UC-NRLF $C IbS 7b2 Single copies of these books (except the last) will be sent free to teachers of mathematics, for their inspection. GEORGE W. JONES, Publisher, No Agents. Ithaca, N. V. f\lA''!'vHjLCv; LOG-AEITHMIC TABLES Prof. GEORGE WILLIAM JONES OP CORNELL UNIVERSITY. SEVENTH EDITION. To promote the detection of errors in the tables, one dollar will be paid for the first notice of every such error. Address Prof. Jones at Ithaca. Uotrtron MACMILLAN AND CO. ITHACA, N. Y. GEORGE W. JONES. 1898. CONTENTS. PAGES. EXPLANATION OF THE TABLES, .... 8-11 I. FOUR-PLACE LOGARITHMS, • - . . . 12-14 A four-place table of logarithms of the natural numbers 1, 2, 8,.. 999, with a table of pro- portional differences in the margin, and of the logarithms of the squares, cubes, square-roots, cube-roots and reciprocals of the numbers 1, 2, 8, ..99. IL FOUR-PLACE TRIGONOMETRIC FUNCTIONS, - - - 15-19 A four-place table of logarithms of the six principal trigonometric functions, with differences for minutes, and of the lengths of arcs in radians. III. LOGARITHMS OF NUMBERS, .... 20-87 A six-place table of logarithms of four-figure numbers, with a table of differences. IV. CONSTANTS OF MATHEMATICS AND OF NATURE— WEIGHTS AND MEASURES, 88-« A table of useful constants, with the logarithms of those in common use. V. ADDITION-SUBTRACTION LOGARITHMS, - . . 42-68 A six-place table of logarithms so related that, by their use, the logarithm of the sum and of the difference of two numbers may be found from their logarithms without taking out the numbers themselves. VL SINES AND TANGENTS OF SMALL ANGLES, 59 A table of the ratios sin A": A, tan A": A for angles 0°-5°, whereby the logarithmic sines and tangents of these small angles are found more exactly than by Table VII. VII. TRIGONOMETRIC FUNCTIONS, .... 60-104 A five-place table of natural sines, cosines, tangents, and cotangents of angles 0°-lS0°, to minutes, and a six-place table of their logarithms, with differences of logarithms for seconds ex- pressed in units of the sixth decimal place. VIII. NATURAL LOGARITHMS, - - - - - 105-117 A six-place table of natural logarithms of the decimal numbers, .01, .02, .08,.. 9.99, of the natural numbers 1, 2, 8, . . 1218, and of the prime numbers between 1218 and 10000. IX. PRIME AND COMPOSITE NUMBERS, .... 118-137 A table of prime and composite numbers from 1 to 20000, with the factors of the composite numbers that are not divisible by 2 or 5, and ten-place logarithms of the primes. X. SQUARES, ....... 188-189 A table of the squares of the natural numbers 1, 2, 8,. .999. XI. CUBES, - .... 140-141 A table of the cubes of the decimal numbers .1, .2, .8,.. 99.9. XIL SQUARE-ROOTS, ...... ftt-UB A table of the square-roots, to four decimal places, of the natural numbers 1, 2, 8,.. 999, and of the decimal numbers .1, .2, .8, . . 99.9. XIIL CUBE-ROOTS, ...... 146-151 A table of the cube-roots, to four decimal places, of the natural numbers 1, 2, 8,.. 999, of the decimals .1, .2, .8,.. 99.9, and of the decimals .01, .02, .08,.. 9.99. XIV. RECIPROCALS, ...... 152-158 A table of the reciprocals of the decimal numbers .01, .02, .08,. .9.99. XV. QUARTER-SQUARES, .... 154-157 A tablo of tho quarter-squares of the natural numbers 1, 2, 8,. .2000. XVL BESSEL'S COEFFICIENTS, • - - • - 168 A tablo of Bessel's coefficients for second, third, fourth, and tilth differences, for interpolation. XVII. BINOMIAL COEFFICIENTS, ..... 169 A table of binomial coefficients for second, third, fourth, and fifth differences, for interpolation. XVIII. ERRORS OF OBSERVATION, • . • - 160 A table of ordinates of the probability-curve, values of probability integrals, and other values. Copyright, 1889, by George William Jones. EXPLANATION" OF THE TABLES. COMMON LOGARITHMS. FORM OF A LOGARITHM. The logarithm of a number is the exponent of that power to which another num- ber, the base, must be raised to give the number first named. The base commonly used in computation is 10, and as most numbers are incom- mensurable powers of 10, a common logarithm, in general, consists of an integer, the characteristic, and an endless decimal, the mantissa. If a number be resolved into two factors, of which one is an integer power of 10 and the other lies between 1 and 10, then the integer exponent of 10 is the charac- teristic, and the logarithm of the other factor is the mantissa. The characteristic is positive if the number be larger than unity, and negative if it be smaller ; the man- tissa is always positive. A negative characteristic is indicated by the sign — above it. E.g., 7770 = 10 3 x 7.77, and log 7770 = 3.890421, .0777 = 10- 2 x 7.77, and log .0777 = 2.890421. The logarithms of all numbers expressed by the same figures in the same order have different characteristics but the same mantissa ; for since all such numbers may be got one from another by multiplying or dividing by some integer power of 10, their logarithms differ by integers. In particular : if the decimal point stand after the first figure of a number, counting from the left, the characteristic is ; if after two figures, it is 1 ; if after three figures, it is 2, and so on. So, if the decimal point stand before the first sig- nificant figure, the characteristic is 1 ; if one zero follow the decimal point, it is 2. E.g., log 3649 = 3.562174, log 3.649 = 0.562174, log .003649 = 3.562174. TABLES OF LOGARITHMS. The logarithms of any set of consecutive numbers, arranged in a form convenient for use, constitute a table of logarithms. Such a table, to the base 10, need give only the mantissas ; the characteristics are evident. In this book there are three tables of common logarithms : Table I, pp. 12, 13, gives the logarithms of all three-figure numbers correct to four decimal places. Table III, pp. 20-37, gives the logarithms of all four-figure numbers correct to six decimal places. Table IX, pp. 118-137, gives the logarithms of all prime numbers below 20000 correct to ten decimal places. All these tables are arranged upon the same general plan, that of double entry, the last figure of a number standing at the top of the page, above the logarithm, and the other figures at the extreme left and on a line with the logarithm. The explanations that follow apply particularly to Table III ; but, with slight changes, they may serve also for Tables I and IX. TABLE III. In Table III, the first three figures of a number stand at the left of the page, and the fourth figure at the top ; the mantissa of the logarithm is found on a line with the first three figures of the number, and under the fourth figure. EXPLANATION OF THE TABLES. The mantissas, though endless decimals, are carried to six places only ; the sixth figure, being that which is nearest to the true value, is in error by less than half a unit. Of these six figures the last four are always printed in full, but the first two appear in the first column only, and at intervals of ten, or when they change. If a change occur in the middle of a line, warning is given by stars, and then the first two figures are read from the line below. E.g., on page 32 the mantissas of all numbers from 7000 to 7079 begin with 84 ; of numbers from 7080 to 7244, with 85 ; and the change to 86 takes place in the logarithm of 7245. The four-figure numbers found in the table are tabular numbers, and their loga- rithms are tabular logarithms. The differences of consecutive tabular logarithms, the tabular differences, are printed in the column of differences with multiples of their tenth parts below them. TO TAKE OUT THE LOGARITHM OF A NUMBER. For a four-figure number. Take out the tabular mantissa that lies in line with the first three figures of the number and under the fourth figure ; the characteristic is the exponent of that integer power of 10 which lies next below the number. E.g., log 72.44 = 1.859978, log .7245=1.860038, log .007246 = 3.860098. For a number of less than four figures. Make the number a four-figure number by annexing zeros ; and follow the rule above. E.g., log 700 = 2.845098, log 72 = 1.857332, log 702 =2.846337, log .007 = 3.845098, log .72 = 1.857332, log .000702 = 4.846337. For a number of more than four figures. Take out the tabular mantissa of the first four figures, subtract this mantissa from the next greater tabular mantissa, multiply the difference so found by the remaining figures, as a decimal, and add the product, as a correction, to the mantissa of the first four figures. E.g., to take out log 8513.64 : The characteristic is 3, and the mantissa of log 8513 is .930083. The tabular difference is .000051, and the product of .000051 by .64 is .000033. The corrected logarithm (3.930083 + .000033) is 3.930116. The work may take this form : 3.930134 51 3.930083 83 51 .64 32.64 33 3.930116 The labor of multiplying is shortened by finding the tabular difference in the col- umn of differences and adding mentally that part of this difference which lies oppo- posite the fifth figure of the number, a tenth of that which lies opposite the sixth figure, a hundredth of that which lies opposite the seventh figure, and so on. E.g., in the example above, under 51 and opposite 6 is 31 ; opposite 4 is 20, whose tenth part is 2, and the sum is 33. So, to take out log .001386137 : man. log 1386 = .14 1763, tab. dif . = 313, 313 x. 137 =43, and the logarithm sought is 3. 1 1 1 806. This process of finding logarithms of numbers of more than four figures is inter- polation by proportional parts ; it rests upon this property of logarithms : that the differences of logarithms are very nearly proportional to the differences of their numbers when those differences are small. EXPLANATION OF THE TABLES. TO TAKE OUT A NUMBER FROM ITS LOGARITHM. For a mantissa found exactly in the table. Join the figure at the top that lies above the given mantissa to the three figures upon the same line at the extreme left ; in the four-figure number thus found, so place the decimal point that the number shall be the product of some number that lies between 1 and 10 by a power of 10 whose ex- ponent is the characteristic of the logarithm. E.g., to take out log -1 3.583652 : [log -1 is read antilogarithm. The mantissa .583652 lies in line with 383 and under 4 ; and since the character- istic is 3, there are four integer figures, and the number is 3834. So, log-* 0.583652 = 3.834, log- 1 3.583652 = .003834. To take out log- 1 1.780029: The mantissa. 780029 lies in line with 602 and under 6, and since the characteristic is — 1, the number sought is .6026. So, log- 1 3.780029 = . 006026, log- 1 2.780029 = 602.6. For a mantissa not found exactly in the table. Take out the four-figure antiloga- rithm of the tabular mantissa next less than the given mantissa, and to it join the quotient of the difference of these two mantissas by the tabular difference. E.g., to take out log- 1 3.583700 : The next less tabular mantissa is .583652, whose four-figure antilogarithm is 3834, 583700 583765 48 : 113 = .425 nearly, 583652 48 583652 113 and the number sought is 3834.425 nearly. To take out log- 1 1.780089 : The next less tabular mantissa is .780029, whose four-figure antilogarithm is 6026, 780089 780101 60 : 72 = .83 nearly, 29 60 29 72 and the number sought is .602683 nearly. To take out log- 1 6.471197 : The next less tabular mantissa is .471145, whose four figure antilogarithm is 2959, 471197 471292 52 : 147 = 35 nearly, 45 52 145 147 and the number sought is 2959350 nearly. The labor of dividing is shortened by finding the tabular difference in the column of differences, and using the multiples of its tenth part for the several products in the course of the division. Thus shortened, the whole work may in most cases be done mentally, and only the complete antilogarithm is then written down. E.g., in dividing 48 by 113, the table of differences shows that 45 is 4 tenths of 113, and that the remainder, 3, is nearly 3 hundredths of 113. POSSIBLE ERRORS. The possible error of any logarithm, as printed in this table, is half a millionth, and the possible error of any tabular difference is a millionth ; but the probable error is much less. If several logarithms be added, or if a logarithm be multiplied by the exponent of a high power, the resulting logarithm may be in error by more than a EXPLANATION OF THE TABLES. millionth. In such a case the fifth figure of the antilogarithm, the first got by di- vision, is generally trustworthy, the sixth figure is often in doubt, and the seventh figure is rarely to be used. The possible error in the result is nearly ten times greater if the logarithm be near the end of the table than if near the beginning ; for then the tabular difference, the divisor, is much smaller, and an error either in it or in the dividend has greater effect. If greater accuracy be desired, larger tables must be used. LABOR-SAVING DEVICES. If the number whose logarithm is sought lie nearer the larger of two tabular num- bers, the correction may be applied, by subtraction, to the larger tabular mantissa; and so, if a given logarithm lie nearer the larger of two tabular mantissas, the correction may be applied, by subtraction, to the larger tabular number. To avoid straining the eyes the logarithms are grouped in blocks of five, and, instead of tracing the lines of figures across the page and down the columns, the computer may guide himself by correspondences of position in the blocks. To divide a logarithm whose characteristic is negative : Write down, as first quo- tient figure, the number of times the divisor is contained in that negative multiple of itself which is equal to, or next larger than, the negative characteristic ; carry the positive remainder to the mantissa and divide for the mantissa of the quotient. To avoid negative characteristics : Modify the logarithms by adding 1 to such characteristics. Use the sums, differences, or multiples of the modified logarithms where the subject-matter is such that the general magnitude of the results cannot be mistaken. To divide a modified logarithm : Add such a multiple of 1 as will make the sum exceed the true logarithm by 1 times the divisor ; divide, and the quotient is the true logarithm, modified. The arithmetical complement of a logarithm is the excess of 1 over the given log- arithm ; it is the modified logarithm of the reciprocal of the number. The arithme- tical complement of a tabular logarithm may be read directly from the table, subtract- ing the first figures of the logarithm from 9 and the last from 10. CONSTANTS.— WEIGHTS AND MEASURES. TABLE IV. Table IV gives the principal constants of mathematics and of nature, with the log- arithms of such of them as are in common use. If the characteristic of a logarithm be negative the modified logarithm is used. In addition to the constants of mathe- matics, certain formulae are shown by which these constants may be determined. In chemistry, Professor Clarke is the authority. In physics, Professors Everett, Landolt and BSrnstein are the principal author When there have been several determinations of a constant, either the range has been given, where space permitted, or that one of them has been chosen which seemed most reliable. Here the meter is taken as 39.370432 inches. In the conversion tables for " Weights and Measures," the meter has been takon as 39.3700 inches, with a very small possible error, on the authority of Professor Rogers and of Professor Mendenhall, the superintendent of the United States Coast and Geodetic Survey. This value is also the legal value of the meter in the United States. The kilogram, by the determinations of the International Bureau of Weights and Measures, is 15432.35639 grains. EXPLANATION OF THE TABLES. ADDITION-SUBTRACTION LOGARITHMS. TABLE V. Addition-subtraction logarithms (Gaussians) are of use in finding the logarithm of the sum or difference of two numbers directly from their logarithms. They are known as A-logarithms, B-logarithms, and C-logarithms. The table is divided into three parts : pp. 42-51, 52-53, 54-58. The formulae at the bottom of any page show how to use the logarithms on that page : for addition, at the left ; for subtraction, at the right. All cases of addition can be solved by the use of part 1, and part 2 need be used only for subtraction ; part 3 is for subtraction only. This table is arranged on the same general plan as Table III : the A-logarithms in parts 1, 2 take the place of numbers in that table, and the B-logarithms that of loga- rithms ; the B-logarithms in part 3 take the place of numbers, and the C-logarithms that of logarithms. In parts 1, 2, A, B are so related that log -1 B= 1 +log -1 A. Given log a, log b, and log a greater than log b, to find log (a + b). From log b subtract log a and add 1 ; enter the table with this sum as A, take out B, as a logarithm is found from its number ; to B add log a. Or, from log a subtract log b, and if the remainder be less than .2, enter the table with this remainder as A, take out B, and add log b- The work may take this form : A 9.216000 [part 1 A 0.110925 [part 2 log b 3.091175 log a 3.875175 • B 0.066116 log (a + 6) 3.941291 A 0.110925 log a 3.847129 logb 3.736204 B 0.360024 log (a + *) 4.096228 Given log a, log b, and log a greater than log b, to find log (a — ft). From log a subtract log b, then : (a) If the remainder be less than .4, enter the table with this remainder as B, and and take out A, as a number is found from its logarithm ; to A add log b. B 0.230162 [part 1 B 0.340079 [part 2 log a 1.517893 logo, 1.683719 log* 1.287731 log* T.343640 A 9.844400 A 0.074875 \og( a -b) 1.132131 log (a-*) 1.418515 (*) If the remainder be more than .4, enter the table with this remainder as B, and take out C, as a logarithm is found from its number ; to C add log a. B 0.450700 B 0.600311 [part 3 log b 1.916429 log a 2.367129 C 9.810070 log {a -b) 2.177199 B 0.600311 log* 0.196834 log a 0.797145 C 9.874476 log (a - -b) 0.671621 EXPLANATION OF THE TABLES. TRIGONOMETRIC FUNCTIONS. In this book there are two tables of trigonometric functions : Table II, pp. 15-19, gives the angles in degrees, and in radians, to five minutes for the first five degrees and the last five degrees of a right angle, and to ten minutes for the rest ; and it gives four-place logarithms of the six principal functions of these an- gles, with differences for minutes. Table VI, page 59, is a supplementary table whose object is to make more exact such computations as involve very small angles. Table VII, pp. 60-104, gives the angles to minutes for two right angles, with their natural sines, cosines, tangents, and cotangents, correct to five places, and six-place logarithms of these functions, with differences for seconds. The explanations that follow apply particularly to Table VII ; with slight changes they may serve also for Table II. For explanations of Table VI, see page 10. TABLE VII. If the angle be less than 45° or more than 135°, the name of the function and the number of degrees in the angle are found at the top of the page, and the minutes at the side of the page below the degrees ; if the angle lie between 45° and 135°, the name of the function and the number of degrees are found at the bottom of the page, and the minutes above the number of degrees. The functions are given for every degree and minute from 0° to 180°, and they lie in line with the minutes of the angle. The functions themselves, called the natural functions, and their logarithms, the logarithmic functions, are printed side by side, the first in small type, and the other in larger type as being more important. If a logarithm be negative, then the modi- fied logarithm is used. At the right of the columns of logarithmic sines and cosines and between those of logarithmic tangents and cotangents are printed the sixtieth parts of the differences of consecutive logarithms ; they are the tabular differences for seconds. Logarithmic secants and cosecants are found by subtracting from 10 the modified logarithms of cosines and sines. The tables do not distinguish between positive and negative functions, and every function is some function of four different angles : every sine is the sine of two angles that are supplementary, and the cosine of their complements, and so with every co- sine, tangent, and cotangent. E.g., on page 71 the decimal .19652 is the sine of 11° 20' and of 168° 40', and the cosine of 78° 40' and of 101° 20' ; and 9.293399 is its logarithm. TO TAKE OUT A FUNCTION OF AN ANGLE. For an angle given in degrees and minutes. If the degrees be at the top of the page, find the minutes under the degrees and take out the number, or its logarithm, that lies in line with the minutes and below the name of the function sought. If the degrees be at the bottom of the page, find the minutes over the degrees and the function sought above its name. E.g., to take ©ut nat-sin 16° 10' : Under 16° and nat-sine, and in line with 10' on the left, read .27843. So, to take out log-cot 107° 34' : Over 107° and log-cotangent, and in line with 34' on the left, read 9.500481. EXPLANATION" OF THE TABLES. 9 For an angle given in degrees, minutes, and seconds. Take out, as above, the functions of the two tabular angles between which the given angle lies ; and to the function of the less angle add such part of the excess of the function of the greater angle over that of the less, as the seconds are of one minute. The correction for seconds may be computed and applied mentally. "With loga- rithmic functions the corrections sought are the products of the tabular differences for seconds by the number of seconds. If the function of the greater angle be the greater function, the correction is posi- tive ; but if it be the less function, the correction is negative. E.g., to take out nat-tan 106° 33' 47" : nat-tan 106° 34' = 3.3616 3.3652 nat-tan 106° 33' = 3.3652, -36x££=-28 28 3.3624 So, to take out log-cot 107° 34' 25" : log-cot 107° 34'= 9.500481 7.32x25 = 183. 183 9.500664 TO TAKE OUT AN ANGLE FROM ITS FUNCTION. The function found exactly in the table. If the name of the function be found at the top of the column, read the degrees at the top of the page, and the minutes in line with the function under the degrees. If the name of the function be found at the bottom of the column, read the degrees at the bottom of the page, and the minutes in line with the function over the degrees. For every sine, the table gives two angles, supplements ; and which of them shall be taken is made known in practice by other considerations. So with the other func- tions if the signs of the functions be disregarded. E.g., to take out nat-cos -1 .51279 : The function is found on page 90, over 120° and in line with 51', and over 59° and in line with 9'. So, to take out log-sin -1 9.716224 : The function is found on page 91, under 31° and in line with 21', and under 148° and in line with 39'. So, to take out log-tan -1 .206744 : The function is found on page 91, over 58° and in line with 9', and over 121° and in line with 51'. The function not found exactly in the table. Take out the two tabular functions between which the given function lies and to the smaller tabular angle add such part of sixty seconds as the difference between the function of the less angle and the given function is a part of the tabular difference. "With logarithmic functions the number of seconds is the quotient of this difference by the tabular difference for seconds. E.g., to take out nat-cos -1 . 51267 : nat-cos 59° 10' = . 51254 .51267 60"x|£=29* 59° 9' 29", nat-cos 59° 9'=. 51279 -25 .51279 -12 120° 50' 31". So, to take out log-sin -1 9.716300 : 31° 21' 22", log-sin 31° 21" = 9.716224 , 76 : 3.47 = 22'. 148° 38' 38". With practice the seconds may be computed mentally, and the whole angle is then read directly from the table. 10 EXPLANATION OF THE TABLES. SINES AND TANGENTS OF SMALL ANGLES. TABLE VI. If an angle be very small, its sine and tangent are also very small ; but their loga- rithms are negative and very large, and they change rapidly and at rapidly varying rates. Such logarithms, therefore, are not convenient for use where interpolation is necessary, and in their stead the logarithms given in Table VI may be used ; they are based on the following considerations : An angle whose bounding arc is just as long as a radius is a radian ; it is equal to 57° 17' 44".8, i. e., to 206264".8, and the number of seconds in an angle is 206264.8 times the number of radians. For a small angle the number of radians in the bounding arc is a little larger than the sine of the angle and a little smaller than its tangent : it follows that, if A be a small angle expressed in radians, the ratio sin A : A is a little smaller, and the ratio tan A : A is a little larger, than unity ; but both these ratios approach unity closer and closer as the angle grows smaller. If the angle be expressed in seconds, then the ratio sin A" : A is a little smaller than the reciprocal of 206264.8, and the ratio tan A" : A is a little larger than this reciprocal. These ratios change very slowly, and hence interpolation is always possi- ble ; the table gives their logarithms for every minute from 0° to 5°. The cosine and cotangent of an angle near 90° are the sine and tangent of the complementary small angle. The logarithm of the cotangent of a small angle is found by subtracting the modified logarithm of the tangent of the angle from 10 ; that of the tangent of an angle near 90°, by subtracting the modified logarithm of the tangent of the complementary small angle from 10. TO TAKE OUT THE SINE OR TANGENT OF A SMALL ANGLE. Take out the logarithm that lies below the number of degrees and in line with the minutes ; interpolate for seconds, and add the logarithm of the whole number of seconds in the angle. Let A be the number of seconds in an angle ; then sin A" = (sin A": A)-A, and log-sin A" = log (sin A": A) + log A, tan A" = (tan A" : A) A, and log-tan A" = log (tan A" : A) + log A. E.g., log-sin 10' 30" = log (sin 630": 630)+ log 630, = 4.685574 + 2.799341 = 7.484915. [pp. 59, 30. So, log-tan 3° 13' 40" = log (tan 11620": 11620) + log 11620, = 4.686034 + 4.065206 = 8.751240. The angle is found by a reverse process. E.g., to take out log-sin- 1 8.414317, and log-tan- 1 8.414317 : From Table VII, page 61, it appears that the angles sought lie between 1° 29 / and 1° 30', and nearer to 1° 29' ; and by the formula log-sin A" — log (sin A" : A) = log A ; log-tan A" — log (tan A" : A) = log A : 8.414317-4.685526 = 3.728791, 8.414317-4.685672 = 3.728645, and the angle is 5355" ; i.e.,l° 29' 15". 5354" ; i.e., 1° 29' 14". So, to take out log-sin-' 8.806231 : log-tan- 1 8.806231 : The angle lies between 3° 40' and 3° 41' ; between 3° 39' and 3° 40' ; [p. 63 8.806231-4.685278 = 4.120953, 8.806231-4.686167 = 4.120064, and the angle is 13212" ; i.e., 3° 40' VI". 13185" ; i.e., 3° 39' 45". EXPLANATION OF THE TABLES. MINOR TABLES. VIII. NATURAL LOGARITHMS. In table VIII, pp. 105-117, the natural logarithms (sometimes improperly called Naperian, and sometimes hyperbolic, logarithms) follow their numbers in parallel columns. The characteristics are given ; and a change in the position of the decimal point in the number changes both the mantissa and the characteristic of the logarithm. IX. PRIME AND COMPOSITE NUMBERS. Table IX, pp. 118-137, gives all the prime factors of composite numbers less than 20 000 that are not divisible by 2 or 5, and the ten -place common logarithms of the primes. It is a double entry table, and to find primes it is sufficient to look for numbers whose logarithms are given. The ten-place logarithms of all composite numbers whose prime factors are smaller than 20 000 are found by adding the loga- rithms of the factors, and of prime numbers greater than 20 000 by interpolation. X-XIV. SQUARES, CUBES, SQUARE-ROOTS, CUBE-ROOTS AND RECIPROCALS. Table X, pp. 138-139, gives the squares of all three-figure numbers in full ; and a change in the position of the decimal point in the number makes twice as great a change in the square, and in the same direction. Table XI, pp. 140-141, gives the cubes of three-figure numbers correct to six figures. Table XII, pp. 142-145, in two parts, gives the square-roots of all three-figure num- bers to four places, and by interpolation it gives the square-roots of all other numbers. Table XIII, pp. 146-151, in three parts, gives the cube-roots of all three-figure numbers to four places, and, by interpolation, of all other numbers. Table XIV, pp. 152-153, gives the reciprocals of all three-figure numbers to four places, and, by interpolation, of all other numbers. XV. QUARTER-SQUARES. Table XV, pp. 154-157, makes it possible, without logarithms, to find the product of any two numbers whose sum does not exceed 2000, by addition and subtraction. For if a, b be any two numbers, then ^(a + by — \(a — b)* = a b. The quarter-square of an even number is an integer, and that of an odd number ends always with the fraction i ; .but as the sum and difference of any two integers are either both even or both odd, these fractions cancel each other in the subtraction. XVI-XVII. COEFFICIENTS FOR INTERPOLATION. Let a, b, c, d, e,f, - - - be any series ; a v b v c v d v $' • * -. their first differences ; a i-> ^a> G i? d& • • • their second differences, and so on ; and let n be the number of any term, T n , between c and d, counting c as T ; then G^ — n, and with Bessel's coefficients T n = c + G 1 c l + \ C 2 (b 9 + c 9 ) + C s b 3 + \ C 4 (a 4 + bj + C b a b ; with the binomial coefficients T n = c + C t c x + C 2 c 2 -f O s c s + - - - Of Bessel's coefficients C 2 is negative throughout, and C 4 positive, C 3 is negative for values of G 1 above .5, and C 5 for values below .5. Of the binomial coefficients all values of C 2 and C 4 are negative. XVIII. ERRORS OF OBSERVATION. Table XVIII, page 160, is in three parts : The first part gives ordinates of the probability-curve, and its area. The second part gives the probability that the abso- lute magnitude of the error does not exceed the indicated fraction of the probable error. The third part tabulates four factors that give the probable error of a single observation, and the probable error of the mean of n observations : Multiply the first two factors into the square root of the sums of the squares of the discrepancies be- tween the n observations and their mean ; or multiply the last two factors into the sum of the absolute values of the discrepancies. 12 L FOUR-PLACE LOGARITHMS. 1 1 2 3 4 5 6 7 8 9 Differences. 1 0000 0000 0000 0414 3010 0792 4771 1139 6021 1461 6990 1761 7782 2041 8451 2304 9031 2553 9542 2788 43 1 4 2 9 42 4 8 41 4 8 40 4 8 M 4 8 2 3010 3222 3424 3617 3802 3979 4150 4314 4472 4624 8 18 13 12 12 12 3 4 4771 6021 4914 6128 5051 6232 5185 6335 5315 6435 5441 6532 5563 6628 5682 6721 5798 6812 5911 6902 4 17 5 22 6 26 17 21 25 16 21 25 16 20 24 16 20 23 5 6990 7076 7160 7243 7324 7404 7482 7559 7634 7709 7 30 8 84 29 34 29 38 28 32 27 31 6 7782 7853 7924 7993 8062 8129 8195 8261 8325 8388 9 89 88 37 86 80 7 8451 8513 8573 8633 8692 8751 8808 8865 8921 8976 38 37 36 35 34 8 9 9031 9542 9085 9590 9138 9638 9191 9685 9243 9731 9294 9777 9345 9823 9395 9868 9445 9912 9494 9956 1 4 2 8 3 11 4 7 11 4 7 11 4 7 11 3 7 10 10 11 0000 0414 0043 0453 0086 0492 0128 0531 0170 0569 0212 0607 0253 0645 0294 0682 0334 0719 0374 0755 4 15 5 19 6 23 15 19 22 J* 18 22 14 18 21 14 20 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 7 27 26 25 25 24 13 14 1139 1461 1173 1492 1206 1523 1239 1553 1271 1584 1303 1614 1335 1644 1367 1673 1399 1703 1430 1732 8 80 9 34 33 80 33 32 29 32 81 28 32 30 27 81 29 15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 1 3 2 7 3 10 3 6 10 3 6 9 3 6 9 3 6 9 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 4 13 13 12 12 12 18 19 2553 2788 2577 2810 2601 2833 2625 2856 2648 2878 2672 2900 2695 2923 2718 2945 2742 2967 2765 2989 5 17 6 20 7 28 16 19 22 16 19 22 15 IS 21 15 17 20 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 8 26 9 30 26 29 25 28 24 27 28 26 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 28 1 3 27 3 26 3 25 3 24 2 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 6 5 5 5 5 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 3 8 4 11 8 11 8 10 S 10 7 10 25 26 3979 4150 3997 4166 4014 4183 4031 4200 4048 4216 4065 4232 4082 4249 4099 4265 4116 4281 4133 4298 5 14 6 17 7 20 14 16 19 13 16 18 13 15 18 12 14 17 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 8 22 22 21 20 19 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 9 25 24 23 28 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 28 1 2 22 2 21 2 20 2 19 2 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 2 5 4 4 4 6 8 4 6 8 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 8 7 4 9 7 9 6 8 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 5 12 11 11 10 10 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 6 14 7 16 8 IS 13 15 18 18 15 17 a 14 16 11 13 15 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 9 21 20 19 IS 17 36 37 5563 5682 5575 5694 5587 5705 5599 5717 5611 5729 5623 5740 5635 5752 5647 5763 5658 .5775 5670 5786 18 1 2 2 4 17 1 8 10 •_> 1 15 2 8 14 1 8 38 39 5798 5911 5809 5922 5821 5933 5832 5944 5843 5955 5855 5966 5866 5977 587 7 5988 5888 5999 5899 6010 8 5 4 7 5 9 5 7 9 5 6 S 5 6 8 4 6 : 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6 11 7 18 8 14 10 II 14 10 11 13 9 11 12 s 10 11 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 9 16 15 14 14 18 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 13 12 11 10 9 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 65 S3 1 1 1 B 1 2 1 I 1 2 1 2 45 46 6532 6628 6542 6637 6551 6646 6561 6656 6571 6665 6580 6675 6590 6684 6599 6693 6609 6702 6618 6712 3 4 4 5 5 7 4 5 6 8 4 6 3 4 | 3 4 5 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 6 S 7 7 6 B 48 49 6812 6902 6821 6911 6830 6920 6839 6928 6848 6937 6857 6946 6866 6955 6875 6964 6884 6972 6893 6981 7 9 S 10 9 12 S 10 11 8 9 10 7 8 9 6 7 8 50 1 2 3 4 5 6 7 8 9 Differences. I. FOUR-PLACE LOGARITHMS. 13 " 50 1 2 3 4 5 6 7 8 9 Differences. 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 i 8 1 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 2 2 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 3 4 2 3 56 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 5 4 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 6 1 5 6 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 8 6 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 9 7 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896. 7903 7910 7917 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 1 2 3 1 1 2 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 4 5 3 4 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 6 4 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 7 8 9 5 6 6 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 6 1 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 1 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 2 1 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 3 4 2 2 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 5 6 7 3 4 4 76 8808 8814 8820 8825 8831 8-&S7 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 V 8904 8910 8915 8 5 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 9 5 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 1 2 5 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 1 1 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 3 2 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 4 5 2 3 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 6 3 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 7 8 4 4 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 9 5 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 4 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 1 2 3 1 1 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727- 4 2 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 5 6 2 2 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 7 3 96 9^23 9827 9832 9836 9841 9845 9850 9854 9859 9863 8 9 3 4 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 99 19956 9961 9965 9969 9974 9978 9983 9987 9991 9996 100 1 2 3 4 5 6 7 8 9 Differences. 14 I. FOUR-PLACE LOGARITHMS. •— ' Square. Cube. So,. Root. Cu. Root. Recip. 50 Square. Cube. So.. Root. Cu. Root. i Recip. • CO CO CO CO CO 50 3.3979 5.0969 0.8495 0.5663 8.3010 l 0.0000 0.0000 0.0000 0.0000 0.0000 51 4151 1227 8538 5692 2924 2 6021 9031 1505 1003 9.6990 52 4320 1480 8580 5720 2840 3 9542 1.4314 2386 1590 5229 53 4486 1728 8621 5748 2757 4 1.2041 8062 3010 2007 3979 54 4648 1972 8662 5775 2676 5 3979 2.0969 3495 2330 3010 55 4807 2211 8702 5801 2596 6 5563 3345 3891 2594 2218 56 4964 2446 8741 5827 2518 7 6902 5353 4225 2817 1549 57 5117 2676 8779 5853 2441 8 8062 7093 4515 3010 0969 58 5269 2903 8817 5878 2366 9 9085 8627 4771 3181 0458 59 5417 3126 8854 5903 2291 10 2.0000 3.0000 0.5000 0.3333 9.0000 60 3.5563 5.3345 0.8891 0.5927 8.2218 11 0828 1242 5207 3471 8.9586 61 5707 3560 8927 5951 2147 12 1584 2375 5396 3597 9208 62 5848 3772 8962 5975 2076 13 2279 3418 5570 3713 8861 63 5987 3980 8997 5998 2007 14 2923 4384 5731 3820 8539 64 6124 4185 9031 6021 1938 15 3522 5283 5880 3920 8239 65 6258 4387 9065 6043 1871 16 4082 6124 6021 4014 7959 66 6391 4586 9098 6065 1805 17 4609 6913 6152 4101 7696 67 6521 4782 9130 6087 1739 18 5105 7658 6276 4184 7447 68 6650 4975 9163 6108 1675 19 5575 8363 6394 4263 7212 69 6777 5165 9194 6129 1612 20 2.6021 3.9031 0.6505 0.4337 8.6990 70 3.6902 5.5353 0.9225 0.6150 8.1549 21 6444 9667 6611 4407 6778 71 7025 5538 . 9256 6171 1487 22 6848 4.0273 6712 4475 6576 72 7147 5720 9287 6191 1427 23 7235 0852 6809 4539 6383 73 7266 5900 9317 6211 1367 24 7604 1406 6901 4601 6198 74 7385 6077 9346 6231 1308 25 7959 1938 6990 4660 6021 75 7501 6252 9375 6250 1249 26 8299 2449 7075 4717 5850 76 7616 6424 9404 6269 1192 27 8627 2941 7157 4771 5686 77 7730 6595 9432 6288 1135 28 8943 3415 7236 4824 5528 78 7842 6763 9460 6307 1079 29 9248 3872 7312 4875 5376 79 7953 6929 9488 6325 1024 30 2.9542 4.4314 0.7386 0.4924 8.5229 80 3.8062 5.7093 0.9515 0.6344 8.0969 31 9827 4741 7457 4971 5086 81 8170 7255 9542 6362 0915 32 3.0103 5154 7526 5017 4949 82 8276 7414 9569 6379 0862 33 0370 5555 7593 5062 4815 83 8382 7572 9595 6397 0809 34 0630 5944 7657 5105 4685 84 8486 7728 9621 6414 0757 35 0881 6322 7720 5147 4559 85 8588 7883 9647 6431 0706 36 1126 6689 7782 5188 4437 86 8690 8035 9672 644S 0655 37 1364 7046 7841 5227 4318 87 8790 8186 9698 6465 0605 33 1596 7394 7899 5266 4202 88 8890 8334 9722 6483 0555 39 1821 7732 7955 5304 4089 89 8988 8482 9747 6498 0506 40 3.2041 4.8062 0.8010 0.5340 8.3979 90 3.9085 5.8627 0.9771 0.6514 8.0458 41 ' 2256 8384 8064 5376 3872 91 9181 8771 9795 6530 0410 42 2465 8697 8116 5411 3768 92 9276 8914 9819 6546 0362 43 2669 9004 8167 5445 3665 93 9370 9054 9843 6562 0315 44 2869 9304 8217 5*478 3565 94 9463 9194 9866 6577 0269 45 3064 9596 8266 5511 3468 95 9554 9332 9889 6592 02S8 46 3255 9883 8314 5543 3372 96 9645 9468 9911 6608 0177 47 3442 5.0163 8360 5574 3279 97 9735 9603 9934 6623 0132 48 3625 0437 8406 5604 3188 98 9825 9737 9966 6637 0088 49 3804 0706 8451 5634 3098 99 9913 9869 9978 6652 0044 log, r= 0.4971, log £tt= 0.1961, log^-7r = 9.895 I, log^TT = 9.7190, logfir— 0.6L >1 J1. l II. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. 15 Deg. Rad. Sin. DlF. Csc. Cos. Dip. Sec. Tan. Dip. Cot. Rad. Deg. 0° 00' 0.0000 00 QO 00 0.0000 .0 0.0000 00 00 CO 1.5708 90° 00' 05 0015 7.1627 602 2.8373 0000 0000 7.1627 602 2.8373 5693 55 10 0029 4637 352 5363 0000 0000 4637 352 5363 5679 50 15 0044 6398 260 3602 0000 0000 6398 250 3602 5664 45 20 0058 7648 194 2352 0000 0000 7648 194 2352 5650 40 25 0073 8617 158 1383 0000 0000 8617 158 1383 5635 35 30 0087 9408 134 0592 0000 0000 9409 184 0591 5621 30 35 0102 8.0078 116 1.9922 0000 0000 8.0078 116 1.9922 5606 25 40 0116 0658 102 9342 0000 0000 0658 102 9342 5592 20 45 0131 1169 91.6 8831 0000 0000 1170 91.4 8830 5577 15 50 0145 1627 82.8 8373 0000 .2 0000 1627 82.8 8373 5563 10 55 0160 2041 75.6 7959 9.9999 .0 0001 2041 75.6 7959 5548 05 1° 00' 0.0175 8.2419 69.4 1.7581 9.9999 .0 0.0001 8.2419 69.6 1.7581 1.5533 89° 00' 05 0189 2766 64.4 7234 9999 0001 2767 64.4 7233 5519 55 10 0204 3088 60.0 6912 9999 0001 3089 60.0 6911 5504 50 15 0218 3388 56.0 6612 9999 0001 3389 56.0 6611 5490 45 20 0233 3668 52.6 6332 9999 0001 3669 52.6 6331 5475 40 25 0247 3931 49.6 6069 9999 0001 3932 49.8 6068 5461 35 30 0262 4179 47.0 5821 9999 .2 0001 4181 47.0 5819 5446 30 35 0276 4414 44.6 5586 9998 .0 0002 4416 44.4 5584 5432 25 40 0291 4637 42.2 5363 9998 0002 4638 42.6 5362 5417 20 45 0305 4848 40.4 5152 9998 0002 4851 40.4 5149 5403' 15- 50 0320 5050 38.6 4950 9998 0002 5053 38.6 4947 5388 10 55 0335 5243 87.0 4757 9998 .2 0002 5246 87.0 4754 5373 05 2° 00' 0.0349 8.5428 35.4 1.4572 9.9997 .0 0.0003 8.5431 35.4 1.4569 1.5359 88° 00' 05 0364 5605 34.2 4395 9997 0003 5608 34.2 4392 5344 55 10 0378 5776 32.6 4224 9997 0003 5779 82.8 4221 5330 50 15 0393 5939 31.6 4061 9997 .2 0003 5943 31.6 4057 5315 45 20 0407 6097 30.6 3903 9996 .0 0004 6101 30.6 3899 5301 40 25 0422 6250 29.4 3750 9996 0004 6254 29.4 3746 5286 35 30 0436 6397 28.4 3603 9996 0004 6401 28.6 3599 5272 30 35 0451 6539 27.6 3461 9996 .2 0004 6544 27.6 3456 5257 25 40 0465 6677 26.6 3323 9995 .0 0005 6682 26.6 3318 5243 20 45 0480 6810 26.0 3190 9995 0005 6815 26.0 3185 5228 15 50 0495 6940 25.2 3060 9995 .2 0005 6945 25.2 3055 5213 10 55 0509 7066 24.4 2934 9994 .0 0006 7071 24.6 2929 5199 05 3° 00' 0.0524 8.7188 23.8 .1.2812 9.9994 .0 0.0006 8.7194 23.8 1.2806 1.5184 87° 00' 05 0538 . 7307 23.2 2693 9994 .2 0006 7313 23.2 2687 5170 55 10 0553 7423 22.4 2577 ' 9993 .0 0007 7429 22.6 2571 5155 50 15 0567 7535 22.0 2465 9993 0007 7542 22.0 2458 5141 45 20 0582 7645 21.4 2355 9993 .2 0007 7652 21.6 2348 5126 40 25 0596 7752 21.0 2248 9992 .0 0008 7760 21.0 2240 5112 35 30 0611 7857 20.4 2143 9992 0008 7865 20.4 2135 5097 30 35 0625 7959 20.0 2041 9992 .2 0008 7967 20.0 2033 5083 25 40 0640 8059 19.4 1941 9991 .0 0009 8067 19.6 1933 5068 20 45 0654 8156 19.0 1844 9991 .2 0009 8165 19.2 1835 5053 15 50 0669 8251 18.8 1749 9990 .0 0010 8261 18.8 1739 5039 10 55 0684 8345 18.2 1655 9990 .3 0010 8355 18.2 1645 5024 05 4° 00' 0.0698 8.8436 17.8 1.1564 9.9989 .0 0.0011 8.8446 18.0 1.1554 1.5010 86° 00' 05 0713 8525 17.6 1475 9989 0011 8536 17.6 1464 4995 55 10 0727 8613 17.2 1387 9989 .2 0011 8624 17.4 1376, 4981 50 15 0742 8699 16.8 1301 9988 .0 0012 8711 16.8 1289 4966 45 20 0756 8783 16.4 1217 9988 .2 0012 8795 16.6 1205 4952 40 25 0771 8865 16.2 1135 9987 .0 0013 8878 16.4 1122 4937 35 30 0785 8946 16.0 1054 9987 .2 0013 8960 16.0 1040 4923 30 35 0800 9026 15.6 0974 9986 .0 0014 9040 15.6 0960 4908 25 40 0814 9104 15.4 0896 9986 .2 0014 9118 0882 4893 20 45 0829 9181 15.0 0819 9985 .0 0015 9196 15.2 0804 4879 15 50 0844 9256 14.8 0744 9985 .2 0015 9272 14.8 0728 4864 10 55 0858 9330 14.6 0670 9984 0016 9346 0654 4850 05 5° 00' 0.0873 8.9403 1.0597 9.9983 0.0017 8.9420 1.0580 1.4835 85° 00' Deg. Rad. Cos. DlF. Sec. Sin. Dip. Csc. Cot. Dip. Tan. Rad. Deg. 16 II. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. Deg. Ead. Sin. Dif. Csc. Cos. Dif. Sec. Tan. Dif. Cot. Km,. Deo. 5° 00' 0.0873 8.9403 14.2 1.0597 9.9983 .1 0.0017 8.9420 14.3 1.0580 1.4835 85° 00* 10 0902 9545 18.7 0455 9982 0018 9563 18.8 0437 4806 50 20 0931 9682 13.4 0318 9981 0019 9701 18.5 0299 4777 40 30 0960 9816 12.9 0184 9980 0020 9836 18.0 0164 4748 30 40 0989 9945 12.5 0055 9979 .2 0021 9966 12.7 0034 4719 20 50 1018 9.0070 12.2 0.9930 9977 .1 0023 9.0093 12.3 0.9907 4690 10 6° 00' 0.1047 9.0192 11.9 0.9808 9.9976 .1 0.0024 9.0216 12.0 0.9784 1.4661 84° 00' 10 1076 0311 11.5 9689 9975 .2 0025 0336 11.7 9664 4632 50 20 1105 0426 11.8 9574 9973 .1 0027 0453 11.4 9547 4603 40 30 1134 0539 10.9 9461 9972 0028 0567 11.1 9433 4573 30 40 1164 0648 10.7 9352 9971 .2 0029 0678 10.8 9322 4544 20 50 1193 0755 10.4 9245 9969 .1 0031 0786 10.5 9214 4515 10 7° 00' 0.1222 9.0859 10.2 0.9141 9.9968 .2 0.0032 9.0891 10.4 0.9109 1.4486 83° 00' 10 1251 0961 9.9 9039 9966 0034 0995 10.1 9005 4457 50 20 1280 1060 9.7 8940 9964 .1 0036 1096 9.8 8904 4428 40 30 1309 1157 9.5 8843 9963 .2 0037 1194 9.7 8806 4399 30 40 1338 1252 9.3 8748 9961 0039 1291 9.4 8709 4370 20 50 1367 1345 9.1 8655 9959 .1 0041 1385 9.3 8615 4341 10 8° 00' 0.1396 9.1436 8.9 0.8564 9.9958 .2 0.0042 9.1478 9.1 0.8522 1.4312 82° 00' 10 1425 1525 8.7 8475 9956 0044 1569 8.9 8431 4283 50 20 1454 1612 8.5 8388 9954 0046 1658 8.7 8342 4254 40 30 1484 1697 8.4 8303 9952 0048 1745 8.6 8255 4224 30 40 1513 1781 8.2 8219 9950 0050 1831 8.4 8169 4195 20 50 1542 1863 8.0 8137 9948 0052 1915 8.2 8085 4166 10 9° 00' 0.1571 9.1943 7.9 0.8057 9.9946 .2 0.0054 9.1997 8.1 0.8003 1.4137 81° 00' 10 1600 2022 7.8 7978 9944 0056 2078 8.0 7922 4108 50 20 1629 2100 7.6 7900 9942 0058 2158 7.8 7842 4079 40 30 1658 2176 7.5 7824 9940 0060 2236 7.7 7764 4050 30 40 1687 2251 7.3 7749 9938 0062 2313 7.6 7687 4021 20 50 1716 2324 7676 9936 0064 2389 7.4 7611 3992 10 10° 00' 0.1745 9.2397 7.1 0.7603 9.9934 .8 0.0066 9.2463 7.8 0.7537 1.3963 80° 00' 10 1774 2468 7.0 7532 9931 .2 0069 2536 7464 3934 50 20 1804 2538 6.8 7462 9929 0071 2609 7.1 7391 3904 40 30 1833 2606 7394 9927 .3 0073 2680 7.0 7320 3875 30 40 1862 2674 6.6 7326 9924 .2 0076 2750 6.9 7250 3846 20 50 1891 2740 7260 9922 .3 0078 2819 6.8 7181 3817 10 11° 00' 0.1920 9.2806 6.4 0.7194 9.9919 .2 0.0081 9.2887 6.6 0.7113 1.3788 79° on' 10 1949 2870 7130 9917 .3 0083 2953 6.7 7047 3759 50 20 1978 2934 6.3 7066 9914 .2 0086 3020 6.5 6980 3730 40 30 2007 2997 6.1 7003 9912 .8. 0088 3085 6.4 6915 3701 30 40 2036 3058 6942 9909 .2 0091 3149 6.3 6851 3612 20 50 2065 3119 6.0 6881 9907 .8 0093 3212 6788 3643 10 12° 00' 0.2094 9.3179 5.9 0.6821 9.9904 .3 0.0096 9.3275 6.1 0.6725 1.3614 78° 00' 10 2123 3238 5.8 6762 9901 .2 0099 3336 6664 3584 50 20 2153 3296 5.7 6704 9899 .8 0101 3397 6603 3555 40 30 2182 3353 6641 9896 0104 3458 5.9 6542 3526 :;n 40 2211 3410 5.6 6590 9893 0107 3517 6483 3497 20 50 2240 3466 5.5 6534 9890 0110 3576 5.8 6424 3468 10 13° 00' 0.2269 9.3521 5.4 0.6479 9.9887 .8 0.0113 9.3634 5.7 0.6366 1.3439 77° 00' 10 2298 3575 6425 9884 0116 3691 6309 ::ilu 50 20 2327 3629 5.3 6371 9881 0119 3748 5.6 6259 3381 10 30 2356 3682 5.2 6318 9878 0122 3804 5.5 6196 3352 30 40 2385 3734 6266 9875 0125 3859 8141 3328 2n 50 2414 3786 5.1 6214 9872 0128 3914 5.4 6086 3294 10 14° 00' 0.2443 9.3837 5.0 0.6163 9.9869 .8 0.0131 9.3968 6.3 o. tin:! 2 1.3265 76° 00' 10 2473 3887 6113 9866 0134 102 1 5919 3235 50 20 2502 3937 4.9 6063 9863 .4 0137 4074 5926 3206 i" 30 2531 3986 60] I 9859 .3 0141 4127 6.1 5873 ::i77 30 40 2560 4035 4.8 5965 9856 0144 4178 5.2 5822 3148 •2H 50 2589 4083 4.7 5917 9853 .4 0147 4230 6.1 5770 3119 10 15° 00' 0.2618 9.4130 0.5870 9.9849 0.0151 9.4281 0.5719 1.3090 75° 00' Deo. Km-. Cos. Dir. Sec. Sin. Dif. Cso. Cot. Dif. Tan. Km-. Deo. II. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. 17 Deg. Ead. Sin. DlF. Csc. Cos. Dip. Sec. Tan. Dif. Cot. Rad. Deg. 15° 00' 0.2618 9.4130 4.7 0.5870 9.9849 .3 0.0151 9.4281 5.0 0.5719 1.3090 75° 00' 10 2647 4177 4.6 5823 9846 0154 4331 5669 3061 50 20 2676 4223 5777 9843 .4 0157 4381 4.9 5619 3032 40 30 2705 4269 4.5 5731 9839 .3 0161 4430 5570 3003 30 40 2734 4314 5686 9836 .4 0164 4479 4.8 5521 2974 20 50 2763 4359 4.4 5641 9832 0168 4527 5473 2945 10 16° 00' 0.2793 9.4403 4.4 0.5597 9.9828 .3 0.0172 9.4575 4.7 0.5425 1.2915 74° 00' 10 2822 4447 5553 9825 .4 0175 4622 5318 2886 50 20 2851 4491 4.2 5509 9821 0179 4669 5331 2857 40 30 2880 4533 4.3 5467 9817 .3 0183 4716 4.6 5284 2828 30 40 2909 4576 4.2 5424 9814 .4 0186 4762 5238 2799 20 50 2938 4618 4.1 5382 9810 0190 4808 4.5 5192 2770 10 17° 00' 0.2967 9.4659 4.1 0.5341 9.9806 .4 0.0194 9.4853 4.5 0.5147 1.2741 73° 00' 10 2996 4700 5300 9802 0198 4898 5102 2712 50 20 3025 4741 4.0 5259 9798 0202 4943 4.4 5057 2683 40 30 3054 4781 5219 9794 0206 4987 5013 2654 30 40 3083 4821 5179 9790 0210 5031 4969 2625 20 50 3113 4861 3.9 5139 9786 0214 5075 4.3 4925 2595 10 18° 00' 0.3142 9.4900 3.9 0.5100 9.9782 .4 0.0218 9.5118 4.3 0.4882 1.2566 72° 00' 10 3171 4939 3.8 5061 9778 0222 5161 4.2 4839 2537 50 20 3200 4977 5023 9774 0226 5203 4797 2508 40 30 3229 5015 3.7 4985 9770 .5 0230 5245 4755 2479 30 40 3258 5052 8.8 4948 9765 .4 0235 5287 4713 2450 20 50 3287 5090 3.6 4910 9761 0239 5329 4.1 4671 2421 10 19° 00' 0.3316 9.5126 3.7 0.4874 9.9757 .5 0.0243 9.5370 4.1 0.4630 1.2392 71° 00' 10 3345 5163 3.6 4837 9752 .4 0248 5411 4.0 4589 2363 50 20 3374 5199 4801 9748 .5 0252 5451 4549 2334 40 30 3403 5235 3.5 4765 9743 .4 0257 5491 4509 2305 30 40 3432 5270 3.6 4730 9739 .5 0261 5531 4469 2275 20 50 3462 5306 3.5 4694 9734 .4 0266 5571 4429 2246 10 20° 00' 0.3491 9.5341 3.4 0.4659 9.9730 .5 0.0270 9.5611 3.9 0.4389 1.2217 70° 00' 10 3520 5375 4625 9725 .4 0275 5650 4350 2188 50 20 3549 5409 4591 9721 .5 0279 5689 3.8 4311 2159 40 30 3578 5443 4557 9716 0284 5727 3.9 4273 2130 30 40 3607 5477 3.3 4523 9711 0289 5766 3.8 4234 2101 20 50 3636 5510 4490 9706 .4 0294 5804 4196 2072 10 21° 00' 0.3665 9.5543 3.3 0.4457 9.9702 .5 0.0298 9.5842 3.7 0.4158 1.2043 69° 00' 10 3694 5576 4424 9697 0303 5879 3.8 4121 2014 50 20 3723 5609 3.2 4391 - 9692 0308 5917 3.7 4083 1985 40 30 3752 5641 4359 9687 0313 5954 4046 1956 30 40 3782 5673 3.1 4327 9682 0318 5991 4009 1926 20 50 3811 5704 3.2 4296 9677 0323 6028 3,6 3972 1897 10 22° 00' 0.3840 9.5736 3.1 0.4264 9.9672 .5 0.0328 9.60G4 3.6 0.3936 1.1868 68° 00' 10 3869 5767 4233 9667 .6 0333 6100 3900 1839 50 20 3898 5798 3.0 4202 9661 .5 0339 6136 3864 1810' 40 30 3927 5828 3.1 4172 9656 0344 6172 3828 1781 30 40 3956 5859 3.0 4141 9651 0349 6208 3.5 3792 1752 20 50 3985 5889 4111 9646 .6 0354 6243 3.6 3757 1723 10 23° 00' 0.4014 9.5919 2.9 0.4081 9.9640 .5 0.0360 9.6279 3.5 0.3721 1.1694 67° 00' 10 4043 5948 3.0 4052 9635 .6 0365 6314 3.4 3686 1665 50 20 4072 5978 2.9 4022 9629 .5 0371 6348 3.5 3652 1636 40 30 4102 6007 3993 9624 .6 0376 6383 3.4 3617 1606 30 40 4131 6036 3964 9618 .5 0382 6417 3.5 3583 1577 20 50 4160 6065 2.8 3935 9613 .6 0387 6452 3.4 3548 1548 10 24° 00' 0.4189 9.6093 2.8 0.3907 9.9607 .5 0.0393 9.6486 3.4 0.3514 1.1519 66° 00' 10 4218 6121 3879 9602 .6 0398 6520 3.3 3480 1490 50 20 4247 6149 3851 9596 0404 6553 3.4 3447 1461 40 30 4276 6177 3823 9590 0410 6587 3.3 3413 1432 30 40 4305 6205 2.7 3795 9584 .5 0416 6620 3.4 3380 1403 20 50 4334 6232 3768 9579 .6 0421 6654 3.3 3346 1374 10 25° 00' 0.4363 9.6259 0.3741 9.9573 0.0427 9.6687 0.3313 1.1345 65° 00' Deg. Rad. Cos. DlF. Sec. Sin. Die. Csc. Cot. Dif. Tan. Rad. Deg. 18 II. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. Deo. Had. Sin. DlF. Csc. Cos. Dnr. Ski:. Tan. Dik. Cot. Rad. Deo. 25° 00' 0.4363 9.6259 2.7 0.3741 9.9573 .6 0.0427 9.6687 3.3 0.3313 1.1345 65° 00' 10 4392 6286 3714 9567 0433 6720 3.2 3280 1316 50 20 4422 6313 3687 9561 0439 6752 '.',:■; 3248 1286 40 30 4451 6340 2.6 3660 9555 0445 6785 8.2 3215 1257 30 40 4480 6366 3634 9549 0451 6817 3.3 3183 1228 20 50 4509 6392 3608 9543 0457 6850 8.2 3150 1199 10 26° 00' 0.4538 9.6418 2.6 0.3582 9.9537 .7 0.0463 9.6882 8.2 0.3118 1.1170 64° 00' 10 4567 6444 3556 9530 .6 0470 6914 3086 1141 50 20 4596 6470 2.5 3530 9524 0476 6946 8.1 3054 1112 40 30 4625 6495 2.6 3505 9518 0482 6977 3.2 3023 1083 30 40 4654 6521 2.5 3479 9512 .7 0488 7009 3.1 2991 1054 20 50 4683 6546 2.4 3454 9505 .6 0495 7040 3.2 2960 1025 10 27° 00' 0.4712 9.6570 2.5 0.3430 9.9499 .7 0.0501 9.7072 3.1 0.2928 1.0996 63° 00' 10 4741 6595 3405 9492 .6 0508 7103 2897 0966 50 20 4771 6620 2.4 3380 9486 .7 0514 7134 2866 0937 40 30 4800 6644 3356 9479 .6 0521 7165 2835 0908 30 40 4829 6668 3332 9473 .7 0527 7196 3.0 2804 0879 20 50 4858 6692 3308 9466 0534 7226 3.1 2774 0850 10 28° 00' 0.4887 9.6716 2.4 0.3284 9.9459 .6 0.0541 9.7257 8.0 0.2743 1.0821 62° 00' 10 4916 6740 2.3 3260 9453 .7 0547 7287 2713 0792 50 20 4945 6763 2.4 3237 9446 0554 7317 8.1 2683 0763 40 30 4974 6787 2.3 3213 9439 0561 7348 8.0 2652 0734 30 40 5003 6810 3190 9432 0568 7378 2622 0705 20 50 5032 6833 3167 9425 0575 7408 2592 0676 10 29° 00' 0.5061 9.6856 2.2 0.3144 9.9418 .7 0.0582 9.7438 2.9 0.2562 1.0647 61° 00' 10 5091 6878 2.8 3122 9411 0589 7467 8.0 2533 0617 50 20 5120 6901 2.2 3099 9404 0596 7497 2.9 2503 0588 40 30 5149 6923 2.3 3077 9397 0603 7526 8.0 2474 0559 30 40 5178 6946 2.2 3054 9390 0610 7556 2.9 2444 0530 20 50 5207 6968 3032 9383 .8 0617 7585 2415 0501 10 30° 00' 0.5236 9.6990 2.2 0.3010 9.9375 .7 0.0625 9.7614 8.0 0.2386 1.0472 60° 00' 10 5265 7012 2.1 2988 9368 0632 7644 2.9 2356 0443 50 20 5294 7033 2.2 2967 9361 .8 0639 7673 2.8 2327 0414 40 30 5323 7055 2.1 2945 9353 .7 0647 7701 2.9 2299 0385 30 40 5352 7076 2924 9346 .8 0654 7730 2270 0356 20 50 5381 7097 2903 9338 .7 0662 7759 2241 0327 10 31° 00' 0.5411 9.7118 2.1 0.2882 9.9331 .8 0.0669 9.7788 2.8 0.2212 1.0297 59° 00' 10 5440 7139 2861 9323 0677 7816 2.9 2184 0268 50 20 5469 7160 2840 9315 .7 0685 7845 2.3 2155 0239 40 *t 30 5498 7181 2.0 2819 9308 .8 0692 7873 2.9 2127 0210 ^ 40 5527 7201 2.1 2799 9300 0700 7902 2.8 2098 0181 2( m 50 5556 7222 2.0 2778 9292 0708 7930 2070 0152 10 " 32° 00' 0.5585 9.7242 2.0 0.2758 9.9284 .8 0.0716 9.7958 2.8 0.2042 1.0123 58° 00' 10 5614 7262 2738 9276 0724 7986 2014 0094 50 20 5643 7282 2718 9268 0732 8014 1986 0065 40 30 5672 7302 2698 9260 0740 8042 1958 0036 30 40 5701 7322 2678 9252 0748 8070 2.7 1930 0007 20 50 5730 7342 1.9 2658 9244 0756 8097 2.8 1903 0.9977 10 33° 00' 0.5760 9.7361 1.9 0.2639 9.9236 .8 0.0764 9.8125 2.8 0.1875 0.9948 57° 00' 10 5789 7380 2.0 2620 9228 .9 0772 8153 2.7 1847 9919 50 20 5818 7400 1.9 2600 9219 .8 0781 8180 2.8 1820 9890 40 30 5847 7419 . 2581 9211 0789 8208 2.7 1792 9861 30 40 5876 7438 2562 9203 .9 0797 8235 2.8 1765 9832 20 50 5905 7457 2543 9194 .8 0806 8263 2.7 1737 9803 10 34° 00' 0.5934 9.7476 1.8 0.2524 9.9186 .9 0.0814 9.8290 2.7 0.1710 0.9774 56° 00' 10 5963 7494 1.9 2506 9177 .S 0823 8317 1683 9745 50 20 5992 7513 1.8 2487 9169 .9 0831 8344 1656 9716 40 30 6021 7531 1.9 2469 9160 0840 8371 L629 9687 30 40 6050 7550 1.8 2450 9151 0849 8398 1602 9657 20 50 6080 7568 2432 9142 .8 0858 8425 l B 1 S 9628 10 35° 00' 0.6109 9.7586 0.241 I 9.9134 0.0866 9.8452 0.1548 0.9599 55° 00' Deo. Had. Cos. Dip. Sec. MS. DlF. Cso. Cot. DlF. Tan. Rad. Deo. II. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. 19 Deg. Rad. Sin. DlF. Csc. Cos. Dif. Sec. Tan. Dif. Cot. Rad. Deg. 35° 00' 0.6109 9.7586 1.8 0.2414 9.9134 .9 0.0866 9.8452 2.7 0.1548 0.9599 55° 00' 10 6138 7604 2396 9125 0875 8479 1521 9570 50 20 6167 7622 2378 9116 0884 8506 1494 9541 40 30 6196 7640 1.7 2360 9107 0893 8533 2.6 1467 9512 30 40 6225 7657 1.8 2343 9098 0902 8559 2.7 1441 9483 20 50 6254 7675 1.7 2325 9089 0911 8586 1414 9454 10 36° 00' 0.6283 9.7692 1.8 0.2308 9.9080 1.0 0.0920 9.8613 2.6 0.1387 0.9425 54° 00' 10 6312 7710 1.7 2290 9070 .9 0930 8639 2.7 1361 9396 50 20 6341 7727 2273 9061 0939 8666 2.6 1334 9367 40 30 6370 7744 2256 9052 1.0 0948 8692 1308 9338 30 40 6400 7761 2239 9042 .9 0958 8718 2.7 1282 9308 20 50 6429 7778 2222 9033 1.0 0967 8745 2.6 1255 9279 10 37° 00' 0.6458 9.7795 1.6 0.2205 9.9023 .9 0.0977 9.8771 2.6 0.1229 0.9250 53° 00' 10 6487 7811 1.7 2189 9014 1.0 0986 8797 2.7 1203 9221 50 20 6516 7828 1.6 2172 9004 .9 0996 8824 2.6 1176 9192 40 30 6545 7844 1.7 2156 8995 1.0 1005 8850 1150 9163 30 40 6574 7861 1.6 2139 8985 1015 8876 1124 9134 20 50 6603 7877 2123 8975 1025 8902 1098 9105 10 38° 00' 0.6632 9.7893 1.7 0.2107 9.8965 LI 0.1035 9.8928 2.6 0.1072 0.9076 52° 00' 10 6661 7910 1.6 2090 8955 1045 8954 1046 9047 50 20 6690 7926 1.5 2074 8945 1055 8980 1020 9018 40 30 6720 7941 1.6 2059 8935 1065 9006 0994 8988 30 40 6749 7957 2043 8925 1075 9032 0968 8959 20 50 6778 7973 2027 8915 1085 9058 0942 8930 10 39° 00' 0.6807 9.7989 1.5 0.2011 9.8905 1.0 0.1095 9.9084 2.6 0.0916 0.8901 51° 00' 10 6836 8004 1.6 1996 8895 1.1 1105 9110 2.5 0890 8872 50 20 6865 8020 1.5 1980 8884 1.0 1116 9135 2.6 0865 8843 40 30 6894 8035 1965 8874 1126 9161 0839 8814 30 40 6923 8050 1.6 1950 8864 1.1 1136 9187 2.5 0813 8785 20 50 6952 8066 1.5 1934 8853 1.0 1147 9212 2.6 0788 8756 10 40° 00' 0.6981 9.8081 1.5 0.1919 9.8843 1.1 0.1157 9.9238 2.6 0.0762 0.8727 50° 00' 10 7010 8096 1904 8832 1168 9264 2.5 0736 8698 50 20 7039 8111 1.4 1889 8821 1179 9289 2.6 0711 8668 40 30 7069 8125 1.5 1875 8810 1.0 1190 9315 0685 8639 30 40 7098 8140 1860 8800 1.1 1200 9341 2.5 0659 8610 20 50 7127 8155 1.4 1845 8789 1211 9366 2.6 0634 8581 10 41° 00' 0.7156 9.8169 1.5 0.1831 9.8778 1.1 0.1222 9.9392 2.5 0.0608 0.8552 49° 00' 10 7185 8184 1.4 1816 8767 1233 9417 2.6 0583 8523 50 ^ 20 7214 8198 1.5 1802 ' 8756 1244 9443 2.5 0557 8494 40 ^ 30 7243 8213 1.4 1787 8745 1.2 1255 9468 2.6 0532 8465 30 m 40 7272 8227 1773 8733 1.1 1267 9494 2.5 0506 8436 20 '] 50 7301 8241 1759 8722 1278 9519 0481 8407 10 42° 00' 0.7330 9.8255 14 0.1745 9.8711 1.2 0.1289 9.9544- 2.6 0.0456 0.8378 48° 00' 10 7359 8269 1731 8699 1.1 1301 9570 2.5 0430 8348 50 20 7389 8283 1717 8688 1.2 1312 9595 2.6 0405 8319 40 30 7418 8297 1703 8676 1.1 1324 9621 2.5 0379 8290 . 30 40 7447 8311 1.3 1689 8665 1.2 1335 9646 0354 8261 20 50 7476 8324 1.4 1676 8653 1347 9671 2.6 0329 8232 10 43° 00' 0.7505 9.8338 1.3 0.1662 9.8641 1.2 0.1359 9.9697 2.5 0.0303 0.8203 47° 00' 10 7534 8351 1.4 1649 8629 1.1 1371 9722 0278 8174 50 20 7563 8365 1.3 1635 8618 1.2 1382 9747 0253 8145 40 30 7592 8378 1622 8606 1394 9772 2.6 0228 8116 30 40 7621 8391 1.4 1609 8594 1406 9798 2.5 0202 8087 20 50 7650 8405 1.3 1595 8582 1.3 1418 9823 0177 8058 10 44° 00' 0.7679 9.8418 1.8 0.1582 9.8569 1.2 0.1431 9.9848 2.6 0.0152 0.8029 46° 00' 10 7709 8431 1569 8557 1443 9874 2.5 0126 7999 50 20 7738 8444 1556 8545 1.3 1455 9899 0101 7970 40 30 7767 8457 1.2 1543 8532 1.2 1468 9924 0076 7941 30 40 7796 8469 1.3 1531 8520 1.3 1480 9949 2.6 0051 7912 20 50 7825 8482 1518 8507 1.2 1493 9975 2.5 0025 7883 10 45° 00' 0.7854 9.8495 0.1505 9.8495 0.1505 0.0000 0.0000 0.7854 45° 00' Deg. Rad. Cos. DlF. Sec. Sin. Dif. Csc. Cot. Dif. Tan. Rad. Deg. 20 III. LOGARITHMS OK NUMBERS. 100 1 2 3 4 5 6 7 8 9 Differences. 100 00 0000 0434 0868 1301 1734 2166 2598 3029 3461 989] i 435 44 87 430 425 MO 01 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 43 gf 48 85 42 84 02 8600 9026 it 15 1 9876 *0300 *0724 *1147 *1570 *1993 *2415 :; 131 12'.) 128 126 03 01 2837 3259 3680 4100 4521 4940 5360 5779 6197 6616 4 5 i 174 172 170 168 04 7033 7451 7868 8284 8700 9116 9532 9947 *0361 *0775 218 261 215 258 213 255 210 252 05 02 1189 1603 2016 2428 2841 3252 3664 4075 4486 4896 7 s 306 348 301 344 340 29 1 888 06 5306 5715 6125 0533 6942 7350 7757 8164 8571 8978 it 392 887 888 878 07 9384 9789 *0195 *0600 *1004 *1408 *1812 *2216 *2619 *3021 415 410 in.", 400 08 03 3424 3826 4227 4628 5029 5430 5830 6230 6629 7028 1 42 41 41 40 09 7426 7825 8223 8620 9017 9414 9811 *0207 *0602 *0998 2 SB 125 82 123 -1 122 80 120 110 11 04 1393 5323 1787 5714 2182 2576 2969 6105 6495 6885 3362 3755 4148 7275 7664 8053 4540 8442 4932 8830 i 5 6 166 208 249 164 205 246 162 248 160 888 240 12 9218 9606 9993 *0380 *0766 *1153. *1538 *1924 *2309 *2694 : 291. 2-7 2-1 13 05 3078 3463 3846 4230 4613 4996 5378 5760 6142 6524 9 it 332 874 369 324 365 320 860 14 6905 7286 7666 8046 8426 8805 9185 9563 9942 *0320 895 390 385 830 15 16 06 0698 ■1158 1075 4832 1152 1829 2206 5206 5580 5953 2582 2958 3333 6326 6699 7071 3709 7443 4083 7815 ! 2 8 40 79 119 V.I 78 117 39 77 116 88 76 114 17 8186 8557 8928 9298 9668 *0038 *0407 *0776 *1145 *1514 1 (58 188 154 152 18 07 1882 2250 2617 2985 3S52 3718 4085 4451 4816 5182 5 «; 7 198 237 '.'77 195 284 273 198 281 878 190 19 5547 5912 6276 6640 7004 7368 7731 8094 8457 8819 266 120 07 9181 9543 9904 *0266 *0626 *0987 *1347 *1707 *2067 *2426 8 it 316 356 312 851 347 888 21 08 2785 3144 3503 3861 4219 ( 4576 4934 5291 5647 6004 375 370 865 37 86 22 6360 6716 7071 7426 7781 8136 8490 8845 9198 9552 1 88 37 23 9905 *0258 *0611 *0963 *1315 *1667 *2018 *2370 *2721 *3071 2 :s 4 75 113 150 74 72 24 09 3422 3772 4122 4471 4820 5169 5518 5866 6215 6562 111 148 Hit 146 108 144 25 6910 7257 7604 7951 8298 8644 8990 9335 9681 *0026 5 <; 7 188 ase 988 185 222 259 188 219 256 180 216 26 10 0371 0715 1059 1403 1747 2091 2434 2777 3119 3462 27 3804 4146 4487 4828 5169 5510 5851 6191 6531 6871 s 300 898 288 28 7210 7549 7888 8227 8565 8903 9241 9579 9916 *0253 9 838 333 829 29 11 0590 0926 1263 1599 1934 2270 2605 2940 3275 3609 1 355 36 350 35 845 35 888 -A 130 11 3943 4277 4611 4944 5278 5611 5943 6276 6608 6940 2 :t 4 71 107 142 70 105 140 88 104 138 102 31 7271 7603 7934 8265 8595 8926 9256 9586 9915 *0245 32 12 0574 0903 1231 1560 1888 2216 2544 2871 3198 :\:ri:> 5 178 175 173 170 33 3852 4178 4504 4830 5156 5481 5806 6131 6466 6781 6 7 8 213 •J lit 2-1 210 245 880 207 242 276 204 288 272 34 7105 7429 7753 8076 8399 8722 9045 9368 9690 *0012 35 13 0334 0655 0977 1298 1619 1939 2260 2580 2900 3219 9 320 815 311 36 3539 3858 4177 4496 4814 5133 5451 5769 6086 6403 1 ;u 330 33 82 37 6721 7037 7364 7671 7987 8303 86 IS 8934 9249 9664 •-' 67 66 65 & 38 39 9879 14 3015 *0194 3327 *0508 *0822 *1 136 3639 39*1 4263 *1450 *1763 *2076 157 1 4885 5196 •2389 5507 *2*02 5818 8 4 5 101 188 08 132 K If;! 140 11 8128 6438 6748 7058 7367 7676 7985 8294 8603 8911 1 7 a 201 198 881 41 9219 9521 9835 *0142 *04 ID ♦0756 *10«3 *1370 ••1676 •1982 988 884 880 42 15 2288 2594 2! 3206 3510 3815 4120 4424 4728 5032 9 2>.<7 43 5336 5640 5943 6246 6649 6852 7154 7457 7759 8061 8)8 816 888 44 8362 8664 8965 '."-'lit; 9567 9868 *0168 *0469 *0769 not;s 1 ■J N 31 61 45 it; 1368 1667 1967 2266 2664 2863 3161 3460 3768 4055 :! 1 '.t;> 120 158 88 124 92 120 46 4353 4650 1947 5244 55 11 6838 6134 6430 r.7 2<; 7022 6 158 47 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 6 188 183 48 17 0262 0555 0848 114 1 11.". 1 17 26 20 lit 2311 2t; it:; •J Si' 5 7 8 9 221 2M 217 MB 214 210 49 3186 3478 3769 4060 4351 hill 49S2 5222 5 5 12 5802 270 150 1 2 3 1 5 6 7 8 9 Different III. LOGARITHMS OF NUMBERS. 21 150 1 2 3 4 5 6 7 8 9 Differences. 150 17 6091 6381 6670 6959 7248 7536 7825 8113 8401 8689 295 290 285 280 51 8977 9264 9552 9839 *0126 *0413 *0699 *0986 *1272 *1558 i 30 59 29 58 29 57 28 56 52 18 1844 2129 2415 2700 2985 3270 3555 3839 4123 4407 a 89 87 86 84 53 54 4691 7521 4975 7803 5259 8084 5542 8366 5825 8647 6108 8928 6391 9209 6674 9490 6956 9771 7239 *0051 4 6 8 118 14S 177 116 145 174 114 143 171 112 140 168 55 19 0332 0612 0892 1171 1451 1730 2010 2289 2567 2846 7 S 207 236 203 232 200 228 196 224 56 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 B 266 261 257 252 57 5900 6176 6453 6729 7005 7281 7556 7832 8107 8382 275 270 265 260 58 8657 8932 9206 9481 9755 *0029 *0303 *0577 *0850 *1124 1 23 27 27 26 59 20 1397 1670 1943 2216 2488 2761 3033 3305 3577 3848 2 3 55 83 54 81 53 80 52 78 160 61 20 4120 6826 4391 7096 4663 7365 4934 7634 5204 7904/ 5475 8173 5746 8441 6016 8710 6286 8979 6556 9247 4 5 6 110 138 165 108 135 162 106 133 159 104 180 156 62 9515 9783 *005l *0319 *0586 *0853 *1121 *1388 *1654 *1921 7 193 189 186 182 63 21 2188 2454 2720 2986 3252 3518 3783 4049 4314 4579 8 9 220 248 216 243 212 239 208 234 64 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 255 250 248 246 65 7484 7747 8010 8273 8536 8798 9060 ' 9323 9585 9846 l 26 51 77 25 50 75 25 50 74 25 66 22 0108 0370 0631 0892 1153 1414 1675 1936 2196 2456 i 3 49 74 67 2716 2976 3236 3496 3755 4015 4274 4533 4792 5051 4 102 100 99 98 68 5309 5568 5826 6084 6342 6600 6858 7115 7372 7630 5 128 125 124 123 69 7887 8144 8400 8657 8913 9170 9426 9682 9938 *0193 6 7 153 179 150 175 149 174 148 172 170 23 0449 0704 0960 1215 1470 1724 1979 2234 2488 2742 8 9 204 230 200 225 198 223 197 221 71 2996 3250 3504 3757 4011 4264 4517 4770 5023 5276 244 24 242 24 240 24 238 24 72 5528 5781 6033 6285 6537 6789 7041 7292 7544 7795 1 73 8046 8297 8548 8799 9049 9299 9550 9800 *0050 *0300 2 49 4S 48 48 74 24 0549 0799 1048 1297 1546 1795 2044 2293 2541 2790 3 4 73 98 73 97 72 96 71 95 75 3038 3286 3534 3782 4030 4277 4525 4772 5019 5266 5 6 7 122 146 171 121 145 169 120 144 168 119 143 167 76 5513 5759 6006 6252 6499 6745 6991 7237 7482 7728 77 7973 8219 8464 8709 8954 9198 9443 9687 9932 *0176 8 195 194 192 190 78 25 1)420 0664 0908 1151 1395 1638 1881 2125 2368 2610 9 220 218 216 214 79 2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 1 236 24 234 23 232 23 230 23 180 25 5273 5514 5755 5996 6237 6477 6718 6958 7198 7439 2 3 4 . 4 7 71 94 47 70 94 46 70 93 46 69 92 81 7679 7918 8158 8398 8637 8877 9116 9355 9594 9833 82 26 0071 0310 0548 0787 1025 1263 .1501 1739 1976 2214 5 118 117 116 115 83 84 2451 4818 2688 5054 2925 5290 3162 5525 3399 , 5761 3636 5996 3873 6232 4109 6467 4346 6702 4582 6937 6 7 8. 142 165 189 140 164 1S7 139 162 186 138 161 184 85 7172 7406 7641 7875 8110 8344 8578 8812 9046 9279 9 212 211 209 207 86 9513 9746 9980 *0213 *0446 *0679 *0912 ♦1144 *1377 *1609 1 22S 23 226 23 224 22 222 22 •^ 27 1842 2074 2306 2538 2770 3001 3233 3464 3696 3927 2 46 45 45 44 4158 4389 4620 4850 5081 5311 5542 5772 6002 6232 3 4 5 68 91 114 68 90 113 67 90 112 67 89 111 89 6462 6692 6921 7151 7380 7609 7838 8067 8296 8525 190 27 8754 8982 9211 9439 9667 9895 *0123 *0351 *0578 *0806 6 1 137 160 136 158 134 157 133 155 191 28 1033 1261 1488 1715 1942 2169 2396 2622 2849 3075 8 182 1S1 179 17S 92 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 B 205 203 202 200 93 5557 5782 6007 6232 6456 6681 6905 7130 7354 7578 220 218 216 214 94 7802 8026 8249 8473 8696 8920 9143 9366 9589 9812 1 2 22 44. 22 44 22 43 21 43 95 29 0035 0257 0480 0702 0925 1147 1369 1591 1813 2034 3 4 66' SS 65 87 65 S6 64 S6 96 2256 2478 2699 2920 3141 3363 3584 3804 4025 4246 5 110 109 108 107 97 4466 4687 4907 5127 5347 5567 5787 6007 6226 6446 6 132 131 130 12S 98 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 7 g 154 176 19S 158 174 151 173 150 171 99 8853 9071 9289 9507 9725 9943 *0161 *0378 *0595 *0813 9 196 194 193 200 1 2 3 4 5 6 7 8 9 Differences. 22 III. LOGARITHMS OF NUMBERS. 200 1 2 3 4 5 6 7 8 9 Differences. 200 01 30 1030 3196 1247 3412 1464 3628 1681 3844 1898 4059 2114 4275 2331 4491 2547 4706 8764 4921 2980 5136 i 2 220 22 44 218 22 44 216 28 43 21 48 02 5351 5566 5781 5996 6211 6425 6639 6854 7068 7282 3 66 65 OB 64 , 03 7496 7710 7924 8137 8351 8564 8778 8991 9204 9417 4 5 6 88 87 98 86 , 04 9630 9843 *0056 *0268 *0481 *0693 *0906 *1 118 *1330 ♦1542 110 132 109 181 108 180 107 05 31 1754 1966 2177 2389 2600 2812 3023 3234 3445 3656 7 8 154 176 153 174 151 118 150 , 171. 06 3867 4078 4289 4499 4710 4920 5130 5340 5551 5760 9 198 1M 1M 19$ 07 5970 6180 6390 6599 6809 7018 7227 7436 7646 7854 212 210 808 f 206 08 >8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 1 2 3 21 21 81 .21 09 - 32 0146 0354 0562 0769 0977 1184 1391 1598 1805 2012 42 64 42 m 42 64 41 62 2ip 11 3'2 2219 4282 2426 4488 2633 4694 2839 4899 3046 5105 3252 5310 3458 5516 3665 5721 3871 5926 4077 6131 4 5 6 SB 106 127 84 1*5 126 98 104 125 82 103 124 12 6336 6541 6745 .6950 7155 7359 7563 7767 7972 8176 7 148 147 146 13 8380 8583 8787 8991 9194 9398 9601 9805 *0008 ♦0311 8 170 191 168 189 166 187 165 14 33 0414 0617 0819 1022 1225 1427 1630 1832 2034 2236 204 202 200 198 15 2438 2640 2842 3044 3246 3447 3649 3850 4051 4253, 1 20 20 20 20 16 4454 4655 4856 5057 5257 5458 5658 5859 6059 62«0 2 3 41 61 40 61 40 60 40 59 17 6460 6660 6860 7060 7260 7459 7659* 7858 8058 8257 4 82 81 80 18 8456 8656 8855 9054 9253 9451 9650 9849 *0047 *0246 5 102 101 KM) 99 19 34 0444 0642 0841 1039 1237 1435 1632 1830 2028 2225 6 7 122 143 121 141 120 140 119 189 220 34 2423 2620 2817 3014 3212 3409 3606 3802 3999 4196 8 9 163 184 162 182 160 180 158 178 21 22 4392 6353 4589 6549 4785 6744 4981 6939 5178 7135 5374 7330 5570 7525 5766 7720 5962 7915 6157 8110 1 196 20 194 19 192 19 190 19 23 8305 8500 8694 8889 9083 9278 9472 9666 9860 *0054 2 89 39 88 24 35 0248 0442 0636 0829 1023 1216 1410 1603 1796 1989 3 4 59 78 58 78 77 57 76 25 26 2183 4108 2375 4301 2568 4493 2761 4685 2954 4876 3147 5068 3339 5260 3532 5452 3724 5643 3916 5834 5 6 7 98 118 137 97 110 136 96 115 134 95 114 188 27 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 8 157 155 154 152 28 7935 8125 8316 8506 8696 8886 9076 9266 9456 9646 9 176 175 171 29 9835 *0025 *0215 *0404 *0593 *0783 *0972 *1161 *1350 *1539 1 188 19 186 19 181 18 18 230 31 36 1728 3612 1917 3800 2105 3988 2294 4176 2482 4363 2671 4551 2859 4739 3048 4926 3236 5113 3424 5301 2 3 4 88 56 37 56 74 37 OB 74 86 55 78 32 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 5 M 93 Bfl 33 34 7356 9216 7542 9401 7729 9587 7915 97 7 2 8101 9958 8287 *0143 8473 *0328 8659 *0513 8845 *0698 9030 *0883 7 8 118 132 m 112 130 149 110 110 147 35 37 1068 1253 1437 1622 1806 1991 2175 2360 2. Ml 2728 B 168 167 m 36 2912 3096 3280 3464 3647 3831 4015 4198 4382 4565 1 180 is 178 1- 170 18 175 37 4748 4932 5115 5298 5481 5664 5846 6029 6212 6394 2 86 36 85 38 6577 6759 G942 7124 7306 7488 7670 7852 8034 8216 3 4 5 H 53 70 88 39 8398 8580 8761 8943 9124 9306 !> 1ST 9668 9849 *0030 90 71 89 38 240 38 0211 0392 0573 0754 0934 1115 1296 1476 L656 1837 6 1 108 1 '.'»'. 107 1(M> 188 128 41 2017 2197 2377 2557 2737 2917 3097 8871 3456 3636 8 144 MS ill 42 3815 3995 4174 4353 4533 4712 4891 507 5849 6438 9 UN 160 108 43 5606 5785 5964 6142 6321 6499 6677 6856 7084 7813 171 178 178 44 7390 7568 7746 7923 8101 8279 8456 8634 881 1 8989 1 1 17 85 17 80 17 34 45 9166 9343 9520 9698 9875 *0051 *0228 •0405 *0582 •0758 8 4 Til 52 69 88 68 86 46 39 0935 1112 1288 1464 1641 1817 1998 2169 3845 383] .'' -7 -T 88 47 2697 2873 3048 3224 3400 ::;,:;, 3751 8936 1 1 1 12 7 7 6 MM 104 108 108 48 4452 4627 4802 4977 5152 5386 5501 5678 8036 7 § m 181 l'.'l 188 187 49 6199 831 1 6548 6722 6896 7071 7841 7419 7593 7766 9 187 156 155 151 250 1 2 3 4 5 6 7 8 9 Differences. _ a HI. LOGARITHMS OF NUMBERS. 23 2.50 1 2 3 4 5 6 7 8 9 Differences. 250 39 7940 8114 8287 8461 8634 8808 8981 9154 9328 9501 i 2 170 17 34 169 17 34 168 17 34 167 17 33 51 9674 9847 *0020 *0192 *0365 *0538 *0711 *0883 *1056 *1228 52 40 1401 1573 1745 1917 2089 2261 2433 2605 2777 2949 B 51 51 50 50 53 3121 3292 3464 3635 3807 3978 4149 4320 4492 4663 4 68 68 67 67 > 5 85 85 84 84 54 4834 5005 5176 5346 5517 5688 5858 6029 6199 6370 6 102 101 101 100 55 .6540 6710 6881 7051 7221 7391 7561 7731 7901 8070 7 8 119 136 118 135 118 134 117 134 56 8240 8410 8579 8749 8918 9087 9257 9426 9595 9764 g 153 152 151 150 57 9933 *0102 *0271 *0440 *0609 *0777 *0946 *1114 *1283 *1451 166 165 164 163 58 41 1620 1788 , 1956 2124 2293 2461 2629 2796 2964 3132 1 2 17 &3 17 33 16 33 16 33 59 3300 3467 '8635 3803" 3970 4137 4305 4472 4639 4806 3 4 50 66 50 66 49 66 49 65 260 41 4973 5140 -5307 5^474 5641 5808 5974 6141 6308 6474 5 83 83 82 82 61 6641 680? 6973 7139 7306 7472 7638 7804 7970 8135 6 100 99 98 98 62 8301 8467 8633 8798 8964 9129 9295 9460 9625 9791 7 8 9 116 133 149 116 132 149 115 131 148 114 130 147 63 9956 *0121 *0286 *0451 *0616 *0781 *0945 *1110 *1275 *1439 64 42 1604 1768 1933 2097 2261 2426 2590 2754 2918 3082 162 161 160 159 . B ^ 3246 3410 3574 3737 3901 4065 4228 4392 4555 4718 1 16 16 16 16 2 32 32 32 32 '•66 4882 5045 5208 5371 5534 5697 5860 6023 6186 6349 3 49 48 48 48 67 6511 6674 6836 6999 7161 7324 7486 7648 7811 7973 4 65 64 64 64 68 . ...8135 8297 8459 8621 8783 8944 9106 9268 9429 9591 5 81 97 81 97 80 96 Si) 95 69 9752 9914 *0075 *0236 *0398 *0559 *0720 *0881 *1042 *1203 7 8 113 180 113 129 112 128 111 127 270 43 1364 1525 1685 L846 2007 2167 2328 2488 2649 2809 9 146 145 144 143 71 2969 3130 3290 3450 3610 3770 3930 4090 4249 4409 158 157 156 155 72 4569 4729 4888 5048 5207 526*7 5£26 % 5685 5844 6004 1 16. 16 • 16 .. 16- 73 6163 6322 6481 6640 6799 6957 7116 7275 7433 7592 - • A 3 -32 47 •31 47 31 47 31 47 62 '74 7751 7909 8067 8226 8384 8542 8701 8859 901-7 "9175 4 63 63 62 75 9333 9491 9648 9806 9964 *0122 *0279 *0437 *0594 *0752 B 8 79 ^95 79 94 78 94 78 93 76 44 0909 1066 1224 1381 1538 1695 1852 2009 2166 2323 T 111 110 109 109 77 2480 2637 2.793 2950 3106 3263 3419 3576 3732 3889 8 9 126 142 126 141 125 140 124 140 78 4045 4201 4357 4513 4669 4825 " 4981 5137 5293 5449 79 5604 5760 5915 6071 6226 6382 6537 6692 6848 7003 1 154 15 153 15 152 15 151 15 280 44 7158 7313 7468 7623 7778 7933 8088 8242 8397 8552 2 31 46 31 46 30 46 30 45 81 8706 8861 9015 9170 9324 9478 9633 9787 994-1 *0095 4 62 61 61 60 82 45 024!) 0403 0557 0711 0865 1018 1172 1326 1479 1633 5 77 77 76 76 83 1786 1940 2093 2247 2400 2553 2706 2859 30JX 3165 6 7 92 108 92 107 91 106 91 106 84 3318 3471 3624 3777 3930 4082 4235 4387 4540 4692 S 8 128 139 122 138 122 137 121 136 85 4845 4997 5150 5302 5454 5606 5758 5910 6062 6214 86 6366 6518 6670 6821 6973 7125 7276 7428 7579 ' 7731 1 150 15 149 15 148 15 147 15 87 7882 8033 8184 8336 8487 8638 8789 8940 9091 9242 2 30 30 30 29 88 9392 9543 9694 9845 9995 *0146 *0296 *0447 *0597 *0748 8 4 45 60 45 60 44 59 44 59 89 46 0898 1048 1198 1348 1499 1649 1799 1948 2098 2248 B 75 75 74 74 290 46 2398 2548 2697 2847 2997 3146 3296- 3445 3594 3744 6 7 90 105 89 104 89 104 88 103 91 3893 4042 4191 4340 4490 4639 4788 4936 5085 5234 S 120 119 118 118 92 5383 5532 5680 5829 5977 6126 6274 6423 6571 6719 9 135 134 133 182 93 6868 7016 7164 7312 7460 7608 7756 7904 8052 8200 146 145 144 94 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675 1 2 15 29 15 29 14 29 95 9822 9969 *0116 *0263 *0410 *0557 *0704 *0851 *0998 *1145 3 4 44 58 44 58 13 >8 96 47 1292 1438 1585 1732 1878 2025 2171 2318 2464 2610 5 73 73 r2 97 2756 2903 3049 3195 3341 3487 3633 3779 3925 4071 6 88 87 56 98 4216 4362 450.8 4653 4799 4944 5090 , 5235 5381 5526 7 102 102 101 8 117 116 115 99 5671 5816 5962 6107 6252 6397 6542 6687 6832 6976 9 131 131 130 300 1 2 3 4 5 6 7 8 9 Differences 24 HI. LOGARITHMS OF NUMBERS. _......_ 300 1 2 3 4 5 6 7 8 9 Differences. 300 47 7121 7266 7411 7555 7700 7844 7989 8133 8278 8422 01 8566 8711 8855 8999 9143 9287 9431 9575 9719 9863 145 144 143 142 02 48 0007 0151 0294 0438 0582 0725 0869 1012 1156 1299 i 2 15 14 14 29 29 29 14 86 03 1443 1586 1729 1872 2016 2159 2302 2445 2588 2731 3 44 43 43 43 04 2874 3016 3159 3302 3445 3587 3730 3872 4015 4157 4 5 58 5S 57 73 72 72 57 71 05 4300 4442 4585 4727 4869 5011 5153 5295 5437 5579 6 87 86 86 85 06 5721 5863 6005 6147 6289 6430 6572 6714 6855 6997 7 g 102 101 100 116 115 114 99 114 07 7138 7280 7421 7563 7704 7845 7986 8127 8269 8410 9 131 130 129 128 08 8551 8692 8833 8974 9114 9255 9396 9537 9677 9818 «» 09 9958 *0099 *0239 *0380 *0520 *0661 *0801 *0941 *1081 *1222 141 140 189 188 310 49 1362 1502 1642 "^182 19 22 '2062 '2201 2341* 318! 2621 1 2 14 14 14 28 28 28 42 42 42 14 28 41 11 2760 2900 3040 3179 3319 3458 3597 3737 3876 4015 3 12 4155 4294 4433 4572 4711 4850 4989 5128 5267 5406 4 56 56 56 55 13 5544 5683 5822 5960 6099 6238 6376 6515 6653 «-.7*U 5 6 71 70 70 85 84 88 69 si 14 6930 7068 7206 7344 7483 7621 7759 7897 8035 817* 9550 7 99 98 97 97 15 8311 8448 8586 8724 8862 8999 9137 9275 9412 l| ^13 112 111 Ukt 126 125 110 124 16 9687 9824 9962 *0099 *0236 *0374 *0511 *0648 *0785 *0922 V 17 50 1059 1196 1333 1470 1607 1744 1880 2017 2154 2291 137 136 135 14 14 14 134 18 2427 2564 2700 2837 2973 3109 3246 3382 3518 3655 1 13 19 3791 3927 4063 4199 4335 4471 4607 4743 4878 5014 2 3 27 27 27 41 41 41 27 40 320 50 5150 5286 5421 5557 5693 5828 5964 6099 6234 6370 4 55 54 54 54 21 22 6505 7856 6640 7991 6776 8126 6911 8260 7046 8395 ' 7181 7316 8530 8664 7451 8799 7586 8934 7721 9068 5 6 7 69 68 68 82 82 SI 96 95 95 67 80 94 23 9203 9337 9471 9606 9740 9874 *0009 *0143 *0277 *0411 8 110 109 108 24 51 0545 0679 0813 0947 1081 1215 1349 1482 1616 1750 9 123 122 122 1 _ 1 25 1883 2017 2151 2284 2418 2551 2684 2818 2951 3084 188 182 181 13 13 13 130 18 26 3218 3351 3484 3617 3750 3883 4016 4149 428 * 1415 1 27 4548 4681. 4813 4946 5079 5211 5344 5476 56«* 693$ 4-741 2 27 26 26 26 28 5874 6006 6139 6271 6403 6535 6668 6800 fc<)64 3 4 40 40 39 53 53 U 89 52 29 7196 7328 7460 7592 7724 7855 7987 8119 8251 ' Jf382 5 67 66 66 65 330 51 8514 8646 8777 8909 9040 9171 9303 9434 1 6 7 80 79 IS 98 98 M 78 91 31 32 9828 52 1138 9959 1269 *0090 1400 *0221 1530 *0353 1661 *04H4 *0615 1792 1922 *0745 2053 *0876 2183 MOO? 2314 8 9 106 106 105 120 119 118 104 117 33 2444 2575 2705 2835 2966 3096 3226 3356 3486 3616 34 3746 3876 4006 4136 4266 4396 45.26 4656 4785 4915 188 L88 tfl 1 18 13 18 35 5045 5174 5304 5434 5563 5693 5822 5951 6081 6210 2 M 36 6339 6469 6598 6727 6856 6985 7114 7243 7372 7501 4 52 51 51 37 7630 7759 7888 8016 8145 8274 8402 8531 8660 8788 5 65 M M 38 8917 9045 9174 9302 9430 9559 9687 9815 9943 *0072 6 77 77 7.: 39 53 0200 0328 0456 0584 0712 0840 0968 1096 1223 1351 7 90 90 89 a km tog toa 340 53 1479 1607 1734 1862 1990 2117 2245 2372 2500 2627 9 116 115 111 41 2754 2882 3009 3136 3264 3391 3518 3645 3773 3899 42 4026 4153 4280 4407 4534 4661 4787 4914 .Mill 5167 186 186 m 43 5294 5421 5547 5674 5800 5927 6053 6180 6306 8483 1 18 18 U 44 6558 6685 6811 6937 7063 7189 7315 7441 7567 7693 45 7819 7945 8071 8197 8322 8448 8574 8699 8825 8951 60 50 68 a 61 46 9076 9202 9327 9452 9578 9708 9829 9964 *0079 + 0201 6 T6 r 47 54 0329 0455 0580 0705 0830 0956 1080 12 05 L380 1454 7 68 83 87 s loi 100 '.".• 113 118 112 48 1579 1704 1829 1953 2078 22»>; 2 ■''-' 2452 2576 2701 49 2825 2950 3074 3199 3323 .3/f7 Mi 3696 3820 3944 350 1 2 3 4 4 G 7 8 9 Differences. III. LOGARITHMS OF NUMBERS. 25 350 1 2 3 4 5 6 7 8 9 Differences. 350 54 4068 4192 4316 4440 4564 4688 4812 4936 5060 5183 51 5307 5431 5555 5678 5802 5925 6049 6172 6296 6419 124 123 122 52 6543 6666 6789 6913 7036 7159 7282 7405 7529 7652 i 2 12 12 25 25 12 24 53 7775 7898 8021 8144 8267 8389 8512 8635 8758 8881 3 37 37 37 54 9003 9126 9249 9371 9494 9616 9739 9861 9984 *0106 4 5 50 49 62 62 49 61 55 55 0228 0351 0473 0595 0717 0840 0962 1084 1206 1328 6 74 74 73 56 1450 1572 1694 1816 1938 2060 2181 2303 2425 2547 7 8 87 86 99 98 85 98 57 2668 2790 2911 3033 3155 3276 3398 3519 3640 3762 9 112 111 110 58 . 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 59 5094 5215 5336 5457 5578 5699 5820 5940 6061 6182 121 120 119 360 55 6303 6423 6544 6664 6785 6905 7026 7146 7267 7387 1 2 12 12 24 24 12 24 61 7507 7627 7748 7868 798.8 8108 8228 8349 8469 8589 3 36 36 36 62 8709 8829 8948 9068 9188 9308 9428 9548 9667 9787 4 48 48 48 63 9907 *0026 #146 *0265 *0385 *0504 *0624 *0743 *0863 *0982 5 6 61 60 73 72 60 71 64 56 1101 1221 1340 1459 1578 1698 1817 1936 2055 2174 7 85 84 83 65 2293 2412* 2531 2650 2769 2887 3006 3125 3244 3362 8 9 97 96 109 108 95 107 66 3481 3600 3718 3837 3955 4074 4192 4311 4429 4548 67 4666 4784 4903 5021 5139 5257 5376 5494 5612 5730 118 117 116 68 5848 5966 6084 6202 6320 6437 6555 6673 6791 6909 1 12 12 12 69 7026 7144 7262 7379 7497 7614 7732 7849 7967 8084 2 3 24 23 35 35 23 35 370 56 8202 8319 8436 8554 8671 8788 8905 9023 9140 9257 4 47 47 46 71 9374 9491 9608 9725 9842 9959 *0076 *0193 *0309 *0426 5 6 59 59 71 70 58 70 7 2 57 0543 0660 0776 0893 1010 1126 1243 1359 1476 1592 7 83 82 81 73 1709 1825 1942 2058 2174 2291 2407 2523 2639 2755 8 9 94 94 106 105 93 104 74 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 75 4031 4147 4263 4379 4494 4610 4726 4841 4957 5072 115 114 113 76 5188 5303 5419 553JK 5650 5765 5880 5996 6111 6226 1 12 11 11 77 6341 6457 6572 Lt>$1 77 2*2 Sfe 886$aW<83 6802 6917 7032 7147 7262 7377 2 23 23 23 78 7492 7607 7951 8066 8181 8295 8410 8525 3 4 35 34 46 46 34 45 79 8639 8754 9097 9212 9326 9441 9555 9669 5 58 57 57 380 57 9784 9898 * 1 *0012 0126 *0241 *0355 *0469 *0583 *0697 *0811 6 7 69 68 81 80 68 79 81 58 0925 1039 1153 1267 1381 1495 1608 1722 1836 1950 8 92 91 90 82 2063 2177 2291 2404 2518 2631 2745 2858 2972 3085 9 104 103 102 83 3199 3312 3426 3539 3652 3765 3879 3992 4105 4218 84 4331 4444 4557 4670 4783 4896 5009 5122 5235 5348 1 112 111 11 11 110 11 85 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 2 22 22 22 86 6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 3 4 34 33 45 44 33 44 87 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 5 56 56 55 88 8832 8944 9056 9167 9279 9391 9503 9615 9726 9838 • 6 67 67 06 89 9950 *0061 *0173 *0284 *0396 *0507 *0619 *0730 *0842 *0953 7 8 78 78 90 89 77 88 390 59 1065 1176 1287 1399 1510 1621 1732 1843 1955 2066 9 101 100 99 91 2177 2288 2399' 2510 2621 2732 2843 2954 3064 3175 92 3286 3397 3508 3618 3729 3840 3950 4061 4171 4282 109 108 93 4393 4503 4614 4724 4834 4945 5055 5165 5276 5386 1 2 11 11 22 22 94 5496 5606 5717 5827 5937 6047 6157 6267 6377 6487 3 33 32 95 6597 6707 6817 6927 7037 7146 7256 7366 7476 7586 4 5 44 43 55 54 96 7695 7805 7914 8024 8134 8243 8353 8462 8572 8681 6 65 65 97 8791 8900 9009 9119 9228 9337 9446 9556 9665 9774 7 8 76 76 87 86 .98 9883 9992 *0101 *0210 *0319 *0428 *0537 *0646 *0755 *0864 9 98 97 99 60 0973 1082 1191 1299 1408 1517 1625 1734 1843 1951 400 1 2 3 4 5 6 7 8 9 Differences. 26 HI. LOGARITHMS OF NUMBERS. 400 1 2 3 4 5 6 7 8 9 Differences. 400 60 2060 2169 2277 2386 2494 2603 2711 2819 2928 3036 01 3144 3253 3361 3469 3577 3686 3794 3902 4010 4118 109 108 107 02 4226 4334 4442 4550 4658 4766 4874 4982 5089 5197 i 2 11 22 11 11 22 21 03 5305 5413 5521 5628 5736 5844 5951 6059 6166 6274 8 88 82 82 04 6381 6489 6596 6704 6811 6919 7026 7133 7241 7348 4 5 44 OB 48 48 54 54 05 7455 7562 7669 7777 7884 7991 8098 8205 8312 8419 6 65 65 64 06 8526 8633 8740 8847 8954 9061 9167 9274 9381 9488 7 8 76 87 76 75 86 86 07 9594 9701 9808 9914 ♦0021 *0128 *0234 *0341 *0447 *0554 9 IB ;»7 N 08 61 0660 0767 0873 0979 1086 1192 1298 1405 1511 1617 09 1723 1829 1936 2042 2148 2254 2360 2466 2572 2678 106 105 104 410 61 2784 2890 2996 3102 3207 3313 3419 3525 3630 3736 1 2 11 21 11 10 21 21 11 3842 3947 4053 4159 4264 4370 4475 4581 4686 4792 3 82 82 81 12 4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 4 42 42 42 13 5950 6055 6160 6265 6370 6476 6581 6686 6790 6895 5 B8 64 53 52 68 62 74 78 14 7000 7105 7210 7315 7420 7525 7629 7734 7839 7943 7 74 15 8048 8153 8257 8362 8466 8571 8676 8780 8884 8989 8 9 85 95 95 94 16 9093 9198 9302 9406 9511 9615 9719 9824 9928 *0032 17 62 0136 0240 0344 0448 0552 0656 0760 0864 0968 1072 108 10 102 10 18 1176 1280 1384 1488 1592 1695 1799 1903 2007 2110 1 19 2214 2318 2421 2525 2628 2732 2 8 85 2939 3042 3146 2 3 •21 31 20 81 420 62 3249 3353 3456 3559 3663 :;7>c 3869 3973 4076 4179 4 41 41 21 22 4282 5312 4385 5415 4488 5518 4591 5621 4695 5724 43o i 5827 *>9Z9 5004 (1032 5107 6135 5210 6238 5 6 7 52 62 72 51 61 71 23 6340 6443 6546 6648 6751 6853 6956 7058 7161 7263 8 82 a 24 7366 7468 7571 7673 7775 7878 7980 8082 8185 8287 9 93 92 25 8389 8491 8593 8695 8797 8900 9002 9104 9206 9308 101 10 100 10 26 9410 9512 9613 9715 9817 9919 *0021 *0123 *0224 *0326 1 27 63 0428 0530 0631 0733 0835 0936 1038 1139 1241 1342 2 20 20 28 1444 1545 1647 1748 1849 1951 2052 2153 2255 2356 3 4 30 40 80 40 29 2457 2559 2660 2761 2862 2963 3064 3165 3266 3367 5 51 50 430 63 3468 3569 3670 3771 3872 3973 4074 4175 4276 4376 6 7 61 71 60 70 31 4477 4578 4679 4779 4880 4981 5081 5182 5283 5383 8 -1 80 .32 5484 5584 5685 5785 5886 5986 6087 6187 6287 6388 9 91 90 33 6488 6588 6688 6789 6889 6989 7089 7189 7290 7390 34 7490 7590 7690 7790 7890 7990 8090 8190 8290 8389 1 99 10 n id 35 8489 8589 8689 8789 8888 8988 9088 9188 9287 9387 2 20 20 36 9486 9586 9686 9785 9885 9984 *0084 *0183 *0283 *0382 3 4 80 40 •-'<" M 37 64 0481 0581 0680 0779 0879 0978 1077 1177 1276 1375 5 50 49 38 1474 1573 1672 1771 1871 1970 2069 2168 2267 2366 6 .v.< 59 39 2465 2563 2662 2761 2860 2959 3058 3156 3255 3354 7 m 79 88 ra 440 64 3453 3551 3650 3749 3847 3946 4044 4143 4242 4340 9 S9 ^> 41 4439 4537 4636 4734 4832 4931 5029 5127 5226 5824 42 5422 5521 5619 5717 5815 5913 6011 6110 6208 6306 ;»7 96 43 6404 6502 6600 6698 6796 6894 6992 7089 7187 7286 1 10 19 10 19 44 7383 7481 7579 7676 7774 7872 7969 8067 8165 8262 3 29 -•;> 45 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 4 5 49 88 1^ 46 9335 9432 9530 9627 9724 9821 9919 *0016 *0113 *0210 6 68 47 65 0308 0405 0502 0599 0696 0793 0890 0987 1084 1181 7 8 9 88 7^ ~7 n 77 48 1278 1375 1412 1569 1666 1762 1859 L966 •jo;.:; 2150 49 2246 2343 2440 2536 2683 2730 2826 2923 3019 9 1 1 6 450 1 2 3 4 5 6 7 8 9 Differences. III. LOGARITHMS OF NUMBERS. 27 450 1 2 3 4 5 6 7 8 "9 Differences. 450 65 3213 3309 3405 3502 3598 3695 3791 3888 3984 4080 51 4177 4273 4369 4465 4562 4658 4754 4850 4946 5042 97 96 52 5138 5235 5331 5427 5523 5619 5715 5810 5906 6002 i 2 10 19 10 19 53 6098 6194 6290 6386 6482 6577 6673 6769 6864 6960 3 29 29 54 7056 7152 7247 7343 7438 7534 7629 7725 7820 7916 4 5 39 49 3S 48 55 8011 8107 8202 8298 8393 8488 8584 8679 8774 8870 6 58 58 56 8965 9060 9155 9250 9346 9441 9536 9631 9726 9821 7 8 68 78 67 77 57 9916 *0011 *0106 *0201 *0296 *0391 *0486 *0581 *0676 *0771 9 S7 86 58 66 0865 0960 1055 1150 1245 1339 1434 1529 1623 1718 59 1813 1907 2002 2096 2191 2286 2380 2475 2569 2663 95 94 460 66 2758 2852 2947 3041 3135 3230 3324 3418 3512 3607 1 2 10 19 9 19 61 3701 3795 3889 3983 4078 4172 4266 4360 4454 4548 3 29 28 62 4642 4736 4830 4924 5018 5112 5206 5299 5393 5487 4 38 38 63 5581 5675 5769 5862 5956 6050 6143 6237 6331 6424 5 6 4S 57 47 56 64 6518 6612 6705 6799 6892 6986 7079 7173 7266 7360 7 67 66 65 7453 7546 7640 7733 7826 7920 8013 8106 8199 8293 8 9 76 86 75 85 66 8386 8479 8572 8665 8759 8852 8945 9038 9131 9224 67 9317 9410 9503 9596 9689 9782 9875 9967 *0060 *0153 93 92 68 67 0246 0339 0431 0524 0617 0710 0802 0895 0988 1080 1 9 9 69 1173 1265 1358 1451 1543 1636 1728 1821 1913 2005 2 3 19 28 IS 28 470 67 2098 2190 2283 2375 2467 £6$ L'652 2744 2836 2929 f 4 37 37 71 3021 3113 3205 3297 3390 3+0 Z 35 74 3666 3758 3850 5 g 47 56 46 55 72 3942 4034 4126 4218 4310 ♦402 4494 4586 4677 4769 7 65 64 .73 4861 4953 5045 5137 5228 . 5320 5412 5503 5595 5687 8 74 74 74 5778 5870 5962 6053 6145 6236 6328 6419 6511 6602 9 84 83 75 6694 6785 6876 6968 7059 7151 7242 7333 7424 7516 91 9 90 9 76 7607 7698. 7789 7881 7972 8063 8154 8245 8336 8427 1 77 8518 8609 8700 8791 8882 8973 9064 9155 9246 9337 2 18 18 78 9428 9519 9610 9700 9791 9882 9973 *0063 *0154 *0245 3 4 27 36 27 36 79 68 0336 0426 0517 0607 0698 0789 0879 0970 1060 1151 5 46 45 480 68 1241 1332 1422 1513 1603 1693 1784 1874 1964 2055 6 7 55 64 54 63 81 2145 2235 2326 241-6 250'6 2596 2686 2777 2867 2957 8 78 72 82 3047 3137 3227 3317 3407 3497 3587 3677 3767 3857 9 82 81 83 3947 4037 4127 4217 4307 4396 4486 4576 4666 4756 84 4845 4935 5025 5114 5204 5294 5383 5473 5563 5652 1 89 g 88 9 85 5742 5831 5921 6010 6100 6189 6279 6368 6458 6547 2 18 18 86 6636 6726 6815 6904 6994 7083 7172 7261 7351 7440 3 4 27 36 26 85 87 7529 7618 7707 7796 7886 7975 8064 8153 8242 8331 5 45 44 88 8420 8509 8598 8687 8776 8865 8953 9042 9131 9220 6 53 53 89 9309 9398 9486 9575 9664 9753 9841 9930 *0019 *0107 7 8 62 71 62 70 490 69 0196 0285 0373 0462 0550 0639 0728 0816 0905 0993 9 80 79 91 1081 1170 1258 1347 1435 1524 1612 1700 1789 1877 92 1965 2053 2142 2230 2318 2406 2494 2583 2671 2759 ' 87 86 93 2847 2935 3023 3111 3199 3287 3375 3463 3551 3639 i 2 9 17 9 17 94 3727 3815 3903 3991 4078 4166 4254 4342 4430 4517 3 26 26 95 4605 4693 4781 4868 4956 5044 5131 5219 5307 5394 4 5 35 44 34 43 96 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 6 52 52 97 6356 6444 6531 6618 6706 6793 6880 6968 7055 7142 7 8 61 70 60 69 98 7229 7317 7404 7491 7578 7665 7752 7839 7926 8014 9 78 77 99 8101 8188 8275 8362 8449 8535 8622 8709 8796 8883 500 1 2 3 4 5 6 7 8 9 Differences. 28 III. LOGARITHMS OF NUMBERS. ■-' 500 1 2 3 4 5 6 7 8 9 Differences. 500 69 8970 9057 9144 9231 9317 9404 9491 9578 9664 9751 01 9838 9924 *0011 *0098 *0184 *0271 *0358 *0444 *0531 *0617 02 70 0704 0790 0877 0963 1050 1136 1222 1309 1395 1482 87 86 03 1568 1654 1741 1827 1913 1999 2086 2172 2258 2344 i 9 9 04 2431 2517 2603 2689 2775 2861 2947 3033 3119 3205 2 3 17 26 17 26 05 3291 3377 3463 3549 3635 3721 3807 3893 3979 4065 4 35 34 06 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 5 | 44 52 43 52 07 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 7 61 60 08 5864 5949 6035 6120 6206 6291 6376 6462 6547 6632 8 70 at 09 6718 6803 6888 6974 7059 7144 7229 7315 7400 7485 9 78 77 510 70 7570 7655 7740 7826 7911 7996 8081 8166 8251 8336 11 8421 8506 8591 8676 8761 8846 8931 9015 9100 9185 12 9270 9355 9440 9524 9609 9694 9779 9863 9948 *0033 85 84 13 71 0117 0202 0287 0371 0456 0540 0625 0710 0794 0879 1 2 9 17 8 17 14 0963 1048 1132 1217 1301 1385 1470 1554 1639 1723 3 4 26 34 25 34 15 1807 1892 1976 2060 2144 2229 2313 2397 2481 2566 5 43 42 16 2650 2734 2818 2902 2986 3070 3154 3238 3323 3407 6 51 50 17 3491 3575 3659 3742 3826 3910 3994 4078 4162 4246 7 8 60 68 59 67 18 4330 4414 4497 4581 4665 4749 4833 4916 5000 5084 9 77 76 19 5167 5251 5335 5418 5502 5586 5669 5753 5836 5920 520 71 6003 6087 6170 6254 6337 6421 6504 6588 6671 6754 21 6838 6921 7004 7088 7171 7254 7338 7421 7504 7587 88 82 22 7671 7754 7837 7920 8003 8086 8169 8253 8336 8419 1 8 8 23 8502 8585 8668 8751 8834 8917 9000 9083 9165 9248 2 17 16 25 33 24 9331 9414 9497 9580 9663 9745 9828 9911 9994 *0077 3 4 25 33 25 72 0159 0242 0325 0407 0490 0573 0655 0738 0821 0903 5 6 7 48 50 58 41 49 57 26 0986 1068 1151 1233 1316 1398 1481 1563 1646 1728 27 1811 1893 1975 2058 2140 2222 2305 2387 2469 2552 8 66 66 28 2634 2716 2798 2881 2963 3045 3127 3209 3291 3374 9 75 74 29 3456 3538 3620 3702 3784 3866 3948 4030 4112 4194 530 72 4276 4358 4440 4522 4604 4685 4767 4849 4931 5013 31 5095 5176 5258 5340 5422 5503 5585 5667 5748 5830 -1 BQ 32 5912 5993 6075 6156 6238 6320 6401 6483 6564 6646 1 2 8 16 8 16 33 6727 6809 6890 6972 7053 7134 7216 7297 7379 7460 8 24 M 34 7541 7623 7704 7785 7866 7948 8029 8110 8191 8273 4 5 82 41 n 40 35 8354 8435 8516 8597 8678 8759 8841 8922 9003 9084 6 49 48 36 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 7 g 57 65 M 64 37 9974 *0055 *0136 *0217 *0298 *0378 *0459 *0540 *0621 *0702 9 78 72 38 73 0782 0863 0944 1024 1105 1186 1266 1347 1428 1508 39 1589 1669 1750 1830 1911 1991 2072 2152 2233 2313 540 73 2394 2474 2555 2635 2715 2796 2876 2956 3037 3117 19 8 41 3197 3278 3358 3438 3518 3598 3679 3759 3839 3919 1 42 3999 4079 4160 4240 4320 4400v 4480 4560 4640 17 'JO 2 16 43 4800 4880 4960 5040 5120 5200 5279 5359 5439 5619 4 M 44 5599 5679 5759 5838 5918 5998 6078 6157 6881 6317 5 40 45 6397 6476 6556 6635 6715 6795 6874 6954 7034 T113 6 7 47 06 46 7193 7272 7352 7431 7511 7590 7670 7749 7829 7908 8 ' 47 7987 8067 8146 8225 8305 8384 8463 8543 8622 8701 9 71 48 8781 8860 8939 9018 9097 !>177 9256 9335 9414 9493 49 9572 9651 9731 9810 9889 9968 *0047 *0126 *0205 *0284 550 1 2 3 4 5 (5 7 8 !> Differences. ni. LOGARITHMS OF NUMBERS. 29 550 1 2 3 4 5 6 7 8 9 Differences. 550 74 0363 0442 0521 0600 0678 0757 0836 0915 0994 1073 51 1152 1230 1309 1388 1467 1546 1624 1703 1782 1860 52 1939 2018 2096 2175 2254 2332 2411 2489 2568 2647 79 78 53 2725 2804 2882 2961 3039 3118 3196 3275 3353 3431 i 8 8 54 3510 3588 3667 3745 3823 3902 3980 4058 4136 4215 2 3 16 24 16 23 55 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 4 32 31 56 5075 5153 5231 5309 5387 5465 5543 5621 5699 5777 5 6 40 47 39 47 57 5855 5933 6011 6089 6167 6245 6323 6401 6479 6556 7 56 55 58 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 8 63 62 59 7412 7489 7567 7645 7722 7800 7878 7955 8033 8110 9 71 70 560 74 8188 8266 8343 8421 8498 8576 8653 8731 8808 8885 61 8963 9040 9118 9195 9272 9350 9427 9504 9582 9659 62 9736 9814 9891 9968 *0045 *0123 *0200 *0277 *0354 *0431 77 76 63 75 0508 0586 0663 0740 0817 0894 0971 1048 1125 1202 1 2 8 15 8 15 64 1279 1356 1433 1510 1587 1664 1741 1818 1895 1972 3 4 23 31 23 30 65 2048 2125 2202 2279 2356 2433 2509 2586 2663 2740 5 39 38 66 2816 2893 2970 3047 3123 3200 3277 3353 3430 3506 6 46 46 67 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 7 8 54 62 53 61 68 4348 4425 4501 4578 4654 4730 4807 4883 4960 5036 9 69 68 69 5112 5189 5265 5341 5417 5494 5570 5646 5722 5799 570 75 5875 5951 6027 6103 6180 6256 6332 6408 6484 6560 71 6636 6712 6788 6864 B940 7016 7092 7168 7244 7320 75 8 74 7 72 7396 7472 7548 7624 7700 7775 7851 7927 8003 8079 1 73 8155 8230 8306 8382 8458 8533 8609 8685 8761 8836 2 15 15 74 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 3 4 23 30 22 30 75 76 9668 76 0422 9743 0498 9819 0573 9894 0649 9970 0724 *0045 0799 *0121 0875 *0196 0950 *0272 1025 *0347 1101 5 6 7 38 45 53 37 44 52 77 1176 1251 1326 1402 1477 1552 1627 1702 1778 1853 8 60 59 78 1928 2003 2078 2153 2228 2303 2378 2453 2529 2604 9 68 67 79 2679 2754 2829 2904 2978 3053 3128 3203 3278 3353 580 76 3428 3503 3578 3653 3727 3802 3877 3952 4027 4101 81 4176 4251 4326 4400 4475 4550 4624 4699 4774 4848 73 82 4923 4998 5072 5147 5221 5296 5370 5445 5520 5594 1 2 7 15 83 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 3 22 84 6413 6487 6562 6636 6710 6785 6859 6933 7007 7082 4 5 29 37 44 85 7156 7230 7304 7379 7453 7527 7601 7675 7749 7823 6 86 4 7898 7972 8046 8120 8194 8268 8342 8416 8490 8564 7 8 51 58 87 8638 8712 8786 8860 8934 9008 9082 9156 9230 9303 9 66 88 9377 9451 9525 9599 9673 9746 9820 9894 9968 *0042 89 77 0115 0189 0263 0336 0410 0484 0557 0631 0705 0778 590 77 0852 0926 0999 1073 1146 1220 1293 1367 1440 1514 72 91 1587 1661 1734 1808 1881 1955 2028 2102 2175 2248 1 7 92 2322 2395 2468 2542 2615 2688 2762 2835 2908 2981 2 8 4 14 22 29 93 3055 3128 3201 3274 3348 3421 3494 3567 3640 3713 94 3786 3860 3933 4006 4079 4152 4225 4298 4371 4444 5 36 95 4517 4590 4663 4736 4809 4882 4955 5028 5100 5173 6 7 43 50 96 5246 5319 5392 5465 5538 5610 5683 5756 5829 5902 8 58 65 97 5974 6047 6120 6193 6265 6338 6411 6483 6556 6629 9 98 6701 6774 6846 6919 6992 7064 7137 7209 7282 7354 » 99 7427 7499 7572 7644 7717 7789 7862 7934 8406 8079 600 1 2 3 4 5 6 7 8 9 Differences. 30 III. LOGARITHMS OF NUMBERS. 600 1 2 3 4 5 6 7 8 9 Differences. 600 77 8151 8224 8296 8368 8441 8513 8585 8658 8730 8802 01 8874 8947 9019 9091 9163 9236 9308 9380 9452 9524 02 9596 9669 9741 9813 9885 9957 *0029 ♦0101 *0173 *0245 73 72 03 78 0317 0389 0461 0533 0605 0677 0749 0821 0893 0965 i 7 7 04 1037 1109 1181 1253 1324 1396 1468 1540 1612 1684 2 8 15 22 14 22 05 1755 1827 1899 1971 2042 2114 2186 2258 2329 2401 4 29 29 06 2473 2544 2616 2688 2759 2831 2902 2974 3046 3117 5 6 37 44 36 07 3189 3260 3332 3403 3475 3546 3618 3689 3761 3832 7 51 50 08 3904 3975 4046 4118 4189 4261 4332 4403 4475 4546 8 9 08 66 58 65 09 4617 4689 4760 4831 4902 4974 5045 5116 5187 5259 610 78 5330 5401 5472 5543 5615 5686 5757 5828 5899 5970 11 6041 6112 6183 6254 6325 6396 6467 6538 6609 6680 12 6751 6822 6893 6964 7035 7106 7177 7248 7319 7390 1 71 7 70 7 13 7460 7531 7602 7673 7744 7815 7885 7956 8027 8098 2 14 14 14 8168 8239 8310 8381 8451 8522 8593 8663 8734 8804 8 4 21 2S 21 28 15 8875 8946 9016 9087 9157 9228 9299 9369 9440 9510 5 36 35 16 9581 9651 9722 9792 9863 9933 *0004 *0074 *0144 *0215 6 7 48 50 42 49 17 79 0285 0356 0426 0496 0567 0637 0707 0778 0848 0918 8 57 H 18 0988 1059 1129 1199 1269 1340 1410 1480 1550 1620 9 64 68 19 1691 1761 1831 1901 1971 2041 2111 2181 2252 2322 620 79 2392 2462 2532 2602 2672 2742 2812 2882 2952 3022 21 3092^3162 3231 3301 3371 3441 3511 3581 3651 3721 69 68 22 3»lf* man 3930 4000 4070 4139 4209 4279 4349 4418 1 7 7 23 448J? ' $058 4627 4697 4767 4836 4906 4976 5045 5115 2 3 14 •21 14 20 24 5185 5254 5324 5393 5463 5532 5602 5672 5741 5811 4 28 27 25 5880 5949 6019 6088 6158 6227 6297 6366 6436 6505 5 6 85 11 84 41 26 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 7 18 48 27 7268 7337 7406 7475 7545 7614 7683 7752 7821 7890 8 9 55 62 54 61 28 7960 8029 8098 8167 8236 8305 8374 8443 8513 8582 29 8651 8720 8789 8858 8927 8996 9065 9134 9203 9272 630 79 9341 9409 9478 9547 9616 9685 9754 9823 9892 9961 31 80 0029 0098 0167 0236 0305 0373 0442 0511 0580 0648 1 67 7 32 0717 0786 0854 0923 0992 1061 1129 1198 1266 1335 a 18 33 1404 1472 1541 1609 1678 1747 1815 1884 1952 2021 3 4 5 20 27 84 34 2089 2158 2226 2295 2363 2432 2500 2568 2637 2705 35 2774 2842 2910 2979 3047 3116 3184 3252 3321 3389 6 40 47 54 36 3457 3525 3594 3662 3730 3798 3867 3935 4003 4071 8 37 4139 4208 4276 4344 4412 4480 4548 4616 4685 4753 9 tx» 38 4821 4889 4957 5025 5093 5161 5229 5297 5365 5433 39 5501 5569 5637 5705 5773 5841 5908 5976 6044 6112 640 80 6180 6248 6316 6384 6451 6519 6587 6655 6723 6790 66 41 6858 6926 6994 7061 7129 7197 7264 7332 7400 7467 1 7 42 7535 7603 7670 7738 7806 7873 7941 8008 8076 8143 ■- 18 20 43 8211 8279 8346 8414 8481 8549 8616 8684 8751 8818 4 26 44 8886 8953 9021 9088 9156 9223 9290 9358 9425 9492 5 88 40 45 9560 9627 9694 9762 9829 9896 9964 *0031 *0098 *0165 7 46 46 81 0233 0300 0367 0434 0501 0569 0636 0703 0770 0837 8 9 58 09 •47 0904 0971 1039 1106 1173 1240 1307 1374 1441 1508 48 1575 1642 1709 1776 1843 1910 1977 2044 2111 •J ! 7 B 49 2245 2312 2379 2445 2512 2579 2646 2713 2780 2847 650 1 2 3 4 5 6 7 8 9 Differences. in. LOGARITHMS OF NUMBERS. 31 650 1 2 3 4 5 6 7 8 9 Differences. 650 81 2913 2980 3047 3114 3181 3247 3314 3381 3448 3514 51 3581 3648 3714 3781 3848 3914 3981 4048 4114 4181 6T 52 4248 4314 4381 4447 4514 4581 4647 4714 4780 4847 i 2 7 13 53 4913 4980 5046 5113 5179 5246 5312 5378 5445 5511 3 20 54 5578 5644 5711 5777 5843 5910 5976 6042 6109 6175 4 5 27 34 55 6241 6308 6374 6440 6506 6573 6639 6705 6771 6838 6 40 56 6904 6970 7036 7102 7169 7235 7301 7367 7433 7499 7 8 47 54 57 7565 7631 7698 7764 7830 7896 7962 8028 8094 8160 9 60 58 8226 8292 8358 8424 8490 8556 8622 8688 8754 8820 59 8885 8951 9017 9083 9149 9215 9281 9346 9412 9478 66 660 81 9544 9610 9676 9741 9807 9873 9939 *0004 *0070 *0136 1 2 7 13 61 82 0201 0267 0333 0399 0464 0530 0595 0661 0727 0792 3 20 62 0858 0924 0989 1055 1120 1186 1251 1317 1382 1448 4 26 63 1514 1579 1645 1710 1775 1841 1906 1972 2037 2103 5 6 38 40 64 2168 2*233 2299 2364 2430 2495 2560 2626 2691 2756 7 46 65 2822 2887 2952 3018 3083 3148 3213 3279 3344 3409 8 9 53 59 66 3474 3539 3605 3670 3735 . 3800 3865 3930 3996 4061 67 4126 4191 4256 4321 4386 4451 4516 4581 4646 4711 65 68 4776 4841 4906 4971 5036 5101 5166 5231 5296 5361 1 7 69 5426 5491 5556 5621 5686 5751 5815 5880 5945 6010 2 8 13 20 670 82 6075 6140 6204 6269 6334 6399 6464 6528 6593 6658 4 26 71 6723 6787 6852 6917 6981 7046 7111 7175 7240 7305 33 39 72 7369 7434 7499 7563 7628 7692 7757 7821 7886 7951 46 73 8015 8080 8144 8209 8273 8338 8402 8467 8531 8595 52 59 74 8660 8724 8789 8853 8918 8982 9046 9111 9175 9239 75 9304 9368 9432 9497 9561 9625 9690 9754 9818 9882 64 6 76 9947 *0011 *0075 *0139 *0204 *0268 *0332 *0396 *0460 *0525 1 77 83 0589 0653 07.17 0781 0845 0909 1 0973 1037 1102 1166 2 13 78 1230 1294 1358 1422 1486 1550 1614 1678 1742 1806 3 4 19 26 79 1870 1934 1998 2062 2126 2189 2253 2317 2381 2445 5 82 680 83 2509 2573 2637 2700 2764 2828 2892 2956 3020 3083 6 7 38 45 81 3147 3211 3275 3338 3402 3466 3530 3593 3657 3721 8 51 82 3784 3848 3912 3975 4039 4103 4166 4230 4294 4357 9 58 83 4421 4484 4548 4611 4675 4739 4802 4866 4929 4993 84 5056 5120 5183 5247 5310 5373 5437 5500 5564 5627 1 68 6 85 5691 5754 5817 5881 5944 6007 6071 6134 6197 6261 2 13 86 6324 6387 6451 6514 6577 6641 6704 6767 6830 6894 8 4 19 25 87 6957 7020 7083 7146 7210 7273 7336 7399 7462 7525 5 32 88 7588 7652 7715 7778 7841 7904 7967 8030 8093 8156 6 38 89 8219 8282 8345 8408 8471 8534 8597 8660 8723 8786 7 8 44 50 690 83 8849 8912 8975 9038 9101 9164 9227 9289 9352 9415 9 57 91 9478 9541 9604 9667 9729 9792 9855 9918 9981 *0043 92 84 0106 0169 0232 0294 0357 0420 0482 0545 0608 0671 62 93 0733 0796 0859 0921 0984 1046 1109 1172 1234 1297 1 2 6 12 94 1359 1422 1485 1547 1610 1672 1735 1797 1860 1922 3 19 95 1985 2047 2110 2172 2235 2297 2360 2422 2484 2547 4 5 25 81 96 2609 2672 2734 2796 2859 2921 2983 3046 3108 3170 6 37 97 3233 3295 3357 3420 3482 3544 3606 3669 3731 3793 7 8 43 50 98 3855 3918 3980 4042 4104 4166 4229 4291 4353 4415 9 56 99 4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 700 1 2 3 4 5 6 7 8 9 Differences. 32 III. LOGARITHMS OF NUMBERS. 700 1 2 3 4 5 6 7 8 9 Differences. 700 84 5098 5160 5222 5284 5346 5408 5470 5532 5594 5656 01 5718 5780 5842 5904 5966 6028 6090 6151 6213 6275 02 8337 6399 6461 6523 6585 6646 6708 6770 6832 6894 62 61 03 6955 7017 7079 7141 7202 7264 7326 7388 7449 7511 1 6 6 04 7573 7634 7696 7758 7819 7881 7943 8004 8066 8128 2 12 3 19 12 18 05 8189 8251 8312 8374 8435 8497 8559 8620 8682 8743 4 26 24 06 8805 8866 8928 8989 9051 9112 9174 9235 9297 9358 5 81 6 37 81 87 07 9419 9481 9542 9604 9665 9726 9788 9849 9911 9972 7 43 08 85 0033 0095 0156 0217 0279 0340 0401 0462 0524 0585 8 50 9 56 49 55 09 0646 0707 0769 0830 0891 0952 1014 1075 1136 1197 710 85 1258 1320 1381 1442 1503 1564 1625 1686 1747 1809 11 1870 1931 1992 2053 2114 2175 2236 2297 2358 2419 12 2480 2541 2602 2663 2724 2785 2846 2907 2968 3029 1 2 60 6 12 13 3090 3150 3211 3272 3333 3394 3455 3516 3577 3637 14 3698 3759 3820 3881 3941 4002 4063 4124 4185 4245 : 1 3 4 5 18 24 30 15 4306 4367 4428 4488 4549 4610 4670 4731 4792 4852 16 4913 4974 5034 5095 5156 5216 5277 5337 5398 5459 6 36 17 5519 5580 5640 5701 5761 5822 5882 5943 6003 6064 7 1 42 ■4^ 18 6124 6185 6245 6306 6366 6427 6487 6548 6608 6668 9 54 19 6729 6789 6850 6910 6970 7031 7091 7152 7212 7272 720 85 7332 7393 7-143 1WX 7634 7694 7755 7815 7875 21 7935 7995 8056 8ns 8236 8297 8357 8417 8477 59 22 8537 8597 860. 8M4 .^778 8838 8898 8958 9018 9078 1 6 23 9138 9198 9258 •j:;!fc 9379 9439 9499 9559 9619 9679 2 8 4 12 18 •24 24 9739 9799 9859 9918 9978 *0038 *0098 *0158 *0218 *0278 25 86 0338 0398 0458 0518 0578 0637 0697 075 7 0817 0877 5 6 30 85 26 0937 0996 1056 1116 1176 1236 1295 1355 1415 1475 7 41 27 1534 1594 1654 1714 1773 1833 1893 1952 2012 2072 8 47 58 28 2131 2191 2251 2310 2370 2430 2489 2549 2608 2668 9 29 2728 2787 2847 2906 2966 3025 3085 3144 3204 3263 730 86 3323 3382 3442 3501 3561 3620 3680 3739 3799 3858 31 3917 3977 4036 4096 4155 4214 4274 4333 4392 4452 5S 32 4511 4570 4630 4689 4748 4808 4867 4926 4985 5045 1 2 6 VI 33 5104 5163 5222 5282 5341 5400 5459 5519 5578 no:; 7 8 17 34 5696 5755 5814 5874 5933 5992 6051 6110 6169 6228 4 5 M 35 6287 6346 6405 6465 6524 6583 6642 6701 6760 6819 6 85 36 6878 6937 6996 7055 7114 7173 7232 7291 7350 7 100 7 8 41 4t; 37 7467 7526 7585 7644 7703 7762 7821 7880 7939 7998 9 38 8056 8115 8174 8233 8292 8350 8409 8468 S.VJ7 8586 39 8644 8703 8762 8821 8879 8938 8997 9056 9114 9173 740 86 9232 9290 9349 9408 9466 9525 9584 9642 9701 9760 .. 41 9818 9877 8936 9994 ♦0053 *0111 *0170 *0228 *0287 *0345 1 6 42 87 0404 0462 0521 0579 0638 0696 (i7.-.;, 0813 0872 0930 I a 4 11 17 43 0989 1047 1106 1164 1223 1281 1339 1398 i i.-.c i ;. l B 44 1573 1631 1690 1748 1806 1865 1923 1981 •JUKI 2098 5 as 45 2156 2215 2273 2331 2389 2448 2506 2064 2622 2681 6 7 10 46 2739 2797 2855 2913 2972 3030 3088 3146 .•'.•_MM 3262 g 46 51 47 3321 3379 3437 3495 3553 3611 3969 :s7-J7 3785 38 I I 9 48 3902 3960 4018 4076 4134 4192 4250 4308 4366 1424 49 4482 4540 4598 4656 4714 4772 4830 4888 4945 5003 750 1 2 3 4 5 6 7 8 9 Different III. LOGARITHMS OF NUMBERS. 33 ( — 1 750 1 2 3 4 5 6 7 8 9 Differences. 750 87 5061 5119 5177 5235 5293 5351 5409 5466 5524 5582 51 5640 5698 5756 5813 5871 5929 5987 6045 6102 6160 52 6218 6276 6333 6391 6449 6507 6564 6622 6680 6737 68 53 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314 i 6 54 7371 7429 7487 7544 7602 7659 7717 7774 7832 7889 2 3 12 17 55 7947 8004 8062 8119 8177 8234 8292 8349 8407 8464 4 23 56 8522 8579 8637 8694 8752 8809 8866 8924 8981 9039 5 g 29 35 57 9096 9153 9211 9268 9325 9383 9440 9497 9555 9612 7 41 58 9669 9726 9784 9841 9898 9956 *0013 *0070 *0127 *0185 8 46 59 88 0242 0299 0356 0413 0471 0528 0585 0642 0699 0756 9 52 760 88 0814 0871 0928 0985 1042 1099 1156 1213 1271 1328 61 1385 1442 1499 1556 1613 1670 1727 1784 1841 1898 62 1955 2012 2069 2126 2183 2240 2297 2354 2411 2468 57 63 2525 2581 2638 2695 2752 2809 2866 2923 2980 3037 1 2 6 11 64 3093 3150 3207 3264 3321 3377 3434 3491 3548 3605 3 17 23 29 65 3661 3718 3775 3832 3888 3945 4002 4059 4115 4172 4 5 66 4229 4285 4342 4399 4455 4512 4569 4625 4682 4739 6 34 67 4795 4852 4909 4965 5022 5078 5135 5192 5248 5305 7 8 40 46 68 5361 5418 5474 5531 5587 5644 5700 5757 5813 5870 9 51 69 5926 5983 6039 6096 6152 6209 6265 6321 6378 6434 770 88 6491 6547 6604 6660 6716 6773 6829 6885. *m-^te>s 71 7054 7111 7167 7223 7280 7336 7392 744|; 4*63 56 72 7617 7674 7730 7786 7842 7898 7955 8011 £f>**v *8123 1 6 73 8179 8236 8292 8348 8404 8460 8516 8573 8«§9 8685 2 3 4 11 17 22 74 8741 8797 8853 8909 8965 9021 9077 9134 9190 9246 75 9302 9358 9414 9470 9526 9582 9638 9694 9750 9806 5 g 28 34 76 9862 9918 9974 *0030 *0086 *0141 *0197 *0253 *0309 *0365 7 39 77 89 0421 0477 0533 0589 0645 0700 0756 0812 0868 0924 8 45 78 0980 1035 1091 1147 1203 1259 1314 1370 1426 1482 9 50 79 1537 1593 1649 1705 1760 1816 1872 1928 1983 2039 780 89 2095 2150 2206 2262 2317 2373 2429 2484 2540 2595 81 2651 2707 2762 2818 2873 2929 2985 3040 3096 3151 55 82 3207 3262 3318 3373 3429 3484 3540 3595 3651 3706 1 2 6 11 83 3762 3817 3873 3928 3984 4039 4094 4150 4205 4261 3 17 84 4316 4371 4427 4482 4538 4593 4648 4704 4759 4814 4 5 22 28 85 4870 4925 4980 5036 5091 5146 5201 5257 5312 5367 6 33 86 5423 5478 5533 5588 5644 5699 5754 5809 5864 5920 7 8 89 44 87 • 5975 6030 6085 6140 6195 6251 6306 6361 6416 6471 9 50 88 6526 6581 6636 6692 6747 6802 6857 6912 6967 7022 89 7077 7132 7187 7242 7297 7352 7407 7462 7517 7572 790 89 7627 7682 7737 7792 7847 7902 7957 8012 8067 8122 54 91 8176 8231 8286 8341 8396 8451 8506 8561 8615 8670 1 5 92 8725 8780 8835 8890 8944 8999 9054 9109 9164 9218 2 3 4 11 16 22 93 9273 9328 9383 9437 9492 9547 9602 9656 9711 9766 94 9821 9875 9930 9985 *0039 *0094 *0149 *0203 *0258 *0312 5 27 95 90 0367 0422 0476 0531 0586 0640 0695 0749 0804 0859 6 7 32 38 96 0913 0968 1022 1077 1131 1186 1240 1295 1349 1404 8 43 97 1458 1513 1567 1622 1676 1731 1785 1840 1894 1948 9 49 98 2003 2057 2112 2166 2221 2275 2329 2384 2438 2492 99 2547 2601 2655 2710 2764 2818 2873 2927 2981 3036 800 1 2 3 4 5 6 7 8 9 Differences. ._ .- 34 III. LOGARITHMS OF NUMBERS. '"" 800 1 .2 3 4 5 6 7 8 9 Differences. 800 90 3090 3144 3199 3253 3307 3361 3416 3470 3524 3578 01 3633 3687 3741 3795 3849 3904 3958 4012 4066 4120 02 4174 4229 4283 4337 4391 4445 4499 4553 4607 4661 55 03 4716 4770 4824 4878 4932 4986 5040 5094 5148 5202 i 6 04 5256 5310 5364 5418 5472. 5526 5580 5634 5688 5742 2 3 11 17 05 5796 5850 5904 5958 6012 6066 6119 6173 6227 6281 4 22 06 6335 6389 6443 6497 6551 6604 6658 6712 6766 6820 5 6 28 33 07 6874 6927 6981 7035 7089 7143 7196 7250 7304 7358 7 39 08 7411 7465 7519 7573 7626 7680 7734 7787 7841 7895 8 9 44 50 09 7949 8002 8056 8110 8163 8217 8270 8324 8378 8431 810 90 8485 8539 8592 8646 8699 8753 8807 8860 8914 8967 11 9021 9074 9128 9181 9235 9289 9342 9396 9449 9503 12 9556 9610 9663 9716 9770 9823 9877 9930 9984 *0037 54 13 91 0091 0144 0197 0251 0304 0358 0411 0464 0518 0571 1 2 5 11 14 0624 0678 0731 0784 0838 0891 0944 0998 1051 1104 3 4 5 16 22 27 15 1158 1211 1264 1317 1371 1424 1477 1530 1584 1637 16 1690 1743 1797 1850 1903 1956 2009 2063 2116 2169 6 82 17 2222 2275 2328 2381 2435 2488 2541 2594 2647 2700 7 8 88 43 18 2753 2806 2859 2913 2966 3019 3072 3125 3178 3231 9 49 19 3284 3337 3390 3443 3496 3549 3602 3655 3708 3761 820 91 3814 3867 3920 3973 4026 4079 4132 4184 4237 4290 21 4343 4396 4449 4502 4555 4608 4660 4713 4766 4819 53 22 4872 4925 4977 5030 5083 5136 5189 5241 5294 5347 1 5 23 5400 5453 5505 5558 5611 5664 5716 5769 5822 5875 2 8 4 11 16 21 24 5927 5980 6033 6085 6138 6191 6243 6296 6349 6401 25 6454 6507 6559 6612 6664 6717 6770 6822 6875 6927 5 g 27 82 26 6980 7033 7085 7138 7190 7243 7295 7348 7400 7453 7 37 27 7506 7558 7611 7663 7716 7768 7820 7873 7925 7978 8 42 28 8030 8083 8135 8188 8240 8293 8345 8397 8450 8502 9 48 29 8555 8607 8659 8712 8764 8816 8869 8921 8973 9026 830 91 9078 9130 9183 9235 9287 9340 9392 9444 9496 9549 31 9601 9653 9706 9758 9810 9862 9914 9967 ♦0019 *0071 1 2 52 5 10 32 92 0123 0176 0228 0280 0332 0384 0436 0489 0541 0593 33 0645 0697 0749 0801 0853 0906 0958 1010 1062 1114 8 16 34 1166 1218 1270 1322 1374 1426 1478 1530 1582 1634 4 5 21 26 35 1686 1738 1790 1842 1894 1946 1998 2050 2102 2154 6 7 8 81 86 4'J 36 2206 2258 2310 2362 2414 2466 2518 2570 2622 2674 37 2725 2777 2829 2881 2933 2985 3037 3089 3140 3192 9 47 38 3244 3296 3348 3399 3451 3503 3555 3607 3658 3710 39 3762 3814 3865 3917 3969 4021 4072 4124 4176 4228 840 92 4279 4331 4383 4434 4486 4538 4589 4641 4693 17 11 a 41 4796 4848 4899 4951 5003 5054 5106 5157 5209 5261 1 5 42 5312 5364 5415 5467 5518 5570 5621 5673 5725 5776 2 1 10 15 43 5828 5879 5931 5982 6034 6085 6137 6188 6240 6291 4 M 44 6342 6394 6445 6497 6548 6600 6651 6702 6754 6805 5 6 7 M 81 45 6857 6908 6959 7011 7062 7114 7165 7216 7268 7319 46 7370 7422 7473 7521 7576 7627' 7678 7730 7781 7882 8 9 41 4('i 47 7883 7935 7986 8037 8088 8140 8191 8242 8293 8345 48 8396 8447 8498 8549 8601 8652 8703 8754 8805 .8857 49 8908 8959 9010 9061 9112 9163 9215 9266 9317 9368. 850 1 - ,._ 1 2 3 4 5 6 7 8 9 Differences. 1 HI. LOGARITHMS OF NUMBERS. 35 1 850 1 2 3 4 5 6 7 8 9 Differences. 850 92 9419 9470 9521 9572 9623 9674 9725 9776 9827 9879 51 9930 9981 *0032 *0083 *0134 *0185 *0236 *0287 *0338 *0389 52 93 0440 0491 0542 0592 0643 0694 0745 0796 0847 0898 52 53 0949 1000 1051 1102 1153 1204 1254 1305 1356 1407 i 5 54 1458 1509 1560 1610 1661 1712 1763 1814 1865 1915 2 3 10 16 55 1966 2017 2068 2118 2169 2220 2271 2322 2372 2423 4 21 56 2474 2524 2575 2626 2677 2727 2778 2829 2879 2930 5 6 26 31 57 2981 3031 3082 3133 3183 3234 3285 3335 3386 3437 7 36 58 3487 3538 3589 3639 3690 3740 3791 3841 3892 3943 8 9 42 . 47 59 3993 4044 4094 4145 4195 4246 4296 4347 4397 4448 860 93 4498 4549 4599 4650 4700 4751 4801 4852 4902 4953 61 5003 5054 5104 5154 5205 5255 5306 5356 5406 5457 62 5507 5558 5608 5658 5709 5759 5809 5860 5910 5960 1 2 51 5 10 63 6011 6061 6111 6162 6212 6262 6313 6363 6413 6463 64 6514 6564 6614 6665 6715 6765 6815 6865 6916 6966 3 4 5 15 20 26 65 7016 7066 7117 7167 7217 7267 7317 7367 7418 7468 66 7518 7568 7618 7668 7718 7769 7819 7869 7919 7969 6 31 67 8019 8069 8119 8169 8219 8269 8320 8370 8420 8470 7 8 36 41 68 8520 8570 8620 8670 8720 8770 8820 8870 8920 8970 9 46 69 9020 9070 9120 9170 9220 9270 9320 9369 9419 9469 870 93 9519 9569 9619 9669 9719 9769 9819 9869 9918 9968 71 94 0018 0068 0118 0168 0218 0267 0317 0367 0417 0467 50 72 0516 0566 0616 0666 0716 0765 0815 0865 0915 0964 1 5 73 1014 1064 1114 1163 1213 1263 1313 1362 1412 1462 2 3 4 10 15 20 74 1511 1561 1611 1660 1710 1760 1809 1859 1909 1958 75 2008 2058 2107 2157 2207 2256 2306 2355 2405 2455 5 g 25 30 76 2504 2554 2603. 2653 2702 2752 2801 2851 2901 2950 7 35 77 3000 3049 3099 3148 3198 3247 3297 , 3346 3396 3445 8 9 40 45 78 3495 3544 3593 3643 3692 3742 3791 3841 3890 3939 79 3989 4038 4088 4137 4186 4236 4285 4335 4384 4433 880 94 4483 4532 4581 4631 4680 4729 4779 4828 4877 4927 81 4976 5025 5074 5124 5173 5222 5272 5321 5370 5419 49 82 5469 5518 5567 5616 5665 5715 5764 5813 5862 5912 1 2 5 10 83 5961 6010 6059 6108 6157 6207 6256 6305 6354 6403 3 15 84 6452 6501 6551 6600 6649 6698 6747 6796 6845 6894 4 5 20 25 85 6943 6992 7041 7090 7140 7189 7238 7287 7336 7385 6 29 86 7434 7483 7532 7581 7630 7679 7728 7777 7826 7875 7 8 34 39 87 7924 7973 8022 8070 8119 8168 8217 8266 8315 8364 9 44 88 8413 8462 8511 8560 8609 8657 8706 8755 8804 8853 89 8902 8951 8999 9048 9097 9146 9195 9244 9292 9341 • 890 94 9390 9439 9488 9536 9585 9634 9683 9731 9780 9829 48 91 9878 9926 9975 *0024 *0073 *0121 *0170 *0219 *0267 *0316 1 5 92 95 0365 0414 0462 0511 0560 0608 0657 0706 0754 0803 2 3 10 14 93 0851 0900 0949 0997 1046 1095 1143 1192 1240 1289 4 19 94 1338 1386 1435 1483 1532 1580 1629 1677 1726 1775 5 6 7 24 29 34 95 1823 1872 1920 1969 2017 2066 2114 2163 2211 2260 96 2308 2356 2405 2453 2502 2550 2599 2647 2696 2744 8 9 38 43 97 2792 2841 2889 2938 2986 3034 3083 3131 3180 3228 98 3276 3325 3373 3421 3470 3518 3566 3615 3663 3711 99 3760 3808 3856 3905 3953 4001 4049 4098 4146 4194 900 1 2 3 4 5 6 7 8 9 Differences. 36 III. LOGARITHMS OF NUMBERS. 900 1 2 3 4 5 6 7 8 9 Differences. 900 95 4243 4291 4339 4387 4435 4484 4532 4580 4628 4677 01 4725 4773 4821 4869 4918 4966 5014 5062 5110 5158 02 5207 5255 5303 5351 5399 5447 5495 5543 5592 5640 49 03 5688 5736 5784 5832 5880 5928 5976 6024 6072 6120 i 5 04 6168 6216 6265 6313 6361 6409 6457 6505 6553 6601 2 3 10 15 05 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 4 20 06 7128 7176 7224 7272 7320 7368 7416 7464 7512 7559 5 6 25 29 07 7607 7655 7703 7751 7799 7847 7894 7942 7990 8038 7 34 08 8086 8134 8181 8229 8277 8325 8373 8421 8468 8516 8 9 n 09 8564 8612 8659 8707 8755 8803 8850 8898 8946 8994 44 910 95 9041 9089 9137 9185 9232 9280 9328 9375 9423 9471 11 9518 9566 9614 9661 9709 9757 9804 9852 9900 9947 12 9995 *0042 *0090 *0138 *0185 *0233 *0280 *0328 *0376 *0423 48 13 96 0471 0518 0566 0613 0661 0709 0756 0804 0851 0899 1 2 5 10 14 0946 0994 1041 1089 1136 1184 1231 1279 1326 1374 3 4 5 14 19 24 15 1421 1469 1516 1563 1611 1658 1706 1753 1801 1848 16 1895 1943 1990 2038 2085 2132 2180 2227 2275 2322 6 29 17 2369 2417 2464 2511 2559 2606 2653 2701 2748 2795 7 8 34 38* 18 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 9 43 19 3316 3363 3410 3457 3504 3552 3599 3646 3693 3741 920 96 3788 3835 3882 3929 3977 4024 4071 4118 4165 4212 21 4260 4307 4354 4401 4448 4495 4542 459<4 5061 4637 4684 47 22 4731 4778 4825 4872 4919 4966 5013 5108 5155 1 5 23 5202 5249 5296 5343 5390 5437 5484 5531 5578 5625 2 8 4 9 14 19 24 5672 5719 5766 5813 5860 5907 5954 6001 6048 6095 25 6142 6189 6236 6283 6329 6376 6423 6470 6517 6564 5 6 7 24 28 S3 26 6611 6658 6705 6752 6799 6845 6892 6939 6986 7033 27 7080 7127 7173 7220 7267 7314 7361 7408 7454 7501 8 as 28 7548 7595 7642 7688 7735 7782 7829 7875 7922 7969 9 42 29 8016 8062 8109 8156 8203 8249 8296 8343 8390 8436 930 96 8483 8530 8576 8623 8670 8716 8763 8810 8856 8903 31 8950. 8996 9043 9090 9136 9183 9229 9276 9323 9369 46 32 9416 9463 9509 9556 9602 9649 9695 9742 9789 9835 1 2 5 9 33 9882 9928) 9975 *0021 *0068 *0114 *0161 *0207 *0254 *0300 3 14 34- 97 0347 0393 0440 0486 0533 0579 0626 0672 0719 0765 4 5 18 28 35 0812 0858 0904 0951 0997 1044 1090 1137 1183 1229 6 n 36 1276 1322 1369 1415 1461 1508 1554 1601 1647 1693 7 8 a 37 37 1740 1786 1832 1879 1925 1971 2018 2064 2110 2157 1 41 38 2203 2249 2295 2342 2388 2434 2481 2527 2573 2619 39 2666 2712 2758 2804 2851 2897 2943 298.9 3035 3082 940 97 3128 3174 3220 3266 3313 3359 3405 3451 3497 3543 45 41 3590 3636 3682 3728 3774 3820 3866 3913 3959 4005 1 42 4051 4097 4143 4189 4235 4281 4327 4374 4420 4466 2 1 43 4512 4558 4604 4650 4696 4742 4788 4834 4880 4926 9 4 14 18 44 4972 5018 5064 5110 5156 5202 5248 5294 5340 5386 S 45 5432 5478 5524 5570 5616 5662 5707 5753 5799 5845 1 7 n 82 46 5891 5937 5983 6029 6075 6121 6167 6212 6258 6304 8 47 6350 6396 6442 6488 6533 6579 6625 6671 6717 6763 9 41 48 6808 6854 6900 6946 6992 7037 7083 7129 7175 7220 49 7266 7312 7358 T408 7449 7495 7541 7586 7632 7678 950 1 2 3 4 5 6 7 8 9 Differences. III. LOGARITHMS OF NUMBERS. 3T f- — — 950 1 2 3 4 5 6 7 8 9 Differences. 950 97 7724 7769 7815 7861 7906 7952 7998 8043 8089 8135 51 8181 8226 8272 8317 8363 8409 8454 8500 8546 8591 52 8637 8683 8728 8774 8819 8865 8911 8956 9002 9047 53 9093 9138 9184 9230 9275 9321 9366 9412 9457 9503 54 9548 9594 9639 9685 9730 9776 9821 9867 9912 9958 46 55 98 0003 0049 0094 0140 0185 0231 0276 0322 0367 0412 i 2 5 9 56 0458 0503 0549 0594 0640 0685 0730 0776 0821 0867 3 14 57 0912 0957 1003 1048 1093 1139 1184 1229 1275 1320 4 18 58 1366 1411 1456 1501 1547 1592 1637 1683 1728 1773 5 6 23 28 59 1819 1864 1909 1954 2000 2045 2090 2135 2181 2226 7 82 960 98 2271 2316 2362 2407 2452 2497 2543 2588 2633 2678 8 9 37 41 61 2723 2769 2814 2859 2904 2949 2994 3040 3085 3130 62 3175 3220 3265 3310 3356 3401 3446 3491 3536 3581 63 3626 3671 3716 3762 3807 3852 3897 3942 3987 4032 64 4077 4122 4167 4212 4257 4302 4347 4392 4437 4482 65 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 66 4977 5022 5067 5112 5157 5202 5247 5292 5337 5382 1 45 5 67 5426 5471 5516 5561 5606 5651 5696 5741 5786 5830 2 9 68 5875 5920 5965 6010 6055 6100 6144 6189 6234 6279 8 4 5 14 18 23 69 6324 6369 6413 6458 6503 6548 6593 6637 6682 6727 970 98 6772 6817 6861 6906 6951 6996 7040 7085 7130 7175 6 7 27 32 71 7219 7264 7309 7353 7398 7443 7488 7532 7577 7622 8 36 72 7666 7711 7756 7800 7845 7890 7934 7979 8024 8068 9 41 73 8113 8157 8202 8247 8291 8336 8381 8425 8470 8514 74 8559 8604 8648 8693 8737 8782 8826 8871 8916 8960 75 9005 9049 9094 9138 9183 9227 9272 9316 9361 9405 76 9450 9494 9539 9583 9628 9672 9717 9761 9806 9850 77 9895 9939 9983 *0028 *0072 *0117 *0161 *0206 *0250 *0294 44 78 99 0339 0383 0428 0472 0516 0561 0605 0650 0694 0738 1 4 79 0783 0827 0871 0916 0960 1004 1049 1093 1137 1182 2 3 9 13 980 99 1226 1270 1315 1359 1403 1448 1492 1536 1580 1625 4 5 6 18 22 26 81 1669 1713 1758 1802 1846 1890 1935 1979 2023 2067 82 2111 2156 2200 2244 2288 2333 2377 2421 2465 2509 1 31 83 2554 2598 2642 2686 2730 2774 2819 2863 2907 2951 8 9 35 40 84 2995 3039 3083 3127 3172 3216 3260 3304 3348 3392 85 3436 3480 3524 3568 3613 3657 3701 3745 3789 3833 86 3877 3921 3965 4009 4053 4097 4141 4185 4229 4273 87 4317 4361 4405 4449 4493 4537 4581 4625 4669 4713 88 4757 4801 4845 4889 4933 4977 5021 5065 5108 5152 89 5196 5240 5284 5328 5372 5416 5460 5504 5547 5591 1 48 4 990 99 5635 5679 5723 5767 5811 5854 5898 5942 5986 6030 2 3 4 9 13 17 91 6074 6117 6161 6205 6249 6293 6337 6380 6424 6468 92 6512 6555 6599 6643 6687 6731 6774 6818 6862 6906 5 22 93 6949 6993 7037 7080 7124 7168 7212 7255 7299 7343 6 26 94 7386 7430 7474 7517 7561 7605 7648 7692 7736 7779 7 8 30 34 95 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 9 39 96 8259 8303 8347 8390 8434 8477 8521 8564 8608 8652 97 8695 8739 8782 8826 8869 8913 8956 9000 9043 9087 98 9131 9174 9218 9261 9305 9348 9392 9435 9479 9522 "99 9565 9609 9652 9696 9739 9783 9826 9870 9913 9957 999 1 2 3 4 5 6 7 8 9 Differences. 38 IV. MATHEMATICAL CONSTANTS. BERNOULLI'S NUMBERS. These numbers are defined by the equation a)/(e*-l)=ayI 8 /6 I +)=1+E a x'/2 !+E* x*/4 \-\ and found, in succession, by the formula E »n =C 2n'8 E Sn-a — C 2»'* E 2n-4+ • • • + C 2n>* E * TC Sn>8 E a ±:1 S then E 2 =l, E 4 =5, E 6 =61, E 8 =13S5, E lo =50521, E la =27 02765, E 14 =1993 60981, E la =l 93915 12145. r-FUNCTIONS— LOG r p. Euler's constant, y, 0.577215664901532 86061. p 01234 5 6789 1.0 9.99753 518 280 053 9.98834 621 415 215 021 1.1 9.97834 653 478 310 147 9.96990 889 694 554 421 1.2 9.96292 169 052 *940 *S33 9.95732 636 545 459 878 1.8 9.95802 281 165 104 047 9.94995 948 905 868 884 1.4 9.94805 781 761 745 734 727 724 725 731 741 1.5 754 772 794 820 850 884 921 963 *008 *057 1.6 9.95110 167 227 291 359 9.95430 505 583 665 750 1.7 839 931 *027 *126 *229 9.96335 444 556 672 791 1.8 9.96918 *038 *167 *298 *433 9.97571 712 856 *004 *154 1.9 9.98307 463 622 784 949 9.99117 288 462 638 818 HYPERBOLIC FUNCTIONS. * c = l+x + x*/2 !+asV8! + asV4!-HB75! ••• e~ x =l~X + X a /2 !-x 3 /8 ! -\-x*/4 !-a? 6 /5 H sinh x=i («*- e~ x )=x+x 3 /S 1 +a: 8 /5 1 +* 7 /7 H cosha;=J(« a: +e -:c )=l+a;V2!+a;V4!+a; s /6!H tanh x=2 a (2 a -l) B 2 cc/2 !-2«(2«-l) B 4 a: 3 /4 ! -\ cotha:=l/x+2 a B„a;/2 1-2* B 4 a: 3 /4 1 +2 8 B e x"/6 1 secha:=l-E 2 a:V2 l + E 4 a;V4 !-E e a:° 18406 0161 l') a /2!= .0 7 423 07974 9703s (1°) 8 = .0"989669962fl l')» = .0**94618 78910 (l°) 8 /tt!= .0'*89 96881 98674 l') 3 /8!= .0' '4102 29702 (1°) T = .0 ,a 4988S4.V.' 70806 l')« = .0»«7159S6 (1°)V7!= .0»*978S88486 !')*/*'■= .0»»29888 (1°)*= .0 14 8 61061 80890 l')» = .0**908 tl >*/8! = .0»*21 85494 80859 l') 8 /51= .0 ,B 2 (1°)»= .0**160978819 .017453292.") 19913 29577 '1 >" 1»)» « .0*8046174 1078670860 (1°)"= .0»°4 57773 91668 sinl°=- .017469406487984 loffatal*- - S.2US5581S4 sin 1' = - .00029 0SSS2 04563 log sin 1' = - 6.4687961111 sinl"= - .000004848186811 log sin 1" = - 4.68661 IV. CHEMISTRY, ENGINEERING, AND PHYSICS. 39 CHEMISTRY. "Weight of 1 liter of hydrogen in grams, ... - .0896 of 1 liter of air, at sea level, under pressure of 760 mm., lat. 45°, 1.293052 Ratio of atomic weight of gases to specific heat, - - 6.25 Expansion of gases for 1 degree centigrade, - - - .00867 ATOMIC WEIGHTS. Aluminium, Al., 27 Manganese, Mn., 55 Antimony, Sb., 120 Mercury, Hg., 200 Arsenic, As., 75 Molybdenum, Mo., 96 Barium, Ba., 137 Nickel, Ni.. 58.7 Bismuth, Bi., 208.9 Nitrogen, N., 14.03 Boron, B., 11 Oxygen, O., 16 Bromine, Br., 79.95 Phosphorus, P-, 31 Cadmium, Cd., 112 Platinum, Pt., 195 Calcium, Ca., 40 Potassium, K., 39.11 Carbon, C, 12 Selenium, Se., 79 Chlorine, CI., 35.45 Silicon Si., 28.4 Chromium, Cr., 52.1 Silver, Ag., 107.92 Cobalt, Co., 59 Sodium, Na., 23.05 Copper, Cu., 63.4 Strontium, Sr., 87.6 Fluorine, F-, 19 Sulphur, 8., 32.06 Gold, Au. 197.3 Tellurium, Te., 125 Hydrogen, H., 1.007 Tin, Sn., 119 Iodine, L, 126.85 Titanium, Ti., 48 Iron, Fe., 56 Tungsten, W., 184 Lead, Pb., 206.95 Uranium, U., 239.6 Lithium, Li., 7.02 Zinc, Zn., 65.3 Magnesium, Mg. 24.3 Zirconium. Zr., 90.6 ENGINEERING. FRICTION. Let F. R. be the coefficient of friction if the body be at rest, F. M. if in motion, and A the angle of repose. F. R. F. M, A. Clay, dry, - - - . .S8-.65 21-33° wet, --- - .25-.31 14-17 Gravel, .... .70-1.00 35-45 Iron on iron, or brass, .16-.25 .15-.20 [oiled, .05-.08] 9-14 on wood, - - .40-.60 .25-.40 [oiled, .06-.08] 22-31 Masonry, dry, - .60-70 31-35 on clay, - • - .30-.50 17-27 Sand, .58-.S4 30-40 Wood on stone, - .18-.58 10-30 on wood, - -. 25-.50 .25-.50 [oiled, .06- .08] 14-27 MODULUS OP ELASTICITY. Let A be the elongation, p the force in tons, I the original length,/ the cross section in square inches, e the modulus of elasticity ; then \—pl//e. Brass, .... '5500 Iron, steel, - • 12000^13000 wire, - - - 6400 wrought, - 12000-13000 Copper, cast, - - 7000 Lead, .... 1000 wire, hard drawn, 8000 Phosphor-bronze, 6000 Gun metal, - - - 4500-6000 Timber, - - - 600-950 Iron, cast, - - - 5000-6000 Zinc, rolled, - 5500 STRENGTH OP MATERIALS. Let T be the ultimate tenacity in pounds per square inch and L the crushing load, per square inch, for short blocks. T. L. Brick, ordinary, 1500-6000 pressed, 8000-15000 Copper, cast, 18000-25000 9000-12000 rolled, 30000-50000 wire, 45000-60000 Iron, cast, 13000-28000 65000-110000 steel, 55000-175000 60000-175000 wrought, 45000-60000 40000-55000 Rope, hemp, 11000-13000 manilla, 7000-10000 Timber, oak and pine, - - 5000-15000 4000-12000 WEIGHT OP MATERIALS TN POUNDS PER CUBIC FOOT. Aluminium, - - - 160-170 Iron, cast, - - - - 435-455 Brass, 475-525 steel, - - - 485-495 Brick, common, - - 110-130 wrought, - - 475-490 Clay, compact, - - 120-135 Platinum, - - - 1300-1375 Copper, 535-560 Stone, 130-170 Earth, loose, - - - 75-90 Timber, .... 30-65 Glass, 150-180 "Water, pure, at 32° F., 62.42 Gravel and sand, - 90-120 Zinc, 425-450 PHYSICS. DENSITY OF AIR. Let t stand for the temperature centigrade, h for the height of the barometer column expressed in millimeters, M for the mass in grams of one cubic centimeter of air ; then M = .001293/(14-.00367 1) A/760. DENSITY AND VOLUME OP WATER. Let C be the temperature in centigrade degrees ; D, the density ; V, the volume of 1 gram in cubic centimeters ; then : C. D. V. C. D. V. C. D. V. 0° 0.99987 1.00013 13°0.99943 1.00057 25°0.99712 1.00289 1 9993 0007 14 9930 O070 26 9687 0314 2 9997 0003 15 9916 0084 27 9660 0341 3 9999 0001 16 9900 0100 28 9633 0368 4 1.00000 0000 17 9884 0116 29 9605 0396 5 0.9 9999 0001 18 9865 0135 30 9577 0425 6 9997 0003 19 9846 0151 40 9235 0770 7 9993 0007 20 9826 0174 50 8819 1195 8 9989 0011 21 9805 0196 60 8338 1691 9 9982 0018 22 9783 0218 70 7794 2256 10 9975 0025 23 9760 0240 80 7194 2887 11 9965 0034 24 9737 0264 90 6556 3567 12 9955 0045 100 5866 4312 ELECTRICITY. Resistance of 1 mil-ft. of soft copper at 0° C, 9.612 legal ohms, at 15.5° 10.20 legal ohms. Electro-motive force of a Clark cell at 15.5° C, 1.435 volts. Loss by hysteresis for wrought iron, .002B 1-6 ergs per cycle per cubic centimeter. PRACTICAL UNITS EXPRESSED IN C. G. 8. UNITS. Let V be the velocity of light, about 3-10 10 cm. per sec. Electromagnetic. Electrostatic. Practical. C.G.S. C.G.S. Quantity, - - - 1 coulomb. 1/10, V/10 i.e., 310 9 Current, - - - 1 ampere, 1/10, V/10 3-10 9 Potential, - - - 1 volt, 10 8 , 10 8 /V l/(3-10 a ) Resistance, - - 1 ohm, 10 9 , 10 9 /V 2 l/(9-10 11 ) Capacity, - - - 1 farad, 1/10 9 , V710 9 9-10 11 . Self induction, 1 henry, 10 9 . UNITS OP RESISTANCE. Let L be the length of a mercury column, 1 millimeter square, at 0° C, and R the resistance in true ohms. L. R. L. R., True ohm, 106.3 cm. 1.0000 B. A. Unit, 104.9 cm. .9867 Legal ohm, 106.0 .9972 Siemen's unit, 100.0 .9407 ELECTRO-CHEMICAL EQUIVALENTS. Hydrogen, .... .0*1038 gram per coulomb. Copper, (cupric), ... 1.177 grams per ampere per hour. Silver, ....... 4.025 grams per ampere per hour. ELECTRICAL RESISTANCES OF METALS. The values given in this table are made to conform to the value of the specific resistance of copper adopted as the stan- dard by the American Institute of Electrical Engineers at their meeting, September, 1890. [Trans. A. I. E. E., vol. 7, p. 346. Let the specific resistance at 0° C. in C. G. S. units be R ; the resistance at 0° C. in legal ohms of a wire 1 mm. in di- ameter and 1 m. long, R'. If R be the resistance of a wire at 0° C, and o the temperature coefficient ; then the resis- tance at t° C. is found by the formula Rt=R (1 + <*<)• R. R'. a. Aluminium, annealed, 2913 .0371 Antimony, pressed, 35500 .4514 .00389 Bismuth, pressed, 13114 1.6680 .00354 Copper, annealed, 1598 .0203 .003SS hard drawn, 1634 .020S German Silver, 20940 .2662 .00044 Gold, annealed, 2059 .0262 .00365 hard drawn, 2095 .0267 Iron, annealed, 9718 .1235 .004- .005 Lead, pressed, 19636 .2494 .00387 Mercury, 95114 1.2093 00072 Nickel, annealed, 12457 .1584 Platinum, annealed, 9056 .1151 .0014-.0036 Silver, annealed, 1505 .0191 .00377 hard drawn, 1634 .0208 Tin, pressed, 13215 .1680 .00365 Zinc, pressed, 562S .0716 .00365 40 IV. PHYSICS. GRAVITY. Length of the seconds pendulum at height A above sea level : in inches, - - - 89 .012540+ .208268 sin* lat. -3 A/10 7 in feet, 8.251045+.017356 sin" lat.-3 A/10 7 in meters, - - - - 0.990910+ .005290 sin* lat. -3 A/10 7 Acceleration by gravity, per second of mean solar time : in feet, 32.086528+.171293 sin' lat.-3 A/10 8 in meters, - - - - 9.7798S6+.052210 sin* lat.-3 A/10« HEAT. Energy required to heat 1 gram of water from 20° to 21° C, 4.18-10' ergs. to heat 1 kg. of water from 20° to 21° - - 426.4 kg-m. to heat 1 lb. of water from 6S° to 69° F., • 778 ft-lbs. 1 British thermal unit, B. T. U., 0.2521 calories. 1 watt=l joule per second =.239 minor calories per second. Heat of vaporization of water at 100° C, 537 calories per kg. 966.6 B. T. U. per lb. COEFFICIENTS OF EXPANSION. If temperatures be measured in centigrade degrees, lengths at temperature t° are expressed in terms of the lengths at 0° by the formula h=l (l-\-af), and volumes by the formula Vt=V (l+3a*). If the Fahrenheit scale be used, these formulae become h = l 31 [l + a'(«-32)], Vt=V 32 [1 +3a' (<-82)]. Aluminium, - - Bismuth, - - - Brass, - - - - Brick, - - - - Cadmium, - - - Carbon, gas coke, graphite, - Gopper, - - - - Glass, - - - - Gold, Iron, cast, - • - wrought, Lead, - - - Magnesium, Nickel, - - Platinum, - Silver, - - Stone, - - Tin, - - - Wood, - - Zinc, - - - .0*231- 132 1S4 054 307 054 079 167 070 144 117 110 108 280 269 128 088 192 045 .0*235 133 191 090 816 055 172 092 147 144 122 117 312 276 091 194 117 .0*128- .0*130 073 074 036 063 290 298 102 030 170 030 044 093 039 080 065 061 060 155 149 071 049 107 025 125 020 160 106 050 175 031 106 051 081 080 068 065 160 153 051 108 065 160 035 165 CONDUCTIVITIES FOR HEAT. Let the thickness of a plate of any substance be p centime- ters, the area of one face A square centimeters, the tempera- tures of the two faces 1 °, 9 2 ° C, and Q the quantity of heat in minor calories that flows through the plate in t seconds ; then: Q = K • A-t-(0 1 -9 1 )/p. K. K. Brass, .... .302 Ice, 0057 Copper, .... 1.108 Iron, .164 Fire-brick, - - - .00174 Parafflne, - - - .00014 German silver, - .109 Water, .... .0014 Glass; - - - .0005-.002 Zinc .807 HEATS OF FUSION. Cal. B.T.U. per kg. per lb. * Bismuth, Cadmium, Ice, - - Lead, Mercury, 12.6 13.6 5.4 2.82 22.7 24.5 144 9.7 5.08 Nickel, - Platinum, Silver, - Tin, - - Zinc, - - Cal. B.T.U. per kg. per lb. - 4.6 8.3 • 27.2 - 24.7 - 14.6 - 28.1 49 44.5 26.8 60.6 MELTING POINTS. C. F. Aluminium, about 600° 1100' Bismuth, - - - 260 500 Cadmium, - - - 815 600 Copper, .... 1054 1980 Gold, - - Ice, - - - Iridium, - - - 1950 8540 Iron, pig, about 1075 1970 Iron, cast stee Lead, Mercury, Nickel, - 1045 1910 Parafflne, 82 Platinum, Silver, - Tin, - - pure, about 1600 2900 Zinc, C. F. - 1870° 2500° - 826 620 . _40 -40 - 1450 2640 - 54 129 - 1775 8280 • 954 1750 - 280 446 - 412 774 Aluminium, 15-97' Bismuth, - 20-48 Brass, - - 14-98 Cadmium, - 0-100 Carbon, charcoal, 20 diamond, 20 graphite, 20 Copper, - - 15-100 Gold, - Ice, - - Iron, pure, SPECIFIC HEATS. C, .212 Iron, steel, ord. tern., .116-.119 .0805 wrought, ord. temp., .108 .086 Lead, - - 19-48° C, .0315 0-100 -20-0 0-100 .055 Magnesium, 20-60 .245 .164 Mercury, - 5-86 .083 .121 Nickel, - 14-97 .109 .167 Platinum, - 0-100 .032 .093 Silver, - - 0-100 .056 .032 Steam, at constant press., .478 .504 Tin, - - 0-100° C, .056 .118 Zinc, - - 0-100 .0985 LIGHT. Units of Light : one candle power, British, is the light from a spermaceti candle burning 120 grains an hour ; 1 carcel is 9J candles, nearly, and the unit of light of 1S90 (bougie deci- male) is a twentieth of 2.08carcels, and nearly 1 candle power. Velocity of Light : in miles per second, • • 1S6887±50 in kilometers per second., 299878±80 INDEX OF REFRACTION FOR THE D LINE. Alcohol at 15° C. 1.3638 Diamond, - - Benzine, 15 1.5002 Fluorite, - - Carbon, disul., 15 1.6308 Glass, - - - • Chloroform, 10 1.4490 Rock salt, - - • Ether, 15 1.3566 Sylvine, - - - Water, 15 1.3833 Canada Balsam, 2.4'V.'- 1.4339 1.5-1.8 1.5442 1.4903 1.5-2? ROWLAND'S VALUES FOR WAVE LENGTHS OF FRAUNHOFER'S LINES. B, 6827.46; C, 6563.06; D„ 5896.16; D„ 5890.19 ; E lt 5270.56; E„, 5269.72; b t , 51S3.79; b t , 5172 .86 ; 6 3 , 5169.16; b t , 5167.58; F, 4861.58; G, 4293.25. SOUND. Velocity of sound in feet, and in meters, per second : Feet. Meters. Feet. Meters. InairatO°C. 1084.84 830.7 In lead, - 3937 1200 copper, - 12303 3750 water, at 8° 4703 1435 glass, - 17060 5200 steel wire. - 15700 48N For temperatures other than 0° C, the velocity of sound in air is expressed by the formula V= 830.7 y (1+ .0037 1). SPECIFIC GRAVITIES. Aluminium, pure, 2.583 Iron, steel, - - - 7.60-7.S0 commercial, - 2.7-2.S wrought, - - 7.79-7.S5 Bismuth, - - - - 9.76-9.93 Lead, .... ll.21-ll.4r. Cadmium, - - - 8.54-8.69 Magnesium, - - 1.09-1.75 Carbon, charcoal, - 1.45-1.70 Mercury at 0° C, - 13.590 diamond, - - 3.49-3.53 Nickel, - - - - B.t gas coke, - - 1.88 Platinum, cast, 21.4S-21.50 graphite, - - 2.17-2.32 wire and foil, - 21. 2-21. 7 Copper, cast, - - 8.S8-S.92 Silver, - - - - 10.42-10.57 electrolytic, - 8.88-8.95 Sulphur, amorphous, 1.92 wire, - - - - 8.93-8.95 monoelinic, - 1.96 Gold, --- - 19.30-19.34 rhombic, - 2.07 Iron, cast, - - - 7.03-7.78 Tin, 6.97-7.87 pure, .... 7.85-7.88 Zinc, 6.MJ-7.24 THERMOMETER SCALES. Let C be the temperature in centigrade degrees and F in Fahrenheit degrees, then C = 5(F-82)/9, F = 82+9C/5; and for interpolation 1° C = 1.8° F, 1° F = 56° C. C. F. C. F. C. F. C. F. C. F. 200 892 150 802 100 212 50 122 82 195 8S3 145 298 95 203 45 118 - 5 28 190 874 140 2S4 90 194 40 104 -10 14 185 865 185 275 85 185 35 95 -15 5 180 856 180 266 80 176 80 86 -M - 4 175 847 125 257 75 167 25 77 -25 -13 170 888 120 248 70 158 20 68 -80 -22 165 829 115 289 65 149 15 59 -85 -81 160 820 110 280 60 140 10 50 -40 -40 155 811 105 221 55 181 5 41 -45 -49 UNITS OF FORCE, POWER, PRESSURE, AND WEIGHT. Dynes in the weight of 1 gram, lat. 45°, .... 980.6 in the weight of 1 pound avoirdupois, ... 4447W Foot-pounds per minute in 1 horse-power, - . - 88000 in 1 kilogram-meter per minute, 7.2880 Grains par cubic inch in 1 1:1:1111 per cubic centimeter, 252.39 Grams per square centimeter in 1 pound per square inch, 70.807 Pounds per cubic foot in 1 kilogram per cubic meter, .062428 Watts in 1 horse-power, Mi IV. WEIGHTS AND MEASURES. 41 MEASURES OF LENGTH. Num. Centimeters in 1 inch, 2.54001 Chains in 1 meter, 1/20, .049710 in 1 mile, 80 Feet in 1 chain, --.....-. 66 in 1 meter, 13/4, 3.28083 in 1 mile, 5280 in 1 nautical mile, 6080.26 Inches in 1 link, 7.92 in 1 meter, 39.37 Kilometers in 1 mile, .... 8/5, 1.60935 in 1 nautical mile, ....... 1.85327 Meters in 1 chain, 20.1168 in 1 foot, 4/13, .304801 in 1 yard, 12/13, .914402 Miles in 1 kilometer, .... 5/8, .621370 Yards in 1 meter, - - - - 13/12, 1.09361 in 1 mile, 1760 MEASURES OF AREA. l Acres in 1 hectar, 5/2, 2.47104 in 1 square mile, ....... 640 Ars in 1 acre, .......... 40.4687 Square centimeters in 1 square inch, - • 6.45163 Square feet in 1 square chain, .... 4356 in 1 square meter, ....... 10.7639 Hectars in 1 square mile, ...... 259.000 Square inches in 1 square meter, ... 1550.00 Square meters in 1 square foot, • 1/11, .092903 in 1 square yard, 5/6, .836131 Square yards in 1 acre, ----... 4840 in 1 square meter, ----- 6/5, 1.19599 MEASURES OF VOLUME. Cubic centimeters in 1 cubic inch, - - - 16.3872 Cubic feet in 1 cubic meter, ..... 35.3145 Cubic meters in 1 cubic yard, • • 3/4, .764559 Cubic yards in 1 cubic meter, ... 4/3, 1.30794 MEASURES OF CAPACITY. Bushels imperial in 1 liter, • - • .027510 United States in 1 liter, .028377 Gallons imperial in 1 liter, .220083 United States in 1 liter, ..... .264170 Cubic inches in 1 bushel imperial, ... 2218.19 in 1 bushel United States, .... 2150.42 in 1 gallon imperial, 277.274 in 1 gallon United States, .... 231 in 1 liter, 61.0234 Liters in 1 bushel imperial, 86.3499 in 1 bushel United States, .... 85.2393 in 1 gallon imperial, ...... 4.54873 in 1 gallon United States, ... - 8.78543 in 1 cubic inch, .016887 WEIGHTS. Grains in 1 gram, ......... 15.4324 Grams in 1 grain, ---....-. .064799 in 1 ounce avoirdupois, ..... 28.3495 in 1 ounce Troy, 31.1035 Kilograms in 1 pound avoirdupois, 5/11, .458592 in 1 pound Troy, 8/8, .373242 Ounces avoirdupois in 1 gram, .... .03527 in lVrnnce Troy, 11/10, 1.09714 Troy in 1 ounce avoirdupois, 10/11, .911458 Pounds avoirdupois in 1 kilogram, 11/5, 2.20462 in 1 pound Troy, 5/6, .822357 Pounds Troy in 1 kilogram, - - - 8/3, . 2.67923 in 1 pound avoirdupois, - - . 6/5, 1.21528 COMPOUND UNITS. Centimeter-seconds in 1 foot-second, • - 30.4801 in 1 kilometer-hour, 27.7778 in 1 mile-hour, • • 44.7041 Foot-pounds in 1 kilogram-meter, - - • 7.23800 Foot-seconds in 1 centimeter-second, - • .032808 Kilogram-meters in 1 foot-pound, - • • .138255 Kilometer-hours in 1 centimeter-second, • .036000 in 1 mile-hour, 1.60935 Mile-hours in 1 centimeter-second- - - - .022869 in 1 kilometer-hour, .621370 Loo. .404885 8.6964 40 1.9080 90 1.819544 .5159 84 3.7226 34 3.7839 22 .8987 25 1.5951 65 .2066 50 .2679 39 1.3035 60 9.4840 16 9.9611 37 9.7983 50 .0388 63 3.245513 .3928 80 2.8061 80 1.6071 20 .8096 69 3.6390 88 1.0319 68 2.4133 00 3.190331 8.9680 82 9.9222 74 8.684845 .0777 26 1.2145 04 1.5479 53 9.883411 .1165 89 8.4394 97 8.4529 73 9.8425 87 9.4218 84 3.3459 99 3.832523 2.4429 09 2.3636 12 1.7854 96 1.560503 1.5470 27 .657413 .5781 16 8.214504 1.188432 8.8115 68 1.452546 1.4928 09 9.6566 66 9.5719 90 8.547454 .0402 63 9.9597 37 .348334 9.9153 24 .4280 10 .0846 76 1.4840 16 1.4436 97 1.6503 47 .8593 18 8.5159 84 9.1406 82 8.5563 03 .2066 50 8.349653 9.7933 50 Inches Cm. inl inl cm. inch. .39870 2.5400 .78740 5.0800 1.1811 7.6200 1.5748 10.160 1.9685 12.700 2.3622 15.240 2.7559 17.780 3.1496 20.320 3.5433 22.860 MEASURES OF LENGTH. Feet Meters Yards Meters Miles inl meter. 3.2808 inl foot. inl meter. in 1 in 1 yard, kilom. 91440 .62137 .30480 l.i 6.5617 .60960 2.1872 1.8288 1.2427 9.8425 .91440 3.2808 2.7482 1.8641 13.123 1.2192 4.3744 3.6576 2.4855 16.404 1.5240 5.4681 4.5720 8.1068 19.685 1.8283 6.5617 5.4864 3.7282 22.966 2.1336 7.6553 6.4008 4.8496 26.247 2.4384 8.7489 7.3152 4.9710 29.528 2.7432 9.8425 8.2296 5.5923 Sq. in. inl sq. cm. .15500 .31000 ..46500 ,62000 .77500 .93000 1.0850 1.2400 1.3950 Sq.cm. inl sq. in. 6.4516 12.903 19.355 25.807 32.258 38.710 45.161 51.613 58.065 MEASURES Sq.ft. Sq.m. inl inl sq. m. sq. ft. 10.764 .09290 21.528 .18581 32.292 .27871 43.055 .37161 53.819 .46452 64.583 .55742 75.347 .65032 86.111 .74323 96.875 .83613 OF AREA. Sq.yds. inl sq.m. 1.1960 2.3920 3.5880 4.7839 5.9799 7.1759 8.3719 9.5679 10.764 Sq. m. inl sq. yd. 1.6723 2.50S4 3.3445 4.1S07 5.0168 5.8529 6.6890 7.5252 Acres inl hectar. 2.4710 4.9421 7.4131 9.8842 12.355 14.826 17.297 19.768 22.289 Kilom inl mile. 1.6093 8.2187 4.8280 6.4374 8.0467 9.6561 11.265 12.875 14.484 Hectar inl acre. .40469 .80937 1.2141 1.6187 2.0234 2.4281 2.8328 3.2375 3.6422 MEASURES OF VOLUME. Cu. in. Cu. cm. Cu. ft. Cu. m. inl inl inl inl cu.cm. cu. in. cu. m. cu. ft. 1 .06102 16.387 35.314 .02832 2 .12205 32.774 70.629 .05663 8 .18307 49.161 105.94 .08495 4 .24409 65.549 141.26 .11327 5 .30512 81.936 176.57 .14159 e .36614 98.323 211.89 .16990 7 .42716 114.71 247.20 .19822 8 .48819 131.10 2S2.52 .22654 y .54921 147.48 317.83 .25485 MEASURES OF Flu. oz. Cu.cm. U.S. Liters inl inl gals, in inl cu.cm. flu. oz. Hit. U.S.gal l .03331 29.574 .26417 3.7854 2 .06763 59.147 .52834 7.5709 3 .10144 88.721 .79251 11.356 4 .13526 118.29 1.0567 15.142 5 .16907 147.87 1.3209 18.927 6 .20288 177.44 1.5850 22.713 7 .23670 207.02 1.8492 26.498 8 .27051 236.59 2.1134 30.288 9 .30432 266.16 2.3775 34.069 nl cu. m. 1.3079 2.6159 3.9238 5.2318 6.5397 7.S477 9.1556 10.464 11.771 Cu. m. inl cu. yd. .76456 1.5291 2.2937 3.0582 3.8228 4.5874 5.3519 6.1165 6.8810 CAPACITY. Imp. Liters gals, in in 1 1 lit. imp.gal. .22008 4.5487 .44017 9.0875 .66025 13.631 18.175 1.1004 22.719 1.3205 27.262 1.5406 31.806 1.7607 36.850 1.9807 40.S94 U.S. H.lits. bu. in in 1 lh.lit.U.S.bu. 2.8377 .35239 5.6755 .70479 8.5132 1.0572 11.851 1.4096 14.189 1.7620 17.026 2.1144 19.864 2.4667 22.702 2.8191 25.540 3.1715 Grains inl gram. 15.432 30.865 46.297 61.729 77.162 6 92.594 7 108.03 8 123.46 9 138.89 Ft-lbs. inl kg-m. 1 7.2330 2 14.466 3 21.699 4 28.932 5 36.165 6 43.398 7 50.631 8 57.864 9 65.097 Grams inl grain. .06480 .12960 .19440 .25920 .32899 .38878 .45359 .51839 .58319 WEIGHTS. Oz. Grams Oz. av. Troy in in 1 inl lgm. oz.tr. gram. .03215 81.103 .03527 .06430 62.207 .07055 .09645 93.310 .10582 .12860 124.41 .14110 .16075 155.52 .17637 .19290 186.62 .21164 .22506 217.72 .24692 .25721 248.83 .28219 .28986 279.93 .31747 Grams inl oz. av. 28.350 56.699 85.049 113.40 141.75 170.10 198.45 226.80 255.15 Lb.av. inl kilog. 2.2046 4.4092 6.6139 8.8185 11.023 13.228 15.432 17.637 19.842 Kilog. inl lb. av. .45359 .90718 1.3608 1.8144 2.2680 2.7216 3.1751 3.6287 4.0S23 COMPOUND UNITS. Kg-m. Cm- Ft-secs. Cm- Mi-hrs in 1 sees, in in 1 sees, in in 1 ft-lb. 1 ft-sec. cm -sec. 1 mi-hr. cm-sec .13826 30.480 .03281 44.704 .02237 .27651 60.960 .06562 89.408 .04474 .41477 91.440 .09842 134.11 .06711 .55302 121.92 .13128 178.82 .0894S .69128 152.40 .16404 228.52 .11185 .S2953 1S2.S8 .196S5 268.22 .13422 .96779 213.36 .22966 312.93 .15659 1.1060 243.84 .26247 357.63 .17895 1.2443 274.32 .2952S 402.34 .20132 Mi-hrs Km-hrs inl inl . km-hr. mi-hr. .62137 1.6093 1.2427 8.2187 1.8641 4.8280 2.4855 6.4374 3.1068 8.0467 3.7282 9.6561 4.3496 11.265 4.9710 12.875 5.5923 14.484 42 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 4 5 6 7 8 9 , l Differences. 4. 0.00 0000 0001 0001 0001 0001 0001 0002 0002 0003 0003 5.0 0.00 0004 0004 0005 0005 0005 0005 0005 0005 0005 0005 5.1 0005 0006 0006 0006 0006 0006 0006 0006 0007 0007 5.2 0007 0007 0007 0007 0008 0008 0008 0008 0008 0008 5.3 0009 0009 0009 0009 0010 0010 0010 0010 0010 0011 5.4 0011 0011 0011 0012 0012 0012 0013 0013 0013 0013 5.5 0014 0014 0014 0015 0015 0015 0016 0016 0017 0017 5.6 0017 0018 0018 0019 0019 0019 0020 0020 0021 0021 i 5.7 0022 0022 0023 0023 0024 0024 0025 0026 0026 0027 1 5.8 0027 0028 0029 0029 0030 0031 0031 0032 0033 0034 2 5.9 0034 0035 0036 0037 0038 0039 0040 0041 0041 0042 3 4 6.0 0.00 0043 0044 0045 0047 0048 0049 0050 0051 0052 0053 5 1 6.1 0055 0056 0057 0059 0060 0061 0063 0064 0066 0067 6 1 7 1 8 1 6.2 0069 0070 0072 0074 0075 0077 0079 0081 0083 0085 6.3 0087 0089 0091 0093 0095 0097 0099 0102 0104 0107 9 1 6.4 0109 0112 0114 0117 0120 0122 0125 0128 0131 0134 6.5 0137 0141 0144 0147 0151 0154 0158 0161 0165 0169 6.6 0173 0177 0181 0185 0190 0194 0198 0203 0208 0213 6.7 0218 0223 0228 0233 0239 0244 0250 0256 0262 0268 6.8 0274 0280 0287 0294 0300 0307 0315 0322 0329 0337 6.9 0345 0353 0361 0369 0378 0387 0396 0405 0415 0424 7.0 0.00 0434 0444 0455 0465 0476 0487 0498 0510 0522 0534 7.1 0546 0559 0572 0585 0599 0613 0627 0642 0657 0672 7.20 0.00 0688 0689 0691 0693 0694 0696 0697- 0699 0701 0702 2 1 2 21 0704 0705 0707 0709 0710 0712 0714 0715 0717 0718 22 0720 0722 0723 0725 0727 0728 0730 0732 0734 0735 3 1 23 0737 0739 0740 0742 0744 0745 0747 0749 0751 0753 4 1 24 0754 0756 0758 0759 0761 0763 0765 0766 0768 0770 5 1 6 1 25 0772 0773 0775 0777 0779 0781 0782 0784 0786 0788 7 1 26 0790 0791 0793 0795 0797 0799 0801 0802 0804 0806 8 2 9 2 27 0808 0810 0812 0814 0815 0817 0819 0821 0823 0825 28 0827 0829 0831 0832 0834 0836 0838 0840 0842 0844 29 0846 0848 0850 0852 0854 0856 0858 0860 0862 0864 7.30 0.00 0866 0868 0870 0872 0874 0876 0878 0880 0882 0884 31 0886 0888 0890 0892 0894 0896 0898 0900 0902 0904 32 0906 0909 0911 0913 0915 0917 0919 0921 0923 0925 33 0928 0930 0932 0934 0936 0938 0940 0943 0945 0947 34 0949 0951 0953 0956 0958 0960 0962 0964 0967 0969 35 0971 0973 0976 0978 0980 0982 0985 0987 0989 0991 8 36 0994 0996 0998 1001 1003 1005 1008 1010 1012 1015 1 2 1 8 1 37 1017 1019 1022 1024 1026 1029 1031 1033 1036 1038 38 1041 1043 1045 1048 1050 1053 1055 1057 1060 1062 4 1 39 1065 1067 1070 1072 1075 1077 1080 1082 1085 1087 5 2 7.40 0.00 1090 1092 1095 1097 1100 1102 1105 1107 1110 1112. 6 2 7 2 41 1115 1117 1120 1123 1125 1128 1130 1133 1136 1138 8 2 42 1141 1143 1146 1149 1151 1154 1157 1159 1162 1165 9 3 43 1167 1170 1173 1175 1178 1181 1184 1186 1189 1192 44 1195 1197 1200 1203 1206 1208 1211 1214 1217 1219 45 1222 1225 1228 1231 1234 1236 1239 1242 1245 1248 46 1251 1254 1256 1259 1262 1265 1268 1271 1274 1277 47 1280 1283 1286 1289 1292 1295 1298 1301 1304 1307 48 1310 1313 1316 1319 1322 1325 1328 1331 1334 1337 49 1340 1343 1346 1349 1352 1356 1359 1362 1365 1368 A = log b - log a, loga + B = log (a + *). B = log a-log b, log/H -A = log (>-£). V. ADDITION-SUBTRACTION LOGARITHMS. 43 A B 1 2 3 4 5 6 7 8 9 Differences. 7.50 0.00 1371 1374 1378 1381 1384 1387 1390 1393 1397 1400 51 1403 1406 1410 1413 1416 1419 1423 1426 1429 1432 52 1436 1439 1442 1446 1449 1452 1456 1459 1462 1466 3 4 53 1469 1472 1476 1479 1483 1486 1489 1493 1496 1500 i 54 1503 1507 1510 1514 1517 1521 1524 1528 1531 1535 2 3 1 1 1 1 55 1538 1542 1545 1549 1552 1556 1560 1563 1567 1570 4 1 2 56 1574 1578 1581 1585 1589 1592 1596 1600 1603 1607 5 6 7 2 2 2 2 2 3 57 1611 1614 1618 1622 1625 1629 1633 1637 1640 1644 58 1648 1652 1656 1659 1663 1667 1671 1675 1679 1682 8 2 3 59 1686 1690 1694 1698 1702 1706 1710 1714 1718 1722 9 8 4 7.60 0.00 1726 1729 1733 1737 1741 1745 1749 1754 1758 1762 61 1766 1770 1774 1778 1782 1786 1790 1794 1798 1803 62 1807 1811 1815 1819 1823 1828 1832 1836 1840 1844 5 6 63 1849 1853 1857 1861 1866 1870 1874 1879 1883 1887 1 2 1 1 1 1 64 1892 1896 1900 1905 1909 1913 1918 1922 1927 1931 8 2 2 65 1936 1940 1945 1949 1953 1958 1962 1967 1972 1976 4 5 2 3 2 8 66 1981 1985 1990 1994 1999 2003 2008 2013 2017 2022 6 3 4 67 2027 2031 2036 2041 2045 2050 2055 2059 2064 2069 7 g 4 4 4 5 68 2074 2078 2083 2088 2093 2098 2102 2107 2112 2117 9 5 5 69 2122 2127 2132 2137 2141 2146 2151 2156 2161 2166 7.70 0.00 2171 2176 2181 2186 2191 2196 2201 2206 2211 2217 71 2222 2227 2232 2237 2242 2247 2252 2258 2263 2268 7 1 8 1 72 2273 2278 2284 2289 2294 2300 2305 2310 2315 2321 1 73 2326 2331 2337 2342 2348 2353 2358 2364 2369 2375 2 1 2 74 2380 2386 2391 2397 2402 2408 2413 2419 2424 2430 3 4 2 3 2 3 75 2435 2441 2447 2452 2458 2463 2469 2475 2481 2486 5 6 7 4 4 5 4 5 6 76 2492 2498 2503 2509 2515 2521 2527 2532 2538 2544 77 2550 2556 2562 2567 2573 2579 2585 2591 2597 2603 8 6 6 78 2609 2615 2621 2627 2633 2639 2645 2651 2657 2663 9 6 7 79 2670 2676 2682 2688 2694 2700 2707 2713 2719 2725 7.80 0.00 2732 2738 2744 2750 2757 2763' 2769 2776 2782 2789 81 2795 2801 2808 2814 2821 2827 2834 2840 2847 2853 9 82 2860 2866 2873 2880 2886 2893 2900 2906 2913 2920 1 2 1 2 83 2926 2933 2940 2947 2953 2960 2967 2974 2981 2987 3 3 84 2994 3001 3008 3015 3022 3029 3036 3043 3050 3057 4 5 6 4 5 5 85 3064 3071 3078 3085 3092 3099 3106 3113 3120 3128 86 3135 3142 3149 3156 3164 3171 3178 3186 3193 3200 7 8 9 6 7 8 87 3208 3215 3222 3230 3237 3245 3252 3260 3267 3275 88 3282 3290 3297 3305 3312 3320 3328 3335 3343 3350 89 3358 3366 3374 3381 3389 3397 3405 3413 3420 3428 7.90 0.00 3436 3444 3452 3460 3468 3476 3484 3492 3500 3508 10 1 91 3516 3524 3532 3540 3548 3556 3565 3573 3581 3589 1 92 3597 3606 3614 3622 3631 3639 3647 3656 3664 3672 2 2 93 3681 3689 3698 3706 3715 3723 3732 3740 3749 3758 3 4 3 4 94 3766 3775 3783 3792 3801 3810 3818 3827 3836 3845 5 5 95 3854 3862 3871 3880 3889 3898 3907 3916 3925 3934 6 7 6 7 96 3943 3952 3961 3970 3979 3988 3997 4007 4016 4025 8 8 97 4034 4044 4053 4062 4071 4081 4090 4100 4109 4118 9 9 98 4128 4137 4147 4156 4166 4175 4185 4195 4204 4214 99 4223 4233 4243 4253 4262 4272 4282 4292 4302 4311 A = log£-log«, log a + B = log (a + b). B = log a — log£ log/H -Azzlog (a- by, , 44 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 4 5 6 7 8 9 Differences. 8.00 0.00 4321 4331 4341 4351 4361 4371 4381 4391 4401 4411 10 11 12 18 14 01 4422 4432 4442 4452 4462 4472 4483 4493 4503 4514 i 2 1 2 1 2 1 2 1 1 3 3 4 4 02 4524 4534 4545 4555 4566 4576 4587 4597 4608 4618 3 1 8 4 03 4629 4639 4650 4661 4671 4682 4693 4704 4714 4725 4 4 4 5 5 6 04 4736 4747 4758 4769 4780 4791 4802 4813 4824 4835 5 6 5 6 6 7 6 7 7 7 8 8 05 06 4846 4958 4857 4969 4868 4981 4879 4992 4890 5004 4902 5015 4913 5027 4924 5038 4935 5050 4947 5061 7 8 9 7 8 9 8 9 10 8 U 11 9 10 10 11 12 13 07 5073 5084 5096 5108 5119 5131 5143 5155 5167 5178 15 Lfl 17 18 19 08 5190 5202 5214 5226 5238 5250 5262 5274 5286 5298 1 2 2 2 2 2 09 5310 5323 5335 5347 5359 5372 5384 5396 5409 5421 2 8 8 5 I 5 3 5 4 4 5 6 8.10 0.00 5433 5446 5458 5471 5483 5496 5508 5521 5534 5546 4 6 6 7 7 8 11 5559 5572 5585 5597 5610 5623 5636 5649 5662 5675 B 6 8 9 8 10 9 10 9 10 11 11 12 5688 5701 5714 5727 5740 5753 5766 5780 5793 5806 7 11 11 19 13 18 13 14 5819 5954 5833 5968 5846 5981 5859 5995 5873 6009 5886 6022 5900 6036 5913 6050 5927 6064 5940 6078 8 9 19 14 20 13 11 n 14 18 88 14 15 16 17 28 24 15 6092 6106 6120 6134 6148 6162 6176 6190 6204 6218 1 2 2 2 2 2 16 6233 6247 6261 6275 6290 6304 6319 6333 6348 6362 2 3 4 6 4 6 4 7 5 5 7 7 17 6377 6391 6406 6421 6435 6450 6465 6479 6494 6509 4 8 8 9 9 10 18 6524 6539 6554 6569 6584 6599 6614 6629 6644 6660 5 10 11 11 12 12 19 6675 6690 6705 6721 6736 6752 6767 6782 6798 6814 6 7 12 14 18 15 18 LB 14 14 16 17 8.20 0.00 6829 6845 6860 6876 6892 6908 6923 6939 6955 6971 8 9 lfl is 17 18 18 88 18 19 21 22 21 6987 7003 7019 7035 7051 7067 7083 7100 7116 7132 25 8 88 8 •27 8 28 29 8 3 22 7148 7165 7181 7197 7214 7230 7247 7264 7280 7297 1 23 7313 7330 7347 7364 7381 7397 7414 7431 7448 7465 2 B 5 B 6 6 24 7482 7499 7517 7534 7551 7568' 7586 7603 7620 7638 8 4 8 10 8 10 8 11 8 9 11 12 25 7655 7673 7690 7708 7725 7743 7761 7778 7796 7814 5 6 7 u 15 18 18 lfl 18 14 lfl u 14 15 17 17 20 20 26 7832 7850 7868 7886 7904 7922 7940 7958 7976 7994 27 8013 8031 8049 8068 8086 8104 8123 8142 8160 8179 8 20 21 22 22 23 28 8197 8216 8235 8254 8273 8291 8310 8329 8348 8367 9 23 88 24 25 26 29 8387 8406 8425 8444 8463 8483 8502 8522 8541 8560 1 30 3 31 3 32 8 33 34 3 3 8.30 0.00 8580 8600 8619 8639 8659 8678 8698 8718 8738 8758 •> 6 9 6 6 10 7 7 10 10 18 14 31 8778 8798 8818 8838 8858 8878 8899 8919 8939 8960 4 u lfl 18 32 8980 9001 9021 9042 9062 9083 9104 9125 9145 9166 5 15 It) Lfl 17 17 33 9187 9208 9229 9250 9271 9292 9314 9335 9356 9378 6 7 8 18 .1 in 22 lfl 22 20 20 BB 24 M 27 34 9399 9420 9442 9463 9485 9507 9528 9550 9572 9594 M BB 88 35 9615 9637 9659 9681 9703 9726 9748 9770 9792 9814 9 27 88 29 80 81 36 9837 9859 9882 9904 9927 9949 9972 9995 *0018 *0040 1 85 4 86 4 81 4 38 89 4 4 37 0.01 0063 0086 0109 0132 0155 0179 0202 0225 0248 0272 2 7 7 7 8 8 38 39 0295 0532 0318 0556 0342 0580 0366 0604 0389 0628 0413 0652 0437 0677 0460 0701 0484 0725 0508 0750 8 4 5 11 11 18 11 14 18 11 IB LB 11 12 15 16 19 20 8.40 0.010774 0799 0823 0848 0873 0897 0822 0947 0972 0997 6 1 21 BB 88 BB 22 98 28 23 27 27 41 1022 1047 1072 1097 1123 1148 1173 1199 1224 1250 8 28 29 88 30 81 42 1275 1301 1327 1353 1378 1404 1430 1456 1482 1508 9 M 89 88 84 85 43 1535 1561 1587 1614 1640 1666 1693 1720 1746 1773 40 41 12 48 44 44 1800 1827 1853 1880 1907 1934 1962 1989 2016 2043 1 2 4 S 4 8 4 8 4 4 9 9 45 2071 2098 2126 2153 2181 2209 2236 2264 229'2 2320 3 4 5 lfl LB 86 Lfl 16 81 18 17 18 18 17 18 22 22 46 2348 2376 2404 2432 2461 2489 2517 2546 2574 2603 21 47 2631 2660 2689 2718 2747 2776 2805 2834 2863 2892 M 25 BB 26 26 48 2921 2951 2980 3010 3039 3069 3098 3128 3158 3188 7 g 2> 29 80 81 34 85 49 3218 3248 3278 3308 3338 3369 3399 3429 3460 3490 9 88 81 88 89 40 A = log b- log a, loga + B = log (a + *). B = loga- og£, log^H -Az = log( a - -b). V. ADDITION-SUBTRACTION" LOGARITHMS. 45 A B 1 2 3 4 5 6 7 8 9 Differences. 8.50 0.01 3521 3552 3582 3613 3644 3675 3706 3737 3768 3800 45 48 47 48 49 51 3831 3862 3894 3925 3957 3989 4020 4052 4084 4116 1 5 2 9 5 9 5 5 5 9 10 10 52 4148 4180 4212 4244 4277 4309 4341 4374 4407 4439 3 14 14 14 14 16 53 4472 4505 4538 4571 4604 4637 4670 4703 4737 4770 4 18 18 19 19 20 54 4803 4837 4871 4904 4938 4972 5006 5040 5074 5108 5 23 6 27 23 28 24 24 25 28 29 29 55 5142 5177 5211 5245 5280 5315 5349 5384 5419 5454 7 32 8 36 9 41 32 87 41 33 84 84 88 88 39 42 43 44 56 5489 5524 5559 5594 5630 5665 5700 5736 5772 5807 57 5843 5879 5915 5951 5987 6023 6059 6096 6132 6169 50 51 52 58 54 58 6205 6242 6279 6316 6352 6389 6427 6464 6501 6538 t 5 5 5 5 5 59 6576 6613 6651 6688 6726 6764 6802 6840 6878 6916 2 10 3 15 10 15 10 11 11 16 16 16 8.60 0.01 6954 6993 7031 7070 7108 7147 7186 7224 7263 7302 4 20 20 21 21 22 61 7341 7381 7420 7459 7499 7538 7578 7618 7657 7697 5 25 6 30 26 81 26 27 27 31 82 82 62 7737 7777 7817 7858 7898 7938 7979 8020 8060 8101 7 35 86 36 37 38 63 8142 8183 8224 8265 8306 8348 8389 8430 8472 8514 8 40 9 45 41 40 42 42 43 47 48 49 57 58 59 64 8556 8597 8639 8681 8724 8766 8808 8851 8893 8936 55 66 65 8978 9021 9064 9107 9150 9193 9237 9280 9324 9367 1 6 6 6 6 6 66 9411 9455 9498 9542 9586 9631 9675 9719 9764 9808 2 11 3 17 11 17 11 12 12 17 17 18 67 9853 9897 9942 9987 *0032 *0077 *0123 *0168 *0213 *0259 4 22 39 23 28 24 68 0.02 0305 0350 0396 0442 0488 0534 0580 0627 0673 0720 5 28 28 29 29 30 69 0766 0813 0860 0907 0954 1001 1048 1096 1143 1191 6 33 7 39 34 80 34 35 85 40 41 41 8.70 0.02 1238 1286 1334 1382 1430 1478 1527 1575 1624 1672 8 44 9 50 45 50 46 46 47 51 52 53 71 1721 1770 1819 1868 1917 1966 2016 2065 2115 2164 60 (il 62 63 64 72 2214 2264 2314 2364 2414 2465 2515 2566 2617 2667 1 6 6 6 6 6 73 74 2718 3234 2769 3286 2820 3338 2872 3390 2923 3443 2975 3495' 3026 3548 3078 3601 3130 3654 3182 3707 2 12 3 18 4 24 12 18 12 13 13 19 19 19 25 25 26 75 3760 3813 3867 3920 3974 4028 4082 4136 4190 4244 5 30 6 36 7 42 31 37 43 31 82 32 37 88 38 43 44 45 76 4298 4353 4408 4462 4517 4572 4627 4682 4738 4793 77 4849 4904 4960 5016 5072 5128 5184 5241 5297 5354 8 48 a 50 50 51 78 5411 5468 5525 5582 5639 5696 5754 5812 5869 5927 9 54 55 56 57 58 79 5985 6043 6102 6160 6219 6277 6336 6395 6454 6513 65 1 7 66 7 67 68 70 7 7 7 8.80 0.02 6572 6632 6691 6751 6811 6871 6931 6991 7051 7112 2 13 3 20 4 26 18 20 u 13 14 14 20 20 21 27 27 28 81 7172 7233 7294 7355 7416 7477 7539 7600 7662 7724 82 7785 7847 7910 7972 8034 8097 8160 8223 8286 8349 5 33 33 34 34 35 83 8412 8475 8539 8603 8666 8730 8794 8859 8923 8987 6 39 7 46 8 52 40 46 53 40 41 42 47 48 49 54 54 56 84 9052 9117 9182 9247 9312 9377 9443 9508 9574 9640 85 9706 9772 9839 9905 9972 *0039 *0105 *0172 *0240 *0307 9 59 60 60 61 63 86 0.03 0374 0442 0510 0578 0646 0714 0782 0851 0920 0988 72 1 7 74 7 76 78 80 8 8 8 87 1057 1126 1196 1265 1335 1404 1474 1544 1614 1684 2 14 15 15 16 16 88 1755 1825 1896 1967 2038 2109 2181 2252 2324 2396 3 22 4 29 5 36 ■>■> 30 37 23 23 24 80 31 32 38 39 40 89 2468 2540 2612 2684 2757 2830 2903 2976 3049 3122 8.90 0.03 3196 3269 3343 3417 3491 3566 3640 3715 3789 3864 6 43 7 50 44 69 46 47 48 53 55 56 91 3939 4015 4090 4166 4241 4317 4393 4470 4546 4622 S 58 60 61 62 64 92 4699 4776 4853 4930 5008 5085 5163 5241 5319 5397 9 65 07 68 70 72 93 5475 5554 5632 5711 5790 5870 5949 6028 6108 6188 82 84 86 88 90 94 6268 6348 6429 6509 6590 6671 6752 6833 6914 6996 1 8 2 16 8 IT 9 9 9 17 18 18 95 7078 7160 7242 7324 7406 7489 7572 7655 7738 7821 3 25 4 83 25 :>4 26 26 27 34 35 36 96 7905 7988 8072 8156 8241 8325 8409 8494 8579 8664 5 41 42 43 44 45 97 8749 8835 8921 9006 9092 9179 9265 9351 9438 9525 6 49 60 52 53 54 98 9612 9699 9787 9874 9962 *0050 *0138 *0227 *0315 *0404 7 57 8 66 DO 67 60 62 63 69 70 72 99 0.04 0493 0582 0671 0761 0851 0941 1031 1121 1211 1302 9 74 70 77 79 81 A = log£- log a, log a + B = log (a + b). B = log a - log ft log^H -A = log( .-*). 46 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 4 5 6 7 8 9 Differences. 9.00 0.04 1393 1484 1575 1666 1758 1850 1942 2034 2126 2219 95 100 105 110 01 2311 2404 2497 2591 2684 2778 2872 2966 3060 3155 i 2 10 19 10 20 11 21 32 11 22 38 02 3249 3344 3439 3535 3630 3726 3822 3918 4014 4111 8 29 80 03 4207 4304 4401 4498 4596 4694 4792 4890 4988 5086 4 38 40 42 44 04 5185 5284 5383 5483 5582 5682 5782 5882 5982 6083 5 6 48 57 50 60 53 63 55 66 05 6184 6285 6386 6487 6589 6691 6793 6895 6997 7100 7 8 9 67 70 86 70 80 90 74 84 M 77 88 99 06 7203 7306 7409 7513 7617 7721 7825 7929 8034 8139 07 8244 8349 8454 8560 8666 8772 8878 8985 9092 9199 115 120 125 180 08 9306 9413 9521 9629 9737 9845 9954 *0063 *0172 *0281 1 12 12 13 18 09 0.05 0390 0500 0610 0720 0830 0941 1052 1163 1274 1385 2 3 23 85 24 86 25 83 26 89 9.10 0.05 1497 1609 1721 1833 1946 2059 2172 2285 2399 2513 4 46 48 50 52 11 2627 2741 2855 2970 3085 3200 3316 3431 3547 3663 5 6 58 69 60 72 63 75 65 78 12 3780 3896 4013 4130 4247 4365 4483 4601 4719 4837 7 81 S4 88 91 13 4956 5075 5194 5314 5434 5554 5674 5794 5915 6036 8 9 92 104 185 96 108 140 100 118 145 104 117 150 14 6157 6278 6400 6522 6644 6766 6889 7012 7135 7259 15 7382 7506 7630 7755 7879 8004 8129 8255 8380 8506 1 14 14 15 15 16 8632 8759 8886 9012 9140 9267 9395 9523 9651 9779 2 8 27 41 28 42 29 44 80 45 17 9908 *0037 *0166 *0296 *0426 *0556 *0686 *0816 *0947 *1078 4 54 56 58 00 18 19 0.06 1210 2537 1341 2672 1473 2806 1605 2941 1738 3076 1870 3211 2003 3347 2136 3483 2270 3619 2404 3755 1 6 7 68 81 95 70 84 93 73 87 102 75 90 105 9.20 0.06 3892 4029 4166 4304 4441 4579 4718 4856 4995 5134 8 B 108 122 112 126 116 181 120 135 21 5274 5413 5553 5694 5834 5975 6116 6257 6399 6541 155 16 160 16 165 17 170 17 22 6683 6826 6968 7111 7255 7398 7542 7686 7831 7976 1 23 8121 8266 8412 8557 8704 8850 8997 9144 9291 9439 2 81 82 33 84 24 9587 9735 9883 *0032 *0181 *033l' *0480 *0630 *0780 ♦0931 8 4 47 62 48 64 50 66 51 68 25 0.07 1082 1233 1384 1536 1688 1840 1993 2146 2299 .2453 5 6 T 78 93 109 80 96 112 88 99 116 85 102 119 26 2606 2761 2915 3070 3225 3380 3536 3692 3848 4004 27 4161 4318 4476 4633 4791 4950 5108 5267 5427 5586 8 124 128 182 136 28 5746 5906 6067 6228 6389 6550 6712 6874 7037 7199 9 140 144 149 153 29 7362 7526 7689 7853 8017 8182 8347 8512 8678 8844 1 175 18 180 18 185 19 190 19 9.30 0.07 9010 9176 9343 9510 9678 9845 ♦0014 *0182 *0351 *0520 2 3 4 35 58 70 36 54 72 87 56 74 88 57 76 31 0.08 0689 0859 1029 1199 1370 1541 1712 1884 2056 2228 32 2401 2574 2747 2921 3095 3269 3444 3619 3794 3970 5 88 90 98 95 33 34 4146 5924 4322 6104 4499 6284 4676 6464 4853 6645 5031 6826 5209 7007 5387 7189 5566 7371 5745 7553 6 7 8 105 123 140 10S 126 144 111 180 148 114 188 35 7736 7919 8103 8286 8470 8655 8840 9025 9210 9396 9 158 162 167 171 36 9583 9769 9956 *0143 *0331 *0519 *0707 *0896 *1085 *1274 1 195 20 200 20 205 u 210 21 37 0.09 1464 1654 1844 2035 2226 2418 2610 2802 2995 3188 2 89 40 41 42 38 3381 3574 3768 3963 4158 4353 4548 4744 4940 5137 1 4 5 59 78 9S 60 80 100 6-1 82 103 68 84 105 39 5334 5531 5728 5926 6125 6324 6523 6722 6922 7122 9.40 0.09 7323 7524 7725 7927 8129 8331 8534 8737 8941 9145 6 7 117 187 120 140 128 144 IM 147 41 9349 9554 9759 9964 ♦0170 *0376 *0583 *0790 *0997 *1205 8 156 160 1C4 168 42 0.10 1413 1621 1830 2039 2249 2459 2669 2880 3091 3302 9 176 180 185 1S9 43 3514 3726 3939 4152 4366 4579 4794 5008 5223 5438 215 220 280 240 44 5654 5870 6087 6304 6521 6739 6957 7175 7394 7614 1 2 22 43 22 44 ■-'•'! M 24 48 45 7033 8053 8274 . .95 8716 8938 9160 9382 9605 9828 3 4 65 N 66 88 N 92 72 96 46 0.11 0052 0276 0500 072« 0950 1176 1402 1629 1855 2083 5 108 110 115 120 47 48 2310 4609 2538 4842 2767 5074 2996 5307 3225 5540 3455 5774 3685 6008 3915 6243 4146 6478 4378 6714 6 7 s 129 151 172 132 154 176 188 161 184 144 168 1M 49 6949 7186 7422 7660 7897 8135 8373 8612 8851 9091 9 104 198 207 216 A = log£- log a, logfl ! + B = log(d + *> B = log a - log*, log b- f A_= log (a -*) ' V. ADDITION-SUBTRACTION LOGARITHMS. 47 A B 1 2 3 4 5 6 ( 8 9 Differences. 9.50 0.11 9331 9572 9812 *0054 *0295 *0538 *0780 *1023 *1267 ♦1510 245 250 255 260 51 0.12 1755 1999 2244 2490 2736 2982 3229 3476 3724 3972 i 2 25 49 25 50 26 51 26 52 52 4221 4470 4719 4969 5219 5470 5721 5973 6225 6477 8 74 75 77 78 53 6730 6983 7237 7491 7746 8001 8256 8512 8769 9025 4 98 100 102 104 54 9283 9540 9799 *0057 *0316 *0576 *0835 *1096 *1357 ♦1618 5 6 123 147 125 150 12S 153 180 156 55 0.13 1879 2142 2404 2667 2931 3195 3459 3724 3989 4255 7 3 172 196 175 200 179 204 182 208 234 56 4521 4787 5054 5322 5590 5858 6127 6396 6666 6936 9 221 225 230 57 7207 7478 7750 8022 8294 8567 8841 9114 9389 9663 270 280 290 800 58 9939 *0214 *0491 *0767 *1044 *1322 *1600 *1878 *2157 *2437 1 27 2S 29 80 59 0.14 2716 2997 3277 3559 3840 4123 4405 4688 4972 5256 2 8 54 SI 56 84 58 87 60 90 9.60 0.14 5540 5825 6111 6397 6683 6970 7257 7545 7833 8122 4 108 112 116 120 61 8411 8701 8991 9282 9573 9865 *0157 *0449 *0742 *1036 5 6 135 162 140 168 145 174 150 180 62 0.15 1330 1624 1919 2215 2511 2807 3104 3401 3699 3997 7 1S9 196 203 210 63 4296 4595 4895 5195 5496 5797 6099 6401 6704 7007 8 9 216 243 224 252 282 261 240 270 340 64 7310 7615 7919 8224 8530 8836 9142 9449 9757 *0065 810 820 880 65 0.16 0374 0683 0992 1302 1613 1924 2235 2547 2859 3172 1 81 62 98 82 38 34 66 3486 3800 4114 4429 4745 5061 5377 5694 6011 6329 2 8 64 96 66 99 68 102 67 6648 6967 7286 7606 7926 8247 8569 8891 9213 9536 4 124 128 132 186 68 9860 *0183 *0508 *0833 *1158 *1484 *1811 *2138 *2465 *2793 5 155 160 165 170 69 0.17 3122 3451 3780 4110 4441 4772 5104 5436 5768 6101 6 7 1S6 217 192 224 198 281 204 288 9.70 0.17 6435 6769 7104 7439 7774 8111 8447 8784 9122 9460 8 9 24S 279 256 288 264 297 272 306 71 9799 *0138 *0478 *0818 *1159 *1501 *1842 *2185 *2528 *287l 350 35 360 36 370 37 380 38 72 0.18 3215 3559 3904 4250 4596 4942 5289 5637 5985 6334 1 73 6683 7033 7383 7733 8085 8436 8789 9141 9495 9849 a 70 72 74 76 74 0.19 0203 0558 0913 1269 1626 1983' 2340 2699 3057 3416 3 4 105 140 108 144 111 148 114 152 75 76 3776 7402 4136 7767 4497 8133 4858 8500 5220 8867 5582 5945 9235 9603 6308 9972 6672 *0341 7037 *0711 5 6 7 175 210 245 180 216 252 185 222 259 190 228 266 77 0.20 1081 1452 1823 2195 2568 2941 3315 3689 4063 4438 8 280 288 296 304 78 4814 5190 5567 5945 6323 6701 7080 7459 7839 8220 9 315 824 383 342 79 8601 8983 9365 9748 *0131 *0515 *0900 *1284 *1670 *2056 1 390 39 400 40 410 41 420 42 9.80 0.21 2443 2830 3217 3606 3994 4384 4774 5164 5555 5947 2 8 4 78 117 156 SO 120 160 82 128 164 84 126 168 81 6339 6731 7124 7518 7912 8307 8703 9098 9495 9892 82 0.22 0289 0688 1086 1485 1885 2286 2686 3088 3490 3892 5 195 200 205 210 83 4296 4699 5103 5508 5913 6319 6726 7133 7540 7948 6 7 8 284 273 812 240 2S0 820 246 287 328 252 294 836 84 8357 8766 9176 9586 9997 *0409 *0821 *1233 *1646 *2060 85 0.23 2474 2889 3304 3720 4137 4554 4971 5389 5808 6227 9 851 860 369 878 86 6647 7067 7488 7910 8332 8755 9178 9602 *0026 *0451 1 480 43 440 44 450 45 460 46 87 0.24 0876 1302 1729 2156 2584 3012 3441 3870 4300 4730 2 86 ss 90 92 88 89 5162 9503 5593 9941 6025 *0379 6458 *0817 6891 *1256 7325 7760 *1696 *2136 8195 *2576 8630 *3018 9067 *3459 8 4 5 129 172 215 132 176 220 135 180 225 138 184 230 9.90 0.25 3902 4345 4788 5233 5677 6122 6568 7015 7462 7909 6 7 25S 801 264 308 270 315 276 322 91 8357 8806 9255 9705 *0155 *0606 *1058 *1510 *1962 *2416 8 844 852 860 36S 92 0.26 2869 3324 3779 4234 4690 5147 5604 6062 6520 6979 9 887 896 405 414 93 7439 7899 8360 8821 9283 9745 *0208 *0671 *1135 *1600 470 4S0 490 500 94 0.27 2065 2531 2998 3464 3932 4400 4869 5338 5808 6278 1 2 47 94 48 96 49 9S 50 100 95 6749 7221 7693 8165 8639 9113 9587 *0062 *0538 *1014 8 4 141 188 144 192 147 196 150 200 96 0.28 1490 1968 2445 2924 3403 3882 4363 4843 5325 5807 5 285 240 245 250 97 6289 6772 7256 7740 8225 8710 9196 9682 *0169 *0657 6 282 288 294 800 98 0.29 1145 1634 2123 2613 3104 3595 4086 4579 5071 5565 7 g 829 876 336 884 843 392 350 400 99 6059 6553 7048 7544 8040 8537 9035 9533 *0031 *0530 9 423 432 441 450 A = log b - log a, log a + B = log (# + £). B = loga — log b, log b- Y.A - = log (a -b) 48 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 . 4 5 6 7 8 9 Differences. 0.000 0.30 1030 1080 1130 1180 1230 1280 1330 1380 1430 1480 001 1530 1580 1630 1680 1731 1781 1831 1881 1931 1981 002 2031 2081 2131 2182 2232 2282 2332 2382 2432 2482 50 5 003 2533 2583 2633 2683 2733 2784 2834 2884 2934 2984 i 004 3035 3085 3135 3185 3236 3286 3336 3386 3437 3487 2 3 10 15 005 3537 3587 3638 3688 3738 3789 3839 3889 3940 3990 4 20 006 4040 4091 4141 4191 4242 4292 4343 4393 4443 4494 5 6 7 u 80 35 007 4544 4595 4645 4695 4746 4796 4847 4897 4948 4998 008 5048 5099 5149 5200 5250 5301 5351 5402 5452 5503 8 40 009 5553 5604 5654 5705 5755 5806 5857 5907 5958 6008 9 45 0.010 0.30 6059 6109 6160 6211 6261 6312 6362 6413 6464 6514 Oil 6565 6615 6666 6717 6767 6818 6869 6919 6970 7021 012 7071 7122 7173 7224 7274 7325 7376 7426 7477 7528 51 013 7579 7629 7680 7731 7782 7832 7883 7934 7985 8036 1 2 5 10 014 8086 8137 8188 8239 8290 8341 8391 8442 8493 8544 3 15 015 8595 8646 8696 8747 8798 8849 8900 8951 9002 9053 4 5 20 26 016 9104 9155 9206 9256 9307 9358 9409 9460 9511 9562 6 81 017 9613 9664 9715 9766 9817 9868 9919 9970 *0021, *0072 7 g 36 41 41 018 0.31 0123 0174 0225 0276 0327 0378 0430 0481 0532 0583" 9 46 019 0634 0685 0736 0787 0838 0889 0941 0992 1043 1094 0.020 0.31 1145 1196 1247 1299 1350 1401 1452 1503 1555 1606 021 1657 1708 1759 1811 1862 1913 1964 2016 2067 2118 52 5 022 2169 2221 2272 2323 2374 2426 2477 2528 2580 2631 1 023 2682 2734 2785 2836 2888 2939 2990 3042 3093 3144 2 10 024 3196 3247 3299 3350 3401 3453 3504 3556 3607 3658 3 4 16 21 025 3710 3761 3813 3864 3916 3967 4019 4070 4122 4173 5 6 7 26 31 86 026 4225 4276 4328 4379 4431 4482 4534 4585 4637 4688 027 4740 4791 4843 4894 4946 4998 5049 5101 5152 5204 8 42 028 5256 5307 5359 5410 5462 5514 5565 5617 5669 5720 9 4T 029 5772 5824 5875 5927 5979 6030 6082 6134 6186 6237 0.030 0.31 6289 6341 6392 6444 6496 6548 6599 6651 6703 6755 031 6807 6858 6910 6962 7014 7066 7117 7169 7221 7273 63 032 7325 7377 7428 7480 7532 7584 7636 7688 7740 7791 1 2 5 ]1 033 7843 7895 7947 7999 8051 8103 8155 8207 8259 8311 3 16 ' 034 8363 8415 8467 8519 8571 8622 8674 8726 8778 8830 4 5 6 21 27 82 035 8882 8935 8987 9039 9091 9143 9195 9247 9299 9351 036 9403 9455 9507 9559 9611 9663 9715 9768 9820 9872 7 8 9 87 42 48 037 9924 9976 *0028 *0080 *0132 *0185 *0237 *0289 *0341 *0393 038 0.32 0445 0498 0550 0602 0654 0706 0759 0811 0863 0915 039 0968 1020 1072 1124 1177 1229 1281 1333 1386 1438 0.040 0.32 1490 1543 1595 1647 1700 1752 1804 1857 1909 1961 54 5 041 2014 2066 2118 2171 2223 2276 2328 2380 2433 2485 1 042 2538 2590 2642 2695 2747 2800 2852 2905 2957 3009 2 11 043 3062 3114 3167 3219 3272 3324 3377 3429 3482 3534 8 4 16 22 044 3587 3640 3692 3745 3797 3850 3902 3955 4007 4060 B 27 045 4113 4165 4218 4270 4323 4376 4428 4481 4533 4586 6 7 82 88 046 4639 4691 4744 4797 4849 4902 4955 5007 5060 6113 8 48 047 5165 5218 5271 5324 5376 5429 5482 5535 5587 5640 9 49 048 5693 5746 5798 5851 5904 5957 6009 6062 6115 6168 049 6221 6274 6326 6379 6432 6485 6538 6591 6643 6696 A = log a- log£, log* + B = log (a + *). B = log a - log*, log*- hA = log( .-,). V. ADDITION-SUBTRACTION LOGARITHMS. 49 A B 1 2 3 4 5 6 7 8 9 Differences. 0.050 0.32 6749 6802 6855 6908 6961 7014 7067 7119 7172 7225 051 7278 7331 7384 7437 7490 7543 7596 7649 7702 7755 052 7808 7861 7914 7967 8020 8073 8126 8179 8232 8285 053 8338 8391 8444 8497 8550 8603 8656 8709 8763 8816 054 8869 8922 8975 9028 9081 9134 9187 9241 9294 9347 055 9400 9453 9506 9560 9613 9666 9719 9772 9826 9879 i 53 5 056 9932 9985 *0038 *0092 *0145 *0198 *0251 *0305 *0358 *0411 2 11 057 0.33 0464 0518 0571 0624 0678 0731 0784 0838 0891 0944 3 4 16 21 058 0998 1051 1104 1158 1211 1264 1318 1371 1424 1478 5 27 059 1531 1585 1638 1691 1745 1798 1852 1905 1958 2012 6 7 32 37 0.060 0.33 2065 2119 2172 2226 2279 2333 2386 2440 2493 2547 8 42 061 2600 2654 2707 2761 2814 2868 2921 2975 3028 3082 9 48 062 3135 3189 3243 3296 3350 3403 3457 3511 3564 3618 063 3671 3725 3779 3832 3886 3940 3993 4047 4101 4154 064 4208 4262 4315 4369 4423 4476 4530 4584 4637 4691 065 4745 4799 4852 4906 4960 5014 5067 5121 5175 5229 066 5283 5336 5390 5444 5498 5552 5605 5659 5713 5767 54 067 5821 5875 5928 5982 6036 6090 6144 6198 6252 6306 1 2 3 5 11 16 068 6360 6413 6467 6521 6575 6629 6683 6737 6791 6845 069 6899 6953 7007 7061 7115 7169 7223 7277 7331 7385 4 22 0.070 0.33 7439 7493 7547 7601 7655 7709 7763 7817 7871 7925 5 6 27 32 071 7979 8033 8087 8142 8196 8250 8304 8358 8412 8466 7 38 072 8520 8575 8629 8683 8737 8791 8845 8899 8954 9008 8 9 48 49 073 9062 9116 9170 9225 9279 9333 9387 9441 9496 9550 074 9604 9658 9713 9767 9821 9876 9930 9984 *0038 *0093 075 0.34 0147 0201 0256 0310 0364 0419 0473 0527 0582 0636 076 0690 0745 0799 0853 0908 0962 1017 1071 1125 1180 077 1234 1289 1343 1398 1452 1506 1561 1615 1670 1724 55 078 1779 1833 1888 1942 1997 2051 2106 2160 2215 2269 1 2 3 6 11 17 079 2324 2378 2433 2487 2542 2597 2651 2706 2760 2815 0.080 0.34 2869 2924 2979 3033 3088 3142 3197 3252 3306 3361 4 5 22 28 081 3416 3470 3525 3580 3634 3689 3744 3798 3853 3908 6 33 082 3962 4017 4072 4127 4181 4236 4291 4346 4400 4455 7 39 083 4510 4565 4619 4674 4729 4784 4838 4893 4948 5003 8 9 44 50 084 5058 5113 5167 5222 5277 5332 5387 5442 5496 5551 085 5606 5661 5716 5771 5826 5881 5936 5990 6045 6100 086 6155 6210 6265 6320 6375 6430 6485 6540 6595 6650 087 6705 6760 6815 6870 6925 6980 7035 7090 7145 7200 088 7255 7310 7365 7420 7475 7530 7.585 7641 7696 7751 089 7806 7861 7916 7971 8026 8081 8137 8192 8247 8302 1 56 6 0.090 0.34 8357 8412 8468 8523 8578 8633 8688 8743 8799 8854 2 3 11 17 091 8909 8964 9020 9075 9130 9185 9241 9296 9351 9406 4 22 092 9462 9517 9572 9627 9683 9738 9793 9849 9904 9959 5 28 093 0.35 0015 0070 0125 0181 0236 0291 0347 0402 0457 0513 6 7 34 39 094 0568 0624 0679 0734 0790 0845 0901 0956 1012 1067 8 45 095 1122 1178 1233 1289 1344 1400 1455 1511 1566 1622 9 50 096 1677 1733 1788 1844 1899 1955 2010 2066 2121 2177 097 2233 2288 2344 2399 2455 2510 2566 2622 2677 2733 098 2788 2844 2900 2955 3011 3067 3122 3178 3234 3289 099 3345 3401 3456 3512 3568 3623 3679 3735 3790 3846 A = log a - log*, log* + B = log (a + b). B = log a — log*, log*H -A = log( a-b). 50 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 4 5 6 7 8 9 Differences. 0.100 0.35 3902 3958 4013 4069 4125 4181 4236 4292 4348 4404 101 4459 4515 4571 4627 4683 4738 4794 4850 4906 4962 102 5018 5073 5129 5185 5241 5297 5353 5409 5465 5520 • 103 5576 5632 5688 5744 5800 5856 5912 5968 6024 6080 104 6136 6192 6248 6304 6360 6416 6472 6528 6584 6640 66 105 6696 6752 6808 6864 6920 6976 7032 7088 7144 7200 i 6 106 7256 7312 7368 7424 7480 7536 7593 7649 7705 7761 2 8 11 17 107 7817 7873 7929 7985 8042 8098 8154 8210 8266 8322 4 22 108 8379 8435 8491 8547 8603 8660 8716 8772 8828 8884 5 28 109 8941 8997 9053 9109 9166 9222 9278 9335 9391 9447 6 7 88 39 0.110 0.35 9503 9560 9616 9672 9729 9785 9841 9898 9954 *0010 8 9 44 60 111 0.36 0067 0123 0179 0236 0292 0349 0405 0461 0518 0574 112 0630 0687 0743 0800 0856 0913 0969 1026 1082 1138 113 1195 1251 1308. 1364 1421 1477 1534 1590 1647 1703 114 1760 1816 1873 1929 1986 2043 2099 2156 2212 2269 115 2325 2382 2439 2495 2552 2608 2665 2722 2778 2835 116 2891 2948 3005 3061 3118 3175 3231 3288 3345 3401 1 56 6 117 3458 3515 3572 3628 3685 3742 3798 3855 3912 3969 2 11 118 4025 4082 4139 4196 4252 4309 4366 4423 4480 4536 8 4 5 17 22 28 119 4593 4650 4707 4764 4820 4877 4934 4991 5048 5105 0.120 0.36 5162 5218 5275 5332 5389 5446 5503 5560 5617 5674 6 7 34 89 121 5730 5787 5844 5901 5958 6015 6072 6129 6186 6243 8 45 122 6300 6357 6414 6471 6528 6585 6642 6699 6756 6813 9 60 123 6870 6927 6984 7041 7098 7155 7212 7269 7326 7384 124 7441 7498 7555 7612 7669 7726 7783 7840" 7898 7955 125 8012 8069 8126 8183 8240 8298 8355 8412 8469 8526 126 8584 8641 8698 8755 8812 8870 8927 8984 9041 9099 127 9156 9213 9270 9328 9385 9442 9500 9557 9614 9671 R 128 9729 9786 9843 9901 9958 *0015 *0073 *0130 *0187 *0245 1 2 8 6 11 17 129 0.37 0302 0360 0417 0474 0532 0589 0646 0704 0761 0819 0.130 0.37 0876 0934 0991 1048 1106 1163 1221 1278 1336 1393 4 5 28 29 34 131 1451 1508 1566 1623 1681 1738 1796 1853 1911 1968 6 132 2026 2083 2141 2198 2256 2314 2371 2429 2486 2544 7 40 133 2602 2659 2717 2774 2832 2890 2947 3005 3062 3120 8 9 46 51 134 3178 3235 3293 3351 3408 3466 3524 3581 3639 3697 135 3755 3812 3870 3928 3985 4043 4101 4159 4216 4274 136 4332 4390 4448 4505 4563 4621 4679 4736 4794 4852 137 4910 4968 5026 5083 5141 5199 5257 5315 5373 5431 138 5488 5546 5604 5662 5720 5778 5836 5894 5952 6010 139 6067 6125 6183 6241 6299 6357 6415 6473 6531 6589 1 58 6 0.140 0.37 6647 6705 6763 6821 6879 6937 6995 7053 7111 7169 2 8 u 17 141 7227 7285 7343 7401 7459 7518 7576 7634 7692 7750 4 28 142 7808 7866 7924 7982 8040 8099 8157 8215 8273 8331 5 M 143 8389 8447 8506 8564 8622 8680 8738 8797 8855 8913 8 7 86 41 144 8971 9029 9088 9146 9204 9262 9321 9379 9437 9495 8 9 46 145 9554 9612 9670 9728 9787 9845 9903 9962 *0020 *0078 62 146 0.38 0137 0195 0253 0312 0370 0428 0487 0545 0603 0662 147 0720 0778 0837 0895 0954 1012 1070 1129 1187 1246 148 1304 1363 1421 1480 1538 1596 1655 1713 1772 1830 149 1889 1947 2006 2064 2123 2181 2240 2298 2357 2416 A = log a — log£, log£ + B = log (a + b). B = loga-l og£, log^H -A = log( a-b). V. ADDITION-SUBTRACTION LOGARITHMS. 51 A B 1 2 3 4 5 6 7 8 9 Differences. 0.150 0.38 2474 2533 2591 2650 2708 2767 2825 2884 2943 3001' 151 3060 3118 3177 3236 3294 3353 3412 3470 3529 3588 152 3646 3705 3764 3822 3881 3940 3998 4057 4116 4174 153 4233 4292 4351 4409 4468 4527 4585 4644 4703 4762 154 4821 4879 4938 4997 5056 5114 5173 5232 5291 5350 69 155 5409 5467 5526 5585 5644 5703 5762 5820 5879 5938 i 6 156 5997 6056 6115 6174 6233 6292 6351 6409 6468 6527 2 3 12 18 157 6586 6645 6704 6763 6822 6881 6940 6999 7058 7117 4 24 158 7176 7235 7294 7353 7412 7471 7530 7589 7648 7707 5 30 159 7766 7825 7884 7943 8002 8062 8121 8180 8239 8298 6 7 36 41 0.160 0.38 8357 8416 8475 8534 8593 8653 8712 8771 8830 8889 8 9 47 53 161 8948 9007 9067 9126 9185 9244 9303 9363 9422 9481 162 9540 9599 9659 9718 9777 9836 9896 9955 *0014 *0073 163 0.39 0133 0192 0251 0311 0370 0429 0488 0548 0607- 0666 164 0726 0785 0844 0904 0963 1022 1082 1141 1201 1260 165 1319 1379 1438 1497 1557 1616 1676 1735 1795 1854 166 1913 1973 2032 2092 2151 2211 2270 2330 2389 2449 1 60 167 2508 2568 2627 2687 2746 2806 2865 2925 2984 3044 2 12 168 3103 3163 3222 3282 3342 3401 3461 3520 3580 3640 3 4 5 18 24 30 169 3699 3759 3818 3878 3938 3997 4057 4117 4176 4236 0.170 0.39 4296 4355 4415 4475 4534 4594 4654 4713 4773 4833 6 7 8 36 42 48 171 4892 4952 5012 5072 5131 5191 5251 5311 5370 5430 172 5490 5550 5609 5669 5729 5789 5849 5908 5968 6028 9 64 173 6088 6148 6208 6267 6327 6387 6447 6507 6567 6627 174 6686 6746 6806 6866 6926 6986 7046 7106 7166 7226 175 7286 7346 7405 7465 7525 7585 7645 7705 7765 7825 176 7885 7945 8005 8065 8125 8185 8245 8305 8365 8425 177 8485 8546 8606 8666 8726 8786 8846 8906 8966 9026 61 178 9086 9146 9206 9267 9327 9387 9447 9507 9567 9627 1 6 179 9688 9748 9808 9868 9928 9988 *0049 *0109 *0169 *0229 2 3 12 18 0.180 0.40 0289 0350 0410 0470 0530 0591 0651 0711 0771 0832 4 5 6 24 31 37 181 0892 0952 1012 1073 1133 1193 1254 1314 1374 1435 182 1495 1555 1616 1676 1736 1797 1857 1917 1978 2038 7 43 183 2098 2159 2219 2280 2340 2400 2461 2521 2582 2642 8 9 49 55 184 2703 2763 2823 2884 2944 3005 3065 3126 3186 3247 185 3307 3368 3428 3489 3549 3610 3670 3731 3791 3852 186 3912 3973 4033 4094 4155 4215 4276 4336 4397 4457 187 4518 4579 4640 4700 4761 4821 4882 4942 5003 5064 188 5124 5185 5246 5306 5367 5428 5488 5549 5610 5670 189 5731 5792 5853 5913 5974 6035 6096 6156 6217 6278 1 62 6 0.190 0.40 6339 6399 6460 6521 6582 6642 6703 6764 6825 6886 2 3 4 12 19 25 191 6947 7007 7068 7129 7190 7251 7312 7372 7433 7494 192 7555 7616 7677 7738 7799 7859 7920 7981 8042 8103 5 31 193 8164 8225 8286 8347 8408 8469 8530 8591 8652 8713 6 7 8 87 43 50 194 8774 8835 8896 8957 9018 9079 9140 9201 9262 9323 195 9384 9445 9506 9567 9628 9689 9750 9811 9872 9933 9 56 196 9994 *0056 *0117 *0178 *0239 *0300 *0361 *0422 *0483 *0545 197 0.41 0606 0667 0728 0789 0850 0911 0973 1034 1095 1156 198 1217 1279 1340 1401 1462 1524 1585 1646 1707 1768 199 1830 1891 1952 2014 2075 2136 2197 2259 2320 2381 A = log a - log£, log£ + B = log (a + b). B - log a — log b, log^H -A = log( a-b). 52 V. ADDITION-SUBTRACTION LOGARITHMS. B C 1 2 3 4 5 6 7 8 9 Differences. 0.400 9.77 9519 9585 9651 9717 9784 9850 9916 9982 *0048 *0113 401 9.78 0179 0245 0311 0377 0443 0508 0574 0640 0706 0771 6T H 402 0837 0903 0968 1034 1099 1165 1230 1296 1361 1427 i 7 7 403 1492 1557 1623 1688 1753 1819 1884 1949 2014 2080 2 3 13 20 13 20 404 2145 2210 2275 2340 2405 2470 2535 2600 2665 2730 4 27 26 405 2795 2860 2925 2990 3054 3119 3184 3249 3313 3378 5 6 34 40 33 40 406 3443 3507 3572 3636 3701 3766 3830 3895 3959 4024 7 47 46 407 4088 4152 4217 4281 4345 4410 4474 4538 4602 4667 8 9 54 60 58 59 408 4731 4795 4859 4923 4987 5051 5115 5179 5243 5307 409 5371 5435 5499 5563 5627 5690 5754 5818 5882 5945 65 64 0.410 9.78 6009 6073 6136 6200 6264 6327 6391 6454 6518 6581 1 2 3 7 13 20 6 13 19 411 6645 6708 6772 6835 6898 6962 7025 7088 7151 7215 412 7278 7341 7404 7467 7531 7594 7657 7720 7783 7846 4 26 26 413 7909 7972 8035 8098 8160 8223 8286 8349 8412 8474 5 6 7 83 39 46 82 38 45 414 8537 8600 8663 8725 8788 8851 8913 8976 9038 9101 415 9163 9226 9288 9351 9413 9475 9538 9600 9662 9725 8 9 52 59 51 58 416 9787 9849 9912 9974 *0036 *0098 *0160 *0222 *0284 *0346 417 9.79 0409 0471 0533 0594 0656 0718 0780 0842 0904 0966 63 62 418 1028 1089 1151 1213 1275 1336 1398 1460 1521 1583 1 6 6 419 1644 1706 1768 1829 1891 1952 2013 2075 2136 2198 2 3 13 19 12 19 0.420 9.79 2259 2320 2382 2443 2504 2565 2627 2688 2749 2810 4 25 25 421 2871 2932 2993 3054 3116 3177 3238 3298 3359 3420 5 6 32 88 31 37 422 3481 3542 3603 3664 3725 3785 3846 3907 3968 4028 7 44 43 423 4089 4150 4210 4271 4331 4392 4453" 4513 4574 4634 8 9 50 57 50 56 424 4694 4755 4815 4876 4936 4996 5057 5117 5177 5238 425 5298 5358 5418 5478 5538 5599 5659 5719 5779 5839 61 60 426 5899 5959 6019 6079 6139 6198 6258 6318 6378 6438 1 6 6 427 6498 6557 6617 6677 6737 6796 6856 6915 6975 7035 2 3 12 18 12 18 428 7094 7154 7213 7273 7332 7392 7451 7511 7570 7629 4 24 24 429 7689 7748 7807 7867 7926 7985 8044 8103 8163 8222 5 6 7 81 87 43 80 86 42 0.430 9.79 8281 8340 8399 8458 8517 8576 8635 8694 8753 8812 431 8871 8930 8989 9048 9106 9165 9224 9283 9342 9400 8 9 49 55 48 54 432 9459 9518 9576 9635 9694 9752 9811 9869 9928 9986 433 9.80 0045 0103 0162 0220 0278 0337 0395 0454 0512 0570 434 0628 0687 0745 0803 0861 0919 0978 1036 1094 1152 1 59 6 58 6 435 1210 1268 1326 1384 1442 1500 1558 1616 1674 1732 2 3 12 18 12 17 H 436 1789 . 1847 1905 1963 2021 2078 2136 2194 2251 2309 4 24 437 2367 2424 2482 2540 2597 2655 2712 2770 2827 2885 5 80 29 438 2942 2999 3057 3114 3171 3229 3286 3343 3401 3458 6 7 8 85 41 47 85 41 46 439 3515 3572 3630 3687 3744 3801 3858 3915 3972 4029 0.440 9.80 4086 4.143 4200 4257 4314 4371 4428 4485 4542 4598 9 n 52 441 4655 4712 4769 4826 4882 4939 4996 5052 5109 5166 442 5222 5279 5335 5392 5448 5505 5561 5618 5674 5731 1 2 57 6 11 56 6 11 443 5787 5844 5900 5956 6013 6069 6125 6181 6238 6294 444 445 6350 6911 6406 6967 6462 7023 6519 7079 6575 7135 6631 7191 6687 7246 6743 7302 6799 7358 6855 7414 8 4 5 17 28 29 17 22 28 446 7470 7526 7581 7637 7693 7748 7804 7860 7915 7971 6 7 8 84 40 46 84 89 45 447 8027 8082 8138 8193 8249 8304 8360 8415 8471 8526 448 8582 8637 8692 8748 8803 8858 8914 8969 9024 9079 9 51 50 449 9134 9190 9245 9300 9355 9410 9465 9520 9575 9630 B = log a — log b. log a + C: = log( a-b). V. ADDITION-SUBTRACTION LOGARITHMS. 53 B C 1 2 3 4 5 6 7 8 9 Differences. 0.450 9.80 9685 9740 9795 9850 9905 9960 *0015 *0070 *0125 *0179 451 9.81 0234 0289 0344 0399 0453 0508 0563 0617 0672 0727 452 0781 0836 0890 0945 1000 1054 1109 1163 1218 1272 55 54 5 453 1326 1381 1435 1490 1544 1598 1652 1707 1761 1815 i 6 454 455 1870 2411 1924 2465 1978 2519 2032 2573 2086 2627 2140 2681 2194 2735 2249 2788 2303 2842 2357 2896 2 3 4 11 17 22 11 16 22 456 2950 3004 3058 3111 3165 3219 3273 3326 3380 3434 5 6 7 28 33 89 27 32 88 457 3487 3541 3595 3648 3702 3755 3809 3862 3916 3969 458 4023 4076 4130 4183 4237 4290 4343 4397 4450 4503 8 44 43 459 4556 4610 4663 4716 4769 4823 4876 4929 4982 5035 9 50 49 0.460 9.81 5088 5141 5194 5247 5300 5353 5406 5459 5512 5565 461 5618 5671 5724 5777 5829 5882 5935 5988 6041 6093 462 6146 6199 6251 6304 6357 6409 6462 6514 6567 6620 1 2 53 52 463 6672 6725 6777 6830 6882 6934 6987 7039 7092 7144 5 11 5 10 464 465 7196 7719 7249 7771 7301 7823 7353 7875 7406 7927 7458 7979 7510 8031 7562 8083 7614 8135 7667 8187 3 4 5 16 • 21 27 16 21 26 466 8239 8291 8343 8395 8447 8499 8551 8603 8655 8706 6 32 31 467 8758 8810 8862 8914 8965 9017 9069 9120 9172 9224 7 8 37 42 36 42 468 9275 9327 9378 9430 9482 9533 9585 9636 9688 9739 9 48 47 469 9790 9842 9893 9945 9996 *0047 *0099 *0150 *0201 *0253 0.470 9.82 0304 0355 0406 0458 0509 0560 0611 0662 0713 0764 471 0815 0867 0918 0969 1020 1071 1122 1173 1223 1274 51 50 472 1325 1376 1427 1478 1529 1580 1630 1681 1732 1783 1 5 5 473 1833 1884 1935 1985 2036 2087 2137 2188 2239 2289 2 3 4 10 15 20 10 15 20 474 2340 2390 2441 2491 2542 2592 2643 2693 2743 2794 475 2844 2895 2945 2995 3046 3096 3146 3196 3247 3297 5 6 7 26 31 25 30 35 476 3347 3397 3447 3498 3548 3598 3648 3698 3748 3798 36 477 3848 3898 3948 3998 4048 4098 4148 4198 4248 4298 8 41 40 478 4347 4397 4447 4497 4547 4596 4646 4696 4746 4795 9 46 45 479 4845 4895 4944 4994 5044 5093 5143 5192 5242 5291 0.480 9.82 5341 5390 5440 5489 5539 5588 5638 5687 5736 5786 481 5835 5885 5934 5983 6032 6082 6131 6180 6229 6279 49 48 482 6328 6377 6426 6475 6524 6573 6622 6671 6721 6770 1 2 5 10 5 10 483 6819 6868 6917 6965 7014 7063 7112 7161 7210 7259 3 15 14 484 485 7308 7795 7357 7844 7405 7892 7454 7941 7503 7990 7552 8038 7600 8087 7649 8135 7698 8184 7746 8232 4 5 6 20 25 29 19 24 29 486 8281 8329 8378 8426 8475 8523 8572 8620 8668 8717 7 8 34 89 34 38 487 8765 8813 8862 8910 8958 9007 9055 9103 9151 9199 9 44 43 488 9248 9296 9344 9392 9440 9488 9536 9584 9632 9680 489 9728 9776 9824 9872 9920 9968 *0016 *0064 *0112 *0160 0.490 9.83 0208 0256 0303 0351 0399 0447 0494 0542 0590 0638 47 46 491 0685 0733 0781 0828 0876 0923 0971 1019 1066 1114 1 5 5 492 1161 1209 1256 1304 1351 1399 1446 1493 1541 1588 2 9 9 493 1636 1683 1730 1778 1825 1872 1919 1967 2014 2061 3 4 14 19 14 18 494 495 2108 2579 2156 2626 2203 2674 2250 2721 2297 2767 2344 2814 2391 2861 2438 2908 2485 2955 2532 3002 5 6 7 24 28 83 23 28 32 496 3049 3096 3143 3190 3236 3283 3330 3377 3424 3470 8 38 37 497 3517 3564 3610 3657 3704 3750 3797 3844 3890 3937 9 42 41 498 3983 4030 4076 4123 4170 4216 4262 4309 4355 4402 499 4448 4495 4541 4587 4634 4680 4726 4773 4819 4865 B =log a - log b- log a + C: = log( %-by 54 V. ADDITION-SUBTRACTION LOGARITHMS. B C 1 8 9 Differences. 0.50 51 52 53 54 55 56 57 58 59 0.60 61 62 63 64 65 66 67 68 69 0.70 71 72 73 74 75 76 77 78 79 0.80 81 82 83 84 85 86 87 88 89 0.90 91 92 93 94 95 96 97 98 99 9.83 4911 9459 9.84 3858 8115 9.85 2234 6222 9.86 0085 3826 7452 9.87 0966 9.87 4372 7676 9.88 0880 3989 7006 9933 9.89 2775 5535 8215 9.90 0818 9.90 3347 5804 8192 9.91 0513 2769 4963 7096 9170 9.92 1188 3150 9.92 5060 6918 8725 9.93 0485 2198 3865 5488 7068 8607 9.94 0105 9.94 1565 2986 4371 5720 7034 8314 9562 ).95 0778 1962 3117 5373 9906 4290 8533 2639 6614 0464 4194 7808 1311 4707 8001 1195 4295 7302 *0221 3055 5807 8479 1074 3596 6046 8427 0742 2991 5179 7306 9374 1386 3344 5248 7101 8904 0658 2366 4029 5648 7224 8759 0253 1709 3126 4507 5853 7163 8440 9685 0897 2079 3231 5833 *0351 4721 8949 3042 7005 0842 4560 8163 1655 5041 8325 1510 4600 7598 *0508 3334 6077 8742 1330 3844 6287 8662 0969 3213 5394 7515 9578 1584 3536 5435 7283 9081 0831 2535 4193 5807 7379 8910 0400 1852 3266 4644 5985 7293 8566 9807 1017 2196 3344 6292 *0795 5150 9365 3444 7394 1220 4926 8517 1999 5374 8648 1823 4903 7893 *0795 3612 6347 9004 1585 4092 6528 8895 1197 3434 5609 7724 9781 1782 3729 5622 7465 9258 1004 2703 4356 5966 7534 9061 0547 1995 3405 4779 6118 7421 8692 9930 1136 2312 3458 6749 *1237 5578 9778 3845 7782 1595 5290 8870 2341 5706 8969 2135 5206 8187 *1080 3889 6617 9265 1839 4338 6768 9128 1423 3654 5823 7932 9984 1979 3920 5809 7647 9435 1176 2870 4519 6125 7689 9211 0694 2138 3544 4915 6250 7550 8817 *0052 1255 2428 3571 7205 7659 8111 8562 9011 *1677 *2116 *2554 *2990 *3425 6004 6429 6852 7275 7695 *0191 0602 *1012 *1421 *1828 4244 4642 5039 5435 5829 8169 8554 8939 9322 9704 1970 2344 2716 3087 3457 5653 6015 6376 6736 7094 9222 9573 9923 *0272 *0619 2682 3022 3361 3699 4036 6037 6367 6696 7023 7350 9290 9610 9929 *0247 *0564 2446 2757 3066 3375 3682 5509 5810 6110 6409 6708 8480 8773 9064 9355 9644 *1365 *1649 *1932 *2214 *2495 4165 4441 4716 4990 5263 6885 7153 7419 7685 7951 9526 9786 *0045 *0304 *0561 2092 2344 2596 2847 3097 4584 4830 5074 5318 5562 7007 7245 7483 7720 7956 9361 9593 9824 *0054 *0284 1649 1874 2099 2323 2546 3874 4093 4311 4529 4746 6037 6250 6462 6674 6885 8140 8347 8554 8760 8965 *0186 *0387 *0588 *0788 *0988 2176 2372 2567 2762 2956 4111 4302 4492 4682 4871 5995 7828 9611 1347 3037 4682 6283 7843 9361 0840 2280 3683 5050 6381 7678 8942 *0174 1374 2543 3683 6180 8008 9787 1518 3203 4844 6441 7996 9511 0986 2422 3821 5184 6512 7806 9067 *0295 1492 2659 3796 6365 6550 6734 8188 8368 8547 9962 *0137 *0311 1689 1859 2028 3369 3535 3700 5006 5167 5328 6599 6755 6912 8150 8302 8455 9660 9809 9957 1131 1276 1421 2564 3959 5319 6643 7934 9191 *0416 1610 2774 3908 2705 2846 4097 4234 5453 5586 6774 6904 8061 8188 9*315 9439 *0537 *0657 1728 1845 2888 3003 4020 4131 460 46 92 138 184 230 276 322 9 414 420 42 84 126 168 210 n 294 336 378 76 114 152 190 228 266 804 342 840 34 68 102 136 170 204 238 272 806 90 120 150 180 210 240 270 450 440 m 45 44 m 90 88 86 135 132 129 180 176 172 225 220 215 270 264 253 315 308 801 360 352 :«4 405 896 887 410 400 390 41 40 89 82 M 78 123 U0 117 164 160 156 205 200 195 246 240 234 287 2S0 328 320 812 369 360 351 870 360 350 37 36 85 74 72 70 111 108 105 148 144 140 185 180 175 222 216 210 259 252 245 296 288 280 383 324 815 830 820 810 33 32 81 66 64 62 99 96 98 182 m IM 165 160 155 198 192 186 281 224 •JIT 264 256 248 297 288 290 . 2S0 270 29 28 27 N 56 54 87 84 81 116 112 108 145 140 185 174 168 m 282 261 196 224 252 240 24 48 n 96 IM 144 16S 10-.' 9 234 225 216 260 250 26 25 52 50 78 75 104 100 180 125 156 150 182 175 '.'lis 200 220 22 44 66 88 110 154 176 198 210 21 l.' 68 84 100 126 147 168 1S9 200 40 60 80 100 190 140 160 ISO 216 248 280 28 46 69 92 115 m 161 184 m 190 19 8S 57 76 95 114 133 152 171 B = log a — log b. log a + C = log (a - b). V. ADDITION-SUBTRACTION LOGARITHMS. 55 B C I 2 3 4 5 6 7 8 9 Differences. 1.00 9.95 4243 4353 4464 4575 4685 4795 4904 5013 5122 5231 180 170 160 150 01 5340 5448 5556 5663 5771 5878 5984 6091 6197 6303 i 18 86 17 34 16 15 32 30 02 6409 6514 6620 6724 6829 6933 7038 7141 7245 7348 8 54 51 48 45 03 7451 7554 7657 7759 7861 7963 8064 8166 8267 8367 4 72 68 64 60 04 8468 8568 8668 8768 8867 8966 9065 9164 9263 9361 90 108 85 102 80 75 96 90 05 9459 9556 9654 9751 9848 9945 *0041 *0138 *0234 *0329 7 s 126 144 119 136 112 105 128 120 144 135 06 9.96 0425 0520 0615 0710 0805 0899 0993 1087 1181 1274 •j 162 153 07 1367 1460 1553 1645 1737 1829 1921 2013 2104 2195 140 130 120 110 08 2286 2376 2467 2557 2647 2737 2826 2915 3004 3093 1 14 13 12 11 09 3182 3270 3358 3446 3534 3621 3709 3796 3882 3969 2 8 28 42 26 39 24 22 86 33 1.10 11 9.96 4055 4908 4142 4992 4228 5076 4313 5159 4399 5243 4484 5326 4569 5409 4654 5492 4739 5574 4823 5657 4 E 6 56 70 84 52 65 78 48 44 60 55 72 66 12 5739 5821 5903 5984 6066 6147 6228 6308 6389 6469 T 98 91 84 77 13 6550 6629 6709 6789 6868 6947 7026 7105 7184 7262 8 9 112 126 104 117 96 88 108 99 14 7340 7418 7496 7574 7651 7728 7805 7882 7959 8035 100 90 85 80 75 15 8112 8188 8264 8339 8415 8490 8565 8640 8715 8790 1 2 3 10 20 30 9 9 18 17 27 26 8 8 16 15 24 23 16 8864 8938 9013 9086 9160 9234 9307 9380 9453 9526 17 9598 9671 9743 9815 9887 9959 *0030 *0102 *0173 *0244 4 40 86 84 32 30 18 9.97 0315 0385 0456 0526 0596 0666 0736 0806 0875 0944 5 6 7 60 60 70 45 43 54 51 63 60 40 38 19 1013 1082 1151 1220 1288 1356 1425 1492 1560 1628 48 45 56 53 1.20 9.97 1695 1762 1830 1897 1963 2030 2096 2163 2229 2295 8 9 80 90 72 68 81 77 64 60 72 68 21 2360 2426 2492 2557 2622 2687 2752 2817 2881 2945 72 70 68 66 64 22 3010 3074 3138 3201 3265 3328 3391 3455 3518 3580 1 7 7 7 7 6 23 24 3643 4261 3705 4322 3768 4383 3830 4444 3892 4504 3954 4565 4016 4625 4077 4685. 4139 4745 4200 4805 S 8 4 14 22 29 14 14 21 20 28 27 13 13 20 19 26 26 25 4864 4924 4983 5042 5101 5160 5219 5278 5336 5395 5 g 36 43 35 34 42 41 33 32 40 38 26 5453 5511 5569 5627 5684 5742 5799 5857 5914 5971 7 50 49 48 46 45 27 28 6027 6588 6084 6643 6141 6699 6197 6754 6253 6809 6309 6863 6365 6918 6421 6972 6477 7027 6533 7081 8 9 58 65 56 54 63 61 53 51 59 58 29 7135 7189 7243 7297 7350 7404 7457 7510 7564 7617 1 62 6 60 58 6 6 56 54 6 5 1.30 9.97 7669 7722 7775 7827 7879 7932 7984 8036 8087 8139 2 3 12 19 12 12 18 17 11 11 17 16 31 8191 8242 8293 8345 8396 8447 8497 8548 8599 8649 4 25 24 23 22 22 32 8699 8750 8800 8850 8900 8949 8999 9048 9098 9147 5 31 30 29 28 27 33 9196 9245 9294 9343 9391 9440- 9488 9537 9585 9633 6 7 37 43 36 35 42 41 34 32 39 38 34 35 9681 9.98 0154 9729 0201 9776 0247 9824 0294 9872 0340 9919 0387 9966 0433 *0013 0479 *0060 0525 *0107 0570 8 9 50 56 52 5 48 46 54 52 50 48 5 5 45 43 50 49 46 44 5 4 36 0616 0662 0707 0753 0798 0843 0888 0933 0978 1023 1 37 1067 1112 1156 1200 1245 1289 1333 1376 1420 1464 2 10 10 10 9 9 38 1507 1551 1594 1637 1681 1724 17*67 1809 1852 1895 8 4 16 21 15 14 20 19 14 13 18 18 39 1937 1980 2022 2064 2106 2148 2190 2232 2274 2315 5 26 25 24 23 22 1.40 9.98 2357 2398 2440 2481 2522 2563 2604 2645 2685 2726 6 7 31 36 30 29 35 34 28 26 32 31 41 2767 2807 2847 2888 2928 2968 3008 3048 3087 3127 8 42 40 88 37 86 42 3167 3206 3245 3285 3324 3363 3402 3441 3480 3518 9 47 45 43 41 40 43 3557 3596 3634 3672 3711 3749 3787 3825 3863 3901 1 2 42 4 40 88 4 " 4 36 34 4 8 44 3938 3976 4014 4051 4088 4126 4163 4200 4237 4274 8 8 8 7 7 45 4311 4347 4384 4421 4457 4493 4530 4566 4602 4638 3 4 13 17 12 11 16 15 11 10 14 14 46 4674 4710 4746 4782 4817 4853 4888 4923 4959 4994 5 21 20 19 18 17 47 48 5029 5376 5064 5410 5099 5444 5134 5478 5169 5512 5203 5546 5238 5580 5273 5613 5307 5647 5341 5681 6 7 8 25 29 34 24 28 28 27 82 80 22 20 25 24 29 27 49 5714 5747 5781 5814 5847 5880 5913 5946 5979 6012 9 38 86 84 32 31 B = log a — log b. log a + C-. = log( a- *> 56 V. ADDITION-SUBTRACTION LOGARITHMS. B C 1 2 3 4 5 6 7 8 9 Differences. 1.50 9.98 6045 6077 6110 6142 6175 6207 6239 6271 6303 6335 51 6367 6399 6431 6463 6494 6526 6557 6589 6620 6651 33 82 81 80 52 6682 6713 6745 6775 6806 6837 6868 6899 6929 6960 1 3 7 3 6 8 6 8 6 53 6990 7021 7051 7081 7111 7141 7171 7201 7231 7261 8 10 10 9 9 54 7291 7320 7350 7379 7409 7438 7468 7497 7526 7555 4 D 18 17 13 16 12 16 12 15 55 7584 7613 7642 7671 7700 7728 7757 7785 7814 7842 8 20 19 19 18 56 7871 7899 7927 7955 7983 8012 8039 8067 8095 8123 7 g 23 26 30 22 26 29 22 25 28 21 24 27 57 8151 8178 8206 8233 8261 8288 8315 8343 8370 8397 •J 58 8424 8451 8478 8505 8532 8558 8585 8612 8638 8665 59 8691 8717 8744 8770 8796 8822 8848 8874 8900 8926 29 28 27 26 1.60 9.98 8952 8977 9003 9029 9054 9080 9105 9131 9156 9181 1 2 3 6 9 8 6 8 5 8 8 5 8 61 9206 9231 9257 9282 9306 9331 9356 9381 9406 9430 8 62 9455 9480 9504 9528 9553 9577 9601 9626 9650 9674 4 12 11 11 10 63 9698 9722 9746 9770 9793 9817 9841 9865 9888 9912 8 a 7 15 17 20 14 17 20 14 16 19 18 16 18 64 9935 9959 9982 *0005 *0028 *0052 *0075 *0098 *0121 *0144 65 9.99 0167 0190 0213 0235 0258 0281 0303 0326 0348 0371 S I 23 26 22 25 22 24 21 23 66 0393 0416 0438 0460 0482 0504 0526 0548 0570 0592 67 68 0614 0830 0636 0851 0658 0873 0680 0894 0701 0915 0723 0936 0744 0957 0766 0978 0787 0999 0809 1020 1 25 3 24 2 28 2 22 2 69 1041 1062 1083 1103 1124 1145 1165 1186 1206 1227 3 5 8 10 5 7 10 5 4 7 9 1.70 9.99 1247 1267 1288 1308 1328 1348 1368 1388 1408 1428 4 9 71 1448 1468 1488 1508 1527 1547 1567 1586 1606 1625 > 6 7 13 15 18 12 14 17 12 11 72 1645 1664 1684 1703 1722 1741 1761 1780 1799 1818 14 16 18 15 73 1837 1856 1875 1894 1912 1931 1950 1969 1987 2006 8 20 19 18 18 74 2024 2043 2061 2080 2098 2116 2135 2153 2171 2189 'J 23 22 21 20 75 2208 2226 2244 2262 2280 2298 2315 2333 2351 2369 76 2386 2404 2422 2439 2457 2474 2492 2509 2527 2544 1 21 2 20 2 19 2 18 2 77 2561 2579 2596 2613 2630 2647 2664 2681 2698 2715 '.' 4 4 4 4 78 2732 2749 2766 2782 2799 2816 2833 2849 2866 2882 3 4 6 g 6 g 6 g 5 7 9 79 2899 2915 2932 2948 2964 2981 2997 3013 3029 3046 5 11 10 10 1.80 9.99 3062 3078 3094 3110 3126 3142 3158 3174 3189 3205 7 13 15 12 14 11 18 11 18 81 3221 3237 3252 3268 3284 3299 3315 3330 3346 3361 8 17 16 15 14 82 3376 3392 3407 3422 3438 3453 3468 3483 3498 3513 it 19 18 17 16 83 3528 3543 3558 3573 3588 3603 3618 3633 3647 3662 84 3677 3691 3706 3721 3735 3750 3764 3779 3793 3807 1 17 2 16 2 15 2 14 1 85 3822 3836 3850 3865 3879 3893 3907 3921 3935 3949 I 3 8 ;; 8 86 87 3963 4102 3977 4115 3991 4129 4005 4143 4019 4156 4033 4170 4047 4183 4060 4197 4074 4210 4088 4223 4 5 7' 9 5 6 s 5 6 8 4 6 7 88 4237 4250 4263 4277 4290 4303 4316 4330 4343 4356 6 10 10 9 8 89 4369 4382 4395 4408 4421 4434 4447 4459 4472 4485 7 8 12 14 11 13 11 12 10 11 1.90 9.99 4498 4511 4523 4536 4549 15(11 4574 4586 4599 4611 8 15 14 14 13 91 4624 4636 4649 4661 4673 4686 4698 4710 4723 4735 92 4747 4769 4771 4783 4795 4807 4819 4831 4843 4855 18 V> 11 10 93 4867 4879 4891 4903 4915 4926 4938 4950 4962 4973 1 1 1 2 4 1 2 8 1 2 8 94 4985 4996 5008 5020 5031 5043 5054 5065 5077 5088 2 3 4 95 5100 5111 5122 5134 5145 5156 5167 5178 5190 5201 4 S 6 5 7 8 5 6 7 4 4 5 96 5212 5223 5234 5245 5256 5267 5278 5289 5300 5310 7 6 97 5321 5332 5343 5354 5364 5375 5386 5397 5407 5418 7 9 8 8 7 8 9 98 5428 5439 5450 5460 5471 5481 5491 5502 5512 5523 -- 9 10 11 10 11 9 10 99 5533 5543 5554 5564 5574 5584 5595 5605 5615 5625 B = log a - log b. log a + G = log( (I - d). V. ADDITION-SUBTRACTION LOGARITHMS. 57 B C 1 2 3 4 5 6 7 8 9 Differences. 2.00 9.99 5635 5645 5655 5665 5675 5685 5695 5705 5715 5725 01 5735 5745 5755 5765 5774 5784 5794 5804 5813 5823 02 5833 5842 5852 5861 5871 5881 5890 5900 5909 5918 03 5928 5937 5947 5956 5965 5975 5984 5993 6003 6012 04 6021 6030 6039 6049 6058 6067 6076 6085 6094 6103 10 9 05 6112 6121 6130 6139 6148 6157 6166 6174 6183 6192 i 2 1 2 1 2 06 6201 6210 6218 6227 6236 6245 6253 6262 6271 6279 3 8 3 07 6288 6296 6305 6313 6322 6330 6339 6347 6356 6364 4 4 4 08 6373 6381 6389 6398 6406 6414 6423 6431 6439 6447 5 6 5 6 5 5 09 6455 6464 6472 6480 6488 6496 6504 6512 6520 6528 7 7 6 2.10 9.99 6537 6544 6552 6560 6568 6576 6584 6592 6600 6608 8 9 8 9 7 8 11 6616 6623 6631 6639 6647 6655 6662 6670 6678 6685 12 6693 6701 6708 6716 6723 6731 6739 6746 6754 6761 13 6769 6776 6783 6791 6798 6806 6813 6820 6828 6835 14 6842 6850 6857 6864 6871 6879 6886 6893 6900 6907 15 6914 6922 6929 6936 6943 6950 6957 6964 6971 6978 8 7 16 6985 6992 6999 7006 7013 7020 7026 7033 7040 7047 1 1 1 17 7054 7061 7067 7074 7081 7088 7094 7101 7108 7114 2 3 2 2 1 2 18 7121 7128 7134 7141 7148 7154 7161 7167 7174 7180 4 3 3 19 7187 7193 7200 7206 7213 7219 7226 7232 7238 7245 . 5 6 7 4 5 6 4 2.20 9.99 7251 7257 7264 7270 7276 7283 7289 7295 7301 7308 4 5 21 7314 7320 7326 7332 7339 7345 7351 7357 7363 7369 8 9 6 7 6 6 22 7375 7381 7387 7393 7399 7405 7411 7417 7423 7429 23 7435 7441 7447 7453 7459 7465 7470 7476 7482 7488 24 7494 7499 7505 7511 7517 7522 7528 7534 7540 7545 25 7551 7557 7562 7568 7573 7579 7585 7590 7596 7601 26 7607 7612 7618 7623 7629 7634 7640 7645 7651 7656 27 7661 7667 7672 7678 7683 7688 7694 7699 7704 7710 1 6 5 28 7715 7720 7725 7731 7736 7741 7746 7751 7757 7762 2 1 1 29 7767 7772 7777 7782 7787 7793 7798 7803 7808 7813 3 4 2 2 2 2 2.30 9.99 7818 7823 7828 7833 7838 7843 7848 7853 7858 7863 5 3 3 31 7868 7873 7878 7882 7887 7892 7897 7902 7907 7912 6 7 8 4 4 5 3 4 4 32 7916 7921 7926 7931 7935 7940 7945 7950 7954 7959 33 7964 7969 7973 7978 7983 7987 '7992 7997 8001 8006 9 5 5 34 8010 8015 8020 8024 8029 8033 8038 8042 8047 8051 35 8056 8060 8065 8069 8074 8078 8082 8087 8091 8096 36 8100 8104 8109 8113 8118 8122 8126 8131 8135 8139 37 8143 8148 8152 8156 8160 8165 8169 8173 8177 8182 38 8186 8190 8194 8198 8202 8207 8211 8215 8219 8223 4 3 39 8227 8231 8235 8239 8243 8247 8252 8256 8260 8264 1 2 1 1 2.40 9.99 8268 8272 8276 8280 8284 8287 8291 8295 8299 8303 3 1 1 41 8307 8311 8315 8319 8323 8327 8330 8334 8338 8342 4 5 6 2 2 2 1 2 42 8346 8350 8353 8357 8361 8365 8368 8372 8376 8380 2 43 8383 8387 8391 8395 8398 8402 8406 8409 8413 8417 7 3 2 44 8420 8424 8428 8431 8435 8438 8442 8446 8449 8453 8 9 3 4 2 3 45 8456 8460 8463 8467 8471 8474 8478 8481 8485 8488 46 8492 8495 8498 8502 8505 8509 8512 8516 8519 8523 47 8526 8529 8533 8536 8539 8543 8546 8550 8553 8556 48 8560 8563 8566 8569 8573 8576 8579 8583 8586 8589 49 8592 8596 8599 8602 8605 8609 8612 8615 8618 8621 B = log a — log b. log a + C: = log( d-b). 58 V. ADDITION-SUBTRACTION LOGARITHMS. B 2.50 51 52 53 54 55 56 57 58 59 2.60 61 62 63 64 65 66 67 68 69 2.70 71 72 73 74 75 76 77 78 79 2.8 9 3.0 1 2 3 4 5 6 7 8 9 4.0 1 2 3 4 5 6 C 8 9 Differences. 9.99 8624 8656 8686 8716 8746 8774 8802 8830 8856 8882 9.99 8908 8933 8957 8981 9004 9027 9049 9071 9092 9112 9.99 9133 9152 9172 9191 9209 9227 9245 9262 9279 9295 9.99 9311 9453 9.99 9565 9655 9726 9782 9827 9863 9891 9913 9931 9945 9.99 9957 9966 9973 9978 9983 9986 9989 9991 9993 9995 9.99 9996 8628 8659 8689 8719 8749 8777 8805 8832 8859 8885 8910 8935 8959 8983 9006 9029 9051 9073 9094 9114 9135 9154 9174 9192 9211 9229 9246 9264 9280 9297 9327 9465 9575 9663 9732 9787 9831 9866 9893 9915 9933 9947 9958 9966 9973 9979 9983 .9987 9989 9992 9993 9995 9997 8631 8662 8693 8722 8751 8780 8808 8835 8861 8887 8913 8938 8962 8985 9009 9031 9053 9075 9096 9116 9137 9156 9175 9194 9213 9231 9248 9265 9282 9298 9342 9478 9585 9670 9738 9792 9835 9869 9896 9917 9934 9948 9959 9967 9974 9979 9983 9987 9990 9992 9993 9995 9997 8634 8665 8696 8725 8754 8783 8810 8838 8864 8890 8915 8940 8964 8988 9011 9033 9055 9077 9098 9118 9139 9158 9177 9196 9214 9232 9250 9267 9284 9300 9357 9489 9595 9678 9744 9797 9839 9872 9898 9919 9936 9949 9959 9968 9974 9980 9984 9987 9990 9992 9994 9995 9998 8637 8668 8699 8728 8757 8786 8813 8840 8867 8893 8918 8942 8967 8990 9013 9036 9058 9079 9100 9121 9141 9160 9179 9198 9216 9234 9252 9269 9285 9302 9372 9501 9604 9685 9750 9801 9842 9875 9900 9921 9937 9950 9960 9969 9975 9980 9984 9987 9990 9992 9994 9995 9998 8640 8643 8671 8674 8702 8705 8731 8734 8760 8763 8788 8791 8816 8819 8843 8846 8869 8872 8895 8898 8920 8923 8945 8947 8969 8971 8992 8995 9015 9018 9038 9040 9060 9062 9081 9083 9102 9104 9123 9125 9143 9145 9162 9164 9181 9183 9200 9202 9218 9220 9236 9238 9253 9255 9270 9272 9287 9289 9303 9305 9386 9400 9512 9524 9613 9622' 9692 9699 9756 9761 9806 9810 9846 9849 9878 9880 9903 9905 9923 9925 9939 9940 9951 9952 9961 9962 9969 9970 9976 9976 9981 9981 9985 9985 9988 9988 9990 9990 9992 9992 9994 9994 9995 9995 9999 9999 8646 8677 8708 8737 8766 8794 8821 8848 8874 8900 8925 8950 8974 8997 9020 9042 9064 9085 9106 9127 9146 9166 9185 9204 9222 9239 9257 9274 9290 9306 9414 9534 9630 9706 9767 9815 9853 9883 9907 9926 9941 9953 9963 9971 9977 9981 9985 9988 9991 9993 9994 9995 9999 8650 8653 8680 8683 8710 8713 8740 8743 8769 8771 8797 8799 8824 8827 8851 8854 8877 8880 8903 8905 8928 8930 8952 8955 8976 8978 8999 9002 9022 9024 9044 9047 9066 9068 9087 9090 9108 9110 9129 9131 9148 9150 9168 9170 9187 9189 9205 9207 9223 9225 9241 9243 9258 9260 9275 9277 9292 9293 9308 9310 9427 9440 9545 9555 9639 9647 9713 9720 9772 9777 9819 9823 9856 9859 9886 9888 9909 9911 9928 9930 9943 9944 9955 9956 9964 9965 9971 9972 9977 9978 9982 9982 9986 9986 9989 9989 9991 9991 9993 9/998 9994 9994 9995 9996 9999 9999 10 9 11 11 18 12 14 14 B = log a-log b. log a + C = log (a - b). VI. SINES AND TANGENTS OF SMALL ANGLES. 59 10 + LOO (8IN A" A) 10 + LOG (tan A" :A) MlN. Sec. 0° 1° 2° 3° 4° 0° 1° 2° 3° 4° 0' 4.68 5575 5553 5487 5376 5222 4.68 5575 5619 5751 5972 6281 0" 1 5575 5552 5485 5374 5219 5575 5620 5754 5976 6287 60 2 5575 5551 5484 5372 5216 5575 5622 5757 5981 6293 120 3 5575 5551 5482 5370 5213 5575 5623 5760 5985 6299 180 4 5575 5550 5481 5367 5210 5575 5625 5763 5990 6305 240 5 5575 5549 5479 5365 5207 5575 5627 5766 5994 6311 300 6 5575 5548 5478 5363 5204 5575 5628 5769 5999 6317 360 7 5575 5547 5476 5361 5201 5575 5630 5773 6004 6323 420 8 5574 5547 5475 5358 5198 5576 5632 5776 6008 6329 480 9 5574 5546 5473 5356 5195 5576 5633 5779 6013 6335 540 10 4.68 5574 5545 5471 5354 5192 4.68 5576 5635 5782 6017 6341 600 11 5574 5544 5470 5351 5189 5576 5637 5785 6022 6348 660 12 5574 5543 5468 5349 5186 5577 5638 5788 6027 6354 720 13 5574 5542 5467 5347 5183 5577 5640 5792 6031 6360 780 14 5574 5541 5465 5344 5180 5577 5642 5795 6036 6366 840 15 5573 5540 5463 5342 5177 5578 5644 5798 6041 6372 900 16 5573 5539 5462 5340 5173 5578 5646 5802 6046 6379 960 n 5573 5539 5460 5337 5170 5578 5648 5805 6051 6385 1020 18 5573 5538 5458 5335 5167 5579 5649 5808 6055 6391 1080 19 5573 5537 5457 5332 5164 5579 5651 5812 6060 6398 1140 20 4.68 5572 5536 5455 5330 5161 4.68 5580 5653 5815 6065 6404 1200 21 5572 5535 5453 5327 5158 5580 5655 5818 6070 6410 1260 22 5572 5534 5451 5325 5154 5581 5657 5822 6075 6417 1320 23 5572 5533 5450 5322 5151 5581 5659 5825 6080 6423 1380 24 5571 5532 5448 5320 5148 5582 5661 5829 6085 6430 1440 25 5571 5531 5446 5317 5145 5583 5663 5833 6090 6436 1500 26 5571 5530 544* 5315 5141 5583 5665 5836 6095 6443 1560 ' 27 5570 5529 5443 5312 5138 5584 5668 5840 6100 6449 1620 28 5570 5527 5441 5310 5135 5584 5670 5843 6105 6456 1680 29 5570 5526 5439 5307 5132 5585 5672 5847 6110 6462 1740 30 4.68 5569 5525 5437 5305 5128 4.68 5586 5674 5851 6116 6469 1800 31 5569 5524 5435 5302 5125 5587 5676 5854 6121 6476 1860 32 5569 5523 5433 5300 5122 5587 5679 5858 6126 6482 1920 33 5568 5522 5431 5297 5118 5588 5681 5862 6131 6489 1980 34 5568 5521 5430 5294 5115 5589 5683 5866 6136 6496 2040 35 5567 5520 5428 5292 5112 5590 5685 5869 6142 6503 2100 36 5567 5518 5426 5289 5108 5591 5688 5873 6147 6509 2160 37 5566 5517 5424 5286. 5105 5592 5690 5877 6152 6516 2220 38 ' 5566 5516 5422 5284 5101 5593 5693 5881 6158 6523 2280 39 5566 5515 5420 5281 5098 5593 5695 5885 6163 6530 2340 40 4.68 5565 5514 5418 5278 5095 4.68 5594 5697 5889 6168 6537 2400 41 5565 5512 5416 5276 5091 5595 5700 5893 6174 6544 2460 42 5564 5511 5414 5273 5088 5596 5702 5897 6179 6551 2520 43 . 5564 5510 5412 5270 5084 5597 5705 5900 6185 6557 2580 44 5563 5509 5410 5268 5081 5599 5707 5905 6190 6564 2640 45 5562 5507 5408 5265 5077 5600 5710 5909 6196 6571 2700 46 5562 5506 5406 5262 5074 5601 5713 5913 6201 6578 2760 47 5561 5505 5404 5259 5070 5602 5715 5917 6207 6585 2820 48 5561 5503 5402 5256 5067 5603 5718 5921 6212 6593 2880 49 5560 5502 5400 5254 5063 5604 5720 5925 6218 6600 2940 50 4.68 5560 5501 5398 5251 5060 4.68 5605 5723 5929 6224 6607 3000 51 5559 5499 5396 5248 5056 5607 5726 5933 6229 6614 3060 52 5558 5498 5394 5245 5053 5608 5729 5937 6235 6621 3120 53 5558 5497 5392 5242 5049 5609 5731 5942 6241 6628 3180 54 5557 5495 5389 5239 5045 5611 5734 5946 6246 6635 3240 55 5556 5494 5387 5237 5042 5612 5737 5950 6252 6643 3300 56 5556 5492 5385 5234 5038 5613 5740 5955 6258 6650 3360 57 5555 5491 5383 5231 5034 5615 5743 5959 6264 6657 3420 58 5554 5490 5381 5228 5031 5616 5745 5963 6269 6665 3480 59 5554 5488 5379 5225 5027 5618 5748 5968 6275 6672 3540 60 4.68 5553 5487 5376 5222 5024 4.68 5619 5751 5972 6281 6679 3600 Mix. 0" 3600" 7 200" 10800" 14400" 0" 3600" 7 200" 10800" 14400" Sec. 60 VII. TRIGONOMETRIC FUNCTIONS. 0° Sines. Cosines. Tangents. Dif. Cotangents. 179° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .00 000 00 00 1.0000 0.00 0000 .00 .00 000 00 00 00 00 60' i 029 6.46 3726 5017. 000 0000 029 6.46 3726 5017. 3.53 6274 3437.7 .V.i 2 058 6.76 4756 2985. 000 0000 058 6.76 4756 2935. 3.23 5244 171S.9 .V- 3 087 6.94 0847 2082. 000 0000 087 6.94 0847 2082. 3.05 9153 1145.9 57 4 116 7.06 5786 1615. 000 0000 116 7.06 5786 1615. 2.93 4214 859.44 56 5 145 7.16 2696 1820. 000 0000 .02 145 7.16 2696 1320. 2.83 7304 687.55 55 6 175 7.24 1877 1116. 000 9.99 9999 .00 175 7.24 1878 1116. 2.75 8122 572.96 54 7 204 7.30 8824 967. 000 9999 204 7.30 8825 967. 2.69 1175 491.11 53 8 288 7.36 6816 858. 000 9999 283 7.36 6817 853. 2.63 3183 429.72 52 9 262 7.41 7968 763. 000 9999 .02 262 7.41 7970 763. 2.58 2030 881.97 51 10 .00 291 7.46 3726 690. 1.0000 9.99 9998 .00 .00 291 7.46 3727 090. 2.53 6273 848.77 50 11 820 7.50 5118 680. .99 999 9998 .02 820 7.50 5120 680. 2.49 4880 312.52 49 12 349 7.54 2906 579. 999 9997 .00 349 7.54 2909 579. 2.45 7091 286.48 48 13 878 7.57 7668 586. 999 9997 .02 878 7.57 7672 586. 2.42 2328 264.44 47 14 407 7.60 9853 499. 999 9996 .00 407 7.60 9857 499. 2.39 0143 245.55 46 15 436 7.63 9816 467. 999 9996 .02 436 7.63 9820 467. 2.36 0180 229.18 45 16 465 7.66 7845 489. "999 9995 .00 465 7.66 7849 439. 2.33 2151 214.86 44 17 495 7.69 4173 414. 999 9995 .02 495 7.69 4179 414. 2.30 5821 202.22 43 18 524 7.71 8997 391. 999 9994 524 7.71 9003 891. 2.28 0997 190.98 42 19 553 7.74 2478 371. 99S 9993 .00 558 7.74 2484 871. 2.25 7516 180.98 41 20 .00 582 7.76 4754 358. .99 998 9.99 9993 .02 .00 582 7.76 4761 853. 2.23 5239 171.89 40 21 611 7.78 5943 837. 998 9992 611 7.78 5951 887. 2.214049 163.70 39 22 640 7.80 6146 322. 998 9991 640 7.80 6155 322. 2.19 3845 156.26 38 23 669 7.82 5451 808. 998 9990 669 7.82 5460 808. 2.17 4540 149.47 37 24 698 7.84 3934 295. 998 9989 .00 69S 7.84 3944 296. 2.15 6056 143.24 36 25 727 7.86 1662 284. 997 9989 .02 727 7.86 1674 2S4. 2.13 8326 137.51 35 26 756 7.87 8695 273. 997 9988 756 7.87 8708 273. 2.12 1292 132.22 34 27 785 7.89 5085 268. 997 9987 785 7.89 5099 268. 2.10 4901 127.82 33 28 814 7.91 0879 254. 997 9986 815 7.91 0894 254. 2.08 9106 122.77 32 29 844 7.92 6119 245. 996 9985 .03 644 7.92 6134 245. 2.07 3866 118.54 31 30 .00 873 7.94 0842 237. .99 996 9.99 9983 .02 .00 873 7.94 0858 287. 2.05 9142 114.59 30 31 902 7.95 5082 230. 996 9982 902 7.95 5100 230. 2.04 4900 110.89 29 32 931 7.96 8870 223. 996 9981 931 7.96 8889 223. 2.03 1111 107.43 18 33 960 7.98 2233 216. 995 9980 960 7.98 2253 216. 2.01 7747 104.17 27 34 9S9 7.99 5198 210. 995 9979 .03 989 7.99 5219 210. 2.00 4781 101.11 26 35 .01 018 8.00 7787 204. 995 9977 .02 .01 018 8.00 7809 204. 1.99 2191 98.218 25 36 047 8.02 0021 198. 995 9976 047 8.02 0044 198. 1.97 9956 95.4S9 24 37 076 8.03 1919 193. 994 9975 .03 076 8.03 1945 198. 1.96 8055 92.908 23 38 105 8.04 3501 188. 994 9973 .02 105 8.04 3527 188. 1.95 6473 90.463 22 39 184 8.05 4781 183. 994 9972 135 8.05 4809 183. 1.94 5191 88.144 21 40 .01 164 8.06 5776 179. .99 993 9.99 9971 .08 .01 164 8.06 5806 179. 1.93 4194 85.940 20 41 198 8.07 6500 174. 993 9969 .02 198 8.07 6531 174. 1.92 3469 88.844 19 42 222 8.08 6965 170. 998 9968 .03 222 8.08 6997 170. 1.91 3003 81.847 18 43 251 8.09 7183 166. 992 9966 251 8.09 7217 166. 1.90 2783 79.948 17 44 280 8.10 7167 163. 992 9964 .02 280 8.10 7203 168. 1.89 2797 7S.126 16 45 809 8.11 6926 159. 991 9963 .08 809 8.11 6963 159. 1.88 3037 76.890 15 46 888 8.12 6471 156. 991 9961 888 8.12 6510 156. 1.87 3490 74.729 14 47 867 8.13 5810 152. 991 9959 .02 867 8.13 5851 152. 1.86 4149 78.189 13 48 896 8.14 4953 149. 990 9958 .08 896 8.14 4996 149. 1.85 5004 71.615 12 49 425 8.15 3907 146. 990 9956 425 8.15 3952 146. 1.84 6048 70.158 11 50 .01454 8.16 2681 143. .99 989 9.99 9954 .08 .01455 8.16 2727 148. 1.83 7273 68.750 10 51 483 8.17 1280 141. 989 9952 484 8.17 1328 141. 1.82 8672 67.402 9 52 513 9713 188. 989 9950 518 9763 18S. 0237 66.105 8 53 542 8.18 7985 185. 988 9948 542 8.18 8036 185. 1.81 1964 64.858 7 54 571 8.19 6102 183. 988 9946 571 8.19 6156 183. 1.80 3844 68.657 6 55 600 8.20 4070 180. 987 9944 600 8.20 4126 180. 1.79 5874 62.499 5 56 629 8.21 1895 128. 987 9942 629 8.21 1953 12S. 1.78 8047 61.888 4 57 658 9581 120. 986 9940 658 9641 126. 0359 60.806 3 58 687 8.22 7134 124. 986 9938 687 8.22 7195 124. 1.77 2805 69.266 2 59 716 8.23 4557 122. 985 9936 716 8.23 4621 122. 1.76 5379 58.261 1 60 .01 745 8.24 1855 .99 985 9.99 9934 .01 746 8.24 1921 1.75 8079 57.290 90° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 89° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 61 1° SlNE8. Cosines. Tangents. Dif. Cotangents. 178° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .01745 8.24 1855 120. .99 985 9.99 9934 .03 .01 746 8.24 1921 120. 1.75 8079 57.290 60' 1 774 9033 118. 984 9932 .05 775 9102 11s. 0898 56.351 59 2 803 8.25 6094 116. 984 9929 .03 804 8.25 6165 116. 1.74 3835 55.442 58 3 832 8.26 3042 114. 983 9927 833 8.26 3115 114. 1.73 6885 54.561 57 4 862 9881 112. 983 9925 .05 862 9956 112. 0044 53.709 56 5 891 8.27 6614 110. 9S2 9922 .03 891 8.27 6691 111. 1.72 3309 52.882 55 6 920 8.28 3243 109. 982 9920 920 8.28 3323 109. 1.716677 .081 54 7 949 9773 107. 981 9918 .05 949 9856 107. 0144 51.303 53- 8 . 978 8.29 6207 106. 980 9915 .03 978 8.29 6292 106. 1.70 3708 50.549 52 9 .02 007 8.30 2546 104. 980 9913 .05 .02 007 8.30 2634 104. 1.69 7366 49.816 51 10 .02 036 8.30 8794 103. .99 979 9.99 9910 .05 .02 036 8.30 8884 103. 1.69 1116 49.104 50 11 065 8.31 4954 101. 979 9907 .03 066 8.31 5046 101. 1.68 4954 48.412 49 12 094 8.32 1027 99.8 978 9905 .05 095 8.32 1122 99.9 1.67 8878 47.740 48 13 123' 7016 98.5 977 9902 124 7114 98.5 2886 .085 47 14 152 8.33 2924 97.2 977 9899 .03 153 8.33 3025 97.2 1.66 6975 46.449 46 15 181 8753 95.9 976 9897 .05 182 8856 95.9 1144 45.829 45 16 211 8.34 4504 94.6 976 9894 211 8.34 4610 94.7 1.65 5390 .226 44 17 240 8.35 0181 93.4 975 9891 240 8.35 0289 93.4 1.64 9711 44.639 43 18 269 5783 92.2 974 9888 269 5895 92.3 4105 .066 42 19 298 8.36 1315 91.0 974 9885 298 8.36 1430 91.1 1.63 8570 43.508 41 20 .02 327 8.36 6777 89.9 .99 973 9.99 9882 .05 .02 828 8.36 6895 90.0 1.63 3105 42.964 40 21 356 8.37 2171 88.8 972 9879 857 8.37 2292 8S.8 1.62 7708 .433 39 22 385 7499 87.7 972 9876 386 7622 87.8 2378 41.916 38 23 414 8.38 2762 86.7 971 9873 415 8.38 2889 86.7 1.61 7111 .411 37 24 443 7962 S5.7 970 9870 444 8092 85.7 1908 40.917 36 25 472 8.39 3101 84.6 969 9867 473 8.39 3234 84.7 1.60 6766 .436 35 26 501 8179 83.7 969 9864 502 8315 83.7 1685 39.965 34 27 530 8.40 3199 82.7 968 9861 531 8.40 3338 82.8 1.59 6662 .506 - 33 28 560 8161 81.8 967 9858 .07 560 8304 81.8 1696 .057 32 29 589 8.41 3068 80.9 966 9854 .05 589 8.41 3213 80.9 1.58 6787 38.618 31 30 .02 618 8.41 7919 80.0 .99 966 9.99 9851 .05 .02 619 8.41 8068 80.0 1.58 1932 88.188 30 31 647 8.42 2717 79.1 965 9848 .07 648 8.42 2869 79.2 1.57 7131 37.769 29 32 676 7462 78.2 964 9844 .05 677 7618 78.3 2382 .858 28 33 705 8.43 2156 77.4 963 9841 706 8.43 2315 77.5 1.56 7685 36.956 27 34 734 6800 .76.6 963 9838 .07 735 6962 76.6 3038 .563 26 35 763 8.44 1394 75.8 962 9834 .05 764 8.44 1560 75.8 1.55 8440 .178 25 36 792 5941 75.0 961 9831 .07 793 6110 75.1 3890 85.801 24 37 821 8.45 0440 74.2 960 9827 .05 822 8.45 0613 74.3 1.54 9387 .431 23 38 850 4893 73.5 959 9824 .07 851 5070 78.5 4930 .070 22 39 879 9301 72.7 959 9820 881 9481 72.8 0519 34.715 21 40 .02 908 8.46 3665 72.0 .99 958 9.99 9816 .05 .02 910 8.46 3849 72.1 1.53 6151 34.368 20 41 938 7985 71.3 957 9813 .07 939 8172 71.4 1828 .027 19 42 967 8.47 2263 70.6 956 9809 968 8.47 2454 70.7 1.52 7546 33.694 18 43 996 6498 69.9 955 9805 997 6693 70.0 3307 .866 17 44 .03 025 8.48 0693 69.3 954 9801 .03 026 8.48 0892 69.3 1.51 9108 .045 16 45 .03 054 4848 68.6 953 9797 .05 055 5050 68.7 4950 82.730 15 46 083 8963 68.0 952 9794 .07 084 9170 68.0 0830 .421 14 47 112 8.49 3040 67.3 952 9790 114 8.49 3250 67.4 1.50 6750 .118 13 48 141 7078 66.7 951 9786 143 7293 66.8 2707 31.821 12 49 170 8.50 1080 66.1 950 9782 172 8.50 1298 66.2 1.49 8702 .528 11 50 .03 199 8.50 5045 65.5 .99 949 9.99 9778 .07 .03 201 8.50 5267 65.6 1.49 4733 31.242 10 51 228 8974 64.9 948 9774 .08 230 9200 65.0 0800 30.960 9 52 257 8.51 2867 64.3 947 9769 .07 259 8.51 3098 64.4 1.48 6902 .683 8 53 286 6726 68.8 946 9765 288 6961 63.8 3039 .412 7 54 316 8.52 0551 63.2 945 9761 317 8.52 0790 68.8 1.47 9210 .145 6 55 345 4343 62.7 944 9757 346 4586 62.7 5414 29.882 5 56 374 8102 62.1 943 9753 .08 376 8349 62.2 1651 .624 4 57 403 8.53 1828 61.6 942 9748 .07 405 8.53 2080 61.7 1.46 7920 .871 3 58 432 5523 61.1 941 9744 434 5779 61.1 4221 .122 2 59 461 9186 60.6 940 9740 .08 463 9447 60.6 0553 28.877 1 60 .03 490 8.54 2819 .99 939 9.99 9735 .03.492 8.54 3084 1.45 6916 2S.636 91° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 88° Cosines. Sines. . 62 VII. TRIGONOMETRIC FUNCTIONS. 2° Sines. Cosines. Tangents. Dif. Cotangents. 177° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat 0' .03 490 8.54 2819 / 60.1 .99 939 9.99 9735 .07 .03 492 8.54 3084 60.1 1.45 6916 28.636 60' i 519 6422 59.6 988 9731 .08 521 6691 59.6 3309 .899 59 2 548 9995 59.1 937 9726 .07 650 8.55 0268 59.2 1.44 9732 .166 58 3 577 8.55 3539 68.6 986 9722 .08 579 3817 58.7 6183 27.987 57 4 606 7054 5S.1 985 9717 .07 609 7336 68.2 2664 .712 56 5 685 8.56 0540 57.7 934 97i3 .08 638 8.56 0828 57.7 1.43 9172 .490 55 6 664 3999 57.2 988 9708 .07 667 4291 57.8 5709 .271 54 7 693 7431 56.8 932 9704 08 696 7727 56.8 2273 .057 53 8 723 8.57 0836 56.3 931 9699 725 8.57 1137 56.4 1.42 8863 26.845 52 9 752 4214 55.9 930 9694 754 4520 66.0 5480 .637 51 10 .03 781 8.57 7566 55.4 .99 929 9.99 9689 07 .03 783 8.57 7877 55.5 1.42 2123 26.432 50 11 810 8.58 0892 65.0 927 9685 08 812 8.58 1208 65.1 1.41 8792 .280 49 12 839 4193 64.6 926 9680 842 4514 54.7 5486 .031 48 13 868 7469 54.2 925 9675 871 7795 64.3 2205 25.835 47 14 897 8.59 0721 68.8 924 9670 900 8.59 1051 63.9 1.40 8949 .642 46 15 926 3948 53.4 923 9665 929 4283 53.5 5717 .452 45 16 .955 7152 53.0 922 9660 958 7492 53.1 2508 .264 44 17 984 8.60 0332 52.6 921 9655 987 8.60 0677 52.7 1.39 9323 .080 43 18 .04 013 3489 52.2 919 9650 .04 016 . 3839 52.8 6161 24.898 42 19 042 6623 51.9 918 9645 046 6978 51.9 3022 .719 41 20 .04 071 8.60 9734 51.5 .99 917 9.99 9640 08 .04 075 8.61 0094 51.6 1.38 9906 24.542 40 21 100 8.61 2823 51.1 916 9635 10 104 3189 51.2 6811 .868 39 22 129 5891 60.8 915 9629 OS 133 6262 60.9 3738 .196 38 23 159 8937 50.4 913 9624 162 9313 60.5 0687 .026 37 24 188 8.62 1962 50.1 912 9619 191 8.62 2343 60.2 1.37 7657 23.859 36 25 217 4965 49.7 911 9614 10 220 5352 49.8 4648 .695 35 26 246 7948 49.4 910 9608 08 250 8340 49.5 1660 .582 34 27 275 8.63 0911 49.1 909 9603 .10 279 8.63 1308 49.1 1.36 8692 .372 33 28 304 3854 48.7 907 9597 .03 308 4256 48.8 5744 .214 32 29 883 6776 48.4 906 9592 .10 337 7184 48.5 2816 .058 31 30 .04 362 8.63 9680 48.1 .99 905 9.99 9586 08 .04 366 8.64 0093 4S.2 1.35 9907 22.904 30 31 891 8.64 2563 4T.8 904 9581 .10 395 2982 47.9 7018 .752 29 32 420 5428 47.4 902 9575 .08 424 5853 47.5 4147 .602 28 33 449 8274 47.1 901 9570 .10 454 8704 47.2 1296 .454 27 34 478 8.65 1102 46.8 900 9564 4S3 8.65 1537 46.9 1.34 8463 .808 26 35 507 3911 46.5 898 9558 .08 512 4352 46.6 5648 .164 25 36 586 6702 46.2 897 9553 .10 541 7149 46.3 2851 .022 24 37 565 9475 45.9 896 9547 570 9928 46.0 0072 21.881 23 38 594 8.66 2230 45.6 894 9541 599 8.66 2689 45.7 1.33 7311 .743 22 39 623 4968 45.4 898 9535 623 5433 45.5 4567 .606 21 40 .04 653 8.66 7689 45.1 .99 892 9.99 9529 .08 .04 658 8.66 8160 45.2 1.33 1840 21.470 20 41 682 8.67 0393 44.8 S90 9524 .10 687 8.67 0870 44.9 1.32 9130 .887 19 42 711 3080 44.5 889 9518 716 3563 44.6 6437 .205 18 43 740 5751 44.2 888 9512 745 6239 44.4 3761 .075 17 44 769 8405 44.0 886 9506 774 8900 44.1 1100 20.946 ' 16 45 798 8.68 1043 48.7 885 9500 .12 803 8.68 1544 43.8 1.31 8456 .819 15 46 827 3665 48.5 883 9493 .10 888 4172 43.5 5828 .698 14 47 856 6272 48.2 882 9487 862 6784 48.8 3216 .669 13 48 885 8863 42.9 881 9481 891 9381 48.0 0619 .446 12 49 914 8.69 1438 42.7 879 9475 920 8.69 1963 42.8 1.30 8037 .825 11 50 .04 948 8.69 3998 42.4 .99 878 9.99 9469 .10 .04 949 8.69 4529 42.5 1.30 5471 20.206 10 51 972 6543 42.2 876 9463 .12 978 7081 42.8 2919 .087 9 52 .05 001 9073 41.9 875 9456 .10 .05 007 9617 42.0 0383 19.970 8 53 030 8.70 1589 41.7 878 9450 .12 087 8.70 2139 41.S 1.29 7861 .855 7 54 059 4090 41.5 872 9443 .10 066 4646 41.6 5354 .740 6 55 088 6577 41.2 870 9437 095 7140 41.3 2860 .627 5 56 117 9049 41.0 869 9431 .12 124 9618 41.1 0382 .516 4 57 146 8.71 1507 40.8 867 9424 .10 158 8.71 2083 40.9 1.28 7917 .405 3 58 175 3952 40.5 866 9418 .12 182 4534 40.6 5466 .296 •J 59 205 6383 40.8 864 9411 212 6972 40.4 3028 .188 1 60 .05 284 8.71 8800 .99S68 9.99 9404 .05 241 8.71 9396 1.28 0604 IMS! 92° Nat. Log. Dlf. Nat. Log. Dlf. Nat. Log. Cotangents. Dlf. Log. Nat. 87° Cosines. Sines. Tangents. VII. TRIGONOMETRIC FUNCTIONS. 63 1 1 3° Sines. COSINES. Tangents. Dif. Cotangents. 176° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .05 2*4 8.71 8800 40.1 .99 863 9.99 9404 .10 .05 241 8.71 9396 40.2 1.28 0604 19.081 60' i 263 8.72 120*4 89.9 861 9398 .12 270 8.72 1806 40.0 1.27 8194 18.976 59 2 292 3595 89.6 860 9391 299 4204 39.7 5796 .871 58 3 821 5972 39.4 858 9384 .10 328 6588 39.5 3412 .768 57 4 350 8337 89.2 857 9378 .12 357 8959 39.3 1041 .666 56 5 379 8.73 0688 39.0 855 9371 387 8.73 1317 39.1 1.26 8683 .564 55 6 408 3027 88.8 854 9364 416 3663 38.9 6337 .464 54 7 437 5354 38.6 852 9357 445 5996 88.7 4004 .366 53 8 466 7667 88.4 851 9350 474 8317 88.5 1683 .268 52 9 495 9969 88.2 849 9343 503 8.74 0626 88.3 1.25 9374 .171 51 10 .05 524 8.74 2259 88.0 .99 847 9.99 9336 .12 .05 533 8.74 2922 38.1 1.25 7078 18.075 50 11 553 4536 37.8 846 9329 562 5207 37.9 4793 17.980 49 12 582 6802 87.6 844 9322 591 7479 37.7 2521 .886 48 13 611 9055 87.4 842 9315 620 9740 87.5 0260 .793 47 14 640 8.75 1297 87.2 841 9308 649 8.75 1989 87.3 1.24 8011 .702 46 15 669 3528 37.0 839 9301 678 4227 87.1 5773 .611 45 16 698 5747 36.8 838 9294 708 6453 86.9 3547 .521 44 17 727 7955 86.6 836 9287 .13 787 8668 36.7 1332 .431 43 18 756 8.76 0151 36.4 834 9279 .12 766 8.76 0872 36.6 1.23 9128 .343 42 19 785 2337 86.2 833 9272 795 3065 36.4 6935 .256 41 20 .05 814 8.76 4511 36.1 .99 831 9.99 9265 .13 .05 824 8.76 5246 86.2 1.23 4754 17.169 40 21 844 6675 85.9 829 9257 .12 854 7417 86.0 2583 .084 39 22 873 8828 35.7 827 9250 .13 883 9578 35.8 0422 16.999 38 23 902 8.77 0970 85.5 826 9242 .12 912 8.77 1727 35.7 1.22 8273 .915 37 24 931 3101 35.4 824 9235 .13 941 3866 85.5 6134 .882 36 25 960 5223 35.2 822 9227 .12 970 5995 85.8 4005 .750 35 26 989 7333 85.0 821 9220 .13 .05 999 8114 85.1 1886 .668 34 27 .06 018 9434 84.8 819 9212 .12 .06 029 8.78 0222 35.0 1.219778 .587 33 28 047 8.78 1524 84.7 817 9205 .13 058 2320 843 7680 .507 32 29 076 3605 34.5 815 9197 087 4408 846 5592 .428 31 30 .06 105 8.78 5675 84.4 .99 818 9.99 9189 .18 .06 116 8.78 6486 845 1.21 3514 16.350 30 31 134 7736 842 812 9181 .12 145 8554 848 1446 .272 29 32 163 9787 840 810 9174 .18 175 8.79 0613 84.2 1.20 9387 .195 28 33 192 8.79 1828 83.9 808 9166 204 2662 340 7338 .119 27 34 221 3859 88.7 806 9158 233 4701 33.8 5299 .043 26 35 250 5881 83.6 804 9150 262 6731 88.7 3269 15.969 25 36 279 7894 88.4 803 9142 291 8752 83.5 1248 .895 24 37 80S 9897 83.3 801 9134 321 8.80 0763 88.4 1.19 9237 .821 23 38 337 8.80 1892 33.1 799 - 9126 850 2765 88.2 7235 .748 22 39 866 3876 82.9 797 9118 879 4758 88.1 5242 .676 21 40 .06 395 8.80 5852 82.8 .99 795 9.99 9110 .13 .06 408 8.80 6742 32.9 1.19 3258 15.605 20 41 424 7819 82.6 793 9102 438 8717 82.8 1283 .584 19 42 453 9777 32.5 792 9094 467 8.81 0683 32.6 1.18 9317 .464 18 43 482 8.81 1726 82.4 790 9086 .15 496 2641 32.5 7359 .894 17 44 511 3667 82.2 788 9077 .13 525 4589 82.3 5411 .825 16 45 540 5599 32.1 786 9069 554 6529 32.2 3471 .257 15 46 569 7522 31.9 784 9061 584 8461 82.1 1539 .189 14 47 593 9436 81.8 782 9053 .15 613 8.82 0384 81.9 1.17 9616 .122 13 48 627 8.82 1343 31.6 780 9044 .13 642 2298 8L8 7702 .056 12 49 656 3240 31.5 778 9036 .15 671 4205 81.6 5795 14990 11 50 .06 6S5 8.82 5130 31.4 .99 776 9.99 9027 .13 .06 700 8.82 6103 31.5 1.17 3897 14.924 10 51 714 7011 81.2 774 9019 .15 730 7992 81.4 2008 .860 9 52 743 8884 31.1 772 9010 .13 759 9874 81.2 0126 .795 8 53 773 8.83 0749 31.0 770 9002 .15 788 8.83 1748 31.1 1.16 8252 .782 7 54 802 2607 80.8 768 8993 817 3613 81.0 6387 .669 6 55 831 4456 30.7 766 8984 .13 847 5471 80.8 4529 .606 5 56 860 6297 80.6 764 8976 .15 876 7321 80.7 2679 .544 4 57 889 8130 80.4 762 8967 905 9163 30.6 0837 .482 3 58 918 9956 80.8 760 8958 .13 934 8.84 0998 80.5 1.15 9002 .421 2 59 947 8.84 1774 80.2 75S 8950 .15 963 2825 30.3 7175 .361 1 60 .06 976 8.84 3585 .99 756 9.99 8941 .06 993 8.84 4644 1.15 5356 14.801 93° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat 86° Cosines. Sines. Tangents. 64 VII. TRIGONOMETRIC FUNCTIONS. 4° Sines. Cosines. Tangents. Dif. Cotangents. 175° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .06 976 8.84 3585 80.0 .99 756 9.99 8941 .15 .06 998 8.84 4644 80.2 1.15 5356 14.801 60* i .07 005 5387 29.9 754 8932 .07 022 6455 80.1 3545 .241 59 2 084 7183 29.8 752 8923 051 8260 80.0 1740 .182 58 3 068 8971 29.7 750 8914 080 8.85 0057 29.8 1.14 9943 .124 5? 4 092 8.85 0751 29.6 748 8905 110 1846 29.7 8154 .065 56 5 121 2525 29.4 746 8896 139 3628 29.6 6372 .008 IS 6 150 4291 29.8 744 8887 168 5403 29.5 4597 13.951 54 7 179 6049 29.2 742 8878 197 7171 29.4 2829 .894 53 8 208 7801 29.1 740 8869 227 8932 29.2 1068 .888 52 9 287 9546 29.0 738 8860 256 8.86 0686 29.1 1.13 9314 .782 51 10 .07 266 8.86 1283 28.9 .99 736 9.99 8851 .17 .07 285 8.86 2433 29.0 1.13 7567 18.727 50 11 295 3014 28.7 734 8841 .15 314 4173 28.9 5827 .672 49 12 324 4738 28.6 731 8832 844 5906 28.8 4094 .617 48 13 858 6455 28.5 729 8823 .17 873 7632 28.7 2368 .568 47 14 882 8165 28.4 727 8813 .15 402 9351 28.6 0649 .510 46 15 411 9868 28.8 725 8804 431 8.87 1064 28.4 1.12 8936 .457 45 16 440 8.87 1565 28.2 723 8795 .17 461 2770 28.8 7230 .404 44 17 469 3255 28.1 721 8785 .15 490 4469 28.2 5531 .352 43 18 498 4938 28.0 719 8776 .17 519 6162 28.1 3838 .800 42 19 527 6.615 27.8 716 8766 .15 548 7849 28.0 2151 .248 41 20 .07 556 8.87 8285 27.7 .99 714 9.99 8757 .17 .07 578 8*87 9529 27.9 1.12 0471 18.197 40 21 585 9949 27.6 712 8747 .15 607 8.88 1202 27.8 1.11 8798 .146 39 22 614 8.88 1607 27.5 710 8738 .17 686 2869 27.7 7131 .096 38 23 643 3258 27.4 708 8728 665 4530 27.6 5470 .046 37 24 672 4903 27.3 705 8718 695 6185 27.5 3815 12.996 36 25 701 6542 27.2 703 8708 .15 724 7833 27.4 2167 .947 35 26 780 8174 27.1 701 8699 .17 753 9476 27.8 0524 .898 34 27 759 9801 27.0 699 8689 782 8.89 1112 27.2 1.10 8888 .850 33 28 788 8.89 1421 26.9 696 8679 812 2742 27.1 7258 .801 32 29 817 3035 26.8 694 8669 841 4366 27.0 5634 .754 31 30 .07 846 8.89 4643 26.7 .99 692 9.99 8659 .17 .07 870 8.89 5984 26.9 1.10 4016 12.706 30 31 875 6246 26.6 689 8649 899 7596 26.8 2404 .659 29 32 904 7842 26.5 687 8639 929 9203 26.7 0797 .612 28 33 933 9432 26.4 685 8629 958 8.90 0803 26.6 1.09 9197 .566 27 34 962 8.90 1017 26.3 6S3 8619 987 2398 26.5 7602 .620 26 35 991 2596 26.2 680 8609 .08 017 3987 26.4 6013 .474 25 36 .08 020 4169 26.1 678 8599 046 5570 26.8 4430 .429 2 1 37 049 5736 26.0 676 8589 .18 075 7147 26.2 2853 .384 23 38 078 7297 25.9 673 8578 .17 104 8719 26.1 1281 .839 2 2 39 107 8853 671 8568 184 8.91 0285 26.0 1.08 9715 .295 21 40 .08 186 8.91 0404 25.8 .99 668 9.99 8558 .17 .08 168 8.91 1846 25.9 1.08 8154 12.251 20 41 165 1949 25.7 666 8548 .18 192 3401 25.8 6599 .207 19 42 194 3488 25.6 664 8537 .17 221 4951 25.7 5049 .168 18 43 228 5022 25.5 661 8527 .18 251 6495 3505 .120 17 44 252 6550 25.4 659 8516 .17 280 8034 25.6 1966 .077 16 45 281 8073 25.8 657 8506 .18 309 9568 25.5 0432 .085 15 46 810 9591 25.2 654 8495 .17 389 8.92 1096 25.4 1.07 8904 11.992 14 47 839 8.92 1103 25.1 652 8485 .18 868 2619 25.8 7381 .960 13 48 868 2610 25.0 649 8474 .17 897 4136 25.2 5864 .909 12 49 397 4112 647 8464 .18 427 5649 25.1 4351 .867 11 50 .08 426 8.92 5609 24.9 .99 644 9.99 8453 .18 .08 456 8.92 7156 25.0 1.07 2844 11.826 10 51 455 7100 24.8 .642 8442 485 8658 1342 .785 9 52 484 8587 24.7 689 8431 .17 514 8.93 0155 24.9 1.06 9845 .745 8 53 518 8.93 0068 24.6 687 8421 .18 544 1647 24.8 8353 .705 7 54 542 1544 24.5 685 8410 578 3134 247 6866 12 49 767 3388 223 2214 .40 106 1174 8826 389 11 50 .18 795 9.27 4049 11.0 .98 218 9.99 2190 .40 .19 186 9.28 1858 11.4 0.71 8142 6.2257 10 51 824 4708 212 2166 166 2542 1458 174 9 52 852 5367 207 2142 197 3225 •;7 7;> 092 8 53 881 6025 10.9 201 2118 .42 227 3907 6093 011 7 54 910 6681 196 2093 .40 257 4588 11.8 5412 :..i ;»•-".» 6 55 988 7337 190 2069 .42 2S7 5268 4732 848 5 56 967 7991 185 2044 .40 817 5947 4053 7i',7 4 57 995 8645 179 2020 847 6624 3376 686 3 58 .19 024 9297 174 1996 .42 878 7301 2699 606 2 59 052 9948 168 1971 .40 408 7977 2023 626 1 60 .19 081 9.28 0599 .98 168 9.99 1947 .19 488 9.28 8652 0.71 1348 .\nir, 100° Nat. Log. Dif. Nat. Log. Dif. Nat Log. Dif. Cotangents. Log. Nat. Tangents. 79° Cosines. Sines. 1 — VII. TRIGONOMETRIC FUNCTIONS. 71 11° SINE8. Cosines. Tangents. Cotangents. 168° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .19 081 9.28 0599 10.8 .98 163 9.99 1947 .42 .19 438 9.28 8652 11.2 0.71 1348 5.1446 60' 1 109 1248 157 1922 468 9326 0674 366 59 2 138 1897 152 1897 .40 498 9999 0001 286 58 3 167 2544 146 1873 .42 529 9.29 0671 0.70 9329 207 57 4 195 3190 140 1848 559 1342 8658 128 56 5 224 3836 10.7 135 1823 .40 589 2013 7987 049 55 6 252 4480 129 1799 .42 619 2682 11.1 7318 5.0970 54 7 281 5124 124 1774 649 3350 6650 892 53 8 309 5766 118 1749 680 4017 5983 814 52 9 338 6408 112 1724 710 4684 5316 736 51 10 .19 366 9.28 7048 10.7 .98 107 9.99 1699 .42 .19 740 9.29 5349 11.1 0.70 4651 5.0658 50 11 395 7688 10.6 101 1674 770 6013 3987 581 49 12 423 8326 096 1649 801 6677 11.0 3323 504 48 13 452 ' 8964 090 1624 831 7339 2661 427 47 14 481 9600 084 1599 861 8001 1999 350 46 15 509 9.29 0236 079 1574 891 8662 1338 273 45 16 538 0870 073 1549 921 9322 0678 197 44 17 566 1504 067 1524 .43 952 9980 0020 121 43 18 595 2137 10.5 061 1498 .42 982 9.30 0638 0.69 9362 045 42 19 623 2768 056 1473 .20 012 1295 10.9 8705 4.9969 41 20 .19 652 9.29 3399 10.5 .98 050 9.99 1448 .43 .20 042 9.30 1951 10.9 0.69 8049 4.9894 40 21 680 4029 044 1422 .42 073 2607 7393 819 39 22 709 4658 039 1397 103 3261 6739 744 38 23 737 5286 033 1372 .43 133 3914 6086 669 37 24 766 5913 10.4 027 1346 .42 164 4567 5433 594 36 25 794 6539 021 1321 .43 194 5218 4782 520 35 26 823 7164 016 1295 .42 224 5869 10.8 4131 446 34 27 851 7788 010 1270 .43 254 6519 3481 372 33 28 880 8412 004 1244 285 7168 2832 298 32 29 908 9034 .97 998 1218 .42 315 7816 2184 225 31 30 .19 937 9.29 9655 10.4 .97 992 9.99 1193 .43 .20 345 9.30 8463 10.8 0.69 1537 4.9152 30 31 965 9.30 0276 10.3 987 1167 376 9109 0891 078 29 32 994 0895 981 1141 406 9754 0246 006 28 33 .20 022 1514 975 1115 .42 436 9.31 0399 10.7 0.68 9601 4.8933 27 34 051 2132 969 1090 .43 466 1042 8958 860 26 35 079 2748 963 1064 497 1685 8315 788 25 36 108 3364 958 1038 527 2327 7673 716 24 37 136 3979 10.2 952 1012 557 2968 7032 644 23 38 165 4593 946 . 0986 588 3608 6392 573 22 39 193 5207 940 0960 618 4247 10.6 5753 501 21 40 .20 222 9.30 5819 10.2 .97 934 9.99 0934 .43 .20 648 9.31 4885 10.6 0.68 5115 4.8430 20 41 250 6430 928 0908 679 5523 4477 359 19 42 279 7041 922 0882 .45 709 6159 3841 288 18 43 307 7650 916 0855 .43 739 6795 3205 218 17 44 836 8259 10.1 910 0829 770 7430 2570 147 16 45 364 8867 905 0803 800 8064 1936 077 15 46 393 9474 899 0777 .45 830 8697 1303 007 14 47 • 421 9.31 0080 893 0750 .43 861 9330 10.5 0670 4.7937 13 48 450 0685 887 0724 .45 891 9961 0039 867 12 49 478 1289 881 0697 .43 921 9.32 0592 0.67 9408 798 11 50 .20 507 9.31 1893 10.0 .97 875 9.99 0671 .43 .20 952 9.32 1222 10.5 0.67 8778 4.7729 10 51 535 2495 869 0645 .45 982 1851 8149 659 9 52 563 3097 863 0618 .21 013 2479 7521 591 8 53 592 3698 9.98 857 0591 .43 043 3106 6894 522 7 54 620 4297 10.0 851 0565 .45 073 3733 10.4 6267 453 6 55 649 4897 9.97 845 0538 104 4358 5642 385 5 56 677 5495 9.95 839 0511 .43 134 4983 5017 317 4 57 706 6092 833 0485 .45 164 5607 4393 249 3 58 734 6689 9.92 827 0458 195 6231 3769 181 2 59 763 7284 821 0431 225 6853 3147 114 1 60 .20 791 9.31 7879 .97 815 9.99 0404 .21 256 9.32 7475 0.67 2525 4.7046 101° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Cotangents. Log. Nat. * 78° Cosines. Sines. Tangents. 72 VII. TRIGONOMETRIC FUNCTIONS. 12° Sinks. Cosines. Tangents. Dlf. Cotangents. 167° Nat. Log. Dlf. Nat. Log. Dlf. Nat Log. Log. Nat 0' .20 791 9.31 7879 9.90 .97 815 9.99 0404 .43 .21 256 9.32 7475 10.8 0.67 2625 t.T'i ji; 60' l 820 8473 9.88 809 0378 .45 286 8095 1905 4.6979 59 2 848 9066 9.87 808 0351 316 8715 1285 912 58 3 877 9658 9.85 797 0324 347 9334 0666 845 57 4 905 9.32 0249 791 0297 877 9953 0047 779 56 5 988 0840 9.83 784 0270 408 9.33 0570 0.66 9430 712 55 6 962 1430 9.82 778 0243 .47 438 1187 8813 646 54 7 990 2019 9.80 772 0215 .45 469 1803 8197 580 53 8 .21 019 2607 9.78 766 0188 499 2418 7582 514 B2 9 047 3194 9.77 760 0161 529 3033 10.2 6967 448 51 10 .21 076 9.32 3780 9.77 .97 754 9.99 0134 .45 .21560 9.33 3646 10.2 0.66 6354 4.6382 50 11 104 4366 9.73 748 0107 .47 590 4259 5741 817 49 12 182 4950 742 0079 .45 621 4871 5129 252 48 13 161 5534 9.72 735 0052 651 5482 4518 187 47 14 189 6117 729 0025 .47 682 6093 3907 122 46 15 218 6700 9.68 723 9.98 9997 .45 712 6702 3298 057 45 16 246 7281 717 9970 .47 743 7311 10.1 2689 4.5998 44 17 275 7862 9.67 711 9942 .45 773 7919 2081 928 43 18 803 8442 9.65 705 9915 .47 804 8527 1473 864 42 19 331 9021 9.63 698 9887 .45 834 9133 0867 800 41 20 .21 860 9.32 9599 9.62 .97 692 9.98 9860 .47 .21864 9.33 9739 10.1 0.66 0261 4.5786 40 21 888 9.33 0176 686 9832 895 9.34 0344 0.65 9656 678 39 22 417 0753 9.60 680 9804 .45 925 0948 9052 609 38 23 445 1329 9.57 673 9777 .47 956 1552 8448 546 37 24 474 1903 9.58 667 9749 986 2155 10.0 7845 488 36 25 502 2478 9.55 661 9721 .22 017 2757 7243 420 35 26 580 3051 655 9693 047 3358 6642 357 34 27 559 3624 9.62 648 9665 078 3958 6042 294 33 28 587 4195 9.53 642 9637 .45 108 4558 9.98 5442 282 32 29 616 4767 9.60 636 9610 .47 139 5157 9.97 4843 169 31 30 .21644 9.33 5337 9.48 .97 680 9.98 9582 .48 .22 169 9.34 5755 9.97 0.65 4245 4.5107 30 31 672 5906 628 9553 .47 200 6353 9.98 3647 045 29 32 701 6475 9.47 617 9525 281 6949 3051 4.4983 28 33 729 7043 9.45 611 9497 261 7545 2455 922 27 34 758 7610 9.43 604 9469 292 8141 9.90 1859 860 26 35 786 8176 598 9441 822 8735 1265 799 25 36 814 8742 9.42 592 9413 853 9329 9.88 0671 787 24 37 848 9307 9.40 585 9385 .48 888 9922 9.87 0078 676 23 38 871 9871 9.88 579 9356 .47 414 9.35 0514 0.64 9486 Ufl 22 39 899 9.34 0434 9.87 678 9328 444 1106 9.85 8894 655 21 40 .21 928 9.34 0996 9.87 .97 566 9.98 9300 .48 .22 475 9.35 1697 9.83 0.64 8303 4.4494 20 41 956 1558 9.85 660 9271 .47 505 2287 9.82 7713 484 19 42 985 2119 9.83 658 9243 .48 686 2876 7124 878 18 43 .22 018 2679 547 9214 .47 567 3465 9.80 6535 313 17 44 041 3239 9.80 541 9186 .48 597 4053 9.78 5947 268 16 45 070 3797 684 9157 628 4640 5360 194 15 46 098 4355 9.28 528 9128 .47 658 5227 9.77 4773 184 14 47 126 4912 521 9100 .48 689 5813 9.75 4187 075 13 48 155 5469 9.26 515 9071 719 6398 9.78 3602 015 12 49 188 6024 508 9042 .47 750 6982 3018 4.8956 11 50 .22 212 9.34 6579 9.25 .97 502 9.98 9014 .48 .22 781 9.35 7566 9.72 0.64 2434 4.8897 10 51 240 7134 9.22 496 8985 811 8149 9.70 1851 888 9 52 268 7687 489 8956 842 8731 1269 779 8 • 53 297 8240 9.20 488 8927 872 9313 9.67 0687 721 7 54 825 8792 9.18 476 8898 908 9893 9.68 0107 662 6 55 858 9343 9.17 470 8869 984 9.36 0474 9.66 0.63 9526 604 5 56 882 9893 468 8840 964 1053 8947 646 4 57 410 9.35 0443 9.15 467 8811 995 1632 9.68 8368 488 3 58 488 0992 9.18 460 8782 .23 026 2210 9.62 7790 480 2 59 467 1540 444 8763 066 2787 7213 872 1 60 .22 495 9.35 2088 .97 487 9.98 8724 .28 087 9.36 3364 0.63 6636 4.8815 102° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Cotangents. Dif. Log. Nat Tangents. 77° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 73 " 13° Sines. Cosines. Tangents. Dif. Cotangents. 166° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .22 495 9.35 2088 9.12 .97 437 9.98 8724 .48 .23 087 9.36 3364 9.60 0.63 6636 4.8315 60' i 523 2635 9.10 430 8695 117 3940 9.58 6060 257 59 2 552 3181 9.08 424 8666 .50 148 4515 5485 200 58 3 580 3726 417 8636 .48 179 5090 9.57 4910 143 57 4 60S 4271 9.07 411 8607 209 5664 9.55 4336 086 56 5 637 4815 9.05 404 8578 .50 240 6237 3763 029 55 6 665 5358 398 8548 .48 271 6810 9.53 3190 4.2972 54 7 693 5901 9.03 391 8519 .50 301 7382 9.52 2618 916 53 8 722 6443 9.02 384 8489 AS 382 7953 2047 S59 52 9 750 6984 9.00 378 8460 .50 363 8524 9.50 1476 8(8 51 10 .22 778 9.35 7524 9.00 .97 871 9.98 8430 .48 .23 393 9.36 9094 9.48 0.63 09C6 4.2747 50 11 807 8064 8.98 365 8401 .50 424 9663 0337 691 49 12 835 8603 8.97 358 8371 .48 455 9.37 0232 9.45 0.62 9768 635 48 13 863 9141 a95 351 8342 .50 485 0799 9.47 9201 580 47 14 892 9678 345 8312 516 1367 9.48 8633 524 46 15 920 9.36 0215 388 8282 547 1933 8067 468 45 16 948 0752 8.92 331 8252 .48 578 2499 9.42 7501 418 44 17 977 1287 325 8223 .50 608 3064 6936 358 43 18 .23 005 1822 8.90 318 8193 639 3629 9.40 6371 303 42 19 033 2356 8.88 811 8163 670 4193 9.88 5807 248 41 20 .23 062 9.36 2889 8.88 .97 304 9.98 8133 .50 .23 700 9.37 4756 9.88 0.62 5244 4.2193 40 21 090 3422 8.87 298 8103 731 5319 9.87 4681 139 39 22 118 3954 8.S5 291 8073 762 5881 9.35 4119 084 38 23 146 4485 284 8043 793 6442 3558 080 37 24 175 5016 8.83 278 8013 823 7003 9.83 2997 4.1976 36 25 203 5546 8.82 271 7983 854 7563 9.82 2437 922 35 26 231 6075 264 7953 .52 885 8122 1878 868 34 27 260 6604 &78 257 7922 .50 916 8681 9.80 1319 814 33 28 288 7131 8.80 251 7892 946 9239 0761 760 32 29 316 7659 8.77 244 7862 977 9797 9.28 0203 706 31 30 .23 345 9.36 8185 8.77 .97 237 9.98 7832 .52 .24 008 9.38 0354 9.27 0.61 9646 4.1658 30 31 373 8711 8.75 230 7801 .50 089 0910 9090 600 29 32 401 9236 228 7771 .52 069 1466 9.23 8534 547 28 33 429 9761 8.73 217 7740 .50 100 2020 9.25 7980 493 27 34 458 9.37 0285 a72 210 7710 .52 181 2575 9.23 7425 441 26 35 486 0808 8.70 203 7679 .50 162 3129 9.22 6871 388 25 36 514 1330 196 7649 .52 193 3682 9.20 6318 835 24 37 542 1852 8.68 189 7618 .50 223 4234 5766 282 23 38 571 2373 182 . 7588 .52 254 4786 9.18 5214 230 22 39 599 2894 8.67 176 7557 • 285 5337 4663 178 21 40 .23 627 9*37 3414 8.65 .97 169 9.98 7526 .50 .24 816 9.38 5888 9.17 0.614112 4.1126 20 41 656 3933 162 7496 .52 847 6438 9.15 3562 074 19 42 684 4452 8.63 155 7465 377 6987 3013 022 18 43 712 4970 8.62 148 7434 408 7536 9.13 2464 4.0970 17 44 740 5487 8.60 141 7403 439 8084 9.12 1916 918 16 45 769 6003 134 7372 470 8631 1369 867 15 46 797 6519 127 7341 501 9178 9.10 0822 815 14 47 825 7035 8.57 120 7310 582 9724 0276 764 13 48 853 7549 113 7279 562 9.39 0270 9.08 0.60 9730 713 12 49 882 8063 106 7248 593 0815 9185 662 11 50 .23 910 9.37 8577 8.53 .97 100 9.98 7217 .52 .24 624 9.39 1360 9.05 0.60 8640 4.0611 10 51 938 9089 093 7186 655 1903 9.07 8097 560 9 52 966 9601 086 7155 686 2447 9.03 7553 509 8 53 995 9.38 0113 8.52 079 7124 .53 717 2989 7011 459 7 54 .24 023 0624 8.50 072 7092 .52 747 3531 6469 408 6 55 051 1134 8.48 065 7061 778 4073 9.02 5927 358 5 56 079 1643 058 7030 .53 809 4614 9.00 5386 808 4 57 10S 2152 051 6998 .52 840 5154 4846 257 3 58 136 2661 8.45 044 6967 871 5694 8.98 4306 207 2 59 164 3168 . 037 6936 .53 902 6233 8.97 3767 158 1 60 .24 192 9.38 3675 .97 080 9.98 6904 .24 933 9.39 6771 0.60 3229 4.0108 103° Nat. Log. Dif. Nat. Log. Dif. Nat, Log. Cotangents. Dif. Log. Nat. 76° Cosines. Sines. Tangents. 74 VII. TRIGONOMETRIC FUNCTIONS. 14° Sines. Cosines. Tangents. Dif. Cotangents. 165° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .24 192 9.38 3675 8.45 .97 030 9.98 6904 .52 .24 983 9.39 6771 8.97 0.60 3229 4.0108 60' l 220 4182 8.42 023 6873 .53 964 7309 8.95 2691 058 59 2 249 4687 015 6841 995 7846 2154 009 58 3 277 5192 008 6809 .52 .25 026 8383 8.98 1617 8.9959 57 4 805 5697 8.40 001 6778 .53 056 8919 1081 910 56 5 888 6201 8.88 .96 994 6746 087 9455 8.92 0545 861 55 6 362 6704 987 6714 .52 118 9990 8.90 0010 812 54 7 390 7207 8.87 980 6683 .53 149 9.40 0524 0.59 9476 768 53 8 418 7709 8.85 973 6651 180 1058 8.88 8942 714 52 9 446 8210 966 6619 211 1591 8409 665 51 10 .24 474 9.38 8711 8.38 .96 959 9.98 6587 .53 .25 242 9.40 2124 8.87 0.59 7876 3.9617 50 11 503 9211 952 6555 278 2656 8.85 7344 563 49 12 531 9711 8.32 945 6523 304 .3187 6813 520 48 13 559 9.39 0210 8.30 987 6491 885 3718 6282 471 47 14 587 0708 930 6459 366 4249 8.82 5751 428 46 15 615 1206 8.28 923 6427 397 4778 8.88 5222 375 45 16 644 1703 8.27 916 6395 428 5308 8.80 4692 827 44 17 672 2199 909 6363 459 5836 4164 279 43 18 700 2695 902 6331 490 6364 3636 282 42 19 728 3191 8.28 894 6299 .55 521 6892 8.78 3108 184 41 20 .24 756 9.39 3685 8.23 .96 887 9.98 6266 .53 .25 552 9.40 7419 8.77 0.59 2581 3.9186 40 21 784 4179 880 6234 583 7945 2055 089 39 22 813 4673 8.22 873 6202 .55 614 8471 8.75 1529 042 38 23 841 5166 8.20 866 6169 .53 645 8996 1004 8.8995 37 24 869 5658 858 6137 .55 676 9521 8.78 0479 947 36 25 897 6150 8.18 851 6104 .53 707 9.41 0045 0.58 9955 900 35 26 925 6641 844 6072 .55 738 0569 8.72 9431 854 34 27 954 7132 8.15 887 6039 .53 769 1092 8908 807 33 28 982 7621 8.17 829 6007 .55 800 1615 8.70 8385 760 32 29 .25 010 8111 8.15 822 5974 .53 831 2137 8.68 7863 714 31 30 .25 038 9.39 8600 8.13 .96 815 9.98 5942 .55 .25 862 9.41 2658 8.68 0.58 7342 8.8667 30 31 066 9088 8.12 807 5909 893 3179 8.67 6821 621 29 32 094 9575 800 5876 924 3699 6301 575 28 33 122 9.40 0062 793 5843 .53 955 4219 8.65 5781 528 27 34 151 0549 8.10 786 5811 .55 986 4738 5262 482 26 35 179 1035 8.08 778 5778 .26 017 5257 8.68 4743 486 25 36 207 1520 771 5745 048 5775 4225 891 24 37 285 2005 8.07 764 5712 079 6293 8.62 3707 845 23 38 263 2489 8.05 756 5679 110 6810 8.60 3190 299 22 39 291 2972 749 5646 141 7326 2674 254 21 40 .25 820 9.40 3455 8.05 .96 742 9.98 5613 .55 .26 172 9.41 7842 8.60 0.58 2158 8.8208 20 41 848 3938 8.08 734 5580 208 8358 8.58 1642 163 19 42 876 4420 8.02 727 5547 235 8873 8.57 1127 118 18 43 404 4901 719 5514 .57 266 9387 0613 078 17 44 482 5382 8.00 712 5480 .55 297 9901 0099 028 16 45 460 5862 7.98 705 5447 828 9.42 0415 8.58 0.57 9585 8.79S8 15 46 488 6341 697 5414 859 0927 8.55 9073 988 14 47 516 6820 690 5381 .57 390 1440 8.53 8560 §98 13 48 545 7299 7.97 682 5347 .55 421 1952 8.52 8048 843 IS 49 578 7777 7.95 675 5314 .57 452 2463 7537 804 11 50 .25 601 9.40 8254 7.95 .96 667 9.98 5280 .55 .26 483 9.42 2974 8.50 0.57 7026 8.7760 10 51 629 8731 7.98 660 5247 .57 515 3484 8.48 6516 715 9 52 657 9207 7.92 658 5213 .55 546 3993 8.50 6007 071 8 53 685 9682 645 5180 .57 577 4503 8.47 5497 M 7 54 718 9.41 0157 688 5146 .55 608 5011 4989 538 6 55 741 0632 7.90 680 5113 .57 689 5519 4481 589 5 56 769 1106 7.88 628 5079 670 6027 8.45 3973 495 4 57 798 1579 615 5045 701 6534 3466 451 3 58 826 2052 7.87 608 5011 .55 788 7041 8.48 2969 408 2 59 854 2524 600 4978 .57 764 7547 8.42 2453 864 1 60 .25 882 9.41 2996 .96 598 9.98 4944 .26 795 9.42 8052 0.57 1948 8.7821 104° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 75° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 75 f— — — — 1 15° Sines. Cosines. Tangents. Dif. Cotangents. 164° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .25 882 9.41 2996 7.85 .96 593 9.98 4944 .57 .26 795 9.42 8052 8.48 0.57 1948 3.7321 60' i 910 3467 585 4910 826 8558 8.40 1442 277 59 2 938 3938 7.83 578 4876 857 9062 0938 234 58 3 966 4408 570 4842 888 9566 0434 191 57 4 994 4878 7.82 562 4808 920 9.43 0070 8.88 0.56 9930 148 56 5 .26 022 5347 7.80 555 4774 951 0573 8.87 9427 105 55 6 050 5815 547 4740 982 1075 8925 062 - 54 7 079 6283 540 4706 .27 013 1577 8423 019 53 8 107 6751 7.77 532 4672 044 2079 8.85 7921 3.6976 52 9 135 7217 7.78 524 4638 .58 076 2580 8.83 7420 933 51 10 .26 163 9.41 7684 7.77 .96 517 9.98 4603 .57 .27 107 9.43 3080 8.88 0.56 6920 3.6891 50 11 191 8150 7.75 509 4569 138 3580 6420 848 49 12 219 8615 7.73 502 4535 .58 169 4080 8.82 5920 806 48 13 247 9079 7.75 494 4500 .57 201 4579 5421 764 47 14 275 9544 7.72 486 4466 232 5078 8.80 4922 722 46 15 303 9.42 0007 479 4432 .58 263 5576 8.28 4424 680 45 16 331 0470 471 4397 .57 294 6073 3927 638 44 17 359 0933 7.70 463 4363 .58 826 6570 3430 596 43 18 387 1395 456 4328 .57 857 7067 8.2T 2933 554 42 19 415 1857 7.68 448 4294 .58 388 7563 2437 512 41 20 .26 443 9.42 2318 7.67 .96 440 9.98 4259 .58 .27 419 9.43 8059 8.25 0.56 1941 3.6470 40 21 471 2778 433 4224 .57 451 8554 8.23 1446 429 39 22 500 3238 7.65 425 4190 .58 482 9048 8.25 0952 387 38 23 528 3697 417 4155 513 9543 8.22 0457 346 37 24 556 4156 410 4120 545 9.44 0036 0.55 9964 305 36 25 584 4615 7.63 402 4085 576 0529 9471 264 35 26 612 5073 7.62 394 4050 607 1022 8.20 8978 222 34 27 640 5530 386 4015 .57 638 1514 8486 181 33 28 668 5987 7.60 379 3981 .58 670 2006 8.18 7994 140 32 29 696 .6443 371 3946 701 2497 7503 100 31 30 .26 724 9.42 6899 7.58 .96 363 9.98 3911 .60 .27 732 9.44 2988 818 0.55 7012 3.6059 30 31 752 7354 355 3875 .58 764 3479 8.15 6521 018 29 32 780 7809 7.57 347 3840 795 3968 8.17 6032 8.5978 28 33 808 8263 340 3805 826 4458 8.15 5542 937 27 34 836 8717 7.55 832 3770 858 4947 8.18 5053 897 26 35 864 9170 324 3735 889 5435 4565 856 25 36 892 9623 7.53 816 3700 .60 921 5923 4077 816 24 37 920 9.43 0075 808 3664 .58 952 6411 8.12 3589 776 23 38 948 0527 7.52 301 ' 3629 983 6898 8.10 3102 786 22 39 976 0978 293 3594 .60 .28 015 7384 2616 696 21 40 .27 004 9.43 1429 7.50 .96 285 9.98 3558 .58 .28 046 9.44 7870 8.10 0.55 2130 3.5656 20 41 032 1879 277 3523 .60 077 8356 8.08 1644 616 19 42 060 2329 7.48 269 3487 .58 109 8841 1159 576 18 43 088 2778 7.47 261 3452 .60 140 9326 8.07 0674 536 17 44 116 3226 7.48 253 3416 .58 172 9810 0190 49T 16 45 144 3675 7.45 246 3381 .60 203 9.45 0294 8.05 0.54 9706 457 15 46 172 4122 238 3345 234 0777 9223 418 14 47 200 4569 230 3309 266 1260 8740 379 13 48 228 5016 7.43 222 3273 .58 297 1743 8.03 8257 839 12 49 256 5462 214 3238 .60 329 2225 8.02 7775 300 11 50 .27 284 9.43 5908 7.42 .96 206 9.98 3202 .60 .28 360 9.45 2706 8.02 0.54 7294 3.5261 10 51 812 6353 198 3166 391 3187 6813 222 9 52 840 6798 7.40 190 3130 423 3668 8.00 6332 183 8 53 368 7242 182 3094 454 4148 5852 144 7 54 396 7686 7.38 174 3058 486 4628 7.98 5372 105 6 55 424 8129 166 3022 517 5107 4893 067 5 56 452 8572 7.87 158 2986 549 5586 7.97 4414 028 " 4 57 480 9014 150 2950 580 6064 3936 8.4989 3 58 508 9456 7.85 142 2914 612 6542 7.95 3458 951 2 59 536 9897 134 2878 643 7019 2981 912 1 60 .27 564 9.44 0338 .96 126 9.98 2842 .28 675 9.45 7496 0.54 2504 8.4874 105° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 740 Cosines. Sines. TANGENT8. I VII. TRIGONOMETRIC FUNCTIONS. 16° Sines. Cosines. Tangents. Dif. Cotangents. 163° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .27 564 9.44 0338 7.88 .96 126 9.98 2842 .62 .28 675 9.45 7496 7.95 0.54 2504 3.4874 60' 1 592 0778 118 2805 .60 706 7973 7.98 2027 886 59 2 620 1218 110 2769 788 8449 1551 798 58 3 648 1658 7.30 102 2733 .62 769 8925 7.92 1075 760 57 4 676 2096 7.82 094 2696 .60 801 9400 0600 722 56 5 704 2535 7.80 086 2660 832 9875 7.90 0125 684 55 6 781 2973 7.28 078 2624 .62 864 9.46 0349 0.53 9651 646 54 7 759 3410 070 2587 .60 895 0823 9177 608 53 8 787 3847 062 2551 .62 927 1297 7.88 8703 570 52 9 815 4284 7.27 054 2514 958 1770 7.87 8230 533 51 10 .27 848 9.44 4720 7.25 .96 046 9.98 2477 .60 .28 990 9.46 2242 7.88 0.53 7758 3.4495 50 11 871 5155 037 2441 .62 .29 021 2715 7.85 7285 458 49 12 899 5590 029 2404 058 3186 7.87 6814 420 48 13 927 6025 7.23 021 2367 .60 084 3658 7.88 6342 888 47 14 955 6459 013 2331 .62 116 4128 7.85 5872 846 46 15 988 6893 7.22 005 2294 147 4599 7.88 5401 80S 45 16 .28 Oil 7326 .95 997 2257 179 5069 4931 271 44 17 089 7759 7.20 989 2220 210 5539 7.82 4461 284 43 18 067 8191 981 2183 242 6008 3992 197 42 19 095 8623 7.18 972 2146 274 6477 7.80 3523 160 41 20 .28 123 9.44 9054 7.18 .95 964 9.98 2109 .62 .29 805 9.46 6945 7.80 0.53 3055 3.4124 40 21 150 9485 7.17 956 2072 837 7413 7.78 2587 087 39 22 178 9915 948 2035 368 7880 2120 050 38 23 206 9.45 0345 940 1998 400 8347 1653 014 37 24 234 0775 7.15 931 1961 482 8814 7.77 1186 8.8977 36 25 262 1204 7.18 928 1924 .63 463 9280 0720 941 35 26 290 1632 915 1886 .62 495 9746 7.75 0254 904 34 27 818 2060 907 1849 526 9.47 0211 0.52 9789 868 33 28 346 2488 7.12 898 1812 .63 558 0676 9324 882 32 29 374 2915 890 1774 .62 590 1141 7.73 8859 796 31 30 .28 402 9.45 3342 7.10 .95 882 9.98 1737 .62 .29 621 9.47 1605 7.73 0.52 8395 8.8759 30 31 429 3768 874 1700 .63 658 2069 7.72 7931 723 29 32 457 4194 7.08 865 1662 .62 685 2532 7468 687 28 33 485 4619 857 1625 .63 716 2995 7.70 7005 652 27 34 513 5044 849 1587 748 3457 6543 616 26 35 541 5469 r.07 841 1549 .62 780 3919 6081 580 25 36 569 5893 7.05 882 1512 .63 811 4381 7.68 5619 544 24 37 597 6316 824 1474 843 4842 5158 509 23 38 625 6739 816 1436 .62 875 5303 7.67 4697 478 22 39 652 7162 7.03 807 1399 .63 906 5763 4237 488 21 40 .28 680 9.45 7584 7.03 .95 799 9.98 1361 .63 .29 988 9.47 6223 7.67 0.52 3777 8.8402 20 41 708 8006 7.02 791 1323 970 6683 7.65 3317 867 19 42 736 8427 782 1285 .80 001 7142 2858 882 18 43 764 8848 7.00 774 1247 088 7601 7.68 2399 297 17 44 792 9268 766 1209 065 8059 1941 261 16 45 820 9688 757 1171 097 8517 1483 226 15 46 847 9.46 0108 6.98 749 1133 128 8975 7.62 1025 191 14 47 875 0527 740 1095 160 9432 0568 156 13 48 908 0946 6.97 782 1057 192 9889 7.60 0111 122 12 49 981 1364 724 1019 224 9.48 0345 0.51 9655 087 11 50 .28 959 9.46 1782 6.96 .95 715 9.98 0981 .65 .80 255 9.48 0801 7.60 0.51 9199 LMM 10 51 987 2199 707 0942 .68 287 1257 7.58 8743 017 9 52 .29 015 2616 6.98 698 0904 819 1712 8288 8.2988 8 53 042 3032 690 0866 .65 851 2167 7.57 7833 948 7 54 070 3448 681 0827 .68 882 2621 7379 914 6 55 098 3864 6.92 678 0789 .65 414 3075 6925 879 5 56 126 4279 664 0750 .68 446 3529 7.55 6471 846 4 57 154 4694 6.90 656 0712 .65 478 3982 6018 811 3 58 182 5108 647 0673 .68 509 4435 7.68 5565 111 2 59 209 5522 6.88 689 0835 .65 541 4887 5113 743 1 60 .29 287 9.46 5935 .95 680 9.98 0596 .80 578 9.48 5339 0.51 4661 LSTM 106° Nat. Log. Dif Nat. Log. Dif. Nat. Log. • Dif. Log. Nat 73° Cosines. Sink*. Tangents. VII. TRIGONOMETRIC FUNCTIONS. 77 .— 17° Sines. Cosines. Tangents. Cotangents. 162° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .29 237 9.46 5935 6.88 .95 630 9.98 0596 63 .30 573 9.48 5339 7.53 0.51 4661 3.2709 60' i 265 6348 622 0558 65 605 5791 7.52 4209 675 59 2 293 6761 6.87 613 0519 637 6242 3758 641 58 3 321 7173 605 0480 63 669 6693 7.50 3307 607 57 4 848 7585 6.85 596 0442 65 700 7143 2857 573 56 5 376 7996 588 0403 732 7593 2407 539 55 6 404 8407 6.88 579 0364 764 8043 7.4S 1957 506 54 7 432 8817 571 0325 796 8492 1508 472 53 8 460 9227 562 0286 828 8941 1059 438 52 9 487 9637 6.82 554 0247 860 9390 7.47 0610 405 51 10 .29 515 9.47 0046 6.82 .95 545 9.98 0208 65 .30 891 9.48 9838 7.47 0.51 0162 3.2371 50 11 543 0455 6.80 536 0169 928 9.49 0286 7.45 0.50 9714 338 49 12 571 0863 528 0130 955 0733 9267 805 48 13 599 1271 519 0091 987 1180 8820 272 47 14 626 1679 6.78 511 0052 67 .31 019 1627 7.43 8373 238 46 15 654 2086 6.77 502 0012 65 051 2073 7927 205 45 16 682 2492 493 9.97 9973 083 2519 7481 172 44 17 710 2898 485 9934 115 2965 7.42 7035 139 43 18 737 3304 476 9895 .67 147 3410 7.40 6590 106 42 19 765 3710 6.75 467 9855 .65 178 3854 7.42 6146 073 41 20 .29 793 9.47 4115 6.73 .95 459 .9.97 9816 .67 .31 210 9.49 4299 7.40 0.50 5701 8.2041 40 21 821 4519 450 9776 .65 242 4743 7.38 5257 008 39 22 849 4923 441 9737 .67 274 5186 7.40 4814 3.1975 38 23 876 5327 6.72 483 . 9697 .65 306 5630 7.38 4370 943 37 24 904 5730 424 9658 .67 338 6073 7.37 3927 910 36 25 932 6133 415 9618 .65 370 6515 3485 878 35 26 960 ' 6536 6.70 407 9579 .67 402 6957 3043 845 34 27 987 6938 398 9539 434 7399 2601 813 33 28 .30 015 7340 6.68 389 9499 466 7841 7.85 2159 780 32 29 043 7741 380 9459 .65 498 8282 7.33 1718 748 31 30 .80 071 9.47 8142 6.67 .95 872 9.97 9420 .67 .31530 9.49 8722 7.85 0.50 1278 8.1716 30 31 098 8542 363 9380 562 9163 7.33 0837 684 29 32 126 8942 354 9340 594 9603 7.32 0397 652 28 33 154 9342 6.65 345 9300 626 9.50 0042 0.49 9958 620 27 34 182 9741 387 9260 658 0481 9519 588 26 35 209 9.48 0140 328 9220 690 0920 9080 556 25 36 237 0539 6.63 819 9180 722 1359 7.30 8641 524 24 37 265 0937 6.62 310 9140 754 1797 8203 492 23 38 292 1334 301 9100 68 786 2235 7.28 7765 460 22 39 320 1731 293 9059 67 818 2672 7328 429 21 40 .30 348 9.48 2128 6.62 .95 284 9.97 9019 .67 .81 850 9.50 3109 7.28 0.49 6891 3.1397 20 41 376 2525 6.60 275 8979 882 3546 7.27 6454 366 19 42 403 2921 6.58 266 8939 68 914 3982 6018 834 18 43 481 3316 6.60 257 8898 67 946 4418 5582 303 17 44 459 3712 6.58 248 8858 68 978 4854 7.25 5146 271 16 45 486 4107 6.57 240 8817 67 .32 010 5289 4711 240 15 46 514 4501 281 8777 042 5724 4276 209 14 47 542 4895 222 8737 68 074 6159 7.28 3841 178 13 48 570 5289 6.55 213 8696 106 6593 3407 146 12 49 597 5682 204 8655 67 139 7027 7.22 2973 115 11 50 .30 625 9.48 6075 6.53 .95 195 9.97 8615 .68 .82 171 9.50 7460 7.22 0.49 2540 8.1084 10 51 653 6467 6.55 186 8574 203 7893 2107 053 9 52 680 6860 6.52 177 8533 .67 235 8326 1674 022 8 53 708 7251 6.58 168 8493 .68 267 8759 7.20 1241 8.0991 7 54 736 7643 6.52 159 8452 299 9191 7.18 0809 961 6 55 768 8034 6.50 150 8411 331 9622 7.20 0378 930 5 56 791 8424 142 8370 863 9.51 0054 7.18 0.48 9946 899 4 57 819 8814 133 8329 396 0485 9515 868 3 58 846 9204 6.48 124 8288 428 0916 7.17 » 9084 838 2 59 874 9593 115 8247 460 1346 8654 807 1 60 .30 902 9.48 9982 .95 106 9.97 8206 .82 492 9.51 1776 0.48 8224 8.0777 107° Nat. Log. Dif. Nat. Log. I )if. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 72° Cosines. S1NE8. 78 VII. TRIGONOMETRIC FUNCTIONS. 18° Sines. Cosines. Tangents. Dif. Ootunm 161° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .30 902 9.48 9982 6.48 .95 106 9.97 8206 .« .32 492 9.51 1776 7.17 0.48 8224 8.0777 60' i 929 9.49 0371 6.47 097 8165 524 2206 7.15 7794 746 59 2 957 0759 088 8124 556 2635 7365 716 58 3 985 1147 079 8083 588 3064 6936 686 57 4 .31 012 1535 6.45 070 8042 621 3493 7.18 6507 655 56 5 040 1922 6.48 061 8001 .70 658 3921 6079 625 55 6 068 2308 6.45 052 7959 .68 685 4349 5651 595 54 7 095 2695 6.43 048 7918 717 4777 7.12 5223 565 53 8 128 3081 6.42 033 7877 .70 749 5204 4796 535 52 9 151 3466 024 7835 .68 782 5631 7.10 4369 505 51 10 .81 178 9.49 3851 6.42 .95 015 9.97 7794 .70 .32 814 9.51 6057 7.12 0.48 3943 8.0475 50 11 206 4236 006 7752 .68 846 6484 7.10 3516 445 49 12 233 4621 6.40 .94 997 7711 .70 878 6910 7.08 3090 415 48 13 261 5005 6.38 988 7669 .68 911 7335 7.10 2665 885 47 14 289 5388 6.40 979 7628 .70 943 7761 7.08 2239 356 46 15 316 5772 6.37 970 7586 975 8186 7.07 1814 826 45 16 344 6154 6.38 961 7544 .68 .33 007 8610 1390 296 44 17 372 6537 6.37 952 7503 .70 040 9034 0966 267 43 18 399 6919 943 7461 072 9458 0542 287 42 19 427 7301 6.85 933 7419 104 9882 7.05 0118 208 41 20 .31454 9.49 7682 6.37 .94 924 9.97 7377 .70 .33 136 9.52 0305 7.05 0.47 9695 8.0178 40 21 482 8064 6.83 915 7335 169 0728 9272 149 39 22 510 8444 6.85 906 7293 201 1151 7.08 8849 W 38 23 537 8825 6.32 897 7251 288 1573 8427 090 37 24 565 9204 6.33 888 7209 266 1995 8005 061 36 25 593 9584 6.82 878 7167 298 2417 7.02 7583 032 35 26 620 9963 869 7125 330 2838 7162 003 34 27 648 9.50 0342 860 7083 363 3259 6741 2.9974 33 28 675 0721 6.30 851 7041 395 3680 7.00 6320 945 32 29 703 1099 6.28 842 6999 427 4100 5900 916 31 30 .31 730 9.50 1476 6.30 .94 832 9.97 6957 .72 .33 460 9.52 4520 7.00 0.47 5480 2.9887 30 31 758 1854 6.28 823 6914 .70 492 4940 6.93 5060 858 29 32 786 2231 6.27 814 6872 524 5359 4641 829 gfl 33 813 2607 6.28 805 6830 .72 557 5778 4222 S00 27 34 841 2984 6.2T 795 6787 .70 589 6197 6.97 3803 772 26 35 868 3360 6.25 786 6745 .72 621 6615 3385 743 25 36 896 3735 777 6702 .70 654 7033 2967 714 24 37 928 4110 768 6660 .72 686 7451 6.95 2549 686 23 38 951 4485 758 6617 718 7868 2132 657 22 39 979 4860 6.28 749 6574 .70 751 8285 1715 629 21 40 .32 006 9.50 5234 6.23 .94 740 9.97 6532 .72 .88 783 9.52 8702 6.95 0.47 1298 2.9600 20 41 034 5608 6.22 730 6489 816 9119 6.93 0881 Rl 19 42 061 5981 721 6446 .70 848 9535 0465 544 18 43 089 6354 712 6404 .72 881 9951 6.92 0049 515 17 44 116 6727 6.20 702 6361 913 9.53 0366 0.46 9634 487 16 45 144 7099 693 6318 945 0781 9219 459 15 46 171 7471 684 6275 978 1196 8804 481 14 47 199 7843 6.18 674 6232 .84 010 1611 6.90 8389 403 13 48 227 8214 665 6189 048 2025 7975 875 12 49 254 8585 656 6146 075 2439 7561 847 11 50 .82 282 9.50 8956 6.17 .94 646 9.97 6103 .72 .34 108 9.53 2853 6.88 0.46 7147 2.9819 10 51 809 9326 687 6060 140 3266 6734 291 9 52 887 9696 6.15 627 6017 178 3679 6321 M s 53 864 9.51 0065 618 5974 .78 205 4092 6.87 5908 285 7 54 892 0434 609 5930 .72 288 4504 5496 208 6 55 419 0803 699 5887 270 4916 5084 180 5 56 447 1172 6.18 590 5844 .78 808 5328 6.85 4672 152 4 57 474 1540 6.12 580 5800 .72 885 5739 4261 1 -'.-> 3 58 502 1907 6.18 571 5757 868 6150 3850 097 ■2 59 529 2275 6.12 561 5714 .78 400 6561 3439 070 1 60 .82 557 9.51 2642 .94 552 9.97 5670 .84 438 9.53 6972 0.46 3028 2.9042 108° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat Tangents. 71° Cosines. Sines. ,, _, .. VII. TRIGONOMETRIC FUNCTIONS. 79 19° Sines. Cosines. Tangents. Dif. Cotangents. 160° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .32 557 9.51 2642 6.12 .94 552 9.97 5670 .72 .34 483 9.53 6972 6.83 0.46 3028 2.9042 60' i 584 3009 6.10 542 5627 .78 465 7382 2618 015 59 2 612 3375 583 5583 498 7792 2208 2.8987 58 3 639 3741 523 5539 .72 530 8202 6.82 1798 960 57 4 667 4107 6.08 514 5496 .78 568 8611 1389 933 56 5 694 4472 504 5452 596 9020 0980 905 55 6 722 4837 495 5408 .72 628 9429 6.80 0571 878 54 7 749 5202 6.07 485 5365 .73 661 9837 0163 851 53 8 777 5566 476 5321 693 9.54 0245 0.45 9755 824 52 9 804 5930 466 5277 726 0653 9347 797 51 10 .32 &32 9.51 6294 6.05 .94 457 9.97 5233 .78 .34 758 9.54 1061 6.78 0.45 8939 2.8770 50 11 859 6657 447 5189 791 1468 8532 748 49 12 887 7020 6.03 438 5145 824 1875 6.77 8125 716 48 13 914 7382 6.05 428 5101 856 2281 6.78 7719 689 47 14 942 7745 6.03 418 5057 889 2688 6.77 7312 662 46 15 969 8107 6.02 409 5013 922 3094 6.75 6906 636 45 16 997 8468 399 4969 954 3499 6.77 6501 609 44 17 .33 024 8829 390 4925 .75 987 3905 6.75 6095 582 43 18 051 9190 380 4880 .73 .35 020 4310 5690 556 42 19 079 9551 6.00 370 4836 052 4715 6.78 5285 529 41 20 .33 106 9.51 9911 6.00 .94 361 9.97 4792 .73 .85 085 9.54 5119 6.75 0.45 4881 2.8502 40 21 134 9.52 0271 351 4748 .75 118 5524 6.78 4476 476 39 22 161 0631 5.98 342 4703 .78 150 5928 6.72 4072 449 38 23 1S9 0990 882 4659 .75 183 6331 6.73 3669 423 37 24 216 1349 5.97 322 4614 .73 216 6735 6.72 3265 397 36 25 244 1707 5.98 313 4570 .75 248 7138 6.70 2862 370 35 26 271 2066 5.97 308 4525 .73 281 7540 6.72 2460 344 34 27 298 2424 5.95 293 4481 .75 314 7943 6.70 2057 318 33 28 326 2781 284 4436 346 8345 1655 291 32 29 353 3138 274 4391 .73 379 8747 1253 265 31 30 .33 881 9.52 3495 5.95 .94 264 9.97 4347 .75 .35 412 9.54 9149 6.68 0.45 0851 2.8239 30 31 408 3852 5.93 254 4302 445 9550 0450 213 29 32 436 4208 245 4257 477 9951 0049 187 28 33 463 4564 235 4212 510 9.55 0352 6.67 0.44 9648 161 27 34 490 4920 5.92 225 4167 543 0752 6.68 9248 135 26 35 518 5275 215 4122 576 1153 6.65 8847 109 25 36 545 5630 5.90 206 4077 608 1552 6.67 8448 083 24 37 573 5984 5.92 196 4032 641 1952 6.65 8048 057 23 38 600 6339 5.90 186 3987 674 2351 7649 032 22 39 627 6693 5.88 176 3942 707 2750 7250 006 21 40 .33 655 9.52 7046 5.90 .94 167 9.97 3897 .75 .35 740 9.55 3149 6.65 0.44 6851 2.7980 20 41 682 7400 5.88 157 3852 772 3548 6.63 6452 955 19 42 710 7753 5.87 147 3807 .77 805 3946 6054 929 18 43 737 8105 5.88 137 3761 .75 838 4344 6.62 5656 908 17 44 764 8458 5.87 127 3716 871 4741 6.68 5259 878 16 45 792 8810 5.85 118 3671 .77 904 5139 6.62 4861 852 15 46 819 9161 5.87 108 3625 .75 937 5536 4464 827 14 47 846 9513 5.85 098 3580 969 5933 6.60 4067 801 13 48 874 9864 088 3535 .77 .36 002 6329 3671 776 12 49 901 9.53 0215 5.83 078 3489 .75 085 6725 3275 751 11 50 .33 929 9.53 0565 5.83 .94 068 9.97 3444 .77 .36 068 9.55 7121 6.60 0.44 2879 2.7725 10 51 956 0915 058 3398 101 7517 2483 700 9 52 983 1265 5.82 049 3352 .75 184 7913 6.58 2087 675 8 53 .84 011 1614 039 3307 .77 167 8308 1692 650 7 54 038 1963 029 3261 199 8703 6.57 1297 625 6 55 065 2312 019 3215 232 9097 0903 600 5 56 093 2661 5.80 009 3169 .75 265 9491 0509 575 4 57 120 3009 .93 999 3124 .77 298 9885 0115 550 3 58 147 3357 5.78 989 3078 381 9.56 0279 0.43 9721 525 2 59 175 3704 5.80 979 3032 364 0673 6.55 9327 500 1 60 .84 202 9.53 4052 .93 969 9.97 2986 .36 397 9.56 1066 0.43 8934 2.7475 109° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 70° Cosines. Sines. Tangents. 80 VII. TRIGONOMETRIC FUNCTIONS. 20° Sines. Cosines. Tangents. Dif. Cotangents. 159° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .34 202 9.53 4052 5.78 .93 969 9.97 2986 .77 .86 397 9.56 1066 6.55 0.43 8934 2.7475 60' i 229 4399 5.77 959 2940 480 1459 6.58 8541 450 59 2 257 4745 5.78 949 2894 463 1851 '6.55 8149 425 58 3 284 5092 5.77 939 2848 496 2244 6.53 7756 400 57 4 811 5438 5.75 929 2802 .78 529 2636 7364 876 56 5 889 5783 5.77 919 2755 .77 562 3028 6.52 6972 851 55 6 866 6129 5.75 909 2709 595 3419 6.58 6581 326 54 7 898 6474 5.73 899 2663 628 3811 6.52 6189 802 53 8 421 6818 5.75 889 2617 .78 661 4202 5798 277 52 9 448 7163 5.78 879 2570 .77 694 4593 6.50 5407 253 51 10 .84 475 9.53 7507 5.73 .93 869 9.97 2524 .77 .86 727 9.56 4983 6.50 0.43 5017 2.7228 50 11 508 7851 5.72 859 2478 .78 760 5373 4627 204 49 12 580 8194 5.73 849 2431 .77 793 5763 4237 179 •1- 13 557 8538 5.70 839 2385 .78 826 6153 6.48 3847 155 47 14 584 8880 5.72 829 2338 859 6542 6.50 3458 180 46 15 612 9223 5.70 819 2291 .77 892 6932 6.47 3068 106 45 16 689 9565 809 2245 .78 925 7320 6.48 2680 082 •14 17 666 9907 799 2198 958 7709 2291 058 43 18 694 9.54 0249 5.68 789 2151 .77 991 8098 6.47 1902 034 42 19 721 0590 779 2105 .78 .87 024 8486 6.45 1514 009 41 20 .34 748 9.54 0931 5.68 .93 769 9.97 2058 .78 .87 057 9.56 8873 6.47 0.43 1127 2.6985 40 21 775 1272 759 2011 090 9261 6.45 0739 961 39 22 808 1613 5.67 748 1964 123 9648 0352 937 38 23 830 1953 738 1917 157 9.57 0035 0.42 9965 913 37 24 857 2293 5.65 728 1870 190 0422 9578 889 36 25 884 2632 718 1823 223 0809 6.48 9191 S65 35 26 912 2971 708 1776 256 1195 8805 841 34 27 939 3310 698 1729 289 1581 8419 818 33 28 966 ' 3649 5.63 688 1682 322 1967 6.42 8033 794 32 29 993 3987 • 677 1635 855 2352 6.43 7648 770 31 30 .35 021 9.54 4325 5.63 .98 667 9.97 1588 .80 .87 888 9.57 2738 6.42 0.42 7262 2.6746 30 31 048 4663 5.62 657 1540 .78 422 3123 6.40 6877 723 29 32 075 5000 5.63 647 1493 455 3507 6.42 6493 699 28 33 102 5338 5.60 637 1446 .80 488 3892 6.40 6108 675 27 34 180 5674 5.62 626 1398 .78 521 4276 5724 652 26 35 157 6011 5.60 616 1351 .80 554 4660 5340 628 25 36 184 6347 606 1303 .78 588 5044 6.88 4956 605 24 37 211 6683 596 1256 .80 621 5427 4573 581 23 38 239 7019 5.58 585 1208 .78 654 5810 4190 558 22 39 266 7354 575 1161 .80 687 6193 3807 534 21 40 .85 293 9.54 7689 5.58 .93 565 9.97 1113 .78 .87 720 9.57 6576 6.88 0.42 3424 2.6511 20 41 320 8024 555 1066 .80 754 6959 6.37 3041 488 19 42 847 8359 5.57 544 1018 787 7341 2659 464 18 43 875 8693 534 0970 820 7723 6.85 2277 441 17 44 402 9027 5.55 524 0922 858 8104 6.87 1896 418 16 45 429 9360 514 0874 .78 887 8486 6.85 1514 895 15 46 456 9693 503 0827 .80 920 8867 1133 871 14 47 484 9.55 0026 493 0779 958 9248 0752 848 13 48 511 0359 483 0731 986 9629 6.88 0371 825 LS 49 588 0692 5.58 472 0683 .88 020 9.58 0009 0.41 9991 802 11 50 .85 565 9.55 1024 5.58 .98 462 9.97 0635 .82 .88 053 9.58 0389 6.88 0.41 9611 ton 10 51 592 1356 5.52 452 0586 .80 086 0769 9231 256 9 52 619 1687 441 0538 120 1149 6.82 8851 238 8 53 647 2018 481 0490 158 1528 8472 210 7 54 674 2349 420 0442 186 1907 8093 187 6 55 701 2680 5.50 410 0394 .82 220 2286 771 1 165 5 56 728 3010 5.52 400 0345 .80 258 2665 7335 142 4 57 755 3341 5.48 889 0297 286 3044 6.80 6956 119 3 58 782 3670 6.50 879 0249 .82 820 3422 6578 096 •j 59 810 4000 5.48 868 0200 .80 858 3800 6.28 6200 074 1 60 .85 887 9.55 4329 .93 858 9.97 0152 .88 886 9.58 4177 0.41 5823 MOB] 110° Nat Log. Dif. Nat. Log. Dlf. Nat Log. Cotangents. Dif. Log. Nat Tangents. 69° Cosines. Sines. 1 VII. TRIGONOMETRIC FUNCTIONS. 81 21° Sines. Cosines. TANGENT8. Dif. Cotangents. 158° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .35 837 9.55 4329 5.48 .93 358 9.97 0152 .82 .38 386 9.58 4177 6.30 0.41 5823 2.6051 60' i 864 4658 348 0103 .80 420 4555 6.28 5445 028 59 2 891 4987 5.47 337 0055 .82 453 4932 5068 006 58 3 918 5315 327 0006 487 5309 4691 2.5983 57 4 945 5643 316 9.96 9957 .80 520 5686 6.27 4314 961 56 5 973 5971 306 9909 .82 553 6062 6.28 3938 938 55 6 .36 000 6299 5.45 295 9860 587 6439 6.27 3561 916 54 7 027 6626 285 9811 620 6815 6.25 3185 893 53 8 054 6953 274 9762" .80 654 7190 6.27 2810 871 52 9 0S1 728.0 5.43 264 9714 .S2 687 7566 6.25 2434 848 51 10 .36 108 9.55 7606 5.43 .93 253 9.96 9665 .82 .38 721 9.58 7941 6.25 0.41 2059 2.5826 50 11 135 7932 243 9616 754 8316 1684 804 49 12 162 8258 5.42 232 9567 787 8691 1309 782 48 13 190 8583 5.43 222 9518 821 9066 6.23 0934 759 47 14 217 8909 5.42 211 9469 854 9440 0560 737 46 15 244 9234 5.40 201 9420 .&3 8S8 9814 0186 715 45 16 271 9558 5.42 190 9370 .82 921 9.59 0188 0.40 9812 693 44 IT 298 9883 5.40 180 9321 955 0562 6.22 9438 671 43 18 325 9.56 0207 169 9272 988 0935 9065 649 42 19 352 0531 159 9223 .S3 .39 022 1308 8692 627 41 20 .36 379 9.56 0855 5.38 .93 148 9.96 9173 .82 .39 055 9.59 1681 6.22 0.40 8319 2.5605 40 21 406 1178 137 9124 0S9 2054 6.20 7946 583 39 22 434 1501 127 9075 .83 122 2426 6.22 7574 561 38 23 461 1824 5.37 116 9025 .82 156 2799 6.20 7201 539 37 24 488 2146 106 8976 .83 190 3171 6.18 6829 517 36 25 515 2468 095 8926 .82 223 3542 6.20 6458 495 35 26 542 2790 084 8877 .83 257 3914 6.18 6086 473 34 27 569 3112 5.35 074 8827 290 4285 5715 452 33 28 596 3433 5.37 063 8777 .82 324 4656 5344 430 32 29' 623 3755 5.33 052 8728 .83 357 5027 4973 408 31 30 .36 650 9.56 4075 5.35 .93 042 9.96 8678 .83 .39 391 9.59 5398 6.17 0.40 4602 2.5386 30 31 677 4396 5.33 031 8628 425 5768 4232 365 29 32 704 4716 020 8578 458 6138 3862 348 28 33 731 5036 010 8528 .82 492 6508 3492 322 27 34 758 5356 .92 999 8479 .83 526 6878 6.15 3122 300 26 35 785 5676 5.82 988 8429 559 7247 2753 279 25 36 812 5995 978 8379 593 7616 2384 257 24 37 839 6314 5.30 967 8329 .85 626 7985 2015 236 23 38 867 6632 6.32 956 - 8278 .83 660 8354 6.13 1646 214 22 39 894 6951 5.30 945 8228 G34 8722 6.15 1278 193 21 40 .36 921 9.56 7269 5.30 .92 935 9.96 8178 .83 .39 727 9.59 9091 6.13 0.40 0909 2.5172 20 41 948 7587 5.28 924 8128 761 9459 0541 150 19 42 975 7904 5.30 913 8078 .85 795 9827 6.12 0173 129 18 43 .37 002 8222 5.28 902 8027 .83 829 9.60 0194 6.13 0.39 9806 108 17 44 029 8539 892 7977 862 0562 6.12 9438 086 16 45 056 8856 5.27 881 7927 .85 896 0929 9071 065 15 46 083 9172 870 . 7876 .83 930 1296 8704 044 14 47 . 110 9488 859 7826 .85 963 1663 6.10 8337 023 13 48 137 9804 849 7775 .83 997 2029 7971 002 12 49 164 9.57 0120 5.25 838 7725 .85 .40 081 2395 7605 2.4981 11 50 .37 191 9.57 0435 5.27 .92 827 9.96 7674 .83 .40 065 9.60 2761 6.10 0.39 7 239 2.4960 10 51 218 0751 5.25 816 7624 .85 098 3127 6873 939 9 52 245 1066 5.23 805 7573 132 3493 6.08 6507 918 8 53 272 1380 5.25 794 7522 166 3858 6142 897 7 54 299 1695 5.23 784 7471 .83 200 4223 5777 876 6 55 326 2009 773 7421 .85 234 4588 5412 855 5 56 353 2323 5.22 762 7370 267 4953 6.07 5047 834 4 57 380 2636 5.23 751 7319 301 5317 6.08 • 4683 813 3 58 407 2950 5.22 740 7268 835 5682 6.07 4318 792 2 59 434 3263 5.20 729 7217 369 6046 3954 772 1 60 .37 461 9.57 3575 .92 718 9.96 7166 .40 403 9.60 6410 0.39 3590 2.4751 111° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 68° Cosines. Sines. Cotangents. Tangents. 1 — J 82 VII. TRIGONOMETRIC FUNCTIONS. 22° siMEs. Cosines. Tangents. Dlf. Cotangents. 157° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .87 461 957 3575 5.22 .92 718 9.96 7166 .85 .40 403 9.60 6410 6.05 0.39 3590 2.4751 60' l 488 3888 5.20 707 7115 486 6773 6.07 3227 780 59 2 515 4200 697 7064 470 7137 6.05 2863 709 58 3 542 4512 686 7013 .87 504 7500 2500 689 57 4 569 4824 675 6961 ^.85 588 7863 6.08 2137 668 56 5 595 5136 5.18 664 6910 572 8225 6.05 1775 648 55 6 622 5447 658 6859 606 8588 6.03 1412 627 54 7 649 5758 642 6808 .87 640 8950 1050 606 53 8 676 6069 5.17 631 6756 .85 674 9312 0688 686 52 9 703 6379 620 6705 .87 707 9674 0326 666 51 10 .37 730 9.57 6689 5.17 .92 609 9.96 6653 .85 .40 741 9.61 0036 6.02 0.38 9964 2.4545 50 11 757 6999 598 6602 .87 775 0397 6.03 9603 525 49 12 784 7309 5.15 587 6550 .85 809 0759 6.02 9241 604 48 ' 13 811 7618 576 6499 .87 848 1120 6.00 8880 484 47 14 838 7927 565 6447 877 1480 6.02 8520 464 46 15 865 8236 554 6395 .85 911 1841 6.00 8159 448 45 16 892 8545 5.18 543 6344 .87 945 2201 7799 428 44 17 919 8853 5.15 532 6292 979 2561 7439 403 43 18 946 9162 5.13 521 6240 .41 018 2921 7079 388 42 19 973 9470 5.12 510 6188 047 3281 6719 862 41 20 .37 999 9.57 9777 5.13 .92 499 9.96 6136 .85 .41 0S1 9.61 3641 5.98 0.38 6359 2.4842 40 21 .38 026 9.58 0085 5.12 488 6085 .87 115 4000 6000 322 39 22 053 0392 477 6033 149 4359 5641 302 38 23 080 0699 5.10 466 5981 183 4718 5282 282 37 24 107 1005 5.12 455 5929 .88 217 5077 5.97 4923 262 36 25 134 1312 5.10 444 5876 .87 251 5435 4565 242 35 26 161 1618 432 5824 285 5793 4207 222 34 27 188 1924 5.08 421 5772 319 6151 3849 202 33 28 215 2229 5.10 410 5720 353 6509 3491 182 32 29 241 2535 5.08 399 5668 .88 387 6867 5.95 3133 162 31 30 .38 26S 9.58 2840 5.08 .92 8$S 9.96 5615 .87 .41 421 9.61 7224 5.97 0.38 2776 2.4142 30 31 295 3145 5.07 377 5563 455 7582 5.95 2418 122 29 32 322 3449 5.08 366 5511 .88 490 7939 5.93 2061 102 28 33 349 3754 5.07 855 5458 .87 524 8295 5.95 1705 083 27 34 376 4058 5.05 848 5406 .88 558 8652 5.98 1348 068 26 35 403 4361 5.07 882 5353 .87 592 9008 0992 043 25 36 430 4665 5.05 321 5301 .88 626 9364 0636 028 24 37 456 4968 5.07 310 5248 660 9720 0280 004 23 38 483 5272 5.08 299 5195 .87 694 9.62 0076 0.37 9924 2.3984 . 22 39 510 5574 5.05 287 5143 .88 728 0432 5.92 9568 964 21 40 .38 537 9.58 5877 5.03 .92 276 9.96 5090 .88 .41 768 9.62 0787 5.92 0.37 9213 2.3945 20 41 564 6179 5.05 265 5037 797 1142 8858 925 19 42 591 6482 5.02 254 4984 881 1497 8503 906 18 43 617 6783 5.08 243 4931 .87 865 1852 8148 886 17 44 644 7085 5.02 231 4879 .88 899 ' 2207 5.90 7793 867 16 45 671 7386 5.03 220 4826 983 2561 7439 847 15 46 698 7688 5.02 209 4773 968 2915 7085 828 14 47 725 7989 5.00 198 4720 .90 .42 002 3269 6731 808 13 48 752 8289 5.02 1S6 4666 .88 036 3623 5.88 6377 789 12 49 778 8590 5.00 175 4613 070 3976 5.90 6024 TO 11 50 .88 805 9.58 8890 5.00 .92 164 9.96 4560 .88 .42 105 9.62 4330 5.88 0.37 5670 2.8750 10 51 832 9190 4.98 152 4507 139 4683 5317 TS1 9 52 859 9489 5.00 141 4454 .90 173 5036 6.87 4964 Tl'J 8 53 886 9789 4.98 130 4400 .88 207 5388 6.88 4612 698 7 54 912 9.59 0088 119 4347 242 5741 5.87 4259 678 <•> 55 939 0387 107 4294 .90 276 6093 3907 654 5 56 966 0686 4.97 096 4240 .88 810 6445 3555 636 4 57 993 0984 085 4187 .90 845 6797 3203 616 3 58 .89 020 1282 073 4133 .88 879 7149 2851 697 2 59 046 1580 0«9 4080 .90 418 7501 5.86 2499 678 1 60 .39 073 9.59 1878 .92 050 9.96 4026 ,1-' 117 9.62 7852 0.37 2148 2.3559 112° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Cotangents. Dlf. Log. Nat 67° Cosines. Sinks. Tangents. VII. TRIGONOMETRIC FUNCTIONS. 83 23° Sines. Cosines. Tangents. Dif. Cotangents. 156° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .89 073 9.59 1878 4.97 .92 050 9.96 4026 .90 .42 447 9.62 7852 5.85 0.37 2148 2.3559 60' i 100 2176 4.95 039 3972 .88 482 8203 1797 539 59 2 127 2473 028 3919 .90 516 8554 1446 520 58 3 153 2770 016 3865 551 8905 5.83 1095 501 57 4 180 3067 4.98 005 3811 585 9255 5.85 0745 483 56 5 207 3363 .91 994 3757 .88 619 9606 5.88 0394 464 55 6 234 3659 982 3704 .90 654 9956 0044 445 54 7 260 3955 971 3650 688 9.63 0306 0.36 9694 426 53 8 287 4251 959 3596 722 0656 5.82 9344 407 52 9 314 4547 4.92 948 3542 757 1005 5.83 8995 388 51 10 .39 341 9.59 4842 4.92 .91 936 9.96 3488 .90 .42 791 9.63 1355 5.82 0.36 8645 2.3369 50 11 367 5137 925 3434 .92 826 1704 8296 351 49 12 394 5432 914 3379 .90 860 2053 7947 332 48 13 421 5727 4.90 902 3325 894 2402 5.80 7598 313 47 14 448 6021 891 3271 929 2750 5.82 7250 294 46 15 474 6315 879 3217 968 3099 5.80 6901 276 45 16 501 6609 868 3163 .92 998 3447 6553 257 44 17 528 6903 4.88 856 3108 .90 .43 032 3795 6205 238 43 18 555 7196 4.90 845 3054 .92 067 4143 5.78 5857 220 42 19 581 7490 4.88 833 2999 .90 101 4490 5.80 5510 201 41 20 .39 608 9.59 7783 4.87 .91 822 9.96 2945 .92 .43 136 9.63 4838 5.78 0.36 5162 2.8188 40 21 635 8075 4.88 810 2890 .90 170 5185 4815 164 39 22 661 8368 4.87 799 2836 .92 205 5532 4468 146 38 23 688 8660 787 2781 .90 239. 5879 4121 127 37 24 715 8952 775 2727 .92 274 6226 5.77 3774 109 36 25 741 9244 764 2672 308 6572 5.78 3428 090 35 26 768 9536 4.85 752 2617 343 6919 5.77 3081 072 34 27 795 9827 741 2562 .90 378 7265 2735 053 33 28 822 9.60 0118 729 2508 .92 412 7611 5.75 2389 035 32 29 848 0409 718 2453 447 7956 5.77 2044 017 31 30 .39 875 9.60 0700 4.88 .91 706 9.96 2398 .92 .43 481 9.63 8302 5.75 0.36 1698 2.2998 30 31 902 0990 694 2343 516 8647 1353 980 29 32 928 1280 683 2288 550 8992 1008 962 28 33 955 1570 671 2233 585 9337 0663 944 27 34 982 1860 660 2178 620 9682 0318 925 26 35 .40 008 2150 4.82 648 2123 .93 654 9.64 0027 5.73 0.35 9973 907 25 36 035 2439 636 2067 .92 689 0371 5.75 9629 889 24 37 062 2728 625 2012 724 0716 5.73 9284 871 23 38 088 3017 4.80 613 - 1957 758 1060 8940 853 22 39 115 3305 4.82 601 1902 .93 793 1404 5.72 8596 835 21 40 .40 141 9.60 3594 4.80 .91 590 9.96 1846 .92 .43 828 9.64 1747 5.73 0.35 8253 2.2817 20 41 168 3882 578 1791 .93 862 2091 5.72 . 7909 799 19 42 195 4170 4.78 566 1735 .92 897 2434 7566 781 18 43 221 4457 4.80 555 1680 .93 932 2777 7223 763 17 44 248 4745 4.78 543 1624 .92 966 3120 6880 745 16 45 275 5032 531 1569 .93 .44 001 3463 6537 727 15 46 301 5319 519 1513 .92 036 3806 5.70 6194 709 14 47 328 5606 4.77 508 1458 .93 071 4148 5852 691 13 48 355 5892 4.78 496 1402 105 4490 5510 673 12 49 381 6179 4.77 484 1346 140 4832 5168 655 11 50 .40 408 9.60 6465 4.77 .91 472 9.96 1290 .92 .44175 9.64 5174 5.70 0.35 4826 2.2637 10 51 434 6751 4.75 461 1235 .93 210 5516 5.68 4484 620 9 52 461 7036 4.77 449 1179 244 5857 5.70 4143 602 8 53 488 7322 4.75 437 1123 279 6199 5.68 3801 584 7 54 514 7607 425 1067 314 6540 3460 566 6 55 541 7892 414 1011 349 6881 3119 549 5 56 567 8177 4.73 402 0955 384 7222 5.67 2778 531 4 57 594 8461 390 0899 418 7562 5.68 2438 513 3 58 621 8745 378 0843 .95 453 7903 5.67 2097 496 2 59 647 9029 366 0786 .93 488 8243 1757 478 1 60 .40 674 9.60 9313 .91 355 9.96 0730 .44 523 9.64 8583 0.35 1417 2.2460 113° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 66° ^Cosines. Sines. Tangbntb. 84 VII. TRIGONOMETRIC FUNCTIONS. 24° Sines. Cosines. Tangents. Dif. Cotangents. 155° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .40 674 9.60 9313 4.73 .91855 9.96 0730 .93 .44 523 9.64 8583 5.67 0.35 1417 2.2460 60' l 700 9597 4.72 343 0674 558 8923 1077 448 59 2 727 9880 4.73 831 0618 .95 593 9263 5.65 0737 425 58 3 758 9.61 0164 4.72 819 0561 .93 627 9602 5.67 0398 408 57 4 780 0447 4.70 807 0505 .95 662 9942 5.65 0058 890 56 5 806 0729 4.72 295 0448 .93 697 9.65 0281 0.34 9719 m 55 6 883 1012 4.70 283 0392 .95 732 0620 9380 866 54 7 860 1294 272 0335 .98 767 0959 5.68 9041 888 53 8 886 1576 260 0279 .95 802 1297 5.65 8703 820 52 9 913 1858 248 0222 837 1636 6.68 8364 808 51 10 .40 939 9.61 2140 4.68 .91 236 9.96 0165 .93 .44 872 9.65 1974 5.63 0.34 8026 2.2286 50 11 966 2421 224 0109 .95 907 2312 7688 268 49 12 992 2702 212 0052 942 2650 7350 251 48 13 .41 019 2983 200 9.95 9995 977 2988 7012 234 47 14 045 3264 188 9938 .93 .45 012 3326 5.62 6674 216 46 15 072 3545 4.67 176 9882 .95 047 3663 6337 199 45 16 098 3825 164 9825 082 4000 6000 182 44 17 125 4105 152 9768 117 4337 5663 165 43 18 151 4385 140 9711 152 4674 5326 148 42 19 178 4665 4.65 128 9654 .97 187 5011 4989 130 41 20 .41 204 9.614944 4.65 .91 116 9.95 9596 .95 .45 222 9.65 5348 5.60 0.34 4652 2.2118 40 21 231 5223 104 9539 257 5684 4316 096 39 22 257 5502 092 9482 292 6020 3980 079 38 23 284 5781 080 9425 327 6356 3644 062 37 24 310 6060 4.63 068 9368 .97 362 6692 3308 045 36 25 337 6338 056 9310 .95 397 7028 2972 028 35 26 363 6616 044 9253 .97 432 7364 5.58 2636 011 34 27 890 6894 032 9195 .95 467 7699 2301 2.1994 33 28 416 7172 020 9138 .97 502 8034 1966 977 32 29 443 7450 4.62 008 9080 .95 538 8369 1631 960 31 30 .41 469 9.61 7727 4.62 .90 996 9.95 9023 .97 .45 573 9.65 8704 5.58 0.34 1296 2.1948 30 31 496 8004 984 8965 .95 608 9039 5.57 0961 926 29 32 522 8281 972 8908 .97 643 9373 5.58 0627 909 28 33 549 8558 4.60 960 8850 678 9708 5.57 0292 892 27 34 575 8834 948 8792 713 9.66 0042 0.33 9958 876 26 35 602 9110 936 8734 .95 748 0376 9624 859 25 36 628 9386 924 8677 .97 784 0710 5.56 9290 842 24 37 655 9662 911 8619 819 1043 5.57 8957 825 23 38 681 9938 4.58 899 8561 854 1377 5.55 8623 808 22 39 707 9.62 0213 887 8503 889 1710 8290 792 21 40 .41 784 9.62 0488 4.58 .90 875 9.95 8445 .97 .45 924 9.66 2043 5.55 0.33 7957 2.1775 20 41 760 0763 863 8387 960 2376 7624 758 19 42 787 1038 851 8329 995 2709 7291 741 18 43 813 1313 4.57 839 8271 .46 030 3042 6958 :-.'.-. 17 44 840 1587 826 8213 .98 065 3375 5.68 6625 708 16 45 866 1861 814 8154 .97 101 3707 6293 MS 15 46 892 2135 802 8096 186 4039 5961 675 14 47 919 2409 4.55 790 8038 .98 171 4371 5629 659 13 48 945 2682 4.57 778 7979 .97 206 4703 5297 Ml 12 49 972 2956 4.55 766 7921 242 5035 6.52 4965 625 11 50 .41 998 9.62 3229 4.55 .90 753 9.95 7863 .98 .4(1 277 9.66 5366 6.68 0.33 4634 2.1609 10 51 .42 024 3502 4.53 741 7804 .97 812 5698 5.52 4302 :>!»•-' 9 52 051 3774 4.55 729 7746 .98 848 6029 3971 576 8 53 077 4047 4.58 717 3687 888 6360 3640 660 7 54 104 4319 704 7628 .97 418 k 6691 5.60 3309 648 6 55 180 4591 692 7570 .98 454 7021 5.52 2979 627 5 56 156 4863 680 7511 489 T862 5.60 2648 610 4 57 188 5135 4.52 668 7452 525 7682 6.52 2318 M i 3 58 209 5406 656 7393 .97 560 8013 5.60 1987 478 2 59 285 5677 648 7335 .98 595 8343 1657 461 1 60 .49 '262 9.62 5948 .90 681 9.95 7276 .46 631 9.66 8673 0.33 1327 2.1445 114° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat Tangents. 65° Cosines. Sinks. VII. TRIGONOMETRIC FUNCTIONS. 85 25° SlNE8. Cosines. Dif. Tangents. Cotangents. 154° Nat. Log. Dif. Nat. Log. Nat. Log. Dif. Log. Nat. 0' .42 262 9.62 5948 4.52 .90 681 9.95 7276 .98 .46 631 9.66 8673 5.48 0.33 1327 2.1445 60' i 238 6219 618 7217 666 9002 5.50 0998 429 59 2 315 6490 450 606 7158 702 9332 5.48 0668 413 58 3 841 6760 594 7099 737 9661 5.50 0339 896 57 4 367 7030 582 7040 772 9991 5.48 0009 380 56 5 394 7300 569 6981 1.00 808 9.67 0320 0.32 9680 364 55 6 420 7570 557 6921 .98 848 0649 5.47 9351 348 54 7 446 7840 4.48 545 6862 879 0977 5.48 9023 382 53 8 473 8109 532 6803 914 1306 8694 815 52 9 499 8378 520 6744 1.00 950 1635 5.47 8365 299 51 10 .42 525 9.62 8647 4.48 .90 507 9.95 6684 .98 .46 985 9.67 1963 5.47 0.32 8037 2.1283 50 11 552 8916 495 6625 .47 021 2291 7709 267 49 12 578 9185 4.47 483 6566 1.00 056 2619 7381 251 48 13 604 9453 470 6506 .98 092 2947 5.45 7053 235 47 14 631 9721 458 6447 1.00 128 3274 5.47 6726 219 46 15 657 9989 446 6387 163 3602 5.45 6398 203 45 16 683 9.63 0257 4.45 433 6327 .98 199 3929 5.47 6071 187 44 n 709 0524 4.47 421 6268 1.00 234 4257 5.45 5743 171 43 18 736 0792 4.45 408 6208 270 4584 5416 155 42 19 762 1059 396 6148 .98 305 4911 5.43 5089 139 41 20 .42 788 9.63 1326 4.45 .90 383 9.95 6089 1.00 .47 841 9.67 5237 5.45 0.32 4763 2.1123 40 21 815 1593 4.43 371 6029 377 5564 5.43 4436 107 39 22 841 1859 358 5969 412 5890 5.45 4110 092 38 23 867 2125 4.45 346 5909 448 6217 5.48 3783 076 37 24 894 2392 4.43 834 5849 483 6543 3457 060 36 25 920 2658 4.42 321 5789 519 6869 5.42 3131 044 35 26 946 2923 4.43 309 5729 555 7194 5.48 2806 028 34 27 972 3189 4.42 296 5669 590 7520 2480 013 33 28 999 3454 284 5609 1.02 626 7846 5.42 2154 2.0997 32 29 .43 025 3719 271 5548 1.00 662 8171 1829 981 31 30 .43 051 9.63 3984 4.42 .90 259 9.95 5488 1.00 .47 698 9.67 8496 5.42 0.32 1504 2.0965 30 31 077 4249 246 5428 733 8821 1179 950 29 32 104 4514 4.40 233 5368 1.02 769 9146 0854 934 28 33 130 4778 221 5307 1.00 805 947 1 5.40 0529 918 27 34 156 5042 208 5247 1.02 840 9795 5.42 0205 903 26 35 182 5306 196 5186 1.00 876 9.68 0120 5.40 0.31 9880 887 25 36 209 5570 183 5126 1.02 912 0444 9556 872 24 37 235 5834 4.88 171 5065 1.00 948 0768 9232 856 23 38 261 6097 158 5005 1.02 984 1092 8908 840 22 39 287 6360 146 4944 .48 019 1416 8584 825 21 40 .48 313 9.63 6623 4.38 .90 133 9.95 4883 1.00 .48 055 9.68 1740 5.38 0.31 8260 2.0809 20 41 340 6886 4.37 120 4823 1.02 091 2063 5.40 7937 794 19 42 366 7148 4.38 108 4762 127 2387 5.88 7613 778 18 43 392 7411 4.37 095 4701 163 2710 7290 763 17 44 418 7673 082 4640 198 3033 6967 748 16 45 445 7935 070 4579 234 3356 6644 732 15 46 471 8197 4.35 057 4518 270 3679 5.37 6321 717 14 47 497 8458 4.37 045 4457 306 4001 5.38 5999 701 13 48 523 8720 4.35 032 4396 342 4324 5.37 5676 686 12 49 549 8981 019 4335 878 4646 5354 671 11 50 .43 575 9.63 9242 4.35 .90 007 9.95 4274 1.02 .48 414 9.68 4968 5.37 0.31 5032 2.0655 10 51 602 9503 .89 994 4213 450 5290 4710 640 9 52 628 9764 4.88 981 4152 1.03 486 5612 4388 625 8 53 654 9.64 0024 968 4090 1.02 521 5934 5.85 4066 609 7 54 680 0284 956 • 4029 557 6255 5.37 3745 594 6 55 706 0544 943 3968 1.03 593 6577 5.85 3423 579 5 56 733 0804 930 3906 1.02 629 6898 3102 564 4 57 759 1064 918 3845 1.03 665 7219 2781 549 3 58 785 1324 4.32 905 3783 1.02 701 7540 2460 533 2 59 811 1583 892 3722 1.03 737 7861 2139 518 1 60 .43 887 9.64 1842 .89 879 9.95 3660 .48 773 9.68 8182 0.31 1818 2.0503 115° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 64° Cosines. Sines. 86 VII. TRIGONOMETRIC FUNCTIONS. 26° Sines. Cosines. Tangents. Dif. Cotangents. 153° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .48 837 9.64 1842 4.82 .89 879 9.95 3660 1.02 .48 773 9.68 8182 5.38 0.31 1818 2.0508 60' i 868 2101 867 3599 1.08 809 8502 5.85 1498 488 59 2 889 2360 4.80 854 3537 845 8823 5.88 1177 473 58 3 916 2618 4.82 841 - 3475 881 9143 0857 458 57 4 942 2877 4.80 828 3413 1.02 917 9463 0537 448 56 5 968 3135 816 3352 1.03 958 9783 0217 428 55 6 994 3393 4.28 803 3290 989 9.69 0103 0.30 9897 418 54 7 .44 020 3650 4.80 790 3228 .49 026 0423 5.82 9577 898 53 8 046 3908 4.28 777 3166 062 0742 5.88 9258 888 M 9 072 4165 4.80 764 3104 098 1062 5.82 8938 868 51 10 .44 098 9.64 4423 4.28 .89 752 9.95 3042 1.03 .49 134 9.69 1381 5.82 0.30 8619 2.0853 50 11 124 4680 4.27 789 2980 170 1700 8300 838 49 12 151 4936 4.28 726 2918 1.05 206 2019 7981 828 48 13 177 5193 713 2855 1.03 242 2338 5.80 7662 808 47 14 208 5450 4.27 700 2793 278 2656 5.32 7344 298 46 15 229 5706 687 2731 815 2975 5.80 7025 278 45 16 255 5962 674 2669 1.05 851 3293 5.82 6707 263 44 17 281 6218 662 2606 1.03 887 3612 5.80 6388 248 43 18 807 6474 4.25 649 2544 1.05 423 3930 6070 238 42 19 833 6729 636 2481 1.03 459 4248 5752 219 41 20 .44 859 9.64 6984 4.27 .89 623 9.95 2419 1.05 .49 495 9.69 4566 5.28 0.30 5434 2.0204 40 21 385 7240 4.23 610 2356 1.03 532 4883 5.80 5117 189 39 22 411 7494 4.25 597 2294 1.05 568v 5201 5.28 4799 174 38 23 487 7749 584 2231 604 5518 5.30 4482 160 37 24 464 8004 4.28 571 2168 1.03 640 5836 5.28 4164 146 36 25 490 8258 558 2106 1.05 677 6153 3847 130 35 26 516 8512 545 2043 713 6470 3530 115 34 27 542 8766 582 1980 749 6787 5.27 3213 101 33 28 568 9020 519 1917 786 7103 5.28 2897 086 32 29 594 9274 4.22 506 1854 822 7420 5.27 2580 072 31 30 .44 620 9.64 9527 4.23 .89 493 9.95 1791 1.05 .49 858 9.69 7736 5.28 0.30 2264 2.0057 30 31 646 9781 422 480 1728 894 8053 5.27 1947 042 29 32 672 9.65 0034 467 1665 981 8369 1631 028 28 33 698 0287 4.20 454 1602 967 8685 1315 013 27 34 • 724 0539 4.22 441 1539 .50 004 9001 5.25 0999 1.9999 26 35 750 0792 4.20 428 1476 1.07 040 9316 6.27 0684 984 25 36 776 1044 4.22 415 1412 1.05 076 9632 5.25 0368 970 24 37 802 1297 4.20 402 1349 113 9947 5.27 0053 955 23 38 828 1549 4.18 889 1286 1.07 149 9.70 0263 5.25 0.29 9737 941 22 39 854 1800 4.20 876 1222 1.05 185 0578 9422 926 21 40 .44 880 9.65 2052 4.20 .89 868 9.95 1159 1.05 .50 222 9.70 0893 5.25 0.29 9107 1.9912 20 41 906 2304 4.18 850 1096 1.07 258 1208 8792 897 19 42 982 2555 837 1032 295 1523 5.23 8477 888 18 43 958 2806 324 0968 1.05 381 1837 5.25 8163 868 17 44 984 3057 311 0905 1.07 868 2152 6.28 7848 854 16 45 .45 010 3308 4.17 298 0841 1.05 404 2466 5.25 7534 840 15 46 086 3558 285 0778 1.07 441 2781 5.28 7219 825 14 47 062 3808 4.18 272 0714 477 3095 6905 811 13 48 088 4059 4.17 259 0650 514 3409 6.22 6591 797 12 49 114 4309 4.15 245 0586 550 3722 5.28 6278 782 11 50 .45 140 9.65 4558 4.17 .89 282 9.95 0522 1.07 .50 587 9.70 4036 5.28 0.29 5964 1.9768 10 51 166 4808 219 0458 628 4350 5.22 5650 7.'4 9 52 192 5058 4.15 206 0394 660 4663 5337 NO 8 53 218 5307 198 0330 696 4976 5.28 5024 725 7 54 248 5556 180 0266 788 5290 5.22 4710 711 6 55 269 5805 167 0202 769 5603 4397 697 5 56 296 6054 4.18 158 0138 806 5916 5.20 4084 688 4 57 821 6302 4.15 140 0074 848 6228 5.22 3772 669 3 58 847 6551 4.18 127 0010 1.08 879 6541 3459 664 ■J 59 878 6799 114 9.94 9945 1.07 916 6854 5.20 3146 640 1 60 .45 899 9.65 7047 .89 101 9.94 9881 ..M> m 9.70 7166 0.29 2834 1.9626 116° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 63° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 87 27° Sines. Cosines. Tangents. Dif. Cotangents. 152° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .45 399 9.65 7047 4.13 .89 101 9.94 9881 1.08 .50 953 9.70 7166 5.20 0.29 2834 1.9626 60' i 425 7295 4.12 087 9816 1.07 989 7478 2522 612 59 2 451 7542 4.13 074 9752 .51 026 7790 2210 598 58 3 477 7790 4.12 061 9688 1.08 063 8102 1898 584 57 4 503 8037 048 9623 099 8414 1586 570 56 5 529 8284 035 9558 1.07 136 8726 5.18 1274 556 55 6 554 8531 021 9494 1.08 173 9037 5.20 0963 542 54 7 580 8778 008 9429 209 9349 5.18 0651 528 53 8 606 9025 4.10 .88 995 9364 1.07 246 9660 0340 514 52 9 632 9271 981 9300 1.08 288 9971 0029 500 51 10 .45 658 9.65 9517 4.10 .88 968 9.94 9235 1.08 .51 319 9.71 0282 5.18 0.28 9718 1.9486 50 11 684 9763 955 9170 356 0593 9407 472 49 12 710 9.66 0009 942 9105 393 0904 9096 458 48 13 736 0255 928 9040 430 1215 5.17 8785 444 47 14 762 0501 4.08 915 8975 467 1525 5.18 8475 430 46 15 787 0746 902 8910 503 1836 5.17 8164 416 45 16 813 0991 888 8845 540 2146 7854 402 44 17 839 1236 875 8780 577 2456 7544 388 43 18 865 1481 862 8715 614 2766 7234 375 42 19 891 1726 4.07 848 8650 1.10 651 3076 6924 361 41 20 .45 917 9.66 1970 4.07 .88 835 9.94 8584 1.08 .51 688 9.71 3386 5.17 0.28 6614 1.9347 40 21 942 2214 4.08 822 8519 724 3696 5.15 6304 388 39 22 968 2459 4.07 808 8454 1.10 761 4005 5995 319 38 23 994 2703 4.05 795 8388 1.08 798 4314 5.17 5686 306 37 24 .46 020 2946 4.07 782 8323 1.10 835 4624 5.15 5376 292 36 25 046 3190 4.05 768 8257 1.08 872 4933 5067 278 35 26 072 3433 4.07 755 8192 1.10 909 5242 4758 265 34. 27 097 3677 4.05 741 8126 946 5551 4449 251 33 28 123 3920 728 8060 1.08 983 5860 5.18 4140 237 32 29 149 4163 715 7995 1.10 .52 020 6168 5.15 3832 223 31 30 .46 175 9.66 4406 4.03 .88 701 9.94 7929 1.10 .52 057 9.71 6477 5.18 0.28 3523 1.9210 30 31 201 4648 4.05 688 7863 094 6785 3215 196 29 32 226 4891 4.03 674 7797 131 7093 2907 183 28 33 252 5133 661 7731 168 7401 2599 169 27 34 278 5375 647 7665 1.08 205 7709 2291 155 26 35 804 5617 634 7600 1.12 242 8017 1983 142 25 36 330 5859 4.02 620 7533 1.10 279 8325 1675 128 24 37 355 6100 4.03 607 7467 816 8633 5.12 1367 115 23 38 381 6342 4.02 593 7401 353 8940 5.18 1060 101 22 39 407 6583 580 7335 390 9248 5.12 0752 088 21 40 .46 433 9.66 6824 4.02 .88 566 9.94 7269 1.10 .52 427 9.71 9555 5.12 0.28 0445 1.9074 20 41 458 7065 4.00 558 7203 1.12 464 9862 0138 061 19 42 484 7305 4.02 589 7136 1.10 • 501 9.72 0169 0.27 9831 047 18 43 510 7546 4.00 526 7070 538 0476 9524 084 17 44 536 7786 4.02 512 7004 1.12 575 0783 5.10 9217 020 16* 45 561 8027 4.00 499 6937 1.10 613 1089 5.12 8911 007 15 46 587 8267 3.98 485 6871 1.12 650 1396 5.10 8604 1.8993 14 47 613 8506 4.00 472 6804 1.10 687 1702 5.12 8298 980 13 48 639 8746 458 6738 1.12 724 2009 5.10 7991 967 12 49 664 8986 8.98 445 6671 761 2315 7685 953 11 50 .46 690 9.66 9225 3.98 .88 431 9.94 6604 1.10 .52 798 9.72 2621 5.10 0.27 7379 1.8940 10 51 716 9464 417 6538 1.12 886 2927 5.08 7073 927 9 52 742 9703 404 6471 878 3232 5.10 6768 913 8 53 767 9942 390 6404 910 3538 6462 900 7 54 793 9.67 0181 8.97 377 6337 947 3844 5.08 6156 887 6 55 819 0419 3.98 363 6270 985 4149 5851 878 5 56 844 0658 3.97 349 6203 .53 022 4454 5.10 5546 860 4 57 870 0896 336 6136 059 4760 5.08 5240 847 3 58 896 1134 322 6069 096 5065 4935 834 2 59 921 1372 3.95 808 6002 134 5370 5.07 4630 820 1 60 .46 947 9.67 1609 .88 295 9.94 5935 .53 171 9.72 5674 0.27 4326 1.8807 117° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 62° Cosines. Sines. Tangents. 1 88 VII. TRIGONOMETRIC FUNCTIONS. — 1 28° Sines. Cosines. Tangents. Dif. Cotangents. 151° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .46 947 9.67 1609 8.97 .88 295 9.94 5935 1.12 .53 171 9.72 5674 5.08 0.27 4326 1.8807 60' i 978 1847 8.95 281 5868 1.13 208 5979 4021 794 59 2 999 2084 267 5800 1.12 246 6284 5.07 3716 781 58 3 .47 024 2321 254 5733 288 6588 3412 768 . 57 4 050 2558 240 5666 1.13 820 6892 5.08 3108 755 56 5 076 2795 226 5598 1.12 858 7197 5.07 2803 741 55 6 101 3032 8.98 213 5531 895 7501 2499 728 54 7 127 3268 8.95 199 5464 1.13 482 7805 2195 715 53 8 153 3505 8.93 185 5396 470 8109 5.05 1891 702 52 9 178 3741 172 5328 1.12 507 8412 5.07 1588 689 51 10 .47 204 9.67 3977 3.93 .88 158 9.94 5261 1.13 .53 545 9.72 8716 5.07 0.27 1284 1.8676 50 11 229 4213 8.92 144 5193 582 9020 5.05 0980 663 49 12 255 4448 8.98 130 5125 1.12 620 9323 0677 650 48 13 281 4684 8.92 117 5058 1.13 657 9626 0374 637 47 14 806 4919 8.93 103 4990 694 9929 5.07 0071 624 46 15 332 5155 3.92 089 4922 732 9.73 0233 5.03 0.26 9767 611 45 16 358 5390 3.90 075 4854 769 0535 5.05 9465 598 44 17 383 5624 3.92 062 4786 807 0838 9162 585 43 18 409 5859 048 4718 844 1141 8859 572 42 19 434 6094 3.90 034 4650 882 1444 5.08 8556 559 41 20 .47 460 9.67 6328 3.90 .88 020 9.94 4582 1.13 .53 920 9.73 1746 5.03 0.26 8254 1.8546 40 21 486 6562 006 4514 957 2048 5.05 7952 538 39 22 511 6796 .87 993 4446 1.15 995 2351 5.03 7649 520 38 23 587 7030 979 4377 1.13 .54 032 2653 7347 507 37 24 562 7264 965 4309 070 2955 7045 495 36 25 588 7498 8.88 951 4241 1.15 107 3257 5.02 6743 482 35 26 614 7731 937 4172 1.18 145 3558 5.08 6442 469 34 27 639 7964 923 4104 183 3860 6140 456 33 28 665 8197 909 4036 1.15 220 4162 5.02 5838 443 32 29 690 8430 896 3967 1.13 258 4463 5537 4S0< 31 30 .47 716 9.67 8663 3.87 .87 882 9.94 3899 1.15 .54 296 9.73 4764 5.03 0.26 5236 1.8418 30 31 741 8895 8.88 868 3830 333 5066 5.02 4934 405 29 32 767 9128 8.87 854 3761 1.13 371 5367 4633 392 28 33 793 9360 840 3693 1.15 409 5668 4332 879 27 34 818 9592 826 3624 446 5969 5.00 4031 867 26 35 844 9824 812 3555 484 6269 5.02 3731 854 25 36 869 9.68 0056 798 3486 522 6570 5.00 3430 841 24 37 895 0288 8.85 784 3417 560 6870 5.02 3130 829 23 38 920 0519 770 3348 597 7171 5.00 2829 816 22 39 946 0750 8.87 756 3279 635 7471 2529 808 21 40 .47 971 9.68 0982 8.85 .87 748 9.94 3210 1.15 .54 678 9.73 7771 5.00 0.26 2229 1.8291 20 41 997 1213 8.88 729 3141 711 8071 1929 278 19 42 .48 022 1443 8.85 715 3072 748 8371 1629 265 18 43 048 1674 701 3003 786 8671 1329 258 17 44 078 1905 8.88 687 2934 1.17 824 8971 1029 240 16 45 099 2135 673 2864 1.15 862 9271 498 0729 228 15 46 124 2365 659 2795 900 9570 5.00 0430 215 14 47 150 2595 645 2726 1.17 988 9870 4.98 0130 202 13 48 175 2825 631 2656 1.15 975 9.74 0169 0.25 9831 190 12 49 201 3055 8.82 617 2587 1.17 .55 018 0468 9532 177 11 50 .48 226 9.68 3284 8.83 .87 608 9.94 2517 1.15 .55 051 9.74 0767 4.98 0.25 9233 1.8165 10 51 252 3514 8.82 589 2448 1.17 089 1066 8934 152 9 52 277 3743 575 2378 127 1365 8635 140 8 53 808 3972 561 2308 1.15 165 1664 4.97 8336 MR 7 54 828 4201 546 2239 1.17 208 1962 4.98 8038 115 6 55 854 4430 8.80 582 2169 241 2261 4.97 7739 108 5 56 879 4658 8.82 518 2099 279 2559 4.93 7441 090 1 57 405 4887 8.80 504 2029 817 2858 4.97 7142 078 3 58 480 5115 490 1959 855 3156 6844 065 2 59 456 5343 476 1889 898 3454 6546 058 1 60 .48 481 9.68 5571 .87 462 9.94 1819 .65 481 9.74 3752 0.25 6248 1.8040 118° Nat Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat 61° COSINES. Sines. Tangents. VII. TRIGONOMETRIC FUNCTIONS. 89 29° Sines. Cosines. Tangents. Dif. Cotangents. 150° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .48 481 9.68 5571 3.80 .87 462 9.94 1819 1.17 .55 431 9.74 3752 4.97 0.25 6248 1.8040 60' i 506 5799 448 1749 469 4050 5950 028 59 2 532 6027 3.78 434 1679 507 4348 4.95 5652 016 58 3 557 6254 3.80 420 1609 545 4645 4.97 5355 003 57 4 583 6482 3.78 406 1539 583 4943 4.95 5057 1.7991 56 5 008 6709 391 1469 1.18 621 5240 4.97 4760 979 55 6 634 6936 377 1398 1.17 659 5538 4.95 4462 966 54 7 659 7163 3.77 363 1328 697 5835 4165 954 53 8 684 7389 3.78 349 1258 1.18 736 6132 3868 942 52 9 710 7616 335 1187 1.17 774 6429 3571 930 51 10 .48 735 9.68 7843 3.77 .87 321 9.94 1117 1.18 .55 812 9.74 6726 4.95 0.25 3274 1.7917 50 11 761 8069 306 1046 850 7023 4.93 2977 905 49 12 786 8295 292 0975 1.17 888 7319 4.95 2681 893 48 13 811 8521 278 0905 1.18 926 7616 2384 881 47 14 837 8747 8.75 264 0834 964 7913 4.93 2087 868 46 15 862 8972 8.77 250 0763 1.17 .56 003 8209 1791 856 45 16 888 9198 3.75 235 0693 1.18 041 8505 1495 844 44 17 913 9423 221 0622 079 8801 1199 882 43 18 938 9648 207 0551 117 9097 0903 820 42 19 964 9873 193 0480 156 9393 0607 808 41 20 .48 989 9.69 0098 3.75 .87 178 9.94 0409 1.18 .56 194 9.74 9689 4.98 0.25 0311 1.7796 40 21 .49 014 0323 164 0338 232 9985 0015 783 39 22 040 0548 3.73 150 0267 270 9.75 0281 4.92 0.24 9719 771 38 23 065 0772 136 0196 309 0576 4.93 9424 759 37 24 090 0996 121 0125 347 0872 4.92 9128 747 36 25 116 1220 107 0054 1.20 385 1167 8833 735 35 26 141 1444 093 9.93 9982 1.18 424 1462 8538 723 34 27 166 1668 079 9911 462 1757 8243 711 33 28 192 1892 8.72 064 9840 1.20 501 2052 7948 699 32 29 217 2115 3.73 050 9768 1.18 539 2347 7653 687 31 30 .49 242 9.69 2339 3.72 .87 036 9.93 9697 1.20 .56 577 9.75 2642 4.92 0.24 7358 1.7675 30 31 268 2562 021 9625 1.18 616 2937 4.90 7063 663 29 32 293 2785 007 9554 1.20 654 3231 4.92 6769 651 28 33 318 3008 .86 993 9482 693 3526 4.90 6474 639 27 34 344 3231 3.70 "978 9410 1.18 731 3820 4.92 6180 627 26 35 369 3453 8.72 964 9339 1.20 769 4115 4.90 5885 615 25 36 394 3676 3.70 949 9267 808 4409 5591 603 24 37 419 3898 935 9195 846 4703 5297 591 23 38 445 4120 921 ' 9123 1.18 885 4997 5003 579 22 39 470 4342 906 9052 1.20 923 5291 4709 567 21 40 .49 495 9.69 4564 3.70 .86 892 9.93 8980 1.20 .56 962 9.75 5585 4.88 0.24 4415 1.7556 20 41 521 4786 8.68 878 8908 .57 000 5878 4.90 4122 544 19 42 546 5007 3.70 863 8836 1.22 039 6172 4.88 3828 532 18 43 571 5229 8.68 849 8763 1.20 078 6465 4.90 3535 520 17 44 596 5450 834 8691 116 6759 4.88 3241 508 16 45 622 5671 820 8619 155 7052 2948 496 15 46 647 5892 805 8547 193 7345 2655 485 14 47 672 6113 791 8475 1.22 232 7638 2362 473 13 48 697 6334 3.67 777 8402 1.20 271 7931 2069 461 12 49 723 6554 8.68 762 8330 309 8224 1776 449 11 50 .49 748 9.69 6775 3.67 .86 748 9.93 8258 1.22 .57 348 9.75 8517 4.88 0.24 1483 1.7487 10 51 773 6995 733 8185 1.20 386 8810 4.87 1190 426 9 52 798 7215 719 8113 1.22 425 9102 4.88 0898 414 8 53 824 7435 3.65 704 8040 464 9395 4.87 0605 402 7 54 849 7654 3.67 690 7967 1.20 503 9687 0313 391 6 55 874 7874 675 7895 1.22 541 9979 4.88 0021 379 5 56 899 8094 8.65 661 7822 580 9.76 0272 4.87 0.23 9728 367 4 57 924 8313 646 7749 619 0564 9436 355 3 58 950 8532 632 7676 1.20 657 0856 9144 344 2 59 975 8751 617 7604 1.22 696 1148 4.85 8852 - 332 1 60 .50 000 9.69 8970 .86 603 9.93 7531 .57 735 9.76 1439 0.23 8561 1.7321 119° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. TANGENT8. 60° Cosines. Sines. 90 VH. TRIGONOMETRIC FUNCTIONS. 30° Sines. Cosines. Tangents. Dlf. Cotangents. 149° Nat. Log. Dlf. Nat. Log. Dlf. Nat. Log. Log. Nat. 0' .50 000 9.69 8970 8.65 .86 603 9.93 7531 1.22 .57 735 9.76 1439 4.87 0.23 8561 1.7821 60' i 025 9189 8.68 588 7458 774 1731 8269 809 59 2 050 9407 8.65 573 7385 818 2023 4.85 7977 297 58 3 076 9626 8.68 559 7312 1.23 851 2314 4.87 7686 286 57 4 101 9844 544 7238 1.22 890 2606 4.85 7394 274 56 5 126 9.70 0062 580 7165 929 2897 7103 262 55 6 151 0280 515 7092 968 3188 6812 251 54 7 176 0498 501 7019 .58 007 3479 6521 289 53 8 201 0716 8.62 486 6946 1.23 046 3770 6230 228 52 9 227 0933 8.66 471 6872 1.22 085 4061 5939 216 51 10 .50 252 9.70 1151 8.62 .86 457 9.93 6799 1.28 .58 124 9.76 4352 4.85 0.23 5648 1.7205 50 11 277 1368 442 6725 1.22 162 4643 4.88 5357 198 49 12 802 1585 427 6652 1.23 201 4933 4.85 5067 182 48 13 327 1802 418 6578 1.22 240 5224 4.88 4776 170 47 14 352 2019 898 6505 1.28 279 5514 4.85 4486 159 46 15 377 2236 8.60 384 6431 818 5805 4.88 4195 147 45 16 403 2452 8.62 369 6357 1.22 357 6095 3905 186 44 17 428 2669 3.60 354 6284 1.23 896 6385 3615 124 43 18 453 2885 340 6210 435 6675 3325 118 42 19 478 3101 825 6136 474 6965 3035 102 41 20 .50 503 9.70 3317 3.60 .86 310 9.93 6062 1.23 .58 518 9.76 7255 4.88 0.23 2745 1.7090 40 21 528 3533 295 5988 552 7545 4.82 2455 079 39 22 553 3749 3.58 281 5914 591 7834 488 2166 067 38 23 578 3964 266 5840 631 8124 1876 056 37 24 608 4179 3.60 251 5766 670 8414 4.82 1586 045 36 25 628 4395 8.58 287 5692 709 8703 1297 033 35 26 . 654 4610 222 5618 1.25 748 8992 1008 022 34 27 679 4825 207 5543 1.23 787 9281 4.88 0719 011 33 28 704 5040 8.57 192 5469 826 9571 4.82 0429 1.6999 32 29 729 5254 3.58 178 5395 1.25 865 9860 4.80 0140 988 31 30 .50 754 9.70 5469 3.57 .86 163 9.93 5320 1.23 .58 905 9.77 0148 4.82 0.22 9852 1.6977 30 31 779 5683 8.58 148 5246 1.25 944 0437 9563 965 29 32 804 5898 3.57 138 5171 1.23 983 0726 9274 954 28 33 829 6112 119 5097 1.25 .59 022 1015 4.80 8985 943 27 34 854 6326 3.55 104 5022 1.23 061 1303 4.82 8697 982 26 35 879 6539 3.57 089 4948 1.25 101 1592 4.80 8408 920 25 36 904 6753 074 4873 140 1880 8120 909 24 37 929 6967 8.55 059 4798 179 2168 4.82 7832 898 23 38 954 7180 045 4723 1.23 218 2457 4.80 7543 887 22 39 979 7393 080 4649 1.25 258 2745 7255 875 21 40 .51 004 9.70 7606 8.55 .86 015 9.93 4574 1.25 .59 297 9.77 3033 4.80 0.22 6967 1.6864 20 41 029 7819 000 4499 886 3321 478 6679 858 19 42 054 8032 .85 985 4424 876 3608 4.80 6392 842 18 43 079 8245 970 4349 415 3896 6104 S81 17 44 104 8458 8.58 956 4274 454 4184 4.78 5816 820 16 45 129 8670 941 4199 1.27 494 4471 4.80 5529 808 15 46 154 8882 926 4123 1.25 588 4759 4.78 5241 797 14 47 179 9094 911 4048 578 5046 4954 786 13 48 204 9306 896 3973 612 5333 4.80 4667 775 . 12 49 229 9518 881 3898 1.27 651 5621 4.78 4379 764 11 50 .51 254 9.70 9730 8.52 .85 866 9.93 3822 1.25 .59 691 9.77 5908 4.78 0.22 4092 1.6758 10 51 279 9941 8.58 851 3747 1.27 780 6195 3805 742 9 52 804 9.71 0153 8.52 886 3671 1.25 770 6482 4.77 3518 781 8 53 829 0364 821 3596 1.27 809 6768 4.78 3232 TSO 7 54 854 0575 806 3520 1.25 849 7055 2945 709 6 55 879 0786 792 3445 1.27 888 7342 4.77 2658 69S 5 56 404 0997 777 3369 928 7628 4.78 2372 687 4 57 429 1208 762 3293 967 7915 4.77 2085 676 3 58 454 1419 8.50 747 3217 .60 007 8201 4.78 1799 665 2 59 479 1629 782 3141 1.25 046 8488 4.77 1512 654 1 60 .51504 9.71 1839 .85 717 9.93 3066 .60 086 9.77 8774 0.22 1226 1.6648 120° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Cotangents. Dif. Log. Nat Tangents. 59° COSINES. Sines. VII. TRIGONOMETRIC FUNCTIONS. 91 1 __ 31° Sines. Cosines. Tangents. Dif. Cotangents. 148° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .51 504 9.71 1839 3.52 .85 717 9.93 3066 1.27 .60 086 9.77 8774 4.77 0.22 1226 1.6643 -60' i 529 2050 8.50 702 2990 126 9060 0940 632 59 2 554 2260 8.48 687 2914 165 9346 0654 621 58 3 579 2469 8.50 672 2838 205 9632 0368 610 57 4 604 2679 657 2762 1.28 245 9918 4.75 0082 599 56 5 628 2889 3.48 642 2685 1.27 284 9.78 0203 4.77 0.219797 588 55 6 653 3098 8.50 627 2609 324 0489 9511 577 54 7 678 3308 8.48 612 2533 364 0775 4.75 9225 566 53 8 703 3517 597 2457 1.28 403 1060 4.77 8940 555 52 9 728 3726 582 2380 1.27 448 1346 4.75 8654 545 51 10 .51753 9.71 3935 8.48 .85 567 9.93 2304 1.27 .60 483 9.78 1631 4.75 0.21 8369 1.6534 50 11 778 4144 8.47 551 2228 1.28 522 1916 8084 523 49 12 803 4352 8.48 536 2151 1.27 562 2201 7799 512 48 13 828 4561 3.47 521 2075 1.28 602 2486 7514 501 47 14 852 4769 8.48 506 1998 642 2771 7229 490 46 15 877 4978 8.47 491 1921 1.27 681 3056 6944 479 45 16 902 5186 476 1845 1.28 721 3341 6659 469 44 17 927 5394 461 1768 761 3626 4.78 6374 458 43 18 952 5602 8.45 446 1691 801 3910 475 6090 447 42 19 977 5809 3.47 431 1614 841 4195 4.78 5805 436 41 20 .52 002 9.71 6017 3.45 .85 416 9.93 1537 1.28 .60 881 9.78 4479 4.75 0.21 5521 1.6426 40 21 026 6224 8.47 401 1460 921 4764 4.78 5236 415 39 22 051 6432 8.46 385 1383 960 5048 4952 404 38 23 076 6639 370 1306 .61 000 5332 4668 393 37 24 101 6846 355 1229 040 5616 4384 383 36 25 126 7053 8.48 340 1152 080 5900 4100 872 35 26 151 7259 8.45 825 1075 120 6184 3816 361 34 21 175 7466 810 0998 160 6468 3532 351 33 28 200 7673 3.43 294 0921 1.30 200 6752 3248 840 32 29 225 7879 279 0843 1.28 240 7036 4.72 2964 329 31 30 .52 250 9.71 8085 3.43 .85 264 9.93 0766 1.30 .61 280 9.78 7319 4.78 0.21 2681 1.6319 30 31 275 8291 249 0688 1.28 320 7603 4.72 2397 308 29 32 299 8497 284 0611 1.30 360 7886 4.78 2114 297 28 33 324 8703 218 0533 1.28 400 ■8170 4.72 1830 287 ' 27 34 349 8909 3.42 203 0456 1.30 440 8453 1547 276 26 35 374 9114 3.48 188 0378 480 8736 1264 265 25 36 399 9320 8.42 173 0300 1.28 520 9019 0981 255 24 37 423 9525 157 0223 1.80 561- 9302 0698 244 23 38 448 9730 142 - 0145 601 9585 0415 234 22 39 473 9935 127 0067 641 9868 0132 223 21 40 .52 498 9.72 0140 3.42 .85112 9.92 9989 1.30 .61 681 9.79 0151 4.72 0.20 9849 1.6212 20 41 522 0345 8.40 096 9911 721 0434 4.70 9566 202 19 42 547 0549 3.42 081 9833 761 0716 4.72 9284 191 18 43 572 0754 8.40 066 9755 801 0999 4.70 9001 181 17 44 597 0958 051 9677 842 1281 8719 170 16 45 621 1162 035 9599 882 1563 4.72 8437 160 15 46 646 1366 020 9521 1.32 922 1846 4.70 8154 149 14 47 671 1570 005 9442 1.30 962 2128 7872 139 13 48 696 1774 .84 989 9364 .62 003 2410 7590 128 12 49 720 1978 8.88 974 9286 1.32 043 2692 7308 118 11 50 .52 745 9.72 2181 8.40 .84 959 9.92 9207 1.30 .62 083 9.79 2974 4.70 0.20 7026 1.6107 10 51 770 2385 3.38 943 9129 1.32 124 3256 6744 097 9 52 794 2588 928 9050 1.30 164 3538 4.68 6462 087 8 53 819 2791 913 8972 1.32 204 3819 4.70 6181 076 7 54 844 2994 897 8893 1.80 245 4101 5899 066 6 55 869 3197 882 8815 1.32 285 4383 4.68 5617 055 5 56 893 3400 866 8736 825 4664 4.70 5336 045 4 57 918 3603 • 8.87 851 8657 866 4946 4.68 5054 034 3 58 943 3805 886 8578 406 5227 4773 024 2 59 967 4007 8.88 820 8499 446 5508 4492 014 1 60 .52 992 9.72 4210 .84 805 9.92 8420 .62 487 9.79 5789 0.20 4211 1.6003 121° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 58° Cosines. Sines. _ „ 92 VII. TRIGONOMETRIC FUNCTIONS. 32° SlNES. Cosines. Tangents. Dif. Cotangents. 147° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .52 992 9.72 4210 3.87 .84 805 9.92 8420 1.80 .62 487 9.79 5789 4.68 0.20 4211 1.6008 60' i .68 017 4412 789 8342 1.82 527 6070 3930 1.5993 59 2 041 4614 774 8263 1.83 568 6351 3649 983 58 3 066 4816 3.35 759 8183 1.32 608 6632 3368 972 57 4 091 5017 3.37 743 8104 649 6913 3087 962 56 5 115 5219 3.35 728 8025 689 7194 4.67 2806 952 55 6 140 5420 3.37 712 7946 730 7474 4.68 2526 941 54 7 164 5622 8.85 697 7867 1.33 770 7755 2245 931 53 8 189 5823 681 7787 1.32 811 8036 4.67 1964 921 52 9 214 6024 666 7708 852 8316 1684 911 51 10 .53 238 9.72 6225 8.85 .84 650 9.92 7629 1.33 .62 892 9.79 8596 4.68 0.20 1404 1.5900 50 11 263 6426 3.33 635 7549 1.32 933 8877 4.67 1123 890 49 12 288 6626 8.85 619 7470 1.83 973 9157 0843 880 48 13 812 6827 8.88 604 7390 .63 014 9437 0563 869 47 14 837 7027 3.85 588 7310 1.32 055 9717 0283 859 46 15 361 7228 8.88 578 7231 1.33 095 9997 0003 849 45 16 386 7428 557 7151 136 9.80 0277 0.19 9723 839 44 17 411 7628 542 7071 177 0557 4.65 9443 829 43 18 435 7828 8.82 526 6991 217 0836 4.67 9164 318 42 19 460 8027 8.83 511 6911 258 1116 8884 808 41 20 .53 484 9.72 8227 3.83 .84 495 9.92 6831 1.33 .63 299 9.80 1396 4.65 0.19 8604 1.5798 40 21 509 8427 3.82 480 6751 840 1675 4.67 8325 788 39 22 534 8626 464 6671 880 1955 4.65 8045 778 38 23 558 8825 448 6591 421 2234 7766 768 37 24 588 9024 483 6511 462 2513 7487 757 36 25 607 9223 417 6431 503 2792 4.67 7208 747 35 26 632 9422 402 6351 1.35 544 3072 4.65 6928 737 34 27 656 9621 386 6270 1.33 584 3351 6649 727 33 28 681 9820 8.80 370 6190 625 3630 6370 717 32 29 705 9.73 0018 3.32 355 6110 1.85 666 3909 4.63 6091 707 31 30 .53 730 9.73 0217 8.30 .84 339 9.92 6029 1.33 .68 707 9.80 4187 4.65 0.19 5813 1.5697 30 31 754 0415 324 5949 1.35 748 4466 5534 • 687 29 32 779 0613 308 5868 1.33 789 4745 4.68 5255 677 28 33 804 0811 292 5788 1.35 880 5023 4.65 4977 667 27 34 828 1009 3.28 277 5707 871 5302 4.63 4698 657 26 35 853 1206 3.80 261 5626 912 5580 4.65 4420 647 25 36 877 1404 245 5545 1.83 953 5859 4.68 4141 637 24 37 902 1602 8.28 230 5465 1.35 994 6137 3863 627 23 38 926 1799 214 5384 .64 035 6415 3585 617 22 39 951 1996 198 5303 076 6693 3307 607 21 40 .58 975 9.73 2193 8.28 .84 182 9.92 5222 1.85 .64 117 9.80 6971 4.68 0.19 3029 1.5597 20 41 .54 000 2390 167 5141 158 7249 2751 587 19 42 024 2587 151 5060 199 7527 2473 577 18 43 049 2784 8.27 185 4979 1.87 240 7805 2195 567 17 44 078 2980 8.28 120 4897 1.85 281 8083 1917 557 16 45 097 3177 8.27 104 4816 822 8361 4.62 1639 547 15 46 122 3373 088 4735 868 8638 4.68 1362 587 14 47 146 3569 072 4654 1.37 404 8916 4.62 1084 527 13 48 171 3765 057 4572 1.35 446 9193 4.68 0807 517 12 49 195 3961 041 4491 1.87 487 9471 4.62 0529 .-o7 11 50 .54 220 9.73 4157 8.27 .84 025 9.92 4409 1.85 .64 528 9.80 9748 4.62 0.19 0252 LMM 10 51 244 4353 009 4328 1.87 569 9.81 0025 0.18 9975 487 9 52 269 4549 8.25 .88 994 4246 610 0302 4.68 9698 477 9 53 298 4744 978 4164 1.85 652 0580 4.62 9420 468 7 54 817 4939 8.27 962 4083 1.87 698 0857 9143 458 6 55 842 5135 8.25 946 4001 784 1134 4.60 8866 448 5 56 866 5330 980 3919 775 1410 4.62 8590 488 1 57 891 5525 8.28 915 3837 817 1687 8313 428 3 58 415 5719 8.25 899 3755 858 1964 8036 418 2 59 440 5914 888 3673 899 2241 4.60 7759 408 1 60 .54 464 9.73 6109 .88 867 9.92 3591 .64 941 9.81 2517 0.18 7483 1.5899 122° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Cotangents. Dif. Log. Nat Tangents. 57° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 93 33° Sines. Cosines. Tangents. Dif. Cotangents. 146° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .54 464 9.73 6109 3.23 .83 867 9.92 3591 1.37 .64 941 9.81 2517 4.62 0.18 7483 1.5399 60' i 488 6303 3.25 851 ' 3509 982 2794 4.60 7206 389 59 2 513 6498 3.23 835 3427 .65 024 3070 4.62 6930 379 58 3 587 6692 819 3345 065 3347 4.60 6653 369 57 4 561 6886 804 3263 106 3623 6377 359 56 5 586 7080 788 3181 1.38 148 3899 4.62 6101 350 55 6 610 7274 3.22 772 3098 1.37 189 4176 4.60 5824 340 54 7 635 7467 3.23 756 3016 1.38 231 4452 5548 380 53 8 659 7661 740 2933 1.37 272 4728 5272 320 52 9 683 7855 3.22 724 2851 1.38 314 5004 4996 311 51 10 .54 708 9.73 8048 3.22 .83 708 9.92 2768 1.37 .65 355 9.81 5280 4.58 0.18 4720 1.5301 50 11 732 8241 692 2686 1.38 397 5555 4.60 4445 291 49 12 756 8434 676 2603 438 5831 4169 282 48 13 781 8627 660 2520 1.37 480 6107 4.58 3893 272 47 14 805 8820 645 2438 1.38 521 6382 4.60 3618 262 46 15 829 9013 629 2355 563 6658 4.58 3342 253 45 16 854 9206 3.20 613 2272 604 6933 4.60 3067 243 44 17 878 9398 597 2189 646 7209 4.58 2791 233 43 18 902 9590 3.22 581 2106 688 7484 2516 224 42 19 927 9783 3.20 565 2023 729 7759 4.60 2241 214 41 20 .54 951 9.73 9975 3.20 .83 549 9.92 1940 1.38 .65 771 9.81 8035 4.58 0.18 1965 1.5204 40 21 975 9.74 0167 533 1857 813 8310 1690 195 39 22 999 0359 3.18 517 1774 854 8585 1415 185 38 23 .55 024 0550 3.20 501 1691 1.40 896 8860 1140 175 37 24 048 0742 485 1607 1.38 938 9135 0865 166 36 25 072 0934 3.18 469 1524 980 9410 4.57 0590 156 35 26 097 1125 453 1441 1.40 .66 021 9684 4.58 0316 147 34 27 121 1316 3.20 437 1357 1.38 063 9959 0041 187 33 28 145 1508 3.18 421 1274 1.40 105 9.82 0234 4.57 0.17 9766 127 32 29 169 1699 3.17 405 1190 1.38 147 0508 4.58 9492 118 31 30 .55 194 9.74 1889 3.18 .83 389 9.92 1107 1.40 .66 189 9.82 0783 4.57 0.17 9217 1.5108 30 31 218 2080 373 1023 230 1057 4.58 8943 099 29 32 242 2271 356 0939 1.38 272 1332 4.57 8668 089 28 33 266 2462 3.17 340 0856 1.40 314 1606 8394 080 27 34 291 2652 324 0772 356 1880 8120 070 26 35 315 2842 3.18 308 0688 398 2154 4.58 7846 061 25 36 339 3033 3.17 292 0604 440 2429 4.57 7571 051 24 37 363 3223 276 0520 482 2703 7297 042 23 38 388 3413 3.15 260 0436 524 2977 7023 032 22 39 412 3602 3.17 244 0352 566 3251 4.55 6749 023 21 40 .55 436 9.74 3792 3.17 .83 228 9.92 0268 1,40 .66 608 9.82 3524 4.57 0.17 6476 1.5013 20 41 460 3982 3.15 212 0184 1.42 650 3798 6202 004 19 42 484 4171 3.17 195 0099 1.40 692 4072 4.55 5928 1.4994 18 43 509 4361 3.15 179 0015 734 4345 4.57 5655 985 17 44 533 4550 163 9.91 9931 1.42 776 4619 5381 975 16 45 557 4739 147 9846 1.40 818 4893 4.55 5107 966 15 46 581 4928 131 9762 1.42 860 5166 4834 957 14 47 605 5117 115 9677 1.40 902 5439 4.57 4561 947 13 48 630 5306 3.13 098 9593 1.42 944 5713 4.55 4287 938 12 49 654 5494 3.15 082 9508 1.40 986 5986 4014 928 11 50 .55 678 9.74 5683 3.13 .83 066 9.91 9424- 1.42 .67 028 9.82 6259 4.55 0.17 3741 1.4919 10 51 702 5871 3.15 050 9339 071 6532 3468 910 9 52 726 6060 3.13 034 9254 113 6805 3195 900 8 53 750 6248 017 9169 1.40 155 7078 2922 891 7 54 775 6436 001 9085 1.42 197 7351 2649 882 6 55 799 6624 .82 9S5 9000 239 7624 2376 872 5 56 823 6812 3.12 969 8915 282 7897 2103 868 4 57 847 6999 3.13 953 8830 824 8170 4.53 1830 854 3 58 871 7187 3.12 936 8745 1.43 366 8442 4.55 1558 844 2 59 895 7374 3.13 920 8659 1.42 409 8715 4.53 1285 835 1 60 .55 919 9.74 7562 .82 904 9.91 8574 .67 451 9.82 8987 0.17 1013 1.4826 123° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 56° Cosines. Sines. Cotangents. Tangents. 94 VII. TRIGONOMETRIC FUNCTIONS. " 34° Sines. Cosines. Tangents. Dif. Cotangents. 145° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .65 919 9.74 7562 8.12 .82 904 9.918574 1.42 .67 451 9.82 8987 4.55 0.17 1013 1.4826 60' l 943 7749 887 8489 498 9260 4.53 0740 816 59 2 968 7936 871 8404 1.48 536 9532 4.55 0468 807 58 3 992 8123 855 8318 1.42 578 9805 4.58 0195 798 57 4 .56 016 8310 889 8233 1.48 620 9.83 0077 0.16 9923 788 56 5 . 040 8497 8.10 822 8147 1.42 663 0349 9651 779 55 6 064 8683 8.12 806 8062 1.43 705 0621 9379 770 54 7 088 8870 8.10 790 7976 1.42 748 0893 9107 761 53 8 112 9056 8.12 778 7891 1.48 790 1165 8835 751 52 9 136 9243 8.10 757 7805 882 1437 8563 74'.' 51 10 .56 160 9.74 9429 8.10 .82 741 9.91 7719 1.42 .67 875 9.83 1709 4.58 0.16 8291 1.4788 50 11 184 9615 724 7634 1.48 917 1981 8019 724 49 12 208 9801 708 7548 960 2253 7747 715 48 13 232 9987 3.08 692 7462 .68 002 2525 4.52 7475 705 47 14 256 9.75 0172 8.10 675 7376 045 2796 4.53 7204 696 46 15 280 0358 8.08 659 7290 088 3068 4.52 6932 687 45 16 805 0543 8.10 ' 643 7204 130 3339 4.58 6661 678 44 17 829 0729 8.08 626 7118 173 3611 4.52 6389 669 43 18 353 0914 610 7032 215 3882 4.58 6118 659 42 19 377 1099 593 6946 1.45 258 4154 4.52 5846 650 41 20 .56 401 9.75 1284 8.08 .82 577 9.91 6859 1.43 .68 301 9.83 4425 4.52 0.16 5575 1.4641 40 21 425 1469 561 6773 343 4696 5304 632 39 22 449 1654 544 6687 1.45 386 4967 5033 628 38 23 473 1839 8.07 528 6600 1.43 429 5238 4762 614 37 24 497 2023 8.08 511 6514 1.45 471 5509 4491 605 36 25 521 2208 3.07 495 6427 1.43 514 5780 4220 596 35 26 545 2392 478 6341 1.45 557 6051 3949 586 34 27 569 2576 462 6254 600 6322 3678 577 33 28 593 2760 446 6167 1.43 642 6593 3407 568 32 29 617 2944 429 6081 1.45 685 6864 4.50 3136 559 31 30 .56 641 9.75 3128 8.07 .82 413 9.91 5994 1.45 .68 728 9.83 7134 4.52 0.16 2866 1.4550 30 31 665 3312 8.05 896 5907 771 7405 4.50 2595 541 29 32 689 3495 3.07 880 5820 814 7675 4.52 2325 582 28 33 713 3679 8.05 863 5733 857 7946 4.50 2054 528 27 34 736 3862 8.07 847 5646 900 8216 4.52 1784 514 26 35 760 4046 8.05 880 5559 942 8487 4.50 1513 505 25 36 784 4229 814 5472 985 8757 1243 496 24 37 808 4412 297 5385 1.47 .69 028 9027 0973 487 23 38 882 4595 281 5297 1.45 071 9297 4.52 0703 478 22 39 856 4778 8.08 264 5210 114 9568 4.50 0432 469 21 40 .56 880 9.75 4960 8.05 .82 248 9.91 5123 1.47 .69 157 9.83 9838 4.50 0.16 0162 1.4460 20 41 904 5143 231 5035 1.45 200 9.84 0108 0.15 9892 451 19 42 928 5326 8.08 214 4948 1.47 248 0378 9622 442 18 43 952 5508 198 4860 1.45 286 0648 4.48 9352 488 17 44 976 5690 181 4773 1.47 829 0917 4.50 9083 4'_>4 16 45 .57 000 5872 165 4685 1.45 872 1187 8813 415 15 46 024 6054 148 4598 1.47 416 1457 8543 406 14 47 04T 6236 132 4510 459 1727 4.48 8273 897 13 48 071 6418 115 4422 502 1996 4.50 8004 888 LI 49 095 6600 098 4334 545 2266 4.48 7734 879 11 50 .57 119 9.75 6782 8.02 .82 082 9.914246 1.47 .69 588 9.84 2535 4.50 0.15 7465 1.4870 10 51 148 6963 065 4158 631 2805 4.48 7195 861 9 52 167 7144 8.08 048 4070 675 3074 6926 852 8 53 191 7326 8.02 082 3982 718 3343 6657 844 7 54 215 7507 015 3894 761 3612 450 6388 885 6 55 288 7688 .81 999 3806 804 3882 4.4S 6118 826 5 56 262 7869 982 3718 847 4161 5849 817 4 57 286 8050 8.00 965 3630 1.48 891 4420 5580 808 3 58 810 , 8230 8.02 949 3541 1.47 984 4689 5311 299 2 59 884 8411 8.00 982 3453 977 4958 5042 290 1 60 .57 858 9.75 8591 .81 915 9.91 3365 .70 021 9.84 5227 0.15 4773 Lisa 124° Nat. Log. Dif. Nat. Log. Dif. Nat. Lay. C.l VN.JKSTS. Dif. Log. Nat. Tangents. .55° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 95 35° Sines. Cosines. Tangents. Cotangents. 144° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' 57 358 9.75 8591 3.02 .81 915 9.91 3365 1.48 .70 021 9.84 5227 4.48 0.15 4773 1.4281 60' i 381 8772 8.00 899 3276 064 5496 4.47 4504 273 59 2 405 8952 882 3187 1.47 107 5764 4.48 4236 264 58 3 429 9132 865 3099 1.48 151 6033 3967 255 57 4 453 9312 848 3010 1.47 194 6302 4.47 3698 246 56 5 477 9492 882 2922 1.48 288 6570 4.48 3430 237. 55 6 501 9672 815 2833 281 6839 3161 229 54 7 524 9852 2.98 798 2744 325 7108 4.47 2892 220 53 8 548 9.76 0031 3.00 782 2655 368 7376 2624 211 52 9 572 0211 2.98 765 2566 412 7644 4.48 2356 202 51 10 .57 596 9.76 0390 2.98 .81 748 9.91 2477 1.48 .70 455 9.84 7913 4.47 0.15 2087 1.4198 50 11 619 0569 731 2388 499 8181 1819 185 49 12 643 0748 714 2299 542 8449 1551 176 48 13 667 0927 698 2210 586 8717 4.48 1283 167 47 14 691 1106 681 2121 1.50 629 8986 4.47 1014 158 46 15 715 1285 664 2031 1.48 673 9254 0746 150 45 16 738 1464 2.97 647 1942 717 9522 0478 141 44 17 762 1642 2.98 631 1853 1.50 760 9790 4.45 0210 132 43 18 786 1821 2.97 614 1763 1.48 804 9.85 0057 4.47 0.14 9943 124 42 19 810 1999 597 1674 1.50 848 0325 9675 115 41 20 .57 833 9.76 2177 2.98 .81 580 9.91 1584 1.48 .70 891 9.85 0593 4.47 0.14 9407 1.4106 40 21 857 2356 2.97 563 1495 1.50 935 0861 9139 097 39 22 881 2534 546 1405 979 1129 4.45 8871 089 38 23 904 2712 2.95 530 1315 1.48 .71028 1396 4.47 8604 080 37 24 928 2889 2.97 513 1226 1.50 066 1664 4.45 8336 071 36 25 952 3067 496 1136 110 1931 4.47 8069 063 35 26 976 3245 2.95 479 1046 154 2199 4.45 7801 054 34 27 999 3422 2.97 462 0956 198 2466 7534 045 33 28 .58 023 3600 2.95 445 0866 242 2733 4.47 7267 087 32' 29 047 3777 428 0776 285 3001 4.45 6999 028 31 30 .58 070 9.76 3954 2.95 .81 412 9.91 0686 1.50 .71 329 9.85 3268 4.45 0.14 6732 1.4019 30 31 094 4131 895 0596 878 3535 6465 011 29 32 118 4308 378 0506 1.52 417 3802 6198 002 28 33 141 4485 361 0415 1.50 461 4069 5931 1.3994 27 34 165 4662 2.93 844 0325 505 4336 5664 985 26 35 189 4838 2.95 327 0235 1.52 549 4603 5397 976 25 36 212 5015 2.93 810 0144 1.50 593 4870 5130 968 24 37 236 5191 293 0054 1.52 687 5137 4863 959 23 38 260 5367 2.95 276 9.90 9963 1.50 681 5404 4596 951 22 39 288 5544 2.93 259 9873 1.52 725 5671 4329 942 21 40 .58 307 9.76 5720 2.93 .81242 9.90 9782 1.52 .71 769 9.85 5938 4.43 0.14 4062 1.3934 20 41 830 5896 225 9691 1.50 818 6204 4.45 3796 925 19 42 354 6072 2.92 208 9601 1.52 857 6471 4.43 3529 916 18 43 378 6247 2.93 191 9510 901 6737 4.45 3263 908 17 44 401 6423 2.92 174 9419 946 7004 4.48 2996 899 16 45 425 6598 2.93 157 9328 990 7270 4.45 2730 891 15 46 449 6774 2.92 140 9237 .72 084 7537 4.43 2463 882 14 47 472 6949 123 9146 078 7803 2197 874 13 48 496 7124 2.93 106 9055 122 8069 4.45 1931 865 12 49 519 7300 2.92 089 8964 167 8336 4.43 1664 857 11 50 .58 543 9.76 7475 2.90 .81 072 9.90 8873 1.53 .72 211 9.85 8602 4.43 0.14 1398 1.3848 10 51 567 7649 2.92 055 8781 1.52 255 8868 1132 840 9 - 52 590 7824 038 8690 299 9134 0866 831 8 53 614 7999 2.90 021 8599 1.53 344 9400 0600 823 7 54 687 8173 2.92 004 8507 1.52 388 9666 0334 814 6 55 661 8348 2.90 .80 987 8416 1.58 432 9932 0068 806 5 56 684 8522 2.92 970 8324 1.52 477 9.86 0198 0.13 9802 798 4 57 708 8697- 2.90 953 8233 1.53 521 0464 ' 9536 789 3 58 731 8871 936 8141 565 0730 4.42 9270 781 2 59 755 9045 919 8049 1.52 610 0995 4.43 9005 772 1 60 .58 779 9.76 9219 .80 902 9.90 7958 .72 654 9.86 1261 0.13 8739 1.3764 125° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 54° Cosines. Sines. Tangents. 96 VII. TRIGONOMETRIC FUNCTIONS. 36° Sines. Cosines. Tangents. Cotangents. 143° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .58 779 9.76 9219 2.90 .80 902 9.90 7958 1.53 .72 654 9.86 1261 4.43 0.13 8739 1.3764 60' i 802 9393 2.88 885 7866 699 1527 4.42 8473 755 59 2 826 9566 2.90 867 7774 743 1792 4.48 8208 747 58 3 849 9740 2.88 850 7682 788 2058 4.42 7942 739 57 4 873 9913 2.90 833 7590 832 2323 4.43 7677 730 56 5 896 9.77 0087 2.88 816 7498 877 2589 4.42 7411 722 55 6 920 0260 799 7406 921 2854 7146 713 54 7 948 0433 782 7314 966 3119 4.48 6881 705 53 8 967 0606 765 7222 1.55 .78 010 3385 4.42 6615 697 52 9 990 0779 748 7129 1.53 055 3650 6350 688 51 10 .59 014 9.77 0952 2.88 .80 730 9.90 7037 1.53 .73 100 9.86 3915 4.42 0.13 6085 1.8680 50 11 037 1125 713 6945 1.55 144 4180 5820 672 49 12 061 1298 2.87 696 6852 1.53 189 4445 5555 668 48 13 084 1470 2.88 679 6760 1.55 234 4710 5290 655 47 14 108 1643 2.87 662 6667 1.53 278 4975 5025 647 46 15 131 1815 644 6575 1.55 823 5240 4760 638 45 16 154 1987 627 6482 368 5505 4495 630 44 17 178 2159 610 6389 413 5770 4230 622 43 18 201 2331 593 6296 1.53 457 6035 3965 613 42 19 225 2503 576 6204 1.55 502 6300 4.40 3700 605 41 20 .59 248 9.77 2675 2.87 .80 558 9.90 6111 1.55 .73 547 9.86 6564 4.42 0.13 3436 1.8597 40 21 272 2847 2.85 541 6018 592 6829 3171 588 39 22 295 3018 2.87 524 5925 637 7094 4.40 2906 580 38 23 318 3190 2.85 507 5832 681 7358 4.42 2642 572 37 24 342 3361 2.87 489 5739 1.57 726 7623 4.40 2377 564 36 25 865 3533 2.85 472 5645 1.55 771 7887 4.42 2113 555 35 26 389 3704 455 5552 816 8152 4.40 1848 547 34 27 412 3875 438 5459 861 8416 1584 539 33 28 436 4046 420 5366 1.57 906 8680 4.42 1320 531 32 29 459 4217 403 5272 1.55 951 8945 4.40 1055 522 31 30 .59 482 9.77 4388 2.83 .80 886 9.90 5179 1.57 .73 996 9.86 9209 4.40 0.13 0791 1.8514 30 31 506 4558 2.85 368 5085 1.55 .74 041 9473 0527 506 29 32 529 4729 2.83 351 4992 1.57 086 9737 0263 498 28 33 552 4899 2.85 334 4898 131 9.87 0001 0.12 9999 490 27 34 576 5070 2.83 316 4804 1.55 176 0265 9735 481 26 35 599 5240 299 4711 1.57 221 0529 9471 473 25 36 622 5410 282 4617 267 0793 9207 465 24 37 646 5580 264 4523 312 1057 8943 457 23 38 669 5750 247 4429 857 1321 8679 449 22 39 693 5920 230 4335 402 1585 8415 440 21 40 .59 716 9.77 6090 2.82 .80 212 9.90 4241 1.57 .74 447 9.87 1849 4.88 0.12 8151 1.3432 20 41 739 6259 2.88 195 4147 492 2112 4.40 7888 424 19 42 768 6429 2.82 178 4053 588 2376 7624 416 18 43 786 6598 2.88 160 3959 1.58 583 2640 4.88 7360 408 17 44 809 6768 2.82 143 3864 1.57 628 2903 4.40 7097 400 16 45 882 6937 125 3770 674 3167 4.88 6833 892 15 46 856 7106 108 3676 1.68 719 3430 4.40 6570 834 14 47 879 7275 091 3581 1.57 764 3694 4.88 6306 875 13 48 902 7444 078 3487 1.58 810 . 3957 6043 867 12 49 926 7613 2.80 056 3392 1.57 855 4220 4.40 5780 859 11 50 .59 949 9.77 7781 2.82 80 038 9.90 3298 1.58 .74 900 9.87 4484 4.88 0.12 5516 1.8851 10 51 972 7950 021 3203 946 4747 . 5253 848 9 52 995 8119 2.80 003 3108 1.57 991 5010 4990 885 8 53 .60 019 8287 79 986 3014 1.58 .75 037 5273 4.40 4727 827 7 54 042 8455 2.82 968 2919 082 5537 4.88 4463 819 6 55 065 8624 2.80 951 2824 128 5800 4200 811 5 56 089 8792 984 2729 178 6063 3937 808 4 57 112 8960 916 2634 219 6326 3674 295 3 58 185 9128 2.78 899 2539 264 6589 3411 287 2 59 158 9295 2.80 881 2444 810 6852 4.87 3 148 278 1 60 .60 182 9.77 9463 .79 864 9.90 2349 .75 855 9.87 7114 0.12 2886 1.8270 126° Nat. Log. Dif. Nat Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 53° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 97 37° Sines. Cosines. Tangents. Dif. Cotangents. 142° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .60 182 9.77 9463 2.80 .79 864 9.90 2349 1.60 .75 355 9.87 7114 4.38 0.12 2886 1.3270 60' i 205 9631 2.78 846 2253 1.58 401 7377 2623 262 59 2 228 9798 2.80 829 2158 447 7640 2360 254 58 3 251 9966 2.78 811 2063 1.60 492 7903 4.87 2097 246 57 4 274 9.78 0133 793 1967 1.58 588 8165 4.38 1835 238 56 5 298 0300 776 1872 1.60 584 8428 1572 230 55 6 321 0467 758 1776 1.58 629 8691 4.37 1309 222 54 7 344 0634 741 1681 1.60 675 8953 4.88 1047 214 53 8 367 0801 723 1585 1.58 721 9216 4.37 0784 206 52 9 390 0968 2.77 706 1490 1.60 767 9478 4.38 0522 198 51 10 .60 414 9.78 1134 2.78 .79 688 9.90 1394 1.60 .75 812 9.87 9741 4.37 0.12 0259 1.8190 50 11 437 1301 671 1298 858 9.88 0003 0.11 9997 182 49 12 460 1468 2.77 653 1202 904 0265 4.88 9735 175 48 13 483 1634 685 1106 950 0528 4.37 9472 167 47 14 506 1800 618 1010 996 0790 9210 159 46 15 529 1966 600 0914 .76 042 1052 8948 151 45 16 553 2132 583 0818 088 1314 4.38 8686 148 44 17 576 2298 565 0722 134 1577 4.37 8423 135 43 18 599 2464 547 0626 1.62 180 1839 8161 127 42 19 622 2630 530 0529 1.60 226 2101 7899 119 41 20 .60 645 9.78 2796' 2.75 .79 512 9.90 0433 1.60 .76 272 9.88 2363 4.87 0.11 7637 1.8111 40 21 668 29.61 2.77 494 0337 1.62 318 2625 7375 103 39 22 691 3127 2.75 477 0240 1.60 364 2887 4.35 7113 095 38 23 714 3292 2.77 459 0144 1.62 410 3148 4.37 6852 087 37 24 738 3458 2.75 441 0047 1.60 456 3410 6590 079 36 25 761 3623 424 9.89 9951 1.62 502 3672 6328 072 , 35 26 784 3788 406 9854 548 3934 6066 064 34 27 807 3953 388 9757 594 4196 4.35 5804 056 33 28 830 4118 2.73 371 9660 1.60 640 4457 4.87 5543 048 32 29 853 4282 2.75 353 9564 1.62 686 4719 4.85 5281 040 31 30 .60 876 9.78 4447 2.75 .79 335 9.89 9467 1.62 .76 733 9.88 4980 4.37 0.11 5020 1.3082 30 31 899 4612 2.73 818 9370 779 5242 4758 024 29 32 922 4776 2.75 300 9273 825 5504 4.85 4496 017 28 33 945 4941 2.73 282 9176 1.68 871 5765 4235 009 27 34 968 5105 264 9078 1.62 918 6026 4.37 3974 001 26 35 991 5269 247 8981 964 6288 4.35 3712 1.2993 25 36 .61 015 5433 229 8884 .77 010 6549 4.37 3451 985 24 37 038 5597 211 8787 1.63 057 6811 4.35 3189 977 23 38 061 5761 193 ' 8689 1.62 103 7072 2928 970 22 39 084 5925 176 8592 1.63 149 7333 2667 962 21 40 .61 107 9.78 6089 2.72 .79 158 9.89 8494 1.62 .77 196 9.88 7594 4.85 0.11 2406 1.2954 20 41 180 6252 2.73 140 8397 1.68 242 7855 2145 946 19 42 153 6416 2.72 122 8299 1.62 289 8116 4.87 1884 938 18 43 176 6579 105 8202 1.63 335 8378 4.85 1622 931 17 44 199 6742 2.73 087 8104 882 8639 1361 928 16 45 222 6906 2.72 069 8006 428 8900 1100 915 ^** 46 245 7069 051 7908 475 9161 4.83 0839 907 14 47 268 7232 033 7810 521 9421 4.85 0579 900 13 48 291 7395 2.70 016 7712 568 9682 0318 892 12 49 814 7557 2.72 .78 998 7614 615 9943 0057 884 11 50 .61 337 9.78 7720 2.72 .78 980 9.89 7516 1.63 .77 661 9.89 0204 4.35 0.10 9796 1.2876 10 51 360 7883 2.70 962 7418 708 0465 4.88 9535 869 9 52 388 8045 2.72 944 7320 754 0725 4.85 9275 861 8 53 406 8208 2.70 926 7222 1.65 801 0986 9014 853 7 54 429 8370 908 7123 1.63 848 1247 4.33 8753 846 6 55 451 8532 891 7025 1.65 895 1507 4.35 8493 838 5 56 474 8694 873 6926 1.63 941 1768 4.38 8232 830 4 57 497 8856 855 6828 1.65 988 2028 4.35 7972 822 3 58 520 9018 887 6729 1.68 .78 085 2289 4.88 7711 815 2 59 548 9180 819 6631 1.65 082 2549 4.85 7451 807 1 60 .61 566 9.78 9342 .78 801 9.89 6532 .78 129 9.89 2810 0.10 7190 1.2799 127° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 52° Cosines. Sines. Tangents. 98 VII. TRIGONOMETRIC FUNCTIONS. - ' 38° Sines. Cosines. Tangents. Dif. Cotangents. 141° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' 61566 9.78 9342 2.70 .78 801 9.89 6532 1.65 .78 129 9.89 2810 4.88 0.10 7190 1.2799 60' i 589 9504 2.68 788 6433 1.63 175 3070 4.85 6930 792 59 2 612 9665 2.70 765 6335 1.65 222 3331 4.33 6669 784 58 3 685 9827 2.68 747 6236 269 3591 6409 776 57 4 658 9988 729 6137 816 3851 6149 769 56 5 681 9.79 0149 711 6038 863 4111 4.85 5889 761 55 6 704 0310 694 5939 410 4372 4.88 5628 758 54 7 726" 0471 676 5840 457 4632 5368 746 53 8 749 0632 658 5741 1.67 504 4892 5108 788 52 9 772 0793 640 5641 1.65 551 5152 4848 731 51 10 .61 795 9.79 0954 2.68 .78 622 9.89 5542 1.65 .78 598 9.89 5412 4.88 0.10 4588 1.2723 50 11 818 1115 2.67 604 5443 1.67 645 5672 4328 715 49 12 841 1275 2.68 586 5343 1.65 692 5932 4068 708 48 13 864 1436 2.67 568 5244 739 6192 3808 700 47 14 887 1596 2.68 550 5145 1.67 786 6452 3548 693 46 15 909 1757 2.67 532 5045 884 6712 4.82 3288 685 45 16 932 1917 514 4945 1.65 881 6971 4.88 3029 677 44 17 955 2077 496 4846 1.67 928 7231 2769 670 43 18 978 2237 478 4746 975 7491 2509 662 42 19 .62 001 2397 460 4646 .79 022 7751 4.32 2249 655 41 20 .62 024 9.79 2557 2.65 .78 442 9.89 4546 1.67 .79 070 9.89 8010 4.83 0.10 1990 1.2647 40 21 046 2716 2.67 424 4446 117 8270 1730 640 39 22 069 2876 2.65 405 4346 164 8530 4.32 1470 632 38 23 092 3035 2.67 387 4246 212 8789 4.38 1211 624 37 24 115 3195 2.65 869 4146 259 9049 4.82 0951 617 36 25 138 3354 2.67 851 4046 306 9308 4.38 0692 609 35 26 160 3514 2.65 333 3946 854 9568 4.82 0432 602 34 27 183 3673 315 3846 1.68 401 9827 4.88 0173 594 33 28 206 3832 297 3745 1.67 449 9.90 0087 4.82 0.09 9913 587 32 29 229 3991 279 3645 1.68 496 0346 9654 579 31 30 .62 251 9.79 4150 2.63 .78 261 9.89 3544 1.67 .79 544 9.90 0605 4.82 0.09 9395 1.2572 30 31 274 4308 2.65 243 3444 1.68 591 0864 4.88 9136 564 29 32 297 4467 225 3343 1.67 689 1124 4.82 8876 557 28 33 320 4626 2.63 206 3243 1.68 686 1383 8617 549 27 34 342 4784 188 3142 734 1642 8358 542 26 35 365 4942 2.65 170 3041 781 1901 8099 534 25 36 888 5101 2.63 152 2940 829 2160 4.88 7840 BR 24 37 411 5259 134 2839 1.67 877 2420 4.82 7580 519 23 38 483 5417 116 2739 1.68 924 2679 7321 512 ■1 ■! 39 456 5575 098 2638 1.70 972 2938 7062 504 21 40 .62 479 9.79 5733 2.68 .78 079 9.89 2536 1.68 .80 020 9.90 3197 4.82 0.09 6803 1.2497 20 41 502 5891 061 2435 067 3456 4.80 6544 489 19 42 524 6049 2.62 043 2334 115 3714 4.82 6286 482 18 43 547 6206 2.63 025 2233 168 3973 6027 475 17 44 570 6364 2.62 007 2132 1.70 211 4232 5768 467 16 45 592 6521 2.68 .77 988 2030 1.68 258 4491 5509 460 15 46 615 6679 2.62 970 1929 1.70 806 4750 4.80 5250 452 It 47 688 6836 952 1827 1.68 854 5008 4.82 4992 445 13 48 660 6993 984 1726 1.70 402 5267 4733 487 12 49 683 7150 916 1624 1.68 450 5526 4474 430 11 50 .62 706 9.79 7307 2.62 .77 897 9.89 1523 1.70 .80 498 9.90 5785 4.80 0.09 4215 LMM 10 51 728 7464 879 1421 546 6043 4.82 3957 415 9 52 751 7621 2.60 861 1319 594 6302 4.80 3698 408 8 53 774 7777 2.62 843 1217 643 6560 4.82 3440 401 7 54 796 7934 824 1115 690 6819 4.80 3181 898 6 55 819 8091 2.60 806 1013 788 7077 4.82 •j'.fj:; 886 5 56 842 8247 788 0911 786 7336 4.80 l'i;<;i BT8 4 57 864 8403 2.62 769 0809 884 7594 4.82 2406 m 3 58 887 8560 2.60 751 0707 882 7853 4.80 2147 864 1 59 909 8716 788 0605 980 8111 1889 ■M 1 60 .62 982 9.79 8872 .77 715 9.89 0503 .80 978 9.90 8369 0.09 1631 1.2849 128° Nat Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. I VS. N - 51° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 99 39° SlNE8. Cosines. Tangents. Dif. Cotangents. 140° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .62 932 9.79 8872 2.60 .77 715 9.89 0503 1.72 .80 978 9.90 8369 4.82 0.09 1631 1.2349 60' . i 955 9028 696 0400 1.70 .81 027 8628 4.80 1372 342 59 2 977 9184 2.58 678 0298 1.72 075 8886 1114 334 58 3 .63 000 9339 2.60 660 0195 1.70 123 9144 0856 327 57 4 022 9495 641 0093 1.72 171 9402 0598 320 56 5 045 9651 2.58 623 9.88 9990 1.70 220 9660 0340 312 55 6 068 9806 2.60 605 9888 1.72 268 9918 4.32 0082 305 54 7 090 9962 2.58 586 9785 316 9.91 0177 4.80 0.08 9823 298 53 8 113 9.80 0117 568 9682 364 0435 9565 290 52 9 135 027 2 550 9579 1.70 413 0693 9307 283 51 10 .63 158 9.80 0427 2.58 .77 531 9.88 9477 1.72 .81 461 9.91 0951 4.80 0.08 9049 1.2276 50 11 ISO 0582 513 9374 510 1209 8791 268 49 12 203 0737 494 9271 558 1467 8533 261 48 13 225 0892 476 9168 1.73 606 1725 4.28 8275 254 47 14 248 1047 2.57 458 9064 1.72 655 1982 4.30 8018 247 46 15 271 1201 2.58 439 8961 703 2240 7760 239 45 16 293 1356 421 8858 752 2498 7502 232 44 17 316 1511 2.57 402 8755 1.73 800 2756 7244 225 43 18 338 1665 384 8651 1.72 849 3014 4.98 6986 218 42 19 361 1819 366 8548 1.73 898 3271 4.30 6729 210 41 20 .63 383 9.80 1973 2.58 .77 847 9.88 8444 1.72 .81 946 9.91 3529 4.80 0.08 6471 1.2203 40 21 406 2128 2.57 329 8341 1.73 995 3787 4.28 6213 196 39 22 428' 2282 310 8237 1.72 .82 044 4044 4.30 5956 189 38 23 451 2436 2.55 292 8134 1.73 092 4302 5698 181 37 24 473 2589 2.57 273 8030 141 4560 4.28 5440 174 36 25 496 2743 255 7926 190 4817 4.30 5183 167 35 26 518 2897 2.55 236 7822 238 5075 4.28 4925 160 34 27 540 3050 2.57 218 7718 287 5332 4.30 4668 153 33 28 563 3204 2.55 199 7614 336 5590 4.28 4410 145 32 29 585 3357 2.57 181 7510 385 5847 4153 138 31 30 .63 608 9.80 3511 2.55 .77 162 9.88 7406 1.73 .82 434 9.91 6104 4.30 0.08 3896 1.2131 30 31 630 3664 144 7302 483 6362 4.28 3638 124 29 32 653 3817 125 7198 1.75 531 6619 4.30 3381 117 28 33 675 3970 107 7093 1.73 580 6877 4.28 3123 109 27 34 698 4123 088 6989 629 7134 2866 102 26 35 720 4276 2.53 070 6885 1.75 678 7391 2609 095 25 36 742 4428 2.55 051 6780 1.73 727 7648 4.30 2352 088 24 37 765 4581 033 6676 1.75 776 7906 4.28 2094 081 23 38 787 4734 2.53 014 ' 6571 825 8163 1837 074 22 39 810 4886 2.55 .76 996 6466 1.73 874 8420 1580 066 21 40 .63 832 9.80 5039 2.53 .76 977 9.88 6362 1.75 .82 923 9.91 8677 4.28 0.08 1323 1.2059 20 41 854 5191 959 6257 972 8934 1066 052 19 42 877 5343 940 6152 .83 022 9191 0809 045 18 43 S99 5495 921 6047 071 9448 0552 038 17 44 922 5647 903 5942 120 9705 0295 031 16 45 944 5799 884 5837 169 9962 0038 024 15 46 966 5951 866 5732 218 9.92 0219 0.07 9781 017 14 47 989 6103 2.52 847 5627 268 0476 9524 009 13 48 .64 011 6254 2.53 828 5522 1.77 317 0733 9267 002 12 49 033 6406 2.52 810 5416 1.75 366 0990 9010 1.1995 11 50 .64 056 9.80 6557 2.53 .76 791 9.88 5311 1.77 .83 415 9.92 1247 4.27 0.07 8753 1.1988 10 51 078 6709 2.52 772 5205 1.75 465 1503 4.28 8497 981 9 52 100 6860 754 5100 1.77 514 1760 8240 974 8 53 123 7011 2.53 735 4994 1.75 564 2017 7983 967 7 54 145 7163 2.52 717 4889 1.77 613 2274 4.27 7726 960 6 55 167 7314 698 4783 662 2530 4.28 7470 953 5 56 190 7465 2.50 679 4677 1.75 712 2787 7213 946 4 57 212 7615 2.52 661 4572 1.77 761 3044 4.27 6956 939 3 58 234 7766 642 4466 811 3300 4.28 6700 932 2 59 256 7917 2.50 623 4360 860 3557 6443 925 1 60 .64 279 9.80 8067 .76 604 9.88 4254 .83 910 9.92 3814 0.07 6186 1.1918 129° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 50° Cosines. Sines. Tangents. 100 VII. TRIGONOMETRIC FUNCTIONS. 40° Sines. Cosines. Tangents. Dif. Cotangents. 139° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .64 279 9.80 8067 2.52 .76 604 9.88 4254 1.77 .83 910 9.92 3814 4.27 0.07 6186 1.1918 60' l 301 8218 2.50 586 4148 960 4070 4.28 5930 910 59 2 828 8368 2.52 567 4042 .84 009 4327 4.27 5673 903 58 3 846 8519 2.50 548 3936 1.78 059 4583 4.28 5417 896 57 4 868 8669 530 3829 1.77 108 4840 4.27 5160 889 56 5 890 8819 511 3723 158 5096 4904 882 55 6 412 8969 492 3617 1.78 208 5352 4.28 4648 875 54 1 435 9119 473 3510 1.77 258 5609 4.27 4391 868 53 8 457 9269 455 3404 1.78 307 5865 4.28 4135 861 52 9 479 9419 436 3297 1.77 357 6122 4.27 3878 854 51 10 .64 501 9.80 9569 2.48 .76 417 9.88 3191 1.78 .84 407 9.92 6378 4.27 0.07 3622 1.1847 50 11 524 9718 2.50 398 3084 457 6634 3366 840 49 12 546 9868 2.48 380' 2977 1.77 507 6890 4.28 3110 883 48 13 568 9.81 0017 2.50 361 2871 1.78 ' 556 7147 4.27 2853 826 47 14 590 0167 2.48 342 2764 606 7403 2597 819 46 15 612 0316 323 2657 656 7659 2341 812 45 16 635 0465 304 2550 706 7915 2085 806 44 17 657 0614 286 2443 756 8171 1829 799 43 18 679 0763 267 2336 806 8427 4.28 1573 792 42 19 701 0912 248 2229 1.80 856 8684 4.27 1316 785 41 20 .64 723 9.81 1061 2.48 .76 229 9.88 2121 1.78 .84 906 9.92 8940 4.27 0.07 1060 1.1778 40 21 746 1210 2.47 210 2014 956 9196 0804 771 39 22 768 1358 2.48 , 192 1907 1.80 .85 006 9452 0548 764 38 23 790 1507 2.47 173 1799 1.78 057 9708 0292 757 37 24 812 1655 2.48 154 1692 1.80 107 9964 0036 750 36 25 884 1804 2.47 135 1584 1.78 157 9.93 0220 4.25 0.06 9780 743 35 26 856 1952 116 1477 1.80 207 0475 4.27 9525 736 34 27 878 2100 097 1369 257 0731 9269 729 33 28 901 2248 078 1261 808 0987 9013 722 32 29 923 2396 059 1153 1.78 858 1243 8757 715 31 30 .64 945 9.81 2544 2.47 .76 041 9.88 1046 1.80 .85 408 9.93 1499 4.27 0.06 8501 1.1708 30 31 967 2692 022 0938 458 1755 4.25 8245 702 29 32 989 2840 003 0830 509 2010 4.27 7990 695 28 33 .65 Oil 2988 2.45 .75 984 0722 1.82 559 2266 7734 688 27 34 033 3135 2.47 965 0613 1.80 609 2522 7478 681 26 35 055 3283 2.45 946 0505 660 2778 4.25 7222 674 25 36 077 3430 2.47 927 0397 710 3033 4.27 6967 667 24 37 100 3578 2.45 908 0289 1.82 761 3289 6711 660 23 38 122 3725 889 0180 1.80 811 3545 4.25 6455 653 22 39 144 3872 870 0072 1.82 862 3800 4.27 6200 647 21 40 .65 166 9.814019 2.45 .75 851 9.87 9963 1.80 .85 912 9.93 4056 4.25 0.06 5944 1.1640 20 41 188 4166 882 9855 1.82 963 4311 4.27 5689 633 19 42 210 4313 818 9746 .86 014 4567 425 5433 626 18 43 232 4460 794 9637 1.80 064 4822 4.27 5178 619 17 44 254 4607 2.43 775 9529 1.82 115 5078 4.25 v 4922 61 -2 16 45 276 4753 2.45 756 9420 166 - 5333 4.27 4667 606 15 46 298 4900 2.43 788 9311 216 5589 4.25 4411 599 14 47 820 5046 2.45 719 9202 267 5844 4.27 4156 592 13 48 842 5193 2.43 700 9093 818 6100 4.25 3900 585 12 49 864 5339 680 8984 868 6355 4.27 3645 578 11 50 .65 886 9.81 5485 2.45 .75 661 9.87 8875 1.82 .86 419 9.93 6611 4.25 0.06 3389 1.1571 10 51 408 5632 2.48 642 8766 1.88 470 6866 3134 565 9 52 480 5778 628 8656 1.82 521 7121 4.27 2879 558 8 53 452 5924 2.42 604 8547 572 7377 4.25 2623 551 7 54 474 6069 2.48 585 8438 1.88 628 7632 2368 544 6 55 496 6215 566 8328 1.82 674 7887 2113 588 5 56 518 6361 547 8219 1.88 725 8142 4.27 1858 581 4 57 540 6507 2.42 528 8109 776 8398 4.25 1602 524 3 58 562 6652 2.48 509 7999 1.82 827 8653 1347 517 2 59 584 6798 2.42 490 7890 1.88 878 8908 1092 510 1 60 .65 606 9.81 6943 .75 471 9.87 7780 .86 929 9.93 9163 0.06 0837 1.1604 130° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 49° Cosines. Sines. VH. TRIGONOMETRIC FUNCTIONS. 101 41° Sines. Cosines. Tangents. Dif. Cotangents. 138° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .65 600 9.81 6943 2.42 .75 471 9.87 7780 1.88 .86 929 9.93 9163 4.25 0.06 0837 1.1504 60' i 628 7088 452 7670 980 9418 0582 497 59 2 650 7233 2.43 483 7560 .87 031 9673 0327 490 58 3 672 7379 2.42 414 7450 082 9928 0072 483 57 4 694 7524 2.40 395 7340 133 9.94 0183 4.27 0.05 9817 477 56 5 716 7668 2.42 375 7230 • 184 0439 4.25 9561 470 55 6 738 7813 356 7120 236 0694 9306 463 54 7 759 7958 337 7010 1.85 287 0949 9051 456 53 8 781 8103 2.40 318 6899 1.83 338 1204 8796 450 52 9 803 8247 2.42 299 6789 1.85 389 1459 4.23 8541 443 51 10 .65 825 9.81 8392 2.40 .75 280 9.87 6678 1.83 .87 441 9.94 1713 4.25 0.05 8287 1.1436 50 11 847 8536 2.42 261 6568 1.85 492 1968 8032 430 49 12 869 , 8681 2.40 241 6457 1.83 548 2223 7777 423 48 13 891 8825 222 6347 1.85 595 2478 7522 416 47 14 913 8969 203 6236 646 2733 7267 410 46 15 935 9113 184 6125 698 2988 7012 403 45 16 956 9257 165 6014 1.83 749 3243 6757 396 44 17 978 9401 146 5904 1.85 801 3498 4.28 6502 389 43 18 .66 000 9545 126 5793 852 3752 4.25 6248 383 42 19 022 9689 2.38 107 5682 904 4007 5993 876 41 20 .66 044 9.81 9832 2.40 .75 088 9.87 5571 1.87 .87 955 9.94 4262 4.25 0.05 5738 1.1369 40 21 066 9976 069 5459 1.85 .88 007 4517 4.23 5483 363 39 22 088 9.82 0120 2.38 050 5348 059 4771 4.25 5229 356 38 23 109 0263 030 5237 110 5026 4974 349 37 24 131 0406 2.40 011 5126 1.87 162 5281 4.28 4719 848 36 25 153 0550 2.38 .74 992 5014 1.85 214 5535 4.25 4465 336 35 26 175 0693 973 4903 1.87 265 5790 4210 829 34 27 197 0836 953 4791 1.85 317 6045 4.23 3955 323 33 28 218 0979 934 4680 1.87 369 6299 4.25 3701 316 32 29 240 1122 915 4568 421 6554 4.23 3446 310 31 30 .66 262 9.82 1265 2.87 .74 896 9.87 4456 1.87 .88 473 9.94 6808 4.25 0.05 3192 1.1303 30 31 284 1407 2.88 876 4344 524 7063 2937 296 29 32 306 1550 857 4232 1.85 576 7318 4.23 2682 290 28 33 327 1693 2.87 838 4121 1.87 628 7572 4.25 2428 283 27 34 349 1835 818 4009 1.88 680 7827 4.28 2173 276 26 35 371 1977 2.88 799 3896 1.87 732 8081 1919 270 25 36 393 2120 2.37 780 3784 784 8335 4.25 1665 263 24 37 414 2262 760 . 3672 836 8590 4.28 1410 257 23 38 436 2404 741 3560 888 8844 4.25 1156 250 22 39 458 2546 722 3448 1.88 940 9099 4.28 0901 243 21 40 .66 480 9.82 2688 2.87 .74 703 9.87 3335 1.87 .88 992 9.94 9353 4.25 0.05 0647 1.1237 20 41 501 2830 688 3223 1.88 .89 045 9608 4.23 0392 230 19 42 523 2972 664 3110 1.87 097 9862 0138 224 18 43 545 3114 2.35 644 2998 1.88 149 9.95 0116 4.25 0.04 9884 217 17 44 566 3255 2.87 625 2885 201 0371 4.23 9629 211 16 45 588 3397 606 2772 253 0625 9375 204 15 46 610 3539 2.85 586 2659 1.87 306 0879 9121 197 14 47 632 3680 567 2547 1.88 858 1133 4.25 8867 191 13 48 653 3821 2.37 548 2434 410 1388 4.23 8612 184 12 49 675 3963 2.85 528 2321 463 1642 8358 178 11 50 .66 697 9.82 4104 2.85 .74 509 9.87 2208 1.88 .89 515 9.95 1896 4.28 0.04 8104 1.1171 10 51 718 4245 489 2095 1.90 567 2150 4.25 7850 165 9 52 740 4386 470 1981 1.88 620 2405 4.28 7595 158 8 53 762 4527 451 1868 672 2659 7341 152 7 54 783 4668 2.88 481 1755 1.90 725 2913 7087 145 6 55 805 4808 2.85 412 1641 1.88 777 3167 6833 139 5 56 827 4949 392 1528 1.90 830 3421 6579 132 4 57 848 5090 2.33 373 1414 1.88 883 3675 6325 126 3 58 870 5230 2.85 353 1301 1.90 985 3929 6071 119 2 59 891 5371 2.33 334 1187 988 4183 5817 113 1 60 .66 913 9.82 5511 .74 814 9.87 1073 .90 040 9.95 4437 0.04 5563 1.1106 131° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 48° Cosines. Sines. Tangents. 102 VII. TRIGONOMETRIC FUNCTIONS. ~ 42° Sines. Cosines. Tangents. Dif. Cotangents. 137° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .66 913 9.82 5511 2.88 .74 814 9.87 1073 1.88 .90 040 9.95 4437 4.28 0.04 5563 1.1106 60' l 935 5651 295 0960 1.90 093 4691 4.25 5309 100 59 2 956 5791 276 0846 146 4946 4.23 5054 093 58 3 978 5931 256 0732 199 5200 4800 087 57 4 999 6071 237 0618 251 5454 4546 080 56 5 .67 021 6211 217 0504 804 5708 4.22 4292 074 55 6 043 6351 198 0390 857 5961 4.28 4039 067 54 7 064 6491 178 0276 1.92 410 6215 3785 061 53 8 086 6631 2.32 159 0161 1.90 463 6469 3531 054 52 9 107 6770 2.33 139 0047 516 6723 3277 048 51 10 .67 129 9.82 6910 2.32 .74 120 9.86 9933 1.92 .90 569 9.95 6977 4.28 0.04 3023 1.1041 50 11 151 7049 2.88 100 9818 1.90 621 7231 2769 035 49 12 172 7189 2.82 080 9704 1.92 674 7485 2515 028 48 13 194 7328 061 9589 727 7739 2261 022 47 14 215 7467 041 9474 1.90 781 7993 2007 016 46 15 237 7606 022 9360 1.92 834 8247 4,22 1753 009 45 16 258 7745 002 9245 887 8500 4.28 1500 003 44 1*? 280 7884 .73 983 9130 940 8754 1246 1.0996 43 18 301 8023 963 9015 993 9008 0992 990 42 19 323 8162 944 8900 .91 046 9262 0738 983 41 20 .67 844 9.82 8301 2.80 .73 924 9.86 8785 1.92 .91 099 9.95 9516 4.22 0.04 0484 1.0977 40 21 366 8439 2.32 904 8670 153 9769 4.23 0231 971 39 22 387 8578 2.30 885 8555 206 9.96 0023 0.03 9977 964 38 23 409 8716 2.32 865 8440 1.93 259 0277 4.22 9723 958 .37 24 430 8855 2.30 846 8324 1.92 313 0530 4.28 9470 951 36 25 452 8993 826 8209 1.93 366 0784 9216 945 35 26 473 9131 806 8093 1.92 419 1038 8962 939 34 27 495 9269 787 7978 1.93 473 1292 4.22 8708 932 33 28 516 9407 767 7862 1.92 526 1545 4.28 8455 926 32 29 538 9545 747 7747 1.93 580 1799 4.22 8201 919 31 30 .67 559 9.82 9683 2.30 .73 728 9.86 7631 1.93 .91633 9.96 2052 4.28 0.03 7948 1.0918 30 31 580 9821 708 7515 687 2306 7694 907 29 32 602 9959 688 7399 740 2560 4.22 7440 900 28 33 623 9.83 0097 2.28 669 7283 794 2813 4.23 7187 894 27 34 645 0234 2.30 649 7167 847 3067 4.22 6933 888 26 35 666 0372 2.28 629 7051 901 3320 4.23 6680 881 25 36 688 0509 610 6935 955 3574 6426 875 24 37 709 0646 2.30 590 6819 .92 008 3828 4.22 6172 869 23 38 730 0784 2.28 570 6703 1.95 062 4081 4.28 5919 862 22 39 752 0921 551 6586 1.93 116 4335 4.22 5665 856 21 40 .67 773 9.83 1058 2.28 .73 531 9.86 6470 1.95 .92 170 9.96 4588 4.28 0.03 5412 L08M 20 41 795 1195 511 6353 1.93 224 4842 4.22 5158 848 19 42 816 1332 491 6237 1.95 277 5095 4.23 4905 887 18 43 837 1469 472 6120 1.93 831 5349 4.22 4651 881 17 44 859 1606 2.27 452 6004 1.95 885 5602 4398 824 16 45 880 1742 2.28 432 5887 489 5855 4.23 4145 818 15 46 901 1879 2.2T 418 5770 498 6109 4.22 3891 812 14 47 923 2015 2.28 393 5653 547 6362 4.23 3638 805 13 48 944 2152 2.27 873 5536 601 6616 4.22 3384 799 12 49 965 2288 2.28 858 5419 655 6869 4.28 3131 798 11 50 .67 987 9.83 2425 2.27 .73 838 9.86 5302 1.95 .92 709 9.96 7123 4.22 0.03 2877 1.0786 10 51 .68 008 2561 814 5185 768 7376 2624 780 9 52 029 2697 294 5068 1.97 817 7629 4.28 2371 774 8 53 051 2833 274 4950 1.95 872 7883 4.22 2117 768 7 54 072 2969 254 4833 926 8136 1864 761 6 55 098 3105 284 4716 1.97 980 8389 4.28 1611 1.0755 5 56 115 3241 215 4598 1.95 .93 034 8643 4.22 1357 749 4 57 186 3377 2.25 195 4481 1.97 088 8896 1104 m 3 58 157 3512 2.27 175 4363 148 9149 4.28 0851 786 ■_> 59 179 3648 2.25 155 4245 197 9403 4.22 0597 780 1 60 .68 200 9.83 3783 .78 185 9.86 4127 .98 252 9.96 9656 0.03 0344 1.0724 132° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 47° Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 103 43° Sines. Cosines. Tangents. Cotangents. 136° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .68 200 9.83 3783 2.27 .73 135 9.86 4127 1.95 .93 252 9.96 9656 4.22 0.03 0344 1.0724 60' i 221 3919 2.25 116 4010 1.97 306 9909 0091 717 59 2 242 4054 096 3892 360 9.97 0162 4.23 0.02 9838 711 58 3 264 4189 2.27 076 3774 415 0416 4.22 9584 705 57 4 285 4325 2.25 056 3656 469 0669 9331 699 56 5 306 4460 036 3538 1.98 524 0922 9078 692 55 6 327 4595 016 3419 1.97 578 1175 4.23 8825 686 54 7 349 4730 .72 996 3301 633 1429 4.22 8571 680 53 8 370 4865 2.23 976 3183 1.98 688 1682 8318 674 52 9 391 4999 2.25 957 3064 1.97 742 1935 8065 668 51 10 .68 412 9.83 5134 2.25 .72 937 9.86 2946 1.98 .93 797 9.97 2188 4.22 0.02 7812 1.0661 50 11 434 5269 2.23 917 2827 1.97 852 2441 4.23 7559 655 49 12 455 5403 2.25 897 2709 1.98 906 2695 4.22 7305 649 48 13 476 5538 2.23 877 2590 961 2948 7052 648 47 14 497 5672 2.25 857 2471 1.97 .94 016 3201 6799 637 46 15 518 5807 2.23 837 2353 1.98 071 3454 6546 630 45 16 539 5941 817 2234 125 3707 6293 624 44 . 17 561 6075 797 2115 180 3960 6040 618 43 18 582 6209 777 1996 235 4213 5787 612 42 19 603 6343 757 1877 290 4466 4.23 5534 606 41 20 .68 624 9.83 6477 2.23 .72 737 9.86 1758 2.00 .94 345 9.97 4720 4.22 0.02 5280 1.0599 40 21 645 6611 717 1638 1.98 400 4973 5027 593 39 22 666 6745 2.22 697 1519 455 5226 4774 587 38 23 688 6878 2.23 677 1400 2.00 510 5479 4521 581 37 24 709 7012 657 1280 1.98 565 5732 4268 575 36 25 730 7146 2.22 687 1161 2.00 620 5985 4015 569 35 26 751 7279 617 1041 1.98 676 6238 3762 562 34 27 772 7412 2.23 597 0922 2.00 731 6491 3509 556 33 28 793 7546 2.22 577 0802 786 6744 3256 550 32 29 814 7679 557 0682 841 6997 3003 544 31 30 .68 835 9.83 7812 2.22 .72 537 9.86 0562 2.00 .94 896 9.97 7250 4.22 0.02 2750 1.0538 30 31 857 7945 517 0442 952 7503 2497 532 29 32 878 8078 . 497 0322 .95 007 7756 2244 526 28 33 899 8211 477 0202 062 8009 1991 519 27 34 920 8344 457 0082 118 8262 1738 513 26 35 941 8477 437 9.85 9962 173 8515 1485 507 25 36 962 8610 2.20 417 9842 2.02 229 8768 1232 501 24 37 983 8742 2.22 397 9721 2.00 284 9021 0979 495 23 38 .69 004 8875 2.20 377 - 9601 2.02 340 9274 0726 489 22 39 025 9007 2.22 357 9480 2.00 395 9527 0473 488 21 40 .69 046 9.83 9140 2.20 .72 837 9.85 9360 2.02 .95 451 9.97 9780 4.22 0.02 0220 1.0477 20 41 067 9272 317 9239 2.00 506 9.98 0033 0.01 9967 470 19 42 088 9404 297 9119 2.02 562 0286 4.20 9714 464 18 43 109 9536 277 8998 618 0538 4.22 9462 458 17 44 130 9668 257 8877 673 0791 9209 452 16 45 151 9800 236 8756 729 1044 8956 446 15 46 172 9932 216 8635 785 1297 8703 440 14 47 193 9.84 0064 196 8514 841 1550 8450 484 13 48 214 0196 176 8393 897 1803 8197 428 12 49 235 0328 2.18 156 8272 952 2056 7944 422 11 50 .69 256 9.84 0459 2.20 .72 136 9.85 8151 2.03 .96 008 9.98 2309 4.22 0.01 7691 1.0416 10 51 277 0591 2.18 116 8029 2.02 064 2562 4.20 7438 410 9 52 298 0722 2.20 095 7908 2.03 120 2814 4.22 7186 404 8 53 819 0854 2.18 075 7786 2.02 176 3067 6933 398 7 54 340 0985 055 7665 2.03 232 3320 6680 392 6 55 361 1116 085 7543 2.02 288 3573 6427 385' 5 56 382 1247 . 015 7422 2.08 344 3826 6174 879 4 57. 403 1378 .71 995 7300 400 4079 5921 878 3 58 424 1509 974 7178 457 4332 4.20 5668 367 2 59 445 1640 954 7056 513 4584 4.22 5416 361 1 60 .69 466 9.84 1771 .71 934 9.85 6934 .96 569 9.98 4837 0.01 5163 1.0355 133° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 46° Cosines. Sines. Tangents. 104 VII. TRIGONOMETRIC FUNCTIONS. 44° Sinks. Cosines. Tangents. Dlf. Cotangents. 135° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nut. 0' .69 46G 9.84 1771 2.18 .71984 9.85 6934 2.08 .96 569 9.98 4837 4.22 0.01 5163 1.0855 60' l 487 1902 914 6812 625 5090 4910 849 69 2 608 2033 2.17 894 6690 681 5343 4657 848 58 3 529 2163 2.18 873 6568 788 5596 4.20 4404 887 57 4 549 2294 2.17 858 6446 2.05 794 5848 4.22 4152 881 56 5 570 2424 2.18 833 6323 2.08 850 6101 3899 825 55 6 591 2555 2.17 813 6201 2.05 907 6354 3646 319 54 7 612 2685 792 6078 2.08 968 6607 3393 313 53 8 638 2815 2.18 772 5956 2.05 .97 020 6860 4.20 3140 307 52 9 654 2946 2.17 752 5833 2.08 076 7112 4.22 2888 801 51 10 .69 675 9.84 3076 2.17 .71 782 9.85 5711 2.05 .97 183 9.98 7365 4.22 0.01 2635 1.0295 50 11 696 3206 711 5588 189 7618 2382 289 49 12 717 3336 691 5465 246 7871 4.20 2129 288 48 13 737 3466 2.15 671 5342 302 8123 422 1877 277 47 14 758 3595 2.17 650 5219 359 8376 • 1624 271 46 15 779 3725 630 5096 416 8629 1371 265 45 16 800 3855 2.15 610 4973 472 8882 4.20 1118 259 44 17 821 3984 2.17 590 4850 529 9134 4.22 0866 258 43 18 842 4114 2.15 569 4727 2.07 586 9387 0613 247 42 19 862 4243 549 4603 2.05 648 9640 0360 241 41 20 .69 883 9.84 4372 2.17 .71 529 9.85 4480 2.07 .97 700 9.98 9893 4.20 0.010107 1.0285 40 21 904 4502 2.15 508 4356 2.05 756 9.99 0145 4.22 0.00 9855 280 39 22 925 4631 488 4233 2.07 818 0398 9602 224 38 23 946 4760 468 * 4109 2.05 870 0651 4.20 9349 218 37 24 966 4889 447 3986 2.07 927 0903 4.22 9097 212 36 25 987 5018 427 3862 984 1156 8844 206 35 26 .70 008 5147 407 3738 .98 041 1409 8591 200 34 27 029 5276 886 3614 098 1662 4.20 8338 194 33 28 049 5405 2.18 366 3490 155 1914 4.22 8086 188 32 29 070 5533 2.15 345 3366 213 2167 7833 182 31 30 .70 091 9.84 5662 2.13 .71 825 9.85 3242 2.07 .98 270 9.99 2420 4.20 0.00 7580 1.0176 30 31 112 5790 2.15 805 3118 827 2672 4.22 7328 170 29 32 182 5919 2.13 284 2994 2.08 384 2925 7075 164 28 33 153 6047 264 2869 2.07 441 3178 6822 108 27 34 174 6175 2.15 248 2745 2.08 499 3431 4.20 6569 152 26 35 195 6304 2.18 223 2620 2.07 556 3683 4.22 6317 147 25 36 215 6432 203 2496 2.08 613 3936 6064 141 24 37 236 6560 182 2371 2.07 671 4189 4.20 5811 185 23 38 257 6688 162 2247 2.08 728 4441 4.22 5559 129 22 39 277 6816 141 2122 786 4694 5306 128 21 40 .70 298 9.84 6944 2.12 .71 121 9.85 1997 2.08 .98 848 9.99 4947 4.20 0.00 5053 1.0117 20 41 819 7071 2.18 100 1872 901 5199 4.22 4801 111 19 42 839 7199 080 1747 958 5452 4548 105 18 43 860 7327 2.12 059 1622 .99 016 5705 4.20 4295 099 17 44 881 7454 2.18 039 1497 078 5957 4.22 4043 094 16 45 .70 401 7582 2.12 019 1372 2.10 131 6210 3790 088 15 46 422 7709 .70 998 1246 2.08 189 6463 4.20 3537 082 14 47 448 7836 2.13 978 1121 247 6715 4.22 3285 076 13 48 468 7964 2.12 957 0996 2.10 804 6968 3032 070 IS 49 484 8091 987 0870 2.08 862 7221 4.20 2779 Ml 11 50 .70 505 9.84 8218 2.12 .70 916 9.85 0745 2.10 .99 420 9.99 7473 4.22 0.00 2527 1.0058 10 51 525 8345 896 0619 478 7726 2274 052 9 52 546 8472 875 0493 2.08 586 7979 4.20 2021 047 8 53 567 8599 855 0368 2.10 594 8231 4.22 1769 041 7 54 587 8726 2.10 884 0242 652 8484 1516 085 i 55 608 8852 2.12 818 0116 710 8737 4.20 1263 029 1 56 628 8979 798 9.84 9990 768 8989 4.22 1011 028 4 57 649 9106 2.10 772 9864 826 9242 0758 017 3 58 670 9232 2.12 752 9738 2.12 884 9495 4.20 0505 019 2 59 690 9359 2.10 781 9611 2.10 942 9747 4.22 0253 006 1 60 .70 711 9.84 9485 .70 711 9.84 9485 1.0000 0.00 0000 0.00 0000 1.0000 134° Nat Log. Dlf. Nat Log. Dlf. Nat. Log. Cotangents. Dlf. Log. Nat. Tangents. 45° Cosines. Sines. VIII. NATURAL LOGARITHMS. 105 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. .00 ao .50 9.30 6853 1.00 0.00 0000 1.50 0.40 5465 2.00 0.69 3147 .01 5.39 4830 .51 9.32 6655 .01 0.00 9950 .51 0.41 2110 .01 8135 .02 6.08 7977 .52 9.34 6074 .02 0.01 9803 .52 8710 .02 0.70 3098 .03 6.49 3442 .53 936 5122 .03 0.02 9559 .53 0.42 5268 .03 8036 .04 6.78 1124 .54 9.38 3814 .04 0.03 9221 .54 0.43 1782 .04 0.71 2950 .05 7.00 4268 .55 9.40 2163 .05 0.04 8790 .55 8255 .05 7840 .06 7.18 6589 .56 9.42 0182 .06 0.05 8269 .56 0.44 4686 .06 0.72 2706 .07 7.34 0740 .57 9.43 7881 .07 0.06 7659 .57 0.45 1076 .07 7549 .08 7.47 4271 .58 9.45 5273 .08 0.07 6961 .58 7425 .08 0.73 2368 .09 7.59 2054 .59 9.47 2367 .09 0.08 6178 .59 0.46 3734 .09 7164 .10 7.69 7415 .60 9.48 9174 1.10 0.09 5310 1.60 0.47 0004 2.10 0.74 1937 .11 7.79 2725 .61 9.50 5704 .11 0.10 4360 .61 6234 .11 6688 .12 7.87 9736 .62 9.52 1964 .12 0.11 3329 .62 0.48 2426 .12 0.75 1416 .13 7.95 9779 .63 9.53 7965 .13 0.12 2218 .63 8580 .13 6122 .14 8.03 3887 . .64 9.55 3713 .14 0.13 1028 .64 0.49 4696 .14 0.76 0806 .15 8.10 2880 .65 9.56 9217 .15 9762 .65 0.50 0775 .15 5468 .16 8.16 7419 .66 9.58 4485 .16 0.14 8420 .66 6818 .16 0.77 0108 .17 8.22 8043 .67 9.59 9522 .17 0.15 7004 .67 0.51 2824 .17 4727 .18 8.28 5202 .68 9.61 4338 .18 0.16 5514 .68 8794 .18 9325 .19 8.33 9269 .69 9.62 8936 .19 0.17 3953 .69 0.52 4729 .19 0.78 3902 .20 8.39 0562 .70 9.64 3325 1.20 0.18 2322 1.70 0.53 0628 2.20 0.78 8457 .21 8.43 9352 .71 9.65 7510 .21 0.19 0620 .71 6493 .21 0.79 2993 .22 8.48 5872 .72 9.67 1496 .22 8851 .72 0.54 2324 .22 7507 .23 8.53 0324 .73 9.68 5289 .23 0.20 7014 .73 8121 .23 0.80 2002 .24 8.57 2884 .74 9.69 8895 .24 0.21 5111 .74 0.55 3885 .24 6476 .25 8.61 3706 .75 9.71 2318 .25 0.22 3144 .75 9616 .25 0.81 0930 26 8.65 2926 .76 9.72 5563 .26 0.23 1112 .76 0.56 5314 .26 5365 .27 8.69 0667 .77 9.73 8635 .27 9017 .77 0.57 0980 .27 9780 .28 8.72 7034 .78 9.75 1539 .28 0.24 6860 .78 6613 .28 0.82 4175 .29 8.76 2126 .79 9.76 4278 .29 0.25 4642 .79 0.58 2216 .29 8552 .30 8.79 6027 .80 9.77 6856 1.30 0.26 2364 1.80 0.58 7787 2.30 0.83 2909 .31 8.82 8817 .81 9.78 9279 .31 0.27 0027 .81 0.59 3327 .31 7248 .32 8.86 0566 .82 9.80 1549 .32 7632 .82 8837 .32 0.84 1567 .33 8.89 1337 .83 9.81 3670 .33 0.28 5179 .83 0.60 4316 .33 5868 .34 8.92 1190 .84 9.82 5647 .34 0.29 2670 .84 9766 .34 0.85 0151 .35 8.95 0178 .85 9.83 7481 .35 0.30 0105 .85 0.61 5186 .35 4415 .36 8.97 8349 .86 9.84 9177 .36 7485 .86 0.62 0576 .36 8662 .37 9.00 5748 .87 9.86 0738 .37 0.314811 .87 5938 .37 0.86 2890 .38 9.03 2416 .88 9.87 2167 .38 0.32 2083 .88 0.63 1272 .38 7100 .39 9.05 8391 .89 9.88 3466 .39 9304 .89 6577 .39 0.87 1293 .40 9.08 3709 .90 9.89 4639 1.40 0.33 6472 1.90 0.64 1854 2.40 0.87 5469 .41 9.10 8402 .91 9.90 5689 .41 0.34 3590 .91 7103 .41 9627 .42 9.13 2499 .92 9.91 6618 .42 0.35 0657 .92 0.65 2325 .42 0.88 3768 .43 9.15 6030 .93 9.92 7429 .43 7674 .93 7520 .43 7891 .44 9.17 9019 .94 9.93 8125 .44 0.36 4643 .94 0.66 2688 .44 0.89 1998 .45 9.20 1492 .95 9.94 8707 .45 0.37 1564 .95 7829 .45 6088 .46 9.22 3471 .96 9.95 9178 .46 8436 .96 0.67 2944 .46 0.90 0161 .47 9.24 4977 .97 9.96 9541 .47 0.38 5262 .97 8034 .47 4218 .48 9.26 6031 .98 9.97 9797 .48 0.39 2042 .98 0.68 3097 .48 8259 .49 9.28 6650 .99 9.98 9950 .49 8776 .99 8135 .49 0.91 2283 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 106 VIII. NATURAL LOGARITHMS. Num. Log. Num. Loo. Num. Loo. Num. Loo. Num. Loo. 2.50 0.91 6291 3.00 1.09 8612 3.50 1.25 2763 4.00 1.38 6294 4.50 1.50 4077 .51 0.92 0283 .01 1.10 1940 .51 5616 .01 8791 .51 6297 .52 4259 .02 5257 .52 8461 .02 1.39 1282 .52 8512 .53 8219 .03 8563 .53 1.26 1298 .03 3766 .53 1.51 0722 .54 0.93 2164 .04 1.11 1858 .54 4127 .04 6245 .54 2927 .55 6093 .05 5142 .55 6948 .05 8717 .55 5127 .56 0.94 0007 .06 8415 .56 9761 .06 1.40 1183 .56 7323 .57 3906 .07 1.12 1678 .57 1.27 2566 .07 3643 .57 9513 .58 7789 .08 4930 .58 5363 .08 6097 .58 1.52 1699 .59 0.95 1658 .09 8171 .59 8152 .09 8545 .59 3880 2.60 0.95 5511 3.10 1.13 1402 3.60 1.28 0934 4.10 1.41 0987 4.60 1.52 6056 .61 9350 .11 4623 .61 3708 .11 3423 .61 8228 .62 0.96 3174 .12 7833 .62 6474 .12 5853 .62 1.53 0395 .63 6984 .13 1.14 1033 .63 9233 .13 8277 .63 2557 .64 0.97 0779 .14 4223 .64 1.29 1984 .14 1.42 0696 .64 4714 .65 4560 .15 7402 .65 4727 .15 3108 .65 6867 .66 8326 .16 1.15 0572 .66 7463 .16 5515 .66 9015 .67 0.98 2078 .17 3732 .67 1.30 0192 .17 7916 .67 1.54 1159 .68 5817 .18 6881 .68 2913 .18 1.43 0311 .68 3298 .69 9541 .19 1.16 0021 .69 5626 .19 2701 .69 5433 2.70 0.99 3252 3.20 1.16 3151 3.70 1.30 8333 4.20 1.43 5085 4.70 1.54 7563 .71 6949 .21 6271 .71 1.31 1032 .21 7463 .71 9688 .72 1.00 0632 .22 9381 .72 3724 .22 9835 .72 1.55 1809 .73 4302 .23 1.17 2482 .73 6408 .23 1.44 2202 .73 3925 .74 7958 .24 5573 .74 9086 .24 4563 .74 6037 .75 1.01 1601 .25 8655 .75 1.32 1756 .25 6919 .75 8145 .76 5231 .26 1.18 1727 .76 4419 .26 9269 .76 1.56 0248 .77 8847 .27 4790 .77 7075 .27 1.45 1614 .77 2346 .78 1.02 2451 .28 7843 .78 9724 .28 3953 .78 4441 .79 6042 .29 1.19 0888 .79 1.33 2366 .29 6287 .79 6530 2.80 1.02 9619 3.30 1.19 3922 3.80 1.33 5001 4.30 1.45 8615 4.80 1.56 8616 .81 1.03 3184 .31 6948 .81 7629 .31 1.46 0938 .81 1.57 0697 .82 6737 .32 9965 .82 1.34 0250 .32 3255 .82 2774 .83 1.04 0277 .33 1.20 2972 .83 2865 .33 5568 .83 4846 .84 3804 .34 5971 .84 5472 .34 7874 .84 6915 .85 7319 .35 8960 .85 8073 .35 1.47 0176 .85 8979 .86 1.05 0822 .36 1.21 1941 .86 1.35 0667 .36 2472 .86 1.58 1038 .87 4312 .37 4913 .87 3255 .37 4763 .87 3094 .88 7790 .38 7876 .88 5835 .38 7049 .88 5145 .89 1.06 1257 .39 1.22 0830 .89 8409 .39 9329 .89 7192 2.90 1.06 4711 3.40 1.22 3775 3.90 1.36 0977 4.40 1.48 1605 4.90 1.58 9235 .91 8153 .41 6712 .91 3537 .41 3875 .91 1.59 1274 .92 1.07 1584 .42 9641 .92 6092 .42 6140 .92 3309 .93 5002 .43 1.23 2560 .93 8639 .43 840.0 .93 5339 .94 8410 .44 5471 .94 1.37 1181 .44 1.49 0654 .94 7365 .95 1.08 1805 .45 8374 .95 3716 .45 2904 .95 9388 .96 5189 .46 1.24 1269 .96 6244 .46 5149 .96 1.60 1406 .97 8562 .47 4155 .97 8766 .47 7388 .97 3420 .98 1.09 1923 .48 7032 .98 1.38 1282 .48 9623 .98 5430 .99 5273 .49 9902 .99 3791 49 1.50 1853 ,99 7436 Num. Loo. Num. Loo. Num. Loo. Num. Loo. Num. Loo. VIII. NATURAL LOGARITHMS. 107 NUM. Log. Num. Log. Num. Log. Num. Log. Num. Log. 5.00 1.60 9438 5.50 1.70 4748 6.00 1.79 1759 6.50 1.87 1802 7.00 1.94 5910 .01 1.61 1436 .51 6565 .01 3425 .51 3339 .01 7338 .02 3430 .52 8378 .02 5087 .52 4874 .02 8763 .03 5420 .53 1.71 0188 .03 6747 .53 6407 .03 1.95 0187 .04 7406 .54 1995 .04 8404 .54 7937 .04 1608 .05 9388 .55 3798 .05 1.80 0058 .55 9465 .05 3028 .06 1.62 1366 .56 5598 .06 1710 .56 1.88 0991 .06 4445 .07 3341 .57 7395 .07 3359 .57 2514 .07 5860 .08 5311 .58 9189 .08 5005 .58 4035 .08 7274 .09 7278 .59 1.72 0979 .09 6648 .59 5553 .09 8685 5.10 1.62 9241 5.60 1.72 2767 6.10 1.80 8289 6.60 1.88 7070 7.10 1.96 0095 .11 1.63 1199 .61 4551 .11 9927 .61 8584 .11 1502 .12 3154 .62 6332 .12 1.81 1562 .62 1.89 0095 .12 2908 .13 5106 .63 8109 .13 3195 .63 1605 .13 4311 .14 7053 .64 9884 .14 4825 .64 3112 .14 5713 .15 8997 .65 1.73 1656 .15 6452 .65 4617 .15 7112 .16 1.64 0937 .66 3424 .16 8077 .66 6119 .16 8510 .17 2873 .67 5189 .17 9699 .67 7620 .17 9906 .18 4805 .68 6951 .18 1.82 1318 .68 9118 .18 1.97 1299 .19 6734 .69 8710 .19 2935 .69 1.90 0614 .19 2691 5.20 1.64 8659 5.70 1.74 0466 6.20 1.82 4549 6.70 1.90 2108 7.20 1.97 4081 .21 1.65 0580 .71 2219 .21 6161 .71 3599 .21 5469 .22 2497 .72 3969 .22 7770 .72 5088 ..22 6855 .23 4411 .73 5716 .23 9376 .73 6575 .23 8239 .24 6321 .74 7459 .24 1.83 0980 .74 8060 .24 9621 .25 8228 .75 9200 .25 2581 .75 9543 .25 1.98 1001 .26 1.66 0131 .76 1.75 0937 .26 4180 .76 1.91 1023 .26 2380 .27 2030 .77 2672 .27 5776 .77 2501 .27 3756 .28 3926 .78 4404 .28 7370 .78 3977 .28 5131 .29 5818 .79 6132 .29 8961 .79 5451 .29 6504 5.30 1.66 7707 5.80 1.75 7858 6.30 1.84 0550 6.80 1.91 6923 7.30 1.98 7874 .31 9592 .81 9581 .31 2136 .81 8392 .31 9243 .32 1.67 1473 .82 1.76 1300 .32 3719 .82 9859 .32 1.99 0610 .33 3351 .83 3017 .33 5300 .83 1.92 1325 .33 1976 .34 5226 .84 4731 .34 6879 .84 2788 .34 3339 .35 7097 .85 6442 .35 8455 .85 4249 .35 4700 .36 8964 .86 8150 .36 1.85 0028 .86 5707 .36 6060 .37 1.68 0828 .87 9855 .37 1599 .87 7164 .37 7418 .38 2688 .88 1.77 1557 .38 3168 .88 8619 .38 8774 .39 4545 .89 3256 .39 4734 .89 1.93 0071 .39 2.00 0128 5.40 1.68 6399 5.90 1.77 4952 6.40 1.85 6298 6.90 1.93 1521 7.40 2.00 1480 .41 8249 .91 6646 .41 7859 .91 2970 .41 2830 .42 1.69 0096 .92 8336 .42 9418 .92 4416 .42 4179 .43 1939 .93 1.78 0024 .43 1.86 0975 .93 5860 .43 5526 .44 3779 .94 1709 .44 2529 .94 7302 .44 6871 .45 5616 .95 3391 .45 4080 .95 8742 .45 8214 .46 7449 .96 5070 .46 5629 .96 1.94 0179 .46 9555 .47 9279 .97 6747 .47 7176 .97 1615 .47 2.01 0895 .48 1.70 1105 .98 8421 .48 8721 .98 3049 .48 2233 .49 2928 .99 1.79 0091 .49 1.87 0263 .99 4481 .49 3569 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 108 VIII. NATURAL LOGARITHMS. Num. Loo. Num. Log. Num. Log. Num. Loo. Num. Log. 7.50 2.01 4903 8.00 2.07 9442 8.50 2.14 0066 9.00 2.19 7225 9.50 2.25 1292 .51 6235 .01 2.08 0691 .51 1242 .01 8335 .51 2344 .52 7566 .02 1938 .52 2416 .02 9444 .52 3395 .53 8895 .03 3185 .53 3589 .03 2.20 0552 .53 4445 .54 2.02 0222 .04 4429 .54 4761 .04 1659 .54 5493 .55 1548 .05 5672 .55 5931 .05 2*765 .55 6541 .56 2871 .06 6914 .56 7100 .06 3869 .56 7588 .57 4193 .07 8153 .57 8268 .07 4972 .57 8633 .58 5513 .08 9392 .58 9434 .08 6074 .58 9678 .59 6832 .09 2.09 0629 .59 2.15 0599 .09 7175 .59 2.26 0721 7.60 2.02 8148 8.10 2.09 1864 8.60 2.15 1762 9.10 2.20 8274 9.60 2.26 1763 .61 9463 .11 3098 .61 2924 .11 9373 .61 2804 .62 2.03 0776 .12 4330 .62 4085 .12 2.21 0470 .62 3844 .63 2088 .13 5561 .63 5245 .13 1566 .63 4883 .64 3398 .14 6790 .64 6403 .14 2660 .64 5921 .65 4706 .15 8018 .65 7559 .15 3754 .65 6958 .66 6012 .16 9244 .66 8715 .16 4846 .66 7994 .67 7317 .17 2.10 0469 .67 9869 .17 5937 .67 9028 .68 8620 .18 1692 .68 2.16 1022 .18 7027 .68 2.27 0062 .69 9921 .19 2914 .69 2173 .19 8116 .69 1094 7.70 2.04 1220 8.20 2.10 4134 8.70 2.16 3323 9.20 2.21 9203 9.70 2.27 2126 .71 2518 .21 5353 .71 4472 .21 2.22 0290 .71 3156 .72 3814 .22 6570 .72 5619 .22 1375 .72 4186 .73 5109 .23 7786 .73 6765 .23 2459 .73 5214 .74 6402 .24 9000 .74 7910 .24 3542 .74 6241 .75 7693 .25 2.11 0213 .75 9054 .25 4624 .75 7267 .76 8982 .26 1425 .76 2.17 0196 .26 5704 .76 8292 .77 2.05 0270 .27 2635 .77 1337 .27 6783 .77 9316 .78 1556 .28 3843 .78 2476 .28 7862 .78 2.28 0339 .79 2841 .29 5050 .79 3615 .29 8939 .79 1361 7.80 2.05 4124 8.30 2.11 6256 8.80 2.17 4752 9.30 2.23 0014 9.80 2.28 2382 .81 5405 .31 7460 .81 5887 31 1089 .81 3402 .82 6685 .32 8662 .82 7022 .32 2163 .82 4421 .83 7963 .33 9863 .83 8155 .33 3235 .83 5439 .84 9239 .34 2.12 1063 .84 9287 .34 4306 .84 6456 .85 2.06 0514 .35 2262 .85 2.18 0417 .35 5376 .85 7471 .86 1787 .36 3458 .86 1547 .36 6445 .86 8486 .87 3058 .37 4654 .87 2675 .37 7513 .87 9500 .88 4328 .38 5848 .88 3802 .38 8580 .88 2.29 0513 .89 5596 .39 7041 .89 4927 .39 9645 .89 1524 7.90 2.06 6863 8.40 2.12 8232 8.90 2.18 6051 9.40 2.24 0710 9.90 2.29 2535 .91 8128 .41 9421 .91 7174 .41 1773 .91 :;:. i i .92 9391 .42 2.13 0610 .92 8296 .42 2835 .92 4553 .93 2.07 0653 .43 1797 .93 9416 .43 3896 .93 5560 .94 1913 .44 2982 .94 2.19 0536 .44 4956 .94 6567 .95 3172 .45 4166 .95 1654 .45 6015 .95 7.->73 .96 4429 .46 5349 .96 2770 .46 7072 .96 8577 .97 5684 .47 6531 .97 3886 .47 8129 .97 9581 .98 6938 .48 7710 .98 5000 .48 9184 .98 2.30 0583 .99 8191 .49 8889 .99 6113 .49 2.25 0289 .99 1585 Num. Log. Num. Loo. Num. Loo. Num. Loo. Num. Log. VIII. NATURAL LOGARITHMS. 109 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 00 50 3.91 2023 100 4.60 5170 150 5.01 0635 200 5.29 8317 1 0.00 0000 51 3.93 1826 01 4.61 5121 51 7280 01 5.30 3305 2 0.69 3147 52 3.95 1244 02 4.62 4973 52 5.02 3881 02 8268 3 1.09 8612 53 3.97 0292 03 4.63 4729 53 5.03 0438 03 5.31 3206 4 1.38 6294 54 3.98 8984 04 4.64 4391 54 6953 04 8120 5 1.60 9438 55 4.00 7333 05 4.65 3960 55 5.04 3425 05 5.32 3010 6 1.79 1759 56 4.02 5352 06 4.66 3439 56 9856 06 7876 7 1.94 5910 57 4.04 3051 07 4.67 2829 57 5.05 6246 07 5.33 2719 8 2.07 9442 58 4.06 0443 08 4.68 2131 58 5.06 2595 08 7538 9 2.19 7225 59 4.07 7537 09 4.69 1348 59 8904 09 5.34 2334 10 2.30 2585 60 4.09 4345 110 4.70 0480 160 5.07 5174 210 5.34 7108 11 2.39 7895 61 4.11 0874 11 9530 61 5.08 1404 11 5.35 1858 12 2.48 4907 62 4.12 7134 12 4.71 8499 62 7596 12 6586 13 2.56 4949 63 4.14 3135 13 4.72 7388 63 5.09 3750 13 5.36 1292 14 2.63 9057 64 4.15 8883 14 4.73 6198 64 9866 14 5976 15 2.70 8050 65 4.17 4387 15 4.74 4932 65 5.10 5945 15 5.37 0638 16 2.77 2589 66 4.18 9655 16 4.75 3590 66 5.11 1988 16 5278 17 2.83 3213 67 4.20 4693 17 4.76 2174 67 7994 17 9897 18 2.89 0372 68 4.21 9508 18 4.77 0685 68 5.12 3964 18 5.38 4495 19 2.94 4439 69 4.23 4107 19 9123 69 9899 19 9072 20 2.99 5732 70 4.24 8495 120 4.78 7492 170 5.13 5798 220 5.39 3628 21 3.04 4522 71 4.26 2680 21 4.79 5791 71 5.14 1664 21 8163 22 3.09 1042 72 4.27 6666 22 4.80 4021 72 7494 22 5.40 2677 23 3.13 5494 73 4.29 0459 23 4.81 2184 73 5.15 3292 23 7172 24 3.17 8054 74 4.30 4065 24 4.82 0282 74 9055 24 5.41 1646 25 3.21 8876 75 4.31 7488 25 8314 75 5.16 4786 25 6100 26 3.25 8097 76 4.33 0733 26 4.83 6282 76 5.17 0484 26 5.42 0535 27 3.29 5837 77 4.34 3805 27 4.84 4187 77 6150 27 4950 28 3.33 2205 78 4.35 6709 28 4.85 2030 78 5.18 1784 28 9346 29 3.36 7296 79 4.36 9448 29 9812 79 7386 29 5.43 3722 30 3.40 1197 80 4.38 2027 . 130 4.86 7534 180 5.19 2957 230 5,43 8079 31 3.43 3987 81 4.39 4449 31 4.87 5197 81 8497 31 5.44 2418 32 3.46 5736 82 4.40 6719 32 4.88 2802 82 5.20 4007 32 6737 33 3.49 6508 83 4.41 8841 33 4.89 0349 83 9486 33 5.45 1038 34 3.52 6361 84 4.43 0817 34 7840 84 5.21 4936 34 5321 35 3.55 5348 85 4.44 2651 35 4.90 5275 85 5.22 0356 35 9586 36 3.58 3519 86 4.45 4347 36 4.91 2655 86 5747 36 5.46 3832 37 3.61 0918 87 4.46 5908 37 9981 87 5.23 1109 37 8060 38 3.63 7586 88 4.47 7337 38 4.92 7254 88 6442 38 5.47 2271 39 3.66 3562 89 4.48 8636 39 4.93 4474 89 5.24 1747 39 6464 40 3.68 8879 90 4.49 9810 140 4.94 1642 190 5.24 7024 240 5.48 0639 41 3.71 3572 91 4.51 0860 41 8760 91 5.25 2273 41 4797 42 3.73 7670 92 4.52 1789 42 4.95 5827 92 7495 42 8938 43 3.76 1200 93 4.53 2599 43 4.96 2845 93 5.26 2690 43 5.49 3061 44 3.78 4190 94 4.54 3295 44 9813 94 7858 44 7168 45 3.80 6662 95 4.55 3877 45 4.97 6734 95 5.27 3000 45 5.50 1258 46 3.82 8641 96 4.56 4348 46 4.98 3607 96 8115 46 5332 47 3.85 0148 97 4.57 4711 47 4.99 0433 97 5.28 3204 47 9388 48 3.87 1201 98 4.58 4967 48 7212 98 8267 48 5.51 3429 49 3.89 1820 99 4.59 5120 49 5.00 3946 99 5.29 3305 49 7453 NUM. Loo. Num. Log. Num. Log. Num. Log. Num. Log. no VUL NATURAL LOGARITHMS. Num. Loo. Num. Log. Num. Loo. Num. Loo. Num. Loo. 250 5.52 1461 300 5.70 3782 350 5.85 7933 400 5.99 1465 450 6.10 9248 51 5453 01 7110 51 5.86 0786 01 3961 51 6.11 1467 52 9429 02 5.71 0427 52 3631 02 6452 52 3682 53 5i53 3389 03 3733 53 6468 03 8937 53 5892 54 7334 04 7028 54 9297 04 6.00 1415 54 8097 55 5.54 1264 05 5.72 0312 55 5.87 2118 05 3887 55 6.12 0297 56 5177 06 3585 56 4931 06 6353 56 2493 57 9076 07 6848 57 7736 07 8813 57 4683 58 5.55 2960 08 5.73 0100 58 5.88 0533 08 6.01 1267 58 6869 59 6828 09 3341 59 3322 09 3715 59 9050 260 5.56 0682 310 5.73 6572 360 5.88 6104 410 6.01 6157 460 6.13 1226 61 4520 11 9793 61 8878 11 8593 61 3398 62 8345 12 5.74 3003 62 5.89 1644 12 6.02 1023 62 5565 63 5.57 2154 13 6203 63 4403 13 3448 63 7727 64 5949 14 9393 64 7154 14 5866 64 9885 65 9730 15 5.75 2573 65 9897 15 8279 65 6.14 2037 66 5.58 3496 16 5742 66 5.90 2633 16 6.03 0685 66 4186 67 7249 17 8902 67 5362 17 3086 67 6329 68 5.59 0987 18 5.76 2051 68 8083 18 5481 68 B468 69 4711 19 5191 69 5.910797 19 7871 69 6.15 0603 270 5.59 8422 320 5.76 8321 370 5.91 3503 420 6.04 0255 470 6.15 2733 71 5.60 2119 21 5.77 1441 71 6202 21 2633 71 4858 72 5802 22 4552 72 8894 22 5005 72 6979 73 9472 23 7652 73 5.92 1578 23 7372 73 9095 74 5.61 3128 24 5.78 0744 74 4256 24 9733 74 6.16 1207 75 6771 25 3825 75 6926 25 6.05 2089 75 3315 76 5.62 04.01 26 6897 76 9589 26 4439 76 5418 77 4018 27 9960 77 5.93 2245 27 6784 77 7516 78 7621 28 5.79 3014 78 4894 28 9123 78 9611 79 5.63 1212 29 6058 79 7536 29 6.06 1457 79 6.17 1701 280 5.63*4790 330 5.79 9093 380 5.94 0171 430 6.06 3785 480 6.17 3786 81 8355 31 5.80 2118 81 2799 31 6108 81 5867 82 5.64 1907 32 5135 82 5421 32 8426 82 7944 83 5447 33 8142 83 8035 33 6.07 0738 83 6.18 0017 84 8974 34 5.81 1141 84 5.95 0643 34 3045 84 2085 85 5.65 2489 35 4131 85 3243 35 5346 85 4149 86 5992 36 7111 86 5837 36 7642 86 6209 87 9482 37 5.82 0083 87 8425 37 9933 87 8264 88 5.66 2960 38 3046 88 5.96 1005 38 6.08 2219 88 6.19 0315 89 6427 39 6000 89 3579 39 4499 89 2362 290 5.66 9881 340 5.82 8946 390 5.96 6147 440 6.08 6775 490 6.19 4405 91 5.67 3323 41 5.83 1882 91 8708 41 9045 91 6444 92 6754 42 4811 92 5.97 1262 42 6.09 1310 92 sit:' 93 5.68 0173 43 7730 •93 3810 43 3570 93 6.20 0509 94 3580 44 5.84 0642 94 6351 44 5825 94 8586 95 6975 45 3544 95 8886 45 8074 95 4558 96 5.69 0359 46 6439 96 5.98 1414 46 6.10 0319 96 6576 97 3732 47 9325 97 3936 47 2559 97 8590 98 7093 48 5.85 2202 98 6452 48 4793 98 6.21 0600' 99 5.70 0444 49 5072 99 8961 49 7023 99 2606 Num. Loo. Num. Loo. Num. Loo. Num. Loo. Num. Loo. _ VIII. NATURAL LOGARITHMS. Ill Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 500 6.214608 550 6.30 9918 600 6.39 6930 650 6.47 6972 700 6.55 1080 01 6606 51 6.31 1735 01 8595 51 8510 01 2508 02 8600 52 3548 02 6.40 0257 52 6.48 0045 02 3933 03 6.22 0590 53 5358 03 1917 53 1577 03 5357 04 2576 54 7165 04 3574 54 3107 04 6778 05 4558 55 8968 1 05 5228 55 4635 05 8198 • 06 6537 56 6.32 0768 06 6880 56 6161 06 9615 07 8511 57 2565 07 8529 57 7684 07 6.56 1031 08 6.23 0481 58 4359 08 6.41 0175 58 9205 08 2444 09 2448 59 6149 09 1818 59 6.49 0724 09 3856 510 6.23 4411 560 6.32 7937 610 6.41 3459 660 6.49 2240 710 6.56 5265 11 6370 61 9721 11 5097 61 3754 11 6672 12 8325 62 6.33 1502 12 6732 62 5266 12 8078 13 6.24 0276 63 3280 13 8365 63 6775 13 9481 14 2223 64 5054 14 9995 64 8282 14 6.57 0883 15 4167 65 6826 15 6.42 1622 65 9787 15 2283 16 6107 66 8594 16 3247 66 6.50 1290 16 3680 17 8043 67 6.34 0359 17 4869 67 2790 17 5076 18 9975 68 2121 18 6488 68 4288 18 6470 19 6.25 1904 69 3880 19 8105 69 5784 19 7861 520 6.25 3829 570 6.34 5636 620 6.42 9719 670 6.50 7278 720 6.57 9251 21 5750 71 7389 21 6.43 1331 71 8769 21 6.58 0639 22 7668 72 9139 22 2940 72 6.51 0258 22 2025 23 9581 73 6.35 0886 23 4547 73 1745 23 3409 24 6.26 1492 74 2629 24 6150 74 3230 24 4791 25 3398 75 4370 25 7752 75 4713 25 6172 26 5301 76 6108 26 9350 76 6193 26 7550 27 7201 77 7842 27 6.44 0947 77 7671 27 8926 28 9096 78 9574 28 2540 78 9147 28 6.59 0301 29 6.27 0988 79 6.36 1302 29 4131 79 6.52 0621 29 1674 530 6.27 2877 580 6.36 3028 630 6.44 5720 680 6.52 2093 730 6.59 3045 31 4762 81 4751 ' 31 7306 81 3562 31 4413 32 6643 82 6470 32 8889 82 5030 32 5781 33 8521 83 8187 33 6.45 0470 83 6495 33 7146 34 6.28 0396 84 9901 34 2049 84 7958 34 8509 35 2267 85 6.37 1612 35 3625 85 9419 35 9870 36 4134 86 3320 36 5199 - 86 6.53 0878 36 6.60 1230 37 5998 87 5025 37 6770 87 2334 37 2588 38 7859 88 6727 38 8338 88 3789 38 3944 39 9716 89 8426 39 9904 89 5241 39 5298 540 6.29 1569 590 6.38 0123 640 6.46 1468' 690 6.53 6692 740 6.60 6650 41 3419 91 1816 41 3029 91 8140 41 8001 42 5266 92 3507 42 4588 92 9586 42 9349 43 7109 93 5194 43 6145 93 6.54 1030 43 6.61 0696 44 8949 94 6879 44 7699 94 2472 44 2041 45 6.30 0786 95 8561 45 9250 95 3912 45 3384 46 2619 96 6.39 0241 46 6.47 0800 96 5350 46 4726 47 4449 97 1917 47 2346 97 6785 47 6065 48 6275 98 3591 48 3891 98 8219 48 7403 49 8098 99 , 5262 49 5433 99 9651 49 8739 Num. Loo. Num. Log. Num. Log. Num. Log. Num. Log. 112 YIII. NATURAL LOGARITHMS. Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 750 6.62 0073 800 6.68 4612 850 6.74 5236 900 6.80 2395 950 6.85 6462 51 1406 01 5861 51 6412 01 3505 51 7514 52 2736 02 7109 52 7587 02 4615 52 8565 53 4065 03 8355 53 8760 03 5723 53 9615 54 5392 04 9599 54 9931 04 6829 54 6.86 0664 55 6718 05 6.69 0842 55 6.75 1101 05 7935 55 1711 56 8041 06 2084 56 2270 06 9039 56 2758 57 9363 07 3324 57 3438 07 6.81 0142 57 3803 58 6.63 0683 08 4562 58 4604 08 1244 58 4848 59 2002 09 5799 59 5769 09 2345 59 5891 760 6.63 3318 810 6.69 7034 860 6.75 6932 910 6.81 3445 960 6.86 6933 61 4633 11 8268 61 8095 11 4543 61 7974 62 5947 12 9500 62 9255 12 5640 62 9014 63 7258 13 6.70 0731 63 6.76 0415 13 6736 63 6.87 0053 64 8568 14 1960 64 1573 14 7831 64 1091 65 9876 15 3188 65 2730 15 8924 65 2128 66 6.64 1182 16 4414 66 3885 16 6.82 0016 66 3164 67 2487 17 5639 67 5039 17 1107 67 4198 .68 3790 18 6862 68 6192 18 2197 68 5232 69 5091 19 8084 69 7343 19 3286 69 6265 770 6.64 6391 820 6.70 9304 870 6.76 8493 920 6.82 4374 970 6.87 7296 71 7688 21 6.71 0523 71 9642 21 5460 71 8326 72 8985 22 1740 72 6.77 0789 22 6545 72 9356 73 6.65,0279 23 2956 73 1936 23 7629 73 6.88 0384 74 1572 24 4171 74 3080 24 8712 74 1411 75 2863 25 5383 75 4224 25 9794 75 2437 76 4153 26 6595 76 5366 26 6.83 0874 76 3463 77 5440 27 7805 77 6507 27 1954 77 4487 78 6727 28 9013 78 7647 28 3032 78 5510 79 8011 29 6.72 0220 79 8785 29 4109 79 6532 780 6.65 9294 830 6.72 1426 880 6.77 9922 930 6.83 5185 980 6.88 7553 81 6.66 0575 31 2630 81 6.78 1058 31 6259 81 8572 82 1855 32 3832 82 2192 32 7333 82 9591 83 3133 33 5034 83 3325 33 8405 83 6.89 0609 84 4409 34 6233 84 4457 34 9476 84 1626 85 5684 35 7432 85 5588 35 6.84 0547 85 2642 86 6957 36 8629 86 6717 36 1615 86 3656 87 8228 37 9824 87 7845 37 2683 87 4670 88 9498 38 6.73 1018 88 8972 38 3750 88 5683 89 6.67 0766 39 2211 89 6.79 0097 39 4815 89 6694 790 6.67 2033 840 6.73 3402 890 6.79 1221 940 6.84 5880 990 6.89 7705 91 3298 41 4592 91 2344 41 6943 91 8715 92 4561 42 5780 92 3466 42 8005 92 9723 93 5823 43 6967 93 4587 43 9066 93 6.90 0731 94 7083 44 8152 94 5706 44 6.85 0126 94 1737 95 8342 45 9337 95 6824 45 1185 95 2743 96 9599 46 6.74 0519 96 7940 46 2243 96 3747 97 6.68 0855 47 1701 97 9056 47 3299 97 4751 98 2109 48 2881 98 6.80 0170 48 4355 98 5753 99 3361 49 4059 99 1283 49 5409 99 6755 Num. Log. Num. Log. Num. Loo. Num. Log. Num. Log. VIII. NATURAL LOGARITHMS. 113 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 1000 6.90 7755 1050 6.95 6545 1100 7.00 3065 1150 7.04 7517 1200 7.09 0077 01 8755 51 7497 01 3974 51 8386 01 0910 02 9753 52 8448 02 4882 52 9255 02 1742 03 6.91 0751 53 9399 03 5789 53 7.05 0123 03 2574 04 1747 54 6.96 0348 04 6695 54 0989 04 3405 05 2743 55 1296 05 7601 55 1856 05 4235 06 3737 56 2243 06 8505 56 2721 06 5064 07 4731 57 3190 07 9409 57 3586 07 5893 08 5723 58 4136 08 7.01 0312 58 4450 08 6721 09 6715 59 5080 09 1214 59 5313 09 7549 1010 6.91 7706 1060 6.96 6024 1110 7.01 2115 1160 7.05 6175 1210 7.09 8376 11 8695 61 6967 11 3016 61 7037 11 9202 12 9684 62 7909 12 3915 62 7898 12 7.10 0027 13 6.92 0672 63 8850 13 4814 63 8758 13 0852 14 1658 64 9791 14 5712 64 9618 14 1676 15 2644 65 6.97 0730 15 6610 65 7.06 0476 15 2499 16 3629 66 1669 16 7506 66 1334 16 3322 17 4612 67 2606 17 8402 67 2192 17 4144 18 5595 68 3543 18 9297 68 3048 18 4965 19 6577 69 4479 19 7.02 0191 69 3904 23 9062 1020 6.92 7558 1070 6.97 5414 1120 7.02 1084 1170 7.06 4759 1229 7.11 3956 21 8538 71 6348 21 1976 71 5613 31 5582 22 9517 72 7281 22 2868 72 6467 37 7.12 0444 23 6.93 0495 73 8214 23 3759 73 7320 49 7.13 0099 24 1472 74 9145 24 4649 74 8172 59 8073 25 2448 75 6.98 0076 25 5538 75 9023 77 7.15 2269 26 3423 76 1006 26 6427 76 9874 79 3834 27 4397 77 1935 27 7315 77 7.07 0724 83 6956 28 5370 78 2863 28 8201 78 1573 89 7.16 1622 29 6343 79 3790 29 9088 79 2422 91 3172 1030 6.93 7314 1080 6.98 4716 1130 7.02 9973 1180 7.07 3270 1297 7.16 7809 31 8284 81 5642 31 7.03 0857 81 4117 1301 7.17 0888 32 9254 82 6566 32 1741 82 4963 03 2425 33 6.94 0222 83 7490 33 2624 83 5809 07 5490 34 1190 84 8413 34 3506 84 6654 19 7.18 4629 35 2157 85 9335 35 4388 85 7498 21 6144 36 3122 86 6.99 0257 36 5269 86 8342 27 7.19 0676 37 4087 87 1177 37 6148 87 9184 61 7.21 5975 38 5051 88 2096 38 7028 88 7.08 0026 67 7.22 0374 39 6014 89 3015 39 7906 89 0868 73 4753 1040 6.94 6976 1090 6.99 3933 1140 7.03 8784 1190 7.08 1709 1381 7.23 0563 41 7937 91 4850 41 9660 91 2549 99 7.24 3513 42 8897 92 5766 42 7.04 0536 92 3388 1409 7.25 0636 43 9856 93 6681 43 1412 93 4226 23 7.26 0523 44 6.95 0815 94 7596 44 2286 94 5064 27 3330 45 1772 95 8510 45 3160 95 5901 29 4730 46 2729 96 9422 46 4033 96 6738 33 7525 47 3684 97 7.00 0334 47 4905 97 7574 39 7.27 1704 48 4639 98 1246 48 5777 98 8409 47 7248 49 5593 99 2156 49 6647 99 9243 51 7.28 0008 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 114 Yin. NATURAL LOGARITHMS. Num. Log. Num. Loo. Num. Log. Num. Loo. Num. Loo. 1453 7.28 1386 1823 7.50 8239 2221 7.70 5713 2621 7.87 1311 3001 8.00 6701 59 5507 31 7.51 2618 37 7.71 2891 33 5879 11 8.01 0028 71 7.29 3698 47 7.52 1318 39 3785 47 7.88 1182 19 2681 81 7.30 0473 61 8869 43 5570 57 4953 23 4005 83 1822 67 7.53 2088 51 9130 59 5705 37 ' 8625 87 4516 71 4228 67 7.72 6213 63 7209 41 9942 89 5860 73 5297 69 7094 71 7.89 0208 49 8.02 2569 93 8543 77 7430 73 8856 77 2452 61 6497 99 7.31 2553 79 8495 81 7.73 2369 83 4691 67 8455 1511 7.32 0527 89 7.54 3803 87 4996 87 6181 79 8.03 2360 1523 7.32 8437 1901 7.55 0135 2293 7.73 7616 2689 7.89 6925 3083 8.03 3658 31 7.33 3676 07 3287 97 9359 93 8411 89 5603 43 7.34 1484 13 6428 2309 7.74 4570 99 7.90 0637 3109 8.04 2056 49 5365 31 7.56 5793 11 5436 2707 3596 19 5268 53 7944 33 6828 33 7.75 4910 11 5073 21 5909 59 7.35 1800 49 7.57 5072 39 7479 13 5810 37 8.05 1022 67 6918 51 6097 41 8333 19 8019 63 9276 71 9468 73 7.58 7311 47 7.76 0893 29 7.91 1691 67 8.06 0540 79 7.36 4547 79 7.59 0347 51 2596 31 2423 69 1171 83 7077 87 4381 57 5145 41 6078 81 4951 1597 7.37 5882 1993 7.59 7396 2371 7.77 1067 2749 7.91 8992 3187 8.06 6835 1601 8384 97 9401 77 3594 53 7.92 0447 91 8090 07 7.38 2124 99 7.60 0402 81 5276 67 5519 3203 8.07 1843 09 3368 2003 2401 83 6115 77 9126 09 3715 13 5851 11 6387 89 8630 89 7.93 3438 17 6205 19 9564 17 9367 93 7.78 0.303 91 4155 21 7447 21 7.39 0799 27 7.61 4312 99 2807 97 6303 29 9928 27 4493 29 5298 2411 7797 2801 7732 51 8.08 6718 37 7.40 0621 39 7.62 0215 17 7.79 0282 03 8446 53 7333 57 7.41 2764 53 7057 23 2762 19 7.94 4137 57 8562 1663 7.41 6378 2063 7.63 1917 2437 7.79 8523 2833 7.94 9091 3259 8.08 9176 67 8781 69 4821 41 7.80 0163 37 7.95 0502 71 8.09 2851 69 9980 81 7.64 0604 47 2618 43 2615 99 8.10 1375 93 7.43 4257 83 1564 59 7510 51 5425 3301 1981 97 6617 87 3483 67 7.810758 57 7527 07 3797 99 7795 89 4441 73 3187 61 8926 13 5609 1709 7.44 3664 99 9216 77 4803 79 7.96 5198 19 7419 21 7.45 0661 2111 7.65 4917 2503 7.82 5245 87 7973 23 8623 23 1822 13 5864 21 7.83 2411 97 7.97 1431 29 8.11 0431 33 7609 29 7.66 3408 31 6370 2903 3500 31 1028 1741 7.46 2215 2131 7.66 4347 .2539 7.83 9526 2909 7.97 5565 3343 8.11 4624 47 5655 37 7158 43 7.84 1100 17 8311 47 5820 53 9084 41 9028 49 3456 27 .7.98 1733 59 9399 59 7.47 2501 43 9962 51 4241 39 5825 61 9994 77 7.48 2682 53 7.67 4617 57 6590 53 7.99 0577 71 8.12 2965 83 6053 61 8326 79 7.85 5157 57 1931 73 3558 87 8294 79 7.68 6621 91 9799 63 3958 89 8290 89 9412 2203 7.69 7575 93 7.86 0571 69 5980 91 8880 1801 7.49 6097 07 9389 2609 6722 71 6654 3407 8.13 3587 11 7.50 1634 13 7.70 2104 17 9784 99 8.00 6034 13 5347 Num. Loo. Num. Loo. Num. Loo. Num. Loo. Num. Loo. VIII. NATURAL LOGARITHMS. 115 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 3433 8.14 1190 3823 8.24 8791 4241 8.35 2554 4663 8.44 7414 5099 8.53 6800 49 5840 33 8.25 1403 43 3026 73 9557 5101 7192 57 8156 47 5049 53 5380 79 8.45 0840 07 8367 61 9313 51 6088 59 6790 91 3401 13 9542 63 9891 53 6607 61 7259 4703 5956 19 8.54 0714 67 8.15 1045 63 9199 71 9603 21 9776 47 6169 69 1622 77 8.26 2817 73 8.36 0071 23 8.46 0199 53 7334 91 7944 81 3848 83 2409 29 1469 67 8.55 0048 99 8.16 0232 89 5907 89 3809 33 2315 71 0821 3511 3656 3907 8.27 0525 97 5672 51 6110 79 2367 3517 8.16 5364 3911 8.27 1548 4327 8.37 2630 4759 8.46 7793 5189 8.55 4296 27 8203 17 3081 37 4938 83 8.47 2823 97 5837 29 8770 19 3592 39 5399 87 3659 5209 8143 33 9903 23 4612 49 7701 89 4077 27 8.56 1593 39 8.17 1599 29 6140 57 9539 93 4912 31 2358 41 2164 31 6649 63 8.38 0915 99 6163 33 2740 47 3857 43 9697 73 3205 4801 6580 37 3504 57 6673 47 8.28 0711 91 7312 13 9076 61 8076 59 7235 67 5765 97 8678 17 9907 73 8.57 0355 71 8.18 0601 89 8.29 1296 4409 8.39 1403 31 8.48 2809 79 1492 3581 8.18 3397 4001 8.29 4300 4421 8.39 4121 4861 8.48 8999 5281 8.57 1871 83 3956 03 4799 23 4573 71 8.49 1055 97 4896 93 6743 07 5798 41 8635 77 2286 5303 6028 3607 8.19 0632 13 7294 47 9985 89 4743 09 7159 13 2294 19 8788 51 8.40 0884 4903 7603 23 9792 17 3400 21 9286 57 2231 09 8826 33 8.58 1669 23 5058 27 8.30 0777 63 3576 19 8.50 0861 47 4291 31 7263 49 6225 81 7602 31 3297 51 5039 37 8914 51 6719 83 8048 33 3703 81 8.59 0630 43 8.20 0563 57 8199 93 8.41 0276 37 4513 87 1744 3659 8.20 4945 4073 8.31 2135 4507 8.41 3387 4943 8.50 5728 5393 8.59 2857 71 8219 79 3607 13 4717 51 7345 99 3969 73 8764 91 6545 17 5603 57 8556 5407 5450 77 9852 93 7033 19 6046 67 8.51 0571 13 6559 91 8.21 3653 99 8498 23 6931 69 0974 17 7297 97 5277 4111 8.32 1422 47 8.42 2223 73 1779 19 7667 3701 6358 27 5306 49 2663 87 4590 31 9879 09 8518 29 5791 61 5297 93 5792 37 8.60 0983 19 8.22 1210 33 6759 67 6612 99 6993 41 1718 27 3359 39 8209 83 8.43 0109 5003 7793 43 2086 3733 8.22 4967 4153 8.33 1586 4591 8.43 1853 5009 8.51 8992 5449 8.60 3187 39 6573 57 2549 97 3159 11 9391 71 7217 61 8.23 2440 59 3030 4603 4464 21 8.52 1384 77 8313 67 4034 77 7349 21 8366 23 1783 79 8678 69 4565 4201 8.34 3078 37 8.44 1823 39 4963 83 9408 79 7215 11 5455 39 2254 51 7342 5501 8.61 2685 93 8.24 0913 17 . 6879 43 3116 59 8924 03 3049 97 1967 19 7353 49 4407 77 8.53 2476 07 3775 3803 3546 29 9721 51 4838 81 3263 19 5952 21 8267 31 8.35 0194 57 6127 87 4444 21 6314 Num. Loo. Num. Log. Num. Log. Num. Log. Num. Log. 116 VIII. NATURAL LOGARITHMS. Num. Loo. Num. Log. Num. Loo. Num. Loo. Num. Log. 5527 8.61 7400 5953 8.69 1651 6373 8.75 9826 6841 8.83 0689 7307 8.89 6588 31 8124 81 6343 79 8.76 0767 57 3025 09 6862 57 8.62 2814 87 7346 89 2333 63 3900 21 8502 i 63 3893 6007 8.70 0681 97 3584 69 4774 31 9867 79 4971 11 1346 6421 7329 71 5065 33 8.90 0140 73 5689 29 4336 27 8263 83 6810 49 2320 81 7123 37 5662 49 8.77 1680 99 7681 51 2592 91 8913 43 6656 51 1990 6907 8.84 0291 69 5037 5623 8.63 4621 47 7318 69 4777 11 0870 93 8289 39 7462 53 8309 73 5395 17 1737 7411 8.910721 5641 8.63 7817 6067 8.71 0620 6481 8.77 6630 6947 8.84 6065 7417 8.91 1530 47 8880 73 1608 91 8172 49 6353 33 3685 51 9588 79 2595 6521 8.78 2783 59 7791 51 6104 53 9942 89 4239 29 4009 61 8078 57 6908 57 8.64 0649 91 4568 47 6762 67 8940 59 7177 59 1002 6101 6208 51 7373 71 9514 77 9587 69 2768 13 8173 53 7678 77 8.85 0374 81 8.92 0122 83 5235 21 9481 63 9203 83 1234 87 0923 89 6290 31 8.72 1113 69 8.79 0117 91 2379 89 1191 93 6993 33 1439 71 0421 97 3237 99 2525 5701 8.64 8397 6143 8.72 3069 6577 8.79 1334 7001 8.85 3808 7507 8.92 3591 11 8.65 0149 51 4370 81 1942 13 5521 17 4922 17 1199 63 6319 99 4673 19 6376 23 5720 37 4692 73 7940 6607 5885 27 7515 29 6518 41 5389 97 8.73 1821 19 7700 39 9221 37 7580 43 5737 99 2143 37 8.80 0415 43 9789 41 8110 49 6781 6203 2788 53 2823 57 8.86 1775 47 8905 79 8.66 1986 11 4077 59 3725 69 3474 49 9170 83 2678 17 5043 61 4025 79 4888 59 8.93 0494 91 4060 21 5686 73 5825 7103 8273 61 0759 5801 8.66 5786 6229 8.73 6971 6679 8.80 6724 7109 8.86 9117 7573 8.93 2345 07 6819 47 9857 89 8220 21 8.87 0803 77 2873 13 7852 57 8.74 1456 91 8519 27 1646 83 3664 21 9227 63 2415 6701 8.81 0012 29 1926 89 4455 27 8.67 0258 69 . 3372 03 0310 51 5007 91 4719 39 2315 71 3691 09 1205 59 6126 7603 6298 43 3000 77 4647 19 2695 77 8637 07 6824 49 4026 87 6239 33 4776 87 8.88 0029 21 8663 51 4368 99 8146 37 5370 93 0864 39 8.94 1023 57 5393 6301 8464 61 8926 7207 2808 43 1545 5861 8.67 6076 6311 8.75 0049 6763 8.81 9222 7211 8.88 3363 7649 8.94 2330 67 7099 17 1000 79 8.82 1585 13 3640 69 4942 69 7440 23 1949 81 1880 19 4472 73 5463 79 9142 29 2898 91 3353 29 5856 81 6505 81 9482 37 4161 93 3648 37 6962 87 7286 97 8.68 2199 43 5107 6803 5119 43 7791 91 7806 5903 3216 53 6682 23 8055 47 8343 99 8846 23 6598 59 7626 27 8641 53 9170 7703 9365 27 7273 61 7941 29 89,34 83 8.89 3298 17 8.95 1181 39 9296 67 8884 33 9519 97 5219 13 1958 Num. Loo. Num. Loo. . Num. Loo. Num. Loo. Num. Loo. ! VIII. NATURAL LOGARITHMS. 117 Num. Loo. Num. Log. Num. Log. Num. Log. Num. Log. 7727 8.95 2476 8221 9.01 4447 8681 9.06 8892 9127 9.11 8992 9539 9.16 3144 41 4286 31 5663 89 9813 33 9650 47 3982 53 5835 33 5906 93 9.07 0273 37 9.12 0087 51 4401 57 6351 37 6391 99 0963 51 1618 87 8163 59 6609 43 7120 8707 1883 57 2274 9601 9623 89 8.96 0468 63 9543 13 2571 61 2711 13 9.17 0872 93 0981 69 9.02 0269 19 3260 73 4020 19 1496 7817 4056 73 0752 31 4635 81 4891 23 1911 23 4823 87 2443 37 5322 87 5545 29 2535 29 5590 91 2926 41 5780 99 6850 31 2742 7841 8.96 7122 8293 9.02 3167 8747 9.07 6466 9203 9.12 7285 9643 9.17 3988 53 7651 97 3649 53 7152 09 7937 49 4610 67 8.97 0432 8311 5335 61 8065 21 9239 61 5852 73 1194 17 6057 79 9.08 0118 27 9889 77 7507 77 1702 29 7499 83 0573 39 9.13 1189 79 7714 79 1956 53 9.03 0376 8803 2848 41 1405 89 8747 83 2464 63 1572 07 3302 57 3135 97 9572 7901 4745 69 2290 19 4664 77 5293 9719 9.18 1838 07 5504 77 3245 21 4891 81 5725 21 2044 19 7020 87 4438 31 6024 83 5940 33 3277 7927 8.97 8030 8389 9.03 4677 8837 9.08 6703 9293 9.13 7017 9739 9.18 3894 33 8787 8419 8246 39 6929 9311 8952 43 4304 37 9291 23 8721 49 8060 19 9811 49 4920 49 8.98 0801 29 9433 61 9415 23 9.14 0240 67 6765 51 1053 31 9671 63 9641 37 1740 69 6969 63 2561 43 9.04 1093 67 9.09 0092 41 2169 81 8197 93 6321 47 1567 87 2345 43 2383 87 8810 8009 8321 61 3223 93 3020 49 3025 91 9219 11 8571 67 3932 8923 6387 71 5375 9803 9.19 0444 17 9320 8501 7939 29 7060 77 6015 11 1259 8039 8.99 2060 8513 9.04 9350 8933 9.09 7508 9391 9.14 7507 9817 9.19 1871 53 3800 21 9.05 0289 • 41 8403 97 8146 29 3092 59 4545 27 0993 51 9521 9403 8784 33 3499 69 5785 37 2165 63 9.10 0860 13 9847 39 4109 81 7271 39 2399 69 1529 19 9.15 0484 51 5328 87 8013 43 2868 71 1752 21 0697 57 5937 89 8260 63 5206 99 4869 31 1757 59 6140 93 8755 73 6373 9001 5091 33 1969 71 7356 8101 9743 81 7306 07 5757 37 2393 83 8571 11 9.00 0976 97 9169 11 6201 39 2605 87 8976 8117 9.00 1716 8599 9.05 9401 9013 9.10 6423 9461 9.15 4933 9901 9.20 0391 23 2455 8609 9.06 0563 29 8197 63 5145 07 0997 47 5405 23 2188 41 9525 67 5567 23 2611 61 7122 27 2652 43 9746 73 6201 29 3215 67 7857 29 2884 49 9.11 0410 79 6834 31 3416 71 8347 41 4274 59 1514 91 8099 41 4423 79 9325 47 4968 67 2397 97 8731 49 5227 91 9.010791 63 6816 91 5040 9511 9.16 0204 67 7035 8209 2986 69 7509 9103 6359 21 1255 73 7637 19 4204 77 8431 09 7018 33 2515 10000 9.21 0340 Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 118 IX. PRIME AND COMPOSITE NUMBERS. Num. 13 7 9 Num. 13 7 9 000 000 0000 4771212647 845 098 0400 3 2 50 3-167 701567 9851 3-13 2 706 717 7828 1 041392 6862 113 948 8523 230 448 9214 278 753 6010 51 7-73 3 3 -19 11-47 3-173 2 3-7 861727 8860 3 3 462 897 9979 52 716 887 7288 7185016889 17-31 23 s 3 4913616988 3-11 6682017241 3-13 53 3 2 -59 13-41 3-179 7 2 -ll 4 612 783 8567 683 468 4556 672 097 8579 7 2 54 7331972651 3-181 7379873263 3 2 -61 5 3-17 7242758696 3-19 7708520116 55 19-29 7-79 745 8551952 13-43 6 785 829 8850 3 2 -7 826 074 8027 3-23 56 3-11-17 7505088949 3 4 -7 7551122664 7" 851258 8487 863 822 8601 7-11 897 627 0918 57 756 6861082 3-191 7611758182 3-193 8 3 4 919 078 0924 3-29 949 390 0066 58 7-83 11-53 768 6881012 19-31 9 7-13 3-31 986 7717848 3 2 -ll 59 3-197 778 054 6984 3-199 777 426 8224 10 004 8218738 012 837 2247 029 888 7777 087 426 4979 60 778 874 4720 3 2 -67 783188 6911 3-7-29 11 3-37 0530784485 3 2 -13 7-17 61 13-47 787 460 4745 790 2851640 791690 6490 12 ll 2 3-41 103 808 7210 3-43 62 3 3 -23 7-89 3-11-19 17-37 13 117 2712957 7-19 186 720 5672 143 014 8003 63 8000293592 3-211 7 2 -13 3 2 -71 14 3-47 11-13 3-7 2 1781862684 64 806 858 0295 808 210 9729 810 904 2807 11-59 15 178 976 9473 3 2 - 17 195 899 6524 3-53 65 3-7-31 814 9181818 3 2 -73 818 885 4146 16 7-23 212187 6044 222 716 4711 13 2 66 820 2014695 3-13-17 23-29 3-223 17 3 2 -19 238 0461081 3-59 252 853 0310 67 11-61 828 015 0642 880 588 6687 7-97 18 2576785749 3-61 11-17 3 3 -7 68 3-227 884 420 7087 3-229 13-53 19 281088 8672 285 557 8090 294 466 2262 298 858 0764 69 8394780474 3 2 -7-ll 17-41 3-233 20 3-67 7-29 3 2 -23 11-19 70 8457180180 19-37 7-101 8506462852 21 824 282 4558 3-71 7-31 3-73 71 3 2 -79 23-31 3-239 8567288904 22 13-17 848 304 8630 856 025 8572 359 835 4823 72 7-103 3-241 8616844109 3 6 23 3-7-11 8678559210 3-79 8788979009 73 17-43 8651089746 11-67 8686444884 24 382 017 0426 3 5 13-19 3-83 74 3-13-19 8709888188 3 s -83 7-107 25 399 678 7215 11-23 409 933 1288 7-37 75 8756899870 3-251 8790958795 3-11-23 26 3 2 -29 419 955 7485 3-89 429 752 2800 76 881884 6568 7-109 13-59 885 926 8898 27 482 969 2909 3-7-13 442 479 7691 3 2 -31 77 3-257 8881794989 3-7-37 19-41 28 448 7068199 4517864855 7-41 17 2 78 11-71 3 3 -29 8959747324 3-263 29 3-97 4668676204 3 3 -ll 13-23 79 7-113 13-61 9014588214 17-47 30 7-43 3-101 4871888755 3-103 80 3 2 -89 11-73 3-269 9079485216 31 492 760 8890 495 544 8875 501059 2622 11-29 81 9090208642 3-271 19-43 3 2 -7-13 32 3-107 17-19 3-109 7-47 82 914 8481571 915899 8352 917 505 5096 918 554 5306 33 519 827 9988 3 2 -37 527 629 9009 3-113 83 3-277 7 2 -17 3 3 -31 928 7619608 34 11.31 7 3 5408294748 6428254270 84 29 2 3-281 7-11 2 3-283 35 3 8 -13 547774 7064 3-7-17 555 094 4486 85 23-37 930 949 0812 932 980 8219 988 998 1638 36 19 2 3-11 2 5646660648 3 2 -41 86 3-7-41 9860107957 3-17 2 11-79 37 7-53 571 70S 8818 13-29 578 689 2100 87 13-67 3 2 -97 942 999 5984 3-293 38 3-127 588198 7740 3 2 -43 689 949 6018 88 944 975 9084 945 960 7086 947 928 6198 7-127 39 17-23 3-131 698 790 5068 3-7-19 89 3 4 -ll 19-47 3-13-23 29-31 40 6081448726 13-31 11-37 611728 3080 90 17-53 3-7-43 957 6072871 3 S -101 41 3-137 7-59 3-139 622 214 0280 91 959 5188770 11-83 7-131 9688155114 42 6242820958 3 2 -47 7-61 3-11-13 92 3-307 13-71 3 2 -103 9680157140 43 684 477 2702 686 487 8964 19-23 642 464 5202 93 7 2 -19 3-311 971789 5909 3-313 44 3 2 -7 8 646408 7262 3-149 662 246 8410 94 978 589 6284 23-41 976 849 9790 13-73 45 11-41 3-151 669 9162001 3 s - 17 95 3-317 979 092 9006 3-11-29 7-137 46 668 7009264 665 580 9910 669 816 8806 7-67 96 31 9 3 s - 107 9854264741 3- 17-19 47 3-157 11-43 3 2 -53 6808855184 97 987 219 2299 7-139 989 8946687 11-89 48 13-37 3-7-23 687 628 9612 3-163 98 3 2 -109 9926536178 3-7-47 23-43 49 6910814921 17-29 7-71 698100 6466 99 996 073 6546 3-331 9986951588 3 s - 37 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 119 Num. 1 3 7 9 Num. 1 3 7 9 100 7- 11-13 17-59 19-53 003 891 1662 150 19-79 3 2 -167 11-137 3-503 01 3-337 005 609 4454 3 2 -113 008 174 1840 51 179 264 4643 17-89 37-41 7 2 -31 02 009 025 7421 3-11-31 13-79 3-7 3 52 3 2 -13 2 182 699 9083 3-509 11-139 03 013 258 6658 014 100 3215 17-61 016 615 5476 53 184 975 1907 3-7-73 29-53 3 4 -19 04 3-347 7-149 3-349 020 775 4882 54 23-67 188 365 9261 7-13-17 190 051 4178 05 021 602 7160 3 4 -13 7-151 3-353 55 3-11-47 191 171 4557 3 2 -l73 192 846 1152 06 025 715 3889 026 538 2645 11-97 028 977 7052 56 7-223 3-521 195 068 9965 3-523 07 3 2 -7-l7 29-37 3-359 13-83 57 196 176 1850 11 2 -13 19-83 198 382 1300 08 23-47 3-19 2 036 229 5441 3 2 -ll 2 58 3-17-31 199 480 9149 3-23 2 7-227 09 037 824 7506 038 620 1619 040 206 6276 7-157 59 37-43 3 3 -59 203 304 9161 3-13-41 110 3-367 042 575 5124 3 3 -41 044 931 5461 160 204 391 3319 7-229 206 015 8768 206 556 0441 11 11-101 3-7-53 048 053 1731 3-373 61 3 2 -179 207 6348674 3-7 2 -ll 209 246 8488 12 19-59 050 379 7563 7 2 -23 052 693 9419 62 209 783 0148 3-541 211 387 5529 3 2 -181 13 3-13-29 11-103 3-379 17-67 63 7-233 23-71 214 048 6794 11-149 14 7-163 3 2 -127 31-37 3-383 64 3-547 31-53 3 3 -61 17-97 15 061 075 3236 061 829 3073 13-89 19-61 65 13-127 3-19-29 219 322 5084 3-7-79 16 3 3 -43 065 579 7147 3-389 7-167 66 11-151 220 892 2492 221 935 5998 222 456 3367 17 068 556 8951 3-17-23 11-107 3 2 -131 67 3-557 7-239 3-13-43 23-73 18 072 249 8976 7-13 2 074 450 7190 29-41 68 41 2 3 2 -ll-17 7-241 3-563 19 3-397 076 640 4437 3 2 -7-19 11-109 69 19-89 228 656 9581 229 681 8423 230 193 3789 120 079 548 0074 3-401 17-71 3-13-31 170 3 6 -7 13-131 3-569 232 742 0627 21 7-173 083 860 8009 085 290 5782 23-53 71 29-59 3-571 17-101 3 2 -191 22 3-11-37 087 426 4570 3-409 089 551 8829 72 235 780 8703 236 285 2774 11-157 7-13-19 23 090 258 0529 3 2 -137 092 369 6996 3-7-59 73 3-577 238 798 5627 3 2 -193 37-47 24 17-73 11-113 29-43 096 562 4384 74 240 798 7711 3-7-83 242 292 9050 3-11-53 25 3 2 -139 7-179 3-419 100 025 7301 75 17-103 243 781 9161 7-251 245265 8395 26 13-97 3-421 7-181 3 3 -47 76 3-587 41-43 3-19-31 29-61 27 31-41 19-67 106 190 8973 106 870 5445 77 7-11-23 3 2 -197 249 687 4278 3-593 28 3-7-61 108 226 6564 3 2 -ll-13 110 252 9174 78 13-137 251 151 3482 252124 5525 252 610 3406 29 110 926 2423 3-431 112 939 9761 3-433 79 3 2 -199 11-163 3-599 7-257 130 114 277 2966 114944 4157 116 275 5876 7-11-17 180 255 513 7128 3-601 13-139 3 3 -67 31 3-19-23 13-101 3-439 120 244 7955 81 257 918 4503 7 2 -37 23-79 17-107 32 120 902 8176 3 3 -7 2 122 870 9229 3-443 82 3-607 260 786 6687 3 2 -7-29 31-59 33 ll 3 31-43 7-191 13-103 83 262 688 3448 3-13-47 11-167 3-613 34 3 2 - 149 17-79 3-449 19-71 84 7-263 19-97 266 466 8954 43 2 35 7-193 3-11-41 23-59 3 2 -151 85 3-617 17-109 3-619 11.13* 36 133 858 1252 29-47 135 768 5146 37 2 86 269 746 3781 3 4 -23 271144 8179 3-7-89 37 3-457 137 670 5372 3 4 -l7 7-197 87 272 073 7875 272 537 7774 273 464 2726 273 926 7801 38 140 193 6786 3-461 19-73 3-463 88 3 2 -ll-19 7-269 3-17-37 276 231 9579 39 13-107 7-199 11-127 145 817 7145 89 31-61 3-631 7-271 3 2 -211 140 3-467 23-61 3-7-67 148 910 9931 190 278 9.82 1169 11-173 280 350 6930 23-83 41 17-83 3 2 -157 13-109 3-11-43 91 3-7 2 -13 281 714 9700 3 3 -7l 19-101 42 7 2 -29 153 204 9001 154 423 9731 155 032 2288 92 17-113 3-641 41-47 3-643 43 3 3 -53 156 246 1904 3-479 158 060 7939 93 285 782 2788 286 231 8540 13-149 7-277 44 11-131 3-13-37 160 468 5311 3 2 -7-23 94 3-647 29-67 3-11-59 289 811 8391 45 161 667 4124 162 265 6143 31-47 164 055 2919 95 290 257 2694 3 2 -7-31 19-103 3-653 46 3-487 7-11-19 3 2 -163 13-113 96 37-53 13-151 7-281 11-179 47 167 612 6727 3-491 7-211 3-17-29 97 3 3 -73 295 127 0853 3-659 296 445 7942 48 170 555 0585 •171 141 1510 172 810 9685 172 894 6978 98 7-283 3-661 298 197 8671 3 2 -13-l7 49 3-7-71 174 059 8077 3-499 175 801 6328 99 11-181 299 507 2987 800878 0649 800 812 7941 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. _^ 120 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 200 3-23-29 801 680 9493 3 2 -223 7 2 -41 250 41-61 898 460 8496 23-109 13-193 01 303 412 0706 3-11-61 804 705 8982 3-673 51 3 4 -31 7-359 3-839 11-229 02 43-47 7-17 2 306 853 7487 807 282 0470 52 401 572 8457 3-29 2 7-19 2 3 2 -281 03 3-677 19-107 3-7-97 809 417 2258 53 408 292 1452 17-149 43-59 404 662 7009 04 13-157 3 2 -227 23-89 3-683 54 3- 7- II 2 405 346 3602 3 2 -283 406 369 8855 05 7-293 312 888 9494 11 2 -17 29-71 55 406 710 4586 3-23-37 407 730 7280 3-853 06 3 2 -229 814 499 2280 3-13-53 315 760 4907 56 13-197 11-233 17-151 7-367 07 19-109 3-691 31-67 3 3 -7-ll 57 3-857 31-83 3-859 411 451 3421 08 318 272 0802 318 689 2699 319 522 4491 819 938 4400 58 29-89 3 2 -7-41 13-199 3-863 09 3-17-41 7-13-23 3 2 -233 822 012 4386 59 418 467 4180 418 802 5168 7 2 -53 23-113 210 11-191 3-701 7 2 -43 3-19-37 260 3 2 -17 2 19-137 3-11-79 416 474 0791 11 324 488 2333 824 899 4971 29-73 13-163 61' 7-373 3-13-67 417 803 7226 3 3 -97 12 3-7-101 11-193 3-709 828 175 6614 62 418 467 0209 43-61 37-71 11-239 13 828 583 4497 3 3 -79 829 804 5222 3-23-31 63 3-877 420 450 8591 3 2 -293 7-13-29 14 330 616 6673 831 022 1710 19-113 7-307 64 19-139 3-881 422 758 9413 3-883 15 3 2 -239 333 044 0298 3-719 17-127 65 11-241 7-379 424 391 5544 424 718 8873 16 334 654 7669 3-7-103 11-197 3 2 -241 66 3-887 425 871 1664 3-7-127 17-157 17 13-167 41-53 7-311 838 257 2302 67 426 673 8880 3 6 -ll 427 648 8712 3-19-47 18 3-727 37-59 3' 11-199 68 7-383 428 620 6727 429 267 6664 429 590 8022 19 7-313 3-17-43 13 3 3-733 69 3 2 -13-23 430 236 3534 3-29-31 431 202 8846 220 31-71 348 014 4972 343 802 3332 47 2 270 37-73 3-17-53 482 488 2558 3 2 -7-43 21 3-11-67 344 981 4139 3-739 7-317 71 483 129 5176 483 449 7938 11-13-19 434 409 2076 22 346 548 5585 3 2 -13-19 17-131 3-743 72 3-907 7-389 3 3 -101 436 003 5357 23 23-97 7-11-29 849 665 9841 350 054 0986 73 486 321 7001 3-911 7-17-23 3-11-83 24 3 3 -83 850 829 2736 3-7-107 13-173 74 487 909 0355 13-211 41-67 439 174 7398 25 352 375 4950 3-751 37-61 3 2 -251 75 3- 7-331 439 806 2114 3-919 31-89 26 7-17-19 31-73 355 451 5201 355 834 4959 76 11-251 3 2 -307 442 009 1591 3-13-71 27 3-757 356 599 4857 3 2 -ll-23 43-53 77 17-163 47-59 448 575 8798 7-397 28 858 125 2853 3-761 859 266 1646 3-7-109 78 3 3 -103 ll 2 -23 3-929 445 448 5148 29 29-79 360 404 0547 861 160 9952 11 2 -19 79 445 759 8365 3-7 2 -19 446 692 4664 3 2 -311 230 3-13-59 72.47 3-769 363 423 9329 280 447 818 1088 447 623 0978 7-401 53 2 31 368 799 9455 3 2 -257 7-331 3-773 81 3-937 29-97 3 2 -313 450 095 0759 32 11-211 23-101 13-179 17-137 82 7-13.31 3-941 11-257 3.23-41 33 3*- 7-37 867 914 7888 3-19-41 369 030 2218 83 19-149 452 246 5745 452 859 8358 17-167 34 869 401 4187 3-11-71 870 513 0896 3 4 -29 84 3-947 458 776 8597 3-13-73 7-11-37 35 371 252 6291 13-181 372 359 5825 7-337 85 454 997 2178 3 8 -317 455 910 2404 3-953 36 3-787 17-139 3 2 -263 23-103 86 456 517 8578 7-409 47-61 19-151 37 874 931 5540 3-7-113 876 029 1817 3-13-61 87 3 2 -ll-29 13 2 -17 3- 7- 137 459 241 6649 38 876 759 8954 877 124 0423 7-11-31 878 216 1497 88 43-67 3-31 2 460 446 7S39 3 3 -107 39 3-797 878 942 6986 3-17-47 880 030 2480 89 7 2 -59 11-263 461 948 4952 i:<-223 240 7 4 3 3 -89 29-83 3-11-73 290 3-967 462 847 0858 3 2 -17-19 $68 743 7212 41 382 197 2104 19-127 888 276 6504 41-59 91 41-71 3-971 464936 4291 3-7-139 42 3 2 -269 884 858 4141 3-809 7-347 92 23-127 37-79 466 4'."-' T9M 29-101 43 11-13-17 3-811 886 855 5292 3 2 -271 93 3-977 7-419 3-11-89 468 199 5S61 44 887 567 7794 7-349 888 688 9694 31-79 94 17-173 3 S -109 7-421 3-983 45 3-19-43 11-223 3 3 -7-13 890 758 5287 95 13-227 470 268 4470 470 851 8245 11-269 46 23-107 3-821 892 169 1495 3-823 96 3 2 -7-47 471 781 6515 3-23-43 472 610 1976 47 7-353 898 224 1164 898 926 0066 37-67 97 472 902 6518 3-991 13-229 3 s - 331 48 3-827 13-191 3-829 19-131 98 11-271 19-157 29-103 7 2 -61 49 47-53 3 2 -277 11-227 3-7 2 -17 99 3-997 41-73 3 4 -37 476 976 4658 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. • IX. PRIME AND COMPOSITE NUMBERS. 121 Num. 1 3 7 9 Num. 1 3 7 9 300 477 265 9954 3-7-11-13 31-97 3-17-59 350 3 2 -389 31-113 3-7-167 ll 2 - 29 01 478 710 7555 23-131 7-431 479 863 1130 51 545 430 8295 3-1171 546 172 3683 3 2 -17.23 02 3-19-53 480 438 1472 3-1009 13-233 52 7-503 13-271 547 405 4597 547 651 6584 03 7-433 3 2 -337 482 444 7919 3-1013 53 3-11-107 548 143 6374 3 3 -131 548 880 5626 04 483 016 4201 17-179 11-277 484 157 4244 54 549 125 9268 3-1181 549 861 1885 3-7-13 2 05 3 3 -113 43-71 3-1019 7-19-23 55 53-67 11-17-19 551 083 8652 551 327 9880 06 485 8633296 3-1021 486 713 7760 3 2 -ll-31 56 3-1187 7-509 3-29-41 43-83 07 37-83 7-439 17-181 488 409 6889 57 552 789 8502 3 2 -397 7 2 -73 3-1193 08 3-13-79 488 973 5247 32.7s 489 817 9083 58 554 004 3210 554 246 8082 17-211 37-97 09 11-281 3-1031 19-163 3-1033 59 3 3 -7-19 555 457 2172 3-11-109 59-61 310 7-443 29-107 13-239 492 620 7220 360 13-277 3-1201 557 146 1423 3 2 -401 11 3-17-61 11-283 3-1039 494 015 8748 61 23-157 557 867 9616 558 348 5088 7-11-47 12 494 293 7687 3 2 -347 53-59 3-7-149 62 3-17-71 559 068 3340 3 2 -13-31 19-191 13 31-101 13-241 496 514 5187 43-73 63 560 026 2489 3-7-173 560 743 3011 3-1213 14 3 2 -349 7-449 3-1049 47-67 64 11-331 561 459 1712 7-521 41-89 15 23-137 3-1051 7-11-41 3 5 -13 65 3-1217 13-281 3-23-53 563 362 4095 16 29-109 500 099 1919 500 648 0634 500 922 2392 66 7-523 3 2 -ll-37 19-193 3-1223 17 3-7-151 19-167 3 2 -353 11-17 2 67 564 784 3845 565 020 9283 565 493 6299 13-283 18 502 563 6691 3-1061 503 382 0635 3-1063 68 3 2 -409 29-127 3-1229 7-17-31 19 503 926 8042 31-103 23-139 7-457 69 567 144 0452 3-1231 567 849 4506 3 3 -137 320 3-11-97 505 556 9387 3-1069 506 369 7171 370 568 319 0851 7-23 2 11-337 569 256 8333 21 13' 2 -19 3 3 -7-l7 507 451 0609 3-29-37 71 3-1237 47-79 3 2 -7-59 570 426 1784 22 507 990 7248 11-293 7-461 509 068 0450 72 61 2 3-17-73 571 359 3928 3-11-113 23 3 2 -359 53-61 3-13-83 41-79 73 7-13-41 572 057 9899 37-101 572 755 4652 24 7-463 3-23-47 17-191 3 2 -19 2 74 3-29-43 19-197 3-1249 23-163 25 512 016 9695 512 284 0633 512 817 7586 513 084 3605 75 11 2 -31 3 3 -139 13-17 2 3-7-179 26 3-1087 13-251 3 3 -ll 2 7-467 76 575 803 3334 53-71 575 995 6202 576 226 1374 27 514 680 5441 3-1091 . 29-113 3-1093 77 3 2 -419 7 3 -ll 3-1259 577 376 8919 28 17-193 7 2 -67 19-173 11-13-23 78 19-199 3-13-97 7-541 3 2 -421 29 3-1097 37-89 3-7-157 518 382 3155 79 17-223 578 982 8427 579 440 5971 29-131 330 518 645 5243 3 2 -367 519 434 1949 3-1103 380 3-7-181 5801263254 3 4 -47 13-293 31 7-11-43 520 221 4359 31-107 521 007 2524 81 37-103 3-31-41 11-347 3-19-67 32 3 4 -41 521 530 3413 3-1109 522 313 7952 82 582 177 0377 582 404 2980 43-89 7-547 33 522 574 6327 3-11-101 47-71 3 2 -7-53 83 3-1277 583 538 8193 3-1279 11-349 34 13-257 524 136 3766 524 655 7124 17-197 84 23-167 3 2 -7-61 585 122 1863 3-1283 35 3-1117 7-479 3 2 -373 526210 0038 85 585573 5186 585 799 0090 7-19-29 17-227 36 526 468 5125 3-19-59 7-13-37 3-1123 86 3 3 -ll-13 586 924 7081 3-1289 53-73 37 527 758 7525 528 0163412 11-307 31-109 87 7 2 -79 3-1291 588 495 8010 3 2 -431 38 3-7 2 -23 17-199 3-1129 530 071 5688 88 588 943 6427 11-353 13 2 -23 589 a37 9431 39 530 327 7898 3 2 -13-29 43-79 3-11.103 89 3-1297 17-229 3 2 -433 7-557 "340 19-179 41-83 532 372 1336 7-487 390 47-83 3-1301 591 843 4112 3-1303 41 3 2 -379 533 136 2883 3-17-67 13-263 91 592 287 8160 7-13-43 592 953 5715 593 175 2635 42 11-311 3-7-163 23-149 3 3 -127 92 3-1307 593 618 3081 3-7 -11 -17 594 282 0288 43 47-73 535 673 8034 7-491 19-181 93 594503 0438 3 2 -19-23 31-127 3-13-101 44 3-31-37 11-313 3 2 -383 537 693 1944 94 7-563 595 826 7771 596 267 1264 11.359 45 7-17-29 3-1151 538 699 3795 3-1153 95 3 2 -439 59-67 3-1319 37-107 46 539 201 5993 539 452 4915 539 953 8417 540 204 2998 96 17-233 3-1321 598 462 2005 34.72 47 3-13-89 23-151 3-19-61 72.71 97 11-19 2 29-137 41-97 23-173 48 59 2 3 4 -43 11-317 3-1163 98 3-1327 7-569 3 2 -443 600 864 0363 49 542 949 8488 7-499 13-269 543 943 9425 99 13-307 3- 11 s 7-571 3-31-43 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 122 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 400 602 168 6614 602 885 5901 602 819 8424 19-211 450 7-643 3-19-79 658 887 5581 3 3 -167 01 3-7-191 603 4691597 3-13-103 604 118 0062 51 13-347 664 466 3335 654850 0906 666 042 8413 02 604 884 0781 3 3 -149 604 9816296 3-17-79 52 3-11-137 655 426 5877 3 2 -503 7-647 03 29-139 37-109 11-367 7-577 53 23-197 3-1511 13-349 3-17-89 04 3 2 -449 13-311 3-19-71 607 847 7768 54 19-239 7-11-59 657 724 9542 657 915 9868 05 607 562 2482 3-7-193 608 205 0077 3 2 -ll-41 55 3-37-41 29-157 3-7 2 -31 47-97 06 31-131 17-239 7 2 -83 13-313 56 659 060 0722 3 3 -13 2 669 681 0116 3-1523 07 3-23-59 609 914 4101 3 3 -151 610 553 7053 57 7-653 17-269 23-199 19-241 08 7-11-53 3-1361 61-67 3-29-47 58 3 2 -509 661 149 8572 3-11-139 13-353 09 611 829 4795 612 0417446 17-241 612 677 9183 59 661 907 2928 3-1531 662 474 5088 3 2 -7-73 410 3-1367 11-373 3-37* 7-587 460 43-107 663 040 9749 17-271 11-419 11 618 947 4768 3 2 -457 23-179 3-1373 61 3-29-53 7-659 3 S -19 31-149 12 13-317 7-19-31 6156344689 615 844 8829 62 664 735 9685 3-23-67 7-661 3-1543 13 3 5 -l7 616 265 4058 3-7-197 616 895 4264 63 11-421 41-113 666 237 0959 666 424 8725 14 41-101 3-1381 11-13-29 3 2 -461 64 3-7-13-17 666 798 6837 3-1549 667 359 5462 15 7-593 618 361 9311 618 780 0245 618 988 9204 65 667 546 8895 3 2 -ll-47 668 106 2879 3-1553 16 3-19-73 23-181 3 2 -463 11-379 66 59-79 668 665 4155 13-359 7-23-29 17 43-97 3-13-107 620 864 4758 3-7-199 67 3 3 -173 669 595 7810 3-1559 670 153 0452 18 37-113 47-89 53-79 59-71 68 31-151 3-7-223 43-109 3 2 -521 19 3-11-127 7-599 3-1399 13-17-19 69 671 265 4329 13- 19 2 7-11-61 37-127 420 623 862 6815 3 2 -467 7-601 3-23-61 470 3-1567 672 374 9787 3 2 -523 17-277 21 624 885 2414 11-383 625003 6010 625 209 5254 71 7-673 3-1571 53-89 3-ll 2 -13 22 3 2 -7-67 41-103 3-1409 626 237 6851 72 674 084 0004 674 217 9456 29-163 674 769 3140 23 626 448 0258 3-17-83 19-223 3 3 -157 73 3-19-83 675 186 6045 3-1579 7-677 24 627 468 2725 627 673 0318 31-137 7-607 74 11-431 3 2 -17-31 47-101 3-1583 25 3-13-109 628 695 3827 3 2 - 11-43 629 307 6401 75 676 785 0804 7 2 -97 67-71 677 515 7048 26 629 511 5842 3-7 2 -29 17-251 3-1423 76 3 2 -23 2 11-433 3-7-227 19-251 27 630 529 5714 6307828928 7-13-47 11-389 77 13-367 3-37-43 17-281 3 4 -59 28 3-1427 681748 0744 3-1429 632 856 0462 78 7-683 679 700 8809 680 063 4275 680 244 8870 29 7-613 3 4 -53 688165 8537 3-1433 79 3-1597 680 607 4290 3 2 -13-41 6811507499 430 11-17-23 13-331 59-73 31-139 480 681 881 7060 3-1601 11-19-23 3-7-229 31 3 2 -479 19-227 3-1439 7-617 81 17-283 682 415 8617 682 776 6468 61-79 32 29-149 3-11-131 636186 8952 3 2 -13-37 82 3-1607 7-13-53 3-1609 11-439 33 61-71 7-619 687189 4221 637 889 6501 83 684 087 0875 3 S -179 7-691 3-1613 34 3-1447 43-101 3 3 -7-23 688 889 4077 84 47-103 29-167 37-131 . 13-373 35 19-229 3-1451 '689187 5599 3-1453 85 3 2 -7 2 -ll 23-211 3-1619 43.113 36 7 2 -89 639 785 2130 11-397 17-257 86 686 725 6211 3-1621 31-157 3*-541 37 3-31-47 640 779 4778 3-1459 29-151 87 687 618 1296 11-443 688 152 7556 7-17-41 38 13-337 3 2 -487 41-107 3-7-11.19 88 3-1627 19-257 3 3 -181 689 220 0878 39 642 568 4871 23-191 6431564656 53-83 89 67-73 3-7-233 59-83 3-23-71 440 3 3 -163 7-17-37 3-13-113 644 840 0988 490 13 2 -29 690 461 8982 7-701 aMW8 0::-ji 41 11-401 3-1471 7-631 3 2 -491 91 3-1637 17 3 3-11-149 691 876 8226 42 645 520 6149 645 716 9894 19-233 43-103 92 7-19-37 3 s - 547 13-379 3-31-53 43 3-7-211 11-13-31 3 2 -17-29 23-193 93 6929850026 698 111 1166 698 468 1272 11-449 44 647 480 7782 3-1481 648 0671294 3-1483 94 3 4 -61 698 990 6105 3-17-97 7*-101 45 648 457 5948 61-73 649 042 6841 7 3 - 13 95 694 692 9268 3-13-127 695218 9189 3 2 -19-'J!> 46 3-1487 649 626 8868 3-1489 41-109 96 11 2 -41 7-709 696 094 1600 aM MB BM 47 17-263 3 2 -7-71 ll 2 -37 3-1493 97 3-1657 696 618 4592 3 2 -7-79 13-383 48 651 874 9489 651568 7389 7-641 67 2 98 17-293 :i- 1 1 - 151 697 889 8682 3-1663 49 3 s -499 652 686 4186 3-1499 11-409 99 7-23-31 69S 861 5661 19-263 8M B88 me Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. J IX. PRIME AND COMPOSITE NUMBERS. 123 Num. 1 3 7 9 Num. 1 3 7 9 500 3-1667 699 230 5029 3-1669 699 751 0317 550 740 441 6450 740599 5128 740 915 0765 7-787 01 699 924 4027 3 2 -557 29-173 3-7-239 51 3-11-167 37-149 3 2 -613 741 860 3941 02 700 790 2214 700 963 1782 11-457 47-107 52 742 017 7471 3-7-263 742 4S9 4646 3-19-97 03 3 2 -13-43 7-719 3-23-73 702 344 8584 53 742 803 6585 11-503 7 2 -113 29-191 04 71 2 3-41 2 7 2 -103 3 3 -ll-l7 54 3-1847 23-241 3-43 2 31-179 05 703 377 3685 31-163 13-389 704 064 6794 55 7-13-61 3 2 -6l7 744 840 8968 3-17-109 06 3-7-241 61-83 3 2 -563 37-137 56 67-83 745 309 0599 19-293 745 777 2179 07 11-461 3-19-89 705 607 1634 3-1693 57 3 2 -619 746 089 0481 3-11-13 2 7-797 08 705 949 1949 13-17-23 706 461 7376 7-727 58 746 712 0225 3-1861 37-151 3 5 -23 09 3-1697 11-463 3-1699 707 485 0120 59 747 489 4923 7-17-47 29-193 11-509 510 707 655 3235 3 6 -7 708 165 8579 3-13-131 560 3-1867 13-431 3 2 -7-89 71-79 11 19-269 708 675 7927 7-17-43 709 185 1296 61 31-181 3-1871 41-137 3-1873 12 3 2 -569 47-109 3-1709 23-223 62 7-11-73 749 9680885 17-331 13-433 13 7-733 3-29-59 11-467 3 2 -571 63 3-1877 43-131 3-1879 751 202 0946 14 53-97 37-139 711 554 1683 19-271 64 751 856 0997 3 3 -ll-19 751 817 7877 3-7-269 15 3-17-101 712 060 1425 3»-191 7-11-67 65 752125 8078 752 278 9855 752 586 1787 752 739 6939 16 13-397 3-1721 713 288 4615 3-1723 66 3 2 -l7-37 7-809 3-1889 753 506 4570 17 713 574 5378 7-739 31-167 714 245 9110 67 53-107 3-31-61 7-811 3 2 -631 18 3-11-157 71-73 3-7-13-19 715 083 6707 68 13-19-23 754 577 6560 ll 2 -47 755 035 9338 19 29-179 3 2 -577 715 752 7168 3-1733 69 3-7-271 755 8411838 3 3 -211 41-139 520 7-743 ll 2 -43 41-127 716 754 3574 570 755 951 0410 3-1901 13-439 3-11-173 21 3 3 -193 13-401 3-37-47 17-307 71 756 712 1602 29-197 757 168 1922 7-19-43 22 23-227 3-1741 718 252 5001 3 2 -7-83 72 3-1907 59-97 3-23-83 17-337 23 718 584 7200 718 750 7347 719 082 5789 13 2 -31 73 11-521 3 2 -7 2 -13 758 684 8499 3-1913 24 3-1747 7 2 -107 3 2 -ll-53 29-181 74 758 987 5469 759 188 8163 7-821 759 592 3086 25 59-89 3-17-103 7-751 3-1753 75 3 4 -7L 11-523 3-19-101 13-443 26 721 068 8018 19-277 23-229 11-479 76 7-823 3-17-113 73-79 3 2 -641 27 3-7-251 722 057 7718 3-1759 722 551 6620 77 29-199 23-251 53-109 761 852 6945 28 722 716 1675 3 2 -587 17-311 3-41-43 78 3-41-47 762 153 1923 3 2 -643 7-827 29 11-13-37 67-79 724 029 9729 7-757 79 762 753 5649 3-1931 11-17-31 3-1933 530 3 2 -19-31 724 521 6271 3-29-61 725 012 7253 580 763 502 8655 7-829 763 9518260 37-157 31 47-113 3-7-11-23 13-409 3 s - 197 81 3-13-149 764 400 3230 3-7-277 11-23 2 32 17-313 726 156 4662 7-761 73 2 82 764 997 5993 3 2 -647 765 445 0181 3-29-67 33 3-1777 726 971 5837 3 2 -593 19-281 83 73.17 19-307 13-449 766 338 4753 34 7 2 -109 3-13-137 728 110 1841 3-1783 84 3 2 -ll-59 766 635 8863 3-1949 767 081 6214 35 728 434 9510 53-101 11-487 23-233 85 767 2300981 3-1951 767 675 2240 3 3 -7-31 36 3-1787 31-173 3-1789 7-13-59 86 767 971 7214 11-13-41 768 416 0S82 7685641095 37 41-131 3 3 -199 19-283 3-11-163 87 3-19-103 7-839 3 2 -653 769 303 4602 38 780 862 9920 7-769 781 346 9755 17-317 88 769 451 1794 3-37-53 7-29 2 3-13-151 39 3 2 -599 731 830 4208 3-7-257 732 313 3275 89 43-137 71-83 770 631 1278 17-347 540 11-491 3-1801 732 956 3696 3 2 -601 590 3-7-281 771 072 7832 3-11-179 19-311 41 7-773 783 438 0271 733 758 8356 733 919 1510 91 23-257 3 4 -73 61-97 3-1973 42 3-13-139 11-17-29 3 4 -67 61-89 92 31-191 772 541 7326 772 834 9272 72.112 43 734 879 8028 3-1811 735 859 3330 3-7 2 -37 93 3 2 -659 17-349 3-1979 773 713 3253 44 735 678 7259 735 838 3848 13-419 736 316 8079 94 13-457 3-7-283 19-313 3 2 -661 45 3-23-79 7-19-41 3-17-107 53-103 95 11-541 774 735 8826 7-23-37 59-101 46 43-127 3 2 -607 7-11-71 3-1823 96 3-1987 67-89 3 3 -13-17 47-127 47 738066 7148 13-421 788 542 7409 788 7013004 97 7-853 3-11-181 43 -139 3-1993 48 3 3 -7-29 789 018 2459 3-31-59 11-499 98 776 778 8024 31-193 777 209 2581 53-113 49 17 2 -19 3-1831 23-239 3 2 -13-47 99 3-1997 13-461 3-1999 7-857 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 124 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 600 17-353 3 2 -23-29 778 657 6319 3-2003 650 3-11-197 7-929 3 3 -241 23-283 01 778 946 7280 7-859 11-547 13-463 51 17-383 3-13-167 7 3 -19 3-41-53 02 3 3 -223 19-317 3-7 2 -41 780 245 2839 52 814 314 2002 11-593 61-107 814 846 6686 03 37-163 3-2011 780 821 1759 3 2 -ll-61 53 3-7-311 47-139 3-2179 13-503 04 7-863 781252 5942 781 539 9686 23-263 54 31-211 3 2 -727 816 042 8409 3-37-59 05 3-2017 781970 6789 3 2 -673 73-83 55 816 807 5994 8164401680 79-83 7-937 06 11-19-29 3-43-47 782 973 9949 3-7-17 2 56 3 8 817 102 4043 3-11-199 817 499 2619 07 13-467 783408 2811 59-103 783 832 1484 57 817 681 4672 3-7-313 818027 8419 3 2 -17-43 08 3-2027 7-11-79 3-2029 784545 9741 58 818 291 8908 29-227 7-941 11-599 09 784 688 5995 3 2 -677 7-13-67 3-19-107 59 3-13 3 19-347 3 2 -733 819 4781284 610 7854010250 17-359 31-197 41-149 660 7-23-41 3-31-71 820 004 3068 3-2203 11 3 2 -7-97 786 254 8958 3-2039 29-211 61 11-601 17-389 13-509 820 792 3811 12 786 822 8795 3-13-157 11-557 3 3 -227 62 3-2207 37-179 3-47* 7-947 13 787 581 8161 787 672 9647 17- 19 2 7-877 63 19-349 3 2 -ll-67 821 971 8176 3-2213 14 3-23-89 7888805153 3 2 -683 11-13-43 64 29-229 7-13-73 17 2 -23 61-109 15 788 945 7270 3-7-293 47-131 3-2053 65 3 2 -739 823 017 5234 3-7-317 823 409 0149 16 61-101 789 7921677 7-881 31-199 66 823 539 4337 3-2221 59-113 3 3 -13-19 17 3 -ll 2 - 17 790496 2770 3-29-71 37-167 67 7-953 824 821 1249 11-607 824 7114485 18 7-883 3 3 -229 23-269 3-2063 68 3-17-131 41-163 3 2 -743 825361 1960 19 41-151 11-563 792 181 4961 792 321 6364 69 825 4910299 3-23-97 37-181 .'! • 7 • 1 1 • 29 620 3 2 -13-53 792 6017812 3-2069 7-887 670 826 189 6179 826 269 2194 19-353 826 657 7919 21 7981615292 3-19-109 793 580 8674 3 2 -691 71 3-2237 7*-137 3-2239 827 304 6411 22 798 860 2018 I 2 - 127 13-479 794 418 3309 72 11-13-47 3 4 -83 7-31 2 3-2243 23 3-31-67 23-271 3 4 -7-ll 17-367 73 53-127 828 208 6145 828 466 5474 23-293 24 79 2 3-2081 795 671 5059 3-2083 74 3 2 -7-107 11-613 3-13-173 17-397 25 7-19-47 13 2 -37 796 866 1550 11-569 75 43-157 3-2251 29-233 3 2 -751 26 3-2087 796 782 4117 3-2089 7971982698 76 880 010 9359 8801898874 67-101 7-967 27 797 336 8008 3 2 -l7-41 797 752 1287 3-7-13-23 77 3-37-61 13-521 3 3 -251 831 165 6889 28 11-571 61-103 798 443 4604 19-331 78 831 293 7444 3-7-17-19 11-617 3-31-73 29 3 3 -233 7-29-31 3-2099 799 271 6083 79 881 988 7305 832 061 6146 7-971 13-523 630 799 409 4796 3-11-191 7-17-53 3 2 -701 680 3-2267 882 700 4710 3-2269 11-619 31 800 0981802 59-107 800 510 8769 71-89 81 7 2 -139 3 2 -757 17-401 3-2273 32 3-7 2 -43 8009281818 3 2 -19-37 801 835 0957 82 19-359 838 975 3718 834 229 9029 8848571127 33 13-487 3-2111 801 883 7071 3-2113 83 3 3 -ll-23 884 6114207 3-43-53 7-977 34 17-373 802 294 7114 11-577 7-907 84 885119 5904 3-2281 41-167 3*- 761 35 3-29-73 8029788558 3-13-163 808 388 8250 85 13-17-31 7-11-89 836 134 1495 19 3 36 803 525 8956 3 2 -7-101 808 984 8499 3-11-193 86 3-2287 886 518 9989 3 2 -7-109 886 898 5164 37 23-277 804 843 9185 7-911 804 752 6022 87 887 019 9485 3-29-79 13- 23 s 3-2293 38 3 2 -709 13-491 3-2129 805 482 8881 88 7-983 887 777 7696 71-97 B8* 39 7-11-83 3-2131 805 976 3507 3 4 -79 89 3-2297 61-113 3-ll 2 -19 888 786 1449 640 37-173 19-337 43-149 13-17-29 690 67-103 3 2 -13-59 839 2S9 4560 3-7 s -47 41 3-2137 11*. 58 3 2 -23-31 7 2 -131 91 339 540 8980 31-223 839 917 7757 11-17-37 42 807 602 6699 3-2141 808 008 2999 3-2143 92 3 s - 769 7-23-43 3-2309 13*- 41 43 59-109 7-919 41-157 47-137 93 29-239 3-2311 7-991 3 3 -257 44 3-19-113 17-379 3-7-307 809 492 8769 94 11-631 53-131 841 797 2989 S41 922 8117 45 809 627 0419 3 3 -239 11-587 3-2153 95 3-7-331 17-409 3 2 -773 842 546 8865 46 7-13-71 23-281 29-223 810 8871511 96 842 671 6888 3-11-211 848 045S105 3-23-101 47 3 2 -719 811105 6070 3-17-127 11-19-31 97 848 295 0S27 19-367 848 668 7280 7-997 48 811642 0215 3-2161 13-499 3 2 -7-103 98 3- 13-179 MAMS MM 3-17-137 29.241 49 812 8116091 43-151 73-89 67-97 99 844 589 8021 3 8 -7-37 844 911 8789 3-2333 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 125 Num. 1 3 7 9 Num. 1 3 7 9 700 845 160 0777 47-149 7 2 -ll-13 43-163 750 13-577 3-41-61 875 4664159 3-2503 01 3 2 -19-41 845 903 8389 3-2339 846 275 2424 51 7-29-37 11-683 876 0445502 73-103 02 7- 17- 59 3-2341 846 769 9535 3 2 • 1 1 • 7 1 52 3-23-109 8763910618 3-13-193 876 737 2971 03 79-89 13-541 31-227 847 510 9652 53 17-443 3 5 -31 877 198 5153 3-7-359 04 3-2347 847 757 6884 3 5 -29 7-19-53 54 877 428 9408 19-397 877 774 3500 877 889 4254 05 11-641 3-2351 848 6201174 3-13-181 55 3 2 -839 7-13-83 3-11-229 878 464 3458 06 23-307 7-1009 37-191 849 357 9817 56 878 579 2381 3-2521 7-23-47 3 2 -29 2 07 3-2357 11-643 3-7-337 849 9719123 57 67-113 879 267 9568 879 497 2872 11-13-53 08 73-97 3 2 -787 19-373 3- 17- 139 58 3-7-19 2 879 841 0560 3 3 -281 880 184 5528 09 7-1013 41-173 47-151 31-229 59 880 2989914 3-2531 71-107 3-17-149 710 3 3 -263 851 441 8147 3- 23 -103 851808 5142 760 11-691 880 984 9905 881 213 4163 7-1087 11 13-547 3-2371 11-647 3 2 -7-113 61 3-43-59 23-331 3-2539 19-401 12 852 540 9858 17-419 852 906 7588 853 028 6147 62 882 Oil 9616 3 2 .7-ll 2 29-263 3-2543 13 3-2377 7-1019 3 2 -13-61 ll 2 -59 63 13-587 17-449 7-1091 883 036 5100 14 37-193 3-2381 7-1021 3-2383 64 3 3 -283 883 263 8596 3-2549 883 604 6609 15 854 366 7780 23-311 17-421 854 852 8624 65 7-1093 3-2551 13-19-31 3 2 -23-37 16 3-7.11.31 13.19-29 3-2389 67-107 66 47-163 79-97 11-17-41 884 738 7378 17 71-101 3 2 -797 855 942 9462 3-2393 67 3-2557 8849651982 3 2 -853 7-1097 18 43-167 11-653 856 547 6449 7 -13 -79 68 885 417 7651 3-13-197 885756 8811 3-11-233 19 3 2 -17-47 856 910 0603 3-2399 23-313 69 885 982 8114 7 2 -157 43-179 886 434 3196 720 19-379 3-7 4 857 754 5221 3 4 -89 770 3-17-151 886 659 8979 3-7-367 13-593 21 857 995 4956 858 115 9322 7-1031 858 477 0418 71 11-701 3 2 -857 887 448 5002 3-31-83 22 3-29-83 31-233 3 2 -11.73 859 078 2247 72 7-1103 887 786 0348 888 010 9122 59-131 23 7-1033 3-2411 859 558 5726 3-19-127 73 3 2 -859 11-19-37 3-2579 71-109 24 13-557 859 918 4852 860158 2613 11-659 74 888 797 0675 3-29-89 61-127 3 3 -7-41 25 3-2417 860 517 6775 3-41-59 7-17-61 75 23-337 889 469 7840 889 693 7914 889 8057519 26 53-137 3 3 -269 13 2 -43 3-2423 76 3-13-199 7-1109 3 2 -863 17-457 27 11-661 7-1039 19-383 29-251 77 19-409 3-2591 7- 11-101 3-2593 28 3 2 -809 862 310 3100 3.7.347 37-197 78 31-251 43-181 13-599 891 481 7038 29 23-317 3-11-13-17 863144 8463 3 2 -811 79 3-7 2 -53 891 704 6762 3-23-113 11-709 730 7 2 -149 67-109 863 739 1073 863 857 9619 780 29-269 3 3 -l7 2 37-211 3-19-137 31 3-2437 71-103 3 3 -271 -13-563 81 73-107 13-601 893 040 1120 7-1117 32 864 570 4069 3-2441 17-431 3-7-349 82 3 2 -ll-79 893373 3302 3-2609 893 706 2931 33 865 163 2195 865 281 6850 11-23-29 41-179 83 41-191 3-7-373 17-461 3 2 -13-67 34 3-2447 7-1049 3-31-79 8662282474 84 894 371 4589 11-23-31 7-19-59 47-167 35 866 346 4227 3 2 -19-43 7-1051 3-11-223 85 3-2617 895 035 5975 3 4 -97 29-271 36 17-433 37-199 53-139 867 408 5565 86 7-1123 3-2621 895 809 1502 3-43-61 37 3 4 -7-13 73-101 3-2459 47-157 87 17-463 896 140 2514 896 360 8455 896 471 1005 38 11 2 -61 3-23-107 83-89 3 2 -821 88 3-37-71 896 691 5266 3-11-239 7 3 -23 39 19-389 868 820 7062 13-569 7 2 -151 89 13-607 3 2 -877 53-149 3-2633 740 3-2467 11-673 3 2 -823 31-239 790 897 682 0618 7-1129 898 011 7388 11-719 41 869 876 8133 3-7-353 870 228 2790 3-2473 * 91 3 3 -293 41-193 3-7-13-29 8986703480 42 41-181 13-571 7-1061 17-19-23 92 89 2 3-19-139 899 108 8582 3 2 -881 43 3-2477 871 164 1328 3-37-67 43-173 93 7-11-103 899 437 4543 899 656 8803 17-467 44 7-1063 3 2 -827 11-677 3-13-191 94 3-2647 13 2 -47 3 2 -883 900 312 4970 45 872 214 5634 29-257 872 564 1431 872 680 6072 95 900 421 7535 3-11-241 73-109 3-7-379 46 3 2 -829 17-439 3-19-131 7-11-97 96 19-419 901 076 7157 31-257 13-613 47 31-241 3-47-53 873 727 3806 3 3 -277 97 3-2657 7-17-67 3-2659 79-101 48 873 959 6547 7-1069 874 307 8331 874 423 8306 98 23-347 3 2 -887 7 2 -163 3-2663 49 3-11-227 59-127 32.72.i7 875 003 3536 99 61-131 902 709 8130 11-727 19-421 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. . 126 IX. PRIME AKD COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 800 3 2 -7-127 53-151 3-17-157 908 5782987 850 929 470 0162 11-773 47-181 67-127 01 903 686 7817 3-2671 904 0118886 3 6 -ll 51 3-2837 980 082 6884 3-17-167 7-1217 02 13-617 71-113 23-349 7-31-37 52 980 490 5658 3 2 • 947 930 796 2680 3 • 2843 03 3-2677 29-277 3 2 -19-47 905 202 0287 53 19-449 7-23-53 931 805 2814 931 407 0186 04 11-17-43 3-7-383 13-619 3-2683 54 3 2 -13-73 981610 4064 3-7-11-37 83-103 05 83-97 905 957 6991 7-1151 906 2811558 55 17-503 3-2851 43-199 3 3 -317 06 3-2687 11-733 3-2689 906 819 7155 56 7-1223 932 625 9440 13-659 11-19-41 07 7-1153 3 3 -13-23 41-197 3-2693 57 3-2857 988182 8287 3 2 -953 23-373 08 907 465 1068 59-137 907 787 4481 907 894 8354 58 938 587 9020 3-2861 31-277 3-7-409 09 3 2 -29-31 908 109 5404 3-2699 7-13-89 59 ll 2 -7l 13-661 934 346 9267 934 447 9489 810 908 688 6822 3-37-73 ll 2 -67 3 2 -17-53 860 3-47-61 7-1229 3-19-151 984 952 7078 11 909 0744014 7-19-61 909 895 5460 23-353 61 79-109 3 3 -11.29 7-1231 3-13 2 -17 12 3-2707 909 716 4532 3 3 -7-43 11-739 62 37-233 935 658 8861 935 859 7980 935 960 4690 13 47-173 3-2711 79-103 3-2713 63 3 2 -7-137 89-97 3-2879 53-163 14 7-1163 17-479 910 997 7168 29-281 64 986 564 0051 3-43-67 986 865 4590 3 2 -31 2 15 3-11-13-1931.263 3-2719 41-199 65 41-211 17-509 11-787 7-1237 16 911 748 8779 3 2 -907 912 062 5556 3-7-389 66 3-2887 987 668 8144 3 4 -107 987 969 0080 17 912 275 2105 11-743 13-17-37 912 700 2082 67 13-23-29 3-7 2 -59 938 869 5975 3-11-263 18 3 4 -101 7 2 -167 3-2729 19-431 68 988 569 7562 19-457 7-17-73 9389697972 19 918 886 9259 3-2731 7-1171 3 2 -911 69 3-2897 989169 6796 3-13-223 9394698808 820 59-139 13-631 29-283 914 290 2557 870 7-11-113 3 2 -967 989 8685445 3-2903 21 3-7-17-23 43-191 3 2 -ll-83 914 818 9804 71 31-281 940167 7140 23-379 940 466 6777 22 914 924 6482 3-2741 19-433 3-13-211 72 3 3 -17.19 11-13-61 3-2909 7-29-43 23 915 452 6017 915 558 1154 915 769 0660 7-11-107 73 941063 9882 3 -41 -71 941862 8357 3 2 -971 24 3-41-67 916 085 2998 3-2749 73-113 74 9415611202 7-1249 941-8591265 13-673 25 37-223 3 2 -7-131 23-359 3-2753 75 3-2917 9421569285 3 2 -7-139 19-461 26 11-751 917 137 7528 7-1181 9174529919 76 942 553 6803 3-23-127 11-797 3-37-79 27 3 2 -919 917 663 0248 3-31-89 17-487 77 7 2 -179 31-283 67-131 943 445 0490 28 72.132 3-11-251 918 897 8888 3 3 -307 78 3-2927 948 642 8828 3- 29- 101 11-17-47 29 918 606 9151 918 711 6654 918 9210901 43-193 79 59-149 3 2 -977 19-463 3-7-419 830 3-2767 19 2 -23 3 2 -13-7l 7-1187 880 13-677 944 630 7019 944 827 9968 23-383 31 919 658 2823 3-17-163 919 966 7015 3-47-59 81 '3 2 -ll-89 7-1259 3-2939 945419 8426 32 53-157 7-29-41 11-757 920 592 8621 82 945 517 8221 3-17-173 7-13-97 3 4 -109 33 3-2777 13-641 3-7-397 31-269 83 946009 8848 ll 2 - 73 946 804 8550 946 408 1889 34 19-439 3 4 -103 17-491 3-ll 2 -23 84 3-7-421 37-239 3 2 -983 946 8941951 35 7-1193 921 842 4814 61-137 13-643 85 53-167 3-13-227 17-521 3-2953 36 3 2 -929 922 862 0968 3-2789 922 678 5679 86 947 482 7866 947 580 7498 947 776 7085 7 s - 181 37 11-761 3-2791 928 088 5154 3 2 -7 2 -19 87 3"-2957 19-467 3-11-269 13-683 38 17 2 -29 83-101 928 606 6480 928 710 1944 88 83-107 3 3 -7-47 948 7551802 3-2963 39 3-2797 7-11-109 3 3 -311 37-227 89 17-523 9490482928 7-31-41 11-809 840 31-271 3-2801 7-1201 3-2803 890 3 s - 23. 43 29-307 3-2969 59-151 41 13-647 47-179 19-443 925 260 5095 91 7-19-67 3-2971 37-241 3 2 -991 42 3-7-401 925 466 8007 3-53 2 925 7760588 92 11-811 950 510 8980 79-113 950 802 8280 43 925 879 0898 3 9 -937 11-13-59 3-29-97 93 3 -13 -229 950 997 8840 3 s . 331 7-1277 44 23-367 926 496 7898 926 702 4942 7-17-71 94 951886 0949 3-11 -271 23-389 3-19-157 45 3 8 - 313 79-107 3-2819 11-769 95 9518715571 7-1279 13*. 63 17*- 31 46 927 421 6951 3-7 -13-31 927 729 5598 3 2 -941 96 3 -29 -103 952 458 8964 3.7 2 -61 9527440240 47 43-197 37-229 7 2 -173 61-139 97 952 840 8567 3 2 -997 47-191 3-41- 7.: 48 3-11-257 17-499 3 9 - 23-41 13-653 98 7-1283 13-691 U-19-43 89-101 49 7-1213 3-19-149 29-293 3-2833 99 3 6 -37 17-23* 3-2999 954 194 2518 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 127 Num. 1 3 7 9 Num. 1 3 7 9 900 954 290 7617 3-3001 9545801627 3 2 - 7 -11 -13 950 3-3167 13-17-43 3-3169 37-257 01 954 772 9897 954 869 3711 71-127 29-311 51 978 226 1817 3 2 -7-151 31-307 3-19-167 02 3- 31-97 7-1289 3 2 -17-59 955 639 6530 52 978 682 5652 89-107 7-1361 13-733 03 11-821 3-3011 7-1291 3-23-131 53 3 3 -353 979 229 5980 3-11-17 2 979 502 8488 04 956 216 4692 956 812 5308 83-109 956 600 5882 54 7-29-47 3-3181 979 866 9226 3 2 -1061 05 3-7-431 11-823 3-3019 9570802597 55 980 048 8451 41-233 19-503 ll 2 -79 06 13-17-41 3 2 -19-53 957 463 6157 3-3023 56 3-3187 73-131 3 2 -1063 7-1367 07 47-193 43-211 29-313 7-1297 57 17-563 3-3191 61-157 3-31-103 08 3 2 -1009 31-293 3-13-233 61-149 58 11-13-67 7-37 2 981 682 7274 43-223 09 958 611 6578 3-7-433 11-827 3 3 -337 59 3-23-139 53-181 3-7-457 29-331 910 19-479 959 184 5427 7-1301 959 470 7021 960 982 816 4697 3 2 -ll-97 13-739 3-3203 11 3-3037 13-701 3 2 -1013 11-829 61 7-1373 982 858 9423 59-163 983 129 9247 12 7-1303 3-3041 960 828 0505 3- 17- 179 62 3 2 -1069 983 810 4858 3-3209 988 5811867 13 23-397 960 613 4576 960 803 6249 13- 19 -37 63 988 671 3829 3-13 2 -19 23-419 3 4 -7-17 14 3-11-277 41-223 3-3049 7-1307 64 31-311 984 212 1668 11-877 984 482 8064 15 961 468 5554 3 4 -113 961753 2142 3-43-71 65 3-3217 7 2 -197 3 2 -29-37 13-743 16 961 942 8831 7 2 -ll-l7 89-103 53-173 66 985 022 0821 3-3221 7-1381 3-11-293 17 3 2 -1019 962 511 3935 3-7-19-23 67-137 67 19-509 17-569 985 740 7411 985 880 4899 18 962 889 9874 3-3061 963178 7164 3 2 -1021 68 3-7-461 23-421 3-3229 986 278 9559 19 7-13-101 29-317 17-541 963 740 6189 69 11-881 3 3 -359 986 687 8956 3-53-61 920 3-3067 963 929 4220 3 3 -ll-31 964 212 4730 970 89-109 31-313 17-571 7-19-73 21 61-151 3-37-83 13-709 3-7-439 71 3 2 -13-83 11-883 3-41-79 987 621 5821 22 964 778 0220 23-401 965 060 5206 11-839 72 987 710 9481 3-7-463 71-137 3 2 -23-47 23 3-17-181 7-1319 3-3079 965 624 9671 73 37-263 988 246 7234 7-13-107 988 514 3658 24 965 718 9702 3 2 -13-79 7-1321 3-3083 74 3-17-191 988 692 7025 3 3 -19 2 988 960 0704 25 11-29 2 19-487 966 470 2637 47-197 75 7 2 -199 3-3251 11-887 3-3253 26 3 3 -7 3 . 59-157 3-3089 13-23-31 76 43-227 13-751 989 761 1877 989 850 1096 27 73-127 3-11-281 967 407 5566 3 2 -1031 77 3-3257 29-337 3-3259 7-11-127 28 967 594 7727 967 688 3505 37-251 7-1327 78 990 888 2589 3 2 -1087 990 649 5888 3-13-251 29 3-19-163 968 155 9371 3 2 -1033 17-547 79 990 827 0506 7-1399 97-101 41-239 930 71-131 3-7-443 41-227 3-29-107 980 3 4 -ll 2 991 359 0026 3-7-467 17-577 31 968 996 8266 67-139 7- II 3 ' 969 869 8117 81 991 713 2757 3-3271 991 978 7910 3 2 -1091 32 3-13-239 969 555 6842 3-3109 19-491 82 7-23-61 11-19-47 31-317 992 509 3351 33 7-31-43 3 2 -17-61 970207 8588 3-11-283. 83 3-29.113 992 686 0392 3 2 -1093 992 950 9606 34 970 893 3721 970 486 8488 13-719 970 7651598 84 13-757 3-17-193 43-229 3-7 2 -67 35 3 2 -1039 47-199 3-3119 7 2 -l91 85 993 480 3191 59-167 993 744 7566 993 832 8666 36 11-23-37 3-3121 17-19-29 3 3 -347 86 3-19-173 7-1409 3-11- 13- 23 71-139 37 971 785 9879 7- 13- 103 972 068 9160 83-113 87 994 361 1519 3 2 -1097 7-17-83 3-37-89 38 3-53-59 11-853 3 2 -7-149 41-229 88 41-241 994 888 7954 995 064 5342 11-29-31 39 972 711 8405 3-31. 101 972 989 2269 3-13-241 89 3 2 -7-157 13-761 3-3299 19-521 940 7-17-79 973 2664861 23-409 97 2 990 995 679 0605 3-3301 995 942 1680 3 3 -367 41 3-3137 973 728 0587 3-43-73 9740047969 91 11-17-53 23-431 47-211 7-13-109 42 974 097 0038 3 3 -349 11-857 3-7-449 92 3-3307 996 642 9914 3 2 -1103 996 905 5107 43 974 557 7449 974 649 8344 974 833 9550 974 925 9861 93 996 992 9819 3-7-11.43 19-523 3-3313 44 3 2 -1049 7-19-71 3.47-67 11-859 94 997 480 0788 61-163 7 3 -29 997 779 4309 45 13-727 3-23-137 7 2 -193 3 2 -1051 95 3-31-107 37-269 3-3319 23-433 46 975 937 0425 976 028 8401 9762128771 17-557 96 7-1423 3 5 -41 998 564 4588 3-3323 47 3-7-11.41 976487 5373 3 6 -13 976 762 5233 97 13 2 -59 998 825 8190 11-907 17-587 48 19-499 3-29-109 53-179 3-3163 98 3 2 -1109 67-149 3-3329 7-1427 49 977 811 9784 11-863 977 5864380 7-23-59 99 97-103 3-3331 13-769 3 2 -ll-101 Num. log 2 = .301 029 9957. Num. 1 log 5 = .698 970 0043. 128 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 1000 73-137 7-1429 000 808 8998 000 890 6892 1050 021 230 6585 3 3 -389 7-19-79 3-31-113 01 3-47- 71 17-19-31 3 3 -7-53 43-233 51 23-457 021 726 6644 13-809 67-157 02 11-911 3-13-257 37-271 3-3343 52 3 2 -7-167 17-619 3-ll 2 .29 022 887 1257 03 7-1433 79-127 001 603 9241 001 690 4542 53 022 469 6128 3-3511 41-257 3 2 -1171 04 3-3347 ll 2 -83 3-17-197 13-773 54 83-127 13-811 53-199 7-11-137 05 19-23 2 3 2 -1117 89-113 3-7-479 55 3-3517 61-173 3 3 -17-23 028 622 7899 06 002 641 1490 29-347 002 900 0686 002 986 3409 56 59-179 3-7-503 023 951 7074 3-13-271 07 3 3 -373 7-1439 3-3359 003 417 4452 57 11-31 2 97-109 7-1511 71-149 08 17-593 3-3361 7-11-131 3 2 -19-59 58 3-3527 19-557 3-3529 024 854 9483 09 003 984 2062 004 020 2733 23-439 004 278 8722 59 7-17-89 3 2 -ll-107 025 182 9843 3-3533 1010 3-7-13-37 004450 3630 3 2 -1123 11-919 1060 025346 8345 23-461 025592 5689 103 2 11 004 794 1104 3-3371 67-151 3-3373 61 3 4 -131 025 838 1642 3-3539 7-37-41 12 29-349 53-191 13-19-41 7-1447 62 13-19-43 3-3541 026 410 6806 3 2 -1181 13 3-11-307 005 738 0427 3-31-109 005 995 1231 63 026 574 1182 7 3 -31 11-967 026 900 8089 14 006 080 7827 3 2 -7 2 -23 73-139 3-17-199 64 3-3547 29-367 3 2 -7-13 2 23-463 15 006 508 8278 11-13-71 7-1451 006 850 9603 65 027 8908847 3-53-67 027 634 9658 3-11-17-19 16 3 2 -1129 007 021 9256 3-3389 007 278 2473 66 7-1523 027 879 4092 028 042 2951 47-227 17 7-1453 3-3391 007 619 7745 3 3 -13-29 67 3-3557 13-821 3-3559 59-181 18 007 790 4874 17-599 61-167 23-443 68 11-971 3 2 -1187 028 855 8094 3-7-509 19 3-43-79 008 802 0242 3 2 -ll-103 7-31-47 69 029 018 8295 17 2 -37 19-563 13-823 1020 101 2 3-19-179 59-173 3-41-83 1070 3 2 -29-41 7-11-139 3-43-83 029 748 9186 21 009 068 2762 7-1459 17-601 11-929 71 029 830 0198 3-3571 7-1531 3 3 -397 22 3-3407 009 578 3608 3-7-487 53-193 72 71-151 030 816 3060 17-631 030 559 2453 23 13-787 3 3 -379 29-353 3-3413 73 3-7 2 -73 030 721 1294 3 2 -1193 080 963 8424 24 7 2 -ll-19 010 427 1727 010 596 7362 37-277 74 23-467 3-3581 11-977 3-3583 25 3 2 -17-67 010 850 9574 3-13-263 Oil 105 0298 75 13-827 081 529 6458 31-347 7-29-53 26 31-331 3-11-311 011 443 5620 3 2 -7-163 76 3-17-211 47-229 3-37-97 11*. 89 27 Oil 612 7292 011 697 2881 43-239 19-541 77 032 256 0259 3 4 -7-19 13-829 3-3593 28 3-23-149 7-13-113 3 4 -127 012 873 1672 78 032 659 0460 41-263 7-23-67 032 9S1 1931 29 41-251 3-47-73 7-1471 3-3433 79 3 2 -ll-109 43-251 3-59-61 038 888 5412 1030 012 879 3872 012 963 6998 11-937 13 2 -61 1080 7-1543 3-13-277 101-107 3 2 -1201 31 3-7-491 013 385 0177 3-19-181 17-607 81 19-569 11-983 29-373 31-349 32 018 721 7781 3 2 -31-37 23-449 3-11-313 82 3-3607 79-137 3 3 -401 7 2 -13-17 33 014 142 3615 014 226 4294 014 894 5163 7 2 -211 83 084 668 5558 3-23-157 034 909 0734 3-3613 34 3 3 -383 014 646 5247 3-3449 79-131 84 37-293 7-1549 035 809 6402 19-571 35 11-941 3-7-17-29 0152839762 3 2 -1151 85 3-3617 085 549 8030 3-7-11-47 085 789 8881 36 13-797 43-241 7-1481 015 736 8745 86 085 869 8187 3 2 -17-71 086 109 6671 3-3623 37 3-3457 11-23-41 3 2 -1153 97-107 87 7-1553 83-131 73-149 11-23-43 38 7-1483 3-3461 13-17-47 3-3463 88 3 3 -13-31 036 748 6292 3-19-191 086 987 9978 39 016 657 8448 19-547 37-281 016 991 5782 89 087 067 7580 3-3631 17-641 3 s . 7-173 1040 3-3467 101-103 3-3469 7-1487 1090 11-991 087 546 0121 13-839 087 784 9418 41 29-359 3 2 -13-89 11-947 3-23-151 91 3-3637 7-1559 3 2 -1213 61-179 42 17-613 7-1489 018159 8785 018 242 6675 92 67-163 3-11-331 7»-223 3-361;; 43 3 2 -19-61 018 409 2074 3-7 2 -71 11-13-73 93 17-643 13-29 2 088 898 2121 088 977 6228 44 53-197 3-59 2 31-337 3 B -43 94 3-7-521 31-353 3-41- 89 089 874 4558 45 7-1493 019 240 9504 019 407 1080 019 490 1680 95 47-233 3 2 -1217 039 691 6616 3-13-281 46 3-11-317 019 656 2258 3 2 -1163 19 2 -29 96 97-113 19-577 11-997 7-1567 47 37-283 3-3491 020 286 9489 3-7-499 97 3 2 -23-53 040 825 8792 3-3659 040 562 7S51 48 47-223 11-953 020 651 2680 17-617 98 79-139 3-7-523 040 879 1245 3».ii ■:;: 49 3-13-269 7-1499 3-3499 021 147 9857 99 29-379 041 116 22S0 7-1571 17-647 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 129 Num. 1 3 7 9 Num. 1 3 7 9 1100 3-19-193 041 511 1130 3 2 -1223 101-109 1150 7-31-53 060 811 1198 37-311 17-677 01 7- II 2 - 13 3-3671 23-479 3-3673 51 3 2 -1279 29-397 3-11-349 061 414 7783 02 103-107 73-151 042 457 3746 41-269 52 41-281 3-23-167 061 716 2932 3 3 -7-61 03 3-3677 11-17-59 3-13-283 7-19-83 53 13-887 19-607 83-139 11-1049 04 61^181 3 3 -409 043 244 3540 3-29-127 54 3-3847 7-17-97 3 2 -1283 062 544 3813 05 43-257 7-1579 043 637 3096 043 715 8581 55 062 619 5839 3-3851 7-13-127 3-3853 06 3 2 -1229 13-23-37 3-7-17-31 0441088874 56 11-1051 31-373 43-269 23-503 07 044186 8508 3-3691 11-19-53 3 2 -1231 57 3-7-19-29 71-163 3-17-227 063 671 0539 08 7-1583 044 657 3332 044 8140475 13-853 58 37-313 3 4 -ll-13 068 971 0070 3-3863 09 3-3697 045 049 0130 3 4 -137 11-1009 59 67-173 064 195 8359 064 345 6572 7-1657 1110 17-653 3-3701 29-383 3-7-23 2 1160 3 2 -1289 41-283 3-53-73 13-19-47 11 41-271 045 831 3143 045 987 6057 046 065 7302 61 17-683 3-7 2 -79 065 093 9894 3 2 -1291 12 3-11-337 7 2 -227 3-3709 31-359 62 065 243 5012 59-197 7-11-151 29-401 13 046 584 1828 3 2 -1237 7-37-43 3-47-79 63 3-3877 065 691 7281 3 3 -431 103-113 14 13-857 11-1013 71-157 047235 9155 64 7-1663 3-3881 19-613 3-11-353 15 3 3 -7-59 19-587 3-3719 047 6252776 65 61-191 43-271 066 586 7965 89-131 16 047 703 1081 3-61 2 13-859 3 2 -17-73 66 3-13 2 -23 107-109 3-3889 7-1667 17 048 092 0518 048 169 7988 048 825 2509 7-1597 67 11-1061 3 2 -1297 067 331 2802 3-17-229 18 3-3727 53-211 3 2 -ll-113 67-167 68 067 480 0239 7-1669 13-29-31 067 7773586 19 19 2 - 31 3-7 -13-41 0491016782 3-3733 69 3 3 -433 11-1063 3-7-557 068 148 7409 1120 23-487 17-659 7-1601 11-1019 1170 068 222 9793 3-47-83 23-509 3 2 -1301 21 3-37-101 049 721 8222 3-3739 13-863 71 7 2 -239 13-17-53 068 816 4299 068 890 5543 22 7 2 -229 3 2 -29-43 103-109 3-19-197 72 3-3907 19-617 3 2 -1303 37-317. 23 11-1021 47-239 17-661 050 727 6712 73 069 835 0348 3-3911 ll 2 -97 3-7.13-43 24 3 2 -1249 050 882 2107 3-23-163 7-1607 74 59-199 069 779 0609 17-691 31-379 25 051 191 1247 3-ll 2 -31 051422 6661 3 4 -139 75 3-3917 7-23-73 3-3919 11-1069 26 0515769585 7-1609 19-593 59-191 76 19-619 3 2 -1307 7-41 2 3-3923 27 3-13-17 2 052 039 5070 3 2 -7-179 052 270 5967 77 79-149 61-193 071 034 6751 071108 4218 28 29-389 3-3761 052 578 5250 3-53-71 78 3 2 - 7 -11-17 071255 8777 3-3929 071 476 9677 29 7-1613 23-491 11-13-79 053 0400086 79 13-907 3-8931 47-251 3 3 -19-23 1130 3-3767 89-127 3-3769 43-263 1180 0719188104 11-29-37 072 139 5632 7 2 -241 31 053 501 0024 3 3 -419 053 7313159 '3-7 3 -ll 81 3-31-127 072 360 2040 3 2 -13-101 53-223 32 053 884 7904 13 2 -67 47-241 0541915768 82 072 654 2173 3-7-563 072 874 5968 3-3943 33 3 2 -1259 7-1619 3-3779 17-23-29 83 073 021 4544 073 094 8645 7-19-89 073 315 0206 34 11-1031 3-19-199 7-1621 3 2 -13-97 84 3-3947 13-911 3-11-359 17 2 -41 35 055 034 1237 055 110 6379 41-277 37-307 85 7-1693 3 3 -439 71-167 3-59-67 36 3-7-541 11-1033 3 3 -421 055 722 2665 86 29-409 074 194 5304 074 340 9424 11-13-83 37 83-137 3-17-223 31-367 3-3793 87 3 2 -1319 31-383 3-37-107 7-1697 38 19-599 056 256 7359 59-193 7-1627 88 109 2 3-17-233 075072 2627 3 2 -1321 39 3-3797 056 638 0974 3-29-131 056 866 7537 89 11-23-47 7-1699 075 437 4616 73-163 1140 13-877 3 2 -7-181 11-17-61 3-3803 1190 3-3967 075 656 4336 3 5 -7 2 075 875 2953 41 057 323 7054 101-113 7 2 -233 19-601 91 43-277 3-11-19 2 17-701 3-29-137 42 3 5 -47 057 780 1768 3-13-293 11-1039 92 7-13-131 076 885 5440 076 5312193, 79-151 43 7-23-71 3-37-103 058 3121211 3 2 -31-41 93 3-41-97 076 749 6406 3-23-173 076 967 9522 44 17-673 058 539 8979 058 691 6828 107 2 94 077 040 6983 3 2 -1327 13-919 3-7-569 45 3-11-347 13-881 3 2 -19-67 7-1637 95 17-19-37 077 476 9195 11-1087 077 694 8659 46 73-157 3-3821 059 449 8125 3-3823 96 3 3 -443 7-1709 3-3989 078 057 8670 47 059 601 2798 7-11-149 23-499 13-883 97 078 130 4808 3-13-307 7-29-59 3 2 -ll 3 48 3-43-89 060 055 3648 3-7-547 060 282 2294 98 078 493 0682 23-521 078 710 5053 19-631 49 060 357 8246 3 2 -1277 060 584 5814 3-3833 99 3-7-571 67-179 3 2 -31-43 13 2 -71 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 130 IX. PRIME AND COMPOSITE NUMBERS. Num. Num. 9 1200 01 02 03 04 05 06 07 08 09 1210 11 12 13 14 15 16 11 18 19 1220 21 22 23 24 25 26 2*7 28 29 1230 31 32 33 34 35 36 37 38 39 1240 41 42 43 44 45 46 47 48 49 11-1091 079 579 1670 3-4007 53-227 080 662 6564 3 s - 13- 103 7-1723 081 748 2499 3-4027 107-113 082 821 2609 3-11-367 17-23-31 7-1733 3 2 -19-71 29-419 084 969 2885 3-4057 13-937 73-167 3-7 2 -83 086 751 2312 11 2 -101 3 4 -151 087 816 8979 3-4001 41-293 11-1093 3 2 -7-191 080 734 6864 17-709 3-4021 081 815 2006 43-281 3-29-139 7 2 -13-19 083 251 7172 3 3 -449 11-1103 084 325 9950 3-4051 085 040 7067 7-37-47 3-31-131 89-137 086 466 6118 3 2 -23-59 17-719 13-941 3-7-11-53 0881715899 088 242 4335 3-61-67 0885967288 7-1753 3-4091 089 233 7314 71-173 3-17-241 19-647 089 940 4185 3 2 -1367 13-947 7-1759 3 2 -37 2 11-19-59 7-41-43 3-23-179 47-263 89-139 3-4127 090 716 4485 3-4111 091 420 7290 11-1123 3-13-317 092 475 0129 7-29-61 098106 3570 3 6 -17 093 456 7075 79-157 3 2 -7-197 093 876 7554 0941565618 3-41-101 31-401 094 575 9886 3-11-13-29 23-541 095 204 2381 3-7-593 17-733 11 2 -103 3-4157 095 970 9228 7-1783 3 s -19-73 096 597 2084 13-31* 079 434 5106 61-197 3-19-211 080 518 2605 7-1721 3-4019 11-1097 13-929 3 2 -17-79 082 677 6806 083 036 5424 3-7-577 67-181 53-229 3-4049 084 826 4167 23 3 3 3 - 11-41 7-1741 086 258 0288 3-13-313 19-643 087 819 9122 3-4079 37-331 7-17-103 3 2 -29-47 089 092 2558 11-1117 •3-4099 31-397 109-113 3-7-587 13' 2 -73 091 561 4481 3 2 -1373 83-149 092 615 8909 3-4129 7 2 -ll-23 19-653 3-4139 l7 2 -43 094 715 6848 3 8 -461 095 418 4644 7-13-137 3-4159 096 45S 1117 096 805 7698 3-4003 1250 7-17-101 51 23-523 52 3-4013 53 080 951 0044 54 31-389 55 3 4 -149 56 47-257 57 7-11-157 58 3-37-109 59 083 108 2792 1260 083 466 7855 61 3-13-311 62 61-199 63 084 540 5321 64 3 2 -7-193 65 43-283 66 19-641 67 3-17-239 68 11-1109 69 29-421 1270 3-4073 71 7-1747 72 087 745 9348 73 3 2 -1361 74 13-23-41 75 088 809 1665 76 3-4093- 77 089 516 5442 78 7 2 -251 79 3-11-373 1280 97-127 81 090 927 8526 82 3 3 -457 83 53-233 84 17-727 85 3-7-19-31 86 092 685 5629 87 13-953 88 3-4133 89 098 786 7846 1290 11-1129 91 3 2 -1381 92 7-1777 93 59-211 94 3-4153 95 37-337 96 096 179 7847 97 3-23-181 98 29-431 99 3 3 -463 097 292 0241 19-659 3-4177 098 8321678 7-11-163 3-53-79 13-867 23-547 3 2 -1399 100 405 0116 100 749 5257 3-7-601 17-743 101 781 4813 3-4217 11-1151 102 810 8909 3 2 -1409 7 3 -37 13-977 3-19-223 104 521 2526 29-439 3-31-137 41-311 7-1823 3 3 -ll-43 106 564 8348 106 904 4989 3-17-251 23-557 107 921 9002 3-7-13-47 108 598 8460 71-181 3 2 -1429 61-211 11-1171 3-4297 097 014 2312 3-11-379 3-43-97 0975002522 7-1789 097 847 0774 83-151 3 2 -7-199 3-37-113 0985898980 098 747 5288 17-739 3 8 -ll-127 099 784 1966 7 2 -257 3 3-4201 100 818 8957 13-971 3-4211 47-269 29-433 3-59-71 099 577 0609 41-307 •13-17-19 7-1801 11-31-37 3 2 -23-61 101 643 9855 101 987 5186 102 193 5080 3-4219 3 3 -7-67 53-239 19-23-29 7-1811 11-1153 3-4229 3-4231 103 7011196 108 906 2981 104 248 0470 3-4241 7-17-107 105 271 6881 3 2 -13-109 105 952 7692 53-241 3-4261 11-1163 7-31-59 3-4271 107 989 6428 41-313 3 2 -1427 109 004 5075 19-677 3-7-613 13-991 110 858 9827 7-19-97 110 959 8811 3-59-73 67-193 111967 8872 3 s - 1439 13-997 7-17-109 3-4327 11-1181 3 -11 -17- 23 37-349 111863 3448 3 8 -479 7- 43 s 112 870 8655 3-29-149 118 040 41S1 118 875 0571 3-61-71 97-131 3 4 -157 11-13-89 47-271 3-7-607 105 748 5555 17-751 3-4259 19-673 67-191 3 2 -1423 7-1831 101-127 3-11-389 29-443 13-23-43 3-4289 79-163 7 a -263 3»-1433 110 825 8101 111 161 6596 3-31-139 17-761 11»-107 3-7-617 112 889 5108 19-683 3 8 -13-37 41-317 7-1787 3 8 -13-107 11-17-67 098262 9024 3-47-89 19-661 099 8»0 TOM 3-7-599 099 991 2885 43-293 3 3 -467 101 024 9404 73-173 3-11-383 7-13-139 102899 3999 3-41-103 31-409 103 427 8974 3 2 -17-83 71-179 7-23-79 3-4243 105 135 3376 11-19-61 3-4253 113* 13-983 3 2 -7«-29 107 176 0391 107 515 US! 3-4273 108 192 8051 37-347 3-4283 7-11-167 17-757 3 5 -53 110 219 2287 110 556 0428 3-13-331 11122SS9S2 7-1847 3.19-331 23-563 112 5714899 3 8 -n-i:u 118241 an j 31-419 3-7-619 Num.. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 131 Num. 1 3 7 9 Num. 1 3 7 9 1300 113 976 7583 114 043 5625 114 177 1402 114 243 9137 1350 23-587 3-7-643 13-1039 3 2 -19-79 01 3-4337 7-11-13 2 3-4339 47-277 51 59-229 130 751 7768 7-1931 11-1229 02 29-449 3 2 -1447 7-1861 3-43-101 52 3-4507 131 073 0480 3 4 -167 83-163 03 83-157 115 044 3953 115177 6655 13-17-59 53 7-1933 3-13-347 131 522 4289 3-4513 04 3 4 -7-23 115377 4943 3-4349 115 577 2311 54 11-1231 29-46-7 19-23-31 17-797 05 31-421 3-19-229 11-1187 3 2 -1451 55 3-4517 132 0354383 3-4519 7-13-149 06 37-353 116042 9268 73-179 7-1867 56 71-191 3 2 -ll-137 132 483 8250 3-4523 07 3-4357 17-769 3 2 -1453 11-29-41 57 41-331 7 2 -277 132 803 8180 37-367 08 103-127 3-7 2 -89 23-569 3-4363 58 3 3 -503 l7 2 -47 3-7-647 107-127 09 13-19-53 117 039 1679 7-1871 117 238 1421 59 133 251 4125 3-23-197 133 443 0975 3 2 -1511 1310 3-11-397 117 370 7410 3-17-257 117 569 5635 1360 7-29-67 61-223 11-1237 31-439 11 7-1873 3 2 -31-47 13-1009 3-4373 61 3-13-349 133 953 8445 3 2 -l7-89 134 145 2199 12 117 966 9355 11-1193 118165 4852 19-691 62 53-257 3-19-239 134 400 2559 3-7-11.59 13 3 2 -1459 23-571 3-29-151 7-1877 63 43-317 134 591 4347 13-1049 23-593 14 17-773 3-13-337 118 826 6629 3 3 -487 64 3-4547 7-1949 3-4549 135 100 8838 15 118 958 7778 7-1879 59-223 119 222 8869 65 11-17-73 3 2 -37-41 7-1951 3-29-157 16 3-41-107 119 354 8813 3 2 -7-ll-19 13-1013 66 19-719 13-1051 79-173 135 736 7435 17 119 618 7498 3-4391 119 816 5459 3-23-191 67 3 2 -7 2 -31 11 2 -113 3-47-97 136 054 3496 18 7 2 -269 120 014 2521 120 146 0062 11 2 -109 68 136 117 8429 3-4561 136 308 2673 3 4 -13 2 19 3-4397 79-167 3-53-83 67-197 69 136 435 1705 136 498 6082 136 625 4558 7-19-103 1320 43-307 3 4 -163 47-281 3-7-17-37 1370 3-4567 71-193 3 2 -1523 137 005 7764 21 11-1201 73-181 121 132 8900 121 198 6026 71 187 069 1308 3-7-653 11-29-43 3-17-269 22 3 2 -13-113 7-1889 3-4409 121 527 0165 72 137 385 7643 137 449 0633 7-37-53 137 638 9050 23 101-131 3-11-401 7-31-61 3 2 -1471 73 3-23-199 31-443 3-19-241 11-1249 24 121 920 7856 17-19-41 13-1019 122 183 1001 74 7-13-151 3 3 -509 59-233 3-4583 25 3-7-631 29-457 3 3 -491 122 510 7706 75 188 8842821 17-809 138 523 7373 138 586 8707 26 89-149 3-4421 122 772 7291 3-4423 76 3 2 -ll-139 138 713 1099 3-13-353 7 2 -281 27 23-577 13-1021 11-17-71 7 2 -27l 77 47-293 3-4591 23-599 3 2 -1531 28 3-19-233 37-359 3-43-103 97-137 78 189 280 7327 7-11-179 17-811 139 532 7716 29 123 557 6580 3 2 -7-211 123 753 6688 3-11-13-31 79 3-4597 13-1061 3 3 -7-73 139 847 6146 1330 47-283 53-251 7-1901 124 145 4251 1380 37-373 3-43-107 140 099 3249 3-4603 31 3 3 -l7-29 124 275 9320 3-23-193 '19-701 81 7-1973 19-727 41-337 13-1063 32 7-11-173 3-4441 124 7323977 3 2 -1481 82 3-17-271 23-601 3-11-419 140 790 7766 33 124 862 7284 67-199 125 058 1512 125 123 2726 - 83 140 853 5813 3 2 -29-53 101-137 3-7-659 34 3 -4447 11-1213 3 2 -1483 7-1907 84 141 167 4686 109-127 61-227 11-1259 35 13 2 -79 3-4451 19 2 -37 3-61-73 85 3 6 -19 7-1979 3-31 -149 141 731 8948 36 31-431 7-23-83 126 033 9481 29-461 86 83-167 3-4621 7 2 -283 3 2 -23-67 37 3-4457 43-311 3-7 3 -13 17-787 87 11-13-97 142 170 3863 142 295 5883 142 358 1758 38 126 488 5707 3 2 -1487 11-1217 3-4463 88 3-7-661 142 483 3237 3 2 -1543 17-19-43 39 7-1913 59-227 127 007 5574 127 072 3871 89 29-479 3-11-421 13-1069 3-41-113 1340 3 2 -1489 13-1031 3-41-109 11-23-53 1390 143 046 0483 143 108 5228 143 233 4547 7-1987 41 127 461 1625 3-17-263 127 6554198 3 3 -7-71 91 3-4637 143 420 7851 3-4639 31-449 42 127 784 8764 31-433 29-463 13-1033 92 143 670 4335 3 2 -7-13-l7 19-733 3-4643 43 3-ll 2 -37 7-19-101 3 2 -1493 89-151 93 143 982 2922 144 044 6371 7-11-181 53-263 44 128 481 5811 3-4481 7-17-113 3-4483 94 3 2 -1549 73-191 3-4649 13-29-37 45 128 754 5727 11-1223 128 948 2524 43-313 95 7-1993 3-4651 17-821 3 3 -ll-47 46 3-7-641 129 141 8458 3-67 2 129335 3529 96 23-607 144 978 7380 145 103 1381 61-229 47 19-709 3 3 -499 129 593 2284 3-4493 97 3-4657 89-157 3 2 -1553 7-1997 48 13-17-61 97-139 129 9158C75 7-41-47 98 11-31-41 3-59-79 71-197 3-4663 49 3 2 -1499 103-131 3-11-409 130 301 5973 99 17-823 7-1999 146 034 9626 146 097 0135 Num. log 2 = .301 029 9957. Num. log 5 = . 698 970 0043. 132 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 1400 3-13-359 11-19-67 3-7-23-29 146 4071358 1450 17-853 161 457 8470 89-163 11-1319 01 146 469 1881 3 4 -l73 107-131 3-4673 51 3-7-691 23-631 3*. 1613 161936 7052 02 7-2003 37-379 13 2 -83 147 026 7152 52 13-1117 3-47-103 73-199 3-29-167 03 3 2 -1559 147 150 5252 3-4679 101-139 53 11-1321 162 8552786 162 474 7904 7-31-67 04 19-739 3-31-151 11-1277 3 2 -7-223 • 54 3-37-131 162 654 0041 3-13-373 162 883 1489 05 147 707 2888 13-23-47 147 892 6448 17-827 55 162 892 8407 3 3 -7 2 - 11 168 071 8820 3-23-211 06 3-43-109 7*- 41 3 3 -521 11-1279 56 163 191 2019 163 250 8495 7-2081 17-857 07 148 824 9630 3-4691 7-2011 3-13-19 2 57 3 2 -1619 13-19-59 3- 43- 113 61-239 08 148 638 4985 148 695 1793 148 818 5146 73-193 58 7-2083 3-4861 29-503 3 2 -1621 09 3-7-11-61 17-829 3-37-127 23-613 59 164 085 0575 164 144 5825 11-1327 13-1123 1410 59-239 3 2 -1567 149 434 6663 3-4703 1460 3-31-157 17-859 3 3 -541 • 7-2087 11 103-137 11-1283 19-743 7-2017 61 19-769 3-4871 47-311 3-11-443 12 3 3 -523 29-487 3-17-277 71-199 62 164 977 0771 7-2089 165155 2614 165 214 6399 13 13-1087 3-7-673 67-211 3 2 -1571 63 3-4877 165 883 3726 3-7-17-41 1655114108 14 79-179 150 541 5414 7-43-47 150 725 7466 64 ll 4 3 2 -1627 97-151 3-19-257 15 3-53-89 150 848 5067 3 2 -ll 2 -13 151 082 5818 65 7 2 -13-23 165 926 5496 166 045 0879 107-137 16 7 2 -17 2 3-4721 31-457 3-4723 66 3 4 -181 11-31-43 3-4889 166 400 5086 17 37-383 151 461 7871 151 584 3394 11-1289 67 17-863 3-67-73 13-1129 3 2 -7-233 18 3-29-163 13-1091 3-4729 7-2027 68 53-277 166 814 7988 19-773 37-397 19 23-617 3 2 -19-83 152 196 5823 3-4733 69 3-59-83 7-2099 3 2 -23-71 1672877899 1420 11-1291 7-2029 152 502 3805 13-1093 1470 61-241 3-13 2 -29 7-11-191 3-4903 21 3 2 -1579 61-233 3-7-677 59-241 71 47-313 167 701 2350 167 819 2899 41-359 22 152 930 1864 3-11-431 41-347 3 3 -17-31 72 3-7-701 167 996 8121 3-4909 11-13-103 23 7-19-107 43-331 23-619 29-491 73 168 232 2295 3 2 -1637 163 409 0885 3 - 1 7 3 24 3-47-101 158 601 4743 3 2 -1583 153 784 8865 74 168 626 9462 23-641 168703 6802 7 3 -43 25 153 845 3401 3-4751 53-269 3-7 2 -97 75 3 2 -l 1-149 168 880 8424 3-4919 1690569327 26 13-1097 17-839 11-1297 19-751 76 29-509 3-7-19-37 169 292 2749 3 3 -547 27 3-67-71 7-2039 3-4759 109-131 77 169 409 8981 11 • 17 -79 7-2111 169 6450491 28 154 758 6192 3 3 -23 2 7-13-157 3-11-433 78 3-13-379 169 762 5769 3 2 -31-53 23-643 29 31-461 155 123 3987 17- 29 2 79-181 79 7-2113 3-4931 170 173 6788 3-4933 1430 3 2 -7-227 155 427 1886 3-19-251 41-349 1480 19 2 -41 113-131 13-17-67 59-251 31 11-1301 3-13-367 103-139 3 2 -37-43 81 3-4937 170 643 0228 3-11-449 7-29-73 32 155 973 8447 156 038 9919 156 155 2609 7-23-89 82 170 877 5078 3 s - 61 171053 2876 3-4943 33 3-17-281 11-1303 3 5 -59 13-1103 83 171 170 4349 7-13-163 37-401 11-19-71 34 156 579 4358 3-7-683 156 761 0983 3-4783 84 3 2 -17-97 171 521 6875 3-7 2 -101 31-479 35 113-127 31-463 7 2 -293 83-173 85 171 755 6981 3-4951 83-179 3 S -13I1'7 36 3-4787 53-271 3-4789 157 426 5448 86 7-11-193 89-167 172 228 3414 172 2S1 7615 37 7-2053 3 2 -1597 11-1307 3-4793 87 3-4957 107-139 3 s - 19 -29 172 578 7488 38 73-197 19-757 157 970 2436 158 030 6126 88 23-647 3-ll 2 -41 172 80718S4 3-7-709 39 3 3 -13-41 37-389 3-4799 7 • II 2 - 17 89 172 928 8636 53-281 178 098 8178 47-317 1440 158 892 6504 3-4801 158 578 5562 3 2 -1601 1490 3-4967 7-2129 3-4969 17-877 41 158 694 1182 7-29-71 13-1109 158 935 1418 91 13-31-37 3 2 -1657 7-2131 3-4973 42 3-11-19-23 159 055 6085 3 2 -7-229 47-307 92 43-347 178 856 1890 11-23-59 174 030 7180 43 IG98964MV 3-17-283 159 476 9565 3-4813 93 3 8 -7-79 109-137 3-13-383 174 8215278 44 7 -2063 11-13-101 159 777 6728 159 887 7911 94 67-223 3.17-293 1745640845 3- - 1 1 - 1 5 1 45 3-4817 97-149 3-61-79 19-761 95 174 670 2415 19-787 174 8444937 7-2137 46 160198 8261 3 2 -1607 17-23-37 ::-7-13-53 M 3-4987 13-1151 3 s - 1663 175192 7884 47 29-499 41-353 111 • Km 160 738 5681 97 11-1361 3-7-23-31 17-881 3-4993 48 3 2 - 1609 7-2069 3- 'l 1-439 161088 4124 98 71-211 175 598 7795 7-2141 13-1153 49 43-337 3-4831 7-19-109 3 4 -179 99 3- 19- 263 11 -20-17 B.4999 53-283 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. .., IX. PRIME AND COMPOSITE NUMBERS. 133 Num. 1 3 7 9 Num. 1 3 7 9 1500 7-2143 3 2 -1667 43-349 3-5003 1550 3-5167 37-419 3 2 -1723 13-1193 01 17-883 176467 4846 176 583 1808 23-653 51 190 639 7978 3-5171 59-263 3-7-739 02 3 2 -1669 83-181 3-5009 7-19-113 52 11-17-83 19 2 -43 191 087 5530 53-293 03 176 987 8748 3-5011 11-1367 3 3 -557 53 3-31-167 7 2 -3l7 3-5179 41-379 04 13 2 -89 7 2 -307 41-367 101-149 54 191 478 9604 3 2 -ll -157 7-2221 3-71-73 05 3-29-173 177 623 0616 3 2 -7-239 11-37 2 55 191 758 8214 103-151 47-331 191 981 6808 06 177 853 8085 3-5021 13-19-61 3-5023 56 3 2 -7-13-19 79-197 3-5189 192 260 7186 07 7-2153 178 199 6991 178 314 9348 17-887 57 23-677 3-29-179 37-421 3 3 -577 08 3-11-457 If 8 487 7310 3-47-107 79-191 58 192 595 3276 192 651 0707 11-13-109 7-17-131 09 178 718 0191 3 3 -13-43 31-487 3-7-719 59 3-5197 31-503 3 2 -1733 19-821 1510 179 005 7076 11-1373 1791782292 29-521 1560 193 152 4369 3-7-743 193 819 4304 3-ll 2 -43 11 3' 2 -23-73 7-17-127 3-5039 13-1163 61 67-233 13-1201 7-23-97 193 653 2249 12 179 580 5134 3-71 2 7-2161 3 2 -41 2 62 3-41-127 17-919 3-5209 193 931 1912 13 179 867 6313 37-409 180 039 8109 180 097 1890 63 7 2 -ll-29 3 4 -193 19-823 3-13-401 14 3-7 2 -103 19-797 3 4 - 11 -17 180 383 9656 64 194 264 5160 194320 0453 194 431 0826 194 486 5905 15 109-139 3-5051 23-659 3-31-163 65 3 2 -37-47 11-1423 3-17-307 7-2237 16 180 727 8477 59-257 29-523 7-11-197 66 194 819 4896 3-23-227 194 985 8434 3 2 -l741 17 3-13-389 1810714578 3-5059 43-353 67 195 096 7106 7-2239 61-257 1958183601 18 17-19-47 3 2 -7-241 181 471 9929 3-61-83 68 3-5227 195 429 1425 3 3 -7-83 29-541 19 11-1381 181 643 5378 7-13-167 181 815 0150 69 13-17-71 3-5231 11-1427 3-5233 1520 3 3 -563 23-661 3-37-137 67-227 1570 7-2243 41-383 113-139 23-683 21 7-41-53 3-11-461 182 329 0406 3 2 -19-89 71 3-5237 19-827 3-13 2 -31 11-1429 22 31-491 13-1171 182 614 3477 97-157 72 79-199 3 2 -1747 196 645 8868 3-7 2 -107 23 3-5077 182 785 4421 3 2 -1693 7 2 -311 73 196 756 3311 196 811 5427 196 921 9448 196 977 1354 24 183 013 4631 3-5081 79-193 3-13-17-23 74 3 3 -ll-53 7-13-173 3-29-181 197 252 9830 25 101-151 7-2179 11-19-73 183 526 0730 75 19-829 3-59-89 7-2251 3 2 -l7-103 26 3-5087 183 639 9042 3-7-727 183 810 5951 76 197 583 7690 11-1433 197 749 0676 13-1213 27 183 867 4772 3 2 -1697 184 038 0786 3-11-463 77 3-7-751 197 914 3033 3 2 -1753 31-509 28 7-37-59 17-29-31 184 322 2656 184379 0807 78 43-367 3-5261 198 299 6090 3-19-277 29 3 2 -1699 41-373 3-5099 184 663 0446 79 198 409 6335 17-929 198 574 6181 7-37-61 1530 11-13-107 3-5101 184 8900822 3 7 -7 1580 3-23-229 198 739 5401 3-11-479 198 904 3995 31 61-251 185 060 2825 l7 2 -53 185 230 4162 81 97-163 3 2 -7-251 199 124 1146 3-5273 32 3-5107 7-11-199 3 2 - 13- 131 185 513 8242 82 13-1217 199 288 8281 7 2 -17-19 11-1439 33 185 570 4836 3-19-269 7 2 -313 3-5113 83 3 2 -1759 71-223 3-5279 47-337 34 23 2 -29 67-229 103-149 186 080 0861 84 7-31-73 3-5281 13-23-53 3 3 -587 35 3-7-17-43 13-1181 3-5119 186 362 9404 85 11 2 -131 83-191 101-157 200 275 7991 36 186 419 4892 3 3 -569 11 2 -127 3-47-109 86 3-17-311 29-547 3 2 -41-43 7-2267 37 19-809 186 758 6272 186 871 6144 7-13 3 87 59-269 3-11-13-37 2007684448 3-67-79 38 3 2 -1709 187 041 0400 3-23-223 11-1399 88 200 877 8457 7-2269 201 041 8955 201 096 5650 39 187 266 8382 3-7-733 89-173 3 2 . 29-59 89 3-5297 23-691 3-7-757 13-1223 1540 187 548 9209 73-211 7-31-71 19-811 1590 201 424 4376 3 3 -19-31 201 588 2811 3-5303 41 3-11-467 187 887 1784 3 3 -571 17-907 91 7-2273 201 752 0628 11-1447 201 915 7827 42 7-2203 3-53-97 1882814795 3-37-139 92 3 2 -29-61 202 024 8951 3-5309 17-937 43 13-1187 11-23-61 43-359 188 6191672 93 89-179 3-47-113 202 406 5726 3 2 - 7. 11 -23 44 3-5147 188 731 6714 3-19-271 7-2207 94 19-839 107-149 37-431 41-389 45 188 956 5925 3 2 -17-101 13-29-41 3-5153 95 3-13-409 7-43-53 3 4 - 197 203 005 6747 46 189 237 5802 7-47 2 189 406 0855 31-499 96 11-1451 3-17-313 7-2281 3-5323 47 3 4 - 191 189 574 5255 3-7-11-67 23-673 97 203 332 1097 203 386 4917 13-1229 19- 29 2 48 113-137 3-13-397 17-911 3 2 -1721 98 3-7-761 il-1453 3-73 2 59-271 49 7-2213 190 135 5209 190 247 6330 11-1409 99 203 875 6233 3 2 -1777 17-941 3-5333 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. . 134 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 1600 204 147 1252 13-1231 204 809 9449 7-2287 1650 29-569 3-5501 17-971 3-5503 01 3 3 -593 67-239 3-19-281 83-193 51 11-19-79 7 2 -337 83-199 81798 02 37-433 3-7 2 -109 11-31-47 3 2 -13-137 52 3-5507 13-31-41 3-7-787 218 240 :,71>7 03 17-23-41 205 014 7926 7-29-79 43-373 53 61-271 3 2 -11.167 23-719 3-37-149 04 3-5347 61-263 3 2 -1783 11-1459 54 7-17- 139 71-233 218 719 2669 13-19-67 05 7-2293 3-5351 2056644074 3-53-101 55 3 3 -613 218 876 7151 3-5519 29-571 06 205 772 5821 205 826 6594 205 934 7937 205 988 8508 56 219 086 5572 3-5521 219 248 8722 3 2 -7-263 07 3-11-487 206 096 9447 3-23-233 7-2297 57 73-227 219 4011804 11 2 -137 59-281 08 13-1237 3 2 -1787 206 475 0618 3-31-173 58 3-5527 7-23-103 3 2 -19-97 53-313 09 206 583 0848 7-ll 2 -19 2067449441 17-947 59 47-353- 3-5531 7-2371 3-11-503 1610 3 2 -1789 206 906 7929 3-7-13-59 89-181 1660 13-1277 2201865679 220 291 1857 17-977 11 207 122 4977 3-41-131 71-227 3 4 -199 61 3-7 2 -113 37-449 3-29-191 220 604 8878 12 73.47 23-701 207 553 5859 127 2 62 11-1511 3 2 -1847 13-1279 3-23-211 13 3-19-283 13-17-73 3»- 11- 163 207 876 6216 63 220 918 3636 220 970 5875 127-131 7-237 7 14 207 930 4375 3-5381 67-241 3-7-769 64 3 2 -43 2 11-17-89 3-31-179 881 :;-si533 15 31-521 29-557 107-151 11-13-113 65 221 440 8208 3 - 7 • 1 3 • 61 221 596 7857 3 3 -617 16 3-5387 7-2309 3-17-317 19-23-37 66 2217010644 19-877 7-2381 79-211 17 103-157 3 3 -599 7-2311 3-5393 67 3-5557 222 013 7502 3 2 - 17-109 13-1283 18 11-1471 209 059 0341 209 166 3667 209 220 0231 68 7-2383 3-67-83 11-37-41 3-5563 19 3 2 -7-257 209 327 3159 3-5399 97-167 69 222 482 8571 222 584 8934 59-283 288 SM 4647 1620 17-953 3-11-491 19-853 3 2 -1801 1670 3-19-293 222 794 4811 3-5569 7 2 -ll-31 21 13-29-43 31-523 209 970 5167 7 2 -331 71 17-983 3 3 -619 73-229 3-5573 22 3-5407 2101811682 3 3 -601 210 291 7603 72 23-727 7-2389 43-389 223 469 9812 23 210 345 2778 3-7-773 13-1249 3-5413 73 3 2 -ll-13 2 29-577 3-7-797 19-881 24 109-149 37-439 7.11-211 210 826 6387 74 223 7813964 3-5581 223 937 0203 3 2 -1861 25 3-5417 210 933 5854 3-5419 71-229 75 7-2393 11-1523 13-1289 JJ4 -_'4s 1010 26 7-23-101 3 2 - 13 -139 211807 4667 1 -11-17-29 76 3-37 -151 2248517450 3 6 -23 41-409 27 53-307 211467 6244 41-397 73-223 77 31-541 3-5591 19-883 3-7-17.47 28 3 6 -67 19-857 3-61-89 7-13-179 78 97-173 13-1291 224 973 0904 103-163 29 11-1481 3-5431 43-379 3 2 -1811 79 3-29-193 .7-2399 3-11-509 107-157 1630 212 214 2474 7- 17-137 23-709 47-347 1680 53-317 3 2 -1867 7 5 3-13-431 31 3-5437 11-1483 3 2 -7 2 -37 212 693 5424 81 225 593 5482 17-23-43 67-251 11 2 -139 32 19-859 3-5441 29-563 3 - 5443 82 3 3 -7-89 225 903 4449 3-71-79 836 008 UM 33 7-2333 218 065 9621 17-31 2 218 225 4728 83 226 109 9200 3-31-181 113-149 3 s - 1871 34 3-13-419 59-277 3-5449 218 491 1988 84 11-1531 226 419 4486 17-991 7-29-83 35 83-197 3 2 -23-79 11-1487 3.7.19.41 85 3-41-137 19-887 3 2 -1873 23-733 36 213 809 8446 213 862 9304 13-1259 214 022 1487 86 13-1297 3-7-11 -7:: 101-167 3-5623 37 3 2 - 17- 107 7-2339 3-53-103 11-1489 87 227140 8254 47-359 T - J 1 1 1 an mm 7182 38 214 840 4103 3-43-127 7-2341 3 3 -607 88 3-17-331 227 449 6205 3-13-433 an Mswff 39 37-443 13 2 -97 19-863 23 s -31 89 7-19-127 3 2 -1877 61-277 3-43-131 1640 3- 7-11-71 47-349 3 2 -1823 61-269 1690 227 912 4018 227 968 7915 11-29-53 3 7 i;.7 41 215 185 0455 3-5471 215293 7982 3-13-421 91 3 2 - 1879 13-1301 3-5639 7 U 1 7 £2 215 899 6011 11-1493 215 558 2571 7-2347 92 228 426 0255 ::•:><; 11 B8 ">T'.i 9942 3 4 -11.19 43 3-5477 215 716 8552 3-5479 17-967 93 228 6S2 6097 7-11 •■'>:• 228 836 4875 13-1303 44 41-401 3 4 -7-29 216 086 6924 3-5483 94 3-5647 228 990 8108 3*- 7-269 17-997 45 216 192 8024 216 245 0977 7-2351 109-151 95 11-23-67 3-5651 ::i ..vi 7 3-5653 46 3 2 . 31-59 101-163 3-11-499 43-383 96 7 • 2423 229 502 6621 19»-47 71-239 47 7-13-181 3-17 2 -19 216 8781417 3 2 -1831 97 3-5657 11-1543 3-5659 229 912 1088 48 216 988 5594 53-311 2171416879 11-1499 98 229 963 2620 3 3 -17-37 280116 6868 3- 7- 809 49 3-23-239 217 299 6590 3 3 - 13-47 7-2357 99 13-1307 280 270 0574 23-739 89-191 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 135 Num. 1 3 7 9 Num. 1 3 7 9 1700 3 2 -1889 7 2 -347 3-5669 73-233 1750 11-37-43 23-761 7-41-61 248 261 3427 01 230 729 8446 3-53-107 7-11-13-17 3 2 -31-61 51 3-13-449 83-211 3-5839 243 509 3126 02 230 985 0717 29-587 231 138 1360 231 189 1455 52 7-2503 3 3 -ll-59 17-1031 3-5843 03 3-7.811 231 291 1464 3 3 -631 11-1549 53 47-373 89-197 13-19-71 244 004 8281 04 2314950764 3 -13 -19 -2 J 231 647 9612 3-5683 54 3 2 -1949 53-331 3-5849 7-23-109 05 17 2 -59 231 800 7921 37-461 7-2437 55 244 301 8662 3-5851 97-181 3 2 -1951 06 3-ll 2 -47 113-151 3-5689 13 2 -101 56 17-1033 7-13-193 11-1597 244 747 0428 07 43-397 3 2 -7-271 282 411 5784 3-5693 57 3-5857 244 845 9090 3 4 -7-31 2449941661 08 19-29-31 11-1553 7-2441 23-743 58 245 043 5739 3-5861 43-409 3-11-13-41 09 3 4 -211 232 818 2926 3-41-139 232 970 7128 59 7*. 359 73-241 245 438 6340 245 487 9913 1710 7 2 -349 3-5701 233 173 8554 3 2 -1901 1760 3-5867 29-607 3-5869 245 734 6935 11 71-241 109-157 233 427 6507 17-19-53 61 11-1601 3 2 -19-103 79-223 3-7-839 12 3-13-439 233 579 8567 3 2 -ll-l73 7-2447 62 67-263 246 079 8412 246 178 4045 17 2 -61 13 37-463 3-5711 233 934 7967 3-29-197 63 3 3 -653 7-11-229 3-5879 31-569 14 61-281 7-31-79 13-1319 11-1559 64 13-23-59 3-5881 7-2521 3 2 -37-53 15 3-5717 17-1009 3-7-19-43 234 4919742 65 19-929 127-139 246 916 9170 246 966 1066 16 131 2 3 2 -1907 234 694 4071 3-59-97 66 3-7 -29 2 17-1039 3 2 -13-151 247 211 9707 17 7-11-223 13-1321 89-193 41-419 67 41-431 3-43-137 11-1607 3-71-83 18 3 2 -23-83 235 098 9901 3-17-337 235250 6116 68 247 506 8241 247 555 9469 23-769 7 2 -19 2 19 235 301 1403 3-11-521 29-593 3 3 -7 2 -13 69 3-5897 13-1361 3-17-347 11-1609 1720 103-167 235 604 1893 235 705 1587 235 755 6346 1770 31-571 3 2 -7-281 248 144 9873 3-5903 21 3-5737 7-2459 3 2 -1913 67-257 71 89-199 248 292 1226 7-2531 13-29-47 22 17-1013 3-5741 7-23-107 3-5743 72 3 2 -ll-179 37-479 3-19-311 248 684 2400 23 236 310 4824 19-907 11-1567 236 512 0697 73 7-17-149 3-23-257 248 880 1660 3 5 -73 24 3-7-821 43-401 3-5749 47-367 74 113-157 11-1613 249 124 9493 249 173 8894 25 13-1327 3 5 -71 236 965 2991 3-11-523 75 3-61-97 41-433 3 2 -1973 7-43-59 26 41-421 61-283 31-557 7-2467 76 249 467 4143 3-31-191 109-163 3-5923 27 3 2 -19-101 23-751 3-13-443 37-467 77 13-1367 7-2539 29-613 23-773 28 11-1571 3-7-823 59-293 3 2 - 17-113 78 3-5927 250 005 0285 3-7 2 -ll 2 250 151 5351 29 237 820 1108 237 8708415 7 2 -353 23S 020 9987 79 250 200 3597 3 3 -659 13-37 2 3-17-349 1730 3-73-79 11 3 -13 3 3 -641 19-911 1780 7-2543 19-937 250 590 7587 11-1619 31 7-2473 3-29-199 238 472 6569 3-23-251 81 3 2 -1979 47-379 3-5939 103-173 32 238 572 9617 17-1019 238 723 3754 13-31-43 82 71-251 3-13-457 251 078 2645 3 2 -7-283 3t! 3-53-109 238 873 7370 3-5779 7-2477 . 83 11-1621 17-1049 251 321 8123 251 370 5055 34 239 074 1382 3 2 -41-47 11-19-83 3-5783 84 3-19-313 7-2549 3 3 -661 13-1373 35 239 324 5098 7-37-67 17-1021 239 524 7032 85 251 662 5500 3-11-541 7-2551 3-5953 36 3 3 -643 97-179 3-7-827 11-1579 86 53-337 251 954 8982 17-1051 107-167 37 29-599 3-5791 239 974 8011 3 2 -1931 87 3-7-23-37 61-293 3-59-101 19-941 38 7-13-191 240 124 7802 240 224 6541 240 274 6075 88 252 391 8032 3 2 -1987 31-577 3-67-89 39 3-11-17-31 240 3744970 3 2 -1933 127-137 89 252 634 6157 29-617 11-1627 7-2557 1740 240 574 2070 3-5801 13 2 -103 3-7-829 1790 3 4 -13-l7 252 925 8117 3-47-127 253 071 3365 41 23-757 11-1583 240 973 3518 241 023 2192 91 253 119 8339 3-7-853 19-23-41 3 2 -ll-181 42 3-5807 7-19-131 3-37-157 29-601 92 253 862 2398 253 410 7048 7-13-197 253 556 0672 43 241 322 3029 3 2 - 13 -149 7-47-53 3-5813 93 3-43-139 79-227 3 2 -1993 253 798 2299 44 107-163 241 621 1808 73-239 241 770 5426 94 7-11-233 3-5981 131-137 3-31-193 45 3 2 -7-277 31-563 3-11-23 2 13-17-79 95 29-619 13-1381 254 233 7827 254 282 1505 46 19-919 3-5821 242 218 3202 3 3 -647 96 3-5987 11-23-71 3-53-113 7-17-151 47 242 317 7637 101-173 242 466 8862 7-11-227 97 254 572 2442 3 2 -1997 254 717 2184 3-13-461 48 3-5827 242 6159576 3 2 -29-67 242 764 9778 98 254 813 8410 7 2 -367 254 958 7847 255 007 0218 49 242 814 6398 3- 7 3 - 17 242 963 5918 3-19-307 99 3 2 -1999 19-947 3-7-857 41-439 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 136 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 Num. 1 3 7 9 1800 47-383 3-17-353 11-1637 3 3 -23-29 1850 3-7-881 267 242 1488 3-31-199 83-223 01 7-31-83 255 586 0490 43-419 37-487 51 107-173 3 2 -ll 2 -17 267570 6266 3-6173 02 3-6007 67-269 3 2 -2003 ll 2 - 149 52 267 664 4817 267 7118267 97-191 7-2647 03 13-19-73 3-6011 17-1061 3-7-859 53 3 2 -29-71 43-431 3-37-167 268 086 3044 04 256 260 6065 256308 7491 256 405 0188 256 453 1449 54 268 188 1589 3-7-883 17-1091 3 4 -229 05 3-11-547 7-2579 3-13-463 256 693 6980 55 13-1427 268 414 1446 7- 11-241 67-277 06 256 741 7926 3 4 -223 7-29-89 3-19-317 56 3-23-269 19-977 3 2 -2063 31-599 07 17-1063 11-31-53 257126 8580 101-179 57 7 2 -379 3-41-151 13-1429 3-11-563 08 3 2 -7 2 -41 13 2 -107 3-6029 257 414 5588 58 17-1093 269 115 8269 269 209 2989 29-641 09 79-229 3-37-163 257 606 5864 3 2 -2011 59 3-6197 269 849 4693 3-6199 7-2657 1810 23-787 43-421 19-953 7-13-199 1860 11-19-89 3 3 -13-53 23-809 3-6203 11 3-6037 59-307 3 3 -ll-61 258 134 2250 61 37-503 7-2659 269 909 6987 43-433 12 258 182 1604 3-7-863 258 325 9347 3-6043 62 3 2 -2069 11-1693 3-7-887 13-1433 13 258 421 7579 258 469 6616 7-2591 11-17-97 63 31-601 3-6211 270376 0052 3 2 -19-109 14 3-6047 258 709 1006 3-23-263 258 852 7006 64 7-2663 103-181 29-643 17-1097 15 7-2593 3 2 -20l7 67-271 3-6053 65 3-6217 23-811 3 3 -691 47-397 16 11-13.127 41-443 37-491 259 831 0249 66 270 984 9129 3-6221 11-1697 3-7 2 -127 17 3 3 -673 17-1069 3-73-83 7 3 -53 67 271 167 5789 71-263 19-983 271 353 6221 18 259 617 7668 3-11-19-29 13-1399 3 2 -43-47 68 3-13-479 7-17-157 3-6229 11-1699 19 259 856 5789 7-23-113 31-587 260 047 5250 69 271 682 5875 3 2 -31-67 7-2671 3-23-271 1820 3-6067 109-167 3 2 -7-l7 2 131-139 1870 271 864 8302 59-317 13-1439 53-353 21 260 838 7944 3-13-467 260 476 8583 3-6073 71 3 5 -7-ll 272 143 4176 3-17-367 272 282 6448 22 7-19-137 260 619 8752 11-1657 260 762 8449 72 97-193 3-79 2 61-307 3 2 -2081 23 3-59-103 260 858 1320 3-6079 13-23-61 73 272 560 9639 11-13-13141-457 7-2677 24 17-29-37 3 2 -2027 71-257 3-7-11-79 74 3-6247 272 839 1052 3 2 -2083 272 97S 1091 25 261 286 6651 261 834 2538 261 429 4156 19.31 s 75 17-1103 3-7-19-47 278 163 8784 3-13 2 -37 26 3 2 -2029 7-2609 3-6089 261 714 7758 76 73-257 29-647 7 2 -383 137* 27 ll 2 - 151 3-6091 7 2 -373 3 3 -677 77 3-6257 273 533 6802 3-11-569 89-211 28 101-181 47-389 262 142 4649 262 189 9599 78 7-2683 3 2 -2087 273 857 4854 3-6263 29 3-7-13-67 11-1663 3 2 -19-107 29-631 79 19-23-43 273 996 1138 274 088 5414 11-1709 1830 262 474 S210 3-6101 262 617 1815 3-17-359 1880 3 2 -2089 274 227 1460 3-6269 7-2687 31 262 712 0626 262 759 4954 13-1409 7-2617 81 13-1447 3-6271 31-607 3 3 -17-41 32 3-31-197 73-251 3-41-149 268 138 7712 82 11-29-59 7-2689 67-281 1S-991 33 23-797 3 3 -7-97 11-1667 3-6113 83 3-6277 37-509 3 s - 7- 13-23 275 057S461 34 263 423 0109 13-17-83 7-2621 59-311 84 83-227 3-11-571 47-401 3-61-103 35 3 2 -2039 263 707 0646 3-29-211 11-1669 85 7-2693 17-1109 109-173 275 518 6605 36 7-43-61 3-6121 264 088 2260 3 2 -13-157 86 3-6287 13-1451 3-19-331 275 748 8845 37 264 182 7972 19-967 17-23-47 264 821 8778 87 113-167 3 4 -233 43-439 3-7.29- 31 38 3-11-557 31-593 3 4 -227 7-37-71 88 79-239 23-821 11-17-101 13-1453 39 53-347 3-6131 264 747 0084 3.6133 89 8*. 2099 7-2699 3-6299 276 488 8250 1840 264 841 4258 7-11-239 79-233 41-449 1890 41-461 3-6301 7-37-73 3* - 1 1 • 1 9 1 41 3-17 -19 2 265 124 5582 3-7-877 113-163 91 276 714 4946 276 760 4226 276 852 2688 276S9Sn;j 42 13 3 -109 3 2 -23-89 265 454 6858 3-6143 92 3-7-17-53 127-149 3 3 -701 23-823 43 7-2633 265 596 0281 103-179 265 787 3648 93 11-1721 3-6311 29-653 3-69-107 44 3 3 -683 265 881 6663 3-11-13-43 19-971 94 13-31-47 19-997 277 540 4551 7--J7H7 45 266 019 9089 3-6151 266 161 1122 3 2 -7-293 95 3-6317 11-1723 3- 71- 89 277 815 4266 46 266 255 2228 37-499 59-313 11-23-73 96 67-283 3 2 - 7- • I:: 13-1459 3-6323 47 3-47-131 7 2 -13-29 3 2 -2053 17-1087 97 61-311 278 186 0067 7i>711 278278 8258 48 266 725 4670 3-61-101 7-19-139 3-6163 98 3 3 -19-37 41-463 3-6329 17-1117 49 11-41 2 267 007 8697 53-349 13-1423 99 7-2713 3-13-487 1 1-157 3 2 -21U Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 137 - Num. 1 3 7 9 Num. 1 3 7 9 1900 278 776 4580 31-613 83-229 278 959 2707 1950 290 056 8823 3 2 -ll-197 290 190 4840 3-7-929 01 3-6337 279 050 64S2 3 2 -2113 7 -11-13-19 51 109-179 13-19-79 29-673 131-149 02 23-827 3-17-373 53-359 3-6343 52 3 4 -241 7-2789 3-23-283 59-331 03 279 461 6093 7-2719 279 598 5099 79-241 53 290 724 4800 3-17-383 7-2791 3 2 - 13- 167 04 3-11-577 137-139 3-7-907 43-443 54 290 946 7847 290 991 2320 11-1777 113-173 • 05 279 917 7770 3 2 -29-73 •17-19-59 3-6353 55 3-7 3 -19 291 213 4003 3 2 -41-53 291 346 6467 06 7 2 -389 11-1733 23-829 280 327 9187 56 31-631 3-6521 17-1151 3-11-593 07 3 2 - 13- 163 280 419 0088 3-6359 280 555 6080 57 291 613 0169 23 2 -37 291 746 1408 7-2797 08 280 601 1315 3-6361 280 737 6735 3 3 -7-101 58 3-61-107 .291 879 2239 3-6529 19-1031 09 17-1123 61-313 13 2 -113 71-269 59 11-13-137 3 2 -7-311 292 189 5926 3-47-139 1910 3-6367 7-2729 3 2 -ll-193 97-197 1960 17-1153 292 322 5399 7-2801 292 455 4465 11 29-659 3-23-277 7-2731 3-6373 61 3 2 -2179 11-1783 3-13-503 23-853 12 281 510 6015 13-1471 31-617 11-37-47 62 7-2803 3-31-211 19-1033 3 3 -727 13 3-7-911 19 2 -53 3-6379 281 919 2424 63 67-293 29-677 73-269 41-479 14 281 964 6233 3 3 -709 41-467 3-13-491 64 3-6547 13-1511 3 2 -37-59 7 8 -401 15 11-1741 107-179 282 327 4992 7 2 -17-23 65 43-457 3-6551 11-1787 3-6553 16 3 2 -2129 282 463 4996 3-6389 29-661 66 293 605 6032 7-53 2 71-277 13-17-89 17 19-1009 3-7- 11- 83 127-151 3 2 -2131 67 3-79-83 103-191 3-7-937 11-1789 18 282 871 2453 282 916 5268 7-2741 31-619 68 294 047 1613 3 9 294 179 5413 3-6563 19 3-6397 17-1129 3 6 -79 73-263 69 7-29-97 47-419 294 400 0849 294 444 1802 1920 7-13-211 3-37-173 283 459 5364 3-19-337 1970 3 2 -ll-199 17-19-61 3-6569 294 664 5895 21 283 549 9720 283 595 1828 11-1747 288 730 7868 71 23-857 3-6571 294 840 8364 3 2 -7-313 22 3-43-149 47-409 2 -13-17-29 7-41-67 72 13-37-41 11 2 -163 295 061 0446 109-181 23 284 001 8679 3 2 -2137 284 187 3450 3-ll 2 -53 73 3-6577 7-2819 3 3 -17-43 295 825 1470 24 71-271 7-2749 19-1013 2844081725 74 19-1039 3-6581 7 2 -13-31 3-29-227 25 3 3 -23.31 13-1481 3-7 2 -131 284 633 7332 75 295 589 0890 295 633 0637 23-859 295 764 9612 26 11-17-103 3-6421 284 814 0974 3 2 -2141 76 3-7-941 295 852 8706 3-11-599 53-373 27 7-2753 284 949 3214 37-521 13-1483 77 17-1163 3 2 -13 3 296 160 4135 3-19-347 28 3-6427 11-1753 3 2 -2143 285 3Q9 7181 78 131-151 73-271 47-421 7-11-257 29 101-191 3-59-109 23-839 3-7-919 79 3 3 -733 296 511 6247 3-6599 13-1523 1930 285 579 8107 97-199 43-449 285 759 7825 1980 296 687 1238 3-7-23-41 29-683 3 2 -31-7l 31 3-41-157 7-31-89 3-47-137 285 984 6425 81 11-1801 296 950 2395 7-19-149 297 081 7377 32 139 2 3 2 -19-113 7-11-251 3-17-379 82 3-6607 43-461 3 2 -2203 79-251 33 13-1487 286 299 2509 61-317 83-233 83 7-2833 3-11-601 83-239 3-17-389 34 3 2 -7-307 23- 29 2 3-6449 11-1759 84 297 563 5571 297 607 8824 89-223 23-863 35 37-523 3-6451 13-1489 3 4 -239 85 3-13-509 297 826 1426 3-6619 7-2837 36 19-1019 17 2 -67 107-181 7-2767 86 298 001 1114 3 2 -2207 298 132 2918 3-37-179 37 3-11-587 287 196 8785 3 2 -2153 287 331 3627 87 31-641 7-17-167 11-13-139 103-193 38 2ST 376 1816 3-7-13-712875106103 3-23-281 88 3 2 -47 2 59-337 3-7-947 298 612 9478 39 287 600 2064 11-41-43 7-17-163 19-1021 89 298 656 6174 3-19-349 101-197 3 3 -ll-67 1940 3-29-223 287 868 8837 3-6469 13-1493 1990 7-2843 13-1531 17-1171 43-463 41 7-47-59 3 3 -719 288 182 1306 3-6473 91 3-6637 299 136 6937 3 2 -2213 299 267 5316 42 288 271 5883 288 816 8102 288 405 7402 288450 4483 92 11-1811 3-29-229 299 441 9208 3-7-13-73 43 3 2 -17-127 288 539 8507 3-11-19-31 7-2777 93 19-1049 31-643 299 659 8089 127-157 44 288 718 6003 3-6481 288 852 6142 3 2 -2161 94 3-17 2 -23 7 2 -ll-37 3-61-109 299 921 1303 45 53-367 7 2 -397 289 075 8789 11-29-61 95 71-281 3 3 -739 7-2851 3-6653 46 3-13-499 289 209 7826 3 3 -7-103 289 343 6451 96 800 182 2946 300 225 8068 41-487 19-1051 47 289 888 2568 3-6491 289 522 0648 3-43-151 97 3 2 -7-317 300 443 3020 3-6659 300 573 7469 48 7-ll 2 -23 289 655 8305 13-1499 289 789 5556 98 13-29-53 3-6661 11-23-79 3 2 -2221 49 3-73-89 101-193 3-67-97 17-31-37 99 300 834 5192 800 877 9660 300 964 8466 7-2857 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 138 X. SQUARES. 1 2 3 4 5 6 7 8 9 1 4 9 16 25 36 49 64 81 i 100 121 144 169 196 225 256 289 324 361 2 400 441 484 529 576 625 676 729 784 841 3 900 961 1024 1089 1156 1225 1296 1369 1444 1521 4 1600 1681 1764 1849 1936 2025 2116 2209 2304 2401 5 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 6 3600 3721 3844 3969 4096 4225 4356 4489 4624 4761 7 4900 5041 5184 5329 5476 5625 5776 5929 6084 6241 8 6400 6561 6724 6889 7056 7225 7396 7569 7744 7921 9 8100 8281 8464 8649 8836 9025 9216 9409 9604 9801 10 1 0000 1 0201 1 0404 1 0609 1 0816 1 1025 1 1236 1 1449 1 1664 1 1881 11 2100 2321 2544 2769 2996 3225 3456 3689 3924 4161 12 4400 4641 4884 5129 5376 5625 5876 6129 6384 6641 13 6900 7161 7424 7689 7956 8225 8496 8769 9044 9321 14 9600 9881 2 0164 2 0449 2 0736 2 1025 2 1316 2 1609 2 1904 2 2201 15 2 2500 2 2801 3104 3409 3716 4025 4336 4649 4964 5281 16 5600 5921 6244 6569 6896 7225 7556 7889 8224 8561 17 8900 9241 9584 9929 3 0276 3 0625 3 0976 3 1329 3 1684 3 2041 18 3 2400 3 2761 3 3124 3 3489 3856 4225 4596 4969 5344 5721 19 6100 6481 6864 7249 7636 8025 8416 8809 9204 9601 20 4 0000 4 0401 4 0804 4 1209 4 1616 4 2025 4 2436 4 2849 4 3264 4 3681 21 4100 4521 4944 5369 5796 6225 6656 7089 7524 7961 22 8400 8841 9284 9729 5 0176 5 0625 5 1076 5 1529 5 1984 5 2441 23 5 2900 5 3361 5 3824 5 4289 4756 5225 5696 6169 6644 7121 24 7600 8081 8564 9049 9536 6 0025 6 0516 6 1009 6 1504 6 2001 25 6 2500 6 3001 6 3504 6 4009 6 4516 5025 5536 6049 6564 7081 26 7600 8121 8644 9169 9696 7 0225 7 0756 7 1289 7 1824 7 2361 27 7 2900 7 3441 7 3984 7 4529 7 5076 5625 6176 6729 7284 7841 28 8400 8961 9524 8 0089 8 0656 8 1225 8 1796 8 2369 8 2944 8 3521 29 8 4100 8 4681 8 5264 5849 6436 7025 7616 8209 8804 9401 30 9 0000 9 0601 9 1204 9 1809 9 2416 9 3025 9 3636 9 4249 9 4864 9 5481 31 6100 6721 7344 7969 8596 9225 9856 10 0489 10 1124 10.1761 32 10 2400 10 3041 10 3684 10 4329 10 4976 10 5625 10 6276 6929 7584 8241 33 8900 9561 11 0224 11 0889 11 1556 11 2225 11 2896 11 3569 11 4244 11 4921 34 11 5600 11 6281 6964 7649 8336 9025 9716 12 0409 12 1104 12 1801 35 12 2500 12 3201 12 3904 12 4609 12 5316 12 6025 12 6736 7449 8164 8881 36 9600 13 0321 13 1044 13 1769 13 2496 13 3225 13 3956 13 4689 13 5424 13 6161 37 13 6900 7641 8384 9129 9876 14 0625 14 1376 14 2129 14 2884 14 3641 38 14 4400 14 5161 14 5924 14 6689 14 7456 8225 8996 9769 15 0544 15 1321 39 15 2100 15 2881 15 3664 15 4449 15 5236 15 6025 15 6816 15 3609 8404 9201 40 16 0000 16 0801 16 1604 16 2409 16 3216 16 4025 16 4836 16 5649 16 6464 16 7281 41 8100 8921 9744 17 0569 17 1396 17 2225 17 3056 17 3889 17 4724 17 5561 42 17 6400 17 7241 17 8084 8929 9776 18 0625 18 1476 18 2329 18 3184 18 4041 43 18 4900 18 5761 18 6624 18 7489 18 8356 9225 19 0096 19 0969 19 1844 lit 2721 44 19 3600 19 4481 19 5364 19 6249 19 7136 19 8025 8916 9809 20 0704 20 1601 45 20 2500 20 3401 20 4304 20 5209 20 6116 20 7025 20 7936 20 8849 9764 210681 46 21 1600 21 2521 21 3444 214369 21 5296 21 6225 21 7156 21 8089 21 9024 9961 47 22 0900 22 1841 22 2784 22 3729 22 4676 22 5625 22 6576 22 7529 22 8484 22 9441 48 23 0400 23 1361 23 2324 23 3289 23 4256 23 5225 23 6196 23 7169 23 8144 23 9121 49 24 0100 24 1081 24 2064 24 3049 24 4036 24 5025 24 6016 24 7009 24 8004 24 9001 50 1 2 3 4 5 G 7 8 9 X. SQUARES. 139 50 1 2 3 4 5 6 7 8 9 50 25 0000 25 1001 25 2004 25 3009 25 4016 25 5025 25 6036 25 7049 25 8064 25 9081 51 26 0100 26 1121 26 2144 26 3169 26 4196 26 5225 26 6256 26 7289 26 8324 26 9361 52 27 0400 27 1441 27 2484 27 3529 27 4576 27 5625 27 6676 27 7729 27 8784 27 9841 53 28 0900 28 1961 28 3Q24 28 4089 28 5156 28 6225 28 7296 28 8369 28 9444 29 0521 54 29 1600 29 2681 29 3764 29 4849 29 5936 29 7025 29 8116 29 9209 30 0304 30 1401 55 30 2500 30 3601 30 4704 30 5809 30 6916 30 8025 30 9136 31 0249 31 1364 31 2481 56 31 3600 314721 31 5844 31 6969 31 8096 31 9225 32 0356 32 1489 32 2624 32 3761 57 32 4900 32 6041 32 7184 32 8329 32 9476 33 0625 33 1776 33 2929 33 4084 33 5241 58 33 6400 33 7561 33 8724 33 9889 34 1056 34 2225 34 3396 34 4569 34 5744 34 6921 59 34 8100 34 9281 35 0464 35 1649 35 2836 35 4025 35 5216 35 6409 35 7604 35 8801 60 36 0000 36 1201 36 2404 36 3609 36 4816 36 6025 36 7236 36 8449 36 9664 37 0881 61 37 2100 37 3321 37 4544 37 5769 37 6996 37 8225 37 9456 38 0689 38 1924 38 3161 62 38 4400 38 5641 38 6884 38 8129 38 9376 39 0625 39 1876 39 3129 39 4384 39 5641 63 39 6900 39 8161 39 9424 40 0689 40 1956 40 3225 40 4496 40 5769 40 7044 40 8321 64 40 9600 41 0881 41 2164 41 3449 414736 41 6025 41 7316 41 8609 41 9904 42 1201 65 42 2500 42 3801 42 5104 42 6409 42 7716 42 9025 43 0336 43 1649 43 2964 43 4281 66 43 5600 43 6921 43 8244 43 9569 44 0896 44 2225 44 3556 44 4889 44 6224 44 7561 67 44 8900 45 0241 45 1584 45 2929 45 4276 45 5625 45 6976 45 8329 45 9684 46 1041 68 46 2400 46 3761 46 5124 46 6489 46 7856 46 9225 47 0596 47 1969 47 3344 47 4721 69 47 6100 47 7481 47 8864 48 0249 48 1636 48 3025 48 4416 48 5809 48 7204 48 8601 70 49 0000 49 1401 49 2804 49 4209 49 5616 49 7025 49 8436 49 9849 50 1264 50 2681 71 50 4100 50 5521 50 6944 50 8369 50 9796 51 1225 51 2656 514089 51 5524 51 6961 72 51 8400 51 9841 52 1284 52 2729 52 4176 52 5625 52 7076 52 8529 52 9984 53 1441 73 53 2900 53 4361 53 5824 53 7289 53 8756 54 0225 54 1696 54 3169 54 4644 54 6121 74 54 7600 54 9081 55 0564 55 2049 55 3536 55 5025 55 6516 55 8009 55 9504 56 1001 75 56 2500 56 4001 56 5504 56 7009 56 8516 57 0025 57 1536 57 3049 57 4564 57 6081 76 57 7600 57 9121 58 0644 58 2169 58 3696 58 5225 58 6756 58 8289 58 9824 59 1361 77 59 2900 59 4441 59 5984 59 7529 59 9076 60 0625 60 2176 60 3729 60 5284 60 6841 78 60 8400 60 9961 61 1524 61 3089 614656 61 6225 61 7796 61 9369 62 0944 62 2521 79 62 4100 62 5681 62 7264 62 8849 63 0436 63 2025 63 3616 63 5209 63 6804 63 8401 80 64 0000 64 1601 64 3204 64 4809 64 6416 64 8025 64 9636 65 1249 65 2864 65 4481 81 65 6100 65 7721 65 9344 66 0969 66 2596 66 4225 66 5856 66 7489 66 9124 67 0761 82 67 2400 67 4041 67 5684 67 7329 67 8976 68 0625 68 2276 68 3929 68 5584 68 7241 83 68 8900 69 0561 69 2224 69 3889 69 5556 69 7225 69 8896 70 0569 70 2244 70 3921 84 70 5600 70 7281 70 8964 71 0649 71 2336 714025 71 5716 71 7409 71 9104 72 0801 85 72 2500 72 4201 72 5904 72 7609 72 9316 73 1025 73 2736 73 4449 73 6164 73 7881 86 73 9600 74 1321 74 3044 74 4769 74 6496 74 8225 74 9956 75 1689 75 3424 75 5161 87 75 6900 75 8641 76 0384 76 2129 76 3876 76 5625 76 7376 76 9129 77 0884 77 2641 88 77 4400 77 6161 77 7924 77 9689 78 1456 78 3225 78 4996 78 6769 78 8544 79 0321 89 79 2100 79 3881 79 5664 79 7449 79 9236 80 1025 80 2816 80 4609 80 6404 80 8201 90 81 0000 81 1801 81 3604 81 5409 81 7216 81 9025 82 0836 82 2649 82 4464 82 6281 91 82 8100 82 9921 83 1744 83 3569 83 5396 83 7225 83 9056 84 0889 84 2724 84 4561 92 84 6400 84 8241 85 0084 85 1929 85 3776 85 5625 85 7476 85 9329 86 1184 86 3041 93 86 4900 86 6761 86 8624 87 0489 87 2356 87 4225 87 6096 87 7969 87 9844 88 1721 94 88 3600 88 5481 88 7364 88 9249 89 1136 89 3025 89 4916 89 6809 89 8704 90 0601 95 90 2500 90 4401 90 6304 90 8209 910116 91 2025 913936 91 5849 91 7764 919681 96 92 1600 92 3521 92 5444 92 7369 92 9296 93 1225 93 3156 93 5089 93 7024 93 8961 97 94 0900 94 2841 94 4784 94 6729 94 8676 95 0625 95 2576 95 4529 95 6484 95 8441 98 96 0400 96 2361 96 4324 96 6289 96 8256 97 0225 97 2196 97 4169 97 6144 97 8121 99 98 0100 98 2081 98 4064 98 6049 98 8036 99 0025 99 2016 99 4009 99 6004 99 8001 100 1 2 3 4 5 6 7 8 9 140 XL CUBES. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0.000 .001 .008 .027 .064 .125 .216 .343 .512 .729 i 1.000 1.331 1.728 2.197 2.744 3.375 4.096 4.913 5.832 6.859 2 8.000 9.261 10.648 12.167 13.824 15.625 17.576 19.683 21.952 24.389 . 3 27.000 29.791 32.768 35.937 39.304 42.875 46.656 50.653 54.872 59.319 4 64.000 68.921 74.088 79.507 85.184 91.125 97.336 103.823 110.592 117.649 5 125.000 132.651 140.608 148.877 157.464 166.375 175.616 185.193 195.112 205.379 6 216.000 226.981 238.328 250.047 262.144 274.625 287.496 300.763 314.432 328.509 7 343.000 357.911 373.248 389.017 405.224 421.875 438.976 456.533 474.552 493.039 8 512.000 531.441 551.368 571.787 592.704 614.125 636.056 658.503 681.472 704.969 9 729.000 753.571 778.688 804.357 830.584 857.375 884.736 912.673 941.192 970.299 10 1 000.00 1 030.30 1 061.21 1 092.73 1 124.86 1 157.63 1 191.02 1 225.04 1 259.71 1 295.03 11 331.00 367.63 404.93 442.90 481.54 520.88 560.90 601.61 643.03 685.16 12 728.00 771.56 815.85 860.87 906.62 953.13 2 000.38 2 048.38 2 097.15 2 146.69 13 2 197.00 2 248.09 2 299.97 2 352.64 2 406.10 2 460.38 515.46 571.35 628.07 685.62 14 744.00 803.22 863.29 924.21 985.98 3 048.63 3 112.14 3 176.52 3 241.79 3 307.95 15 3 375.00 3 442.95 3 511.81 3 581.58 3 652.26 723.88 796.42 869.89 944.31 4 019.68 16 4 096.00 4 173.28 4 251.53 4 330.75 4 410.94 4 492.13 4 574.30 4 657.46 4 741.63 826.81 17 913.00 5 000.21 5 088.45 5 177.72 5 268.02 5 359.38 5 451.78 5 545.23 5 639.75 5 735.34 18 5 832.00 929.74 6 028.57 6 128.49 6 229.50 6 331.63 6 434.86 6 539.20 6 644.67 6 751.27 19 6 859.00 6 967.87 7 077.89 7 189.06 7 301.38 7 414.88 7 529.54 7 645.37 7 762.39 7 880.60 20 8 000.00 8 120.60 8 242.41 8 365.43 8 489.66 8 615.13 8 741.82 8 869.74 8 998.91 9 129.33 21 9 261.00 9 393.93 9 528.13 9 663.60 9 800.34 9 938.38 10 077.7 10 218.3 10 360.2 10 503.5 22 10 648.0 10 793.9 10.941.0 11 089.6 11 239.4 11 390.6 11 543.2 11 697.1 11 852.4 12 009.0 23 12 167.0 12 326.4 12 487.2 12 649.3 12 812.9 12 977.9 13 144.3 13 312.1 13 481.3 13 651.9 24 13 824.0 13 997.5 14 172.5 14 348.9 14 526.8 14 706.1 14 886.9 15 069.2 15 253.0 15 438.2 25 15 625.0 15 813.3 16 003.0 16 194.3 16 387.1 16 581.4 16 777.2 16 974.6 17 173.5 17 37 4.0 26 17 576.0 17 779.6 17 984.7 18 191.4 18 399.7 18 609.6 18 821.1 19 034.2 19 248.8 19 465.1 27 19 683.0 19 902.5 20 123.6 20 346.4 20 570.8 20 796.9 21 024.6 21 253.9 21485.0 21 717.6 28 21 952.0 22 188.0 22 425.8 22 665.2 22 906.3 23 149.1 23 393.7 23 639.9 23 887.9 24 137.6 29 24 389.0 24 642.2 24 897.1 25 153.8 25 412.2 25 672.4 25 934.3 26 198.1 26 463.6 26 730.9 30 27 000.0 27 270.9 27 543.6 27 818.1 28 094.5 28 372.6 28 652.6 28 934.4 29 218.1 29 503.6 31 29 791.0 30 080.2 30 371.3 30 664.3 30 959.1 31 255.9 31 554.5 31 855.0 32 157.4 88 461.8 32 32 768.0 33 076.2 33 386.2 33 698.3 34 012.2 34 328.1 34 646.0 34 965.8 35 287.6 35 611.3 33 35 937.0 36 264.7 36 594.4 36 926.0 37 259.7 37 595.4 37 933.1 38 272.8 38 614.5 38 958.2 34 39 304.0 39 651.8 40 001.7 40 353.6 40 707.6 41 063.6 41 421.7 41 781.9 42 144.2 42 508.5 35 42 875.0 43 243.6 43 614.2 43 987.0 44 361.9 44 738.9 45 118.0 45 499.3 45 882.7 46 268.3 36 46 656.0 47 045.9 47 437.9 47 832.1 48 228.5 48 627.1 49 027.9 49 430.9 49 836.0 50 243.4 37 50 653.0 51 064.8 51 478.8 51 895.1 52 313.6 52 734.4 53 157.4 53 582.6 54 010.2 54 439.9 38 54 872.0 55 306.3 55 743.0 56 181.9 56 623.1 57 066.6 57 512.5 57 960.6 58411.1 58 863.9 39 59 319.0 59 776.5 60 236.3 60 698.5 61 163.0 61 629.9 62 099.1 62 570.8 63 044.8 63 521.2 40 64 000.0 64 481.2 64 964.8 65 450.8 65 939.3 66 430.1 66 923.4 67 419.1 67 917.3 68 417.9 41 68 921.0 69 426.5 69 934.5 70 445.0 70 957.9 71473.4 71 991.3 72 511.7 73 034.6 73 560.1 42 74 088.0 74 618.5 75 151.4 75 687.0 76 225.0 76 765.6 77 308.8 77 854.5 78 402.8 78 953.6 43 79 507.0 80 063.0 80 621.6 81 182.7 81 746.5 82 312.9 82 881.9 83 453.5 SI 027.7 84 604.5 44 85 184.0 85 766.1 86 350.9 86 938.3 87 528.4 88 121.1 88 716.5 89 314.6 89 915.4 90 518.8 45 91 125.0 91 733.9 92 345.4 92 959.7 93 576.7 94 196.4 94 818:8 95 444.0 96 071.9 96 702.6 46 97 336.0 97 972.2 98 611.1 99 252.8 99 897.3 100 545 101195 101848 102 503 103 162 47 103 823 104 487 105 154 105 824 106 496 107 172 107 850 108 531 109 215 109 902 48 110 592 111 285 111 980 112 679 113 380 114 084 114 791 115 501 116 214 116 930 49 117 649 118 371 119 095 119 823 120 554 121287 122 024 128 768 188 506 1JI 251 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .!» XI. CUBES. 141 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 50 125 000 125 752 126 506 127 264 128 024 128 788 129 554 130 324 131 097 131 872 51 132 651 133 433 134 218 135 006 135 797 136 591 137 388 138 188 138 992 139 798 52 140 608 141 421 142 237 143 056 143 878 144 703 145 532 146 363 147 198 148 036 53 148 877 149 721 150 569 151 419 152 273 153 130 153 991 154 854 155 721 156 591 54 157 464 158 340 159 220 160 103 160 989 161 879 162 771 163 667 164 567 165 469 55 166 375 167 284 168 197 169 112 170 031 170 954 171880 172 809 173 741 174 677 56 175 616 176 558 177 504 178 454 179 406 180 362 181 321 182 284 183 250 184 220 57 185 193 186 169 187 149 188 133 189 119 190 109 191 103 192 100 193 101 194 105 58 195 112 196 123 197 137 198 155 199 177 200 202 201 230 202 262 203 297 204 336 59 205 379 206 425 207 475 208 528 209 585 210 645 211 709 212 776 213 847 214 922 60 216 000 217 082 218 167 219 256 220 349 221 445 222 545 223 649 224 756 225 867 61 226 981 228 099 229 221 230 346 231476 232 608 233 745 234 885 236 029 237 177 62 238 328 239 483 240 642 241 804 242 971 244 141 245 314 246 492 247 673 248 858 63 250 047 251 240 252 436 253 636 254 840 256 048 257 259 258 475 259 694 260 917 64 262 144 263 375 264 609 265 848 267 090 268 336 269 586 270 840 272 098 273 359 65 274 625 275 894 277 168 278 445 279 726 281 Oil 282 300 283 593 284 890 286 191 66 287 496 288 805 290 118 291 434 292 755 294 080 295 408 296 741 298 078 299 418 67 300 763 302 112 303 464 304 821 306 182 307 547 308 916 310 289 311 666 313 047 68 314 432 315 821 317 215 318 612 320 014 321 419 322 829 324 243 325 661 327 083 69 328 509 329 939 331 374 332 813 334 255 335 702 337 154 338 609 340 068 341 532 7.0 343 000 344 472 345 948 347 429 348 914 350 403 351 896 353 393 354 895 356 401 71 357 911 359 425 360 944 362 467 363 994 365 526 367 062 368 602 370 146 371 695 72 373 248 374 805 376 367 377 933 379 503 381 078 382 657 384 241 385 828 387 420 73 389 017 390 618 392 223 393 833 395 447 397 065 398 688 400 316 401 947 403 583 74 405 224 406 869 408 518 410 172 411 831 413 494 415 161 416 833 418 509 420 190 75 421 875 423 565 425 259 426 958 428 661 430 369 432 081 433 798 435 520 437 245 76 438 976 440 711 442 451 444 195 445 944 447 697 449 455 451 218 452 985 454 757 77 456 533 458 314 460 100 461 890 463 685 465 484 467 289 469 097 470 911 472 729 78 474 552 476 380 478 212 480 049 481 890 483 737 485 588 487 443 489 304 491 169 79 493 039 494 914 496 793 498 677 500 566 502 460 504 358 506 262 508 170 510 082 80 512 000 513 922 515 850 517 782 519 718 521 660 523 607 525 558 527 514 529 475 81 531 441 533 412 535 387 537 368 539 353 541 343 543 338 545 339 547 343 549 353 82 551 368 553 388 555 412 557 442 559 476 561 516 563 560 565 609 5,67 664 569 723 83 571 787 573 856 575 930 578 010 580 094 582 183 584 277 586 376 588 480 590 590 84 592 704 594 823 596 948 599 077 601 212 603 351 605 496 607 645 609 800 611 960 85 614 125 616 295 618 470 620 650 622 836 625 026 627 222 629 423 631 629 633 840 86 636 056 638 277 640 504 642 736 644 973 647 215 649 462 651 714 653 972 656 235 87 658 503 660 776 663 055 665 339 667 628 669 922 672 221 674 526 676 836 679 151 . 88 681472 683 798 686 129 688 465 690 807 693 154 695 506 697 864 700 227 702 595 89 704 969 707 348 709 732 712 122 714 517 716 917 719 323 721 734 724 151 726 573 90 729 000 731 433 733 871 736 314 738 763 741 218 743 677 746 143 748 613 751 089 91 753 571 756 058 758 551 761 048 763 552 766 061 768 575 771 095 773 621 776 152 92 778 688 781 230 783 777 786 330 788 889 791453 794 023 796 598 799 179 801 765 93 804 357 806 954 809 558 812 166 814 781 817 400 820 026 822 657 825 294 827 936 94 830 584 833 238 835 897 838 562 841 232 843 909 846 591 849 278 851971 854 670 95 857 375 860 085 862 801 865 523 868 251 870 984 873 723 876 467 879 218 881 974 96 884 736 887 504 890 277 893 056 895 841 898 632 901429 904 231 907 039 909 853 97 912 673 915 499 918 330 921 167 924 010 926 859 929 714 932 575 935 441 938 314 98 941 192 944 076 946 966 949 862 952 764 955 672 958 585 961 505 964 430 967 362 99 970 299 973 242 976 191 979 147 982 108 985 075 988 048 991 027 994 012 997 003 100 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 142 XII. SQUARE ROOTS. . _ ___ — — ' 1 1 2 3 4 5 6 7 8 9 Difference. 0.0000 1.0000 1.4142 1.7321 2.0000 2.2361 2.4495 2.6458 2.8284 3.0000 coo 490 480 470 i 3.1623 3166 4641 6056 7417 8730 *0000 ♦1231 *2426 •35*9 i 2 50 100 49 98 48 96 47 94 2 4.4721 5826 6904 7958 8990 *0000 *0990 *1962 *2915 *3852 3 160 147 144 141 3 5.4772 5678 6569 7446 8310 9161 *0000 *0828 *1644 *2450 4 200 196 192 188 4 6.3246 4031 4807 5574 6332 7082 7823 8557 9282 *0000 6 250 300 245 294 240 288 285 888 5 7.0711 1414 2111 2801 3485 4162 4833 5498 6158 6811 7 8 850 400 343 392 336 329 876 6 7460 8102 8740 9373 *0000 *0623 *1240 *1854 *2462 *3066 9 450 441 432 428 7 8.3666 4261 4853 5440 6023 6603 7178 7750 8318 8882 460 450 440 480 8 9443 *0000 *0554 *1104 *1652 *2195 *2736 *3274 *3808 ♦4340 1 46 45 44 48 9 9.4868 5394 5917 6437 6954 7468 7980 8489 8995 9499 2 3 , 92 188 90 185 88 182 86 129 10 10.0000 0499 0995 1489 1980 2470 2956 3441 3923 4403 4 5 6 184 280 276 180 225 270 176 220 264 172 11 4881 5357 5830 6301 6771 7238 7703 8167 8628 9087 215 258 12 9545 *0000 *0454 *0905 *1355 *1803 *2250 *2694 *3137 *3578 7 822 815 808 801 13 11.4018 4455 4891 5326 5758 6190 6619 7047 7473 7898 8 9 368 414 360 405 852 396 887 888 14 8322 8743 9164 9583 *0000 *0416 *0830 *1244 *1655 *2066 420 410 400 15 12.2474 2882 3288 3693 4097 4499 4900 5300 5698 6095 1 42 41 40 89 16 6491 6886 7279 7671 8062 8452 8841 9228 9615 *0000 2 3 84 126 82 128 80 120 78 117 11 13.0384 0767 1149 1529 1909 2288 2665 3041 3417 3791 4 168 164 160 156 18 4164 4536 4907 5277 5647 6015 6382 6748 7113 7477 5 210 205 200 195 19 7840 8203 8564 8924 9284 9642 *0000 *0357 *0712 ♦1067 6 7 252 •294 246 287 240 280 234 20 14.1421 1774 2127 2478 2829 3178 3527 3875 4222 4568 8 9 336 878 828 869 820 860 312 851 21 22 4914 8324 5258 8661 5602 8997 5945 9332 6287 9666 6629 *0000 6969 *0333 7309 7648 *0665 *0997 7986 *1327 1 8S0 88 370 37 360 88 v850 35 23 15.1658 1987 2315 2643 2971 3297 3623 3948 4272 4596 2 76 74 IS 70 24 4919 5242 5563 5885 6205 6525 6844 7162 7480 7797 3 4 114 152 111 148 108 144 105 140 25 8114 8430 8745 9060 9374 9687 *0000 *0312 *0624 *0935 5 6 7 190 228 266 185 180 175 26 16.1245 1555 1864 2173 2481 2788 3095 3401 3707 4012 222 259 216 252 210 245 27 4317 4621 4924 5227 5529 5831 6132 6433 6733 7033 8 304 296 888 280 28 7332 7631 7929 8226 8523 8819 9115 9411 9706 *0000 9 342 883 824 315 29 17.0294 0587 0880 1172 1464 1756 2047 2337 2627 2916 1 840 34 830 &3 820 88 810 81 30 17.3205 3494 3781 4069 4356 4642 4929 5214 5499 5784 2 68 66 64 62 31 6068 6352 6635 6918 7200 7482 7764 8045 8326 8606 8 4 102 186 99 182 96 188 98 124 32 8885 .9165 9444 9722 *0000 *0278 *0555 *0831 *1108 *1384 5 170 165 160 155 33 18.1659 1934 2209 2483 2757 3030 3303 3576 3848 4120 6 204 198 192 186 34 4391 4662 4932 5203 5472 5742 6011 6279 6548 6815 7 8 288 272 281 264 224 256 217 248 35 7083 7350 7617 7883 8149 8414 8680 8944 9209 9473 9 806 297 288 279 36 9737 *0000 *0263 *0526 *0788 *1050 *1311 ♦1572 *1833 *2094 1 2 800 30 60 290 29 5S 280 2S B8 270 37 19.2354 2614 2873 3132 3391 3649 3907 4165 4422 4679 81 54 38 4936 5192 5448 5704 5959 6214 6469 6723 6977 7 231 3 90 87 84 SI 39 7484 7737 7990 8242 8494 8746 8997 9249 9499 9750 4 5 m 150 116 145 112 140 108 185 40 20.0000 0250 0499 0749 0998 1246 1494 1742 1990 2237 6 180 174 168 41 2485 2731 2978 3224 3470 3715 3961 4206 4450 4695 7 8 210 240 208 888 196 224 189 216 42 4939 5183 5426 5670 5913 6155 6398 6640 6882 7123 9 270 981 243 43 7364 7605 7846 8087 8327 8567 8806 9045 9284 9523 260 250 240 280 44 9762 *0000 *0238 *0476 *0713 *0950 *1187 ♦1424 *1660 *1896 1 2 M 52 25 50 24 48 28 46 45 21.2132 2368 2603 2838 3073 3307 3542 3776 4009 4243 8 78 75 100 125 72 69 46 4476 4709 4942 5174 5407 5639 5870 6102 6333 6564 4 5 104 l:!u 88 1 81 1 92 115 47 6795 7025 7256 7486 7715 7945 8174 8403 8632 8861 6 156 150 144 1SS 48 9089 9317 9545 9773 *0000 *0227 *0454 ♦0681 *0097 *1133 7 182 175 168 161 49 22.1359 1585 1811 2036 2261 2486 2111 2935 3159 3383 > 9 234 200 199 818 1S4 50 1 2 3 4 5 6 7 8 9 Differences. XII. SQUARE ROOTS. 143 50 1 2 3 4 5 6 7 8 9 Differences. 50 22.3607 3830 4054 4277 4499 4722 4944 5167 5389 5610 i 2 220 22 44 215 22 43 210 21 42 208 21 42 51 5832 6053 6274 6495 6716 6936 7156 7376 7596 7816 52 8035 8254 8473 8692 8910 9129 9347 9565 9783 *0000 3 66 65 63 62 53 54 23.0217 2379 0434 2594 0651 2809 0868 3024 1084 3238 1301 1517 3452 3666 1733 3880 1948 2164 4094 4307 4 5 6 88 110 132 86 108 129 84 105 126 83 104 125 55 4521 4734 4947 5160 5372 5584 5797 6008 6220 6432 7 8 154 176 151 172 147 168 146 166 56 6643 6854 7065 7276 7487 7697 7908 8118 8328 8537 9 198 194 189 187 57 8747 8956 9165 9374 9583 9792 *0000 *0208 *0416 *0624 206 204 202 200 58 59 24.0832 2899 1039 3105 1247 3311 1454 3516 1661 3721 1868 2074 3926 4131 2281 4336 2487 2693 4540 4745 1 2 3 21 41 62 20 41 61 20 40 61 20 40 60 60 24.4949 5153 5357 5561 5764 5967 6171 6374 6577 6779 4 5 82 103 124 82 102 122 81 101 121 80 100 120 61 6982 7184 7386 7588 7790 7992 8193 8395 8596 8797 6 62 8998 9199 9399 9600 9800 *0000 *0200 *0400 *0599 *0799 7 144 143 141 140 63 25.0998 1197 1396 1595 1794 1992 2190 2389 2587 2784 8 9 165 185 103 184 162 182 160 ISO 64 2982 3180 3377 3574 3772 3969 4165 4362 4558 4755 198 196 194 192 65 4951 5147 5343 5539 5734 5930 6125 6320 6515 6710 1 '.' 3 20 20 19 19 66 6905 7099 7294 7488 7682 7876 8070 8263 8457 8650 40 59 89 59 39 58 38 58 67 8844 9037 9230 9422 9615 9808 *0000 *0192 *0384 *0576 4 79 78 78 77 68 26.0768 0960 1151 1343 1534 1725 1916 2107 2298 2488 5 99 119 139 98 118 137 97 96 69 2679 2869 3059 3249 3439 3629 3818 4008 4197 4386 6 7 116 136 115 134 70 26.4575 4764 4953 5141 5330 5518 5707 5895 6083 6271 8 9 158 178 157 176 155 175 154 173 71 6458 6646 6833 7021 7208 7395 7582 7769 7955 8142 190 19 188 19 186 19 184 18 72 8328 8514 8701 8887 9072 9258 9444 9629 9815 *0000 1 73 27.0185 0370 0555 0740 0924 1109 1293 1477 1662 1846 '2 38 38 37 37 74 2029 2213 2397 £580 2764 2947 3130 3313 3496 3679 3 4 57 76 56 75 56 74 55 74 75 3861 4044 4226 4408 4591 4773 4955 5136 5318 5500 5 g 7 95 114 133 94 113 132 93 112 130 92 76 5681 5862 6043 6225 6405 6586 6767 6948 7128 7308 110 129 77 7489 7669 7849 8029 8209 8388 8568 8747 8927 9106 a 152 150 149 147 78 9285 9464 9643 9821 *0000 *0179 *0357 *0535 *0713 *0891 a 171 169 167 166 79 28.1069 1247 1425 1603 f 1780 1957 2135 2312 2489 2666 i 182 18 180 18 178 18 176 IS 80 28.2843 3019 3196 3373 3549 3725 3901 4077 4253 4429 2 36 36 36 85 81 4605 4781 4956 5132 5307 5482 5657 5832 6007 6182 8 4 55 73 54 72 53 71 53 70 82 6356 6531 6705 6880 7054 7228 7402 7576 7750 7924 B 91 90 89 88 83 8097 8271 8444 8617 8791 8964. 9137 9310 9482 9655 (i 109 108 107 106 84 9828 *0000 *0172 *0345 *0517 *0689 *0861 *1033 *1204 *1376 7 8 127 146 126 144 125 142 128 141 • 85 29.1548 1719 1890 2062 2233 2404 2575 2746 2916 3087 1) 164 162 160 158 86 3258 3428 3598 3769 3939 4109 4279 4449 4618 4788 174 172 17 34 170 168 87 4958 5127 5296 5466 5635 5804 5973 6142 6311 6479 1 2 17 35 17 34 17 84 88 6648 6816 6985 7153 7321 7489 7658 7825 7993 8161 :! 52 52 51 50 89 8329 8496 8664 8831 8998 9166 9333 9500 9666 9833 4 5 70 87 69 86 68 85 67 84 90 30.0000 0167 0333 0500 0666 0832 0998 1164 1330 1496 6 104 103 102 101 91 1662 1828 1993 2159 2324 2490 2655 2820 2985 3150 7 8 122 139 120 138 119 136 118 184 92 3315 3480 3645 3809 3974 4138 4302 4467 4631 4795 9 157 155 153 151 93 4959 5123 5287 5450 5614 5778 5941 6105 6268 6431 166 164 162 160 94 6594 6757 6920 7083 7246 7409 7571 7734 7896 8058 1 2 17 38 16 33 16 32 16 32 95 96 8221 9839 8383 *0000 8545 *0161 8707 *0322 8869 *0483 9031 9192 *0644 *0805 9354 *0966 9516 9677 *1127 *1288 3 4 5 50 66 83 49 66 82 49 65 81 48 64 80 97 31.1448 1609 1769 1929 2090 2250 2410 2570 2730 2890 100 98 97 96 98 99 3050 4643 3209 4802 3369 4960 3528 5119 3688 5278 3847 4006 5436 5595 4166 5753 4325 4484 5911 6070 7 8 9 116 133 149 115 131 148 113 130 146 112 128 144 100 1 2 3 4 5 6 7 8 9 Differences. 144 XII. SQUARE ROOTS. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 0.0000 3162 4472 5477 6325 7071 7746 8367 8944 9487 1 a 250 25 50 245 240 285 i 1.0000 0488 0954 1402 1832 2247 2649 3038 3416 3784 25 49 24 48 24 47 2 4142 4491 4832 5166 5492 5811 6125 6432 6733 7029 a 75 74 72 71 3 7321 7607 7889 8166 8439 8708 8974 9235 9494 9748 4 100 98 aa 4 2.0000 0248 0494 0736 0976 1213 1448 1679 1909 2136 B 1 125 150 123 147 120 144 118 141 5 2361 2583 2804 3022 3238 3452 3664 3875 4083 4290 T 8 175 200 172 196 168 1M 165 188 6 4495 4698 4900 5100 5298 5495 5690 5884 6077 6268 I 225 221 216 7 6458 6646 6833 7019 7203 7386 7568 7749 7928 8107 280 225 220 215 8 8284 8460 8636 8810 8983 9155 9326 9496 9665 9833 1 23 23 22 22 9 3.0000 0166 0332 0496 0659 0822 0984 1145 1305 1464 1 a 46 69 45 68 44 aa 48 65 10 3.1623 1780 1937 2094 2249 2404 2558 2711 2863 3015 4 6 a 92 115 188 90 113 135 110 182 86 108 129 11 3166 3317 3466 3615 3764 3912 4059 4205 4351 4496 12 4641 4785 4928 5071 5214 5355 5496 5637 5777 5917 7 161 158 154 151 13 6056 6194 6332 6469 6606 6742 6878 7014 7148 7283 a 9 184 207 180 203 176 m 1M 14 7417 7550 7683 7815 7947 8079 8210 8341 8471 8601 210 205 200 15 8730 8859 8987 9115 9243 9370 9497 9623 9749 9875 1 21 21 20 so 16 4.0000 0125 0249 0373 0497 0620 0743 0866 0988 1110 2 8 42 63 41 62 40 60 59 17 1231 1352 1473 1593 1713 1833 1952 2071 2190 2308 4 84 82 80 78 18 2426 2544 2661 2778 2895 3012 3128 3243 3359 3474 .-> 105 108 100 98 19 3589 3704 3818 3932 4045 4159 4272 4385 4497 4609 6 7 126 147 123 144 120 140 117 187 20 4.4721 4833 4944 5056 5166 5277 5387 5497 5607 5717 s 9 168 189 164 185 160 180 156 i n 21 5826 5935 6043 6152 6260 6368 6476 6583 6690 6797 190 19 185 19 22 6904 7011 7117 7223 7329 7434 7539 7645 7749 7854 1 180 18 175 18 23 7958 8062 8166 8270 8374 8477 8580 8683 8785 8888 2 86 87 86 85 24 8990 9092 9193 9295 9396 9497 9598 9699 9800 9900 8 4 57 76 56 74 54 72 58 70 25 5.0000 0100 0200 0299 0398 0498 0596 0695 0794 0892 6 95 93 90 88 26 0990 1088 1186 1284 1381 1478 1575 1672 1769 1865 6 7 114 188 111 180 108 126 105 128 27 1962 2058 2154 2249 2345 2440 2536 2631 2726 2820 8 152 148 144 140 28 2915 3009 3104 3198 3292 3385 3479 3572 3666 3759 9 171 167 162 158 29 3852 3944 4037 4129 4222 4314 4406 4498 4589 4681 1 170 17 165 17 160 16 155 16 30 5.4772 4863 4955 5045 5136 5227 5317 5408 5498 5588 2 84 88 82 81 31 5678 5767 5857 5946 6036 6125 6214 6303 6391 6480 8 4 61 68 50 66 48 64 47 62 32 6569 6657 6745 6833 6921 7009 7096 7184 7271 7359 5 85 83 80 78 33 7446 7533 7619 7706 7793 7879 7966 8052 8138 8224 6 102 aa 96 98 34 8310 8395 8481 8566 8652 i 8737 8822 8907 8992 9076 7 8 119 186 116 182 112 m 109 124 35 9161 9245 9330 9414 9498 9582 9666 9749 9833 9917 9 158 149 144 140 36 6.0000 0083 0166 0249 0332 0415 0498 0581 0663 0745 1 2 150 15 80 145 15 29 140 14 2S 185 14 27 37 0828 0910 0992 1074 1156 1237 1319 1400 1482 1563 38 1644 1725 1806 1887 1968 2048 2129 2209 2290 2370 8 45 44 42 41 39 2450 2530 2610 2690 2769 '2849 2929 3008 3087 3166 4 5 60 75 B8 78 , 66 70 54 63 40 41 6.3246 4031 3325 4109 3403 4187 3482 4265 3561 4343 3640 4420 3718 4498 3797 4576 3875 4653 3953 4730 6 7 8 90 105 120 87 102 116 84 98 112 SI 95 10S 42 4807 4885 4962 5038 5115 5192 5269 5345 5422 5498 9 185 181 1M 122 43 5574 5651 5727 5803 5879 5955 6030 6106 6182 8351 180 125 120 115 44 6332 6408 6483 6558 6633 6708 6783 6858 6933 7007 1 2 13 26 18 25 12 24 12 28 45 7082 7157 7231 7305 7380 7454 7528 7602 7676 7750 a 89 88 aa 85 46 7823 7897 7971 8044 8118 8191 8264 8337 8411 8484 4 5 6 52 65 78 50 63 75 48 60 n 46 68 69 47 8557 8629 8702 8775 8848 8920 8993 9065 9138 9210 48 9282 9354 9426 9498 9570 9642 9714 9785 9857 9929 7 91 88 84 81 49 7.0000 0071 0143 0214 0285 0356 0427 0498 0569 0640 8 9 104 117 100 118 96 108 92 104 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 1 XII. SQUARE ROOTS. 145 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences 108 50 7.0711 0781 0852 0922 0993 1063 1134 1204 1274 1344 i 2 114 . 112 • 11 11 23 22 110 51 1414 1484 1554 1624 1694 1764 1833 1903 1972 2042 11 22 11 22 52 2111 2180 2250 2319 2388 2457 2526 2595 2664 2732 8 34 34 88 82 53 2801 2870 2938 3007 3075 3144 3212 3280 3348 3417 t 6 8 46 45 57 56 68 67 44 43 54 3485 3553 3621 3689 3756 3824 3892 3959 4027 4095 55 66 54 65 55 4162 4229 4297 4364 4431 4498 4565 4632 4699 4766 T 8 80 78 91 90 77 88 76 86 56 4833 4900 4967 5033 5100 5166 5233 5299 5366 5432 103 101 99 97 57 5498 5565 5631 5697 5763 5829 5895 5961 6026 6092 106 104 102 100 58 6158 6223 6289 6354 6420 6485 6551 6616 6681 6746 1 11 10 10 10 59 6811 6877 6942 7006 7071 7136 7201 7266 7330 7395 '2 8 21 21 32 31 20 31 20 30 60 7.7460 7524 7589 7653 7717 7782 7846 7910 7974 8038 4 6 42 42 53 52 41 51 40 50 61 8102 8166 8230 8294 8358 8422 8486 8549 8613 8677 6 64 62 61 60 62 8740 8804 8867 8930 8994 9057 9120 9183 9246 9310 7 74 73 71 70 63 9373 9436 9498 9561 9624 9687 9750 9812 9875 9937 8 9 85 83 95 94 82 92 80 90 64 8.0000 0062 0125 0187 0250 0312 0374 0436 0498 0561 98 96 94 92 90 65 0623 0685 0747 0808 0870 0932 0994 1056 1117 1179 1 10 10 9 9 9 66 1240 1302 1363 1425 1486 1548 1609 1670 1731 1792 2 3 20 19 19 29 29 28 18 28 18 27 67 1854 1915 1976 2037 2098 2158 2219 2280 2341 2401 4 39 38 88 37 36 68 2462 2523 2583 2644 2704 2765 2825 2885 2946 3006 5 49 48 47 46 45 69 3066 3126 3187 3247 3307 3367 3427 3487 3546 3606 6 7 59 58 56 69 67 66 55 64 54 63 70 8.3666 3726 3785 3845 3905 3964 4024 4083 4143 4202 8 9 78 77 75 88 86 85 74 83 72 81 71 4261 4321 4380 4439 4499 4558 4617 4676 4735 4794 88 86 84 82 80 72 •4853 4912 4971 5029 5088 5147 5206 5264 5323 5381 1 9 9 8 8 8 73 5440 5499 5557 5615 5674 5732 5790 5849 5907 5965 2 18 17 17 16 16 74 6023 6081 6139 6197 6255 6313 6371 6429 6487 6545 8 4 26 26 25 85 84 34 25 33 24 82 75 6603 6660 6718 6776 6833 6891 6948 7006 7063 7121 5 6 7 44 43 42 53 52 50 62 60 59 41 40 76 7178 7235 7293 7350 7407 7464 7521 7579 7636 7693 49 57 48 56 77 7750 7807 7864 7920 7977 8034 8091 8148 8204 8261 S 70 69 67 66 64 78 8318 8374 8431 8487 8544 8600 8657 8713 8769 8826 9 79 77 76 74 72 79 8882 8938 8994 9051 9107 9163 9219 9275 9331 9387 1 78 76 74 8 8 7 72 7 70 7 80 8.9443 9499 9554 9610 9666 9722 9778 9833 9889 9944 2 16 15 15 14 14 81 9.0000 0056 0111 0167 0222 0277 0333 0388 0443 0499 3 4 23 23 22 81 80 30 22 29 21 28 82 0554 0609 0664 0719 0774 0830 0885 0940 0995 1049 5 39 38 37 36 35 83 1104 1159 1214 1269 1324 1378 1433 1488 1542 1597 6 47 46 44 43 42 84 1652 1706 1761 1815 1869 1924 1978 2033 2087 2141 7 8 55 53 52 62 '61 59 50 58 49 56 85 2195 2250 2304 2358 2412 2466 2520 2574 2628 2682 9 70 68 67 65 63 86 2736 2790 2844 2898 2952 3005 3059 3113 3167 3220 1 2 68 66 64 7 7 6 14 13 13 62 6 12 60 6 12 87 3274 3327 3381 3434 3488 3541 3595 3648 3702 3755 88 3808 3862 3915 3968 4021 4074 4128 4181 4234 4287 8 20 20 19 19 18 89 4340 4393 4446 4499 4552 4604. 4657- 4710 4763 4816 4 5 27 26 26 34 33 32 25 31 24 80 90 9.4868 4921 4974 5026 5079 5131 5184 5237 5289 5341 6 41 40 38 37 36 91 5394 5446 5499 5551 5603 5656 5708 5760 5812 5864 7 8 48 46 45 54 53 51 43 50 42 48 92 5917 5969 6021 6073 6125 6177 6229 6281 6333 6385 9 61 59 58 56 54 93 6437 6488 6540 6592 6644 6695 6747 6799 6850 6902 5S 56 54 52 50 94 6954 7005 7057 7108 7160 7211 7263 7314 7365 7417 1 2 6 6 5 12 11 11 5 10 5 10 95 7468 7519 7570 7622 7673 7724 7775 7826 7877 7929 3 17 17 16 16 15 96 7980 8031 8082 8133 8184 8234 8285 8336 8387 8438 4 5 23 22 22 29 28 27 21 26 20 25 97 8489 8539 8590 8641 8691 8742 8793 8843 8894 8944 6 35 34 82 31 30 98 8995 9045 9096 9146 9197 9247 9298 9348 9398 9448 7 41 89 88 36 35 99 9499 9549 9599 9649 9700 9750 9800 9850 9900 9950 8 9 46 45 48 52 50 49 42 47 40 45 100 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9' Differences. 146 XIII. CUBE ROOTS. 1 1 2 3 4 5 6 7 8 9 Differences. i 0.0000 2.1544 1.0000 2240 1.2599 2894 1.4422 3513 1.5874 4101 1.7100 4662 1.8171 5198 1.9129 5713 ♦0000 6207 ♦0801 6684 i i 250 25 50 245 25 49 240 24 48 235 24 47 2 7144 7589 8020 8439 8845 9240 9625 *0000 *0366 ♦0723 :; 75 74 72 71 3 4 3.1072 4200 1414 4482 1748 4760 2075 5034 2396 5303 2711 5569 3019 5830 3322 6088 3620 6342 3912 6593 i B a 100 125 150 98 123 147 88 120 144 94 118 141 5 6840 7084 7325 7563 7798 8030 8259 8485 8709 8930 T a 175 200 172 196 168 192 165 18S 6 9149 9365 9579 9791 *0000 *0207 *0412 *0615 *0817 *1016 i 225 221 216 212 7 4.1213 1408 1602 1793 1983 2172 2358 2543 2727 2908 230 225 220 215 8 3089 3267 3445 3621 3795 3968 4140 4310 4480 4647 ; I I 23 46 69 28 45 88 22 44 66 22 48 65 9 4814 4979 5144 5307 5468 5629 5789 5947 6104 6261 10 4.6416 6570 6723 6875 7027 7177 7326 7475 7622 7769 92 115 90 118 88 110 86 108 11 7914 8059 8203 8346 8488 8629 8770 8910 9049 9187 6 188 135 132 129 12 9324 9461 9597 9732 9866 *0000 *0133 *0265 *0397 *0528 7 a a 161 1S4 207 158 180 203 154 151 13 5.0658 0788 0916 1045 1172 1299 1426 1551 1676 1801 176 186 172 194 14 1925 2048 2171 2293 2415 2536 2656 2776 2896 3015 210 205 200 195 15 16 3133 4288 3251 4401 3368 4514 3485 4626 3601 4737 3717 4848 3832 4959 3947 5069 4061 5178 4175 5288 i a > 21 42 63 21 41 62 20 40 60 20 39 59 17 5397 5505 5613 5721 5828 5934 6041 6147 6252 6357 i 84 82 88 78 18 19 6462 7489 6567 7590 6671 7690 6774 7790 6877 7890 6980 7989 7083 8088 7185 8186 7287 8285 7388 8383 B 6 7 105 126 147 103 128 144 100 120 140 98 117 137 20 5.8480 8578 8675 8771 8868 8964 9059 9155 9250 9345 S 8 168 189 164 185 160 ISO 156 176 21 9439 9533 9627 9721 9814 9907 *0000 *0092 *0185 *0277 190 185 180 175 18 22 6.0368 0459 0550 0641 0732 0822 0912 1002 1091 1180 1 19 19 18 23 1269 1358 1446 1534 1622 1710 1797 1885 1972 2058 2 88 37 36 35 24 2145 2231 2317 2403 2488 2573 2658 2743 2828 2912 8 ft 57 76 56 74 54 72 53 70 25 26 2996 3825 3080 3907 3164 3988 3247 4070 3330 4151 3413 4232 3496 4312 3579 4393 3661 4473 3743 4553 5 6 7 95 114 133 93 111 130 90 108 126 88 105 123 27 4633 4713 4792 4872 4951 5030 5108 5187 5265 5343 8 152 148 144 140 28 5421 5499 5577 5654 5731 5808 5885 5962 6039 6115 9 171 167 162 158 29 6191 6267 6343 6419 6494 6569 6644 6719 6794 6869 1 170 17 165 17 160 16 155 16 30 6.6943 7018 7092 7166 7240 7313 7387 7460 7533 7606 ■> 8 4 34 51 68 S3 50 66 82 48 64 81 47 62 31 7679 7752 7824 7897 7969 8041 8113 8185 8256 8328 32 8399 8470 8541 8612 8683 8753 8824 8894 8964 9034 B 85 83 SO 78 33 9104 9174 9244 9313 9382 9451 9521 9589 9658 9727 6 7 8 102 119 136 99 116 182 96 112 128 93 109 124 34 9795 9864 9932 *0000 *0068 *0136 *0203 *0271 *0338 *0406 35 7.0473 0540 0607 0674 0740 0807 0873 0940 1006 1072 9 158 149 144 140 36 1138 1204 1269 1335 1400 1466 1531 1596 1661 1726 \ 150 15 145 15 140 14 135 14 37 1791 1855 1920 1984 2048 2112 2177 2240 2304 2368 2 80 29 86 2T 38 2432 2495 2558 2622 2685 2748 2811 2874 2936 2999 8 45 44 58 78 42 B8 70 41 39 3061 3124 3186 3248 3310 3372 3434 3496 3558 3619 1 5 60 75 54 68 40 7.3681 3742 3803 3864 3925 3986 4047 4108 4169 4229 6 7 8 90 105 198 87 102 116 84 86 112 81 95 108 41 4290 4350 4410 4470 4530 4590 4650 4710 4770 4829 42 4889 4948 5007 5067 5126 5185 5244 5302 5361 5420 9 185 181 IM 199 43 5478 5537 5595 5654 5712 5770 5828 5886 5944 6001 130 125 120 115 44 6059 6117 6174 6232 6289 6346 6403 6460 6517 6574 1 2 18 26 18 25 12 24 12 23 45 6631 6688 6744 6801 6857 6914 6970 7026 7082 7138 8 89 8S 36 4S 60 35 46 5S 46 7194 7250 7306 7362 7418 7473 7529 7584 7639 7695 4 5 6 52 65 50 63 47 7750 7805 7860 7915 7970 8025 8079 8134 8188 8243 78 75 72 69 48 8297 8352 8406 8460 8514 8568 8622 8676 8730 8784 7 91 83 84 96 108 81 92 104 49 8837 8,891 8944 8998 9051 9105 9158 9211 9264 9317 8 9 104 117 100 113 50 1 2 3 4 5 6 7 8 9 Differences. XIII. CUBE ROOTS. 147 50 1 2 3 4 5 6 7 8 9 Differences. 50 7.9370 9423 9476 9528 9581 9634 9686 9739 9791 9843 i 2 110 11 22 105 -11 100 10 20 95 10 19 51 9896 9948 *0000 *0052 *0104 *0156 *0208 *0260 *0311 ♦0363 21 52 8.0415 0466 0517 0569 0620 0671 0723 0774 0825 0876 8 33 32 30 29 53 54 0927 1433 0978 1483 1028 1533 1079 1583 1130 1633 1180 1683 1231 1733 1281 1783 1332 1833 1382 1882 4 5 6. 44 K 6« 42 53 63 40 50 60 38 48 57 55 1932 1982 2031 2081 2130 2180 2229 2278 2327 2377 T 8 71 •86 74 84 70 80 67 76 56 2426 2475 2524 2573 2621 2670 2719 2768 2816 2865 B 9S 95 90 86 57 2913 2962 3010 3059 3107 3155 3203 3251 3300 3348 92 90 88 86 84 58 59 3396 3872 3443 3919 3491 3967 3539 4014 3587 4061 3634 4108 3682 4155 3730 4202 3777 4249 3825 4296 1 2 3 9 18 28 9 18 27 9 18 26 9 17 26 8 17 25 60 8.4343 4390 4437 4484 4530 4577 4623 4670 4716 4763 4 5 37 46 36 45 35 44 34 43 34 42 61 4809 4856 4902 4948 4994 5040 5086 5132 5178 5224 6 55 64 53 52 50 62 63 5270 5726 5316 5772 5362 5817 5408 5862 5453 5907 5499 5952 5544 5997 5590 6043 5635 6088 5681 6132 1 8 9 64 74 83 63 72 81 62 70 79 60 69 77 59 67 76 64 6177 6222 6267 6312 6357 6401 6446 6490 6535 6579 82 80 78 76 74 65 6624 6668 6713 6757 6801 6845 6890 6934 6978 7022 1 i 8 8 16 25 8 16 24 8 16 23 8 15 23 7 15 22 66 7066 7110 7154 7198 7241 7285 7329 7373 7416 7460 67 7503 7547 7590 7634 7677 7721 7764 7807 7850 7893 4 83 32 31 30 30 68 69 7937 8366 7980 8408 8023 8451 8066 8493 8109 8536 8152 8578 8194 8621 8237 8663 8280 8706 8323 8748 6 8 7 41 49 57 40 48 56 39 47 55 38 46 53 37 44 52 70 8.8790 8833 8875 8917 8959 9001 9043 9085 9127 9169 8 9 66 74 04 72 62 70 61 68 59 67 71 9211 9253 9295 9337 9378 9420 9462 9503 9545 9587 72 70 68 66 64 72 9628 9670 9711 9752 9794 9835 9876 9918 9959 *0000 1 7 7 7 7 6 73 9.0041 0082 0123 0164 0205 0246 0287 0328 0369 0410 2 8 4 14 22 29 21 28 14 20 27 13 20 26 13 19 26 74 0450 0491 0532 0572 0613 0654 0694 0735 0775 0816 75 0856 0896 0937 0977 1017 1057 1098 1138 1178 1218 5 36 43 35 4 '2 34 41 as 40 46 32 38 45 76 1258 1298 1338 1378 1418 1458 1498 1537 1577 1617 7 50 4H 48 77 1657 1696 1736 1775 1815 1855 1894 1933 1973 2012 8 58 56 54 53 51 78 2052 2091 2130 2170 2209 2248 2287 2326 2365 2404 9 65 68 61 59 58 79 2443 2482 2521 2560 2599 2638 2677 2716 2754 2793 1 62 6 60 6 58 6 56 6 54 5 80 81 9.2832 3217 2870 3255 2909 3294 2948 3332 2986 337-0 3025 3408 3063 3447 3102 3485 3140 3523 3179 3561 2 8 4 12 19 25 12 18 24 12 17 23 11 17 22 11 16 22 82 3599 3637 3675 3713 3751 3789 3827 3865 3902 3940 5 31 30 29 28 27 83 84 3978 4354 4016 4391 4053 4429 4091 4466 4129 4503 4166 4541 4204 4578 4241 4615 4279 4652 4316 4690 6 7 8 37 43 50 36 42 48 35 41 46 34 39 45 32 38 43 85 4727 4764 4801 4838 4875 4912 4949 4986 5023 5060 9 56 04 52 50 49 86 5097 5134 5171 5207 5244 5281 5317 5354 5391 5427 1 52 5 50 5 48 5 46 5 44 4 87 5464 5501 5537 5574 5610 5647 5683 5719 5756 5792 2 10 10 10 9 9 88 5828 5865 5901 5937 5973 6010 6046 6082 6118 6154 8 16 21 26 15 20 25 14 19 24 14 18 23 13 18 22 89 6190 6226 6262 6298 6334 6370 6406 6442 6477 6513 4 5 90 9.6549 6585 6620 6656 6692 6727 6763 6799 6834 6870 6 7 8 31 36 42 30 88 40 29 34 38 28 32 37 26 31 35 91 6905 6941 6976 7012 7047 7082 7118 7153 7188 7224 92 7259 7294 7329 7364 7400 7435 7470 7505 7540 7575 9 47 45 43 41 40 93 7610 7645 7680 7715 7750 7785 7819 7854 7889 7924 42 40 38 36 34 94 7959 7993 8028 8063 8097 8132 8167 8201 8236 8270 1 2 4 8 4 8 4 8 4 7 3 7 95 96 8305 8648 8339 8683 8374 8717 8408 8751 8443 8785 8477 8819 8511 8854 8546 8888 8580 8922 8614 8956 3 4 5 13 IT 21 12 16 20 11 15 19 11 14 IS 10 14 17 97 8990 9024 9058 9092 9126 9160 9194 9227 9261 9295 6 25 24 23 22 20 98 99 9329 9666 9363 9699 9396 9733 9430 9766 9464 9800 9497 9833 9531 9866 9565 9900 9598 9933 9632 9967 7 8 9 29 34 38 28 32 36 27 30 34 25 29 32 24 27 81 100 1 2 3 4 5 6 7 8 9 Differences. 148 XIII. CUBE ROOTS. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 0.0000 4642 5848 6694 7368 7937 8434 8879 9283 9655 84 1 8 2 17 88 8 17 82 81 80 i 1.0000 0323 0627 0914 1187 1447 1696 1935 2164 2386 8 16 8 8 16 16 2 2599 2806 3006 3200 3389 3572 3751 B92Q 4095 4260 3 25 25 25 24 24 3 4422 4581 4736 4888 5037 5183 5326 5467 5605 5741 4 84 5 42 6 50 88 83 32 82 4 5874 6005 6134 6261 6386 6510 6631 6751 6869 6985 42 50 41 49 41 40 49 48 5 7100 7213 7325 7435 7544 7652 7758 7863 7967 8070 7 59 8 67 58 66 57 66 57 56 65 64 6 8171 8272 8371 8469 8566 8663 8758 8852 8945 9038 9 76 75 74 73 72 7 9129 9220 9310 9399 9487 9574 9661 9747 9832 9916 79 78 77 76 75 8 2.0000 0083 0165 0247 0328 0408 0488 0567 0646 0724 1 8 8 8 8 8 9 0801 0878 0954 1029 1105 1179 1253 1327 1400 1472 2 16 8 24 16 23 15 23 15 15 23 28 10 11 2.1544 2240 1616 2307 1687 2374 1758 2440 1828 2506 1898 2572 1967 2637 2036 2702 2104 2766 2172 2831 4 82 5 40 6 47 31 89 47 31 39 46 80 80 88 S3 46 45 12 2894 2958 3021 3084 3146 3208 3270 3331 3392 3453 7 55 55 54 53 58 13 3513 3573 3633 3693 3752 3811 3870 3928 3986 4044 8 63 9 71 62 70 62 69 61 60 gs H 14 4101 4159 4216 4272 4329 4385 4441 4497 4552 4607 74 73 72 71 70 15 4662 4717 4771 4825 4879 4933 4987 5040 5093 5146 1 7 2 15 3,22 7 15 22 7 7 7 16 5198 5251 5303 5355 5407 5458 5510 5561 5612 5662 14 22 14 14 21 21 17 5713 5763 5813 5863 5913 5962 6012 6061 6110 6159 4 80 29 29 28 28 18 6207 6256 6304 6352 6400 6448 6495 6543 '6590 6637 5 87 6 44 7 52 37 86 86 85 19 6684 6731 6777- 6824 6870 6916 6962 7008 7053 7099 44 51 43 50 43 42 50 49 20 2.7144 7189 7234 7279 7324 7369 7413 7457 7501 7545 8 59 9 67 58 66 5S 65 57 56 64 68 21 22 7589 . 8020 7633 8063 7677 8105 7720 8147 7763 8189 7806 8231 7850 8273 7892 8314 7935 8356 7978 8397 69 1 7 68 7 67 7 66 65 7 7 23 8439 8480 8521 8562 8603 8643 8684 8724 8765 8805 2 14 14 18 18 18 24 8845 8885 8925 8965 9004 9044 9083 9123 9162 9201 3 21 4 28 20 27 20 27 20 20 26 26 25 9240 9279 9318 9357 9395 9434 9472 9511 9549 9587 5 35 6 41 7 48 34 34 33 88 26 9625 9663 9701 9738 9776 9814 9851 9888 9926 9963 41 48 40 47 40 89 46 46 27 3.0000 0037 0074 0111 0147 0184 0221 0257 0293 0330 8 55 54 54 53 52 28 0366 0402 0438 0474 0510 0546 0581 0617 0652 0688 9 62 61 60 59 59 29 0723 0758 0794 0829 0864 0899 0934 0968 1003 1038 64 1 6 68 6 62 6 61 60 6 6 30 3.1072 1107 1141 1176 1210 1244 1278 1312 1346 1380 2 18 18 12 12 12 31. 1414 1448 1481 1515 1548 1582 1615 1648 1682 1715 3 19 4 26 19 25 19 25 18 18 24 24 32 1748 1781 1814 1847 1880 1913 1945 1978 2010 2043 5 32 32 31 31 80 33 2075 2108 2140 2172 2204 2237 2269 2301 2332 2364 6 88 38 87 87 86 34 2396 2428 2460 2491 2523 2554 2586 2617 2648 2679 7 45 8 51 44 50 43 50 48 4J 49 48 35 2711 2742 2773 2804 2835 2866 2897 2927 2958 2989 9 58 57 56 55 54 36 3019 3050 3080 3111 3141 3171 3202 3232 3262 3292 59 1 6 2 12 58 6 12 57 6 11 56 55 6 6 11 11 37 3322 3352 3382 3412 3442 3472 3501 3531 3561 3590 38 3620 3649 3679 3708 3737 3767 3796 3825 3854 3883 8 IS 17 17 17 17 39 3912 3941 3970 3999 4028 4056 4085 4114 4142 4171 4 24 5 80 28 29 23 29 .".» •_>■_> 28 28 40 3.4200 4228 4256 4285 4313 4341 4370 4398 4426 4454 6 85 85 34 84 38 41 4482 4510 4538 4566 4594 4622 4650 4677 4705 4733 7 41 8 47 41 40 40 H 45 44 42 4760 4788 4815 4843 4870 4898 4925 4952 4980 5007 9 53 52 51 50 50 43 5034 5061 5088 5115 5142 5169 5196 5333 5250 5277 54 58 .'■•J 51 50 44 5303 5330 5357 5384 5410 5437 5463 5490 5516 5543 1 5 2 11 5 11 5 10 5 5 10 10 45 5569 5595 5622 5648 5674 5700 5726 5752 5778 5804 8 16 16 21 •j 7 16 21 M 15 15 46 5830 5856 5882 5908 5934 5960 5986 6011 6037 6063 4 M 5 27 20 20 26 25 47 6088 6114 6139 6165 6190 6216 6241 6267 6292 6317 6 82 32 81 31 80 48 6342 6368 6393 6418 6443 6468 6493 6518 6543 6568 7 88 37 86 86 85 49 6593 6618 6643 6668 6692 6717 6742 6766 6791 6816 s I:; 8 49 42 4S 42 47. 11 in 46 45 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. XIII. CUBE ROOTS. 149 50 .0 .1 2 .3 .4 .5 .6 .7 .8 .9 Differences. 50 3.6840 6865 6889 6914 6938 6963 6987 7011 7036 7060 49 1 5 2 10 48 5 10 47 5 9 46 45 5 5 9 9 51 7084 7109 7133 7157 7181 7205 7229 7253 7277 7301 52 7325 7349 7373 7397 7421 7444 7468 7492 7516 7539 3 15 14 14 14 14 53 54 7563 7798 7586 7821 7610 7844 7634 7867 7657 7891 7681 7914 7704 7937 7728 7960 7751 7983 7774 8006 4 20 5 25 6 29 19 24 29 19 24 28 18 18 23 23 2S 27 55 8030 8053 8076 8099 8121 8144 8167 8190 8213 8236 7 84 8 89 34 38 33 38 82 32 37 36 56 8259 8281 8304 8327 8349 8372 8395 8417 8440 8462 9 44 43 42 41 41 57 8485 8508 8530 8552 8575 8597 8620 8642 8664 8687 44 48 42 41 40 58 8709 8731 8753 8775 8798 8820 8842 8864 8886 8908 1 4 2 9 3 13 4 9 13 4 4 4 59 8930 8952 8974 8996 9018 9040 9061 9083 9105 9127 8 13 8 8 12 12 60 3.9149 9170 9192 9214 9235 9257 9279 9300 9322 9343 4 18 5 22 17 22 26 17 21 25 16 16 21 20 25 24 61 9365 9386 9408 9429 9451 9472 9494 9515 9536 9558 6 26 62 9579 9600 9621 9643 9664 9685 9706 9727 9748 9770 7 31 30 29 29 28 63 9791 9812 9833 9854 9875 9896 9916 9937 9958 9979 8 85 9 40 34 39 84 38 33 82 37 36 64 4.0000 0021 0042 0062 0083 0104 0125 0145 0166 0187 39 38 37 36 35 65 66 0207 0412 0228 0433 0248 0453 0269 0474 0290 0494 0310 0514 0331 0534 0351 0555 0372 0575 0392 0595 1 4 2 8 8 12 4 8 11 4 7 11 4 4 7 7 11 11 67 0615 0636 0656 0676 0696 0716 0736 0756 0776 0797 4 16 15 15 14 14 68 69 0817 1016 0837 1035 0857 1055 0876 1075 0896 1095 0916 1114 0936 1134 0956 1154 0976 1174 0996 1193 5 20 6 23 7 27 19 28 27 19 22 26 18 18 22 21 25 25 70 4.1213 1232 1252 1272 1291 1311 1330 1350 1369 1389 8 31 9 35 30 34 30 33 29 28 32 32 71 1408 1428 1447 1466 1486 1505 1524 1544 1563 1582 34 33 82 31 30 3 3 72 1602 1621 1640 1659 1679 1698 - 1717 1736 1755 1774 1 3 3 3 73 1793 1812 1832 1851 1870 1889 1908 1927 1946 1964 2 7 7 6 6 6 74 1983 2002 2021 2040 2059 2078 2097 2115 2134 2153 3 10 4 14 10 13 10 13 9 9 12 12 75 2172 2190 2209 2228 2246 2265 2284 2302 2321 2340 5 17 6 20 7 24 17 20 23 16 19 22 16 15 19 18 22 21 76 2358 2377 2395 2414 2432 2451 2469 2488 2506 2525 77 2543 2562 2580 2598 2617 2635 2653 2672 2690 2708 8 27 26 26 25 24 78 2727 2745 2763 2781 2799 2818 2836 2854 2872 2890 9 81 30 29 28 27 79 2908 2927 2945 2963 2981 2999 3017 3035 3053 3071 29 1 3 28 3 27 3 26 25 3 3 80 4.3089 3107 3125 3142 3160 3178 3196 3214 3232 3250 2 6 3 9 4 12 6 8 11 5 8 11 5 5 8 8 10 10 81 3267 3285 3303 3321 3339 3356 3374 3392 3409 3427 82 3445 3462 3480 3498 3515 3533 3551 3568 3586 3603 5 15 14 14 13 13 83 3621 3638 3656 3673 3691 3708 3726 3743 3760 3778 6 17 7 20 8 23 17 20 22 16 19 22 16 15 18 18 21 20 84 3795 3813 3830 3847 3865 3882 3899 3917 3934 3951 85 3968 3986 4003 4020 4037 4054 4072 4089 4106 4123 9 26 25 24 23 23 86 4140 4157 4174 4191 4208 4225 4242 4259 4276 4293 24 1 2 2 5 23 2 22 2 21 20 2 2 87 4310 4327 4344 4361 4378 4395 4412 4429 4446 4463 5 4 4 4 88 4480 4496 4513 4530 4547 4564 4580 4597 4614 4631 8 7 7 7 6 6 89 4647 4664 4681 4698 4714 4731 4748 4764 4781 4797 4 10 5 12 9 12 9 11 8 8 11 10 90 91 4.4814 4979 4831 4996 4847 5012 4864 5029 4880 5045 4897 5062 4913 5078 4930 5094 4946 5111 4963 5127 6 14 7 17 8 19 14 16 18 13 15 18 13 12 15 14 17 16 92 5144 5160 5176 5193 5209 5225 5241 5258 5274 5290 9 22 21 20 19 18 93 5307 5323 5339 5355 5371 5388 5404 5420 5436 5452 19 18 17 16 15 94 5468 5484 5501 5517 5533 5549 5565 5581 5597 5613 1 2 2 4 2 4 2 3 2 2 3 3 95 96 5629 5789 5645 5804 5661 5820 5677 5836 5693 5852 5709 5868 5725 5884 5741 5900 5757 5915 5773 5931 3 6 4 8 5 10 5 7 9 5 7 9 5 5 6 6 8 8 97 5947 5963 5979 5994 6010 6026 6042 6057 6073 6089 6 11 11 10 10 9 98 99 6104 ' 6261 6120 6276 6136 6292 6151 6307 6167 6323 6183 6338 6198 6354 6214 6369 6229 6385 6245 6400 7 13 8 15 9 17 13 14 16 12 14 15 11 . 11 13 12 14 14 100 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 150 XIII. CUBE ROOTS. . J 1 2 3 4 5 6 7 8 9 Differences .0 0.0000 2154 2714 3107 3420 3684 3915 4121 4309 4481 i 140 185 14 14 130 13 125 13 ,i 4642 4791 4932 5066 5192 5313 5429 5540 5646 5749 ■-' 28 2T 26 25 .2 5848 5944 6037 6127 6214 6300 6383 6463 6542 6619 ■■', 42 41 89 88 .3 6694 6768 6840 6910 6980 7047 7114 7179 7243 7306 i 5 56 54 70 68 52 SB 50 63 .4 7368 7429 7489 7548 7606 7663 7719 7775 7830 7884 •; 84 81 78 75 .5 7937 7990 8041 8093 8143 8193 8243 8291 8340 8387 T a 98 95 112 108 91 104 38 100 .6 8434 8481 8527 8573 8618 8662 8707 8750 8794 8837 u 126 122 117 118 .7 8879 8921 8963 9004 9045 9086 9126 9166 9205 9244 120 115 110 105 .8 9283 9322 9360 9398 9435 9473 9510 9546 9583 9619 i 12 12 11 11 .9 9655 9691 9726 9761 9796 9830 9865 9899 9933 9967 8 24 23 86 35 22 33 21 32 1.0 1.0000 0033 0066 0099 0132 0164 0196 0228 0260 0291 1 5 43 46 60 53 44 55 42 58 1.1 0323 0354 0385 0416 0446 0477 0507 0537 0567 0597 1 72 69 66 63 1.2 0627 0656 0685 0714 0743 0772 0801 0829 0858 0886 7 84 81 77 74 1.3 0914 0942 0970 0997 1025 1052 1079 1106 1133 1160 8 9 96 92 108 104 88 99 84 95 1.4 1187 1213 1240 1266 1292 1319 1344 1370 1396 1422 100 95 90 85 1.5 1447 1473 1498 1523 1548 1573 1598 1623 1647 1672 1 2 10 10 20 19 30 29 9 9 1.6 1696 1720 1745 1769 1793 1817 1840 1864 1888 1911 18 27 17 16 1.7 1935 1958 1981 2005 2028 2051 2074 2096 2119 2142 4 40 38 36 84 1.8 2164 2187 2209 2232 2254 2276 2298 2320 2342 2364 5 6 7 50 48 60 57 70 67 45 54 63 48 51 60 1.9 2386 2407 2429 2450 2472 2493 2515 2536 2557 2578 2.0 1.2599 2620 2641 2662 2683 2703 2724 2745 2765 2785 8 9 80 76 90 86 72 81 68 77 2.1 2806 2826 2846 2866 2887 2907 2927 2947 2966 2986 80 75 70 65 60 2.2 3006 3026 3045 3065 3084 3104 3123 3142 3162 3181 1 8 8 7 7 6 2.3 3200 3219 3238 3257 3276 3295 3314 3333 3351 3370 2 16 15 14 13 1-2 2.4 3389 3407 3426 3444 3463 3481 3499 3518 3536 3554 3 4 24 23 21 32 80 28 20 26 18 M 2.5 3572 3590 3608 3626 3644 3662 3680 3698 3715 3733 5 6 40 88 35 48 45 42 83 39 SO 86 2.6 3751 3768 3786 3803 3821 3838 3856 3873 3890 3908 7 56 53 49 46 42 2.7 3925 3942 3959 3976 3993 4010 4027 4044 4061 4078 8 64 60 56 52 43 2.8 4095 4111 4128 4145 4161 4178 4195 4211 4228 4244 9 72 63 63 59 54 2.9 4260 4277 4293 4309 4326 4342 4358 4374 4390 4406 1 56 55 54 6 6 5 53 5 52 5 3.0 1.4422 4439 4454 4470 4486 4502 4518 4534 4550 4565 2 11 11 11 11 10 3.1 4581 4597 4612 4628 4643 4659 4674 4690 4705 4721 8 4 17 17 16 22 22 22 16 •21 16 21 3.2 4736 4751 4767 4782 4797 4812 4828 4843 4858 4873 5 28 23 27 27 26 3.3 4888 4903 4918 4933 4948 4963 4978 4993 5007 5022 C 84 83 82 82 81 3.4 5037 5052 5066 5081 5096 5110 5125 5139 5154 5168 7 8 89 89 88 45 44 43 87 42 86 42 3.5 5183 5197 5212 5226 5241 5255 5269 5283 5298 5312 9 50 60 49 43 47 3.6 5326 5340 5355 5369 5383 5397 5411 5425 5439 5453 1 51 50 49 5 5 5 43 5 47 5 3.7 5467 5481 5495 5508 5522 5536 5550 5564 5577 5591 2 10 10 10 10 9 3.8 5605 5619 5632 5646 5659 5673 5687 5700 5714 5727 3 15 15 15 14 14 3.9 5741 5754 5767 5781 5794 5808 5821 5834 5848 5861 4 6 20 20 20 26 25 25 19 M 19 24 4.0 1.5874 5887 5900 5914 5927 5940 5953 5966 5979 5992 6 7 8 81 80 29 86 85 34 41 40 89 29 34 88 23 33 8S 4.1 6005 6018 6031 6044 6057 6070 6083 6096 6109 6121 4.2 6134 6147 6160 6173 6185 6198 6211 6223 6236 6249 9 46 45 44 43 42 4.3 6261 6274 6287 6299 6312 6324 6337 6349 6362 6374 46 45 44 43 a 4.4 6386 6399 6411 6424 6436 6448 6461 6473 6485 6497 1 a 5 5 4 9 9 9 4 9 4 S 4.5 6510 6522 6534 6546 6558 6571 6583 6595 6607 6619 8 4 14 14 13 18 18 18 13 17 13 17 4.6 6631 6643 6655 6667 6679 6691 6703 6715 6727 6739 5 6 28 28 22 28 27 26 22 26 21 4.7 6751 6763 6774 6786 6798 6810 6822 6833 6845 6857 25 4.8 6869 6880 6892 6904 6915 6927 6939 6950 6962 6973 7 82 82 81 80 29 4.9 6985 6997 7008 7020 7031 7043 7054 7065 7077 7088 8 9 87 86 35 41 41 40 34 89 34 83 5.0 1 2 3 4 5 6 7 8 9 Differences. XIII. CUBE ROOTS. 151 5.0 1 2 3 4 5 6 7 8 9 Differences. 5.0 1.7100 7111 7123 7134 7145 7157 7168 7179 7190 7202 i 41 4 40 4 39 4 38 4 37 4 5.1 7213 7224 7235 7247 7258 7269 7280 7291 7303 7314 2 8 8 8 8 7 5.2 7325 7336 7347 7358 7369 7380 7391 7402 7413 7424 8 12 12 12 11 11 5.3 7435 7446 7457 7468 7479 7490 7501 7512 7522 7533 4 5 16 21 26 16 20 24 16 20 23 15 19 23 15 19 22 5.4 7544 7555 7566 7577 7587 7598 7609 7620 7630 7641 5.5 7652 7662 7673 7684 7694 7705 7716 7726 7737 7748 7 8 29 88 28 82 27 31 27 30 26 30 5.6 7758 7769 7779 7790 7800 7811 7821 7832 7842 7853 9 37 36 35 84 33 5.7 7863 7874 7884 7894 7905 7915 7926 7936 7946 7957 36 35 34 33 32 5.8 7967 7977 7988 7998 8008 8018 8029 8039 8049 8059 1 2 3 4 7 11 4 7 11 3 7 10 3 7 10 3 6 10 5.9 8070 8080 8090 8100 8110 8121 8131 8141 8151 8161 6.0 1.8171 8181 8191 8201 8211 8222 8232 8242 8252 8262 4 5 14 18 14 18 14 17 13 17 13 16 6.1 8272 8282 8292 8302 8311 8321 8331 8341 8351 8361 6 22 21 20 20 19 6.2 8371 8381 8391 8400 8410 8420 8430 8440 8450 8459 7 s B 25 29 82 25 28 32 24 27 31 23 26 30 22 6.3 8469 8479 8489 8498 8508 8518 8528 8537 8547 8557 26 29 6.4 8566 8576 8586 8595 8605 8615 8624 8634 8643 8653 31 30 29 28 27 6.5 8663 8672 8682 8691 8701 8710 8720 8729 8739 8748 1 a 3 6 9 3 6 9 3 6 9 3 6 8 3 5 8 6.6 8758 8767 8777 8786 8796 8805 8814 8824 8833 8843 6.7 8852 8861 8871 8880 8889 8899 8908 8917 8927 8936 4 12 12 12 11 11 6.8 8945 8955 8964 8973 8982 8992 9001 9010 9019 9029 B 8 T 16 19 22 15 18 21 15 17 20 14 17 20 14 16 19 6.9 9038 9047 9056 9065 9074 9084 9093 9102 9111 9120 7.0 1.9129 9138 9148 9157 9166 9175 9184 9193 9202 9211 S g 25 28 24 27 23 26 22 25 22 24 7.1 9220 9229 9238 9247 9256 9265 9274 9283 9292 9301 26 25 24 23 22 7.2 9310 9319 *9328 9337 9345 9354 9363 9372 9381 9390 i 3 3 2 2 2 7.3 9399 9408 9416 9425 9434 9443 9452 9461 9469 9478 4 5 8 10 5 8 10 5 7 10 5 7 9 4 7 9 7.4 9487 9496 9504 9513 9522 9531 9539 9548 9557 9566 7.5 7.6 9574 9661 9583 9670 9592 9678 9600 9687 9609 9695 9618 9704 9626 9713 9635 9721 9644 9730 9652 9738 5 C, 7 13 16 18 13 15 18 12 14 17 12 14 16 11 13 15 7.7 9747 9755 9764 9772 9781 9789 9798 9806 9815 9823 s 21 20 19 18 18 7.8 9832 9840 9849 9857 9866 9874 9883 9891 9899 9908 '.1 28 28 22 21 20 7.9 9916 9925 9933 9941 9950 9958 9967 9975 9983 9992 1 21 2 20 2 19 2 18 2 17 2 8.0 8.1 2.0000 0083 0008 0091 0017 0100 0025 0108 0033 0116 0042 0124 0050 0132 0058 0141 0066 0149 0075 0157 •1 8 i 4 6 8 4 6 8 4 6 8 4 5 7 3 5 7 8.2 0165 0173 0182 0190 0198 0206 0214 0223 0231 0239 D 11 10 10 9 9 8.3 0247 0255 0263 0271 0279 0288- 0296 0304 0312 0320 1 T a 13 15 17 12 14 16 11 IS 15 11 13 14 10 12 14 8.4 0328 0336 0344 0352 0360 0368 0376 0384 0392 0400 8.5 0408 0416 0424 0432 0440 0448 0456 0464 0472 0480 B 19 18 17 16 15 8.6 0488 0496 0504 0512 0520 0528 0536 0543 0551 0559 l 16 2 15 2 14 1 13 1 12 1 8.7 0567 0575 0583 0591 0599 0606 0614 0622 0630 0638 •> 3 3 3 3 2 8.8 0646 0653 0661 0669 0677 0685 0692 0700 0708 0716 ■i 5 6 8 5 6 8 4 6 7 4 5 7 4 5 6 8.9 0724 0731 0739 0747 0755 0762 0770 0778 0785 0793 4 B 9.0 2.0801 0809 0816 0824 0832 0839 0847 0855 0862 0870 8 T 8 10 11 13 9 11 12 8 10 8 9 7 3 9.1 0878 0885 0893 0901 0908 0916 0923 0931 0939 0946 11 10 10 9.2 0954 0961 0969 0977 0984 0992 0999 1007 1014 1022 9 14 14 13 12 11 9.3 1029 1037 1045 1052 1060 1067 1075 1082 1090 1097 11 10 9 8 7 9.4 1105 1112 1120 1127 1134 1142 1149 1157 1164 1172 1 '2 1 2 1 2 1 2 1 2 1 1 9.5 9.6 1179 1253 1187 1261 1194 1268 1201 1275 1209 1283 1216 1290 1224 1297 1231 1305 1238 1312 1246 1319 3 4 5 3 4 6 8 4 5 3 4 5 2 3 4 2 3 4 9.7 1327 1334 1341 1349 1356 1363 1371 1378 1385 1392 ('. 7 6 5 5 4 9.8 1400 1407 1414 1422 1429 1436 1443 1451 1458 1465 T S 'J 8 9 10 7 8 9 6 7 8 6 6 7 5 6 6 9.9 1472 1480 1487 1494 1501 1508 1516 1523 1530 1537 10.0 1 2 3 4 5 6 7 8 9 Differences. _ J 152 XIV. RECIPROCALS. 1 2 3 4 5 6 7 8 9 Differences. .0 00 100.0 50.00 33.33 25.00 20.00 16.67 14.29 12.50 ii.il i i 98 10 20 96 10 19 94 9 19 92 90 9 9 18 18 .i 10.0000 9.091 8.333 7.692 7.143 6.667 6.250 5.882 5.556 5.263 .2 5.0000 4.762 4.545 4.348 4.167 4.000 3.846 3.704 3.571 3.448 :; 29 29 28 .3 3.3333 3.226 3.125 3.030 2.941 2.857 2.778 2.703 2.632 2.564 1 5 89 49 59 88 48 58 38 47 56 37 86 46 45 55 54 .4 2.5000 2.439 2.381 2.326 2.273 2.222 2.174 2.128 2.083 2.041 .5 2.0000 *9608 *9231 *8868 *8519 *8182 *7857 *7544 *7241 *6949 7 a 69 78 67 77 66 75 64 68 74 '■> .6 1.6667 6393 6129 5873 5625 5385 5152 4925 4706 4493 !) 88 86 85 83 81 .7 4286 4085 3889 3699 3514 3333 3158 2987 2821 2658 88 86 84 S2 80 .8 2500 2346 2195 2048 1905 1765 1628 1494 1364 1236 1 9 9 8 8 8 .9 1111 0989 0870 0753 0638 0526 0417 0> 0309 0204 0101 •■', 18 26 17 26 17 25 16 16 25 24 1.0 1.1 1.0000 0.9091 *9901 9009 *9804 8929 *9709 8850 *9615 8772 *9524 8696 *9434 8621 *9346 8547 *9259 8475 *9174 8403 4 85 44 58 34 43 52 34 42 50 33 82 41 40 49 48 1.2 8333 8264 8197 8130 8065 8000 7937 7874 7813 7752 7 62 60 59 57 56 1.3 7692 7634 7576 7519 7463 7407 7353 7299 7246 7194 s 70 79 69 77 67 T8 66 64 74 72 1.4 7143 7092 7042 6993 6944 6897 6849 6803 6757 6711 78 76 74 72 70 1.5 6667 6623 6579 6536 6494 6452 6410 6369 6329 6289 1 8 16 23 8 7 7 7 1.6 6250 6211 6173 6135 6098 6061 6024 5988 5952 5917 2 15 23 15 22 14 14 22 21 1.7 5882 5848 5814 5780 5747 5714 5682 5650 561,8 5587 4 81 30 30 29 28 1.8 5556 5525 5495 5464 5435 5405 5376 5348 5319 5291 5 39 47 55 38 46 53 37 86 35 1.9 5263 5236 5208 5181 5155 5128 5102 5076 5051 5025 1 7 44 52 4;; H 50 49 2.0 0.5000 4975 4950 4926 4902 4878 4854 4831 4808 4785 a 62 70 61 68 Bf 67 58 56 65 63 2.1 2.2 4762 4545 4739 4525 4717 4505 4695 4484 4673 4464 4651 4444 4630 4425 4608 4405 4587 4386 4566 4367 l 68 7 66 7 G4 6 6 8 2.3 4348 4329 4310 4292 4274 4255 4237 4219 4202 4184 •-» 14 13 13 12 12 2.4 4167 4149 4132 4115 4098 4082 4065 4049 4032 4016 -1 20 27 20 26 19 26 19 18 •J.". -Jl 2.5 4000 3984 3968 3953 3937 3922 3906 3891 3876 3861 B 8 •7 84 41 48 as 32 38 45 81 30 2.6 3846 3831 3817 3802 3788 3774 3759 3745 3731 3717 40 46 87 36 43 42 2.7 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 B 54 Bi 51 50 43 2.8 3571 3559 3546 3534 3521 3509 3497 3484 3472 3460 9 61 59 58 56 54 2.9 3448 3436 3425 3413 3401 3390 3378 3367 3356 3344 1 58 6 56 6 54 5 52 50 5 5 3.0 0.3333 3322 3311 3300 3289 3279 3268 3257 3247 3236 2 12 11 11 10 10 3.1 3226 3215 3205 3195 3185 3175 3165 3155 3145 3135 8 4 17 28 17 22 16 22 16 15 21 20 3.2 3125 3115 3106 3096 3086 3077 3067 3058 3049 3040 5 29 28 27 26 25 3.3 3030 3021 3012 3003 2994 2985 2976 2967 2959 2950 6 85 84 82 31 80 3.4 2941 2933 2924 2915 2907 2899 2890 2882 2874 2865 7 8 41 46 89 45 88 43 36 35 42 40 3.5 2857 2849 2841 2833 2825 2817 2809 2801 2793 2786 8 52 50 49 47 45 3.6 2778 2770 2762 2755 2747 2740 2732 2725 2717 2710 l 2 48 5 10 46 5 9 44 4 9 43 42 3.7 2703 2695 2688 2681 2674 2667 2660 2653 2646 2639 4 4 9 8 3.8 2632 2625 2618 2611 2604 2597 2591 2584 2577 2571 8 14 14 13 13 13 39 2564 2558 2551 2545 2538 2532 2525 2519 2513 2506 4 5 19 M 18 23 IS 17 17 4.0 0.2500 2494 2488 2481 2475 2469 2463 2457 2451 2445 f. 29 28 26 26 25 4.1 2439 2433 2427 2421 2415 2410 2404 2398 2392 2387 7 8 84 88 82 87 81 85 80 29 34 34 4.2 2381 2375 2370 2364 2358 2353 2347 2342 2336 2331 9 48 41 40 89 88 4.3 2326 2320 2315 2309 2304 2299 2294 2288 2283 2278 41 40 39 88 87 4.4 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 1 •J 4 8 4 8 4 8 4 4 8 7 4.5 2222 2217 2212 2208 2203 2198 2193 2188 2183 2179 8 1-.' 19 U 11 11 4.6 2174 2169 2165 2160 2155 2151 2146 2141 2137 2132 4 5 6 16 •Jl 25 16 20 24 16 20 23 15 15 19 19 28 22 4.7 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 4.8 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 7 29 28 27 27 26 4.9 2041 2037 2033 2028 2024 2020 2016 2012 2008 2004 9 88 87 82 36 81 85 30 30 34 88 5.0 1 2 3 4 5 6 7 8 9 Diffei •ences. XIV. RECIPROCALS. 153 5.0 1 2 3 4 5 6 7 8 9 Differences. 5.0 0.2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 j 36 4 35 4 34 3 33 3 7 32 3 6 5.1 1961 1957 1953 1949 1946 1942 1938 1934 1931 1927 2 7 7 7 5.2 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 3 11 11 10 10 10 5.3 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 4 5 C 14 IS 22 14 18 21 14 17 20 13 17 20 13 16 19 5.4 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 5.5 1818 1815 1812 1808 1805 1802 1799 1795 1792 1789 7 S 25 29 25 2S 24 27 23 26 22 26 5.6 1786 1783 1779 1776 1773 1770 1767 1764 1761 1757 S 32 32 31 30 29 5.7 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 31 30 29 28 27 5.8 5.9 1724 1695 1721 1692 1718 1689 1715 1686 1712 1684 1709 1681 1706 1678 1704 1675 1701 1672 1698 1669 1 2 8 3 6 9 3 6 9 3 6 9 3 6 8 3 5 8 6.0 1667 1664 1661 1658 1656 1653 1650 1647 1645 1642 4 5 12 16 12 15 12 15 11 14 11 14 6.1 1639 1637 1634 1631 1629 1626 1623 1621 1618 1616 8 19 18 17 17 16 6.2 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 7 22 21 20 20 19 6.3 1587 1585 1582 1580 1577 1575 1572 1570 1567 1565 S 9 25 2S 24 27 23 26 22 25 22 24 6.4 1563 1560 1558 1555 1553 1550 1548 1546 1543 1541 26 25 24 23 22 6.5 6.6 1538 1515 1536 1513 1534 1511 1531 1508 1529 1506 1527 1504 1524 1502 1522 1499 1520 1497 1517 1495 1 2 8 3 5 8 3 5 8 2 5 7 2 5 7 2 4 7 . 6.7 1493 1490 1488 1486 1484 1481 1479 1477 1475 1473 4 10 10 10 9 9 6.8 6.9 1471 1449 1468 1447 1466 1445 1464 1443 1462 1441 1460 1439 1458 1437 1456 1435 1453 1433 1451 1431 B 8 7 13 16 18 13 15 18 12 14 17 12 14 16 11 13 15 7.0 1429 1427 1425 1422 1420 1418 1416 1414 1412 1410 S 9 21 23 20 23 19 22 IS 21 18 20 7.1 1408 1406 1404 1403 1401 1399 1397 1395 1393 1391 21 20 19 18 17 7.2 1389 1387 1385 1383 1381 1379 1377 1376 1374 1372 1 2 2 2 2 2 7.3 1370 1368 1366 1364 1362 1361 1359 1357 1355 1353 8 3 4 4 6 8 4 6 8 4 6 8 4 5 7 3 7.4 1351 1350 1348 1346 1344 1342 1340 1339 1337 1335 5 7 7.5 1333 1332 1330 1328 1326 1325 1323 1321 1319 1318 5 i; 11 13 10 12 10 11 13 9 11 13 9 10 12 7.6 1316 1314 1312 1311 1309 1307 1305 1304 1302 1300 T 15 14 7.7 1299 1297 1295 1294 1292 1290 1289 1287 1285 1284 8 17 16 15 14 14 7.8 1282 1280 1279 1277 1276 1274 1272 1271 1269 1267 8 19 18 17 16 15 7.9 1266 1264 1263 1261 1259 1258 1256 1255 1253 1252 1 16 2 15 2 14 1 13 1 12 1 8.0 1250 1248 1247 1245 1244 1242 1241 1239 1238 1236 8 8 4 3 5 6 3 5 6 3 4 6 3 4 5 2 8.1 1235 1233 1232 1230 1229 1227 1225 1224 1222 1221 4 5 8.2 1220 1218 1217 1215 1214 1212 1211 1209 1208 1206 B 8 8 7 7 6 8.3 8.4 1205 1190 1203 1189 1202 1188 1200 1186 1199 1185 1198 1183 -1196 1182 1195 1181 1193 1179 1192 1178 8 T 8 10 11 13 9 11 12 8 10 11 8 9 10 7 8 10 8.5 1176 1175 1174 1172 1171 1170 1168 1167 1166 1164 8 14 14 13 12 11 8.6 1163 1161 1160 1159 1157 1156 1155 1153 1152 1151 1 ? 11 1 2 10 2 9 1 2 8 1 2 7 1 1 8.7 1149 1148 1147 1145 1144 1143 1142 1140 1139 1138 2 8.8 1136 1135 1134 1133 1131 1130 1^29 1127 1126 1125 3 3 3 3 2 2 8.9 1124 1122 1121 1120 1119 1117 1116 1115 1114 1112 4 6 4 6 4 5 4 5 3 4 3 4 9.0 9.1 1111 1099 1110 1098 1109 1096 1107 1095 1106 1094 1105 1093 1104 1092 1103 1091 1101 1089 1100 1088 a 7 9 7 8 9 6 7 8 5 6 7 5 6 6 4 5 6 9.2 1087 1086 1085 1083 1082 1081 1080 1079 1078 1076 8 10 9 8 7 6 9.3 1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 6 5 4 3 2 9.4 1064 1063 1062 1060 1059 1058 1057 1056 1055 1054 1 2 1 1 1 1 1 1 9.5 1053 1052 1050 1049 1048 1047 1046 1045 1044 1043 3 2 2 3 2 2 3 1 2 2 1 1 2 1 1 1 9.6 1042 1041 1040 1038 1037 1036 1035 1034 1033 1032 4 5 9.7 1031 1030 1029 1028 1027 1026 1025 1024 1022 1021 6 4 3 2 2 1 9.8 9.9 1020 1010 1019 1009 1018 1008 1017 1007 1016 1006 1015 1005 1014 1004 1013 1003 1012 1002 1011 1001 7 8 9 4 5 5 4 4 5 3 3 4 2 2 3 1 2 2 10.0 1 2 3 4 5 6 7 8 9 Differences. 154 XV. QUARTER-SQUARES. 1 2 3 4 5 6 7 8 9 i 2 4 6 9 12 16 20 i 25 30 36 42 49 56 64 72 81 90 2 100 110 121 132 144 156 169 182 196 210 3 225 240 256 272 289 306 324 342 . 361 380 4 400 420 441 462 484 506 529 552 576 600 5 625 650 676 702 729 756 784 812 841 870 6 900 930 961 992 1024 1056 1089 1122 1156 J190 7 1225 1260 1296 1332 1369 1406 1444 1482 1521 1560 8 1600 1640 1681 1722 1764 1806 1849 1892 1936 1980 9 2025 2070 2116 2162 2209 2256 2304 2352 2401 2450 10 2500 2550 2601 2652 2704 2756 2809 2862 2916 2970 11 3025 3080 3136 3192 3249 3306 3364 3422 3481 3540 12 3600 3660 3721 3782 3844 3906 3969 4032 4096 4160 13 4225 4290 4356 4422 4489 4556 4624 4692 4761 4830 14 4900 4970 5041 5112 5184 5256 5329 5402 5476 5550 15 5625 5700 5776 5852 5929 6006 6084 6162 6241 6320 16 6400 6480 6561 6642 6724 6806 6889 6972 7056 7140 17 7225 7310 7396 7482 7569 7656 7744 7832 7921 8010 18 8100 8190 8281 8372 8464 8556 8649 8742 8836 8930 19 9025 9120 9216 9312 9409 9506 9604 9702 9801 9900 20 1 0000 1 0100 1 0201 1 0302 1 0404 1 0506 1 0609 1 0712 1 0816 1 0920 21 1025 1130 1236 1342 1449 1556 1664 1772 1881 1990 22 2100 2210 2321 2432 2544 2656 2769 2882 2996 3110 23 3225 3340 3456 3572 3689 3806 3924 4042 4161 4280 24 4400 4520 4641 4762 4884 5006 5129 5252 5376 5500 25 5625 5750 5876 6002 6129 6256 6384 6512 6641 6770 26 6900 7030 7161 7292 7424 7556 7689 7822 7956 8090 27 8225 8360 8496 8632 8769 8906 9044 9182 9321 9460 28 9600 9740 9881 2 0022 2 0164 2 0306 2 0449 2 0592 2 0736 2 0880 29 2 1025 2 1170 2 1316 1462 1609 1756 1904 2052 2201 2350 30 2 2500 2 2650 2 2801 2 2952 2 3104 2 3256 2 3409 2 3562 2 3716 2 3870 31 4025 4180 4336 4492 4649 4806 4964 5122 5281 5440 32 5600 5760 5921 6082 6244 6406' 6569 6732 6896 7060 33 7225 7390 7556 7722 7889 8056 8224 8392 8561 8730 34 8900 9070 9241 9412 9584 9756 9929 3 0102 3 0276 3 0450 35 3 0625 3 0800 3 0976 3 1152 3 1329 3 1506 3 1684 1862 2041 2220 36 2400 2580 2761 2942 3124 3306 3489 3672 3856 4040 37 4225 4410 4596 4782 4969 5156 5344 5532 5721 5910 38 6100 6290 6481 6672 6864 7056 7249 7442 7636 7830 39 8025 8220 8416 8612 8809 9006 9204 9402 9601 9800 40 4 0000 4 0200 4 0401 4 0602 4 0804 4 1006 4 1209 4 1412 4 1616 4 1820 41 2025 2230 2436 2642 2849 3056 3264 3472 3681 3890 42 4100 4310 4521 4732 4944 5156 5369 5582 5796 6010 43 6225 6440 6656 6872 7089 7306 7524 7742 7961 8180 44 8400 8620 8841 9062 9284 9506 9729 9952 5 0176 5 0400 45 5 0625 5 0850 5 1076 5 1302 5 1529 5 1756 5 1984 5 2212 2441 2670 4G 2900 3130 3361 3592 3824 4056 4289 4522 4756 4990 47 5225 5460 5696 5932 6169 6406 6644 6882 7121 7360 48 7600 7840 8081 8322 8564 8806 9049 9292 9536 9780 49 6 0025 6 0270 6 0516 6 0762 6 1009 6 1256 6 1504 6 1752 6 2001 6 2250 \(a + d) '-*(«■ -b)' = ad. XV. QUARTER-SQUARES. 155 50 1 2 3 4 5 6 7 8 9 50 6 2500 6 2750 6 3001 6 3252 6 3504 6 3756 6 4009 6 4262 6 4516 6 4770 51 5025 5280 5536 5792 6049 6306 6564 6822 7081 7340 52 7600 7860 8121 8382 8644 8906 9169 9432 9696 9960 53 7 0225 7 0490 7 0756 7 1022 7 1289 7 1556 7 1824 7 2092 7 2361 7 2630 54 2900 3170 3441 3712 3984 4256 4529 4802 5076 5350 55 5625 5900 6176 6452 6729 7006 7284 7562 7841 8120 56 8400 8680 8961 9242 9524 9806 8 0089 8 0372 8 0656 8 0940 57 8 1225 8 1510 8 1796 8 2082 8 2369 8 2656 2944 3232 3521 3810 58 4100 4390 4681 4972 5264 5556 5849 6142 6436 6730 59 7025 7320 7616 7912 8209 * 8506 8804 9102 9401 9700 60 9 0000 9 0300 9 0601 9 0902 9 1204 9 1506 9 1809 9 2112 9 2416 9 2720 61 3025 3330 3636 3942 4249 4556 4864 5172 5481 5790 62 6100 6410 6721 7032 ' 7344 7656 7969 8282 8596 8910 63 9225 9540 9856 10 0172 10 0489 10 0806 10 1124 10 1442 10 1761 10 2080 64 10 2400 10 2720 10 3041 3362 3684 4006 4329 4652 4976 5300 65 5625 5950 6276 6602 6929 7256 7584 7912 8241 8570 66 8900 9230 9561 9892 11 0224 11 0556 11 0889 11 1222 11 1556 11 1890 67 11 2225 11 2560 11 2896 11 3232 3569 3906 4244 4582 4921 5260 68 5600 5940 6281 6622 6964 7306 7649 7992 8336 8680 69 9025 9370 9716 12 0062 12 0409 12 0756 12 1104 12 1452 12 1801 12 2150 70 12 2500 12 2850 12 3201 12 3552 12 3904 12 4256 12 4609 12 4962 12 5316 12 5670 71 6025 6380 6736 7092 7449 7806 8164 8522 8881 9240 72 9600 9960 13 0321 13 0682 13 1044 13 1406 13 1769 13 2132 13 2496 13 2860 73 13 3225 13 3590 3956 4322 4689 5056 5424 5792 6161 6530 74 6900 7270 7641 8012 8384 8756 9129 9502 9876 14 0250 75 14 0625 14 1000 14 1376 14 1752 14 2129 14 2506 14 2884 14 3262 14 3641 4020 76 4400 4780 5161 5542 5924 6306 6689 7072 7456 7840 77 8225 8610 8996 9382 9769 15 0156 15 0544 15 0932 15 1321 15 1710 78 15 2100 15 2490 15 2881 15 3272 15 3664 4056 4449 4842 5236 5630 79 6025 6420 6816 7212 7609 8006 8404 8802 9201 9600 80 16 0000 16 0400 16 0801 16 1202 1G 1604 16 2006 16 2409 16 2812 16 3216 16 3620 81 4025 4430 4836 5242 5649 6056 6464 ' 6872 7281 7690 82 8100 8510 8921 9332 9744 17 0156 17 0569 17 0982 17 1396 17 1810 83 17 2225 17 2640 17 3056 17 3472 17 3889 4306 4724 5142 5561 5980 84 6400 6820 7241 7662 8084 8506 8929 9352 9776 18 0200 85 18 0625 18 1050 18 1476 18 1902 18 2329 18 2756 18 3184 18 3612 18 4041 4470 86 4900 5330 5761 6192 6624 7056 7489 7922 8356 8790 87 9225 9660 19 0096 19 0532 19 0969 19 1406 19 1844 19 2282 19 2721 19 3160 88 19 3600 19 4040 4481 4922 5364 5806 6249 6692 7136 7580 89 8025 8470 8916 9362 9809 20 0256 20 0704 20 1152 20 1601 20 2050 90 20 2500 20 2950 20 3401 20 3852 20 4304 20 4756 20 5209 20 5662 20 6116 20 6570 91 7025 7480 7936 8392 8849 9306 9764 21 0222 21 0681 21 1140 92 21 1600 21 2060 21 2521 21 2982 21 3444 21 3906 21 4369 4832 5296 5760 93 6225 6690 7156 7622 8089 8556 9024 9492 9961 22 0430 94 22 0900 22 1370 22 1841 22 2312 22 2784 22 3256 22 3729 22 4202 22 4676 5150 95 5625 6100 6576 7052 7529 8006 8484 8962 9441 9920 96 23 0400 23 0880 23 1361 23 1842 23 2324 23 2806 23 3289 23 3772 23 4256 23 4740 97 5225 5710 6196 6682 7169 7656 8144 8632 9121 9610 98 24 0100 24 0590 24 1081 24 1572 24 2064 24 2556 24 3049 24 3542 24 4036 24 4530 99 5025 5520 6016 6512 7009 7506 8004 8502 9001 9500 \{a + br-\{a- -by = ab 1 156 XV. QUARTER-SQUARES. 100 1 2 3 4 5 6 7 8 9 100 25 0000 25 0500 25 1001 25 1502 25 2004 25 2506 25 3009 25 3512 25 4016 25 4520 01 5025 5530 6036 6542 7049 7556 8064 8572 9081 9590 02 26 0100 26 0610 26 1121 26 1632 26 2144 26 2656 26 3169 26 3682 26 4196 26 4710 03 5225 5740 6256 6772 7289 7806 8324 8842 9361 9880 04 27 0400 27 0920 27 1441 27 1962 27 2484 27 3006 27 3529 27 4052 27 4576 27 5100 05 5625 6150 6676 7202 7729 8256 8784 9312 9841 28 0370 06 28 0900 28 1430 28 1961 28 2492 28 3024 28 3556 28 4089 28 4622 28 5156 5690 07 6225 6760 7296 7832 8369 8906 9444 9982 29 0521 29 1060 08 29 1600 29 2140 29 2681 29 3222 29 3764 29 4306 29 4849 29 5392 5936 6480 09 7025 7570 8116 8662 9209 9756 30 0304 30 0852 30 1401 30 1950 110 30 2500 30 3050 30 3601 30 4152 30 4704 30 5256 30 5809 30 6362 30 6916 30 7470 11 8025 8580 9136 9692 31 0249 31 0806 31 1364 31 1922 31 2481 31 3040 12 31 3600 314160 314721 31 5282 5844 6406 6969 7532 8096 8660 13 9225 9790 32 0356 32 0922 32 1489 32 2056 32 2624 32 3192 32 3761 32 4330 14 32 4900 32 5470 6041 6612 7184 7756 8329 8902 9476 33 0050 M 33 0625 33 1200 33 1776 33 2352 33 2929 33 3506 33 4084 33 4662 33 5241 5820 16 6400 6980 7561' 8142 8724 9306 9889 34 0472 34 1056 34 1640 17 34 2225 34 2810 34 3396 34 3982 34 4569 34 5156 34 5744 6332 6921 7510 18 8100 8690 9281 9872 35 0464 35 1056 35 1649 35 2242 35 2836 35 3430 19 35 4025 35 4620 35 5216 35 5812 6409 7006 7604 8202 8801 9400 120 36 0000 36 0600 36 1201 36 1802 36 2404 36 3006 36 3609 36 4212 36 4816 36 5420 21 6025 6630 7236 7842 8449 9056 9664 37 0272 37 0881 37 1490 22 37 2100 37 2710 37 3321 37 3932 37 4544 37 5156 37 5769 6382 6996 7610 23 8225 8840 9456 38 0072 38 0689 38 1306 38 1924 38 2542 38 3161 38 3780 24 38 4400 38 5020 38 5641 6262 6884 7506 8129 8752 9376 39 0000 25 39 0625 39 1250 39 1876 39 2502 39 3129 39 3756 39 4384 39 5012 39 5641 6270 26 6900 7530 8161 8792 9424 40 0056 40 0689 40 1322 40 1956 40 2590 27 40 3225 40 3860 40 4496 40 5132 40 5769 6406 7044 7682 8321 8960 28 9600 41 0240 41 0881 41 1522 41 2164 41 2806 41 3449 414092 414736 41 5380 29 41 6025 6670 7316 7962 8609 9256 9904 42 0552 42 1201 42 1850 130 42 2500 42 3150 42 3801 42 4452 42 5104 42 5756 42 6409 42 7062 42 7716 42 8370 31 9025 9680 43 0336 43 0992 43 1649 43 2306 43 2964 43 3622 43 4281 43 4940 32 43 5600 43 6260 6921 7582 8244 8906 9569 44 0232 44 0896 44 1560 33 44 2225 44 2890 44 3556 44 4222 44 4889 44 5556 44 6224 6892 7561 8230 34 8900 9570 45 0241 45 0912 45 1584 45 2256 45 2929 45 3602 45 4276 45 4950 35 45 5625 45 6300 6976 7652 8329 9006 9684 46 0362 46 1041 46 1720 36 46 2400 46 3080 46 3761 46 4442 46 5124 46 5806 46 6489 7172 7856 8540 37 9225 9910 47 0596 47 1282 47 1969 47 2656 47 3344 47 4032 47 4721 47 5410 38 47 6100 47 6790 7481 8172 8864 9556 48 0249 48 0942 48 1636 48 2330 39 48 3025 48 3720 48 4416 48 5112 48 5809 48 6506 7204 7902 8601 9300 140 49 0000 49 0700 49 1401 49 2102 49 2804 49 3506 49 4209 49 4912 49 5616 49 6320 41 7025 7730 8436 9142 9849 50 0556 50 1264 50 1972 50 2681 50 3390 42 50 4100 50 4810 50 5521 50 6232 50 6944 7656 8369 9082 9796 610510 43 51 1225 51 1940 51 2656 51 3372 514089 514806 51 5524 5] 6249 51 6961 7680 44 8400 9120 9841 52 0562 52 1284 52 2006 52 2729 52 3452 52 4176 52 4900 45 52 5625 52 6350 52 7076 7802 8529 9256 9984 53 0712 53 1441 53 2170 46 53 2900 53 3630 63 4361 53 5092 53 5824 53 6556 53 7289 8022 8756 9490 47 54 0225 54 0960 54 1696 54 2432 54 3169 54 3906 54 4644 54 5382 54 6121 54 6860 48 7600 8340 9081 9822 55 0564 55 1306 55 2049 55 2792 55 3536 55 4280 49 55 5025 55 5770 55 6516 55 7262 8009 8756 9504 56 0252 66 1001 56 1750 *(« + *)'-*(«- -b? = ab XV . QUARTER-SQUARES. 15T 150 1 2 3 4 5 6 7 8 9 150 56 2500 56 3250 56 4001 56 4752 56 5504 56 6256 56 7009 56 7762 56 8516 56 9270 51 57 0025 57 0780 57 1536 57 2292 57 3049 57 3806 57 4564 57 5322 57 6081 57 6840 52 7600 8360 9121 9882 58 0644 58 1406 58 2169 58 2932 58 3696 58 4460 53 58 5225 58 5990 58 6756 58 7522 8289 9056 9824 59 0592 59 1361 59 2130 54 59 2900 59 3670 59 4441 59 5212 59 5984 59 6756 59 7529 8302 9076 9850 55 60 0625 60 1400 60 2176 60 2952 60 3729 60 4506 60 5284 60 6062 60 6841 60 7620 56 8400 9180 9961 61 0742 61 1524 61 2306 61 3089 61 3872 61 4656 61 5440 57 61 6225 61 7010 61 7796 8582 9369 62 0156 62 0944 62 1732 62 2521 62 3310 58 62 4100 62 4890 62 5681 62 6472 62 7264 8056 8849 9642 63 0436 63 1230 59 63 2025 63 2820 63 3616 63 4412 63 5209 63 6006 63 6804 63 7602 8401 9200 160 64 0000 64 0800 64 1601 64 2402 64 3204 64 4006 64 4809 64 5612 64 6416 64 7220 61 8025 8830 9636 65 0442 65 1249 65 2056 65 2864 65 3672 65 4481 65 5290 62 65 6100 65 6910 65 7721 8532 9344 66 0156 66 0969 66 1782 66 2596 66 3410 63 66 4225 66 5040 66 5856 66 6672 66 7489 8306 9124 9942 67 0761 67 1580 64 67 2400 67 3220 67 4041 67 4862 67 5684 67 6506 67 7329 67 8152 8976 9800 65 68 0625 68 1450 68 2276 68 3102 68 3929 68 4756 68 5584 68 6412 68 7241 68 8070 66 8900 9730 69 0561 69 1392 69 2224 69 3056 69-3889 69 4722 69 5556 69 6390 67 69 7225 69 8060 8896 9732 70 0569 70 1406 70 2244 70 3082 70 3921 70 4760 68 70 5600 70 6440 70 7281 70 8122 8964 9806 71 0649 71 1492 71 2336 71 3180 69 71 4025 71 4870 71 5716 71 6562 71 7409 71 8256 9104 9952 72 0801 72 1650 170 72 2500 72 3350 72 4201 72 5052 72 5904 72 6756 72 7609 72 8462 72 9316 73 0170 71 73 1025 73 1880 73 2736 73 3592 73 4449 73 5306 73 6164 73 7022 73 7881 8740 72 9600 74 0460 74 1321 74 2182 74 3044 74 3906 74 4769 74 5632 74 6496 74 7360 73 74 8225 9090 9956 75 0822 75 1689 75 2556 75 3424 75 4292 75 5161 75 6030 74 75 6900 75 7770 75 8641 9512 76 0384 76 1256 76 2129 76 3002 ."6 3876 76 4750 75 76 5625 76 6500 76 7376 76 8252 9129 77 0006 77 0884 77 1762 77 2641 77 3520 76 77 4400 77 5280 77 6161 77 7042 77 7924 8806 9689 78 0572 78 1456 78 2340 77 78 3225 78 4110 78 4996 78 5882 78 6769 78 7656 78 8544 9432 79 0321 79 1210 78 79 2100 79 2990 79 3881 79 4772 79 5664 79 6556 79 7449 79 8342 9236 80 0130 79 80 1025 80 1920 80 2816 80 3712 80 4609 80 5506 80 6404 80 7302 80 8201 9100 180 81 0000 81 0900 81 1801 81 2702 81 3604 81 4506 81 5409 81 6312 81 7216 81 8120 81 9025 9930 82 0836 82 1742 82 2649 82 3556 82 4464 82 5372 82 6281 82 7190 82 82 8100 82 9010 9921 83 0832 83 1744 83 2656 83 3569 83 4482 83 5396 83 6310 83 83 7225 83 8140 83 9056 9972 84 0889 84 1806 84 2724 84 3642 84 4561 84 5480 84 84 6400 84 7320 84 8241 84 9162 85 0084 85 1006 85 1929 85.2852 85 3776 85 4700 85 85 5625 85 6550 85 7476 85 8402 9329 86 0256 86 1184 86 2112 86 3041 86 3970 86 86 4900 86 5830 86 6761 86 7692 86 8624 9556 87 0489 87 1422 87 2356 87 3290 87 87 4225 87 5160 87 6096 87 7032 87 7969 87 8906 9844 88 0782 88 1721 88 2660 88 88 3600 88 4540 88 5481 88 6422 88 7364 88 8306 88 9249 89 0192 89 1136 89 2080 89 89 3025 89 3970 89 4916 89 5862 89 6809 89 7756 89 8704 9652 90 0601 90 1550 190 90 2500 90 3450 90 4401 90 5352 90 6304 90 7256 90 8209 90 9162 910116 91 1070 91 91 2025 91 2980 91 3936 91 4892 91 5849 91 6806 91 7764 918722 9681 92 0640 92 92 1600 92 2560 92 3521 92 4482 92 5444 92 6406 92 7369 92 8332 92 9296 93 0260 93 93 1225 93 2190 93 3156 93 4122 93 5089 93 6056 93 7024 93 7992 93 8961 9930 94 94 0900 94 1870 94 2841 94 3812 94 4784 94 5756 94 6729 94 7702 948676 94 9650 95 95 0625 95 1600 95 2576 95 3552 95 4529 95 5506 95 6484 95 7462 95 8441 95 9420 96 96 0400 96 1380 96 2361 96 3342 96 4324 96 5306 96 6289 96 7272 96 8256 96 9240 97 97 0225 97 1210 97 2196 97 3182 97 4169 97 5156 97 6144 97 7132 97 8121 97 9110 98 98 0100 98 1090 98 2081 98 3072 98 4064 98 5056 98 6049 98 7042 98 8036 98 9030 99 99 0025 99 1020 99 2016 99 3012 99 4009 99 5006 99 6004 99 7002 99 8001 99 9000 \(a+by-\(a- -6)*=al . 158 XVI. BESSEL'S COEFFICIENTS. c, c 2 c 3 c 4 c 5 c, c 2 c 3 c, c 5 .00 0.00000 0.00000 0.00000 0.00000 .50 0.12500 0.00000 0.02344 0.00000 .01 0495 0081 0083 0008 .51 2495 0042 2343 0005 .02 0980 0157 0165 0016 .52 2480 0083 2340 0009 .03 1455 0228 0246 0023 .53 2455 0125 2334 0014 .04 1920 0294 0326 0030 .54 2420 0166 2327 0019 .05 2375 0356 0405 0036 .55 2375 0206 2318 0023 .06 2820 0414 0483 0043 .56 2320 0246 2306 0028 .07 3255 0467 0560 0048 .57 2255 0286 2293 0032 .08 3680 0515 0636 0053 .58 2180 0325 2277 0036 .09 4095 0560 0710 0058 .59 2095 0363 2260 0041 .10 0.04500 0.00600 0.00784 0.00063 .60 0.12000 0.00400 0.02240 0.00045 .11 4895 0636 0856 0067 .61 1895 0436 2218 0049 .12 5280 0669 0926 0070 .62 1780 0471 2195 0053 .13 5655 0697 0996 0074 .63 1655 0505 2169 0056 .14 6020 0722 1064 0077 .64 1520 0538 2141 0060 .15 6375 0744 1130 0079 .65 1375 0569 2111 0063 .16 6720 0762 1195 0081 .66 1220 0598 2080 0067 .17 7055 0776 1259 0083 .67 1055 0626 2046 0070 .18 7380 0787 1321 0085 .68 0880 0653 2011 0072 .19 7695 0795 1381 0086 .69 0695 0677 1973 0075 .20 0.08000 0.00800 0.01440 0.00086 .70 0.10500 0.00700 0.01934 0.00077 .21 8295 0802 1497 0087 .71 0295 0721 1892 0079 .22 8580 0801 1553 0087 .72 0080 0739 1849 0081 .23 8855 0797 1607 0087 .73 0.09855 0756 1804 0083 .24 9120 0790 1659 0086 .74 9620 0770 1758 00'84 .25 9375 0781 1709 0085 .75 9375 0781 1709 0085 .26 9620 0770 1758 0084 .76 9120 0790 1659 0086 .27 9855 0756 1804 0083 .77 8855 0797 1607 0087 .28 0.10080 0739 1849 0081 .78 8580 0801 1553 0087 .29 0295 0721 1892 0079 .79 8295 0802 1497 0087 .30 0.10500 0.00700 0.01934 0.00077 .80 0.08000 0.00800 0.01440 0.00086 .31 0695 0677 1973 007.5 .81 7695 0795 1381 0086 .32 0880 0653 2011 0072 .82 7380 0787 1321 0085 .33 1055 0626 2046 0070 .83 7055 0776 1259 0083 .34 1220 0598 2080 0067 .84 6720 0762 1195 0081 .35 1375 0569 2111 0063 .85 6375 0744 1130 0079 .36 1520 0538 2141 0060 .86 6020 0722 1064 0077 .37 1655 0505 2169 0056 .87 5655 0697 0996 0074 .38 1780 0471 2195 0053 .88 5280 0669 0926 0070 .39 1895 0436 2218 0049 .89 4895 0636 0856 0067 .40 0.12000 0.00400 0.02240 0.00045 .90 0.04500 0.00600 0.00784 0.00063 .41 2095 0363 2260 0041 .91 4095 0560 0710 0058 .42 2180 0325 2277 0036 .92 3680 0515 0636 0053 43 2255 0286 2293 0032 .93 3255 0467 0560 0048 .44 2320 0246 2306 0028 .94 2820 0414 0483 0043 .45 2375 0206 2318 0023 .95 2375 0356 0405 0036 .46 2420 0166 2327 0019 .96 1920 0294 0326 0030 .47 2455 0125 2334 0014 .97 1455 0228 0246 0023 .48 2480 0083 2340 0009 .98 0980 0157 0165 0016 .49 2495 0042 2343 0005 .99 0495 0081 0083 0008 1 3„ C 5 , Negative. c „ C,, Negative. XVII. BINOMIAL COEFFICIENTS. 159 Cx c 2 C 3 c t c 6 0, c 2 c 3 c 4 c 5 .00 0.00000 0.00000 0.00000 0.00000 .50 0.12500 0.06250 0.03906 0.02734 .01 0495 0328 0245 0196 .51 2495 6206 3863 2696 .02 0980 0647 0482 0384 .52 2480 6157 3817 2657 .03 1455 0955 0709 0563 .53 2455 6103 3769 2615 .04 1920 1254 0928 0735 .54 2420 6044 3717 2572 .05 2375 1544 1139 0899 .55 2375 5981 3664 2528 .06 2820 1824 1340 1056 .56 2320 5914 3607 2482 .07 3255 2094 1534 1206 .57 2255 5842 3549 2434 .08 3680 2355 1719 1348 .58 2180 5765 3488 2386 .09 4095 2607 1897 1483 .59 2095 5685 3425 2336 .10 0.04500 0.02850 0.02066 0.01612 .60 0.12000 0.05600 0.03360 0.02285 .11 4895 3084 2228 1733 .61 1895 5511 3293 2233 .12 5280 3309 2382 1849 .62 1780 5419 3224 2180 .13 5655 3525 2529 19<58 .63 1655 5322 3154 2125 .14 6020 3732 2669 2060 .64 1520 5222 3081 2071 .15 6375 3931 2801 2157 .65 1375 5119 3007 2015 .16 6720 4122 2926 2247 .66 1220 5012 2932 1958 .17 7055 4304 3045 2332 .67 1055 4901 2855 1901 .18 7380 4477 3156 2412 .68 0880 4787 2777 1844 .19 7695 4643 3261 2485 .69 0695 4670 2697 1785 .20 0.08000 0.04800 0.03360 0.02554 .70 0.10500 0.04550 0.02616 0.01727 .21 8295 4949 3452 2617 .71 0295 4427 2534 1668 .22 8580 5091 3538 2675 .72 0080 4301 2451 1608 .23 8855 5224 3618 2728 .73 0.09855 4172 2368 1548 .24 9120 5350 3692 2776 .74 9620 4040 2283 1488 .25 9375 5469 3760 2820 .75 9375 3906 2197 1428 .26 9620 5580 3822 2859 .76 9120 3770 2111 1368 .27 9855 5683 3879 2893 .77 8855 3631 2024 1308 .28 0.10080 5779 3930 2924 .78 8580 3489 1937 1247 .29 0295 5868 3976 2950 .79 8295 3346 1848 1187 .30 0.10500 0.05950 0.04016 0.02972 .80 0.08000 0.03200 0.01760 0.01126 .31 0695 6025 4052 2990 .81 7695 3052 1671 1066 .32 0880 6093 4082 3004 .82 7380 2903 1582 1006 .33 1055 6154 4108 3015 .83 7055 2751 1493 0946 .34 1220 6208 4129 3022 .84 6720 2598 1403 0887 .35 1375 6256 4145 3026 .85 6375 2444 1314 0828 .36 1520 6298 4156 3026 .86 6020 2288 1224 0769 .37 1655 6333 4164 3023 .87 5655 2130 1134 0710 .38 1780 6361 4167 3017 .88 5280 1971 1045 0652 .39 1895 6384 4165 3007 .89 4895 1811 0955 0594 .40 0.12000 0.06400 0.04160 0.02995 .90 0.04500 0.01650 0.00866 0.00537 .41 2095 6410 4151 2980 .91 4095 1488 0777 0480 .42 2180 6415 4138 2962 .92 3680 1325 0689 0424 .43 2255 6413 4121 2942 .93 3255 1161 0601 0369 .44 2320 6406 4100 2919 .94 2820 0996 0513 0314 .45 2375 6394 4076 2894 .95 2375 0831 0426 0260 .46 2420 6376 4049 2866 .96 1920 0666 0339 0206 .47 2455 6352 4018 2836 .97 1455 0500 0254 0154 .48 2480 6323 3984 2804 .98 0980 0333 0168 0102 .49 2495 6289 3946 2770 .99 0495 0167 0084 0050 eg c 4 , k r egath re. ._ 160 XVIII. ERRORS OF OBSERVATION. 1 t. JLe't' J- f'e-i'at t ± Ce-'at n. 0.6745 0.6745 'i.vir;i 0.8458 V" V"J .4769 V*J V(n-\) v n ( a — i) yn(n-l) flV(»-l) 0.0 .56419 0.000000 0.0 0.0000 2 0.6745 0.4769 0.5978 0.4227 0.1 .55858 112463 0.1 0538 3 4769 2754 3451 1993 0.2 .54207 222703 0.2 1073 4 3894 1947 2440 1220 0.3 .51563 328627 0.3 1604 0.4 .48077 428392 0.4 2127 5 3372 1508 1890 0845 6 3016 1231 1543 0630 0.5 .43939 520500 0.5 2641 7 2754 1041 1304 0493 0.6 .39362 603856 0.6 3143 8 2549 0901 1130 0399 0.7 .34564 677801 0.7 3632 9 2385 0795 0996 0332 0.8 .29749 742101 0.8 4105 0.9 .25098 796908 0.9 4562 10 0.2248 0.0711 0.0891 0.0282 11 2133 0643 0806 0243 1.0 .20755 0.842701 1.0 0.5000 12 2034 0587 0736 0212 1.1 .16824 880205 1.1 5419 13 1947 0540 0677 0188 1.2 .13367 910314 1.2 5817 14 1871 0500 0627 0167 1.3 .10410 934008 1.3 6194 1.4 .07947 952285 1.4 6550 15 1803 0465 0583 0151 16 1742 0435 0546 0136 1.5 .05947 966105 1.5 6883 17 1686 0409 0513 0124 1.6 .04361 976348 1.6 7195 18 1636 0386 0483 0114 1.7 .03136 983790 1.7 7485 19 1590 0365 0457 0105 1.8 .02210 .989090 1.8 7753 1.9 .01526 '992790 1.9 8000 20 0.1547 0.0346 0.0434 0.0097 21 1508 0329 0412 0090 2.0 .01033 0.995322 2.0 0.8227 22 1472 0314 0393 0084 2.1 .0 2 6858 997020 2.1 8433 23 1438 0300 0376 0078 2.2 .0 2 4461 998137 2.2 8622 24 1406 0287 0360 0073 2.3 .0 2 2845 998857 2.3 8792 2.4 .0 2 1778 999310 2.4 8945 25 1377 0275 0345 0069 26 1349 0265 0332 0065 2.5 .0 2 1089 999593 2.5 9082 27 1323 0255 0319 0061 2.6 .0 3 6540 999764 2.6 9205 28 1298 0245 0307 0058 2.7 .0 3 3850 999866 2.7 9314 29 1275 0237 0297 0055 2.8 .0 3 2221 999925 2.8 9411 2.9 .0 3 1256 999959 2.9 9495 30 0.1252 0.0229 0.0287 0.0052 31 1231 0221 0277 0050 3.0 .0 4 6963 0.9999779 3.0 0.9570 32 1211 0214 0268 0047 3.1 .0 4 3783 9999884 3.1 9635 33 1192 0208 0260 0045 3.2 .0 4 2015 9999940 3.2 9691 34 1174 0201 0252 0043 3.3 .0 4 1052 9999969 3.3 9740 3.4 .0 5 5382 9999985 3.4 9782 35 1157 0196 0245 0041 36 1140 0190 0238 0040 3.5 .0 5 2700 9999993 3.5 9818 37 1124 0185 0232 0038 3.6 .0H327 9999996 3.6 9848 38 1109 0180 0225 0037 3.7 .0 6 6396 9999998 3.7 9874 39 1094 0175 0220 0035 3.8 .0 6 3021 9999999 3.8 9896 3.9 .0«1399 9999999 3.9 9915 40 0.1080 0.0171 0.0214 0.0034 41 1066 0167 0209 0033 4.0 .0'6349 4.0 0.9930 42 1053 0163 0204 0031 4.1 .0'2824 4.1 9943 43 1041 0159 0199 0030 4.2 .0 1 1232 4.2 9954 44 1029 0155 0194 0029 4.3 .0 8 5264 4.3 9963 4.4 .0 8 2205 4.4 9970 45 1017 0152 0190 0028 46 1005 0148 0186 0027 4.5 .0 9 9057 4.5 9976 47 0994 0145 0182 0027 4.6 .0 9 3645 4.6 9981 48 0984 0142 0178 0026 4.7 .0 9 1438 4.7 9985 49 0974 0139 0174 0025 4.8 .0 I0 5563 4.8 9988 4.9 .0 10 2109 4.9 9991 50 0.0964 0.0136 0.0171 0.0024 55 0918 0124 0155 0021 5.0 .0"7835 5.0 0.9993 60 0878 0113 0142 0018 65 70 0843 0812 0105 0097 0131 0122 0016 0015 PROPORTIONS OP THE DIFFER ENT C< 3N ST ANTS. Let M. be modulus ; M. E., mean er ror; E. M. S., error of 75 0784 0091 0113 0013 mean square ; P. E. probable error ; the i : 80 0759 0085 0106 0012 M. M. E. E. 1 1. S. P. E. 85 0736 0080 0100 0011 Modulus, .... 1.000000 0.564190 0.7(1 7107 0.476986 90 0715 0075 0094 0010 Mean error, - - 1.772454 1.000000 1.2{ 8814 0.845848 95 0696 0071 0089 0009 Error mean square, 1.414214 0.797885 1.0C •0000 0.674490 Probable error, 2.096716 1.182945 1.46 2602 1.000000 100 0.0678 0.0068 0.0085 0.0008 ( l£<9lfiSil nm 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. RENEWALS ONLY-TEL. NO. 642-3405 Th, s book is due on the last date stamped below or on the date to which renewed w ' or Renewed books are subject «, iSSdte recall. ftN 1 4 1962 LD21A-60w-6,'69 (J9096sl0)476-A-32 General Library University of California Berkeley ^EP 12 1960 K LD 21-100to-1,'54(1887s1(>) 476 UN 8 '67 -10 AM f *^V/V "*»\3fc.7--. . 4