78 


2.19 


10.77 


2.24 


11 


12 


11.78 


2.29 


11.77 


2.34 


11.7-6 


2.39 


11.75 


2.44 


12 


13 


12.76 


2.48 


12.75 


2.54 


12.74 


2.59 


12.73 


2.65 


13 


14 


13.74 


2.67 


13.73 


2.73 


13.72 


2.79 


13.71 


2.85 


14 


15 


14.72 


2.86 


14.71 


2.93 


14.70 


2.99 


14.69 


3.06 


15 


16 


15.71 


3.05 


15.69 


3.12 


15.68 


3.19 


15.66 


3.26 


16 


17 


16.69 


3.24 


16.67 


3.32 


16.66 


3.39 


16.64 


3.46 


17 


18 


17.67 


3.43 


17.65 


3.51 


17.64 


3.59 


17.62 


3.66 


18 


19 


18.65 


3.63 


18.63 


3.71 


18.62 


3.79 


18.60 


3.87 


19 


20 1 19.63 


3.82 


19.62 


3.90 


19.60 


3.99 


19.58 


4.07 


20 


21 


20.61 


4.01 


20.60 


4.10 


20.58 


4.19 


20.. 56 


4.28 


21 


22 


21.60 


4.20 


21.58 


4.29 


21.56 


4.39 


21.54 


4.48 


22 


23 


22.58 


4.39 


22.56 


4.49 


22.54 


4.59 


22.52 


4.68 


23 


24 


23.56 


4.58 


23.54 


4.68 


23.52 


4.78! 


23.50 


4.89 


24 


25 


24.54 


4.77 


24.52 


4.88 


24.50 


4.98 i 


24.48 


5.09 


25 


26 


25.52 


4.96 


25.50 


5.07 


25.48 


5.18 


25.46 


5.30 


26 


27 


20.50 


5.15 


26.48 


5.27 


26.46 


5.38 


26.43 


5.50 


27 


28 


27.49 


5.34 


27.46 


5.46 


27.44 


5.58 


27.41 


5.70 


28 


29 


28.47 


5.53 


28.44 


5.66 


28.42 


5.78 


28.39 


5.91 


29 


30 


29.45 


5.72 


29.42 


5.85 


29.40 


5.98 


29.37 


6.11 


30 


31 


30.43 


5.92 


30.40 


6.05 


30.38 


6.18 


30.35 


6.31 


31 


32 


31.41 


6.11 


31.39 


6.24 


31.36 


6.38 


31.33 


6.52 


32 


33 


32.39 


6-30 


32.37 


6.44 


32.34 


6.58 


32.31 


6.72 


33 


34 


33.38 


6.49 


33.35 


6.63 


33.32 


6.78 


33.29 


6.92 


34 


35 


34.36 


6.68 


34.33 


6.83 


34.30 


6.98 


34.27 


7.13 


35 


36 


35.34 


6.87 


35.31 


7.02 


35.28 


7.18 


35.25 


7.33 


36 


37 


36.32 


7.06 


36.29 


7.22 


36.26 


7.38 


36.22 


7.53 


37 


38 


37.30 


7.25 


37.27 


7.41 


37.24 


7.58 


37.20 


7.74 


38 


39 


38.28 


7.44 


38.25 


7.61 


38.22 


7.78 


.38.18 


7.94 


39 


40 


39.27 


7.63 


39.23 


7.80 


39.20 


7.97 


39.18 


8.15 


40 


41 


40.25 


7.82 


40.21 


8.00 


40.18 


8.17 


40.14 


8.35 


41 


42 


41 23 


8.01 


41.19 


8.19 


41.16 


8.37 


41.12 


8.55 


42 


43 


42.21 


8.20 


42.17 


8.39 


42.14 


8.57 


42.10 


8.76 


43 


44 


43.19 


8.40 


43.15 


8.58 


43.12 


8.77 


43.08 


8.96 


44 


45 


44.17 


8.59 


44.14 


8.78 


44.10 


8.97 


44.06 


9.16 


45 


46 


45.15 


8.78 


45.12 


8.97 


45.08 


9.17 


45.04 


9.37 


46 


47 


46.14 


8.97 


46.10 


9.17 


46.06 


9.37 


46.02 


9.57 


47 


48 


47.12 


9.16 


47.08 


9.36 


47.04 


9.57 


46.99 


9.78 


48 


49 


48.10 


9.35 


48.06 


9.56 


48.02 


9.77 


47.97 


9.98 


49 


Jl 


49.08 


9.54 


49.04 


Lat. 


49.00 


9.97 


48.95 


10.18 


50 

.2 


i 

a 

(0 

Q 


Dep. 

1 


Lat. 


Dtjp. 


Dep. 


Lat. 


Dep. 


Lat. 


1 
1 

79 


Deg. 


7P.| De^. 


"Sx 


Deg. 


78J Deg. 



TKAVtRSi! TA^LS* 



29 



n 
a 

"51 


11 Deg. 


lU Degr. 


IH Deg. 


111 Deg. 


i 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50.06 


9.73 


50.02 


9.95 


49.98 


10.17 


49.93 


10.39 


51 


52 


51.04 


9.92 


51.00 


10.14 


50.96 


10.37 


50.91 


10,59 


52 


53 


52.03 


10.11 


51.98 


10.34 


51.94 


10.57 


51.89 


10.79 


53 


51 


53.01 


10.30 


52.96 


10.53 


52.92 


10.77 


52.87 


11.00 


54 


65 


53.99 


10.49 


53.94 


10.73 


53.90 


10.97 


53.85 


11.20 


55 


56 


54.97 


10.69 


54.92 


10.93 


54.88 


11.16 


54.83 


11.40 


56 


67 


55.95 


10.88 


55.90 


11.12 


55.86 


11.36 


55.81 


11.61 


57 


68 


56.93 


11.07 


56.89 


11.32 


56.84 


11.56 


56.78 


11.81 


58 


59 


57.92 


11.26 


57.87 


11.51 


57.82 


11.76 


57.76 


12.01 


59 


60 
61 


58.90 


11.45 


58.85 


11.71 


58.80 


11.96 


58.74 


12.22 


60 


59.88 


11.64 


59.83 


11.90 


59.78 


12.16 


59.72 


12.42 


61 


63 


60.86 


11.83 


60.81 


12.10 


60.76 


12.36 


60.70 


12.63 


62 


63 


61.84 


12.02 


61.79 


12.29 


61.74 


12.56 


61.68 


12.83 


63 


64 


62.82 


12.21 


62.77 


12.49 


62.72 


12.76 


1 62.66 


13.03 


64 


65 


63.81 


12.40 


63.75 


12.68 


63.70 


12.96 


1 63.64 


13.24 


65 


66 


64.79 


12.59 


64.73 


12.88 


64.68 


13.16 


64.62 


13.4^1 


66 


67 


65.77 


12.78 


65.71 


13.07 


65.66 


13.36 


65.60 


13.64 


67 


68 


66.75 


12.98 


66.69 


13.27 


66.63 


13.56 


66.68 


13.85 


68 


69 


67.73 


13.17 


67.67 


13.46 


67.61 


13.76 


67.55 


14.05 


69 


70 
71 


68.71 


13.36 


68.66 


13.66 


63.59 


13.96 


68.53 


14.25 


70 


69.70 


13.55 


69.64 


13.85 


69.57 


14.16 


69.51 


14.46 


71 


72 


70.68 


13.74 


70.62 


14.05 


70.55 


14.35 


70.49 


14.66 


72 


73 


71.66 


13.93 


71.60 


14.24 


71.53 


'4.55 


71.47 


14.87 


73 


74 


72.64 


14.12 


72.58 


14.44 


72.51 


14.75 


72.45 


15.07 


74 


75 


73.62 


14.31 


73.56 


14.63 


73.49 


14.95 


73.43 


15.27 


75 


76 


74.60 


14.50 


74.54 


14.83 


74.47 


15.15 


74.41 


15.48 


76 


77 


75.59 


14.69 


75.52 


15.02 


75.45 


15.35 


75 39 


15.68 


77 


78 


76.57 


14.88 


76.50 


15.22 


76.43 


15.55 


76.37 


15.88 


78 


79 


77.55 


15.07 


77.48 


15.41 


77.41 


15.75 


77.34 


16.09 


79 


80 
81 


78.53 


15.26 


78.48 


15.61 


78.39 


15.95 


78.32 


16.29 


80 


79.51 


15.46 


79.44 


15.80 


79.37 


16.15 


79.30 


16.49 


81 


82 


80.49 


15.65 


80.42 


16.00 


80.35 


16.35 


80.28 


16.70 


82 


83 


81.48 


15.84 


81.41 


16.19 


81.33 


16.55 


81.36 


16.90 


83 


84 


82.46 


16.03 


82.39 


16.39 


82.31 


16.75 


82.24 


17.11 


84 


85 


83.44 


16.22 


83.37 


16.58 


83.29 


16.95 


83.22 


17.31 


85 


86 


84.42 


16.41 


84.35 


16.78 


84.27 


17.15 


84.20 


17.51 


86 


87 


85.40 


16.60 


85.33 


16.97 


85.25 


17.35 


85.18 


17.72 


87 


88 


86.38 


16.79 


86.31 


17.17 


86.23 


17.54 


86.16 


17.92 


88 


89 


87.36 


16.98 


87.29 


17.36 


87.21 1 


17.74 


87.14 


18.12 


89 


90 
91 


88.35 


17.17 


88.27 


17.56 


88.19 


17.94 


88.11 


18.33 


90 


89.33 


17.36 


89.25 


17.75 


89.17 


18.14 


89.09 


18.53 


91 


92 


90.31 


17.55 


90.23 


17.95 


90.15 


18.34 


90.07 


18.74 


92 


93 


91.29 


17.75 


91.21 


18.14 


91.13 


18.54 


91.05 


18.94 


93 


94 


92.27 


17.94 


92.19 


18.34 


92.11 


18.74 


92.03 


19.14 


94 


95 


93.25 


18.13 


93.17 


18.53 


93.09 


18.94 


93.01 


19.35 


95 


96 


94.24 


18.32 


94.16 


18.73 


94.07 


19.14 


93.99 


19.55 


96 


97 


95.22 


18.51 


95.14 


18.92 


95.05 


19.34 


94.97 


19.75 


97 


98 


96.20 


18.70 


96.12 


19.12 


96.03 


19.54 


95.95 


19.96 


98 


99 


97.18 


18.89 


97.10 


19.31 


97.01 


19.74 


96.93 


20.16 


99 


100 


98.16 


19.08 


98.08 


19.51 


97.99 


19.94 


97.90 


20.36 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


S 

s 

■(0 


79 Deg. 


781 Deg. 


78| Deg. 

1 


78i Deg. 



ts 



TRAVERSE TABLE. 



1 

p 


12 Deg 


12i Deg. 


12i Deg. 


1 
12| Deg. 




Lai. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. ! Dep. j 


3 


1 


0.98 


0.21 


0.98 


0.21 


0.98 


0.22 


0.98 


0.22 


1 


2 


1.96 


0.42 


1.95 


0.42 


1.95 


0.43 


1.95 


0.44 


2 


3 


2.93 


0.62 


2.93 


0.64 


2.93 


0.65 


2.93 


0.66 


3 


4 


3.91 


0.83 


3.91 


0.85 


3.91 


0.87 


3.90 


0.88 


4 


5 


4.89 


1.04 


4.89 


1.06 


4.88 


1.08 


4.88 


1.10 


5 


6 


5.87 


1.25 


5.86 


1.27 


5.86 


1.30 


5.85 


1.32 


6 


7 


6.85 


1.46 


6.84 


1.49 


6.83 


1.52 


6.83 


1.54 


7 


8 


7.83 


1.66 


7.82 


1.70 


7.81 


1.73 


7.80 


1.77 


8 


9 


8.80 


1.87 


8.80 


1.91 


8.79 


1.95 


8.78 


1.99 


9 


10 
11 


9.78 


2.08 


9.77 


2.12 
2.33 


9.76 


2.16 


9.75 


2.21 


10 


10.76 


2.29 


10.75 


10.74 


2.38 


10.73 


2.43 


11 


12 


11.74 


2.49 


11.73 


2.55 


11.72 


2.60 


11.70 


2.65 


13 


13 


12.72 


2.70 


12.70 


2.76 


12.69 


2.81 


12.68 


2.87 


13 


14 


13.69 


2.91 


13.68 


2.97 


13.67 


3.03 


13.65 


3.09 


14 


15 


14.67 


3.12 


14.66 


3.18 


14.64 


3.25 


14.63 


3.31 


15 


16 


15.65 


3.33 


15.64 


3.39 


15.62 


3.46 


15.61 


3.53 


16 


17 


16.63 


3.. 53 


16.61 


3.61 


16.60 


3.68 


16.58 


3.75 


17 


18 


17.61 


3.74 


17.59 


3.82 


17.. 57 


3.90 


17.56 


3.97 


18 


19 


18.. 58 


3.95 


18.57 


4.03 


18.55 


4.11 


18.53 


4.19 


19 


20 
21 


19.56 


4.16 


19.54 


4.24 


19.53 


4.33 


19.51 


4.41 


20 


20.54 


4.37 


20.. 52 


4.46 


20.50 


4.55 


20.48 


4.63 


21 


22 


21.52 


4.57 


21.50 


4.67 


21.48 


4.76 


21.46 


4.86 


%% 


23 


22.50 


4.78 


22.48 


4.88 


22.45 


4.98 


22.43 


5.08 


23 


24 


23.48 


4.99 


23.45 


5.09 


23.43 


5.19 


23.41 


5.30 


24 


25 


24.45 


5.20 


24.43 


5.30 


24.41 


5.41 


24.38 


5.52 


25 


26 


25.43 


5.41 


25.41 


5.52 


25.33 


5.63 


25.36 


5.74 


26 


27 


26.41 


5.61 


26.39 


5.73 


26.36 


5.84 


26.33 


5.96 


27 


28 


27.39 


5.82 


27.36 


5.94 


27.34 


6.06 


27.31 


6.18 


28 


29 


28.37 


6.03 


28.34 


6.15 


28.31 


6.28 


28.28 


6.40 


29 


30 


29.34 


6.24 


29.32 


6.. 37 


29.29 


6.49 


29.26 


6.62 


30 


31 


30.32 


6.45 


30.29 


6.58 


30.27 


6.71 


30.24 


6.84 


31 


32 


31. .30 


6.65 


31.27 


6.79 


31.24 


6.93 


31.21 


7.06 


32 


33 


32.28 


6.86 


32.25 


7.00 


32.22 


7.14 


32.19 


7.28 


33 


34 


33.26 


7.07 


33.23 


7.21 


33.19 


7.36 


33.16 


7.50 


34 


35 


34.24 


7.28 


34.20 


7.43 


34.17 


7.58 


34.14 


7.72 


35 


36 


35.21 


7.48 


35.18 


7.64 


35.15 


7.79 


35.11 


7.95 


36 


5 37 


36.19 


7.69 


36.16 


7.85 


36.12 


8.01 


36.09 


8.17 


37 


38 


37.17 


7.90 


37.13 


8.06 


37.10 


8.22 


37.06 


8.39 


38 


39 


38.15 


8.11 


38.11 


8.27 


38.08 


8.44 


38.04 


8.61 


39 


40 
41 


39.13 


8.32 


39.09 


8.49 
8.70 


39.05 


8.66 


39.01 


8.83 


40 


40.10 


8.52 


40.07 


40.03 


8.87 


39.99 


9.05 


41 


42 


41.08 


8.73 


41.04 


8.91 


41.00 


9.09 


40.96 


9.27 


42 


43 


42.06 


8.94 


4?. 02 


9.12 


41.98 


9.31 


41.94 


9.49 


43 


44 


43.04 


9.15 


43.00 


9.34 


42.96 


9., 52 


42.92 


9.71 


44 


45 144.02 


9.36 


43.98 


9.55 


43.93 


9.74 


43.89 


9.93 


45 


46 144.99 


9.56 


44.95 


9.76 


44.91 


9.96 ii44.87 


10.15 


46 


47 145.97 


9.77 


45.93 


9.97 


45.89 


10.17 ij 45.84 


10.37 


47 


48 i 46.95 


9.98 


46.91 


10.18 


46.86 


10.39 46.82 


10.. 59 


48 


49 47.93 


10.19 


47.88 


10.40 


47.84 


10.61 ; 47.79 


10.81 


49 


50 

i 

s 

.2 
Q 


48.91 


10.40 


48.86 


10.61 


48.81 
Dep. 


10.82 
Lat. 


i 48.77 


11.03 


50 

6 
o 

a 


Dep. 


Lat. 


Dep. 


L:it. 


1 Dep. 


Lat. 


78 Deg 


77f 


Deg. 


771 


Deg. ' 77 J Deg. 



TRAVERSE TABLE. 



27 



9. 

o 
~5l 


12 Deg. 


12i Deg. 


12A Deg. 


12| Deg. 


r 


Lat. 
49.89 


Dep. 
To ".GO" 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


~5i 


49.84 


16.82 


49.79 


11.04 


49.74 


11.26 


52 


50.86 


10.81 


50.82 


11.03 


50.77 


11.25 


50.72 


11.48 


62 


53 


51.84 


11.02 


51.79 


11.25 


51.74 


11.47 


51.69 


11.70 


53 


54 


52.82 


11.23 


52.77 


11.46 


52.72 


11.69 


52.67 


11.92 


54 


55 


53.80 


11.44 


.53.75 


^1.67 


53.70 


11.90 


53.64 


12.14 


55 


56 


54.78 


11.64 


54.72 


I? 88 


54.67 


12.12 


54.62 


12.36 


50 


57 


55.75 


11.85 


55.70 


12.09 


55.65 


12.34 


55.59 


12.. 58 


57 


58 


56.73 


12.06 


56.68 


12.31 


56.63 


12.55 


56.57 


12.80 


58 


59 


57.71 


12.27 


57.66 


12.52 


57.60 


12.77 


57.55 


13.02 ; 59 


60 
61 


58.69 


12.47 


58.63 


12.73 


58.58 


12.99 


.58.52 


13.24 1 60 


59.67 


12.68 


59.61 


12.94 


159.55 


13.20 


59.50 


13.46 1 61 


62 


60.65 


12.89 


60.59 


13.16 


60.53 


13.42 


60.47 


13.68 


02 


63 


61.62 


13.10 


61.57 


13.37 


61.51 


13.64 


61.45 


13.90 


63 


64 


62.60 


13.31 


62.54 


13.58 


62.48 


13.85 


62.42 


14.12 


64 


65 


63.58 


13.51 


63.. 52 


13.79 


63.46 


14.07 


63.40 


14.35 


65 


66 


£4.56 


13.72 


64.50 


14.00 


64.44 


14.29 


64.37 


14.57 


66 


67 


65.54 


13.93 


65.47 


14.22 


65.41 


14.50 


65.35 


14.79 


67 


68 


66.51 


14.14 


66.45 


14.43 


66.39 


14.72 


66.32 


15.01 


68 


69 


67.49 


14.35 


67.43 


14.64 


67.36 


14.93 


67.30 


15.23 


69 


70 

71 


68.47 


14.55 


68.41 


14.85 


68.34 


15.15 


68.27 


15.45 


70 

71 


69.45 


14.76 


69.38 


15.06 


69.32 


15.. 37 


69.25 


15.67 


72 


70.43 


14.97 


70.36 


15.28 


70.29 


15.58 


70.22 


15.89 


72 


73 


71.40 


15.18 


71.34 


15.49 


71.27 


15.80 


71.20 


16.11 


73 


74 


72.38 


15.39 


72.32 


15.70 


72.25 


16.02 


72.18 


16.33 


74 


75 


73.36 


15.59 


73.29 


15.91 


73.22 


16.23 


73.15 


16.55 


75 


76 


74.34 


15.80 


74.27 


16.13 


74.20 


16.45 


74.13 


16.77 


76 


77 


75.32 


16.01 


75.25 


16.34 


75.17 


16.67 


75.10 


16.99 


77 


78 


76.30 


16.22 


76.22 


16.. 55 


76.15 


16.88 


76.08 


17.21 


78 


79 


77.27 


16.43 


77.20 


16.76 


77.13 


17.10 


77.05 


17.44 


79 


80 
81 


78.25 


16.63 


78.18 


16.97 
17.19 


78.10 


17.32 


78.03 


17.66 


80 


79.23 


16.84 


79.16 


79.08 


17.. 53 


79.00 


17.88 


"81 


82 


80.21 


17.05 


80.13 


17.40 


80.06 


17.75 


79.98 


18.10 


82 


S3 


81.19 


17.26 


81.11 


17.61 


81.03 


17.96 


80.95 


18.32 


83 


84 


82.16 


17.46 


82.09 


17.82 


82.01 


18.18 


81.93 


18.54 


84 


85 


83.14 


17.67 


83.06 


18.04 


82.99 


18.40 


82.90 


18.76 


85 


86 


84.12 


17.88 


84.04 


18.25 


83.96 


18.61 


83.88 


18.98 


86 


87 


85.10 


18.09 


85.02 


18.46 


84.94 


18.83 


84.85 


19.20 


87 


88 


86.08 


18.30 


86.00 


18.67 


85.91 


19.05 


85.83 


19.42 


88 


89 


87.06 


18.50 


86.97 


18.88 


86.89 


19.26 


86.81 


19.64 


89 


90 
91 


88.03 


18.71 


87.95 
88.93 


19.10 


87.87 


19.48 


87.78 


19.86 


90 


89.01 


18.92 


19.31 


88.84 


19.70 


88.76 


20.08 


91 


92 


89.99 


19.13 


89.91 


19.52 


89.82 


19.91 


89.73 


20.30 


92 


93 


90.97 


19.34 


90.88 


19.73 


90.80 


20.13 


90.71 


20.52 


93 


94 


91.95 


19.54 


91.86 


19.94 


91.77 


20.35 


91.68 


20 . 75 


94 


95 


92.92 


19.75 


92.84 


20.16 


92 . 75 


20.56 


92.66 


20.97 


95 


96 


93.90 


19.96 


93.81 


20.37 


93.72 


20.78 


93.63 


21.19 


96 


97 


94.88 


20.17 


94.79 


,20.58 


94.70 


20.99 


94.61 


21.41 


97 


98 


95.86 


20.38 


95.77 


20.79 


95.68 


21.21 


95.58 


21.63 


98 


99 


96.84 


20.58 


96.75 


21.01 


96.65 


21.43 


96.56 


21.85 


99 


100 

o 
c 
S 


97.81_ 
Dep. 


20.79 
Lat. 


97.72 


21.22 


97.63 


21.64 


97.53 


22.07 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

1 

.2 
Q 


78 Deg. 


77| Deg 


771 Deg. 


m Deg. 



28 



TRAVl KSE TABLE. 



5 

CO 

P 

3 
O 
CD 

T 


13 Deg. 


13:t Deg. 


13A] 


Deg. 


13! Deg. 


o 
o 


Lat. 1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.97 


0.23 


0.97 


0.23 


0,*97 


0.23 


0.97 


0.24 


1 


2 


1.95 1 


0.4.'; 


1 . 95 


0.46 


1.95 


0.47 


1.94 


0.48 


2 


3 


2.93 


0.67 


2.92 


0.69 


2.92 


0.70 


2.91 


0.71 


3 


4 


3.90 


0.90 


3.89 


0.92 


3.89 


0.93 


3.89 


0.95 


4 


f) 


4.87 


1.12 


4.87 


1.15 


4.86 


1.17 


4.86 


1.19 


5 


6 


5.85 


1.35 


5.84 


1.38 


5.83 


1.40 


5.83 


1.43 


6 


7 


6.82 


1.57 


0.81 


1.60 


6.81 


1.63 


6.80 


1.66 


7 


8 


7.80 


1.80 


7.79 


1.83 


7.78 


1.87 


7.77 


1.90 


8 


9 


8.77 


2.02 


8.76 


2.06 


8.75 


2.10 


8.74 


2.14 


9 


10 
11 


9.74 


2.25 


9.73 


2.29 


9.72 


2.33 


9.71 


2.38 


10 
11 


10.72 


2.47 


10.71 


2.52 


10.70 


2.57 


10.68 


2.61 


1? 


11.69 


2.70 


11.68 


2.75 


11.67 


2.80 


11.66 


2.85 


12 


13 


12.67 


2.92 


12.65 


2.98 


12.64 


3.03 


12.63 


3.09 


13 


14 


13.64 


3.15 


13.63 


3.21 


13.61 


3.27 


13.60 


3.33 


14 


15 


14.62 


3.37 


14.60 


3.44 


14.59 


3.50 


14.57 


3.. 57 


15 


16 


15.59 


3.60 


15.. 57 


3.67 


15.56 


3.74 


15.54 


3.80 


16 


17 


16.57 


3.82 


16.55 


3.90 


16.53 


3.97 


16.51 


4.04 


17 


18 


17.54 


4.05 


17. .52 


4.13 


17.50 


4.20 


17.48 


4.28 


18 


19 


18.51 


4.27 


18.49 


4.35 


18.48 


4.44 


18.46 


4.52 


19 


20 


19.49 


4.50 


19.47 


4.58 


19.45 
20.42 


4.67 
4.90 


19.43 


4.75 


20 
21 


21 


20.46 


4.72 


27). 44 


4.81 


20.40 


4.99 


29, 


21.44 


4.95 


21.41 


5.04 


21.39 


5.14 


21.37 


5.23 


22 


23 


22.41 


5.17 


22.39 


5.27 


22.36 


5.37 


22.34 


5.47 


23 


24 


23.38 


5.40 


23.36 


5.50 


23.34 


5.60 


23.31 


5.70 


24 


25 


24.36 


5.62 


24.33 


5.73 


24.31 


5.84 


24.28 


5.94 


25 


26 


25.33 


5.85 


25.31 


5.96 


25.28 


6.07 


25.25 


6.18 


26 


27 


26.31 


6.07 


26.28 


6.19 


26.25 


6.30 


26.23 


6.42 


27 


28 


27.28 


6.30 


27.25 


6.42 


27.23 


6.. 54 


27.20 


6.66 


28 


29 


28.26 


6.52 


28.23 


6.65 


28.20 


6.77 


28.17 


6.89 


29 


30 
31 


29.23 
30.21 


6.75 


29.20 


6.88 


29.17 


7.00 


29.14 


7.13 


30 


6.97 


30.17 


7.11 


30.14 


7.24 


30.11 


7.37 


31 


32 


31.18 


7.20 


31.15 


7.33 


31.12 


7.47 


31.08 


7.61 


32 


33 


32.15 


7.42 


32.12 


7.56 


32.09 


7.70 


32.05 


7.84 


33 


34 


.33.13 


7.65 


33.09 


7.79 


33.06 


7.94 


33.03 


8.08 


,31 


35 


34.10 


7.87 


34.07 


8.02 


34.03 


8.17 


34.00 


8.32 


35 


36 


35.08 


8.10 


35.04 


8.25 


35.01 


8.40 


34.97 


8.56 


36 


37 


36.05 


8.32 


36.02 


8.48 


35.98 


8.64 


35.94 


8.79 


37 


38 


37.03 


8.55 


36.99 


8.71 


36.95 


8.87 


36.91 


9.03 


38 


39 


38.00 


8.77 


37.96 


8.94 


37.92 


9.10 


37.88 


9.27 


39 


40 
41 


38.97 


9.00 


38.94 


9.17 


38.89 


9.34 


38.85 


9.51 


40 

41 


39.95 


9.22 


39.91 


9.40 


39.87 


1 9.57 


39.83 


9.75 


42 


40.92 


9.45 


40.88 


9.63 


40.84 


1 9.80 


40.80 


9.98 


42 


43 


41.90 


9 67 


41.86 


9.86 


41.81 


10.04 


41.77 


10.22 


43 


44 


42.87 


9.90 


42.83 


19.08 


42.78 


10.27 


42.74 1 10.46 


44 


45 


43.85 


10.12 


43.80 


10.31 


43.76 


10.51 


43.71 


10.70 


45 


46 


44.82 


10.35 


44.78 


10.54 


44.73 


10.74 


44.68 


10.93 


46 


47 


45.80 


10.57 


45.75 


10.77 


45.70 


1 10.97 


45.65 


11.17 


47 


48 


46.77 


10.80 


46.72 


11.00 


46.67 


11.21 


46.62 


11.41 


48 


49 


47.74 


11.02 


47.70 


11.23 


4-7.65 


1 11.44 


47.60 


11.65 


49 


50 


48.72 


11.25 


48.67 


11.46 


48.62 


11.67 


48 . 57 


11.88 


50 


§ 

a 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


8 

c 

1 

s 


77 Deg. 


76J Deg. 


76J 


Deg. 


76i Deg. 



TRAVERSE TABLE. 



29 



E 


13 Deg. 


13i Deg. 


13i Deg. 


131 Deg. 


s 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


49.69 


11.47 


49.64 


Tr.69' 


49.59 


11.91 


49.54 


12.12 


52 


50.67 


11.70 


50.62 


11.92 


50.66 


12.14 


50.51 


12.36 


53 


63 


51.64 


11.92 


51.59 


12.16 


51.54 


12.37 


61.48 


12.60 


53 


54 


52.62 


12.15 


52.56 


12.38 


52.51 


12.61 


52.46 


12.84 


54 


55 


53.59 


12.37 


53.54 


12.61 


63.48 


12.84 


53.42 


13.07 


55 


56 


54.56 


12.60 


54.51 


12.84 


64.45 


13.07 


64.40 


13.31 


56 


57 


55.54 


12.82 


65.48 


13.06 


56.43 


13.31 


56.37 


13.56 


57 


58 


56.51 


13.05 


56.46 


13.29 


.56.40 


13.54 


56 34 


13.79 


58 


59 


57.49 


13.27 


57.43 


13.52 


57.37 


13.77 


67.31 


14.02 


59 


60 
'61 


58.46 


13.. 50 


68.40 


13.75 


68.34 
59.31 


14.01 
14.24 


68.28 
59.25 


14.26 


60 


59.44 


13.72 


59.38 


13.98 


14.50 


61 


62 


60.41 


13.95 


60.35 


14.21 


60.29 


14.47 


60.22 


14.74 


62 


63 


61.39 


14.17 


61.32 


14.44 


61.26 


14.71 


61.19 


14.97 


63 


64 


62.36 


14.40 


62.30 


14.67 


62.23 


14.94 


62.17 


15.21 


64 


65 


63.33 


14.62 


63.27 


14.90 


63.20 


15.17i 


63.14 


15.46 


65 


66 


64.31 


14.85 


64.24 


15.13 


64.18 


16.41 ! 


64.11 


15.69 


66 


67 


65. 2S 


15.07 


66.22 


15.36 


65.15 


15.64 1 


65.08 


15.93 


67 


68 


66.26 


15.30 


66.19 


15.69 


66.12 


16.87 


66.05 


16.16 


68 


69 


67.23 


15.52 


67.16 


15.81 


67.09 


16.11 


67.02 


16.40 


69 


70 
71 


68.21 


15.75 


68.14 


16.04 


68.07 


16.34 


67.99 


16.64 


70 


69.18 


16.97 


69.11 


16.27 


69.04 


16.67 1 


68.97 


16.88 


71 


72 


70.15 


16.20 


70.08 


16.. 50 


70.01 


16.81 1 


69.94 


17.11 


72 


73 


71.13 


16.42 


71.06 


16.73 


70.98 


17.04 


70.91 


17.35 


73 


74 


72.10 


16.65 


72.03 


16.96 


71.96 


17.28 1 


71.88 


17.59 


74 


76 


73.08 


16.87 


73.00 


17.19 


72.93 


17.50! 


72.85 


17.83 


75 


76 


74.05 


17.10 


73.98 


17.42 


73.90 


17.74 i 


73.82 


18.06 


76 


77 


75.03 


17.32 


74.95 


17.65 


74.87 


17.98 \ 


74.79 


18.30 


77 


78 


76.00 


17.56 


76.92 


17.88 


75.84 


18.21 


75.76 


18.64 


78 


79 


70.98 


17.77 


76.90 


18.11 


76.82 


18.44 


76.74 


18.78 


79 


80 


77.95 


18.00 


77.87 


18.34 1 


77.79 


18.68 


77.71 


19.01 


80 


81 


78.92 


18.22 


78.84 


18. .57 1 


78.76 


18.91 


78.68 


19.26 


81 


82 


79.90 


18.45 


79.82 


18.79 


79.73 


19.14 


79.65 


19.49 


82 


83 


80.87 


18.67 


80.79 


19.02 1 


80.71 


19.38 


80.62 


19.73 83 1 


84 


81.85 


18.90 


81.76 


19.25 


81.68 


19.61 


81.69 


19.97 


84 


85 


82 . 82 


19.12 


82.74 


19.48 


82.65 


19.84 


82.. 56 


20 . 20 


86 


86 


83.80 


19.35 


83.71 


19.71 


83.62 


20.08 


83.54 


20.44 


86 


87 


84.77 


19.57 


84.68 


19.94' 


84.60 


20.31 


84.51 


20.68 


87 


88 


85.74 


19.80 


85.66 120.17 


85.57 


20.54 185.48 


20.92 


88 


89 


86.72 


20.02 


86.63 


20.40 


86.54 


20.78 I! 86.45 


21.15 


89 


90 
91 


87.69 
88.67 


20.25 


87.60 

88.58 


20.63 
20.86 


87.51 


21.01 i: 87.42 


21. .39 


90 


20.47 


88.49 21.24:] 88.39 


21.63 


91 


92 


89.64 


20.70 


89.66 


21.09 


89.46 21.48 89.36 


21.87 


92 


93 


90.62 


20 . 92 


90.62 21.32 90.43 1 21.71 i! 90.33 


22.10 


93 


94 


91.. 59 


21.15 


91.60 


21. .54 91.40 1 21.94 1) 91.31 


22.34 


94 


95 


92.57 


21.37 11 92.47 


21.77 92.38 122.18 92.28 


22.58 


95 


96 


93.54 


21.60 ! 93.44 


22.00 93.35! 22.41 '! 93.25 


22.82 


96 


97 


94.51 


21.82 


94.42 


22.23 94.32 


22.64 ij 94.22 


23 . 06 


97 


98 


95.49 


22.05 


95.39 


22.46 95.29 


22.88 li 95.19 


23 . 29 


98 


99 


96.46 


22.27 


96.36 


22.69 96.26 


23.11 !! 96.16 


23.53 


99 


100 

6 

V 

n 
% 

b 


97.44 
Dcp. 


22.50 
Lat. 


97.34 


22.92 


97.24 1 23.34 1 
Dep. 1 Lat. 


97.13 


23 . 77 


ICO 


Dcp. 


Lat. 


Dop. 


Lat. 


CJ 


77 Deer. 


76f Dng. l^ Deg. i! 76i Deg. 


5 



19 



'AU 



TKAVfiRSE TABLE. 



oi 


— 

14 Deg. 


14i Deg. 


14^ Deg. 


1 
141 Dog. 1 


5 


p 

1 
















n 
9 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.97 


24 


0.97 


0.25 


0.97 


0.25 


0.97 


0.25 


2 


1.94 


0.48 


1.94 


0.49 


1.94 


0.50 


1.93 


0.51 


2 


3 


2.91 


0.73 


2.91 


0.74 


2.90 


0.75 


2.90 


0.76 


3 


4 


3.88 


0.97 


3.88 


0.98 


3.87 


1.00 


3.87 


1.02 


4 


5 


4.85 


1.21 


4.85 


1.23 


4.84 


1.25 


4.84 


1.27 


5 


6 


5.82 


1.45 


5-. 82 


1.48 


5.81 


1.50 


5.80 


1.53 


6 


7 


6.79 


1.69 


6.78 


1 72 


6.78 


1.75 


6.77 


1.78 


7 


8 


7.76 


1.94 


7.75 


1.97 


7.75 


2.00 


7.74 


2.04 


8 


9 


8.73 


2.18 


8.72 


2.22 


8.71 


2.25 


8.70 


2.29 


9 


10 


9.70 


2.42 


9.69 


2.46 


9.68 


2., 50 


9.67 


2.55 


JO 


11 


10.67 


2.66 


10.66 


2.71 


10.65 


2.75 


10.64 


2.80 


11 


12 


11.64 


2.90 


11.63 


2.95 


11.62 


3.00 


11.60 


3.06 


12 


13 


12.61 


3.15 


12.60 


3.20 


12.59 


3.25 


12.57 


3.3] 


13 


14 


13.58 


3.39 


13.57 


3.45 


13.55 


3.51 


13.54 


3.56 


14 


15 


14.55 


3.63 


14.54 


3.69 


14.52 


3.76 


14.51 


3.82 


15 


16 


15.52 


3.87 


15.51 


3.94' 


15.49 


4.01 


15.47 


4.07 


16 


17 


16.50 


4.11 


16.48 


4.18 


16.46 


4.26 


16.44 


4.33 


17 


18 


17.47 


4.35 


17.45 


4.43 


17.43 


4.51 


17.41 


4.58 


18 


19 


18.44 


4.60 


18.42 


4.68 


18.39 


4.76 


18.37 


4.84 


19 


20 

21 


19.41 


4.84 


19.38 


4.92 


19.36 


5.01 


19.34 


5.09 


20 
21 


20.38 


5.08 


20.35 


5.17 


20.33 


5.26 


20.31 


5.35 


22 


21.35 


5.32 


21.32 


5.42 


21.30 


5.51 


21.28 


5.60 


22 


23 


22.32 


5.56 


22.29 


5.66 


22.27 


5.76 


22.24 


5.86 


23 


24 


23.99 


5.81 


23.26 


5.91 


23.24 


6.01 


23.21 


6.11 


24 


25 


24.26 


6.05 


24.23 


6.15 


24.20 


6.26 


24.18 


6.37 


25 


26 


25.23 


6.29 


25.20 


6.40 


25.17 


6.51 


25.14 


6.62 


26 


27 


26.20 


6.53 


26.17 


6.65 


26.14 


6.76 


26.11 


6.87 


27 


28 


27.17 


6.77 


27.14 


6.89 


27.11 


7.01 


27.08 


7.13 


28 


29 


28.14 


7.02 


28.11 


7.14 


28.08 


7.26 


28.04! 7.38 


29 


30 
31 


29.11 


7.26 


29.08 


7.38 


29.04 


7.51 


29.01 


7.64 


30 
31 


30.08 


7.50 


30.05 


7.63 


.30.01 


7.76 


29 . 98 


7.89 


32 


31.05 


7.74 


31.02 


7.88 


30.98 


8.01 


30.95 


8.15 


32 


33 


32.03 


7.98 


31.98 


8.12 


31.95 


8.26 


31.91 


8.40 


33 


34 


32.99 


8.23 


32.95 


8.37 


32.92 


8.51 


32.88 


8.66 


31 


35 


.33.96 


8.47 


33.92 


8.62 


33.89 


8.76 


33.85 


8.91 


35 


36 


34.93 


8.71 


34.89 


8.86 


34.85 


9.01 


34.81 


9.17 


38 


37 


35.90 


8.95 


35.86 


9.11 


35.82 


9.26 


35.78 


9.42 


37 


38 


36.87 


9.19 


.36.83 


9.35 


36.79 


9.51 


36.75 


9.67 


38 


39 


37.84 


9.44 


37.80 


9.60 


37.76 


9.76 


37.71 


9.93 


39 


40 
ll 


38.81 


9.68 


38.77 


9.85 


38.73 


10.02 


38.68 


10.18 


40 
41 


39,78 


9.93 


39.74 


10.09 


39.69 


10.27 


39.65 


10.44 


42 


40.75 


10.16 


40.7] 


10.34 


40.66 


10.52 


40.62 


10.69 


42 


43 


41.72 


10.40 


41.68 


10.. 58 


41.63 


10.77 


41.58 


10.95 


43 


44 


42 . 69 


10.64 


42.65 


10.83 


42.60 


11.02 


42.55 


11 .20 


44 


45 


43.66 


10.89 


43.62 


11.08 


43.57 


11.27 


43.52 


11.46 


45 


46 


44.63 


11.13 


44.. 58 


11.32 


44.53 


11.52 


44.48 


11.71 


46 


47 


45.60 


11.37 


45.55 


11.57 


45.50 


11.77 


45.45 


11.97 


47 


48 


46.57 


11.61 


46.52 


11.82 


46.47 


12.02 


46.42 


12.22 


48 


49 


47.54 


11.85 


47.49 


12.06 


47.44 


12.27 


47.39 


12.48 


49 


50 


48.51 


12.10 


48.46 


12.31 


48.41 


12.52 


48.35 


12.73 


50 

i 

c 

ri 


i 

c 


Dep. 


Lat. 


..^':;_ 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


5 
5 


76 


Dog 


75] 


D.'-. 


16\ Dejr. 


i 

75 V D-Lr. 








i 




1 


U 





TRAVERSE TABLE. 



31 



o 


14 Deg. 


14i Deg. 


14| Deg. 


j 14| Deg. ! D 1 


? 










? 












61 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


? 


49.49 


12.34 


49.43 


12.55 


49.38 


12.77 


49.32 


12.98 i 51 1 


52 


50.46 


12.58 


50.40 


12.80 


50.34 


13.02 


60.29 


13.24 


52 


53 


51.43 


12.82 


51.37 


13.05 


51.31 


13.27 


61.25 


13.49 


53 


54 


52.40 


13.06 


52.34 


13.29 


62.28 


13.62 


52.22 


13.76 


54 


55 


53.37 


13.31 


53.31 


13.54 


63.25 


13.77 


63.19 


14.00 


55 


56 


54.34 


13.55 


54.28 


13.78 


54.22 


14.02 


54.16 


14.26 


66 


57 


55.31 


13.79 


55.25 


14.03 


56.18 


14.27 


55.12 1 14.51 


57 


58 


56.28 


14.03 


.56.22 


14.28 


66.16 


14.52 


56.09 


14.77 


58 


59 


.57.25 


14.27 


57.18 


14.52 


67.12 


14.77 


57.06 


16.02 


59 


60 
61 


58.22 


14.52 


68.15 


14.77 


58.09 


15.02 


68.02 


16.28 


60 


59.19 


14.76 


59.12 


15.02 


.59.06 


15.27 


58.99 


16.. 63 


61 


62 


60.16 


15.00 


60.09 


15.26 


60.03 


16.62 


59.96 


16.79 


62 


63 


61.13 


15.24 


61.06 


16.51 


60.99 


16.77 


60.92 


16.04 


63 


64 


62.10 


15.48 


62.03 


15.75 


61.96 


16.02 


61.89 


16.29 


64 


65 


63.07 


15.72 


63.00 


16.00 


62.93 


16.27 


62.86 


16.65 


65 


66 


64.04 


15.97 


63.97 


16.26 


63.90 


16.63 


163.83 


16.80 


66 


67 


65.01 


16.21 


64.94 


16.49 


64.87 


16.78 


64.79 


17.06 


67 


68 


65.98 


16.45 


65.91 


16.74 


65.83 


17.03 


66.76 


17.31 


68 


69 


66.95 


16.69 


66.88 


16.98 


66.80 


17.28 


66.73 


17.67 


69 


70 

71 


67.92 


16.93 


67.85 


17.23 


67.77 


17.63 

17.78 


67.69 


17.82 70 1 


68.89 


17.18 


68.82 


17.48 


68.74 


68.66 


18.08 


71 


72 


69.86 


17.42 


69.78 


17.72 


69.71 


18.03 


69.63 


18.. 33 


72 


73 


70.83 


17.66 


70.75 


17.97 


70.67 


18.28 


70.. 69 


18.59 


73 


74 


71.80 


17.90 


71.72 


18.22 


71.64 


18.53 


71.56 


18.84 


74 


75 


72 77 


18.14 


72.69 


18.46 


72.61 


18.78 


72.53 


19.10 


75 


76 


73.74 


18.39 


73.66 


18.71 


73.58 


19.03 


73.60 


19.35 


76 


77 


74.71 


18.63 


74.63 


18.96 


74.. 65 


19.28 


74.46 


19.60 


77 


78 


75.68 


18.87 


75.60 


19.20 


75.62 


19.63 


75.43 


19.86 78| 


79 


76.65 


19.11 


76.57 


19.46 


76.48 


19.78 


76.40 


20.11 


79 


80 
81 


77.62 
78.59 


19.35 


77.54 


19.69 


77.45 


20.03 


77.36 


20.37 


80 


19.60 


78.51 


19.94 


78.42 


20.28 


78.33 


20.62 


81 


82 


79.56 


19.84 


79.48 


20.18 


79.39 


20.63 


79.30 


20.88 


82 


83 


80.53 


20.08 


80.45 


20.43 


80.36 


20.78 


80.26 


21.13 


83 


84 


81.50 


20.32 


81.42 


20.68 


81.32 


21.03 


81.23 


21.39 


84 


85 


82.48 


20.56 


82.38 


20.92 


82.29 


21,28 


82.20 


21.64 


85 


86 


83.45 


20.81 


83.35 


21.17 


83.26 


21.63 


83.17 


21.90 


86 


87 


84.42 


21.05 


84.32 


21.42 


84.23 


21.78 


84.13 


22.16 


87 


88 


85.39 


21.29 


85.29 


21.66 


86.20 


22.03 


85.10 


22.41 


88 


89 


86.36 


21.53 


86.26 


21.91 


86.17 


22.28 


86.07 


22.66 1 89 


90 
91 


87.33 


21.77 


87.23 
88.20 


22.16 


87.13 


22.. 53 


87.03 


22.91 : 90 


88.30 


22.01 


22.40 


88.10 


22 . 78 


88.00 


23.17 1 91 


92 


89.27 


22.26 


89.17 


22.66 


89.07 


23.04 


88.97 


23.42 , 92 


93 


90.24 


22.50 


90.14 


22.89 


90.04 


23.29 


89.94 


23.68 93 


94 


91.21 


22.74 


91.11 


23.14 


91.01 


23.. 54 


90.90 


23.93 1 94 


95 


92.18 


22.98 


92.08 


23.38 


91.97 


23.79 


91.87 


24.19 i 95 


96 


93.15 


23.22 


93.05 


23.63 


92.94 


24.04 


92.84 


24.44; 96 


97! 


94.12 


23.47 


94.02 


23.88 


93.91 


24.29 


93.80 


24.70 97 


98! 


95.09 


23.71 


94.98 


24.12| 


94.88 


24.54 


94.77 


24.95 1 98 


99 ! 


96.06 


23 95 


96.95 


24.37; 


95.85 


24.79 


95.74 


25.21 , 99 


100 1 


97.03 


24.19 


96.92 
Dep. 


24.62 


96.81 


26.04 


96.70 


26.46 100 


Dep. j Lat. 


Lat. i 


Dep. 


Lat. 


Dep. 


Lat. 


»■ 
c 


5j 


76 Deg. 


75^ Deg i 

i 


751 Dej:. 


75^ Deg 


%, 

Q 



32 



TRAVERSE TABLC. 



! 

1 


15 Deg. 


15i Deg. 


15^ 


Deg. 


151 Deg. 




La.. 

0.97 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.26 1 


0.96 


0.26 


0.96 


0.27 


0.96 


0.27 


1 


2 


1.93 


0.52 1 


1.93 


0..53 


1.93 


0.53 


' 1.92 


0.54 


2 


3 


2.90 


0.78 


2.89 


0.79 


2.89 


0.80 


2.89 


0.81 


3 


4 


3.86 


1.04 


3.86 


1.05 


3.85 


1.07 


3.85 


1.09 


4 


5 


4.83 


1.29 1 


4.82 


1.32 


4.82 


1.34 


4.81 


1.36 


5 


6 


5.80 


1.55 I 


5.79 


1.58 


5.78 


1.60 


5.77 


1,63 


6 


7 


0.76 


1.81 


6.75 


1.84 


6.75 


1.87 


6.74 


1.90 


7 


8 


7.73 


2.07 1 


7.72 


2.10 


7.71 


2.14 


7.70 


2.17 


8 


9 


8.69 


2.33! 


8.68 


2.. 37 


8.67 


2.41 


8.66 


2.44 


9 


10 

11 


9.66 


2.59 


9.65 


2.63 


9.64 


2.67 


9.62 


2.71 


10 


10.63 


2.85 j 
3.11 1 


10.61 


2.89 


10.60 


2.94 


10.59 


2.99 


11 


12 


11.59 


11.58 


3.16 


11.56 


3.21 


11.55 


3.26 


12 


13 


12.56 


3.36 j 


12.54 


3.42 


12.53 


3.47 


12.51 


3.53 


13 


14 


13.52 


3.62 


13.51 


3.68 


13.49 


3.74 


13.47 


3.80 


14 


15 


14.49 


3.88 


14.47 


3.95 


14.45 


4.01 


14.44 


4.07 


15 


16 


15.45 


4.14 


15.44 


4.21 


15.42 


4.28 


15.40 


4.34 


16 


17 


16.42 


4.40 1 


16.40 


4.47 


16.38 


4.54 


16.36 


4.61 


17 


18 


17.39 


4.66 


17.37 


4.73 


17.35 


4.81 


17.32 


4.89 


18 


19 


18.35 


4.92 


18.33 


5.00 


18.31 


5.08 


18.29 


5.16 


19 


20 


19.32 


5.18 i 


19.30 


5.26 


19.27 


5.34 'i 19.25 


5.43 


20 


21 


20.28 


5.44 1 


20.26 


5.52 


20.24 


5.61 


20.21 


5.70 


21 


22 


21.25 


5.69 


21.23 


5.79 


21.20 


5.88 


21.17 


5.97 


22 


23 


22.22 


5.95 


22.19 


6.05 


22.16 


6.15 


22.14 


6.24 


23 


24 


23.18 


6.21 


23.15 


6.31 


23.13 


6.41 


23.10 


6.51 


24 


25 


24.15 


6.47 


24.12 


6.58 


24.09 


6.68 


24.06 


6.79 


25 


26 


25.11 


6.73 


25.08 


6.84 


25.05 


6.95 


25.02 


7.06 


26 


27 


26.08 


6.99 


26.05 


7.10 


26.02 


7.22 


25.99 


7.33 


27 


28 


27,05 


7.25 


27.01 


7.36 


26.98 


7.48 


26.95 


7.60 


28 


29 


28.01 


7.61 


27.98 


7.63 


27.95 


7.75 


27.91 


7.87 


29 


30 
31 


28.98 


7.76 


28.94 


7.89 


28.91 


8.02 


28.87 


8.14 


30 


29.94 


8.02 


29.91 


8.151 


29.87 


8.28 


29.84 


8.41 


31 


32 


30.91 


8.28 


30.87 


8.42 1 


30.84 


8.55 


30.80 


8.69 


32 


33 


31.88 


8.54 


31.84 


8.68 1 


31.80 


8.82 


31.76 


8.96 


33 


34 


32.84 


8.80 


32.80 


8.94 


32.76 


9.09 


32.72 


9.23 


34 


35 


33.81 


9.06 


33.77 


9.21 


33.73 


9.35 


33.69 


9.50 


35 
36 
37 


36 


34.77 


9.32 


34.73 


9.47 


34.69 


9.62 


34.65 


9.77 


37 


35.74 


9.58 


35.70 


9.73 


35.65 


9.89 


35.61 


10.04 


38 


36.71 


9.84 


36.66 


10.00 


36.62 


10.16 


36.57 


10.31 


38 


39 


37.67 


10.09 


37.63 


10.26 


37.58 


10.42 


37.54 


10.59 


39 


40 


38.64 


10.35 


38.59 


10.52 


38.55 


10.69 


38.50 


10,86 


40 


41 


39.60 


10.61 


39.56 


10.78 


39.51 


10.96 


39.46 


11.13 


41 


42 


40.57 


10.87 


40.52 


11.05 


40.47 


11.22 


40.42 


11.40 


42 


43 41.53 


11.13 


141.49 


11.31 


41.44 


11.49 


41.39 


11.67 


43 


44 42.50 


11.39 


42.45 


11.57 


42.40 


11.76 


42.35 


11.94 


44 


45 43.47 


11.65 


43.42 


11.84 


43.36 


12.03 


43.31 


12.21 


45 


46 44.43 


11.91 


44.38 


12.10 


44.33 


12.29 1144.27 


12.49 


40 


47 45.40 


12.16 45.35 


12.36 


45.29 


12.56 1 45.24 


12.76 


47 


48 46.36 


12.42 46.31 


12.63 


46.25 


12.83 46.20 
13.09 !!47.16 


13.03 


48 


49 


47.33 


12.68 47.27 


12.89 


47.22 


13.30 


49 


50 


48.30 


12.94 48.24 


13.15 


48.18 


13.36 
Lat. 


|| 48.12 


, 13.57 


50 




Dep. 


Lat. Dep. 


Lat. 


Dep. 


Dop. 


Lat. 


6 
o 

c 

"tia 

Q 


75 

1 


Dog. :4\ 


Deg. 


1^ 


Deg. ' 74i 


Deg. 



TRAVERSE TABLE. 



33 



p 

9 
o 
? 

"5\ 


15 Dog. 


15i Deg. 


15| Deg. 


) 
151 Deg. 


p' 

o 
p 

"5]' 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. [ 
13.63 1 


Lat. 


Dep. 


49.26 


13.20 


4'9720" 


13.41 


49.15 


49.09 


13.84 


52 


50.23 


13.46 


50.17 


13.68 


.50.11 


13.90! 


.50.05 


14.11 


52 


53 


51.19 


13.72 


51.13 


13.94 


51.07 


14.16 


51.01 


14.39 


53 


54 


52.16 


13.98 


52.10 


14.20 


.52.04 


14.43! 


51.97 


14.66 


54 


55 


53.13 


14.24 


53.06 


14.47 


.53.00 


14.70 i 


.52.94 


14.93 


55 


56 


54.09 1 14.49! 


54.03 


14.73 


53.96 


14.97 i 


.53.90 


15.20 


56 


57 


55.06] 14.75 1 


54.99 


14.99 


54.93 


15.23 1 


54.86 


15.47 


57 


58 


56.02 


15.01 


55.96 


15.26 


55.89 


15..50: 


55.82 


15.74 


58 


59 


.56.99 


15.27 


56.92 


15.52 


56.85 


15.77 1 


56.78 


16.01 


59 


60 
61 


57.96 


15.53 


57.89 


15.78 


57.82 
58.78 


16.03; 


57.75 


16.29 


60 
61 


.58.92 


15.79 


58.85 


16.04 


18.30 1 


58.71 


16.56 1 


62 


59.89 


16.05 


59.82 


16.31 


59 . 75 


16.57 


59.67 


16.83 


62 


63 


60.85 


16.31 


60.78 


16.57 


60.71 


16.84 


60.63 


17.10 


63 


64 


61.82 


16.56 


61.75 


16.83 


61.67 


17.10 


01.60 


17.37 


64 


65 


62.79 


16.82 


62.71 


17.10 


62.64 


17.37 


62.. 56 


17.64 


65 


66 


63.75 


17.08 


63.68 


17.35 


63.60 


17.64: 


63.52 


17.92 


66 


67 


64.72 


17.34 


64.64 


17.62 


64.56 


17.90' 


64.48 


18.19 


67 


68 


65.68 


17.60 


65.61 


17.89 


65.53 


18.17 


65.45 


18.46 


68 


69 


66.65 


17.86 


66.57 


18.15 


06.49 


18.44' 


66.41 


18.73 


69 


70 
71 


67.61 


18.12 


67.. 54 


18.41 


67.45 


18.71 


67.37 
68.33 


19.00 
19.27 


70 
71 


68.58 


18.38 


68.. 50 


18.68 1 


68.42 


18.97 


72 


69.55 


18.63 


09.46 


18.94 


69.38 


19.24 


69.30 19.. 54 


72 


73 


70.51 


18.89 


70.43 


19.20 


70.35 


19.51 


70.26 19.82 


73 


74 


71.48 


19.15 


71.39 


19.46 


71.31 


19.78 


71.22 20.09 


74 


75 


72.44 


19.41 


72.36 


19.73 


72.27 


20.04 


72.18 20.36 


75 


76 


73.41 


19.67 


73.32 


19.99 


73.24 


20.31 1 73.15 20.63 


76 


77 


74.38 


19.93 


74.29 


20.25 


74.20 


20.58 74.11 


20.90 


77 


78 


75.34 


20.19 


75.25 


20.52 


75.16 


20.84! 75.07 


21.17 


78 


79 


76.31 


20.45 


76.22 


20.78 


76.13 


21.11 


76.03 


21.44 


79 


80 
'81 


77.27 


20.71 


77.18 


21.04 


77.09 

78.05 


21.38 


77.00 


21.72 


80 
81 


78.24 


20.96 


78.15 


21.31 


21.65 


77.96 


21.99 


82 


79.21 


21.22 


79.11 


21.. 57 


79.02 


21.91 


78.92 


22.26 


82 


83 


80.17 


21.48 


80.08 


21.83 


79.98 


22.18 


79.88 


22.53 


83 


84 


81.14 


21.74 


81.04 


22.09 


80.94 


22.45 


80.85 


22.80 


84 


85 


82.10 


22.00 


82.01 


22.36 


81.91 


22.72 


1 81.81 


23.07 


85 


86 


83.07 


22.26 


82.97 


22.62 


82.87 


22.98 


182.77 


23.34 


86 


87 


84.04 


22.52 


83.94 


22.88 


83.84 


23.25 


i 83.73 


23.62 


87 


88 


85-00 


22.78 


84.90 


23.15 


84.80 


23.. 52 


84.70 


23.89 


88 


89 


85.97 


23-03 


85.87 


23.41 


85.76 


23.78 


85.66 


24.16 


89 


90 
91 


86.93 


23.29 


86.83 


23.67 


86.73 


24.05 


86.62 


24.43 


90 
91 


87.90 


23.55 


87.80 


23.94 


87.69 


24.32 


87.. 58 


24.70 


92 


88.87 


23.81 


88.76 


24.20 


88.65 


24.59 


88.55 


24.97 


92 


93 


89.83 


24.07 


89.73 


24.46 


89.62 


24.85 


89.51 


25.24 


93 


94 


90.80 


24.33 


90.69 


24.72 


90.58 


25.12 


90.47 


25.52 


94 


95 


91.76 


24.59 


91.65 


24.99 


91.54 


25 . 39 


191.43 


25.79 


95 


96 


92 73 


24.85 


92.62 


25.25 


92.51 


25 . 65 


192.40 


26.06 


96 


97 


93.69 


25.11 


93.58 


25.51 


93.47 


25 . 92 


i 93.36 


26.33 


97 


98 


94.66 


25.36 


94.. 55 


25.78 


94.44 


26.19 


94.32 


26.60 


98 


99 


95.63 


25.62 


195.51 


26.04 


95.40 


26.46 


i 95.28 


26.87 


99 


100 

c 

.2 


96.59 


25.88 


1 36.48 


26.30 
Lat. 


96.36 


26.72 


96.25 
Dep. 


27.14 
Lat. 


100 

ci 
c 

1 Q 

1 


Dep. 


Lat. 


Dep. 


Dep. 


Lat. 


75 Deg. 


741 Deg. 


74j Deg. 


1 

m Deg. 

'i 



34 



traversjE table. 



5 

00 

o 

a 


16 Deg. 


I6i Deg. 


161 Deg. 


161 Deg. 


§ 


Lat. 


D&p. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.96 


0.28 


0.90 


0.28 


0.96 


28 


0.96 


0.29 


1 


2 


I 92 


0.55 


1.92 


0.56 


1.92 


0.67 


1.92 


0.58 


2 


3 


2. 88 


0.83 


2.88 


0.84 


2.88 


0.85 


2.87 


0.86 


3 


4 


3.85 


1.10 


3.84 


1.12 


3.84 


1.14 


3.83 


1.15 


4 


5 


4.81 


1.38! 


4.80 


1.40 


4.79 


1.42 


4.79 


1.44 


5 


6 


5.77 


1.65 1 


5.76 


1.68 


5.75 


1.70 


5.75 


1.73 


6 


7 


6.73 


1.93 1 


0.72 


1.96 


6.71 


1.99 


6.70 


2.02 


7 


8 


7.69 


2.21 


7.68 


2.24 


7.67 


2.27 


7.66 


2.31 


8 


9 


8.&5 


2.48 


8.64 


2.52 


8.63 


2.. 56 


8.62 


2.59 


9 


10 
11 


9.61 


2.76 i 


9.60 


2.80 


9.59 


2.84 


9.58 


2.88 


10 


10.57 


3.03 


10.56 


3.08 


10.55 


3.12 


10.53 


3.17 


11 


12 


11.54 


3.31 1 


11.52 


3.36 


11.51 


3.41 


11.49 


3.46 1 12 


13 


12.50 


3.581 


12.48 


3.64 


12.46 


3.09 


12.45 


3.75 13 


U 


13.40 


3.86 


13.44 


3.92 


13.42 


3.98 


13.41 


4.03 14 


15 


14.42 


4.13 i 


14.40 


4.20 


14.38 


4.26 


14.36 


4.;^ 15 


16 


15.38 


4.41 


15.36 


4.48 


15.34 


4.54 


15.32 


4.01 1 16 


17 


16.34 


4.69 


16.32 


4.76 


16.30 


4.83 


16.28 


4.90 17 


18 


17.30 


4.96 1 


17.28 


5.04 


17.26 


5.11 


17.24 


5.19! 18 


19 


18.26 


5.24 1 


18.24 


5.32 


18.22 


5.40 


18.19 


5.48 1 19 


20 


19.23 


5.51 


19.20 


5.60 


19.18 


5.68 I 


19.15 


5.76 20 


21 


20.19 


5.79 


20.16 


5.88 


20.14 


5.96 


20.11 


6.05 21 


22 


21.15 


6.06 


21.12 


6.16 


21.09 


6.25 


21.07 


6.34 1 22 


23 


22.11 


6.341 


22.08 


6.44 


22.05 


6.53 


22.02 


6.63 


23 


24 


23.07 


6.62 


23.04 


6.72 


23.01 


6.82 


22.98 


6.92 


24 


25 


24.03 


6.89 


24.00 


7.00 


23.97 


7.10 


23.94 


7.20 


25 


2fi 


24.99 


7.17 


24.96 


7.28 


24.93 


7.38 


24.90 


7.49 1 26 1 


27 


25.95 


7.44 


25.92 


7.56 


25.89 


7.67 


25.85 


7.78 


27 


28 


20 . 92 


7.72 


20.88 


7.84 


26.85 


7.95 


20.81 


8.07 


28 


29 


27.83 


7.99 


27.84 


8.11 


27.81 


8.24 


27.77 


8.36 


29 


30 
31 


28.84 


8.27 


28.80 


8.39 


28.76 


8.52 


28.73 


8.65 


30 


29.80 


8.54 


29 . 76 


8.67 


29.72 


8.80 


29.68 


8.93 


31 


32 


30.76 


8.82 


30.72 


8.95 


30.68 


9.09 


30.64 


9.22 


32 


33 


31.72 


9.10 


31.68 


9.23 


31.64 


9.37 


31.60 


9.51 


33 


34 


32.68 


9.37 


32.64 


9.51 


32.60 


9.66 


32.56 


9.80 


34 


35 


.33.64 


9.65 


33.60 


9.79 


33.58 


9.94 


33.51 


10.09 j 35 


3fi 


31.61 


9.92 


34.56 


10.07 


34.52 


10.22 


34.47 


10.38 36 


37 


35.57 


10.20 


35.52 


10.35 


35.48 


10.51 


35.43 


10.66 37 


38 


36.53 


10.47 


36.48 


10.63 


36.44 


10.79 


36.. 39 


10.95 38 


39 


37.49 


10.75 


37.44 


10.91 


37.39 


11.08 


37.35 


11.24 1 39 


40 
41 


38.45 


11.03 


38.40 


11.19 


38.35 


11.36 


38.30 


11.53 


40 


39.41 


11.30 


39.36 


11.47 


39.31 


11.64 


39.26 


11.82 


41 


42 


40.37 


11.58 


40.32 


11.75 


40.27 


11.93 


40.22 


12.10 1 42 


43 


41.33 


11.85 


41.28 


12.03 


41.23 


12.21 


41.18 


12.39 43 


44 


42.30 


12.13 


42.24 


12.31 


42.19 


12.50 


42.13 


12.68 1 44 


45 


43.26 


12.40 


43.20 


12.59 


43.15 


12.78 


43.09 


12.97 


45 


46 


44.22 


12.68 


44.16 


12.87 


44.11 


13.06 


44.05 


13.26 


46 


47 


45.18 


12.95 


45.12 


13.15 


45.00 


13.35 


45.01 


13.55 


47 


48 


46.14 


13.23 


46.08 


13.43 


46.02 


13.63 


45.96 


13.83 


48 


49 


47.10 


13.51 


47.04 


13.71 


46.98 


13.92 


46 . 92 


14.12 


49 


_50_ 

6 

a 
.2 


48 . 06 


13.78 


48.00 


13.99 


47.94 


14.20' 


47.88 


14.41 


50 

03 
O 

c 

.2 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


74 


Deg. 


731 


Deg. 


731 


Deg. 


73^ Deg. 



TRWKRSF- TABLE. 



5 


16 Deg. 


16^ Deg. 


16^- 


Deg 


1 
161 Deg. 


3 
o 

CD 

~5l 


p 
3 
a 
a 


Lat. 
49.02 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


M 


14.06 


48.96 


14.27 


48.90 


14.48 


48.84 


14.70 


52 


49.99 


14.33 


49.92 


14.55 


49.86 


14.77 


49.79 


14.99 


52 


53 


50.95 


14.61 


50.88 


14.83 


.50.82 


15.05 


50.75 


15.27 


53 


54 


51.91 


14.88 


51.84 


15.11 


51.78 


15.34 


51.71 


15.. 56 


54 


55 


52.87 


15.16 


52.80 


15.39 


52.74 


15.62 


52.67 


15.85 


55 


56 


53.83 


15.44 


53.76 


15.67 


53.69 


15.90 


53.62 


16.14 


56 


57 54.79 1 


15.71 


54.72 


15.95 


54.65 


16.19 


54.58 


16.43 


57 


58 


55.75 


15.99 


55.68 


16.23 


55.61 


16.47 1 


55.54 


16.72 


58 


59 


56.71 


16.26 


56.64 


16.51 


56.57 


16.76! 


56.50 


17.00 


59 


60 


57.68 


16.54 


57.60 


16.79 


57 . 53 


17.04 
17.32 1 


57.45 


17.29 
17.58 


60 
61 


61 


58.64 


16.81 


58.56 


17.07 


58.49 


68.41 


62 


59.60 


17.09 


59.52 


17.35 


59.45 


17.61 i 


59.37 


17.87 


G2 


63 


60.56 


17.37 


60.48 


17.63 


60.41 


17.89 i 


60.33 


18.16 


63 


64 


61.52 


17.64 1 


61.44 


17.91 


61.36 


18.18 


61.28 


18.44 


04 


65 


62.48 


17.92 1 


62.40 


18.19 


62.32 


18.46 1 


62.24 


18.73 


05 


66 


63.44 


iS.lOJ 


63.-36 


18.47 


63.28 


18.74! 


63.20 


19.02 


1)6 


67 


64.40 1 


18.47 


64.32 


18.75 


64.24 


19.03' 


64.16 


19.31 


67 


68 


65.37 


18.74 i 


65.28 


19.03 


65.20 


19.31 i 


65.11 


19.60 


68 


69 


66.33 


19.02 


66.24 


19.31 


66.16 


i9.r,0: 


66.07 


19.89 


69 


70 


67.29 


19.29 ! 


67.20 


19.59 


67.12 

68.08 


19.88 
20.17 1 


G7.03 


20.17 


70 

71 


71 


68.25 


19.57 


68.16 


19.87 


67.99 


20.46 


72 


69.21 


19.85 


69.12 


20.15 


69.03 


20.45 1 


68.95 


20.75 


72 


73 


70.17 


20.12 


70.08 


20.43 


69.99 


20.73 i 


69.90 


21.04 


73 


74 


71.13 


20.40 


71.04 


20.71 


70.95 


21.02 


70.86 


21.33 74 


75 


72.09 


20.67 


72.00 


20.99 


71.91 


21.30 


71.82 


21.61 75 


76 


73.06 


20.1/5 


72.96 


21.27 


72.87 


21.. 59 


72.78 


21.90 


76 


77 


74.02 


21.22 


73.92 


21.55 


73.83 


21.87 


73.73 


22.19 


77 


78 


74.98 


21. .50 


74.88 


21.83 


74.79 


22.15 


j 74.69 


22.48 


78 


79 


75.94 


21.78 


75.84 


22.11 


75.75 


22.44 


! 75.65 


22.77 


79 


8.0 


76.90 


22.05 


76.80 


22.39 


76.71 


22.72 


176.61 


23.06 


80 
81 


81 


77.86 


22.33 


77.76 


22.67 


77.66 


23.01 


77.56 


23.34 


82 


78.82 


22.60 


78.72 


22.95 


78.62 


23.29 


78.52 


23.63 


82 


83 


79.78 


22.88 


79.68 


23.23 


79.58 


23.57 


79.48 


23.92 


83 


84 


80.75 


23.15 


80.64 


23.51* 


80.54 


23.86 


80.44 


24.21 


84 


85 


81.71 


23.43 


81.60 


23.79 


81.50 


24.14 


181.39 


24.50 


85 


86 


82.67 


23.70 


82.56 


24.07 


82.46 


24.43 


182.35 


24.78 


86 


87 


83.63 


23.98 


83.52 


24.35 


83.42 


24.71 


183.31 


25.07 


87 


88 


84.59 


24.26 


84.48 


24.62 


84.38 


24.99 


184.27 


25.36 


88 


89 


85.55 


24.53 


85.44 


24.90 


85.33 


25.28 


1 85.22 


25.65 


89 


90 


8G.51 24.81 


86.40 


25.18 


86.29 


25.56 


86.18 


25.94 


90 
91 


91 


87.47 


25.08 


87.36 


25.46 


87.25 


25.85 


87.14 


26.23 


92 


88.44 


25.36 


88.32 


25.74 


88.21 


26.13 


88.10 


26.51 


92 


93 


89.40 


25.63 


89.28 


26.02 


89.17 


26.41 


89.05 


26.80 


y3 


94 


90. £6 


25.91 


90.24 


26.30 


90.13 


26.70 


90.01 


27.09 


94 


95 


91.32 


26.19 


91.20 


26.58 


91.09 


26.98 


90.97 


27.38 


95 


96 


92.28 


26.46 


92.16 


26.86 


92.05 


27.27 


91.93 


27.67 


96 


97 


93.24 


26.74 


93.12 


27.14 


93.01 


27.55 


92.88 


27.95 


97 


98 


94.20 


27.01 


94.08 


27.42 


93.96 


27.83 


93.84 


28.24 


98 


99 


95.16 


27.29 


95.04 


27.70 


94.92 128.12 


94.80 


28.. 53 


99 


100 


96.13 


27.56 


96.00 


27.98 


95.88} 28.40 


95.76 


28.82 


100 


i 


Dep. 


Lat. 


Dep. Lat. 
731 Deg. 


Dep. 
73^ 


Lat. 


Dep. 


Lat. 


8 


c4 
.2 

Q 


; ^4 


Deg. 


De^ 


:3-i 


Deg. 


s 



36 



TKAVl'KSi: TADLH. 





17 Deg. 


17i Deg. 


I7i 
I^t. 


Dog. ' 
Dep. 


171 


Deg 


ST 

s 
o 


3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.95 


Dep. 


1 


0.96 


0.29 


0.95 


0.30 


0.95 


0.30 


0.30 


2} 1.91 


0..58 


1.91 


0.59 


1.91 


0.60 


1.90 


0.61 


2 


3 2. 87 


0.88 


2.87 


0.89 


2.86 


0.90 


2.86 


0.91 


3 


4 


3.83 


1.17 


3.82 


1.19 


3.81 


1.20 


3.81 


1.22 


4 


5 


t.78 


1.46 


4.78 


1.48 


4.77 


1.50 


4.76 


1.52 


5 


6 


5.74 


1.75 


5.73 


1.78 


5.72 


1.80 


5.71 


1.83 


6 


7 


6.69 


2.05 


6.69 


2.08 


6.68 


2.10 


6.67 


2 13 


7 


8 


7.65 


2.34 


7.64 


2.37 


7.63 


2.41 


7.62 


2.44 


8 


9 


8.61 


2.63 


8.60 


2.67 


8.58 


2.71 


8.57 


2.74 


9 


10 
11 


9.. 56 


2.92 


9.55 


2.97 


9.54 


3.01 


9.. 52 


3.05 


_12 
11 


10.52 


3.22 


10.51 


3.26 


10.49 


3.31 


10.48 


3.35 


12 


1.1.48 


3.51 


11.46 


3.56 


11.44 


3.61 


11.43 


3.66 


12 


13 12.43 


3.80 


12.42 


3.85 


12.40 


3.91 


12.38 


3.96 


13 


14 


13.39 


4.09 


13.37 


4.15 


13.35 


4.21 


13.33 


4.27 


14 


15 


14.34 1 4.39 


14,33 


4.45 


14.31 


4.51 


14.29 


4.57 


15 


16 


15.30 1 4.68 


15.28 


4.74 


15.26 


4.81 


15.24 


4.88 


16 


17 


16.20 1 4.97 


16.24 


5.04 


16.21 


5.11 


16.19 


5.18 


17 


18 


17.21 j 5.26 


17.19 


5.34 


17.17 


5.41 


17.14 


5.49 


18 


19 


18.17 5.56 


18.15 


5.63 


18.12 


5.71 


18.10 


5.79 


19 


20 


19.13 1 5.85 


19.10 


5.93 


19.07 


6.01 


19.05 


6.10 


20 
21 


21 


20.08 


6.14 


20.06 


6.23 


20.03 


6.31 


20.00 


6.40 


22 [21.04 


6.43 


21.01 


6.. 52 


20.98 


6.62 


20.95 


6.71 


22 


23 21.99 


6.72 


21.97 


6.82 


21.94 


6.92 


21.91 


7.01 


23 


24 22.95 1 7.02 


22.92 


7.12 


22.89 


7.22 


22.86 


7.32 


24 


25 23.91 j 7.31 


23.88 


7.41 j 


23.84 


7.. 52 


23.81 


7.62 


25 


26 24.86 7.60 


24.83 


7.71 1 


24.80 


7.82 


24.76 


7.93 


26 


27 


25.82 7.89 


25.79 


8.01 


25.75 


8.12 


25.71 


8.23 


27 


28 


26.78i 8.19 


26.74 


8.30 


26.70 


8.42 


26.67 


8.54 


28 


29 


27.73 1 8.48 


27.70 


8.60 


27.66 


8.72 


27.62 


8.84 


29 


30 
31 


28 . 09 i 8 . 77 


28.65 


8.90 


28.61 


9.02 


28.57 


9.15 


30 
31 


29.65: 9.06 


29.61 


9.19 


29.57 


9.32 


29.52 


9.45 


32 


30.60 j 9.36 


30.56 


9.49 


30.52 


9.62 


30.48 


9.76 


32 


33 


31.56! 9.65 


31.. 52 


9.79 


31.47 


9.92 


31.43 


10.06 


33 


34 


32.51 [ 9.94 


32.47 


10.08 


.32.43 


10.22 


32.38 


10.37 


34 


35 


33.47! 10.23 


33.43 


10.38 


33.38 


10.52 


33.33 


10.67 


35 


36 


34.43 10.53 


.34.. 38 


10.68 


34.33 


10.83 


34.29 


10.98 


36 


37 


35.38 1 10.82 


35.34 


10.97 


35.29 


11.13 


35 24 


11.28 


37 


38 


36.34! 11.11 


36.29 


11.27 


36.24 


11.43 


36.19 


11.58 


38 


39 


37.30! 11.40 


37.25 


11.57 


37.19 


11.73 


37.14 


11.89 


39 


40 
41 


38.25 11.09 


38.20 


11.86 


38.15 


12.03 


38.10 


12.19 


40 
41 


39.21 11.99 


139.16 


12.16 


39.10 


12.33 


39.05 


12.50 


42 


40.16 12.28 


40.11 


12.45 


40.06 


12.63 


40.00 


12.80 


42 


43 


41.12 12.57 


41.07 


12.75 


41.01 


12.93 


40.95 


13.11 


43 


44 


42.08 12.86 


42.02 


13.05 


41.96 


13.23 


41.91 


13.41 


44 


45 


43.03 13.16 


42.98 


13.34 


42.92 


13.53 


42.86 


13.72 


45 


46 


43.99 13.45 


43.93 


13.64 


43.87 


13.83 


43.81 


14.02 


46 


47 


44.95 18.74 


44.89 


13.94 


44.82 


14.13 


44.76 


14.33 


47 


48 


45.90 14.03 


45.84 


14.23 


45.78 


14.43 


45.71 


14.63 


48 


49 


46.86 14.33 | 46.80 


14.53 


46.73 


14.73 


46.67 


14.94 


49 


50 

Q 


47.82 


14.62,147.75 


14.83 


47.69 


15.04 


47.62 


15.24 


50 

6 
c 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


73 Deg. 


721 Deg. 


721 


Deg. 


m Deg. 



TRAVERSE TABLE. 



37 





a 
P 
51 


17 Deg. 


m Deg. 


17A Deg. 


1?| Deg. 


3 
o 
a 


Lat. 


Dep. 


Lat. 
48.71 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


48.77 


14.91 


16.12 


48.64 


15.34 


48.57 


15.55 


"51 


52 


49.73 


15.20 


49.66 


15.42 


49.59 


15.64 


49.52 


15.85 


52 


53 


50.68 


15.50 


50.62 


15.72 


50.55 


15.94 


50.48 


16.16 


53 


54 


51.64 


15.79 


51.57 


16.01 


51.50 


16.24 


51.43 


16.46 


54 


55 


52.60 


16.08 


52.53 


16.31 


52.45 


16.54 


52.38 


16.77 


55 


56 


53.55 


16.37 


53.48 


16.61 


53.41 


16.84 


53.33 


17.07 


56 


57 


54.51 


16.67 


54.44 


16.90 


54.36 


17.14 


54.29 


17.38 


57 


58 


55.47 


16.96 


55.39 


17.20 


55.32 


17.44 


55.24 


17.68 


58 


59 


56.42 


17.25 


56.35 


17.50 


56.27 


17.74 


56.10 


17.99 


59 


60 
61 


57.. 38 


17.54 


57.30 


17.79 


57.22 


18.04 


57.14 


18.29 


60 


58.33 


17.83 


58.26 


18.09 


58.18 


18.34 


58.10 


18.60 


61 


62 


59.29 


18.13 


59.21 


18.39 


59.13 


18.64 


59.05 


18.90 


62 


63 


60.25 


18.42 


60.17 


18.68 


60.08 


18.94 


60.00 


19.21 


63 


64 


61.20 


18.71 


61.12 


18.98 


61.04 


19.25 


60.95 


19.51 


64 


65 


62.16 


19.00 


62.08 


19.28 


61.99 


19.55 


61.91 


19.82 


65 


66 


63.12 


19.30 


63.03 


19.57 


62.95 


19.85 


62.86 


20.12 


66 


67 


64.07 


19.59 


63.99 


19.87 


63.90 


20.15 


63.81 


20.43 


67 


68 


65.03 


19.88 


64.94 


20.16 


64.85 


20.45 


64.76 


20.73 


68 


69 


65.99 


20.17 


65.90 


20.46 


65.81 


20.75 


65.72 


21.04 


69 


70 
71 


66.94 


20.47 


66.85 


20.76 


66.76 
67.71 


21.05 


66.67 


21.34 
21.65 


70 

71 


67.90 


20.76 


67.81 


21.05 


21.35 


67.62 


72 


68.85 


21.05 


68.76 


21.35 


68.67 


21.65 


68.57 


21.95 


72 


73 


69.81 


21.34 


69.72 


21.65 


69.62 


21.95 


69.52 


22.26 


73 


74 


70.77 


21.64 


70.67 


21.94 


70.58 


22.25 


70.48 


22.56 


74 


75 


71.72 


21.93 


71.63 


22.24 


71.53 


22.55 


71.43 


22.86 


75 


76 


72.68 


22.22 


72.58 


22.54 


72.48 


22.85 


72.38 


23.17 


76 


77 


73.64 


22.51 


73.54 


22.83 


73.44 


23.15 


73.33 


23.47 


77 


78 


74.59 


22.80 


74.49 


23.13 


74.39 


23.46 


74.29 


23.78 


78 


79 


75.55 


23.10 


75.45 


23.43 


75.34 


23.76 


75.24 


24.08 


79 


80 
81 


76.50 
77.46 


23.39 


76.40 


23.72 


76.30 


24.06 
24.36 


76.19 


24.39 


80 


23.68 


77.36 


24.02 


77.25 


77.14 


24.69 


81 


&2 


78.42 


23.97 


78.31 


24.32 


78.20 


24.66 


78.10 


25.00 


82 


83 


79.37 


24.27 


79.27 


24.61 


79.16 


25.96 


79.05 


25.30 


83 


84 


80.33 


24.56 


80.22 


24.91 


80.11 


25.26 


80.00 


25.61 


84 


85 


81.29 


24.85 


81.18 


25.21 


81.07 


25.56 


80.95 


25.91 


85 


86 


82.24 


25.14 


82.13 


25.50 


82.02 


25.86 


81.91 


26.22 


86 


87 


83.20 


25.44 


83.09 


25.80 


82.97 


26.16 


82.86 


26.52 


87 


88 


84.15 


25.73 


84.04 


26.10 


83.93 


26.46 


83.81 


26.83 


88 


89 


85.11 


26.02 


85.00 


26.39 


84.88 


26.76 


84.76 


27.13 


89 


90 
91 


86.07 


26.31 


85.95 


26.69 


85.83 


27.06 


85.72 


27.44 

27.74 


90 
91 


87.02 


26.61 


86.91 


26.99 i 86.79 


27.36 


86.67 


92 


87.98 


26.90 


87.86 


27.28 


87.74 27.66 


87.62 


28.05 


92 


93 


88.94 


27.19 


88.82 


27.58 


88.70 27.97 


88.57 


38.35 


93 


94 


89.89 


27.48 


89.77 


27.87 


89.65 28.27 


89.53 


28.66 


94 


95 


90.85 


27.78 


90.73 


28.17 


90.60 


28.57 


90.48 


28.96 


95 


96 


91.81 


28.07 


91.68 


28.47 


, 91.56 


28.87 


91.43 


29.27 


96 


97 


92.76 


28.36 


92.64 


28.76 


92.51 


29.17 


92.38 


29.57 


97 


98 


93.72 


28.65 


93.59 


29.06 


93.46 


29.47 


93.33 


29.88 


98 


99 


94.67 


28.94 


94.55 


29.36 


94.42 


29.77 


94.29 


30.18 


99 


100 

.2 


95.63 


29.24 


95.50 


29.65 


95.37 


30.07 


95.24 


30.49 


100 


Dep. 


Lat. 


Dep. 


L.t. 


Dep. 


T.at. 


Dep. 


Lat. 


(6 
u 

c 

so 

Q 


73 Deg. 


721 Deg. 


72^ Deg. 


m Deg. 



38 



TBAVERSE TABLE 



5 

o 

a 


18 Deg. 


18i Deg. 


18i Deg. 


18| Deg. 


g 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.95 


0.31 


0.95 


0.31 


1 0.95 


0.32 


0.96 


0.32 


2 


2 


1.90 


0.62 


1.90 


0.63 


1.90 


0.63 


1.89 


0.64 


2 


3 


2.85 


0.93 


2.85 


0.94 


2 84 


0.95 


2.84 


0.96 


3 


4 


3.80 


1.24 


3.80 


1.25 


3 79 


1.27 


3.79 


1.29 


4 


5 


4.76 


1.55 


4.75 


1.57 


4.74 


1.59 


4.73 


1.61 


5 


6 


5.71 


1.85 


6.70 


1.88 


5.69 


1.90 


5.68 


1.93 


6 


7 


6.66 


2.16 


6.65 


2.19 


6.64 


2.22 


6.63 


2.25 


7 


8 


7.61 


2.47 


7.60 


2.51 


7.59 


2.54 


7.58 


2.57 


8 


9 


8.56 


2.78 


8.55 


2. 82 


8.53 


2.86 


8.52 


2.89 


9 


10 


9.51 


3.09 


9.50 
10.45 


3.13 


9.48 


3.17 


9.47 


3.21 


10 


11 


10.46 


3.40 


3.44 


10.43 


3.49 


10.42 


3.54 


11 


12 


11.41 


3.71 


11.40 


3.76 


11.38 


3 81 


11.36 


3.86 


12 


13 


12.36 


4.02 


12.35 


4.07 


12.33 


4 12 


12.31 


4.18 


13 


14 


13.31 


4.33 


13.30 


4.38 


13.28 


4.44 


13.26 


4.50 


14 


15 


14.27 


4.64 


14.25 


4.70 


14.22 


4.76 


14.20 


4.82 


15 


16 


15.22 


4.94 


15.20 


5.01 


15.17 


5.08 


15.15 


5.14 


16 


17 


16.17 


5.25 


16.14 


5.32 


16.12 


5.39 


16.10 


5.46 


17 


18 


17.12 


5.56 


17.09 


5.64 


17.07 


5.71 


17.04 


5.79 


18 


19 


18.07 


5.87 


18.04 


5.95 


18.02 


6.03 


17.99 


6.11 


19 


20 
21 


19.02 


6.18 


18.99 


6.26 


18.97 


6.35 


18.94 


6.43 


20 


19.97 


6.49 


19.94 


6.58 


19.91 


6.66 


19.89 


6.75 


21 


22 


20.92 


6.80 


20.89 


6.89 


20.86 


6.98 


20.83' 7.07 


22 


23 


21.87 


7.11 


21.84 


7.20 


21.81 


7.30 


21.78 i 7.39 


23 


24 


22.83 


7.42 


22.79 


7.52 


22.76 


7.62 


22.73 


7 71 


24 


25 


23.78 


7.73 


23.74 


7.83 


23.71 


7.93 


23.67 


8.04 


25 


26 


24.73 


8.03 


24.69 


8.14 


24.66 


8.25 


24.62 


8.36 26 


27 


25.68 


8.34 


25.64 


8.46 


25.60 


8.57 


25.57 


8.68 ' 27 


28 


26.63 


8.65 


26.59 


8.77i 


26.55 


8.88 


26.51 


9.00 28 


29 


27.58 


8.96 


27.54 


9.08 


27.50 


9.20 


27.46 


9.32 


29 


30 


28.53 


9.27 


28.49 


9.39 


28.45 


9.52 


28.41 


9.64 


30 
31 


31 


29.48 


9.58 


29.44 


9.71 


29.40 


9.84 


29.35 


9.96 


32 


30.43 


9.89 


30.39 


10.02 


30.35 


10.15 


30.30 


10.29 


32 


33 


31.38 


10.20 


31.34 


10.33 


31.29 


10.47 


31.25 


10.61 


33 


34 


.32.34 


10.51 


32.29 


10.65 


32.24 


10.79 


32.20 


10.93 


34 


35 


33.29 


10.82 


33.24 


10.96 


33.19 


11.11 


.33.14 


11.25 


35 


36 


.34.24 


11.12 


34.19 


11.27 


34.14 


11.42 


34.09 


11.57 


36 


37 


35.19 


11.43 


35.14 


11.59 


35.09 


11.74 


36.04 


11.89 


37 


38 


36.14 


11.74 


36.09 


11.90 


36.04 


12.06 


35.98 


12.21 


38 


39 


37.09 


12.05 


37.04 


12.21 


36.98 


12.37 


36.93 


12.64 


39 


40 38.04 1 


12.36 


37.99 


12.53 


37.93 


12.69 


37.88 


12.86 


40 


41 


38.99 


12.67 


38.94 


12.84 


38.88 


13.01 


38.82 


13.18 


41 


42 


39.94 


12.98 


39.89 


13.15 


39.83 


13.33 


39.77 


13.50 


42 


43 


40.90 


13.29 


40.84 


13.47 


40.78 


13.64 


40.72 


13.82 


43 


44 


41.85 


13.60 


41.79 


13.78 


41.73 


13.96 


41.66 


14.14 


44 


45 42.80 1 


13.91 


42.74 


14.09 


42.67 


14.28 


42.61 


14.46 


45 


46 


43.75 


14.21 


43.69 


14.41 


43.62 


14.60 


43.66 


14.79 


46 


47 


44.70 


14.. 52 


44.64 


14.72 


44.57 


14.91 


44.51 


15.11 


47 


48 


45.65 


14.83 


45.59 


15.03 


45.52 


15.23 


45.45 


15.43 


48 


49 


46.60 


15.14 


46.54 


15.35 


46.47 


15.55 


46.40 


15.75 49 


50 


47.55 


15.45 


47.48 


15.66 


47.42 


15.87 


47.35 


16.07 50 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. ! 


o 

c 


^1 


72 Deg. 


71| Deg. 


7HI 


)eg. 


1 
7U Deg. 

1 



TRAVBKSE TABr>F. 



39 



P 

51 


18 Deg. 


184 Deg. 


m Deg. 


18| Deg. 


1 
~51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

48.29 


Dep. 
16.39 


48.50 


15.76 


48.43 


15.97 


48.36 


16.18 


53 


49.45 


16.07 


49.38 


16.28 


49.31 


16.50 


49.24 


16.71 


52 


53 


50.41 


16.38 


50.33 


16.60 


50.26 


16.82 


50.19 


17.04 


53 


54 


51.36 


16.69 


51.28 


16.91 


51.21 


17.13 


51.13 


17.36 


54 


55 '52.31 


17.00 


52.23 


17.22 


52.16 


17.45 


52.08 


17.68 


55 


56 


53.26 


17.30 


53.18 


17.. 54 


53.11 


17.77 


53.03 


18.00 


56 


57 


54.21 


17.61 


54.13 


17.85 


54.05 


18.09 


53.98 


18.32 


57 


58 


55.16 


17.92 


55.08 


18.16 


55.00 


18.40 


54.92 


18.64 


58 


59 


56.11 


18.23 


56.03 


18.48 


55.95 


18.72 


55.87 


18.96 


59 


60 
61 


67.06 


18.54 


56.98 


18.79 


56.90 


19.04 


56.82 


19.29 


60 


58.01 


18 85 


57.93 


19.10 


57.85 


19.36 


57.76 


19.61 


61 


62 


58.97 


19.16 


58.88 


19.42 


58.80 


19.67 


58.71 


19.93 


62 


63 


59.92 


19.47 


59.83 


19.73 


59.74 


19.99 


59.66 


20.25 


63 


64 


60.87 


19.78 


60.78 


20.04 


60.69 


20.31 


60.60 


20.57 


64 


65 


61.82 


20.09 


61.73 


20.36 


61.64 


20.62 


61.55 


20.89 


65 


66 


62.77 


20.40 


62.68 


20.67 


62.59 


20.94 


62.50 


21.22 


66 


67 


63.72 


20.70 


63.63 


20.98 


63.54 


21.26 


63.44 


21.54 


67 


68 


64.67 


21.01 


64.58 


21.30 


64.49 


21.58 


64.39 


21.86 


68 


69 


65.62 


21.32 


65.53 


21.61 


65.43 


21.89 


65.34 


22.18 


69 


70 
71 


66.57 


21.63 


66.48 


21.92 


66.38 


22.21 


66.29 


22.50 


70 
71 


67.53 


21.94 


67.43 


22.23 


67.33 


22.53 


67.23 


22.82 


72 


68.48 


22.25 


68.38 


22.55 


68.28 


22.85 


68.18 


23.14 


72 


73 


69.43 


22.56 


69.33 


22.86 


69.23 


23.16 


69.13 


23.47 


73 


74 


70.38 


22.87 


70.28 


23.17 


70.18 


23.48 


70.07 


23.79 


74 


76 


71.33 


23.18 


71.23 


23.49 


71.12 


23.80 


71.02 


24.11 


75 


76 


72.28 


23.49 


72.18 


23.80 


72.07 


24.12 


71.97 


24.43 


76 


77 


73.23 


23.79 


73.13 


24.11 


73.02 


24.43 


72.91 


24.75 


77 


78 


74.18 


24.10 


74.08 


24.43 


73.97 


24.75 


73.86 


25.07 


78 


79 


75.13 


24.41 


75.03 


24.74 


74.92 


25.07 


74.81 


25.39 


79 


80 
81 


76.08 
77.04 


24.72 
25.03 


75.98 


25.05 


75.87 


25.38 


75.75 


25.72 


80 


76.93 


25.37 


76.81 


25.70 


76.70 


26.04 


81 


82 


77.99 


25.34 


77.88 


25.68 


77.76 


26.02 


77.65 


26.36 


82 


83 


78.94 


25.65 


78.83 


25.99 


78.71 


26.34 


78.60 


26.68 


83 


84 


79.89 


25.96 


79.77 


26.31 


79.66 


26.65 


79.54 


27.00 


84 


85 


80.84 


26.27 


80.72 


26.62 


80.61 


26.97 


80.49 


27.. 32 


85 


86 


81.79 


26.58 


81.67 


26.93 


81.56 


27.29 


81.44 


27.64 


86 


87 


82.74 


26.88 


82.62 


27.25 


82.50 


27.61 


82.38 


27.97 


87 


88 


83.69 


27.19 


83.57 


27.56 


83.45 


27.92 


83.33 


28.29 


88 


89 


84.64 


27.50 


84.52 


27.87 


84.40 


28.24 


84.28 


28.61 


89 


90 
91 


85.60 


27.81 


85.47 


28.18 


85.35 


28.56 


85.22 


28.93 


90 


86.55 


28.12 


86.42 


28.50 


86.30 


28.37 


86.17 


29.25 


91 


92 


87.50 


28.43 


87.37 


28.81 


87.25 


29.19 


87.12 


29.57 


92 


93 


88.45 


28.74 


88.32 


29.12 


88.19 


29.51 


88.06 


29.89 


93 


94 


89.40 


29.05 


89.27 


29.44 


89.14 


29.83 


89.01 


30.22 


94 


95 


90.35 


29.36 


90.22 


29.75 


90.09 


30.14 


89.96 


.30.54 


95 


96 


91.30 


29.67 


91.17 


30.06 


91.04 


30.46 


1.0.91 


30.86 


96 


97 


92.25 


29.97 


92.12 


30.38 


91.99 


30.78 


91.85 


31.18 


97 


98 


93.20 


30.28 


93.07 30.69 1 


92.94 


31.10 


92.80 


31.50 


98 


99 


94.15 


30.59 


94.02 


31.00 


93.88 


31.41 


93.75 


31.82 


99 


100 

1 

5 


95.11 


30.90 


94.97 


31.32 


94.83 


31.73 


94.69 


32.14 


100 

a 

3 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 


72 Deg. 


711 Deg. 

! 


711 Deg. 


7U Deg. 



40 



TKAVFKSE TARLF-. 



I 
r 


19 Deg. 


19i Deg. 


19^ Deg. 


191 Deg. 


p 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.95 


0.33 


0.94 


0.33 


0.94 


0.33 


0.94 


0..34 


1 


2 


1.89 


0.65 


1.89 


0.66 


1.89 


0.67 


1.88 


0.68 


2 


3 


2.84 


0.98 


2.83 


0.99 


2.83 


1.00 


2 82 


1.01 


3 


4 


3.78 


1.30 


3.78 


1.32 


3.77 


1.34 


3.76 


1.36 


4 


5 


4.73 


1.63 


4.72 


1.65 


4.71 


1.67 


4.71 


1.69 


6 


6 


6.67 


1.95 


6.66 


1.98 


5.66 


2.00 


5.65 


2.03 


6 


7 


6.62 


2.28 


6.61 


2.31 


6.60 


2.34 


6.59 


2.. 37 


7 


8 


7.56 


2.60 


7.55 


2.64 


7.54 


2.67 


7.63 


2.70 


8 


9 


8.51 


2.93 


8.50 


2.97 


8.48 


3.00 


8.47 


3.04 


9 


10 


9.46 


3.26 


9.44 


3.30 


9.43 


3.34 


9.41 


3.38 


10 


11 


10.40 


3.58 


10.38 


3.63 


10.37 


3.67 


10.35 


3.72 


11 


12 


11.35 


3.91 


11.33 


3.96 


11.31 


4.01 


11.29 


4.06 


12 


13 


12.29 


4.23 


12.27 


4.29 


12.25 


4.. 34 


12.24 


4.39 


13 


14 


13.24 


4.56 


13.22 


4.62 


13.20 


4.67 


13.18 


4.73 


14 


15 


14.18 


4.88 


14.16 


4.95 


14.14 


5.01 


14.12 


5.07 


15 


16 


15.13 


5.21 


15.11 


5.28 


15.08 


6.34 


15.06 


5.41 


16 


17 


16.07 


5.53 


16.05 


5.60 


16.02 


6.67 


16.00 


5.74 


17 


18 


17.02 


6.86 


16.99 


5.93 


16.97 


6.01 


16.94 


6.08 


18 


19 


17.96 


6.19 


17.94 


6.26 


17.91 


6.34 


17.88 


6.42 


19 


20 


18.91 


6.51 


18.88 


6.59 


18.85 


6.68 


18.82 


6.76 


20 


21 


19.86 


6.84 


19.83 


6.92 


19.80 


7.01 


19.76 


7.10 


21 


22 


20.80 


7.16 


20.77 


7.25 


20.74 


7.34 


20.71 


7.43 


22 


23 


21.75 


7.49 


21.71 


7.58 


21.68 


7.68 
8.01 


21.65 


7.77 


23 


24 


22.69 


7.81 


22.66 


7.91 


22.62 


22.59 


8.11 


24 


25 


23.64 


8.14 


23.60 


8.24 


23.57 


8.35 


23.53 


8.45 


25 


26 


24.58 


8.46 


24.66 


8.57 


24.51 


8.68 


24.47 


8.79 


26 


27 


25.53 


8.79 


25.49 


8.90 


25.45 


9.01 


26.41 


9.12 


27 


28 


26.47 


9.12 


26.43 


9.23 


26.39 


9.35 


26.35 


9.46 


28 


29 


27.42 


9.44 


27.38 


9.56 


27.34 


9.68 


27.29 


9.80 


29 


30 
31 


28.37 


9.77 


28.32 
29.27 


9.89 
10.22 


28.28 


10.01 


28.24 


10.14 


30 


29.31 


10.09 


29.22 


10.. 35 


29.18 


10.48 


3i 


32 


30.26 


10.42 


30.21 


10.55 


30.16 


10.68 


30.12 


10.81 


32 


33 


31.20 


10.74 


31.15 


10.88 


31.11 


11.02 


31.06 


11.15 


33 


34 


32.15 


11.07 


32.10 


11.21 


32.05 


11.35 


32.00 


11.49 


34 


35 


33.09 


11.39 


33.04 


11.54 


32.99 


11.68 


32.94 


11.83 


35 


36 


34.04 


11.72 


33.99 


11.87 


33.94 


12.02 


33.88 


12.17 


36 


37 


34.98 


12.05 


34.93 


12.20 


34.88 


12.35 


34.82 


12.50 


37 


38 


35.93 


12.37 


35.88 


12.53 


35.82 


12.68 


35.76 


12.84 


38 


39 


36.88 


12.70 


36.82 


12.86 


36.70 


13.02 


36.71 


13.18 


39 


40 


37.82 


13.02 


37.76 
38.71 


13.19 
13.. 52 


37.71 


13.. 35 


37.65 


13.. 52 


40 


41 


38.77 


13.35 


38.05 


13.69 


38.59 


13.85 


41 


42 


39.71 


13.67 


39.65 


13.85 


39.59 


14.02 


39.53 


14.19 


42 


43 


40.66 


14.00 


40.60 


14.18 


40., 53 


14.35 


40.47 


14.53 


43 


44 


41.60 


14.32 


41.54 


14.51 


41.48 


14.69 


41.41 


14.87 


44 


45 


42.55 


14.65 


42.48 


14.84 


42.42 


15.02 


42.35 


15.21 


46 


46 


43.49 


14.98 


43.43 


15.17 


43.36 


15.36 


43.29 


15.54 


46 


47 


44.44 


15.30 


44.37 


15.. 50 


44.30 


15.69 


44.24 


15.88 


47 


48 


45.38 


15.63 


45.32 


16.83 


45.25 


16.02 


45.18 


16.22 


48 


49 


46.33 


16.95 


46.26 


16.15 


46.19 


16.36 


46.12 


16.56 


49 


50 


47.28 


16.28 


47.20 


16.48 


47.13 


16.69 


47.06 


16.90 


50 


1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lai. 


i 

c 

s 

.52 


711 


>e. 


701 Deg. 


70 i Deg. 


70J Deg. 



TRAVEIlSfi TABLE. 



41 



5 
1 ■ 


19 Deg. 


m Deg. 

1 


19A Dog. 


191 Deg. 


3 

51 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


48.22 


16.60 


48.15 


16.81 


48.07 


17.02 


48.00 


17.23 


52 


49.17 


16.93 


49.09 


17.14 


49.02 


17.36 


48.94 


17.57 


52 


53 


50.11 


17.26 


50.04 


17.47 


49.96 


17.69 


49.88 


17.91 


53 


54 


51.06 


17.58 


50.98 


17.80 


50.90 


18.03 


.50.82 


18.25 


54 


55 


52.00 


17.91 


51.92 


18.13 


51.85 


18.36 


51.76 


18.59 


55 


56 


52.95 


18.23 


52.87 


18.46 


52.79 


18.69 


52.71 


18.92 


56 


57 


53.89 


18.56 1 


53.81 


18.79 


53.73 


19.03 


53.65 


19.26 


57 


58 


.54.84 


18.88 


54.76 


19.12 


54.67 


19.36 


54.59 


19.60 


58 


59 


55.79 


19.21 


55.70 


19.45 


55.62 


19.69 


55.53 


19.94 


59 


60 
61 


50.73 


19.53 


56.65 


19.78 


56.56 


20.03 


56.47 


20.27 


00 
61 


57 . 68 


19.86 


57.59 


20.11 


57.50 


20.36 


57.41 


20.61 


62 


58.62 


20.19 


58.53 


20.44 


58.44 


20.70 


58.35 


20.95 


62 


63 


.59.57 


20.51 


59.48 


20.77 


59.39 


21.03 


59.29 


21.29 


63 


64 


60.51 


20.84 


60.42 


21.10 


60.33 


21.361 


60.24 


21.63 


64 


65 


61.46 


21.16 


61.37 


21.43 


01.27 


21.70 


61.18 


21.96 


65 


66 


62.40 


21.49 


62.31 


21.76 


62.21 


22.03 


62.12 


22.30 


66 


67 


63.35 


21.81 


63.25 


22.09 


63.16 


22.37 


63.06 


22 . 64 


67 


68 


64.30 


22.14 


64.20 


22.42 


04.10 


22.70 


64.00 


22.98 


68 


69 


65.24 


22.40 


65.14 


22.75 


05.04 


23.03 


64.94 


23.32 


69 


70 
71 


66.19 


22.79 


66.09 


23.08 


65.98 


23.37 


65.88 


23.65 


70 

71 


67.13 


23.12 


07.03 


23.41 


66.93 


23.70 


66.82 


23.99 


72 


68.08 


23.44 


67.97 


23.74 


07.87 


24.03 


67.76 


24.33 


72 


73 


69.02 


23.77 


68.92 


24.07 


68.81 


24.37 


68.71 


24.67 


73 


74 


69.97 


24.09 


69.86 


24.40 


69.76 


24.70 


69.65 


25.01 


74 


75 


70.91 


24.42 


70.81 


24.73 


70.70 


25.04 


70.59 


25.34 


75 


76 


71.86 


24.74 


71.75 


25.06 


71.64 


25.37 


71.53 


25.68 


76 


77 


72.80 


25.07 


72.69 


25.39 


72.58 


25.70 


72.47 


26.02 


77 


78 


73.75 


25.39 


73.84 


25.72 


73.53 


26.04 


73.41 


26.36 


78 


79 


74.70 


25.72 


74.58 


26.05 


74.47 


26.37 


74.35 


26.70 


79 


80 
81 


75.64 


26.05 


75.53 


26.38 


75.41 


26.70 


75.29 


27.03 


80 
81 


76.59 


26.37 


76.47 


26.70 


76.35 


27.04 


76.24 


27.37 


82 


77.53 


26.70 


77.42 


27.03 


77.30 


27.37 


77.18 


27.71 


82 


83 


78.48 


27.02 


78.36 


27.36 


78.24 


27.71 


78.12 


28.05 


83 


84 


79.42 


27.35 


79.30 


27.69 


79.18 


28.04 


79.06 


28.39 


84 


85 


80.37 


27.67 


80.25 


28.02 


80.12 


28.37 


80.00 


28.72 


85 


86 


81.31 


28.00 


81.19 


28.35 


81.07 


28.71 


80.94 


29.06 


86 


87 


82-26 


28.32 


82.14 


28.68 


82.01 


29.04 


81.88 


29.40 


87 


88 


83.21 


28.65 


83.08 


29.01 


92.95 


29.37 


82.82 


29.74 


88 


89 


84.15 


28.98 


84.02 


29.34 


83.90 


29.71 


83.76 


30.07 


89 


90 
91 


85.10 


29.30 


84.97 


29.67 


84.84 


30.04 


84.71 


30.41 


90 


86.04 


29.63 


85.91 


30.00 


85.78 


30.38 


85.65 


.30.75 


91 


92 


86.99 ',29.95 


86.86 


30.33 


86.72 


30.71 


86.59 


31.09 


92 


93 


87.93 


30.28 


87.80 


30.66 


87.67 


31.04 


87.53 


31.43 


93 


94 


88.88 


30.60 


88.74 


30.99 


88.61 


31.38 


88.47 


31.76 


94 


95 


89.82 


30.93 


89.69 


31.32 


89.55 


31.71 


89.41 


32.10 


95 


96 


90.77 


31.25 


90.63 


31.65 


90.49 


32.05 


90.35 


32.44 


96 


97 


91.72 


31.58 


91.58 


31.98 


91.44 


32.38 


91.29 


32.78 


97 


98 


92.66 


31.91 


92.52 


32.31 


92.38 


32.71 


92.24 


33.12 


98 


99 


93.61 


32.23 


93.46 


32.64 


93.32 


33.05 


93.18 


33.45 


99 


100 


94.55 


32.56 


94.41 


32.97 


94.26 


33.38 


94.12 


33.79 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

1 

.2 


71 Deg. 


701 Deg. 


701 Deg. 


m Deg. 



42 



TRAVERSE TABLE. 



o 
~1 


i 

20 


Deg. 


20i Deg. 


20i Deg. 


20^ 


Deg. 


n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.94 


0.34 


0.94 


0.35 


0.94 


0.35 


0.94 


0.35 


2 


1.88 


0.68 


1.88 


0.69 


1.87 


0.70 


1.87 


0.71 


2 


3 


2.82 


1.03 


2.81 


1.04 


2.81 


1.05 


2.81 


1.06 


3 


4 


3.76 


1.37 


3.75 


1.38 


3.75 


1.40 


3.74 


1.42 


4 


5 


4.70 


1.71 


4.69 


1.73 


4.68 


1.75 


4.68 


1.77 


6 


6 


5.64 


2.05 


5.63 


2.08 


5.62 


2.10 


5.61 


2.13 


6 


7 


6.58 


2.39 


6.57 


2.42 


6.56 


2.45 


6.55 


2.48 


7 


8 


7.52 


2.74 


7.51 


2.77 


7.49 


2.80 


7.48 


2.83 


8 


9 


8.46 


3.08 


8.44 


3.12 


8.43 


3.15 


8.42 


3.19 


9 


10 
11 


9.40 


3.42 


9.38 


3.46 


9.37 


3.50 


9.35 


3.. 54 


10 
11 


10.34 


3.76 


10.32 


3.81 


10.30 


3.85 


10.29 


3.90 


12 


11.28 


4.10 


11.26 


4.15 


11.24 


4.20 


11.22 


4.25 


12 


13 


12.22 


4.45 


12.20 


4.50 


12.18 


4.55 


12.16 


4.61 


13 


14 


13.16 


4.79 


13.13 


4.85 


13.11 


4.90 


13.09 


4.96 


14 


15 


14.10 


5.13 


14.07 


5.19 


14.05 


5.25 


14.03 


5.31 


15 


16 


15.04 


5.47 


15.01 


5.54 


14.99 


5.60 


14.96 


5.67 


16 


17 15.97 


5.81 


15.95 


5.88 


15.92 


5.95 


15.90 


6.02 


17 


18 16.91 


6.16 


16.89 


6.23 


16.86 


6.30 


16.83 


6.38 


18 


19 


17.85 


6.50 


17.83 


6.58 


17.80 


6.65 


17.77 


6.73 


19 


20 
21 


18.79 


6.84 


18.76 


6.92 


18.73 


7.00 


18.70 


7.09 


20 
21 


19.73 


7.18 


19.70 


7.27 


19.67 


7.35 


19.64 


7.44 


22 


20.67 


7.52 


20.64 


7.61 


20.61 


7.70 


20.. 57 


7.79 


M'lO 


23 


21.01 


7.87 


21.58 


7.96 


21.54 


8.05 


21.51 


8.15 


23 


24 


22.. 55 


8.21 


22.52 


8.31 


22.48 


8.40 


22.44 


8.50 


24 


25 


23.49 


8.55 


23.45 


8.65 


23.42 


8.76 


23.38 


8.86 


25 


26 


24.43 


8.89 


24.39 


9.00 


24.35 


9.11 


24.31 


9.21 


26 


27 


25.37 


9.23 


25.33 


9.35 


25.29 


9.46 


25.25 


9.57 


27 


28 


26.31 


9.58 


26.27 


9.69 


26.23 


9.81 


26.18 


9.92 


28 


29 


27.25 


9.92 


27.21 


10.04 


27.16 


10.16 


27.12 


10.27 


29 


30 
31 


28.19 


10.26 


28.15 


10.38 


28.10 


10.51 


28.05 


10.63 


30 
31 


29.13 


10.60 


29.08 


10.73 


29.04 


10.86 


28.99 


10.98 


32 


30.07 


10.94 


30.02 


11.08 


29.97 


11.21 


29.92 


11.34 


32 


33 


31.01 


11.29 


30.96 


11.42 


30.91 


11.56 


.30.86 


11.69 


33 


34 


31.95 


11.63 


31.90 


11.77 


31.85 


11.91 


31.79 


12.05 


34 


35 32.89 


11.97 


32.84 


12.11 


.32.78 


12.26 


32.73 


12.40 


35 


36 


33.83 


12.31 


33.77 


12.46 


33.72 


12.61 


33.66 


12.75 


36 


37 


34.77 


12.65 


34.71 


12.81 


34.66 


12.96 


34.60 


13.11 


37 


38 


35.71 


13.00 


35.65 


13.15 


35.59 


13.31 


35.54 


13.46 


38 


39 


36.65 


13.34 


36.59 


13.50 


36.53 


13.66 


36.47 


13.82 


39 


40 

41 


37.59 


13.68 


37.53 


13.84 


37.47 


14.01 


37.41 


14.17 


40 
41 


38.53 


14.02 


38.47 


14.19 


38.40 


14.36 


38.34 


14.53 


42 


39.47 


14.36 


39.40 


14.54 


39.34 


14.71 


39.28 


14.88 


42 


43 


40.41 


14.71 


40.34 


14.88 


40.28 


15.06 


40.21 


15.23 


43 


44 


41.35 


15.05 


41.28 


15.23 


41.21 


15.41 


41.15 


15.59 


44 


45 


42.29 


15.39 


42.22 


15.58 


42.15 


15.76 


42.08 


15.94 


45 


46 143.23 


15.73 


43.16 


15.92 


43.09 


16.11 


43.02 


16., 30 


46 


47 i44.17 


16.07 !i 44.09 


16.27 


44.02 


16.46 


43.95 


16.65 


47 


48 


45.11 


16.42 i! 45.03 


16.61 


44.96 


16.81 


44.89 


17.01 


48 


49 


46.04 


16.76 !| 45.97 


16.96 


45.90 


17.16 


45.82 


17.36 


49 


50 

s 

c 

X 


46.98 


17.10 


46.91 


17.31 


46.83 


17.51 


46.76 


17.71 


50 

o 

c 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

69^ 


Lat. 
Dfg 


70] 


Deg. 


69| Deg. 


69i Deg. 



TRAVERSE TABLE. 



43 



d 

% 

p 

3 
o 
a 

"51 


20 Deg. 


20t Deg. 


20A Deg. 


201 Deg. 


O 

3 
§ 

51 


Lat. 


Dep. 


Lat. 


Dep. 
17 .'65 


Lat. 


Dep. 


Lat. 


Dep. 


47.92 


17.44 i 


47.35 


47.77 


17.86 


47.69 


18.07 


52 


48.86 


17.79 1 


48.79 


18.00 


48.71 


18.21 


48.63 


18.42 


52 


53 


49.80 


18.13 


49.72 


18.34 


49.64 


18.56 


49.56 


18.78 


53 


54 


50.74 


18.47 1 


50.66 


18.69 


50.58 


18.91 


50.50 


19.13 


54 


55 


51.68 


18.81 1 


51.60 


19.04 


51.52 


19.26 


51.43 


19.49 


55 


56 


52.62 


19.15! 


52.54 


19.38 


52.45 


19.61 


52.37 


19.84 


56 


57 


53.56 


19.50 


63.48 


19.73 


53.39 


19.96 


53.30 


20.19 


57 


58 


54.50 


19.84 


54.42 


20.07 


54.33 


20.31 ! 


54.24 


20.55 


58 


59 


55.44 


20.18 


55.35 


20.42 


55.26 


20.66 1 


55.17 


20.90 


59 


60 

61 


56.38 


20.. 52 


56.29 


20.77 


56.20 
57.14 


21.01 1 
21.36 1 


56.11 


21.26 


60 
61 


57.32 


20.86 


57.23 


21.11 


.57.04 


21.61 


62 


58.26 


21.21 


58.17 


21.46 


58.07 


21.71 


57.98 


21.97 


62 


63 


59.20 


21.55 1 


59.11 


21.81 


59.01 


22.06 


58.91 


22.32 


63 


64 


60.14 


21.89 


60.04 


22.15 


59.95 


22.41 


59.85 


22.67 


64 


65 


61.08 


22.23 


60.98 


22.50 


60.88 


22.76 


60.78 


23.03 


65 


66 


62.02 


22.57 


61.92 


22.84 


61.82 


23.11 


61.72 


23.33 


66 


67 


62.96 


22.92 


62.86 


23.19 


62.76 


23.46 


62.65 


23.74 


67 


68 


63.90 


23.26 


63.80 


23.54 


63.69 


23.81 


63.59 


24.09 


68 


69 


64.84 


23.60 


64.74 


23.88 


64.63 


24.16 


64.52 


24.45 


69 


70 
71 


65.78 
66.72 


23.94 

24.28 


65.67 


24.23 


,65.57 


24.51 


65.46 


24.80 


70 
71 


66.61 


24.5? 


,66.50 


24.86 


66.39 


25.15 


72 


67.66 


24.63 


67.55 


24.92 


167.44 


25.21 


67.33 


25.51 


72 


73 


63.60 j 24.97 


63.49 


25.27 


163.33 


25.57 


68.26 


25.86 


73 


74 


69.54 25.31 : 


69.43 


25.61 


69.31 


25.92 


69.20 


26 . 22 


74 


75 


70.48 25.65 


70.36 


25.96 


70.25 


26.27 


|70.14 


26.57 


75 


76 


71.42,25.99 


71.30 


26.30 


71.19 


26.62 


! 71.07 


28.93 


76 


77 


72.36 


26.34 


72.24 


26.65 


72.12 


26.97 


72.01 


27.28 


77 


78 


73.30 


26.68 


73.18 


27.00 


73.06 


27.32 


! 72.94 


27.63 


78 


79 


74.24 


27.02 


74.12 


27.34 


74.00 


27.67 


1 73.88 


27.99 


79 


80 
81 


75.18 


27.36 


75.06 { 27.69 


74.93 


28.02 


i 74.81 


28.-34 


80 
81 


76.12 


27.70 


75.99 


28.04 


75.87 1 28.37 


j 75.75 


28.70 


S3 


77.05 


28.05 


76.93 


23.33 


76.81 


23.72 


'76.68 


29.05 


82 


>^3 


77.99 


28.39 


77.87 


28.73 


77.74 


29.07 


! 77.62 


29.41 


83 


84 


78.93 


28.73 


78.81 


29.07 


78.68 


29.42 


73.55 


29.76 


84 


85 


79.87 


29.07 


79.75 


29.42 


79.62 


29.77 


! 79.49 


30.11 


85 


86 


80.81 


29.41 


80.68 


29.77 


80.55 


30.12 


80.42 


30.47 


86 


87 


81.75 


29.76 


81.62 


30.11 


81.49 


30.47 


;81.36 


30.82 


87 


88 


82.69 


30.10 


82.56 


30.46 


82.43 


30.82 


82.29 


31.18 


88 


89 


83.63 


30.44 


83.50 


30.80 


83.36 


31.17 


83.23 


31., 53 


89 


90 
91 


84.57 


30.78 


84.44 


31.15 


84.30 


31.52 


[84.16 


31.89 


90 
91 


85.51 


31.12 


85.38 


31.50 


85.24 


31.87 


[85.10 


32.24 


92 


86.45 


31.47 


86.31 


31.84 


86.17 


32.22 


86.03 


32.59 


92 


93 


87.39. 31.81 


87.25 


32.19 


87.11 


32.57 


86.97 


32.93 


93 


94 


88.33' 32.15 


88.19 


32.54 


88.05 


32.92 


87.90 


33.30 


94 


95 


89.27, 32.49 


89.13 


32.88 


88.98 


33.27 


88.84 


33.66 


95 


96 


90.21 


32.83 


90.07 


33.23 


89.92 


33.62 


89.77 


34.01 


96 


97 


91.15 


33.18 


91.00 


33.57 


90.86 


33.97 


90.71 


34.37 


97 


98 


92.09 


33.52 


91.94 


33.92 


91.79 


34.32 


91.64 


.34.72 


98 


99 


93.03 


33.86 


92.88 


34.27 


92.73 


34.67 


92.58 


35.07 


99 


100 

i 

s 

.2 

Q 


1 93.97 


34.20 


93.82 


34.61 


93.67 


35.02 


93.51 


35.43 


100 

u 

c 


1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


! 70 Deg. 


69| Deg. 


69^ Deg 


69i Deg 



44 



TRAVEKSE TAHLE. 



a 
a 
a 


21 
Lat. 


Deg. 
Dep. 


2H Deg. 


211 


Deg. 


21| Deg. 


g 

3 

2 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.93 


0.36 


0.93 


0.36 


0.93 


0.37 


0.93 


0.37 


1 


ii 


1.87 


0.72 


1.86 


0.72 


1.86 


0.73 


1.86 


0.74 


2 


3 


2.80 


1.08 


2.80 


1.09 


2.79 


1.10 


2.79 


1.11 


3 


4 


3.73 


1.43 


3.73 


1.45 


3.72 


1.47 


3.72 


1.48 


4 


6 


4.67 


1.79 


4.66 


1.81 


4.65 


1.83 


4.64 


1.85 


5 


6 


5.60 


2.15 


6.59 


2.17 


5.58 


2.20 


6.57 


2.22 


6 


7 


6.54 


2.51 


6.52 


2.54 


6.51 


2.57 


6.50 


2.59 


7 


8 


7.47 


2.87 


7.46 


2.90 


7.44 


2.93 


7.43 


2.96 


8 


9 


8.40 


3.23 


8.39 


3.26 


8.37 


3.30 


8.36 


3.34 


9 


10 


9.34 


3.58 


9.32 


3.62 


9.30 


3.67 


9.29 


3.71 


10 
11 


U 


10.27 


3.94 


10.25 


3.99 


10.23 


4.03 


10.22 


4.08 


]2 


11.20 


4.30 


11.18 


4.35 


11.17 


4.40 


11.15 


4.45 


12 


13 


13.14 


4.66 


12.12 


4.71 


12.10 


4.76 


12.07 


4.82 


13 


14 


13.07 


5.02 


13.05 


5.07 


13.03 


5.13 


13.00 


5.19 


14 


15 


14.00 


5.38 


13.98 


5.44 


13.96 


5.. 50 


13.93 


5.56 


15 


IG 


14.94 


5.73 


14.91 


5.80 


14.89 


5.86 


14.86 


5.93 


16 


17 


15.87 


6.09 


15.84 


6.16 


15.82 


6.23 


15.79 


6.30 


17 


18 


16.80 


6.45 


16.78 


6.52 


16.75 


6.60 


16.72 


6.67 


18 


19 


17.74 


6.81 


17.71 


6.89 


17.68 


6.96 


17.65 


7.04 


19 


20 


18.67 


7.171 


18.64 


7.25 


18.01 


7.33 


18.. 58 


7.41 


20 


21 


19.61 


7.53 


19.57 


7.61 


19.54 


7.70 


19.50 


7.78 


21 


22 


20.. 54 


7.88 


20.50 


7.97 


20.47 


8.06 


20.43 


8.15 


22 


23 


21.47 


8.24 1 


21.44 


8.34 


21.40 


8.43 1 


21.36 


8.52 


23 


24 


22.41 


8.60 1 


22.37 


8.70 


22.33 


8.80 


22.29 


8.89 


24 


25 


23.34 


8.96 


23.30 


9.06 


23.26 


9.16 


23.22 


9.26 


25 


26 


24.27 


9.32 


24.23 


9.42 


24.19 


9.53 


24.15 


9.63 


26 


27 


25.21 


9.68 


25.16 


9.79 


25.12 


9.90 


25.08 


10.01 


27 


28 


26.14 


10.03 


26.10 


10.15 


26.05 


10.26 


26.01 


10.38 


28 


29 


27.07 


10., 39 


27.03 


10.51 


26.98 


10.63 


26.94 


10.75 


29 


30 
31 


28.01 


10.75 


27.96 


10.87 


27.91 


11.00 


27.86 


11.12 


30 


28.94 


11.11 


28.89 


11.24 


28.84 


11.36 


28.79 


11.49 


31 


32 


29.87 


11.47 


29.82 


11.60 


29.77 


11.73 


29 . 72 


11.86 


32 


33 


30.81 


11.83 


30.76 


11.96 


30.70 


12.09 


30.65 


12.23 


33 


34 


31.74 


12.18 


31.69 


12.32 


31.63 


12.46 


31.58 


12.60 


34 


35 


32.68 


12.54 


32.62 


12.69 


32.56 


12.83 


32.51 


12.97 


35 


36 


33.61 


12.90 


33.55 


13.05 


33.50 


13.19 


33.44 


13.34 


36 


37 


34.54 


13.26 


34.48 


13.41 


34.43 


13.. 56 


34.37 


13.71 


37 


38 


35.48 


13.62 


35.42 


13.77 


35.36 


13.93 


35.29 


14.08 


38 


39 


36.41 


13.98 


36.35 


14.14 


36.29 


14.29 


36.22 


14.45 


39 


40 

41 


37.34 


14.33 


37.28 


14.50 


37.22 


14.66 


37.15 


14.82 


40 
41 


38.28 


14.69 


38.21 


14.86 


38.15 


15.03 


38.08 


15.19 


42 


39.21 


15.05 


39.14 


15.22 


39.08 


15.09 


39.01 


15.56 


42 


43 


40.14 


15.41 


40.08 


15.58 


40.01 


15.76 


39.94 


15.93 


43 


44 


41.08 


15,77 


41.01 


15.95 


40.94 


16.13 


40.87 


16.30 


44 


45 


42.01 


16.13 


41.94 


16.31 


41.87 


16.49 


41.80 


16.68 


45 


46 


42.94 


16.48 


42.87 


16.67 


42.80 


16.86 


42.73 


17.05 


46 


47 


43. SS 


16.84 


43.80 


17.03 


43.73 


17.23 


43.65 


17.42 


47 


48 


44.81 


17.20 


44.74 


17.40 


44.66 


17.59 


44.58 


17.79 


48 


49 


45.75 


17.56 


45.67 


17.76 


45.59 


17.96 


45.51 


18.16 


49 


50^ 

.2 


46.68 


17.92 


46.60 


18.12 


46.52 


18.33 


46.44 


18.53 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 

c 

i 


69] 


Deg. 


68f Deg. 


681 


Deg. 

1 


68i Deg. 



TK>^ VERSE TABLE. 



45 



'51 


21 Deg. 


2U Deg. 


21A Deg. 


211 De.. 


O 

a 
? 

5: 


Lat. 


Dep. 

18.28 


Lat. 


Dep. 


Lat. Dep. 


Lat. 

47.37 


Dep. 
18.90 


47.61 


47.53 


18.48 


47.45 


18.69 


52 


48.55 


18.64 


48.46 


18.85 


I48..38 


19.06 


48.30 


19.27 


52 


63 


49.48 


18.99 


49.40 


19,21 


49.31 


19.42 


49.23 


19.64 


53 


64 


50.41 


19.35 


50.33 


19.57 


50.24 


19.79 


50.16 


20.01 


54 


55 


51.35 


19.71 


51.26 


19.93 


51.17 


20.16 


51.08 


20.38 


55 


56 


52 28 


20.07 


52.19 


20.30 


.52.10 


20.52 


52.01 


20.75 


58' 


57 


53 21 


20.43 


53.12 


20.66 


53.03 


20.89 


.52.94 


21.12 


57 


58 


54.15 


20.79 


54.06 


21.02 


53.96 


21.26 


53.87 


21.49 


58 


59 


55.08 


21.14 


54.99 


21.38 


54.89 


21.62 


,54.80 


21.86 


59 


GO 
61 


56.01 


21.50 


55.92 


21.75 


55.83 


21.99 


55.73 


22.23 


60 


56.95 


21.86 


58.85 


22.11 


58.78 


22.36 


56.66 


22.60 


81 


62 


57.88 


22.22 


57.78 


22.47 


57.69 


22.72 


57.59 


22,97 


62 


63 


58.82 


22.58 j 


58.72 


22.83 


58.62 


23.09 


.58.52 


23.35 


63 


64 


59.75 


22.94 


59.65 


23.20 


59.55 


23.40 


59.44 


23.72 


84 


65 


60.68 


23.29 


60.. 58 


23.56 


60.48 


23.82 


60.37 


24.09 


85 


66 


61.62 


23.65 1 


61.51 


23.92 


01.41 


24.19 


61.30 


24.46 


66 


07 


62.55 


24.01 


62.44 


24.28 


62.34 


24.. 56 


62.23 


24.83 


67 


68 


63.48 


24.37 


63.38 


24.65 


83.27 


24.92 


63.16 


25.20 


68 


69 


64.42 


24.73 


64.31 


25.01 


64.20 


25.29 


64.09 


25.57 


69 


70 
"71 


65.35 


25.09 

25.44 1 


65.24 


25.37 


65.13 


25.66 


65.02 


25.94 


70 
71 


6 b. 28 


66.17 


25.73 


! 66.06 


26.02 


65.95 


26.31 


72 


67.22 


25.80 


67.10 


26.10 


166.99 


26.39 


68.87 


26.68 


72 


73 


68.15 


26.16 


68.04 


26.46 


67.92 


28.75 


87.80 


27.05 


73 


74 


69.08 


26.. 52 


68.97 


26.82 


68.85 


27.12 


68.73 


27.42 


74 


75 


70.02 


26.88 


69.90 


27.18 


69.78 


27.49 


69.68 


27.79 


75 


76 


70.95 


27.24 


70.83 


27.55 


70.71 


27.85 


70.59 


28.16 


76 


77 


71.89 


27.59 


71.76 


27.91 


71.64 


28.22 


71.52 


28.53 


77 


78 


72.82 


27.95 


72.70 


28.27 


72.57 


28.59 


72.45 


28.90 


78 


79 


73.75 


28.31 


73.63 


28.63 


73.50 


28.95 


73.38 


29.27 


79 


80 
81 


74.69 


28.67 


74.56 


29.00 


74.43 


29.32 
29.89 


74.30 


29.84 


80 


75.62 


29.03 


75.49 


29.36 


75.38 


75.23 


30.02 


81 


82 


76.. 55 


29.39 


76.42 


29.72 


76.29 


30.05 


78.16 


30.39 


82 


83 


77.49 


29.74 


77.36 


30.08 


77.22 


30.42 


77.09 


30.76 


83 


84 


78.42 


30.10 


78.29 


30.44 !| 78.16 


30.79 


78.02 


31.13 


84 


85 


79.35 


30.46 


79.22 


30.81 179.09 


31.15 


78.95 


31.50 


85 


86 


80.29 


30.82 


80.15 


31.17 80.02 


31.52 


79.88 


31.87 


86 


87 


81.22 


31.18 


81.08 


31.53 ii 80.95 


31.89 


80.81 


32.24 


87 


88 


82.10 


31 54 


82.02 


31.89 81.88 


32.25 


81.74 


32.61 


88 


89 


83.09 


31.89 


82.95 


32.28 ! 82.81 


32.62 i' 82.66 


32.98 


r.9 


90 
91 


84.02 


32.25 


83.88 


32.62 83.74 


32.99 , 83.59 


33.35 
33 . 72 


90 
'91 


84.96 


32.61 


84.81 


32.98 -84.07 


33.35 i 84.52 


92 


85.89 


32.97 


85.74 


33.34 85.60 


33.72 i; 85.45 


34.09 


92 


93 


86.82 


33.33 


86.68 


33.71 86.53 


34.08 86. 3S 


34.48 


.^3 


94 


87.76 


33.89 


87.61 


34.07 87.46 


34.45 i 87.31 


34.83 


94 


95 


88.69 


34.04 


j 88.. 54 


34.43 88.39 


34.82 1 88.24 


35.20 


95 


96 


89.62 


34.40 


89.47 


34.79 89.32 


35.18 ,89.17 


35.57 


98 


97 


90.. 56 


34.76 


90.40 


35.18 90.25 


35.55 ii 90.09 


35.94 


97 


98 


91.49 


35.12 


91.34 


35. .52 91.18 


35.92 91.02 


30.31 


98 


99 


92.42 


35.48 


92.27 


35.88 92.11 


36.28 ; 91.95 


36.69 


99 


100 

O 

c 


93.36 


35.84 


93.20 


36.24 


93.04 36.85 
Dep. 1 Lat. 

68^ Deg. 


; 92.88 


37.00 


100 


Dep. 


Lat. 


Dep. 


Lat. 


: Dep. 


Lat. 


a 
Q 


69. 


Deg. 


681 


Deg. 


j 68i 

'1 


Dog. 



20 



u> 



TRAVERSE TABLE, 



I 

3 
? 
1 


22 Deg. 


22i Dog. 


221 


Deg. 


22t Deg. 


5 

go' 

3 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 


Dep. 


Lat. 


Dep. 


0.93 


0.37 


0.93 


0.38 


0.92 


0.38 


0.92 


0.39 


2 


1.85 


0.75 


1.85 


0.76 


1.85 


0.77 


1.84 


0.77 


2 


3 


2.78 


1.12 


2.78 


1.14 


2.77 


1.15 


2.77 


1.16 


3 


4 


3.71 


1.50 


3.70 


1.51 


3.70 


1.53 


3.69 


1.55 


4 


5 


4.64 


1.87 


4.63 


1.89 


4.62 


1.91 


4.61 


1.93 


5 


.6 


5.56 


2.25 


5.55 


2.27 


5.54 


2.30 


5.53 


2.32 


6 


7 


6.49 


2.62 


6.48 


2.65 


6.47 


2.68 


6.40 


2.71 


7 


8 


7.42 


3.00 


7.40 


3.03 


7.39 


3.06 


7.38 


3.09 


8 


9 


8.34 


3.37 


8.33 


3.41 


8.31 


3.44 


8.30 


3.48 


9 


10 
11 


9.27 


3.75 


9.26 


3.79 


9.24 


3.83 


9.22 


3.87 


10 


10.20 


4.12 


10.18 


4.17 


10.16 


4.21 


10.14 


4.25 


11 


12 


11.13 


4.50 


11.11 


4.54 


11.09 


4.59 


11.07 


4.64 


12 


13 


12.05 


4.87 


12.03 


4.92 


12.01 


4.97 


11.99 


5.03 


13 


14 


12.98 


5.24 


12.96 


5.30 


12.93 


5.36 


12.91 


5.41 


14 


15 


13.91 


5.62 


13.88 


5.08 


13.86 


5.74 


13.83 


5.80 


15 


16 


14.83 


5.99 


14.81 


6.06 


14.78 


6.12 


14.76 


6.19 


16 


17 


15.76 


6.37 


15.73 


6.44 


15.71 


6.51 


15.68 


6.. 57 


17 


18 


16.69 


6.74 


16.66 


6.82 


16.63 


6.89 


16.60 


6.96 


18 


19 


17.62 


7.12 


17.59 


7.19 


17.55 


7.27 


17.52 


7.35 


19 


20 
21 


18.54 


7.49 


18.51 


7.57 


18.48 


7.65 


18.44 


7.73 


20 


19.47 


7.87 


19.44 


7.95 


19.40 


8.04 


19.37 


8.12 


21 


22 


20.40 


8.24 


20.36 


8.33 


20.33 


8.42 


20.29 


8.51 


^2 


23 


21.33 


8.62 


21.29 


8.71 


21.25 


8.80 


21.21 


8.89 


23 


24 


22.25 


8.99 


22.21 


9.09 


22.17 


9.18 '22.13 


9.28 


24 


25 


23.18 


9.37 


23.14 


9.47' 


23.10 


9.57 i 23.05 


9.67 


25 


26 


24.11 


9.74 


24.06 


9.84 


24.02 


9.95 123.98 


10.05 


26 


27 


25.03 


10.11 


24.99 


10.22 


24.94 


10.33 : 24.90 


10.44 


27 


28 


25.96 


10.49 


25.92 


10.60 


25.87 


10.72 1 25.82 


10.83 


28 


20 


26.89 ' 10.86 


26.84 


10.98 


26.79 


11.10 1 26.74 


11.21 


29 


30 


27.82 i 11.24 


27.77 


11. .36 


27.72 


11.48 i 27.67 


11.60 


30 


31 


28.74 1 11.61 


28.69 


11.74 


28.64 


11.86 i|28.59 


11.99 


31 


32 


29.67 11.99 


29.62 


12.12 


29.56 


12.25 |! 29.51 


12.37 


32 


33 


.•50.60 i 12.36 


30.. 54 


12.50 


30.49 


12.63 30.43 


12.76 


33 


34 


31.52 ! 12.74 


31.47 


12.87 


31.41 


13.01 t: 31.35 


13.15 


34 


35 


32.45 ! 13.11 


32.39 


13.25 


32.34 


13.39 1132.28 


13.53 


35 


36 


33.33 1 13.49 


33.32 


13.63 


33.26 


13.78 133.20 


13.92 


36 


37 


34.31 1 13.86 


34.24 


14.01 


34.18 


14.16 


134.12 


14.31 


37 


38 


35.23 14.24 


35.17 


14.39 


35.11 


14.54 


35.04 


14.70 


38 


39 


36.16 14.61 


36.10 


14.77 


36.03 


14.92 


35.97 


15.08 


39 


40 


37.09 ! 14.98 


37.02 


15.15 


36.96 


15.31 


36.89 


15.47 


40 


4! 


38.01 15.36 


37.95 


15.52 |i 37.88 


15.69 


37.81 


15.86 


41 


42 


.38.94 ; 15.73 


38.87 


15.90 


38.80 


16.07 


138.73 


16.24 


42 


43 


39.87 16.11 


39.80 


16.28 


39 . 73 


16.46 


! 39.65 


16.63 


43 


44 


40.80 ' 16.48 


40.72 


16.66 


40. C5 


16.84 1140.58 


17.02 


44 


45 


41.72 


16.86 


41.65 


17.04 


41.57 


17.22 41.50 


17.40 


45 


46 


42.65 


17.23 


42.57 


17.42 


42.50 


17.60 ,42.42 


17.79 


46 


47 


43.58 


17.61 


43.50 


17.80 


43.42 


17.99 


43.31 


18.18 


47 


48 144.50 


17.98 


44.43 


18.18 


44.35 


18.37 


44.27 


18.56 


48 


49 145.43 


, 18.36 


45.35 


18.55 


45.27 


18.75 


45.19 


18.95 


49 


50 


46.36 


18.73 


46.28 


18.93 


46.19 


19.13 


46.11 


19.34 


60 


§ 

c: 

10 


Dep. 


1 Lat. 


Dep. 


L:.t, 


Dep. 


Lat. i| Dep. 


Lat. 


© 

a 

1 


68 Dog. 


67! 


Deg. 


C71 

1 


Deg. 


67i 


Deg. 



TRAVEKSE TABLE. 



47 



c 

g 
? 

61 


22 Deg. 


22i Deg. 1 


22A Deg. 


221 Deg. 


a 

s 
51 1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


47.29 


19.10 


47.20 


19.31 


47.12 


19.52 


47.03 


19.72 


52 


48.21 


19.48 


48.13 


19.69 


48.04 


19.90 


47.95 


20.11 


52 


53 


49.14 


19.85 


49.05 


20.07 


48.97 


20.28 


48.88 


20.50 


53 


64 


50.07 


20.23 


49.98 


20.45 


49.89 


20.66 


49.80 


20.88 


54 


55 


51.00 


20.60 


50.90 


20.83 


50.81 


21.05 


.50.72 


21.27 


55 


56 


51.92 


20.98 


51.83 


21.20 


51.74 


21.43 


51.64 


21.66 


56 


57 


52.85 


21.35 


52.76 


21.. 58 


.52.66 


21.81 


52.57 


'7,2.04 


57 


58 


53.78 


21.73 


53.68 


21.96 


53.59 


22.20 


.53.49 


22.43 


58 


59 


54.70 


22.10 


54.61 


22.34 


54.51 


22.58 


.54.41 


22.82 


59 


60 
61 


55.63 


22.48 


55.53 


22.72 


55.43 
56.36 


22.96 


55.33 


23.20 


60 

61 


.56.56 


22.85 


56.47 


23.10 


23.34 


56.25 


23.59 


62 


57.49 


23.23 


57.38 


23.48 


57.28 


23.73 


57.18 


23.98 


62 


63 


58.41 


23.60 


58.31 


23.85 


58.20 


24.11 


58.10 


24.38 


63 


64 


.59.34 


23.97 


.59.23 24.23 1 


59.13 


24.49 1 


59.02 


24.75 


64 


65 


60.27 


24.35 


60.16 


24.61 


60.05 


24.87 


59.94 


25.14 


65 


66 


61.19 


24.72 


61.09 


24.99 


60.98 


25.26 


60.87 


25.52 


66 


67 


62.12 


25.10 


62.01 


25.37 


61.90 


25.64 


61.7^ 


25.91 


67 


68 


63.05 


25.47 


62.94 


25 . 75 


62.82 


26.02 


62.71 


26.30 


^I 


69 


63.98 


25.85 


63.86 


26.13 


63.75 


26.41 


63.63 


26.68 


69 


70 
71 


64.90 


26.22 


64.79 


26.51 


64.67 


26.79 


64.55 


27.07 


70 
71 


65.83 


26.60 


65.71 126.88 


65.60 


27.17 


65.48 


27.46 


72 


66.76 


26.97 


66.64 


27.26 


66 52 


27.55 


66.40 


27.84 


72 


73 


67.68 


27.35 


67.56 


27.64 


67.44 


27.94 


67.32 


28.23 


73 


74 


68.61 


27.72 


68.49 


28.02 


68.37 


28.32 


68.24 


28.62 


74 


75 


69.54 


28.10 


69.42 


28.40 


69.29 


28.70 


69.17 


29.00 


^^ 


76 


70.47 


28.47 


70.34 


28.78 


70.21 


29.08 


70.09 


29.39 


76 


77 


71.39 


28.84 


71.27 


29.16 


71.14 


29.47 


71.01 


29.78 


77 


78 


72.32 


29.22 


72.19 


29.53 


72.06 


29.85:171.93 


30.16 


78 


79 


73.25 


29.59 


73.12 


29.91 


72.99 


30.23 


72.85 


30.55 


I^ 


80 
81 


74.17 


29.97 


74.04 


30.29 


73.91 


30.61 


73.78 


30.94 


80 


75.10 


30.34 


74.97 


30.67 


74.83 


31.00 


74.70 


31.32 


82 


76.03 


30.72 


75.89 


31.05 


75.76 


31.38 


75.62 


31.71 


82 


83 


76.96 


31.09 


76.82 


31.43 


76.68 


31.76 


76.54 


,32.10 


1 83 


84 


77.88 


31.47 


77.75 


31.81 


77.61 


32.15 


77.46 


32.48 


84 


85 


78.81 


31.84 


78.67 


32.19 


78.53 


32.53 


78.39 


32.87 


85 


86 


79.74 


32.22 


79.60 


32.56 


79.45 


32.91 


79.31 


33.26 


86 


87 


80.60 


32.59 


80.52 


32.94 


80.38 


33.20 


80.23 


33.64 


i l^ 


88 


81.59 


32.97 


81.45 


33.32 


81.30 


33.68 


81.15 


34.03 


88 


89 


82.52 


33.34 


82.37 


33.70 


82.23 


34.06 


82.08 


34.42 


89 


90 
91 


83.45 


33.71 


83.30 


34.08 


83.15 


34.44 


83.00 


34.80 


90 

i 91 


84.37 


34.09 


9^1.22 


34.46 


84.07 


34.82 


83.92 


35.19 


92 


85.30 


34.46 


85.15 1 34.84 


85.00 


35.21 


84.84 


35.58 


92 


93 


86.23 


34.84 


86.08 35.21 


85.92 


35.59 


85.76 


35.96 


93 


94 


,87.16 


35.21 


87.00-35.59 


86.84 


35.97 


86.69 


36.35 


94 


95 


88.08 


35.59 


87.93 135.97 


87.77 


36.35 


87.61 


36.74 


95 


96 


i 89.01 


35.96 


88.85 1 36.35 


88.69 


36.74 


88.53 


37.12 


96 


97 ' 89.94 


.36.34 


89.78 36.73 


89.62 


37.12 


89.45 


37.51 


! 97 


98 90.86 


36.71 


90.70 37.11 


90.54 


37.50 


90.38 


37.90 


; 98 


99 i 91.79 


37.09 


91.63 37.49 


191.46 


37.89 


91.30 


38.28 


i 99 


100 


1 92.72 


37.46 


92.55 37.86 


[92.39 


38.27 


1 92.22 


38.67 


!100 

1 

i 


6 
o 

c 


Dep. 


Lat. 


Dep. Lat. 

1 


Dep. 


'•"•• 


i! Dep. 

|i 


Lat. 


" 


68 


Degr. 


671 


Deor. 


67^ 


Dog. 


: 67i 


i >•••/. 




48 



tRAVEitsK 'Table. 





23 Deg. 

1 


23k Deg. 


23^ 


Deg. 


m Deg. 




Lat. 


Dcp. 


Lat. 
0.92 


Dop. 

0.39 


Lat. 


Dep. 

0.40 


Lat. 


Dep. 


1 


0.92 


0.39 


0.92 


0.92 


0.40 


1 


2 


1.84 


0.78 


1.84 


0.79 


1.83 


0.80 


1.83 


0.81 


2 


3 


2.76 


1.17 


2.76 


1.18 


2.75 


1.20 


2.75 


1.21 


3 


4 


3.68 


1.56 


3.68 


1.58 


3.67 


1.59 


3.66 


1.61 


4 


5 


4.60 


1.95 


4.59 


1.97 


4.. 59 


1.99 


4.58 


2.01 


6 


6 


6.52 


2.34 


5.51 


2.37 


5.50 


2.39 


5.49 


2.42 


6 


7 


6. '14 


2.74 


6.43 


2.76 


6.42 


2.79 


6.41 


2.82 


7 


8 


7.36 


3.13 


7.35 


3.16 


7.. 34 


3.19 


7.32 


3.22 


8 


9 


8.28 


3.52 


8.27 


3.55 


8.25 


3.59 


8.24 


3.62 


9 


iO 


9.20 


3.91 


9.10 


3.95 


9.17 


3.99 


9.15 


4.03 


10 


11 


10.13 


4.30 


10.11 


4.34 


10.09 


4.39 


10.07 


4.43 


11 


12 


11.05 


4.69 


11.03 


4.74 


11.00 


4.78 


10.98 


4.83 


12 


13 


11.97 


5.08 


11.94 


5.13 


11.92 


5.18 


11.90 


6.24 


13 


14 


12.89 


5.47 


12.86 


5.63 


12.84 


5.58 


12.81 


5.64 


14 


15 


13.81 


6.86 


13.78 


5.92 


13.76 


5.98 


13.73 


6.04 


15 


16 


14.73 


6.25 


14.70 


6.32 


14.67 


6.38 


14.64 


6.44 


16 


17 


15.65 


6.. 64 


15.62 


6.71 


15.59 


6.78 


15.66 


6.85 


17 


18 


16.57 


7.03 


16.54 


7.11 


16.51 


7.18 


16.48 


7.25 


18 


19 


17.49 


7.42 


17.46 


7.50 


17.42 


7.58 


17.39 


7.65 


19 


20 


18.41 


7.81 


18.38 


7.89 


18.. 34 


7.97 


18.31 


8.05 


20 


21 


19.33 


8.21 


19.29 


8.29 


19.26 


8.37 


19.22 


8.46 


21 


22 


20.25 


8.60 


20.21 


8.68 


20.18 


8.77 


20.14 


8.86 


22 


23 21.17 


8.99 


21.13 


9.08 


21.09 


9.17 


21.05 


9.2f) 


23 


24 22.09 


9..?8 ! 


22.05 


9.47 


22.01 


9.67 


21.97 


9.67 


24 


25 123.01 


9.77 


22.97 


9.87 


22.93 


9.97 


22.88 


10.07 


25 


26 


23.93 


10.16 


23.89 


10.26 


23.84 


10.37 


23.80 


10.47 


26 


27 


24.85 


10.55 


24.81 


10.66 


24.76 


10.77 


24.71 


10.87 


27 


28 


25.77 


10.94 


25.73 


11.05 


25.68 


11.16 


25.63 


1.1.28 


28 


29 


26.69 


11.33 


26.64 


11.45 


26.59 


11.56 


26.54 


11.68 


29 


30 


27.62 


11.72 


27.56 


11.84 


27.51 


11.96 


27.46 


12.08 


30 


31 


28.54 


12.11 


28.48 


12.24 


28.43 


12.36 


28.37 


12.49 


31 


32 


29.46 


12.50 


29.40 


12.63 


29.35 


12.76 


29.29 


12.89 


32 


33 


30.38 


12.89 


30.32 


13.03 


30.26 


13.16 


30.21 


13.29 


33 


34 


31.30 


13.28 


31.24 


13.42 


31.18 


13.56 


31.12 


13.69 


34 


35 


32.22 


13.68 


32.16 


13.82 


32.10 


13.96 


32.04 


14.10 


35 


36 


33.14 


14.07 


33.08 


14.21 


33.01 


14.35 


32.95 


14.50 


36 


37 


34.06 


14.46 


34.00 


14.61 


.33.93 


14.75 


33.87 


14.90 


37 


38 


34.98 


14.85 


34.91 


15.00 


34.85 


15.15 


34.78 


15.30 


38 


39 


35.90 


15.24 


35.83 


15.39 


35.77 


15.55 


35.70 


15.71 


39 


40 


36.82 


15.63 


36.75 
37.67 


15.79 


36.68 
37.60 


15.95 


36.61 


16.11 


40 

41 


41 


37.74 


16.02 


16.18 


16.35 


37.63 


16.61 


42 


38.66 


16.41 


38.59 


16.58 


38.. 52 


16.76 


38.44 


16.92 


42 


43 


39.58 


16.80 


39.51 


16.97 


39.43 


17.15 


39.36 


17.32 


43 


44 


40.50 


17.19 


40.43 


17.37 


40.35 


17.. 54 


40.27 


17.72 


44 


45 41.42 


17., 58 


41.35 


17.76 


41.27 


17.94 


141.19 


1.^. ,2 


46 


46 


,42.34 


; 17.97 


,42.26 


, 18.16 


42.18 


18.34 


!42.10 


is.;;3 


46 


47 


143.26 


i 18.36 


143.18 


18.55 


43.10 


18.74 


43.02 


18.93 


47 


48 


144.18 


1 18.76 


144.10 


18.95 


44.02 


19.14 


143.93 


19. na 


48 


49 


145.10 


1 19.15 


1 45.02 


19.34 


44.94 


19.64 


:44.S5 


r).;3 


49 


50 

S 

e 

1 

5 


46.03 
' Dep. 


; 19.54 
1 Lat. 

7V^ 


|| 45.94 


19.74 


45.85 


19.94 
Lat. 


'45.77 


20.14 


50 

03 

U 

c 

rt 


Dop. Lat. 


Dep. 


, Dep. 


Lat. 


67 


!i ■■ 

66J Deg. 


OSi 


Deg. 6G^ 


Deg. 



TRAVERSE TABLE. 



p 

O 

P 


23 Deg. 1 

i 


23i Deg. 


23A Deg. 


231 Deg. 


6 
"51 


Lat. 


Dep. 


Lat. 


Dep. 

20. i3 


Lat. 


Dep. 


Lat. Dep. 

1 


46.95 


19.93! 


46.86 


46.77 


20.34 


46.68 120.54 


52 


47.87 


20.32 1 


47.73 


20 ■^3 


47.69 


20.73 


47.60 


20.94 


52 


53 


48.79 


20.71 


48.70 


20. M2 


48.60 


21.13 


48.51 


21.35 


53 


54 


49.71 


21.10 


49.61 


21. '52 


49.52 


21.53 


49.43 


21.75 


54 


55 


50.63 


21.49 


50.53 


21.71 


.50.44! 21.93 1 


50.34 


22.15 


55 


56 


51.55 


21.88 


51.45 


22.11 


51.36 ! 22.33 


51.26 


22.55 


56 


57 


52.47 


22.27 


52.37 


22 . 50 


52.27 


22.73 


52.17 


22.98 


57 


53 


53.39 


22.68 


53.29 


22.90 


53.19 


23.13 


53.09 


23.36 


58 


59 


54.31 


23.05 


54.21 


23.29 


54.11 


23.53 


54.00 


23.76 


59 


60 
61 


.55.23 


23.44 


55.13 


23.63 


55.02 


23.92 


54.92 


24.16 


60 


56.15 


23.83 


56.05 


24.03 


55.94 


24.32 


55.83 


24.57 


61 


62 


57.07 


24.23 


56.97 


24.47 


56.88 


24.72 


56.75 


24.97 


62 


63 


57.99 


24.62 


57.83 


24.87 


57.77 


25.12 


.57.66 


25.37 63 


64 


53.91 


25.01 


58 . 80 


25.26 


58.69 


25 . 52 


58.58 


25.78 ! 64 


65 


59.83 


25.40 


59.72 


25.66 


59.61 


25.92 


.59.50 


26.18 1 65 


66 


60.75 


25 . 79 


60.64 


26.05 


60.53 


26.32 


60.41 


26.58 I 66 


67 


61.67 


26.18 


61. .56 


2T.45 


61.44 


26 . 72 


61.33 


26.98 


67 


68 


62.59 


26.57 


62.48 


28.84 


62.36 


27.11 


62.24 


27.39 


68 


69 


63.51 


26.96 


63.40 


27.24 


63.28 


27.51 


63.16 


27.79 


69 


70 
71 


61.44 


27.35 


64.32 


27.63 


64.19 


27.91 


64.07 


28.19 


70 


65.36 


27.74 


65.23 


23.03 


65 . 1 1 


23.31 


64.99 


23.59 


71 


72 


66 . 2a 


28.13 


66.15 


28.42 


66.03 


23.71 


65.90 


29.00 


72 


73 


67.20 


28.52 


67.07 


28.82 


66.95 


29.11 
29.51 


66.32 


29.40 


73 


74 


63.12 


28.91 


67.99 


29.21 


67.86 


67.73 


29.80 


74 


75 


69.04 


29.. 30 


63.91 


29.61 


68.73 


29.91 


68.65 


30.21 


75 


76 


69.96 


29.70 


69.83 


30.00 i 


69.70 


30.30 


69.. 56 


30.61 


76 


77 


70.88 


30.09 


70 . 75 


30.40 


70.61 


30.70 


70.43 


31.01 


77 


78 


71.80 


30.43 


n.67 


30.79 


71.53 


31.10 


71.39 


31.41 


78 


79 


72.72 


30.37 


72 . 53 


31.18 


72.45 


31.50 


72.31 


31.82 


79 


80 

81 


73.64 


31.26 


73.50 


31.53 


73.36 


31.90 


73.22 


32.22 


80 
81 


74.56 


31.65 


74.42 


31.97 


74.23 


32.30 


74.14 


32.62 


82 


75.48 


32.04 


75.34 


32.37 


75 . 20 1 32 . 70 


75.03 


33.03 ; 82 


83 


76.40 


32.43 


76.26 


32.76 


76.12 


33.10 


75.97 


33.43 1 83 


84 


77.32 


32.82 


77.18 


33.16 


77.03 


33.49 


76.89 


.33.83! 84 


85 


78.24 


33.21 


73.10 


33.. 55 


77.95 


.33.89 


77.80 


.34.23 


85 


86 


79.16 


33.60 


79.02 


33.95 


78.87 


34.29 


78.72 


34.64 


86 


87 


80.08 


33.99 


79 . 93 


34.34 


79.78 


34.69 


79.63 


35.04 


87 


88 


81.00 


34.38 


80.85 


34.74 


80.70 135.09 


80.55 


35.44 


as 


89 


81.92 


34.78 


81.77 


.35.13 


81.62 


35.49 


81.46 


35.84 i 89 1 


90 
91 


82.85 


35.17 


82.69 


35.53 


82.54 


.35.89 


82. 3S 


36.25 


90 


83.77 


35.56 


83.61 


35.92 


83.45 


36.29 


83.29 


36.65 


"91 


92 


84.69 1 35.95 


84.53 


36.32 


84.37 


36.63 


84.21 


37.05 1 92 


93 


85.61 1 36.34 


85.45 


35.71 


85.29 


37.08 


85.12 


37.46 1 93 


94 


86.53 1 36.73 


86.37 


37.11 1 


86.20 137.48 


86.04 


37.86! 94 


95 


87.45 37.12 


87.29 


37.50 


87. 12 i 37.88 


86.95 


38.26 


95 


96 


83.37 1 37.51 


88.20 


37.90 1 


88.04 j 38.28 


87.87 


38.66 


96 


97 


89.29 '37.90 


89.12 


38.29' 


88.95 38.68 


88.79 


39.07 


97 


98 


90.21 ■ 38.29 


90.04 


33.68 i 


89.87 1 39.08 


89.70 


39.47 


98 


99 


91.13! 38.68 


90.96 


39.08; 


90.79 139.48 


90.62 


.39.87 


99 


100 

1 
,2 


92.05 139.07 
Dep. 1 Lat. 


91.88 


39.47 


91.71 1 39.87 


91.53 


40.27 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep 


Lat. 


i 
s 

.2 

Q 


67 r 


)eg. 


66| De?. 


661 Deg. 


661 oeg. 



60 



TBAVERSE TABLK, 



p 

3 
? 
1 


24Deg. 


24i Deg. 


1 24A Deg. 


241 Deg. 




s 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lai. 


Dep. 


Lat. 


Dep. 


~o79r 


0.41 


0.91 


0.41 


0.91 


0.41 


0.91 


0.42 


2 


1.83 


0.81 


1.82 


0.82 


1.82 


0.83 


1.82 


0.84 


2 


3 


2.74 


1.22 


2.74 


1.23 


2.73 


1.24 


2.72 


1.26 


3 


4| 3.65 


1.63 


3.65 


1.64 


3.64 


1.66 


3.63 


1.67 


4 


5 4.57 


2.03 


4.56 


2.05 


4.55 


2.07 


4.64 


2.09 


5 


6 5.48 


2.44 


5.47 


2.46 


5.46 


2.49 


5.45 


2.51 


6 


7 


6.39 


2.85 


6.38 


2.87 


6.37 


2.90 


6.36 


2.93 


7 


8 


7.31 


I 3.25 


7.29 


3.29 


7.28 


3.32 


7.27 


3.35 


8 


9 


8.22 


i 3.66 


8.21 


3.70 


8.19 


3.73 


8.17 


3.77 


9 


10 
11 


9.14 
10.05 


4.07 
4.47 


9.12 


4.11 
4.52 


9.10 


4.15 


9.08 


4.19 


10 
"11 


10.03 


10.01 


4.56 


9.99 


4.61 


12 


10.96 


4.88 


10.94 


4.93 


10.92 


4.98 


10.90 


6.02 


12 


13 


11.88 


5.29 


11.85 


5.34 


11.83 


5.39 


11.81 


5.44 


13 


14 


12.79 


5.69 


12.76 


5.75 


12.74 


6.81 


12.71 


5.86 


14 


15 


13.70 


6.10 


13.68 


6.16 


13.65 


6.22 


13.62 


6.28 


15 


J6 


14.62 


6.51 


14.59 


6.57 


14.56 


6.64 


14.53 


6.70 


16 


17 


15.53 


6.92 


15.50 


6.98 


15.47 


7.05 


15.44 


7.12 


17 


18 


16.44 


7.32 


16.41 


7.39 


16.38 


7.46 


16.35 


7.54 


18 


19 


J7.36 


7.73 


17.32 


7.80 


17.29 


7.88 


17.25 


7.95 


19 


20 

21 


18.27 


8.13 


18.24 


8.21 


18.20 


8.29 


18.16 


8.37 


20 
21 


19.18 


8.54 


19.15 


8.63 


19.11 


8.71 


19.07 


8.79 


22 


20.10 


8.95 


20.06 


9.04 


20.02 


9.12 


19.98 


■9.21 


22 


23 


21.01 


9.35 


20.97 


9.45 


20.93 


9.. 54 


20.89 


9.63 


23 


24 


21.93 


9.76 


21.88 


9.86 


21.84 


9.95 


21.80 


10.05 


24 


25 


22.84 


10.17 


22.79 


10.27 


22.75 


10.37 


22.70 


10.47 


25 


26 


23.75 


10.58 


23.71 


10.68 


23.66 


10.78 


23.61 


10.89 


26 


27 


24.67 


10.98 


24.62 


11.09 


24.57 


11.20 


24.52 


11.30 


27 


28 


25.58 


11.39 


25.53 


11.50 


25.48 


11.61 


25.43 


11.72 


28 


29 


26.49 


11.80 


26.44 


11.91 


26.39 


12.03 


26.34 


12.14 


29 


30 
31 


27.41 


12.20 


27.35 


12.32 


27.30 


12.44 


27.24 


12.56 


30 
31 


28.32 


12.61 


28.26 


12.73 


28.21 


12.86 


28.15 


12.68 


32 


29.23 


13.02 


29.18 


13.14 


29.12 


13.27 


29.06 


13.40 


32 


33 


30.15 


13.42 


30.09 


13.55 


30.03 


13.68 


29.97 


13.82 


33 


34 


31.06 


13.83 


31.00 


13.96 


30.94 


14.10 


30.88 


14.23 


34 


35 


31.97 


14.24 


31.91 


14.38 


31.85 


14.51 


31.78 


14.65 


35 


36 


32.89 


14.64 


32.82 


14.79 


32.76 


14.93 


32.69 


15.07 


36 


37 


33.80 


15.05 


33.74 


15.20 


33.67 


1 5.. 34 


33.60 


15.49 


37 


38 


34.71 


15.46 


34.65 


15.61 


34.58 


15.76 


34.51 


15.91 


38 


39 


35.63 


15.86 


35.56 


16.02 


35.49 


16.17 


35.42 


16.33 


39 


40 
41 


36.54 16.27 1 


36.47 


16.43 


36.40 


16.59 


36.33 


16.75 


40 
41 


37.46 i 


16.68 


37.38 


16.84 


■37T31 


17.00 


37.23 


17.16 


42 


38.37 


17.08 


38.29 


17.25 


38.22 


17.42 


38.14 


17.58 


42 


43 


39.28 


17.49 


39.21 


17.60 


39.13 


17.83 


39.05 


18.00 


43 


44 


40.20 1 17.90 


40.12 


18.07 


40.04 


18.25 


39.96 


18.42 


44 


45 


41.11 118.30 


41.03 


18.48 


40.95 


18.66 


40.87 


18.84 


45 


46 


42.02 


18.71 


41.94 


18.89 


41.86 


19.08 


41.77 


19.26 


46 


47 


42.94 


19.12 


42.85 


19.30 


42.77 


19.49 


42.68 


19.68 


47 


48 


43.85 


19.52 


43.76 


19.71 


43.68 


19.91 


43.59 


20.10 


48 


49 


44.76 


19.93 


44.68 


20.13 


44.59 


20.32 


44.50 


20.51 


49 


50 

y 
1 


45.68 120.34 


45.59 


20.. ^.4 


45.. 50 


20.73 


45.41 
Dep. 


20.93 
Lat. 


50 

6 


en 

a 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


66 Deg. 


65f DejT. 

! 


65^ 1 


3e.. 


65i Deg. 



TRAVF.USF. TAHLi?:. 



51 



m' 

P 

51 


24 Deg. 


24i Deg. 


24i 


Deg. 


24| Deg. 


C 
51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


46.59 


20.74 


46.50 


20.95 


46.41 


21.15 


46.32 


21.35 


52 


47.50 


21.15 


47.41 


21.36 


47.32 


21.56 


47.22 


21.77 


52 


53 


48.42 


21.56 


48.32 


21.77 


48.23 


21.98 


48.13 


23.19 


53 


54 


49.33 


21.96 


49.24 


22.18 


49.14 


22.39 


49.04 


22.61 


54 


55 


50.24 


22.37 


50.15 


22.59 


50.05 


22.81 


49.95 


23.03 


55 


56 


51.16 


22.78 


51.06 


23.00 


50.96 


23.22 


50.86 


23.44 


56 


57 


52.07 


23.18 


51.97 


23.41 


51.87 


23.64 


51.76 


23.86 


57 


58 


52.99 


23.59 


52.88 


23.82 


52.78 


24.05 


52.67 


24.28 


58 


59 


53.90 


24.00 


53.79 


24.23 


53.69 


24.47 


53.58 


24.70 


59 


60 
61 


54.81 


24.40 


54.71 


24.64 


54.60 


24.88 


54.49 


25.12 


60 
61 


55.73 


24.81 


55.62 


35.05 


55.51 


25.30 


.55.40 


25.54 


62 


56.64 


25.22 


56.53 


25.46 


56.42 


25.71 


56.30 


25.96 


62 


63 


57.55 


25.62 


57.44 


25.88 


57.33 


26.13 


.57.21 


23.38 


63 


64 


58.47 


26.03 


58.35 


26.29 


,58.24 


26.54 


.58.12 


26.79 


64 


65 


59.38 


26.44 


59.26 


26.70 


59.15 


26.96 


59.03 


27.21 


65 


66 


60.29 


26.84 


60.18 


27.11 


60.06 


27.37 


59.94 


27.63 


66 


67 


61.21 


27.25 


61.09 


27.52 


60.97 


27.78 


60.85 


28.05 


67 


68 


62.12 


27.66 


02.00 


27.93 


61.88 


28.20 


61.75 


28.47 


68 


69 


63.03 


28.06 


62.91 


28.34 


62.79 


28.61 


62.66 


28.89 


69 


70 
71 


63.95 


28.47 


63. &2 


28.75 


63.70 


29.03 


63.57 


29.31 


70 

71 


64.86 


28.88 


64.74 


29.16 


64.61 


29.44 


04.48 


29.72 


72 


65.78 


29.28 


65.65 


29.57 


65.52 


29.86 


65.39 


30.14 


72 


73 


66.69 


29.69 


66.56 


29.98 


66.43 


30.27 


66.29 


30.56 


73 


74 


67.60 


30.10 


67.47 


30.39 


67.34 


30.69 


67.20 


30.98 


74 


75 


68.. 52 


.30.51 


68.38 


30.80 


68.25 


31.10 


i 68.11 


31.40 


75 


76 


69.43 


30.91 


69.29 


31.21 


69.16 


31.52 


i 69.02 


31.82 


76 


77 


70.34 


31.32 


70.21 


31.63 


70.07 


31.93 


69.93 


32.24 


77 


78 


71.26 


31.73 


71.12 


32.04 


70.98 


.32.35 


i 70.84 


32.66 


78 


79 


72.17 


32.13 


72.03 


32.45 


71.89 


32.76 


171.74 


33.07 


79 


80 

81 


73.08 


.32.54 


72.94 


32.86 


72.80 


33.18 


172.65 


33.49 


80 
81 


74.00 


32.95 


73.85 


33.27 


73.71 


33.59 


j 73.56 


33.91 


82 


74.91 


33.35 


74.76 


33.68 


74.62 


34.00 


! 74.47 


34.33 


82 


83 


75.82 


33.76 


75.68 


34.09 


75.53 


34.42 


75.38 


34.75 


83 


84 


76.74 


34.17 


70.59 


34.50 


76.44 


34.83 


76.28 


35.17 


84 


85 


77.65 


34.57 


77.50 


34.91 


77.35 


35.25 


177.19 


35.59 


85 


86 


78.56 


34.98 


78.41 


35.32 


78 26 


35.66 


78.10 


36.00 


86 


87 


79.48 


35.39 


79.32 


35.73 


79.17 


36.08 


79.01 


36.42 


87 


88 


80.39 


35.79 


80.24 


36.14 


80.08 


36.49 


79.92 


36.84 


88 


89 


81.31 


36.20 


81.15 


36.55 


80.99 


36.91 


80.82,37 26 


S9 


90 
'91 


82.22 


36.61 


82.06 


36.96 


81.90 
82.81 


37.32 


81.73 
82.64 


37.68 


90 
9l' 


83.13 


37.01 


82.97 


.37.38 


37.74 


38.10 


92 


84.05 


37.42 


83.88 


37.79 


83.72 


38.15 


83.55 


38.. 52 


92 


93 


84.96 


37.83 


84.79 


38.20 


84.63 


38.57 


84.46 


38.94 


93 


94 


85.87 


38.23 


85.71 


38.61 


85.54 


38.98 


85.37 


39.35 


94 


95 


86.79 


38.64 


86.62 


39.02 


86.45 


39.40 


86.27 


39.77 


95 


96 


87.70 


39.05 


87.53 


39.43 


87.36 


39.81 


87.18 


40.19 


96 


97 


88.61 


39.45 


88.44 


39.84 


88.27 


40.23 


88.09 


40.61 


97 


98 


89.53 


39.86 


89.35 


40.25 


89.18 


40.64 


89.00 


41.03 


98 


99 


90.44 


40.27 


90.26 


40.66 


90.09 


41.05 


89.91 


41.45 


99 


100 

6 
o 

c 

xn 

± 


91.35 
Dep. 


40.67 


91.18 


41.07 


91.00 


41.47 


90.81 


41.87 


100 

d 
c 

1 
a. 

Q 


Lat. 


Dop. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


63 De;:-. 


r 

' 65| 


Deg. 


e5\ Deg. 


65\ Deg. 



62 



TRAVJbRSE TAIJLE. 



S' 

p 

a 
o 
re 


23 Deg. ' 


25i Deg. 


25h Deg. 


25 f Deg. 


CO 

2 
J 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.91 


0.42 


O.SO 


0.43 


0.90 


0.43 


0.90 


0.43 


2 


1.81 


0.85 


1.81 


0.85 


1.81 


0.86 


1.80 


0.87 


2 


3 


2.72 


1.27 


2.71 


1.28 


2.71 


1.29 


2.70 


1.30 


3 


4 


3.63 


1.69 


3.62 


1.71 


3.61 


1.72 


3.60 


1.74 


4 


5 


4.53 1 2.11 


4.52 


2.13 


4.51 


2.15 


4.50 


2.17 


5 


6 


5.44 


2.54 


5.43 


2.56 


5.42 


2.58 


5.40 


2.61 


6 


7 


6.34 


2.96 


G.33 


2.99 


6.32 


3.01 


6.30 


3.04 


7 


8 


7.25 


3.38 


7.24 


3.41 


7.22 


3.44 


7.21 


3.48 


8 


9 


8.16 


3.80 


8.14 


3.84 


8.12 


3.87 


8.11 


3.91 


9 


10 


9.06 


4.23 


9.04 


4.27 


9.03 


4.31 


9.01 


4.34 

4.78 


10 
11 


11 


9.97 


4.65 


9.95 


4.69 


9.93 


4.74 


9.91 


12 


10.88 


5.07 


10.85 


5.12 


10.83 


5.17 


10.81 


5.21 


12 


13 


11.78 


5.49 


11.76 


5.55 


11.73 


5.60 


11.71 


5.65 


13 


14 


12. G9 


5.92 


12.66 


5.97 


r^.64 


6.03 


12.61 


6.08 


14 


15 


13.r,9 


6.34 


13.57 


6.40 


13.54 


6.46 


13.51 


6.. 52 


15 


16 


14.50 


6.76 


14.47 


6.83 


14.44 


6.89 


14.41 


6.95 


16 


17 


15.41 


7.18 


15.38 


7.25 


15.34 


7.32 


15.31 


7.. 39 


17 


18 


16.31 


7.61 


16.28 


7.68 


16.25 


7.75 


16.21 


7.82 


18 


19 


17.22 


8.03 


17.18 


8.10 


17.15 


8.18 


17.11 


8.25 


19 


20 
21 


18.13 
19.03 


8.45 


18.09 


8.53 


18.05 


8.61 


18.01 


8.69 


20 

21 


8.87i 


18.99 


8.96 


18.95 


9.04 


18.91 


9.12 


22 


19.94 


9.30 


19.90 


9.38 


19.86 


9.47 


19.82 


9.56 


22 


23 


20.85 


9.72! 


20.80 


9.81 


20.76 


9.90 


20.72 


9.99 


23 


24 


21.75 


lO.Hi 


21.71 


10.24 


21.66 


10.33 


21.62 


10.43 


24 


25 


22.66 


10.57 


22.61 


10.66 


22.56 


10.76 


22.52 


10.86 


25 


2G 


23.56 


10.99 


23.52 


11.09 


23.47 


11.19 


23.42 


11.30 


26 


27 


24.47 


11.41 


24.42 


11.52 


24.37 


11.62 


24.32 


11.73 


27 


28 


25 . 38 


11.83 


25.32 


11.94 


25.27 


12.05 


25.22 


12.16 


28 


2S 


2G.28 


12.26 


26.23 


12.37 


26.17 


12. 4S 


26.12 


12.60 


29 


30 
31 


27.19 


12.68 


27.13 


12.80 


27.08 


12.92 


27.02 
27.92 


13.03 
13.47 


30 
31 


2S.10 


13.10 


28.04 


13.22 


27.98 


13.35 


32 


29.00 


13.52 


28.94 


13.65 


28.88 


13.78 


28.82 


13.90 


32 


33 


29.91 


13.95 


29.85 


14.08 


29.79 


14.21 


29.72 


14.34 


33 


34 


30.81 


14.37 


30.75 


14.50 


30.69 


14.64 


30.62 


14.77 


34 


35 


31.72 


14.79 


31.66 


14.93 


31.59 


15.07 


31.52 


15.21 


35 


36 


32 . 63 


15.21 


32.56 


15.36 


32.49 


15.. 50 


32.43 


15.64 


36 


37 


33.53 


15.64 


33.46 


15.78 


33.40 


15.93 


33.33 


16.07 


37 


38 


34.44 


16.06 


34.37 


16.21 


34.30 


16.36 


34.23 


16.51 


38 


39 


35.35 


16.48 


35.27 


16.64 


35.20 


16.79 


35.13 


16.94 


39 


40 
41 


36.25 


16.90 


36.18 


17.06 


36.10 


17.22 


,36.03 


17.38 
17.81 


40 
41 


37.16 


17.33 


37.08 


17.49 


37.01 


17.65 


36.93 


42 


38.06 


17.75 


37.99 


17.92 


37.91 


18.08 


37.83 


18.25 


42 


43 


38.97 


18.17 


38.89 


18.34 


38.81 


18.51 


38.73 


18.68 


43 


44 


39.88 


18.60 


39.80 


18.77 


39.71 


18.94 


39.63 


19.12 


44 


45 


40.78 


19.02 


40.70 


19.20 


40.62 


19.37 


40.53 


19.55 


45 


46 


41.69 


19.44 


41.60 


19.62 


41.52 


19.80 


41.43 


19.98 


46 


47 


42.60 


19.86 


42.51 


20.05 


42.42 


20.23 


42.33 


20.42 


47 


48 


43.50 


20.29 


43.41 


20.48 


43.32 


20.66 


43.23 


20.85 


48 


49 


44.41 


20.71 


44.32 


20.90 


44.23 


21.10 


44.13 


21.29 


49 


50 


45.32 


21.13 


45.22 


21.33 


45.13 


21.63 


45.03 


21.72 


50 


i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


03 
O 

c 
C 


65 Deg. 


64| Deg. 


64i 


Deg. 


64i Deg. 



TRAVERSE TABLE. 



63 





^' 

p 

a 

? 
51 


25 Deg. 


25i Deg. 


25i Deg. 


25| Deg. 


5 

o 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


46.22 


21.55 


46.13 


21.75 


46.03 


21.96 


45.94 


22.16 


51 


52 


47.13 


21.98 


47.03 


22.18 


46.93 


22.39 


46.84 


22.59 


52 


53 


48.03 


22.40 


47.94 


22.01 


47.84 


22.82 


47.74 


23.03 


53 


54 


48.94 


22.82 


48.84 


23.03 


48.74 


23.25 


48.64 


23.46 


54 


55 


49.85 


23.24 


49.74 


23.46 


49.64 


23.68 


49.54 


23.89 


55 


56 


50 . 75 


23.67 


50.65 


23.89 


50.. 54 


24.11 


50.44 


24.33 


56 


57 


51.66 


24.09 


51.55 


24.31 


51.45 


24.54 


51.34 


24.76 


57 


58 


.52.57 


24.51 


52.46 


24.74 


.52.35 


24.97 


52.24 


25.20 


68 


59 


53.47 


24.93 


53.36 


25.17 


53.25 


25.40 


53.14 


25.63 


59 


60 
61 


54.38 


25.36 


54.27 


25.59 


54.16 


25.83 


54.04 


26.07 


60 


55.28 


25.78 


55.17 


26.02 


55.06 


26.26 


54.94 


26.50 


61 


62 


56.19 


26.20 


56.08 


26.45 


55.96 


^.69 


55.84 


26.94 


62 


63 


57.10 


26.62 


.56.98 


26.87 


56.86 


27.12 


.56.74 


27.37 


63 


64 


58.00 


27.05 


57.89 


27.30 


57.77 


27.55 


57.64 


27.80 


64 


65 


58.91 


27.47 


58.79 


27.73 


58.67 


27.98 


58.. 55 


28.24 


65 


66 


59.82 


27.89 


59.69 


28.15 


59.57 


28.41 


.59.45 


28.67 


66 


67 


60.72 


28.32 1 


60.60 


28.58 


60.47 


28.84 


60.35 


29.11 


67 


68 


61.63 


28.74 


61.50 


29.01 


61.38 


29.27 


61.25 


29.54 


68 


69 


62.54 


29.16 


62.41 


29.43 


62.28 


29.71 


62.15 


29.98 


69 


70 
71 


63.44 


29.58 


63.31 


29.86 


63.18 


30.14 


63.05 


30.41 


70 
71 


64.35 


30.01 


64.22 


30.29 


64.08 


30.57 


63.95 


30.85 


72 


65.25 


30.43 


65.12 


30.71 


64.99 


31.00 


64.85 


31.28 


72 


73 


66.18 


.30.85 


66.03 


31.14 


65.89 


31.43 


65.75 


31.71 


73 


74 


67.07 


31.27 


66.93 


31.57 


66.79 


31.86 


66.65 


32.15 


74 


75 


67.97 


31.70 


67.83 


31.99 


67.69 


32.29 


67.55 


32.58 


75 


76 


68.88 


32.12 


68.74 


32.42 


68.60 


32.72 


68.45 


33.02 


76 


77 


69.79 


32.54 


69.64 


32.85 


69.50 


33.15 


69.35 


33.45 


77 


78 


70.69 


32.96 


70.55 


33.27 


70.40 


33.. 58 


70.25 


33.89 


78 


79 


71.60 


33.39 


71.45 


33.70 


71.30 


34.01 


71.16 


34.32 


79 


80 

81 


72.50 
73.41 


33.81 


,72.36 
73.26 


34.13 


72.21 


34.44 


72 06 


34.76 


80 


34.23 


34.55 


73.11 


34.87 


72.96 


35.19 


81 


82 


74.32 


34.65 


74.17 


34.98 


74.01 


35.30 


73.86 


35.62 


82 


83 


75.22 


35.08 


75.07 


35.41 


74.91 


35.73 


74.76 


38.06 


83 


84 


76.13 


35.50 


75.97 


.35.83 


75.82 


36.16 


75.66 


36.49 


84 


85 


77.04 


35.92 


76.88 


36.26 


76.72 


36.59 


76.56 


36.93 


85 


86 


77.94 


36.35 


77.78 


36.68 


77.62 


37.02 


77.46 


37.36 


86 


87 


78.85 


36.77 


78.69 


37.11 


78.52 


37.45 


78.36 


37.80 


87 


88 


79.76 


37.19 


79.59 


37.54 


79.43 


37.88 


79.26 


38.23 


88 


89 


80.66 


37.61 


80.50 


37.96 


80.33 


.38.32 


80.16 


38.67 


89 


90 
91 


81.57 


38.04 


81.40 


38.39 


81.23 


38.75 


81.06 


39.10 


90 


82.47 


38.46 


82.31 


38.82 


82.14 


39.18 


81.96 


39.53 


91 


92 


83.38 


38.88 


83.21 


39.24 


83.04 


39.61 


82.86 


39.97 


92 


93 


84.29 


39.30 


84.11 


39.67 


83.94 


40.04 


83.70 


40.40 


93 


94 


85.19 


39.73 


85.02 


40.10 


84.84 


40.47 


84.67 


40.84 


94 


95 


86.10 


40.15 


85.92 


40.52 


85.75 


40.90 


85.57 


41.27 


95 


96 


87.01 


40.57 


86.83 


40.95 


86.65 


41.33 


86.47 


41.71 


96 


97 


87.91 


40.99 


87.73 


41.38 


87.55 


41.76 


87.37 


42.14 


97 


98 


88.82 


41.42 


88.64 


41.80 


88.45 


42.19 


88.27 


42.58 


98 


99 


89.72 


41.84 


89.54 


42.23 


89.36 


42.62 


89.17 


43.01 


99 


100 

6 

.2 

Q 


90.63 


42.26 


90.45 


42.66 


90.26 


43.05 


90.07 


43.44 


100 

g 

c 

d 

.2 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


65 Deg. 


64| Deg. 


64i Deg. 


m Dog. 



54 



TRAVERSE TABLE. 



1 


26 Deg. 


264 Deg. 


26h Deg. 


26| Deg. 


a 

a 

s 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


1 


0.90 


0.44 


0.90 


0.44 


0.89 1 0.45 


0.89 


0.45 


1 


2 


1.80 


0.88 


1.79 


0.88 


1.79 


0.89 


1.79 


0.90 


2 


3 


2.70 


1.32 


2.69 


1.33 


2.68 


1.34 


2.68 


1.35 3 1 


4 


3.60 


1.75 


3.59 


1.77 


3.58 


1.78 


3.57 


1.80 ! 4| 


5 


4.49 


2.19 


4.48 


2.21 


4.47 


2.23 


4.46 


2.25 


5 


6 


5.39 


2.63 


5.38 


2.65 


5.37 


2.68 


5.36 


2.70 


6 


7 


6.29 


3.07 


6.28 


3.10 


6.26 


3.12 


6.25 


3.15 


7 


8 


7.19 


3.51 


7.17 


3.. 54 


7.16 


3.57 


7.14 


3.60 


8 


9 


8.09 


3.95 


8.07 


3.98 


8.05 


4.02 


8.04 


4.05 


9 


10 


8.99 


4.38 


8.97 


4.42 


8.95 


4.46 


8.93 


4.50 


10 
11 


11 


9.89 


4.82 


9.87 


4.87 


9.84 


4.91 


9.82 


4.95 


12 


10.79 


5.26 


10.76 


5.31 


10.74 


5.35 


10.72 


5.40 


12 


13 


11.68 


5.70 


11.66 


5.75 


11.63 


5.80 


11.61 


5.85 


13 


14 


12.58 


6.14 


12.56 


6.19 


12.53 


6.25 


12.50 


6.30 


14 


15 


13.43 


6.58 


13.45 


6.63 


13.42 


6.69 


13.39 


6.75 


15 


16 


14.38 


7.01 


14.35 


7.08 


14.32 


7.14 


14.29 


7.20 


16 


17 


15.28 


7.45 


15.25 


7.52 


15.21 


7.59 


15.18 


7.65 


17 


18 


16.18 


7.89 


16.14 


7.96 


16.11 


8.03 


16.07 


8.10 


18 


19 


17.08 


8.33 


17.04 


8.40 


17.00 


8.48 


16.97 


8.55 


19 


20 

21 


17.98 


8.77 


17.94 


8.85 


17.90 


8.92 


17.86 


9. GO 


20 
21 


18.87 


9.21 


18.83 


9.29 


18.79 


9.37 


18.75 


9.45 


22 


19.77 


9.64 


19.73 


9.73 


19.09 


9.82 


19.65 


9.90 


22 


23 


20.67 


10.08 


20.63 


10.17 


20.58 


10.26 


20.54 


10.35 


23 


24 


21.57 


10.52 


21.52 


10.61 


21.48 


10.71 


21.43 


10.80 


24 


25 


22.47 


10.96 


22.42 


11.06 


22.37 


11.15 


22.32 


11.25 


25 


26 


23.37 


11.40 


23.32 


11.50 


23.27 


11.60 


23.22 


11.70 


26 


27 


24.27 


11.84 


24.22 


11.94 


24.16 


12.05 


24.11 


12.15 


27 


28 


25.17 


12.27 


25.11 


12.38 


25.06 


12.49 


25.00 


12.60 


28 


29 


26.06 


12.71 


26.01 


12.83 


25.95 


12.94 


25.90 


13.05 


29 


30 


26.96 


13.15 


26.91 


13.27 


26.85 


13.39 
13.83~ 


26.79 


13.50 


30 


31 


27.86 


13.59 


27.80 


13.71 


27.74 


27.68 


13.95 


31 


32 


28.76 


14.03 


28.70 


14.15 


28.64 


14.28 


28.58 


14.40 


32 


33 


29.66 


14.47 


29.60 


14.60 


29.. 53 


14.72 


29.47 


14.85 


33 


34 


30.56 


14.90 


30.49 


15.04 


30.43 


15.17 


30.36 


15.30 


34 


35 


31.46 


15.34 


31.39 


15.48 


31.32 


15.62 


31.25 


15.75 


35 


36 


32.36 


15.78 


32.29 


15.92 


32.22 


16.06 


32.15 


16.20 


36 


37 


33.26 


16.22 


.33.18 


16.36 


33.11 


16.51 


33.04 


16.65 


37 


38 


34.15 


16.66 


34.08 


16.81 


34.01 


16.96 


33.93 


17.10 


38 


39 


35.05 


17.10 


34.98 


17.25 


34.90 


17.40 


34.83 


17.55 


39 


40 


35.95 


17.53 


35.87 


17.69 


35.80 


17.85 


35.72 


18.00 


40 


41 


36.85 


17.97 


36.77 


18.13 


36.69 


18.29 


36.61 


18.45 


41 


42 


37.75 


18.41 


37.67 


18.58 


37.59 


18.74 


37.51 


18.90 


42 


43 


38.65 


18.85 


38.57 


19.02 


38.48 


19.19 


38.40 


19.. 35 


43 


44 


39.55 


19.29 


39.46 


19.46 


39.38 


19.63 


39.29 


19.80 


44 


45 


40.45 


19.73 


40.36 


19.90 


40.27 


20.08 


40.18 


20.25 


45 


46 


41.34 


20.17 


41.26 


20.35 


41.17 


20.53 


41.08 


20 . 70 


46 


47 


43.24 


20.60 


42.15 


20.79 


42.06 


20.97 


41.97 


21.15 


47 


48 


43.14 


21.04 


43.05 


21.23 


42.96 


21.42 


42.86 


21.60 


48 


49 


44.04 


21.48 


43.95 


21.67 


43.85 


21.86 


43.76 


22.05 


49 


50 

8 


4^.94 


21.92 


44.84 


22.11 


44.75 


22.31 


44.65 


22.50 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 


1 














Q 












.s 


64 Deg. 


631 


Deg. 


6Sh Deg. 


63t Deg. 



TRAVERSE TABLE. 



55 



s 

s. 
p 


26 Dog. 


26k Deg. 


26i Deg. 


26| 


Deg. 


i 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


45.84 


22.36 


45.74 


22.56 


45.64 


22.76 


15T64 


22.96 


51 


52 


46.74 


22.80 


46.64 


23.00 


46.54 


23.20 


46.43 


23.41 


52 


53 


47.64 


23.23 


47.53 


23.44 


47.43 


23.65 


47-33 


23.88 


53 


54 


48.53 


23.67 


48.43 


23.88 


48.33 


24.09 1 48 22 


24.31 


54 


55 


49.43 


24.11 


49.33 


24.33 


49.22 


24.54 49.11 


24.76 


55 


56 


50.33 


24.55 


50.22 


24.77 


50.12 


24.09 


60.01 


25.21 


56 


57 


51.23 


24.99 


51.12 


25.21 


51.01 


25.43 


50.00 


25.66 


57 


58 


52.13 


25.43 


52.02 


25.65 


51.91 


25 88 


51.79 


26.11 


58 


59 


53.03 


25.86 


52.92 


26.09 


52.80 


26.33 


52.69 


26.56 


59 


60 
61 


53.93 


26.30 


53.81 


26.54 


53.70 


26-77 


.53.58 


27.01 


60 


54.83 


26.74 


54.71 


26.98 


54.59 


27.22 


54.47 


27.46 


61 


62 


55.73 


27.18 


55.61 


27.42 


55.49 


27.66 


55.36 


27.91 


62 


63 


56.62 


27.62 


56.50 


27.86 


56.38 


28.11 


56.26 


28.36 


63 


64 


57.52 


23.06 


57.40 


28.31 


57.28 


28.56 


57.15 


28.81 


64 


65 


58.42 


28.49 


58.30 


28.75 


58.17 


29.00 


58.04 


29.26 


65 


66 


59.32 


28.93 


59.19 


29.19 


59.07 


29.45 


58.94 


29.71 


66 


67 


60.22 


29.37 


60.09 


29.63 


59.96 


29.90 


59.83 


30.16 


67 


68 


61.12 


29.81 


60.99 


30.08 


60.86 


30.34 


60.72 


30.61 


68 


G9 


62.02 


30.25 


61.88 


30.52 


61.75 


30.79 


61.62 


31.06 


69 


70 
71 


62.92 


30.69 


62.78 


30.96 


62.65 


31.23 


62.51 


31.51 


70 


63.81 


31.12 


63.68 


31.40 


63.54 


31.68 


63.40 


31.96 


71 


72 


64.71 


31.56 


64.57 


31.84 


64.44 


32.13 


64.29 


32.41 


72 


73 


65.61 


32.00 


65.47 


32.29 


65.33 


32.57 


65.19 


32.86 


73 


74 


66.51 


32.44 


66.37 


32.73 


66.23 


33.02 


66.08 


33.31 


74 


75 


67.41 


32.88 


67.27 


33.17 


67.12 


33.46 


66.97 


33.76 


75 


76 


68.31 


33.32 


68.16 


33.61 


68.01 


33.91 


67.87 


34.21 


76 


77 


69.21 


33.75 


69.06 


34.06 


68.91 


34.36 


68.76 


34.66 


77 


78 


70.11 


34.19 


69.96 


34.. 50 


69.80 


34.80 


69.65 


35.11 


78 


79 


71.00 134.63 


70.85 


34.94 


70.70 


35.25 


70.55 


35.56 


79 


80 
81 


71.90 
72.8.0 


35.07 
35.51 


71.75 


35.38 


71.59 


35.70 


71.44 


36.01 


80 


72.65 


35.83 


72.49 


36.14 


72.33 


36.46 


81 


82 


73.70 


35.95 


73.54 


36.27 


73.38 


36.. 59 


73.22 


36.91 


82 


83 


74.60 


36.38 


74.44 


.36.71 


74.28 


37.03 


74.12 


37.36 


83 


84 


75.50 


36.82 


75.34 


37.15 


75.17 


37.48 


75.01 


.37.81 


84 


85 


76.40 


37.26 


76.23 


37.59 


76.07 


37.93 


75.90 


38.26 


85 


86 


77.30 


37.70 


77.13 


38.04 


76.96 


38.37 


76.80 


38.71 86| 


87 


78.20 


38.14 


78.03 


38.48 


77.86 


38.82 


77.69 


39.16 


87 


88 


79.09 


38.58 


78.92 


.38.92 


78.75 


39.27 


78.58 


39.61 


88 


89 


79.99 


39.01 


79.82 


39.36 


79.65 


39.71 


79.48 


40.06 


89 


90 
91 


80.89 


39.45 


80.72 


39.81 


80.54 


40.16 


80.37 


40.51 


90 


81.79 


39.89 


81.62 


40.25 


81.44 


40.60 


81.26:40.96 


91 


92 


82.69 40.33 


82.51 


40.69 


82.33 


41.05 


82.15 41.41 


92 


93 


83.59 40.77 


83.41 


41.13 


83.23 


41.50 


83.05 


41.86 


93 


94 


84.49 1 41.21 


84.31 


41.58 


84.12 


41.94 


83.94 


42.31 


94 


95 


85.39 41.65 


85.20 


42.02 


85.02 


42.39 


84.83 


42.76 


95 


96 


86.28 42.08 


86.10 


42.46 


85.91 


42.83 


85.73 


43.21 ! 96| 


97 


87.18 42.52 


87.00 


42.90 


86.81 


43.28 


86.62 


43.66 


97 


98 


88.08 


42.96 


87.89 


43.34 


87.70 


43.73 


187.51 


44.11 


98 


99 


88.98 


43.40 


88.79 


43.79 


88.60 


44.17 


188.40 


44.56 


99 


^00 

6 

1 


89.88 


43.84 


89.69 


44.23 


89.49 


44.62 


89.30 145.01 


100 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


64 Deg. 


631 Deg. 


631 Deg. 


63i Deg. 



56 



niAVEK.E TABLE. 





27 Deg. 


27i Deg. 


271 


Deg. 


27;| Deg. 


»• 

s 

-1 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 


Dep. 


0.89 


0.45 


0.89 


0.46 


0.89 


0.46 


0.88 


0.47 


2 


1.78 


0.91 


1.78 


0.92 


1.77 


0.92 


1.77 


0.93 


2 


3 


2.67 


1.36 


2.67 


1.37 


2.66 


1.39 


2.65 


1.40 


3 


4 


3.56 


1.82 


3.56 


1.83 


3.55 


1.85 


3.54 


1.86 


4 


5 


4.45 


2.27 


4.45 


2.29 


4.44 


2.31 


4.42 


2.33 


5 


6 


5.35 


2.72 


5.33 


2.75 


5.32 


2,77 


5.31 


2.79 


6 


7 


6.24 


3.18 


6.22 


3.21 


6.21 


3.23 


6.19 


3.26 


7 


8 


7.13 


3.63 


7.11 


3.66 


7.10 


3.69 


7.08 


3.72 


8 


9 


8.02 


4.09 


8.00 


4.12 


7.98 


4.16 


7.96 


4.19 


9 


10 

11 


8.91 


4.54 


8.89 
9.78 


4.58 


8.87 


4.62 


8.85 


4.66 


10 
11 


9.80 


4.99 


5.04 


9.76 


5.08 


9.73 


5.12 


12 


10.69 


5.45 


10.67 


5.49 


10.64 


5.54 


10.62 


5.59 


12 


13 


11. .58 


5.90 


11.56 


5.95 


11.53 


6.00 


11.. 50 


6.05 


13 


14 


12.47 


6.36 


12.45 


6.41 


12.42 


6.46 


12.39 


6.52 


14 


15 


13.37 


6.81 


13.34 


6.87 1 


13.31 


6.93 


13.27 


6.98 


15 


16 


14.26 


7.26 


14.22 


7.33 


14.19 


7.39 


14.16 


7.45 


16 


17 


15.15 


7.72 


15.11 


7.78 


15.08 


7.85 


15.04 


7.92 


17 


18 


16.04 


8.17 


16.00 


8.24 


15.97 


8.31 


15.93 


8..3« 


18 


19 


16.93 


8.63 


16.89 


8.70 


16.85 


8.77 


16.81 


8.85 


19 


20 
21 


17.82 


9.08 


17.78 


9.16 1] 17.74 


9.23 


17.70 


9.31 


20 
21 


18.71 


9.53 


18.67 


9.62 1 


18.63 


9.70 


18.58 


9.78 


22 


19.60 


9.99 


19.56 


10.07 


19.51 


10.16 


19.47 


10.24 


22 


23 


20.49 


10.44 


20.45 


1.0.53 


20.10 


10.62 


20.35 


10.71 


23 


24 


'^1.38 


10.90 


21.34 


10.99 


21.29 


11.08 


21.24 


11.17 


24 


25 


22.28 


11.35 


22.23 


11.45 


22.18 


11.54 


22.12 


n.64 


25 


26 


23.17 


11.80 


23.11 


11.90 


23.06 


12.01 


23.01 


12.11 


26 


27 


24.06 


12.26 


24.00 


12.36 


23.95 


12.47 


23.89 


12.57 


27 


28 


24.95 


12.71 


24.89 


12.82 


24.84 


12.93 


24.78 


13.04 


28 


29 


25.84 


13.17 


25.78 


13.28 


25.72 


13.39 


25.66 


13.50 


29 


30 
31 


26.73 


13.62 


26.67 
27.56 


13.74 
14.19 


26.61 


13.85 


26.55 


13.97 


30 
31 


27.62 


14.07 


27.50 


14.31 


27.43 


14.43 


32 


28.51 


14.53 


28.45 


14.65 


28.38 


14.78 


28.32 


14.90 


32 


33 


29.40 


14.98 


29.34 


15.11 


29.27 


15.24 


29.20 


15.37 


33 


34 


30.29 


15.44 


30.23 


15.57 


30.16 


15.70 


30.09 


15.83 


34 


35 


31.19 


15.89 


31.12 


16.03 


31.05 


16.16 


30.97 


16.30 


35 


36 


32.08 


16.34 


32.00 


16.48 


31,93 


16.62 


31.86 


16.76 


36 


37 


32.97 


16.80 


32.89 


16.94 


i .32.82 


17.08 


32.74 


17.23 


37 


38 


33.80 


17.25 


33.78 


17.40 


33.71 


17.55 


33.63 


17.69 


38 


39 


34.75 


17.71 


34.67 


17.86 


34.59 


18.01 


34.51 


18.16 


39 


40 
41 


35.64 


18.16 


35.56 
36.45 


18.31 

18.77 


35.48 


18.47 


35.40 


18.62 


40 
41 


36.53 


18.6] 


36.37 


18.93 


36.28 


19.09 


42 


37.42 


19.07 


37.34 


19.23 


37.25 


19.39 


.37.17 


19.56 


42 


43 


38.31 


19.52 


38.23 


19.69 


38.14 


19.86 


38.05 


20.02 


43 


44 


39.20 


19.98 


39.12 


20.15 


39.03 


20.32 


38.94 


20.49 


44 


45 


40.10 


20.43 


40.01 


20.60 


39.92 


20.78 


39.82 


20 . 95 


45 


46 


40.99 


20.88 


40.89 


21.06 


40.80 


21.24 


40.71 


21.42 


46 


47 


41.88 


21.34 


41.78 


21.52 


41.69 


21.70 


41.59 


21.88 


47 


48 


42.77 


21.79 


42.67 


21.98 


42.58 


22.16 


42.48 


22.35 


48 


49 


43.66 


22.25 


43.56 


22.44 


43.46 


22.63 


43.36 


22.82 


49 


50 

§ 

1 
.2 


44.55 


22.70 


44.45 


22.89 


44.35 


23.09 


44.25 
Dep. 


23.28 


50 

o 

1 

to 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


63] 


Oeg. 


«.f 


Deg. 


62^ 


Deg. 


62i Deg. 



TRAVERSE TABtfi. 



£7 



a 
o 
? 

"51 


27 Deg. 


2n Deg. 


271 Deg. 


27J Deg. 


51 


L 


at. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


45" 


44 


23.15 


45.34 


23.35 


45.24 


23.55 


45.13 


23 


75 


52 


46 


33 


23.61 


46.23 


23.81 


46.12 


24.01 


46.02 


24 


21 


52 


53 


47 


.22 


24.06 


47.12 


24.27 


47.01 


24.47 


46.90 


24 


68 


53 


54 


48 


11 


24.52 


48.01 


24.73 


47.90 


24.93 


47.79 


25 


14 


54 


55 


49 


01 


24.97 


48.90 


25.18 


48.79 


25.40 


48.67 


25 


61 


55 


5G 


49 


90 


25.42 


49.78 


25.64 


49.67 


25.86 


49.. 56 


26 


07 


56 


57 


50 


.79 


25.88 


50.67 


26.10 


50.56 


26.32 


50.44 


26 


54 


57 


58 


51 


69 


26.33 


51.56 


26.. 56 


51.45 


26.78 


51.33 


27 


01 


58 


59 


52 


57 


26.79 


52.45 


27.01 


52.33 


27.24 


52.21 


27^ 


47 


59 


60 
61 


53 


46 


27.24 


53.34 


27.47 


53.22 


27.70 


.53.10 


27 


94 


60 
61 


54 


.35- 


27.69 


54.23 


27.93 


54.11 


28.17 


53.93 


28 


40 


62 


55 


24 


28.15 


55.12 


28.39 !l 54.99 


28.63 


.54.87 


23 


87 


62 


63 


56 


.13 


28 . 60 


.56.01 


28.85 


155.88 


29.09 


55.75 


29 


33 


63 


64 


57 


02 


29.06 


56.90 


29.30 


56.77 


29.55 


56.64 


29 


80 


64 


65 


57 


92 


29.51 


57.79 


29.76 


57.66 


30.01 


57.. 52 


30 


36 


65 


66 


58 


81 


29.96 


.58 . 68 


30.22 ll 58.54 


30.48 


58.41 


30 


73 


66 


67 


59 


70 


30.42 


.59.56 


30.68 |i 59.43 


30.94 


59.29 


31 


20 


67 


68 


60 


59 


30.87 


60.45 


31.14! 60.32 


31.40 


60.18 


31 


66 


68 


69 


61 


48 


31.33 


61.34 


3] .59 i 61.20 


31.86 


61.06 


32 


13 


69 


70 

71 


62 


.37 


31.78 


62.23 


32.05 J 62.09 


32.32 


61.95 


32 


59 


70 
71 


63 


26 


32.23 


63.12 


32.51 ji 62.98 


32.78 


62.83 


33 


06 


7^2 


64 


15 


32.69 


64.01 


32.97 63.86 


33.25 


63.72 


33 


52 


72 


73 


65 


.04 


33.14 


64.90 


33.42 


64.75 


.33.71 


64.60 


33 


99 


73 


74 


65 


93 


33.60 


65.79 


33.88 


65.64 


34.17 


65.49 


34 


46 


74 


75 


06 


83 


34.05 


66.68 


34.34 


66 . 53 


34.63 


66.37 


34 


92 


75 


76 


67 


72 


.34.50 


67.57 


34.80 


67.41 


35.09 


i 67.26 


35 


39 


76 


77 


68 


61 


34.96 


68.45 


35.26 


68.30 


35.55 


68.14 


35 


85 


77 


78 


69 


50 


35.41 


69.34 


35.71 


69.19 


.36.02 


69.03 


36 


32 


78 


79 


70 


39 


35.87 


70.23 


36.17 


70.07 


36.48 


69.91 


36 


78 


79 


80 
81 


71 


28 


36.32 


71.12 
72.01 


36.63 
37.09 


70.96 


36.94 


70.80 
71.68" 


37 
37 


25 
71 


80 
81 


72 


17 


36.77 


71.85 


37.40 


82 


73 


06 


37.23 


72.90 


37.-05 


72.73 


37.86 


72 . 57 


38 


18 


82 


83 


73 


95 


37.68 


73.79 


33.00 


73.62 


38.33 


73.45 


38 


65 


83 


84 


74 


84 


38.14 


74.68 


38.46 


74.51 


38.79 


74.34 


39 


11 


84 


85 


75 


74 


38.59 


75.57 


38.92 


75.40 


39.25 


75.22 


39 


58 


85 


86 


76 


63 


39.04 


76.46 


39.38 


76.28 


39.71 


76.11 


40 


04 


86 


87 


77 


52 


39.50 


77.34 


39.83 


77.17 


40.17 


76.99 


40 


51 


87 


88 


78 


41 


39.95 


78.23 


40 .29 


78.06 


40.63 


77.88 


40 


97 


88 


89 


79 


30 


40.41 


79.12 


40.75 


78.94 


41.10 


1 78.76 


41 


44 


89 


90 
91 


80 


19 


40.86 


»0.01 


41.21 


79.83 


41. ..56 


79.65 


41 


91 


90 
91 


81 


08 


41.31 


80.90 


41.67 


80.72 


42.02 


80.53 


42 


37 


92 


81 


97 


41.77 


81.79 


42.12 


81.60 


42.48 


81.42 


42 


84 


92 


93 


82 


86 


42.22 


82.68 


42.58 


82.49 


42.94 


82.30 


43 


30 


93 


94 


83 


75 


42.68 


83.57 


43.04 


83.38 


43.40 


83.19 


43 


77 


94 


95 


84 


65 


43.13 


84.46 


43.50 


84.27 


43.87 


84.07 


44 


23 


95 


96 


85 


54 


43.58! 


85.35 


43.96 


85.15 


44.33 


84.96 


44 


70 


96 


97 


86 


43 


44.04 


86.23 


44.41 


86.04 


44.79 


85.84 


45 


16 


97 


98 


87 


32 


44.49 


87.12 


44.87 


86.93 


45.25 


86.73 


45 


63 


98 


J) 9 


88 


21 


44.95 


88.01 


45.33 


87.81 


45.71 


87.61 


46 


10 


99 


100 

V 

o 

s 
a 

.2 
Q 


89 
Dt 


10 


45.40 


88.90 


45.79 


88.70 


46.17 


88.50 


46 


56 


100 

o 

a 
a 


jp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


63 Deg. 


62f Deg. 

i 


62}j Deg. 


62; Deg. 



58 



TRAVERSE TABLE. 





28 Deg. 


28i Deg. 


2H Deg. 


281 Deg. 




i! 


Lat. 


Dep. 


Lat. 

0.88 


Dep. 

0.47 


Lai. 


Dep. 


Lat. 1 Dep. 


i 


1 


0.88 


0.47 


0.88 


0.48 


0.88 0.48 


1 


2 


1.77 


0.94 


1.76 


0.95 


1.76 


0.95 


1.75 0.96 


2 


3 


2.65 


1.41 


2.64 


1.42 


2.64 


1.43 


2.63 


1.44 


3 


4 


3.53 


1.88 


3.52 


1.89 


3.52 


1.91 


3.51 


1.92 


4 


5 


4.41 


2.35 


4.40 


2.37 


4.39 


2.39 


4.38 


2.40 


5 


6 


5.^0 


2.82 


5.29 


2.84 


5.27 


2.86 


5.26 


2.89 


6 


7 


6.18 


3.29 


6.17 


3.31 


6.15 


3.34 


6.14 


3.37 


7 


8 


7.06 


3.76 


7.05 


3.79 


7.03 


3.82 


7.01 


3.85 


8 


9 


7n95 


4.23 


7.93 


4.26 


7.91 


4.29 


7.89 


4.33 


9 


10 
11 


8.83 


4.69 


8.81 


4.73 


8.79 


4.77 


8.77 


4.81 


10 


9.71 


5.16 


9.69 


5.21 


9.67 


5.25 


9.64 


5.29 


11 


12 


10.60 


5.63 


10.57 


5.68 


10.55 


5.73 


10.52 


5.77 


12 


13 


11.48 


6.10 


11.45 


6.15 


11.42 


6.20 ! 


11.40 


6.25 


13 


14 


12.36 


6.57 


12.33 


6.63 


12.30 


6.68 1 


12.27 


6.73 


14 


15 


13.24 


7.04 


13.21 


7.10 


13.18 


7.16 


13.15 


7.21 


15 


16 


14.13 


7.51 


14.09 


7.57 


14.06 


7.63 


14.03 


7.70 


16 


17 


15.01 


7.98 


14.98 


8.05 


14.94 


8.11 


14.90 


8.18 


17 


18 


15.89 


8.45 


15.86 


8.52 


15.82 


8.59 


15.78 


8.66 


18 


19 


16.78 


8.92 


16.74 


8.99 


16.70 


9.07!! 16.66 


9.14 


19 


20 


17.66 


9.39 1 17.62 


9.47 


17.58 


9.54 : 

10.02 


17.53 


9.62 


20 


21 


18.54 


9.86 


18.50 


9.94 


18.46 


18.41 


10.10 


21 


22 


19.42 


10.33 


19.38 


10.41 


19.33 


10.50 , 19.29 


10.58 


22 


23 


20.31 


10.80 


20.26 


10.89 


20.21 


10.97 20.16 


11.06 


23 


24 


21.19 


11.27 


21.14 


11.36 


21.09 


11.45 1 21.04 


11.54 


24 


25 


22.07 


11.74 


22.02 


11.83 


21.97 


11.93 


21.92 


12.02 


25 


26 


22.96 


12.21 


22.90 


12.31 


22.85 


12.41 


22.79 


12.51 


26 


27 


23.84 


12.68 


23.78 


12.78 


23.73 


12.88 


23.67 


12.99 


27 


28 


24.72 


13.15 


24.66 


13.25 


24.61 


13.36 


24.55 


13.47 


28 


29 


25.61 


13.61 


25.55 


13.73 


25.49 


13.84 


25.43 


13.95 


29 


30 


26.49 


14.08 


26.43 


14.20 


26.36 


14.31 


26.30 


14.43 


30 
31 


31 


27.37 


14.55 


27.31 


14.67 


27.24 


14.79 


27.18 


14.91 


32 


28.25 


15.02 


28.19 


15.15 


28.12 


15.27 


28.06 


15.39 


32 


33 


29.14 


15.49 


29.07 


15.62 


29.00 


15.75 


28.93 


15.87 


33 


34 


30.02 


15.96 


29.95 


16.09 


29.88 


16.22 


29.81 


16.35 


34 


35 


30.90 


16.43 


30.83 


16.57 


30.76 


16.70 


30.69 


16.83 


35 


36 


31.79 


16.90 


31.71 


17.04 


31.64 


17.18 


31.56 


17.32 


36 


37 


32.67 


17.37 


32.59 


17.51 


32.52 


17.65 


32.44 


17.80 


37 


38 


33.55 


17.84 


33.47 


17.99 


33.39 


18.13 


33.32 


18.28 


38 


39 


34.43 


18.31 


34.35 


18.46 


34.27 


18.61 


34.19 


18.76 


39 


40 


35.32 


18.78 


35.24 


18.93 


35.15 


19.09 


35.07 


19.24 


40 
41 


41 


36.20 


19.25 


36.12 


19.41 


36. OQ 


19.56 


"35.95 


19.72 


42 


37.08 


19.72 


37.00 


19.88 


36.91 


20.04 


36.82 


20.20 


42 


43 


37.97 


20.19 


37.88 


20.35 


37.79 


20.52 


37.70 


20.68 


43 


44 


38.85 


20.66 


38.76 


20.83 


38.67 


20.99 


38.58 


21.16 


44 


45 


39.73! 21.13 


39.64 


21.30 


39.55 


21.47 


.33.45 


21.64 


45 


46 


40.62 21.60 11 40.52 


21.77 


40.43 


21.95 


! 40.33 


22.13 


46 


47 141.50! 22.07 


41.40 


22.25 


41.30 


22.43 


141.21 


22.61 


47 


48 


42.38 122.53 


42.28 


22.72 


42.18 


22.90 


'42.08 


23.09 


48 


49 


43.26 1 23.00 


143.16 


23.19 


43.06 


23.38 


; 42.96 


23.57 


49 


50 

1 

o 


44.15 1 23.47 
Dep. Lat. 


1 44.04 


23.67 


43.94 


23.86 
Lat. 


1 43.84 


24.05 


50 


Dep. 


Lat. 


Dep. 


; Dep. 


Lat. 


5 


62 


Deg. 


61J Deg. 

i 


6HDeg. 


6U Deg. 

i 



TRAVERSE TABLE. 



f)! 



! 7 

? 

s 
n 
a 

"51 


28 Ueg. 


28i Deg. 


28i Deg. 


281 De.r. 


a 

? 

~51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


45.03 


23.94! 


44.93 


24.14 


44.82 


24.34 1 


44.71 


24.. 53 


52 


45.91 


24.41 ' 


45.81 


24.61 


45.70 


24.81 


45.59 


25.01 


52 


53 


46.80 


24.88 i 


46.69 


25.09 


46.58 


25.29 


46.47 


25.49 


53 


54 


47.68 


25.35 i 


47.57 


25.56 


47.46 


25.77 


47.34 


25.97 


54 


55 


48.56 


25.82 i 


48.45 


26.03 


48.33 


26.24 


48.22 


26.45 


56 


56 j 


49.45 


26.29 1 


49.33 


26.51 


49.21 


26.72 


49.10 


26.94 


56 


57 


50.33 


26.76 


50.21 


26.98 


50.09 


27.20 


49.97 


27.42 


57 


58 


51.21 27.23; 


51.09 


27.45 


50.97 


27.68 


50.85 


27.90 


58 


59 


52.09 


27.70 1 


51.97 


27.93 


51.85 


28.151 


51.73 


28,38 


59 


60 
61 


.52.98 


28.17! 


52.85 


28.40 


52.73 


28.63 J 


52.60 


28.86 


60 
61 


53.86 


28.64; 


53.73 


28.87 


53.61 


29.11 ! 


53.48 


29.34 


62 


54.74 


29.11 1 


54.62 


29.35 


54.49 


29.58' 


54.36 


29.82 


62 


63 


55.63 


29. 5s : 


55.50 


29.82 


.55.37 


30.06' 


55.23 


30.30 


63 


64 


56.51 


30.05 


56.38 


30.29 


56.24 


30.54! 


56.11 


30.78 


64 


65 


57.39 


30.52 i 


57.26 


30.77 


57.12 


31.02 


56.99 


31.26 


65 


66 


.58.27 


30.99' 


58.14 


31.24 


58.00 


31.40 


57.86 


31.75 


66 


67 


59.16 


31.45' 


59.02 


31.71 


58.88 


31.97 


58.74 


32.23 


67 


68 


60.04 


31.92 


59.90 


.32.19 


59.76 


32.45 


59.62 


32.71 


68 


69 


60.92 


32.39 


60.78 


32.66 


60.04 


32.92 


60.49 


33.19 


69 


70 


61.81 


32.86 


61.66 


33.13 


61.52 


33.40 


61.37 


33.67 


70 


7) 


62.69 33.33 


62.54 


33.61 


62.40 


33.88 


62.25 


34.15 


71 


72 


63.57 


33.80 


63.42 


34.08 


63.27 


34.36 


63.12 


34.63 


72 


73 


64.46 


34.27 


64.30 


34.55 


64.15 


.34.83 


64.00 


35.11 


73 


74 


65.34 


34.74 


65.19 
66.07 


35.03 


65.03 


35.31 


64.88 


35.59 


74 


75 


66.22 


35.21 


35.50 


65.91 


35.79 


65.75 


36.07 


75 


76 


67.10 


35.68 


66.95 


35.97 


66.79 


36.26 


66.63 


36.56 


76 


77 


67.99 


36.15 


67.83 


30.45 


67.67 


36.74 


67.51 


37.04 


77 


78 


68.87 


36.62 


68.71 


36.92 


68.. 55 


37.22 


68.38 


37.52 


78 


79 


69.75 


37.09 


69.59 


37.39 


69.43 


37.70 


69.26 


38.00 


79 


80 
81 


70.64 


37.56 


70.47 


37.87 


70.31 


38.17 


1 70.14 


38.48 


80 
'81 


71.52 


38.03 


71.. 35 


38.34 


71.18 


38.65 


'71.01 


38.96 


82 


72.40 


38.50 


72.23 


38.81 


72.06 


39.13 


',71.89 


.39.44 


82 


83 


73.28 


38.97 


73.11 


39.29 


72.94 


39.60 


1 72.77 


3.9.92 


83 


84 


74.17 


39.44 


73.99 


39.70 


73.82 


40.08 


: 73.64 


40.40 


84 


85 


75.05 


39.91 


74.88 


40.23 


74.70 


40.. 56 


174.. 52 


40.88 


85 


86 


75 . 93 


40.37 


75.76 


40.71 


75 58 


41.04 


! 75.40 


41.36 


86 


87 


76.82 


40.84 


76.64 


41.18 


76.46 


41.51 


1 76.28 


41.85 


87 


88 


77.70 


41.31 


77.52 


41.65 


77.34 


41.99 


177.15 


42.33 


88 


89 


78.58 


41.78 


78.40 


42.13 


78.21 


42.47 


,78.03 


42.81 


89 


90 


79.47 


42.25 


79.28 


42.60 


79.09 


42.94 


! 78.91 


43.29 


90 


91 


80.35 


42.72 


80.16 


43.07 


79.97 


43.42 


i 79.78 


43.77 


91 


92 


81.23 


43.19 


81.04 


43.55 


80.85 


43.90 


80.66 


44.25 


92 


93 


82.11 


43.66 


81.92 


44.02 


81.73 


44.38 


81.54 


44.73 


93 


94 


83.00 


44.13 


82.80 


44.49 


82.61 


44.85 


82.41 


45.21 


94 


95 


83.88 


44.60 


83.68 


44.97 


83.49 


45.33 


83.29 


45.69 


95 


96 


84.76 


45.07 


84.57 


45.44 


84.37 


45.81 


84.17 


46.17 


96 


97 


85.65 


45.54 


85.45 


45.91 


85.25 


46.28 


85.04 


46.66 


97 


98 


86.53 146.01 


86.33 


46.39 


86.12 


46.76 


85.92 


47.14 


98 


99 


87.41 


46.48 


87.21 


46.86 


87.00 


47.24 


86.80 


47.62 


99 


100 
1 

5 


88.29 


46.95 


88.09 


47.33 


87.88 


47.72 


87.67 


48.10 


lOO 

i 
1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 


Dep. 


Lat. 


1 62 Deg. 


61| Deg. 


eu Dfig- 


6U Deg. 



60 



TRAVERSE TABLE. 



o 

o 
? 

1 


29 De^r. 


29^ Deg. ! 


29i Deg. 


291 


Deg. 


5 

a 
o 
9 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 


Dep. 


Lat. 


Dop. 




0.87 


0.48 


0.87 


0.49 


0.87 1 


0.49 1 


0.87 


. 50 


1 




2 


1.75 


0.07 


1.74 


0.98 


.1.74 


0.98 


1.74 


0.99 


2 




3 


2.62 


1.45 


2.62 


1.47 


2.61 


1.48 


2.00 


1.49 


3 




4 


3.50 


1.94 


3.49 


1.95 


3.48 


1.97 


3.47 


1.98 


4 




5 


4.37 


2.42 


4.36 


2.44 


4.35 


2.46 


4.34 


2.48 


5 




6 


6.25 


2.91 


5.23 


2.93 


5.22 


2.95 


6.21 


2.98 


6 




7 


6.12 


3.. 39 


6.11 


3.42 


6.09 


3.45 


6.08 


3.47 


7 




8 


7.00 


3.88 


6.98 


3.91 


6.96 


3.94 


6.95 


3.97 


8 




9 


7.87 


4.36 


7.85 


4.40 


7.83 


4.43 


7.81 


4.47 


9 




10 


8.75 


4.85 


8.72 


4.89 


8.70 
9.57 


4.92 
5.42 


8.68 


4.90 


10 
11 




11 


9.62 


5.33 


9.60 


5.37 


9.55 


5.46 




12 


10.50 


6.82 


10.47 


5.86 


10.44 


6.91 


10.42 


5.95 


12 




13 


11.37 


6.30 


11.34 


6.35 


11.31 


6.40 


11.29 


6.45 


13 




14 


12.24 


6.79 


12.21 


6.84 


12.18 


6.89 


12.16 


6.95 


14 




15 


13.12 


7.27 


13.09 


7.33 


13.06 


7.39 


13.02 


7.44 


15 




16 


13.99 


7.76 


13.96 


7.82 


13.93 


7.88 


13.89 


7.94 


16 




17 


14.87 


8.24 


14.83 


8.31 


14.80 


ft.. 37 


14.76 


8.44 


17 




18 


15.74 


8.73 


15.70 


8.80 


15.67 


8.86 


15.63 


8.93 


18 




19 


16.62 


9.21 


16.58 


9.28 


16. .54 


9.36 


16.50 


9.43 


19 




20 
21 


17.49 
18.37 


9.70 
10.18! 


17.45 
18.32 


9.77 
10.26 


17.41 

18.23 


9.85 
10.34 


17.36 


9.92 


20 




18.23 


10.42 


21 




22 


19.24 


10.67 1 


19.19 


10.75 


19.15 


10.83 


19.10 


10.92 


22 




23 


20.12 


11.15 1 


20.07 


11.24 


20.02 


11.33 


19.97 


11.41 


23 




24 


20.99 


11.64 


20.94 


11.73 


20.89 


11.82 


20.84 


11.91 


24 




25 


21.87 


12.12 


21.81 


12.22 


21.76 


12.31 


21.70 


12.41 


25 




26 


22.74 


12.60 


22.68 


12.70 


22.63 


12.80 


22.57 


12.90 


26 




27 


23.61 


13.09 


23.56 


13.19 


23.50 


13.30 


23.44 


13.40 


27 




28 


24.49 


13.57 


24.43 


13.68 


24.37 


13.79 


24.31 


13.89 


28 




29 


25.36 


14.06 


25.30 


14.17 


25.24 


14.28 


25.18 


14.39 


29 




30 
31 


26.24 


14.54 


26.17 


14.66 


26.11 


14.77 


26.05 
26.91 


14.89 
15.38 


30 
31 




27.11 


15.03 


27.05 


15.15 


26.98 


15.27 




32 


27.99 


15.51 


27.92 


15.64 


27.85 


15.76 


27.78 


15.88 


32 




33 


28.86 


16.00 


28.79 


16.12 


28.72 


16.25 


28.65 


16.38 


33 




34 


29.74 


16.48 


29.66 


16.61 


29.59 


16.74 


29.52 


16.87 


34 




35 


30.61 


16.92 
17. 4d 


30.54 


17.10 


30.46 


17.23 


.30.39 


17.37 


35 




36 


31.49 


31.41 


17.59 


31.33 


17.73 


31.26 


17.86 


36 




37 


32.36 


17.94 


32.28 


18.08 


32.20 


18.22 


32.12 


18.36 


37 




38 


33.24 


18.42 


33.15 


18.57 


33.07 


18.71 


32.99 


18.86 


38 




39 


34.11 


18.91 


34.03 


19.06 


33.94 


19.20 


33.86 


19.35 


39 




40 
41 


34.98 


19.39 


34.90 
35.77 


19.54 
20.03 


34.81 


19.70 


34.73 


19.85 


40 

1 41 




35.86 


19.88 


35 . 68 


20.19 


35.60 


20.34 




42 


36.73 


20.36 


36.64 


20.52 


36.55 


20.68 


36.46 


20.84 


! 42 




43 


37.61 


20.85 


37.52 


21.01 


37.43 


21.17 


37.. 33 


21.34 


1 43 




44 


3S.48 


21.33 


38.39 


21.50 


38.. 30 


21.67 


38.20 


21.83 


1 44 




45 


39.36 


21.82 


39.26 


21.99 


39.17 


22.16 


39.07 


22.33 


i 45 




46 


40.23 


22.30 


40.13 


22.48 


140.04 


22.65 


39.94 


22.83 


1 46 




47 


41.11 


22.79 


41.01 


22.97 


1 40.91 


23.14 


40.81 


23.3? 


i 47 




48 


41.98 


23.27 


41.88 


23.45 


41.78 


23.68 


41.67 


23.82 


! 48 




49 


42.86 


1 23.76 


42.75 


23.94 


42.65 


24.13 


42.54 


24.31 


1 49 




50^ 


43.73 


! 24.24 


43.62 


24.43 


43.. 52 


24.62 


43.41 


24.81 


1 50 




1 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




61 


Deg. 


601 Deg. 


60,^ 


Deg. 


60i 


Deg. 


(5 





TRAVKRSE TABLE. 



61 



s 
51 


29 Deg. 


29i Deg. 


29^ Deg. 


291 Deg. 


1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 




44.61 


24.73 


44.50 


24.92 


44.39 


25.11 


44.28 


25.31 


51 




52 


45.48 


25.21 


45.37 


25.41 


45.26 


25.01 


45.15 


25.80 


52 




53 


46.35 


25.69 


46.24 


25.90 


46.13 


26.10 


46.01 


26.30 


53 




54 


47.23 


26.18 


47.11 


26.39 


47.00 


26.59 


46.88 


26.80 


54 




55 


48.10 


26.66 


47.99 


26.87 


47.87 


27.08 


47.75 


27.29 


55 




50 


48.98 


27.15 


48.86 


27.36 


48.74 


27.. 58 


48.62 


27.79 


50 




57 


49.85 


27.63 


49.73 


27.85 


49.61 


28.07 


49.49 


28.28 


57 




58 


50.73 


28.12 


50.60 


28.34 


50.48 


28.56 


50.36 


28.78 


58 




59 


51.60 


28.60 


51.48 


28.83 


51.35 


29.05 


51.22 


29.28 


59 




60 
61 


52.48 
53.35 


29.09 
29.57 


.52.35 


29.32 


52.22 


29.55 


52.09 


29.77 1 


60 
61 




53.22 


29.81 


53.09 


30.04 


52.96 


30.2? 




62 


54.23 


30.06 


54.09 


30.29 


53.96 


30., 53 


53.83 


30.77 


62 




63 


55.10 


30.54 


54.97 


30.78 


.54.83 


31.02 


54.70 


31.26 


63 




64 


55.98 


31.03 


55.84 


31.27 


55.70 


31.52 


55.56 


31.76 


64 




65 


56.85 


31.51 


.56.71 


31.76 


56.57 


32.01 


56.43 


32.25 


05 




66 


.57.72 


32.00 


57.58 


32.25 


57.44 


32.50 


.57.30 


32.75 


66 




67 


.58.60 


32.48 


.58.46 


32 . 74 


.58.31 


32.99 


58.17 


33.25 


67 




68 


.59.47 .32.97 1 


59.33 


33.23 


.59.18 


33.48 


59.04 


33.74 


68 




69 


60.35 


33.45 


60.20 


33.71 


60.05 


33.98 


59.91 


34.24 


69 




70 
71 


61.22 


33.94 


61.07 


34.20 
34.69 


00.92 


34.47 


60.77 
61.64 


34.74 


_70 




62.10 


34.42 


61.95 


61.80 


34.96 


35.23 


71 




72 


62.97 


34.91 


62.82 


35.18 


62.67 


35,45 


62.51 


35.73 


72 




73 


63.85 


35.39 


63.69 


35.67 


63.54 


35.95 


63.38 


.36.22 


73 




74 


64 . 72 


35.88 


64.. 56 


36.16 


64.41 


36.44 


64.25 


36.72 


74 




75 


65.60 


36.36 


65.44 


36.65 


65.28 


36.93 


65.11 


37.22 


75 




76 


66.47 


36.85 


66.31 


37.14 


66.15 


37.42 


65.98 


37.71 


76 




77 


67.35 


37.33 


67.18 


37.62 


67.02 


37.92 


66.85 


38.21 


77 




78 


68.22 


37.82 


68.05 


38.11 


67.89 


38.41 


67.72 


38.70 


78 




79 


69.09 


38.. 30 


68.93 


38.60 


68.76 


38.90 


68.59 


39.20 


79 




80 
81 


69.97 
70.84 


38 . 78 


69.80 


39.09 
39.58 


69.63 


39.39 


69.46 


39.70 


80 
81 




39.27 


70.67 


70.. 50 


39.89 


70.32 


40.19 




82 


71.72 


39.75 


71.54 


40.07 


71.37 


40.38 


71.19 


40.69 


82 




83 


72.59 


40.24 


72.42 


40.56 


72.24 


40.87 


72.06 


41.19 


83 




84 


73.47 


40.72 


73.29 


41.04 


73.11 


41.36 


72.93 


41.68 


84 




85 


74.:i4 


41.21 


74.16 


41.. 53 


73.98 


41.86 


1 73.80 


42.18 


85 




86 


75.22 


41.69 


75.03 


42.02 


74.85 


42.35 


74.67 


42.67 


86 




87 


76.09 


42.18 


75.91 


42.51 


75.72 


42.84 


75.53 


43.17 1 87 




88 


76.97 


42.63 


76.78 


43.00 


76.59 


43.33 


76.40 


43 . 67 


88 




89 


77.84 


43.15 


77.65 


43.49 


77.46 


43.83 


77.27 


44.10 


89 




90 
91 


78.72 


43.63 


78 . 52 


43.98 


78.33 


44.32 


178.14 


44.60 


90 




79.59 


44.12 


79.40" 


44.46 


79.20 


44.81 


79.01 


45.10 


91 




92 


80.46 


44.60 


80.27 


44.95 


80.07 


45.30 


79.87 


45.05 


92 




93 


81.34 


145.09 


81.14 


45.44 


80.94 


45.80 


1 80.74 


46.15 


93 




94 


82.21 


1 45 . 57 


82.01 


45.93 


81.81 


46.29 


1 81.61 


46.64 


94 




95 


83.09 


46.06 


82.89 


46.42 


82.68 


46.78 


ii 82.48 


47.14 


95 




96 


83.96 


1 46 . 54 


83.70 


46.91 


83.55 


47.27 


; 83.35 


47,64 


96 




97 


84.84 


47.03 


84.63 


47.40 


84.42 


47.77 


f- 84.22 


48.13 


97 




9S 


85.71 


47.51 


85.50 


47.88 


1 85.29 


48.20 


: 85.08 


48.63 


98 




99 


86., 59 


: 48.00 


86.38 


48.37 


Ij 80.17 


48.75 


S 85.95 


49.13 


99 




100 


187.46 


'48.48 


87.25 
Dep. 


48.86 
Lat. 


! 87.04 


49.24 


ii 86.82 


49.62 


100 

i 

.2 

O 




Dep. 


1 

j Lat. 


1 Dep, 


Lat. 


! Dep. 


Lat. 




61 


Deg. 


60! DefT. 


60* Deg. 


ll 

il eOi Deg. 





21 



i.<y 



TRAVERSE TABLE. 



x' 

3 
? 
1 


1 
30 Deg. 


301 Deg. 


30| 


Deg. 


30| Deg. 


55' 

1 
P 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.87 


0..50 


0.86 


0.50 


0.86 


0.51 


0.86 


0.51 


2 


1.73 


1.00 


1.73 


1.01 


1.72 


1.02 


1.72 


1.02 


2 


3 


2.60 


1.50 


2.59 


1.51 


2.58 


1.52 1 


2.58 


1.53 


3 


4 


3.46 


2.00 


3.46 


2.02 


3.45 


2.03 


3.44 


2.05 


4 


5 


4.33 


2.50 


4.32 


2.52 


4.31 


2.54 


4.30 


2.56 


5 


6 


5.20 


3.00 


5.18 


3.02 


5.17 


3.05 


5.16 


3^7 


6 


7 


6.06 


3.50 


6.05 


3.53 


6.03 


3.55 


6.02 


3.58 


7 


8 


6.93 


4.00 


6.91 


4.03 


6.89 


4.06 


6.88 


4.09 


8 


9 


7.79 


4.50 


7.77 


4.53 


7.75 


4.57 


7.73 


4.60 


9 


10 
11 


8.66 


5.00 


8.64 


6.04 


8.62 


5.08 


8.59 


5.11 


10 
11 


9.53 


5.50 


9.50 


5.54 


9.48 


5.58 


9.45 


5.62 


12 


10.39 


6.00 


10.37 


6.05 


10.34 


6.09 


10.31 


6.14 


12 


13 


11.26 


6.50 


11.23 


6.55 


11.20 


6.60 


11.17 


6.65 


13 


14 


12.12 


7.00 


12.09 


7.05 


12.06 


7.11 


12.03 


7.16 


14 


15 


12.99 


7.50 


12.96 


7.56 


12.92 


7.61 


12.89 


7.67 


15 


16 


13.86 


8.00 


13.82 


8.06 


13.79 


8.12 


13.75 


8.18 


16 


17 


14.72 


8.50 


14.69 


8.56 


14.65 


8.63 


14.61 


8.69 


17 


18 


15.59 


9.00 


15.55 


9.07 


15.51 


9.14 


15.47 


9.20 


18 


19 


16.45 


9.50 


16.41 


9.57 


16.37 


9.64 


16.33 


9.71 


19 


20 
21 


17.32 


10.00 


17.28 


10.08 


17.23 


10.15 
10.66 


17.19 


10.23 


20 

21 


18.19 


10.50 


18.14 


10.58 i 


18.09 


18.05 


10.74 


22 


19.05 


11.00 


19.00 


11.08 


18.96 


11.17 


18.91 


11.25 


22 


23 


19.92 


11.50 


19.87 


11.59! 


19.82 


11.67 


19.77 


11.76 


23 


24 


20.78 


12.00 


20.73 


12.09, 


20.68 


12.18 


20.63 


12.27 


24 


25 


21.65 


12.. 50 


21.60 


12.59 


21.54 


12.69 


21.49 


12.78 


25 


26 


22.52 


13.00 


22.46 


13.10 


22.40 


13.20 


22.34 


13.29 


26 


27 


23.38 


13.. 50 


23.32 


13.60 


23.26 


13.70 


23.20 


13.80 


27 


28 


24.25 


14.00 


24.19 


14.11 


24.13 


14.21 


24.06 


14.32 


28 


29 


25.11 


14.50 


25.05 


14.61 


24.99 


14.72 


24.92 


14.83 


29 


30 
31 


25.98 


15.00 


25.92 


15.11 


25.85 


15.23 


25.78 


15.34 


30 
31 


26.85 


15.50 


26.78 


15.62 


26.71 


15.73 


26.64 


15.85 


32 


27.71 


16.00 


27.64 


16.12 


27.57 


16.24 


27.50 


16.36 


32 


33 


28.58 


16.50 


28.51 


16.62 


28.43 


16.75 


28.36 


16.87 


33 


34 


29.44 


17.00 


29.37 


17.13 


29.30 


17.26 


29.22 


17.38 


34 


35 


30.31 


17.50 


30.23 


17.63 


30.16 


17.76 


30.08 


17.90 


35 


36 


31.18 


18.00 


31.10 


18.14 


31.02 


18.27 


30.94 


18.41 


36 


37 


32.04 


18.50 


31.96 


18.64 


31.88 


18.78 


31.80 


18.92 


37 


38 


32.91 


19.00 


32.83 


19.14 


32.74 


19.29 


.32.66 


19.43 


38 


39 


33.77 


19.50 


33.69 


19.65 


33.60 


19.79 


,33.52 


19.94 


39 


40 
41 


34.64 


20.00 


34.55 


20.15 


34.47 


20.30 


34.38 


20.45 


40 
41 


35.51 


20.. 50 


35.42 


20.65 


35.33 


20.81 


35.24 


20.96 


42 


36.37 


21.00 


36.28 


21.16 


36.19 


21.32 


36.10 


21.47 


42 


43 


37.24 


21.50 


37.14 


21.66 


37.05 


21.82 


36.95! 21.99 


43 


44 


38.11 


22.00 


38.01 


22.17 


37.91 


22.33 


37.81 I 22.50 


44 


45 


38.97 


22.50 


38.87 


22.67 


.38.77 


22.84 


38.67 


23.01 


45 


46 


39.84 


23.00 


139.74 


23.17 


39.63 


23.. 35 


.39.53 


23.52 


46 


47 


40.70 


23.50 


40.60 


23.68 


40.50 


23.85 


40.39 


24.03 


47 


48 


41.57 


24.00 


41.46 


24.18 


41.36 


24.36 


41.25 


24.54 


48 


49 


42.44 


24.50 


42.33 


24.68 


42.22 


24.87 


42.11 


25.05 


49 


50 

1 

.2 


43.30 


25.00 


43.19 


25.19 


43.08 


25.38 


42.97 


25. 5G 


_50 

3 
.2 


Dep. 


Lat. 


Dep. 

591 


Lat. 
Dog. 


Dep. 


Lat. 


Dep. 


Lat. 


60 I 


3eg. 


59^, 


Deg. 


59 i D^yr. 



TRAVT:T?sr; TAHLE. 



63 



o 
s 

p 

3 

? 

51 


30 Deg. 


30i Deg. 


SOi Deg. 


301 Deg. 


O 

• 

51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


44.17 


25.50 


44.06 


25.69 


43.94 


25.88 


43.83 


26.08 


52 


45.03 


26.00 


44.92 


26.20 


44.80 


26.39 


44.69 


26.59 


52 


53 


45.90 


26.50 


45.78 


26.70 


45.67 


26.90 


45.55 


27.10 


53 


54 


46.77 


27.00 


46.65 


27.20 


46.53 


27.41 


46.41 


27.61 


54 


55 


47.63 


27.50 


47.51 


27.71 


47.39 


27.91 


47.27 


28.12 


55 


56 


48.50 


28.00 


48.37 


28.21 


48.25 


28.42 


48.13 


28.63 


56 


57 


49.36 


28.50 


49.24 


28.72 


49.11 


28.98 


48.99 


29.14 


57 


58 


50.23 


29.00 


50.10 


29.22 


49.97 


29.44 


49.85 


29.65 


58 


59 


51.10 


29.50 


50.97 


29.72 


50.84 


29.94 


50.70 


30.17 


59 


60 
61 


51.96 


30.00 


51.83 


30.23 


51.70 


30.45 


51.56 

52.42 


30.68 


60 


52.83 


30.50 


52.69 


30.73 


52.. 56 


30.96 


31.19 


61 


62 


53.69 


31.00 


53.56 


31.23 


53.42 


31.47 


53.28 


31.70 


62 


63 


54.56 


31.50 


54.42 


31.74 


54.28 


31.97 


54.14 


32.21 


63 


64 


55.43 


32.00 


55.29 


.32.24 


55.14 


32.48 


55.00 


32.72 


64 


65 


56.29 


32.50 


56.15 


32.75 


56.01 


32.99 


55.86 


33.23 


65 


66 


57.16 


33.00 


57.01 


33.25 


.56.87 


33.50 


56.72 


33.75 


66 


67 


58.02 


33.50 


57.88 


33.75 


.^7.73 


34.01 


57.58 


34.26 


67 


68 


58.89 


34.00 i 


58.74 


34.26 


58.59 


34.51 


.58.44 


34.77 


68 


69 


59.76 


34.50 


59.60 


34.76 


59.45 


35.02 


59.30 


35.28 


69 


70 

71 


60.62 


35.00 1 


60.47 


35.26 


60.31 


35.53 


60.16 


35.79 


70 


61.49 


35.50 


61.33 


35.77 


61.18 


36.04 1 


61.02 


36.30 


71 


72 


62.35 


36.00 


62.20 


36.27 


62.04 


.36.54 


61.88 


36.81 


72 


73 


63.22 


36.50 


63.06 


36.78 


62.90 


37.05 


62.74 


37.32 


73 


74 


64.09 


37.00 


63.92 


37.28 


63.76 


37.56 


63.60 


37.84 


74 


75 


64.95 


37.. 50 


64.79 


37.78 


64.62 


38.07 


64.46 


38.35 


75 


76 


65.82 


38.00 


65.65 


38.29 


65.48 


38.57 


65.31 


38.86 


76 


77 


66.68 


38.. 50 


66.52 


38.79 


66.35 


39.08 


66.17 


39.37 


77 


78 


67.55 


39.00 


67.38 


39.29 


67.21 


39.59 


67.03 


39.88 


78 


79 


68.42 


39.50 


68.24 


39.80 


68.07 


40.10 


67.89 


40.39 


79 


80 
81 


69.28 


40.00 


69.11 


40.30 1 


68.93 


40.60 


68.75 


40.90 
41.41 


80 
81 


70.15 


40.50 


69.97 


40.81 


69.79 


41.11 


69.61 


82 


71.01 


41.00 


70.83 


41.31 


70.65 


41.62 


70.47 


41.93 


82 


83 


71.88 


41.50 


71.70 


41.81 


71.52 


42.13 


71.33 


42.44 


83 


84 


72.75 


42.00 


72.56 


42.32 


72.38 


42.63 


72.19 


42.95 


84 


85 


73.61 


42.50 


73.43 


42.82 


73.24 


43.14 


73.05 


43.46 


85 


86 


74.48 


43.00 


74.29 


43.32 1 


74.10 


43.65 


73.91 


43.97 


86 


87 


75.34 


43.50 


75.15 


43.83 ! 


74.96 


44.16 


74.77 


44.48 


87 


88 


76.21 


44.00 


76.02 


44.33 ' 


75.82 


44.66 


75.63 


44.99 


88 


89 


77.08 


44.50 


76.88 


44.84 


76.68 


45.17 


76.49 


45.51 


89 


90 
91 


77.94 


45.00 


77.75 


45.34 


77.55 


45.68 


77.35 


46.02 


90 


78.81 


45.50 


78.61 


45.84 


78.41 


46.19 


78.21 


46.53 


91 


92 


79.67 


46.00 


79.47 


48.35 


79.27 


46.69 


79.07 


47.04 


92 


93 


80.54 


46.50 


80.34 


46.85 


80.13 


47.20 


79.92 


47.55 


93 


94 


81,41 


47.00 


81.20 


47.35 


80.99 


47.71 


80.78 


48.06 


94 


95 


82.27 


47.50 


82.06 


47.86 


81.85 


48.22 


81.64 


48.57 


95 


96 


83.14 


48.00 


82.93 


48.36 82.72 


48.72 


82.50 


49.08 


96 


97 


84.00 


48.50 


83.79 


48.87 83.58 


49.23 


83.36 


49.60 


97 


98 


84.87 


49.00 


84.66 


49.37 84.44 


49.74 


84.22 


50.11 


98 


99 


85.74 


49.50 


85.52 


49.87 85.30 


50.25 


85.08 


50.62 


99 


100 

§ 

c 

to 


86.60 


50.00 


86.38 


50.38 86.16 


50.75 


85.94 


51.13 


100 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


c 

(5 


60 Deg. 


59| Deg. 69i Deg. 


59i Deg. 



64 



TRAVERSE TABLE. 



g 
s 


31 Deg. 

1 


31i Dog. 


3U Deg. 


311 Deg. 


5 
1 


s 
s 


Lai. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.86 


0.51 


0.85 


0.52 


0.85 


0.52 


0.85 


0..53 


2 


1.71 


1.03 


1.71 


1.04 


1.71 


1.04 


1.70 


1.05 


2 


3 


2. .57 


1..55 


2.56 


1..56 


2.56 


1.57 


2.55 


1.58 


3 


4 


3.43 


2.06 


3.42 


2.08 


3.41 


2.09 


3.40 


2.10 


4 


5 


4.29 


2.58 


4.27 


2.59 


4.26 


2.61 


4.25 


2.63 


5 


6 


5.14 


3.09 


5.13 


3.11 


5.12 


3.13 


5.10 


3.16 


6 


7 


6.00 


3.61 


5.98 


3.63 


5.97 


3.66 


5.95 


3.68 


7 


8 


6.86 


4.12 


6.84 


4.15 


6.82 


4.18 


6.80 


4.21 


8 


9 


7.71 


4.64 


7.09 


4.67 


7.67 


4.70 


7.65 


4.74 


9 


10 


8.57 


5.15 


8.55 


5.19 


8.. 53 


5.22 


8.50 


5.26 


10 


11 


9.43 


5.67 


9. 40 


5.71 


9.38 


5.75 


9.35 


5.79 


11 


12 


10.29 


6.18 


10.26 


6.23 


10.23 


6.27 


10.20 


6.31 


12 


13 


11.14 


6.70 


11.11 


6.74 


11.08 


6.79 


11.05 


6.84 


13 


14 


12.00 


7.21 


11.97 


7.26 


11.94 


7.31 


11.90 


7.37 


14 


15 12.86 


7.73 


12.82 


7.78 


12.79 


7.84 


12.76 


7.89 


15 


16 


13.71 


8.24 


13.68 


8.30 


13.64 


8.36 


13.61 


8.42 


16 


17 


14.57 


8.76 


14.53 


8.82 


14.49 


8.88 


14.46 


8.95 


17 


18 


15.43 


9.27 


15.39 


9.34 


15.35 


9.40 


15.31 


9.47 


18 


19 


16.29 


9.79 


16.24 


9.86 


16.20 


9.93 


16.16 


10.00 


19 


20 


17.14 


10.30 


17.10 


10.38 


17.05 


10.45 


17.01 


10.. 52 


20 


21 


18.00 


10.82 


17.95 


10.89 


17.91 


10.97 


17.86 


11.05 


21 


22 


18.86 


11.33 


18.81 


11.41 


18.76 


11.49 


18.71 


11.58 


22 


23 


19.71 


11.85 


19.66 


11.93 


19.61 


12.02 


19.56 


12.10 


23 


24 


20.57 


12.36 


20.52 


12.45 


20.46 


12.54 


20.41 


12.63 


24 


25 


21.43 


12.88 


21.37 


12.97 


21.32 


13.06 


|21.26 


13.16 


25 


26 


22.29 


13.39 


22.23 


13.49 


22.17 


13.. 58 


l22.ll 


13.68 


26 


27 


23.14 


13.91 


23.08 


14.01 


23.02 


14.11 


i22.96 


14.21 


27 


28 


24.00 


14.42 


23.94 


14.53 


23.87 


14.63 


23.81 


14.73 


28 


29 


24.86 


14.94 


24.79 


15.04 


24.73 


15.15 


24.66 


15.26 


29 


30 


2'5.71 


15.45 


25.65 


15.. 50 


25.58 


15.67 


25.51 


15.79 


30 


31 


26.57 


15.97 


26.50 


16.08 


26.43 


16.20 


26.36 


16.31 


31 


32 


27.43 


16.48 


27.36 


16.60 


27.28 


16.72 


27.21 


16.84 


32 


33 


28.29 


17.00 


28.21 


17.12 


28.14 


17.24 


28.06 


17.37 


33 


34 


29.14 


17.51 


29.07 


17.64 


23.99 


17.76 


28.91 


17.89 


3-1 


35 


30.00 


18.03 


29.92 


18.16 


29.84 


18.29 


29.76 


18.42 


35 


36 


30.86 


18.. 54 


30.78 


18.68 


30.70 


18.81 


30.61 


18.94 


36 


37 


31.72 


19.06 


31.63' 19.19 


31.55 


19.33 


31.46 


19.47 


37 


38 


32.57 


19.57 


32.49 


19.71 


32.40 


19.85 


32.31 


20.00 


33 


39 


33.43 


20.09 


33.34 


20.23 


33.25 


20.38 


33.16 


20.52 


39 


40 


34.29 


20.60 


34.20 


20.75 


34.11 


20.90 


34.01 


21.05 


40 


41 


35.14 


21.12 


35.05 


21.27 


34.96 


21.42 


34.86 


21.57 


41 


42 


36.00 


21.63 


35.91 


21.79 


35.81 


21.94 


35.71 


22.10 


42 


43 


36.86 


22.15 


36.76 


22.31 


36.66 


22.47 


36.57 


22.63 


43 


44 


37.72 


22,66 


37.62 


22.83 


37.. 52 


22.99 


37.42 


23.15 


44 


45 


38.57 


23.18 


i 38.47 


23.34 


38.37 


23.51 


38.27 


23.63 


45 


46 


39.43 


23.69 


39.33 


23.86 


39.22 


24.03 


39.12 


24.21 


46 


47 


40.29 


24.21 


40.18 


24.38 


40.07 


24.. 56 


39.97 


24.73 


47 


48 


41.14 


24.72 


41.04 


24.90 


40.93 


25.08 


40.82 


25 . 26 


48 


49 


42.00 


25.24 


41.89 


25.42 


41.78 


25.60 


41.67 


25.78 


49 


50^ 


42.86 


25.75 


42.75 


25.94 


42.63 


26.12 


42.52 


26.31 


50 


6 
a 

a 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




59 


Deg. 


58| Deg. 


58^ 


Deg. 


58i Deg. 


1 



TBAVERSE TABLE 



65 



1 

9 
61 


31 Deg. 


3U Deg. 


311 Deg. 


3U Deg. 



~5T 


Lat. 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


43.72 


26.27 


43.60 


26.46 


43.48 


26.65 


43.37 


26.84 


52 


44.57 


26.78 


44.46 


26.98 


44.34 


27.17 


44.22 


27.36 


52 


53 


45.43 


27.30 


45.31 


27.49 


45.19 


27.69 


45.07 


27.89 


53 


54 


46.29 


27.81 


46.17 


28.01 


46.04 


28.21 


45.92 


28.42 


64 


55 


47.14 


28.33 


47.02 


28.63 


46.90 


28.74 


46.77 


28.94 


55 


56 


4S.00 


28.84 


47.88 


29.05 


47.76 


29.26 


47.62 


29.47 


66 


67 


48.86 


29.36 


48.73 


29.67 


48.60 


29.78 


48.47 


29.99 


67 


58 


49 . 72 


29.87 


49.58 


30.09 


49.45 


.30.30 


49.32 


30.. 52 


58 


59 


50.57 


30.39 


50.44 


30.61 


50.31 


30.83 


.50.17 


31.05 


59 


60 
61 


51.43 30.90 1 


51.29 


31.13 


51.16 


31.35 


51.02 


31.57 
32.10 


60 
61 


52.29 31.42 


.52.15 


31.66 


52.01 


31.87i 


51.87 


62 


53.14 


31.93 


53.00 


32.16 


.52.86 


32.39 


52.72 


32.63 


62 


63 


54.00 


32.45 


53.86 


32.68 


53.72 


32.92 


.53.57 


33.15 


63 


64 


54.86 


32.96 


54.71 


.33.20 


64.57 


33.44 


64.42 


33.68 


64 


65 


55.72 


33.48 


55.57 


33.72 


55.42 


33.96 


55.27 


34.20 


65 


66 


56.57 


33.99 


66.42 


34.24 


.56.27 


34.48 


56.12 


.34.73 


66 


67 


57.43 


34.51 


57.28 


34.76 


57.13 


35.01 


56.98 


35.26 


67 


68 


58.29 


35.02 


58.13 


36.28 


67.98 


35.63 


57.82 


35.78 


68 


69 


59.14 


35.54 


58.99 


35.80 


58.83 


36.05 


58.67 


36.31 


69 


70 
71 


60.00 


36.05 


59.84 


36.31 


59.68 


36.57 


59.52 
60.37 


36.83 
37.36 


70 

71 


60.86 


36.57 i 


60.70 


36.83 1 


60.54 


37.10 


72 


01.72 


37.08 j 


61.55 


37.35 


61.39 


37.62 1 


61.23 


37.89 


72 


73 


62.57 


37.60 1 


62.41 


37.87 


62 . 24 


38.14 1 


62.08 


38.41 


73 


74 


63.43 


38.111 


63.26 


38.89 


63.10 


38.66] 


62.93 


38.94 


74 


75 


64.29 


38.63! 


64.12 


38.91 


63.95 


39.191 


63.78 


39.47 


75 


76 


65.14 


39.14; 


64.97 


39.43 


64.80 


39.71 


64.63 


39.99 


76 


77 


66.00 


39.66 


65.83 


39.95 


65.65 


40.23 


65.48 


40.. 52 


77 


78 


06.86 


40.17 


66.68 


40.46 


66.51 


40.75 


66.33 


41.04 


78 


79 


07.72 


40.69 


67.54 


40.98 


67.36 


41.28 


07.18 


41. .57 


79 


80 
81 


68.. 57 


41.20 


68.39 


41. .50 


68.21 


41.80 


38.03 


42.10 


80 
81 


69.43 Ul. 72' 


69.25 


42.02 


69.06 


42.32 


68.88 


42.62 


82 


70.29 42.23 1 


70.10 


42.54 


69.92 


42.84 


69.73 


43.15 


82 


83 


71.14 


42.75 


70.96 


43.06 


70.77 


43.37 


70.58 


43.68 


83 


84 


72.00 


43.26 


71.81 


43.58 


71.62 


43.39 


71.43 


44.20 


84 


85 


72.86 


43 . 78 


•72.67 


44.10 


72.47 


44.41 


72.28 


44.73 


85 


86 


73.72 


44.29 


73.52 


44.61 


73.33 


44.93 


73.13 


45.25 


86 


87 


74.57 


44.81 


74.38 


45.13 


74.18 


46.46 


73.98 


45.78 


87 


88 


75.43 


45.32 


75.23 


46.65 


75.03 


45.98 


74.83 


46.31 


88 


89 


76.29 


45.84 


76.09 


46.17 


75.88 


46.. 50 


75.68 


46.83 


89 


90 
91 


77.15 


46.35 


76.94 


46.69 


76 . 74 


47.02 


76. 5Z 


47.36 


90 
91 


78.00 


46.87 


77.80 


47.21 


77.59 


47.65 


77.38 


47.89 


92 


78.86 


47.38 


78.65 


47.73 


78.44 


48.07 


78.23 


48.41 


92 


93 


79.72 


47.90 


79.51 


48.25 


79.30 


48.59 


79.08 


48.94 


93 


94 


80.. 57 


48.41 


80.36 


48.76 


80.15 


49.11 


79.93 


49.47 


94 


95 


81.43 


48.93 


81.22 


49.28 


81.00 


49.64 


80.78 


49.99 


95 


96 


82.29 


49.44 


82.07 


49.80 


81.86 


50.16 


81.63 


50.62 


96 


97 


83.15 


49.96 


82.93 


50.32 


82.71 


50.68 


82.48 


51.04 


97 


98 


84.00 150.47 


83.78 


50.84 


83.56 


51.20 


83.33 


51.57 


98 


99 


84.86 1.50.99 


84.64 


51.36 


84.41 


51.73 


84.18 


52.10 


99 


100 

o 

C 


85.72 151.50 


85.49 


61.88 


85.26 


52.25 


85.04 


52.62 


100 




c 

s 

"cc 

5 
! 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




59 De^. 


58| Deg. 


5^ Deg. 


58i 


Deg. 



66 



TKAVERSE TABLE. 



o 

o 
a 


32 Deg. 


32i Deg. 


32i Deg. 


321 Deg. 




i 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.85 


0.53 


0.85 


0.53 


0.84 


0.54 


0.84 


0.54 


1 


2 


1.70 


1.06 


1.69 


1.07 


1.09 


1.07 


1.68 


1.08 


2 


3 


2.54 


1.59 


2.54 


1.60 


2.53 


1.61 


2.52 


1.62 


3 


4 


3.39 


2.12 


3.38 


2.13 


3.37 


2.15 


3.36 


2.16 


4 


5 


4.24 


2.65 


4.23 


2.67 


4.22 


2.69 


4.21 


2.70 


5 


6 


5.09 


3.18 


5.07 


3.20 


5.06 


3.22 


5.05 


3.25 


6 


7 


5.94 


3.71 


5.92 


3.74 


5.90 


3.76 


5.89 


3.79 


7 


8 


6.78 


4.24 


6.77 


4.27 


6.75 


4.30 


6.73 


4.33 


8 


9 


7.63 


4.77 


7.61 


4.80 


7.59 


4.84 


7.57 


4.87 


9 


10 
11 


8.48 


5.30 


1 8.46 


5.34 


8.43 


5.37 


8.41 


5.41 


10 


9.33 


5.83 


9.30 


5.87 


9.28 


5.91 


9.25 


5.95 


11 


12 


10.18 


6.36 


10.15 


6.40 


10.12 


6.45 


10.09 


6.49 


12 


1^ 


11.02 


6.89 


10.99 


6.94 


10.96 


6.98 


10.93 


7.03 


13 


14 


11.87 


7.42 


11.84 


7.47 


11.81 


7.52 


11.77 


7.57 


14 


15 


12.72 


7.95 


12.69 


8.00 


12.65 


8.06 


! 12.62 


8.11 


15 


16 


13.57 


8.48 


13.53 


8.54 


13.49 


8.60 


13.46 


8.66 


16 


17 


14.42 


9.01 


14.38 


9.07 


14.34 


9.13 


14.30 


9.20 


17 


18 


15.26 


9.54 


15.22 


9.61 


15.18 


9.67 


15.14 


9.74 


18 


19 


16.11 


10.07 


16.07 


10.14 


10.02 


10.21 


15.98 


10.28 


19 


20 


16.96 


10.60 


16.91 
17.76 


10.67 


16.87 


10.75 


16.82 


10.82 


20 


21 


17.81 


11.13 


11.21 


17.71 


11.28 


17.66 


11.36 


21 


22 


18.66 


11.66 


18.61 


11.74 


18.55 


11.82 


18.50 


11.90 


22 


23 


19.51 


12.19 


19.45 


12.27 


19.40 


12.36 


19.34 


12.44 


23 


24 


20.35 


12.72 


20.30 


12.81 


20.24 


12.90 


20.18 


12.98 


21 


25 


21.20 


13.25 


21.14 


13.34 


21.08 


13.43 


21.03 


13.52 


25 


26 


22.05 


13.78 


21.99 


13.87 


21.93 


13.97 


21.87 


14.07 


26 


27 


22.90 


14.31 


22.83 


14.41 


22.77 


14.51 


22 71 


14.61 


27 


28 


23.75 


14.84 


23.68 


14.94 


23.61 


15.04 


23.55 


15.15 


28 


29 


24.59 


15.37 


24.53 


15.47 


24.46 


15.58 


24.. 39 


15.69 


29 


30 


25.44 


15.90 


25.37 


16.01 


25.30 


16.12 


25.2.'^ 


16.23 


30 


31 


26.29 


16.43 


26.22 


16.54 


26.15 


16.66 


26.07 


16.77 


31 


32 


27.14 


16.96 


27.06 


17.08 


26.99 


17.19 


26.91 


17.31 


32 


33 


27.99 


17.49 


27.91 


17.61 


27.83 


17.73 


27.75 


17.85 


33 


34 


28.83 


18.02 


28.75 


18.14 


28.68 


18.27 


28.60 


18.39 


34 


35 


29.68 


18.55 


29.60 


18.68 


29.52 


18.81 


29.44 


18.93 


35 


36 


30.53 


19.08 


30.45 


19.21 


30.36 


19.34 


30.28 


19.48 


36 


37 


31.38 


19.61 


31.29 


19.74 


31.21 


19.88 


31.12 


20.02 


37 


38 


32.23 


20.14 


32.14 


20.28 


32.05 


20.42 


31.96 


20.56 


38 


39 


33.07 


20.67 


32.98 


20.81 


32.89 


20.95 


32.80 


21.10 


39 


40 


33.92 


21.20 


33.83 


21.34 


33.74 


21.49 


33.64 


21.64 


40 
41 


41 


34.77 


21.73 


34.67 


21.88 


34.58 


22.03 


34.48 


22.18 


42 


35.62 


22.26 


35.52 


22.41 


35.42 


22.57 


35.32 


22.72 


42 


43 


36.47 


22.79 


36.37 


22.95 


36.27 


23.10 


.36.16 


23.26 


43 


44 


37.31 


23.32 


37.21 


23.48 


37.11 


23.64 


37.01 


23.80 


44 


45 


38.16 


23.85 


38.06 


24.01 


37.95 


24.18 


37.85 


24.-34 


45 


46 


39.01 


24.38 


38.90 


24.55 


38.80 


24.72 


38.69 


24.88 


46 


47 


39.86 


24.91 


39.75 


25.08 


39.64 


25.25 


39.53 


25.43 


47 


48 


40.71 


25.44 


40.59 


25.61 


40.48 


25.79 


40.37 


25.97 


48 


49 


41.55 


25.97 


41.44 


26.15 


41.33 


26.33 


41.21 


26.51 


49 


50 


42.40 


26.50 


42.29 


26.68 


42.17 


26.86 


42.05 


27.05 


50 


.2 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

c 

d 



58 Deg. 


57| Deg. 


67iDeg. 


571 I 


)eg. 



TRAVERSE TABLE. 



67 





32 Deg. 


32i Deg. 

II 


i 
32i Deg. 1 


321 Deg. 


f 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 


Dep. 


"51 


43.25 


27.03 


43.13 


27.21 


43". of 


27.40 


42.89 


27.. 59 


■"51 


52 


44.10 


27.56 


43.98 


27.75 


43.86 


27.94! 


43.73 


28.13 


52 


53 


4-1.95 


28.09 


44.82 


28.28 


44.70 


28.48 1 


44.58 


28.67 


53 


54 


45.79 


28.62 


45.67 


28.82 


45.54 


29.01 


45.42 


29.21 


54 


55 


46.64 


29.15 


46.51 


29,35 


46.. 39 


29.55 


46.26 


29.75 


55 


56 


47.49 


29.68 


47.36 


29.88 


47.23 


30.09 


47.10 


30.29 


56 


57 


48.34 


30.21 


48.21 


30.42 


48.07 


30.63 


47.94 


30.84 


57 


58 


49.19 


30.74 


49.05 


30.95 


48.92 


31.16 


48.78 


31.38 


58 


59 


50.03 


31.27 


49.90 


31.48 


49.76 


31.70 


49.62 


31.92 


59 


60 
61 


50.88 


31.80 


50.74 


32.02 


50.60 
51.45 


32.24 

32.78 


50.46 


32.46 


60 
61 


51.73 


32.. 33 


51.59 


32.55 


51.30 


33.00 


62 


52.58 


32.85 


52.44 


33.08 


52.29 


33.31 


52.14 


33.54 


62 


63 


53.43 


33.38 


53.28 


33.62 


53.13 


33.85 


52.99 


34.08 


63 


64 


54.28 


33.91 


54.13 


34.15 


53.98 


34.39 


.53.83 


34.62 


64 


65 


55.12 


34.44 


54.97 


34.68 


.54.82 


34.92 


54.67 


35.16 


65 


60 


55.97 


34.97 


55.82 


35.22 


55.66 


35.46 


55.51 


35.70 


66 


67 


56.82 


35.50; 


56.66 


35.75 


56.51 


36.00 


56.35 


36.25 


67 


68 


57.67 


36.03 1 


57.51 


36.29 


57.35 


^.54 


57.19 


36.79 


68 


69 


58.52 


36.56 


58.36 


36.82 


58.19 


37.07 


.58.03 


37.33 


69 


70 
"71 


59.36 


37.09 


59.20 


37.35 


59.04 


37.61 


58.87 


37.87 


70 
71 


60.21 


37.62' 


60.05 


37.89 


59.88 


38.15 


59.71 


38.41 


72 


61.06 


38.15 1 


60.89 


38.42 


60.72 


38.69 


60.55 


38.95 


72 


73 


61.91 


38.68 


61.74 


38.95 


61.57 


39.22 


61.40 


39.49 


73 


74 


62.76 


39.21 


62.58 


39.49 


62.41 


39.76 


62.24 


40.03 


74 


75 


63.60 


39.74 


63.43 


40.02 


63.25 


40.30 


'63.08 


40.57 


75 


76 


64.45 


40.27 


64.28 


40.55 


64.10 


40.83 


163.92 


41.11 


76 


77 


65.30 


40.80 


65.12 


41.09 


64.94 


41.37 


64.76 


41.65 


77 


78 


66.15 


41.33 


65.97 


41.62 


65.78 


41.91 


65.60 


42.20 


78 


79 


67.00 


41.86 


66.81 


42.16 


66.63 


42.45 


66.44 


42.74 


79 


80 


67.84 


42.39 


67.66 


42.69 


67.47 


42.98 


67.28 


43.28 


80 


81 


68.69 


42.92 


68.50 


43.22 


68.31 


43.52 


68.12 


43.82 


81 


82 


69.. 54 


43.45 


69.35 


43.76 


69.16 


44.06 


68.97 


44.30 


82 


83 


70.39 


43.98 


70.20 


44.29 


70.00 


44.60 


69.81 


44.90 


83 


84 71.24 


44.51 


71.04 


44.82 


70.84 


45.13 


70.65 


45.44 


84 


85 72.08 


45.04 


71.89 


45.36 


71.69 


45.67 


171.49 


45.98 


85 


86 72.93 


45.57 


72.73 


45.89 


72.53 


46.21 


72.33 


46.52 


86 


87 173.78 


46.10 


73.58 


46.42 


73.38 


46.75 


73.17 


47.06 


87 


88 


74.63 


46.63 


74.42 


40.96 


74.22 


47.28 


174.01 


47.61 


88 


89 


75.48 


47.16 


75.27 


47.49 


75.06 


47.82 


174.85 


48.15 


89 


90 
91 


76.32 


47.69 


76.12 


48.03 


75.91 


48.36 


[75.69 
76.53 


48.69 


90 
91 


77.17 


48.22 


76.96 


48.56 


76.75 


48.89 


49.23 


92 


78.02 


48.75 


77.81 


49.09 


77.59 


49.43 


77.38 


49 77 


92 


93 


78.87 


49.28 


78.65 


49.63 


78.44 


49.97 


78.22 


.50.31 


93 


94 


79.72 


49.81 


79.50 


50.16 


79.28 


50.51 


79.06 


50.85 


94 


95 


80.56 


50.34 


80.34 


.50.69 


80.12 


51.04 


79.90 


51.39 


95 


96 


81.41 


50.87 


81.19 


51.23 


80.97 


51.58 


80.74 


51.93 


96 


97 


82.26 


51.40 


82.04 


51.70 


81.81 


52.12 


81.58 


.52.47 


97 


98 


83.11 


51.93 


82.88 


52.29 


82.65 


52.66 


82.42 


53.02 


98 


99 


83.96 


.52.46 


83.73 


52.83 


83.50 


53.19 


183.26 


53.56 


99 


100 


84.80 


52.99 


84.57 


53.36 
Lat. 


84.34 


53.73 


84.10 


54.10 


100 

C 


Dep. 


Lat. 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


1 68 Deg. 


571 De^. 

It 


57^ Deg 


57i Deg. 



68 



TRAVERSE TABLE. 



""""■ 










—— • 


5 


33 Deg. 


33^ Deg. 


33i Deg. 


33 i Deg. O 


3 

n 


Lat. 


Dep. 


Lat. 


Dep. 




Lat. 


Dep. 


Lat. 


Dep. 


5 

o 

(6 
1 


0.84 


0.54 


0.84 


0.55 


0.83 


0.55 


0.83 


0.56 


2 


1.68 


1.09 


1.67 


1. 10 


1.67 


1.10 


1.60 


1.11 


2 


3 


2.52 


1.63 


2.51 


1.64 


2.50 


1.66 


2.49 


1.67 


3 


4 


3.35 


2.18 


3.35 


2.19 


3.34 


2.21 


3.33 


2.22 


4 


5 


4.19 


2.72 


4.18 


2.74 


4.17 


2.76 


4.16 


2.78 


5 


6 


5.03 


3.27 


5.02 


3.29 


5.00 


3.31 


4.99 


3.33 


6 


7 


5.87 


3.81 


5.85 


3.84 


5.84 


3.86 


5.82 


3.89 


7 


8 


6.71 


4.36 


6.69 


4.39 


6.67 


4.42 


6.65 


4.44 


8 


9 


7.. 55 


4.90 


7.. 53 


4.93 


7.50 


4.97 


7.48 


5.00 


9 


10 


8.39 


5.45 


8.36 
9.20 


5.48 
6.03 


8.. 34 
9.17 


5.52 


8.31 


5.56 


10 


11 


9.23 


5.99 


6.07 


9.15 


6.11 


11 


12 


10.06 


6.54 


10.04 


6.58 


10.01 


6.62 


9.98 


6.67 


12 


13 


10.90 


7.08 


10.87 


7.13 


10.84 


7.18 


10.81 


7.22 


13 


14 


11.74 


7.62 


11.71 


7.68 


11.67 


7.73 


11.64 


7.78 


14 


1.) 


12.58 


8.17 


12.54 


8.22 


12.51 


8.28 


12.47 


8.33 


15 


16 


13.42 


8.71 


13.38 


8.77 


13.34 


8.83 


13.30 


8.89 


16 


17 


14.26 


9.20 


14.22 


9.32 


14.18 


9.38 


14.13 


9.44 


17 


18 


15.10 


9.80 


15.05 


9.87 


15.01 


9.93 


14.97 


10.00 


18 


19 


15.93 


10.35 


15.89 


10.42 


15.84 


10.49 


15.80 


10.56 


19 


20 


16.77 


10.89 


16.73 


10.97 


16.68 


11.04 


16.63 


11.11 


20 


21 


17.61 


11.44 


17.56 


11.51 


17.51 


11. .59 


17.46 


11.67 


21 


22 


18.45 


11.98 


18.40 


12.06 


)8.35 


12.14 


18.29 


12.22 


22 


23 


19.29 


12.53 


19.23 


12.61 


19.18 


12.69 


19.12 


12.78 


23 


24 


20.13 


13.07 


20.07 


13.16 


20.01 


13.25 


19.96 


13.33 


24 


25 


20.97 


13.62 


20.91 


13.71 


20.85 


13.80 


20.79 


13.89 


25 


26 


21.81 


14.16 


21.74 


14.26 


21.68 


14.35 


21.62 


14.44 


26 


27 


22.64 


14.71 


22.58 


14.80 


22.51 


14.90 


22.45 


15.00 


27 


2S 


23.48 


15.25 


23.42 


15.35 


23.35 


15.45 


23.28 


15.56 


28 


29 


24.. 32 


15.79 


24.25 


15.90 


24.18 


16.01 


24.11 


16.11 


29 


30 
31 


25.16 


16.34 


25.09 


16.45 


25.02 


16.56 


24.94 


16.67 


30 


26.00 


16.88 


25.92 


17.00 


25.85 


17.11 


25.78 


17.22 31 \ 


32 


26.84 


17.43 


26.76 


17.55 


26.68 


17.66 


26.61 


17.78 


32 


33 


27.68 


17.97 


27.60 


18.09 


27.52 


18.21 


27.44 


18.33 


33 


34 


28.51 


18.52 


28.43 


18.64 


28.35 


18.77 


28.27 


18.89 


34 


35 


29.35 


19.06 


29.27 


19.19 


29.19 


19.32 


29.10 


19.44 


35 


36 


30.19 


19.61 


30.11 


19.74 


30.02 


19.87 


29.93 


20.00 


36 


37 


31.03 


20.15 


30.94 


20.29 


30.85 


20.42 


.30.76 


20.. 56 


37 


3S 


31.87 


20.70 


31.78 


20.84 


31.69 


20.97 


31.60 


21.11 


38 


39 32 71 1 


21.24 


32.62 


21.. 38 


32.52 


21.53 


32.43 


21.67 


39 


40 
41 


33.. 55 
34.39 


21.79 


33.45 
34.29 


21.93 

22.48 


33.. 36 
34.19 


22.08 


33.26 


22.22 


40 
41 


22.33 


22.63 


34.09 


22.78 


42 


35.22 


22.87 


35.12 


23.03 


35.02 


23.18 


34.92 


23.33 


42 


43 


36.06 


23.42 


35.96 


23.58 


35.86 


23.73 


35.75 


23.89 


43 


44 


36.90 


23.96 


36.80 


24.12 


36.69 


24.29 


.36.58 


24.45 


44 


45 


37.74 


24.51 


37.63 


24.67 


37.52 


24.84 


37.42 


25 00 


45 


46 


38.58 


25.05 


38.47 


25.22 


38.36 


25.39 


38.25 


25.56 


46 


47 


39.42 


25.60 


39.31 


25.77 


.39.19 


25.94 


39.08 


26.11 


47 


48 


40 . 28 


26.14 


40.14 


26.32 


40.03 


26.49 


39.91 


26 . 67 


48 


49 


41.09 


26.69 


40.98 


26.87 


40.86 


27.04 


40.74 


27.22 


49 


50 

o 

.2 

Q 


41.93 


27.23 


41.81 


27.41 


41.69 


27.60 


41.57 


27.78 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
o 

c 

s 


57 Deg. 


56| Deg. 


56i Deg. 


56 i Deg. 



TRAVERSE TABLE. 



69 



s 
s 

? 

51 


33 Deg. 


33i Deg. 


33^ Deg. 


33i Deg. 


g 

61 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


42.77 


27.78 


42.65 


27.98 


42.53 


28.15 


42.40 


28.33 


52 


43.61 


28.32 


43.49 


28.51 


43.36 


28.70 


43.24 


28.89 


52 


53 


44.45 


28.87 


44.32 


29.06 


44.20 


29.25 


44.07 


29.45 


53 


54 


45.29 


29.41 


45.16 


29.61 


45.03 


29.80 


44.90 


30.00 


64 


55 


46.13 


29.96 


46.00 


30.16 


45.86 


30.36 


45.73 


30.66 


65 


56 


46.97 


30.50 


46.83 


30.70 


46.70 


30.91 


46.56 


31.11 


66 


67 


47.80 


31.04 


47.07 


31.25 


47.53 


31.46 


47.39 


31.67 


67 


58 


48.64 


31.59 


48.50 


31.80 


48.37 


32.01 


48.23 


32.22 


68 


59 


49.48 


32.13 


49.34 


32.35 


49.20 


32.56 


49.06 


32.78 


69 


60 
61 


50.32 


32.68 


50.18 


32.90 


50,03 


33.12 


49.89 


33.33 


60 
61 


51.16 


33.22 


51.01 


33.45 


50.87 


33.67 


50.72 


33.89 


62 


52.00 


33.77 


51.85 


33.99 


51.70 


34.22 


51.55 


34.45 


62 


63 


52.84 


34.31 


52.69 


34.54 


52.53 


34.77 


52.38 


35.00 


63 


64 


53.67 


34.86 


53.52 


35.09 


53.37 


35.32 


53.21 


35.66 


64 


65 


54.51 


35.40 


54.36 


.35.64 


54.20 


35.88 


54.05 


36.11 


65 


66 


55.. 35 


35.95 


55.19 


36.19 


55.04 


36.43 


54.88 


36.67 


66 


67 


56.19 


36.49 


56.03 


36.74 


55.87 


36.98 


55.71 


37.22 


67 


68 


57.03 


37.04 


56.87 


37.28 


56.70 


37.53 


56.54 


37.78 


68 


69 


57.87 


37.58 


57.70 


37.83 


57.54 


38.08 


57.37 


38.33 


69 


70 
71 


58.71 


38.12 


.58.54 


38.38 


68.37 


38.64 


58.20 


38.89 
39.45 


70 

71 


59.55 


38.67 


59.. 38 


38.93 


59.21 


39.19 


.59.03 


72 


00.38 


39.21 


60.21 


39.48 


60.04 


39.74 


.59.87 


40.00 


72 


73 


61.22 


39.76 


61.05 


40.03 


60.87 


40.29 


60.70 


40.56 


73 


74 


62.06 


40.30 


61.89 


40.57 


61.71 


40.84 


61.53 


41.11 


74 


75 


62.90 


40.85 


62.72 


41.12 


62.. 54 


41.40 


62.. 36 


41.67 


75 


76 


63.74 


41.39 


63.56 


41.67 


63.38 


41.95 


63.19 


42.22 


76 


77 


64.58 


41.94 


64.39 


42.22 


64.21 


42.. 50 


64.02 


42.78 


77 


78 


65.42 


42.48 


65.23 


42.77 


65.04 


43.05 


64.85 


43.33 


78 


79 


86.25 


43.03 


66.07 


43.32 


65.88 


43.60 


65.69 


43.89 


79 


80 
81 


67.09 
67.93 


43.57 

44.12 


66.90 


43.86 


66.71 


44.15 


66.52 


44.45 


80 


67.74 


44.41 


67.54 


44.71 


67.35 


45.00 


8l 


82 


68.77 


44.66 


68.58 


44.96 


68.38 


45.26 


68.18 


45.56 


82 


83 


69.61 


45.20 


69.41 


45.51 


69.21 


45.81 


69.01 


46.11 


83 


84 


70.45 


45.75 


70.25 


46.06 


70.05 


46.36 


69.84 


46.67 


84 


85 


71.29 


46.29 


71.08 


46.60 


70.88 


46.91 


70.67 


47.22 


86 


86 


72.13 


46.84 


71.92 


47.15 


71.71 


47.47 


71.51 


47.78 


86 


87 


72.96 


47.38 


72.76 


47.70 


72.55 


48.02 


72.34 


48.33 


87 


88 


73.80 


47.93 


73.59 


48.25 


73.38 


48.57 


73.17 


48.89 


88 


89 


74.64 


48.47 


74.43 


48.80 


74.22 


49.12 


74.00 


49.45 


89 


90 
91 


75.48 


49.02 


75.27 


49.35 


75.05 


49.67 


74.83 
75.66 


.50.00 


90 


76.32 


49.56 


76.10 


49.89 


75.88 


50.23 


50.56 


91 


92 


77.16 


.50.11 


76.94 


.50.44 


76.72 


60.78 


76.50 


61.11 


92 


93 


78.00 


50.65 


77.77 


50.99 


77.55 


51.33 


77.33 


51.67 


93 


94 


78.83 


51.20 


78.61 


51.54 


78.39 


51.88 


78.16 


52.22 


94 


95 


79.67 


51.74 


79.45 


52.09 


79.22 


52.43 


78.99 


62.78 


95 


96 


80.51 


52.29 


80.28 


52.64 


80.05 


52.99 


79.82 


63.33 


96 


97 


81.35 


52.83 


81.12 


.53.18 


80.89 


53.54 


80.65 


53.89 


97 


98 


82.19 


53.37 


81.96 


.53.73 


81.72 


54.09 


81.48 


54.45 


98 


99 


83.03 


53.92 


82.79 


54.28 


82.55 


54.64 


82.32 


65.00 


99 


^00 


83.87 


54.46 


83.63 


.54.83 


83.39 


55.19 


83.15 


.55.56 


100 

1 

CC 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


57 Deg. 


561 Deg. 


561 Deg. 


56i Deg. 


1 


1 




.. ...„..1.,.J 



70 



TK AVERSE TABLE. 



1 


34 Deg. 


34i Deg. 


34^ Deg. 


341 Deg. 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

"O.W 


Dep. 


Lat. 


Dep. 


1 


0.83 


0.56 


0.83 


0.56 


0.67 


0.82 


0.57 


1 


2 


1.66 


1.12 


1.65 


1.13 


1.65 


1.13 


1.64 


1.14 


2 


3 


2.49 


1.68 


2.48 


1.69 


2.47 


1.70 


2.46 


1.71 


3 


4 


3.32 


2.24 


3.31 


2.25 


3.30 


2.27 


3.29 


2.28 


4 


5 


4.15 


2.80 


4.13 


2.81 


4.12 


2.83 


4.11 


2.85 


5 


6 


4.97 


3.36 


4.96 


3.38 


4.94 


3.40 


4.93 


3.42 


6 


7 


5.80 


3.91 


6.79 


3.94 


5.77 


3.96 


5.75 


3.99 


7 


8 


6.63 


4.47 


6.61 


4.50 


6.59 


4.. 53 


6.57 


4.56 


8 


9 


7.46 


5.03 


7.44 


5.07 


7.42 


5.10 


7.39 


5.13 


9 


10 


8.29 


5.59 


8.27 


5.63 


8.24 


5.66 1 


8.22 


5.70 


10 
11 


11 


9.12 


6.15 


9.09 


6.19 


9.07 


6.23 


9.04 


6.27 


12 


9.95 


6.71 


9.92 


6.75 


9.89 


6.80 


9.86 


6.84 


12 


13 


10.78 


7.27 


10.75 


7.32 


10.71 


7.36 


10.68 


7.41 


13 


14 


11.61 


7.83 


11.57 


7.88 


11.54 


7.93 


11.50 


7.98 


14 


15 


12.44 


8.39 


12.40 


8.44 


12.36 


8.50 


12.32 


8.55 


15 


16 


13.26 


8.95 


13.23 


9.00 


13.19 


9.06 


13.15 


9.12 


16 


17 


14.09 


9.51 


14.05 


9.57 


14.01 


9.63 


13.97 


9.69 


17 


18 


14.92 


10.07 


14.88 


10.13 


14.83 


10.20 


14.79 


10.26 


18 


19 


15.75 


10.62 


15.71 


10.69 


15.66 


10.76 


15.61 


10.83 


19 


20 


16.58 


11.18 


16.53 


11.26 


16.48 


11.33 


16.43 


11.40 


20 


21 


17.41 


11.74 


17.36 


11.82 


17.31 


11.89 


17.25 


11.97 


21 


22 


18.24 


12.. 30 


18.18 


12.38 


18.13 


12.46 


18.08 


12.54 


22 


23 


19.07 


12.86 


19.01 


12.94 


18.95 


13.03 


18.90 


13.11 


23 


24 


19.90 


13.42 


19.84 


13.51 


19.78 


13.59 


19.72 


13.68 


24 


25 


20.73 


13.98 


20.66 


14.07 


20.60 


14.16 


20.54 


14.25 


25 


26 


21.55 


14.54 


21.49 


14.63 


21.43 


14.73 


21.36 


14.82 


26 


27 


22.38 


15.10 


22.32 


15.20 


22.25 


15.29 


22.18 


15.39 


27 


28 


23.2] 


15 66 


23.14 


15.76 


23.08 


15.86 


23.01 


15.96 


28 


29 


24.04 


16.22 


23.97 


16.32 


23.90 


16.43 


23.83 


16.53 


29 


30 


24.87 


16.78 


24.80 


16.88 


24.72 


16.99 


24.65 


17.10 


30 


31 


25.70 


17.33 


25.62 


17.45 


25.55 


17.56 


25.47 


17.67 


31 


32 


26.53 


17.89 


26.45 


18.01 


26.37 


18.12 


26.29 


18.24 


32 


33 


27.36 


18.45 


27.28 


18.. 57 


27.20 


18.69 


27.11 


18.81 


33 


34 


28.19 


19.01 


28.10 


19.14 


28.02 


19.26 


27.94 


19.38 


34 


35 


29.02 


19.57 


28.93 


19.70 


28.84 


19.82 


28.76 


19.95 


35 


36 


29.85 


20.13 


29.76 


20.26 


29.67 


20.39 


29.58 


20.52 


36 


37 


30.67 


20.69 


30.58 


20.82 


30.49 


20.96 


30.40 


21.09 


37 


38 


31.50 


21.25 


31.41 


21.39 


31.32 


21.52 


31.22 


21.66 


38 


39 


32.33 


21.81 


32.24 


21.95 


32.14 


22.09 


32.04 


22.23 


39 


40 


33.16 


22.37 


33.06 


22.51 


.32.97 


22.06 


32.87 


22.80 


40 


41 


33.99 


22.93 


33.89 


23.07 


33.79 


23.22 


33.69 


23.37 


41 


42 


34.82 


23.49 


34.72 


23.64 


34.61 


23.79 


34.51 


23.94 


42 


43 


35.65 


24.05 


35.54 


24.20 


35.44 


24.36 


36.33 


24.51 


43 


44 


36.48 


24.60 


36.37 


24.76 


36.26 


24.92 


36.15 


25.08 


44 


45 


37.31 


25.16 


37.20 


25.. 33 


37.09 


25.49 


36.97 


25.65 


45 


46 


38.14 


25.72 


38.02 


25.89 


37.91 


26.05 


37.80 


26.22 


46 


47 


38.96 


26.28 


38.85 


26.45 


38.73 


26.62 


38. G2 


26.79 


47 


48 


39.79 


26.84 


39.68 


27.01 


39.56 


27.19 


39.44 


27.36 


48 


49 


40.62 


27.40 


40.50 


27.58 


40.38 


27.75 


40.26 


27.93 


49 


50 


41.45 


27.96 


41.33 


28.14 


41.21 
Dep. 


28.32 


41.08 


28.50 


50 


.2 
Q 


Dop. 


Lat. 


Dep. 


Lat. 


Lat. 


Dep. 


Lat. 


c 
Q 


56 Deg. 


551 Deg. 


55iDeg. 


5oi 


Deg. 



TRAVERSE TABLE. 



71 



t 

.51 


34 Deg. 


34iDeg. 


34i Deg. 


341 Deg. 


S 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
42.03 


Dep. ! 


Lat. 


Dep. 


42.28 


28.52 


42.16 


28.70 


28.89 


41.90 


29.07 


52 


43.11 


29.08 


42.98 


29.27 


42.85 


29.45 


42.73 


29.64 


52 


53 


43.94 


29.64 


43.81 


29.83 


43.68 


30.02 


43.. 55 


30.21 


53 


54 


44.77 


30.20 


44.64 


30.39 


44.. 50 


30.59 


44.37 


30.78 


54 


55 


45.60 


30.76 


45.46 


30,95 


45.33 


31.15 


45.19 


31.35 


55 


56 


46.43 


31.31 


46.29 


31.52 


46.15 


31.72 


46.01 


31.92 


56 


57 


47.26 


31.871 


47.12 


32.08 


46.98 


32.29 


46.83 


32. 4« 


57 


58 


48.08 


32.43 


47.94 


32.64 


47.80 


.32.85 


47.66 


33. OG 


58 


59 


48.91 


32.99 


48.77 


33.21 


48.62 


33.42 


48.48 


33.63 


59 


60 
61 


49.74 


33.55 


49.60 


33.77 


49.45 


33.98 


49.30 


34.20 


60 
61 


50.57 


34.11 


50.42 


34.33 


50.27 


34.55 


.50.12 


34.77 


62 


51.40 


34.67 


51.25 


34.89 


51.10 


35.12 


50.94 


35.34 


62 


63 


52.23 


35.23 


52.08 


35.46 


51.92 


35.68 


51.76 


35.91 


63 


64 


53.06 


35.79 


52.90 


36.02 


52.74 


36.25 


52.59 


36.48 


64 


65 


53.89 


36.35 


53.73 


36.58 


53.57 


36.82 


53.41 


37.05 


65 


66 


54.72 


36.91 


54.55 


37.15 


54.39 


37.38 


54.23 


37.62 


66 


67 


55.55 


37.46 


55.38 


37.71 


55.22 


37.95 


55.05 


38.19 


67 


68 


.56.37 


38.03 


56.21 


38.27 


56.04 


38.52 


55.87 


38.76 


68 


69 


57.20 


38.58 


57.03 


38.83 


56.86 


39.08 


56.69 


39.33 


69 


70 

■ 71 


58.03 


39.14 


57.86 


39.40 


57.69 


39.65 


57.52 


39.90 


70 

71 


58.86 


39.70 


58.69 


39.96 


58.51 


40.21 


58.34 


40.47 


72 


59.69 


40.26 


59.51 


40.. 52 


59.34 


40.78 


59.16 


41.04 


72 


73 


60.52 


40.82 


60.34 


41.08 


60.16 


41.35 


59.98 


41.61 


73 


74 


61.35 


41.38 


61.17 


41.65 


60.99 


41.91 


60.80 


42.18 


74 


75 


62.18 


41.94 


61.99 


42.21 


61.81 


42.48 


61.62 


42.75 


75 


76 


63.01 


42.50 


62.82 


42.77 


62.63 


43.05 


62.45 


43.. 32 


76 


77 


63.84 


43.06 


63.65 


43.34 


63.46 


43.61 


63.27 


43.89 


77 


78 


64.66 


43.62 


64.47 


43.90 


64.28 


44.18 


64.09 


44.46 


78 


79 


65.49 


44.18 


65.30 


44.46 


65.11 


44.75 


64.91 


45.03 


79 


80 
81 


66.32 


44.74 


66.13 


45.02 


65.93 


45.31 


65.73 


45 . 60 
46.17 


80 
81 


67.15 


45.29 


66.95 


45.59 


66.75 


45.88 


66.55 


82 


67.98 


45.85 


67.78 


46.15 


67.58 


46.45 


67.37 


46.74 


82 


83 


68.81 


46.41 


68.61 


46.71 


68.40 


47.01 


68.20 


47.31 


83 


84 


69.64 


46.97 


69.43 


47.28 


69.23 


47.58 


69.02 


47.88 


84 


85 


70.47 


47.53 


70.26 


47.84 


70.05 


48.14 


69.84 


48.45 


85 


86 


71.30 


48.09 


71.09 


48.40 


70.87 


48.71 


70.66 


49.02 


86 


87 


72.13 


48.65 


71.91 


48.96 


71.70 


49.28 


71.48 


49.59 


87 


88 


72.96 


49.21 


72.74 


49.53 


72.52 


49.84 


72.30 


50.16 


88 


89 


73.78 


49.77 


73.57 


50.09 


73.35 


50.41 


73.13 


50.73 


89 


90 
91 


74.61 


50.33 


74.39 


50.65 


74.17 


50.98 


73.95 


51.30 


90 
91 


75.44 


50.89 


75.22 


51.22 


75.00 


51.54 


74.77 


51.87 


92 


76.27 


51.45 


76.05 


51.78 


75.82 


52.11 


75.59 


52.44 


92 


93 


77.10 


52.00 


76.87 


52.34 


76.64 


52.68 


76.41 


53.01 


93 


94 


77.93 


52.56 


77.70 


52.90 


77.47 


53.24 


77.23 


53.58 


94 


95 


78.76. 
79.59* 


53.12 


78.53 


53.47 


78.29 


53.81 


78.06 


54.15 


95 


96 


53.68 


79.35 


54.03 


179.12 


54.37 


78.88 


54.72 


96 


97 


80.42 


54.24 


80.18 


54.59 


79.94 


54.94 


79.70 


55.29 


97 


98 


81.25 


,54.80 


81.01 


55.15 


80.76 


55.51 


80.52 


.55.86 


98 


99 


82.07 


55.36 


81.83 


55.72 


81.59 


,56.07 


81. .34 


56.43 


99 


100 

"oa 

Q 


82.90 


55.92 


82.66 


.56.28 


82.41 


56.64 


82.16 


.57.00 


100 

<u 
c 

.2 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


56 Deg. 


55| Deg. 


551 Deg. 


55i Deg. 



72 



TRAVERSE TABLE. 



o 

3 
9 


35 Deg. 

1 


351 Deg. 


35i Deg. 


351 Deg. 


1 

o 
p 


Lat. 


Dcp. 


Lat. 
0.82 


Dep. 


Lat. 

0.81 


Dep. 


Lat. 


Dep. 


1 


0.82 


0.57 


0.58 


"(Tss" 


0.81 


"0^58" 


I 


2 


1.64 


1.15 


1.63 


1.15 


1.63 


1.16 


1.62 


1.17 


2 


3 


2.46 


1.72 


2.45 


1.73 


2.44 


1.74 


2.43 


1.75 


3 


4 


3.28 


2.29 


3.27 


2.31 


3.26 


2.32 


3.25 


2. .34 4 1 


5 


4.10 


2.87 


4.08 


2.89 


4.07 


2.90 


4.06 


2.92 


5 


6 


4.91 


3.44 


4.90 


3.46 


4.88 


3.48 


4.87 


3.51 


6 


7 


5.73 


4.01 


5.72 


4.04 


5.70 


4.06 


5.68 


4.09 


7 


8 


6.. 55 


4.59 


6.53 


4.62 


6.51 


4.65 


6.49 


4.67 


8 


9 


7.37 


5.16 


7.35 


5.19 


7.33 


5.23 


7.30 


5.26 


9 


10 
' 11 


8.19 


5.74 


8.17 


5.77 


8.14 


5.81 


8.12 


5.84 


10 


9.01 


6.31 


8.98 


6.35 


8.96 


6.39 


8.93 


6.43 


11 


12 


9.83 


6.88 


9.80 


6.93 


9.77 


6.97 


9.74 


7.01 12 1 


13 


10.65 


7.46 


10.62 


7.50 


10.. 58 


7.55 


10.55 


7.60 


13 


14 


11.47 


8.03 


11.43 


8.08 


11.40 


8.13 


11.36 


8. IS 


14 


15 


12.29 


8.60 


12.25 


8.6.6 


12.21 


8.71 


12.17 


8.76 


15 


16 


13.11 


9.18 


13.07 


9.23 


13.03 


9.29 


12.99 


9.35 


16 


17 


13.93 


9.75 


13.88 


9.81 


13.84 9.87i 


13.80 


9.93 


17 


18 


14.74 


10.32 


14.70 


10.39 


14.65 


10.45 


14.61 


10.. 52 


18 


19 


15.56 


10.90 


15.. 52 


10.97 


15.47 


11.03 


15.42 


11.10 


19 


20 


16.38 


11.47 


16.33 


11. .54 


16.28 


11.61 i 


16.23 


11.68 


20 


21 


17.20 


12.05 


17.15 


12.12 


17.10 


12.19 1 


17.04 


12.27 


21 


22 


13.02 


12.62 


17.97 


12.70 


17.91 


12.78 


17.85 


12.85 


22 


23 


18.81 


13.19 


18.78 


13.27 


18.72 


13.36 


18.67 


13.44 


23 


24 


19.66 


13.77 


19.60 


13.85 


19.54 


13.94 


19.48 i 14.02 


24 


25 


20.48 


14.34 


20.42 


14.43 


20.. 35 


14.52 


120.29 


14.61 


25 


26 


21.30 


14.91 


21.23 


15.0' 


21.17 


15.10 


121.10 


15.19 


26 


27 


22.12 


15.49 


22.05 


15.58 


21.98 


15.68 


21.91 


15.77 


27. 


23 


22.94 


16.06 


22.87 


16. IS 


22.80 


16.26 


122.72 


16.36 


28 


29 


23.76 


16.63 


23.68 


16.74 


23.61 


16.84 


123.54 


16.94 


29 


30 
31 


24.57 


17.21 


24.50 


17. &1 


24.42 


17.42 


124.35 


17.53 


30 


25.39 


17.7S 


25.32 


17.89 


25.24 


18.00 


[25.16 
125.97 


18.11 


31 


32 


28.21 


18.. 35 


26.13 


18.47 


26.05 1 18.58 


18.70 


32 


33 


27.03 


18.93 


26.95 


19.05 


26.87 


19.16 


126.78 


19.28 


33 


34 


27.85 


19.50 


27.77 


19.62 


27.68 


19.74 


127.59 


19.86 


34 


35 


28 . 67 


20.08 


28.58 


20.20 


28.49 


20.32 


28.41 


20.45 


35 


36 


29.49 


20.65 


29.40 


20.78 


29.31 


20.91 


'29.22 


21.03 


36 


37 


30.31 


21.22 


30.22 


21.35 


30.12 


21.49 


30.03 


21.62 


37 


38 


31.13 


21.80 


31.03 


21.93 


30.94 


22.07 


30.84 


22.20 


38 


39 


31.95 


22.37 


31.85 


22.51 


31.75 


22.65 


31.65 


22.79 


39 


40 


32.77 


22.94 


32.67 


23.09 


32.56 


23.23 


1 32.46 


23.37 


40 


41 


33.59' 


23.52 


33.48 


23.66 


33. 3S 


23.81 


133.27 


23.95 


41 


42 


34.40 


24.09 


34.30 


24.24 


34.19 


24.39 


34.09 


24.. 54 


42 


43 


35.22 


24.66 


35.12 


24.82 


35.01 


24.97 


34.90 


25.12 


43 


44 


36.04 


25.24 


35.93 


25.39 


35.82 


25.55 


35.71 


25.71 


44 


45 


36.86 


25.81 


36.75 


25.97 


36.64 


26.13 


36.. 52 


«6.29 


45 


46 


37.68 


26.38 


.37.57 


26.55 


37.45 


26.71 


37.33 


26.88 


46 


47 


3S..50 


26.96 


.38.38 


27.13 


38.26 


27.29 


38.14 


27.46 


47 


48 


39.32 


27.53 


.39.20 


27.70 


.39.08 


27.87 


38.96 


28.04 


48 


49 


40.14 


28.11 


40.02 


28. as 


39.89 


28.45 


39.77 


28.63 


49 


50 


40.96 


28.68 


40.83 


28.86 
Lat. 


40.71 


29.04 


40.58 


29.21 


50 


6 


Dep. 


Lat. 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


§ 

c 

"an 

5 


.2 

Q 


55 Deg. 


541 


Deg. 


54^ Deg. 


544 Deg. 



TnAVERSE TABLE. 



73 



51 


35 Deg. 


35i Deg. 


35i Deg. 


351 Deg. 


C 

1' 
s 

n 
a 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

41.. 39 


Dep. 

29.80 


41.78 


29.25 


41.65 


29.43 


41.52 


29.62 


52 


42.60 


29.83 


42.47 


30.01 


42.. 33 


30.20 


42.20 


30.38 


62 


53 


43.42 


30.40 


43.28 1 30.59 


43.15 


30.78 


43.01 


80.97 


53 


54 


44.23 


30.97 


44.10 


31.17 


43.96 


31.36 


43.82 


3i..55 


54 


55 


45.05 


31.55 


44.92 


31.74 


44.78 


31.94 


44.64 


32.13 


55 


56 


45.87 


32.12 


45.73 


32.32 


45.. 59 


32.52 


45.45 


32 . 72 


66 


57 


46.69 


32.69 


46.55 


32.90 


46.40 


33.10 


46,26 


33-30 


57 


58 


47.51 


.33.27 


47.37 


33.47 


47.22 


33.68 


47.07 


33.89 


58 


59 


48.33 


33.84 


48.18 


34.05 


48.03 


34.26 


47-88 


34.47 


69 


60 
61 


49.15 


34.41 


49.00 


34.63 


48.85 


34.84 


48.69 
49.51 


35.05 
35.64" 


60 
61 


49.97 


34.99 


49.82 


.35.21 


49.66 


35.42 


62 


60.79 


35.56 


50.63 


.35.78 


50.48 


36.00 


50.32 


36.22 


62 


63 


51.61 


36.14 


51.45 


36.36 


51.29 


36.58 


51.13 


36.81 


63 


64 


52.43 


36.71 


.52.27 


36.94 


.52.10 


37.16 


51.94 


37-39 


64 


65 


53.24 


37.28 


53.08 


37.51 


52.92 


37.75 


52.75 


37.98 


65 


66 


54.06 


37.86 


53.90 


38.09 


,53.73 


.38.33 


53.. 56 


38.56 


66 


67 


54.88 


38.43 


.54.71 


38.67 


.54.55 


38.91 


54.38 


39.14 


67 


68 


55.70 


39.00 


55.. 53 


39.55 


.55.36 


39.49 


55.19 


39.73 


68 


69 


56.. 52 


39.58 


56.35 


39.82 


,56.17 


40.07 i 56.00 


40.31 


69 


70 
71 


57.34 


40.15 


57.10 


40 40 


56.99 


40.65 ' 56.81 


40.90 
41.48 


70 
71 


58.16 


40.72 


57.98 


40.98 


57.80 


41.23 


57 - 62 


72 


58.98 


41.30 


58.80 


41.. 55 


58 . 62 


41.81 


58-43 


42.07 


72 


73 


.59.80 


41.87 


59.61 


42.13 


59.43 


42.39 


59-24 


42.65 


73 


74 


60.62 


42.44 


60.43 


42.71 


60.24 


42.97 


60-06 


43.23 


74 


75 


61.44 


43.02 


61.25 


43.29 


61.06 


43.55 


60-87 


43.82 


75 


76 


62.26 


43.59 


62.06 


43.86 


61.87 


44.13 


61.68 


44.40' 76 1 


77 


63.07 


44.17 


62.88 


44.44 


62.69 


44.71 


62.49 


44.99 


77 


78 


63.89 


44.74 


63.70 


45.02 


63.50 


45.29 


63.30 


45.57 


78 


79 


64.71 


45.31 


64.51 


45.59 


64.32 


45.88 


64.11 


40.16 


79 


80 
81 


65.. 53 


45.89 


65.. 33 
66.15 


46.17 
46.75 


65.13 


46.46 


64.93 
65.74 


46.74 


80 
81 


6H.35 


46.46 


65.94 


47.04 


47.32 


82 


67.17 


47.03 


66.90 


47.33 


66.76 


47.62 


66.. 55 


47.91 


82 


83 


67.99 


47.61 


67.78 


47.90 


67.. 57 


48.20 


67.36 


48.49 


83 


84 


6S.81 


48.18 


68.60 


48.48 1 


68.. 39 


48.78 


68.17 


49.08 


84 


85 


09.63 


48.75 


69.41 


49.06 1 


69.20 


49.-36 


68.98 


49.66 


85 


86 


70.45 


49.33 


70.23 


49.63 


70.01 


49.94 


69.80 


,50.25 


86 


87 


71.27 


49.90 


71.05 


50.21 


70.83 


.50.-52 


70.61 


50.83 


87 


88 


72.09 


50 47 


71.86 


.50.79 


71.64 


51.10 


71-42 


51.41 


88 


89 


72.90 


51.05 


72.68 


51.37 


72.46 


51.68 


72-23 


52.00 


89 


90 
91 


73.72 


51.62 


73.50 


51.94 


73^7. 


.52.26 


73.04 


,52.58 


90 


74.54 


52.20 


74.31 


.52.52 


74.08 


.52.84 


73.85 


53.17 


91 


92 


75.36 


52.77 


75.13 


53.10 


74.90 


53.42 


74.66 


53.75 


92 


93 


76.18 


53., 34 


75.95 


53.67 


75.71 


54.01 


75.48 


54.34 


93 


94 


77.00 


53.92 


76.76 


54.25 


76.-53 


.54.. 59 


76.29 


54.92 


94 


95 


77.82 


54.49 


77.58 


54.83 


77.34 


55.17 


77.10 


55.50 


95 


96 


78.64 


55.06 


78.40 


.55.41 


78.16 


55.75 


77.91 


56.09 


96 


97 


79.46 


55.64 


79.21 


.55.98 


7S 97 


56.33 


78.72 


.56.67 


97 


98 


80.28 


56.21 


80.03 


.56.. 56 


79.78 56.91 


79.53 


57.26 


98 


99 


81.10 


56.78 


80.85 


57.14 


80.60 57.49 


80.35 


-57.84 


99 


J 00 


81.92 


57.36 


81.66 


57.71 


81.41 


58.07 


81.16 


58.42 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat- 


c 


55 Deg. 


541 Deg. 


1 
54i Deg. 


54i Deg. 



u 



TTIAVEKSr. TAHI-H. 



o 


1 36 Deg. 


36i Deg. 


36^ Deg. 


361 Deg. 


C 


? 

1 


1 








3 

? 

' 1 


I Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.81 


"~0".59" 


0.81 


0.59 


0.80 


0.59 


0.80 


0.60 


2 


1.62! 1.18 


1.61 


1.18 


1.61 


1.19 


1.60 


1 20 


2 


3 


2.43 1.76 


2.42 


1.77 


2.41 


1.78 


2.40 


1.79 


3 


4 


3.24 2.35 


3.23 


2.37 


3.22 


2.38 


3.20 


2.39 


4 


5 


4.05! 2.94 


4.03 


2.96 


4.02 


2.97 


4.01 


2.99 


5 


6 


4.85 1 3.53 


4.84 


3.55 


4.82 


3.57 


4.81 


3.59 


6 


7 


5.66 4.11 


5.65 


4.14 


5.63 


4.16 


5.61 


4.19 


7 


8 


6.47, 4.70 


6.45 


4.73 


6.43 


4.76 


6.41 


4.79 


8 


9 


7.28 1 5.29 


7.26 


5.32 


7.23 


5.35 


7.21 


5. 38 


9 


10 

11 


8.09 1 5.88 


8.06 


5.91 


8.04 


5.95 


8.01 


5.98 


10 
11 


8.90; 6.47 


8.87 


6.. 50 


8.84 


6.54 


8.81 


6.58 


12 


9.71 


7.05 


9.68 


7.10 


9.65 


7.14 


9.61 


7.18 


12 


13 


10.52 


7.64 


10.48 


7.69 


10.45 


7.73 


10.42 


7.78 


13 


14 


11.33 


8.23 


11.29 


8.28 


11.25 


8.33 


11.22 


8.38 


14 


15 


12.14 


8.82 


12.10 


8.87 


12.06 


8.92 


12.02 


8.97 


15 


16 


12.94 


9.40 


12.90 


9.46 


12.86 


9.53 


12.82 


9.57 


16 


17 


13.75 


9.99 


13.71 


10.05 


13.67 


10.11 


13.62 


10.17 


17 


18 


14.50 


10.58 


14.52 


10.64 


14.47 


10.71 


14.42 


10.77 


18 


19 


15.37 


11.17 


15.32 


11.23 


15.27 


11.30 


15.22 


11.37 


19 


20 
21 


16.18 


11.76 


16.13 


11.83 


16.08 


11.90 


16.03 


11.97 
12.56 


20 
.21 


16.99 


12. .34 


16.94 


12.42 


16.88 


13.49 


16.83 


22 


17.80 


12.93 


17.74 


13.01 


17.68 


13.09 


17.63 


13.16 


22 


23 


18.61 


13.52 


18.55 


13.60 


18.49 


13.68 


18.43 


13.76 


23 


24 


19.42 


14.11 


19.35 


14.19 


19.29 


14.28 


19.23 


14.36 


24 


25 


20.23 


14.69 


20.16 


14.78 


20.10 


14.87 


20.03 


14.96 


25 


26 


21.03 


15.28 


20.97 


15.37 


20.90 


15.47 


20.83 


15.66 


26 


27 


21.84 


15.87 


21.77 


15.97 


21.70 


16.06 


21.63 


16.15 


27 


28 


22.65 


16.46 


22.58 


16.56 


22.51 


16.65 


22.44 


16.75 


28 


29 


23.46 


17.05 


23.39 


17.15 


23.31 


17.25 


23.24 


17.35 


29 


30 
31 


24.27 


17.63 


24.19 


17.74 


24.12 


17.84 


24.04 


17.95 


30 
31 


25.08 


18.22 


25.00 


18.33 


24.92 


18.44 


24.84 


18.55 


32 


25.89 


18.81 


25.81 


18.92 


25.72 


19.03 


25.64 


19.15 


32 


33 


26.70 


19.40 


26.61 


19.51 


26.53 


19.63 


26.44 


19.74 


33 


34 


27.51 


19.98 


27.42 


20.10 


37.33 


20.22 


27.24 


20.34 


34 


35 


28.32 


20.57 


28.23 


20.70 


38.13 


20.82 


28.04 


20.94 


35 


36 


29.12 


21.16 


29.03 


21.29 


38.94 


21.41 


28.85 


21.54 


36 


37 


29.93 


21.75 


29.84 


21.88 


39.74 


22.01 


29.65 


22.14 


37 


38 


30.74 


23.34 


30.64 


22.47 


30.55 


22.60 


30.45 


22.74 


38 


39 


31.55 


22.92 


31.45 


23.06 


31.35 


23.20 


31.25 


23.33 


39 


40 
41 


32.36 


23.51 


32.26 


23.65 


32.15 


23.79 


32.05 


23.93 


40 
41 


33.17 


24.10 


33.06 


24.24 


32.96 


24.39 


32.85 


24.53 


42 


33.98 


24.69 


33.87 


24.83 


33.76 


24.98 


33.65 


25.13 


42 


43 


34.79 


25.37 


34.68 


25.43 


34.57 


25.58 


34.45 


25.73 


43 


44 


35.60 


25.86 


35.48 


26.02 


35.37 


36.17 


35.26 


26.33 


44 


45 


3G.41 


26.45 


36.29 


26.61 


36.17 


36.77 


36.06 


26.92 


45 


46 


37.21 


27.04 


37.10 


27.20 


36.98 


37.36 


36.86 


27.52 


46 


47 


38.03 


27.63 


37.90 


27.79 


37.78 


37.96 


37.66 


28.12 


47 


48 


38.83 


28.21 


38.71 


28.38 


38.59 


28.55 


38.46 


28.72 


48 


49 


39.64 


28.80 


39.52 


28.97 


39.39 


29.15 


39.26 


29.33 


49 


50 


40.45 


29.39 


40.32 


29.57 


40.19 


29.74 


40.06 


39.92 


50 
a 

■s 


1 


Dop. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


54 Deg. 


53| Deg. 


53i Deg. 


53i Deg. 



TEAVERSE TABLE. 



75 



o 

1 

? 

51 


36 Deg. 


11 
36i Deg. 


36i Deg. 


361 Deg. 


O 

3 
? 

'51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep 


Lat. 


Dep. 


41.26 


29.98 


41.13 


ToTTe" 


41.00 


30.34! 


40.86 


30.51 


52 


42.07 


30.56 


41.94 


30.75 


41.80 


30.93 


41.67 


31.11 


52 


63 


42.88 


31.15 


42.74 


31.34 


42.60 


31.53 


42.47 


31.71 


63 


54 


43.69 


31.74 


43.55 


31.93 


43.41 


32.12 


43.27 


32.31 


64 


65 


44.50 


32.33 


44.35 


32.52 


44.21 


32.72 


44.07 


32.91 


55 


56 


45.30 


32.92 


45.16 


33.11 


45.02 


33.31 


44.87 


33.51 


56 


57 


46.11 


33.50 


45.97 


33.70 


45.82 


33.90 


45.67 


34.10 


57 


58 


46.92 


34.09 


46.77 


34.30 


46.62 


34.50 


46.47 


34.70 


68 


59 


47.73 


.34.68 


47.58 


34.89 


47.43 


35 09 


47.27 


35.30 


69 


GO 
61 


48.. 54 


35.27 


48.39 


.35.48 


48.23 


35.69 


48.08 


35.90 


60 
61 


49.35 


35.85 


49.19 


3G.07 


49.04 


36.28 1 


48.88 


36.50 


62 


50.16 


36.44 


.50.00 


36.66 


49.84 


36.88 


49.68 


37.10 


62 


63 


50.97 


37.03 


50.81 


37.25 


50.64 


37.47 


50.48 


37.69 


63 


64 


51.78 


37.62 


51.61 


37.84 


51.45 


38.07 


51.28 


38.29 


64 


65 


52.59 


38=21 


52.42 


38.44 


52.25 


3S.66 


52.08 


38.89 


65 


66 


53.40 


38.79 


53.23 


39.03 


53.05 


39.26 


52.88 


39.49 


66 


67 


54.20 


39.38 


54.03 


39.62 


53.86 


39.85 


53.68 


40.09 


67 


68 


55.01 


39.97 


54.84 


40.21 


64.66 


40.45 


54.49 


40.69 


68 


69 


55.82 


40.56 


55.04 


40.80 


55.47 


41.04; 


55.29 


41.28 


69 


70 
71 


50.63 


41.14 


56.45 


41.39 


56.27 


41.64* 


56.09 


41.88 

42.48 


70 

71 


57.44 


41.73 


57.26 


41.98 


57.07 


42.23 


56.89 


72 


58.25 


42.32 


58.06 


42.57 


57.88 


42.83 


57.69 


43.08 


72 


73 


59.06 


42.91 


.58.87 


43.17 


58.68 


43.42 


58.49 43.68 


73 


74 


59.87 


43.50 1 


59.68 


43.76 


59.49 


44.02 


69.29 44.28 


74 


75 


60.68 


44.08 


60.48 


44.35 


60.29 


44.61 


60.09 44.87 


75 


76 


61.49 


44.67 


61.29 


44.94 


61.09 


45.21 


60.90 


45.47 


76 


77 


62.29 


45.26 


62.10 


45.53 


61.90 


45.80 


61.70 


46.07 


77 


78 


63.10 


45.85 


62.90" 


46.12 


62.70 


46.40 


62.50 


46.67 


78 


79 


63.91 


46.43 


63.71 


46.71 


63.50 


46.99 


63.30 


47.27 


79 


80 
81 


64.72 


47.02 


64.52 


47.30 


64.31 


47.59 


! 64.10 


47.87 


80 
81 


65.53 


47.61 


65.32 


47.90 


65.11 


48.18 


i 64.90 


48.46 


82 


66.34 


48.20 


66.13 


48.49 


65.92 


48.78 


'65.70 


49.06 


82 


83 


67.15 


48.79 


66.93 


49.08 


66.72 


49.37 


66.50 


49.66 


83 


84 


67.96 


49.37 


67.74 


49.67 


67.52 


49.97 


'67.31 


50.26 


84 


85 


68.77 


49.96 


68.55 


.50.26 


68.33 


50.56 


68.11 


50.86 


85 


86 


69.58 


50.55 


60.35 


50.85 


69.13 


51.15 


'68.91 


51.46 


86 


87 


70.38 


51.14 


70.16 


51.44 


69.94 


51.75 


69.71 


52.05 


87 


88 


71.19 


51.73 


70.97 


52.04 


70.74 


52.34 


70.51 


62.65 


88 


89 


72.00 


52.31 


71.77 


52.63 


71.54 


52.94 


171.31 


53.25 


89 


90 
91 


72.81 


52.90 


72.58 


53.22 


72.35 


53.53 


i72.11 


53.85 


90 
91 


73.62 


53.49 


73.39 


53.81 


73.15 


54.13 


72.91 


64.45 


92 


74.43 


54.08 


74.19 


54.40 


73.95 


54.72 


73.72 


55.05 


92 


93 


75.24 


.54.66 


75.00 


54.99 


74.76 


55.32 


! 74.52 


55.64 


93 


94 


76.05 


55.25 


75.81 


55.. 58 


75.56 


55.91 


1 75.32 


56.24 


94 


95 


76.86 


55.84 


76.61 


56.17 


76.37 


66.51 


76.12 


56.84 


95 


96 


77.67 


56.43 


77.42 


.56.77 


77.17 


57.10 


76.92 


57.44 


96 


97 


78.47 


57.02 


78.23 


57.38 


77.97 


57.70 


77.72 


58.04 


97 


98 


79.28 


57.60 


79.03 


57.95 


78.78 


58.29 


78.. 52 


58.64 


98 


99 80.09 


58.19 


79.84 


58.54 


79.58 


58.89 


79-32 


59.23 


99 


100 

8 

a 

Li 


80.90 


58.78 


80.64 


59.13 


80.39 


59.48 


80.13 
Dep. 


59.83 
Lat. 


100 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


54 Deg. 


531 Deg. 


53i Deg. 


53i Deg. 



?6 



TRAVERSE TAHLK. 



if 


37 Deg. 1 


37;^ Deg. 


37i Deg. 


37| Deg. 


in' 
n 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 
0.79 


Dep. 


0.80 


0.60 


0.80 0.61 


0.79 


0.61 


0.61 


1 


2 


1.60 


1.20 


1..59 


1.21 


1.59 


1.22 


1.58 


1.22 


2 


3 


2.40 


1.81 


2.39 


1.82 


2.38 


1.83 


2.37 


1.84 


3 


4 


3.19 


2.41 


3.18 


2.42 


3.17 


2.13 


3.16 


2.45 


4 


5 


3.99 


3.01 


3.98 


3.03 


3.97 


3.04! 


3.95 


3.06 


5 


6 


4.79 


3.61 


4.78 


3.63 


4.76 


3.65 


4.74 


3.67 


6 


7 


5.59 


4.21 


5.57 


4.24 


5.. 55 


4.26 


5.53 


4.29 


7 


8 


6.39 


4.81 


6.37 


4.84 


6.35 


4.87 


6.33 


4.90 


8 


9 


7.19 


5.42 


7.16 


5.45 


7.14 


5.48 


7.12 


5.51 


9 


10 


7.99 


6.02 


7.96 


6.05 


7.93 


6.09 1 
6.70 


7.91 


6.12 


10 
11 


11 


8.78 


6.62 


8.70 


6.66 


8.73 


8.70 


6.73 


12 


9.58 


7.22 


9.55 


7.26 


9.52 


7.31 
7.91 


9.49 


7.35 


12 


13 


10.33 


7.82 


10.35 


7.87 


10.31 


10.28 


7.96 


13 


14 


11.18 


8.43 


11.14 


8.47 


11.11 


8..52I 


11.07 


8.57 


14 


15 


11.98 


9.03 


11.94 


9.08 


11.90 


9.131 


11.86 


9.18 


15 


16 


12.78 


9.63 


12.74 


9.68 


12.69 


9.74! 


12.65 


9.80 


16 


17 


13.. 58 


10.23 


13.53 


10.29 


13.49 


10.35 


13.44 


10.41 


17 


18 


14.38 


10.83 i 


14.33 


10.90 


14.28 


10.96 


14.23 


11.02 


18 


19 


15.17 


11.43 1 


15.12 


11.50 


15.07 


11.57 


15.02 


11.63 


19 


20 

21 


15.97 
16.77 


12.04 1 


15.92 


12.11 


15.87 


12.18 


15.81 


12.24 


20 


12.641 


16.72 


12.71 


16.66 


12.78 


16.60 


12.80 


21 


22 


17.57 13.24! 


17.51 


13.32 


17.45 


13.39 


17.40 


13.47 


22 


23 


18.37 


13.84 


18.31 


13.92 


18.25 


14.00 


18.19 


14.08 


23 


24 


19.17 


14.44 


19.10 


14.53 


19.04 


14.61 


18.98 


14.69 


24 


25 


19.97 


15.05 


19.90 


15.13 


19.83 


15.22 


19.77 


15.31 


25 


26 


20.76 


15.65 


20.70 


15.74 


20.63 


15.83 


20.56 


15.92 


26 


27 


21. .56 


16.25 


21.49 


16. .34 


21.42 


16.44 


21.35 


16.. 53 


27 


28 


22.33 


16.85 


22.29 


16.95 


22.21 


17.05 


22.14 


17.14 


28 


29 


23.16 


17.45 


23.08 


17.55 


23.01 


17.65 


22.93 


17.75 


29 


30 
31 


23.96 
24.76 


18.05 


23.88 


18.16 


23.80 


18.26 


23.72 


18.37 


30 


18.06 


24.68 


18.76 


24.. 59 


18.87 


24.51 


18.98 


31 


32 


25.. 56 


19.26 


25.47 


19.37 


25.39 


19.48 


25.30 


19.59 


33 


33 


26.35 


19. 8G 


26.27 


19.97 


26.18 


20.09 


26.09 


20.20 


33 


34 


27.15 


20.46 


27.06 


20.58 


26.97 


20.70 


26.88 


20.82 


34 


35 


27.95 


21.06 


27.86 


21.19 


27.77 


21.31 


27.67 


21.43 


35 


36 


28.75 


21.67 


28.66 


21.79 


28.-56 


21.92 


28.46 


22.04 


36 


37 


29.55 


22.27 


29.45 


22.40 


29.35 


22.. 52 


29.26 


22.65 


37 


38 


30.35 


22.87 


30.25 


23.00 


30.15 


23.13 


30.05 


23.26 


38 


39 


31.15 


23.47 


31.04 


23.61 


30.94 


23.74 


30.84 


23.88 


39 


40 
41 


31.95 
32.71 


24.07 


31.84 


24.21 


31.73 


24.35 


31.03 


24.49 


40 
41 


24.67 


32.64 


24.82 


32 53 


24.96 


32.42 


25.10 


42 


33.54 


25.28 


33.43 


25.42 


33 32 


25.57 


33.21 j 25.71 


42 


43 


34.34 


25 . 88 


34.23 


26.03 


34.11 


26.18 


34.00 '26.-33! 43 | 


44 


35.14 


20.48 


35.02 


26.63 


34.91 


26.79 


34.79 


26.94 


44 


45 


35.94 


27.08 


35.82 


27.24 


35.70 


27.39 


35.58 


27.55 


45 


40 


36.74 


27.68 


38.62 


27.84 


36.49 28.00 


36.37 


28. ;6 


46 


47 


37.54 


28.29 


37.41 


28.45 


37.29 28.61 


37.16 


28.77 


47 


48 


38.33 


28.89 


38.21 


29.05 


.38.08 29.22 


37.95 


29.39 


48 


49 


39. 13 


29.49 


39.00 


29.66 


38.87, 29,83 


38.74 


30.00 


i9 


50 

o 
u 

C 


39.93 


30.09 


39.80 


30.26 


39.67 
Dep. 


j 30.44 


39 . 53 


30.61 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


Dep. 


Lat. 


6 



53 Deg. 


521 Deg. 


52i Deg. 


52k Dog. 



TRAVKRSE TABLE. 



77 



05 
P 

3 

8 

"51 


37 Deg. 


31^ Deg. 


37^ Deg. 


37| Deg. 


D 

s 

p 

51 


Lat. 


Dcp. 


Lat. 


Dep. 

30.87 


Lat. 


Dcp. 
31.05 


Lat. 


Dep. 


40.73 


.30.69 


40.60 


40.46 


40.33 


31.22 


52 


41. .53 


31.29 


41.. 39 


31.48 


41.25 


31.66 


41.12 


31.84 


52 


53 


42.33 131.90 


42.19 


32 . 08 


42.05 


32.26 


41.91 


32.45 


53 


54 43.13 


b2.50 


42.98 


32.69 


42.84 


32.87 


42.70 


33.06 


54 


55 43.92 


33.10 


43.78 


33.29 


43.63 


33.48 


43.49 


33.67 


55 


56 44.72 


33.70 


44.58 


33.90 


44.43 


34.09 


44.28 


34.28 


66 


57 45.52 


34.. 30 


45.37 


34., 50 


45.22 


34.70 


45.07 


34.90 


57 


.58 46.32 


34.91 


46.17 


35 . 1 1 


46.01 


35.31 


45.86 


35.51 


58 


.59 47.12 


35.51 


46.96 


35.71 


46.81 


35.92 


46.65 


36.12 


59 


60 
61 


47.92 


36.11 


47.76 


36.32 


47.60 


36.53 
37.13 


47.44 


36.73 


60 


48.72 


36.71 


48.56 


,36.92 


48.39 


48.23 


37.35 


61 


62 


49.52 


37.31 


49.35 


37.53 


49.19 


37.74 


49.02 


37.96 


62 


63 


.50.31 


37.91 


50.15 


38.13 


49.98 


38.35 


49.81 


38.57 


63 


64 


51.11 


38.. 52 


50.94 


38.74 


.50.77 


38.96 


.50.60 


.39.18 


64 


65 


51.91 


39.12 


51.74 


39.34 


51.57 


39.57 


51.39 


39.79 


66 


66 


52.71 


39.72 


.52.54 


39.95 


52.36 


40.18 


52.19 


40.41 


06 


67 


53.51 


40.32 


.53.33 


40.55 


53.15 


40.79 


.52.98 


41.02 


67 


6S 


54.31 


40.92 


54.13 


41.16 


53.95 


41.40 


53.77 


41.63 


68 


69 


.55.11 


41.53 


.54.92 


41.77 


54.74 


42.00 


.54.56 


42.24 


69 


70 

'71 


.05.90 
.56.70 


42.13 
42.73 


55.72 


42.37 


.55.. 53. 


42.61 


.55.35 


42 86 
43.47 


70 
71 


.56.52 


42.98 


.56.33 


43.22 


.56.14 


72 


57.. 50 


43.33 


57.31 


43.. 58 


57.12 


43.83 


,56.93 


44.08 


72 


73 


58.30 


43.93 


.58.11 


44.19 


57.91 


44.44 


57.72 


44.69 


73 


74 


.59.10 


44.. 53 
45.14: 


.58.90 


44.79 


.58.71 


45.05 


58.51 


45.30 


74 


75 


59 . 90 


59.70 


45.40 


.59., 50 


45.66 


59., 30 


45.92 


7f. 


76 


60.70 


45.74 1 


60.. 50 


46.00 


60.29 


46.27 


60.09 


46.. 53 


76 


77 


61.40 |46.34| 


61.29 


46.61 


61.09 


46.8/ 


60.88 


47.14 


77 


78 


62.29 146.94! 


62.09 


47.21 


61.88 


47.48 


61.67 


47.75 


78 


79 


63.09 147.54! 


62.88 


47.82 


62.67 


48.09 


62.46 


48.. 37 


79 


80 

81 


63.89 
64.89 


48.151 


63.68 


48.42 


63.47 


48.70 
49.31 


63.20 


48.98 


80 

81 


48.75! 


64.48 


49.03' 


<i4 . 26 


04 . 05 


49.59 


82 


65.49 149.35 


65.27 


49.63 


65.05 


49.92 


64.84 


50.20 


82 


83 


66.29 149.95 


66.07 


.50.24 


65.85 


5=0.. 53 


65.63 


.50.81 


83 


84 


67.09 50.55 


66.86 


.50.84 


66.64 


51.14 


66.42 


51.43 


84 


85 


67.88 151.15 


67.66 


51.45 


67.43 


51.74 


67.21 


.52.04 


86 


86 


68.68 151.76 


68.46 


52.06 1 


G8.23 


.52.35 


68.00 


.52.65 


86 


87 


69.48 ; 52.36 


69.25 


,52.66! 


69.02 


52.96 


68.79 


.53.26 


87 


88 


70.28 1.52.96 


70.05 


.53.27 1 


69.82 53.57 


69.. 58 


,53.88 


88 


89 


71.08 : ,53.56 


70.84 


.53.87 


70.61 i 54.18 


70.07 


.54. •19 


89 


90 
"91 


71.83 i .54.16 


71.64 


.54.48 


71.40 
72.20 


.54.79 
.55.40 1 


71.16 


55 . 1 


90 


72. 6S , .54.77 


72.44 


55.08 1 


71.95 


.55.71 


91 


92 


73.47 55.37 


73.23 


55.69! 


72.99 


56.01 1 


72.74 


.56.32 


92 


93 


74.27 55.97 


74.03 


.56.29! 


73.78 


56.61 


73.. 53 


56.94 


93 


94 


75.07 ; 56.57 


74.82 


56.90 


74.58 


57.22 


74.32 


,57.. 55 


94 


95 


75.87 157.17 


75.62 


57.. 50 


75.37 


57.83 


75.12 


.58.16 


95 


96 


76. 67 .57. 77 


76.42 


.58.111 


76.16 


58.44 


75.91 


68 . 77 


96 


97 


77.47 58.38 


77.21 


.58.71 1 


76.96 j 59.05 1 


76.70 


59.39 


97 


98 


78.27 ' 58,98 


78.01 


59.32 1 


77.75 1 59.66 


77.49 


60.00 


98 


99 


79.06 .59.58 


78.80 


59.92 1 


78.54 1 60.27 


78.28 


60.61 


99 


100 

6 

V 


79.86 60.18 


79.60 


60.53 i 


79.34 60.88 1 
Dep Lai, 


79.07 


6). 22 


100 

6 

o 

c 


Dcp. 1 Lat. 


Dep. 


Lat. 1 


Dcp. 


Lat. 




1 


ll 


■£ 


53 Deg. 


521 Deg. 


52^ Deg. 1, 52ii Deg. 


2 



22 



TRAVTCRSE TABLE. 



2 


38 Deg. 


3S\ Deg. 


38i Deg. 


38; D.-jj. j 


r.' 

P 
S 
o 


3 
o 
o 


Lai. I Dep. 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


"T" " 


0.79 


0.62 


0.79 


0.62 


0.78 


0.62 


0.78 


0.63 


1 


9, 


1.58 


1.23 


1.57 


1.24 


1.57 


1.24 


1.56 


1.25 


2 


3 


2.36 


1.85 


2.36 


1.86 


2.35 


1.87 


2.34 


1.88 


3 


4 


3.15 


2.46 


3.14 


2.48 


3.13 


2.49 


3.12 


2.60 


4 


f) 


3.94 


3.08 


3.93 


3.10 


3.91 


3 11 


3.90 


3.13 


5 


r» 


4.73 


3.69 


4.71 


3.71 


4.70 


3.74 


4.68 


3.76 


6 


7 


5.52 


4.31 


5.50 


4.33 


5.48 


4.36 


5.46 


4.38 


7 


8 


6.30 


4.93 


6.28 


4.95 


6.26 


4.98 


6.24 


5.01 


8 


q 


7.09 


5.54 


7.07 


5.57 


7.04 


5.60 


7.02 


5.63 


9 


10 

11 


7.88 6.161 


7.85 


6.19 


7.83 


6.23 


7.80 


6.26 


10 


8.67 


6.77 


8.64 


6.81 


8.61 


6.85 


8.58 


6.89 


11 


l?r 


9.46 


7.39 


9.42 


7.43 


9.39 


7.47 


9.36 


7.51 


12 


13 


10.24 


8.00 


10.21 


8.05 


10.17 


8.09 


10.14 


8.14 


13 


14 


11.03 


8.62 


10.99 


8.67 


10.96 


8.72 


10.92 


8.70 


14 


15 11.82 


9.23 


11.78 


9.29 


11.74 


9.34 


11.70 


9.39 


15 


16 12.61 


9.85 


12.57 


9.91 


12.52 


9.96 


12.48 


10.01 


16 


17 13.40 10.47 1 


13.35 


10.52 


13.30 


10.58 


13.26 


10.64 


17 


18 I 14.18 


11.08 


14.14 


11.14 


14.09 


11.21 


14.04 11.27 


18 


19 1 14.97 


11.70 


14.92 


11.76 


14.87 


11.83 


14.82 11.89 


19 


20 


15.76 


12.31 


15.71 


12.38 


15.65 


12.45 


15.60 


12.52 


20 

21 


?.1 


16.55 


12.93 


16.49 


13.00 


16.43 


13.07 


16.38 


13.14 


9,9, 


17.34 


13.54 


17.28 


13.62 


17.22 


13.70 


17.16 


13.77 


22 


93 


18.12 


14.16 


18.06 


14.24 


18.00 


14.32 


17.94 


14.40 


23 


24 


18.91 


14.78 


18.85 


14.86 


18.78 


14.94 


,18.72 


15.02 


24 


95 


19.70 


15.39 


19.63 


15.48 


19.. 57 


15.56 


19.50 


15.65 


25 


96 


20.49 


16.01 


20.42 


16.10 


20.35 


16.19 


20.28 


16.27 


26 


97 


21.28 


16.62 


21.20 


16.72 


21.13 


16.81 


21.06 


16.90 


27 


98 


22.06 


17.24 


21.99 


17.33 


21.91 


17.43 


121.84 


17.-53 


28 


99 


22.85 


17.85 


22.77 


17.95 


22.70 


18.05 


22.62 


18.15 


29 


30 


23.64 1 18.47 


23.56 


18.57 


23.48 


18.68 


23.40 


18.78 


30 


31 


24.43 


19.09 


24.34 


19.19 


24.26 
25.04 


19.30 


;24.18 


19.40 


31 


39 


25.22 


19.70 


25.13 


19.81 


19.92 


; 24.96 


20.03 


32 


33 


26.00 


20.32 


25.92 


20.43 


25.83 


20.54 


^25.74 


20.66 


33 


34 


26.79 


20.93 


26.70 


21.05 


26.61 


21.17 


26.52 


21.28 


34 


35 


27.58 


21.55 


27.49 


21.67 


27.39 


21.79 


127.30 


21.91 


35 


36 


28.37 


22.16 


28.27 


22.29 


28.17 


22.41 


28.08 


22.53 


36 


37 


29.16 


22.78 


29.06 


22.91 


28.96 


23.03 


128.86 


23.16 


37 


38 


29.94 


23.40 


29.84 


23.53 


29.74 


23.66 '129.64 


23.79 


38 


39 


30.73 


24.. 01 


30.63 


24.14 


.30.52 


24.28 


,30.42 


24.41 


39 


40 


31.52 


24 .-.63 


31.41 


24.76 


31.30 


24.90 


31.20 


25.04 


1 40 
41 


41 


32.31 


25.24 


32.20 


25.38 


32.09 


25.52 


1131.98 


25.66 


49 


33.10 125.86 


32.98 


26.00 


1 32.87 


26.15 ! 32.76 


26.29 


42 


43 


33. 8S 


26.47 


33.77 


26.62 


1 33.65 


26.77 j 33.53 


26.91 


43 


44 


34 . 67 


27.09 


34.55 


27.24 


! 34.43 


27.39 (.34. 31 


27.54 


44 


45 


35.46 


27.70 


35.34 127.86 


1 35.22 


28.01 


35.09 


28.17 


45 


46 


36.25 


28.32 


36.12 1 28.48 


36.00 


28.64 


35. 8J 


28.79 


46 


47 


37.04 


28.94 


36.91 29.10 


36.78 


29.26 


36.65 


29.42 


47 


48 


37.82 


29.55 


37.70 29.72 


37.57 


29.88 li 37.43 


30.04 


i 48 


49 


38.61 


30.17 


38.48 30.34 


38.35 


30.50 


1 38.21 


30.67 


49 


50 


39.40 


30.78 


39.27 1 30.95 


39.13 


31.13 


38.99 


31.30 


50 


6 
o 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


La,. 


J3 

C 

'A 


■'- '■"-■ 


51! Deg. 


513 


Deg. 


5U D«a. 



TIIAVKUSE TAnLl\ 



79 



5 
% 

2 
51 


38 Deg. 


38i Deg. 


38^ Deg. 


381 Deg. 


1 
O 

I 

n 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


40.19 


31.40 


40.05 


31.57 


39.91 


31.75 


39.77 


31.92 


51 


62 


40.98 


32.01 


40.84 


32.19 


40.70 


32.37 


40.65 


32.. 55 


52 


53 


41.76 


32.63 


41.62 


32.81 


41.48 


32.99 


41.33 


33.17 


53 


54 


42.55 


33.25 


42.41 


33.43 


42.26 


33.62 


42.11 


33.80 


54 


55 


43.34 


33.86 


43.19 


34.06 


43,04 


34.24 


42.89 


34.43 


55 


56 


44.13 


34.48 


43.98 


34.67 


43.83 


34.86 


43.67 


35.05 


56 


57 


44.92 


35.09 


44.76 


35.29 


44.61 


35.48 


44.45 


35.68 


57 


58 


45.70 


35.71 


45.65 


35.91 


45.39 


36.11 


45.23 


36.30 


58 


59 


46.49 


36.32 


46.33 


36.53 


46.17 


.36.73 


46.01 


36.93 


59 


60 
61 


47.28 


36.94 


47.12 


37.16 


46.96 


37.36 


46.79 


37.56 


60 


48.07 


37.66 


47.90 


37.76 


47.74 


37.97 


47.57 


38.18 


61 


62 


48.86 


38.17 


48.69 


38.38 


48.52 


38.60 


48.35 


38.81 


62 


63 


49.64 


38.79 


49.47 


39.00 


49.30 


39.22 


49.13 


39.43 


63 


64 


50.43 


39.40 


50.26 


39.62 


50.09 


39.84 


49.91 


40.06 


64 


65 


51.22 


40.02 


51.05 


40.24 


60.87 


40.46 


50.69 


40.68 


65 


66 


52.01 


40.63 


51.83 


40.86 


51.65 


41.09 


51.47 


41.31 


66 


67 


62.80 


41.25 


52.62 


41.48 


52.43 


41.71 


52.25 


41.94 


67 


68 


53.58 


41.86 


53.40 


42.10 


.53.22 


42.33 


53.03 


42.66 1 68 1 


69 


54.37 


42.48 


54.19 


42.72 


64.00 


42.95 


,53.81 


43.19, 69 1 


70 
71 


55.16 


43.10 


54.97 


43.34 


54.78 


43.58 
44.20 


.54.. 59 


43.81 


70 


55.95 


43.71 


55.76 


43.96 


65.. 57 


55.37 


44 44 


71 


72 


56.74 


44.33 


56.54 


44.67 


56.35 


44.82 


56.15 


45 07 1 72 1 


73 


57.52 


44.94 


57.33 


45.19 


57.13 


45.44 


.56.93 


45.69 


73 


74 


58.31 


45.56 


58.11 


45.81 


67.91 


46.07 


57.71 


46.32 


74 


75 


.59.10 


46.17 


58.90 


46.43 


58.70 


46.69 


.58.49 


46.94 


75 


76 


59.89 


46.79 


69.68 


47.05 


59.48 


47.31 


69.27 


47.57 


76 


77 


00.68 


47.41 


60.47 


47.67 


60.26 


47.93 


60 05 


48.20 


77 


78 


61.46 


48.02 


61.25 


48.29 


61.04 


48.56 


60 83 


48.82 


78 


79 


62.25 


48.64 


62.04 


48.91 


61.83 


49.18 


61.61 


49.45 1 79 


80 
81 


63.04 


49.25 


62.83 


49.. 53 


62.61 


49.80 


62.39 


60.07 1 80 


63.83 


49.87 


63.61 


.50.15 i 


63.39 


50.42 


63.17 60.70 1 81 


82 


64.62 


50.48 


64.40 


50.77 i 


64.17 


51.05 


63.95 51.33 1 82 


83 


65.40 


51.10 


65.18 


51.38 i 


64.96 


51.67 


64.73 


61.95 ! 83 1 


84 


66.19 


51.72 


65.97 


.52.00 ' 


65.7^ 


.52.29 


65.51 


52.. 58 


84 


85 


66.98 


52.33 


66.75 


.52.62 


66.52 


62.91 


66.29 


63.20 


85 


86 


67.77 


52.95 


67.54 


.53.24 


67.30 


63.54 


67.07 


53.83 


86 


87 


68.56 


53.56 


68.32 


53.86 ' 


68.09 


54.16 


67.85 


54.46 


87 


88 


69.34 


54.18 


69.11 


54.48 ; 


68.87 


.54.78 


68.63 


55.08 


88 


89 


70.13 


54.79 


69.89 


55.10 1 


69.65 


.56.40 


69.41 


55.71 


89 


90 
91 


70.92 


55.41 


70.68 


.55.72 : 


70.43 


56.03 


70.19 


66.33 


90 
91 


71.71 


56.03 


71.46 


56.34 i 


71.22 


56.66 


70.97 


50.96 


92 


72.50 


56.64 


72.25 


56.96 : 


72.00 


67.27 


71.75 


57.68 


92 


93 


73.28 


.57.26 


73.03 


57.58 


72.78 


57.8-9 


72.53 


.58.21 


93 


94 


74.07 


57.87 


73.82 


58.19 


73.57 


68.52 


73.31 


58.84 


94 


95 


74.86 


58.49 


74.61 


.58.81 74.35 


59.14 


74.09 


59.46 1 


95 


96 


75.65 


59.10 


75.39 


59.43 75.13 


59.76 


74.87 


60.09 


96 


97 


76.44 


59.72 


76.18 


60.05 75.91 


60.33 


75.65 


60.71 


97 


98 


77.22 


60.. 33 


76.96 


60.67 76.70 


61.01 


76.43 


61.34 


98 


99 


78.01 


60.95 


77.75 


61.29 77.48 


61.63 


77.21 


61.97 


99 


100 

i 

S 

X 

1 


78.80 


61.57 


78.53 


61.91 78.26 


62.25 


77.99 


62.59 


] 00 

s 

c 

5 


Dep. 


Lat. 


Dep. 


Lat. 


! 11 

Dep. 1 Lat. j 


Dep. 


Lat. { 

1 


52 Deg. 


51 J Dog. 


.-,iu 


Jeer. 1; 


5UI 


)eg. i 

i 



80 



TRAVERSE TABLB. 




TRAVEUSK TAJILE. 



8J 







tl 11 < \ 


1" 


39 Deg. 


391 Deg. 


39^ Deg. 


39J Deg. 


D 
^ 


3 
o 
n 

~5T 


Lat. Dep. 
39.63 32.10 


Lat. 


Dep. 


Lat. 
39.35 


Dep. 
32.44 


Lat. 
39.21 


Dep. 
32.6; 


s 
"51 


39.49 


32.27 


52 


40.41 32.72 


40.27 


32.90 


40.12 


33.08 


39 . 9S 


33.25 


52 


53 


41.19 33.35 


41 04 


33.53 


40.90 


.33.71 


40.75 


33.89 


53 


G4 


41.97 33.98 


41,82 


34.17 


41.67 


34.35 


41.52 


34.. 53 


54 


56 


42.74 3-1. 61 ; 


42.59 


34.80 


42.44 


34.98 


42.29 


.35.17 


55 


66 


43.52 ■• 35.24 i 


43.37 


35.43 


43.21 


35.62! 


43.06 


35.81 


56 


57 


44. .30 35.87 i 


44.14 


36.06 


43.98 


36.26 1 


43.82 


36.45 


57 


58 


45.07 1 36.50 


44.91 


36.70 1 


44.75 


36.89 1 


44.59 


37.09 


58 


59 


45.85 1 37.13 '■ 


45.69 


^7.33 1 


45.53 


37.53 1 


45.36 


37.73 


59 


60 


43.63! 37.76 \ 


46.46 
47.24 


37.96! 
38.60 


46.30 
47.07 


38.16 1 


48.13 


38.37 


60 
61 


47.41 ! 38.39 1 


38.80 


46.90 


39.01 


62 


4S.18 39.02 


48.01 


39.23 


47. S4 


39.44 


47.67 


39.65 


62 


63 


48.96 39.65 


48.79 


39.86 


48.61 


40.07 


48.44 


40.28 


63 


64 


49.74 


40.28 j 


49.56 


40.49 


49.38 


40.71 


49.21 


40.92 


64 


65 


50.51 


40.91 1 


50.34 


41.13 


.50.16 


41.35! 


49.97 


41. .56 


65 


66 


51.29 


41.54 1 


51.11 


41.76 


.50.93 


41.981 


50.74 


42.20 


66 


67 


52.07 


42.16 


51.88 


42.39 


51.70 


42.62! 


51.51 


42.84 


67 


68 


52 . 85 


42.79- 


52.66 


43.02 


52.47 


43.25 1 


52.28 


43.48 


08 


69 


53.52 


43.42 1 


.53.43 


43.66 


.53.24 


43.89 


53.05 


44.12 


69 


70 


.'■)4.40 


44.05 ' 


54.21 


44.29 


54.01 


44.5.3, 


53.82 


44.76 


70 


71 


55.18| 44.08 1 


54.98 


44.92 


.54.79 


45.16' 


.54.59 


45.40 


71 


72 


55.95 45.31 


55.70 


45.55 


55.56 


45.80 


55.36 


46.04 


72 


73 


.56.73 


45.94; 


56.53 


46.19 


56.33 


46.43 


56.13 


46.68 


73 


74 


57.51 


46.57 1 


.57.31 


46.82 


57.10 


47.07 


56.89 


47.32 


74 


75 


58.29 


47.20 1 


58 . 08 


47.45 


57.87 


47.71 


57.66 


47.96 


75 


76 


.59.00 


47.83 1 


58.85 


48.09 


58.64 J48..34 


58.43 


48.60 


76 


77 


59 . 84 


48.46 1 


59.63 


48.72 


59.42 I 48.98 


,59.20 


49.24 


77 


78 


60.62 


49.09 


00.40 


49.35 


60.19 


49.61 


59.97 


49.88 


78 


79 


61.39 


49.72 


61.18 


49 . 98 


00.96 


50.25 


160.74 


.50.. 52 


79 


80 
81 


62.17| 50.35] 


61.95 
62.73 


50.62 
51.25' 


61.73 
62.. 50 


.50.89 


161.51 


51.16 
51.79 


80 


62.95 50.97 


51.52 


; 62.28 


81 


82 


63.73 51.60 


63.50 


51.88 


63.27 1.52.16 


63.04 


52.43 


82 


83 


64..50I 52.23 


64.27 


52»51 


64.04 1-52.79 


! 63.81 


53.07 


83 


84 


65.28 1 52.86 


65.05 


53.15 


64.82 1.53.43 


64.58 


53.71 


84 


85 


66.06 .'=,3.49 1 


65.82 


.53.78 


65.59 


.54.07 


65.35 


.54.35 


85 


86 


66.83 


54.12 


66.60 


.54.41 


66.36 


64.70 


66.12 


.54.99 


86 


87 


67.61 


54.75 


67.37 


55.05 


67.13 


55.34 


66.89 


55 . 63 


87 


88 


68.39 


55.38 


68.15 


55.68 


67.90 


.55.97 


67.66 


56.27 


88 


89 


69.17 


56.01 


68.92 


56.32 


68.67 


66.61 


68.43 


.56.91 


89 


90 
91 


69.94 


56 . 64 


69.70 


.56.94 


69.45 

70.22 


.57.25 


69.20 


57.. 55 


90 


70 . 72 


57.27 


70.47 


57.. 58 


57.88 


69.96 


.58.19 


91 


92 


71.50 


57.90 


71.24 


58.21 


70.99 


58.52 


1 70.73 


.58.83 


92 


93 


72.27! 58.. 53 


72.02 


58.84 


71.76 


59.16 


i 71.50 


.59.47 


93 


94 


73.05 


59.16 


72.79 


59.47 


72.53 


59.79 


' 72.27 


60.11 


94 


95 


73.83 


59.79 


73.57 


60.11 


73.30 


60.43 


; 73.04 


60.75 


95 


96 


74.61 


60.41 


74.34 


60.74 


74.08 


61.06 


173.81 


61.39 


90 


97 


75.38 


61.04 


75.12 


61.37 


74.85 


61.70 


74.58 


62.03 


97 


98 


76.16 


61.67 


75.89 


62.01 


75.62 


62.34 


75.35 


62.66 


98 


99 


76.94 


62.30 


76.66 


62.64 


76.39 


62.97 


76.12 


63.30 


99 


100 


77.71 


62.93 


77.44 


63.27 


77.16 


63.61 


76.88 


63.94 


100 


Dep. 


Lat. 


Dep. 1 Lat. 


Dep. 


1 i.t. 


Dep. 


1 Lat. 


6 
1 




1 


i 51 


Deg. 


501 


Deg. 


50i 


Deg 


50i 


Deg. 



82 



TRAVERSE TABLE 



% 

3 
o 
a 


40 Deg. 


40J Deg. 


40i Deg. 


401 Deg. 


5 


Lat. Dep. 
~0:77 0.64 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. ' 


0.76 


0.65 


0.76 


0.65 


0.76 


0.65 


1 


2 


1.53 1.29 


1.53 


1.29 


1..52 


1.30 


1..52 


1.3! 


2 


3 


2.30 


1.93 


2.29 


1.94 


2.28 


1.95 


2.27 


1.96 


3 


4 


3.(»6 


2.57 


3.05 


2.58 


3.04 


2.60 


3.03 


2.61 4 


5 


3.83 


3.21 


3.82 


3.23 


3.80 


3.25 


3.79 


3.26 6 


6 


4.60 


3.86 


4.58 


3.88 


4.56 


3.90 


4.55 


3-92 


6 


7 


5.36 


4.50 


5.34 


4.52 


5.32 


4.55 


5., 30 


4.57 


7 


8 


6.13 


5.14 


6.11 


5.17 


6.08 


5 . 20 1 


6.06 


5. 22 


8 


9 


6.89 


5.79 


6.87 


5.82 


6.84 


5.84 


6.82 


5.87 


9 


10 


7.66 


6.43 


7.63 


6.46 


7.60 


6.49 


7.. 58 
8.33 


6.53 
7.18 


10 
11 


11 


8.43 


7.07 


8.40 


7.11 


8.36 


' 7.14 


12 


9.19 


7.71 


9.16 


7.75 


9.12 


7.79 


9.09 


7.83 


12 


13 


9.96 


8.36 


9.92 


8.40 


9.89 


8.14 


9.85 


8.49 


13 


14 


10.72 


9.00 


10.69 


9.05 


10.65 


9.09 


10.61 


9.14 


14 


15 


11.49 


9.64 


11.45 


9.69 


11.41 


9.74 1 


11.36 


9.79 


15 


16 


12.26 


10.28 


12.21 


10.34 


12.17 


10.39 


12.12 


10.44 


16 


17 


13.02 


10.93 


12.97 


10.98 


12.93 


11.04 


12.88 n.io 


17 


18 


13.79 


11.57 


13.74 


11.63 


13.69 


11.69 


13.64 


11.75 


18 


19 


14.55 


12.21 


14.50 


12.28 


14.45 


12.34 i 


14.39 


12.40 


19 


20 


15., 32 


12.86 


15.26 


12.92 


15.21 


12.99 


15.15 


13.06 


20 


21 


10.09 


13.50 


16.03 


13.57 


15.97 


13.64 


15.91 


13.71 


21 


22 


16.85 


14.14 


16.79 


14.21 


16.73 


14.29 


16.67 


14.36 


22 


23 


17.62 


14.78 


17.55 


14.86 


17.49 


14.94 


17.42 


\5.01 


23 


24 


18.39 


15.43 


18.32 


15.51 


18.25 


15.59 1 


18.18 


15.67 


24 


25 


19.15 


16.07 


19.08 


16.15 


19.01 


16.24 1 


18.94 


16.32 


25 


26 


19.92 


16.71 


19.84 


16.80 


19.77 


16.89 


19.70 


16.97 


26 


27 


20.68 


17.36 


20.61 


17.45 


20.53 


17. .54 1 


20.45 


17.62 


27 


28 


21.45 


18.00 


21.37 


18.09 


21.29 


18.18 


21.21 


18.28 


28 


29 


22.22 


18.64 


22.13 


18.74 


22.05 


18.83 


21.97 


18.93 


29 


30 


22.98 


19.28 


22.90 


19.38 


22.81 


19.48 


22.73 
23.48 


19.. 58 


30 


31 


23.75 


19.93 


23.66 


20.03 


23.. 57 


20.13 


20.24 31 


32 


24.51 


20.. 57 


24.42 


20.68 


24.33 


2Q.78 


24.24 


20.89 32 


33 


25.28 


21.21 


25.19 


21.32 


25.09 


21.43 


25.00 


21.54 .33 


34 


26.05 


21.85 


25.95 


21.97 


25.85 


22.08 


25.76 


22.19 34 


35 


26.81 


22.50 


26.71 


22.61 


26.61 


22.73 


26.51 


22.85 35 


30 


27.58 


23.14 


27.48 


23.26 


27.37 


23.38 


27.27 


23.50 j .36 


37 


28.34 


23.78 


28.24 


23.91 


28.13 


24.03 


28.03 


24.15 


37 


38 


29.11 


24.43 


29.00 


24.. 55 


28.90 


24.68 


28.79 


24.80 


38 


39 


29.88 


25.07 


29.77 


25.20 


29.66 


25.33 


29.54 


25.46 


39 


40 


30.64 


25.71 


30.53 


25.84 


30.42 


25.98 


30.30 


26.11 


40 


41 


31.41 


26.35 


31.29 


26.49 


31.18 


26.03 


31.06 


26.76 


41 


42 


32.17 


27.00 


32.06 


27.14 


31.94 


27.28 


31.82 


27.42 


42 


43 


32.94 


27.64 


32.82 


27.78 


32.70 


27.93 


32.58 


28.07 


43 


44 


33.71 


28.28 


33.58 


28.43 


33.46 


28.58 


33.33 


28.72 


44 


45 


34.47 


28.93 


34.35 


29.08 


34.22 


29.23 


34.09 


29.37 


45 


46 


35.24 


29.57 


35 . 1 1 


29.72 


34.98 


29.87 


34.85 


30.03 


46 


47 


36.00 


30.21 


35.87 


30.37 


35.74 


30.52 


35.61 


30.68 


47 


48 


36.77 


30.85 


36.64 


31.01 


36.. 50 


31.17 


36.36 


31. .33 


48 


49 


37.54 


31.50 


37.40 


31.66 


37.26 


31.82 


37.12 


31.99 


49 


50 


.38.30 


32.14 


^.16^ 


32.31 


38.02 


32.47 


37.88 


32.64 


Jl 


a>' 
o 

C 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

2 


50 Deg. 


49| Deg. 


49h Deg. 


49^ Deg. 



TRAVERSE TABLE. 



83 



o 
o 


40 Deg. 




40i Deg. 


40^ Deg. 1 


401 Deg. 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


39.07 


32.78 


38.92 


32.95 


38?/8' 


33.12 


38.64 


33.29 


52 


39.83 


.33.42 


.39.69 


.33.60 


39.. 54 


33.77 


39.39 


33.94 


52 


53 


40.60 


34.07 


40.45 


34.^4 


40.30 


34.42 


40.15 


34.60 


53 


5-1 


41.37 


34.71 


41.21 


34.89 


41.06 


35.07 


40.91 


35.25 


54 


55 


42.13 


.35.35 


41.98 


35.54 


41.82 


35.72 


41.67 


35.90 


55 


56 


42.90 


36.00 


42.74 


36.18 


42.58 


.36.37 


42.42 


36.55 


56 


57 


43.66 


36.64 


43.50 


36.83 


43.34 


37.02 


43.18 


37.21 


57 


58 


44.43 


37.28 


44.27 


37.48 


44.10 


37.67 


43.94 


37.86 


58 


59 


45.20 


37.92 


45.03 


38.12 


44.86 


38^.32 


44.70 


38.51 


59 


60 
61 


45.96 


38.57 


45.79 


38.77 


45.62 


38.97 


45.45 


39.17 


60 


46.73 


39.21 


46.56 


39.41 


46.38 


39". 62 


46.21 


39.82 


61 


62 


47.49 


39.85 


47.32 


40.06 


47.15 


40.27 


46.97 


40.47 


62 


63 


48 . 26 


40.50 


48.08 


40.71 


47.91 


40.92 


47.73 


41.12 


63 


64 


49.03 


41.14 


48.85 


41.35 


48.67 


41.. 56 


48.48 


41.78 


64 


65 


49 . 79 


41.78 


49.61 


42.00 


49.43 


42.21 ' 49.24 


42.43 


65 


66 


50.56 


42.42 


50,37 


42.64 


.50.19 


42.86 1 
43.51 


50.00 


43.08 


66 


67 


51.32 


43.07 


51.14 


43.29 


50.95 


50.76 


43.73 


67 


6S 


52 . 09 


43.71 


51.90 


43.94 


51.71 


44.16] 


51.51 


44.39 


68 


69 


52.86 


44.. 35 


52.66 


44.58 


52.47 


44.81 


.52.27 


45.04 


69 


70 
71 


53.62 


45.00 


53.43 


45.23 


53.23 


45.46 53.03 


45.69 


70 


.54.39 


45.64 


.54.19 


45.87 


53.99 


46.11 53.79 


46.35 


71 


72 


.55.16 


46.28 


,54.95 


46 . 52 


54.75 


46.76 ; 54.54 


47.00 


72 


73 


55.92 


46.92 


55.72 


47.17 


55.51 


47.41 i 55.30 


47.65 


73 


74 


56.69 


47.. 57 


56.48 


47.81 


56.27 


48.06 


56.06 


48.. 30 


74 


75 


57.45 


48.21 


57.24 


48.46 


57.03 


48.71 


.56.82 


48.96 


75 


76 


58.22 


48.85 


58.01 


49 . 1 1 


57.79 


49.36 


.57.57 


49.61 


76 


77 


.58 . 99 


49.49 


58.77 


49 . 75 


58.55 


50.01 


.58.33 


50.26 


77 


78 


59 . 75 


50.14 


59,53 


50.40 


59.31 


.50.66 


,59.09 


.50.92 


78 


79 


60.52 


50.78 


60.30 


51.04 


60.07 


51.31 


.59.85 


51.57 


79 


80 
8 1 


61.28 


51.42 


61.06 


51.69 


60.83 


51.96 


60.61 


52.22 


80 


62.05 


52.07 


61.82 


.52.34 


61.59 


52.61 


61.36 


52.87 


81 


82 


62.82 


52.71 


62.59 


.52 . 98 


62.35 


53.25 


62.12 


53.53 


82 


83 


63.. 58 


53.35 


63.35 


.53.63 


63.11 


.53.90 


62.88 


.54.18 


83 


84 


64.35 


53.99 


64.11 


.54.27 


63.87 


54.55 


63.64 


54.83 


84 


85 


65.11 


.54.64 


64.87 


.54.92 


64 63 


55.20 


64.39 


55.48; 85 1 


86 


65.88 


.55.28 


65.64 


55.. 57 


65 39 


55.85 


65.15 


56.14' 


86 


87 


66.65 


.55.92 


66.40 


56.21 


66 16 


56.50 


65.91 


56.79 


87 


88 


67.41 


56.57 


67.16 


56.86 


66 92 


57.15 


66.67 


57.44 


88 


89 


68.18 


.57.21 


67.93 


57.50 


67 68 


57.80 


67.42 


58.10 


89 


90 
91 


68 . 94 


57.85 


68.69 


58.15 


68.44 


58.45 


68.18 


58.75 
59.40 


90 
91 


69.71 


58.49 


69.45 


58.80 


69.20 


59.10 


68.94 


92 


70.48 


59.14 


70.22 


59 . 44 


69.96 


59.75 


69.70 


60.05 


92 


93 


71.24 


.59.78 


70.98 


60.09 


70.72 


60.40 


70.45 


60.71 


93 


94 


72.01 


60.42 


71.74 


60.74 


71.48 


61.05 


71.21 


61.36 


94 


95 


72.77 


61.06 


72.51 


61.38 


72.24 


61.70 


71.97 


62.01 


95 


96 


73.54 


61.71 


73.27 


62.03 


73.00 


63.35 


72.73 


62.66 


96 


97 


74.31 


62.35 


74.03 


62.67 


73.76 


63.00 


73.48 


63.32 


97 


98 


75.07 


62.99 


74.80 


63.32 


74.52 


63.65 


74.24 


63.97 


98 


99 


75.84 


63.64 


75 . 56 


63.97 


75.28 


64.30 


75.00 


64.62 


99 


ioe 

o 

c 

.2 


76.60 


64.28 


76.32 


64.61 


76.04 


64.94 


75/r6_ 


65.28 


100 


Dep. 


Lat. 


Dep. 


Lat.. 


Dep. 


Lat. 


Dep. 


Lat. 


o 


50 


Deg. 


49 1 Deg. 


49.\ Deg. 


49i Deg. 



84 



TRAVERSE TABLE. 





! 

41 Deg. 


4U Deg. 


1 4U- Deg. 

i 


4I| Deg 


o 


s 
n 

~1 


Lat. 1 Dep. 


Lat. 
0.75 


Dep. 


Lat. 


Dep. 
0.66 


Lat 
0.75 


Dep. 
~0T67 


0.75 0.66 


! 0.75 


2 


1.51 ! 1.31 


1.50 


1.32 


1.50 


1.33 


1.49 


1.33 


2 


3 


2.26 1.97 


2.26 


1.98 


2.25 


1.99 


2.24 


2.00 


3 


4 


3.02 2.62 


3.01 


2.64 


3.00 


2.65 


2.98 


2.06 


4 
5 


5 


3.77 3.28 


3.76 


3.30 


3.74 


3.31 


3.73 


3.33 


6 


4.53! 3.94 


4.51 


3.96 


4.49 


3.98 


4.48 


4.00 


6 


7 


5.28 1 4.59 


5.26 


4.62 


5.24 


4.64 


5.22 


4.66 


7 


8 


6.04! 5.25 


6.01 


5.27 


5 99 


5.30 


5.97 


5.33 


8 


9 


6.79^ 5.90 


6.77 


5.93 


6.74 


5.96 


6.71 


5.99 


9 


10 
11 


7.55 6.56 

8.30, 7.2^ 


7.52 


6.59 


7.49 


6.63 


7.46 
8.21 


6.66 
7.32 


10 
11 


8.27 


7.25 


8.24 


7.29 


12 


9.06 i 7.87 


9.02 


7.91 


8.99 


7.95 


8.95 


7.99 


12 


13 


9.81 i 8.53 


9.77 


8.57 


9.74 


8.61 


9.70 


8.66 


13 


14 


10.57 9.18 


10.53 


9.23 


10.49 


9.28 


10.44 


9.32 


14 


15 


11.32 9.84 


11.28 


9.89 


11.23 


9.94 


11.19 


9.99 


15 


16 


12.08 10.. 50 


12.03 


10.55 


11.98 


10.60 


11.94 


10.65 


16 


17 1 12.83 11.15 1 


12.78 


11.21 


12.73 


11.26 


12.68 


11.32 


17 


18 13.58 11.81 


13.. 53 


11.87 


13.48 


11.93 


13.43 


11.99 


L8 


19 14.34 12.47! 


14.28 


12.. 53 


14.23 


12.59 


14.18 


12.65 


19 


20 15.09 13.12! 

21 [ 15.85 13.78 


15.04 


13.19 


14.98 


13.25 


14.92 


13.32 


_20 
21 


15.79 


13.85 


15.73 


13791 


15.67 


13.98 


22 16.60 14.43 


16.54 


14.51 


16.48 


14.58 


16.41 


14.65 


22 


23 17.36 15.09 


17.29 


15.16 


17.23 


15.24 


17.16 


15.32 


23 


24 18.11 15.75 ' 


18.04 


15.82 


17.97 


'5.90 


17.91 


15.98 


24 


25 


18.87 16.40 


18.80 


16.48 


18.72 


16.. 57 


18.65 


16.65 


25 


26 


19.62 17.06 


19.55 


17.14 


19.47 


17.23 


19.40 


17.31 


26 


27 


20. .38 17.71 


20.30 


17.80 


20.22 


17.89; 


20.14 


17.98 


27 


28 


21.13 18.37 


21.05 


18.46 


20.97 


18.. 55 


20.89 


18.64 


28 


29 


21.89 19.03 


21.80 


19.12 


21.72 


19.22 


21.64 


19.31 


29 


30 


22.64 19.68 


22.56 


19.78 


22.47 


19.88 


22.38 


19.98 


30 


"31 


23.40 20.34 


23.31 


20.44 


23.22' 


20.. 54 


23.13 


20.64 


31 


32 


24.15 20.99 


24.06 


21.10 


23.97 


21.20 


23.87 


21.31 


32 


33 


24.91 21.65 


24.81 


21.76 


24.72 


21.87 


24.62 


21.97 


33 


34 


25.66 ,22.31 


25.56 


22.42 


25.4JB 


22.. 53 


25.37 


22.64 


34 


35 


26.41 22.96 


26.31 


23.08 


26.21 


23.19 


26.11 


23.31 


35 


36 


27.17 23.62 


27.07 


23.74 


26.96 


23.85 


26.86 


23.97 


36 


37 


27.92 24.27 


27.82 


24.40 


27.71 


24.52 


27.60 


24.64 


37 


38 


28.68 124.93 


28.57 


25.06 


28.46 


25.18 


28.35 


25.30 


38 


39 


29.43 '25.59 


29.32 


25.71 


29.21 


25.84 


29.10 


25.97 


39 


40 
41 


30.19 126.24 


30.07 


26.37 


29.96 
30.71 


26.50 

27.17 


29.84 
30.. 59 


26.64 
27.30 


40 
41 


30.94 26.90 


30.83 


27.03 


42 


31.70 127.55 


31.58 


27.69 


31.46 


27.83 


31.33 


27.97 


42 


43 


32.45 128.21 


32.33 


28.35 


.32.21 


28.49 


32.08 


28.63 


43 


44 33.21 128.87 | 


33.08 


29.01 


32 . 95 


29.16 


32.83 


29.30 


44 


45 


33.96 129.52 


33.83 


29.67 


33.70 


29.82 


33.57 


29.97 


45 


46 


34.72 130.18 


34.58 


30.33 


34,45 


30.48 


34.32 


.30.63 


46 


47 


35.47 130.83 


35.34 


30.90 


35.20 


31.14 


.35.06 


3 1 . 30 


47 


48 136.23 ! 31.49 ; 


36.09 


31.65; 


35.95 


31.81 


35.81 


31.96 


4S 


49 


36.98 32.15 1 


36.84 


32.31 


36.70 


.32.47 


36.56 


32 . 63 


49 


50 

"i 
S 

.2 

Q 

! 


37.74 j 32.80 


.37.59 


32.97 


37.45 


.33.13 


37.30 


33.29 


_50 

6 
o 

c 

CO 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


49 Deg, 


481 Deg. 


48i Deg. 


48i Deg. 



TRAVERSE TABLE. 



85 



3 

s 

51 


41 Deg. 


4U Deg. 


4li Deg. 


411 Deg. 


3 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


33.49 


33.46 


.38.34 


33.63 


38.20 


33.79 


38.05 


33.96 51 1 


52 


39.24 


34.12 


39.10 


34.29 


38.95 


34.46 


.38.79 


34.63 


52 


53 


40.00 


34.77 


39.85 


34.95 


.39.69 


35.12 


39.54 


35.29 


53 


54 


40.75 


35.43 


40.60 


35.60 


40.44 


35.78 


40.29 


35.96 


54 


55 


41.51 


36.08 


41.35 


36.26 


41.19 


36.44 


41.03 


36.62 


55 


56 


42.26 


36.74 


42.10 


36.92 


41.94 


37.11 


41.78 


37.29 


56 


57 


43.02 


37.40 


42.85 


37.58 


42.69 


37.77 


42.53 


37.96 


57 


58 


43.77 


38.05 


43.61 


38.24 


43.44 


38.43 


43.27 


.38.62 


58 


59 


44.53 


38.71 


44.36 


38.90 


44.19 


39.09 


44.02 


39.29 


59 


00 
61 


45. 2S 


39.36 


45.11 


39.56 


44.94 


39.76 


44.76 


39.95 


60 
61 


46.04 


40.02 


45.86 


40.22 


45.69 


40.42 


45.51 


40.62 


62 


46.79 


40.68 


46.61 


40.88 


46.44 


41.08 


46.26 


41.28 


62 


63 


47.55 


41.33 


47.37 


41.54 


47.18 


41.75 


47.00 


41.95 


63 


64 


4S.30 


41.99 


48.12 


42.20 


47.93 


42.41 


47.75 


42.62 


64 


65 


49.06 


42.64 


48.87 


42.86 


48.68 


43.07 


48.49 


43.28 


65 


66 


49.81 


43.30 


49.62 


43.52 


49.43 


43.73 


49.24 


43.95 


66 


87 


50.57 


43.90 


50.37 


44.18 


50.18 


44.40 


49.99 


44.61 


67 


68 


51.33 


44.61 


51.13 


44.84 


.50.93 


45.06 


50.73 


45.28 


68 


69 


52.07 


45.27 


51.88 


45.49 


51.68 


45.72 


51.48 


45.95 


69 


70 
71 


52.83 
.53.58 


45.92 
46.58 


52.63 


46.15 


.52.43 


46.38 


52.22 


46.61 


70 


53.38 


46.81 


53.18 


47.05 


52.97 


47.28 


71 


72 


.54.34 


47.24 


54.13 


47.47 


.53.92 


47.71 


53.72 


47.94 


72 


73 


55.09 


47.89 


.54.88 


48.13 


54.67 


48.37 


54.46 


48.61 


73 


74 


.55.85 


48.. 55 


55.64 i 48.79, 


.55.42 


49.03 


55.21 


49.28 


74 


75 


56.60 


49.20 


56.39 


49.45 


56.17 


49.70 


55.95 


49.94 


75 


76 


57.36 


49.86 


57.14 


.50.11 


56.92 


50.36 


56.70 


.50.61 


76 


77 


.58.11 


50.52 


57.89 


50.77 


57.67 


51.02 


57.45 


51.27 


77 


78 


58.87 


51.17 


.58.64 


51.43 


58.42 


51.68 


58.19 


51.94 


78 


79 


59.62 


51.83 


59.40 


52.09 


59.17 


52.35 


58.94 


52.60 


79 


80 

81 


60.38 


.52.48 


60.15 


52 . 75 


.59.92 


53.01 


59.68 


53.27 


80 

IT 


61.13 


53.14 


60.90 


53.41 


60.67 


53.67 


60.43 


53.94 


82 


61.89 


.53.80 


61.65 


.54.07 


61.41 


.54.33 


61.18 


54.60 


82 


83 


62.64 


54.45 


62.40 


54.73 


62.16 


.05.00 


61.92 


.55.27 


83 


84 


63.40 


55.11 


63.15 


55.38 


62.91 


55.66 


62.67 


55.93 


84 


85 


64.15 


55.76 


63.91 


56.04 


63.66 


56.32 


63.41 


56.60 


85 


86 


64.90 


56.42 


64.66 


56.70 


64.41 


56.99 


64.16 


57.27 


86 


87 


65.66 


57.08 


65.41 


57.36 


65.16 


57.65 


64.91 


57.93 


87 


88 


66.41 


.57.73 


66.16 


58.02 


65.91 


58.31 


65.65 


.58.60 


88 


89 


67.17 


58.39 


66.91 


,58.68 


66.66 


58.97 


66.40 


59.26 


89 


90 
91 


67.92 


59.05 
.59.70 


67.67 


59.34 


67.41 


59.64 
60.30 


67. 15 159.93 


90 


68.68 


68.42 


60.00 


68.15 


67.89 


60.60 


91 


92 


69.43 


60.36 


69.17 


60.68 


68.90 


60.96 


68.64 


61.26 


92 


93 


70.19 1 61.01 


69.92 


61.32 


69.65 


61.62 


69.38 


61.93 


93 


94 


70.94 161.67 


70.67 


61.98 


70.40 


62.29 


70.13 


62.59 


94 


95 


71.70 


62.33 


71.43 


62.64 


71.15 


6