oninr OF

the estate of Professor William F. Meyer

TABLES OF LOGARITHMS

TO

FIVE PLACES OF DECIMALS,

WITH AUXILIARY TABLES.

EDITED BY

EDWIN S. CRAWLEY, PH.D.,

- THOMAS A. SCOTT PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF PENNSYLVANIA

E. S. CRAWLEY,

UNIVERSITY OF PENNSYLVANIA,

PHILADELPHIA,

1905.

COPYRIGHT, 1890,

BY EDWIN S. CRAWLKY.

ELECTROTVPEO AND PHINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA. U.S. A

EDITOR'S NOTE.

THIS collection of logarithmic tables has been prepared to accompany the editor's Elements of Trigonometry^ in response to the demand of a number of teachers using the latter, who prefer a text bound with tables. In commending the tables to the use of educational institutions and the mathematical public in general, the editor wishes to state that great care has been taken to secure accuracy. The proof has been com- pared twice, number by number, with different standard tables (Yega's seven-place Tables, the 74th edition, edited by W. L. F. Fischer; and Gauss's five-place Tables, the 20th edition), and the method of differences was applied as a further check. Besides these, other tests were applied to parts of the tables, as in the case of Table III., where the log tan column was checked by taking the difference of log sin and log cos, and the log cot column was checked by taking the arithmetical complement of log tan.

Should any errors be discovered, the editor will be glad to be informed of them.

EDWIN S. CKAWLEY.

UNIVERSITY OF PENNSYLVANIA, January, 1899.

C8

M577188

TABLE OF CONTENTS.

EXPLANATION or THE TABLES vii

TABLE I. — Logarithms of Numbers 1

" II.— Important Constants and their Logarithms 20

" III.— Logarithms of the Sine, Cosine, Tangent, Cotangent

for every Minute of the Quadrant 21

" IV.— Table for Computing the Log Sin and Log Tan of

Small Angles 67

" V. — Natural Sines, Cosines, Tangents, and Cotangents . . 69

" VI. — Circular Arcs, expressed in Kadians 74

*• VII. — Napierian Logarithms of Numbers 75

EXPLANATION OF THE TABLES.

1. Definitions and Rules. If three numbers n, a, x have such values that the equation

n = a* (1)

is true, then x is called the logarithm of n to the base a. If, without changing a, we give to n and x all possible values, con- sistent with this equation, the values of x thus obtained form a system of logarithms to the base a.

Hence : — The logarithm of a number to a given base is the ex- ponent of the power to which the base must be raised to produce the number.

Suppose 9 is taken for the base, then

log 81 = 2, because 92 = 81 11 729= 3, " 93 =729 « i = -l, -" 9~!= i " 3= i, « 9* = 3 " 9= 1, " 91 = 9 " 1= 0, " 9° = 1

In every system the logarithm of the base is 1, and the logarithm of 1 is 0. This follows directly from the definition, or from (1) ; for if n = a, x must be 1 ; and if n = 1, x must be 0, without respect to the value of a.

It is plain, since any number will serve as the base of a system of logarithms, that the number of such systems is indefinite.

vii

Vlll EXPLANATION OF THE TABLES.

The systems of logarithms commonly used are :

(1.) The common or Briggian* system, with the base 10.

(2.) The natural or Napierianf system with the base

6 = 2.7182818285 ____ defined by the convergent infinite series

e=1 + 1 + r2 + ii3+i^-4 + ---

Of these two systems, the first is used for all purposes of numerical computation, and the second for purely analytical purposes.

The logarithms of these tables (except in Table VII.) are common or Briggian logarithms.

The corresponding logarithms of any two systems are in a constant ratio to each other. Thus the relation between com- mon and Napierian logarithms is

(This equation is read : " Logarithm of n to the base 10 equals the reciprocal of the logarithm of 10 to the base e, multiplied

bv the logarithm of n to the base e.") The factor - is

log . 10

called the modulus of the common system. It is represented by M, and its value to ten places is 0.4342944819.

The rules governing the use of logarithms in computation are the following : —

I. To multiply numbers, find the logarithm of each factor, and add them ; the sum is the logarithm of the product.

II. To divide one number by another, subtract the logarithm of the divisor from the logarithm of the dividend ; the difference is the logarithm of the quotient.

III. To raise a number to any power multiply the logarithm of the number by the exponent of the power ; the product is the log- arithm of the required power of the number.

* Named for Henry Briggs (1666-1631), who first suggested the use of the base 10.

f Named for John Napier, Baron of Merchiston, in Scotland (1560- 1617), the inventor of logarithms.

EXPLANATION OF THE TABLES. IX

IY. To extract any root of a number, divide the logarithm of the number by the index of the root ; the quotient is the logarithm of the required root of the number.

These statements and rules .are given without proof, as the purpose here is simply to familiarize the student with the mechanism and use of the tables. The theory of logarithms is set forth in text-books on algebra, to which the student is referred. In the same place will be found an explanation of how logarithms are computed.

TABLE I. Common Logarithms of Numbers. (Pages 1-19)

2. Characteristic and Mantissa. A logarithm consists, usually, of two parts : a whole number, called the characteristic, and an incommensurable decimal fraction, called the mantissa. The table gives only the mantissa ; the characteristic, which may be positive, negative, or zero, must be supplied in every case by the computer. The mantissa is always positive, ex- cept in the logarithms of exact powers of 10, when it is zero.

Since 10 is the base we have :

log 100Q = 3, because 103 = 1000

log 100= 2, " 102 = 100

log 10= If " 10l = 10

log 1= 0, " 10° = 1

log a = — 1, " 10 ~l = .1

log .01=— 2, " 10-2= .01

log .001 = —3, " 10 ~3 = .001

(a)

This series of equations can be extended indefinitely in both directions.

Let us now consider two numbers which contain the same sequence of figures, with different positions of the decimal point, say 72.936 and .72936. Now 72.936 = 100 X .72936. Hence, by Eule I, § 1 log 72.936 = log 100 -f log .72936,

or, by (a) = 2 + log .72936.

Hence, since any change in the position of the decimal

X EXPLANATION OF THE TABLES.

point in a number is equivalent to multiplication or division by a power of 10, the effect produced upon the logarithm of the number by a change of this kind is to increase it or diminish it by a whole number ; that is, the characteristic is affected by such a change, but not the mantissa. We have, therefore, the following important fact :

I. The mantissa of the logarithm of a number depends only upon the sequence of figures in the number.

Referring again to (a), we note that for all numbers greater than 1 and less than 10 (all numbers with one significant figure before the decimal point) the logarithm is greater than 0 and less than 1, that is, its characteristic is 0 ; for all num- bers greater than 10 and less than 100 (all numbers with two significant figures before the decimal point) the logarithm is greater than 1 and less than 2, that is, its characteristic is 1 ; for all numbers greater than 100 and less than 1000 (all -num- bers with three significant figures before the decimal point) the logarithm is greater than 2 and less than 3, that is, its characteristic is 2; and so on. Hence, we have the following rule:

II. The characteristic of the logarithm of a number greater than unity is one less than the number of significant figures preceding the decimal point.

Again, from (#) it will be seen that if a number is greater than .1 and less than 1, its logarithm is between 0 and — 1 ; that is, using a positive mantissa, which we always do, it is — 1 -f the mantissa, hence the characteristic is — 1 ; if the number is greater than .01 and less than .1, the logarithm is between — 1 and — 2, which is written — 2 -f- the mantissa, that is, the characteristic is — 2 ; if the number is greater than .001 and less than .01, the logarithm is between — 2 and — 3, which is written — 3 -f- the mantissa, that is, the characteristic is — 3, and so on. Hence, we have the following rule :

III. The characteristic of the logarithm of a number less than unity is negative, and is numerically one greater than the number of ciphers between the decimal point and the first significant figure.

EXPLANATION OF THE TABLES. XI

Verify the following statements :

characteristic of log 763.92 = 2

" " log 1.9841— 0

*' "log .07296 = — 2

" " log 26 = 1

" " log 400000= 5

" " log .9426 = —!

" " log 3869= 3

" " log .00042 = — 4

" " log .005 = — 3 '

" " log 62893= 4

3. To Find the Logarithm of a Number of Four Figures or Less.

If the number has less than four figures add ciphers on the right until it has four figures, and then proceed in the manner described below.

If the number has four figures, enter the table in the left hand column of the page, the column marked N, with the first three figures (the first three significant figures if the number is a decimal fraction) and with the fourth figure in the line running across the page at the extreme top or bottom. Go across the page, in the line containing the first three figures, until the column marked by the fourth figure is reached. The three figures found at this point are the last three figures of the mantissa. The first two figures of the mantissa are printed only in the first column of the body of the table, and if they are not found in the same line with the last three figures they will be found a few lines above.

Suppose the number is 48.65. We find 486 in the N column on page 9 ; and the column marked 5 at the top and bottom is the one to the right of the heavy line down the middle of the page. The three figures in this column and on the same line with 486 are 708, which are the last three figures of the mantissa; the first two figures are 68. Hence, mantissa of log 48.65 is .68708. By II. § 2 characteristic of log 48.65 is 1. Hence, log 48.65 = 1.68708.

Find log 6.2. Annexing two ciphers, this becomes 6.200.

Xll EXPLANATION OF THE TABLES.

Proceeding then as above, we find that the mantissa is 79239. Hence, log 6.2 = 0.79239.

Find log 431. Annexing one cipher this becomes 431.0. Hence, the mantissa is 63448; and log 431. = 2.63448.

An important exception in one point of the usual procedure is exemplified below. Find log .07416. Entering the table on page 14, line 741, we find in the column marked 6, the figures *017. The asterisk is inserted to indicate that the first two figures of the mantissa are to be taken from the line below, instead of from above. Hence, the mantissa of log .07416 is .87017 ; and by III. § 2 log .07416 = 2.87017. The negative sign is written over the characteristic, instead of before it, as it applies to the characteristic only, the mantissa being positive.

The reason for placing this asterisk in the table is easily seen. The last logarithm that begins with 86 is 86999. The next one in order is 87005, but as this comes in the middle of the page there is not room to print 87 in the same column with 005, so the asterisk is inserted to call the computer's attention to this fact and bid him take the first two figures from below.

Verify the following statements :

log 863.2 =2.93611 log 3 =0.47712

log 1.29 =0.11059 log 2758 =3.44059

log 18000 =4.25527 log 64.58 =1.81010

log .92 =1.96379 log .00006 = 5.77815

log .04312 = 2.63468 log .00183 = 3.26245

It is proper at this point to explain that in practical com- putation negative characteristics are very rarely used. Their use is avoided by adding 10 to the characteristic and writing — 10 after the logarithm. In this way the true value of the logarithm is not changed. With this modification the four logarithms above with negative characteristics become

log .92 =9.96379 — 10 log .00006 = 5.77815 — 10

log .04312 = 8.63468 — 10 log .00183 = 7.26245 — 10

This method will be used exclusively in the examples which follow. After a little practice the — lO's written after the log- arithm may be omitted without danger of error in the final

EXPLANATION OF THE TABLES.

result. Eule III. § 2 can be changed, therefore, to the fol- lowing:

The characteristic of the logarithm of a number less than unity is formed by subtracting from 9 the number of ciphers between the decimal point and the first significant figure, and writing — 10 after the logarithm.

Verify the following statements :

log .3628 = 9.55967 — 10 log .0026 = 7.41497 — 10

log .0796 = 8.90091 — 10 log .007 =7.84510 — 10

4. To Find the Number to Four Figures which Corresponds to a Given Logarithm.

The method is best explained by an example. Given log x = 1.79683, to find x. Disregarding the characteristic for the moment, we enter the table with the first two figures of the mantissa, 79, looking for them in the column headed with 0. We find them on page 12. We then look in that part of the body of the table which contains the logarithms beginning with 79, for the number nearest to 683 ; we find 685.

The logarithm in the table nearest to our given logarithm is now located. The first three figures of the corresponding number are taken from the column JV, on the same line with 685. They are 626. The fourth figure of the number is that which stands at the top of the column containing 685. It is 4. Hence, the number is 6264. To insert the decimal point we note that the characteristic of the given logarithm is 1 ; hence, we must have two figures before the decimal point. We have, therefore, x = 62.64.

Given log x = 7.14168 — 10 find x. The nearest logarithm in the table is .14176, on page 2 (notice the asterisk). The corresponding number is 1386. The real value of the charac- teristic is 7 — 10 = — 3. Hence by III. § 2 there must be two ciphers between the decimal point and the first significant figure. We can also obtain the number of ciphers by sub- tracting the augmented characteristic 7, from 9, according to the rule above. The result is, therefore, x = .001386.

XIV . EXPLANATION OF THE TABLES.

Verify the following statements :

log x = 1.73682, x = 54.55 log x = 9.74464 — 10, x = .5554

log x = 5.41621, x = 260700 log x = 4.48493, x = 30540

log x = 8.91929 — 10, x = .08304 log x = 3.14139, x = 1385

log x = 2.43625, x = 273.1 log x = 7.79012 — 10, x = .006168

log x = .64443, x = 4.41 log x = 6.56822 — 10, x = .00037

5. Exercises and Examples.

1. Compute the value of (1.789)5.

By III. § 1, we have log (1.789)6 = 5 X log 1.789. log 1.789 = .25261

5

log (1.789)5 = 1.26305 .-. (1.789)* = 18.33

2. Compute the value of 728 X 63.86 X -4792

log 728= 2.86213 log 63.86= 1.80523 log .4792 = 9.68052 — 10

by I. § 1, log (728 X 63.86 X -4792) = j 14-34788 - 10

>• or 4.34/88. Hence 728 X 63.86 X -4792 = 22280.

3. Compute the value of V 73.

log 73 = 1.86332.

By IV. \ 1, log ^]T¥= * log 73 = .62111,

^'73= 4.179

In dividing log 73 by 3, the division is not exact. Such cases arise with great frequency in logarithmic work ; and the student must carefully observe the two following rules :

(1.) Never carry the work beyond the number of decimal places given in the table, that is with this table, five places.

(2.) When the division is not exact, always take in the last place the figure that is nearest to the true result.

Thus, in the case just above, where we divide 1.86332 by 3, the last step of the division is 2 divided by 3. Now 3 goes into 2 more nearly once than no times ; hence, we take 1 for the last figure. Sometimes, when the divisor is an even number, the result falls just half way between two integers in the last place. We then take at pleasure either the larger or smaller of these two figures for the last figure. The following example illustrates this :

4. Find 1/471L log 4711 = 3.67311,

.-. log V/4711 J log 4711 = 1.83655 or 1.83656.

Both of these logarithms give 68.64 as the result to four figures.

EXPLANATION OF THE TABLES. XV

5. Find y/.06398.

log .06398 = 8.80604 — 10.

We cannot divide this logarithm by 7 without getting an awk- ward result. But if we add and subtract 60, we have

log .06398 = 68.80604 — 70,

where the number subtracted from the logarithm is now ten times the number by which we must divide ; and hence, after the divi- sion, it will be reduced to 10. This is the best practice for such cases. Performing the division, we have

log >/.06398 = 9.82943 — 10, .'. 1/.06398 = .6752.

log l/"27" = £log27 =* X 1.43136= .71568 log (9.261)? = f log 9.261 = f X 0.96666 = .41428 BylLgl logz = .30140

x = 2.002.

7. x= 68.96X^^228 ^

39 X (8.642)* X (.96)2

log 68.96= 1.83860

log f .4228 = I log (.4228) = £ X 29.62613 — 30 = 9.87538 — 10 log of numerator = 11.71398 — 10

log 39 = 1.59106

log (8.642)* = f log 8.642 = f X 0.93661 = 1.56102 log (.96)2 = 2 log (.96) = 2 X 9.98227 — 10 = 19.96454 — 20

f 23.11662-20 log of denominator = { QJ. Q U662

log x = log of numerator — log of denominator = 8.59736 — 10. Hence x = .03957.

In order to explain clearly each step in working this example, the amount of written work set down is much greater than is allowable in ordinary practice. The work for the same example is arranged below in more concise form, and at the same time the — 10's are omitted from the logarithms with negative character- istics.

log 39 = 1.59106 log 68.96 = 1.83860

log (8.642) * =1.56102 log ^.4228 =9.87538

log (.96)2 = 9.96454 log of num. = 1.71398

log of denom. = 3.11662 3.11662

x= .03957 log a; = 8.59736

XVI EXPLANATION OF THE TABLES.

EXAMPLES.

Find the values of the following numerical expressions, and give the results to four significant figures :

1. 839.6 X /6129. Ans. 65730 5 21 . 38 X 6.296 X. 412. Ans. .2292

7 X ^ 41290

2. 19.63X^6^2. ^n, 173.4 4.19X6.2X^^67

(3.339)s X 142.9

7 298.7 X 563 X/TT Am. 7266

(2.96)*

. ft (9.8)3X^.4621X18.

F 12 X Vl7 1/41.63 X (2.649)5

6. The Arithmetical Complement of the Logarithm

or Co-logarithm. To compute the value of - by log-

b

arithms, we may take either log a — log b, or log a -f- log-.

b

Log - = log 1 — log b = 0 — log b is called the co-logarithm of b

b. We have, therefore, the following rule :

To form the co-logarithm of a given number subtract the log- arithm of the number from 0.

It is customary in practice to subtract the logarithm from 10 instead of from 0, and then to write — 10 after the result ; that is, the logarithm is subtracted from 0, written in the form 10.00000 — 10. If the logarithm is one which has been itself augmented by 10, the two — 10's, that in the subtrahend and that in the minuend, cancel each other.

Ex. Find colog 729.6. Log 728.6 = 2.86308. Subtracting this from 10.00000 — 10, the result is colog 729.6 = 7.13692 — 10.

Ex. Find colog .0641. Log .0641 = 8.80686 — 10. Subtracting this from 10.00000— 10, the result is colog .0641 = 1.19314.

Verify the following statements :

colog 9986 = 6.00061, colog 3.9 = 9.40894,

colog 7.298 = 9.130SI ), colog 380.6 = 7.41953,

colog .4682 = .32957, colog .005 == 2.30103.

EXPLANATION OF THE TABLES. XV11

With a little practice the student can write down the colog directly from the table, as readily as the log itself. The prac- tical rule is to subtract each figure of the logarithm, beginning at the left, from 9, except the last or right-hand figure, which must be subtracted from 10. When the characteristic of the logarithm is 0, care must be taken not to forget to subtract this from 9, just as any other characteristic would be sub- tracted.

The practical advantage of using cologs consists in the fact that thereby the number of separate operations required to obtain the log of the result is reduced. For example, suppose

we wish to calculate log —^ — ^-^. Without using co = logs three operations are required :

(1.) to find log a + log 6 -4- log c, (2.) « logd + loge + log/, (3.) to subtract (2) from (1).

If, on the other hand, cologs are used, these three opera- tions are reduced to one, viz. : to find log a -4- log b -\- log c -f- colog d -f- colog e -f colog /.

Ex. By using cologs the work of Ex. 7, p. xv., may be arranged in the following concise form :

log 68.96 = 1.83860 log 1^.4228 = 9.87538 colog 39 =8.40894 colog (8.642)1 =8.43898 colog (.96)2 == 0.03546 logo; =8.59736

7. To Find the Logarithm of a Number which Consists of Five Figures.

This is accomplished by the aid of the operation known as interpolation. Let the given number be 31.687. The table gives log 31.68 = 1.50079 and log 31.69 = 1.50092. To find log 31,687 a small correction must either be added to log 31.68 or subtracted from log 31.69.

The whole difference between two consecutive logarithms in

XV111 EXPLANATION OF THE TABLES.

the table is called the tabular difference. In this case the tabular difference is 13. That is, the logarithm increases by 13 for a change of unity in the fourth place in the number. Hence, for 7 in the fifth place the proportional change in the logarithm will be seven-tenths of 13, or 9.1, the nearest integer to which is 9 ; hence, 9 is the correction to be added to log 31.68 to obtain 31.687. Therefore,

log 31.687 = 1.50079 + .00009 = 1.50088

This method of determining the correction for the fifth figure is not theoretically correct, for it assumes that log- arithms vary proportionally with the corresponding numbers; but while this is not true, it is applied here for such a small interval that no appreciable error arises from its use.

The work of computing corrections for the fifth figure is performed in the little auxiliary tables in the column headed Prop. Pts. (Proportional Parts). On the same page with log 31.68 we find one of these tables headed by the tabular differ- ence 13. In this table we look in the column to the left of the vertical line for the fifth figure, 7, of the given number. The corresponding number to the right of the vertical line, which is 9.1, is the required correction, the nearest integer to which must be added to the logarithm corresponding to the first four figures of the given number.

The student should accustom himself to apply the correc- tion for the fifth figure mentally, and to write nothing on the paper except the corrected logarithm.

Verify the following statements :

log 414.23 = 2.61724, log 69.426 = 1.84152,

log 3.8642 = 0.58706, log 1418.1 = 3.15171 ,

log .43007 = 9.63354, log 85672. = 4.93284.

8. To Find the Number to Five Figures Corres- ponding to any Logarithm.

Let logo; = 2.38647. Look in the table for the nearest man- tissa that is less than 38647, not for that which is absolutely

EXPLANATION OF THE TABLES. XIX

nearest, as when only four figures are required. This is found to be 38632, which corresponds to the natural number 2434. These are the first four figures of x. Next find the tabular difference, which is 18. Then subtract the mantissa taken from the table (38632) from the mantissa of the given log- arithm (38647); the difference is 15. Hence, we have the problem: If a difference of 18 in the mantissse makes a change of a unit in the fourth figure of the number, what change will be made by a difference of 15 in the mantissse ? Evidently we have the proportion

18 : 1 = 15 : difference required or difference = i-f = | = .8 ;

that is, the correction is .8 of a unit in the fourth place, or 8 units in the fifth place. Hence, the figures in the number x are 24348, and inserting the point after the 3, because the characteristic is 2, we have x = 243.48.

The work of determining the fifth figure is performed in the marginal tables of Prop. Pts. Find the one correspond- ing to the tabular difference IS^and look on the right of the vertical column for the number nearest to 15, the difference between the given log and the next smaller one in the table. We find 14.4 and the corresponding number on the left of the vertical line, which is 8, is the required fifth figure.

Verify the following statements :

log x = 3.28642, x = 1933.8 log x = 7.63419 — 10, x = .0043072

log x = 1.46010, x = 28.847 log x = 2.31419, x = 206.15

log x = 9.38642 — 10, x = .24346 log x = .76787, x = 5.8596

9. Exercises and Examples.

_ (36.842)* X. (1.6272)' X &_ - ~ 1/.062416 X 72.983 X ^189*

log (36.842)4 = 1.56634 X*= -52211 log (1.6272)2 = .21144 X 2 = .42288

log 87 =1.93952

colog V .062416 = 1.20471 -s- 2 = .60235

colog 72.983 — 8.13678

colog ^189 = 7.72354 -=- 3 = 9.24118

x = 7.3252 log*= .86482

XX EXPLANATION OF THE TABLES.

EXAMPLES.

In working these examples use cologs wherever necessary, and arrange the work as on preceding page.

67.284 X .10003 L f 74^99X6.7843' ^..10953

63.842 X (42.32)* X(.02478)3- 1/2

(7.2S43)8 X 1^.00067894 3" (620.01)* X 489.62 ^m. 306.49

1986.1 X ff 92.836

3.403.75

5.

a

V 1000000 7. 1/IO~X ^100 X HOW! ^m. 82.542

10. Numbers with Six Figures. As a general rule, we cannot work to six figures in natural numbers with a table of five-place logarithms, for when the correction for the sixth figure is applied it will usually be too small to make any difference in the logarithm. On the first page or two of the table, however, where the logarithms vary rapidly, it can be done with approximate accuracy.

The correction for the sixth figure is always one-tenth of the correction for the same figure in the fifth place.

Ex. To find log 13.9647.

log 13.96 = 1.14489 correction for fifth figure = 12.4

" " sixth " = 2.17

total correction = 14.57, nearest integer = _ 15

log 13 9647 =1.14504

EXPLANATION OF THE TABLES. XXi

Ex. Find a, given log x — 2.21647,

nearest log in table = .21643, corresponding to 1646

difference 4

nearest smaller prop.1

pt. under tab. diff. 26 / = ^ J corresponding to 1

difference remaining ~IA * for the fafth ^

1.4 X 10 (because sixth figure is required) = 14, corresponding to 5 for the sixth figure. Hence, x = 164.615.

Verify the following:

log 1219.35 = 3.08613. log x = 3.12964, x = 1347.84.

log 10.7642 = 1.03198. log x = 0.06432, x = 1.15963.

TABLE II. Constants and Their Logarithms. (Page #0.)

11. No description of this table is necessary. The loga- rithms are given to seven places, instead of five, in case a greater degree of accuracy should be required. If only the first five places are used, the fifth figure must be increased by 1, if the sixth figure is 5, or more.

TABLE III. Logarithmic Sines, Cosines, Tangents and Cotangents. (Pages 21-66.)

12. The logarithms of the trigonometric functions are used in computation much more frequently than the functions them- selves, which are called natural functions. For this reason this table is given more prominence than that of the natural func- tions. The table gives the logarithms of the functions for each minute from 0° to 90°. The functions of angles not expressed evenly in minutes can be found by interpolation, as explained below.

Since sec and esc are the reciprocals of cos and sin respec- tively, their logs can always be found by taking the cologs of the latter.

The sin and cos of all angles and the tan of angles less than 45° are less than unity ; hence, their logarithms have negative characteristics. For this reason the characteristics of all these logarithms are increased by 10 in the tables.

XXU EXPLANATION OF THE TABLES.

13. To Find the Logarithmic Function of an Angle Less than 90°.

Enter the table with the given number of degrees, which will be found at the top of the page, if it is 44° or less, but at the bottom of the page, if it is greater than 44°. The func- tion required is read at the top or bottom of the page, accord- ing as the number of degrees is at the top or bottom, and the required logarithm is taken from the corresponding column. The minutes are read in the left hand column of the page, if the degrees are read at the top, but in the extreme right hand column of the body of the table if the degrees are read at the bottom.

EXERCISES.

1. Find log sin 24° 38'. 24° is at the top of page 46, and the log sin column for 24° is the first column of logarithms on the page. Running dow.n the page until we corne to 38', we find log-sin 24° 38' = 9.61994.

2. Find log tan 57° 16'. 57° is at the bottom of page 54. Run- ning up the page in the column marked at the bottom log tan, until we come to the line with 16' on the right, we find log tan 57° IV = 0.19192.

Verify the following statements:

log sin 39° 16' = 9.80136, log cos 8° 19' = 9.99541,

log tan 63° 24' = 0.30037, log cot 54° 9' = 9.85887,

log cos 41° 31' = 9.87434, log tan 82° 56' = 0.90670,

log cot 26° 12' = 0.30798, log cot 7° = 0.91086,

log cos 31° = 9.93307, log sin 19° 12' = 9.51702.

14. Interpolating for Seconds.

Find the logarithmic functions for the degrees and minutes as before; then apply a correction for the seconds, as explained below. This correction must be added if the function is sin or tan, and subtracted if the function is cos or cot.

Find log sin 16° 28' 35".

log sin 16° 28' = 9.45249, and the tabular difference is 43 ; that is, the log sin increases by 43, while the angle increases by 1'. Hence, the proportional increase for 1" is f $ , and for 35" it is U X 35 = JVVL = 25.08 . . . , the nearest integer to which is the required correction. Hence,

log sin 16° 28' 35" = 9.45249 + .00025 = 9.45274.

EXPLANATION OF THE TABLES. XX111

The auxiliary table of proportional parts for tabular differ- ence 43 will give the same result. The column to the left of the vertical line in these auxiliary tables gives the number of seconds, arranged in the order 6, 7, 8, 9, 10, 20, 30, 40, 50. If the correction for 1, 2> 3, 4, or 5 seconds is required it is obtained by taking one-tenth of that for 10, 20, 30, 40, or 50 respectively. The work can be arranged concisely as follows, but it is desirable in actual practice to compute the correction mentally and to write only the complete logarithm :

log sin 16° 28' = 9.45249 correction for 30" = 21.5 " " 5" = 3.58

log sin 16° 28' 35" = 9.45274

Find log cot 61° 13' 19". log cot 61° 13' = 9.73987

correction for 10" (tab. diff. 30) = 5.0

u u g// « « __ 45

nearest integer to total correction = 10.0

Subtract correction because function is cot, 10

log cot 61° 13' 19" = 9.73977

On pages 22 to 27 of the table, on account of the large number of differences which occur, owing to the rapid varia- tion of the logarithms, different arrangements of the tables of Prop. Pts. are made. If the logarithm required falls on pages 25 to 27, and it happens that the tabular difference is one for which a table of proportional parts is given, the pro- cedure is the same as above; otherwise as follows:

Find log tan 3° 51' 26"

log tan 3° 51' = 8.82799, tab. diff. = 188.

This tabular difference is not given, so we use the auxiliary tables for 185 and 3 (because 185 -f 3 = 188) instead.

tab. diff. 185 ( Correction for 20" = 61.7 " 6" = 18.5

tab. diff. 3 { ' »?" 1-0

I " " 6"= 0.3

81.5 Hence, the total correction to be added is 82 and log tan 3°

61' 26" = 8.82881.

XXIV EXPLANATION OF THE TABLES.

In a case of this kind it is, perhaps, just as easy to compute the correction without using the auxiliary tables.

On pages 22 to 24 the Prop. Pt. is given for one second for each tabular difference for log sin, log tan, and log cot. Log cos varies so slowly in this part of the table that no auxiliary tables are necessary. Find log sin 1° 48' 53".

log sin 1° 48' = 8.49708, tab. diff. = 400 Prop. pt. for 1" (tab. diff. 400) = 6.67 " " 53" = 6.67X53 =353.51 . \ correction to be added = 354. and log sin 1° 48' 53" = 8.49708 + .00354 = 8.50062 On account of the very rapid variation in the log sin and log tan at the beginning of the table, the theory that the varia- tion of the log is proportional to that of the angle, leads to results which are sometimes appreciably in error. For this reason, when great precision is required, Table IV., pp. 67, 68, should be used in finding the log sin and log tan of angles less than 4°. An explanation of this table is given below, § 19. Yerify the following statements :

log cos 17° 38' 42" = 9. 97907, log tan 5° 38' 5" = 8.99416,

log tan 84° 9' 13" = 0.98972, ^log sin 1° 12' 38" = 8.32482, log sin 61° 41' 31" = 9.94469, log cos 26° 28' 37" = 9.95188,

log cos 87° 6' 14" = 8.70351, log cot 9° 1' 43" = 0.79889,

log cot 86° 53' 34" = 8.73467, log sin 45° 43' 28" = 9.85491.

15. To Find the Logarithmic Function of an Angle >90°.

According to the theorems demonstrated in Elements of Trigonometry §§ 28-31, and the rules on page 40, summariz- ing the results, the functions of any angle can be found if those of all angles less than 90° are known. These results are given here in the form of the following rules:

I. To find the function of an angle between 90° and 180° sub- tract the angle from 180° and look for the same function of the difference, or subtract 90° from the angle and look for the co-function of the difference.

II. To find a function of an angle between 180° and 270° sub- tract the angle from 270° and look for the co-function of the differ-

EXPLANATION OF THE TABLES. XXV

ence, or subtract 180° from the angle and look for the same function of the difference.

III. To find a function of an angle between 270° and 360° sub- tract the angle from 360° and look for the same function of the differ- ence, or subtract 270° from the angle and look for the co-function of the difference.

The second alternative in each of these rules is better if the angle has minutes and seconds, for there is less danger of making a mistake in taking the difference.

EXERCISES.

1. Find log cos 117° 19' 35".

By rule I. log cos 117° 19' 35" = log (—sin 27° 19' 35").

NOTE.— In taking the logarithm of a negative quantity we pro- ceed as if the quantity were positive. To the logarithm when found, we prefix the symbol (— ) or annex the symbol n. Neither of these signs affect the operations to which the logarithm may be subjected, but are used merely to remind the computer that the corresponding numbers are negative.

log sin 27° 19' 35" = 9.66187, log cos 117° 19' 35" = (— ) 9.66187.

2. Find log tan 242° 20' 17".

By rule II. log tan 242° 20' 17" = log tan 62° 20' 17" = 0.28054.

Verify the following statements :

log sin 300° 24' = (— ) 9.93577 log cot 200° 30' 30" = 0.42707 log cos 216° 14' 33" = (— ) 9.90662 log sin 138° 48' 6" = 9.81867 log tan 101° 6' 52" = (— ) 0.70674 log cos 342° 38' 15" = 9.97975

16. To Find an Angle Given one of its Logarith- mic Functions.

A further glance at the general constitution of the table is first necessary. Upon each page of the table are four columns of logarithms, the first and fourth are logarithmic sines and cosines, the second and third are logarithmic tangents and cotangents. The logarithms increase, going toward the back of the table in the first and second columns, and then passing into the fourth and third columns respectively, they increase, going toward the front of the table. Eemembering this, the place of any given logarithm in the table can be found readily.

XXVI EXPLANATION OF THE TABLES.

The rules for finding an angle from its logarithmic function are as follows:

If the given function is log sin or log cos look for the nearest smaller logarithm in the first or fourth column ; if it is log tan or log cot, look in the second or third column.

Read the degrees at the top or bottom of the page, according as the name of the given function is at the top or bottom of the column in which the given logarithm is located.

Head the minutes on the left or right according as the degrees are read at the top or bottom of the page, and in the same line with the nearest logarithm smaller than the given one.

Determine the number of seconds by proportion and add them to the degrees and minutes found, if the given function is log sin or log tan, but subtract them if it is log cos or log cot.

EXERCISES.

1. Given log sin 6 = 9.86592, what is 6?

In the fourth column on p. 64 we find 9.86589, and log sin is read at the bottom. Hence, the degrees and minutes are 47° 15'. The tabular difference is 11 and the difference between the given log and log sin 47° 15' is 3. Hence, 0 exceeds 47° 15' by T3T of one minute. This fraction reduced to seconds is T3T X 60 — 16". Hence, 0 = 47° 15' 16".

To use the auxiliary table to find the number of seconds, we arrange the work as follows, using table for tabular difference 11. whole difference = 3

nearest smaller prop. pt. = 1.8, corresponding to 10" difference remaining = 1.2 " " 6"

whole number of seconds 16"

NOTE. — The number of seconds corresponding to 1.2 under tabular difference 11 is, according to the table, either 6" or 1" ; but 6" is really a little nearer than 7", as we found above.

2. Given log cot 0 = 0.72654, find 0.

On p. 32, in the third column, we find 0.72643, and log cot is

read at the top ; hence, the degrees and minutes are 10° 38'. The

tabular difference is 70, and the difference between log cot 6 and

0.72643 is 11. Hence, using table of proportional parts, we have

whole difference =11

nearest smaller prop. pt. = 10.5, corresponding to 9" difference remaining = .6,

EXPLANATION OF THE TABLES. XXV11

as this is less than half the prop. pt. for 1" (1.17), the entire correc- tion is 9", which is subtracted from 10° 38', giving 0 = 10° 37' 51".

3. Given log tan 6 = 8.61246, find 6. On page 24, log tan 2° 20' = 8.61009.

difference = 237, tab. diff. = 310, prop. pt. for 1" = 5.17,

no. of seconds = ^- = 46". .-.0 = 2° 20' 46". 5.17

In these three exercises the results are incomplete, because we know from Trigonometry that there are always two angles less than 360° corresponding to any given trigonometric function. The complete answers are as follows : 1. 6 = 47° 15' 16" and 180°— 47° 15' 16" = 132° 44' 44", because sin 6 is positive in the first and second quadrants. 2. 6 = 10° 37' 51" and 180° -f 10° 37' 51" = 190° 37' 51". 3. 6 = 2° 20' 46" and 180° + 2° 20' 46" = 182° 20' 46", be- cause tan 0 and cot 6 are positive in the first and third quadrants.

4. Given log cos 6 = (— ) 9.62983, find 0.

Assume that cos 6 is positive and find the angle corresponding to it in the first quadrant. We find on p. 47 log cos 64° 46' = 9.62972. whole difference = 11

nearest smaller prop. pt. = 9.0, corresponding to 20" difference remaining = 2.0 " " 4"

number of seconds to be subtracted, 24"

Hence, log cos 64° 45' 36" = 9.62983. Since the cos is negative in the second and third quadrants,

we have d - / 180° ~ 64° 45/ 36// = 115° 14/ 24//

\ 180° + 64° 45' 36" = 244° 45' 36".

When one or both values of the required angle are not in the first quadrant, the following rules are to be followed :

To find an angle in the second quadrant, subtract the angle taken from the table from 180°.

To find an angle in the third quadrant, add the angle taken from, the table to 180°.

To find an angle in the fourth quadrant, subtract the angle taken from the table from 360°.

Verify the following statements :

log sin 0= 9.28642, 0= 11° 9' 1" and 168° 50' 59". log cos 0= 8.46321, 0= 88° 20' 6" " 271° 39' 54". log tan 0= 0.12983, 0= 53° 26' 22" " 233° 26' 22". log cot 0= 9.62412, 0 ±= 67° 10' 36" " 247° 10' 36". log sin 0 = (— ) 9.96419, 0 = 247° 3' 0" " 292° 57' 0". log cos 0 = (— ) 9.78416, 0 = 127° 28' 15" " 232° 31' 45". log tan 0=(— ) 9.42317, 0 = 165° 9' 36" " 345° 9' 36". log cot 0 = (— ) 8.76432, 0 = 93° 19' 35" " 273° 19' 35".

XXV111 EXPLANATION OF THE TABLES.

17. Functions of Negative Angles. To find the log- arithmic functions of negative angles, follow the formulae given in § 31, Elements of Trigonometry.

18. General Remarks. In using a five-place table of logarithmic functions the computer should remember that the seconds in his results will be, in general, only approximately correct. Nevertheless, angles can be determined in most parts of the table more closely than to tenths of a minute ; so that it seems preferable to give tables of proportional parts for seconds, rather than for tenths of a minute.

Attention is here called to the fact that throughout all the tables a final five is sometimes marked with a small dash over it, thus 5, and sometimes it is not so marked. This mark is used to indicate that if, for any reason, the computer wishes to use a smaller number of decimal places than are gwen in the table, the 5 is to be dropped without increasing the pre- ceding figure by unity. If the 5 is not marked in this way the preceding figure must be increased by unity if the 5 is dropped.

The student may vary somewhat the procedure in the matter of interpolation as he becomes accustomed to using the tables. For example : in finding log 18769 he may take log 1877 from the tables and subtract the correction for 1, instead of taking log 1876 and adding the correction for 9. Again, in finding log cos 78° 38' 56" he may take log cos 78° 39' and add the correction for 4" instead of taking log cos 78° 38' and sub- tracting the correction for 56". Numerous points of this kind, which in many cases will shorten the work, will 'suggest them- selves, and need not be specified here.

EXAMPLES. Find 0 in each of the following examples :

1 n 0 - 6-2984 8ip' 63° 18/ W 6 = / 127° l/ 7"

" 7.5692 cot 116° 36' 12" " 1 307° 1' 1"

o 2.93 tan 48° 6' 38" 0=/121°34' 3"

" 14.12 sin 26° 13' 42" " i 238° 25' 57"

EXPLANATION OF THE TABLES. XXIX

7° 58' VI" 172° 1' 43"

I sin3 146° 12' 19" X tan 78° 12' 32" a _ 8- 8m ° := \ cot* 12° 14' 6" X cos 64° 4' 55" '

352° V 43"

. a _ .93862 cos2 312° 38' 40" e= f 32° 55' 19" 4. cot a : _ -

TABLE IY. (Pages 67 and 68.)

19. Sine and Tangent of Small Angles. This table derives its usefulness from the fact that when an angle (a) is

small the ratios ?!5L? and ^-^ vary but slowly. The quan-

a a

tities S and T in the table are the logarithms (increased by 10) of these ratios, where the angle is expressed in seconds. Hence, to find log sin and log tan of a small angle we have the formulae

log sin a = log a" + S

log tan a = log a" + T and to find a small angle from its log sin or log tan we have

log a" = log sin a — S

log a" •=. log tan a — T

Ex. Find log tan 0° 26' 51".

0° 26' 51" = 1611" log 1611 = 3.20710

T (for 0° 270=4.68558

.-. log tan 0° 26' 51" = 7.89268

(the same calculated from Table III. is 7.89264, which is thus shewn to be in error four units in the fifth place). Ex. Given log sin a = 8.36892, find a. From Table III. we find that a = 1° 207 approximately ; hence, the proper value of S (from Table IY) is 4.68554. We have, therefore, log sin a _ s= 3>68338 = log a//

a = 4824" -=1° 20/24". Yerify the following statements, by means of Table IY :

log sin 0° 57' 36" = 8.22412.

log tan a = 8.19632, a = 0° 54' 1".

To find the cosine or cotagent of an angle nearly 90° use the same table, taking the sine or tangent, as the case may be, of the complement of the given angle.

XXX EXPLANATION OF THE TABLES.

TABLE V. Natural Functions. (Pages 69-78.)

20. By the terms natural sine, cosine, etc., are meant the actual values of these functions. The table is used compara- tively seldom, and for that reason the functions are given for every five minutes only. To find the functions for inter- mediate minutes the process of interpolation by simple pro- portion is used. Thus, to find sin 51° 18', we have

sin 51° 20' = .78079

sin 51° 15' = .77988 difference for 5' = 91 hence, correction for 3' = f of 91 = 55, and sin 51° 18' = .77988 + .00055 = .78043.

The rules given above, for adding and subtracting correc- tions and for finding functions of angles greater than 90°, apply here the same as in the case of Table III.

The results of interpolating minutes in that part of the table which gives the cot of angles less than 15° and the tan- gents of angles between 75° and 90° will, in general, not be correct in the last place. Hence, when considerable .precision is required in these cases the function should be found by taking the natural number corresponding to the logarithm found in Table III.

TABLE VI. Circular Arcs Expressed in Radians. (Page 74.) This table gives to seven decimal places the number of radians for every degree up to 180°, with auxiliary tables for minutes and seconds.

EXERCISES. L How many radians in 126° 38' 19" ? From the table we have

number of radians in 126° =2.1991149

38' = .0110538

" " 19"= .0000921

" " 126° 38' 19" = 2.2102608

2. How many degrees, minutes and seconds in 4.6832964 radians ? As this number of radians exceeds 180, we subtract the number of

EXPLANATION OF THE TABLES. XXXI

radians in 180° and find the degrees, minutes and seconds in the remainder. This last added to 180° is the result :

Given number of radians = 4.6832964 Radians in 180° =3.1415927

Difference =1.5417037

Radians in 88° = 1.5358897

.0058140

Radians in 19' = .0055269

.0002871

Radians in 59" = 2860

Result = 268° 19' 59" .0000011

The last difference, .0000011, corresponds to less than half a second.

TABLE VII. Napierian Logarithms of Numbers. (Pages

75, 76.)

Although these logarithms are not used for purposes of practical computation, their values are sometimes required in calculating values of transcendental functions, and for other purposes. -The table gives the logarithm of each number from 1 to 1000. As the value of the characteristic does not depend upon the position of the decimal point, nor the value of the mantissa solely upon the sequence of figures in the corres- ponding number, we cannot use the table just as we do a table of common logarithms. If log 363.8 is required we can find it by interpolating between log 363 and log 364 ; but if log 3638 is required we must find log 363.8 in the manner just indicated, and then add log 10. The work is as follows :

log 363 =5.89440

log 364 = 5.89715

difference = 275

.8 of difference = 220

adding this to log 363 gives log 363.8 = 5.89660

log 10 = 2.30259 log 3638 = 8.19919

To find the number corresponding to a given Napierian logarithm we first subtract as many times log 10 as may be necessary to bring the logarithm within the limits of the

XXX11 EXPLANATION OF THE TABLES.

table. Then find the number corresponding to this difference and multiply it by the power of 10, whose logarithm was subtracted at the beginning. Thus, to find the number whose Napierian logarithm is 9.62983 :

log 100 = 2 log 10 = 4.60517

9.62983 — 4.60517 = 5.02466

5.02466 is the logarithm of some number between 152 and 153. Given log =5.02466

log 152 =5.02388

difference 78

tabular difference = 656 78 -4- 656 = .12.

5.02466 is the logarithm of 152.12. Hence, 9.62983 is the logarithm of 152.12 X 100 = 15212.

TABLE I.

COMMON LOGARITHMS OF NUMBERS.

If.	O	l	2	3	4	5	6 7	8	9	Prop. Pts.
100	00 000	043	087	130	173	217	260	303	346	389
01	432	475	518	561	604	647	689	732	775	817		44	43	42
02 03	860 oi 284	903 326	945 368	988 410	452	*072 494	*ii5 536	*I57 578	*i99 620	*242 662	i 2	4.4 8.8	4-3 8.6	&
04	703	745	787	828	870	912	953	995	*o36	*078	3	13.2	I2.9	12.6
05	02 119	160	202	243	284	325	366	407	449	490	4	17.6	17.2	16.8
06	531	572	612	653	694	735	776	816	857	898	i	22. 0 26 A	21.5	21.0 25.2
07 08 09	938 03 342 743	979 383 782	423 822	*o6o 463 862	*IOO 503 902	*i4i 543 941	*i8i 583 981	*222 623 *O2I	*262 663 *o6o	*3<>2 703 *IOO	I 9	*v.«| 30-8 35-2 39.6	30.1 38.7	29.4 33-6 37.8
110	04 139	179	218	258	297	336	376	415	454	493
II	532	57 i	610	650	689	727	766	805	*844	*883		41	40	39
12	922	961	999	*o38	*o77	*II5	*i54	*I92			i	4.1	4.0	7.0
13	05 308	346	385	423	461	500	538	576	614	652	2	8.2	8.0	O :? 7.8
14 15	690 06 070	729 108	767 145	805 183	843 221	88l 258	918 296	956 333	994	*032 408	3 4	12.3 12.0 16.4 16.0	ii. 7 15-6
16	446	483		558	595	633	670	707	744	781	5	20.5	20. o	19-5
											6	24.6	24.0	23.4
17	819	856	893	930	967	*oo4	*o4 1	^078	*"5	^151		28.7	28.0	27.3
18	07 188	225	262	298	335	372	408	445	482	518	g	•3.2.8	72. 0	31.2
19	555		628	664	700	737	773	809 | 846	882	9 36.9 36-0	35-1
120	918	954	990	*027	*o63	*099	*I35	*i7i	*207 *243
21	08 279	314	350	386	422	458	493	529	565 600		38	37	36
22	636	672	707	743	*778	814	849	884	920	*955	i	' 3-8	3-7	3-6
23	991	*026	*o6i	*o96		*i67	202	*237	*272		2	7-6	7-4	7.2
24	09 342	377	412	447	482	517	552	587	621	*656	3	11.4 ii. i _ _ _ _ . o	10.8
25 26	691 10 037	726 072	760 106	795 140	830 175	864 209	899 243	934 278	968 312	346	4 1	15.2 14.8 19.0 18.5 22.8 22.2	14.4 18.0 21.6
27	380	415	449	483	517	55i	585	619	653	687	7	26.6 25.9 25.2
28	721	755	789	823	857	890	924	958	992	*025	8	30.4 29.6 28.8
29	ii 059	093	126	160	193	227	26l	294	327	361	9	34-2 33-3! 32.4
180	394	428	461	494 528	561	594	628	661	694
31	727	760	793	826 860	893	926	959	992	*O24		35	34	33
32	12 057	090	123	156 189	222	254	287	320	352	i	3-5	3-4	3.3
33	385	418	450	483 5*6	548	581	613	646	678	2	7.0	6.8	6.6
34	710	743	775	808	840	872	905	937	969	*OOI	3	10.5	IO.2 _ _ £	9-9
II	13 033 354	066 386	098 418	130 450	162 481	194 513	226 545	258 577	290 609	322 640	4 5 6	14.0 17-5 21.0	13.6 17.0 20.4	13-2 16.5 I9.8
37	672	704	735	767	799	830	862	893	925	956	7	24.5	23-8	23.1
38	988	'o 1 9	*05I	*082	*ii4	*i45	*I76	*20S	*239	*270	8	28.0		26.4
39	14 301	333	364	395	426	457	489	520		582	9	31.5	30.6	29-7
140	613	644	675	706	737	768	799	829	860	891
41	922	953	983	*oi4	*Q45	•076	*io6	*I37	*i68	*ig8		32	31	30
_ 42	15 229	259	290	320	351	381	412	442	473	503	i	3-2	3-1	3-°
43	534	564	594	625	655	685	715	746	776	806	2	6.4	6.2	6.0
44 45 46	836 16 137 435	866 167 465	897 197 495	927 227 524	957 256 554	987 286 584	*OI7 £3	346 643	*o77 376 673	406 702	3 4 6	9.6 12.8 16.0 19.2	9-3 12.4 m	9.0 12. 0 15.0 18.0
47	732	761	791	820	850	879	909	938	967	997	7	22.4	21.7	21.0
48	17 026	056	085	114	'43	173	202	231	260	289	S	25-6	24.8	24.0
49	319	34?	377	406	435				551	5-So	9	28.8	27.9	27.0
150	609	638	667	696	725	754	7S2	811		S69
N.	o i 'z :* 4	5,0 7 8	•	Prop. Pi.-.

N.	0	1 2	3 4	o	6 | 7	8	9	Prop. Pts.
150	17 609	638	667	696	725	754	782	811	840	869
5i	898	926	955	984	*oi3	*o4i	*o7o	*099	*I27	*i56		29	25
52	18 184	213	241	270	298	327	355	384	412	441	I	2.Q	2.8
53	469	498	526	554	583	611	639	667	696	724	2	-/ 5-8	5-6
54	752	780	808	837	865	893	921	949	977	*cx>5	3	• 8.7	8.4
55	19 °33	06 1	089	117	145	173	2OI	229	257	285	4	ii. 6	II. 2
56	312	340	368	396	424	45i	479	507	535	562	5 6	14-5 17.4	14.0 16.8
57	59°	618	645	673	700	728	756	783	811	838	7	20.3	19.6
58	866	893	921	948	976	*oo3	*030	*o58	*o8s	*II2	8	23.2	22.4
59	20 140	167	194	222	249	276	303	330	358	385	9	26.1	25-2
160	412	439	466	493	520	548	575	602	629	656
61	683	710	737	763	790	817	844	871	898	925		27	20
62	952	978	*005	*032	*°59	*o8s	*II2	*i39	*i65	*I92	i	2-7	2.6
63	21 219	245	272	299	325	352	378	405	431	458	2	5-4	5-2
64	484-	5ii	537	564	590	617	643	669	696	722	3	8.1 o	7.8
65	748	775	80 1	827	854	880	906	932	958	985	4	10.8	10.4
66	22 Oil	037	063	089	"5	141	167	194	220	24C	5 6	13-5 16.2	13.0- 15.6
67	272	298	324	350	376	401	427	453	479	505	7	18.9	18.2
68	531	557	583	608	634	660	686	712	737	763	8	21.6	20.8
69	789	814	840	866	891	917	943	968	994	*oi9	9	24.3	23.4
170	23 045	070	096	121	147	172	198	223	249	274
7i	300	325	35o	376	401	426	452	477	502	528	25
72	553	578	603	629	654	679	704	729	754	779	i 2.5
73	^805	830	855	880	905	930	955	980	*oo5	*030	2 5-0
74	24 055	080	105	130	155	180	204	229	254	279	3 7-5
75 •'	^3<H	329	353	378	403	428	452	477	502	527	4 10.0
76	55i	576	601	625	650	674	699	724	748	773	5 12.5 6 15.0
77	797	822	846	871	895	920	944	969	993	*oi8	7 17-5
78	25 042	066	091	115	139	164	1 88	212	237	261	8 20.0
79	285	310	334	358	382	406	43i	455	479	503	9 22.5
180	527	551	575	600	624	648	672	696	720	744
81	768	792	816	840	864	888	912	935	959	983		24	23
82	26 007	031	055	079	102	126	150	174	198	221	i	2.4	2.3
83	245	269	293	316	340	364	387	411	435	458	2	4.8	4.6
84	482	505	529	553	576	600	623	647	670	694	3	7.2 /-	6.9
85	717	74i	764	788	8l I	834	858	881	9°5	928	4	9.6	9.2
86	95i	975	998 |*02I	*Q45	*o68	*O9 1	*n4	*i38	*i6i	5	12. 0	n-5 _ _ o
												14.4	13.8
87	27 184	207	231	254	277	300	323	346	37o	393	7	16.8	16.1
88	416	439	462	485	508	53i	554	577	600	623	8	19.2	18.4
89	646	669	692	715	738	761	784	807	830	852	9	21.6	20.7
190	875	898	921	944	967	989	*OI2	*035	*os8	*o8i
91	28 103	126	149	171	194	217	240	262	285	3°7		22	21
92	330	353	375	398	421	443	466	488	5"	533	i	2.2	2.1
93	556	578	601	623	646	668	69I	713	735	758	2	4.4	4.2
94	780	803	825	847	870	892	914	937	959	.981	3	6.6 80	si
95	29 003	026	048	070	092	H5	137	!59	181	203	4	.0	8.4
96	226	248	270	292	3H	336	358	380	403	425	6	II. O 13.2	10.5 12.6
97	447	469	49 1	513	535	557	579	601	623	645	7	15.4	14.7
98	667	688	710	732	754	776	798	820	842	863	8	17.6	16.8
99	885	907	929	95i	973	994	*oi6	*o38	*o6o	*o8i	9	19.8	18.9
200	30 103	125	146	1 68	190	211	233	255	276	298
N.	0	1	2	3	4	5	6	n	8	9	Prop. Pts.

IV.	0	1	2	3	4	5	6	7	8	9	Pro	p. Pts.
200	30 103	125	146	168	190	211	233	255	276	298
01 02 °3 04 05 06 07 08 09	320 535 750 963 3i 175 387 597 806 32 015	34i 557 771 984 197 408 618 827 035	363 578 792 *oo6 218 429 056	384 600 814 *027 239 450 660 869 077	406 621 835 260 681 890 098	428 856 *o69 281 492 702 911 118	449 664 878 302 513 723 139	471 685 899 *II2 323 534 744 952 160	492 707 920 *I33 345 555 765 973 181	728 942 *i54 366 576 785 994 201	2 I 2 2 4 3 6o 4 8 5 " 6 13 7 IS 8 17 9 *9	2 21 .2 2.1 •4 4.2 .6 6.3 .8 8.4 .0 10.5 .2 12.6 .4 14.7 .6 16.8 .8 18.9
210	222	243	263	284	305	325	346	366	387	408
ii 12 13 M It 17 18 19	428 634 838 33 041 244 445 646 846 34 044	449 654 858 062 264 465 666 866 064	469 675 879 082 284 486 686 885 084	490 695 899 102 304 506 706 905 104	715 919 122 S3 726 925 124	736 940 143 345 546 746 945 143	552 756 960 163 365 566 766 965 163	572 777 980 183 $ 786 985 183	593 797 *OOI 203 405 606 806 203	613 818 *02I 224 425 626 826 *025 223	i 2 3 4 5 6 9	20 2.0 4.0 6.0 8.0 10.0 12. 0 I4.O 16.0 18.0
220	242	262	282	301	321	34 1	361	380	400	420
21 22 23 24 25 26 27 28 29	439 635 830 35 025 218 411 603 793 984	459 655 850 044 238 430 622 *813	479 674 869 064 257 449 641 832 *02I	498 694 889 083 276 468 660 *851	518 713 908 102 295 488 679 870	537 733 928 122 315 507 ^078	557 753 947 141 334 526 717 *9°8	577 772 967 160 353 545 736 927 *n6	596 792 986 180 372 564 755 946 *I35	616 811 199 392 583 774 *f5	* i 2 3 4 5 6 1 9	19 1.9 3.8 5-7 7-6 9-5 11.4 13.3 15-2 17.1
230	36 173	192	211	229	248	267	286	305	324	342
32 33 34 35 36 37 38 39	549 736 922 37 107 291 475 658 840	380 568 754 940 125 310 i	399 586 773 959 144 328 694 876	4l8 605 791 977 162 346 530 712 894	436 624 810 996 181 365 548 912	455 642 829 *oi4 199 383 566 749 931	474 661 847 *o33 218 401 585 767 949	493 680 866 236 420 603 785 967	254 438 621 803 985	717 903 *o88 273 457 639 822 *oo3	i 2 3 4 5 i	18 1.8 3.6 5-4 7.2 9.0 10.8 12.6 14-4 16.2
240	38 021	039	057	075	093	112	130	148	166	184
42 43 44 45 46 47 48 49	202 382 56l 739 917 39 °94 270 445 620	220 399 578 757 934 in 287 463 637	238 417 596 775 952 129 3? 480 655	256 435 614 792 970 146 322 498 672	274 453 632 810 987 164 340 515 690	292 471 650 828 *oo5 182 358 533 707	310 846 199 375 550 724	328 507 686 863 *04I 217 393 568 742	346 525 703 881 *o58 235 410 585 759	364 543 721 *8" 252 428 602 777	i 2 3 4 6 8 9	3-4 6.'8 10.2 II.O 13.6 15-3
250	794	811	829	846	863	881	898	915	933	95o
N.	0	1	2	1	1	B	6	7	*	9	Pro	p. Pts.

N.	O	1	2	3	4	5	6	7	8	9	Pro	p. Pts.
250	39 794	811	829	846	863	881	898	915	933	950
52 53 54 55 56 11 59	967 40 140 312 483 654 824 993 41 162 330	985 157 329 500 67 1 841 *OIO 179 347	*OO2 175 346 518 688 858 *027 196 363	192 364 535 705 875 212 380	*o37 209 552 722 892 *o6i 229 397	226 398 569 739 909 246 414	243 415 586 756 926 *°95 263 430	*o88 261 432 603 773 943 *in 280 447	*io6 278 449 620 79° 960 *I28 296 464	11 637 807 976 *I45 313 481	i 2 3 4 5 6 8 9	18 1.8 3-6 5-4 7-2 9.0 10.8 12.6 14.4 16.2
260	497	5H	531	547	564	58i	597	614	631	647
61 62 63 64 65 66 67 68	664 830 996 42 160 325 488 651 813	681 847 *OI2 177 341 504 667 830	697 *863 193 357 521 684 846	880 210 374 537 700 862	731 896 *062 226 39° 553 716 878	747 913 *o78 243 406 570 732 894	764 *929- 259 423 586 749 911	780 946 *in 275 439 602 765 927	797 *9 3 292 455 619 781 943	814 979 *I44 308 472 635 797 959	i 2 3 4 5 6 8	17 1.7 3-4 6.S 8.5 10.2 II.9 13.6
69	975	991	*oo8	*024	040	^056	072		104		9	15.3
270	43 136	152	169	185	201	217	233	249	265	281
72 73 74 75 76 77 78 79	297 457 616 775 933 44 091 248 404 560	313 473 632 791 949 107 264 420 576	329 489 648 807 965 122 279 436 592	345 505 664 823 981 138 295 607	361 521 680 838 996 154 3" 467 623	377 537 696 854 *OI2 170 326 483 638	393 553 712 870 *028 185 342 498 654	409 569 727 886 201 358 5H 669	425 584 743 *9°2 217 373 529 685	441 600 759 *oI? 232 389 545 700	i 2 3 4 6 I 9	16 1.6 43i 6.4 8.0 9-6 * II. 2 12.8 14.4
280	716	73 1	747	762	778	793	809	824	840	855
81 82 83 84 85 86 87 88 89	871 45 025 179 332 484 637. 788 939 46 090	886 040 194 347 500 652 803 954 105	902 056 209 362 667 818 969 120	917 071 225 378 530 682 834 984 135	932 086 240 393 545 697 849 *ooo 150	948 IO2 255 408 561 712 864 £65	963 117 271 423 576 728 879 ^030 180	979 439 59 i 743 894 *°45 195	994 148 301 454 606 758 909 *o6o 210	*OIO 163 317 469 621 773 ^924 225	i 2 3 4 5 6 8 9	15 i-5 4-5 6.0 7-5 9.0 10.5 12.0 13.5
290	240	255	270	285	300	315	33°	345	359	374
92 93 94 - 9£ 96 97 98 99	389 538 687 835 982 47 129 276 422 567	404 553 702 850 997 144 290 436 582	419 568 7l6 864 *OI2 159 305 451 596	434 583 731 879 *026 173 3J9 465 611	449 598 746 49i 188 334 480 625	464 6'3 761 *9°9 202 349 494 640	479 627 776 *923 217 363 509 654	494 642 790 *938 232 378 524 669	509 657 805 953 *IOO 246 392 538 683	f3 672 820 967 *ii4 261 407 553 698	i 2 3 4 5 6 I 9	14 1.4 2.8 4.2 5-6 7.0 8-4 9.8 II. 2 12.6
300	712	727	741	756	770	784	799	813	828	842
N.	0	1	2	3	4	5	6	;	8	9	Pro	p. Pts.

N.	0 1	2 3	4	5	678	9	Prop. Pts.
300	47 712	727	741	756	770	784 799 813	828	842
OI	857	871	885	900	914	929 943 958	972	986
02	48 ooi	015	029	044 058	073 087 | 101	116	130
03	144	159	173	187	202	216 230	244	259	273		15
04	287	302	316	330	344	359 373	387	401	416
05	430	444	458	473	487	5oi 515	530	544	558		!-5
06	572	586	601	615	629	643 657	671	686	700	2 3	3-° 4-5
07	714	728	742	756	770	785 799	813	827	841	4	6.0
08	855	869	883	897	911	926	940	954	968	982	5	7-5
09	996	*OIO	*024	*Q38	*052	*o66	*o8o	*094	*io8	*I22	6	9.0
310	49 136	150	164	178	192	206	220	234	248	262	7	10.5
ii	276	290	304	3i8	332	346	360	374	388	4O2		12. 0 T ^ C
12 13	4i5 554	$	443 582	457 596	471 610	485 624	499 638	513 651	527 665	541 679		1O-0
14	693	707	721	734	748	762	776	790	803	8l7
15	8ji	845	859	872	886	900	914	927	941	955		14
16	969	982	996	*OIO	*O24	*o37	*05I	*o6s	*079	*092	i	1.4
17	50 106	1 20	133	147	161	174	188	202	215	229	2	2.8
18	243	256	270	284	297	3ii	325	338	352	365	3	4.2
19	379	393	406	420	433	447	461	474	488	501	4	5-6
320	515	529	542	556	569	583	596	610	623	637	5	7.0 0 .
21 22	651 786	664 799	678 813	69! 826	705 840	718 853	732	745 880	759 893	772 907	6 g	8.4 9.8 112
23	920	934	947	9*1	974	987	*OOI	*oi4	*028	*o4i	9	12.6
24	5i 055	068	081	095	108	121	135	148	162	175
25	188 202	215	228	242	255	268	282	295	308
,26	322 335 348	362	375	388	402	415	428	441
27	455 468	481	495	508	521	534	548	56i	574		13
28	587	601	614	627	640	654	667	680	693	706	i	1.3
29	720	733	746	759	772	786	799	812	825	838	2	2.6
330	85i	865	878	891	904	917	930	943	957	970	3	3.9 5M
3i	983	996	*oo9	*O22	*°35	*048	*o6i	*°75	*o88	*IOI	4	•2 6-5
32	52 114	127	140	153	1 66	179	192	205	218	231	6
33	244	257	270	284	297	310	323	336	349	362	7	7.0 9-1
34	375	388	401	414	427	440	453	466	479	492	8	10.4
35	504	517	530	543	556	569	582	595	608	621	9	ii. 7
36	634	647	660	673	686	699	711	724	737 75o
37	7^3	776	789	802	815	827	840	853	866 879
38	892	905	917	930	943	956	969	982	994	*007		12
39	53 020	033	046	058	071	084	097	no	122	135
340	148	161	173	186	199	212	224	237	250	263	i	1.2 2j
4i	275	288	301	314	326	339	352	364	377	390	•i	•4 3.6
42 43	403 529	415 542	428 555	441 567	453 580	466 593	479 605	491 618	504 631	643	O 4 5	4-8 6.0
44	656	668	681	694	706	719	732	744	757	769	6 7-2
45	782	794	807	820	832	845	857	870	882	895	I 81
46	908	920	933	945	958	970	983	995	•008	*020	8 9.6
47	54 033	045	058	070	083	095	108	120	133	145	9 10.8
48		170	183	195	208	220	233	245	258	270
49	283	295	307	320	332	345	357	370	382	39-1
350	407	419	432	IU	456	469	481	494	5</>	Si*
N.	0	1	2	:* 4	5 <»	7 8 i>	Prop. I'ts.

N. '	0	1	2	3	4	5	6	7	8	9	Pro	p. Pts.
350	54 407	419	432	444	456	469	481	494	506	5i8
5i 52 53 54 55 56 57 58 59	53i 654 777 900 55 023 145 267 388 509	543 667 790 913 035 157 279 400 522	555 679 802 925 047 169 291 413 534	568 691 814 937 060 182 303 425 546	58o 704 827 949 072 194 315 437 558	593 716 839 962 084 206 328 449 570	605 728 851 974 096 218 340 461 582	617 741 864 986 108 230 352 473 594	630 753 876 998 121 242 364 485 606	642 765 888 *OII 133 255 376 497 618	i 2 3 4 5 6	13 1-3 2.6 3-9 5-2 6.5 7.8
860	630	642	654	666	678	691	703	715	727	739	z	9-1
61 62 63 64 65 66 67 68 69	75i 871 991 56 no 467 585 703	763 883 *oo3 122 241 360 478 597 714	775 895 *ois 134 253 372 490 608 726	787 907 *027 146 265 384 502 62O 738	799 919 *038 158 277 396 5H 632 750	811 93i *o5o 170 289 407 526 644 761	823 943 *062 182 301 419 538 656 773	835 955 *074 194 312 43i 549 667 785	847 967 *o86 205 324 443 56i 679 797	859 979 *098 217 336 455 573 691 808	O 9 i 2 3 4	10.4 ii. 7 12 1.2 2-4 3-6 4.8
370	820	832	844	855	867	879	891	902	914	926	5	6.0
7i 72 73 74 75 76 77 78 79	937 57 054 171 287 403 519 634 749 864	949 066 183 299 415 530 646 761 875	961 078 194 310 426 542 657 772 887	972 089 206 322 438 553 669 784 898	984 101 217 334 449 565 680 795 910	996 H3 229 345 461 576 692 807 921	*oo8 124 241 357 473 588 703 818 933	*oi9 136 252 368 484 600 7*5 830 944	*03I 148 264 380 496 6n 726 841 955	*<H3 159 276 392 507 623 738 852 967	9 i 2	7-2 8.4 9.6 10.8 ii i.i 2.2
380	978	990	*OOI	*OI3	*024	*o35	*047	*os8	*o7o	*o8i	3	3-3
Si 82 83 84 85 86 87 88 89	58 092 206 320 433 546 659 771 883 995	104 218 33i 444 557 670 782 894 *oo6	115 229 343 456 569 681 794 906 *oi7	127 240 354 467 580 692 805 917 *028	138 252 365 478 59i 704 816 928 *o4o	149 263 377 49° 602 715 827 939 *osi	161 274 501 614 726 838 950 *062	172 286 399 512 625 737 850 961 *Q73	184 297 410 524 636 749 861 973 *o84	195 309 422 535 647 760 872 984 *095	4 5 6 8 9	4.4 5-5 6.6 1:1 9-9 10
390	59 i°6	118	129	140	151	162	173	184	195	207	i	I.O
9i 92 93 94 95 96 97 98 99	218 329 439 550 660 770 879 988 60 097	229 34o 450 56i 671 780 890 999 108	240 351 461 III 791 901 *OIO 119	251 362 472 583 693 802 912 *O2I 130	262 373 483 594 704 813 923 *032 141	273 384 494 605 715 824 934 *043 152	284 395 506 616 726 835 945 *054 163	295 406 517 627 737 846 956 *o6s 173	306 417 528 638 748 857 966 *076 184	3i8 428 539 649 759 868 977 *o86 195	3 4 5 6 8 9	3-0 4.0 5-0 6.0 7.0 8.0 9.0
400	206	217	228	239	249	260	271	282	293	304
N.	O	1	2,	3	4	5	6	7	8	9	Pro	p. Pts.

N.	o	1	2	3	4	5	6	7	8	9	Pro	p. Pts.
400	60 206	217	228	239	249	260	271	282	293	304
01 02 03 04 a 07 08 09	314 423 531 638 746 853 959 61 066 172	325 433 54i 649 % 970 077 183	336 444 552 660 767 874 981 087 194	347 455 563 670 778 885 991 098 204	3g 466 574 68 1 788 895 *002 109 215	369 477 584 692 799 906 *oi3 119 225	379 487 595 703 810 917 *023 130 236	390 498 606 713 821 927 *<>34 140 247	401 509 617 724 831 938 *o45 151 257	412 520 627 735 842 949 *055 162 268	i 2 3	IX i.i 2.2 3-3
410	278	289	300	310	321	33i	342	352	363	374	4	4.4
ii 12 13 14 15 16 17 18 19	384 49° 595 700 805 909 62 014 118 221	395 500 606 711 815 920 024 128 232	.405 •511 616 721 826 930 034 138 242	416 521 627 III 941 045 149 252	426 532 637 742 847 951 055 159 263	437 542 648 752 857 962 066 170 273	448 658 763 868 972 076 180 284	458 563 669 773 878 982 086 190 294	469 574 679 784 888 993 097 20 1 304	479 584 690 794 899 *oo3 107 211 315	8 9	•o 6.6 1:1 9-9
420	325	335	346	356	366	377	387	397	408	4l8
21 22 23 24 25 26 27 28 29	428 I3' 634 737 839 941 63 043 144 246	439 542 644 747 849 95i 053 155 256	449 552 655 757 859 961 063 165 266	459 66\ 767 870 972 073 175 276	469 572 675 778 880 982 083 185 286	480 583 685 992 094 195 296	49° 593 696 798 900 *OO2 I04 205 306	500 603 706 808 910 *OI2 114 215 317	5ii 613 716 818 921 *022 124 225 327	521 624 726 829 931 *o33 134 236 337	• I 2 3 4 6 8 9	10 I.O 2.0 3-o 4.0 5.0 6.0 7.0 8.0 9.0
430	347	357	367	377	387	397	407	417	428	438
3i 32 33 34 35 36 37 38 39	448 548 649 749 849 949 64 048 H7 246	458 558 659 759 859 959 058 157 256	468 568 669 769 869 969 068 167 266	478 579 679 779 879 979 078 J77 276	488 $ 789 889 988 088 I87 286	498 599 699 799 899 998 098 '97 296	508 609 709 809 909 *oo8 108 207 306	518 619 719 819 919 *oi8 118 217 316	528 629 729 829 929 *028 128 227 326	538 639 739 839 939 *o38 137 237 335	i 2 3	9 0.9 1.8 2.7
440	345	355	365	375	385	395	404	414	424	434	4	3-6
4i 42 43 44 45 46 47 48 49	444 542 640 738 836 933 65 031 128 225	454 552 650 748 846 943 040 137 234	464 562 660 758 856 953 050 147 244	473 572 670 768 865 963 060 157 254	483 582 680 777 875 972 070 >*7 263	493 59i 689 787 885 982 079 176 273	£? 699 992 089 186 283	513 611 709 807 904 *002 099 I96 292	523 621 719 816 914 *OII 108 205 302	532 631 729 826 924 *02I 118 215 312	i 9	4-5 5-4 6.3 7.2 8.1
450	321	33i	34i	35<>	360	369	379	389	39«	408
N.	O	1	2	:j	1	5	6	7	8	«)	Prop	. Pts.

N.	O	1	2	3	4	5	6	7	8	9	Proi	p. Pts.
450	65 321	331	341	350	36o	369	379	389	398	408
5i 52 53 54 55 56 57 58 59	418 514 610 706 801 896 66 087 181	427 523 619 715 811 906 *OOI 096 191	437 533 629 725 820 916 *OII 106 200	447 543 639 734 830 925 *O2O H5 210	456 552 648 744 839 935 *030 124 219	466 562 658 753 849 944 *o39 134 229	475 57i 667 763 858 954 *049 M3 238	485 58i 677 772 868 963 *o58 153 247	495 591 686 782 877 973 *o68 162 257	504 600 696 792 887 982 *077 172 266	i 2 3	IO 1.0 2.0 3-0
460	276	285	295	304	314	323	332	342	35i	36i	4 c	4.0 e o
61 62 63 64 65 66 67 68 69	370 464 558 652 745 839 932 67 025 117	380 474 567 661 755 848 941 034 127	389 483 577 671 764 857 950 043 136	398 492 586 680 III 960 052 145	408 502 596 689 783 876 969 062 154	417 5ii 605 699 978 071 164	427 521 614 708 801 894 987 080 173	436 530 624 717 811 904 997 089 182	445 539 633 727 820 913 *oo6 099 191	455 549 642 736 829 922 *oi5 108 201	6 8 9	M 7.0 8.0 9.0
470	210	219	228	237	247	256	265	274	284	293
7i 72 73 74 75 76 11 79	302 394 486 578 669 761 852 943 68 034	3ii 403 495 679 770 861 952 043	321 413 504 779 870 961 052	330 422 514 605 697 788 879 970 06 1	339 43i 523 614 706 797 888 979 070	348 440 532 624 7i5 806 897 988 079	357 449 54i 633 724 815 906 997 088	367 459 550 642 733 825 916 *oo6 097	376 468 560 651 742 834 925 *ois 106	385 477 569 660 752 843 934 *O24 115	i 2 3 4 5 6 8 9	9 0.9 1.8 2.7 3-6 4-5 5-4 6-3 7.2 8.1
480	124	133	142	151	160	169	178	187	196	205
81 82 83 84 85 86 87 88 89	215 305 395 485 574 664 753 842 93i	224 3H 404 494 583 673 762 851 940	233 323 413 502 592 681 771 860 949	242 332 422 511 601 690 780 869 958	251 34i 43i 520 610 699 789 878 966	260 350 440 529 619 708 797 886 975	269 359 449 538 628 717 806 895 984	278 368 458 547 637 726 815 904 993	287 377 467 556 646 735 824 913 *002	476 565 655 744 833 922 *OII	i 2 3	8 0.8 1.6 2.4
490	69 020	028	037	046	055	064	073	082	090	099	4	3-2
9i 92 93 94 95 96 97 98 99	108 197 285 373 461 548 636 723 810	117 205 294 38i 469 557 644 732 819	126 214 302 390 478 566 653 740 827	135 223 3ii 399 487 574 662 749 836	144 232 320 408 496 583 671 758 845	152 241 329 417 504 592 679 767 854	161 $ 425 513 601 688 775 862	170 258 346 434 522 609 697 784 871	179 267 355 443 531 618 705	188 276 364 452 539 627 714 80 1 888	6 8 9	4.0 4.8 5.6 6.4 7.2
500	897	906	914	923	932	940	949	958	966	975
N.	0	1	2	3	4	5	6	7	8	9	Pro]	>. Pts.

IO

N.	0	1	2	3	4	5	6	7	8	9	Pro]	). PtS.
500	69 897	906	914	923	932	940	949	958	966	975
or 02 03 04 05 06 07 08 09	984 70 070 157 243 329 415 501 586 672	992 079 165 252 338 424 509 595 680	*OOI 088 174 260 346 432 5i8 603 689	*OIO 096 183 269 355 441 526 612 697	*oi8 105 191 278 364 449 535 621 706	*O27 114 200 286 372 458 544 629 7H	*o36 122 209 295 381 467 552 638 723	*044 131 217 303 389 475 56i 646 73i	*o53 140 226 312 398 484 569 655 740	*062 148 234 32i 406 492 578 663 749	I 2 3	9 0.9 1.8 2-7
510	757	766	774	783	791	800	808	817	825	834	4	3-6 4e
ii 12 13 14 15 16 17 18 19	842 927 71 012 096 181 265 349 433 517	851 935 020 105 I89 273 357 441 525	859 944 029 113 282 366 450 533	868 952 037 122 206 290 374 458 542	876 961 046 130 214 299 383 466 55o	885 969 054 139 223 307 39i 475 559	893 978 063 147 231 315 399 483 567	902 986 071 155 240 324 408 492 575	910 995 079 164 248 332 416 500 584	919 *oo3 088 172 257 341 £3 592	6 I 9	5-4 6-3 7.2 8.1
520	600	609	617	625	634	642	650	659	667	675
21 22 23 24 25 26 27 28 29	684 767 850 933 72 016 099 181 263 346	692 775 858 941 024 107 189 272 354	700 784 867 950 032 H5 362	709 792 875 958 041 123 206 288 370	717 800 883 966 049 132 214 296 378	725 809 892 975 057 140 222 304 387	734 817 900 983 066 148 230 313 395	742 825 908 991 074 156 239 321 403	750 834 917 999 082 165 247 329 411	759 842 925 *oo8 090 173 255 337 419	* i 2 3 4 I 8 9	8 0.8 1.6 2.4 3-2 4.0 4-8 5-6 6.4 7.2
580	428	436	444	452	460	469	477	485	493	501
3i 32 33 34 35 36 37 38 39	509 59i 673 754 835 916 997 73 078 159	5i8 599 681 762 843 925 *oo6 086 167	526 607 689 770 852 933 *OI4 094 175	534 616 697 779 860 941 *022 102 183	542 624 705 787 868 949 *o3o in 191	550 632 713 795 876 957 *o38 119 199	558 640 722 803 884 965 *046 127 207	567 648 730 811 892 973 *°54 135 215	575 656 738 819 900 981 *062 143 223	583 665 746 827 908 989 *070 151 231	i 2 3	7 0.7 1.4 2.1
540	239	24?	255	263	272	280	288	296	304	312	4	2.8
41 42 43 44 8 47 48 49	320 400 480 560 640 719 799 878 957	328 408 488 568 648 727 807 886 965	336 416 496 576 656 735 8i5 894 973	344 424 5«>4 584 664 743 823 902 981	352 432 5" 592 672 751 830 910 989	360 440 520 600 679 759 838 918 997	368 448 528 608 687 767 846 926 •00|	376 456 536 616 695 775 854 933 *oi3	384 464 544 624 703 783 862 941 *020	392 472 552 632 711 791 870 949 *028	1 8 9	3-5 4-2 4-9 5-6 6.3
550	74 036	"44	052	060	068	076	084	092	099	107
N.	0	1 1	9	3	4	5	6	7	8	9	Pro]	». Pis.

II

N.	O	1	2	3	4	5	G	7 8	9	Prop. Pts.
550 51 52 53 54 P 57 58 59 560 61 62 63 64 65 66 3 69 570 7i 72 73 74 3 £ 79 580 81 82 83 84 85 86 87 88 89 590 9i 92 93 94 95 96 97 98 99 600	74 036	044	052	060	068	076	084	092	099	107	I 2 3 4 5 6 8 9 i 2 '3 4 5 6 8 9	8 0.8 1.6 2.4 3-2 4.0 4.8 5-6 6.4 7.2 7 0.7 1.4 2.1 2.8 3-5 4.2 4-9 5-6 6.3
H5 194 273 35i 429 50? 586 663 74i	123 202 280 359 437 515 593 671 749	131 2IO 288 367 445 523 601 679 757	139 218 296 374 453 53i 609 687 764	147 225 304 382 461 539 617 695 772	155 233 312 39° 468 547 624 702 780	162 241 320 398 476 554 632 710 788	170 249 327 406 484 562 640 718 796	178 257 335 414 492 570 648 726 803 881	186 265 343 421 500 578 656 733 811
819	827	834	842	850	858	865	873	889
896 974 75 051 128 205 282 358 435 5ii	904 981 059 136 213 289 366 442 5i9	912 £ i43 220 297 374 450 526	920 997 074 151 228 305 38i 458 534	927 *oo5 082 159 236 312 389 465 542	935 *OI2 089 166 243 320 397 473 549	943 *O2O 097 174 251 328 404 48l 557	950 *028 105 182 259 335 412 488 565	958 *035 "3 343 420 496 572	966 *°43 120 197 274 351 427 504 580
587	595	603	610	618	626	633	641	648	656
664 740 815 89r 967 76 042 118 193	671 747 823 899 974 050 ^25 200 275	679 755 831 906 982 057 133 208 283	686 762 838 914 989 065 140 215 290	694 770 846 921 997 072 148 223 298	702 778 853 929 *oo5 080 155 230 305	709 785 861 937 *OI2 087 163 238 313	717 793 868 944 *O2O 095 170 245 320	724 800 876 952 *O27 103 178 253 328	732 808 884 959 *°35 no 185 260 335
343	350	358	365	373	380	388	395	403	410
418 492 567 641 716 790 864 938 77 012 085	425 500 574 649 723 797 871 945 019	433 507 582 656 730 805 879 953 026	440 515 589 664 738 812 886 960 034	448 522 597 671 745 819 893 967 041	455 530 604 678 753 827 901 975 048	462 537 612 686 760 834 908 982 056	470 545 619 693 768 842 916 989 063	477 552 626 701 775 849 923 997 070	485 559 634 708 782 856 930 *oo4 078
093	100	107	H5	122	129	137	144	151
159 232 305 379 452 525 597 670 743 815	166 240 313 386 459 532 605 677 750	173 247 320 393 466 539 612 685 757	181 254 327 401 474 546 619 692 764	1 88 262 335 408 481 554 627 699 772	195 269 342 415 488 561 634 706 779	203 276 349 422 495 568 641 714 786	210 283 357 430 503 576 648 721 793	217 291 364 437 5io 583 656 728 801	225 298 37i 444 517 59° 663 735 808
822	830	837	844	851	859	866	873	880
N.	0 | 1	2	3	4	5	6	7	8	9	Prop. Pts.

12

N.	0	1	2	3	4	5	6	7	8	9	Pro]	p. Pts.
600	77 8i5	822	830	837	844	85I	859	866	873	880
01 02 03 04 05 06 07 08 09	887 960 78 032 104 176 247 319 390 462	895 967 039 in 183 254 326 398 469	902 974 046 118 190 262 333 405 476	909 981 053 125 197 269 340 412 483	916 988 061 132 204 276 347 419 490	924 996 068 140 211 283 355 426 497	931 *oo3 075 147 219 290 362 433 504	938 *OIO 082 154 226 297 369 440 512	945 *oi7 089 161 233 305 376 447 519	952 *025 097 1 68 240 312 383 455 526	I 2 3	8 0.8 1.6 2.4
610	533	54o	547	554	56i	569	576	583	590	597	4 5	3-2 A O
ii 12 13 14 15 16 17 18 19	604 675 746 817 888 958 79 029 099 169	611 682 753 824 895 965 036 106 176	618 689 760 831 902 972 043 H3 183	625 696 767 838 909 979 050 120 190	633 704 774 845 916 986 057 127 197	640 711 78i 852 923 993 064 134 204	647 718 789 859 930 *000 071 141 211	654 725 796 866 937 *oo7 078 148 218	661 732 803 873 944 *oi4 085 155 225	668 739 810 880 *951 *O2I 092 162 232	6 8 9	4.8 5-6 6.4 7.2
620	239	246	253	260	267	274	28l	288	295	302
21 22 23 24 25 26 27 28 29	309 379 449 5i8 657 727 796 865	3i6 386 456 525 595 664 734 803 872	323 393 463 532 602 671 741 810 879	330 4OO 470 539 609 678 748 817 886	337 407 477 546 616 685 754 824 893	344 414 484 553 623 692 761 831 900	351 421 491 560 630 699 768 837 906	358 428 498 567 637 706 775 844 913	365 435 505 574 644 713 782 851 920	372 442 5H 581 650 720 789 858 927	i 2 3 4 5 6 8 9	7 0.7 1.4 2.1 2.8 3-5 4.2 4-9 5-6 6.3
680	934	94i	948	955	962	969	975	982	989	996
3i 32 33 34 11 § 39	80 003 072 140 209 277 346 414 482 550	010 079 147 216 284 353 421 489 557	017 085 154 223 291 359 428 496 564	024 092 161 229 298 366 434 502 570	030 099 1 68 236 305 373 441 509 577	037 106 175 243 312 38o 448 5i6 584	044 "3 182 250 3i8 387 455 523 59i	051 120 188 257 325 393 462 53° 598	058 127 195 264 332 400 468 536 604	065 134 2O2 271 339 407 475 543 611	i 2 3	6 0.6 1.2 1.8
640	618	625	632	638	645	652	659	665	672	679	4	2.4
4i 42 43 44 45 46 47 48 49	686 754 821 889 956 8 1 023 090 158 224	693 760 828 895 963 030 097 164 231	699 767 835 9°2 969 037 104 171 238	706 ffi 909 976 043 in 178 245	713 78i 848 916 983 050 117 184 251	720 787 855 922 990 057 124 I9o 258	726 794 862 929 S6 064 131 %	733 801 868 936 *oo3 070 137 20.} 271	740 808 875 943 *OIO 077 144 211 278	747 814 882 949 *oi7 084 151 218 285	8 9	3-o 3-6 4.2 4.8 5-4
650	291	298	305	3ii	3i8	325	331	33«	345	35i
N.	0	1	2	3	1	5	G	7	8	9	Proj	. Pts.

N.	O	1	2	3	4	5	6	7 8	9	Prop. Pts.
650 51 52 53 54 55 56 57 58 59 660 61 62 63 64 65 66 67 68 69 670 72 73 74 75 76 77 78 79 680 81 82 83 84 85 86 87 88 89 690 92 93 94 9 9 99 700	81 291	298	305	311	318	325	331	338	345	351 418 485 551 617 684 750 816 882 948	i 2 3 4 6 I 9 i 2 3 4 5 6 8 9	7 0.7 1.4 2.1 2.8 3-5 4.2 4.9 5-6 6.3 6 0.6 1.2 1.8 2.4 3.o 3-6 4.2 4.8 5-4
358 425 491 558 624 690 757 823 889	365 431 498 564 631 697 763 829 895	37i 438 505 637 704 770 836 902	378 445 578 644 710 776 842 908	385 451 518 584 651 717 915	391 458 525 591 657 723 790 856 921	398 465 531 598 664 730 796 862 928	405 471 538 604 671 737 803 869 935	411 478 544 611 677 743 809 875 941
954	961	968	974	981	987	994	*ooo	*oo7	*oi4
82 020 086 151 217 282 347 413 478 543	027 092 158 223 289 354 419 484 549	033 099 164 230 295 360 426 491 556	040 105 171 236 302 367 432 497 562 627	046 112 I78 243 308 373 439 504 569	053 119 184 249 315 380 445 575	060 125 191 256 321 387 452 517 582	066 132 197 263 328 393 458 523 588	073 138 204 269 334 400 465 530 595	079 210 276 341 406 471 536 601
607	614	620	633	640	646	653	659	666
672 737 802 866 930 995 83 059 123 187	679 743 808 872 937 *OOI 065 129 193	685 750 814 879 943 *oo8 072 136 200	692 756 821 885 078 142 206	698 763 827 892 956 *020 085 149 213	705 769 834 898 963 *027 091 155 219	711 776 840 905 969 *o33 097 161 225	718 782 847 911 *975 104 168 232	724 789 853 918 982 no 174 238	730 795 924 *f2 117 181 245
251 315 378 442 506 569 632 696 759 822	257	264	270	276	283	289	296	302	308
321 385 448 512 575 639 702 765 828	327 391 455 582 645 708 771 835	334 3f 461 525 651 715 778 841	340 404 467 531 594 658 721 784 847	347 410 474 537 601 664 727 790 853	353 417 480 544 607 670 734 797 860	359 423 487 550 613 677 740 i	366 429 493 556 620 683 746 809 872	372 436 499 563 626 689 753 816 879
885	891	897	904	910	916	923	929	935	942
948 84 on 073 136 198 261 323 386 448	954 017 080 142 205 267 330 392 454	960 023 086 148 211 273 336 398 460	967 029 092 155 217 280 342 404 466	973 036 098 161 223 286 348 410 473	979 042 105 167 230 292 354 417 479	985 048 in 173 236 298 423 485	992 055 117 180 242 305 367 429 491	998 061 123 186 248 311 373 435 497	067 130 192 255 317 379 442 504
5io	5i6	522	528	535	54i	547	553	559	566
N.	0	1	2	3	4	5	6	7	8	9	Prop. Pts.

N.	0	1	2	\ 3	4	5	6	7	8	9	Pro	). Pts.
700	84 510	5i6	522	528	535	541	547	553	559	566
01 02 03 04 05 06 07 08 09	572 634 696 757 819 880 942 85 003 065	578 640 702 763 825 887 948 009 071	584 646 708 770 831 893 954 016 077	590 652 7H 776 837 899 960 022 083	597 658 720 782 844 905 967 028 089	603 665 726 788 850 911 973 034 095	609 671 733 794 856 917 979 040 101	615 677 739 800 862 924 985 046 .107	621 683 745 807 868 930 991 052 114	628 689 751 813 874 936 997 058 120	I 2 3	7 0.7 1.4 2.1
710	126	132	138	144	150	156	163	169	175	181	4	2.8 •7 C
ii 12 13 14 15 16 17 18 19	187 248 309 37o 43i 491 552 612 673	193 254 3i5 376 437 497 558 618 679	199 260 321 382 443 503 564 625 685	205 266 327 388 449 509 570 63i 691	211 272 333 394 455 5i6 576 637 697	217 278 339 400 461 522 582 643 703	224 285 345 406 467 528 588 649 709	230 291 352 412 473 534 594 655 715	236 297 358 418 479 540 600 661 721	242 303 364 425 485 546 606 667 727	6 9	O'O 4-2 4-9 5-6 6-3
720	733	739	745	75i	757	763	769	775	78i	788
21 22 23 24 25 26 27 28 29	794 854 9M 974 86 034 094 153 213 273	800 860 920 980 040 100 159 219 279	806 866 926 986 046 106 165 225 285	812 872 932 992 052 112 171 231 291	818 878 938 998 058 118 177 237 297	824 884 944 *oo4 064 124 183 243 303	830 890 950 *OIO 070 130 189 249 308	836 896 956 *oi6 076 136 195 255 3H	842 902 962 *O22 082 141 201 26l 320	848 908 968 *028 088 147 207 267 326	* i 2 3 4 1 8 9	6 0.6 1.2 1.8 2.4 3-0 3-6 4-2 4.8 5-4
730	332	338	344	350	356	362	368	374	380	386
3i 32 33 34 35 36 37 38 39	392 45i 5io 570 629 688 747 806 864	398 457 5i6 576 635 694 753 812 870	404 463 522 58i 641 700 759 817 876	410 469 528 587 646 705 764 823 882	4i5 475 534 593 652 711 770	421 481 540 717 776 835 894	427 487 546 605 664 723 782 841 900	433 493 552 611 670 729 738 847 906	439 499 558 617 676 735 794 853 911	445 504 564 623 682 74i 800 859 917	i 2 3	5 0-5 I.O i-5
740	923	929	935	941	947	953	958	964	970	976	4	2.0
4i 42 43 44 45 46 47 48 49	982 87 040 099 157 216 274 332 390 448	988 046 105 163 221 280 338 396 454	994 052 in 169 227 286 344 402 460	999 058 116 175 233 291 349 408 466	*oo5 064 122 181 239 297 355 413 47i	*OI I 070 128 186 245 303 36i 419 477	*oi7 075 134 192 251 309 367 425 483	*023 081 140 198 256 315 373 $	*029 087 146 204 262 320 379 437 495	*o35 093 151 210 268 326 384 442 500	9	2.5 3-0 3-5 4.0 4-5
750	506	5"	5i8	523	529	535	54i	547	552	558
N.	0	1	•z	:*	t	5	6	7	N	9	I'roi	). I'tS.

N.	O 1 2 3	4	5	6	7	8	9	Prop. Pts.
750 5i 52 53 54 55 56 11 59 760 61 62 63 64 65 66 6? 68 69 770 7i 72 73 74 75 76 77 78 79 780 81 82 83 84 85 86 87 88 89 790 9i 92 93 94 95 96 97 98 99 800	87 506	512	5i8	523	529	535	541	547	552	558	I 2 3 4 6 8 9 i 2 3 4 5 6 8 9	6 0.6 1.2 1.8 2.4 3-0 3-6 4.2 4-8 54 5 o.5 I.O 1.5 2.0 2-5 3-0 3-5 4.0 4-5
564 622 679 737 795 852 910 967 88 024	570 628 685 743 800 858 915 973 030	576 633 691 749 806 864 921 978 036	58i 639 697 754 812 869 927 984 041	587 645 703 760 818 875 933 990 047	593 651 708 766 823 881 938 996 053	599 656 714 772 829 887 944 *OOI 058	604 662 720 777 835 892 950 *oo7 064	610 668 726 783 841 898 955 *OI3 070	616 674 73i 789 846 904 961 *oi8 076
081	087	093	098	104	no	116	121	127	133
138 195 252 309 366 423 480 536 593	144 201 258 315 372 429 485 542 598	150 207 264 321 377 434 491 547 604	156 213 270 326 383 440 497 553 610	161 218 275 332 389 446 502 559 615	167 224 281 338 395 45i 508 564 621	173 230 287 343 400 457 513 570 627	I78 235 292 349 406 463 519 576 632	184 241 298 355 412 468 525 58i 638	190 247 304 360 417 474 530 587 643
649	655	660	666	672	677	683	689	694	700
705 762 818 874 930 986 89 042 098 154	711 767 824 880 936 992 048 IO4 159	717 773 829 885 941 997 053 109 165	722 779 835 891 947 *oo3 059 H5 170	728 784 840 897 953 *009 064 120 176	734 790 846 902 958 *oi4 070 126 182	739 795 852 908 964 *020 076 I3I 187	745 801 857 913 969 *025 081 137 193	750 807 863 919 975 *o3i 087 198	756 812 868 925 981 *o37 092 148 204
209	215	221	226	232	237	243	248	254	260
265 321 376 432 487 542 597 653 708	271 326 382 437 492 548 603 658 713	276 443 498 553 609 664 719	282 337 393 448 504 559 614 669 724	287 343 398 454 509 564 620 675 73°	348 404 459 515 57o 625 680 735	298 354 409 465 520 575 631 686 741	304 360 415 470 526 58i 636 691 746	310 365 421 476 531 586 642 697 752	315 37i 426 481 537 592 647 702 757
763	768	774	779	785	79°	796	801	807	812
818 873 927 982 90 037 091 146 200 255	823 878 933 988 042 097 151 206 260	829 883 938 993 048 102 157 211 266	834 889 944 998 053 108 162 217 271	840 894 949 *oo4 059 "3 168 222 276	845 900 955 *oo9 064 119 173 227 282	851 905 960 -015 069 124 179 233 287	856 911 966 *O2O 075 I29 184 238 293	862 916 971 *026 080 135 189 244 298	867 922 977 *03I 086 140 *95 249 304
309	3i4	320	325	331	336	342	347	352	358
N.	0 1	2	3	4	5	6	7	8	9	Prop. Pts.

i6

N.	0	1	2	3	4	5	6	7	8	9	Pro]	[>. PtS.
800	90 309	314	320	325	331	336	342	347	352	358
OI 02 03 04 05 06 07 08 09	363 417 472 526 634 687 741 795	369 423 477 585 639 693 747 800	374 428 482 536 590 644 698 752 806	380 434 488 542 596 650 703 757 811	385 439 493 547 601 655 709 763 816	39° 445 499 553 607 660 768 822	396 450 504 558 612 666 720 773 827	401 455 509 563 6i7 671 725 779 832	407 461 515 569 623 677 730 784 838	412 466 520 574 628 682 736 789 843
810	849	854	859	865	870	875	881	886	891	897
ii 12 14 II 17 18 19	902 956 91 009 062 116 169 222 275 328	907 961 014 068 121 174 228 28l 334	020 % 180 339	918 972 025 078 132 185 238 291 344	924 977 030 084 137 190 243 297 350	929 982 036 089 142 196 249 302 355	041 094 148 201 254 307 360	940 993 046 100 153 206 259 312 365	945 998 052 105 158 212 265 318 371	950 *oo4 057 1 10 164 217 270 323 376	I 2 3 4 6 8	6 0.6 1.2 1.8 2.4 3-o 3-6 4-2 4-8
820	381	387	392	397	403	408	413	418	424	429	9	5-4
21 22 23 24 25 26 27 28 29	434 487 593 803 855	440 492 545 598 651 703 756 808 861	445 498 603 656 709 761 814 866	450 609 66 1 714 766 819 871	614 666 719 772 824 876	461 514 566 619 672 724 777 829 882	466 519 572 624 677 730 782 834 887	47i 524 577 630 682 735 787 840 892	477 529 582 635 687 740 793 845 897	482 535 640 693 745 798 850 903
880	908	913	918	924	929	934	939	944	950	955
32 33 34 37 38 39	960 92 OI2 065 117 169 221 273 324 376	965 018 070 122 174 226 278 330 381	971 023 075 127 179 231 283 335 387	976 028 080 132 184 236 288 340 392	981 033 085 137 189 241 293 345 397	986 038 091 143 195 247 298 350 402	991 044 096 148 200 252 304 355 407,	997 049 101 153 205 257 309 412	*002 054 106 158 210 262 366 4l8	*oo7 059 in 163 215 267 319 37i 423	i 2 3 4 5 6 7	5 I.O i-5 2.0 2.5 3-0 3-5
840	428	433	438	443	449	454	459	464	469	474	8	4.0
' 42 43 44 45 46 47 48 49	480 531 583 634 686 737 788 840 891	s 588 639 691 742 793	490 542 593 645 747 799 850 901	495 547 598 650 701 752 8°-	500 655 706 758 809 860 911	505 557 609 660 711 763 814 865 916	5" 562 614 665 716 768 819 870 921	567 619 670 722 773 824 875 927	521 572 624 675 727 778 829 881 932	526 578 629 681 732 783 834 886 937	9	4-5
850	942	947	952	957	962	967	973	978	983	988
N.	0	1	2	3	I	I	;	7	8	»	Pro]	). PtS.

N.	0	1	2	3	4	5	6	7	8	9	Pro	p. Pts.
850	92 942	947	952	957	962	967	973	978	983	988
5i 52 53 54 55 56 57 58 59	993 93 044 095 146 197 247 298 349 399	998 049 IOO 151 202 252 303 354 404	*oo3 054 105 156 207 258 308 359 409	*oo8 059 no 161 212 263 313 364 414	*oi3 064 H5 166 217 268 3i8 369 420	"018 069 120 171 222 273 323 374 425	*024 075 125 176 227 278 328 379 430	*029 080 I31 181 232 283 334 384 435	*034 s 1 86 237 288 339 389 440	*039 090 141 192 242 293 344 394 445	i 2 3	6 0.6 1.2 1.8
860	450	455	460	465	470	475	480	485	490	495	4 5	2.4 •7 O
61 62 63 64 65 66 67 68 69	500 55i 601 651 702 752 802 852 902	505 556 606 656 707 757 807 857 907	5io 56i 611 661 712 762 812 862 912	515 566 616 666 717 767 817 867 917	520 57i 621 671 722 772 822 872 922	526 576 626 676 727 777 827 877 927	53i 58i 631 682 732 782 832 882 932	536 586 636 687 737 787 837 887 937	54i 59i 641 692 742 792 842 892 942	546 596 646 697 747 797 847 897 947	6 1 9	1.6 4.2 4.8 5-4
870	952	957	962	967	972	977	982	987	992	997
7i 72 73 74 75 76 77 78 79	94 002 052 101 151 201 250 300 349 399	007 057 106 156 206 255 305 354 404	012 062 III 161 211 260 310 359 409	017 067 116 166 216 265 315 364 414	022 072 121 171 221 270 320 369 419	027 077 126 176 226 275 325 374 424	082 131 181 231 280 330 379 429	037 086 136 186 236 285 384 433	042 091 141 191 240 290 34o	047 096 146 196 245 295 345 394 443	i 2 3 4 5 6 8 9	5 0.5 I.O i-5 •2.O 2-5 3.0 3-5 4.0 4-5
880	448	453	458	463	468	473	478	483	488	493
81 82 83 84 85 86 87 88 89	498 547 596 645 694 743 792 841 890	503 552 601 650 797 846 895	507 557 606 655 704 753 802 851 900	512 562 611 660 709 758 807 856 905	517 567 616 665 714 763 812 861 910	522 57i 621 670 719 768 817 866 9*5	527 576 626 675 724 773 822 871 919	532 58i 630 680 729 778 827 876 924	537 586 635 685 734 783 832 880 929	542 59i 640 689 738 787 836 885 934	i 2 3	4 0.4 0.8 1.2
890	939	944	949	954	959	963	968	973	978	983	4	1.6
91 92 93 94 95 96 97 98 99	988 95 036 085 134 182 231 279 328 376	993 041 090 139 187 236 284 332 38i	998 046 095 143 192 240 289 337 386	*002 051 IOO 148 197 245 294 342 39°	*007 056 105 153 202 250 299 347 395	*OI2 061 109 158 207 255 303 352 400	*oi7 066 114 163 211 260 308 357 405	*022 071 119 168 216 265 313 36i 410	*027 075 124 173 221 270 318 366 415	*032 080 129 177 226 274 323 371 419	6 8 9	2.O 2-4 2.8 11
900	424	429	434	439	444	448	453	458	463	468
N.	O	1	*	3	4	5	6	7	8	9	Proj	>. Pts.

i8

w.	0123	4	5	6	7	8	9	Prop. Pts.
900 01 02 03 04 05 06 07 08 09 910 ii 12 13 14 15 16 17 18 920 21 22 23 24 25 26 27 28 29 930 32 33 34 35 36 37 38 39 940 42 43 44 45 46 47 48 49 950	95 424	429	434	439	444	448	453	458	.463	468	I 2 3 4 6 8 9 i 2 3 4 6 8 9	5 0-5 I.O 1-5 2.0 2-5 3-o 3.5 4.0 4.5 4 0.4 0.8 1.2 1.6 2.O 2-4 2.8 3-2 3-6
472 521 569 617 665 713 76i 809 856	477 525 574 622 670 718 766 813 86 1	482 530 578 626 674 722 770 818 866	437 535 583 679 727 775 823 871	492 540 588 636 684 732 780 828 875	497 545 593 641 689 737 785 832 880	SGI 550 598 646 694 742 789 837 885	506 650 698 746 794 842 890	559 607 655 703 751 799 847 895	516 564 612 660 708 756 804 852 899
904	909	914	918	923	928	933	938	942	947
952 999 96 047 095 142 190 237 284 332	957 *OQ4 052 099 147 194 242 289 336	961 *oc>9 057 104 152 199 246 294	06 1 109 156 204 251 298 346	066 114 161 209 256 303 350	976 *023 071 118 166 213 261 308 355	980 *028 076 123 171 218 265 313 360	*985 *o8o 128 175 223 270 317 365	990 *o38 085 133 180 227 275 322 369	*o9! 090 137 185 232 280 327 374
_379_ 426 473 520 ' 614 661 708 755 802	384	388	393	398	402	407	412	417	421
43i 478 525 572 619 666 713 759	435 483 530 577 624 670 717 764 811	440 487 534 58i 628 675 722 769 816	445 492 539 586 633 680 727 774 820	450 497 544 638 685 778 825	454 501 548 595 642 689 736 783 830	459 506 553 600 647 694 741 788 834	464 558 605 652 699 745 792 839	468 515 562 609 656 703 750 797 844
848	853	858	862	867	872	876	881	886	890
895 942 988 97 035 08 1 1*8 220 267	900 946 993 039 086 132 179 225 271	904 95i 997 044 090 137 183 230 276	909 956 *002 049 095 142 188 234 280	914 960 *oo7 053 IOO 146 192 239 285	918 965 *OII 058 104 151 197 243 290	923 970 *oi6 063 109 155 202 248 294	928 974 *02I 067 114 160 206 253 299	932 *979 072 118 165 211 257 304	937 *984 077 123 169 216 262 308
_3Jf3_ 359 405 45i 497 543 589 727	317	322	327	331	336	340	345	350	354
364 410 456 502 548 594 640 685	368 414 460 506 552 598 644 690 736	373 419 465 557 603 649 695 740	377 424 470 607 §9 745 791"	382 428 474 520 566 612 658 704 749	387 433 479 525 617 663 708 754	391 437 483 529 575 621 667 759	396 442 488 534 580 626 672 717	400 447 493 539 630 676 722
772	777	7*2	786	Soo	804	809	813
N.	0 1	2 :j i	5 0	7	8 0	Proi	.. Pis.

N.	o	1	2	3 4	5	6 | 7	8	9	Prop. Pts.
950 5i 52 53 - 54 55 56 57 58 59 OGO 61 62 63 64 65 66 67 68 69 970 7i 72 73 74 75 76 11 79 980 81 82 83 84 85 86 87 88 89 990 9i 92 93 94 95 96 .97 98 99 1000	97 772	777	782	786	791	795	800	804	809	8i3	i 2 3 4 5 6 9 i 2 3 4 5 6 8 9	5 0.5 I.O i-5 2.0 2-5 3-o 3-5 4.0 4-5 4 0.4 0.8 1.2 1.6 2.0 2.4 2.8 %
818 864 909 955 98 ooo 046 091 137 182	823 868 914 959 005 050 096 141 186	827 873 918 964 009 055 100 146 191	832 877 923 968 014 059 105 150 195	836 882 928 973 019 064 109 155 200	841 886 932 978 023 068 114 159 204	845 891 937 982 028 073 118 164 209	850 896 941 987 032 078 123 1 68 214	855 900 946 991 037 082 127 173 218	859 9°5 950 996 041 087 132 177 223
227	232	236	241	245	250	254	259	263	268
272 3i8 363 408 453 498 543 588 632	277 322 367 412 457 502 547 592 637	281 327 372 417 462 507 552 597 641	286 331 376 421 466 5ii 556 601 646	290 336 381 426 471 516 561 605 650	295 340 385 430 475 520 565 610 655	299 345 390 435 480 525 57o 614 659	3°4 349 394 439 484 529 574 619 664	308 354 399 444 489 534 579 623 668	313 358 403 448 493 538 583 628 673
677	682	686	691	695	700	704	709	713	717
722 767 8x1 856 900 945 989 99 034 078	726 771 816 860 9°5 949 994 038 083	73i 776 820 865 909 954 998 043 087	825 869 914 958 -003 047 092	740 784 829 874 9l8 963 *007 052 096	744 789 834 878 923 967 *OI2 056 100	749 793 838 883 927 972 *oi6 061 105	753 798 843 887 932 976 *02I 065 I09	758 802 847 892 936 981 *025 069 114	762 807 851 896 941 985 *029 074 118
123	127 131	136	140	145	149	154	158	162
167 211 255 300 344 388 432 476 520	171 216 260 304 348 392 436 480 524	176 220 264 308 352 396 441 484 528	180 224 269 313 357 401 445 489 533	185 229 273 317 361 405 449 493 537	I89 233 277 322 366 410 454 498 542	193 238 282 326 370 414 458 502 546	I98 242 286 330 374 419 463 506 550	202 247 291 335 379 423 467 5u 555	207 251 295 427 471 515 559
564	568	572	577	58i	585	590	594	599	603
607 651 695 739 782 826 870 913 957	612 656 699 743 787 830 874 917 961	616 660 704 747 791 835 878 922 965	621 664 708 752 795 839 883 926 970	625 669 712 756 800 843 887 930 974	629 673 717 760 804 848 891 935 978	634 677 721 765 808 852 896 939 983	638 682 726 769 813 856 900 944 987	642 686 730 774 817 861 904 948 991	647 691 734 778 822 865 909 952 996
00 000	004	009	013	017	022	026	030	035	039
N. ,	O	1	2	3	4	5	6	7	8	9	Prop. Pts.

20

TABLE II.
CONSTANTS WITH THEIR LOGARITHMS.
	Number.	Logarithm.
TT (ratio of circumference to diameter) . . . 7T2 ...	3.14159265 9.86960440 1.77245385 0.31830989 O.IOI32II8 0.56418958 3600 2i6oo/ I 296000" 57°.2957795 3437^74677 206264". 806 .01745329 .00029089 .000004848 2.718281828 0.434294482 3.8197186 3963.296 3949.790 3956. 39-37 39.37079 39.37043 5280. 6080.290 1.466667 0.681818	0.49714 99 0.99429 97 0.24857 49 9.50285 01 — 10 9.00570 03 — 10 9.75142 51—10 2.55630 25 4-33445 38 6.11260 50 1.75812 26 3-53627 39 5.31442 51 8.24187 74 — 10 6.46372 61 — 10 4.68557 49—10 0.43429 45 9.63778 43—10 0.58203 14 3-59805 65 3-59657 4o 3.59725 63 i.595i6 54 I.595I7 4i I.595I7 oi 3.72263 39 3-78392 43 .16633 15 9.83366 86—10
V*
I
I
I
v« ' Number of degrees in circumference .... minutes .... seconds " .... Degrees in arc equal to radius .
Minutes " " " ....
Seconds " " "
Length of arc of i degree
" " i minute
" " i second
Napierian base
Modulus of common logarithms . . .
Hours in which earth revolves through arc equal to radius
Equat. radius of earth, miles (Clarke, 1878) Polar " " " " " Mean " " "
Inches in i metre (U. S. Standard) " i " (British Standard) .... " i " (Clarke 1866)
Feet in i mile . . ....
Feet in i nautical mile (U. S. Coast Survey) Feet per second in i mile per hour
Miles per hour in i foot per second ....

21

TABLE III.

LOGARITHMS

OF THE

SINE, COSINE, TANGENT, AND COTANGENT

EACH MINUTE OF THE QUADRANT.

22

r	L. Sin.	d.	L.Tarig. c. d. L.Cotg.	L. Cos.		Prop. Pts.
O i 2 3 4	6.46 373 6.76 476 6.94 085 7.06 579	30103 17609 12494 9691 7918 6694 5800 5"5 4576 4*39 3779 3476 3218	6.46 373 6.76 476 6.94 085 7.06 579	30103 17609 12494 9691 7918 6694 5800 5"5 4576 4139 3779 3476 3219 2996 2803 2633 2482 2348 2228 2119 2O2O J93i 1848 1773 1704 1639 1579 *524 1473 1424 1379 1336 1297 "59 1223 1190 "59 1128 IIOO 1072 1047 1022 998 976 955 934 9^5 895 878 860 843 828 812 797 782 769 756 742 73<>	3-53 627 3-23 524 3-05 915 2.93 421	o.oo ooo 0.00 000 o.oo ooo 0.00 000 o.oo ooo	6O 59 58 57 56	d. I336 1297 1259 1223 1190 "59 1158 1128 IIOO 1072 1047 1046 IO22 999 998 976 955 954 934	d. 30103 17609 12494 9691 7918 6694 5800 5"5 4576 4139 3779 3476 3219 3218 2997 2996 2803 2802 2633 2483 2482 2348 2228 2227 2119 3021 2020 1931 1930 1848 1773 1704 1639 1579 1524 1473 1472 1424 1379 p.p.1" 22.27 21.62 20.98 20.38 19.83 19.32 19.30 18.80 18.33 17.87 17.45 17-43 17.03 16.65 16.63 16.27 15-92 15.90 15-57	p.p.l 501.7 293-4 208.^ l6i.e I3I.9 111.5 96.6 85-2 76.2 68.9 62.9 57-9 53.^ 53-^ 49-9 49-9 46.7 46.7 43-8 41.3 41-3 39-1 37-1 37-1 35-3 33-^ 33^ 32.1 32.1 30.8 29.= 28.4 27-3 26.3 25.4 24-5 24-5 23-7 22.9 d. 9i5 914 896 895 878 877 860 843 828 827 812 797 782 769 756 755 743 742 73°	2 8 3 2 7 7 7 5 7 8 8 3 5 3 5 3 2 O 8 8 7 3 3 2 2 8 7 8 7 0 5 o 2 2 0 5 3 3 8 P-P-1" 15-25 15-23 14-93 14.92 14-63 14.62 14-33 14-05 13.80 13-78 13-53 13.28 13-03 12.82 12.60 12.58 12.38 12.37 12.17
6 7 8 9	7.16 270 7.24 188 7.30 882 7.36 682 7.41 797	7.16 270 7.24 188 7.30 882 7.36 682 7.41 797	2.83 730 2.75 812 2.69 118 2.63 318 2.58 203	0.00 000 o.oo ooo 0.00 000 o.oo ooo 0.00 000	55 54 53 52 5i
10 ii 12 13 14	7-46 373 7-50 512 7-54 291 7-57 707 7.60 985	7-46 373 7-50 512 7-54 291 7-57 767 7.60 986	2.53 627 2.49 488 2.45 709 2.42 233 2.39 014	o.oo ooo o.oo ooo 0.00 000 o.oo ooo 0.00 000	50 49 48 47 46
15 16 17 18 19	7.63 982 7.66 784 7.69 417 7.71 900 7-74 248	2802 2633 2483 2348	7.63 982 7.66 785 7.69 418 7.71 900 7-74 248	2.36 018 2-33 215 2.30 582 2.28 100 2.25 752	0.00 000 o.oo ooo 9-99 999 9-99 999 9-99 999	45 44 43 42 4i
20 21 22 23 24	7.76 475 7.78 594 7.80 615 7-82 545 7-84 393	2119 202 1 *93o 1848 1773 1704 1639 J579 1524 1472 1424 1379 1336 1297	.7.76 476 7-78 595 7.80 615 7-82 546 7-84 394	2.23 524 2.21 405 2.19 385 2.17 454 2.15 606	9-99 999 9-99 999 9-99 999 9-99 999 9-99 999	40 39 38 37 36
25 26 27 28 29	7.86 166 7.87 870 7.89 509 7.91 088 7.92 612	7.86 167 7.87 871 7-89 510 7.91 089 7.92 613	2.13 833 2.12 129 2.IO 490 2.08 911 2.07 387	9.99 999 9-99 999 9-99 999 9-99 999 9-99 998	35 34 33 32 3i
30 3i 32 33 34	7-94 084 7-95 508 7.96 887 7.98 223 7-99 520	7.94 086 7-95 5io 7.96 889 7.98 225 7-99 522	2.05 914 2.04 490 2.03 III 2.01 775 2.00 478	9-99 998 9-99 998 9-99 998 9-99 998 9-99 998	30 29 28 27 26
33i 37 38 39	8.00 779 8. 02 002 8.03 192 8.04 350 8.05 478	1259 1223 1190 1158 1128	8.00781 8.02 004 8.03 194 8.04 353 8.05 481	1.99 219 1.97 996 1.96 806 1.95 647 1-94 519	9-99 998 9-99 998 9-99 997 9-99 997 9.99 997	25 24 23 22 21
40 4i 42 43 44	8.06 578 8.07 650 8.08 696 8.09 718 8.10717	1072 1046 1022 999 976 954 934 914 896 877 860 843 827 812 797 782 769 755 743 73°	8.06 581 8.07 653 8.08 700 8.09 722 8.10 720	1-93 419 1.92 347 1.91 300 1.90 278 1.89 280	9-99 997 9-99 997 9.99 997 9.99 997 9-99 996	20 19 18 17 16
45 46 47 48 49	8. 1 1 693 8.12 647 8.13 581 8.14 495 8.IS 39i	8. 1 1 696 8.12 651 8.13 585 8.14 500 8.15 305'	1.88 304 1.87 349 1.86 415 1.85 500 1.84 605	9.99 996 9-99 996 9-99 996 9-99 996 9.99 996	15 14 13 12 II
50 Si 52 53 54	8.16 268 8.17 128 8.17 971 8.18 798 8.19 610	8.16 273 8.17 133 8.17 976 8.18 804 8.19 616	1.83 727 1.82 867 1.82 024 1.81 196 x.8o 384	9-99 995 9-99 995 9-99 995 9-99 995 9-99 995	10 9 8 7 6
55 56 57 58 59	8.20 407 8.21 189 8.21 958 8.22713 8.23 456	8.20 413 8.21 195 8.21 964 8.22 720 8.23 462	i-79 587 1-78 805 1.78 036 1.77 280 1.76 538	9-99994 9-99 994 9-99 994 9-99 994 9-99 994	5 4 3 2
00	8.24 1 86	8.24 192	1.75 808	9-99 993	0
	I,. ( os. d.	L. Cotg.	C. d.	L.Tniic.	JL. Sin.	f	Prop. Pts.

if	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.			Prop.	Pts
o I 2 3 4	8.24 186 8.24 903 8.25 609 8.26 304 8.26 988	717 706 695 684 (,-~	8.24 192 8.24 910 8.25 616 8.26 312 8.26 996	* 706 696 684 fit?	1.75 808 1.75 090 1.74 384 1.73 688 1.73 004	9-99 993 9-99 993 9-99 993 9-99 993 9-99 992	GO II 11
5 6 7 8 9	8.27 661 8.28 324 8.28 977 8.29 621 8.30 255	663 653 644 634 624.	8.27 669 8.28 332 8.28 986 8.29 629 8.30 263	°73 663 654 643 634 62 e	1.72 331 1.71 668 1.71 014 1.70 371 1.69 737	9.99 992 9.99 992 9.99 992 9-99 992 9.99 991	55 54 53 52 5i	d.	P. D. 1"	d.	n TJ \"
10 ii 12 13 14	8.30 879 8-31 495 8.32 103 8.32 702 8-33 292	616 608 599 590	8.30 888 8-31 505 8.32 112 8.32711 8.33 302	6l7 607 599 59i -0 .	1.69 112 1.68 495 1.67 888 1.67 289 1.66 698	9-99 991 9-99 991 9-99 990 9.99 990 9-99 990	5O 49 48 47 46	718 717 706 696 605	11.97 n-95 11.77 1 1. 60 11.58	485 480 475 474 470	8.08 8.00 7.92 7.90 7 8q
15 16 17 18 19	8-33 875 8-34 450 8 35 018 8-35 578 8.36 131	5°3 575 568 560 553	8.33 886 8.34 461 8-35 029 8-35 590 8.36 143	5°4 575 568 56i 553 e/ifi	1.66 114 1-65 539 1.64 971 1.64 410 1.63 857	9-99 99° 9.99 989 9-99 989 9-99 989 9.99 989	45 44 43 42 4i	684 673 663 654 653	11.40 11.22 11.05 10.90 10.88	t/v 464 460 459 455 450	7.73 7.67 7.65 7.58 7.50
20 21 22 23 24	8.36 678 8.37 217 8-37 750 8.38 276 8.38 796	539 533 526 520	8.36 689 8.37 229 8.37 762 8.38 289 8.38 809	540 533 527 520	1.63 311 1.62 771 1.62 238 1.61 711 1.61 191	9.99 988 9-99 988 9.99 988 9-99 987 9-99 987	40 39 38 37 36	644 643 634 625 624	10.73 10.72 io.57 10.42 10.40	446 445 441 437 436	7.43 7.42 7.35 7.28 7.27
25 26 27 28 29	8.39 3io 8.39 818 8.40 320 8.40 816 8.41 307	508 502 496 491 ,0.	8-39 323 8.39 832 8.40 334 8.40 830 8.41 321	509 502 496 491 A&6	i. 60 677 .60 168 .59 666 •59 170 .58 679	9-99 987 9.99 986 9.99 986 9.99 986 9-99 985	35 34 33 32 3i	617 616 608 607 599	10.28 10.27 10.13 IO.I2 9.98 o 8^	433 432 428 427 424	7.22 7.20 7.13 7.12 7.07
30 3i 32 33 34	8.41 792 8.42 272 8.42 746 8.43 216 8.43 680	480 474 470 464	8.41 807 8.42 287 8.42 762 8.43 232 8-43 696	480 475 470 464	•58 193 •57 713 •57 238 •56 768 •56 304	9.99 985 9-99 985 9-99 984 9-99 984 9-99 984	30 29 28 27 26	590 584 583 575 568	9-83 9-73 9.72 9.58 9-47	419 416 412 411 408	6.98 6.93 6.87 6.85 6.80
35 36 37 38 39	8.44 139 8.44 594 8.45 044 8.45 489 8-45 930	459 455 450 445 441	8.44 156 8.44 611 8.45 061 8-45 507 8.45 948	400 455 450 446 441	•55 844 •55 389 •54 939 •54 493 •54 052	9-99 983 9-99 983 9-99 983 9-99 982 9.99 982	25 24 23 22 21	56i 560 553 547 546	9-35 9-33 9.22 9.12 9.10	404 401 400 397 396	6.73 6.68 6.67 6.62 6.60
4O 4i 42 43 44	8.46 366 8.46 799 8.47 226 8.47 650 8.48 069	43° 433 427 424 419 A,f.	8.46 385 8.46 817 8-47 245 8.47 669 8.48 089	437 432 428 424 420 Atft	•53 615 •53 183 1-52 755 •52 33i .51 911	9-99 982 9-99 981 9.99 981 9-99 98i 9-99 98o	20 19 18 17 16	540. 539 533 527 526	9.00 8.98 8.88 8.78 8-77	393 39° 386 383 382	£'55 6.50 6-43 6.38 6-37
45 46 47 48 49	8.48 485 8.48 896 8.49 304 8.49 708 8.50 108	411 408 404 400 qo6	8.48 505 8.48 917 8-49 325 8.49 729 8.50 130	412 408 404 401	•5i 495 •Si 083 •50 675 .50 271 .49 870	9.99 980 9-99 979 9-99 979 9-99 979 9-99 978	15 14 13 T2 II	520 514 5<>9 508 502 4O6	O.O7 8-57 8.48 8.47 8.37 8.27	380 379 376 373 370 q6o	6-33 6.32 6.27 6.22 6.17 6 15
5O Si 52 53 54	8.50 504 8.50 897 8.51 287 8-51 673 8.52 055	393 39° 386 382	8.50 527 8.50 920 8.51 310 8.51 696 8.52 079	393 390 386 383	•49 473 .49 080 .48 690 .48 304 •47 921	9-99 978 9-99 977 9.99 977 9.99 977 9.99 976	10 9 8 7 6	491 486	8.18 8.10	* 367 363	6.12 6.05
55 56 57 58 59	8.52 434 8.52 810 8-53 183 8-53 552 8-53 919	379 376 373 369 367 •36-3	8.52 459 8.52 835 8.53 208 8-53 578 8-53 945	3°° 376 373 37° 367 •afii	•47 541 •47 165 .46 792 .46 422 •46 055	9-99 976 9-99 975 9-99 975 9-99 974 9-99 974	5 4 3 2 I
6O	8.54 282		8.54 308		1.45 692	9-99 974	O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	/•		Prop.	Pts,

88<

/•	I.. Sin.	d.	L.Taiig.	c. d.	L. Cotg.	L. Cos.		Prop. Pts.
o I 2 3 4	8.54 282 8.54 642 8.54 999 8-55 354 8.55 705	360 357 355 35i 349 346 343 34i 337 336 332 33<> 328 325 323 320 3i8 316 313 3" 3°9 307 3°5 302 301 298 296 294 293 290 288 287 284 283 281 '	8.54 308 8.54 669 8-55 027 8.55 382 8-55 734	361 358 355 352 349 346' 344 34i 338 336 333 33° 328 326 323 321 3i9 316 314 3" 310 3°7 3<>5 303 301 299 297 295 292 291 289 287 285 284 28-1 280 278 276 274 273 271 269 268 266 .264 263 261 260 258 257 255 254 252 251 249 248 246 245 244 *43	1.45 692 i-45 33i 1-44 973 1.44 618 1.44 266	9 99 974 9-99 973 9-99 973 9.99 972 9.99 972	6O 59 58 57 56		P-P-1' 6. 02 6.00 5-97 5-95 5-92 5.87 5.85 5-82 5-77 5-73 5-72 5-68 5-63 ^.62 5-6o 5-55 5-53 5-5° 5*47 5-43 5-42 5-38 5-35 5.33 5-32 5-3° 5-27 5-23 5.22 5-i8 5.17 5-15 5-12 5-08 5-05 5.03 5.02 4.98 4-97 4-95 4-93 4.92 4.90 4.88 4-87	d. 291 290 289 288 287 285 284 283 281 280 279 278 277 276 274 273 272 271 270 269 268 267 266 264 263 261 260 259 258 257 256 255 254 253 252 251 250 249 248 247 246 245 244 243 242	p.p.l" 4-85 4-83 4.82 4.80 4.78 4-75 4-73 4.72 4.68 4.67 4.65 4-63 4.62 4.60 4-57 4-55 4-53 4-52 4-50 4.48 4-47 4-45 4-43 4.40 4.38 4-35 4-33 i32 4-30 4.28 4.27 4-25 4-23 4.22 4.20 4.18 4.17 4-15 4-13 4-1? 4.10 4.08 4.07 4-05 4-03
1 7 8 9	8.56 054 8.56 400 8.56 743 8-57 084 8.57 421	8.56 083 8.56 429 8-56 773 8.57 114 8-57 452	1-43 917 1-43 57i 1-43 227 1.42 886 1.42 548	9-99 971 9.99 971 9-99 970 9.99 970 9-99 969	55 54 53 52 5i	d.
1O ii 12 13 14	8-57 757 8.58 089 8.58 419 8.58 747 8.59 072	8.57 788 8.58 121 8-58 451 8.58 779 8-59 105	1.42 212 1.41 879 1.41 549 I.4I 221 1.40 895	9-99 969 9-99 968 9-99 968 9-99 967 9.99 967	5O 49 48 47 46	361 360 358 357 355 352 35i 349 346 344 343 34i 338 337 336 333 332 33° 328 326 325 323 321 320 319 3i8 316 3*4 3i3 3" 310 3°9 307 3°5 303 302 301 299 298 297 296 295 294 293 292
15 16 17 18 19	8-59 395 8-59 715 8.60 033 8.60 349 8.60 662	8.59 428 8-59 749 8.60 068 8.60 384 8.60 698	1.40 572 1.40 251 1-39 932 1.39 616 1-39 3°2	9-99 967 9.99 966 9.99 966 9-99 965 9.99 964	45 44 43 42 41
20 21 22 23 24	8.60 973 8.61 282 8.61 589 8.61 894 8.62 196	8.61 009 8.61 319 8.61 626 8.61 931 8.62 234	1.38 991 1.38 681 1-38 374 1.38 069 1.37 766	9.99 964 9-99 963 9-99 963 9-99 962 9-99 962	40 39 38 37 36
25 26 27 28 29	8.62.497 8.62 795 8.63 091 8.63 385 8.63 678	8.62 535 8.62 834 8.63 131 8.63 426 8.63 718	*-37 465 1.37 166 1.36 869 1-3.6 574 1.36 282	9-99 96i 9-99 961 9-99 96o 9-99 960 9-99 959	35 34 33 32 3i
30 3i 32 33 34	8.63 968 8.64 256* 8-64 543 8.64 827 8.65 no	8.64 009 8.64 298 8.64 585 8.64 870 8.65 154	i-35 99i 1.35 70^ 1.35 415 1-35 130 1.34 846	9-99 959 9-99 958 9-99 958 9-99 957 9-99 956	30 29 28 27 26
35 36 37 38 39	8.65 391 8.65 670 8.65 947 8.66 223 8.66 497	'279 277 276 274 272 270 269 267 266 263 263 260 259 258	8-65 435 8-65 715 8-65 993 8.66 269 8.66 543	i-34 565 i-34 285 1.34 007 1-33 73i 1-33 457	9-99 956 9-99 955 9-99 955 9-99 954 9-99 954	25 24 23 22 21
40 4i. 42 43 44	8.66 769 8.67 039 8.67 308 8.67 575 8.67 841	8.66 816 8.67 087 8.67 35-6 8. "67 624 8.67 890	1-33 184 1.32 913 1.32 644 1.32 376 1.32*110	9-99 953 9-99 952 9-99 952 9-99 951 9-99 95 !	20 19 18 17 16
45 46 47 48 49	8.68 104 8.68 367 8.68 627 8.68 886 8.69 144	8.68 154 8.68 417 8.68 678 8.68 938 8.69 196	1.31 846 1-31 583 1.31 322 1.31 062 1.30 804	9-99 950 9-99 949 9.99 949 9-99 948 . 9-99 948	15 14 13 12 II
50 Si 52 53 54	8.69 400 8.69 654 8.69 907 8.70 159 8.70 409	250 254 253 252 250	8-69 453 8.69 708 8.69 962 8.70 214 8.70 46?	1-30 547 1.30 292 1.30 038 1.29.786 1-29 535	9-99 947 9.99 946 9-99 946 9-99 945 9-99 944	10 9 8 7 6
55 56 57 58 59	8.70 658 8.70 90? 8.71 151 8-71 395 8.71 638	249 247 246 244 243	8.70 714 8.70 962 8.71 208 8-71 453 8.71 697	1.29 286 1.29 038 1.28 792 1.28 547 1.28 303	9-99944 9-99 943 9-99 942 9.99 942 9.99 941	5 4 3 2 I 0
GO	8.71 880	243	8.71 940	1.28 060	9-99 940
	L. Cos.	d.	L. Cotg.	c. d.	L.Taiif;.	L. Sin.	/	Prop. Pts.

87<

r	L,. Siu.	d.	L.Tang.jc. d.| L. Cotg.	L. Cos.		Prop.	Pts.
0 i 2 3 4	8.71 880 8.72 120 8.72 359 8.72 597 8.72 834	240 239 238 237 235 234 232 232 230 229 228 226 226 224 223 222 220 220 2I9 2I7 216 216 2I4 2I3 212 2X1 210 209 208 208 206 205 204 203 2O2 2OI 201 I99 199 197 197 I96 195 I94 life I92 192 I90 190 189 188 187 187 1 86 185 184 183 183 181 181	8.71 940 8.72 181 8.72 420 8.72 659 8.72 896	241 239 239 237 236 234 234 232 231 229 229 227 226 225 224 222 222 220 2I9 2I9 2I7 2l6 215 214 213 211 211 < 210 209 208 206 206 205 204 2*3 202 2O I 201 I99 I98 I98 I96 I96 '95 194 193 192 192 190 190 189 188 188 186 186 185 184 184 182 182	1.28 060 1.27 819 1.27 580 1.27 341 1.27 104	9-99 940 9.99 940 9-99 939 9-99 938 9-99 938	60 59 58 1	6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 4° 50 6 7 8 "9 10 20 30 40 50	438 23.8 27-8 31-7 35-7 39-7 79-3 119.0 158.7 198-3 225 22.5 26.3 30.0 33-8 37-5 75-0 112.5 150.0 187.5 212 "21.2 24.7 28.3 3L8 35-3 70.7 106.0 141-3 176.7 2OI 20.1 23-5 26.8 30.2 33-5 67.0 100.5 134.0 167.5 189 18.9 22.1 25.2 28.4 SI'S 63.0 94-5 126.0 157.5 4 6.4 c 0.5 c 0.5 c 0.6 c 0.7 c i-3 i 2.0 J 2.7 i 3-3 '-	234 23-4 27-3 31.2 35-1 39-o 78.0 117.0 156.0 195-0 220 22.0 25-7 29-3 33-o 36.7 73-3. IIO.O 146.7 183-3 208 20.8 24-3 27.7 31.2 34-7 69-3 104.0 138.7 173-3 197 19.7 23.0 26.3 29.6 32.8 65-7- 98.5 I3L3 164.2 185 18.5 21.6 24.7 27.8 30.8 61.7 92.5 123-3 1542 3 « )-3 0.2 )-4 0.2 >-4 0.3 >-5 0.3 >-5 0.3 .0 0.7 •5 1.0 ..o 1.3 '•5 i-7	229 22.9 26.7 30.5 34-4 38.2 76.3 "4-5 152.7 190.8 216 21.6 25.2 28.8 32.4 t 36.0 72.0 108.0 144.0 180.0 204 20.4 23.8 27.2 30.6 34-0 68.0 102.0 136.0 170.0 193 19-3 22-5 25.7 29.0 32.2 6J.3 96.5 128.7 160.8 181 18.1 21. 1 24.1 27.2 30.2 60.3 9°-5 120.7 150.8 z O.I O.I O.I 0.2 O.2 0-3 0.5 0.7 0.8
6 7 8 9	8.73 069 8-73 303 8-73 535 8-73 767 8-73 997	8.73 132 8.73 366 8.73 600 8.73 832 8.74 063	1.26 868 1.26 634 1.26 400 1.26.168 1.25 937	9-99 937 9.99 936 9-99 936 9-99 935 9-99 934	55 54 53 52 5i
10 ii 12 13 14	8.74 226 8-74 454 8.74 680 8.74 906 8-75 130	8.74 292 8.74 52i 8.74 748 8.74 974 8-75 199	1.25 708 1.25 479 1.25 252 1.25 026 1.24 801	9-99 934 9-99 933 9.99 932 9.99 932 9-99 931	50 49 48 47 46
15 16 17 18 19	8-75 353 8-75 575 8-75 795 8.76 015 8.76 234	8-75 423 8-75 645 8.75 867 8.76 087 8.76306	1-24 577 1-24 355 1-24 133 1.23 913 1.23 694	9-99 930 9.99 929 9.99 929 9-99 928 9-99 927	45 44 43 42 4i,
20 21 22 23 24	8.76 451 8.76 667 8.76 883 8-77 097 8.77 310	8.76 525 8.76 742 8.76 958 8.77 173 8.77 387	1.23 475 1.23 258 1.23 042 ' 1.22 827 1.22 613	9.99 926 9-99 926 9-99 925 9.99 924 9.99 923	40 39 38 %
25 26 27 28 29	8.77 522 8.77 733 8-77 943 8.78 152 8.78 360	8.77 600 8.77 811 8.78 022 8.78 232 8.78 441	1.22 400 1.22 189 " I.2I 978 I.2I 768 i.2i 559	9-99 923 9 99 922 9.99 921 9.99 920 9.99 920	35 34 33 32 3i
30 31 32 33 34	8.78 568 8.78 774 8.78 979 8.79 183 8.79 386	• 8.78 649 8.78 855 8.79 061 8.79 266 8.79 470	1. 21 351 ' I.2I 145 1.20 939 1.20 734 1.20 530	9-99 919 9-99 9i8 9.99 917 9-99 917 9.99 916	3O 29 28 27 26
It 37 38 39	8.79 588 8-79 789 8-79 990 8.80 189 8.80 388	8.79 673 8-79 875 8.80 076 8.80 277 8.80 476	1.20 327 1.20 I2g I.I9 924 I.I9 723 I.I9.524	9-99 9*5 9-99 914 9-99 913 9-99 9*3 9-99 912	25 24 23 22 21
40 4i 42 43 44	8.80 585 8.80 782 8.80 978 8.81 173 8.81 367	8.80 674 8.80 872 8.81 c68 8.81 264 8.81 459	I.I9 326 I.I9 128 1.18 932 1.18 736 1.18 541	9.99 911 9-99 9io 9-99 909 9.99 909 9-99 9°8	20k 19 18 17 16
45 46 47 48 49	8.81 560 8.81 752 8.81 944 8.82 134 8.82 324	8.81 653 8.8l 846 8.82 038 8.82 230 8.82 420	1.18 347 1.18 154 1.17 962 1.17 770 1.17 580	9-99 9°7 9-99 9°6 9 99 9°5 9-99 904 9.99904	15 H 13 12 II
50 5i 52 53 54	8.82513 8.82 701 8.82 888 8.83 075 8.83 261	8.82 610 8.82 799 8.82 987 8-83 175 8.83 361	1.17 390 I.I7 201 I.I7 OI3 1.16 825 1.16 639	9.99 903 9.99 902 9-99 90i 9-99 900 9-99 ^99	10 9 8 7 6
55 56 57 58 59	8.83 446 8.83 630 8.83 813 8.83 996 8.84 177	8.83 547 8.83 732 8.83 916 8.84 100 8.84 282	1-16 453 1.16 268 1.16 084 1.15900 1.15 718	9.99 898 9-99 898 9-99 897 9-99 896 9.99 895	5 4 3 2 I
60	8.84 358	8.84 464	I.I5 536	9-99 894	0
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	/•	Prop. Pts.

86C

26

/•	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	T,. Cos.			Pro	p. Ft;-
o I 2 3 4	8.84 358 8-84 539 8.84 718 8.84 897 8.85 075	181 179 179 178	8.84 464 8.84 646 8.84 826 8.85 006 8.85 185	182 180 180 179	1-15 536 I-I5 354 I.I5 174 1.14 994 1.14815	9.99 894 9.99 893 9-99 892 9-99 891 9-99 891	60 59 58 57 56	6 7 8	1 80 18.0 2I.O 24.0	177 17.7 20.7 23-6	174 17.4 20.3 23.2
5 6 7 8 9	8.85 252 8.85 429 8.85 605 8.85 780 8-85 955	177 177 176 i75 *75	8.85 363 8.85 540 8-85.717 8.85 893 8.86 069	178 177 177 176 176	1.14 637 1.14 460 1.14 283 1.14 107 I-I3 93i	9-99 890 9-99 889 9.99 888 9-99 887 9.99 886	55 54 53 52 Si	9 10 20 30 40	27.0 30.0 6o.O 90.0 I2O.O	26.6 29-5 59-° 88.5 118.0	26.1 29.0 58.0 87.0 116.0
10 ii 12 13 14	8.86 128 8.86 301 8.86 474 8.86 645 8.86 816	173 173 173 171 171	8.86 243 8.86 417 8.86 591 8.86 763 8.86 935	*74 174 174 172 172	1.13 757 I.I3 583 1.13 409 1.13 237 1.13 065	9-99 885 9-99 884 9-99 883 9.99 882 9.99 881	5O 49 48 47 46	5° 6 7 8	171 I7.I 20.0 22.8	X47-S 169 16.9 19.7 22.5	I45-° 167 16.7 19-5 22.3
15 16 17 18 19	8.86 987 8.87 156 8.87 325 8.87 494 8.87 661	171 169 169 169 167 ififi	8.87 106 8.87 277 8.87 447 8.87 616 8.87 785	171 171 170 J69 169	1. 12 894 1. 12 723 i.i2 553 1. 12 384 1. 12 215	9.99 880 9-99 879 9-99 879 9.99 878 9.99 877	45 44 43 42 4i	9 10 20 30 40	25-7 28.5 57-0 85-5 114.0	25-4 28.2 56.3 84.5 112.7 T in R	25.1 27.8 55-7 83-5 111.3
20 21 22 23 24	8.87 829 8.87 995 8.88 161 8.88 326 8.88 490	166 166 165 164	8.87 953 8.88 120 8.88 287 8.88 453 8.88 618	167 167 166 165	1. 12 047 I. II 880 I. II 713 i. ii 547 i. n 382	9.99 876 9-99 875 9.99 874 9-99 873 9.99 872	40 39 38 37 36	5° 6 7 8	142.5 165 16.5 19-3 22.0	140.8 I63 I6.3 19.0 21.7	139.2 1 60 16.0 18.7 21.3
25 26 27 28 29	8 88 654 8.88 817 8.88 980 8.89 142 8.89 304	163 163 162 162 160	8.88 783 8.88 948 8.89 in 8.89 274 8.89 437	105 165 163 163 163 161	i. n 217 i. n 052 I. 10 889 i. 10 726 i.io 563	9-99 871 9-99 870 9 99 869 9.99 868 9-99 867	35 34 33 32 3i	9 10 20 3° 40	24.8 27-5 55-0 82.5 IIO.O	24-5 27.2 54-3 81.5 108.7	24.0 26.7 53-3 80.0 106.7
30 3i 32 33 34	8.89 464 8.89 625 8.89 784 8.89 943 8.90 102	161 159 159 J59	8.89 598 8.89 760 8.89 920 8.90 080 8.90 240	162 160 160 160	i.io 402 i.io 240 i.io 080 1.09 920 1.09 760	9.99 866 9-99 865 9-99 864 9-99 863 9.99 862	30 29 28 27 26	-5° 6 7 8	J37-5 i57 iS-7 18.3 20.9	I35-° 155 15-5 18.1 20.7	J33-3 153 15-3 17.9 20.4
35 36 37 38 39	8.90 260 8.90 417 8.90 574 8.90 730 8.90 885	158 157 »57 156 155	8.90 399 8.90 557 8.90 715 8.90 872 8.91 029	T59 158 158 157 157 tcfi	1.09 60 1 1.09 443 1.09 285 1.09 128 i. 08 971	9 99 861 9.99 860 9-99 859 9-99 858 9-99 857	25 24 23 22 21	9 10 20 30 40	23.6 26.2 52.3 78.5 104.7	23-3 25-8 51-7 77-5 103-3	23.0 25-5 51.0 76.5 102.0
40 4i 42 43 44	8.91 040 8.91 195 8.91 349 8.91 502 8-91 655	!55 »55 *54 153 »53	8.91 185 8.91 340 8.91 495 8.91 650 8.91 803	155 155 155 153	1.08 815 i. 08 660 i. 08 505 i. 08 350 1.08 197	9-99 856 9-99 855 9-99 854 9-99 853 9-99 852	20 19 18 17 16	b° 6 7 8	130.0 151 I5A I7.6 20.1	149 14.9 17-4 19.9	I27-5 147 14.7 17.2 19.6
45 46 47 48 49	8.91 807 8.91 959 8.92 no 8.92 261 8.92 411	152 152 151 151 150	8.91 957 8.92 no 8.92 262 8.92 414 8.92 565	X54 153 i52 152 *5i	i. 08 043 1.07 890 1.07 738 1.07 586 1-07 435	9-99 851 9 99 850 9-99 848 9-99 847 9.99 846	15 14 13 12 II	9 10 20 30 40	22.7 25-2 50-3 75-5 100.7	22.4 24.8 49-7 74-5 99-3	22.1 24-5 49.0 73-5 98.0
50 Si 52 53 54	8.92 561 8.92 710 8.92 859 893007 8-93 154	150 *49 1 49 148 M7	8.92 716 8.92 866 8.93 016 8-93 I65~ 8.93 313	X5X 150 150 149 148	1.07 284 1.07 134 i. 06 984 1.06 835 i. 06 687	9-99 845 9-99 844 9-99 843 9.99 842 9-99 841	10 9 8 7 6	i>°	146 6 14- 7 17- 8 19-	a 6 0.2 0 0.2 5 0.3	122.5 i O.I O.I O.I
55 56 57 58 59	8.93 3oi 8.93 448 8-93 594 8.93 740 8.93 885	'47 '47 146 146 MS	8.93 462 8.93 609 8-93 756 8 93 903 8.94 049	J49 »47 »47 »47 146	1.06 538 1.06 391 i. 06 244 i. 06 097 1-05 951	9-99 840 9-99 839 9.99 838 9-99 837 9-99 836	5 4 3 2 I	i 2 3 4	9 21. o 24. o 48. o 73- o 97.	9 o-3 3 °-3 7 0.7 0 I.O 3 1-3	0.2 0.2 0-3 0-5 0.7
60	8.94 030	145	8.94 195	140	1.05 805	9-99 834	0	b	O 121.	7 1-7	o.o
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85C

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.			Pro]	>. PtH	•
O i 2 3 4	8.94 030 8.94 174 8.94 317 8.94 461 8.94 603	144 143 i44 142	8.94 195 8.94 340 8.94 485 8.94 630 8-94 773	145 145 145 143	1.05 805 1.05 660 1.05 5i5 1.05 370 1.05 227	9-99 834 9-99 833 9-99 832 9.99 831 9-99 830	6O 59 58 |	6 7 8	MS 14-5 16.9 19-3	'43 14-3 I6.7 I9.I	141 I4-I 16.5 18.8
5 6 7 8 9	8.94 746 8.94 887 8.95 029 8.95 170 8-95 3io	141 142 141 140	8.94 917 8.95 060 8.95 202 8-95 344 8.95 486	143 142 142 142	1.05 083 1.04 940 1.04 798 1.04 656 1.04 514	9-99 829 9.99 828 9.99 827 9-99 825 9-99 824	55 54 53 52 5i	9 10 20 30 40	21.8 24.2 48.3 72.5 96.7 I2O 8	21-5 23-8 47-7 71.5 95-3	21.2 23-5 47.0 70.5 94.0 117 ^
10 ii 12 13 14	8-95 450 8-95 589 8.95 728 8-95 867 8.96 005	139 139 139 138 j-,0	8.95 627 8-95 767 8.95 908 8.96 047 8.96 187	140 141 139 140 Tl8	1-04 373 1.04 233 1.04 092 1-03 953 1.03 813	9-99 823 9.99 822 9.99 821 9.99 820 9-99 819	50 49 48 47 46	6 7 8	139 13.9 16.2 18.5	138 13-8 16.1 18.4	I36 13-6 15-9 18.1
15 16 17 18 19	8.96 143 8.96 280 8.96 417 8.96 553 8.96 689	137 137 136 136 176	8.96 325 8 96 464 8.96 602 8.96 739 8.96 877	I3° 139 138 137 138 lift	1.03 675 1.03 536 1.03 398 1.03 261 1.03 123	9-99 817 9.99 816 9-99 815 9-99 814 9 99 813	45 44 43 42 4i	9 10 20 30 40	20.9 23.2 46.3 69.5 92.7 TTC 8	20.7 23.0 46.0 69.0 92.0	20.4 22.7 45-3 68.0 90.7
2O 21 22 23 24	8.96 825 8.96 960 8-97 095 8.97 229 8-97 363	135 J35 134 J34	8.97 013 8.97 150 8.97 285 8.97 421 8-97 556	137 135 136 135	1.02 987 1.02 850 1.02 715 1.02 579 1.02444	9.99 812 9.99 810 9.99 809 9.99 808 9.99 807	40 39 38 P	5° 6 7 8	135 13-5 15.8 18.0	133 13-3 15-5 17.7	iAO J 131 I3-I 15-3 17.5
25 26 27 28 29	8.97 496 8.97 629 8.97 762 8.97 894 8.98 026	133 133 132 132	8.97 691 8.97 825 8-97 959 8.98 092 8.98 225	134 134 133 133	1.02 309 1.02 175 1.02 041 i.oi 908 i. oi 775	9.99 806 9-99 804 9.99 803 9.99 802 9.99 801	35 34 33 32 3i	9 10 20 30 40	20.3 22.5 45-0 67.5 90.0	20.0 22.2 44-3 66.5 88.7	19.7 21.8 43-7 65.5 87.3
30 3i 32 33 34	.8.98 157 8.98 288 8.98 419 8.98 549 8.98 679	131 131 130 130	8.98 358 8.98 490 8.98 622 8.98 753 8.98 884	J33 132 132 »3i 131	i.oi 642 i.oi 510 i.oi 378 i.oi 247 i.oi 116	9.99 800 9.99 798 9-99 797 9-99 796 9-99 795	30 29 28 27 26	Su 6 7 8	112.5 129 12.9 iS-i 17.2	128 12.8 14.9 17.1	126 12.6 14.7 16.8
H 37 38 39	8.98 808 8.98 937 8.99 066 8.99 194 8.99 322	129 129 128 128 128	8.99 015 8-99 145 8.99 275 8.99 405 8-99 534	I31 130 130 130 129 128	i.oo 985 i.oo 855 i.oo 725 i.oo 595 I.OO 466	9-99 793 9.99 792 9.99 791 9-99 790 9-99 788	25 24 23 22 21	9 10 20 30 40	19.4 21.5 43-o 64.5 86.0	19.2 21.3 42.7 64.0 85.3	18.9 21.0 42.0 63.0 84.0
40 41 42 43 44	8-99 450 8-99 577 8-99 704 8.99 830 8-99 956	127 127 126 126 126	8.99 662 8-99 79i 8.99 919 9.00 046 9.00 174	129 128 127 128	i.oo 338 i.oo 209 i.oo 081 0.99 954 0.99 826	9-99 787 9.99 786 9-99 785 9-99 783 9-99 782	20 19 18 17 16	50 6 7 8	i°7-5 «5 12.5 14.6 16.7	123 12.3 14.4 16.4	122 12.2 14.2 I6.3
45 46 47 48 49	9.00 082 9.00 207 9.00 332 9.00 456 9.00 581	125 125 124 125	9.00 301 9.00 427 9-00 553 9.00 679 9.00 805	126 126 126 126	0.99 699 o-99 573 o.99 447 0.99 321 0.99 195	9-99 78i 9.99 780 9.99 778 9-99 777 9-99 776	IS 14 13 12 II	9 10 20 3° 40	18.8 20.8 41.7 62.5 83-3	18.5 20.5 41.0 61.5 82.0	I8.3 20.3 40.7 61.0 81.3
5O 5i 52 53 54	9.00 704 9.00 828 9.00 951 9.01 074 9.01 196	124 123 123 122	9.00 930 9.01 055 9.01 179 9.01 303 9.01 427	125 124 124 124	0.99 070 0.98 945 0.98 821 0.98 697 0.98 573	9-99 775 9-99 773 9-99 772 9-99 771 9-99 769	10 9 8 7 6	50 e	121 i I2.I r 14.1 5 16.1	I2O I2.C I4.C i6.c	z O.I O.I O.I
55 56 57 58 59	9.01 318 9.01 440 9.01 561 9.01 682 9.01 803	122 121 121 121	9.01 550 9.01 673 9.01 796 9.01 918 9.02 040	123 123 123 122 122	0.98 450 0.98 327 0.98 204 0.98 082 o 97 960	9.99 768 9-99 767 9-99 765 9-99 764 9-99 763	5 4 3 2 I	c 1C 2C 3< 4<	) 18.2 ) 2O.2 > 40-3 ) 60.5 ) 80.7	i8.c 2O.C 40.c 6o.c 8o.c	0.2 O.2 » 0.3 > 0.5 > 0.7
6O	9.01 923		9.02 162		0.97 838	9.99 761	O	b<	) 100.8	IOO.C	> 0.8
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	/•		Pro]	p. PtB

84(

6°

/•	L. Sin.	d.	L.Taug.	c. d.	L. Cotg.	L. Cos.		Prop. Pts.
o I 2 3 4	9.01 923 9.02 043 9.02 163 9.02 283 9.02 402	20 20 20 19 18 '9 18 117 118 117 117 116 xx6 116 116 "5 "5 114 "5 "3 114 114 "3 113 "3 112 112 112 III III III 110 110 110 no 109 109 109 108 109 1 08 107 1 08 107 107 106 107 1 06 105 106	9.02 162 9.02 283 9.02 404 9.02 525 9.02 645	121 121 121 120 121 II9 120 II9 118 119 118 118 117 118 116 117 116 116 116 "5 "5 "5 "5 114 114 "3 114 "3 112 II3 112 112 112 III III III 1 10 III no 109 no 109 109 1 08 109 1 08 1 08 107 108 107 106 107 106 1 06 106 1 06 105 105 105 104	0.97 838 0.97 717 0.97 596 0.97 475 0-97 355	9.99 761 9-99 76o 9-99 759 9-99 757 9-99 756	60 59 58 57 56	6 7 8 9 10 20 3° 40 50 6 8 9 10 20 3° 40 50 6 7 8 9 10 20 3° 40 So 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 8 9 10 20 30 40 50	121 I2.I I4.I 16.1 18.2 20.2 40-3 00.5 80.7 100.8 iiS 11.8 13-8 15-7 17.7 19.7 39-3 59'° 78.7 98.3 «5 "•5 13-4 15-3 17-3 19.2 38.3' 57-5 76.7 95-8 112 II. 2 I3-I 14.9 16.8 18.7 37-3 56.0 74-7 93-3 109 10.9 12.7 14-5 16.4 18.2 36.3 54-5 72.7 90.8 106 10.6 12.4 14.1 15-9 17.7 35-3 53-0 70.7 88.3	120 I2.C I4.c i6.c i8.c 20.C 40.c 6o.c 8o.c IOO.C 117 11.7 13-7 15-6 17.6 19-5 39-o 58.5 78.0 97-5 114 11.4 13-3 15-2 17.1 19.0 38.0 57-0 76.0 95-0 in n. i 13-0 14.8 !6.7 18.5 37-0 55-5 74.0 92.5 108 10.8 12.6 14.4 16.2 18.0 36.0 54-0 72.0 90.0 105 io-5 12.3 14.0 15-8 17-5 35-0 52.5 70.0 87.5	iig > 11.9 > 13-9 > 15-9 > 17-9 ) 19.8 > 39-7 > 59-5 > 79-3 > 99-2 116 11.6 13-5 15-5 17-4 19-3 38.7 58.0 77-3 96.7 113 "•3 13.2 15-1 17.0 18.8 37-7 56.5 75-3 94.2 'no II.O 12.8 14-7 16.5 18.3 36.7 55-0 73-3 91.7 107 10.7 12.5 14-3 16.1 17-8 35-7 53-5 71-3 89.2 104 10.4 12. 1 13-9 15-6 17-3 34-7 52.0 69-3 86.7
I 7 8 9	9.02 520 9.02 639 9.02 757 9.02 874 9.02 992	9.02 766 9.02 885 9.03 005 9.03 124 9.03 242	0.97 234 0.97 115 0.96 995 0.96 876 0.96 758	9-99 755 9-99 753 9-99 752 9-99 75i 9-99 749	55 54 53 52 5i
1O ii 12 13 14	9.03 109 9.03 226 9-03 342 9-03 458 9-03 574	9.03 361 9-03 479 9-03 597 9.03 714 9.03 832	0.96 639 0.96 521 0.96 403 0.96 286 0.96 168	9-99 748 9-99 747 9-99 745 9-99 744 9-99 742	5O 49 48 47 46
15 16 17 18 19	9.03 690 9.03 805 9.03 920 9.04 034 9.04 149	9.03 948 9.04 065 9.04 181 9.04 297 9.04 413	0.96 052 o-95 935 0.95 819 0-95 703 0-95 587	9-99 74i 9-99 74° 9-99 738 9-99 737 9-99 736	45 44 43 42 41
20 21 22 23 24	9.04 262 9.04 376 9.04 490 9.04 603 9-04 715	9.04 528 9.04 643 9.04 758 9.04 873 9.04 987	0.95 472 0-95 357 0.95 242 0.95 127 0.95 013	9-99 734 9-99 733 9-99 731 9-99 730 9-99 728	40 39 38 37 36
25 26 27 28 29	9.04 828 9.04 940 9.05 052 9.05 164 9-05 275	9.05 101 9-05 214 9.05 328 9.05 441 9-05 553	0.94 899 0.94 786 0.94 672 o-94 559 0.94 447	9-99 727 9-99 726 9.99 724 9-99 723 9-99 721	35 34 33 32 3i
30 3i 32 33 34	9.05 386 9-05 497 9.05 607 9.05 717 9-05 827	9.05 666 9.05 778 9-05 890 9.06 002 9.06 113	o-94 334 0.94 222 0.94 no 0.93 998 0.93 887	9.99 720 9-99 7i8 9.99 717 9-99 7i6 9 99 714	30 29 28 27 26
11 37 38 39	9-05 937 9.06 046 9-o6 155 9.06 264 9.06 372	9.06 224 9-o6 335 9.06 445 9.06 556 9.06 666	0.93 776 0.93 665 o-93 555 0-93444 0-93 334	9-99 713 9.99711 9-99 7io 9-99 708 9-99 707	25 24 23 22 21
4O 4i 42 43 44	9.06 481 9-o6 589 9.06 696 9.06 804 9.06 911	9.06 775 9.06 885 9.06 994 9.07 103 9.07 211	0.93 225 o-93 "5 0.93 006 0.92 897 0.92 789	9-99 705 9-99 704 9-99 702 9-99 7°i 9.99 699	20 19 18 17 16
45 46 47 48 49	9.07 018 9.07 124 9.07 231 9-07 337 9.07 442	9.07 320 9.07 428 9-07 536 9.07 643 9-07 751	0.92 680 0.92 572 0.92 464 0-92 357 0.92 249	9-99 698 9-99 696 9-99 695 9-99 693 9-99 692	15 14 13 12 II
50 Si 52 53 54	9.07 548 9-07 653 9-°7 758 9.07 863 9.07968	105 105 105 105	9.07 858 9.07 964 9.08 071 9.08 177 9.08 283	0.92 142 0.92 036 0.91 929 0.91 823 0.91 717	9.99690 9.99 689 9-99 687 9.99 686 9.99 684	10 9 8 7 6
P 57 58 59	9.08 072 9.08 176 9.08 280 9.08 383 9.08 486	104 104 103 103 103	9-o8 389 9.08 495 9.08 600 9.08 705 9.08 810	0.91 611 0-91 505 0.91 400 0.91 295 0.91 190	9-99 683 9.99 681 9.99 680 9-99 678 9-99 677	5 4 3 2 I
60	9.08 589	9.08 914	0.91 086	9-99 675	0
	L. COM. d.	L. Cotg. c. d. L.Tang.	L. Sin.	f	Prop. Pts.

83(

29

/•	L. Sin.	d.	JL.Tang.	c. d.	L.Cotg.	L. Cos.			Prop	. Pts
0 I 2 3 4	9.08 589 9.08 692 9.08 795 9.08 897 9.08 999	103 103 102 IO2	9.08 914 9.09 019 9.09 123 9.09 227 9.09 330	105 104 104 103	0.91 086 0.90 981 0.90 877 0.90 773 0.90 670	9-99 675 9.99 674 9-99 672 9.99 670 9.99 669	60 59 58 57 56	6 7 8	105 10.5 12.3 14.0	104 10.4 12. 1 13-9	103 10.3 I2.O 13-7
5 6 7 8 9	9.09 101 9.09 202 9.09 304 9.09 405 9.09 506	OI O2 OI OI	9.09 434 9-°9 537 9.09 640 9.09 742 9.09 845	103 103 IO2 103	0.90 566 0.90 463 0.90 360 0.90 258 0.90 155	9.99 667 9.99 666 9.99 664 9.99 663 9.99 661	55 54 53 52 5i	9 10 20 30 40 CQ	15.8 17.5 35-0 52-5 70.0 j 87 <;	15-6 17-3 34-7 52.0 69.3 86 7	15-5 17.2 34-3 51-5 68.7 8c 8
10 ii 12 13 14	9.09 606 9.09 707 9.09 807 9.09 907 9.IO OO6	101 IOO IOO 99	9.09 947 9.10 049 9.10 150 9.10 252 9-10 353	102 101 102 IOI	0.90 053 0.89 951 0.89 850 0.89 748 0.89 647	9-99 659 9.99 658 9-99 656 9-99 655 9-99 653	5O 49 48 47 46	6 7 8	102 IO.2 II.9 13-6	IOI IO.I n.8 13-5	zoo IO.O 11.7 13.3
15 16 17 18 19	9.10 106 9.10 205 9.10 304 9.10 402 9.10 501	99 99 98 99	9.10 454 9-i° 555 9.10 656 9.10 756 9.10 856	IOI IOI IOO IOO	0.89 546 0.89 445 0.89 344 0.89 244 0.89 144	9.99 651 9-99 650 9.99 648 9.99 647 9-99 645	45 44 43 42 41	9 10 20 30 40	15-3 17.0 34-0 51.0 68.0 85 o	15-2 16.8 33-7 50.5 67-3 8d 2	15.0 16.7 33-3 50.0 66.7 8-3 q
20 21 22 23 24	9.10 599 9.10 697 9.10 795 9.10 893 9.10 990	98 98 98 98 97	9.10 956 9.11 056 9-ii 155 9.11 254 9- " 353	IOO 99 99 99	0.89 044 0.88 944 0.88 845 0.88 746 0.88 647	9-99 643 9-99 642 9.99 640 9-99 638 9-99 637	4O 39 38 37 36	6 8	99 9.9 ii. 6 13.2	98 9-8 11.4 I3-I	97 9-7 «.3 12.9
25 26 27 28 29	9.11 087 9.11 184 9.11 281 9.11 377 9.11 474	97 97 97 96 97 nfi	9.11 452 9-ii 551 9.11 649 9. 1 1 747 9. 1 1 845	99 99 98 98 98 08	0.88 548 0.88 449 0.88 351 0.88 253 0.88 155	9-99 635 9-99 633 9.99 632 9-99 630 9-99 629	35 34 33 32 3i	9 10 20 30 40	14.9 16.5 33-0 49-5 66.0 82 c;	14.7 16.3 32.7 49.0 65-3 81 7	14.6 16.2 32.3 48.5 64.7 80 8
3O 3i 32 33 34	9.11 570 9 ii 666 9.11 761 9.11 857 9.11 952	9° 96 95 96 95	9- 1 1 943 9.12 040 9.12 138 9.12 235 9.12 332	9° 97 98 97 97 06	0.88 057 0.87 960 0.87 862 0.87 765 0.87 668	9.99 627 9-99 625 9-99 624 9.99 622 9.99 620	30 29 28 27 26	6 7 8	96 9-6 II. 2 12.8	95 9-5 n. I 12.7	94 9-4 II.O 12.5
P 37 38 39	9.12 047 9.12 142 9.12 236 9.12 331 9.12 425	95 95 94 95 94	9.12 428 9.12 525 9.12 621 9.12717 9.12 813	9° 97 96 96 96	0.87 572 0.87 475 0.87 379 0.87 283 0.87 187	9.99 618 9.99 617 9-99 615 9-99 613 9.99 612	25 24 23 22 21	9 10 20 3° 40	14.4 16.0 32.0 48.0 64.0	14-3 15-8 3i-7 47-5 63.3	14.1 15-7 31-3 47-0 62.7 78 3
40 4i 42 43 44	9.12519 9.12 612 9.12 706 9 .12 799 9.12 892	94 93 94 93 93	9.12 909 9.13 004 9.13 099 9-13 194 9.13 289	9° 95 95 95 95	0.87 091 0.86 996 0.86 901 0.86 806 0.86 711	9.99 610 9.99 608 9-99 6°7 9-99 605 9.99 603	20 19 18 17 16	Ou 6 7 8	93 9-3 10.9 12.4	ga 9-2 10.7 12.3	9i 9-i 10.6 I2.I
45 46 47 48 49	9.12 985 9.13 078 9.13 171 9.13 263 9-13 355	93 93 93 92 92	9-!3 384 9.13 478 9.13 573 9.13 667 9.13 761	95 94 95 94 94	0.86 616 0.86 522 0.86 427 0.86 333 0.86 239	9.99 601 9.99 600 9-99 598 9.99 596 9-99 595	15 14 13 12 II	9 10 20 3° 40	14.0 15.5 31-0 46.5 62.0	13.6 15-3 3°-7 46.0 61.3 76 7	13-7 15.2 3°-3 45-5 60.7 7c. «
50 5i 52 53 54	9-13 447 9-13 539 9.13 630 9.13 722 9-13 813	92 92 91 92 9l	9-i3 854 9.13 948 9 14 041 9-14 134 9.14 227	93 94 93 93 93	0.86 146 0.86 052 0.85 959 0.85 866 0.85 773	9-99 593 9-99 591 9-99 589 9.99 588 9-99 586	10 9 8 7 6	ou 6 8	9° 9.0 10.5 I2.O	t 0.2 O.2 0-3	I O.I O.I O.I
S 57 58 59	9.13 904 9-13 994 9.14085 9-14 175 9.14 266	91 90 91 90 91	9.14 320 9.14 412 9.14 504 9-14 597 9.14 688	93 92 92 93 91	0.85 680 0.85 588 0.85 496 0.85 403 0.85 312	9-99 584 9-99 582 9-99 58i 9-99 579 9-99 577	5 4 3 2 I	9 1C 2C 3C 4c	13-5 15.0 3O.O 45-o 60.0	0-3 o-3 0.7 I.O i-3	0.2 0.2 o-3 0.5 0.7 o 8
60	9-14 356	90	9.14780	92	0.85 220	9-99 575	0	5^
	L. Cos.	d.	L,. Cotg.	c. d.	L.Tang.	L. Sin.	A		Prop	. Pt!	!•

82<

8<

/•	L. Sin. | d.	L.Taug. c. d.	L. Cotg.	L. Cos.		Prop. Pts.
0 I 2 3 4	9-i4 356 9-H445 9-i4 535 9.14624 9.14 714	89 90 89 90 89 88 89 89 88 88 88 88 87 88 87 87 87 87 86 86 87 86 85 86 85 86 85 85 85 84 85 84 84 84 84 83 84 83 83 83 83 83 82 82	9.14780 9.14 872 9.14963 9-i5 °54 9-iS 145	92 91 9^ 91 91 91 90 91 90 90 89 90 89 90 89 89 88 89 88 88 88 88 88 87 88 87 87 87 86 87 86 86 86 86 86 85 86 85 85 85 85 84 85 84 84 84 84 83 84 83 83 83 83 83 83 82 82 82 82 82	0.8S 220 0.85 128 0.85 037 0.84 946 0.84 855	9-99 575 9-99 574 9-99 572 9-99 570 9-99 568	6O 59 58 57 56	6 7 8 9 IO 20 3° 40 50 " 6 7 8 9 10 20 3° 4° 50 i 6 7 8 9 10 20 30 40 5°	9 9 10 12 13 15 30 46 6 1 76 6 7 8 9 10 20 3° *o 50 8 8 IO ii 13 14 29 43 58 72 6 7 8 9 to 20 3° 10 50 8 8 9 10 12 13 27 41 54 08 6 7 8 9 10 20 3" 40 50	I .2 •7 -3 .8 •3 •7 .0 •3 • 7 { 8 1C ii 13 14 29 44 59 74 1 •7 .2 .6 .1 • 5 .6 •5 .0 •5 i 8 9 ii 12 14 28 42 56 70 1 .2 6 •9 •3 •7 • 3 .0 •7 •3 0 c 0 0 0 c I I I	9 ! K ii i^ i« 3r 45 6c 7: ^ •9 •4 9 •4 .8 •7 •5 •3 .2 8 £ 1C i] i: 14 •2t 4'- 53 71 k •4 .8 .2 .6 .0 .0 .0 .0 .0 8 S 9 1C 12 13 2? 4c 54 6) 2 .2 .2 •3 •3 •3 •7 .0 •3 •7	i .1 >.6 .1 •7 .2 •3 -5 • 7 .8 8 8 10 II 13 14 29 44 58 73 6 .6 .0 •5 •9 ^•3 •7 .0 •3 •7 8 8 9 ii 12 13 27 41 55 69 i .1 •5 .8 .2 •5 .0 •5 .0 •5 X 0. 0. 0. 0. 0. o. 0. 0.' 0.	90 9-o 10.5 12.0 13-5 15.0 30.0 45-0 60.0 75-0 3 .8 •3 •7 .2 •7 •3 .0 •7 •3 85 . 8-5 9-9 ii-3 12.8 14.2 28.3 42.5 56.7 70.8 3 •3 -7 .1 .8 •7 •5 •3 .2 80 8.0 9-3 10.7 12.0 13-3 26.7 4O.O 53-3 66.7 1 [ c i i j 7 J
6 7 8 9	9.14803 9.14 891 9.14 980 9.15 069 9-i5 157	9.15 236 9-i5 327 9-i5 4i7 9-i5 508 9-i5 598	0.84 764 0.84 673 0.84 583 0.84 492 0.84 4O2	9-99 566 9-99 565 9-99 563 9-99 56i 9-99 559	55 54 53 52 5i
10 ii 12 J3 14	9-i5 245 9-15 333 9.15 421 9.15 508 9-iS 596	9.15 688 9-15 777 9.15 867 9-15 956 9.16 046	0.84 312 0.84 223 0.84 I33 0.84 044 0-83 954	9-99 557 9-99 556 9-99 554 9-99 552 9-99 550	50 49 48 47 46
15 16 17 18 19	9-15 683 9.15 770 9-15 857 9-15 944 9.16 030	9-i6 135 9.16 224 9.16 312 9.16 401 9.16 489	0.83 865 0.83 776 0.83 688 0-83 599 0.83 511	9-99 548 9-99 546 9-99 545 9-99 543 9-99 54i	45 44 43 42 4i
20 21 22 23 24	9.16 116 9.16 203 9.16 289 9.16 374 9.16 460	9.16 577 9.16 665 9-i6 753 9.16 841 9.16 928	0.83 423 0-83 335 0.83 247 0.83 159 0.83 072	9-99 539 9-99 537 9-99 535 9-99 533 9-99 532	40 39 38 %
25 26 27 28 29	9-i6 545 9.16 631 9.16 716 9.16 801 9.16 886	9.17 016 9.17 103 9.17 190 9.17 277 9-17 363	0.82 984 0.82 897 0.82 810 0.82 723 0.82 637	9-99 530 9.99 528 9-99 526 9-99 524 9-99 522	35 34 33 32 31
3O 3i 32 33 34	9.16 970 9-17 055 9.17 139 9.17 223 9.17 307	9 17 450 9-17 536 9.17 622 9.17 708 9.17 794	0.82 550 0.82 464 0.82 378 0.82 292 0.82 206	9-99 520 9-99 5i8 9-99 517 9-99 515 9-99 513	30 29 28 27 26
35 36 37 38 39	9.17 391 9.17 474 9-17 558 9.17 641 9.17 724	9.17 880 9.17 965 9.18 051 9.18 136 9.18 221	0.82 120 O.82 035 o 81 949 0.81 864 0.8 1 779	9.99 511 9.99 509 9-99 507 9-99 5°5 9-99 503	25 24 23 22 21
40 4i 42 43 44	9.17 807 9.17 890 9-17 973 9-i8 055 9.18 137	9.18 306 9 18 391 9-i8 475 9.18 560 9.18 644	0.81 694 0.81 609 0.81 525 0.81 440 0.81 356	9.99 501 9-99 499 9-99 497 9-99 495 9-99 494	2O 19 18 17 16
11 47 48 49	9.18 220 9.18 302 9-18 383 9.18 465 9.18 547	83 82 8z 82 82 81 81 81 81 81 0-	9.18 728 9.18 812 9.18 896 9.18 979 9.19 063	0.81 272 0.81 188 0.8 1 104 0.81 021 0.80 937	9.99 492 9.99 490 9-99 488 9.99 486 9-99 484	IS 14 13 12 II
50 5i 52 53 54	9.18 628 9.18 709 9.18 790 9.18 871 9-i8 952	9.19 146 9.19 229 9.19 312 9-19 395 9.19 478	0.80 854 0.80 771 0.80 688 0.80 605 0.80 522	9-99 482 9-99 48o 9-99 478 9-99 476 9.99 474	10 9 8 7 6
11 57 58 59	9-19 033 9.19 113 9.19 193 9.19 273 9-19 353	80 80 80 80 0-.	9-19 S^i 9.19 643 9.19 725 9.19 807 9.19 889	0.80 439 0.80 357 0.80 275 0.80 193 0.80 in	9-99 472 9-99 470 9 99 468 9.99 466 9-99 464	5 4 3 2 I
GO	'.."- m		9.19 971	0.80 029	9-99 462	o
	L. Cos. j d.	L. Cotg. c. d.JL.Tang.	L. Sin.	f	Prop. Pts.

81°

9'

/	L. Sin.	d.	L.Tang.	c. d.	L. Cots.	JL. Cos.		Prop. Pts.
0 I 2 3 4	9-19 433 9-19 513 9.19 592 9.19 672 9-I975I	80 79 80 79 79 79 79 79 78 78 79 78 78 77 78 78 77 77 77 77 77 77 76 77 -f.	9.19 971 9.20 053 9-20 134 9.20 216 9.20 297	82 81 82 81 81 81 81 81 80 81 80 80 80 80 80 79 80 79 79 79 79 79 78 79 78 78 78 78 78 78 77 78 77 77 77 77 77 76 77 76 76 77 76 76 75 76 75 76 75 75 75 75 75 74 75 74 75 74 74 74	0.80 029 0.79 947 0.79 866 0.79 784 0.79 703	9.99 462 9-99 460 9-99 458 9.99 456 9-99 454	60 59 58 57 56	8 6 8 7 S 8 ic	2 .2 .6 •9 •3 •7 •3 .0 •7 •3 7 7 9 1C ii 13 2C 35 S^ 6 = 7 7 5 1C ii 12 25 38 51 64 7 7 8 10 ii 12 25 37 50 62 3 •3 •5 •7 .0 .2 •3 -5 •7 .8 o 0 0 0 0 I I 2 2	{ i c 1C 1: i: 2: 4C 5^ 6; 9 •9 .2 •5 •9 .2 •3 •5 • 7 .8 7 •7 .0 •3 .6 .8 •7 •5 •3 .2 5 •5 .8 .0 •3 •5 .0 •5 .0 •5 7 7 g 9 1C 12 24 3^ 48 6c 3 •3 •4 •4 •5 .0 • 5 .0 •5	i 5.i )-5 ).8 J.2 !-5 '.0 '•5 [.0 '•5 7 7 5 1C ii 13 2e 35 52 6 = 7 7 8 1C ii 12 25 38 50 63 7 7 8 9 ii 12 24 37 49 61 2 .2 •4 .6 .8 .0 .0 .0 .0 .0 2 o.: o.: O.' o-: o-: o.; I.C i-: i.;	so 8.0 9-3 10.7 I2.O 13-3 26.7 40.0 53-3 66.7 8 .8 .1 •4 •7 .0 .0 .0 .0 .0 6 .6 •9 .1 •4 •7 •3 .0 •7 •3 4 •4 .6 •9 .1 •3 •7 .0 •3 •7 7i 7-1 8-3 9-5 10.7 H.8 23-7 35-5 47-3 59-2 z z J 3 J T ) J 7
5 6 7 8 9	9.19 830 9.19 909 9.19 988 9.20 067 9.20 145	9.20 378 9.20 459 9.20 540 9.20 621 9.20 701	0.79 622 0.79 541 0.79 460 0.79 379 0.79 299	9-99 452 9-99 450 9-99 448 9-99 446 9.99 444	55 54 53 52 5i	9 is 10 13 20 27 30 41 4° 54 50 68 6 7 8
10 ii 12 13 14	9.20 223 9.20 302 9.20 380 9.20 458 9-20 535	9.20 782 9.20 862 9.20 942 9.21 022 9-21 IO2	0.79 218 0.79 138 0.79 058 0.78 978 0.78 898	9-99 442 9-99 440 9-99 438 9-99 436 9-99 434	50 49 48 47 46
15 16 17 18 19	9.20 613 9.20 691 9.20 768 9-20 845 9.20 922	9.21 182 9-21 26l 9-21 341 9.21 420 9.21 499	0.78 818 0.78 739 0.78 659 0.78 580 0.78 501	9-99 432 9-99 429 9-99 427 9-99 425 9-99 423	45 44 43 42 4i	9 10 20 30 40 CQ
2O 21 22 23 24	9-20 999 9.21 076 9-21 153 9.21 229 9.21 306	9-21 578 9.21 657 9.21 736 9.21 814 9.2! 893	0.78 422 0.78 343 0.78 264 0.78 186 0.78 107	9-99 421 9-99 419 9-99 417 9-99 415 9-99 413	40 39 38 37 36	6 8
25 26 27 28 29	9.21 382 9.21 458 9-21 534 9.21 610 9.21 685	76 76 76 75 76 75 76 75 75 75 74 75 75 74 74 74 74 74 74 73 74 73 73 73 73 73 73 72 73 72 72 73 71 72 72	9.21 971 9.22 049 9.22 127 9-22 2O5 9-22 283	0.78 029 0.77 951 o.77 873 0-77 795 0.77 717	9.99 411 9-99 409 9.99 407 9.99 404 9-99 402	35 34 33 32 3i	9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 7 6 7 7 8 8 9 9 " 10 12 20 24 30 36 40 48 50 60 6 7 8 9 10 20 30 40 50
30 3i 32 33 34	9.21 761 9.21 836 9.21 912 9.21 987 9.22 062	9.22 361 9.22 438 9-22 516 9-22 593 9.22 670	0.77 639 0.77 562 0.77 484 0.77 407 0.77 330	9.99 400 9-99 398 9-99 396 9-99 394 9-99 392	30 29 28 27 26
35 36 37 38 39	9.22 137 9-22 211 9-22 286 9-22 361 9-22 435	9.22 747 9.22 824 9.22 901 9.22 977 9-23 054	0.77 253 0.77 176 0.77 099 0.77 023 0.76 946	9.99 390 9-99 388 9-99 385 9-99 383 9-99 38i	25 24 23 22 21
40 4i 42 43 44	9.22 509 9-22 583 9.22 657 9-22 731 9.22 805	9.23 130 9.23 206 9.23 283 9-23 359 9-23 435	0.76 870 0.76 794 0.76 717 0.76 641 0.76 565	9-99 379 9-99 377 9-99 375 9.99 372 9-99 370	20 19 18 17 16
45 46 47 48 49	9.22 878 9.22 952 9.23 025 9.23 098 9.23 171	9.23 510 9.23 586 9.23 661 9-23 737 9.23 812	0.76 490 0.76 414 0.76 339 0.76 263 0.76 188	9-99 368 9-99 366 9-99 364 9.99 362 9-99 359	15 14 13 12 II
50 Si 52 53 54	9.23 244 9-23 317 9.23 390 9.23 462 9-23 535	9-23 887 9.23 962 9.24 037 9.24 112 9.24 186	0.76 113 0.76 038 o.75 963 0.75 888 0.75 814	9-99 357 9-99 355 9-99 353 9-99 35i 9-99 348	10 9 8 6
55 56 57 58 59	9.23 607 9.23 679 9-23 752 9.23 823 9-23 895	9.24 261 9-24 335 9.24 410 9.24 484 9-24 558	0.75 739 0.75 665 0-75 590 0-75 5i6 0.75 442	9.99 346 9-99 344 9-99 342 9.99 340 9-99 337	5 4 3 2 I
60	9.23 967	9.24 632	0.75 368	9-99 335	0
	JL. Cos.	d.	L,. Cotg.	C. d.	L.Tang.	L. Sin.	/•	Prop. Pts.

8OC

10'

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Pi	op. 1	*ts.
0 I 2 3 4	9.23 967 9.24 039 9.24 no 9.24 181 9-24 253	72 71 7* 72	9.24 632 9.24 706 9.24 779 9-24 853 9.24 926	74 73 74 73	0.75 368 0.75 294 0.75 221 0-75 147 o.7S 074	9-99 335 9-99 333 9-99 331 9.99 328 9-99 326	2 2 3 2	60 59 58 57 56	6 7 8	74 7-4 8.6 9-9	73 7-3 8-5 9-7
5 6 7 8 9	9.24 324 9-24 395 9.24 466 9-24 536 9.24 607	71 7i 7i 70 7i	9.25 ooo 9-25 073 9.25 146 9-25 219 9.25 292	74 73 73 73 73	0.75 ooo 0.74 927 0.74 854 9.74 781 0.74 708	9-99 324 9-99 322 9-99 319 9-99 3J7 9-99 315	2 3 2 2	55 54 53 52 51	y 10 20 30 40 CO	II. I 12.3 24.7 37-0 49-3 6l 7	n.o 12.2 24-3 36.5 48.7- 60 8
10 ii 12 13 14	9.24 677 9.24 748 9.24 818 9.24 888 9.24 958	70 7i 70 TO 70	9-25 365 9-25 437 9-25 5io 9-25 582 9-25 655	73 72 73 72 73	0.74 635 0.74 563 0.74 490 0.74 418 0.74 345	9-99 313 9.99 310 9-99 308 9-99 306 9-99 3°4	3 2 2 2	50 49 48 47 46	6 8	72 7.2 8.4 9.6	7i 7-1 8-3 9-5
15 16 17 18 19	9.25 028 9.25 098 9.25 168 9-25 237 .9-25 307	70 70 69 70 fm	9.25 727 9-25 799 9.25 871 9-25 943 9.26 015	72 72 72 72 72	0.74 273 0.74 201 0.74 129 0.74 057 0-73 985	9.99 301 9.99 299 9-99 297 9-99 294 9-99 292	3 2 2 3 2	45 44 43 42 4i	9 10 20 30 40 CQ	10.8 12.0 24.0 36.0 48.0 60 o	10.7 11.8 23-7 35-5 47-3
20 21 22 23 24	9-25 376 9-25 445 9-25 514 9-25 583 9.25 652	09 69 69 69 69	9.26 086 9.26 158 9.26 229 9.26 301 9.26 372	71 72 7i 72 7i	0-73 9M 0.73 842 0.73 771 0.73 699 0.73 628	9.99 290 9.99 288 9-99 285 9-99 283 9.99 281	2 3 2 2	40 39 38 1	6 7 8	70 7.0 8.2 9-3	69 6.9 8.1 9-2
5 27 28 29	9-25 721 9.25 790 9.25 858 9.25 927 9-25 995	°9 69 68 69 68 68	9.26 443 9.26 514 9.26 585 9.26 655 9.26 726	71 71 7i 70 7i	o.73 557 0.73 486 0-73 415 0-73 345 0.73 274	9-99 278 9.99 276 9.99 274 9-99 271 9-99 269	2 2 3 2	35 34 33 32 .31	y 10 20 30 40 CQ	10.5 11.7 23-3 35-o 46.7 cR q	10.4 "•5 23.0 34-5 46.0 C,7 e
30 3i 32 33 34	9.26 063 9.26 131 9.26 199 9.26 267 9-26 335	68 68 68 68 68	9.26 797 9.26 867 9.26 937 9.27 008 9.27 078	70 70 7i 70	0.73 203 0-73 133 0.73 063 0.72 992 0.72 922	9-99 267 9.99 264 9.99 262 9.99 260 9-99 257	3 2 2 3	30 29 28 27 26	6 7 8	68 6.8 7-9 9-i	67 6-7 7-8 8.9
35 36 37 38 39	9.26 403 9.26 470 9.26 538 9.26 605 9.26 672	67 68 67 67 £.-	9.27 148 9.27 218 9.27 288 9-27 357 9.27 427	70 70 70 69 70	0.72 852 0.72 782 0.72 712 0.72 643 0.72 573	9-99 255 9-99 252 9-99 250 9-99 248 9-99 243	3 2 2 3	25 24 23 22 21	9 10 20 30 40	IO.2 "•3 22.7 34-0 45-3 c.6 7	IO.I II. 2 22.3 33-5 44-7 re 8
40 4i 42 43 44	9.26 739 9.26 806 9.26 873 9.26 940 9.27 007	O7 67 67 67 67	9.27 496 9.27 566 9-27 635 9-27 704 9.27 773	09 70 69 69 69	0.72 504 0.72 434 0.72 365 0.72 296 0.72 227	9-99 243 9-99 241 9-99 238 9-99 236 9-99 233	2 3 2 3	20 19 18 17 16	6 7 8	66 6.6 7-7 8.8	65 6-5 7.6 8-7
45 46 47 48 49	9.27 073 9.27 14° 9.27 206 9.27 273 9-27 339	67 66 67 66	9.27 842 9.27 911 9.27 980 9.28 049 9.28 117	69 69 69 69 68	0.72 158 0.72 089 0.72 020 0.71 951 0.71 883	9-99 231 9-99 229 9.99 226 9-99 224 9.99 221	2 3 2 3	IS 14 13 12 II	9 10 20 30 40	y-y n.o 22.0 S3-0 44.0	9.8 10.8 21.7 32.5 43-3
5O 5i 52 53 54	9x27 405 9.27 471 9-27 537 9.27 602 9.27 668	66 66 65 66	9.28 186 9.28 254 9.28 323 9-28 391 9.28 459	69 68 69 68 68	0.71 814 0.71 746 0.71 677 0.71 609 0.71 541	9-99 219 9-99 217 9-99 214 9.99 212 9-99 209	2 3 2 3	10 9 8 7 6	ou 6 \7 8	33-v 3 0-3 0.4 0.4	a 0.2 O.2 0-3
55 56 57 58 59	9-27 734 9.27 799 9.27 864 9.27 930 9-27 995	65 65 66 65	9.28 527 9-28 59? 9.28 662 9.28 730 9.28 798	68 67 63 68 fit	0.71 473 0.71 405 0.71 338 0.71 270 0.71 202	9-99 207 9.99 204 9.99 202 9.99 200 9-99 197	3 2 2 3	5 4 3 a i	9 10 20 30 40	0-5 0-5 z.o 1-5 2.0 2 ^	0-3 0-3 0.7 1.0 i-3 I 7
GO	9.28 060	°5	9.28 865	07	0.71 135	9-99 195		0
	L. Cos.	d.	L. Cotg.	c. d.	L.TniiK.	L. Sin.	d.	r	Pr	op. 1	Ms.

79<

11'

33

/•	L. Sin.	d.	L.Tang.	c. d.! L. Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9.28 060 9.28 125 9.28 190 9.28 254 9.28 319	65 65 64 65 65 64 64 65 64 64 64 64 63 64 64 63 63 64 63 63 63 63 63 62	9.28 865 9-28 933 9.29 ooo 9.29 067 9.29 134	68 67 67 67 67 67 67 67 66 67 66 67 66 66 66 66 66 66 66 65 66 65 65 66 65 65 65 65 65 64 65 64 65 64 64 65 64 64 64 64 63 64 63 64 63 64 63 63 63 63 63 63 63 62 63 62 63 62 62 62	0-71 135 0.71 067 0.71 ooo 0.70 933 0.70 866	9-99 195 9.99 192 9.99 190 9.99 187 9.99 185	3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 ,3 2 3 2 3 3 2 3 2 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3	60 59 58 57 56	6 7 8 9 10 20 30 40 50 6 7 8 9 10 "20 3° 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 8 9 10 20 30 40 50	68 6.8 7-9 9-i 10.2 "•3 22.7 34-° 45-3 56.7 66 6.6 7-7 8.8 9-9 II.O 22.0 33-° 44.0 55.0 64 6.4 7-5 8-5 9.6 10.7 21.3 32.0 42.7 53-3 62 6.2 7.2 8-3 9-3 10.3 20.7 31.0 41-3 51-7 60 6.0 7.0 8.0 9.0 IO.O 20.0 30.0 4O.O 50.0 3 o-3 0.4 0.4 0.5 o.S I.O Jt-S 2.0 2.5	67 6-7 7.8 8.9 10. 1 II.2 22.3 33-5 44-7 55-8 65 6-5 7.6 8.7 9-8 10.8 21.7 32.5 43-3 54-2 63 6-3 7-4 8.4 9-5 10.5 21.0 31-5 42.0 52.5 61 6.1 7-1 8.1 9-2 10.2 20.3 30.5 40.7 50.8 59 5-9 6-9 7-9 8.9 9.8 19.7 29-5 39-3 49.2 2 0.2 0.2 0-3 °-3 0-3 0.7 I.O i-3 1-7
6 .7 8 '9	9.28 384 9.28 448 9.28 512 9.28 577 9.28 641	9.29 2OI 9.29 268 9-29 335 9.29 402 9.29 468	0.70 799 0.70 732 0.70 665 0.70 598 0.70 532	9.99 182 9.99 180 9.99 177 9-99 175 9.99 172	55 54 53 52 5i
10 ii 12 13 14	9.28 705 9.28 769 9.28 833 9.28 896 9.28 960	9-29 535 9.29 601 9.29 668 9-29 734 9.29 800	0.70 465 .0-7° 399 0.70 332 0.70 266 0.70 200	9.99 170 9.99 167 9.99 165 9.99 162 9.99 160	50 49 48 47 46
15 16 17 18 19	9.29 024 9.29 087 9-29 150 9.29 214 9.29 277	9.29 866 9.29 932 9.29 998 9.30 064 9.30 130	0.70 134 0.70 068 0.70 002 0.69 936 0.69 870	9-99 157 9-99 155 9.99 152 9-99 ISO 9.99 147	45 44 43 42 4i
20 21 22 23 24	9.29 340 9.29 403 9.29 466 9.29 529 9.29 591	9-3° 195 9.30 261 9.30 326 9-30 391 9-30 457	0.69 805 0.69 739 0.69 674 0.69 609 0-69 543	9-99 145 9-99 142 9-99 140 9-99 137 9-99 135	40 39 38 37 36
25 26 27 28 29	9.29 654 9.29 716 9.29 779 9.29 841 9.29 903	°3 62 63 62 62	9.30 522 9-30 587 9.30 652 9.30 717 9.30 782	0.69 478 0.69 413 0.69 348 0.69 283 0.69 218	9-99 132 9-99 130 9-99 127 9.99 124 9.99 122	35 34 33 32 3i
30 3i 32 33 34	9.29 966 9.30 028 9.30 090 9-30 151 9.30 213	°3 62 62 61 62	9.30 846 9.30 911 9-30 975 9.31 040 9.31 104	0.69 154 0.69 089 0.69 025 0.68 960 0.68 896	9.99 119 9.99 117 9.99 114 9.99 112 9.99 109	30 29 28 27 26
11 37 38 39	9-30 275 9-30 336 9-30 398 9-30 459 9.30 521	61 62 6x 62 61 61 61 61 61 61 60 61 60 61 60 61 60 60 60 60 59 60 60 59 60	9.31 168 9-31 233 9.31 297 9.31 361 9-31 425	0.68 832 0.68 767 0.68 703 0.68 639 0.68 575	9.99 106 9-99 104 9.99 101 9.99 099 9.99 096	25 24 23 22 21
40 4i 42 43 44	9.30 582 9-30 643 9.30 704 9-30 765 9.30 826	9.31 489 9-3i 552 9.31 616 9.31 679 9-31 743	0.68 511 0.68 448 0.68 384 0.68 321 0.68 257	9.99 093 9-99 °9i 9.99 088 9.99 086 9.99 083	2O 19 18 17 16
45 46 47 48 49	9.30 887 9-30 947 9.31 008 9.31 068 9.31 129	9.31 806 9.31 870 9-3i 933 9.31 996 9-32 059	0.68 194 0.68 130 0.68 067 0.68 004 0.67 941	9.99 080 9-99 078 9-99 075 9-99 072 9.99 070	IS 14 13 12 II
50 5i 52 53 54	9.31 189 9.31 250 9.31 310 9-31 370 9-3i 430	9.32 122 9.32 185 9.32 248 9.32 311 9-32 373	0.67 878 0.67 815 0.67 752 0.67 689 0.67 627	9.99 067 9.99 064 9.99 062 9-99 059 9.99 056	10 9 8 6
55 56 57 58 59	9.31 490 9-3i 549 9.31 609 9.31 669 9.31 728	9-32 436 9.32 498 9.32 561 9.32 623 9.32 685	0.67 564 0.67 502 0.67 439 0.67 377 0.67 315	9-99 054 9.99 051 9.99 048 9.99 046 9-99 043	5 4 3 2 I
60	9.31 788	9-32 747	0.67 253	9.99 040	0
	L. Cos.	d.	L. Cotg. c. d.	L.Tang.	L. Sin.	d.	/•	Prop. Pts.

78(

34

/•	1 . Sin.	d.	L.Taug. c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
0 I 2 3 4	9.31 788 9.31 847 9.31 907 9.31 966 9.32 025	59 60 59 59 59 59 59 59 58 59 59 58 58 59 58 58 58 58 58 58 58 57 58 57 58 57 57 58 57 57 57 56 57 57 57 56 57 56 56 57 56 56 56 56 56 56 55 56 55 56 55 56 55 55 55 55 55 55 55	9-32 747 9.32 810 9-32 872 9-32 933 9-32 995	63 62 61 62 62 62 61 62 61 62 61 61 61 61 61 61 61 61 60 61 60 61 60 60 61 60 60 60 60 60 59 60 60 59 60 59 59 59 60 59 59 59 59 58 59 59 58 59 58 59 58 58 58 58 58 58 58 58 58 57	0.67 253 0.67 190 0.67 128 0.67 067 0.67 005	9.99 040 9.99 038 9-99 035 9-99 032 9-99 030	2 3 3 2 3 3 2 3 3 3 2 3 3 3 2 3 3 3 2 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3- 3	60 59 58 57 56	6 7 8	63 6-3 7-4 8.4	62 6.2 7.2 8-3 93 10.3 20.7 31-0 41-3 5i-7 60 6.0 7.0 8.0 9.0 10.0 20.0 3O.O 40.0 50.0 9 •9 •9 •9 •9 .8 •7 •5 •3 .2 57 5-7 6-7 7-6 8.6 9-5 19.0 28.5 38.0 47-5 55 % 7-3 8-3 9.2 18.3 27-5 36.7 45-8 3 0.2 0.2 0-3 0-3 0-3 0.7 I.O i-3 1-7
6 7 8 9	9.32 084 9-32 M3 9.32 202 9.32 261 9-32 319	9-33 057 9-33 H9 9-33 180 9-33 242 9-33 303	0.66 943 0.66 881 0.66 820 0.66 758 0.66 697	9.99 027 9.99 024 9.99 022 9.99 019 9.99 016	55 54 53 52 5i	9 10 20 3° 40	9-5 10.5 21.0 31-5 42.O 52.5 61 6.1 7-i 8.1 9-2 10.2 20.3 30.5 40.7 50.8 5 6 e 7 * 8 7 9 * 10 9 20 19 30 29 *o 35 50 49 58 5-8 6.8 7-7 8.7 9-7 19-3 29.0 38.7 48.3 56 5-6 6.5 il 93 18.7 28.0 37-3 46.7 3 0-3 0.4 0.4 0-5 0-5 I.O i-5 2.0 3-5
10 ii 12 13 14	9-32 378 9-32 437 9-32 495 9-32 553 9.32 612	9 33 365 9-33 426 9-33 487 9-33 548 9-33 609	0.66 635 0.66 574 0.66 513 0.66 452 0.66 391	9-99 013 9.99 on 9.99 008 9-99 005 9.99 002	50 49 48 47 46	5° 6 7 8
15 16 17 18 19	9.32 670 9.32 728 9.32 786 9.32 844 9.32 902	9-33 670 9-33 731 9-33 792 9-33 853 9-33 913	0.66 330 0.66 269 0.66 208 0.66 147 0.66 087	9.99000 9.98 997 9.98 994 9.98 991 9.98 989	45 44 43 42 4i	9 10 20 3° 40
20 21 22 23 24	9-32 960 9.33 018 9-33 075 9-33 133 9-33 190	9-33 974 9-34 °34 9-34 °95 9-34 155 9-34 215	0.66 026 0.65 966 0.65 905 0.65 845 0.65 785	9.98 986 9.98 983 9.98 980 9.98 978 9-98 975	4O 39 38 |	5° 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50
25 26 27 28 29	9-33 248 9-33 305 9-33 362 9-33 420 9-33 477	9.34 276 9-34 336 9-34 396 9-34 456 9-34 5i6	0.65 724 0.65 664 0.65 604 0-65 544 0.65 484	9.98 972 9.98 969 9.98 967 9.98 964 9.98 961	35 34 33 32 3i
30 3i 32 33 34	9-33 534 9-33 59i 9-33 647 9-33 704 9-33 76i	9-34 576 9-34 635 9-34 695 9-34 755 9-34 814	0.65 424 0.65 365 0.65 305 0.65 245 0.65 186	9.98 958 9-98 955 9-98 953 9.98 950 9.98 947	3O 29 28 27 26
35 36 11 39	9-33 818 9-33 874 9-33 93i 9-33 987 9-34 043	9-34 874 9-34 933 9-34 992 9-35 051 9-35 I"	0.65 126 0.65 067 0.65 008 0.64 949 0.64 889	9.98 944 9.98 941 9.98 938 9.98 936 9-98 933	25 24 23 22 21
40 4i 42 43 44	9-34 ioo 9-34 156 9-34 212 9-34 268 9-34 324	9-35 170 9-35 229 9-35 288 9-35 347 9-35 405	0.64 830 0.64 771 0.64 712 0.64 653 0.64 595	9.98 930 9.98 927 9.98 924 9.98 921 9.98 919	20 19 18 17 16
;t 47 48 49	9-34 38o 9-34 436 9-34 49i 9-34 547 9-34 602	9-35 464 9-35 523 9-35 58i 9-35 640 9-35 698	0.64 536 0.64 477 0.64 419 0.64 360 0.64 302	9.98 916 9.98 913 9.98 910 9.98 907 9.98 904	15 14 13 12 II
:>o 51 52 53 54	9-34 658 9-34 713 9-34 769 9-34 824 9-34 879	9-35 757 9-35 815 9-35 873 9-35 93i 9-35 989	0.64 243 0.64 185 0.64 127 0.64 069 0.64 on	9.98 901 9.98 898 9.98 896 9.98 893 9.98 890	3 2 3 3	10 9 8 7 6
Cn Cn Cn Cn en \O oovj O\cn	9-34 934 9-34 989 9-35 044 9-35 099 9-35 154	9.36 047 9.36 105 9.36 163 9.36 221 9.36 279	0.63 953 0.63 895 0.63 837 0.63 779 0.63 721	9.98 887 9.98 884 9.98 881 9.98 878 9.98 875	3 3 3 3 3	5 4 3 2 I
60	, - . -		9-36 S36	0.63 664	9.98 872		o
	L. Cos. d.	L. < otg. c. d. L.Tang.	L. Sin.	d.	r	Prop. Pts.

77<

35

/•	L. Sin.	d.	L.Taug.	c. d	L. Cotg	L. Cos.	d.		P]	rop.	Pts.
o I 2 3 4	9-35 209 9-35 263 9-35 3i8 9-35 373 9-35 427	54 55 55 54	9-36 336 9-36 394 9-36 452 9-36 509 9.36 566	58 58 57 57 eg	0.63 664 0.63 606 0.63 548 0.63 491 0-63 434	9.98 872 9.98 869 9.98 867 9.98 864 9.98 861	3 2 3 3	GO 59 58 57 56	6 •7 8	58 5-8 6.8 7-7	57 5-7 6.7 7-6
5 6 7 8 9	9-35 48i 9-35 536 9-35 590 9-35 644 9-35 698	55 54 54 54	9.36 624 9.36 681 9-36 738 9-36 795 9.36 852	57 57 57 57	0.63 376 0.63 319 0.63 262 0.63 205 0.63 148	9.98 858 9-98 855 9-98 852 9.98 849 9.98 846	3 3 3 3	55 54 53 52 5i	9 10 20 30 40	8.7 9-7 19-3 29.0 38.7 /ifi o	8.6 9-5 19.0 28.5 38.0
1O ii 12 13 14	9-35 752 9-35 806 9-35 860 9-35 9H 9-35 963	54 54 54 54	9.36 909 9.36 966 9-37 023 9-37 080 9-37 137	57 57 57 57 rfi	0.63 091 0.63 034 0.62 977 0.62 920 0.62 863	9.98 843 9.98 840 9.98 837 9.98 834 9.98 831	3 3 3 3	50 49 48 47 46	5° 6 7 8	4° o 56 5-6 6-5 7-5	47-5 55 5-5 6.4 7-3
15 16 17 18 19	9.36 022 9-36 075 9.36 129 9.36 182 9.36 236	53 54 53 54	9-37 193 9-37 250 9-37 3°6 9-37 363 9-37 419	57 56 57 56	0.62 807 0.62 750 0.62 694 0.62 637 0.62 581	9.98 828 9.98 825 9.98 822 9.98 819 9.98 816	3 3 3 3	45 44 43 42 4i	9 10 20 30 40	8.4 9-3 18.7 28.0	8-3 9.2 18.3 27.5 36.7 A C 8
2O 21 22 23 24	9.36 289 9-36 342 9-36 395 9.36 449 9.36 502	53 53 54 53	9-37 476 9-37 532 9-37 588 9-37 644 9-37 700	56 56 56 56 cfi	0.62 524 0.62 468 0.62 412 0.62 356 0.62 300	9.98 813 9.98 810 9.98 807 9.98 804 9.98 801	3 3 3 3	4O 39 38 37 36	Ou	46.7 5 6 c 7 ^ 8 7	45-° 4 4 •3 .2
25 26 27 28 29	9-36 555 9.36 608 9.36 660 9-36 713 9.36 766	53 52 53 53	9-37 756 9-37 812 9-37 868 9-37 924 9-37 980	56 56 56 56	0.62 244 0.62 188 0.62 132 0.62 076 0.62 020	9.98 798 9-98 795 9.98 792 9.98 789 9.98 786	3 3 3 3	35 34 33 32 3i	,	9 iJ [o 9 20 18 50 27 (.0 36	.1 .O .0 .0 .0
3O 3i 32 33 34	9.36 819. 9.36 871 9.36 924 9.36 976 9-37 028	52 53 52 52	9-38 035 9-38 091 9.38 147 9.38 202 9-38 257	56 56 55 55 rf)	0.61 965 0.61 909 0.61 853 0.61 798 0.61 743	9.98 783 9.98 780 9.98 777 9.98 774 9.98 771	3 3 3 3	30 29 28 27 26	6 7 8	>° 45 53 5-3 6.2 7-i	5» 5-2 6.1 6.9
35 36 37 38 39	9-37 081 9-37 133 9-37 185 9-37 237 9-37 289	52 52 52 52	9-38 313 9.38 368 9-38 423 9-38 479 9-38 534	55 55 56 55	0.61 687 0.61 632 0.61 577 0.61 521 0.61 466	9.98 768 9.98 765 9.98 762 9-98 759 9.98 756	3 3 3 3	25 24 23 22 21	9 10 20 3° 40	8.0 8.8 17.7 26.5 35-3	7-8 8-7 17-3 26.0 34-7
40 4i 42 43 44	9-37 341 9-37 393 9-37 445 9-37 497 9-37 549	52 52 52 52	9-38 589 9.38 644 9.38 699 9-38 754 9.38 808	55 55 55 54	0.61 411 0.61 356 0.61 301 0.61 246 0.61 192	9-98 753 9.98 750 9.98 746 9-98 743 9.98 740	3 4 3 3	20 19 18 17 16	5° 6 7 8	44.2 5i 5-i 6.0 6.8	43-3 4 0.4 0.5 °-5
45 46 47 48 49	9-37 600 9-37 652 9-37 703 9-37 755 9-37 806	52 5i 52 5i	9-38 863 9.38 918 9.38 972 9-39 027 9.39 082	55 54 55 55	0.61 137 0.61 082 0.61 028 0.60 973 0.60 918	9-98 737 9-98 734 9.98 731 9.98 728 9.98 725	3 3 3 3	15 14 13 12 II	9 10 20 3° 40	7-7 8-5 17.0 25.5 34-0	0.6 0.7 1-3 2.0 2.7
50 Si 52 53 54	9-37 858 9-37 9°9 9-37 960 9.38 on 9.38 062	51 5i Si 5i	9-39 I36 9-39 19° 9-39 245 9-39 299 9-39 353	54 54 55 54 54	0.60 864 0.60 810 0.60 755 0.60 701 0.60 647	9.98 722 9.98 719 9-98 715 9.98 712 9.98 709	3 3 4 3 3	10 9 8 7 6	5° 6 7 8	42.5 3 0.3 0.4 0.4	3-3 2 0.2 0.2 0-3
55 56 57 58 59	9-38 113 9.38 164 9-38 215 9.38 266 9-38 317	Si 5i 5i 51	9-39 407 9-39 461 9-39 515 9-39 569 9-39 623 j	54 54 54 54	0.60 593 0.60 539 0.60 485 0.60 431 0.60 377	9.98 706 9.98 703 9.98 700 9.98 697 9 98 694	3 3 3 3 3	5' 4 3 2 I	9 10 20 30 40	o-5 0-5 I.O 1-5 2.0	0-3 0-3 0.7 I.O i-3
60	9.38 368		9-39 677	54	0.60 323	9.98 690	4	0	50	2-5	I-7
	L. Cos.	d.	L.Cotg.	c. d.	L.Tang.	L. Sin.	d.	/•	Pr	>|). I	•ts.

76C

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Pi	op.	Pts.
0 i 2 3 4	9.38 368 9.38 418 9.38 469 9-38 519 9-38 57o	50 51 50 5i	9.39 677 9-39 73i 9-39 785 9-39 838 9.39 892	54 54 53 54	0.60 323 0.60 269 0.60 215 0.60 162 0.60 108	9.98 690 9.98 687 9.98 684 9.98 681 9.98 678	3 3 3 3	GO 59 58 57 56	6 7	54 5-4 6.3	53 5-3 6.2
5 6 8 9	9.38 620 9.38 670 9.38 721 9.38 771 9.38 821	50 5i 5o 50	9-39 945 9-39 999 9.40 052 9.40 106 9.40 159	54 53 54 53	0.60 055 0.60 ooi 0.59 948 0.59 894 0.59 841	9.98 675 9.98 671 9.98 668 9.98 665 9.98 662	4 3 3 3	55 54 53 52 5i	8 9 10 20 30	7-2 8.1 9.0 18.0 27.0	7-1 8.0 8.8 17.7 26.5
10 ii 12 13 14	9-38 871 9.38 921 9.38 971 9-39 02! 9-39 071	So 50 50 50	9.40 212 9.40 266 9.40 319 9.40 372 9.40 425	54 53 53 53	0.59 788 0-59 734 0.59 681 0.59 628 o-59 575	9.98 659 9.98 656 9.98 652 9.98 649 9 98 646	3 4 3 3	50 49 48 47 46	40 50	36.0 45-o 5«	35-3 44.2 5i
15 16 17 18 19	9.39 121 9-39 170 9-39 220 9.39 270 9-39 319	49 50 50 49	9.40 478 9-40 531 9.40 584 9.40 636 9.40 689	53 53 52 53	0.59 522 0.59 469 0.59 416 0-59 364 0-59 3"	9.98 643 9.98 640 9.98 636 9-98 633 9.98 630	3 4 3 3	45 44 43 42 4i	6 7 8 9 10	5-2 6.1 6.9 7.8 8-7	& 6.8 7-7 8-5
20 21 22 23 24	9-39 369 9-39 4i8 9-39 467 9-39 517 9-39 566	5° 49 49 So 49	9.40 742 9-40 795 9.40 847 9.40 900 9.40 952	53 52 53 S2	0.59 258 0.59 205 o-59 153 0.59 100 0.59 048	9.98 627 9.98 623 9.98 620 9.98 617 9.98 614	4 3 3 3	40 39 38 37 36	20 30 40 50	17-3 26.0 34-7 43-3	17.0 25-5 34-o 42-5
25 26 27 28 29	9-39 615 9.39 664 9-39 713 9.39 762 9-39 8n	49 49 49 49	9.41 005 9.41 057 9.41 109 9.41 161 9.41 214	52 52 52 53	o-58 995 0-58 943 0.58 891 0.58 839 0.58 786	9.98 610 9.98 607 9.98 604 9.98 601 9 98 597	3 3 3 4	35 34 33 32 3i	• 6 7 8	5° 5-o 5-8 6-7	49 4-9 5-7 6-5
30 3i 32 33 34	9.39 860 9.39 909 9-39 958 9.40 006 9-40 055	49 49 48 49 j.8	9.41 266 9.41 318 9.41 370 9.41 422 9.41 474	52 52 52 52	0-58 734 0.58 682 0.58 630 0.58 578 0.58 526	9.98 594 9.98 591 9.98 588 9-98 584 9.98 581	3 3 4 3	30 29 28 27 26	9 10 20 30 40 co	7-5 8-3 16.7 25.0 33-3 41.7	7-4 8.2 16.3 24-5 32-7 40 8
!i 37 38 39	9.40 103 9.40 152 9.40 200 9.40 249 9.40 297	49 48 49 48	9.41 526 9-41 578 9.41 629 9.41 681 9-41 733	52 5i S2 52	0.58 474 0.58 422 0.58 37i 0.58 319 0.58 267	9.98 578 9-98 574 9.98 571 9.98 568 9.98 565	4 3 3 3	25 24 23 22 21	6	48 4.8 C fi	47 4-7 c •=• •
40 4i 42 43 44	9.40 346 9-40 394 9.40 442 9.40 490 9-40 538	48 48 48 48 A&	9.41 784 9.41 836 9.41 887 9-4i 939 9.41 990	52 Si 52 5i	0.58 216 0.58 164 0.58 113 0.58 061 0.58 oio	9.98 561 9-98 558 9-98 555 9-98 55i 9.98 548	3 3 4 3 3	20 19 18 17 16	7 8 9 10 20 3°	5-° 6-4 7.2 8.0 16.0 24.0	IS 7-1 7-8 15-7 23.5
45 46 47 48 49	9.40 586 9.40 634 9.40 682 9.40 730 9.40 778	48 48 48 48	9.42 041 9.42 093 9.42 144 9.42 195 9.42 246	52 5i Si Si	0-57 959 0.57 907 0.57 856 0.57 805 o.57 754	9-98 545 9.98 541 9-98 538 9-98 535 9-98 53i	4 3 3 4	15 14 13 12 .11	40 50	32.0 40.0 4	31-3 39-2 3
50 Si 52 53 54	9.40 825 9.40 873 9.40 921 9.40 968 9.41 016	47 48 48 47 48	9.42 297 9.42 348 9.42 399 9.42 450 9.42 501	51 5i 5i 5i 5i	0-57 703 0.57 652 0.57 601 0-57 550 o-57 499	9.98 528 9-98 525 9.98 521 9.98 518 9-98 515	3 4 3 3	10 9 8 7 6	6 8 9 10	0.4 o.5 o.S 0.6 0.7	0.3 0.4 0.4 o.5 o-S
P 57 58 59	9.41 063 9.4! in 9-41 158 9.41 205 9.41 252	47 48 47 47 47	9-42 552 9.42 603 9-42 653 9.42 704 9-42 75?	51 5* So 51 5*	0.57 448 0.57 397 0-57 347 0.57 296 0-57 245	9.98 511 9.98 508 9-98 505 9-98 501 9.98 498	3 3 4 3	5 4 3 2 I	20 3° 40 50	1-3 2.0 2.7 3-3	I.O i-5 2.0 2-5
00	9-41 300	4°	9-42 805	5°	0-57 195	9.98 494		0
	L. Cos.	d.	L. Cot£.	c. d.	L.Taiii;.	1,. Sin.	d.	/	1'r	op. 1	•Is.

75<

37

/•	L. Sin.	d.	L.Tang. c. d.	L. Cotg.	JL. Cos.	d.		Prop. Pts.
0 I 2 3 4	9.41 300 9-41 347 9-41 394 9.41 441 9.41 488	47 47 47 47 47 47 46 47 47 46 47 46 47 46 47 46 46 47 46 46 46 46 46 46 45 46 46 46 45 46 45 46 45 46 45 45 46 45 45 45 45 45 45 45 44 45 45 45 44 45 44 45 44 45 44 44 44 45 44 44	9.42 805 9.42 856 9.42 906 9-42 957 9.43 007	51 50 51 50 5° 51 5° So So 50 So 50 So 5° So 49 50 50 49 50 49 50 49 So 49 49 49 So 49 49 49 49 49 49 49 48 49 49 48 49 49 48 49 48 48 49 48 48 48 49 48 48 48 48 48 48 47 48 48 48	0-57 195 0.57 144 0.57 094 0-57 043 0-56 993	9.98 494 9.98 491 9.98 488 9.98 484 9.98 481	3 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 4 3 4 3 4 3 4 3 4 3 4 4 3 4 3 4 3 4 4 3 4 3 4 4 3 4	60 59 58 57 56	6 8 9 10 20 30 40 50 6 7 8 9 10 20 3<> 40 5° 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 3° 40 50	51 5-1 6.0 6.8 7-7 8.5 17.0 25-5 34-° 42.5 49 4.9 5-7 6-5 7-4 8.2 16.3 24-5 32-7 40.8 47 4-7 5-5 6-3 7-1 7.8 15-7 23-5 3i.3 39-2 45 4-5 5-3 6.0 6.8 7-5 15.0 22.5 30.0 37-5 4 0.4 o.S 0-5 0.6 0.7 i-3 2.0 2.7 3-3	50 S-o 5.8 6.7 7-5 8-3 16.7 25.0 33-3 41.7 48 4.8 5.6 6.4 7-2 8.0 16.0 24.0 32.0 40.0 46 4.6 5-4 6.1 6.9 7-7 15.3 23.0 30.7 38.3 44 4.4 5-i 5-9 6.6 7-3 14.7 22.O 29-3 36.7 3 0-3 0.4 0.4 o.S o.S I.O i-5 2.0 2-5
t 7 8 9 1O ii 12 13 14	9-4i 535 9.41 582 9.41 628 9-4i 675 9.41 722	9-43 057 9-43 i°8 9-43 158 9-43 208 9-43 258	0.56 943 0.56 892 0.56 842 0.56 792 0.56 742	9.98 477 9.98 474 9.98 471 9.98 467 9.98 464	55 54 53 52 5i
9.41 768 9.41 815 9.41 861 9.41 908 9-4i 954	9-43 3°8 9 43 358 9-43 408 9.43 458 9 43 5o8	0.56 692 0.56 642 0.56 592 0.56 542 0.56 492	9.98 460 9-98 457 9-98 453 9.98 450 9.98 447	50 49 48 47 46
IS 16 17 18 19	9.42 ooi 9.42 047 9.42 093 9.42 140 9.42 186	9-43 558 9 43 607 9-43 657 9-43 707 9-43 756	0.56-442 0-56 393 0-56 343 0.56 293 0.56 244	9.98 443 9.98 440 9.98 436 9-98 433 9 98 429	45 44 43 42 41
20 21 22 23 24	9.42 232 9.42 278 9.42 324 9.42 370 9.42 416	9-43 806 9-43 855 9-43 9°5 9-43 954 9.44 004	0.56 194 0.56 145 0.56 095 0.56 046 0-55 996	9.98 426 9.98 422 9.98 419 9.98 415 9.98 412	40 39 38 37 36
25 26 27 28 29	9.42 461 9.42 507 9-42 553 9.42 599 9-42 644	9-44 °53 9.44 102 9-44 I5i 9.44 201 9-44 250	o-55 947 0.55 898 0-55 849 o.55 799 0-55 750	9.98 409 9.98 405 9.98 402 9.98 398 9-98 395	35 34 33 32 3i
30 3i 32 33 34	9.42 690 9-42 735 9.42 781 9.42 826 9.42 872	9-44 299 9.44 348 9-44 397 9.44446 9-44 495	0-55 70i 0-55 652 0.55 603 o-SS 554 o-55 5°5	9.98 391 9.98 388 9.98 384 9.98 381 9-98 377	3O 29 28 27 26
35 36 37 38 39	9.42 917 9.42 962 9-43 °°8 9-43 °53 9-43 098	9-44 544 9.44 592 9-44 641 9.44 690 9-44 738	0-55 456 0.55 408 0-55 359 0-55 3io 0.55 262	9-98 373 9.98 370 9.98 366 9-98 363 9-98 359	25 24 23 22 21
40 4i 42 43 44	9-43 143 9-43 188 9-43 233 9-43 278 9-43 323	9-44 787 9-44 836 9-44 884 9-44 933 9.44981	o-55 213 0.55 164 0.55 116 0.55 067 0.55 019	9-98 356 9 98 352 9-98 349 9-98 345 9.98 342	20 19 18 17 16
45 46 47 48 49	9-43 367 9-43 412 9-43 457 9-43 502 9-43 546	9.45 029 9-45 078 9.45 126 9-45 174 9-45 222	0.54 971 0.54 922 0.54 874 0.54 826 0-54 778.	9.98 338 9-98 334 9-98 33i 9.98 327 9.98 324	15 14 13 12 II
5O Si 52 53 54	9-43 59i 9-43 635 9.43 680 9-43 724 9-43 769	9.45 271 9-45 319 9-45 367 9-45 415 9-45 463	0.54 729 0.54 681 0.54 633 0-54 585 °-54 537	9.98 320 9.98 317 9-98 313 9.98 309 9.98 306	10 '9 8 7 6
55 56 57 58 59	9-43 813 9-43 857 9-43 901 9.43 946 9-43 990	9-45 5ii 9-45 559 9-45 606 9-45 654 9-45 7°2	0.54 489 0.54 441 °-54 394 o-54 346 0.54 298	9.98 302 9.98 299 9.98 295 9.98 291 9.98 288	5 4 3 2 I
60	9.44 034	9-45 750	0.54 250	9.98 284	o
	L. Cos.	d.	L.Cotg.	c, d.JL.Tang.	L. Sin.	d.	r	Prop. Pts.

74<

16'

/•	L. Sin.	d.	L.Tang. c. d. L. Cotg.	L. Cos. d.		Prop. Pts.
o I 2 3 4	9-44 034 9-44 078 9.44 122 9.44 166 9.44 210	44 44 44 44 43 44 44 44 43 44 44 43 43 44 43 44 43 43 43 43 43 44 43 42 43' 43 43 43 43 42 43 42 43 42 43 42 43 42 42 42 43 42 42 42 42 42 42 42 4i 42 42 42 41 42 4i 42 4i 42 4» 42	9-45 750 9-45 797 9-45 845 9-45 892 9-45 940	47 48 47 48 47 48 47 48 47 47 47 48 47 47 47 47 47 47 47 46 47 47 47 46 47 47 46 47 46 46 47 46 46 47 46 46 46 46 46 46 46 46 46 46 46 45 46 46 46 45 46 45 46 45 45 46 45 45 46 45	0-54 250 0.54 203 0-54 155 0.54 108 0.54 060	9.98 284 9.98 281 9.98 277 9.98 273 9.98 270	3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4	00 59 58 57 56	6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50	48 4.8 5-6 6-4 7.2 8.0 16.0 24.0 32.0 40.0 46 4.6 5-4 6.1 6-9 7-7 15-3 23.0 3°-7 38-3 44 4-4 5-1 5-9 6.6 7-3 147 22.0 29-3 36.7 43 4-2 4-9 5-6 6-3 7-o 14.0 21.0 28.0 35-0 4 0.4 0-5 0.5 0.6 0.7 i-3 2.0 2.7 3-3	47 4-7 il 7.1 7-8 15-7 23-5 31-3 39-2 45 4-5 . 5-3 6.0 6.8 7-5 15-0 22.5 30.0 37-5 43 4-3 5-0 5-7 6-5 7-2 14-3 21-5 28.7 35-8 4i 4.1 4-8 I:! 6.8 13-7 20.5 27-3 34-2 3 0-3 0.4 0.4 0-5 0-5 I.O i-5 2.0 2-5
5 6 7 8 9	9-44 253 9-44 297 9-44 34i 9 44 385 9-44 428	9-45 987 9-46 035 9.46 082 9.46 130 9.46 177	0.54 013 o-53 965 0-53 9i8 0.53 870 0.53 823	9.98 266 9.98 262 9 98 259 9-98 255 9.98 251	55 54 53 52 5i
10 ii 12 13 14	9.44 472 9-44 5i6 9-44 559 9.44 602 9-44 646	9.46 224 9.46 271 9.46 319 9.46 366 9.46 413	o.53 776 0-53 729 0.53 681 0-53 634 0.53 587	9.98 248 9.98 244 9.98 240 9.98 237 9-98 233	50 49 48 47 46
15 16 17 18 19	9.44 689 9-44 733 9.44 776 9-44 819 9.44 862	9.46 460 9.46 507 9-46 554 9.46 601 9.46 648	0-53 540 0-53 493 0-53 446 0-53 399 o.53 352	9.98 229 9.98 226 9.98 222 9.98 218 9.98 215	45 44 43 42 41
20 21 22 23 24	9-44 9°5 9-44 948 9-44 992 9-45 035 9-45 077	9.46 694 9.46 741 9.46 788 9-46 835 9.46 881	0.53 306 o.53 259 0.53 212 0-53 165 0.53 "9	9.98 211 9.98 207 9.98 204 9.98 2OO 9.98 196	40 39 38 H
25 26 27 28 29	9-45 120 9-45 163 9-45 206 9-45 249 9.45 292	9.46 928 9.46 975 9.47 021 9.47 068 9-47 "4	0.53 072 0.53 025 0.52 979 0.52 932 0.52 886	9.98 192 9.98 189 9.98 I8f 9.98 181 9.98 177	35 34 33 32 3i
3O 3i 32 33 34	9-45 334 9-45 377 9-45 419 9-45 4°2 9-45 504	9.47 160 9.47 207 9-47 253 9-47 299 9-47 346	0.52 840 0.52 793 .0.52 747 0.52 701 0.52 654	9.98 174 9.98 170 9.98 166 9.98 162 9.98 159	30 29 28 27 26
35 36 37 38 39	9-45 547 9-45 589 9-45 632 9-45 674 9-45 7i6	9-47 392 9-47 438 9.47 484 9-47 530 9-47 576	0.52 608 0.52 562 0.52 516 0.52 470 0.52 424	9-98 155 9.98 151 9.98 147 9.98 144 9.98 140	25 24 23 22 21
40 4i 42 43 44	9-45 758 9-45 801 9-45 843 9-45 885 9-45 927	9.47 622 9.47 668 9-47 7H 9-47 760 9.47 806	0.52 378 0.52 332 0.52 286 0.52 240 0.52 194	9.98 136 9.98 132 9.98 129 9-98 125 9.98 121	20 19 18 17 16
45 46 47 48 49	9-45 969 9.46 on 9-46 °53 9.46 095 9.46 136	9-47 852 9-47 897 9-47 943 9-47 989 9-48 035	0.52 148 0.52 103 0.52 057 0.52 on 9-Si 965 0.51 920 0.51 874 0.51 829 0.51 783 0.51 738	9.98 117 9.98 II3 9.98 no 9.98 106 9.98 102	15 14 13 12 11
50 Si 52 53 54	9.46 178 9.46 220 9.46 262 9-46 303 9-46 345	9.48 080 9.48 126 9.48 171 9.48 217 9.48 262	9.98 098 9.98 094 9.98 090 9.98 087 9-98 083	10 9 8 7 6
55 56 57 58 59	9-46 386 9.46 428 9.46 469 9.46 511 9-46 552	9.48 307 9-48 353 9.48 398 9-48 443 9.48 489	0.51 693 0.51 647 0.51 602 0-51 557 0.51 5"	9.98 079 9.98 075 9.98 071 9.98 067 9-98 063	5 4 3 a
00	9-46 594	9-48 534	0.51 466	9.98 060		0
	L. Cos. | d.	L. Cotg. C. d. L.TMIIU.	L. Sin. d.	/	Prop. Pts.

73C

17'

39

/-	L. Sin.	d.	L. Tang.	c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9.46 594 9-46 635 9.46 676 9.46 717 9.46 758	41 41 41 41 42 41 41 41 41 41 40 41 41 41 41 40 41 40 41 40 41 40 41 40 40 41 40 40 40 40 40 40 40 40 40 40 40 39 40 40 39 40 40 39	9-48 534 9-48 579 9.48 624 9.48 669 9.48 714	45 45 45 45 45 45 45 45 45 45 45 44 45 45 44 45 44 45 44 45 44 45 44 44 45 44 44 44 44 44 44 44 44 44 44 44 44 43 44 44 44 43 44 43 44 43 44 43 44 43 43 44 43 43 43 43 43 44 43 43	0.51 466 0.51 421 0.51 376 0-51 33i 0.51 286	9.98 060 9.98 056 9.98 052 9.98 048 9.98 044	4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4	6O 59 58 fa	6 7 8 9 10 20 3°	4 $ 5 6 6 1 15 25 3^ 37 6 7 8 9 10 20 30 40 50 4 4 A 5 6 7 14 21 28 35 4 4 4 6 6 13 20 26 33 5 5-5 ).6 )-7 ).8 ).8 •7 »-s i-3 \.2	5 •5 •3 .0 .8 •5 .0 •5 .0 • 5 4 4 c 1 ( 7 M 23 2£ 3 = * .2 •9 .6 •3 .0 .0 .0 .0 .0 0 .0 •7 •3 .0 •7 •3 .0 •7 •3 4 o. 0. o. o 0. I. 2. 2. 3-	44 4.4 S-i 5.9 6.6 7-3 14-7 22.0 29-3 36.7 3 k3 .0 •7 •5 .2 \-3 •5 .7 .8 4i 4.1 4.8 5-5 6.2 6.8 13-7 20.5 27-3 34-2 39 3-9 4.6 5-2 5-9 6-5 13.0 19.5 26.0 32-5 3 4 0.3 5 0.4 5 0.4 6 0.5 7 0.5 3 i-o o 1.5 7 2.0 3 2.5
6 7 8 9	9.46 800 9.46 841 9.46 882 9.46 923 9.46 964	9-48 759 9.48 804 9.48 849 9.48 894 9.48 939	0.51 241 0.51 196 0.51 151 0.51 106 0.51 061	9.98 040 9.98 036 9.98 032 9.98 029 9.98 025	55 54 53 52 5i
10 ii 12 13 14	9.47 005 9-47 045 9.47 086 9-47 127 9.47 168	9.48 984 9.49 029 9-49 073 9.49 118 9-49 163	0.51 016 0.50 971 0.50 927 0.50 882 0.50 837	9.98 021 9 98 017 9 98 013 9.98 009 9.98 005	50 49 48 47 46	40 50
15 16 17 18 19	9-47 209 9-47 249 9-47 290 9-47 330 9-47 37i	9-49 207 9-49 252 9.49 296 9-49 341 9-49 385	0.50 793 0.50 748 0.50 704 0.50 659 0.50 615	9.98 ooi 9-97 997 9-97 993 9 97 989 9-97 986	45 44 43 42 4i
20 21 22 23 24	9.47411 9 47 452 9.47 492 9-47 533 9-47 573	9-49 430 9.49 474 9-49 519 9-49 563 9.49 607	0.50 570 0.50 526 0.50 481 0.50 437 0.50 393	9-97 982 9.97 978 9-97 974 9-97 970 9-97 966	40 39 38 37 36	6 7 8
25 26 27 28 29	9.47 613 9-47 654 9-47 694 9-47 734 9-47 774	9.49 652 9-49 696 9.49 740 9.49 784 9.49 828	0.50 348 0.50 304 0.50 260 0.50 216 0.50 172	9-97 962 9-97 958 9-97 954 9-97 950 9-97 946	35 34 33 32 3i
3O 3i 32 33 34	9.47 814 9-47 854 9.47 894 9-47 934 9.47 974	9 49 872 9.49 916 9.49 960 9.50 004 9.50 048	0.50 128 0.50 084 0.50 040 0.49 996 0.49 952	9.97 942 9-97 938 9-97 934 9-97 930 9-97 926	3O 29 28 27 26	9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 c 7 < 8 c 9 < 10 C 20 1 30 '. 40 : 50 t
35 36 37 38 39	9.48 014 9.48 054 9.48 094 9-48 133 9.48 173	9.50 092 9.50 136 9.50 180 9.50 223 9.50 267	0.49 908 0.49 864 o 49 820 0.49 777 0-49 733	9.97 922 9-97 9i8 9.97 914 9-97 910 9.97 906	25 24 23 22 21
40 4i 42 43 44	9.48 213 9.48 252 9.48 292 9-48 332 9-48 37i	9-503II 9 So 355 9-50 398 9.50 442 9-5° 485	0.49 689 0.49 645 0.49 602 0-49 558 049515	9-97 902 9.97 898 9-97 894 9-97 890 9.97 886	20 19 18 17 16
45 46 47 48 49	9.48 411 9.48 450 9.48 490 9.48 529 9.48 568	40 39 40 39 39	9-5° 529 9-So 572 9.50 616 9-50 659 9-50 7°3	0.49 471 0.49 428 0.49 384 0-49 34i 0.49 297	9.97 882 9-97 878 9-97 874 9-97 870 9.97 866	15 14 13 12 II
5O Si 52 53 54	9.48 607 9.48 647 9.48 686 9.48 725 9.48 764	39 40 39 39 39	9.50 746 9.50 789 9-50 833 9.50 876 9.50919	0.49 254 0.49 211 0.49 167 0.49 124 0.49 08 1	9.97 861 9-97 857 9-97 853 9-97 849 9-97 845	4	10 9 8 7 6
55 56 57 58 59	9.48 803 9.48 842 9.48 881 9.48 920 9.48 959	39 39 39 39 39 39	9.50 962 9.51 005 9.51 048 9.51 092 9-51 135	0.49 038 0.48 995 0.48 952 0.48 908 0.48 865	9.97 841 9-97 837 9-97 833 9-97 829 9.97 825	4 4 4 4 4	5 4 3 2 I
60	9.48 998	9.51 178	0.48 822	9.97 821		O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	r	Prop. Pts.

72<

r	! . Sill.	d.	L.Taiig.	c. d.	L. Cotg.	L. Cos.	d.		Pi	01	>.	Pts.
O i 2 3 4	9.48 998 9-49 °37 9.49 076 9-49 US 9-49 153	39 39 39 38	9.51 178 9.51 221 9-51 264 9.51 306 9-51 349	43 43 42 43	0.48 822 0.48 779 0.48 736 0.48 694 0.48 651	9.97 821 9-97 817 9.97 812 9.97 808 9-97 804	4 5 4 4	60 59 58 57 56	6 7	4 4 5	3 •3 .0	4» 4-2 4-9
5 6 7 8 9	9-49 192 9-49 231 9-49 269 9-49 3o8 9-49 347	39 38 39 39 •38	9-5i 392 9-5i 435 9.51 478 9-5i 520 9-5i 563	43 43 43 42 43	0.48 608 0.48 565 0.48 522 0.48 480 0.48 437	9.97 800 9-97 796 9-97 792 9.97 788 9-97 784	4 4 4 4	55 54 53 52 5i	8 9 10 20 30	\ 7 M 21	-7 •5 .2 •3 •5	5-6 6-3 7.0 14.0 2C.O
10 ii 12 13 14	9-49 385 9-49 424 9-49 462 9-49 5oo 9-49 539	39 38 38 39 -0	9.51 606 9.51 648 9.51 691 9-5i 734 9.51 776	43 42 43 43 42	0.48 394 0.48 352 0.48 309 0.48 266 0.48 224	9-97 779 9-97 775 9-97 771 9-97 767 9-97 763	4 4 4 4	50 49 48 47 46	40 50	2b 35	•7 .8 4	28.0 35-0 i
15 16 17 18 19	9-49 577 9-49 615 9.49 654 9.49 692 9-49 730	38 39 38 38 _Q	9.51 819 9.51 861 9-5i 903 9.51 946 9.51 988	43 42 42 43 42	0.48 181 0.48 139 0.48 097 0.48 054 0.48 012	9-97 759 9-97 754 9-97 75° 9-97 746 9-97 742	5 4 4 4	45 44 43 42 4i		6 7 8 9 10	t A c I t	kl ki •s ).2 .8
20 21 22 23 24	9-49 768 9.49 806 9-49 844 9.49 882 9.49 920	38 38 38 38	9.52 031 9-52 073 9-52 115 9-52 157 9.52 200	43 42 42 42 43	0.47 969 0.47 927 0.47 885 0.47 843 0.47 800	9-97 738 9-97 734 9.97 729 9-97 725 9-97 721	4 5 4 4	40 39 38 37 36		20 30 P >0	\.-. 2C ^ 3-1	•7 '•5 •3 ^•2
5 27 28 29	9-49 958 9-49 996 9-5° 034 9.50 072 9.50 no	38 38 38 38 38	9.52 242 9.52 284 9.52 326 9.52 368 9.52 4IO	42 42 42 42 42	0.47 758 0.47 7l6 0.47 674 0.47 632 0.47 590	9-97 717 9-97 713 9-97 708 9-97 704 9-97 700	4 5 4 4	35 34 33 32 3i	. 6 7 8	3 3 4 5	9 •9 .6 .2	38 3-8 4-4 5-i
3O 3i 32 33 34	9.50 148 9-50 185 9.50 223 9.50 261 9.50 298	3° 37 38 38 37	9-52 452 9-52 494 9-52 536 9-52 578 9.52 620	42 42 42 42 42	0.47 548 0.47 506 0.47 464 0.47 422 0.47 380	9-97 696 9.97 691 9-97 687 9 97 683 9-97 679	5 4 4 4	30 29 28 27 26	9 10 20 30 40 CQ	i 6 13 19 at	•9 •5 .0 •5 .0	5-7 6-3 12.7 19.0 25-3
35 36 37 38 39	9-50 336 9-5° 374 9.50 411 9-50 449 9.50 486	S8 38 37 38 37	9.52 661 9-52 703 9-52 745 9.52 787 9.52 829	41 42 42 42 42	0-47 339 0.47 297 0-47 255 0.47 213 0.47 171	9-97 674 9-97 670 9.97 666 9.97 662 9-97 657	5 4 4 4 5	25 24 23 22 21	6	3 3	7 •7	36 3-6
40 4i 42 43 44	9-5° 523 9.50 561 9-50 598 9-50 635 9-50 673	37 38 37 37 38	9.52 870 9.52 912 . 9-52 953 9-52 995 9-53 °37	41 42 4» 42 42	0.47 130 0.47 088 0.47 047 0.47 005 0.46 963	9-97 653 9-97 649 9-97 645 9.97 640 9-97 636	4 4 5 4	2O 19 18 17 16	7 8 9 10 20 3°	4 4 I 12 Ifi	•3 •9 .6 .2 •3 c	4.2 4.8 5-4 6.0 12.0 18.0
45 46 47 48 49	9.50 710 9-5° 747 9.50 784 9.50 821 9.50 858	37 37 37 37 37	9-53 078 9-53 120 9-53 161 9-53 202 9-53 244	41 42 4i 4» 42	0.46 922 0.46 880 0.46 839 0.46 798 0.46 756	9-97 632 9.97 628 9 97 623 9.97 619 9-97 615	4 5 4 4	15 14 13 12 II	40 50	24 30	.7 .8	24.0 30.0
50 Si 52 53 54	9.50 896 9-5° 933 9.50 970 9.51 007 9-Si 043	38 37 37 37 36	9-53 285 9-53 327 9-53 368 9-53 409 9-53 450	4X 42 4* 4* 4i	0.46 715 0.46 673 0.46 632 0.46 591 0.46 550	9.97 610 9.97 606 9.97 602 9-97 597 9-97 593	4 4 5 4	10 9 8 7 6	6 7 8 9 10	0 o 0° 0	S •7 .8 s	0.4 0-5 0-5 0.6 0.7
H 57 58 59	9.51 080 9-Si "7 9-Si 154 9.51 191 9-Si 227	37 37 37 37 36	9-53 492 9-53 533 9-53 574 9-53 6i5 9-53 656	42 4i 4' 4i 4»	0.46 508 0.46 467 0.46 426 0.46 385 0.46 344	9-97 589 9-97 584 9-97 58o 9-97 576 9-97 571	5 4 4 5	5 4 3 2	20 30 40 50	J 2 4	•7 s 3 i	1-3 2.0 2-7 3-3
00	9.51 264	37	9-53 697	41	0.46 303	9-97 567		o
	L. Cos.	d.	L. Cotg.	C. d.	L.Tang.	L. Sin.	d.	r	Tr	<M	. 1	Ms.

71°

19C

r	L. Sin.	d.	L.Tang.	c. d.	L.Cotg.	L. Cos.	d.		Pr	op.	Pts.
0 i 2 3 4	9.51 264 9-Si 301 9-5i 338 9-Si 374 9-51 4"	37 37 36 37 ofi	9-53 697 9-53 738 9-53 779 9-53 820 9-53 861	41 41 4i 4*	0.46 303 0.46 262 0.46 221 0.46 180 0.46 139	9-97 567 9-97 563 9-97 558 9-97 554 9-97 550	4 5 4 4	GO 59 58 57 56	6 7	41 4.1 4.8	40 4.0 4-7
6 7 8 9	9-Si 447 9.51 484 9-51 520 9-5i 557 9-5i 593	3° 37 36 37 36 ifi	9-53 902 9-53 943 9-53 984 9-54 025 9-54 065	4i 41 4i 40	0.46 098 0.46 057 0.46 016 o.45 975 0-45 935	9-97 545 9-97 541 9-97 536 9-97 532 9.97 528	4 5 4 4	55 54 53 52 Si	8 9 10 20 30	5-5 6.2 6.8 13-7 20.5	5-3 6.0 6-7 13-3 2O.O
10 ii 12 13 14	9.51 629 9.51 666 9.51 702 9-51 738 9-5i 774	3° 37 36 36 36	9.54 106 9-54 147 9-54 187 9-54 228 9-54 269	4i 40 4i 41	0.45 894 0-45 853 0.45 813 0.45 772 o-45 73i	9-97 523 9-97 519 9-97 515 9-97 5io 9.97 506	4 4 5 4	50 49 48 47 46	40 50	27.3 34-2 3	26.7 33-3 9
15 16 17 18 19	9-51 811 9.51 847 9-51 883 9.51 919 9-Si 955	37 36 36 36 36	9-54 3°9 9-54 350 9-54 390 9-54 43i 9-54 47i	4° 4i 40 4i 40	0.45 691 0.45 650 0.45 610 o-45 569 o-45 529	9-97 501 9-97 497 9-97 492 9.97 488 9.97 484	4 5 4 4	45 44 43 42 4i	]	6 3 7 4 8 5 9 5 :o 6	•9 .6 .2 •9 •5
20 21 22 23 24	9-Si 99i 9.52 027 9.52 063 9.52 099 9-52 135	3° 36 36 36 36 ifi	9-54 512 9-54 552 9-54 593 9-54 633 9-54 673	41 40 41 40 40	0.45 488 0.45 448 0.45 407 o-45 367 o-45 327	9-97 479 9-97 475 9.97 470 9.97 466 9-97 461	4 5 4 5	40 39 38 37 36	t i	to 13 jo 15 [0 26 ;o 32	.0 •5 .0 •5
25 26 27 28 29	9.52 171 9.52 207 9.52 242 9-52 278 9-52 3H	3° 36 35 36 .36 •36	9-54 714 9-54 754 9-54 794 9-54 835 9-54 875	40 40 41 40	0,45 286 0.45 246 0.45 206 0.45 165 0-45 125	9-97 457 9-97 453 9.97 448 9.97 444 9-97 439	4 5 4 5	35 34 33 32 3i	6 7 8	37 3-7 4-3 4-9	36 3-6 4-2 4.8
3O 3i 32 33 34	9-52 350 9-52 385 9-52 421 9-52 456 9.52 492	3° 35 36 35 36 .	9-54 915 9-54 955 9-54 995 9-55 035 9-55 °75	4° 40 40 40 40	0.45 085 0-45 045 0.45 005 0.44 965 0.44 925	9-97 435 9-97 430 9.97 426 9.97 421 9-97 417	5 4 5 4	30 29 28 27 26	9 10 20 3° 40 CQ	5-o 6.2 12.3 18.5 24.7 qo 8	5-4 6.0 12.0 18.0 24.0 qo O
35 36 37 38 39	9-52 527 9-52 563 9-52 598 9-52 634 9.52 669	35 36 35 36 35	9-55 H5 9-55 155 9-55 195 9-55 235 9-55 275	40 40 40 4° 40	0.44 885 0.44 845 0.44 805 0.44 765 0.44 725	9-97 412 9-97 4°8 9-97 403 9-97 399 9-97 394	4 5 4 5	25 24 23 22 21	6	35 3-5	34 3-4
40 4i 42 43 44	9-52 705 9.52 740 9-52 775 9.52 811 9-52 846	3° 35 35 36 35	9-55 315 9-55 355 9-55 395 9-55 434 9-55 474	4° 40 40 39 40	0.44 685 o.44 645 0.44 605 0.44 566 0.44 526	9-97 39° 9-97 385 9-97 38i 9-97 376 9-97 372	5 4 5 4	20 19 18 17 16	7 8 9 10 20 30	4.1 4-7 5-3 5-8 11.7 17.5	4.0 4-5 S-i 5-7 ".3 17.0
45 46 47 48 49	9.52 881 9.52 916 9-52 95i 9.52 986 9-53 021	35 35 35 35 35	9-55 5H 9-55 554 9-55 593 9-55 633 9-55 673	40 40 39 40 40	0.44 486 0.44 446 0.44 407 0.44 367 0.44 327	9-97 367 9-97 363 9-97 358 9-97 353 9-97 349	4 5 5 4	15 14 13 12 II	40 So	23-3 29.2	22.7 28.3
5O Si 52 53 54	9-53 056 9-53 092 9-53 126 9-53 161 9-53 196	35 36 34 35 35	9-55 712 9-55 752 9-55 791 9-55 831 9-55 870	39 40 39 40 39	0.44 288 0.44 248 0.44 209 0.44 169 0.44 130	9-97 344 9-97 340 9-97 335 9-97 331 9-97 326	4 5 4 5	10 9 8 7 6	6 7 8 9 10	o.5 0.6 0.7 0.8 08	0.4 o-5 o-5 0.6 0.7
55 56 57 58 59	9-53 231 9-53 a66 9-53 301 9-53 336 9-53 370	35 35 35 35 34	9-55 9Jo 9-55 949 9-55 989 9.56 028 9.56 067	40 39 4° 39 39	0.44 090 0.44 051 0.44 on 0.43 972 0-43 933	9-97 322 9-97 317 9 97 312 9-97 308 9-97 3«>3	5 5 4 5	5 4 3 2 I	20 3° 4° So	1.7 2-5 3-3 4.2	i-3 2.O 2.7 3-3
60	9-53 405	35	9.56 107	4°	0-43 893	9-97 299		o
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	r	Pi	op. 1	Pts.

70<

20<

/•	L. Sin.	(1.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Pi	op.	Pts.
o 2 3 4	9-53 4°5 9-53 44° 9-53 475 9-53 509 9-53 544	35 35 34 35	9.56 107 9.56 146 9.56 185 9.56 224 9.56 264	39 39 39 40	0-43 893 0-43 854 0.43 815 0.43 776 0.43 736	9.97 299 9.97 294 9-97 289 9.97 285 9.97 280	5 5 4 5	GO 59 58 57 56	6 7	40 4.0 4-7	39 3-9 4.6
5 6 7 8 9	9-53 578 9-53 613 9-53 647 9-53 682 9-53 7i6	35 34 35 34	9-56 303 9-56 342 9.56 381 9.56 420 9-56 459	39 39 39 39	0.43 697 0.43 658 0.43 619 0.43 580 °-43 54i	9-97 276 9-97 271 9.97 266 9.97 262 9-97 257	5 5 4 5	55 54 53 52 5i	8 9 10 20 3°	5-3 6.0 6-7 13-3 2O.O	5-2 5,9 6-5 13.0 19-5
1O ii 12 13 14	9-53 75i 9-53 785 9-53 819 9-53 854 9.53 888	34 34 35 34.	9.56 498 9-56 537 9-56 576 9.56 615 9-56 654	39 39 39 39	0.43 502 0-43 463 0.43 424 0-43 385 o-43 346	9-97 252 9.97 248 9-97 243 9.97 238 9.97 234	4 5 5 4	50 49 48 47 46	40 50	2b.7 33-3 38	26.0 32.5 37
15 16 17 18 19	9-53 922 9-53 957 9-53 99i 9-54 025 9-54 059	35 34 34 34	9-56 693 9-56 732 9.56 771 9.56 810 9.56 849	39 39 39 39 •38	0-43 307 0.43 268 0.43 229 0.43 190 o-43 I51	9.97 229 9-97 224 9.97 220 9-97 215 9.97 210	5 4 5 5	45 44 43 42 4i	6 7 8 9 10	3-8 4-4 5-1 5-7 6-3	3-7 4-3 4-9 5-6 6.2
20 21 22 23 24	9-54 093 9-54 127 9-54 161 9-54 195 9-54 229	34 34 34 34	9.56 887 9.56 926 9-56 965 9-57 004 9.57 042	39 39 39 38	0-43 "3 0.43 074 0-43 035 0.42 996 0.42 958	9.97 206 9-97 201 9-97 196 9.97 192 9.97 187	5 5 4 5	40 39 38 37 36	20 3° 40 50	12.7 19.0 25-3 31-7	12.3 18-5 24-7 30.8
25 26 27 28 29	9-54 263 9-54 297 9-54 33i 9-54 365 9-54 399	34 34 34 34	9-57 081 9-57 120 9-57 158 9-57 197 9-57 235	39 39 38 39 38	0.42 919 0.42 880 0.42 842 0.42 803 0.42 765	9.97 182 9.97 178 9-97 173 9.97 168 9.97 163	4 5 5 5	35 34 33 S2 3i	-	3. 6 3 7 4 8 4	5 •5 .1 •7
30 3i 32 33 34	9-54 433 9-54 466 9-54 5°o 9-54 534 9-54 567	33 34 34 33	9-57 274 9-57 312 9-57 35i 9-57 389 9.57 428	39 38 39 38 39 08	0.42 726 0.42 688 0.42 649 0.42 611 0.42 572	9-97 159 9-97 154 9-97 149 9-97 145 9.97 140	5 5 4 5	30 29 28 27 26	3 <	9 5 o 5 0 II o 17 ^ 23	•3 .8 •7 •5 -3
35 36 37 38 39	9.54 601 9-54 635 9-54 668 9.54 702 9-54 735	34 34 33 34 33	9-57 466 9-57 504 9-57 543 9-57 58i 9-57 619	3° 38 39 38 38	0-42 534 0.42 496 0.42 457 0.42 419 0.42 381	9-97 135 9.97 130 9.97 126 9.97 121 9.97 116	5 4 5 5	25 24 23 22 21	6	34 3-4	33 3-3
4O 41 42 43 44	9-54 769 9-54 802 9-54 836 9-54 869 9-54 903	34 33 34 33 34	9-57 658 9-57 696 9-57 734 9-57 772 9.57810	39 38 38 38 38	0.42 342 0.42 304 0.42 266 0.42 228 0.42 190	9-97 "I 9-97 i°7 9.97 102 9-97 097 9-97 092	4 5 5 5	2O 19 18 17 16	7 8 9 10 20 3O	4.0 4-5 5-i 5-7 H-3 17 o	3-9 4-4 5-o 5-5 II.O 16 <
45 46 47 48 49	9-54 936 9-54 969 9-55 003 9-55 036 9-55 069	33 34 33 33	9-57 849 9-57 887 9-57 925 9-57 963 9.58 ooi	38 38 38 38 ,0	0.42 151 0.42 113 0.42 075 0.42 037 0.41 999	9-97 087 9-97 083 9-97 078 9-97 073 9.97 068	4 5 5 5	15 14 *3 12 II	40 5°	22.7 28.3	22.0 27-5
5O 5i 52 53 54	9-55 102 9-55 IS6 9-55 169 9.55 202 9-55 235	33 34 33 33 33	9-58 039 9.58 077 9-58 115 9-58 153 9.58 191	3° 38 38 38 38 _Q	0.41 961 0.41 923 0.41 885 0.41 847 0.41 809	9.97 063 9-97 059 9-97 054 9-97 049 9.97 044	4 5 5 5	10 9 8 7 6	6 7 8 9 10	0.5 0.6 0.7 0.8 0.8	0.4 0.5 0.5 0.6 0.7
55 56 57 58 59	9-55 268 9-55 301 9-55 334 9-55 367 9-55 400	33 33 33 33 33	9.58 229 9.58 267 9-58 304 9.58 342 9.58 380	38 38 37 38 38 _Q	0.41 771 0.41 733 0.41 696 0.41 658 0.41 620	9-97 039 9-97 035 9-97 030 9-97 025 9.97 020	4 5 5 5	5 4 3* 2 I	20 30 4<> 50	1-7 2-5 3-3 4-2	i-3 2.0 2.7 3-3
GO	9-55 433	33	9-58 418-	38	0.41 582	9-97 015		O
	L. Cos.	d.	L. Coif.	c. d.	L.Tang.	I,. Sin.	d.	r	Pr	«>p, 1	Ms.

69(

r	L. Sin.	d.	L.Tang.	c. d. L. Cotg.	L. Cos.	d.		Prop. Pts.
O i 2 3 4	9-55 433 9-55 466 9-55 499 9-55 532 9-55 564	33 33 33 32 33 33 33 32 33 33 32 33 32 33 32 33 32 33 32 32 33 32 32 33 32 32 32 32 32 33 32 32 32 32	9.58 418 9-58 455 9-58 493 9.58 53i 9.58 569	37 38 38 38 37 38 37 38 38 37 38 37 38 37 37 38 37 38 37 37 37 38 37 37 37 37 38 37 37 37 37 37 37 37 37 37 37 36 37 37 37 37 36 37 37 37 36 37 37 36 37 36 37 36 37 36 37 36 37 36	0.41 582 0.41 545 0.41 507 0.41 469 0.41 431	9-97 015 9.97 010 9.97 005 9.97 ooi 9.96 996	5 5 4 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5	60 59 58 57 56	6 7	38 3-8 4-4 S-i 5-7 6.3 12.7 19.0 25-3 31-7 36 3-6 4-2 4.8 5-4 6.0 12.0 18.0 24.0 30.0 '9 6 3 7 3 8 4 9 4 o 5 0 10 o 16 O 21 o 26 31 iS 4.1 4.7 5-2 10.3 15.5 20.7 25.8 5 0-5 0.6 0.7 0.8 0.8 1-7 2.5 3-3 4.2	37 3-7 4-3 4-9 5-6 6.2 12.3 18.5 24.7 30.8 33 3-3 3-9 4.4 5-0 5.5 II.O 16.5 22.O 27-5 2 .2 •7 •3 .8 •3 •7 .0 •3 •7 6 0.6 0.7 0.8 0.9 I.O 2.0 3-0 4.0 5-0 4 0.4 o.S 0-5 0.6 0.7 1-3 2.0 2.7 3-3
5 6 7 8 9	9-55 597 9-55 630 9-55 663 9-55 695 9-55 728	9.58 606 9.58 644 9.58 681 9.58 719 9-58 757	0.41 394 0.41 356 0.41 319 0.41 281 0.41 243	9.96 991 9.96 986 9.96 981 9.96 976 9.96 971	55 54 53 52 Si	8 9 10 20 30
10 ii 12 13 14	9-55 761 9-55 793 9-55 826 9-55 858 9-55 891	9-58 794 9.58 832 9.58 869 9.58 907 9.58 944	0.41 206 0.41 168 0.41 131 0.41 093 0.41 056	9.96 966 9.96 962 9-96 957 9.96 952 9.96 947	50 49 48 47 46	40 50 6 8 9 10 20 30 40 50 I c ! c 6 8 9 10 20 30 40' 50 6 7 8 9 10 20 30 40 50
15 16 17 18 19	9-55 923 9-55 956 9-55 988 9.56 021 9-56 053	9.58 981 9-59 OI9 9-59 056 9-59 °94 9-59 131	0.41 019 0.40 981 0.40 944 0.40 906 0.40 869	9.96 942 9-96 937 9.96 932 9.96 927 9.96 922	45 44 43 42 41
2O 21 22 23 24	9.56 085 9.56 118 9.56 150 9.56 182 9.56 215	9.59 168 9-59 205 9-59 243 9.59 280 9-59 317	0.40 832 0.40 795 0.40 757 0.40 720 0.40 683	9.96 917 9.96 912 9-96 907 9.96 903 9.96 898	40 39 38 1
25 26 27 28 29	9.56 247 9.56 279 9-56311 9-56343 9-56 375	9-59 354 9-59 39i 9-59 429 9-59 466 9-59 503	0.40 646 0.40 609 0.40 571 o-40 534 0.40 497	9.96 893 9.96 888 9-96 883 9.96 878 9.96 873	35 34 33 32 3i
30 3i 32 33 34	9.56 408 9.56 440 9.56 472 9.56 504 9-56 536	9-59 540 9-59 577 9-59 614 9-59 651 9-59 688	0.40 460 0.40 423 0.40 386 0.40 349 0.40 3-12	9.96 868 9.96 863 9.96 858 9-96 853 9.96 848	30 29 28 27 26
35 36 37 38 39	9-56 568 9.56 599 9.56 631 9.56 663 9o6 695	32 3i 32 32 32 32 32 3i 32 32 32 3i 32 31 32 32 3i 32 3i 3i 32 3i 32 3i 3i	9-59 725 9-59 762 9-59 799 9-59 835 9-59 872	0.40 275 0.40 238 0.40 201 0.40 165 0.40 128	9.96 843 9.96 838 9.96 833 9.96 828 9.96 823	25 24 23 22 21
40 4i 42 43 44	9.56 727 9-56 759 9.56 790 9.56 822 9-56 854	9.59 909 9-59 946 9-59 983 9.60 019 9.60 056	0.40 091 0.40 054 0.40 017 0.39 981 0.39 944	9.96 818 9.96 813 9.96 808 9.96 803 9.96 798	5 5 5 5	20 19 18 17 16
45 46 47 48 49	9.56 886 9.56 917 9-56 949 9.56 980 9-57 012	9.60 093 9.60 130 9.60 166 9.60 203 9.60 240	0.39 907 0.39 870 0-39 834 0.39 797 0.39 760	9-96 793 9.96 788 9.96 783 9.96 778 9.96 772	5 5 5 6	15 14 13 12 II
50 5i 52 53 54	9.57 044 9-57 075 9.57 107 9-57 138 9-57 169	9.60 276 9.60 313 9.60 349 9.60 386 9.60 422	0.39 724 0.39 687 0.39 651 0.39 614 0-39 578	9-96 767 9.96 762 9-96 757 9.96 752 9.96 747	5 5 5 5 5 5 5 5 5 5	10 9 8 7 6
55 56 57 58 59	9-57 201 9-57 232 9-57 264 9-57 295 9-57 326	9.60 459 9.60 495 9.60 532 9.60 568 9.60 605	0-39 54i o-39 5°5 0.39 468 o-39 432 o-39 395	9.96 742 9.96 737 9.96 732 9-96 727 9.96 722	5 4 3 2 I
60	9-5.7 358	32	9.60 641	°-39 359	9-96 717	5	O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	r	Prop. Pts.

68<

44

22<

r	L. Sin.	d.	L. Tang.	c. d.	L. Cotg.	L,. Cos.	d.		I* i	op. 1	Pts.
O i 2 3 4	9-57 358 9-57 389 9-57 420 9-57 45i 9-57 482	31 31 31 3»	9.60 641 9.60 677 9.60 714 9.60 750 9.60 786	36 37 36 36	o-39 359 0,39 323 0.39 286 0.39 250 0.39 214	9.96 717 9.96 711 9.96 706 9.96 701 9.96 696	6 5 5 5	GO 59 58 57 56	6 7	37 3-7 4-3	36 3-6 4.2
5 6 7 8 9	9-57 5H 9-57 545 9-57 576 9-57 607 9-57 638	3» 3» 3i 3i	9.60 823 9.60 859 9.60 895 9.60 931 9.60 967	37 36 36 36 36	0.39 177 0.39 141 0.39 105 0.39 069 o-39 033	9.96 691 9.96 686 9.96 681 9.96 676 9.96 670	5 5 5 6	55 54 53 52 5i	8 9 10 20 30	4.9 5-6 6.2 12.3 18.5	4.8 & I2.O 18.0
10 ii 12 13 14	9.57 669 9-57 700 9-57 73i 9-57 762 9-57 793	31 3i 3' 3i 3i	9.61 004 9.61 040 9.61 076 9.61 112 9.61 148	37 36 36 36 36 ofi	0.38 996 0.38 960 0.38 924 0.38 888 0.38 852	9.96 665 9.96 660 9-96 655 9.96 650 9.96 645	5 5 5 5	5O 49 48 47 46	40 50	24.7 30.8 3	24.0 30.0 5
15 16 17 18 19	9-57 824 9-57 855 9-57 885 9-57 916 9-57 947	3i 30 3i 3i	9.61 184 9.61 22O 9.61 256 9.61 292 9.6l 328	3° 36 36 36 36	0.38 816 0.38 780 0.38 744 0.38 708 0.38 672	9.96 640 9.96 634 9.96 629 9.96 624 9.96 619	6 5 5 5	45 44 43 42 41	3	6 3 7 4 8 4 9 5 to 5	•5 .1 •7 -3 .8
20 21 22 23 24	9-57 978 9.58 008 9-58 039 9.58 070 9.58 101	31 30 31 31 3i	9.61 364 9.61 400 9.6l 436 9.6l 472 9.6l 508	3° 36 36 36 36 if>	0.38 636 0.38 600 0.38 564 0.38 528 0.38 492	9.96 614 9.96 608 9.96 603 9.96 598 9 96 593	6 5 5 5	4O 39 38 37 36	i	JO II jo 17 \o 23 ;o 29	•7 •5 •3 .2
25 26 27 28 29	9-58 131 9.58 162 9.58 192 9.58 223 9-58 253	3i 30 3i 3"	9.61 544 9.61 579 9.61 615 9.61 651 9.61 687	35 36 36 36	0.38 456 0.38 421 0.38 385 0.38 349 0.38 313	9 96 588 9.96 582 9-96 577 9.96 572 9.96 567	6 5 5 5	35 34 33 32 3i	6 7 8	3* 3-2 3-7 4-3	31 H 4.I
30 3i 32 33 34	9.58 284 9-58 3H 9-58 345 9-58 375 9.58 406	31 30 3i 30 3i	9.61 722 9.61 758 9.61 794 9.61 830 9.61 865	35 36 36 36 35	0.38 278 0.38 242 0.38 206 0.38 170 0-38 135	9.96 562 9-96 556 9-96 55i 9.96 546 9.96 541	6 5 5 5	3O 29 28 27 26	9 10 20 30 40 CQ	4.8 5-3 10.7 16.0 21.3 26 7	4-7 5-2 10.3 15-5 20.7 2c 8
35 36 37 38 39	9-58 436 9.58 467 9-58 497 9-58 527 9-58 557	3° 3» 3° 3<> 30	9.61 901 9.61 936 9.61 972 9.62 008 9.62 043	30 35 36 36 35 ofi	0.38 099 0.38 064 0.38 028 0.37 992 o.37 957	9-96 535 9-96 530 9-96 525 9.96 520 9.96 514	5 5 5 6	25 24 23 22 21	6	30 3-0	29 2.9
4O 4i 42 43 44	9-58 588 9.58 618 9.58 648 9.58 678 9.58 709	31 30 30 3<> 3«	9.62 079 9.62 114 9.62 150 9.62 185 9.62 221	3° 35 36 35 36	0.37 921 0.37 886 0.37 850 0-37 815 0.37 779	9.96 509 9.96 504 9.96 498 9-96 493 9.96 488	5 6 5 5	2O 19 18 17 16	7 8 9 10 20 30	3-5 4.0 4-5 5-0 IO.O 15.0	3-4 3-9 4-4 4.8 9-7 14 c
45 46 47 48 49	9-58 739 9.58 769 9-58 799 9.58 829 9-58 859	3° 3° 30 3<> 30	9.62 256 9.62 292 9.62 327 9.62 362 9.62 398	35 36 35 35* 36	0-37 744 0.37 708 0.37 673 0.37 638 0.37 602	9.96 483 9-96 477 9.96 472 • 9.96 467 9.96 461	6 5 5 6	15 14 13 12 II	40 So	20.0 25.0 5	J9-3 24.2
50 5i 52 53 54	9.58 889 9-58 919 9-58 949 9-58 979 9.59009	30 3° 3° 30 3°	9.62 433 9.62 468 9.62 504 9-62 539 9.62 574	35 35 36 35 35	0-37 567 o.37 532 0.37 496 0.37 461 0.37 426	9.96 456 9.96 451 9-96 445 9.96 440 9-96 435	5 6 5 5	10 9 8 7 6	6 7 8 9 10	0.6 0.7 0.8 0.9 I O	o.S 0.6 0.7 0.8 08
55 56 57 58 59	9-59 <>39 9.59069 9-59 098 9-59 "8 9-59 158	3° 3<> »9 30 3<>	9.62 609 9.62 645 9.62 680 9-62 715 9.62 750	35 36 35 35 35	o 37 391 0-37 355 0.37 320 0.37 285 0.37 250	9.96 429 9.96 424 9.96 419 9 96 413 9.96 408	5 5 6 5	5 4 3 2 I	20 3° 40 50	2.0 3-o 4.0 5-0	i-7 2-5 3-3 4.2
60	9-59 1 88	3°	9.62 785	35	0.37 215	9.96 403	5	O
	L. Cos.	d.	1,. Cotff.	c. d.	L. Ta UK.	L. Sin.	d.	r	Pr	op. I	'ts.

67

23'

45

/•	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
0 I 2 3 4	9-59 188 9-59 218 9-59 247 9-59 277 9-59 3°7	3° 29 30 3° 29 3<> 30 29 30 29 3° 29 3° 29	9.62 785 9.62 820 9.62 855 9.62 890 9.62 926	35 35 35 36 35 35 35 35 35 34 35 35 35 35 35 35 34 35 35 35 35 34 35 35 34 35 34 35 35 34 35 34 35 34 35 34 35 34 34 35 34 34 35 34 34 35 34 34 34 34 35 34 34 34 34 34 34 34 34 34	0.37 215 0.37 180 0-37 M5 0.37 no 0.37 074	9.96 403 9-96 397 9.96 392 9.96 387 9.96 381	6 5 5 6 5 6 5 5 6 5 6 5 5 6 5 6 5 6 5 6 5 5 6 5 6 5 6 5 6	6O 59 58 57 56	6 7	< < i ii U Q.L 3< 6 7 8 9 10 20 30 1° 50 3 • \ A 4 5 1C 15 2C 25 6 7 8 9 [0 >0 5° p 50 < c 0 0 o 2 3 4 5	16 j.6 1-2 j.8 5-4 ).0 J.O 5.o [.0 ).0 3 -1 4 c c IJ «3 22 2g 0 .0 •5 .0 •5 .0 .0 .0 .0 .0 2 2 3 3 4 4 9 14 18 23 i .6 •7 .8 •9 .0 .0 .0 .0 .0	35 3-5 4.1 4-7 5-3 5-8 11.7 17-5 23-3 29.2 4 •4 ^.0 kS I .7 •3 .0 •7 •3 29 2.9 3-4 3-9 4-4 4.8 9-7 14-5 19-3 24.2 8 .8 •3 •7 .2 •7 •3 .0 •7 •3 5 0-5 06 0.7 0.8 0.8 1-7 2-5 3-3 4-2
5 6 7 8 9	9-59 336 9-59 366 9-59 396 9-59 425 9-59 455	9.62 961 9.62 996 9.63 031 9.63 066 9.63 101	0.37 039 0.37 004 0.36 969 0-36 934 0.36 899	9.96 376 9.96 370 9-96 365 9.96 360 9-96 354	55 54 53 52 5i	8 9 10 20 30
1O ii 12 13 14	9.59 484 9-59 5i4 9-59 543 9-59 573 9-59 602	9-63 135 9.63 170 9.63 205 9.63 240 9-63 275	0.36 865 0.36 830 0-36 795 0.36 760 0.36 725	9-96 349 9-96 343 9-96 338 9-96 333 9.96 327	50 49 48 47 46	40 50 6 7 8 9 10 20 3° 40 50 J i 1 6 8 9 10 20 30 40 50
15 16 17 18 19	9-59 632 9-59 661 9-59 690 9-59 720 9-59 749	29 29 3<> 29 29 30 29 29 29 29 30 29 29 29	9.63 310 9-63 345 9-63 379 9.63 414 9.63 449	0.36 690 0.36 655 0.36 621 0.36 586 o-S6 55i	9.96 322 9.96 316 996311 9-96 3<>5 9.96 300	45 44 43 42 4i
2O 21 22 23 24	9-59 778 9-59 808 9-59 837 9-59 866 9-59 895	9.63 484 9-63 519 9-63 553 9-63 588 9.63 623	0.36 516 0.36 481 0.36 447 0.36 412 0.36 377	9.96 294 9.96 289 9.96 284 9.96 278 9.96 273	40 39 38 37 36
2S 26 27 28 29	9-59 924 9-59 954 9-59 983 9.60 012 9.60 041	9-63 657 9.63 692 9.63 726 9.63 761 9.63 796	0-36 343 0.36 308 0.36 274 o 36 239 0.36 204	9.96 267 9.96 262 9.96 256 9.96 251 9.96 245	35 34 33 32 3i
30 3i 32 33 34	9.60 070 9.60 099 9.60 128 9.60 157 9.60 186	29 29 29 29	9.63 830 9.63 865 9.63 899 9-63 934 9.63 968	0.36 170 0.36 135 0.36 101 0.36 066 0.36 032	9.96 240 9.96 234 9 96 229 9.96 223 9.96 218	6 5 6 5 g	30 29 28 27 26
3 37 38 39	9.60 215 9.60 244 9.60 273 9.60 302 9.60 331	29 29 29 29 29 28 29 29 29 28 29 29 29 28 29 28 29 29 28 29 28	9.64 003 9.64 037 9.64 072 9.64 106 9.64 140	o-35 997 0-35 963 0.35 928 o-35 894 0.35 860	9.96 212 9.96 207 9.96 2OI 9.96 196 9.96 190	5 6 5 6 5 6 5 6 6	25 24 23 22 21
40 4i 42 43 44	9-6o 359 9.60 388 9.60 417 9.60 446 9.60 474	9.64 175 9.64 209 9.64 243 9.64 278 9.64 312	0.35 825 o-35 79i o-35 757 0.35 722 0.35 688	9.96 185 9.96 179 9.96 I74 9.96 168 9.96 162	20 J9 18 17 16
45 46 47 48 49	9.60 503 9.60 532 9.60 561 9.60 589 9.60 618	9.64 346 9.64 381 9.64 415 9 64 449 9.64 483	0-35 654 0.35 619 °-35 585 o-35 55i 035 5i7	9.96 157 9 96 151 9.96 146 9.96 140 9-96 135	6 5 6 5	15 14 13 12 II
50 5i 52 53 54	9.60 646 9.60 675 9.60 704 9.60 732 9.60 761	9.64 517 9-64 552 9.64 586 9.64 620 9.64 654	0-35 483 0-35 448 0-35 414 0.35 380 0.35 346	9.96 129 9.96 123 9.96 118 9.96 112 9.96 107	6 5 6 5 6 6 5 6 5	10 9 8 7 6
55 56 57 58 . 59	9.60 789 9.60 818 9.60 846 9.60 875 9.60 903	29 28 29 28	9.64 688 9.64 722 9 64 756 9.64 790 9.64 824	0.35 312 0.35 278 0-35 244 0.35 210 0.35 176	9.96 101 9.96 095 9.96 090 9.96 084 9.96 079	5 4 3 2 I
6O	9.60 931		9.64 858	o-35 142	9.96 073		0
	L. Cos.	d.	L. Cotg.	c. d.	L. Tang.	L. Sin.	d.	/•	Prop. Pts.

66<

46

24'

/	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Proj	.. 1	Pts.
0 I 2 3 4	9.60 931 9.60 960 9.60 988 9.61 016 9.61 045	29 28 28 29 28	9.64 858 9.64 892 9.64 926 9.64 960 9.64 994	34 34 34 34	0-35 142 0.35 108 0-35 074 0.35 040 0.35 006	9.96 073 9.96 067 9.96 062 9.96 056 9.96 050	6 5 6 6	6O 59 58 57 56	3 6 2 7 4	4 •4 .0	33 3-3 3-9
6 7 8 9	9.61 073 9.61 101 9.61 129 9.61 158 9.61 186	28 28 29 28 ?s	9.65 028 9.65 062 9-65 096 9.65 130 9.65 164	34 34 34 34 34	0.34 972 o-34 938 0.34 904 0.34 870 0.34 836	9.96 045 9.96 039 9.96 034 9.96 028 q.q6 022	6 5 6 6	55 54 53 52 51	8 A 9 5 i° £ 20 I] 30 17	•5 .1 •1 •3 .0	4.4 5-o 5-5 II.O 16.5
10 ii 12 13 14	9.61 214 9.61 242 9.61 270 9.61 298 9.61 326	28 28 28 28	9.65 197 9.65 231 9.65 265 9.65 299 9-65 333	33 34 34 34 34	0.34 803 0.34 769 0-34 735 0.34 701 0.34 667	9.96 017 9.96 on 9.96 005 9.96 ooo 9-95 994	6 6 5 6 g	50 49 48 47 46	40 25 50 2g	• 7 •3 2	22.O 27-5 I
15 16 17 18 19	9-6i 354 9.61 382 9.61 411 9.61 438 9.61 466	28 29 27 28	9-65 366 9.65 400 9-65 434 9.65 467 9-65 5oi	33 34 34 33 34	0-34 634 0.34 600 0.34 566 o.34 533 o-34 499	9-95 988 9.95 982 9-95 977 9-95 971 9-95 965	6 5 6 6	45 44 43 42 4i	6 7 8 9 10	2 3 3 4 4	•9 •4 •9 •4 .8
20 21 22 23 24	9.61 494 9.61 522 9-6i 550 9.61 578 9.61 606	28 28 28 28	9-65 535 9.65 568 9.65 602 9.65 636 9.65 669	34 33 34 34 33	o-34 465 0-34 432 0-34 398 0-34 364 o-34 33i	9.95 960 9-95 954 9.95 948 9-95 942 9-95 937	6 6 6 5 g	4O 39 38 |	20 30 40 50	9 14 19 24	•7 •5 •3 .2
25 26 27 28 29	9.61 634 9.61 662 9.61 689 9.61 717 9-6 1 745	28 27 28 28	9-65 703 9-65 736 9.65 770 9.65 803 9-65 837	34 33 34 33 34	0.34 297 0.34 264 0.34 230 0.34 197 0.34 163	9-95 93i 9-95 925 9-95 920 9-95 914 9.95 908	6 5 6 6 g	35 34 33 32 3i	6 7 8	2 2 3 3	B .8 •3 •7
30 3i 32 33 34	9.61 773 9.61 800 9.61 828 9.61 856 9.61 883	27 28 28 27	9.65 870 9.65 904 9-65 937 9-65 971 9.66 004	33 34 33 34 33	0.34 130 0.34 096 0.34 063 0.34 029 0.33 996	9-95 902 9-95 897 9-95 891 9-95 885 9-95 879	5 6 6 6 g	30 29 28 27 26	9 10 20 30 40 CQ	4 4 9 14 18 00	•7 •3 .0 •7 q
35 36 37 38 39	9.61 911 9.61 939 9.61 966 9.61 994 9.62 021	28 27 28 27	9.66 038 9.66 071 9.66 104 9.66 138 9.66 171	34 33 33 34 33	0.33 962 0.33 929 0.33 896 0.33 862 0.33 829	9-95 873 9-95 868 9.95 862 9-95 856' 9-95 850	5 6 6 6 g	25 24 23 22 21	6	a 2	7 •7
40 4i 42 43 44	9.62 049 9.62 076 9.62 104 9.62 131 9.62 IS9	27 28 27 28	9.66 204 9.66 238 9.66 271 9.66 304 9.66 337	33 34 33 33 33	0.33 796 0.33 762 0.33 729 0.33 696 0.33 663	9-95 844 9-95 839 9-95 833 9-95 827 9-95 821	5 6 6 6 g	2O 19 18 17 16	7 8 9 10 20 •5O	3 3 4 4 9 1 -;	.6 .1 •5 .0 .5
45 46 47 48 49	9.62 180 9.62 214 9.62 241 9.62 268 9.62 296	27 28 27 27 28	9.66 371 9.66 404 9-66 437 9.66 470 9.66 503	34 33 33 33 33	0.33 629 0-33 596 0-33 563 o-33 530 o-33 497	9-95 815 9.95 810 9-95 804 9-95 798 9-95 792	5 6 6 6	15 14 13 12 II	40 50	1 8 22	.0 •5
50 5i 52 53 54	9.62 323 9.62 350 9.62 377 9.62 405 9.62 432	27 27 27 28 27	9-66 537 9.66 570 9.66 603 9.66 636 9.66 669	34 33 33 33 33	0-33 463 o-33 430 0-33 397 o-33 364 0-33 331	9.95 786 9-95 78o 9-95 775 9-95 769 9-95 763	6 5 6 6 g	10 9 8 7 6	6 c 7 o 8 c 9 c IO I	.6 •7 .8 •9 o	5 o-5 0.6 0.7 0.8 0.8
H 11 59	9.62 459 9.62 486 9.62 513 9-62 541 9.63 568	27 27 27 28 27	9.66 702 9-66 735 9.66 768 9.66 801 9.66 834	33 33 33 33 33	0.33 298 0.33 265 0.33 232 o-33 199 0.33 166	9-95 757 9-95 75i 9-95 745 9-95 739 9-95 733	6 6 6 6	5 4 3 2 I	20 9 3° 3 40 4 So 5	.0 .0 .0 .0	1-7 2-5 3-3 4.2
GO	9-62 595	27	9.66 867	33	0-33 133	9-95 728		o
	L. Cos.	d •	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	r	1*1 0|	. 1	•ti.

65C

25'

47

r	L. Sin.	d.	L.Tang.c. d.	L.Cotg.	L. Cos.	d.		Prop. Pts.
0 2 3 4	9-62 595 9.62 622 9.62 649 9.62 676 9.62 703	27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 26 27 27 26 27 27 26 27 26 27 26 27 26	9.66 867 9.66 900 9-66 933 9.66 966 9-66 999	33 33 33 33 33 33 33 33 32 33 33 33 33 32 33 33 33 32 33 33 32 33 33 32 33 32 33 33 32 33 32 33 32 33 32 32 33 32 33 32 32 33 32 32 33 32 32 32 33 32 32 32 32 33 32 32 32 32 32 3*	0-33 133 0.33 100 0.33 067 0.33 034 0.33 ooi	9-95 728 9-95 722 9-95 7i6 9.95 710 9-95 704	6 6 6 6 6 6 6 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6 6 6 6 6 6 6 6 6 6 6	6O 59 58 57 56	6 7	3 3 3 4 5 ii 16 22 27	3 32 •3 3-2 •9 3-7 •4 4.3 .0 4.8 •5 5-3 .0 10.7 .5 16.0 .0 21.3 •5 26.7 27 2.7 3-2 3-6 4-1 4-5 9.0 13-5 18.0 22.5 26 2.6 3-o 3-5 3-9 4-3 8.7 13-0 17-3 21.7 7 0.7 0.8 0.9 i.i 1.2 2-3 3-5 4-7 5.8 5 5 6 0.5 .7 0.6 8 0.7 9 0.8 . o 0.8 o 1.7 o 2.5 o 3-3 o 4.2
5 6 7 8 9	9.62 730 9.62 757 9.62 784 9.62 811 9.62 838	9.67 032 9.67 065 9.67 098 9.67 131 9-67 163	0.32 968 0.32 935 0.32 902 0.32 869 0.32 837	9-95 698 9.95 692 9.95 686 9.95 680 9-95 674	55 54 53 52	8 9 10 20 30
10 II 12 13 14	9.62 865 9.62 892 9.62 918 9.62 945 9.62 972	9.67 196 9.67 229 9.67 262 9.67 295 9.67 327	0.32 804 0.32 771 0.32 738 0.32 705 0.32 673	9.95 668 9-95 663 9-95 657 9-95 651 9-95 645	5O 49 48 47 46	40 50
15 16 17 18 19	9.62 999 9.63 026 9.63 052 9.63 079 9.63 106	9.67 360 9-67 393 9.67 426 9.67 458 9.67 491	0.32 640 0.32 607 0.32 574 0.32 542 0.32 509	9-95 639 9-95 633 9-95 627 9-95 621 9-95 615	45 44 43 42	6 8 9 10
20 21 22 23 24	9-63 133 9-63 159 9.63 186 9-63 213 9-63 239	9.67 524 9-67 556 9.67 589 9.67 622 9-67 654	0.32 476 0.32 444 0.32 411 0.32 378 0.32 346	9-95 609 9-95 603 9-95 597 9-95 59i 9-95 585	40 39 38	2 < c I 2 3 A c 6 7 8 9 10 20 3° 40 50	0 o ^° o 6 7 8 9 0 0 o o 0 6 8 9 10 20 30 40 50 0 o 0 0 I 2 3 4 5
25 26 27 28 29	9.63 266 9.63 292 9.63 319 9-63 345 9.63 372	9.67 687 9.67 719 9.67 752 9.67 785 9.67 817	0.32 3:3 0.32 281 0.32 248 0.32 215 0.32 183	9-95 579 9-95 573 9-95 567 9-95 56i 9-95 555	35 34 33 32
30 32 33 34	9-63 398 9-63 425 9.63 451 9.63 478 9-63 504	27 26 27 26 27 26 26 27 26 26 27 26 26 26 27 26 26 26 26	9.67 850 9.67 882 9.67 915 9.67 947 9.67 980	0.32 150 0.32 118 0.32 085 0.32 053 0.32 020	9-95 549 9-95 543 9-95 537 9-95 53i 9-95 525	30 29 28 27 26
37 38 39	9-63 S31 9-63 557 9-63 583 9.63 610 9.63 636	9.68 012 9.68 044 9.68 077 9-68 109 9.68 142	0.31 988 0.31 956 0.31 923 0.31 891 0.31 858	9-95 5i9 9-95 513 9-95 507 9-95 5oo 9-95 494	25 24 23 22 21
40 42 43 44	9.63 662 9.63 689 9.63 715 9.63 741 9.63 767	9.68 174 9.68 206 9.68 239 9.68 271 9-68 303	0.31 826 0.31 794 0.31 761 0.31 729 0.31 697	9.95 488 9-95 482 9-95 476 9-95 470 9-95 464	19 18 17 16
45 46 47 48 49	9-63 794 9.63 820 9.63 846 9.63 872 9.63 898	9.68 336 9.68 368 9.68 400 9.68 432 9.68 465	0.31 664 0.31 632 0.31 600 0.31 568 0.31 535	9-95 458 9-95 452 9-95 446 9-95 440 9-95 434	15 14 13 12 II
50 \ 52 S3 54	9.63 924 9-63 950 9.63 976 9.64 002 9.64 028	26 26 26 26 26	9-68 497 9.68 529 9.68 561 9-68 593 9.68 626	0.31 503 0.31 471 0-31 439 0.31 407 0.31 374	9-95 427 9-95 421 9-95 415 9-95 4°9 9-95 403	7 6 6 6 6 g	10 9 8 7 6
55 56 57 58 59	9.64 054 9.64 080 9.64 106 9.64 132 9.64 158	26 26 26 26 26	9.68 658 9.68 690 9.68 722 9-68 754 9.68 786	0.31 342 0.31 310 0.31 278 0.31 246 0.31 214	9-95 397 9-95 391 9-95 384 9-95 378 9-95 372	6 7 6 6	5 4 3 2 I
6O	9.64 184	9.68 818	0.31 182	9-95 366		O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	'	Prop. Pts.

64C

48

26'

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
0 i 2 3 4	9.64 184 9.64 2IO 9.64 236 9.64 262 9.64 288	26. 26 26 26 25 26 26 26 26 25 26 26 25 26 26 25 26 35 26 25 26 25 26 25 „£.	9.68 818 9.68 850 9.68 882 9.68 914 9.68 946	32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 31 32 32 32 32 31 32 32 32 31 32 32 31 32 32 31 32 31 32 32 31 32 32 33 32 32 32 32 32 32 33	0.31 182 0.31 150 0.31 118 0.31 086 0.31 054	9-95 366 9-95 36o 9-95 348 9-95 34i	6 6 6 7 6 6 6 6 7 6 6 6 6 7 6 6 6 7 6 6 6 7 6 6 6 7 6 6 7 6 6 6 7 6 6 7 6 6 7 6 6 7 6 7	60 59 58 57 56	6 7	3 4 4 c 1C ie 2] zt 6 7 8 9 0 o o o 0 6 7 8 9 o 0 0 0 0 6 7 8 9 o 0 0 0 0 0 0 0 I I 2 3 4 5	3 31 • 2 3.1 •7 3-6 \-3 4-1 ^.8 4.7 •3 5-2 (.7 10.3 '•o 15-5 •3 20.7 >-7 25.8 26 2.6 3-o 3-5 3-9 4-3 8-7 13-0 17-3 21.7 25 2-5 2-9 3-3 3-8 4.2 8-3 12.5 16.7 20.8 24 2.4 2.8 3-2 3.6 4.0 8.0 12. 0 16.0 2O.O 7 6 .7 0.6 .8 0.7 .9 0.8 .1 0.9 .2 I.O •3 2.0 •5 3-0 •7 4-0 .8 5.0
5 6 7 8 9	9^4 313 9-64 339 9 64 3°5 9 64 391 9.64 417	9.68 978 9.69 oio 9.69 042 9.69 074 9.69 106	0.31 022 0.30 990 0.30 958 0.30 926 0.30 894	9-95 335 9-95 329 9-95 323 9-95 317 9-95 3io	55 54 53 52	8 9 10 20 30
10 ii 12 13 14	9.64 442 9.64 468 9.64 494 9.64 519 9-64 545	9.69 138 9.69 170 9.69 202 9.69 234 9.69 266	0.30 862 0.30 830 0.30 798 0.30 766 0.30 734	9-95 304 9.95 298 9-95 292 9.95 286 9-95 279	50 49 48 47 46	40 50
15 16 17 18 19	9.64 571 9.64 596 9.64 622 9.64 647 9.64 673	9.69 298 9.69 329 9.69 361 9-69 393 9.69 425	0.30 702 0.30 671 0.30 639 0.30 607 0.30 575	9-95 273 9-95 267 9-95 261 9-95 254 9-95 248	45 44 43 42 41	I
20 21 22 23 24	9.64 698 9.64 724 9.64 749 9-64 775 9.64 800	9-69 457 9.69 488 9.69 520 9.69 552 9.69 584	0-30 543 0.30 512 0.30 480 0.30 448 0.30 416	9.95 242 9-95 236 9-95 229 9-95 223 9-95 217	40 39 38 37 36	2 3 A 5 i 2 3 4 5 i 2 3 -4 5 6 7 8 9 10 20 30 40 50
25 26 27 28 29	9.64 826 9.64 851 9.64 877 9.64 902 9.64 927	25 26 25 25 26 25 25 26 25	9.69 615 9.69 647 9.69 679 9.69 710 9.69 742	0.30 385 0.30 353 0.30 321 0.30 290 0.30 258	9-95 211 9-95 204 9.95 198 9.95 192 9-95 185	35 34 33 32
30 32 33 34	9-64 953 9.64 978 9.65 003 9.65 029 9-6S 054	9.69 774 9.69 805 9.69 837 9.69 868 9.69 900	0.30 226 0.30 195 0.30 163 0.30 132 0.30 loo	9-95 179 9-95 173 9.95 167 9.95 160 9-95 154	3O 29 28 27 26
35 36 37 38 39	9.65 079 9.65 104 9.65 I3o 9-65 155 9.65 1 80	25 26 25 25	9.69 932 9.69 963 9-69 995 9.70 026 9.70 058	0.30 068 0.30 037 0.30 005 0.29 974 0.29 942	9-95 148 9-95 141 9-95 135 9-95 129 9-95 122	25 24 23 22 21
40 42 43 44	9.65 205 9.65 230 9.65 255 9.65 281 9.65 306	25 25 25 26 25 25 25 25 25 25	9.70 089 9.70 121 9.70 152 9.70 184 9.70 215	0.29 911 0.29 879 0.29 848 0.29 816 0.29 785	9.95 116 9-95 1 10 9-95 103 9-95 097 9-95 090	20 19 18 17 16
45 46 47 48 49	9.65 331 9-65 356 9-65 381 9.65 406	9.70 247 9-70 278 9.70 309 9-70 341 9.70 372	0.29 753 0.29 722 0.29 691 0.29 659 0.29 628	9.95 084 9-95 078 9-95 071 9-95 065 9-95 059	6 7 6 6	15 14 13 12 II
50 5i 52 53 54	9.65 456 9.65 481 9.65 506 9-65 53i 9-65 556	25 25 25 25 25 24 25 25 25 25	9.70 404 9-70 435 9.70 466 9.70 498 9.70 529	0.29 596 0.29 565 0-29 534 0.29 502 0.29 471	9-95 052 9-95 046 9-95 039 9-95 033 9-95 027	6 7 6 6	10 9 8 7 6
55 56 57 58 59	9-65 58o 9.65 605 9.65 630 9-65 655 9.65 680	9.70 560 9.70 592 9.70 623 9.70 654 9.70 685	0.29 440 0.29 408 0.29 377 0.29 346 0.29 315	9-95 020 9-95 014 9.95007 9-95 ooi 9-94 995	6 7 6 6	5 4 3 2 I
00		9.70 717	0.29 283	9-94 988		0
	L. Cos.	d.	L.Cotp.	c. d.	L.Tnng.	L. Sin.	d.	f	Prop. Pts.

63C

27<

49

/•	L. Sin.	d.	L.Tang. c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9-65 7°5 9.65 729 9-65 754 9-65 779 9.65 804	24 25 25 25 24 25 25 24 25 25 24 25 24 25	9.70 717 9.70 748 9.70 779 9.70 810 9.70 841	31 31 3i 3i 32 3i 3i 3i 31 3i 3i 3i 31 32 3i 31 3i 3i 3i 3i 3i 3i 30 31 3i 3i 3i 3i 3i 3i 3i 30 3i 3i 3i 31 3° 3i 3i 30 3i 3i 3i 30 3i 3i 3° 3i 30 3i 3i 30 3i 30 3i 3° 3i 3° 3i 3°	0.29 283 0.29 252 O.29 221 0.29 190 0.29 159	9.94 988 9.94 982 9-94 975 9-94 969 9.94 962	6 7 6 7 6 7 6 7 6 7 6 6 7 6 7 6 7 7 6 7 6 7 6 7 6 7 6 7 7 6 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7	GO 59 58 57 56	6 7 8 9 10 20 30 40 So 3 Z t i 6 7 8 9 10 20 30 40 50 I 2 3 A 5 6 7 8 9 10 20 3° 40 50	3 ' t i 1C ie 2] Zf 6 7 8 9 0 20 !0 P o 3 2 2 2 t A 8 12 16 2C 6 7 8 9 0 o o 0 0 0 0 o I I 2 3 4 5	2 •2 • 7 [-3 \& •3 '•7 ).O •3 •7 a 4 t t 1C If 2C 2^ 5 •5 •9 •3 .8 .2 -3 •5 •7 .8 a 2 2 3 3 3 7 ii IS 19 7 •7 .8 •9 .1 .2 •3 •5 •7 .8	31 3-1 3.6 4.1 4-7 5-2 10.3 15-5 20.7 25.8 0 .0 •5 ^.0 (-5 .0 ).0 .0 ).0 .0 24 2.4 2.8 3-2 3.6 4.0 8.0 12.0 16.0 20.0 3 •3 •7 .1 -5 .8 •7 •5 •3 .2 6 0.6 0.7 0.8 0.9 I.O 2.0 3-o 4.0 5.0
5 6 7 8 9	9.65 828 9-65 853 9.65 878 9.65 902 9.65 927	9.70 873 9.70 904 9-70 935 9.70 966 9.70 997	O.29 127 O.29 096 0.29 065 0.29 034 0.29 003	9-94 956 9.94 949 9-94 943 9-94 936 9.94 930	55 54 53 52 5i
10 ii 12 13 14	9-65 952 9.65 976 9.66 ooi 9.66 025 9.66 050	9.71 028 9.71 059 9.71 090 9.71 121 971 153	0.28 972 0.28 941 0.28 910 0.28 879 0.28 847	9-94 923 9-94 9J7 9-94 9H 9-94 9°4 9-94 898	50 49 48 47 46
15 16 17 18 19	9.66 075 9.66 099 9.66 124 9.66 148 9.66 173	24 25 24 25	9.71 184 9.71 215 9.71 246 9.71 277 9.71 308	0.28 816 0.28 785 0.28 754 0.28 723 0.28 692	9-94 891 9-94 885 9-94 878 9.94 871 9 94 865	45 44 43 42 4i
2O 21 22 23 24	9.66 197 9.66 221 9.66 246 9.66 270 9.66 295	24 25 24 25	9.71 339 9.71 370 9.71 401 9.71 431 9.71 462	0.28 661 0.28 630 0.28 599 0.28 569 0.28 538	9-94 858 9-94 852 9-94 845 9-94 839 9-94 832	40 39 38 37 36
25 26 27 28 29	9.66 319 9-66 343 9.66 368 9.66 392 9.66 416	24 25 24 24	9-7i 493 9-71 524 9-71 555 9.71 586 9.71 617	0.28 507 0.28 476 0.28 445 0.28 414 0.28 383	9.94 826 9-94 819 9-94 813 9.94 806 9-94 799	35 34 33 32 3i
30 3i 32 33 34	9.66 441 9.66 465 9.66 489 9.66 513 9-66 537	25 24 24 24 24 25 24 24 24 24	9.71 648 9.71 679 9.71 709 9.71 740 9.71 771	0.28 352 0.28 321 0.28 291 0.28 260 0.28 229	9.94 793 9-94 786 9.94 780 9-94 773 9.94 767	30 29 28 27 26
35 36 37 38 39	9.66 562 9.66 586 9.66 610 9.66 634 9.66 658	9.71 802 9-7i 833 9.71 863 9.71 894 9.71 925	0.28 198 0.28 167 0.28 137 0.28 106 0.28 075	9-94 76o 9-94 753 9-94 747 9-94 740 9-94 734	25 24 23 22 21 ^O~ 19 18 17 16
40 4i 42 43 44	9.66 682 9.66 706 9.66 731 9-66 755 9.66 779	24 24 25 24 24	9-71 955 9.71 986 9.72 017 9.72 048 9.72 078	0.28 045 0.28 014 0.27 983 0.27 952 0.27 922	9.94 727 9-94 720 9-94 714 9-94 707 9-94 700
45 46 47 48 49	9.66 803 9.66 827 9.66 851 9.66 875 9.66 899	24 24 24 24 24	9.72 109 9.72 140 9.72 170 9.72 201 9.72 231	0.27 891 0.27 860 0.27 830 0.27 799 0.27 769	9-94 694 9.94 687 9.94 680 9-94 674 9.94 667	15 14 13 12 II
5O Si 52 53 54	9.66 922 9.66 946 9.66 970 9.66 994 9.67 018	23 24 24 24 24	9.72 262 9-72 293 9.72 323 9-72 354 9.72 384	0.27 738 0.27 707 0.27 677 0.27 646 0.27 616	9.94 660 9.94 654 9-94 647 9.94 640 9-94 634	10 9 8 \
11 57 58 59	9.67 042 9.67 066 9.67 090 9.67 113 9.67 137	24 . 24 23 24	9-72 415 9-72 445 9.72 476 9.72 506 9-72 537	0.27 585 0.27 555 0.27 524 0.27 494 0.27 463	9.94 627 9.94 620 9-94 614 9-94 607 9.94 600	5 4 3 2 I
60	9.67 161		9.72 567	0.27 433	9-94 593	7	0
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	/•	Prop. Pts.

62<

28<

/•	L. Sin.	d.	L.Tang.	c. d.	L.Cotg.	L. Cos.	d.		Prop. Pts.
0 I 2 3 4	9.67 161 9.67 185 9.67 208 9.67 232 9.67 256	24 23 24 24 24 23 24 23 24 24 23 24 23 24 23 24 23 24 23 24 23 24 23 23 24 23 23 24 23 23 24 23 23 23 23 24 23 23 23 23 23 23 23 23 23 24 23 23 22	9.72 567 9.72 598 9.72 628 9.72 659 9.72 689	31 30 31 30 31 30 30 31 3° 31 3° 3° 3i 3<> 30 3i 30 30 3° 3i 3° 3° 30 30 3i 3° 3° 3° 3° 30 3i 30 30 30 30 3° 3<> 30 3° 30 30 3° 3° i° 3° 30 3° 3° 3° 30 30 3° 29 30 30 30 3<> 3<> 29 30	0.27 433 0.27 402 0.27 372 0.27 341 0.27 311	9-94 593 9-94 587 9-94 58o 9-94 573 9-94 567	6 7 7 6 7 7 7 6 7 7 7 6 7 7 7 7 6 7 7 7 7 6 7 7 7 7 7 6 7 7 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 7 7	60 59 58 57 56	6 7 8 9 10 20 3° 40 50 ] 2 4 c * 6 7 8 9 10 20 30 40 50 I 2 3 4 5	3i 3-1 3-6 4.1 4-7 5-2 10.3 15-5 20.7 25.8 2 6 2 7 3 8 3 9 4 o 4 so 9 o 14 ^o 19 o 24 *4 2-4 2.8 3-2 3-6 4.0 8.0 12.0 16.0 20.0 23 6 2 7 2 8 2 9 3 0 3- o 7 0 II. o 14. o 18 7 o-7 0.8 0.9 i.i 1.2 2-3 3-5 4-7 5-8	30 3-0 3-5 4.0 4-5 5-o IO.O 15.0 2O.O 25.0 9 •9 •4 •9 .8 •7 •5 •3 .2 33 2-3 2.7 I'l 3-8 7-7 "•5 15-3 19.2 2 6 9 3 7 3 o 7 3 6 0.6 0.7 0.8 0.9 I.O 2.0 3-0 4.0 5-0
5 6 7 8 9	9.67 280 9.67 303 9.67 327 9-67 350 9-67 374	9.72 720 9.72 750 9.72 780 9.72 8n 9.72 841	0.27 280 0.27 250 0.27 220 0.27 189 0.27 159	9.94 560 9-94 553 9-94 546 9-94 540 9-94 533	55 54 53 52 5i
1O ii 12 13 14	9.67 398 9.67 421 9-67 445 9.67 468 9.67 492	9.72 872 9.72 902 9.72 932 9.72 963 9.72 993	0.27 128 0.27 098 0.27 068 0.27 037 O.27 OO7	9-94 526 9-94 519 9-94 513 9-94 506 9.94 499	5O 49 48 47 46
li 17 18 19	9-67 515 9-67 539 9.67 562 9.67 586 9.67 609	9.73 023 9-73 054 9-73 084 9-73 "4 9-73 144	0.26 977 0.26 946 0.26 916 0.26 886 0.26 856	9-94 492 9-94 485 9-94 479 9-94 472 9-94 465	45 44 43 42 4i
2O 21 29 23 24	9.67 633 9 67 656 9.67 680 9.67 703 9.67 726	9-73 175 9-73 205 9-73 235 9-73 265 9-73 295	0.26 825 0.26 795 0.26 765 0.26 735 0.26 705	9-94 458 9-94 451 9-94 445 9-94 438 9-94 431	40 39 38 37 36
25 26 27 28 29	9.67 750 9.67 773 9.67 796 9.67 820 9.67 843	9.73 326 9-73 356 9-73 386 9-73 4i6 9-73 446	0.26 674 0.26 644 0.26 614 0.26 584 0.26 554	9.94 424 9-94 417 9-94 4io 9.94 404 9-94 397	35 34 33 32 3i
30 3i 32 33 34	9.67 866 9.67 890 9-67 913 9.67 936 9-67 959	9 73 476 9-73 5°7 9-73 537 9-73 567 9-73 597	0.26 524 0.26 493 0.26 463 0.26 433 0.26 403	9-94 390 9-94 383 9-94 376 9.94 369 9-94 362	30 29 28 27 26
35 36 37 38 39	9.67 982 9.68 006 9.68 029 9.68 052 9-68 075	9.73 627 9-73 657 9-73 687 9-73 717 9-73747	0.26 373 0.26 343 0.26 313 0.26 283 0.26 253	9-94 355 9-94 349 9-94 342 9-94 335 9-94 328	25 24 23 22 21
40 4i 42 43 44	9.68 098 9.68 121 9.68 144 9.68 167 9.68 190	9-73 777 9 73 807 9-73 837 9-73 867 9-73 897	0.26 223 0.26 193 0.26 163 0.26 133 0.26 103	9-94 321 9-94 3H 9-94 307 9.94 300 9-94 293	20 19 18 17 16
45 46 47 48 49	9.68 213 9-68 237 9.68 260 9.68 283 9.68 305	9-73 927 9-73 957 9-73 987 9.74 017 9-74 047	0.26 073 0.26 043 0.26 013 0.25 983 0-25 953	9.94 286 9-94 279 9-94 273 9.94 266 9-94 259	15 14 13 12 II
5O 5i 52 53 54	9.68 328 9-68 351 9-68 374 9.68 397 9.68 420	23 23 23 23 23 23 23 23 23 22 23	9-74 077 9 74 107 9-74 137 9.74 166 9-74 196	0.25 923 0.25 893 0.25 863 0.25 834 0.25 804	9-94 252 9-94 245 9-94 238 9-94 231 9.94 224	10 9 8 7 6	6 7 8 9 10 20 30 40 5°
55 56 57 58 59	9-68 443 9.68 466 9.68 489 9.68 512 9-68 534	9.74 226 9-74 256 9.74 286 9-74 3l6 9-74 345	0.25 774 0.25 744 0.25 714 0.25 684 0-25 655	9.94 217 9.94 210 9-94 203 9-94 I96 9.94 189	5 4 3 2 I
60	9-68 557	9-74 375	0.25 625	9.94 182	7	0
	L. Con.	d.	L.Cotg. c. d. L.Tnng.	L. Sin. d.	/	Prop. Pis.

61

29<

f	JL. Sin.	d.	L.Tang.c. d. L. Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9-68 557 9.68 580 9.68 603 9.68 625 9.68 648	23 23 22 23 23 23 22 23 23 22 23 22 23 23	9-74 375 9-74 405 9-74 435 9-74 465 9.74 494	30 3° 30 29 3° 30 29 30 30 30 29 30 30 29 3° 3° 29 30 29 30 29 30 3° 29 30 29 30 29 30 29 30 29 30 29 29 3° 29 30 29 29 30 29 3° 29 29 30 29 29 29 30 29 29 29 30 29 29 29 3° 29 29	0.25 625 0-25 595 0-25 565 0.25 535 0.25 506	9.94 182 9-94 175 9.94 168 9.94 161 9-94 154	7 7 7 7 7 7 7 7 7 7 7 7 8 7 7 7 7 7 7 7 7 7 7 8 7 7 7 7 7 7 7 8 7 7 7 7 7 8 7 7 7 7 8 7 7 7 8 7 7 7 7 8 7 7	60 59 58 57 56	6 7 8 9 10 20 30	30 3-o 3-5 4.0 4-5 S-o 10.0 15-0 20.0 25.0 29 2.9 3-4 3-9 4-4 4.8 9-7 14.5 19-3 24.2 23 2-3 2-7 3-i 3-5 3-8 7-7 "•5 15-3 19.2 22 2.2 2.6 2-9 3-3 3-7 7-3 II.O 14.7 18.3 8 7 .8 0.7 .9 0.8 .1 0.9 .2 I.I •3 L2 •7 2.3 •o 3-5 •3 4-7 •7 1 5-8
5 6 7 8 9	9.68 671 9.68 694 9.68 716 9.68 739 9.68 762	9-74 524 9-74 554 9-74 583 9.74 613 9-74 643	0.25 476 0.25 446 0.25 417 0.25 387 0.25 357	9-94 147 9-94 140 9-94 133 9.94 126 9-94 U9	55 54 53 52 Si
10 ii 12 13 14	9.68 784 9.68 807 9.68 829 9.68 852 9.68 875	9-74 673 9-74 702 9-74 732 9-74 762 9.74 791	0.25 327 0.25 298 0.25 268 0.25 238 0.25 209	9.94 112 9-94 i°5 9.94 098 9-94 09° 9.94 083	50 49 48 47 46	40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 IO 20 30 ' 40 50 6 7 8 9 10 20 30 40 50 6 o 7 o 8 i 9 i 10 I 20 2 3° 4 40 5 50 6
II 17 18 19	9.68 897 9.68 920 9.68 942 9.68 965 9.68 987	23 22 23 22 23 22 23 22 23	9.74 821 9-74 851 9.74 880 9.74 910 9-74 939	0.25 179 0.25 149 0.25 120 0.25 090 O.25 O6 I	9.94 076 9-94 069 9.94 062 9-94 055 9-94 048	45 44 43 42 41
20 21 22 23 24	9.69 oio 9.69 032 9-69 055 9.69 077 9.69 100	9-74 969 9.74 998 9-75 028 9-75 058 9-75 087	0.25 031 0.25 002 0.24 972 O.24 942 0.24 913	9.94 041 9.94 034 9-94 027 9.94 020 9-94 OI2	40 39 38 i
25 26 27 28 29	9.69 122 9.69 144 9.69 167 9.69 189 9.69 212	22 23 22 23	9-75 "7 9-75 146 9-75 176 9-75 205 9-75 235	0.24 883 0.24 854 0.24 824 0.24 795 0.24 765	9.94 005 9-93 998 9-93 99i 9-93 984 9-93 977	35 34 33 32 3i
30 3i 32 33 34	9-69 234 9.69 256 9.69 279 9.69 301 9.69 323	22 23 22 22 22 23 22 22 22 22 23 22 22 22	9.75 264 9-75 294 9-75 323 9-75 353 9-75 382	0.24 736 0.24 706 0.24 677 0.24 647 0.24 618	9-93 970 9-93 963 9-93 955 9-93 948 9-93 94i	30 29 28 27 26
35 36 37 38 39	9-69 345 9.69 368 9.69 390 9.69 412 9.69 434	9-75 4" 9-75 44i 9-75 470 9-75 500 9-75 529	0.24 589 0.24 559 0.24 530 0.24 500 0.24 471	9-93 934 9-93 927 9-93 920 9-93 912 9-93 905	25 24 23 22 21
4O 4i 42 43 44	9.69 456 9.69 479 9.69 501 9-69 523 9-69 545	9-75 558 9-75 588 9-75 617 9-75 647 9-75 676	0.24 442 0.24 412 0.24 383 0.24 353 0.24 324	9-93 898 9-93 891 9-93 884 9.93 876 9-93 869	»0 *9 18 17 16
45 46 47 48 49	9.69 567 9.69 589 9.69 611 9.69 633 9-69 655	22 22 22 22 22 22 22 22 22	9-75 705 9-75 735 9-75 764 9-75 793 9-75 822	0.24 295 0.24 265 0.24 236 0.24 207 0.24 178	9.93 862 9-93 855 9-93 847 9-93 840 9-93 833	15 14 13 12 II
50 Si 52 53 54	9.69 677 9.69 699 9.69 721 9-69 743 9.69 765	9-75 852 9-75 881 9-75 9io 9-75 939 9-75 969	0.24 148 0.24 119 0.24 090 0.24 06 1 0.24 031	9.93 826 9-93 819 9-93 8n 9-93 804 9-93 797	10 9 8 7 6
3 57 58 59	9.69 787 9.69 809 9-69 831 9-69 853 9.69 875	22 22 22 22 22	9-75 998 9.76 027 9.76 056 9.76 086 9.76 115	0.24 002 0.23 973 0.23 944 0.23 914 0.23 885	9-93 789 9-93 782 9-93 775 9 93 768 9.93 760	7 7 7 8	5 4 3 2 I
60	9.69 897	9.76 144	0.23 856	9-93 753	7	0
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	r	Prop. Pts.

60C

30C

/•	L. Sin.	d.	L.Tang. c. d.' L. Cotg.	L. Cos. j d.		Prop. ]	Pts.
o I 2 3 4	9.69 897 9.69 919 9.69 941 9.69 963 9.69 984	22 22 22 21	9.76 144 9.76 173 9.76 202 9.76 231 9.76 261	29 29 29 3° 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 28 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 .-29 29 28 29 29 29 29 a8 29 29 29 28 29 29 28 29 29 29 28 29 28 29 29 28	0.23 856 0.23 827 0.23 798 0.23 769 0.23 739	9-93 753 9-93 746 9-93 738 9-93 73i 9-93 724	7 8 7 7 7 8 7 7 8 7 7 8 7 8 7 7 8 7 7 8 7 8 7 7 8 7 8 7 8 7 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 8 7 8 7 8 7	GO 59 58 57 56	3 6 3 7 3 8 4 9 A i° 5 20 1C 30 is 4O 2C 50 25 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 30 40 50 6 c 7 c 8 i 9 * 10 I 20 2 3° A 40 5 50 t	o 29 .0 2.9 •5 3-4 .0 3.9 •5 4-4 .0 4.8 .0 9.7 .0 14.5 .0 19.3 .0 24.2 28 2.8 3-3 3-7 4.2 4-7 9-3 14.0 18.7 23-3 22 2.2 2.6 2.9 3-3 3-7 7-3 II.O 14.7 18.3 21 2.1 2-5 2.8 3-2 3.5 7.0 10.5 14.0 17.5 8 7 .8 0.7 .9 0.8 .1 0.9 .2 I.I .3 i.a •7 2-3 •o 3-5 •3 4-7 •7 5-8
1 7 8 9	9.70 006 9.70 028 9.70 050 9.70 072 9.70 093	22 22 22 21 22 22 22 21 22 22 21 22 21 22 22 21 22 21 22	9.76 290 9-76 3*9 9.76 348 9.76 377 9.76 406	0.23 710 0.23 68 1 0.23 652 0.23 623 0-23 594	9-93 717 9-93 709 9-93 702 9-93 695 9-93 687	55 54 53 52 51
1O II 12 13 14	9.70 115 9.70 137 9.70 159 9.70 180 9.70 202	9-76 435 9.76 464 9-76 493 9.76 522 9-76 551	0.23 565 0.23 536 0.23 507 0.23 478 0.23 449	9.93 680 9-93 673 9-93 665 9-93 658 9-93 650	50 49 48 47 46
IS 16 17 18 19	9.70 224 9.70 245 9.70 267 9.70 288 9.70 310	9.76 580 9.76 609 9.76 639 9.76 668 9.76 697	0.23 420 0.23 391 0.23 361 0.23 332 0.23 303	9-93 643 9-93 636 9-93 628 9-93 621 9-93 614	45 44 43 42 41
20 21 22 23 24	9.70 332 9-70 353 9-70 375 9.70 396 9.70 418	9.76 725 9-76 754 9.76 783 9.76 812 9.76 841	0.23 275 0.23 246 0.23 217 0.23 188 0.23 159	9-93 606 9-93 599 9-93 591 9-93 584 9-93 577	40 39 38 11
25 26 27 28 29	9-7° 439 9.70 461 9.70 482 9.70 504 9-70 525	22 21 22 21	9.76 870 9.76 899 9.76 928 9-76 957 9.76 986	0.23 130 0.23 101 0.23 072 0.23 043 0.23 014	9-93 569 9-93 562 9-93 554 9-93 547 9-93 539	35 34 33 32 3i
30 3i 32 33 34	9-70 547 9.70 568 9.70 590 9.70 611 9.70 633	21 22 21 22	9.77 015 9-77 044 9-77 073 9.77 101 9-77 130	0.22 985 0.22 956 0.22 927 O.22 899 0.22 870	9-93 532 9-93 525 9-93 517 9-93 5io 9-93 502	30 29 28 27 26
H 37 38 39	9.70 654 9.70 675 9.70 697 9.70 718 9.70 739	21 22 21 21	9-77 159 9.77 188 9-77 217 9.77 246 9.77 274	0.22 841 O.22 8l2 0.22 783 0.22 754 O.22 726	9-93 495 9-93 487 9-93 48o 9-93 472 9-93 465	25 24 23 22 21
4O 4i 42 43 44	9.70 761 9.70 782 9.70 803 9.70 824 9.70 846	21 21 21 22	9-77 303 9-77 332 9-77 361 9.77 390 9-77 4i8	O.22 697 0.22 668 O.22 639 0.22 6lO O.22 582	9-93 457 9-93 450 9-93 442 9-93 435 9-93 427	20 19 18 17 16
45 46 47 48 49	9.70 867 9.70 888 9.70 909 9.70 931 9.70 952	21 21 22 21 21 21 21 21 22 21 21 21 91 21 21	9-77 447 9-77 476 9-77 505 9-77 533 9-77 562	0.22 553 0.22 524 0.22 495 0.22 467 O.22 438	9-93 420 9-93 412 9-93 405 9-93 397 9-93 390	15 14 13 12 II
50 Si 52 53 54	9.70 973 9.70 994 9.71 015 9-71 036 9.71 058	9-77 59i 9-77 619 9-77 648 9-77 677 9.77 706	O.22 409 0.22 381 0.22 352 0.22 323 0.22 294	9-93 382 9-93 375 9-93 367 9-93 3°° 9-93 352	10 9 8 7 6
55 56 57 58 59	9.71 079 9.71 100 9.71 I2i 9.71 142 9-71 163	9-77 734 9-77 763 9-77 791 9 77 820 9-77 849	0.22 266 0.22 237 0.22 209 0.22 ISO 0.22 151	9-93 344 9-93 337 9-93 329 9.93 322 9-93 314	5 4 3 2 I
60	9.71 184	9-77 877	0.22 123	9-93 3<V	0
	1.. Cog. i d.	L. Cotg. c. d. L.Taiig.	L. Sin. d.	r	I'rop.	Pt8.

59'

31

53

/•	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Pro]	>, Pts.
o I 2 3 4	9.71 184 9-71 205 9.71 226 9.71 247 9.71 268	21 21 21 21	9.77 877 9-77 906 9-77 935 9-77 963 9.77 992	29 29 28 29 28	O.22 123 0.22 094 O.22 065 0.22 037 O.22 OO8	9-93 307 9-93 299 9-93 291 9-93 284 9.93 276	8 8 7 8	60 59 58 57 56	6 7	29 2.9 3.4
5 6 7 8 9	9.71 289 9.71 310 9-71 33i 9-7i 352 9-71 373	21 21 21 21	9.78 020 9.78 049 9.78 077 9.78 106 9.78 135	29 28 29 29 28	0.21 980 O.2I 951 0.21 923 O.2I 894 0.21 865	9.93 269 9.93 26! 9-93 253 9-93 246 9-93 238	8 8 7 8 g	55 54 53 52 5i	8 9 10 20 3°	3-9 4-4 4.8 9-7 14-5
10 ii 12 13 14	9-71 393 9.71 414 9-7i 435 9-7i 456 9.71 477	21 21 21 21	9.78 163 9.78 192 9.78 220 9.78 249 9.78 277	29 28 29 28	O.2I 837 0.21 808 O.2I 780 0.21 751 0.21 723	9.93 230 9-93 223 9-93 215 9-93 207 9.93 200	7 8 8 7 g	5O 49 48 47 46	40 50	19-3 24.2 28
IS 16 17 18 19	9.71 498 9-7i 519 9-7i 539 9.71 560 9.71 581	21 20 21 21	9.78 306 9-78 334 9.78 363 9.78 391 9.78 419	28 29 28 28	0.21 694 0.21 666 O.2I 637 0.21 609 O.2I 581	9-93 192 9-93 184 9-93 177 9.93 169 9-93 161	8 7 8 8	45 44 43 42 4i	6 7 8 9 10	2.8 3-3 3-7 4-2 4-7
20 21 22 23 24	9.71 602 9.71 622 9.71 643 9.71 664 9.71 685	20 21 21 21	9.78 448 9.78 476 9-78 505 9-78 533 9.78 562	29 28 29 28 29	0.21 552 0.21 524 0.21 495 O.2I 467 0.21 438	9-93 154 9-93 X46 9-93 138 9-93 131 9-93 123	7 8 8 7 8 g	40 39 38 37 36	20 30 40 50	9-3 14.0 18.7 23-3
25 26 27 28 29	9.71 705 9.71 726 9.71 747 9.71 767 9.71 788	21 21 20 21	9.78 590 9.78 618 9.78 647 9.78 675 9.78 704	28 29 28 29	O.2I 4IO 0.21 382 0.21 353 0.21 325 O.2I 296	9-93 "5 9-93 108 9-93 ioo 9-93 092 9.93 084	7 8 8 8	35 34 33 32 3i	6 7 8	21 2.1 2-5 2.8
30 3i 32 33 34	9.71 809 9.71 829 9.71 850 9.71 870 9.71 891	20 21 20 21	9.78 732 9.78 760 9.78 789 9.78 817 9.78 845	28 29 28 28	O.2I 268 O.2I 240 0.21 211 0.21 183 0.21 155	9-93 077 9-93 069 9-93 061 9-93 053 9.93 046	8 8 8 7	3O 29 28 27 26	9 10 20 3° 40	3-2 3-5 7.0 10.5 14.0
35 36 37 38 39	9.71 911 9.71 932 9-7i 952 9-7i 973 9.71 994	21 20 21 21	9.78 874 9.78 902 9.78 930 9-78 959 9.78 987	29 28 28 29 28	0.21 126 0.21 098 O.2I 070 0.21 041 O.2I OI3	9-93 038 9-93 030 9.93 022 9-93 014 9-93 007	8 8 8 7	25 24 23 22 21	5° 6	*7-5 20 2.0
40 4i 42 43 44	9.72 014 9.72 034 9-72 055 9.72 075 9.72 096	2O 21 2O 21	9.79 015 9-79 043 9.79 072 9.79 100 9.79 128	28 29 28 28	0.20 985 0.20 957 0.20 928 0.20 900 O.2O 872	9.92 999 9.92 991 9.92 983 9.92 976 9.92 968	8 8 7 8	20 19 18 17 16	7 8 9 10 20	2-3 2.7 3-0 3-3 6-7
45 46 47 48 49	9.72 116 9.72 137 9.72 157 9.72 177 9.72 198	21 20 2O 21	9-79 156 9.79 185 9-79 213 9-79 24i 9.79 269	29 28 28 28	0.20 844 0.20 815 0.20 787 0.20 759 0.20 731	9.92 960 9.92 952 9.92 944 9.92 936 9.92 929	8 8 8 7	15 14 13 12 II	40 50	13-3 16.7
50 5i 52 53 54	9.72 218 9.72 238 9.72 259 9.72 279 9.72 299	20 21 20 2O	9-79 297 9-79 S26 9-79 354 9.79 382 9.79 410	29 28 28 28	O.2O 703 O.2O 674 O.2O 646 0.20 618 O.2O 590	9.92 921 9.92 913 9.92 905 9.92 897 9.92 889	8 8 8 8	10 9 8 6	6 c 7 c 8 i 9 i	7 .8 0.7 (.9 0.8 .1 0.9 .2 I.I
55 56 57 58 59	9.72 320 9.72 340 9.72 360 9.72 381 9.72 401	2O 2O 21 20	9-79 438 9.79 466 9-79 495 9-79 523 9-79 55i	28 29 28 28	O.2O 562 0.20 534 0.20 505 0.20 477 0.20 449	9.92 881 9-92 874 9.92 866 9.92 858 9.92 850	7 8 8 8	5 4 3 2 I	2O 2 30 A 4«> S 50 6	z.a •7 2.3 •o 3-5 •3 4-7 •7 5-8
60	9.72 421		9-79 579		O.2O 421	9.92 842		0
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	/•	Proj	.Pts.

58(

54

32'

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Ft	op. 1	*ts.
0 i 2 3 4	9.72 421 9.72 441 9.72 461 9.72 482 9.72 502	20 20 21 2O	9-79 579 9.79 607 9-79 635 9.79 663 9-79 691	28 28 28 28 28	O.2O 421 0.20 393 O.2O 365 0.20 337 O.2O 309	9.92 842 9.92 834 9.92 826 9.92 818 9.92 810	8 8 8 8	60 59 58 57 56	6 7	29 2-9 0 A	28 2.8 o.o
6 7 8 9	9.72 522 9.72 542 9-72 562 9.72 582 9.72 602	20 20 20 20	9.79 719 9-79 747 9-79 776 9-79 804 9-79 832	28 29 28 28 28	O.2O 28l 0.20 253 O.2O 224 0.20 196 0.20 168	9.92 803 9-92 795 9.92 787 9.92 779 9.92 771	8 8 8 8 g	55 54 53 52 5i	8 9 10 20 30	3-9 4.4 4.8 9-7 14-5	3-7 4.2 4-7 9-3 14.0
1O ii 12 13 14	9.72 622 9.72 643 9.72 663 9.72 683 9.72 703	21 20 20 2O	9.79 860 9.79 888 9-79 9i6 9-79 944 9-79 972	28 28 28 28 28	O.2O 140 O.2O 112 0.20 084 0.20 056 O.2O O28	9.92 763 9-92 755 9.92 747 9.92 739 9.92 731	8 8 8 8 g	50 49 48 47 46	40 50	19-3 24.2 a	18.7 23-3 7
II 17 18 19	9.72 723 9-72 743 9.72 763 9.72 783 9.72 803	2O 20 20 2O	9.80 ooo 9.80 028 9.80 056 9.80 084 9.80 112	28 28 28 28 28	O.2O OOO 0.19 972 0.19 944 0.19 916 0.19 888	9.92 723 9.92 715 9.92 707 9.92 699 9.92 691	8 8 8 8 g	45 44 43 42 4i	]	6 2 7 3 8 3 9 4 [O 4	•7 .2 .6 .1 •5
SO 21 22 23 24	9.72 823 9.72 843 9.72 863 9.72 883 9.72 902	20 20 20 *9	9.80 140 9.80 168 9.80 195 9.80 223 9.80 251	28 27 28 28 28	0.19 860 0.19 832 0.19 805 0.19 777 0.19 749	9.92 683 9.92 675 9.92 667 9.92 659 9.92 651	8 8 8 8	4O 39 38 |	i	jo 9 *o 13 (.0 18 ;o 22	.0 •5 .0 •5
25 26 27 28 29	9.72 922 9.72 942 9.72 962 9.72 982 9.73 002	20 20 20 2O	9.80 279 9.80 307 9-8o 335 9.80 363 9.80 391	28 28 28 28	0.19 721 0.19 693 0.19 665 0.19 637 0.19 609	9.92 643 9-92 635 9.92 627 9.92 619 9.92 611	8 8 8 8	35 34 33 32 3i	6 7 8	ai 2.1 2-5 2.8	20 2.0 2-3 2.7
30 3i 32 33 34	9-73 022 9-73 041 9.73 061 9-73 °8i 9-73 ioi	J9 20 20 2O	9.80 419 9.80 447 9.80 474 9.80 502 9.80 530	28 27 28 28	0.19 581 0-19 553 0.19 526 0.19 498 0.19 470	9.92 603 9-92 595 9.92 587 9-92 579 9.92 571	8 8 8 8	3O 29 28 27 26	9 10 20 30 40	3-2 3-5 7.0 10.5 14.0	3-0 3-3 6-7 10.0 J3'3
35 36 37 38 39	9-73 121 9.73 140 9-73 160 9-73 180 9.73 200	19 2O 20 20	9-80 558 9.80 586 9.80 614 9.80 642 9.80 669	28 28 28 27	0.19 442 0.19 414 0.19 386 0-19 358 0.19 331	9-92 563 9-92 555 9.92 546 9-92 538 9-92 530	8 9 8 8	25 24 23 22 21	5° 6	J7-5 19 1.9	10.7 9 0.9
40 4i 42 43 44	9-73 219 9-73 239 9-73 259 9-73 278 9-73 298	*9 20 20 19 20	9.80 697 9.80 725 9-8o 753 9.80 781 9.80 808	28 28 28 27	0.19 303 0.19 275 0.19 247 0.19 219 0.19 192	9.92 522 9.92 514 9.92 506 9.92 498 9.92 490	8 8 8 8	2O 19 18 17 16	7 8 9 10 20	2.2 2-5 2.9 3-2 6.3	I.I 1.2 1.4 i-S 3-0
45 46 47 48 49	9-73 3i8 9-73 337 9-73 357 9-73 377 9-73 396	»9 20 20 19	9.80 836 9.80 864 9.80 892 9.80 919 9.80 947	28 28 27 28 _o	0.19 164 0.19 136 0.19 108 0.19 081 0.19 053	9.92 482 9-92 473 9.92 465 9-92 457 9.92 449	9 8 8 8 g	15 14 13 12 II	3° 40 50	9-5 12.7 15-8 8,	4-5 6.0 7-5
50 Si 52 53 54	9-73 4i6 9-73 435 9-73 455 9-73 474 9-73 494	19 20 19 2O	9.80 975 9.81 003 9.81 030 9.81 058 9.81 086	28 27 28 28	0.19 025 o.i 8 997 o.i 8 970 o.i 8 942 0.18 914	9.92 441 9-92 433 9.92 425 9.92 416 9.92 408	8 8 9 8 g	10 9 8 7 6	6 8 9 10	0.8 0.9 i.i 1.2 I 3	7 0.7 0.8 0.9 i.i I 2
55 56 57 58 59	9-73 513 9-73 533 9-73 552 9-73 572 9-73 59i	J9 20 i9 20 »9	9.81 113 9.81 141 9.81 169 9.81 196 9.81 224	27 28 28 27 28 QQ	0.18 887 o.i 8 859 0.18 831 o.i 8 804 o.i 8 776	9.92 400 9.92 392 9.92 384 9.92 376 9.92 367	8 8 8 9 |	5 4 3 2 I	20 30 40 50	2.7 4.0 5-3 6-7	2-3 3-5 4-7 5-8
00	9-73 611		9.81 252		o.i 8 748	9-92 359		0
	L. COB.	d.	L. Cotg.	C. d.	I..T.-MI-.	L. Sin.	d.	f	Pi	op. 1	Ms.

57'

33C

55

r	L.. Sin.	d.	L.Tang. c. d.	L.Cotg.	L. Cos.	d.		Prop.	Pts.
O i 2 3 4	9-73 6n 9-73 630 9-73 650 9-73 669 9-73 689	J9 20 19 2O 19 J9 20 X9 19 20 T9 19 20 19 19 20 *9 J9 19 *9 20 '9 19 '9 J9 20 J9 19 r9	9.81 252 9.81 279 9.81 307 9-8i 335 9.81 362	27 28 28 27 28 28 27 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 28 27 27 28 27 28 27 27 28 27 27 28 27 27 28 27 27 27 28 27 27 27 28	o.i 8 748 0.18 721 0.18 693 o.i 8 665 0.18 638	9-92 359 9-92 35i 9-92 343 9-92 335 9-92 326	8 8 8 9 8' 8 8 9 8 8 8 9 8 8 9 8 8 8 9 8 8 9 8 8 9 8 8 9 8 8 9 8 8 9 8 9 8 8 9 8 9 8 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8	6O 59 58 57 56	6 8 9 10 20 30	2 '* ' < <• C ll Ij 2^	8 27 5.8 2.7 !-3 3-2 t-7 3-6 [.2 4.1 \-7 4-5 )-3 9-o ^o 13-5 .7 18.0 1-3 22.5 20 2.0 2-3 2.7 3-0 11 10.0 13-3 16.7 19 i-9 2.2 2-5 2.9 3-2 6-3 9-5 12.7 15-8 18 1.8 2.1 2.4 2.7 3-° 6.0 9.0 12.0 15-0 9 8 .9 0.8 .1 0.9 .2 I.I .4 1.2 •5 i-3 .0 2.7 •5 4-o •o 5-3 •5 6.7
5 6 7 8 9	9-73 708 9-73 727 9-73 747 9-73 766 9-73 785	9.81 390 9.81 418 9.81 445 9-8i 473 9.81 500	0.18 610 0.18 582 0.18 555 0.18 527 0.18 500	9.92 318 9.92 310 9.92 302 9.92 293 9.92 285	55 54 53 52 5i
10 II 12 13 14	9-73 805 9-73 824 9-73 843 9-73 863 9-73 882	9.81 528 9.81 556 9-8i 583 9.81 611 9.81 638	0.18 472 0.18 444 0.18 417 0.18 389 0.18 362	9.92 277 9.92 269 9.92 260 9.92 252 9-92 244	5O 49 48 47 46	40 5°
15 16 17 18 19	9-73 9°i 9-73 921 9-73 94° 9-73 959 9-73 978	9.81 666 9.81 693 9.81 721 9.81 748 9.81 776	0.18 334 o.i 8 307 o.i 8 279 0.18 252 o.i 8 224	9-92 235 9.92 227 9.92 219 9.92 211 9.92 2O2	45 44 43 42 4i	6 7 8 9 10
20 21 22 23 24	9-73 997 9.74 017 9.74 036 9-74 055 9-74 074	9.81 803 9.81 831 9.81 858 9.81 886 9.81 913	0.18 197 0.18 169 o.i 8 142 0.18 114 0.18 087	9.92 194 9.92 186 9.92 177 9.92 169 9.92 161	4O 39 38 37 36	2 3 4 S I 2 3 A 5 i 2 3 4 5 6 7 8 9 10 20 3° 40 So	O o o o 6 7 8 9 0 0 0 0 0 6 7 8 9 o 0 0 0 0 c I I I I 3 4 6 7
25 26 27 28 29	9-74 093 9-74 H3 9.74 132 9-74 151 9-74 170	9.81 941 9.81 968 9.81 996 9.82 023 9.82 051	0.18 059 o.i 8 032 0.18 004 0.17 977 0.17 949	9.92 152 9.92 144 9.92 136 9.92 127 9.92 119	35 34 33 32 3i
30 3i 32 33 34	9.74 189 9.74 208 9.74 227 9.74 246 9-74 265	*9 19 19 19 19 19 19 J9 19 J9	9.82 078 9.82 106 9.82 133 9.82 161 9.82 188	0.17 922 0.17 894 0.17 867 0.17 839 0.17 812	9.92 in 9.92 IO2 9.92 094 9.92 086 9.92 077	30 29 28 27 26
35 36 37 38 39	9-74 284 9-74 303 9-74 322 9-74 341 9.74 360	9.82 215 9.82 243 9.82 270 9.82 298 9.82 325	0.17 785 0.17 757 0.17 73° 0.17 702 0.17 675	9.92 069 9.92 060 9.92 052 9.92 044 9-92 035	25 •24 23 22 21
4O 4i 42 43 44	9.74 379 9-74 398 9-74 417 9-74 436 9-74 455	*9 19 T9 T9 19 19 19 19 19 18 *9 *9 19 19 19 18 19 19 19 18 J9	9.82 352 9.82 380 9.82 407 9-82 435 9.82 462	0.17 648 0.17 620 0.17 593 0.17 565 0.17538	9.92 027 9.92 018 9.92 oio 9.92 002 9-9i 993	2O 19 18 17 16
45 46 47 48 49	9-74 474 9-74 493 9.74 512 ' 9-74 53i 9-74 549	9.82 489 9.82 517 9.82 544 9.82 571 9.82 599	0.17511 0.17483 0.17 456 0.17 429 0.17 401	9.91 985 9.91 976 9.91 968 9-9i 959 9.91 951	15 14 13 12 II
5O 5i 52 53 54	9.74 568 9-74 587 9.74 606 9-74 625 9-74 644	9.82 626 9.82 653 9.82 681 9.82 708 9-82 735	0.17 374 0.17 347 0.17 319 0.17 292 0.17 265	9.91 942 9-9i 934 9.91 925 9.91 917 9.91 908	10 9 8 7 6
55 56 57 58 59	9.74 662 9.74 68 1 9-74 700 9-74 719 9-74 737	9.82 762 9.82 790 9.82 817 9.82 844 9.82 871	0.17 238 O.I7 2IO 0.17 183 O.I7 156 0.17 129	9.91 900 9.91 891 9.91 883 9.91 874 9.91 866	5 4 3 2 I
6O	9-74 756	9.82 899	0.17 ioi	9.91 857	9	O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	/•	Prop. Pts.

56C

34C

r	L. Sin.	d.	L.Tang. c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
0 i 2 3 4	9-74 756 9-74 775 9-74 794 9.74 812 9-74 831	19 19 18 19 19 18 X9 19 18 *9 18 19 J9 18 19 18 19 18 19 18 19 18 '9 18 J9 18 T9 18 18 19 18 19 18 18	9.82 899 9.82 926 9-82 953 9.82 980 9.83 008	27 27 27 28 27 27 27 28 27 27 27 27 27 28 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 27 27 27 27 27	0.17 101 0.17 074 0.17 047 0.17 020 0.16 992	9.91 857 9.91 849 9.91 840 9.91 832 9.91 823	8 9 8 9 g	60 59 58 1	2 6 2 7 3 8 3 9 4 10 4 20 9 30 14 40 18 50 23 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 . 50 6 c 7 i 8 i 9 * 10 I 20 3 3° 4 40 6 50 7	3 37 .8 2.7 •3 3-2 -7 3-6 .2 4.1 •7 4-5 •3 9-° •o 13-5 .7 18.0 •3 22.5 26 2.6 3-o 3-5 3-9 4-3 8-7 13.0 17-3 21.7 19 i-9 2.2 2-5 2.9 i',2 9-5 12.7 15-8 18 1.8 2.1 2.4 2.7 3-o 6.0 9.0 12. 0 15-0 9 8 .9 0.8 .1 0.9 .2 I.I .4 1.2 •5 1-3 .0 2.7 •5 4-0 •o 5-3 •5 6.7
5 6 7 8 9	9-74 850 9.74 868 9-74 887 9-74 9°6 9-74 924	9-83 035 9.83 062 9.83 089 9.83 117 9.83 144	0.16 965 0.16 938 0.16 911 0.16 883 0.16 856	9.91 815 9.91 806 9.91 798 9.91 789 9.91 781	9 8 9 8	55 54 53 52 5i
1O II 12 13 14	9-74 943 9-74 96i 9-74 98o 9-74 999 9-75 oi7	9.83 171 9.83 198 9.83 225 9.83 252 9.83 280	0.16 829 0.16 802 0.16 775 o.i 6 748 o.i 6 720	9.91 772 9.91 763 9-9i 755 9.91 746 9.91 738	9 8 9 8 9 9 8 9 8 9 9 8 9 9 8 9 9 8 9 9 8 9 9 8 9 9 9 8 9 9 8 9 9 9 8 9 9 9 9 g	5O 49 48 47 46
IS 16 17 18 19	9-75 036 9-75 054 9-75 073 9-75 091 9-75 no	9-83 307 9-83 334 9.83 361 9.83 388 9-83 415	0.16 693 0.16 666 0.16 639 0.16 612 0.16 585	9.91 729 9.91 720 9.91 712 9.91 703 9.91 695	45 44 43 42 41
2O 21 22 23 24	9-75 128 9-75 147 9-75 165 9-75 184 9-75 202	9.83 442 9.83 470 9-83 497 9-83 524 9-83 55i	0.16 558 0.16 530 o.i 6 503 o.i 6 476 0.16 449	9.91 686 9.91 677 9.91 669 9.91 660 9.91 651	40 39 38 P
25 26 27 28 29	9-75 221 9-75 239 9-75 258 9-75 276 9-75 294	9-83 578 9.83 605 9.83 632 9-83 659 9.83 686	0.16 422 0.16 395 0.16 368 0.16 341 0.16 314	9.91 643 9.91 634 9.91 625 9.91 617 9.91 608	35 34 33 32 3i
30 3i 32 33 34	9-75 313 9-75 33i 9-75 350 9-75 368 9-75 386	9-83 713 9.83 740 9-83 768 9-83 795 9.83 822	0.16 287 o.i 6 260 0.16 232 0.16 205 0.16 178	9-91 599 9.91 591 9.91 582 9-91 573 9-9i 565	30 29 28 27 26
35 36 37 38 39	9-75 405 9-75 423 9-75 44i 9-75 459 9-75 478	T9 18 18 18 J9 18 18 *9 18 18 18 18 19 •a 18 18 18 18 19 18 18 18 18 18 18 18	9.83 849 9.83 876 9-83 903 9-83 930 9-83 957	0.16 151 0.16 124 0.16 097 o.i 6 070 0.16 043	9-9i 556 9-9i 547 9-9i 538 9-9i 530 9.91 521	25 24 23 22 21
40 4i 42 43 44	9-75 496 9-75 514 9-75 533 9-75 55i 9-75 569	9.83 984 9.84 on 9.84 038 9-84 065 9.84 092	0.16 016 0.15 989 0.15 962 0.15 935 0.15 908	9.91 512 9.91 504 9-9i 495 9.91 486 9.91 477	20 19 18 17 16
45 46 47 48 49	9-75 587 9-75 605 9-75 624 9-75 642 9-75 660	9.84 119 9.84 146 9.84 173 9.84 200 9.84 227	0.15 881 0-15 854 0.15 827 0.15 800 0.15 773	9.91 469 9.91 460 9-9i 451 9.91 442 9.9i 433	15 14 13 12 II
50 5i 52 53 54	9-75 678 9-75 696 9-75 7H 9-75 733 9-75 751	9.84 254 9.84 280 9.84 307 9-84 334 9.84 361	0.15 746 0.15 720 0.15693 0.15 666 0.15 639	9-9i 425 9.91 416 9.91 407 9.91 398 9.91 389	9 9 9 9 g	10 9 8 7 6
55 56 57 58 59	9-75 769 9-75 787 9-75 805 9-75 823 9-75 841	9.84 388 9.84 415 9.84 442 9.84 469 9.84 496	0.15 612 0.15 585 0.15 558 0.15 531 0.15 504	9.91 381 9.91 372 9-9i 363 9-9i 354 9-9i 345	9 9 9 9	5 4 3 2 I
GO	9-75 859	9-84 523	0.15 477	9-9i 336		0
	L. < os.	d.	L*Cotff.	c. d.	L.TniiK.	L. Sin. d.	/•	Prop. 1	'ts.

55C

35C

57

"	L. Sin.	d.	L.Tang.	c. d.	JL. Cotg.	L. Cos.	d.		Prop	. Pt«.
0 I 2 3 4	9-75 859 9-75 877 9-75 895 9-75 9J3 9-75 93i	18 18 18 18	9-84 523 9-84 55o 9.84 576 9.84 603 9.84 630	27 26 27 27	0.15 477 0.15 450 0.15 424 0.15 397 0.15 370	9.91 336 9-91 328 9.91 319 9.91 310 9.91 301	8 9 9 9	60 59 58 57 56	2 6 2 7 3	7 a6 .7 2.6 • 2 3.O
5 6 7 8 9	9-75 949 9-75 967 9-75 985 9.76 003 9.76 021	18 18 18 18	9.84 657 9.84 684 9.84 711 9.84 738 9.84 764	27 27 27 27 26	0.15 343 0.15 316 0.15 289 0.15 262 0.15 236	9.91 292 9-91 283 9 9i 274 9.91 266 9.91 257	9 9 9 8 9	55 54 53 52	8 3 9 4 10 4 20 9 3° J3	•6 3-5 •i 3-9 •5 4-3 .0 8.7 •5 13-0
1O ii 12 13 14	9.76 039 9.76 057 9.76 075 9.76 093 9.76 in	18 18 18 18	9.84 791 9.84 818 9.84 845 9.84 872 9.84 899	27 27 27 27 27	0.15 209 0.15 182 0.15 155 0.15 128 0.15 101	9.91 248 9.91 239 9.91 230 9.91 221 9.9! 212	9 9 9 9	50 49 48 47 46	40 18 50 22	.0 17.3 •5 21.7 18
15 16 17 18 19	9.76 129 9.76 146 9.76 164 9.76 182 9.76 200	17 18 18 18	9.84 925 9.84 952 9.84 979 9.85 006 9-85 033	27 27 27 27 26	0.15 075 0.15 048 0.15 021 0.14 994 0.14 967	9.91 203 9.91 194 9.91 185 9.91 176 9.91 167	9 9 9 9 9	45 44 43 42	6 7 8 9 10	1.8 2.1 2-4 2.7
21 22 23 24	9.76 218 9.76 236 9.76 253 9.76 271 9.76 289	18 18 18	9-85 059 9.85 086 9-85 "3 9.85 140 9.85 166	27 27 27 26	0.14 941 0.14 914 0.14 887 0.14 860 0.14 834	9.91 158 9.91 149 9.91 141 9.9I 132 9.91 123	9 8 9 9	40 39 38 37 36	20 30 40 50	6.0 9.0 12.0 15.0
25 26 27 28 29	9.76 307 9.76 324 9.76 342 9.76 360 9.76 378	17 18 18 18	9-85 193 9.85 220 9.85 247 9-85 273 9.85 300	27 27 26 27	0.14 807 0.14 780 0.14 753 0.14 727 0.14 700	9.91 114 9.91! IO5 9.91 096 9.91 087 9.91 078	9 9 9 9	35 34 33 32	• 6 7 8	17 1-7 2.O 2-3
30 32 33 34	9-76 395 9.76 413 9.76 431 9.76 448 9.76 466	17 18 18 i? 18	9-85 327 9-85 354 9.85 380 9.85 407 9-85 434	27 27 26 27 27 26	0.14 673 0.14 646 0.14 620 0.14 593 0.14 566	9.91 069 9.91 060 9.91 051 9.91 042 9.91 033	9 9 9 9	30 29 28 27 26	9 10 20 30 40 tn	2.6 2.8 5.7 8-5 ".3 14 2
It 37 38 39	9.76 484 9.76 501 . 9.76 519 9-76 537 9-76 554	17 18 18 17	9.85 460 9.85 487 9-85 5H 9-85 540 9-85 567	27 27 26 27	0.14 540 0.14513 0.14 486 0.14 460 0.14 433	9.91 023 9.91 014 9.91 005 9.90 996 9.90 987	9 9 9 9	25 24 23 22 21	6	10 1.0
4O 42 43 44	9-76 57? 9.76 590 9.76 607 9.76 625 9.76 642	18 18 17	9-85 594 9.85 620 9.85 647 9.85 674 9.85 700	27 26 27 27 26	0.14 406 0.14 380 0.14 353 0.14 326 0.14 300	9.90 978 9.90 969 9.90 960 9.90 951 9.90 942	9 9 9 9	20 19 18 17 16	8 9 10 20 qo	1.2 3-3 c o
45 46 47 48 49	9.76 660 9.76 677 9.76 695 9.76 712 9.76 730	17 18 17 18	9.85 727 9-85 754 9-85 78o 9.85 807 9-85 834	27 27 26 27 27	0.14 273 0.14 246 0.14 220 0.14 193 0.14 166	9-9° 933 9.90 924 9.90 915 9.90 906 9.90 896	9 9 9 10	15 14 13 12 II	40 50	6.7 8-3 90
5O 52 53 54	9.76 747 9.76 765 9.76 782 9.76 800 9.76 817	18 17 18 17	9.85 860 9.85 887 9-85 913 9.85 940 9.85 967	27 26 27 27 -£	0.14 140 0.14 113 0.14 087 0.14 060 0.14 033	9.90 887 9.90 878 9.90 869 9.90 860 9.90 85!	9 9 9 9	10 9 8 7 6	6 o 7 i 8 I 9 i IO I	.9 0.8 .1 0.9 .2 I.I .4 1.2 5 * 3
55 56 57 58 59	9.76 835 9.76 852 9.76 870 9.76 887 9.76 904	17 18 17 17	9-85 993 9.86 020 9.86 046 9.86 073 9.86 100	27 26 27 27	0.14 007 0.13 980 0.13 954 0.13 927 0.13 900	9.90 842 9.90 832 9.90 823 9.90 814 9.90 805	10 9 9 9	5 4 3 2 I	20 3 30 4 40 o 50 7	.0 2.7 •5 4-0 •o 5-3 •5 6.7
60	9.76 922		9.86 126		0.13 874	9.90 796	9	O
	L. Cos.	d.	L. Cotg.	c. d.	L.Tang.	L. Sin.	d.	'	Prop	. Pts.

54C

36C

/	L. Sin.	d.	L.Tang.	c. d.| L.Cotg.	L. Cos.	d.		Prop. Pts. ,
0 I 2 3 4	9.76 922 9.76 939 9-76 957 9.76 974 9.76 991	17 18 17 17 18 17 18 17 '7 18 '7 17	9.86 126 9.86 153 9.86 179 9.86 206 9.86 232	27 26 27 26 27 26 27 26 27 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 26 27 26 26 27 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 27 •6 26 26	0.13 874 0.13 847 0.13 821 0.13 794 0.13 768	9.90 796 9.90 787 9.90 777 9.90 768 9-9° 759	9 10 9 9 9 9 10 9 9 9 10 9 9 9 10 9 9 9 10 9 9 10 9 9 9 10 9 9 10 9 9 10 9 10 9 9 10 9 9 10 9 10 9 10 9 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9	60 59 58 57 56	2 6 2 7 3 8 3 9 4 10 4 20 C 30 13 40 18 50 22 6 7 8 9 10 20 3° 40 5° 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 i 7 3 8 i 9 i 10 I 20 3 30 5 40 6 50 -a	1 •7 .2	26 2.6 3.O
6 7 8 9	9.77 009 9.77 026 9-77 043 9.77 061 9.77 078	9.86 259 9.86 285 9.86 312 9.86 338 9.86 365	0.13 741 0.13 715 0.13 688 0.13 662 0.13 635	9.90 750 9.90 741 9.90 731 9.90 722 9.90 713	55 54 53 52	•6 i-5 •i 3-9 •5 4-3 .0 8.7 •5 13-0 .0 17.3 •5 21.7 18 1.8 2.1 2.4 2.7 3-° 6.0 9.0 12.0 15-0 17 2.0 2-3 2.6 2.8 5-7 8-5 "•3 14.2 16 1.6 1-9 2.1 2.4 2-7 5-3 8.0 10.7 13-3 10 9 .0 0.9 .2 I.I •3 1-2 •5 1-4 •7 i-5 •3 3-° •o 4-5 .7 6.0 •3 7-5
1O ii 12 13 14	9-77 095 9.77 112 9.77 130 9-77 147 9-77 164	9-86 392 9.86 418 9-86 445 9.86 471 9.86 498	0.13 608 0.13 582 0.13 555 0.13 529 0.13 502	9.90 704 9.90 694 9.90 685 9.90 676 9.90 667	5O 49 48 47 46
15 16 17 18 19	9.77 181 9.77 199 9.77 216 9-77 233 9-77 250	18 '7 17 17 18 17 17	9-86 524 9.86 551 9.86 577 9.86 603 9.86 630	0.13 476 0.13 449 0.13 423 0.13 397 0.13 370	9.90 657 9.90 648 9.90 639 9.90 630 9.90 620	45 44 43 42
20 21 22 23 24	9.77 268 9-77 285 9-77 302 9-77 319 9-77 336	9.86 656 9.86 683 9.86 709 9.86 736 9.86 762	0.13 344 0.13 317 0.13 291 0.13 264 0.13 238	9.90 611 9.90 602 9.90 592 9-90 583 9.90 574	40 39 38 11
25 26 27 28 29	9-77 353 9-77 370 9-77 387 9-77 405 9-77 422	I7 17 18 17	9.86 789 9.86 815 9.86 842 9.86 868 9.86 894	O.I3 211 0.13 185 0.13 158 0.13 132 0.13 106	9-9° 565 9-9° 555 9.90 546 9-90 537 9.90 527	35 34 33 32
30 31 32 33 34	9-77 439 9-77 456 9-77 473 9-77 49° 9-77 5°7	17 17 17 17 17 17 17 17 17 16 17 17 17 16 >7 »7 16	9.86 921 9.86 947 9.86 974 9.87 ooo 9.87 027	0.13 079 0.13 053 0.13 026 0.13 ooo 0.12 973	9.90 518 9.90 509 9.90 499 9.90 490 9.90 480	30 29 28 27 26
35 36 37 38 39	9-77 524 9-77 541 9-77 558 9-77 575 9-77 592	9-87 053 9.87 079 9.87 106 9.87 132 9.87 158	0.12 947 O.I2 921 0.12 894 0.12 868 0.12 842	9.90 471 9.90 462 9.90 452 9.90 443 9-9° 434	25 24 23 22 21
40 42 43 44	9-77 609 9.77 626 9-77 643 9.77 660 9-77 677	9.87 185 9.87 211 9.87 238 9.87 264 9.87 290	0.12 815 0.12 789 0.12 762 0.12 736 0.12 710	9.90 424 9.90 415 9.90 405 9.90 396 9.90 386	20 19 18 17 16
47 48 49	9.77 694 9-77 7ii 9-77 728 9-77 744 9-77 76i	9.87 317 9-87 343 9-87 369 9.87 396 9.87 422	0.12 683 0.12 657 0.12 631 O.I 2 604 0.12 578	9.90 377 9.90 368 9-9° 358 9.90 349 9-90 339	15 14 13 12 II
5O 51 52 53 54	9.77 778 9-77 795 9.77 812 9-77 829 9-77 846	9.87 448 9-87 475 9.87 501 9.87 527 9-87 554	0.12 552 0.12 525 0.12 499 0.12 473 0.12 446	9.90 330 9.90 320 9.90311 9.90 301 9.90 292	10 9 8 7 6
55 56 57 58 59	9.77 862 9-77 879 9-77 896 9-77 913 9-77 930	9.87 580 9.87 606 9-87 633 9.87 659 9.87 685	0.12 420 0.12 394 0.12 367 0.12 341 0.12 315	9.90 282 9.90 273 9.90 263 9.90 254 9.90 244	5 4 3 2 I
	9-77 946	9.87 711	0.12 289	9-90 235	0
	L. COB. d.	L. Cotg. c. d. L.Tang.	L. Sin. d.	f	Prop. I'IN.

53C

37<

59

r	L. Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
0 i 2 3 4	9-77 946 9-77 963 9-77 98o 9-77 997 9.78 013	17 17 *7 16	9.87 711 9.87 738 9.87 764 9.87 790 9.87 817	27 26 26 27 26 26 26 27 26 26 26 27 26 26 26 26 27 26 26 26 26 27 26 26 26 26 27 26 26 26 26 26 27 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26	O.I2 289 0.12 262 O.I 2 236 0.12 210 0.12 183	9-90 235 9-90 225 9.90 216 9.90 206 9.90 197	10 9 10 9	60 59 58 57 56	6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50	27 2.7 3-2 3-6 4.1 4-5 9.0 13-5 18.0 22.5 26 2.6 3-0 3-? 3-9 4-3 8.7 13-0 17-3 21.7 17 1-7 2.0 2-3 2.6 2.8 5-7 8-5 "•3 14.2 16 1.6 1.9 2.1 2.4 2.7 5-3 8.0 10.7 13-3 io 9 .0 0.9 .2 I.I •3 1.2 •5 1-4 •7 S i.S 1-3 3-0 >.o 4-5 >.7 6.0 •3 7-5
i 7 8 9	9.78 030 9.78 047 9.78 063 9.78 080 9.78 097	*7 i? 16 17 i? 16	9.87 843 9.87 869 9.87 895 9.87 922 9.87 948	0.12 157 0.12 131 0.12 lOg 0.12 078 0.12 052	9.90 187 9.90 178 9.90 168 9.90 159 9.90 149	9 IO 9 10 IO 9 10 9 10 10 9 10 9 10 10 9 10 10 9 10 IO 9 10 10 9 10 IO 9 10 IO 10 ,9 10 10 10 9 10 10 10 9 IO 10 10 10 9 10 10 10 10 IO 9 10 10 IO IO	55 54 53 52 5i
IO ii 12 13 14	9.78 113 9.78 130 9.78 147 9.78 163 9.78 180	17 i? 16 17	9.87 974 9.88 ooo 9.88 027 9.88 053 9.88 079	O.I 2 O26 0.12 000 o.i i 973 o.i i 947 o.ii 921	9.90 139 9.90 130 9.90 120 9.90 III 9.90 ioi	50 49 48 47 46
15 16 17 18 19	9.78 197 9.78 213 9.78 230 9.78 246 9.78 263	16 17 16 X7	9.88 105 9.88 131 9.88 158 9.88 184 9.88 210	o.i i 895 o.ii 869 o.ii 842 o.ii 816 o.ii 790	9.90 091 9.90 O82 9.90 072 9.90 063 9.90 053	45 44 43 42 41
2O 21 22 23 24	9.78 280 9.78 296 9-78 313 9.78 329 9.78 346	16 i? 16 17 16	9.88 236 9.88 262 9-88 289 9-88 315 9.88 341	o.ii 764 o.ii 738 o.ii 711 o.ii 685 o.ii 659	9.90 043 9.90 034 9.90 O24 9.90 014 9.90 005	40 39 38 37 36
25 26 27 28 29	9.78 362 9-78 379 9-78 395 9.78 412 9.78 428	17 16 17 16	9.88 367 9-88 393 9.88 420 9.88 446 9.88 472	o.ii 633 o.ii 607 o.ii 580 o.ii 554 o.ii 528	9.89 995 9.89 985 9.89 976 9.89 966 9.89 956	35 34 33 S2 3i
3O 3i 32 33 34	9-78 445 9.78 461 9.78 478 9.78 494 9.78 510	J7 16 17 16 16	9.88 498 9.88 524 9-88 550 9-88 577 9.88 603	o.ii 502 o.ii 476 o.ii 450 o.ii 423 o.ii 397	9.89 947 9-89 937 9.89 927 9.89 918 9.89 908	30 29 28 27 26
35 36 37 38 39	9.78 527 9-78 543 9.78 560 9.78 576 9.78 592	16 17 16 16	9.88 629 9.88 655 9.88 681 9.88 707 9-88 733	o.ii 371 o.ii 345 o.ii 319 o.ii 293 o.ii 267	9.89 898 9.89 888 9.89 879 9.89 869 9.89 859	25 24 23 22 21
40 41 42 43 44	9.78 609 9.78 625 9.78 642 9.78 658 9.78 674	16 17 16 16	9-88 759 9.88 786 9.88 812 9.88 838 9.88 864	o.ii 241 o.ii 214 o.ii 188 o.ii 162 o.ii 136	9.89 849 9.89 840 9.89 830 9.89 820 9.89 810	20 19 18 17 16
45 46 47 48 49	9.78 691 9.78 707 9.78 723 9-78 739 9.78 756	I7 16 16 16 17 16 16 i? 16 16 16 16 J7 16 16 16	9.88 890 9.88 916 9.88 942 9.88 968 9.88 994	O.II IIO o.n 084 o.n 058 o.n 032 o.n 006	9.89 801 9.89 791 9.89 781 9.89 771 9.89 761	15 14 13 12 II
50 5i 52 53 54	9.78 772 9.78 788 9.78 805 9.78 821 9.78 837	9.89 020 9.89 046 9.89 073 9.89 099 9.89 125	o.io 980 o.io 954 o.io 927 o.io 901 o.io 875	9.89 752 9.89 742 9.89 732 9.89 722 9.89 712	10 9 8 6	6 ] 7 3 8 ] 9 J IO ]
55 56 57 58 59	9-78 853 9.78 869 9.78 886 9.78 902 9.78 918	9.89 151 9.89 177 9.89 203 9.89 229 9-89 255	o.io 849 o.io 823 o.io 797 o.io 771 o.io 745	9.89 702 9.89 693 9.89 683 9.89 673 9.89 663	5 4 3 2 I	20 I 30 f 40 < 50 J
GO	9-78 934	9.89 281	o.io 719	9-89 653	0
	L. Cos.	d.	L,. Cotg.	c. d.	L.Tang.	JL. Sin.	d.	f	Prop. Pts.

52<

6o

38<

r	L. Sin.	d.	L. Tang.	c. d.	JL. Cotg.	L. Cos.	d.		Pi	•oi	>.	Pts.
O i 2 3 4	9-78 934 9.78 950 9.78 967 9.78 983 9.78 999	16 *7 16 16 16	9.89 281 9.89 307 9-89 333 9-89 359 9-89 385	26 26 26 26 26	o.io 719 o.io 693 o.io 667 o.io 641 o.io 615 .	9-89 653 9.89 643 9-89 633 9.89 624 9.89 614	IO 10 9 10	60 59 58 57 56	6 7	2 2 J	5 .6 .0	25 2-5 2.9
5 6 7 8 9	9-79 oi5 9-79 031 9-79 047 9-79 063 9.79 079	16 16 16 16 16	9.89 411 9-89 437 9.89 463 9.89 489 9-89 515	26 26 26 26 26	o.io 589 o.io 563 o.io 537 o.io 511 o.io 485	9.89 604 9-89 594 9.89 584 9-89 574 9.89 564	10 IO IO 10	55 54 53 52 51	8 9 10 20 3°	3 3 4 8 .'3	•5 •9 •3 •7 .0	3-3 3-8 4.2 8-3 12.5
10 ii 12 13 14	9-79 095 9.79 in 9.79 128 9-79 144 9.79 160	16 J7 16 16 16	9.89 541 9.89 567 9-89 593 9.89 619 9.89 645	26 26 26 26 26	o.io 459 o.io 433 o.io 407 o.io 381 o-io 355	9-89 554 9.89 544 9-89 534 9.89 524 9.89 514	IO IO 10 10	50 49 48 47 46	40 50	17 21	•3 •7 i	16.7 20.8 7
15 16 17 18 19	9.79 176 9-79 192 9.79 208 9-79 224 9.79 240	16 16 16 16 16	9.89 671 9.89 697 9.89 723 9.89 749 9-89 775	26 26 26 26 26	o.io 329 o.io 303 o.io 277 o.io 251 o.io 225	9.89 504 9-89 495 9.89 485 9-89 475 9.89 465	9 10 10 IO	45 44 43 42 4i	]	6 7 8 9 to	2 2 2 2	•7 .0 :! .8
2O 21 22 23 24	9-79 256 9-79 272 9.79 288 9-79 304 9-79 319	16 16 16 15 rfi	9.89 801 9.89 827 9-89 853 9-89 879 9.89 905	26 26 26 26 ifi	o.io 199 o.io 173 o.io 147 O.IO 121 o.io 095	9-89 455 9-89 445 9-89 435 9.89 425 9.89 415	10 10 10 IO	40 39 38 37 36	j i i c	>0 50 p )0	5 8 ii H	•7 •5 •3 .2
25 26 27 28 29	9-79 335 9-79 35i 9-79 367 9-79 383 9-79 399	16 16 16 16	9.89 931 9-89 957 9.89 983 9.90009 9-90 035	26 26 26 26	o.io 069 o.io 043 o.io 017 0.09 991 0.09 965	9.89 405 9-89 395 9-89 385 9-89 375 9.89 364	xo IO 10 II	35 34 33 32 3i	6 8	I I I 2	5 .6 •9 .1	15 1.5 1.8 2.0
30 3i 32 33 34	9-79 415 9-79 431 9-79 447 9-79 463 9-79 478	16 16 16 IS 16	9.90 06 1 9.90 086 9.90 112 9.90 138 9.90 164	25 26 26 26 26	0.09 939 0.09 914 0.09 888 0.09 862 0.09 836	9-89 354 9-89 344 9-89 334 9.89 324 9.89 314	IO 10 10 10	30 29 28 27 26	9 10 20 30 40 CO	2 2 5 8 10 70	•4 -7 •3 .0 •7	2-3 2-5 5-0 7.5 10.0 12 ?
!I 37 38 39	9.79 494 9-79 51° 9-79 526 9-79 542 9-79 558	16 16 16 16	9.90 190 9.90 216 9.90 242 9.90 268 9.90 294	26 26 26 26 tfi	0.09 810 0.09 784 0.09 758 0.09 732 0.09 706	9.89 304 9.89 294 9.89 284 9.89 274 9.89 264	10 10 10 IO	25 24 23 22 21		6	i	I I
4O 41 4« 43 44	9-79 573 9-79 589 9.79 605 9.79 621 9-79 636	16 16 16 »5 tfi'	9.90 320 9.90 346 9.90 371 9.90 397 9.90 423	26 25 26 26 ~f	0.09 680 0.09 654 0.09 629 0.09 603 0.09 577	9.89 254 9.89 244 9-89 233 9.89 223 9.89 213	IO XI 10 10	20 19 18 17 16		7 8 9 10 20 TO	3 C	3 7 8 7 C
45 46 47 48 49	9-79 652 9.79 668 9-79 684 9.79699 9-79 715	16 16 IS 16 tfi	9.90 449 9-90 475 9.90 501 9.90 527 9-90 553	26 26 26 26	0.09 551 0.09 525 0.09499 0.09 473 0.09 447	9-89 203 9.89 193 9-89 183 9.89 173 9.89 162	10 10 IO II	15 14 13 12 II		40 50	7 9	3 2
50 51 52 53 54	9-79 731 9-79 746 9-79 762 9-79 778 9-79 793	«5 16 •6 15 ifi	9.90 578 9.90604 9.90 630 9.90 656 9.90 682	25 26 26 26 26 •>fi	0.09 422 0.09 396 0.09 370 0.09 344 0.09 318	9-89 152 9.89 142 9.89 132 9.89 122 9.89 112	10 10 10 10	10 9 8 7 6	6 7 8 9 IO		0 2 3 5 7	0-9 I.I 1.2 1.4 1.5
55 56 57 58 .53-	9-79 809 9-79 825 9.79 840 9-79 856 9-79 872	16 15 16 16	9.90 708 9-90 734 99° 759 9.90 785 9.90 8ll	26 25 26 26 ofi	0.09 292 0.09 266 0.09 241 0.09 215 0.09 189	9.89 ioi 9.89 091 9.89 081 9.89 071 (;.8<y O')0	10 10 10 II	5 4 3 3 I	20 3° 40 50	3 5 6 8	3 0 7 3	3-o 4-5 6.0 7-5
00	9-79 887	J5	9.«,o 837		0.09 163	9.89 050		O
	L. Cos.	d.	I,. cotK.	c. d.	L.TniiK.	L. Sin.	d.	r	Pr	op	•'	Ms.

51'

39C

61

r	L. Sin.	d.	L.Taug. c. d.	L. Cuts.	L,. Cos.	d.		Prop. Pts.
0 1 8 9	9-79 887 9-79 9°3 9-79 9i8 9-79 934 9-79 95°	16 15 16 16 15 16 i5 16 15 16 15 16 15 16 15 16 15 IS 16 iS 16 i5 16 15	9.90 837 9.90 863 9.90 889 9.90 914 9.90 940	26 26 25 26 26 26 26 25 26 26 26 26 25 26 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 25 26 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25	0.09 163 0.09 137 0.09 in 0.09 086 0.09 060	9.89 050 9.89 040 9.89 030 9.89 020 9.89 OO9	10 10 10 ii 10 IO II IO 10 10 II 10 10 II IO 10 II 10 IO II IO IO II 10 IO II 10 II 10 IO II 10 II IO II 10 10 II IO II IO II 10 II 10 II 10 II IO II IO II II 10	6O 59 58 57 56	6 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 50 6 8 9 10 20 30 40 50 6 7 8 9 10 20 3° 40 50 6 i 7 i 8 I 9 I IO I 20 3 3° 5 40 7 50 9	26 2.6 3-° 3-5 3-9 4-3 8-7 13.0 17-3 21.7 »5 2-5 2.9 3-3 3-8 4.2 8-3 12.5 16.7 20.8 16 1.6 1.9- 2.1 2.4 2-7 5-3 8.0 10.7 13-3 »5 1-5 1.8 2.0 2-3 2-5 5-0 7.5 IO.O 12.5 [I 10 .1 I.O .3 1.2 •5 1-3 •7 i-5 .8 1.7 •7 3-3 •5 5-0 •3 6.7 .2 8.3
9-79965 9.79981 9-79 996 9.80 012 9.80 027	9.90 966 9.90 992 9.91 018 9.91 043 9.91 069	0.09 034 0.09 008 0.08 982 0.08 957 0.08 931	9.88 999 9.88 989 9.88 978 9.88 968 9.88 958	55 54 53 52 51
10 ii 12 lj 11 3 19	9.80*043 9.80 058 9.80 074 9.80 089 9.80 105	9.91 095 9.9! 121 9.91 147 9.91 172 9.91 198	0.08 905 0.08 879 0.08 853 0.08 828 0.08 802	9.88 948 9.88 937 9.88 927 9.88 917 9.88 906	50 49 48 47 46
9.80 120 9.80 136 9.80 151 9.80 166 9.80 182	9.91 224 9.91 250 9.91 276 9.91 301 9.91 327	0.08 776 0.08 750 0.08 724 0.08 699 0.08 673	9.88 896 9.88 886 9-88 875 9.88 865 9-88 855	45 44 43 42 4i
20 21 22 23 24 |	9.80 197 9.80 213 9.80 228 9.80 244 9.80 259	9-91 353 9-91 379 9.91 404 9.91 430 9.91 456	0.08 647 0.08 621 0.08 596 0.08 570 0.08 544	9.88 844 9.88 834 9.88 824 9.88 813 9.88 803	40 39 38 11
25 26 27 28 29	9.80 274 9.80 290 9.80 305 9.80 320 9.80 336	16 IS 15 16	9.91 482 9.91 507 9-91 533 9-9i 559 9-91 585	0.08 518 0.08 493 0.08 467 0.08 441 0.08 415	9.88 793 9.88 782 9.88 772 9.88 761 9.88 751	35 34 33 32 3i
30 3i 32 33 34 35 36 37 38 39	9.80 351 9.80 366 9.80 382 9.80 397 9.80 412	*5 16 IS 15	9.91 610 9.91 636 9.91 662 9.91 688 9.91 713	0.08 390 0.08 364 0.08 338 0.08 312 0.08 287	9.88 741 9-88 730 9.88 720 9.88 709 9.88 699	30 29 28 27 26
9.80 428 9.80 443 9.80 458 9.80 473 9.80 489	15 i5 15 16	9-9i 739 9.91 765 9.91 791 9.91 816 9.91 842	0.08 261 0.08 235 0.08 209 0.08 184 0.08 158	9.88 688 9.88 678 9.88 668 9.88 657 9.88 647	25 24 23 22 21
40 41 42 43 44 |	9.80 504 9.80 519 9-8o 534 9.80 550 9.80 565	XS 15 15 16 15 15 15 IS 15 16	9.91 868 9.91 893 9.91 919 9-9i 945 9.91 971	0.08 132 0.08 107 0.08 08 1 0.08 055 0.08 029	9.88 636 9.88 626 9.88 615 9.88 605 9.88 594	20 19 18 17 16
45 46 47 48 49	9.80 580 9-8o 595 9.80 610 9.80 625 9.80 641	9.91 996 9.92 022 9.92 048 9.92 073 9.92 099	0.08 004 0.07 978 0.07 952 0.07 927 0.07 901	9.88 584 9-88 573 9-88 563 9-88 552 9-88 542	15 14 13 12 II
5O 5i 52 53 54 |	9.80 656 9.80 671 9.80 686 9.80 701 9.80 716	*5 15 15 IS 15	9.92 125 9.92 150 9.92 176 9.92 202 9.92 227	0.07 875 0.07 850 0.07 824 0.07 798 0.07 773	9-88 531 9.88 521 9.88 510 9.88 499 9.88 489	10 9 8 7 6
55 56 57 58 59	9.80 731 9.80 746 9.80 762 9.80 777 9.80 792	JS '5 16 15 15 IS	9-92 253 9.92 279 9.92 304 9.92 330 9-92 356	0.07 747 0.07 721 0.07 696 0.07 670 0.07 644	9.88 478 9.88 468 9.88 457 9.88 447 9-88 436	10 II 10 II	5 4 3 2 I
60 1	9.80 807	9-92 381	0.07 619	9-88 425		0
1 L. Cos.	d.	L. Cot&.	C. d.	L.Tang.	L. Sin.	d.	r	Prop. Pts.

50<

62

40°

f	L. Sin.	d.	L.Tang.	c. d.	L.Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9.80 807 9.80 822 9.80 837 9.80 852 9.80 867	15 15 15 15 15 15 15 15 15 15 15 15 15 is 15 15 14 15 15 15 IS 15 15 15 14 15 15 15 15 14 15 15 15 IS 14 IS IS 14 IS	9.92 381 9.92 407 9-92 433 9.92 458 9.92 484	26 26 25 26 26 25 26 26 25 26 25 26 26 25 26 26 25 26 25 26 26 23 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 25 96 as	0.07 619 0.07 593 0.07 567 0.07 542 0.07 516	9.88 425 9-88 415 9.88 404 9.88 394 9-88 383	10 II 10 II II 10 II II IO II II IO II II 10 II II IO II II II 10 II II II 10 II II II IO II II II II	60 59 58 57 56	6 7	26 2.6 3-o 3-5 3-9 4-3 8-7 13.0 17-3 21.7 25 2-5 2.9 3-3 3-8 4-2 8-3 12.5 16.7 20.8 15 i-5 1.8 2.0 2-3 2-5 5-0 7-5 IO.O 12.5 14 i-4 1.6 1.9 2.1 2.3 4-7 7.0 9-3 II- 7 [I 10 .1 I.O .3 1-2 5 1-3 •7 i.S .8 1.7 •7 3-3 •5 5-0 •3 6.7 .2 8.3
5 6 7 8 9	9.80 882 9.80 897 9.80 912 9.80 927 9.80 942	9.92 510 9-92 535 9.92 561 9.92 587 9.92 612	0.07 490 0.07 465 0.07 439 0.07 413 0.07 388	9.88 372 9.88 362 9.88 351 9.88 340 9.88 330	55 54 53 52 5i	8 9 10 20 30
10 ii 12 13 14	9.80 957 9.80 972 9.80 987 9.8l 002 9.8l 017	9.92 638 9.92 663 9.92 689 9.92 715 9.92 740	0.07 362 0.07 337 0.07 311 0.07 285 0.07 260	9.88 319 9.88 308 9.88 298 9.88 287 9.88 276	50 49 48 47 46	40 So
15 16 17 18 19	9.8l 032 9.8l 047 9.81 061 9.81 076 9.81 091	9.92 766 9.92 792 9.92 817 9.92 843 9.92 868	0.07 234 0.07 208 0.07 183 0.07 157 0.07 132	9.88 266 9.88 255 9.88 244 9-88 234 9.88 223	45 44 43 42 41	6 7 8 9 10
20 21 22 23 24	9.81 106 9.81 121 9.81 136 9.81 151 9.81 166	9.92 894 9.92 920 9-92 945 9.92 971 9.92 996	0.07 106 0.07 080 0.07 055 0.07 029 0.07 004	9.88 212 9.88 201 9.88 191 9.88 180 9-88 169	4O 39 38 37 36	20 3° 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 i 7 i 8 I 9 I 10 I 20 3 30 5 40 7 50 9
25 26 27 28 29	9.81 180 9.81 195 9.8l 2IO 9.8l 225 9.8l 240	9-93 022 9.93 048 9-93 °73 9.93 099 9-93 124	0.06 978 0.06 952 0.06 927 0.06 901 0.06 876	9-88 158 9.88 148 9.88 137 9.88 126 9.88 115	35 34 33 32 3i
30 3i 32 33 34	9.8l 254 9.8l 269 9.8l 284 9-81 299 9.8l 314	9-93 150 9-93 175 9-93 201 9.93 227 9-93 252	0.06 850 0.06 825 0.06 799 0.06 773 0.06 748	9.88 105 9.88 094 9.88 083 9-88 072 9.88 061	30 29 28 27 26
35 36 37 38 39	9.8l 328 9- 8 1 343 9.81 358 9.81 372 9.81 387	9.93 278 9-93 303 9-93 329 9-93 354 9-93 38o	0.06 722 0.06 697 0.06 671 0.06 646 0.06 620	9.88 051 9.88 040 9.88 029 9.88 018 9.88 007	II II II II	25 24 23 22 21
40 4i 42 43 44	9.81 402 9.81 417 9.81 431 9.81 446 9.81 461 ,	15 14 15 IS 14 15 15 14 15	9-93 406 9-93 43i 9-93 457 9.93 482 9-93 5o8	0.06 594 0.06 569 0.06 543 0.06 518 0.06 492	9.87 996 9.87 985 9-87 975 9.87 964 9-87 953	II 10 II	20 19 18 17 16
45 46 47 48 49	9-8i 475 9.81 490 9-8i 505 9.81 519 9-8i 534	9-93 533 9-93 559 9-93 584 9.93 610 9.93 636	0.06 467 0.06 441 0.06 416 0.06 390 0.06 364	9.87 942 9.87 931 9.87 920 9.87 909 9.87 898	II II II II	15 14 13 12 II
50 Si 52 53 54	9.81 549 9-8i 563 9.81 578 9-8i 592 9.81 607	14 15 M 15	9-93 66 1 9-93 687 9-93 7" 9-93 738 9-93 763	0.06 339 0.06 313 0.06 288 0.06 262 0.06 237	9.87 887 9.87 877 9.87 866 9-87 855 9.87 844	IO II II II	10 9 8 6
P 57 58 59	9.81 622 9.81 636 9.81 651 9.81 665 9.81 680	14 IS »4 15	9-93 789 9-93 814 9-93 840 9-93 865 9-93 891	0.06 211 0.06 1 86 0.06 160 0.06 135 0.06 109	9-87 833 9.87 822 9.87 811 9.87 800 9.87 789	II II II II	5 4 3 2 I
60	9.81 694		9-93 9i6	0.06 084	9.87 778		0
	L. Con. d.	L. Cotg. c. d. L.Tnng.	L. Sin. | d.	/	Prop. Pts.

49'

41

/•	L. Sin.	d.	L.Tang. c. d.	L.Cotg.	It. Cos.	d.		Prop. Pts.
o I 2 3 4	9.81 694 9.81 709 9.81 723 9.81 738 9.81 752	15 M 15 M 15 14 15 14 15 14 15 H 14 15 14 15 14 15 *4 14 15 14 J4 i5 14 14 15 M 14	9-93 9i6 9-93 942 9-93 967 9-93 993 9.94 018	:: 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 25 26 25 26 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26	0.06 084 0.06 058 0.06 033 0.06 007 0.05 982	9.87 778 9.87 767 9.87 756 9-87 745 9-87 734	iz ii ii ii ii ii ii ii ii ii ii ii ii ii ii 12 II II « II II II II II 12 II II II II II 12 II II II II 12 II II II II 12 II II 12 II II II 12 II II 12 II II 12 II II 12 II II 12	6O 59 58 57 56	6 7	26 2.6 3-o 3-5 3-9 4-3 8-7 13.0 17-3 21.7 «5 2-5 2.9 3-3 3-8 4.2 8-3 12.5 16.7 20.8 15 i-5 1.8 2.0 2-3 2-5 5-o 7-5 10.0 12.5 14 1.4 1.6 1.9 2.1 2-3 4-7 7.0 9-3 11.7 it ii 1.2 I.I 1.4 1-3 1.6 1.5 1.8 1.7 2.0 1.8 *-o 3-7 5-0 5-5 3.0 7.3 xo 9.2
5 6 7 8 9	9.81 767 9.81 781 9.81 796 9.81 810 9.81 825	9.94 044 9.94 069 9-94 095 9.94 120 9.94 146	0.05 956 0.05 931 0.05 905 0.05 880 0.05 854	9.87 723 9.87 712 9.87 701 9.87 690 9.87 679	55 54 53 52 Si	8 9 10 20 3°
10 ii 12 13 14	9.81 839 9.81 854 9.81 868 9.81 882 9.81 897	9-94 I7i 9-94 197 9.94 222 9.94 248 9-94 273	0.05 829 0.05 803 0.05 778 0.05 752 0.05 727	9.87 668 9.87 657 9.87 646 9.87 635 9.87 624	50 49 48 47 46	40 50
15 16 17 18 19	9.81 911 9.81 926 9.81 940 9-8i 955 9.81 969	9.94 299 9-94 324 9-94 350 9-94 375 9-94 4°*	0.05 701 0.05 676 0.05 650 0.05 625 0.05 599	9.87 613 9.87 601 9.87 59<> 9-87 579 9.87 568	45 44 43 42' 4i	• 6 7 8 9 10
20 21 22 23 24	9.81 983 9.81 998 9.82 012 9.82 O26 9.82 041	9.94 426 9-94 452 9-94 477 9-94 5°3 9.94 528	0.05 574 0.05 548 0.05 523 0.05 497 0.05 472	9-87 557 9.87 546 9-87 535 9.87 524 9-87 513	4O 39 38 37 36	20 30 40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 3° 40 50 6 7 8 9 10 20 30 4° 50 i
25 26 27 28 29	9.82 055 9.82 069 9.82 084 9.82 098 9.82 112	9-94 554 9-94 579 9.94 604 9-94 630 9-94 655	0.05 446 0.05 421 0.05 396 o-OS 370 0-05 345	9.87 501 9.87 490 9.87 479 9.87 468 9-87 457	35 34 33 32 3i
3O 3i 32 33 34	9.82 126 9.82 141 9-82 155 9.82 169 9.82 184	15 14 M 15	9.94 68 1 9-94 7o6 9-94 732 9-94 757 9-94 783	0.05 319 0.05 294 0.05 268 0.05 243 0.05 217	9.87 446 9-87 434 9.87 423 9.87 412 9.87 401	3O 29 28 27 26
35 36 37 38 39	9.82 198 9.82 212 9.82 226 9.82 240 9.82 255	H 14 J4 i5 M 14 H 14 15 M *4 14 14 H *4 14 15 14 14 H 14 H H J4 *4	9.94 808 9-94 834 9-94 859 9.94 884 9-94 9io	0.05 192 0.05 166 0.05 141 0.05 116 0.05 090	9.87 390 9.87 378 9.87 367 9-87 356 9.87 345	25 24 23 22 21
40 4i 42 43 44	9.82 269 9.82 283 9.82 297 9.82 311 9.82 326	9-94 935 9-94 961 9.94 986 9.95 OI2 9-95 037	0.05 065 0.05 039 0.05 014 0.04 988 0.04 963	9-87 334 9.87 322 9.87311 9.87 300 9.87 288	20 19 18 17 16
45 46 47 48 49	9.82 340 9-82 354 9.82 368 9.82 382 9.82 396	9-95 062 9.95 088 9-95 "3 9-95 139 9-95 164	0.04 938 0.04 912 0.04 887 0.04 86 1 0.04 836	9.87 277 9.87 266 9-87 255 9.87 243 9.87 232	15 14 J3 12 II
50 5i 52 53 54	9.82 410 9.82 424 9.82 439 9-82 453 9.82 467	9.95 190 9-95 215 9-95 240 9-95 266 9-95 291	0.04 8 10 0.04 785 0.04 760 0.04 734 0.04 709	9.87 221 9.87 209 9.87 198 9.87 187 9-87 175	10 9 8 7 6
55 56 57 58 59	9.82 481 9.82 495 9-82 509 9.82 523 9-82 537	9-95 317 9-95 342 9-95 368 9-95 393 9-95 4i8	0.04 683 0.04 658 0.04 632 0.04 607 0.04 582	9.87 164 9-87 153 9.87 141 9.87 130 9.87 119	5 4 3 2 I
60	9-82 55i	9-95 444	0.04 556	9.87 107	0
	JL. Cos.	d.	L. Cotg. c. d.	L.Tang.	L. Sin.	d.	r	Prop. Pts.

48C

64

42'

/•	L. Sin.	d.	L. Tang.	c. d.j L.Cotg.	L. Cos. d.		Prop. Pts.
0 I 2 3 4	9-82 551 9.82 565 9.82 579 9-82 593 9.82 607	X4 J4 *4 *4 i4 J4 H '4 14 '4 H *4 14 14	9-95 444 9-95 469 9-95 495 9-95 520 9-95 545	25 26 25 25 26 25 26 25 25 26 25 25 26 25 26 25 25 26 25 26 25 25 26 25 25 26 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 36 25 25 26	0.04 556 0.04 531 0.04 505 0.04 480 0.04 455	9.87 107 9.87 096 9-87 085 9.87 073 9.87 062	ii ii 12 II 12 II II 12 II 12 II 12 II 12 II 12 II II 12 II 12 12 II 12 II 12 II 12 II 12 II 12 12 II 12 II 12 12 II 12 12 II 12 12 II 12 12 12 12 12 II 12 12 II 12 12 12 II 12	60 59 58 57 56	6 8 9 10 20 30 40 50 6 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 5° *	26 2.6 3-o 3-5 3-9 4-3 8-7 13.0 17-3 21.7 «5 2-5 2.9 3-3 3-8 4-2 8-3 12.5 16.7 20.8 14 1.4 1.6 i-9 2.1 2-3 4-7 7.0 9-3 11.7 13 i-3 i-S 1-7 2.0 2.2 4-3 6-5 8-7 10.8 ia ii 1.2 I.I 1-4 1-3 1.6 1.5 1.8 1.7 2.0 1.8 4-0 3-7 S.o 5-5 B.o 7.3 o.o 9.2
5 6 7 8 9	9.82 621 9.82 635 9.82 649 9.82 663 9.82 677	9-95 571 9-95 596 9-95 622 9-95 647 9-95 672	0.04 429 0.04 404 0.04 378 0-04 353 0.04 328	9.87 050 9.87 039 9.87 028 9.87 016 9.87 005	55 54 53 52 5i
10 ii 12 13 14	9.82 691 9.82 705 9.82 719 9-82 733 9.82 747	9-95 698 9-95 723 9-95 748 9-95 774 9-95 799	0.04 302 0.04 277 0.04 252 0.04 226 O.O4 2OI	9-86 993 9.86 982 9.86 970 9.86 959 9-86 947	50 49 48 47 46
15 16 17 18 19	9.82 761 9.82 775 9.82 788 9.82 802 9.82 816	*4 13 14 14	9-95 825 9-95 850 9-95 875 9-95 901 9.95 926	0.04 175 0.04 150 O.O4 125 O.O4 099 0.04 074	9.86 936 9.86 924 9.86 913 9.86 902 9.86 890	45 44 43 42 4i
20 21 22 23 24	9.82 830 9.82 844 9.82 858 9.82 872 9.82 885	14 14 14 13 *4 14 14 14 14 13 14 14 14 13 14 14 14 13 14 14 H '3 14 14 13 14 H 13 14 13 14 M »3 »4 »3 14 »4 '3 »4	9-95 952 9-95 977 9.96 002 9.96 028 9-96 053	O.O4 048 O.O4 O23 0.03 998 O.O3 972 0.03 947	9.86 879 9.86 867 9.86 855 9.86 844 9.86 832	40 39 38 37 36
25 26 27 28 29	9.82 899 9.82 913 9.82 927 9.82 941 9-82 955	9.96 078 9.96 104 9.96 129 9-96 J55 9.96 180	0.03 922 0.03 896 0.03 871 0.03 845 0.03 820	9.86 821 9.86 809 9.86 798 9.86 786 9.86 775	35 H 32 3i
30 31 32 33 34	9.82 968 9.82 982 9.82 996 9.83 oio 9.83 023	9.96 205 9.96 231 9.96 256 9.96 281 9.96 307	0.03 795 0.03 769 0.03 744 0.03 719 0.03 693	9.86 763 9.86 752 9.86 740 9.86 728 9.86 717	30 29 28 27 26
35 36 37 38 39	9-83 °37 9.83 051 9.83 065 9.83 078 9.83 092	9.96 332 9-96 357 9-96 383 9.96 408 9-96 433	0.03 668 0.03 643 0.03 617 0.03 592 0.03 567	9.86 705 9.86 694 9.86 682 9.86 670 9.86 659	25 24 23 22 21
40 4i 42 43 44	9.83 106 9.83 120 9-83 133 9.83 147 9.83 161	9-96 459 9.96 484 9.96 510 9-96 535 9.96 560	0.03 541 0.03 516 0.03 490 0.03 465 0.03 440	9.86 647 9.86 635 9.86 624 9.86 612 9.86 600	2O 19 18 17 16
3 47 48 49	9-83 174 9.83 188 9.83 202 9-83 215 9.83 229	9.96 586 9.96 611 9.96 636 9.96 662 9.96 687	0.03 414 0.03 389 0.03 364 0.03 338 0.03 313	9.86 589 9.86 577 9.86 565 9-86 554 9.86 542	15 14 13 12 II
5O 5i 52 53 54	9.83 242 9.83 256 9.83 270 9.83 283 9.83 297	9.96 712 9.96 738 9.96 763 9.96 788 9.96 814	0.03 288 0.03 262 0.03 237 0.03 212 0.03 1 86	9.86 530 9.86 518 9-86 507 9.86 495 9-86 483	10 9 8 7 6
55 56 57 58 59	9.83 310 9.83 324 9.83 338 9.83 351 9.83 365	9.96 839 9.96 864 9.96 800 9.96 915 9.96 940	0.03 161 0.03 136 0.03 no 0.03 085 0.03 060	9.86 472 9.86 460 9.86 448 9.86 436 9-86 425	5 4 3 2 I
00	9.83 378	13	9.96 966	0.03 034	9-86 413	0
	I,. Cos. d.	L. Cotg. ,c. d. L.Tan^.	I,. Sin. ; <l.	r	Prop. Pts.

47'

43<

r	L. Sin.	d.	L.Tang	c. d	L. Cotg.	L. Cos.	d.		Prop. Pts.
O i 2 3 4	9-83 378 9-83 392 9-83 4°5 9.83 419 9-83 432	14 13 *4 *3 J4 13 M T3 14 »3 H 13 14 13 14 13 14 13 J3 H 13 13 H 13	9.96 966 9.96 991 9.97 016 9.97 042 9.97 067	25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26	0.03 034 0.03 009 0.02 984 O.O2 958 0.02 933	9.86 413 9.86 401 9.86 389 9-86 377 9.86 366	12 12 12 II 12 12 12 12 12 II 12 12 12 12 12 12 12 II 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12	60 59 58 57 56	6 7	36 2.6 3-o 3-5 3-9 4-3 8-7 13-0 17-3 21.7 25 2-5 2.9 3-3 3-8 4.2 8-3 12.5 16.7 20.8 14 11 i-9 2.1 2-3 4-7 7.0 9-3 H-7 13 i-3 i.S 1-7 2.0 2.2 ti 8.7 10.8 2 XI :.2 i.i f-4 i-3 .6 1.5 .8 1.7 5.0 1.8 k<> 3-7 >-o 5-5 •o 7-3 >.o 9.2
5 6 7 8 9	9.83 446 9-83 459 9-83 473 9.83 486 9.83 500	9-97 092 9.97 118 9-97 143 9-97 168 9-97 193	0.02 908 0.02 882 0.02 857 0.02 832 0.02 807	9-86 354 9.86 342 9.86 330 9.86 318 9.86 306	55 54 53 52 5i	8 9 10 20 30
in ii 12 13 14	9-83 513 9-83 527 9-83 540 9-83 554 9-83 567	9.97 219 9-97 244 9.97 269 9-97 295 9-97 320	0.02 781 0.02 756 0.02 731 0.02 705 O.O2 680	9.86 295 9.86 283 9.86 271 9.86 259 9.86 247	50 49 48 47 46	40 50 6 8 9 10 20 3° £ 6 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 1 6 ] 7 3 8 ] 9 i 10 S 20 t 30 d 40 S 50 ic
15 16 17 18 19	9-83 58i 9-83 594 9.83 608 9.83 621 9-83 634	9-97 345 9-97 371 9-97 396 9.97 421 9-97 447	0.02 655 O.O2 629 0.02 604 0.02 579 0.02 553	9.86 235 9.86 223 9.86 211 9.86 200 9.86 188	45 44 43 42 4i
20 21 22 23 24	9.83 648 9.83 661 9.83 674 9.83 688 9.83 701	9.97 472 9.97 497 9-97 523 9-97 548 9-97 573	0.02 528 0.02 503 0.02 477 0.02 452 0.02 427	9.86 176 9.86 164 9.86 152 9.86 140 9.86 128	40 39 38 i
25 26 27 28 29	9-83 715 9.83 728 9.83 741 9-83 755 9.83 768	J4 13 13 H 13 *3 H 13 13 13	9-97 598 9-97 624 9.97 649 9-97 674 9-97 700	0.02 402 O.O2 376 0.02 351 O.O2 326 O.O2 300	9.86 116 9.86 104 9.86 092 9.86 080 9.86 068	35 34 33 32 3i
30 3i 32 33 34	9.83 781 9-83 795 9.83 808 9.83 821 9-83 834	9-97 725 9-97 750 9-97 776 9.97 801 9.97 826	0.02 275 O.O2 250 0.02 224 O.O2 199 0.02 174	9.86 056 9.86 044 9.86 032 9.86 020 9.86 008	30 29 28 27 26
35 36 37 38 39	9.83 848 9.83 861 9.83 874 9.83 887 9.83 901	J4 13 13 13 H	9-97 851 9-97 877 9.97 902 9-97 927 9-97 953	O.O2 149 0.02 123 O.O2 098 0.02 073 0.02 047	9.85 996 9.85 984 9.85 972 9.85 960 9.85 948	25 24 23 22 21
40 4i 42 43 44	9.83 914 9.83 927 9.83 940 9-83 954 9.83 967	J3 13 13 14 13 *3 13 13 I4 13 13 13 13 13 13	9-97 978 9.98 003 9.98 029 9.98 054 9.98 079	O.O2 O22 o.oi 997 o.oi 971 o.oi 946 o.oi 921	9-85 936 9.85 924 9.85 912 9-85 900 9.85 888	12 12 12 12	20 19 18 17 16
45 46 47 48 49	9.83 980 9-83 993 9.84 006 9.84 020 9-84 033	9.98 104 9.98 130 9 98 155 9.98 180 9.98 206	o.oi 896 o.oi 870 o.oi 845 o.oi 820 o.oi 794	9.85 876 9-85 864 9-85 851 9-85 839 9-85 827	12 13 12 12	IS 14 13 12 II
50 Si 52 53 54	9.84 046 9.84 059 9.84 072 9.84 085 9.84 098	9.98 231 9.98 256 9.98 281 9.98 307 9-98 332	o.oi 769 o.oi 744 o.oi 719 o.oi 693 o.oi 668	9-85 815 9-85 803 9.85 791 9.85 779 9.85 766	12 12 12 13	10 9 8 6
55 56 57 58 59	9.84 112 9.84 125 9.84 138 9.84 151 9.84 164	13 13 13 13	9-98 357 9-98 383 9.98 408 9-98 433 9.98 458	o.oi 643 o.oi 617 o.oi 592 o.oi 567 o.oi 542	9-85 754 9.85 742 9-85 730 9.85 718 9.85 706	12 12 12 12	5 4 3 2 I
60	9.84 177		9.98 484	o.oi 516	9-85 693	X3	0
	L. Cos.	d.	L. Cotg. |c. d.	L.Tang.	L. Sin.	d.	/•	Prop. Pts.

46C

66

44e

/•	I . Sin.	d.	L.Tang.	c. d.	L. Cotg.	L. Cos.	d.		Prop. Pts.
o I 2 3 4	9.84 177 9.84 190 9.84 203 9.84 216 9.84 229	13 13 »3 13	9.98 484 9.98 509 9-98 534 9 98 560 9-98 585	25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25	o.oi 516 o.oi 491 o.oi 466 o.oi 440 o.oi 415	9-85 693 9.85 681 9.85 669 9-85 657 9.85 645	12 12 12 12	GO 59 58 57 56	6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 8 9 10 20 30 40 ero	26 2.6 £ 3-9 4-3 8-7 13-0 17-3 21.7 35 2-5 2.9 3-3 3-8 4.2 8-3 w-S 16.7 20.8 14 1.4 1.6 1.9 2.1 2-3 4-7 7.0 9-3 11.7 13 i-3 i-S i-7 2.0 2.2 $ 8-7 10.8 13 1.2 1.4 1.6 1.8 2.0 4.0 6.0 8.0 10.0
5 6 7 8 9	9.84 242 9-84 255 9.84 269 9.84 282 9.84 295	J3 13 14 13 13 13 13 13 13 13 13 12 13 13 13	9.98 610 9-98 635 9.98 661 9.98 686 9.98 711	o.oi 390 o.oi 365 o.oi 339 o.oi 314 o.oi 289	9.85 632 9.85 620 9.85 608 9-85 596 9-85 583	12 12 12 13 12 12 12 13 12 12 *3 12 12 J3 12 12 13 12 12 13 12 13 12 12 J3 12 13 12 13 12 12 13 12 *3 12 J3 12 13 12 »3 12 13 12 13 »3 12 13 12 »3 12 ^3 13 12 '3 12	55 54 53 52 5i
10 II 12 13 14	9.84 308 9.84 321 9-84 334 9-84 347 9.84 360	9-98 737 9.98 762 9.98 787 9.98 812 9.98 838	o.oi 263 o.oi 238 o.oi 213 o.oi 188 o.oi 162	9-85 571 9-85 559 9-85 547 9-85 534 9.85 522	50 49 48 47 46
15 16 17 18 19	9-84 373 9-84 385 9 84 398 9.84411 9 84 424	9.98 863 9.98 888 9.98 913 9-98 939 9.98 964	o.oi 137 O.OI 112 o.oi 087 o.oi 061 o.oi 036	9-85 5io 9-85 497 9-85 485 9-85 473 9.85 460	45 44 43 42 41
20 21 22 23 24	9-84 437 9.84 450 9.84 463 9.84 476 9.84 489	J3 13 13 13 »3	9.98 989 9-99 oi5 9 99 040 9-99 065 9.99 090	O.OI Oil o.oo 985 o.oo 960 o.oo 935 o.oo 910	9.85 448 9-85 436 9-85 423 9.85 411 9-85 399	4O 39 38 37 36
25 26 27 28 29	9.84 502 9-84 515 9.84 528 9.84 540 9-84 553	T3 *3 13 12 13 13 13 J3 13 13 12 13 13 13 13 12 13 13 13 12 13 13 *3 12 »3 13 13 12 13 13 12 13 13 12 13 13	9.99 116 9-99 141 9.99 166 9 99 191 9-99 217	o.oo 884 o.oo 859 o.oo 834 o.oo 809 o.oo 783	9.85 386 9-85 374 9-85 361 9-85 349 9-85 337	35 34 33 32 3i
30 3i 32 33 34	9.84 566 9-84 579 9.84 592 9-84 605 9.84 618	9.99 242 9-99 267 9-99 293 9.99 318 9-99 343	o.oo 758 o.oo 733 o.oo 707 o.oo 682 o.oo 657	9-85 324 9-85 312 9.85 299 9-85 287 9.85 274	3O 29 28 27 26
35 36 37 38 39	9-84 630 9-84 643 9.84 656 9.84 669 9.84 682	9.99 368 9-99 394 9-99 419 9.99 444 9-99 469	o.oo 632 o.oo 606 o.oo 581 o.oo 556 o.oo 531	9.85 262 9.85 250 9-85 237 9.85 225 9.85 212	25 24 23 22 21	6
40 4i 42 43 44	9.84 694 9.84 707 9.84 720 9-84 733 9-84 745	9-99 495 9-99 520 9-99 545 9-99 570 9-99 596	o.oo 505 o.oo 480 o.oo 455 o.oo 430 o.oo 404	9.85 200 9.85 187 9-85 175 9.85 162 9.85 150	20 19 18 17 16	7 8 9 10 20 3°
45 46 47 48 49	9.84 758 9.84 771 9.84 784 9.84 796 9.84 809	9.99 621 9-99 646 9-99 672 9-99 697 9-99 722	o.oo 379 o.oo 354 o.oo 328 o.oo 303 o.oo 278	9-85 137 9-85 125 9-85 "2 9.85 ioo 9.85 087	15 H 13 12 II	40 50 6 8 9 10
5O 5i 52 53 54	9.84 822 9-84 835 9.84 847 9.84 860 9.84 873	9-99 747 9-99 773 9-99 798 9-99 823 9-99 848	o.oo 253 o.oo 227 0.00 202 o.oo 177 o.oo 152	9-85 074 9.85 062 9.85 049 9-85 037 9-85 024	10 9 8 6
55 56 57 58 59	9 84 885 9.84 898 9.84911 9.84 923 9.84 936	9-99 874 9-99 899 9-99 924 9-99 949 9-99 975	o.oo 126 O.OO IOI o.oo 076 o.oo 051 o.oo 025	9.85 012 9.84 999 9.84 986 9.84 974 9.84 9°i	5 4 3 2 I	20 30 40 50
00	9.84 9 jrv	0.00 000	O.OO 000	9.84 949	0
	L. Cos.	d.	L. Cot*.	c. d. L.Tang.	L. Sin.	d.	f	Prop. Pts.

45C

o<

TABLE IV.

r r	r	s	T
0 60 120 1 80 240	o i 2 3 4	4-68557 .68557 .68557 .68557 •68557	4-68557 -68557 .68557 .68557 .68558
300 360 420 480 540	5 6 7 8 9	4.68557 .68557 •68557 •68557 .68557	4.68558 .68558 .68558 .68558 .68558
600 660 720 780 840	10 ii 12 13 14	4-68557 •68557 .68557 .68557 .68557	4-68558 .68558 .68558 .68558 .68558
900 960 1020 I080 1140	II 17 18 19	4-68557 .68557 .68557 .68557 .68557	4-68558 .68558 .68558 .68558 • .68558
1200 1260 1320 1380 I440	20 21 22 23 24	4-68557 .68557 .68557 .68557 .68557	4-68558 .68558 .68558 .68558 .68558
1500 1560 1620 1680 1740	25 26 27 28 29	4-68557 .68557 •68557 .68557 .68557	4-68558 .68558 .68558 .68558 •68559
1800 1860 1920 1980 2040	30 31 32 33 34	4-68557. .68557 .68557 .68557 -68557	4-68559 .68559 .68559 •68559 •68559
2100 2160 2220 228O 2340	35 36 37 38 39	4-68557 .68557 .68557 .68557 .68557	4-68559 .68559 .68559 .68559 •68559
2400 2460 2520 2580 2640	40 41 42 43 44	4-68557 .68556 .68556 .68556 .68556	4-68559 .68560 .68560 .68560 .68560
2700 2760 2820 2880 2940	45 46 47 48 49	4-68556 .68556 .68556 .68556 .68556	4.68560 .68560 .68560 .68560 .68560
3OOO 3060 3120 3180 3240	50 51 52 53 54	4.68556 .68556 .68556 .68556 .68556	4.68561 .68561 .68561 .68561 .68561
3300 3360 3420 3480 3540	55 56 57 58 59	4.68556 .68556 .68555 .68555 -68555	4.68561 .68561 .6856! .68562 .68562
3600	60	4-68555	4.68562

r r	r	S	T
3600 3660 3720 3780 3840	0 i 2 3 4	4.68555 •68555 •68555 .68555 •68555	4.68562 .68562 .68562 .68562 .68563
3900 3960 4020 4080 4140	i 7 8 9	4.68555 .68555 .68555 .68555 .68555	4.68563 .68563 .68563 .68563 .68563
4200 4260 4320 4380 4440	10 ii 12 13 14	4-68554 .68554 .68554 •68554 •68554	4.68563 .68564 .68564 .68564 .68564
4500 456o 4620 4680 4740	15 16 17 18 19	4-68554 .68554 •68554 .68554 •68554	4-68564 .68565 .68565 .68565 .68565
4800 4860 4920 4980 5040	20 21 22 23 24	4.68554 .68553 .68553 .68553 •68553	4-68565 .68566 .68566 .68566 .68566
5100 5160 5220 5280 5340	25 26 27 28 29	4-68553 •68553 •68553 •68553 .68553	4.68566 .68567 .68567 .68567 .68567
5400 546o 5520 558o 5640	30 31 32 33 34	4-68553 .68552 .68552 .68552 .68552	4-68567 .68568 .68568 .68568 .68568
5700 576o 5820 5880 5940	CO CO CO CO CO vO OOvj O\Cn	4.68552 .68552 .68552 .68552 .68551	4.68569 .68569 .68569 .68569 .68569
6000 6060 6120 6180 6240	40 42 43 44	4-68551 .68551 .68551 .68551 .68551	4.68570 .68570 .68570 .68570 .68571
6300 6360 6420 6480 6540	45 46 47 48 49	4-68551 .68551 .68550 .68550 .68550	4.68571 .68571 .68572 .68572 .68572
6600 6660 6720 6780 6840	So 51 52 53 54	4.68550 .68550 .68550 .68550 .68550	4-68572 .68573 .68573 .68573 •68573
6900 6960 7020 7080 7140	55 56 57 58 59	4.68549 .68549 .68549 .68549 .68549	4.68574 .68574 .68574 .68575 .68575
7200	60	4.68549	4-68575

Log sin a = log a " -f S.

Log tan a — log a " -j- T.

68

r r	A	S	T
7200 7260 7320 7380 7440	o 2 3 4	4.68549 .68549 .68548 .68548 .68548	4-68575 •68575 .68576 .68576 .68576
7500 7560 7620 7680 7740	5 6 7 8 9	4.68548 .68548 .68548 .68547 .68547	4.68577 .68577 .68577 .68578 .68578
7800 7860 7920 7980 8040	10 ii 12 13 14	4.68547 •68547 .68547 .68547 .68546	4.68578 .68579 •68579 .68579 .68579
8100 8160 8220 8280 8340	15 16 17 18 19	4-68546 .68546 .68546 .68546 .68546	4.68580 .68580 .68580 .68581 .68581
8400 8460 8520 8580 8640	20 21 22 23 24	4-68545 •68545 •68545 •68545 .68545	4.68582 .68582 .68582 .68583 .68583
8700 8760 8820 8880 8940	25 26 27 28 29	4-68545 •68544 .68544 .68544 .68544	4-68583 .68584 .68584 .68584 .68585
9000 9060 9120 9180 9240	30 31 32 33 34	4.68544 .68544 •68543 .68543 .68543	4.68585 .68585 .68586 .68586 .68587
9300 9360 9420 9480 9540	35 36 37 38 39	4-68543 •68543 .68542 .68542 .68542	4.68587 .68587 .68588 .68588 .68588
9600 9660 9720 9780 9840	40 4i 42 43 44	4.68542 .68542 .68541 .68541 .68541	4.68589 .68589 .68590 •68590 .68590
9900 9960 10020 I0080 IOI40	45 46 47 48 49	4-68541 .68541 .68540 .68540 .68540	4.68591 .68591 .68592 .68592 .68592
10200 10260 10320 10380 10440	50 Si 52 53 54	4.68540 .68540 .68539 •68539 •68539	4-68593 •68593 .68594 .68594 •68595
10500 10560 I062O 10680 10740	55 56 57 58 59	4.68539 .68539 .68538 .68538 .68538	4.68595 •68595 .68596 .68596 .68597
10800	60	4.68538	4.68597

rr	r	S	T
10800 10860 10920 10980 11040	0 i 2 3 4	4-68538 .68537 •68537 .68537 .68537	4.68597 .68598 .68598 .68599 .68599
IIIOO 11160 1 1 220 II280 II340	5 6 8 9	4-68537 .68536 .68536 .68536 .68536	4.68599 .68600 .68600 .68601 .68601
II400 II460 II520 II580 11640	10 ii 12 13 14	4-68535 •68535 .68535 •68535 •68534	4.68602 .68602 .68603 .68603 .68604
II7OO II760 II820 II880 II940	IS 16 17 18 19	4-68534 •68534 .68534 .68533 -68533	4.68604 .68605 .68605 .68606 .68606
12000 I2O6O I2I20 I2I80 12240	20 21 22 23 24	4-68533 •68533 .68532 .68532 •68532	4.68607 .68607 .68608 .68608 .68609
12300 12360 I242O 12480 12540	25 26 27 28 29	4-68532 .68531 .68531 .68531 .68531	4.68609 .68610 .68610 .68611 .68611
I26OO 12660 12720 12780 12840	3Q, 31 32 33 34	4.68530 .68530 .68530 •68530 .68529	4.68612 .68612 .68613 .68613 .68614
12900 12960 13020 13080 I3I40	3 37 38 39	4.68529 .68529 .68529 .68528 .68528	4.68614 .68615 .68615 .68616 .68616
13200 13260 13320 13380 13440	40 4i 42 43 44	4.68528 .68528 .68527 .68527 .68527	4.68617 .68617 .68618 .68618 .68619
13500 13560 13620 13680 13740	45 46 47 48 49	4.68526 .68526 .68526 .68526 .68525	4.68620 .68620 .68621 .68621 .68622
13800 13860 13920 13980 14040	50 51 52 53 54	4-68525 .68^25 .68525 .68524 .68524	4.68622 .68623 .68623 .68624 .68625
I4IOO I4I60 14220 14280 14340	55 56 57 58 59	4.68524 .68523 .68^23 .68523 .68522	4.68625 .68626 .68626 .68627 .68628
14400	60	4.68522	4.68628

Log sin a = log a " -f S.

Log tan a — log a "

TABLE V.

NATURAL

SINES, COSINES, TANGENTS, AND COTANGENTS.

o /	N. Sin.	N. Tan.	N. Cot.	N. Cos.		0 /	N. Sin.	N. Tan.	N. Cot.	N. Cos.
0 o 5 10 15 20 25	.00 000 145 291 436 582 727	.00 OOO 145 291 436 582 727	Infinity. 687.55 343-77 229.18 171.89 I37.5I	Unity. •99 999 998 997	90 o 55 5o 45 40 35	230 35 40 45 50 55	.04 362 507 653 798 .04 943 .05 088	.04 366 512 658 803 .04 949 •05 095	22.904 22.164 21.470 20.819 20.206 19.627	•99 905 898 892 885 878 870	87 30 25 20 15 10 5
30 35 40 45 So 55	.00 873 .01 018 164 3°9 454 600	.00873 .01 018 164 309 455 600	114-59 98.218 85.940 76.390 68.750 62.499	•99 996 995 993 991 989 987	3° 25 20 15 10 5	3 o 5 10 15 20 25	•05 234 379 524 669 814 .05 960	.05 241 387 533 678 824 .05 970	19.081 18.564 18.075 17.611 17.169 16.750	.99 863 855 847 839 831 822	87 o 55 So 45 40 35
1 0 5 10 15 20 25	•oi 745 .01 891 .02 036 181 327 472	.01 746 .01 891 .02 036 182 328 473	57.290 52.882 49.104 45-829 42.964 40.436	.99 985 982 979 976 973 969	89 o 55 So 45 40 35	30 35 40 45 So 55	.06 105 250 395 540 685 831	.06 116 262 408 554 700 847	16.350 15.969 .605 15-257 14.924 .606	.99 813 804 795 786 776 766	30 25 20 15 10 5
30 35 40 45 50 55	.02 618 763 .02 908 •°3 °54 199 345	.02 619 764 .02 910 •03 055 201 346	38.188 36.178 34.368 32.730 31.242 29.882	.99 966 962 958 953 949 944	3° 25 20 15 10 5	4 o 5 10 15 20 25	.06 976 .07 121 266 411 556 701	.06 993 .07 139 285 43i 578 724	14.301 14.008 13.727 •457 I3.I97 12.947	•99 756 746 736 . 725 714 703	86 o 55 50 45 40 35
2 o 5 10 15 20 25	.03 490 635 781 .03 926 .04 071 217	.03 492 638 783 .03 929 •04075 220	28.636 27.490 26.432 25-452 24.542 23-695	•99 939 934 929 923 917 911	88 o 55 50 45 40 35	30 35 40 45 So 55	.07 846 .07 991 .08 136 281 426 571	.07 870 .08 017 163 3°9 456 602	12.706 •474 .251 12.035 11.826 .625	.99 692 680 668 657 644 632	30 25 20 IS 10 5
2 30	.04 362	.04 366	22.904	•99 905	87 30	5 o	.08 716	.08 749	11.430	.99 619	85 o
	N. Cos.	N. Cot.	N. Tan.	N. Sin.	o f		N. Cos.	N. Cot.	N. Tan.	N. Sin.	0 /

0 f	X. Sin.	N. Tan.	N. Cot.	N. Cos.		0 1	. Sin.	N.Tan	N. Cot.	N.Cos.
5 o 5 10 15 20 25	.08 716 .08 860 .09005 150 295 440	.08 749 .08 895 .09042 189 335 482	11-430 .242 11.059 10.883 .712 .546	•99 619 607 594 58o 567 553	85 o 55 So 45 40 35	10 o 5 10 15 20 25	7365 508 651 794 7937 8 081	•17 633 783 •17 933 .18 083 233 384	5-6713 •6234 •5764 •5301 .4845 •4397	.98 481 455 430 404 378 352	80 o 55 So 45 - 40 35
30 35 40 45 So 55	-09585 729 .09 874 .10 019 164 308	.09 629 776 .09923 .10 069 216 363	10.385 .229 10.078 9.9310 .7882 •6493	•99 540 526 5" 497 482 467	30 25 20 15 10 5	30 35 40 45 50 55	8 224 367 509 652 795 8 938	.18 534 684 - 835 .18986 .19 136 287	5-3955 •3521 > •3093 .2672 •2257 .1848	•98 325 299 272 245 218 190	30 25 20 15 IO 5
6 o 5 10 15 20 25	•10 453 597 742 .10 887 .11 031 176	.10 510 657 805 .10 952 .11099 246	9-5I44 •3831 •2553 .1309 9.0098 8.8919	•99 452 437 421 406 390 374	84 o 55 So 45 40 35	11 0 5 10 15 20 25	9 061 224 366 509 652 794	.19 438 589 740 .19 891 .20 042 194	5.1446 .1049 .0658 5-0273 4.9894 .9520	.98 163 135 107 079 050 .98 021	79 o 55 So 45 40 35
30 35 40 45 So 55	.11 320 465 609 754 .11 898 .12 043	•ii 394 54i 688 836 .11 983 .12 131	8.7769 .6648 -5555 .4490 •3450 •2434	•99 357 34i 324 307 290 272	30 25 20 15 10 5	30 35 40 45 So 55	9937 o 079 222 364 507 649	•20 345 497 648 800 .20 952 .21 104	4-9I52 .8788 .8430 .8077 .7729 .7385	•97 992 963 934 905 875 845	30 25 20 15 10 5
1 0 5 zo 15 20 25	.12 187 331 476 620 764 .12 908	.12 278 426 574 722 .12 869 .13 017	8-1443 8.0476 7-9530 .8606 .7704 .6821	•99 255 237 219 200 182 I63	83 o 55 So 45 40 35	12 o 5 10 15 20 25	o 791 0933 I 076 218 360 502	.21 256 408 560 712 .21 864 .22 017	4.7046 .6712 .6382 .6057 .5736 .5420	•97 815 784 754 723 692 661	78 o 55 50 45 40 35
3° 35 40 45 50 55	•13 053 197 341 485 629 773	•13 165 313 46! 609 758 .13906	7.5958 •5113 .4287 •3479 .2687 .1912	•99 144 125 106 087 067 047	30 25 20 15 10 5	30 35 40 45 50 55	I 644 786 I 928 2 070 212 353	.22 169 322 475 628 781 .22 934	4-5I07 •4799 .4494 .4194 •3897 .3604	.97 630 598 566 534 502 470	3° 25 20 15 10 5
8 o 5 10 IS 20 25	•13 917 .14 061 205 349 493 637	•14 054 202 351 499 . 648 796	7-II54 7.0410 6.9682 .8969 .8269 .7584	.99 027 .99006 .98 986 965 944 923	82 o 55 50 45 40 35	13 o 5 10 15 20 25	2495 637 778 2 92O 3 062 203	.23 087 240 393 547 700 •23 854	4-33I5 •3029 .2747 .2468 .2193 .1922	•97 437 404 37i 338 304 271	77 o 55 50 45 40 35
3'o 35 40 45 50 55	.14781 •14 925 .15069 212 356 500	•14 945 .15094 243 39i 540 689	6.6912 .6252 - .5606 .4971 .4348 •3737	.98 902 880 858 836 814 79i	30 25 20 15 10 5	30 35 40 45 50 55	3345 486 627 769 3 91° 4051	.24 008 162 316 470 624 778	4-1653 .1388 .1126 .0867 .0611 •0358	•97 237 203 169 134 100 065	30 25 20 15 10 5
9 o 5 10 IS 20 25	•15 643 787 •15 931 .16074 8X8 361	• 15 838 •15 988 .16 137 286 435 585	6.3138 •2549 .1970 .1402 .0844 6.0296	.98 769 746 723 700 676 652	81 o 55 So 45 40 35	14 o 5 10 15 20 25	4 192 333 474 615 756 4897	•24933 .25 087 242 397 552 707	4.0108 3-9861 .9617 •9375 .9136 .8900	.97 030 •96 994 959 923 887 851	76 o 55 50 45 40 35
30 35 40 45 So 55	.16 505 648 792 •16 935 17078 222	•16 734 .16 884 •17 033 183 81	5.9758 .9228 .8708 .8197 .7694 .7199	.98 629 604 580 556 53i 506	30 25 20 15 10 5	30 35 40 45 50 55	5 038 179 320 460 601 741	.25 862 .26 017 172 328 483 639	3-8667 .8436 .8208 .7983 .7760 •7539	.96 815 778 742 70S 667 630	30 25 20 15 10 5
10 o	I736S	•17 633	5.6713	.98 481	80 o	100	5 882	.26 795	3-7321	-96593	75 o
	N.Cos.	N. Cot. |	N.Tan.	N. Sin.	0 /		Cos.	N. Cot.	N.Tan.	N. Sin.	o ;

o /	N. Sin.	N. Tan.	N.Cot.	N.Coa.		o r	N. Sin.	N. Tan.	N. Cot.	N.Cos.
15 o 5 10 15 20 25	.25 882 .26 022 163 303 443 584 .26 724 .26 864 .27004 144- 284 424	.26 795 .26 951 .27 107 263 419 576	3-7321 •7105 .6891 .6680 .6470 .6264	•96 593 555 517 479 440 402	75 o 55 So 45 40 35	20 o 5 10 IS 20 25	• 34 202 339 475 612 748 •34 884	•36 397 562 727 .36 892 •37 057 223	2-7475 .7351 .7228 .7106 .6985 .6865	•93 969 919 869 819 769 718	70 o 55 So 45 40 35
3° 35 40 45 So S5	.27 732 .27 889 .28 046 203 360 517	3-6059 •5K .5656 •5457 .5261 .5067	.96 363 324 28I 246 206 166	30 25 20 15 10 5	30 35 40 45 50 55	•35 021 157 293 429 565 701	•37 388 554 720 •37 887 •38 053 220	2.6746 .6628 .6511 .6395 .6279 .6165	.93 667 616 565 514 462 410	30 25 20 IS IO 5
16 o 5 10 15 20 25	•27 564 704 843 .27 983 .28 123 262	.28 675 832 .28 990 •29 147 305 463	34874 .4684 •4495 •4308 .4124 -3941	.96 126 - 086 046 .96005 •95 964 923	74 o 55 So 45 40 35	21 o 5 10 15 20 25	•35 837 •35 973 .36 108 244 379 515	.38 386 553 721 .38 888 •39 055 223	2.6051 .5938 .5826 .5715 .5605 •5495	•93 358 306 253 201 148 095	69 o 55 50 45 40 35
30 35 40 45 So 55	.28 402 541 680 820 .28 959 .29098	.29 621 780 •29 938 .30 097 255 - 4H	3-3759 .358o .3402 .3226 •3052 .2879	•95 882 841 799 757 715 673	30 25 20 15 10 5	3° 35 40 45 50 55	.36 650 785 .36 921 -37 056 I9J 326	•39 391 559 727 .39 896 .40065 234	2.5386 .5279 •5172 •5065 .4960 .4855	•93 042 .92 988 935 881 827 773	30 25 20 15 10 5
17 o 5 10 15 20 25	.29 237 376 515 654 793 .29 932	•30 573 732 .30 891 •3i 051 210 370	3.2709 •2539 .2371 .2205 .2041 .1878	•95 630 588 545 502 459 415	73 o 55 5o 45 40 35	22 o 5 10 15 20 25	•37 461 595 730 865 •37 999 •38 134	.40 403 572 74i .40 911 .41 081 251	2.4751 .4648 •4545 •4443 •4342 .4242	.92 718 664 609 554 499 444	68 o 55 5o 45 40 35
30 35 40 45 So 55	.30 071 209 348 486 625 763	•31 530 690 •31 850 .32 oio 171 331	3.1716 .1556 .1397 .1240 .1084 .0930	•95 372 328 284 240 195 150	30 25 20 15 10 5	3° 35 40 45 So 55	.38 268 403 537 671 805 -38 939	.41 421 592 763 .41 933 .42 105 276	2.4142 •4043 •3945 .3847 •3750 •3654	.92 388 332 276 220 I64 107	30 25 20 15 10 5
18 o 5 10 15 20 25	.30 902 .31 040 178 316 454 593	.32 492 653 814 •32 975 •33 136 298	3.0777 .0625 .047! .0326 .0178 3.0032	95 106 061 •95 015 •94 970 924 878	72 o 55 So 45 40 35	23 o 5 10 IS 20 25	•39073 207 341 474 608 741	.42447 619 791 .42 963 •43 136 308	2-3559 •3464 .3369 .3276 •3183 .3090	.92 050 .91 994 936 879 822 764	67 o 55 50 45 40 35
30 35 40 45 So 55	•3i 730 .31 868 .32006 144 282 419	•33 46o 621 783 •33 945 •34 108 270	2.9887 •9743 .9600 •9459 •9319 .9180	•94 832 786 740 693 646 599	30 25 20 15 IO 5	30 35 40 45 50 55	•39 875 .40 008 141 275 408 54i	•43 48i 654 .43 828 .44001 175 349	2.2998 .2907 .2817 .2727 .2637 •2549	.91 706 648 590 531 472 414	30 25 20 15 10 5
19 o 5 10 15 20 25	•32 557 694 832 .32 969 .33 106 244	•34 433 596 758 •34 922 •35 085 248	2.9042 .8905 .8770 .8636 .8502 •8370 .	•94 552 504 457 409 361 313	71 o 55 So 45 40 35	24 o 5 10 15 20 25	.40 674 806 •40 939 .41 072 204 337	•44523 697 .44872 •45 047 222 397	2.2460 .2373 .2286 .2199 .2113 .2028	•91 355 295 236 176 116 .91 056	66 o 55 So 45 40 35
30 35 40 45 So 55	•33 38i I1- 655 792 •33 929 •34 065	•35 412 576 740 •35 9°4 .36 068 232	2.8239 .8109 .7980 •7852 •7725 .7600	.94 264 215 167 118 068 •94 019	30 25 20 15 10 5	30 35 40 45 So 55	.41 469 602 734 866 .41 998 .42 130	•45 573 748 •45 924 .46 101 277 454	2-1943 .1859 • 1775 .1692 .1609 • 1527	.90996 936 875 814 753 692	30 25 20 15 10 5
20 o	.34 202	•3J5 397	2-7475	•93 969	70 o	25 o	.42 262	.46 631	2.1445	.90 631	65 o
	N. Cos.	F. Cot. | N. Tan.	N. Sin.	o /		N.Cos.	N. Cot.	N. Tan.	N. Sin.	o /

.

o t	N. Sin.	N. Tan.	N. Cot.	N. Cos.		o /	N. Sin.	N. Tan.	N. Cot.	N. Cos.
25 o 5 10 IS 20 25	.42 262 394 525 657 788 .42 920	.46 631 808 .46 985 •47 163 34i 519	2.1445 .1364 .1283 .1203 .1123 .1044	.90631 569 507 446 383 321	65 o 55 So 45 40 35	30 o 5 10 15 20 25	.50 ooo 126 252 377 503 628	•57 735 •57 929 .58 124 3i8 513 709	1.7321 .7262 .7205 .7147 .7090 .7033	.86 603 530 457 384 310 237	60 o 55 50 45 40 35
30 35 40 45 So 55	•43 051 182 313 445 575 706	.47 698 •47 876 •48 055 234 414 593	2.0965 .0887 .0809 .0732 •0655 •0579	.90 259 196 133 070 .90007 •89 943	3° 25 20 15 10 5	30 35 40 45 So 55	754 .50 879 .51 004 129 254 379	.58 905 .59 ioi 297 494 691 •59 888	1.6977 .6920 .6864 .6808 .6753 .6698	.86 163 089 .86 015 .85 941 866 792	30 25 20 15 10 5
26 o 5 10 15 20 25	•43 837 .43 968 .44098 229 359 490	•48 773 •48 953 •49 134 315 495 677	2.0503 .042,8 •0353 .0278 .0204 .0130	.89 879 816 752 687 623 558	64 o 55 So 45 40 35	31 o 5 10 15 20 25	•51 504 628 753 •Si 877 .52 002 126	.60086 284 483 681 .6© 881 .61 080	1.6643 .6588 •6534 •6479 .6426 •6372	•85 717 642 567 491 416 340	59 o 55 So 45 40 35
30 35 40 45 50 55	.44 620 750 .44880 •45 oio 140 269	•49 858 .50 040 222 404 587 769	2.0057 1.9984 .9912 .9840 .9768 •9697	.89 493 428 363 298 232 167	30 25 20 15 10 5	30 35 40 45 So 55	.52 250 374 498 621 745 869	.61 280 480 68 1 .61 882 .62 083 285	1.6319 .6265 .6212 .6160 .6107 •6055	.85 264 188 112 •85 035 •84 959 882	30 25 20 15 10 5
27 o 5 10 15 20 25	•45 399 529 658 787 •45 917 .46 046	•So 953 .51 136 319 503 688 .51 872	1.9626 •9556 .9486 .9416 .9347 •9278	.89 101 •89 035 .88 968 902 835 768	68 o 55 So 45 40 35	32 o 5 10 15 20 25	•52 992 •53 "5 238 361 484 607	.62 487 689 .62 892 •63095 299 503	1.6003 •5952 .5900 .5849 •5798 •5747	.84 805 728 650 573 495 417	58 o 55 So 45 40 35
3° 35 40 45 50 55	•46 175 304 433 56i 690 819	•52 057 242 427 613 798 •52 985	1.9210 .9142 .9074 .9007 .8940 .8873	.88 701 634 566 499 431 363	30 25 20 15 10 5	30 35 4° 45 50 55	•53 73° 853 •53 975 •54 097 220 342	.63 707 .63 912 .64 117 322 528 734	1.5697 •5647 •5597 •5547 •5497 .5448	•84 339 261 182 104 .84 025 .83 946	30 25 20 15 10 5
28 o 5 10 15 20 25	.46 947 •47 076 204 332 460 588	•53 171 358 545 732 •53 920 •54 107	1.8807 .8741 .8676 .8611 .8546 .8482	.88 295 226 158 089 .88 020 •87 951	62 o 55 So 45 40 35	33 o 5 10 15 20 25	•54 464 586 708 829 •54 95i •55 072	.64 941 •65 148 355 563 771 .65 980	1-5399 •5350 •5301 •5253 .5204 .5156	•83 867 788 708 629 549 469	67 o 55 5o 45 40 35
30 35 40 45 So 55	•47 7i6 844 •47 97i .48099 226 354	•54 296 484 673 .54 862 •55 051 241	1.8418 .8354 .8291 .8228 .8165 .8103	.87 882 812 743 673 603 532	30 25 20 15 10 5	3° 35 40 45 50 55	•55 194 3i5 436 557 678 799	.66 189 398 608 .66 818 .67 028 239	1.5108 .5061 •5013 .4966 .4919 •4872	•83 389 308 228 147 .83066 .82 985	30 25 20 15 10 5
29 o 5 10 IS 20 25	.48 481 608 735 862 .48 989 .49 116	•55 43i 621 •55 812 .56003 194 385	1.8040 •7979 .7917 .7856 .7796 •7735	.87 462 391 321 250 178 107	61 o 55 So 45 40 35	34 o 5 10 15 20 25	•55 9*9 .56 040 160 280 401 521	•67 451 663 .67 875 .68 088 301 514	1.4826 •4779 •4733 •4687 .4641 •4596	.82 904 822 741 659 577 495	56 o 55 50 45 40 35
30 35 40 45 50 55	.49 242 369 495 622 748 •49 874	•56 577 769 .56962 •57 155 348 54i	1.7675 •7615 .7556 .7496 •7437 •7379	.87 036 .86 964 892 820 748 675	30 25 20 IS 10 5	30 35 40 45 So 55	641 760 .56 880 .57000 119 238	.68 728 .68 942 •69 157 372 588 .69804	1-4550 .4505 .4460 .4415 •4370 .4326	.82 413 330 248 165 .82 082 .81 999	30 25 20 15 10 5
30 o	.50 ooo	.57 735	1.7321	.86603	60 o	36 o	•57 358	.70 021	1.4281	.81 915	55 o
	N. Cos.	N. Cot.	N.Tan.	N. Sin.	o /		N. Cos.	N. Cot.	N. Tan.	N. Sin.	0 f

73

0 I	N. Sin.	N. Tan.	N. Cot.	N.Cos.		o t	N. Sin.	N. Tan.	N.Cot.	N.Cos.
35 o 5 10 15 2O 25	•57 358 477 596 7iS 833 •57 952	.70 021 238 455 673 .70 891 .71 no	1.4281 •4237 •4i93 .4150 .4106 .4063	.81 915 832 748 664 580 496	55 o 55 So 45 40 35	40 o 5 10 15 20 25	.64 279 390 501 612 723 834	.83 910 •84 158 407 656 .84 906 •85 i57	1.1918 .1882 .1847 .1812 .1778 •1743	.76 604 5" 4i7 323 229 135	50 o 55 So 45 4° 35
30 35 40 45 5o 55	.58 070 189 307 425 543 66 1	.71 329 549 769 71 99p .72 211 432	1.4019 •3976 •3934 .3891 •3848 .3806	.81 412 327 242 157 .81 072 .80 987	30 25 20 15 10 5	30 35 40 45 50 55	.64 945 •65 055 166 276 386 496	.85 408 660 •85 912 .86 166 419 674	1.1708 .1674 .1640 .1606 • 1571 •1538	.76 041 •75 946 85J 756 661 566	30 25 20 15 10 5
36 o 5 10 15 20 25	•58 779 .58 896 .59014 131 248 365	.72 654 .72 877 •73 I00 323 547 771	1-3764 •3722 .3680 •3638 •3597 •3555	.80 902 816 730 644 558 472	54 o 55 So 45 40 35	41 o 5 10 15 20 25	.65 606 716 « 8^ •65 935 .66 044 153	.86 929 .87 184 441 698 •87 955 .88 214	1.1504 .1470 .1436 .1403 .1369 •1336	•75 47i 375 280 184 •75 088 -74 992	49 o 55 So 45 40 35
30 35 40 45 50 55	.59 482 599 716 832 •59 949 .60 065	•73 996 .74 221 447 674 .74 900 •75 128	I-35H •3473 •3432 •3392 •3351 •33"	.80 386 299 212 125 .80 038 •79 95i	30 25 20 15 10 5	30 35 40 45 50 55	.66 262 37i 480 588 697 805	.88 473 732 .88 992 •89 253 515 .89 777	1.1303 .1270 .1237 .1204 .1171 •"39	.74 896 799 703 606 509 412	30 25 20 15 IO 5
37 o 5 10 15 20 25	.60 182 298 414 529 645 761	•75 355 584 •75 812 .76 042 272 502	1.3270 •3230 .3190 •3151 .3111 .3072	.79 864 776 688 600 512 424	53 o 55 So 45 40 35	42 o 5 10 15 20 25	.66 913 .67 021 129 237 344 452	.90 040 304 569 .90 834 .91 099 366	1.1106 .1074 .1041 .1009 .0977 •0945	•74 314 217 1 20 .74 022 •73 924 826	48 o 55 50 45 40 35
30 35 40 45 50 55	876 .60 991 .61 107 222 337 451	•76 733 .76964 •77 I96 428 661 •77 895	1.3032 •2993 •2954 •2915 .2876 .2838	•79 335 247 Xf .79 069 .78 980 891	30 25 20 15 10 5	3° 35 40 45 50 55	•67 559 666 773 880 .67 987 .68093	•91 633 .91 901 .92 170 439 709 .92 980	1.0913 .0881 .0850 .0818 .0786 •0755	.73 728 629 53i 432 333 234	30 ?5 20 IS 10 5
38 o 5 10 IS 20 25	.61 566 68 1 795 .61 909 .62 024 138	.78 129 363 598 •78 834 .79 070 306	1.2799 .2761 •2723 •2685 .2647 .2609	.78 801 711 622 532 442 35i	52 o 55 So 45 40 35	43 o 5 10 15 20 25	.68 200 306 412 5i8 624 730	•93 252 524 •93 797 •94 071 345 620	1.0724 .0692 .0661 .0630 •0599 •0569	•73 135 •73 036 .72 937 837 737 637	47 o 55 So 45 40 35
30 35 40 45 50 55	.62 251 365 479 592 706 819	•79 544 •79 78i .80 020 258 498 738	1.2572 •2534 .2497 .2460 .2423 .2386	.78 261 170 .78 079 •77 988 897 806	30 25 20 15 10 5	30 35 40 45 5o 55	.68 835 .68 941 .69 046 I5i 256 361	.94 896 •95 173 451 •95 729 .96008 288	1.0538 .0507 .0477 .0446 .0416 •0385	•72 537 437 337 236 136 •72 035	30 25 20 15 10 5
39 o 5 10 15 20 25	.62 932 •63 045 158 271 383 496	.80 978 .81 220 46l 703 .81 946 .82 igO	1.2349 .2312 .2276 •2239 .2203 .2167	•77 715 623 531 439 347 255	51 o 55 So 45 40 35	44 o 5 10 15 20 25	.69 466 570 675 779 883 .69 987	.96 569 .96 850 •97 133 416 700 •97 984	1-0355 •0325 .0295 .0265 •0235 .0206	•7i 934 833 732 630 529 427	46 o 55 5o 45 40 35
30 35 40 45 50 55	.63 608 720 832 .63 944 .64 056 167	.82 434 678 .82 923 .83 169 415 662	1.2131 •2095 .2059 .2024 .1988 •1953	.77 162 .77 070 .76 977 884 791 698	30 25 20 15 10 5	30 35 40 45 So 55	.70 091 195 298 401 505 608	.98 270 556 •98 843 •99 131 420 •99 7io	1.0176 .0147 .0117 .0088 .0058 .0029	•71 325 223 121 .71 019 .70 916 813	30 25 20 IS 10 5
40 o	.64 279	.83 910	1.1918	.76 604	50 o	45 o	.70 711	1. 00 000	1. 0000	.707"	45 o
	N.Cos.	N. Cot	N. Tan.	N. Sin.	o /		N. Cos.	N. Cot.	N. Tan.	N. Sin.	o /

74 TABLE VI. — CIRCULAR ARCS EXPRESSED IN RADIANS.

DEGREES.	MINUTES.	SI < OM>S.
o° I 2 3 4 I 7 8 9 10 ii 12 13 14 15 16 17 18 19 20 21 22 33 24 25 26 27 28 29 30 3i 32 33 34 35 36 37 38 39 40 4i 42 43 44 45 46 47 48 49 50 Si 52 53 54 3 57 58 59 <i(>	o.ooooo oo	60° 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 9i 92 93 94 95 96 97 98 99 10O 101 IO2 103 104 IOI 106 107 108 109 110 in 112 "3 "4 "5 116 H7 118 119 120	1.04719 76	120° 121 122 123 I24 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 I4I 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 I76 177 178 179 1HO	2.09439 51	O' I 2 3 4 5 6 7 8 9 10 ii 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3i 32 33 34 11 37 38 39 40 4i 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 00	0.00000 00	O" I 2 3 4 6 7 8 9 10 ii 12 13 14 15 16 17 18 19 20 21 22 23 24 3 27 28 29 30 3i 32 33 34 35 36 37 38 39 40 4i 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 (10	o.ooooo oo
0.01745 33 0.03490 66 0.05235 99 0.06981 32 0.08726 65 0.10471 98 0.12217 3° 0.13962 63 0.15707 96	1.06465 08 1.08210 41 i -°9955 74 1.11701 07 1.13446 40 1.15191 73 1.16937 06 1.18682 39 1.20427 72	2.11184 84 2.12930 17 2.14675 50 2.16420 83 2.18166 16 2.19911 49 2.21656 82 2.23402 14 2.25147 47	0.00029 °9 0.00058 I 8 0.00087 27 0.00116 36 0.00145 44 0.00174 53 0.00203 62 0.00232 71 0.00261 80	o.ooooo 48 o.ooooo 97 o.ooooi 45 o.ooooi 94 O.OOOO2 42 0.00002 91 0.00003 39 0.00003 88 0.00004 36
0.17453 29	1.22173 °5	2.26892 80	0.00290 89	0.00004 85
0.19198 62 0.20943 95 0.22689 28 0.24434 61 0.26179 94 0.27925 27 0.29670 60 0.31415 93 0.33161 26	1.23918 38 1.25663 71 1.27409 04 1.29154 36 1.30899 69 1.32645 02 1-3439° 35 1.36135 68 1.37881 01	2.28638 13 2.30383 46 2.32128 79 2.33874 12 2.35619 45 2.37364 78 2.39110 ii 2.40855 44 2.42600 77	0.00319 98 0.00349 07 0.00378 15 0.00407 24 0.00436 33 0.00465 42 0.00494 51 0.00523 60 0.00552 69	0.00005 33 0.00005 82 0.00006 30 0.00006 79 0.00007 27 0.00007 76 0.00008 24 0.00008 73 0.00009 2I
0.34906 59	1.39626 34	2.44346 10	0.00581 78	0.00009 7°
0.36651 91 0.38397 24 0.40142 57 0.41887 90 0.43633 23 0.45378 56 0.47123 89 0.48869 22 0.50614 55	1.41371 67 1.43117 oo 1.44862 33 1.46607 66 1.48352 99 1.50098 32 1.51843 64 1-53588 97 1-55334 30	2.46091 42 2.47836 75 2.49582 08 2.51327 41 2.53072 74 2.54818 07 2.56563 40 2-58308 73 2.60054 06	0.00610 87 0.00639 95 0.00669 °4 0.00698 13 0.00727 22 0.00756 31 0.00785 40 0.00814 49 0.00843 S8	o.oooio 18 o.oooio 67 o.oooii 15 o.ooon 64 0.00012 12 O.OOOI2 6l 0.00013 09 0.00013 57 0.00014 06
0.52359 88	1.57079 63	2.61799 39	0.00872 66	0.00014 54
0.54105 21 0.55850 54 0-57595 87 0.59341 19 0.61086 52 0.62831 85 0.64577 1 8 0.66322 51 0.68067 84	1.58824 96 1.60570 29 1.62315 62 1.64060 95 1.65806 28 1.67551 61 1.69296 94 1.71042 27 1.72787 60	2.63544 72 2.65290 05 2.67035 38 2.68780 70 2.70526 03 2.72271 36 2.74016 69 2.75762 02 2.77507 35	0.00901 75 0.00930 84 0.00959 93 0.00989 02 0.01018 ii 0.01047 20 0.01076 29 O.OII05 38 O.OII34 46	0.00015 °3 0.00015 5i 0.00016 oo 0.00016 48 0.00016 97 0.00017 45 0.00017 94 0.00018 42 0.00018 91
0.69813 17	1.74532 93	2.79252 68	0.01163 55	0.00019 39
0.71558 50 0.73303 83 0.75049 16 0.76794 49 0.78539 82 0.80285 15 0.82030 47 0.83775 80 0.85521 13	1.76278 25 1.78023 58 1.79768 91 1.81514 24 1-83259 57 1.85004 90 1.86750 23 1.88495 56 1.90240 89	2.80998 01 2.82743 34 2.84488 67 2.86234 oo 2.87979 33 2.89724 66 2.91469 99 2.93215 31 2.94960 64	0.01192 64 0.01221 73 0.01250 82 0.01279 91 0.01309 oo 0.01338 09 0.01367 17 0.01396 26 0.01425 35	0.00019 88 0.00020 36 0.00020 85 0.00021 33 0.00021 82 0.00022 30 0.00022 79 0.00023 27 0.00023 76
0.87266 46	1.91986 22	2.96705 97	0.01454 44	0.00024 24
0.89011 79 0.90757 12 0.92502 45 0.94247 78 0-95993 « 0.97738 44 0.99483 77 1.01229 I0 1.02974 43	I-9373I 55 1.95476 88 1.97222 21 1.98967 53 2.00712 86 2.02458 19 2.04203 52 2.05948 85 2.07694 1 8	2.98451 30 3.00196 63 3.01941 96 3.03687 29 3.05432 62 3.07177 95 3.08923 28 3.10668 61 3.12413 94	0.01483 53 0.01512 62 0.01541 71 0.01570 80 0.01599 89 0.01628 97 0.01658 06 0.01687 15 0.01716 24	0.00024 73 0.00025 21 0.00025 70 0.00026 1 8 0.00026 66 0.00027 15 0.00027 63 0.00028 12 0.00028 60
1.04719 76	2.09431) M	3.14159 27	3.01745 ;	0.00029 09

TABLE VII. NAPIERIAN LOGARITHMS OF NUMBERS.

75

N.	Log.	N.	Log.	N.	Log.	N.	Log.	N.	Log.
i 2 3 4 5	0.00000 0.69315 1.09861 1.38629 1.60944	21 22 23 24 25	3-04452 3.09104 3-13549 3-17805 3.21888	4i 42 43 44 45	3-7I357 3.73767 3.76120 3-78419 3.80666	61. 62 63- 64 65	4.11087 4.12713 4-14313 4.15888 4-17439	81 82 83 84 85	4-39445 4.40672 4.41884 4-43082 4-44265
6 7 8 9 10	1.79176 1.94591 2.07944 2.19722 2.30259	26 27 28 29 30	3.25810 3-29584 3.33220 3-36730 3.40120	46 47 48 49 50	3.82864 3-85015 3.87120 3.89182 3.91202	66 67 68 69 70	4-18965 4.20469 4.21951 4.23411 4.24850	86 87 88 89 90	4-45435 4.46591 4-47734 4.48864 4.49981
ii 12 13 14 15	2.39790 2.48491 2.56495 2.63906 2.70805	31 32 33 34 35	3-43399 346574 3-49651 3-52636 3-55535	5i 52 53 54 55	3-93183 3-95124 3.97029 3.98898 4-00733	71 72 73 74 75	4.26268 4.27667 4.29046 4.30407 4.31749	91 92 93 94 95	4.51086 4-52I79 4-53260 4.54329 4.55388
16 17 18 19 20	2.77259 2.83321 2.89037 2.94444 2.99573	36 37 38 39 40	3-58352 3.61092 3-63759 3-66356 3.68888	56 57 58 59 60	4-02535 4.04305 4.06044 4-07754 4-09434	76 77 78 79 80	4.33073 4.3438i 4-35671 4-36945 4-38203	96 97 98 99 IOO	4-56435 4.57471 4.58497 4-59512 4.60517

N.	0	1	2	3 | 4	5	6	7	8	9
10 ii 12 13 14	4-6 0517 4.7 0048 8749 4-8 6753 4-9 4164	1512 °953 9579 7520 4876	2497 1850 #0402 8280 5583	3473 2739 #1218 9035 6284	4439 3620 #2028 9784 6981	5396 4493 #2831 #0527 7673	6344 5359 #3628 #1265 8361	7283 6217 #4419 #1998 9043	8213 7068 *52Q3 #2725 972i	9i35 7912 *S98i *3447 *Q395
IS 16 17 18 19	5.0 1064 7517 5-1 358o 9296 5.2 4702	1728 8140 4166 9850 5227	2388 8760 4749 #0401 575"o	3044 9375 5329 #0949 6269	3695 9987 5906 #1494 6786	4343 *0595 6479 #2036 7300	4986 #1199 7048 *2575 7811	5625 #1799 7615 #3111 8320	6260 #2396 8178 #3644 8827	6890 #2990 8739 *4i75 9330
20 21 22 23 24	5-3 9832 5-347II 9363 5.4 3808 8064	*033Q 5186 9816 4242 8480	#0827 5659 *0268 4674 8894	.Wi32i 6129 #0717 5104 9306	#1812 *6S2? *n65 5532 9717	#2301 7064 *i6io 5959 *OI26	#2788 7528 *2Q53 6383 ^533	#3272 7990 *2495 6806 #0939	*37S4 8450 *2935 7227 *i343	#4233 8907 *3372 7646 *I745
25 26 27 28 29	5-5 2146 6068 9842 5-6 3479 6988	2545 6452 #0212 3835 7332	2943 6834 #0580 4191 7675	3339 7215 *0947 4545 8017	3733 7595 *I3I3 4897 8358	4126 7973 *i677 5249 8698	45i8 8350 #2040 5599 9036	4908 .8725 #2402 5948 9373	5296 9099 #2762 6296 9709	5683 947i #3121 6643 #0044
3° 3i 32 33 34	5-7 0378 3657 6832 9909 5.8 2895	0711 3979 7144 #0212 3188	1043 4300 .,7455 ••"0513 348i	1373 4620 7765 #0814 3773	1703 4939 8074 *ni4 4064	2031 5257 8383 *I4I3 4354	2359 5574 8690 #1711 4644	2685 5890 8996 #2008 4932	3010 6205 9301 *2305 5220	3334 6519 9606 %6oo 5507
9 37 38 39	5-8 5793 8610 5-9 1350 4017 66!5	6079 8888 1620 4280 6871	6363 9164 1889 4542 7126	6647 944° 2158 4803 738i	6930 9715 2426 5064 7635	7212 9990 2693 5324 7889	7493 #0263 2959 5584 8141	7774 *o536 3225 5842 8394	8053 *o8o8 3489 6101 8645	8332 *io8o 3754 6358 8896
40	5-9 9146	9396	9645	9894	*oi4i	#0389	*o635	#0881	*II27	*I372
N.	0	1	2	3	4	5	6	7	8	9

76

N.	O	1	2	3	4	5	6	7	8	9
40 4i 42 43 44	5-9 9146 6.0 1616 4025 6379 8677	9396 1859 4263 6611 8904	9645 2102 4501 6843 9131	9894 2345 4737 7074 9357	*oi4i 2587 4973 73°4 9582	*o389 2828 5209 7535 9807	*o635 3069 5444 7764 #0032	*o88i 33°9 5678 7993 *oas6	*II27 3548 5912 8222 •0479	*I372 3787 6146 8450 *0702
45 46 47 48 49	6.1 0925 3"3 5273 7379 9441	1147 3340 5486 7587 9644	1368 3556 5698 7794 9848	1589 3773 59io 8002 $0051	1810 3988 6121 8208 *02S4	2030 4204 6331 8415 •0456	2249 4419 6542 8621 *o658	2468 4633 6752 8826 *o859	2687 4847 6961 9032 *io6o	2905 5060 7170 9236 *I26l
50 51 52 53 54	6.2 1461 3441 5383 7288 9157	1661 3637 5575 7476 9342	1860 3832 5767 7664 9527	2059 4028 5958 7852 9711	2258 4222 6149 8040 9895	2456 4417 6340 8227 *oo79	2654 4611 6530 8413 *0262	2851 4804 6720 8600 *°445	3048 4998 6910 8786 *o628	3245 5190 7099 8972 *o8io
55 56 57 58 59	6.3 0992 2794 4564 6303 8012	"73 2972 4739 6475 8182	1355 3150 4914 6647 8351	1536 3328 5089 6819 8519	1716 35°5 5263 6990 8688	1897 3683 5437 7161 8856	2077 3859 5611 7332 9024	2257 4036 5784 7502 9192	2436 4212 5957 7673 9359	2615 4388 6130 7843 9526
60 61 62 63 64	6.3 9693 6.4 1346 2972 4572 6i47	9859 1510 3133 4731 6303	#0026 1673 3294 4889 6459	*oi92 1836 3455 5047 6614	*03S7 1999 36i5 5205 6770	#0523 2162 3775 5362 6925	*o688 2325 3935 5520 7080	*o853 2487 4095 5677 7235	*IOI7 2649 4254 5834 7389	*Il82 2811 4413 5990 7543
65 66 67 68 69	6.4 7697 9224 6.5 0728 2209 3669	7851 9375 0877 2356 3814	8004 9527 1026 2503 3959	8158 9677 U75 2649 4io3	8311 9828 1323 2796 4247	8464 9979 1471 2942 4391	8616 *OI29 1619 3088 4535	8768 #0279, 1767 3233 4679	8920 *0429 1915 3379 4822	9072 *0578 2062 3524 4965
70 71 72 73 74	6.5 5108 6526 7925 93°4 6.6 0665	5251 6667 8064 9441 0800	5393 6808 8203 9578 0935	5536 6948 8341 9715 1070	5678 7088 8479 9851 1204	5820 7228 8617 9987 1338	5962 7368 8755 *OI23 1473	6103 7508 8893 *02S9 1607	6244 7647 9030 *°394 1740	6386 7786 9167 *0530 1874
75 76 77 78 79	6.6 2007 3332 4639 5929 7203	2141 3463 4769 6058 733°	2274 3595 4898 6185 7456	2407 3726 5028 6313 7582	2539 3857 5157 6441 7708	2672 3988 5286 6568 7834	2804 4118 5415 6696 7960	2936 4249 5544 6823 8085	3068 4379 5673 6950 8211	3200 4509 5801 7077 8336
80 81 82 83 84	6.6 8461 9703 6.7 0930 2143 3340	8586 9827 1052 2263 3459	8711 9950 1174 2383 3578	8835 *oo73 1296 2503 3697	8960 *oi96 1417 2623 3815	9084 %3i9 1538 2743 3934	9208 *044i 1659 2863 4052	9332 *os64 1780 2982 4170	9456 *o686 1901 3102 4288	9580 *o8o8 2O22 3221 4406
85 86 87 88 89	6.7 4524 5693 6849 7992 9122	4641 5809 6964 8106 9234	4759 5926 7079 8219 9347	4876 6041 7194 8333 9459	4993 6i57 7308 8446 9571	5110 6273 7422 8559 9682	5227 6388 7537 8672 9794	5344 6504 7651 8784 9906	5460 6619 7765 8897 *ooi7	5577 6734 7878 9010 •;;:'012S
90 91 92 93 94	6.8 0239 1344 2437 35i8 4588	0351 1454 2546 3626 4694	0461 1564 2655 3733 4801	0572 1674 2763 3841 4907	0683 1783 2871 3948 5013	0793 1892 2979 4055 5118	0904 2OO2 3087 4l62 5224	1014 2III 3195 4268 533°	1124 2220 3303 4375 5435	123? 2329 34" 4482 5541
$ H 99	6.8 5646 6693 773° 8755 9770	5751 6797 7833 8857 9871	5857 6901 7936 8959 9972	596i 7005 8038 9061 *0073	6066 7109 8141 9163 •0174	6171 7213 8244 9264 *0274	6276 7316 8346 9366 *0375	6380 7420 8449 9467 *0475	6485 7523 8551 9568 *0575	6589 7626 8653 £» *o67S
100	6.9 0776	0875	0975	1075	"75	1274	1374	1473	1572	1672
N.	O	1	2	3	4	5	0	7	8	9

UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY

Return to desk from which borrowed. This book is DUE on the last date stamped below.

ASTFIDNOMY LIB

111AJ .->

&& 1 5 1971

ARY

LD 21-100m-ll,'49(B7146sl6)476

YC 1 02260

MATH*.

STAT«

UBftARY