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
0 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 0 ; 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 0 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 0 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 0 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
2.104729 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 0 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 0 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 0 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 0 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
0 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 0 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 0 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 0 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 0 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 0
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 0 on the limb ; and if
the vernier plate be moved l' towards the left, these lines will
coincide, and the second line from 0 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 0 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 0 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 0 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 0 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 0 of the ver-
nier at 0 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 0 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 0 point of the vernier at the
0 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 0 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 0
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 0
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 0 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 0 point, and marked 5, 10, 1 5,
to one extremity, and correspondingly from the other extre
mity 15, 20 and 25, to the 0 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 0 to the left.
The first thing to be done, is to ascertain the point of the
vertical limb at which the 0 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
0 of the limb.
If the instrument be accurately constructed, and the parts
have not been disarranged, this point is the 0 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 0 point of the limb, in the direction of the
greater arc read, gives the true 0 point of the vertical limb ;
that is, the point at which the 0 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 0 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 0 ought to stand at 10°. If it shows a less arc,
the true 0 is between the 0 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 0 point. The half difference
thus found is called the correction. When the true o falls
between the marked 0 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 0 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 0 point of this vernier coincides with the 0
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 0 of the vernier to coincide with the
0 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 0 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 0 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 0 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
0
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 0 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 0 of the eyeglass vernier to
coincide with the 0 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 0 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 0 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
0 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 0 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 0 and 180®, con-
tinues parallel to the base AB, the 0 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 0 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 0 to 360.
At the 0 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 0 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 0 of the index to the 0
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 0 and 180°, on the given line.
Turn the screw that works the index, until the 0 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 0 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 0 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 0 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 - - 9.455044
: 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 0 |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 0 |l|2|3|4|5|6|7|8|9|D. 1
A
FABLE OF LOGARrrllSi
S FROM 1 TO 10,000
3
N. I 0 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 0 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 0 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.
} 0 |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
0
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 0 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 0 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 0 |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 0 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 0 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 0 |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
0 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 0 |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
0 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 0
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.
0 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 0 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
0 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
0 |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 0 |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.
0 il|2|3|4|5'6l7|8l9|n!
A TABLE Of LOGARITHMS FROM I TO 10,000.
15
nn
0 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-
0 |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 0 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
0
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
0
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
0
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
0
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. \ \
0
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
0
_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
0
_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
0
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
0
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
0
,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
0
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
0
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 0
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
0
|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' 0
<■..-:...
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
0
"~
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
0
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
0
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 0
~
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
0
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
0
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
0
1 Cosine
Sine 1
Cotang.
Taiis. 1 AL j
70 DfL'i-
15
38
C-'
0 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
0
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
0
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
0
^
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
0
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
0
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
0
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
0
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
0
CoLiiiie
1 ^i..e 1
Cntani|.
1
j Tang. j M. |
fi3 Degrees.
sixNEs AND TA.NGENTS. (27 Pegrcei
0
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
0
,
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
0
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
0
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
0
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
0 Def;
reea.
48
(30 Dcgr
ees.) A
TABLE OF LOGAniUlMlr
~
Sine 1
n. 1
("ot;ine D. |
Tani;. |
D. 1
Cot .nit:. 1
0
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 0
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
0
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
0
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
0
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
0
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
0
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
0
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
0
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
0
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
0
_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
0
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
0
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
0
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
0
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 \
0
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
0
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 0
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
0
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
0
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
0
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 0
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,^ | ^
0
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
0
~
Cosine
1 ^="« 1
1 Coia,.,'. 1
1 Ta,.g. (M.|
45 DcFrefis.
A TABLE OF JVATURAL SlIVJES.
0 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
99953
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
99725
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. inTc^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
16505198629
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 Peg.
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.«
0 258 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
45127144
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 Peg. ||
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
34175,93979 _
■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
93667
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
0
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
■^ 434451 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
87673
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 Peg.
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 179881!
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
66262
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
65606175471
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 170711
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
0 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
0 . 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
0 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
0
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.
0
■~
Lat.
1.00
Dep.
0.07
Lat.
Dep. 1
Lat.
Dep.
Lat.
Dep.
3
0
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
0 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
0 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
0 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
0
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
0
?
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.
©
0
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.
0
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
0
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
0
^'
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
0
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
0 . 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.
0
~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
0
0
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.
0
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
0
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
0
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 0
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
0
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
62.95
70.88
63.26
95
96
72.45
62.98
72.18
63.. 30
71.90
63.61
71.62
63.92
96
97
73.21
63.64
72.93
63.96
72.65
64.27
72.37
64.59
97
98
73.96
64.29
73.68
64.62
73.40
64.94
73.11
65,26
98
99
74.72
64.95
74.43
65.28
74.15
65.60
73.86
65.92
99
100
1
.2
Q
75.47 i 65.61
75.18
65.93
74.90
66.26
74.61
66.. 59
100
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
D«p.
Lat.
s
c
.2
49 Deg.
48| Deg.
48^ Deg.
48i Deg.
86
TKAVEllSE TABLE.
s
42 Deg.
1
42k Deg.
1
42i Deg,
421 Deg.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
1
0.74
0.67
0.74
0.67
0.74
0.68
0.73
0.68
1
2
1.49
1.34
1.48
1.34
1.47
1.35
1.47
1.36 1
2
3
2.23
2.01
2.22
2.02
2.21
2.03
2.20
2.04!
3
4
2.97
2.68
2.96
2.69
2.95
2.70
2.94
2.72'
4
ft
3.72
3.35 1
3.70
3.36
3.69
3.38
3.67
3.39
5
6
4.46
4.01
4.44
4.03
4.42
4.05
4.41
4.07
6
7
5.20
4.68
5.18
4.71
5.16
4.73
5.14
4.75
7
8
5.95
5.35
5.92
5.38
5.90
5.40
5.87
5.43
8
9
6.69
6.02
6.66
6.05
6.64
6.08
6.61
6.11
9
10
" 11
7.43
6.69
7.40
6.72
7.37
6.76
7.34
6.79
10
8.17
7.36
8.14
7.40
8.11
7.43 1
8.08
7.47
11
12
8.92
8.03
8.88
8.07
8.85
8.11
8.81
8.15
12
13
9.66
8.70
9.62
8.74
9.58
8.78
9.55
8.82
13
H
10.40
9.37
10.36
9.41
10.32
9.46
10.28
9.50
14
15
11.15
10.04
11.10
10.09
11.06
10.13
11.01
10.18
15
16
11.89
10.71
11.84
10.76
11.80
10.81 1
11.75
10.86
16
17
12.63
11.38
12.58
11.43
12.53
11.48 i
12.48
11.54
17
18
13.38
12.04
13.32
12.10
13.27
12.16
13.22
12.22
18
19
14.12
12.71
14.06
12.77
14.01
12.84!
13.95
12.90
19
20
14.86
13.38
14.80
13.45
14.75
13.51 i! 14.69
13.58
20
21
15.61
14.05
15.54
14.12
15.48
14.19 1
15.42
14.25
21
22
16.35
14.72
16.28
14.79
16.22
14.86!
16.16
14.93
22
23
17.09
15.39
17.02
15.46
16.96
15.54 1
16.89
15.61
23
24
17.84
16.06
17.77
16.14
17.69
16.21 i
17.62
16.29
24
25
18.58
16.73
18.51
16.81
18.43
16.89 i
18.36
16.97
25
26
19.32
17.40
19.25
17.48
19.17
17.57,
19.09
17.65
26
27
20.06
18.07
19.99
18.15
19.91
18.241
19.83
18.33
27
2S
20.81
18.74
20.73
18.83
20.64
18.92
20.. 56
19.01
28
29
21.55
19.40
21.47
19.50
21.38
19.59
21.30
19.69
29
30
22.29
20.07
22.21
20.17
22.12
20.27
22.03
20.36
30
31
23.04
20.74
22.95
20.84
22.86
20.94
22.76
21.04
31
32
23.78
21.41
23.69
21.52
23.59
21.62
23.50 121.72
32
33
24.52
22.08
24.43
22.19
24.33
22.29
24.23
22.40
33
34
25.27
22.75
25.17
22.86
25.07
22.97
24.97
23.08
34
35
26.01
23.42
25.91
23.53
25.80
23.65
25.70
23.76
35
36
26.75
24.09
26.65
24.21
26.54
24.32
26.44
24.44
36
37
27 50
24.76
27.39
24.88
27.28
25.00
27.17
25.12
37
38
28.24
25.43
28.13
25.55
28.02
25.07
27.90
25.79
38
39
28.98
26.10
28.87
26.22
28.75
26.35
28.64
26.47
39
40
29.73
26.77
29.61
26.89
29.49
27.02
29.37
27.15
40
41
30.47
27.43
30.35
27.57
30 . 23
27.70
30.11
27.83
41
42
31.21
28.10
31.09
28.24
30.97
28.37
30.84
28.51
42
43
31.96
28.77
31.83
28.91
31.70
29.05
131.58
29.19
43
44
32.70
29.44
32.57
29.58
32.44
29.73
32.31
29.87
44
45
33.44
30.11
33.31
30.26
.33.18
30.40
33.04
30.55
45
46
.34.18
30.78
34.05
30.93
33.91
31.08
33.78
31.22
46
47
34.93
31.45
34.79
31.60
34.65
31.75
34.51
31.90
47
48
35.67
32.12
35.53
32.27
35.39
.32.43
35.25
32.58
48
49
36.41
32.79
36.27
32.95
36.13
33.10
35.98
.33.26
49
50
37.16
33.46
37.01
33.62
36.86
33.78
36.72
33.94
50
s
1
Dcp.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
6
' 1
48 Deg.
471 Deg.
47i Deg.
47i Deg.
TRAVERSE TABLE-
87
p
3
?
51
42Deg.
42k Deg.
42i Deg.
42| Deg.
s
§
"51
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
37.90
34.13
37.75
34.29
37.60
34.46
37.45
34.62
52
38 . 64
34.79
38.49
34.96
38.34
35.13
38.18
35.30
52
53
39.39
35.46
39.23
35.64
39.08
35.81
38.92
35.98
53
54
40.13
36.13
39.97
36.31
39.81
36.48
39.65
36.66
54
55
40.87
36.80
40.71
36.98
40.55
37.16
40.39
37.33
55
56
41.62
37.47
41.45
37.65
41.29
37.83 1
41.12
38.01
56
57
42.36
38.14
42.19
38.32
42.02
38.51
41.86
38.69
57
58
43.10
38.81
42.93
39.00
42.76
39.181
42.59
39.37
58
59
43.85
39.48
43.67
39.67
43.50
39.86 1
43.32
40.05
59
60
"61
44.59
40.15
44.41
40.34
44.24
40.54 1
44.06
40.73
60
61
45.33
40.82
45.15
41.01
44.97
41.21 !
44.79
41.41
62
46.07
41.49
45.89
41.69
45.71
41.89]
45.53
42.09
62
63
46.82
42.16
46.63
42.36
46.45
42.56;
46.26
42.76
63
64
47.56
42.82
47.37
43.03
47.19
43.24
47.00
43.44
64
65
48.30
43.49
48.11
43.70
47.92
43.91
47.73
44.12
65
66
49.05
44.16
48.85
44.38
48.66
44.59 j
48.47
44.80
66
67
49.79
44.83
49.59
45.05
49.40
45.26
49.20
45.48
67
68
50.53
45.50
50.. 33
45.72
50.13
45.94
49.93
46.16
68
69
51.28
46.17
51.07
46.39
.50.87
46.62
50.67
46.84
69
70
71
52.02
46.84
51.82
47.07
51.61
52.35
47.29'
51.40
47.52
70
71
52.76
47.51
52.56
47.74
47.97;
52.14
48.19
72
53.51
48.18
53.30
48.41
1.53.08
48.64
52.87
48.87
72
73
54.25
48.85
54.04
49.08
,53.82
49. y2
53.61
49.55
73
74
54.99
49.52
.54.78
49.76
54.56
49.99
54.34
50.23
74
75
55.74
50.18
55.52
50.43
55.30
50.67
55.07
50.91
75
76
56.48
.50.85
56.26
51.10
56.03
51.34
55.81
51.59
76
77
57.22
51.52
57.00
51.77
56.77 152.02
56.54
52.27
77
78
57.97
52.19
57.74
52.44
.57.51
52.70
: ,57.28
52.95
78
79
58.71
52.86
58.48
53.12
58.24
53.37
.58.01
.53.63
74
80
81
59.45
53.53
59.22
53.79
58.98
59.72
54.05
54.72
'58.75
54.30
8U
60.19
54.20
59.96
54.46
159.48
54.93
81
82
60.94
54.87
60.70
55.13
60.46
55.40
■60.21
55.66
82
83
61.68
55.54
61.44
55.81
61.19
56.07
j 60.95
56.34
83
84
62.42
56.21
62.18
56.48
61.93
.56.75
61.68
57.02
84
85
63.17
56.88
62.92
57.15
62.67
57.43
62.42
57.70
85
86
63.91
57.55
63.66
57.82
63.41
58.10
63.15
58.38
86
87
64.65
58.21
64.40
,58.50
64.14
58.78
63.89
.59.06
87
88
65.40
58.88
65.14
59.17
64.88
59.45
64.62
59.73
88
89
66.14
59.55
65.88
.59.84
65.62
60.13
65., 35
60.41
89
90
91
66.88
60.22
66.62
60.51
66.35 160.80
66.09
61.09
90
67.63
60.89
67.36
61.19
67.09
61.48
66.82
61.77
91
92
68.37
61.56
68.10
61.86
67.83
62.15
67.. 56
62.45
92
93
69.11
62.23
6S.84
62.53
68.57
62.83
168.29
63.13
93
94
69.86
i 62.90
69.. 58
63.20
69.30
63.51
169.03
63.81
94
95
70.60
63.57
70.32
63.87
70.04
64.18
169.76
64.49
95
96
71.34
64.24
71.06
64.55
70.78
64.86
i 70.49
65.16
96
97
72.08
64.91
71.80
65.22
71.52
65.53
71.23
65.84
97
98
72.83
65.57
72.54
65.89
72.25
66.21
71.96
66.52
98
99
73.57
66.24
73.28
66.56
72.99
66.88
72.70
67.20
99
100
s
c
1
2
74.31
66.91
74.02
67.24
73.73
67.56
73.43
67.88
100
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
6
u
a
48 Deg.
47| Deg.
47i Deg.
47i Deg.
.1
Q
83
TUAVERSE TAKLF,.
o
43 Deg.
43i Deg.
43i Deg.
1
431 Deg.
c
%
a
' 1
Lat.
Dep.
Lat.
Dep.
0.69
Lat.
Dep.
Lat.
Dep.
~r
0.73
0.68
0.73
0.73
0.69
0.72
0.69
2
1.40
1.36
1.46
1.37
1.45
1.38
1.44
1.33
2
3
2.19
2.05
2.19
2.06
2.18
2.07
2.17
2.07
3
4
2.93
2.73
2.91
2.74
2.90
2.75
2.89
2.77
4
5
3.66
3.41
3.64
3.43
3.63
3.44
3.61
3.46
5
6
4.39
4.09
4.37
4.11
4.35
4.13
4.33
4.15
6
7
5.12
4.77
5.10
4.80
5.08
4.82
5.06
4.84
7
8
5.85
5.46
5.83
5.48
5.80
5.51
5.78
5.53
8
9
6.58
6.14
0.56
6.17
6.. 53
6.20
6.50
6.22
9
10
7.31
6.82
7.28
6.85
7.25
6.88
7.22
7.95
6 92
7.61
10
11
11
8.04
7.50
8.01
7.. 54
7.98
7.57
12
8.78
8.18
8.74
8.22
8.70
8.26
8.67
8.30
12
13
9.51
8.87
9.47
8.91
9.43
8.95
9.39
8.99
13
14
10.24
9.55
10.20
9.59
10.16
9.64
10.11
9.68
14
15
10.97
10.23
10.93
10.28
10.88
10.33
10.84
10.37
15
16
1 1 . 70
10.91
1 1 . 65
10.96
11.61
11.01
11. .56
11.06
16
17
12.43
11.59
12.33
11.65
12.33
11.70
12.28
11.76
17
18
13.16
12.28
13.11
12.33
13.06
12.39
13.00
12.45
18
19
13.90
12.96
13.84
13.02
13.78
13.08
13.72
13.14
19
20
1 4^63_
13.64
14.57
13.70
14.51
)3.77
14.45
13.83
20
21
15.36"
14.32
15.30
14.39
15.23
14.46
15.17
14.. 52
21
22
16.09
15.00
13.02
15.07
15.96
15.14
15.89
15.21
22
23
16.82
15.69
16.75
15.76
16.68
15.83
16.61
15.90
23
24
17.55
16.37
17.48
16.44
17.41
16.52
17.34
16.60
24
25
18.28 j 17.05
18.21
17.13
18.13
17.21
18.06
17.29
25
26
19.02
17.73
18.94
17.81
18.86
17.90
18.78! 1-7.98
26
27
19.75
18.41
19.67
18 50
19.59
18.59
19.50
18.67
27
28
20.48
19.10
20.39
19.19
20.31
19.27
20.23
19.36
28
29
21.21
19. 7S
21.12
19.87
21.04
19.96
20.95
20.05
29
30
31"
21.94
20.46
21.85
20.56
21.76
20.65
21.67
22.39
20.75
21.44
30
31
^22.67
21.14
22.58
21.24
22.49
21.34
32 23.40
21.82
23.31
21.93
23.21
22.03
23.12
22.13
32
33
24.13
22.51
24.04
22.61
23.94
22.72
23.84
22.82
33
34
24.87
23.19
24.76
23.30
24.66
23.40
24.56
23.51
34
35
25.60
23.87
25.49
23.98
25.39
24.09
25.28
24.20
35
36
26.. 33
24.55
26.22
24.67
26.11
24.78
26.01
24.89
36
37
27.06
25.23
26.95
25.35
26.84
25.47
26.73
25.59
37
38
27.79
25.92
27.68
26.04
27.56
26.16
27.45
26.28
38
39
28.52
26.60
28.41
26.72
28.29
26.85
28.17
26.97
39
40
41
29.25 '27.28
29.13
27.41
29.01
27.53
28.89
27.66
40
29.99 127.96
'29.86
28.09
29.74
28.22
29.62
28.35
"41
42
30.72
28.64
30.59
28.78
30.47
28.91
30.34
29.04
42
43
31.45
29.33
31.32
29.46
31.19
29 . 60
31.06
29.74
43
44
32.18
30.01
32.05
30.15
31.92
30.29
31.78
30.43
44
45
32.91
30.69
32.78
30.83
32.64
30.98
32.51
31.12
45
46
33.64
31.37
.33.51
31.52
33.37
31.66
.33.23
31.81
46
47
34.37
32.05
34.23
32.20
34.09
32.35
33.95
32.50
47
48
35.10
32.74
34.96
32.89
34.82
33.04
34.67
33.19
48
49
35.84
33.42
35.69
33.57
35.. 54
33.73
35.40
33.88
49
_50
36.-57
34.10
36.42
34.26
30.27
34.42
36.12
34.58
50
6
o
a
.2
6
u
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
47 Deg.
4G| Deg.
46i Deg.
m Deg.
TKAVEESt; TABLE.
89
1
u
»•
3
(5
CD
~5l
43 Deg.
4S| Deg.
43i Deg.
431 Deg.
s
?
51
Lat.
Dep.
Lat. 1 Dep.
Lat.
Dep.
Lat.
Dep.
37.30
34.78
37.15 .34.94
36 . 99
35 . 1 1
1T6784
J^.W
52
38.03
35.46
37.88 135.63
.37.72
35.79
.37.56
35.96
52
53
38.76
30.15
38.60 i 36.31
38.44
36.48
38.29
36.65
53
51
39.49
36.83
39.33 137.00
39.17
37.17
39.01
37.34
54
55
40.22
37.51
40.06
37.69
.39.90
37.80
39.73
38.03
55
56
40.96
38.19
40.79
38.37
40.62
38.55
40.45
38.72
56
57
41.69
38.87
41.52
39.00
41.35
39 . 24
41.17
39.42
57
5S
42.42
39.56
42.25
39.74
42.07
39.92
41.90
40.11
58
59
43.15
40.24
42.97 140.43
42.80
40.01
42.62
40.80
59
60
61
43.88
40.92
43.70 1 41.11
43.52
44.25
41.30
41.99
43.34
44.06
41.49
42.18
60
61
44.61
41.60
44.43 41.80
6ii
45.34
42.28
45.16 42.48
44.97
42.68
44.79
42.87
62
63
46.08
42.97
45.89 143.17
45.70
43.37
15.51
'1 3. 57
63
64
46.81
43 . 65
40.02
43.85
46.42
44.05
46.23
44.26
64
65
47.54
44.33
47.34
44.54
47.15
44.74]
46.95
44.95
65
66
48.27 45.01
43.07
45 . 22
47.87
45.43
47.68
45 . 64
66
67
49.00 45.69
48.80
45.91
48.60
46.12
48.40
46.33
67
68
49.73
46.38
49.53
40.. 59
49.33
46.81
49.12
47.02
68
69
50.46
47.06
.50.26
47.28
.50.05
4 7.. 50
49.84
47.71
69
70
51.19
47.74
50.99
47 . 96
50.78
48.18
,50.. 57
48.41
70
"71
51.93
48.42
51.71
48.65!
51.50
48.87
51.29
49.10
71
72
52 . r,H
49.10
52.44
49.33
.52.23
4 9.. 56
.50.25
.50.94
52.01
49.79
72
73
.53.39
49.79
.53.17
50.02
.52.95
.52.73
50.48
73
74
.54.12
.50.47
53.90
50.70
53 . 08
.53.45
51.17
74
75
,54.85
51.15
.54.63
51.39
.54.40
51.63
.54.18
51.86
75
76
55.58
51.83
55.36
.52.07
55.13
.52.31
.54.90
.52.55
76
77
56.31
.52.51
56.08
.52.76
55.85
53.00
55.62
.53 . 25
77
78
57. (»5
53.20
56.81
.53.44
.56.. 58
53.69
! 56.34
,53.94
78
79
57.78
53.88
57.. 54
54.13
57.30
,54.38
157.07
.54.63
79
80
81
58.51
59.24
.54.56
58.27
.59.00
.54.81
55 . 50
.58.03
1.58.76
55.07
55 . 76
157.79
.58.51
55.32
80
55.24
'56'.0fj 81
82
59.97
55.92
59.73
.56.18
1 59.48
.56.45
59.23
.56.70 82
83
60 . 70
50.61
60.45
.56.87
60.21
57.13
1 59.96
.57.40 1 83
84
61.43
57.29
61.18
57 . 56
60.93
57.82
60 . 68
.58.09
84
85
62.17
57.97
61.91
,58.24
61.66
,58.51
61.40
5S.7S
85
86
62.90
.58.65
62.64
58.93
62.38
59.20
62.12
.59.47
86
87
63.63
59.33
63.37
59.61
63 . 1 1
59.89
62.85
60.16
87
88
64.36
60.02
64.10
60.30
63.83
60.. 58
63.57
1 60.85
88
89
05.09
60.70
04.82
60.98
64.56
61.26
64.29
61. .54
89
90
91
05 . 82
61.38
65.55
61.67
65.28
61.95
65.01
65.74
62.24
62.93
90
66.55
62.06
'66.28
62.35
66.01
62.64
91
92
07.28
02.74
67.01
63.04
66.73
63.33
66.46
63.62
92
93
68.02
63.43
67.74
63 . 72
67.46
64.02
|67.18
64.31
93
94
08.75
64.11
68.47
64.41
68.19 '64.71
167.90
65.00
94
95
69.18
64.79
09.20
65.09
68.91
65.39
68.62
65.69
95
96
70.21
65.47
69.92
65.78
69.64
66.08
69.. 35
66.39
96
97
70.94
66.15
70.65
66.46
70.36
66.77
70.07
67.08
97
98
71.67
66.84
71.37
07.15
71.09
67.46
70.79
67.77 i 98
99
72.40
67.52
72.11
67.83
71.81
68.15
71.51
68.46
99
100
§
c
5
to
Q
73.14
68.20
72.84
68.52
72.. 54
68.84
72.24
69.15
_I00
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
O
c
d
47
Deg.
46| Deg.
1
46i Deg.
A0\ Deg.
90
TRAVEUSE TABLE.
5
55'
3
CD
'14 Deg.
44 i Deg.
44i Deg.
44| Deg.
45 Deg.
1
0
55'
Lai.
■ ■-
Dep.
0.69
Lat.
Dep.
Lat.
0.71
Dep.
"oTto
Lat.
Dep.
Lat.
Dep.
3
9 '.
0.72
0.72
0.70
0.71
0.71
0.71
0.71
1
2
1.44
1.39
1.43
1.40
1.43
1.40
1.42
1.41
1.41
1.41
2
3
2.16
2.08
2.15
2.09
2.14
2.10
2.13
2.11
2.12
2.12
3i
4
2.88
2.78
2.87
2.79
2.85
2.80
2.84
2.82
2.83
2.83
^\
f)
3.60
3.47
3.58
3.49
3.57
3.50
3.55
3.52
3.54
3.. 54
5'
6
4.32
4.17
4.. 30
4.19
4.28
4.21
4.26
4.22
4.24
4.24
61
7
5.04
4.86
5.01
4.88
4.99
4.91
4.97
4.93
4.95
4.95
V !
8
5.75
5.56
5.73
5.58
5.71
5.61
5.68
5.631
5.66
5.66
8i
9
6.47
6.25
6.45
6.28
6.42
6.31
6.39
6.34
6.36
6.36
9'
10
7.19
6.95
7.16
7. '88
6.98
7.13
7.01
7.10
7.04
7.07
7.78
7.07
\78
10
11
7.91
7.64
7.68
7.85
7.71
7.81
7.74
11
12
8.63
8.34
8.60
8.37
8.56
8.41
8.52
8.45
8.49
8.49
J 2
13
9.35
9.03
9.31
9.07
9.27
9.11
9.23
9.15
9.19
9.19
13
14
10.07
9.73
10.03
9.77
9.99
9.81
9.94
9.86
9.90
9.90
14
15
10.79
10.43
10.74
10.47
10.70
10.51
10.65
10.56
10.61
10.61
15
16
11.51
11.11
11.46
11.16
11.41
11.21
11.36
11.261
11.31
11.31
16
17112.23
11.81
12.18
11.86
12.13
11.92
12.07
11.971
12.02
12.02
IV
18
12.95
12.50
12.89
12.56
12.84
12.62
12.78
12.67
12.73
12.73
18
19
13.67
13.20
13.61
13.261
13.55
13.32
13.49
13.38
13.43
13.43
19
20
14.39
13.89
14.33
13.96
14.65
14.26
14.02
14.20
14.08
14.14
14.85
14.14
20
21
21
15.11
14.59
15.04
14.98
U 72
14.91
14.78
14.85
29,
15.83
15.28
15.76
15.35
15.69
15.42
15.62
15.49
15.56
15.. 56 22
23
16.54
15.98
16.47
16.05
16.40
16.12
16.33
16.19
16.26
16.26 23
24
17-26
16.67
17.19
16.75
17.12
16.82 '17.04
16.90
16.97
16.97124
25 17.98
17.37
17.91
17.44
17.83
17.52 !l7. 75
17.60
17.68
17.38
25
26 i 18. 70
27 19.42
18.06
18.62
18.14
18.54
18.22 18.46
18.30
18.. 38
18.38
26
18.76
19.34
18.84
19.26
18. 92119.17
19.01
19.09
19.09
27
28 20.14
19.45
20.06
19.54
19.97
19.63ll9.89
19.71
19.80
19.80
28
29i20.86
20.15
20.77
20.24
20.68 20.33
20.60
20.42
20.51
20.51
29
30121.. 58
31 I22.3O
20.84
21.49
20.93
21.40
22.11
21.03
21.31
21.12
21.21
21.92
21.21
21.92
30
31
21.53
22.21
21.63
'^1.73
22.02
21.82
32 23.02
22.23
22.92
22.33
22.82|22.43r22.73
22.53
22.63
22.63
32
33|23.74
22.92
23.64
23.03
23.54123.131 23.44
23.23
23.33
23.33
33
34124.46
23.62
24.35
23.72
24.25
23.83! 24. 15
23.94
24.04
24.04
34
3'>
25.18
24.31
25.07
24.42
24.96
24. 53i 24.86
24.64
24.75
24.75
35
36
25.90
25.01
25.79
25.12
25 . 68
25.23
25.. 57
25.34
25.46
25.46
36
37
26.62
25.70
26.50
25.82
26.39
25.93
26.28
26.05
26.16
26.16
37
38
27.33
26.40
27.22
26.52
27.10
26.63
26.99
26.75
26.87
26.87
38
39
28.05
27.09
27.94
27.21
27.82
27.34
27.70
27.46
27.58
27.58
39
40
41
28.77
29'.49
27.79
28.65
27.91
28 . 53
28,04
28.41
28.16
28.86
28.28
28.28 40
28.99 41
28.48
29.37
28.61
I29.24
28.74
29.12
28.99
4?
30.21
29.18
30.08
29.31
29.96
29.44
29.83
29.57
29.70 29. 70|42
43
30.93
29.87
30.80
30.00
30.67
30.14
30.54
30.27
30.41 30.41
43
44
31.65
30.56
31.52
30.70
31.38
30.84
'31.25
30.98
31.11 31.11
44
45
32.37
31.26
32.23
31.40
.32.10
31.54
31.96
31. 6S
31.8231.82
45
46
33.09
31.95
32.95
32.10
32.81
32.24' 32.67
32.38
32.53,32.53146
47
33.81
32 . 65
33.67
32.80
33.. 52
32.94 33.. 38
33.09
1 33. 23 33.23147
48
34.53
33.34
34.38
33.49
34.24
33.64 3' 'r. 09
33.79
1.33. 94|33. 94148
49
35.25
34.04
3,0.10
34.19
34.95
34.34 3'. .80
34.50
34.65134.65149
50
1
.2
Q
35^7
Dep.
34.73
35.82
134.89
35.66
35.05
'35.51
35.20
35.36 35. 3C
51»
Lat.
Dep. 1 Lat.
Dep.
Lat.
D3p.
\
Lat.
Dep. 1 Lat.
c
46 Dog
45| Deg.
45^ Deg.
45i Deg.
1
45 Deg.
TRAVERSE TABL15.
9}
92
A TABLE
OF RHUMBS.
SHOWING
THE DEGREES, MINUTES, AND SECONDS. THAT EVERY POINT AND QUARTER-
POINT OF THE COMPASS MAKES WITH
TUE
MERIDIAN.
1
NO
N byE.
N. by W.
Pts.
0
1
0
1
qr.
1
2
3
0
o
2
5
8
11
/ //
48 45
37 30
26 15
15 0
|Pts
0
0
0
1
1
2
3
0
SOL
S. by E.
TH.
S. byW.
N.N.E.
N.N.W.
1
1
2
1
2
3
0
14
IB
JO
22
3 45
52 30
41 15
30 0
1
1
1
2
1
2
3
0
S.S.E.
S.S.W.
N.E.byN.
N.W.byN.
2
2
2
3
1
2
3
0
25
23
33
33
13 45
7 30
53 15
45 0
2
2
2
3
1
2
3
0
S.E. by S.
S.W. by S.
N.E.
N.W.
3
3
3
4
1
2
3
0
3i
33
42
43
33 45
22 30
11 15
0 0
3
3
3
4
1
2
3
0
S.E.
S.W.
N.E. by E.
N.W.byW
4
4
4
5
1
2
3
0
47
50
53
56
48 45
37 30
23 15
15 0
4
4
4
5
1
2
3
0
S.E. byE.
S.W. by W.
E.N.E.
W.N W.
5
5
6
6
1
2
3
0
59
61
64
67
3 45
52 30
41 15
30 0
5
5
5
6
2
3
0
E.S.E.
W S.W.
E.byN.
W. by N.
6
G
6
7
1
2
3
0
70
73
75
78
18 45
7 30
C6 15
45 0
6
6
6
7
1
2
3
0
E. by S.
W. by S.
East.
West.
7
7
7
8
I
2
3
0
81
84
87
90
33 45
22 30
1] 15
0 0
7
7
7
8
1
2
3
0
East.
West.
WORKMAN'S TABLE, FOR CORRECTI.\*G THE MIDDLE LATlTDDE. 93
Mid.
i
Lat.
30
40
i 50
1 60
70
. 80
1 90
100
no
o
0 ^
0 '
0 /
0 '
0 /
0 .
0 /
0
0 /
15
0 02
0 08
0 04
0 06
0 09
0 r:
0 15
0 19
0 23
16
0 02
0 03
0 04
0 OG
0 09
0 1-^
0 15
0 18
0 22
17
0 02
0 03
0 04
0 06
0 OS
0 11
0 14
0 17
0 21
18
0 02
0 03
0 04
0 08
0 08
0 11
0 14
0 17
0 20
19
0 02
0 03
0 04
0 00
0 07
0 10
0 13
0 16
0 19
20
0 02
0 03
0 (4
0 06
0 07
0 09
0 12
0 15
0 18
21
0 02
0 03
0 04
0 06
0 07
0 09
0 12
0 15
0 18
22
0 C2
0 03
0 04
0 06
0 07
0 09
0 12
0 16
0 17
23
0 02
0 03
0 04
0 06
0 07
0 09
0 12
0 15
0 17
24
0 02
0 03
0 04
0 06
0 07
0 09
0 11
0 14
0 16
25
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
26
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
27
0 02
0 03
0 04
0 05
0 07
0 08
0 11
0 14
0 16
28
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
29
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
30
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
31
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
32
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
33
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
34
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
36
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
36
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
37
0 '2
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
38
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
39
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
40
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
41
0 02
0 03
0 04
0 05
0 06
0 08
0 10
0 13
0 15
42
0 02
0 03
0 04
0 06
0 06
0 08
0 10
0 13
0 15
43
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
44
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
45
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
46
0 02
0 03
0 04
0 05
0 07
0 09
0 1]
0 14
0 16
.47
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
48
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 16
49
0 02
0 03
n 04
0 05
0 07
0 09
0 11
0 14
0 17
60
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 17
61
0 02
0 03
0 04
0 05
0 07
0 09
0 11
0 14
0 17
52
0 02
0 03
0 04
0 05
0 07
0 09
0 12
0 15
0 18
53
0 02
0 03
0 04
0 06
0 07
0 09
0 12
0 15
0 18
54
0 02
0 03
0 04
0 06
0 08
0 10
0 13
0 16
0 19
55
0 02
0 03
0 04
0 06
0 08
0 10
0 13
0 16
0 19
56
0 02
0 03
0 04
0 06
0 OS
0 10
0 13
0 16
0 20
57
0 02
0 03
0 04
0 ()G
0 OS
0 11
0 14
0 17
0 20
58
0 02
0 03
0 04
0 06
0 09
0 11
0 14
0 17
0 21
69
0 02
0 03
0 04
0 06
0 09
0 12
0 15
0 18
0 22
60
0 02
0 03
0 04
0 06
0 09
0 12
0 15
0 19
0 23
61
0 02
0 03
0 05
0 07
0 09
0 12
0 15
0 19
0 23
62
0 02
0 03
0 05
0 07
0 09
0 12
0 16
0 20
0 24
63
0 02
0 04
0 05
0 07
0 09
0 13
0 16
0 20
0 24
64
0 02
0 04
0 06
0 08
0 09
0 13
0 17
0 21
0 25
65
0 02
0 04
0 06
0 08
0 10
0 13
0 17
0 21
0 25
66
0 02
0 04
0 C6
0 08
0 10
0 14
0 18
0 22
0 26
67
0 02
0 04
0 06
0 08
0 11
0 15
0 18
0 23
0 27
68
0 02
0 04
0 06
0 08
0 11
0 15
0 19
0 24
0 28
69
0 02
0 05
0 06
0 09
0 12
0 16
0 20
0 25
0 30
70
0 03
0 05
0 06
0 09
0 13
0 17
0 21
0 £6
0 31
71
0 04
0 06
0 07
0 09
0 13
0 18
0 22
0 27
0 33
72
0 04
0 06
0 08
0 10
0 14
0 19
0 23
0 29
0 35 J
23
94 workman's table, for correotlvg the middle latitude.
Midr'i
Lat.
120
130 ,
140
ISO ,
160 1
170
180
190
200
o
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
O /
0 27
o /
0 31
O /
0 35
O /
0 40
O /
0 45
O /
0 51
o /
0 58
0 /
1 06
0 /
1 14
0 26
0 25
0 24
0 30
0 34
0 33
0 43
0 49
0 56
1 03
1 11
0 28
0 32
0 37 !
0 42 !
0 48
0 54
1 01
1 08
0 27
0 31
0 36
0 41
0 46
0 52
0 58
1 06
0 23
0 26
0 30
0 34
0 40
0 45
0 50
0 56
1 03
0 22
0 21
0 20
0 20
0 19
0 25
0 29
0 33
0 38
0 43
0 48
0 54
1 00
0 25
0 29
0 33
0 37
0 42
0 47
0 53
0 58
0 24
0 28
0 32
0 36
0 41
0 46
0 51
0 56
0 24
0 28
0 32
0 36
0 40
0 45
0 50
0 55
0 23
0 27
0 31
0 35
0 39
0 44
0 48
0 53
0 19
0 19
0 19
0 18
0 18
0 18
0 18
0 18
0 18
0 18
0 23
0 27
0 31
0 35
0 39
0 43
0 47
0 52
0 22
0 26
0 30
0 34
0 38
0 42
0 47
0 52
0 22
0 26
0 30
0 33
0 38
0 42
0 46
0 51
0 21
0 25
0 29
0 33
0 37
0 41
0 46
0 51
0 21
0 25
0 29
0 32
0 36
0 41
0 45
0 50
0 21
0 25
0 28
0 32
0 36
0 41
0 45
0 50
0 21
0 25
0 28
0 32
0 36
0 41
0 45
0 50
0 21
0 25
0 28
0 31
0 36
0 41
0 45
0 50
0 21
0 24
0 27
0 31
0 35
0 40
0 44
0 49
0 21
0 24
0 27
0 31
0 35
0 40
0 44
0 49
0 18
0 18
0 18
0 18
0 18
0 18
0 21
0 24
0 27
0 31
0 35
0 40
0 44
0 49
0 21
0 24
0 27
0 31
0 35
0 40
0 44
0 49
0 21
0 24
0 27
0 31
0 35
0 40
0 44
0 49
0 21
0 24
0 27
0 31
0 36
0 40
0 45
0 50
0 21
0 25
0 28
0 32
0 36
0 41
0 45
0 50
0 22
0 25
0 28
0 32
0 36
0 41
0 45
0 50
0 18
0 22
0 25
0 28
0 32
0 37
0 41
0 45
0 50
0 18
0 22
0 26
0 29
0 33
0 37
0 42
0 46
0 51
0 19
0 19
0 23
0 26
0 30
0 34
0 38
0 42
0 46
0 51
0 23
0 27
0 30
0 34
0 38
0 43
0 47
0 52
45
46
47
48
49
50
51
52
53
54
0 19
0 19
0 23
0 27
0 31
0 35
0 39
0 43
0 47
0 52
0 23
0 27
0 31
0 35
0 39
0 44
0 48
0 53
0 20
0 23
0 27
0 31
0 35
0 40
0 44
0 49
0 54
0 20
0 23
0 27
0 31
0 35
0 40
0 45
0 50
0 55
0 21
0 24
0 28
0 32
0 36
0 41
0 45
0 51
0 57
0 21
0 24
0 28
0 32
0 36
0 41
0 46
0 52
0 58
0 21
0 24
0 28
0 32
0 37
0 42
0 47
0 53
0 59
0 22
0 25
0 29
0 33
0 37
0 42
0 48
0 54
1 00
0 22
0 25
0 29
0 33
0 38
0 43
0 49
0 55
1 01
0 23
0 26
0 30
0 34
0 39
0 44
0 50
0 56
1 02
55
56
57
58
59
60
61
62
63
64
0 23
0 26
0 30
0 35
0 40
0 45
0 51
0 57
1 03
0 24
0 27
0 31
0 36
0 41
0 46
0 52
0 58
1 04
0 24
0 28
0 32
0 37
0 42
0 48
0 54
1 00
1 06
0 25
0 29
0 33
0 38
0 44
0 50
0 55
1 02
1 08
0 26
0 30
0 34
0 39
0 45
0 51
0 57
1 04
1 10
0 27
0 31
0 35
0 40
0 46
0 52
0 59
1 06
1 13
0 27
0 31
0 36
0 41
0 47
0 54
1 01
1 08
1 15
0 28
0 32
0 37
0 42
0 49
0 56
1 03
1 10
1 18
0 29
0 33
0 39
0 44
0 51
0 58
1 05
1 12
1 21
0 29
0 34
0 40
0 46
0 53
1 00
1 07
1 14
1 24
65
0 30
0 35
0 41
0 48
0 55
1 02
1 09
1 17
1 27
66
0 31
0 37
0 43
0 50
0 58
1 05
1 12
1 21
1 31
67
0 33
0 38
0 45
0 53
1 00
1 07
1 16
1 25
1 35
68
0 34
0 40
0 48
0 55
1 02
1 10
1 19
1 30
1 39
69
70
0 36
0 42
0 50
0 58
1 05
1 13
1 23
1 34
1 44
0 38
0 44
0 52
1 00
1 08
1 17
1 28
1 39
1 50
71
0 40
0 46
0 55
1 03
1 12
1 22
1 32
1 44
1 56
72
0 42
0 49
0 58
1 1 06
1 16
1 27
1 38
1 50
2 04
TABLE OF MERIDIONAL PARTS.
95
mr
fob
n^
20
30
40
50
60 1 70
8^
90
10O| llo| 120| i3o|
0
0
60
120
180
240
300
361
421
482
542
603
664
725 787 1
1
1
61
121
181
241
301
362
422
483
543
604
665
723
788
2
2
62
122
182
242
302
363
423
484
544
605
666
727
789
•A
3
63
123
183
243
303
364
424
485
545
606
867
728
790
'i
4
64
124
184
244
304
365
425
486
546
607
668
729
791
5
5
65
125
185
245
305
366
426
487
547
608
669
730
792
G
6
66
126
186
246
306
367
427
488
548
609
670
731
793
7
7
67
127
187
247
307
368
428
489
549
610
671
732
794
8
8
68
128
188
248
308
369
429
490
550
611
672
734
795
9
9
69
129
189
249
309
370
430
491
551
612
673
735
796
10
10
70
130
190
250
310
371
431
492
552
613
664
736
797
11
11
71
131
191
251
311
372
432
493
553
614
675
737
798
12
12
72
132
192
252
312
373
433
494
554
615
676
738
799
13
13
73
133
193
253
313
374
434
495
555
616
677
739
800
14
14
74
134
194
254
314
375
435
496
556
617
678
740
801
15
15
75
135
195
255
315
376
436
497
557
618
679
741
802
16
16
76
136
196
256
316
377
437
498
558
619
680
742
803
17
17
77
137
197
257
317
378
438
499
559
620
681
743
804
18
18
78
138
198
258
318
379
439
500
560
621
682
744
805
19
19
79
139
199
259
319
380
440
501
561
622
683
745
806
20
20
80
140
200
260
320
381
441
502
562
623
684
746
807
21
21
81
141
201
261
321
382
442
503
563
624
685
747
808
22
22
82
142
202
262
322
383
443
504
584
625
687
748
809
23
23
83
143
203
263
323
384
444
505
565
626
688
749
810
24
24
84
144
204
264
324
385
445
506
567
627
689
750
811
25
25
85
145
205
365
325
386
446
507
568
628
690
751
812
26
26
86
146
203
206
326
387
447
508
569
629
691
752
813
27
27
87
147
207
267
327
388
448
509
570
631
692
753
815
28
28
88
148
208
268
328
389
'149
510
571
632
693
754
816
29
29
89
149
209
269
330
390
450
511
572
633
694
755
817
30
30
90
150
210
270
331
391
451
512
573
634
695
756
818
31
31
91
151
211
271
332
392
452
513
574
635
696
757
819
32
32
92
152
212
272
333
393
453
514
575
636
697
75S
820
33
33
93
153
213
273
334
394
454
515
576
637
698
75^
821
34
34
94
154
214
274
335
395
455
516
577
638
699
760
822
35
35
95
155
215
275
336
396
456
517
578
639
700
761
823
36
36
96
156
216
276
337
397
457
518
579
640
701
762
824
37
37
97
157
217
277
338
398
458
519
580
641
702
763
825
38
38
98
158
218
278
339
399
459
520
581
642
703
764
826
39
39
99
159
219
279
340
400
460
521
582
643
704
765
827
40
40
100
160
220
280
341
401
461
522
583
644
705
76r
823
41
41
101
161
221
281
342
402
462
523
584
645
706
767
829
42
42
102
162
222
282
343
403
463
524
585
646
707
76&
830
43
43
103
163
223
283
344
404
464
525
586
647
708
76C
831
44
44
104
164
224
284
345
405
465
526
587
648
709
77C
832
45
45
105
165
225
285
346
406
466
527
588
649
710
771
833
46
46
106
166
226
286
347
407
467
528
589
650
711
77:^
834
47
47
107
167
227
287
348
408
468
529
590
651
712
773
835
48
48
108
168
228
288
349
409
469
530
591
652
713
774
836
49
49
109
169
229
289
350
410
470
531
592
653
714
77C
837
50
50
110
170
230
290
351
411
471
532
593
654
715
777
838
51
51
111
171
231
291
352
412
472
533
594
655
716
77S
839
52
52
112
172
232
292
353
413
473
534
595
656
717
779
840
53
53
113
173
233
293
354
414
474
535
596
657
718
780
841
54
54
114
174
234
294
355
415
476
536
597
658
719
781
842
55
55
115
175
235
295
356
416
477
537
598
659
720
782
843
56
56
116
176
236
296
357
417
478
538
599
660
721
783
844
57
57
117
177
237
297
358
418
479
539
600
661
722
784
845
58
58
118
178
238
298
359
419
480
540
601
662
723
785
846
59
59
119
179
239
299
360
420
481
541
603
663
724
786
847
96
TABLE OF MERIDIONAL PARTS.
M, 1 140| I50j l6o| 17C| 180| 190| 20O| -^ici 22C| 230| 240| 25©! 260| 27o|
C
8481 9U
) 97r
103f
) 1098
1161
1225 1289
1354
141911484
11550 1616
1684
1
850 911
974
36
) 9S
63
2C
90
55
20
85
51
18
85
2
851 91C
975
3^
' HOC
64
27
'; 91
56
21
86
52
19
86
3
852 9l'j
976
3^
01
65
28
1 92
57
22
87
53
20
87
4
852
9ir
977
3£
02
66
29
93
58
23
88
54
21
88
5
854
916
978
41
03
67
30
95
59
24
90
56
22
89
6
855
917
979
42
05
68
32
96
60
25
91
57
90
7
856
918
980
43
06
69
33
97
61
26
92
58
24
91
8
857
919
981
44
07
70
34
1 98
62
27
93
59
25
93
9
858
920
982
45
08
71
35
1 99
63
28
94
60
26
94
10
859
921
983
1046
1109
1172
1236
:1300
1364
1430
1495
1561
1628
1695
11
800
922
984
47
10
73
37
01
66
31
96
62
29
96
12
861
923
985
48
11
74
38
02
67
32
97
63
30
97
13
862
924
986
49
12
75
39
03
68
33
98
64
31
98
14
863
925
987
50
13
76
40
04
69
34
99
65
32
99
15
864
926
988
51
14
77
41
05
70
35
1500
67
33
1700
16
865
927
989
52
15
78
42
06
71
36
02
68
34
01
17
866
928
990
53
16
79
43
07
72
37
03
69
35
03
18
867
929
991
54
17
81
44
08
73
38
04
70
37
04
19
868
930
993
55
18
82
45
10
74
39
05
71
38
05
20
869
931
994
1056
1119
1183
1246
1311
1375
1440
1506
1572
1639
1706
21
870
932
995
57
20
84
48
12
76
41
07
73
40
07
22
871
933
996
58
2]
85
49
13
77
43
08
74
41
08
23
872
934
997
59
22
86
50
14
79
44
09
75
42
09
24
873
935
998
60
23
87 51
15
80
45
10
77
43
11
25
874
930
999
CI
25
88 52
16
81
46
11
78
44
12
26
875
937
1000
63
26
89
53
17
82
47
13
79
45
13
27
876
938
iOOl
64
27
90
54
18
83
48
14
80
47
14
28
877
939
1002
65
28
91
55
19
84
49
15
81
48
15
29
878
941
1003
66
29
92
56
20
85
50
16
82
49
16
30
879
942
1004
1067
1130
1193
1257
1321
1386
1451
1517
1583
1650
1717
31
880
943
05
68
31
94
58
22
87
52
18
84
51
18
32
882
944
06
69
32
95
59
24
88
53
19
85
52
20
33
883
945
07
70
33
96
60
25
89
55
20
86
53
21
34
884
946
08
71
34
98
61
26
90
56
21
88
54
22
35
885
947
09
72
35
99
62
27
92
57
22
89
56
23
36
886
948
10
73
36
1200
64
28
93
58
24
90
57
24
37
887
949
11
74
37
01
65
29
94
59
25
91
58
25
38
888
950
12
75
38
02
66
30
95
60
26
92
59
26
39
889
951
13
76
39
03
67
31
96
61
27
93
60
27
40
890
952
1014
1077
1140
1204
1268
1332
1397
1462
1528
1594
1661
1729
41
891
953
15
78
41
05
69
33
98
63
29
96
62
30
42
892
954
16
79
42
06
70
34
99
64
30
97
63
31
43
893
955
18
80
44
07
71
35
1400
65
31
98
64
32
44
894
956
19
81
45
08
72
36
01
67
32
99
66
33
45
895
957
20
82
46
09
73
38
02
68
33
1600
67
34
46
896
958
21
84
47
10
74
39
03
69
35
01
68
35
47
897
959
22
85
48
11
75
40
05
70
36
02
69
36
48
898
960
23
86
49
12
76
41
06
71
37
03
70
38
49
899
961
24
87
50
13
77
42
07
72
38
04
71
39
50
900
962
1025
1088
1151
1215
1278
1343
1408
1473
1539
1605
1672
1740
51
901
963
26
89
52
16
80
44
09
74
40
06
73
41
52
902
964
27
90
53
17
81
45
10
75
41
08
75
42
53
903
965
28
91
54
18
82
46
11
76
42
09
76
43
54
904
966
29
92
55
19
83
47
12
77
43
10
77
44
65
905
968
30
93
56
20
84
48
13
79
44
11
78
46
56
906
969
31
94
57
21
85
49
14
80
46
12
79
47
57
907
970
32
95
58
22
86
50
15
81
47
13
80
48
58
908
971
33
96
59
23
87
52
16
82
48
14
81
49
69
909
972
34
97
60
24
88
53
18
83
49
15
82
50
TABLE OF MERIDIONAL PARTS.
97
M.l
280| 290] 30C| 31o| 320| 330j 340| 350| 36o] 370| 380]
3901 40Oi 41oj
0
1751
1819
1888
1958 2028]
2100
2171
2-:44 2318i2393!2468|
2545 2623 2702 I
1
52
21
90
59
30
01
73
46 19|
94
70
46 24!
03
2
53
22
91
60
31
02
74
47
20
95
71
48
25!
04
3
55
23
92
62
32
03
75
48:
22
96
72
49
27|
06
4
56
24
93
63
33
04
76
49;
23
98
73
50
28
07
5
5.7
25
94
64
34
05
78
50
24
99
75
51
29|
08
6
58
26
95
65
35
07
79
52
25
2400
76
53
31
10
7
59
27
96
66
37
08
80
53
27
01
77
54
32
11
8
60
29
98
67
38
09
81
54
28
03
78
55
33
12
9
61
30
99
69
39
10
82
55I
29
04
80
57
34
14
10
1762
1831
1900
1970
2040
2111
2184
2257
2330
2405
2481
2558
2636
2715
11
64
32
01
71
41
13
85
58
32
06
82
59
37
16
12
65
33
02
72
43
14
86
59
33
08
84
60
38
18
13
66
34
03
73
44
15
87
60
34
09
85
62
40
19
14
67
35
05
74
45
16
88
61
35
10
86
63
41
20
15
68
37
06
76
46
17
90
63
37
11
87
64
42
22
16
69
38
07
77
47
19
91
64
38
13
89
66
44
23
17
70
39
08
78
48
20
92
65
39
14
90
67
45
24
18
72
40
09
79
50
21
93
66
40
15
91
68
46
26
19
73
41
10
80
51
22
94
68
42
16
92
69
48
27
20
1774
1842
1912
1981
2052
2123
2196
2269
2343
2418
2494
2571
2649
2728
21
75
43
13
83
53
25
97
70
44
19
95
72
50
29
22
76
45
14
84
54
26
98
71
45
20
96
73
51
31
23
77
46
15
85
56
27
99
72
46
22
98
75
53
32
24
78
47
16
86
57
28
2200
74
48
23
99
76
54
33
25
80
48
17
87
58
29
02
75
49
24
2500
77
55
35
26
81
49
18
88
59
31
03
76
50
25
01
78
57
36
27
82
50
20
90
60
32
04
77
51
27
03
80
58
37
28
83
52
21
91
61
33
05
79
53
28
04
81
59
39
29
84
53
22
92
63
34
07
80
54
29
05
82
61
40
30
1785
1854
1923
1993
2064
2135
2208
2281
2355
2430
2508
2584
2662
2742
31
86
55
24
94
65
37
0')
82
56
32
08
85
63
43
32
87
56
25
95
66
38
10
83
58
33
09
86
65
44
33
89
57
27
97
67
39
11
85
59
34
10
88
66
46
34
90
58
28
98
69
40
13
86
60
35
12
89
67
47
35
91
60
29
99
70
41
14
87
61
37
13
90
69
48
36
92
61
30
2000
71
43
15
88
63
38
14
91
70
50
37
93
62
31
01
72
44
16
90
64
39
15
93
71
51
38
94
63
32
02
73
45
17
91
65
40
17
94
73
52
39
95
64
34
04
75
46
19
92
66
42
18
95
74
54
40
1797
1865
1935
2005
2076
2147
2220
2293
;;368
2443
2519
2597
2675
2755
41
98
66
36
06
77
49
21
95
69
44
21
98
76
56
42
99
68
37
07
78
50
22
96
70
45
22
99
78
58
43
1800
69
38
08
79
51
24
97
71
47
23
2600
79
59
44
01
70
39
10
80
62
25
98
73
48
24
02
80
60
45
02
71
41
11
82
53
26
99
74
49
26
03
82
62
46
03
72
42
12
83
55
27
2301
75
51
27
04
83
63
47
05
73
43
13
84
56
28
02
76
52
28
06
84
64
48
06
75
44
14
85
57
30
03
78
53
30
07
86
66
49
07
76
45
15
86
"58
31
04
79
54
31
08
87
67
50
1808
1877
1946
2017
2088
2159
2232
2306
2380
2456
2532
2610
2688
2768
51
09
78
48
18
89
61
33
07
81
57
33
11
90
70
52
10
79
49
19
90
62
35
08
83
58
35
12
91
71
53
11
80
50
20
91
63
36
09
84
59
36
14
92
72
54
13
81
51
21
92
64
37
11
85
61
37
15
94
74
55
14
83
52
22
94
65
38
12
86
62
38
16
95
75
56
15
84
53
24
95
67
39
13
88
63
40
17
96
76
57
16
85
55
25
96
68
41
14
89
64
41
19
98
78
58
17
86
5G| 26
97
69
42
16
90
66
42
20
99
79
59
18| 67
57 i 27
98
70j 43
17
91
67
44
21
2700
80
98
TABLE OF MERIDIONAL PARTS.
[mT
1 42oj 430| 44oj 450| 460| 47J| 480j 490i 50^| 51o, 520| 530| 54o
550
0
2782
286312946
3030
3116:32031329213382
3474
3569
3665
3764
3885
3968
1
83
1 6^
47
31
17
041 9Hi 84
76
70
67
65
67
70
2
84
' 66
49
33
19
Ub
95 i bji
78
72
68
67
68
71
3
86
67
50
34
20
07
96
87
79
74
70
69
70
73
4
87
69
51
36
21
09
98
88
81
75
72
70
71
75
5
88
70
53
37
23
10
99
90
82
77
73
72
73
77
6
90
71
54
38
24
12
3301
91
84
78
75
74
75
78
7
91
73
56
40
26
13
02
93
85
80
77
75
77
80
8
92
74
57
41
27
14
03
94
87
82
78
77
78
82
9
94
75
58
43
29
16
05
96
88
83
80
79
80
84
10
2795
2877
2960
3044
3130
3217
3306|3397
3^i90
3585
3681
3780
3882
3985
11
97
78
61
46
31
19
08
99
92
86
83
82
83
87
12
98
80
63
47
33
20
09
3400
93
88
85
84
85
89
13
99
81
64
48
34
22
11
02
95
90
86
85
87
91
14
2801
82
65
50
36
23
12
03
96
91
88
87
89
92
15
02
84
67
51
37
25
14
05
98
93
90
89
90
94
16
03
85
68
53
39
26
16
07
99
94
91
90
92
96
17
05
86
70
54
40
28
17
08
3501
96
93
92
94
98
18
06
88
71
55
42
29
19
10
03
98
95
94
95
.99
19
07
89
72
57
43
31
20
11
04
99
96
95
97
4001
20
2809
289!
2974
3058
3144
3232
3322
3413
:3.506
3601
3698
3797
3899
4003
21
10
92
75
60
46
34
24
14
07
02
99
99
3901
05
22
11
93
76
61
47
35
25
16
09
04
3701
3800
02
06
23
13
95
78
63
49
37
26
17
10
06
03
02
04
08
24
14
96
79
04
50
38
28
19
12
07
04
04
08
10
25
15
97
81
65
52
40
29
20
14
09
06
06
07
12
26
17
99
82
67
53
41
31
22
15
10
07
07
09
14
27
18
2900
83
68
55
42
32
23
17
12
09
09
11
15
28
20
02
85
70
56
44
34
25
18
14
11
11
13
17
29
21
03
86
71
57
45
35
27
20
15
13
12
14
19
30
2822
2904
3988
3073
3159
3247
3337
3428
3521
J'Ml
3714
3S14
3916
4021
31
24
06
89
74
60
48
38
30
23
18
16
16
18
22
32
25
07
91
75
62
50
40
31
25
20
17
17
19
24
33
26
08
92
77
63
51
41
33
26
22
19
19
21
26
34
28
10
93
78
65
53
43
34
28
23
21
21
22
28
35
29
11
95
80
66
54
44
36
29
25
22
22
25
29
38
30
13
96
81
68
56
46
37
31
26
24
24
26
31
37
32
14
98
83
69
57
47
39
32
28
26
26
28
33
38
33
15
99
84
71
59
49
40
34
30
27
27
30
35
39
34
17
3000
85
72
60
50
42
36
31
29
29
32
37
40
2836
2918
3002
3087
3173
3262
3352
3443
3537
3633
3731
3 31
3933
4038
41
37
19
03
88
75
63
53
45
39
34
32
32
35
40
42
39
21
05
90
76
65
55
47
40
36
34
34
37
42
43
40
22
06
91
78
66
56
48
42
38
36
36
38
44
44
41
24
07
93
79
68
58
50
43
39
37
38
40
45
45
43
25
09
94
81
69
59
51
45
41
39
39
42
47
46
44
26
10
95
82
71
61
53
47
43
41
41
44
49
47
45
28
12
97
84
72
62
54
48
44
42
43
45
51
48
47
29
13
98
85
74
64 56
50
46
44
44
47
52
49
48
31
14
3100
87
75
65
57
51
47
46
46
49
54
50
2849
2932
3016
3101
3188
3277
3367
3459
3553
3049
3747
384S
3951
4056
61
5i
33
17
03
90
78
68
60
55 i 51
49
49
52
58
52
52
35
19
04 91
80
70
62
56
52
50
51
54
60
53
54
36
20
05 92
81
71
64
58
54
52
53 i 56
61
54
55
37
21
07 94
83
73
65
59
55
54
54
58
63
55
56
39
23
08
95
84
74
67
61
57
55
56
59
65
56
58
40
24
10
97
86
76
68
62
59
57
58
61
67
57
59
42
26i 11
98
87
78
70
64 60
59
60
63
69
58
60
43
27 133200
89
79
71
66 62
60
61
64
70
59
62
44
29 14l 01
90
81
73
67 64
62
631 fi6
72
TABLE
3F MERIDIONAL PARTS.
DD
"Tf. 1 oo"i 5701 5SO| 590| 60O| 6I0I 620| 630| 640| 05O| 66oj Q',o. o«-| <iyo]
0 4074
4183 4294
4409 45271
4649
4775 4905,5039 5179;
5324
5474 5631 5795 |
1 76
84
96
11
29
61
77
07
42 81
26
77
33 97
2 77
86
98
13
31
53
79
09
44 84
28
79
36 5800
3 79
88
4300
15
33
55
81
12
46 86
31
82
39
03
4 81
90
02
17
35
57
84
14
49 88
33
84
42
06
5 83
92
04
19
37
60
86
16
51 91
36
87
44
09
6 85
94
06
21
39
62
88
18
53 93
38
89
47
11
7 86
95
08
23
41
64
90
20
55 95
41
92
50
14
8 88
97
09
25
43
66
92
23
58 98
43
95
52
17
9; 90
99
11
27
45
68
94
25
60 5200
46
97
55
20
10 4092
4201
4313
4429
4547
4670
4796
4927
5062 5203
5348
5500
5658
5823
111 94
03
15
31
49
72
98
29
65
05
51
02
60
25
12' 95
05
17
33
51
74
4801
31
67i
07
53
05
63
28
13' 97
07
19
34
53
76
03
34
69j
10
56
07
66
31
141 99
08
21
36
55
78
05
36
71
12
58
10
68
34
15 4101
10
23
38
57
80
07
38
74
14
61
13
71
37
16| 03
■ 12
25
40
59
82
09
40
76
17
63
15
74
39
17| 04
14
27
42
62
84
11
43
78!
19
66
18
76
42
18! 06
16
28
44
64
87
14
45
81
22
68
20
79
45
19j 08
18
30
46
66
89
16
47
83
24
71
23
82
48
20 4110
4220
4332
4448
4568
4691
4818
4949
5085
5226
5373
5526
5685
5851
21
12
21
34
50
70
93
20
51
88
29
76
28
87
54
22
13
23
36
52
72
95
22
54
90
31
78
31
90
56
23
15
25
38
54
74
97
24
66
92
34
80
33
93
59
24
17
27
40
56
76
99
26
68
95
36
83
36
95
02
25
19
29
42
58
78
4701
29
60
97
38
85
39
98
65
26
21
31
44
60
80
03
31
63
99
41
88
41
5701
68
27
22
32
46
62
82
05
33
65
5102
43
90
44
04
71
28
24
34
47
64
84
07
35
67
04
46
93
46
06
74
29
26
36
49
66
86
10
37
69
06
48
95
49
09
76
30
4128
4238
4351
4468
4588
4712
4839
4972
5108
5250
5398
5552
5712
5879
31
30
40
53
70
90
14
42
74
11
53
5401
54
15
82
32
32
42
55
72
92
16
44
76
13
55
03
57
17
85
33 33
44
57
74
94
18
46
78
15
58
06
59
20
88
34| 35
46
59
76
96
20
48
81
18
60
08
62
23
91
35
37
47
61
78
98
22
50
83
20
63
11
65
25
94
36
39
49
63
80
4600
24
52
85
22
65
13
67
28
96
37
41
51
65l 82
02
26
55
87
25
67
16
70
31
99
38
42
53
67
84
04
28
57
90
27
70
18
73
34
5P02
39
44
55
69
86
06
31
59
92
29
72
21
75
36
05
40
4146
4257
4370
4488
4608
4733
4861
4994
5132
5275
5423
5578
5739
5908
41
48
59
72
90
10
35
63
96
34
77
26
80
42
11
■42
50
60
74
92
12
37
65
99
36
80
28
83
45
14
43
52
62
76
94
14
39
68
5001
39
82
31
86
47
17
44
53
64
78
95
16
41
70
03
41
84
33
88
50
19
45
55
66
80
97
18
43
72
05
43
87
36
91
53
22
46
57
68
82
99
20
45
74
08
46
89
38
94
56
25
47
59
70
84
4501
23
47
76
10
48
92
41
96
58
28
43
61
72
86
03
25
50
79
12
51
94
43
99
61
31
49
62
74
88
05
27
52
81
14
53
97
46
5602
64
34
50 4! 64
4275
4390
4507
4629
4754
4883
5017
5155
5299
5448
5604
5767
5937
511 GG
77! 92
09
31
56
85
19
58
5301
51
07
71
1 10
52
68
79
94
11
33
58
87
21
60
04
54
10
72
1 43
53
70
81
96
13
35
60
90
23
62
06
56
12
75: 4^
54
72
83
98
15
37
62
92
26
65
09
59
15
78 1 48
55
73
85
99
17
39
64
94
28
67
11
61
17
81 -y
56
75
87
4401
19
41
66
96
30
69
14
64
20
83 54
57
77
89
03
21
43
69
98
33
72
16
66
23
86 57
58
79
91
05
23
45
71
4901
35
74
19
69
25
89 60
59
81
92
07
25
47
73
03
37
76
21
71
28
92! 63
iOO
TABLE OF MERIDIONAL PARTS.
M.
70Oj 71o| 720| 730| 740| 750| 760| 770| 780| 790| 80O| 81o| 820
830
0
0966 614616335 6534
674616970,7210
7467l7745;8046j8375:8739 9145
9606
1
6r. 49
38
38
49
74
14
72
49
51
81
45
53
14
2
72 62
41
41
53
78
18
76
54
56
87
52
60
22
3
75; 65
45
45
57
82
22
81
59
61
93
58
67
31
4
78
58
48
48
60
86
27
85
64
67
98
65
74
39
5
81
61
51
52
64
90
31
90
69
72
8404
71
82
47
6
84
64
54
55
68
94
35
94
74
77
10
78
89
55
7
86
67
58
58
71
97
39
98
78
83
16
84
96
64
8
89
70
61
62
75
7001
43
7503
83
88
22
91
9203
72
9
92
73
64
65
79
05
47
07
88
93
27
97
11
81
10
5995
6177
6367
6569
6782
7009
7252
7512
7793
8099
8433
8804
9218
9689
11
98
80
71
72
86
13
56
16
98
8104
39
10
25
97
12,
6001
83
74
76
90
17
60
21
7803
09
45
17
33
9706
1^
04
86
77
79
93
21
64
25
08
15
51
23
40
14
14
07
89
80
83
97
25
68
30
13
20
57
30
48
23
15
10
92
84
86
6801
29
73
35
17
25
63
36
55
31
16
13
95
87
90
04
33
77
39
22
31
69
43
62
40
17
16
98
90
93
08
37
81
44
27
36
74
49
70
48
18
19
6201
94
96
12
41
85
48
32
41
80
56
77
57
19
•22
05
97
6600
15
45
89
53
37
47
86
63
85
65
20
6025
6208
6400
6603
6819
7049
7294
7557
7842
8152
8492
8869
9292
9774
21
28
11
03
07
23
52
98
62
47
58
98
76
9300
83
22
31
14
07
10
26
56
7302
66
52
63
8504
83
07
91
23
34
17
10
14
30
60
06
71
57
68
10
89
15
9800
24
37
20
13
17
^4
64
11
76
62
74
16
96
22
09
25
40
23
17
21
38
68
15
80
67
79
22
8903
30
17
26
43
26
20
24
41
~72
19
85
72
85
28
09
38
26
27
46
30
23
28
45
V€
23
89
77
90
34
16
45
35
28
49
33
27
31
49
80
28
94
82
96
40
23
53
44
29
52
36
30
35
53
84
32
98
87
8201
46
30
60
52
30
6055
6239
6433
6639
6856
7088
7338
76103
7892
8207
8552
8936
9368
9861
31
58
42
37
42
60
92
40
08
97
12
58
43
76
70
32
61
45
40
46
64
96
45
12
7902
18
64
50
83
79
33
64
49
43
49
68
7100
49
17
07
23
71
57
91
88
34
67
52
47
53
71
04
63
22
12
29
77
63
99
97
35
70
55
50
56
75
08
58
26
17
34
83
70
9407
9906
36
73
58
53
60
79
12
62
31
22
40
89
77
14
15
37
76
61
57
63
83
16
66
36
27
45
95
84
22
24
38
79
64
60
67
86
20
71
40
32
,51
8601
91
30
33
39
82
68
63
70
90
24
75
45
37
56
07
98
38
42
40
6085
6271
6467
6674
6894
7128
7379
7650
7942
8262
8614
9005
9445
9951
41
88
74
70
77
98
32
84
54
48
67
20
12
53
60
42
91
77
73
81
6901
36
88
59
53
73
26
18
f)l
69
43
94
80
77
85
05
40
92
64
58
79
32
25
09
78
44
97
83
80
88
09
45
97
68
63
84
38
32
77
87
45
6100
87
83
92
13
49
7401
73
68
90
44
39
85
9996
46
04
90
87
95
17
53
OG
78
73
95
51
46
93
10005
47
06
93
90
99
20
57
10
83
78
8301
57
53
9501
10015
48
09
96
94
6702
24
61
14
87
83
07
63
60
09
10024
49
12
99
97
06
28
65
19
92
89
12
69
67
17
10033
50
6115
6303
6500
6710
6932
7169
7423
7697
7994
8318
8676
9074
9525
10043
51
18
06
04
13
36
73
27
7702
99 1 24
82
81
33
10052
52
21
09
07
17
40
77
32
06
80041 29
88
88
41
10061
53
24
12
11
20
43
81
36
11
09 35
93
96
49
10071
54
27
15
14
24
47
85
41
16
14 41
8701
9103
57
10080
55
30
19
17
28
51
89
45
21
20 47
07
10
65 10089
56
33
22
21
31
55
94
49
25
25 52
14
17
73:10099
67
36
25
24
35
59
98
54
30
30 58
20
24
8l|l0108
58
40
28
28
38
63
7202
58
35
35 64
26
31
89 10118
59
43
32
31
421 66
06
63
40
40 69
33
38
98110127
^ Mf/Hi
'raillB^
W
•^ ^
^
i^
A
1
-;; ,.
-Tjt,^
c
J^
-^
■■^"•■■■;.
-i)r^ .';■ 1
^
k^ V _
UuMMUTaA ,Ul.
A
J^iJA,>miiit . 'J- .Ay
'i l; XJ-I..:
'M^. a
ffii/ti-ry /('/■ f it II n 1 11
Jjcittery Ar Mcrtaiv
Ci>urr//ouse
nttivi Favwry
Tiwern
J^iimiiix
Church pfa J/T/Jtuje
Do. />f/Mhei/
R'uniirif
J'cr</e
Cizi'a/ry
/nfcuUn/
m-use
MM out
/)<>. Suj/-
Vo. b'ti:<i»i
Do. of Stcnf
f/v. ol^^c'd
Pest Office #
Tritfoncmffnail /l>Ou
Telef/rafih
o
AAA AAA 'A
A.AAAA AA
ris^^i - »
I E
-(.*** ■< * V
« « it % «k Ck iL-
* 4 % * * 1^ i
-^ % <i <^ % % i
M
DETAILS or LEAVES
i i i
^^5^;
^C
4^ -^#^^:ig^ iE®y^©S <2!a«
:i^
— ^ ^ — T ] ; H
iWrtwi''-
,,_,,,„
-,-._-. V.
■mpii
AmA'ww ,jv .q:
=r=— ^^ElalL ()
Aui-lmrairf ^
> IWVd Street
1
\ 1
It ,, U ,lu . - i
»
SOUTHEASTERN MASSACHUSETTS UNIVERSITY
3 ETEE D031L Tbl T
A
^( Sp.Coll. TA5i^5 .D26 181^7 oQf^r^
Davies, Charles 6O0D^
Elements of surveying,, ,
/ ? "^ /
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11