Mathematical Text Books. PRICE-LIST, JANUARY i, 1896. I. A DRILL-BOOK IN TRIQONOMETRY. FIRST EDITION. For both the elementary and the advanced work of high-school and college classes. i2mo, cloth, xvi + 193 pp. Single copies by mail, $1.00. All cash orders (carriage at the buyer's cost), 75 cents. II. A DRILL-BOOK IN ALGEBRA. THIRD EDITION. Yor the more advanced classes in the high schools and academies and the lower classes in the colleges. i2mo, cloth, xvi + 272 pp. Single copies by mail, $1.00. All cash orders (carriage at the buyer's cost), 75 cents. AN ANSWER-BOOK^ for teachers only, 25 cents. A BOX OF QUESTION-CA KDS, for the class-room, 75 cents. III. LOQARITHMIC TABLES. SIXTH EDITION. Eighteen tables, (four-place, six-place and ten-place,) with explanations, for use in the class-room, the laboratory, and the office. Large open pages, clear type, fine strong heavy paper. Royal 8vo. cloth, 160 pp. Single copies by mail, $1.00. All cash orders (carriage at the buyer's cost), 75 cents. IV. FOUR-PLACE LOGARITHMS. Two tables : one of the log^ithms of three-figure numbers, the other of trig'o- nometric ratios and tiieir log-arithms for angles differing by ten minutes. i2mo, paper, 8 pp. Single copies by mail, 5 cents. Allcasa orders (carriage at the buyer^s cost), 4 cents. V. FIVE-PLACE LOGARITHMS. IN PREPARATION. VI. PROBLEMS IN ALQEBR^, FOR BEGINNERS. IN PREPARATION. VII. HIGHER ALGEBRA. IN PREPARATION. Single copies of these boots' (except the last) will be sent free to teachers of mathematics, for their inspection. GEORGE W. JONES, Publisher, No Agents. Ithaca, N.Y. m Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924083590962 LOaAEITHMIC TABLES BT Prof. GEOEGE WILLIAM JOI^ES OF CORNELL UNIVERSITY. SIXTH EDITION. To promote the detection of errors in tlie tables, one dollar will be paid for the first notice of every such error. Address Prof. Jones at Ithaca. TLonTron MACMILLAN AND CO- ITHACA, N. Y. GEORGE W. JONES, 1896. CONTENTS. PAGES. EXPLANATION OF THE TABLES, .... 8-11 L FOtJK-PLACE LOGARITHMS, - ... 12-I4 A four-place table of logarithms of the natural numbers 1, 2, 8,.. 999, with ■' 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 FOTTE-FLACE TKIGONOMETEIC FUNCTIONS, ~ - 15-19 A four-placo table of logarithms of the six principal trigonometric functions, with differences for minutes, and of the lengths of arcs in radians. lU. 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, 88-41 A table of useful constants, with the logarithms of those in common use. T. ADDITION-SUBTRACTION LOGARITHMS, - - • 42-58 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, ... 69 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. VIL TRIGONOMETRIC FUNCTIONS, . 60-104 A five-place table of natural sines, cosines, tangents, and cotangents of angles 0°-180°, 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. VIIL NATURAL LOGARITHMS, - . 105-117 A six-place table of natural logarithms of the decimal numbers, .01, .03, .08, . .9.99, of the natural numbers 1, 2, 8, . . 1218, and of the prime numbers beWveen 1218 and 10000. IX. PRIME AND COMPOSITE NUMBERS, - - • 118-187 A table of prime and composite numbers fWim 1 to 20000, with the &ctors of the composite numbers that are not divisible by 2 or 6, and ten-place logarithms of the primes. X. SQUARES, - ..... 188-189 A table of the squares of the natural numbers 1, 2, 8, . .999. XL CUBES, ...... 140-141 A table of the cubes of the decimal numbers .1, .2, .8,.. 99.9. Xn. SQUARE-ROOTS, ...... 142-146 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, .03, . . 9.99. XT?. RECIPROCALS, ...... 162-153 A table of the reciprocals of the decimal numbers .01, .02, .03, . .9.99. XV. QUARTER-SQUARES, .... 164-157 A table of the quarter-squares of the natural numbers 1, 2, 8, . . 2000. XVL BESSEL'S COEFFICIENTS, ..... I68 A table of Bessel's cocflBcients for second, third, fourth, and fifth differences, for Interpolation. XVII. BINOMIAL COEFFICIENTS, ..... 159 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 OP A LOGAEITHM. 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 resqlved 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., '77'70 = 10'x'7.7V, and log 7770 = 3.890421, .0777:= 10-" 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 OP 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 OP 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 1 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 = . 141763, tab. dif. = 313, 313 x. 137 = 43, and the logarithm sought is 3.141806. 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 tlie 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-' 3.583652 : [log"' 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-' 3.583652 = .003834. To takeout log-' 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-'3.780029 = .o66026, log-' 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-' 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-' 1.780089 : 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-' 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 antilogarithiii, 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 10 as will make the sum exceed the true logarithm by 10 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 Bornstein are the principal authorities. 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 taken 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 formulsB 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~' B=: 1 +log-'A. Given log a, log d, 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 3 3.091175 log a 3.875175 B 0.066116 log [a + b) 3.941291 A 0.110925 log« 3.847129 log 5 3.736204 B 0.360024 log{a + b) 4.096228 Given log a, log b, and log a greater than log b, to find log {a — b). 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- [part 1 B 0.340079 [part 2 log« 1.683719 log b 1.343640 A 0.074875 log (a- 3) 1.418515 {b) 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 b 0.196834 log a 2.367129 log « 0.797145 C 9.810070 C 9.874476 log(a-^) 2.177199 log(a-d) 0.671621 B 0.230162 log« 1.517893 log (5 1.287731 A 9.844400 log(a- -b) 1.132131 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 tjrpe 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 out 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. For an angle given in degrees, minutes, and seconds. Take out, as above, the functions of the two tabular angles betweeri 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 2S 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 ANQLE 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"' .51279 : Tlie 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-' 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-'. 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-'.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-' 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 wHoie 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 1 ; 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)-flog 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-' 8.414317, and log-tan-' 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-' 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' 12". 13185" ; i.e., 3° 39' 45". iUJ^Jt'jLAJNATiUN OF THE TABLES. 11 ^ • MINOR TABLES. Vm. NATURAL LOGABITHMS. '^ 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. PHIMK 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 BECIPROCALS. 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 «, b be any two numbers, then ^(a + hy — \(a — hy = ab. The qiiarter-square of an even number is an integer, and that of an odd number ends always with the fraction ^ ; biit 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 ; «_, b^, c^, d^, e, - - their first differences ; a , b , c , d , - ■ ■ their second differences, and so on ; and let Vi be the number of any term, T„, between c and d, counting c as T,, ; then C^ = n, and with Bessel's coefiScients T„ = c -I- C, c, -f 1 0^ (6, -f c,) -f C^ 63 + ^ 0, (a, + 5 J + C^ ce^ ; with the binomial coefficients T„ = c + C, c, -f C^ c^ + C3 c, + ■ - - Of Besspl's coefficients 0^ is negative throughout, and C^ positive, C, is negative for .values of C above .5, and C^ for values below .5. Of the binomial coefficients all values of 0, and G^ are negative. XVIIl. 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 I. FOUR-PLACE LOGARITHMS. 1 1 1 3 4 5 6 7 8 9 Differences. ■ 0000 0000 3010 4771 6021 6990 7782 8451 9031 9542 1 2 43 4 42 4 8 41 4 S 40 89 4 4 8 8 1 0000 0414 0792 1139 1461 1761 2041 2304 2553 2788 9 9 3010 3222 3424 3617 ■ 3802 3979 4150 4314 4472 4624 8 18 17 22 26 18 17 21 25 12 16 21 2S 12 12 16 16 20 20 24 28 ! 3 4771 4914 5051 5185 5315 5441 , 5563 5682 6798 5911 4 8 G ; 4 6021 6128 6232 6335 6435 6532 6628 6721 6812 6902 5 6990 7076 7160 7243 7324 7404 7482 7559 7634 7709 S 80 84 29 84 29 28 27 82 81 6 7782 7853 7924 7993 80G2 8129 8195 8261 8325 8388 9 89 88 37. 86 85 7 8451 8513 8573 8633 8692 8751 8808 8865 8921 8976 3S 87 36 85 34 8 9031 9085 9138 9191 9243 ■ 9294 9345 9395 9443 9494 1 2 3 4 8 11 4 4 7 11 4 8 9 9542 9590 9638 9685 9731 9777 9823 9868 9912 9956 11 7 7 11 10 10 0000 0043 0086 0128 0170 0212 0263 0294 0334 0374 4 . 5 C 15 19 28 15 19 22 14 18 22 14 14 18 17 21 20 11 0414 0453 0492 0531 0569" 0607 0645 0682 0719 0755 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 7 S 9 27 30 34 26 80 88 25 29 32 2S 24 28 27 82 81 13 1139 1173 1206 1239 1-27 L 1303 1335 1367 1399 1430 14 I 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 88 82 31 80 29 ! '» 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 1 2 8 8 7 10 8 6 10 8 6 9 3 8, 6 6 9 9 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 4 18 18 12 12 12 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2766 5 6 7 17 20 28 16 10 22 16 19 22 15 15 13 17 21 20 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 ' 20 3010 3032 3054 307S 3096 3118 3139 3160 3181 3201 8 9 26 80 26 29 26 28 24 28 27 26 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 28 8 27 8 26 8 25 24 8 2 1 22 3424 3444 3464 3483 3502 3522 3541 3560 3679 3598 1 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 ■3784 2 6 6 6 5 5 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 8 4 8 11 8 U 8- 10 . 8 7 10 10 25 3979 3997 4014 .4031 4048 4065 4082 4099 4116 4133 6 6 7 14 17 20 14 16 19 13 16 18 18 12 15 14 18 17 26 4150 4166 4183 '4200 4216 4232 4249 4265 4281 4298 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 28 28 22 29 1 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 Ml. 2^ 2 22 2 21 2 20 19 2 2 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 4 5 4 4 4 4 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 7 9 7 9 6 8 6 6 8 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 18 18 12 11 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 7 8 16 18 15 18 15 17 14 18 16 15 35 5441 5453 5465 5478 5490 5502 5514 5527 6539 5551 9 21 20 19 18 17 36 5563 5575 5587 5599 5611 5623 5635 5647 6668 5670 1 2 18 2 4 17 2 8 16 2 3 15 14 2 1 3 3 37 5682 5694 5705 5717 5729 5740 5752 6763 6775 5786 38 5798 5809 5821 5832 5843 5855 5866 6877 6888 5899 3 5 5 S 5 4 39 5911 5922, 5933 5944 5955 5966 5977 5988 5999 6010 4 5 7 9 7 9 6 8 6 6 8 7 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6 7 8 11 18 14 10 12 14 10 11 13 9 8 U 10 12 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 18 J2 11 10 9 44 6435 6444 6454 6464 6474 6484 6493 6503 6613 6522 1 2 1 8 1 2 1 2 1 1 2 2 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 8 4 4 8 3 8 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 4 5 ■ C 5 7 8 5 6 7 4 6 7 4 4 6 5 6 5 47 6721 6730 6739 6749 6758 6767 6776 G785 •6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 7 9 8 10 11 8 9 10 7 6 . 49 6902 6911 6920 6928 6937. 6946' 6955 6964 6972 6981 8 9 10 12 8 7 9 8 50 1 2 3 4 5 6 7 8 9 Differences. — .. 1 I. FOUE-PLACE LOGARITHMS. 13 50 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 VO 11 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 : 92 93 94 95 96 97 98 99 6990 7076 7160 7243 7324 7404 7482 7559 76.34 7709 7782 7853 7924 7993 8062 8129 8195 8261 8325 8388 8451 6513 8573 8633 8692 8751 8808 8865. 8921 8976 6998 7084 7168 7251 7332 7412 7490 7566 7642 7716 7789 7860 7931 8000 8069 8186 8202 8267 8331 8395 7007 7016 7024 7093 7101 7110 7177 7185 7193 7259 7267 7275 7340 7348 7356 7419 7427 7497 7505 7574 7582 7649 7657 ' 7723 7731 7796 7868 7938 8007 8075 8142 8209 8274 8338 8401 7803 7875 7945 8014 8082 8149 8215 8280 8344 8407 7435 7513 7589 7664 7738 7810 7882 7952 8021 8089 8156 8222 8287 8351 8414 6 V ^8 9 7033 7118 7202 7284 7364 7443 7520 7597 7672 7745 7042 7126 7210 7292 7372 7451 75-28 7604 7679 7752 7050 7135 7218 .7300 7380 7459 7535 7612 7686 7760 8457 8463 8470 8476 8519 8525 8531 8537 8579 8585 8591 8597 8639 8645 8651 8657 8698 8704 8710 8716 8756 8762 8768 8774 8814 8820 8825 8831 8871 8876 8882 8887 8927 8932 8938 8943 8982 8987 8993 8998 9031 9036 9042 9047 9053 9085 9090 9096 9101 9106 9138 9143 9149. 9154 9159 9191 9196 9201 9206 9212 9243 9248 9253 9258 .9263 9294 9299 9304 9309 9315 9345 9350 9355 9360 9365 9395 9400 9405 9410 9415 9445 9450 9455 9460 9465 9494 9499 9504 9509 9513 9542 9547 9552 9557 9562 9590 9595 9600 9605 9609 9638 9643 9647 9652 9657 9685 9689 9694 9699 9703 9731 9736 -9741 9745 9750 9777 9782 9786 9791 9795 9823 9827 9832 9836 9841 9868 9872 9877 9881 9886 9912 9917 9921 9926 9930 9956 9961 9965 9969 9974 7818 7825 7832 7889 7896 7903 7959 7966 7973 8028 8035 8041 8096 8102 8109 8162 8169 8176 8228 8235 8241 8293 8299 8306 8357. 8363 8370 8420 8426 8432 8482 8488 8543 8549 8603 8609 8663 8669 8722 8727 8779 8785 8837 8842 8893 8899 .8949 8954 9004 9009 8494 8555 8615 8675 8733 8791 8848 8904 8960 9015 7059 7067 7143 7152 7226 7235 7308 7316 7388 7396 7466 7474 7543 7551 7619 7627 7694 7701 7767 7774 7839 7846 7910 7917 7980 7987 8048 8055 8116 8122 8182 8189 . 8248 8254 8312 8319 8376 8382 8439 8445 8500 8506 8561 8567 8621 8627 8681 8686 8739 8745 8797 8802 8854 8859 8910 8915 8965 8971 9020 9025 9058 9063 9069 9074 9079 9112 9117 9122 9128 9133 9165 9170 9175 9180 9186 d217 9222 9227 9232 9238 9269 9274 9279 9284 9289 9320 9325 9330 9370 9375 9380 9420 9425 ,9430 9469 9474 9479 9518 9523 9528 9566 9571 9576 9614 9619 9624 9661 9666 9671 9708 9713 "9717 9754 9759 9763 9335 9340 9385 9390 9435 9440 9484 9489' 9533 9538 9581 9586 9628 9633 9675 9680 9722 9727 9768 9773 9800 9805 9809 9814 9818 9845 9850 9854 9859 9863 9890. 9894 9899 9903 9908 9934 9939 9943 9948 9952 9978 9983 9987 9991 9996 Differences. 1 2 1 8 1 4 2 5 2 6 2 7 3 i^tA 100 8 9 Differences. 14 L FOUR-PLACE LOGARITHMS. » Squaek. Cube. Sq. Boot. Cu. KOOT. Kkcip. 50 Sqdare. Cube. Sij. Boot. Cn. Root. ItEOIl". OD 00 00 00 CO 50 3.3979 5.0969 0.8495 0.5663 8.3010 1 0.0000 0.0000 0.0000 0.0000 0.0000 61 4151 1227 8538 6692 2924 2 6021 9031 1505 1003 9.6990 52 4320 1480 8680 5720 2840 3 9542 1.4314 2386 1590 5229 63 4486 1728 8621 6748 2767 4 1.2041 8062 3010 2007 3979 64 4648 1972 8662 5775 2676 5 3979 2.0969 3495 2330 3010 65 4807 2211 8702 5801 2596 6 5563 3345 3891 2594 2218 56 4964 2446 8741 5827 2518 7 6902 6353 4225 2817 1549 57 5117 2676 8779 6863 2441 8 8062 7093 4515 3010 0969 58 5269 2903 8817 5878 2366 9 9085 8627 4771 3181 0468 59 5417 3126 8864 6903 2291 10 2.0000 3.0000 0.5000 0.3333 9.0000 60 3.5563 5.3345 0.8891 0.6927 8.2218 11 0828 1242 6207 3471 8.9686 61 5707 3560 8927 6951 2147 12 1584 2375 6396 3697 9208 62 5848 3772 8962 5975 2076 13 2279 3418 6570 3713 8861 63 5987 3980 8997 5998 2007 14 2923 4384 5731 3820 8539 64 6124 .4186 9031 6021 1938 15 3522 5283 5880 3920 8239 65 6258 4387 9065 6043 1871 16 4082 6124 6021 4014 7959 66 6391 4686 9098 6065 1805 n 4609 6913 6152 4101 7696 67 6521 4782 9130 6087 1739 18 5105 7658 6276 4184 7447 68 6650 4976 9163 6108 1675 19 5575 8363 6394 4263 7212 69 6777 6165 9194 6129. 1612 20 2.6021 3.9031 0.6505 0.4337 8.6990 70 3.6902 5.6363 0.9225 0.6150 8.1649 21 6444 9667 6611 4407 6778 71 7025 5538 9256 6171 1487 22 6848 4.0273 6712 4476 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 948,8 6325 1024 .30 2.9542 4.4314 0.7386 0.4924 8.5229 80 3.8062 6.7093 0.9515 0.6344 8.0969 31 9827 4741 7457 4971 6086 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 9696 6397 0809 34 0630 5944 7657 5105 4685 84 8486 7728 9621 6414 0757 35 0881 6322 7720 5147 4659 85 8588 7883 9647 6431 0706 36 1126 6689 7782 5188 4437 86 8690 8035 9672 6448 0055 37 1364 7046 7841 5227 4318 87 8790 8186 9698 6465 0605 3: 1596 7394 7899 5266 4202 88 8890 8334 9722 6482 0555 39 1821 7732 7955 6304 4089 89 8988 8482 9747 6498 0506 40 3.2041 4.8062 0.8010 0.6340 8.3979 90 3.9085 6.8627 0.9771 0.6514 8.0458 41 2256 8384 8064 6376 3872 91 9181 8771 9795 6630 0410 42 2465 8697 8116 6411 3768 92 9276 8914 9819 6640 0362 43 2669 9004 8167 6446 3665 93 9370 9064 9842 6562 0315 44 2869 9304 8217 6478 3565 94 9463 9194 9866 6577 0269 45 3064 9596 8266 5511 3468 96 9654 9332 9889 6692 0223 46 3255 9883 8314 5543 3372 96 9645 9468 9911 6608 0177 47 3442 5.0163 8360 5674 3279 97 9736 9603 9934 6623 0132 48 3625 0437 8406 6604 3188 98 9825 9737 9956 6637 0088 49 3804 0706 8451 5634 3098 99 9913 9869 9978 6652 0044 log, r= 0.497 1, log|,r= 0.1961, log^ff = 9.895 I, log|,r = 9.7190, log |,r= 0.6221. 1 II. FOim-PLACE TRIGONOMETRIC FUNOTIQNS. 15 1 " ; Deg. Bad. 8lN. DiF. Ceo. Cos. Dir. Sec.' Tak. Dif. Cot. Kad. Deo. 0° 00' 0.0000 00 00 00 0.0000 .0 0.0000 00 00 00 1.5708 90° 00' 05 0015 7.1627 602 2.8373 0000 0000 7.1627 602 2.8373 5693 55 10 0029 4637 852 5363 0000 0000 4637 852 5363 5679 50 15 0044 6398 250 3602 0000 0000 6398 260 3602 5664 45 20 0058 7648 194 2352 0000 0000 7648 194 2352 5650 40 25 0073 8617 15S 1383 0000 0000 8617 168 1383 5635 35 30 0087 9408 184 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 0181 1169 91.6 8831 0000 0000 1170 91.4 8830 5577 15 50 0145 1627 82.8 8373 booo .2 0000 1627 82.8 8373 5563 10 ' 55 0160 2041 76.6 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 66.0 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 i 35 0276 4414 44.6 5586 9998 .0 00O2 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 88.6 4947 5388 10 : 55 0335 5243 87.0 4757 9998 .2 0002 5246 87.0 4754 5373 05 i 2° 00' 0-.0349 8.5428 35.4 1.4572 9.9997 .0 0.0003 8.5431 85.4 1.4569 1.5359 88° 00' 05 0364 5605 84.2 4395 9997 0003 5608 84.2 4392 5344 55 1 10 0378 5776 82.6 4224 9997 0003 5779 82.8 4221 5330 50 15 0393 5939 81.6 4061 9997 .2 0003 5943 81.6 4057 5315 45 : 20 0407 6097 30.6 3903 9996 .0 0004 6101 80.6 3899 5301 40 25 0422 6250 29.4 3750 9996 0004 6254 29.4 3746 5286 35 i 30 0436 6397 28.4 3603 9996 0004 6401 28.6 3599 6272 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 26.2 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 28.8 1.2806 1.5184 87° 00' 05 0538 7307 23.2 2693 9994 .2 0006 7313 28.2 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 .2 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' Deo. ' Bad. Cos. DiF. Seo. Sin. Dif. Cso. Cot. Dif. Tan. Ead. Deg. 16 n. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. Deo. Bad. Sis. DiF. Csc. Cos. DlF. Sko. Tan. DiF. Cot. Bad. Deg. 5° 00' 0.0873 8.9403 14.2 1.0597 9.9983 .1 0.0017 8.9420 14.8 1.0580 1.4835 85° 00' 10 0902 9545 18.7 0455 9982 0018 9563 18.8 0437 4806 50 20 0931 9682 18.4 0318 9981 0019 9701 18.6 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 60 1018 9.0070 12.2 0.9930 9977 .1 0023 9.0093 12.8 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 60 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.T 8806 4399 30 40 1338 1252 9.8 8748 9961 0039 1291 9.4 8709 4370 20 50 1367 1345 9.1 8655 9959 .1 0041 1385 9.8 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.S 7824 9940 0060 2236 7.7 7764 4050 30 40 1687 2251 7.8 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 .8 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 .8 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° 00' 10 1949 2870 7130 9917 .8 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 3672 20 50 2065 3119 6.0 6881 9907 .8 0093 3212 6788 3643 10 12° 00' 0.2094 9.3179 6.9 0.6821 9.9904 .8 0.0096 9.3275 6.1 0.6725 i.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 6647 9896 0104 3458 6.9 6542 3526 30 40 2211 3410 5.6 6590 9893 0107 3517 6483 3497 20 50 2240 3466 6.5 6534 9890 0110 . 3576 6.8 6424 3468 10 13° 00' 0.2269 9.3521 6.4 0.6479 9.9887 .8 0.0113 9.3634 6.7 0.6366 1.3439 77° 00' 10 2298 3575 6425 9884 0116 3691 6309 3410 50 20 2327 3629 6.8 6371 9881 0119 3748 6.6 6252 3381 40 30 2356 3682 5.2 6318 9878 0122 3804 6.5 6196 3352 30 40 2385 3734 6266 9875 0125 3859 6141 3323 20 50 2414 3786 5.1 6214 9872 0128 3914 5.4 6086 3294 10 14° 00' 0.2443 9.3837 6.0 0.6163 9.9869 .8 0.0131 9.3968 6.8 6.6032 1.3265 76° 00' 10 2473 3887 6113 9860 0134 4021 5979 3235 50 20 2502 3937 4.9 6063 9863 .4 0137 4074 5926 3206 40 30 2531 3986 6014 9859 .8 0141 4127 6.1 5873 ■ 3177 30 40 2560 4035 4.8 5965 9856 0144 4178 6.2 5822 3148 20 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' Dec. Bad. Cos. DiF. Bec. Sin. DiF Cso. Cot. DiF Tak. Bad. Deg. 1 . , ■ . 1 n. FOUR-PLACE TRiaONOMETRIO FUNCTIONS. • IT ^ Deo. Ead. Sra. Dip. Cso. 003. Dip. Sue, Tan. Dip. Cor. Ead. , Deg. 15° 00' 0.2618 9.4130 4.7 0.5870 9.9849 .8 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 4.6 5731 9839 .8 0161 4430 5570 3003 30 40 ■2734 4314 5686 9836 .4 0164 4479 48 5521 2974 20 50 2763 4359 4.4 5641 9832 0168 4527 5473 2945 74° 00' 16° 00' 0.2793 9.4403 4.4 0.5597 9.9828 .8 0.0172 9.4575 4.7 0.5425 1.2915 10 2822 4447 5553 9825 .4 0175 4622 5378 2886 50 20 2851 4491 4.2 5509 9821 0179 4669 5331 2857 40 30 2880 4533 4.8 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 4.6 5192 2770 10 n° 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 02a0 5031 4969 2625 20 50 3113 4861 8.9 5139 9786 0214 5075 4.3 4925 2595 10 18° 00' 0.3142 9.4900 8.9 0.5100 9.9782 .4 0.0218 9.5118 4.3 0.4882 1.2566 72° 00' 10 3171 4939 8.8 5061 9778 0222 5161 4.2 4839 2537 50 20 3200 4977 ■5023 9774 0226 5203 4797 2508 40 30 3229 5015 8.7 4985 9770 .5 0230 5245 4755 2479 30 40 3258 5052 8.8 4948 9765 .4 0235 5287 4713 2450 20 50 3287 5090 8.6 4910 9761 0239 5329 4.1 4671 2421 10 19° 00' 0.3316 9.5126 8.7 0.4874 9.9757 .5 0.0243 9.5370 4.1 0.4630 1.2392 71° 00' 10 3345 5163 8.6 4837 9752 .4 0248 5411 4.0 4589 2363 50 20 3374 5199 4801 9748 .6 0252 5451 4549 2334 40 30 3403 5235 8.5 4765 ' 9743 .4 0257 5491 4509 2305 30 40 3432 5270 8.6 4730 9739 .5 0261 5531 4469 2275 20 50 3462 5306 8.6 4694 9734 .4 0266 6571 4429 2246 10 20° 00' ,0.3491 9.5341 8.4 0.4659 9.9730 .5 0.0270 9.5611 8.9 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 8.8 4311 2159 40 30 3578 5443 4557 9716 0284 5727 3.9 4273 2130 30 40 3607 5477 8.8 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 8.8 0.4457 9.9702 .5 0.0298 9.5842 8.7 0.4158 1.2043 69° 00' 10 3694 5576 4424 9697 0303 5879 3.8 4121 2014 50 20 3723 5609 8.2 4391 9692 0308 5917 3.7 4083 1985 40 30 3752 5641 4359 9687 0313 5954 4046 1956 30 40 3782 5673 8.1 4327 9682 0318 5991 4009 1926 20 50 3811 5704 3.2 4296 9677 0323 6028 8.6 3972 1897 10 22° 00' 0.3840 9.5736 3.1 0.4264 9.9672 .5 0.0328 9.6064 3.6 0.3936 1.1868 68° 00' 10 3869 5767 4233 9667 .6 0333 6100 3900 1839 50 20 3898 5798 8.0 4202 9661 .6 0339 6136 3864 1810 40 30 3927 5828 8.1 4172 9656 0344 6172 3828 1781 30 40 3956 5859 8.0 4141 9651 0349 6208 8.5 3792 1752 20 50 3985 5889 4111 9646 .6 0354 6243 8.6 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 8.0 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 8.4 3617 1606 30 40 4131 6036 3964 9618 .6 0382 6417 3.5 3583 1577 20 50 4160 6065 2.8 3935 9613 .6 0387 6452 8.4 3548 1548 10 24° 00' 0.4189 9.6093 2.8 0.3907 9.9607 .5 0.0393 9.6486 8.4 0.3514 1.1519 66° 00' 10 4218 6121 3879 9602 .6 0398 6520 8.3 3480 1490 50 20 4247 6149 3851 9596 0404 6553 8.4 3447 1461 40 30 4276 6177 3823 9590 0410 6587 8.8 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 8.8 3346 1374 10 25° 00' 0.4363 9.6259 0.3741 9.9573 0.0427 9.6687 0.3313 1.1345 65° 00' Deo. Ead. Cos. DiF. Sec. SlH. Dip. Cso. Cot. Dip. Tah. Ead. Des. 18 n. FOUR-PLACE TRIGONOMETRIC FUNCTIONS. 1 Deg. Ead. Sin, Drp. Cso. Cos. Dw. Sec. Tan. DiF Cot. Bad. Deo. 25° 00' 0.4363 9.G259 2.7 0.3741 9.9573 .6 0.0427 9.6687 8.8 0.3313 1.1345 65° 00' 10 4392 6286. 3714 9567 0433 6720 8.2 3280 1316 50 20 4422 6313 3687 9561 0439 6752 8.8 3248 1286 40 30 445] 6340 2.6 3660 9555 0445 6785 8.2 3215 1267 30 40 4480 6366 3634 9549 0451 6817 3.8 3183 1228 20 50 4509 6392 3608 9543 0457 6850 3.2 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 3.1 3054 1112 40 30 4625 6495 2.6 3505 9618 0482 6977 8.2 3023 1083 30 40 4654 6521 2.5 3479 9512 .7 0488 7009 8.1 2991 1054 20 50 4683 6546 2.4 3454 9505 .6 0495 7040 8.2 2960 1025 10 27° 00' 0.4712 9.6570 2.6 0.3430 9.9499 .7 0.0501 9.7072 8.1 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 8.0 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 2.8 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 Q689 7467 8.0 2533 0617 50 20 5120 6901 2.2 3099 9404 0696 7497 2.9 2503 0588 40 30 5149 6923 2.8 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 3,0 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 0366 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 2.8 2155 0239 40 30 5498 7181 2.0 2819 9308 .8 0692 7873 2.9 2127 0210 30 40 5527 7201 2.1 2799 9300 0700 7902 2.8 2098 0181 20 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 07 24 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 67° 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.S 0.2524 9.9186 .9 0.0814 9.8290 2.7 0.1710 0.9774 56° 00' 10 5963 7494 1.9 2506 9177 .8 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 1629 9687 30 40 6050 7550 1.8 2450 9151 0849 8398 1602 9657 20 50 6080 7568 2432 9142 .8 0858 8425 1575 9628 10 35° 00' 0.6109 9.7586 0.2414 9.9134 0.0866 9.8452 0.1548 0.9599 55° 00' Dse. Bad. Cob. DiF. Sec. Sin. DiF. Cso. Cot. DiF. Tan. Bad. Deg. . _l II. EOUR-PLAOE TRIGONOMETEIO FUNCTIONS. 19 . . 1 Deq. Ead. Sin. Dif. Cbo. Cos. Dif. Sec. Tan. Dif. Cor. Ead. Deo. 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 to 0948 8692 1308 9338 30 40 '6400 7761 2239 9042 .8 0958 8718 2.7 1282 9308 20 50 6429 7778 2222 9033 1.0 0967 8745 2.8 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 9.896S to 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 1.6 0.2011 9.8905 to 0.1095 9.9084 2.6 0.0916 0.8901 51° 00' 10 6836 8004 1.6 1996 8895 tl 1105 9110 2.5 0890 8872 50 20 6865 8020 1.6 1980 8884 to 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 1.6 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 2.6 0736 8698 50 20 7039 8111 1.4 1889 8821 1179 9289 2.6 0711 8668 40 30 7069 8125 1.6 1875 8810 to 1190 9315 0685 8639 30 40 7098 8140 1860 8800 tl 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 1.6 0.1831 9.8778 tl 0.1222 9.9392 2.6 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 t2 1255 9468 2.6 0532 8465 30 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 1.4 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 2.6 0430 8348 50 20 7389 8283 1717 8688 t2 1312 9595 2.6 0405 8319 40 "30 7418 8297 1703 8676 1.1 1324 9621 2.6 0379 8290 30 40 7447 8311 1.8 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 1.8 0.1662 9.8641 1.2 0.1359 9.9697 2.5 0.0303 0.8203 47° 00' 10 7534 8351 1.4 1649 ■86^9 1.1 1371 9722 0278 8174 50 20 7563 8365 1.8 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 2.6 0202 8087 20 50 7650 8405 1.8 1595 8582 1.8 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 2.6 0126 7999 50 20 7738 8444 1556 8545 1.8 1455 9899 0101 7970 40 30 7767 8457 1.2 1543 8532 t2 1468 9924 0076 7941 30 40 7796 8469 1.8 1531 8520 1.8 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' Deo. Ead. Cos. DiF. Sec. Sin. Dif. Csc. Cot. Dif Tan. Ead. Deq. 20 III. LOGARITHMS OF NUMBERS. 100 1 2 3 4 5 6 ^ O i 9 Differences. 100 00 0000 0434 0868 1301 1734 2166 2598 3029 3461 3391 1 485 44 480 48 428 420 48 42 01 4321 4751 5181 5609 ^6038 0466 6894 7321 7748 8174 2 87 86 85 84 02 8600 9026 9451 9876 *0300 *0724 *1147 *1570 *1993 *2415 3 181 129 12S 126 03 01 2837 3269 3680 4100 4521 4940 5360 5779 6197 6616 4 5 174 218 172 .216 ITO 168 218 210 04 7033 7461 7868 8284 8700 9110 9532 9947 *036,1 *0775 C 261 258 265 262 05 02 1189 1603 2016 2428 2841 3252 3664 4075- 4486 4896 7 S 305 348 801 844 298 294 340 886 06 5306 6715 6125 6533 6942 7350 7757 81G4 8571 8978 9 892 887 383 878 07 9384 9789 *0195 *0600 *1004 *1408 *1812 *2216 *2619 *3021 41,5 410 406 400 08 03 3424 3826 4227 4628 502? 5430 5830 6230 6629 7028 1 42 41 41 40 09 7426 7825 8223 8620 9017 9414 98ll *0207 *0602 *0998 ■ 2 8 83 125 82 123 81 80 122 120 no' 04 1393 1787 2182 2576 2969 3362 3755 4148 4540 4932 4 5 C 166 208 249 164 206 246 162 160 203 200 248 240 11 5323 6714 6105 6495 6885 7275 7664 8063 8442 8830 12 9218 9606 9993 *0380 *0766 *1163 *1538 *1924 *2309 *2694 7 291 287 284 280 13 05 3078 3463 3846 4230 4613 4996 5378 5760 6142 6524 8 9 382 374 323 869 824 820 365 860 14 6905 7286 7666 8046 8426 8806 9185 9563 9942 *0320 89.'} 890 885 880 15 06 0698 1075 1452 1829 2206 2582 2958 3333 3709 4083 1 2 40 79 89 78 89 88 77 76 16 4458 4832 6206 5680 5963 6326 6699 7071 7443 7815 3 119 117 116 114 17 8186 8557 8928 9298 9668 *0038 *0407 *0776 *1145 *1514 4 158 166 164 162 18 07 1882 2250 2617 2986 3352 3718 4086 4461 4816 6182 5 G 198 287 27T 196 284 278 193 190 281 228 270 266 19 5547 5912 6276 6640 7004 7368 7731 8094 8457 8819 120 OJ 9181 9643 9904 *0266 *0626 *0987 *1347 *1707 *2067 *2426 8 9 816 856 812 861 308 304 847 342 21 08 2785 3144 3603 3861 4219 4576 4934 5291 5647 6004 876 38 370 37 866 360 87 86 22 6360 6716 7071 7426 7781 8136 8490 8845 9198 9662 1 23 9905 *0258 *0611 *0963 *13|5 *1667 *2018 *2370 *2721 *3071 2 8 75 118 74 111 73 72 110 108 24 09 3422 3772 4122 4471 4820 6169 6518 6866 6215 6562 4 150 148 146 144 25 6910 7267 7604 7961 8298 8644 8990 9335 9681 *0026 5 6 7 188 225 268 185 222 269 188 ISO 219 216 266 262 26 10 0371 0715 1059 1403 1747 2091 2434 2777 3119 3462 27 3804 4146 4487 4828 5169 5510 6851 6191 6531 6871 8 300 296 292 288 28 7210 7649 7888 8227 8565 8903 9241 9679 9916 *0253 9 888 833 829 824 29 11 0590 0926 1263 1699 1934 2270 2605 2940 3275 3609 1 865 86 860 86 845 840 85 84 130 11 3943 4277 4611 4944 6278 5611 6943 6276 6608 6940 2 8 4 71 107 142 70 106 140 69 68 104 102 188 186 31 7271 7603 7934 8266 8595 8926 9266 9586 9915 *0245 32 12 0574 0903 1231 1560 1888 2216 2644 2871 3198 3525 6 178 175 173 170 33 3852 4178 4504 ,4830 5156 5481 6806 6131 6456 6781 C 7 8 218 249 284 210 246 280 207 204 • 242 233 276 272 34' 7105 7429 7753 8076 8399 8722 9045 9368 9690 *0012 35 13 0334 0655 0977 1298 1619 1939 2260 2580 2900 3219 9 820 815 811 306 36 3539 3858 4177 4496 4814 6133 5451 5769 6086 6403 1 885 84 830 88 325 320 88 - 82 37 6721 7037 7364 7671 7987 8303 8618 8934 9249 9564 2 67 66 65 64 38 9879 *0194 *0508 *0822 *1136 *1450 *1763 *2076 *2389 *2702 8 4 S 101 184 168 99 182 166 98 96 180 128 168 160 39 14 3015 3327 3639 3961 4263 4574 4885 5196 5607 5818 140 14 6128 6438 6748 7058 7367 7676 7985 8294 8603 8911 6 7 8 201 285 193 281 195/1 192 22^ 224 260 266 41 9219 9527 9835 *0142 *0449 *0756 *1063 *1370 *1676 *1982 268 264 42 15 2288 2694 2900 3205 3510 3816 4120 4424 4728 6032 9 802 297 293 288 43 5336 5640 6943 6246 6549 6862 7154 7457 7769 8061 815 810 806 300 44 8362 8664 8965 9266 9567 9868 *0168 *0469 *0769 *1068 1 2 82 68 81 62 31 30 61 60 45 16 1368 1667 1967 2266 2564 2863 3161 3460 3768 4055 8 4 6 96 126 168 93 124 155 92 90 122 120 168 160 46 4363 4650 4947 5244 5541 5838 6134 6430 6726 7022 47 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 6 189 186 188 180 48 17 0262 0556 0848 1141 1434 1726 2019 2311 2603 2895 7 8 9 221 262 284 217 248 279 214 210 244 240 276 270 49 3186 3478 3769 4060 4351 4641 4932 6222 5512 6802 150 1 2 3 4 5 6 7 8 9 DiiFejences, III. LOGARITHMS OF NUMBERS. ^ 21 150 1 2 3 4 5 G 7 8 9 Dirorences. 150 17 6091 6381 6670 6959 7248 7536 7825 8113 8401 8689 1 1 295 290 285 280 51 8977 9264 9552 9839 *0126 *0413 *0699 *0986 *1272 *1558 1 2 30 59 29 58 29 28 67 56 52 18 1844 2129 2415 2700 2985 3270 3555 3839 4123 4407 3 89 87 86 84 53 54 4691 7521 4975 7803 5259 8084 5542 8366 5825 8647 6108 8928 6391 9209 6674 6956 7239 9490 9771 *0051 4 5 6 118 148 177 116 146 174 114 112 148 140 171 168 55 19 0332 0612 0892 1171 1451 1730 ■2010 2289 2567 2846 7 8 207 286 203 232 200 196 228 224 56 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 9 266 261 257 252 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 8 56 88 54 81 53 52 SO 78 160 20 4120 4391 4663 4934 5204 5475 5746 6016 6286 6556 4 5 6 110 188 165 108 185 162 106 104 183'. 180 159 156 61 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 62 9515 9783 *0051 *0319 *0586 *0853 *1121 *1388 *1654 *1921 1 193 189 186 182 63 21 2188 2454 2720 2986 3252 3518 3783 4049 4314 4579 8 9 220 248 216 243 212, 208 239. 284 64 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 255 250 243 246 65 7484 7747 8010 8273 8536 8798 9060 9323 9585 9846 1 26 25 25. 26 66 22 0108 0370 0631 0892 1153 1414 ■ 167'5 1936 2196 2456 2 3 51 77 50 75 60^ 49 74 74 67 2716 2976 3236 3496 3755 4015 4274 4533 4792 5051 4 102 100 99 93 68' 5309 6568 5826 6084 6342 6600 6858 7115 7372 7630 5 158 125 124 128 69 7887 8144 8400 8657 8913 9170 9426 9682 9938 *0193 C 7 153 179 150 175 149 14S 174 172 170 23 0449 0704 0960 1215 1470 1724 1979 2234 2488 2742 8 9 204 230 200 225 198 197 223 221 71 2996 3250 3504 3757 4011 4264 4517 4770 5023 5276 244 24 242 24 240 288 24 24 72 5528 5781 6033 6285 6537 6789 7041 7292 7544 7795 1 73 74 8046 24 0549 -8-297 0799 8548 104P 8799 1297 9049 1546 9299 1795 ^9550 2044 9800 *0050 *q300 2293 2541 2Y9O 2 8 4 49 73 98 48 78 97 48 48 72 71 96 ■ 96 75 3038 3286 3534 3782 4030 4277 4525 4772 5019 5266 5 6 7 122 146 171 121 145 169 120 119 141 143 168 167 76 5513 5759 6006 6252 6499 6745 6991 7237 7482 7728 77 7973 8219 8464 8709 8954 9198 9443 9687 9932 *0176 8 195 194 193 190 78 25 0420 0664 0908 1151 1395 1638 1881 2125 2368 2610 9 220 21s 216 214 79 2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 1 236 24 234 23 232 ■ 280 23 23 180 81 25 5273 7679 5514 7918 5755 8158 5996 8398 6237 8637 647,7 8877 6718 9116 6958 7198 7439 . 9355 9594 9833 2 ■3 4 47 71 94 47 70 94 46 46 70 69 93 92 82 26 0071 0310 0548 0787 1025 1263 1501 1739 1976 2214 5 118 117 116 116 83 84 2451 4818 2688 5054 2925 5290 3162 5525 3399 5761 3636 5996 3873 6232 4109 4346 4582 6467 6702 6937 C T 8 142 165 189 140 164 187 139 133 162 161 186 184 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 \ 228 23 226 23 46 224 222 22 22 45 44 87 27 1842 2074 2306 2538 2770 3001 3233 3464 3696 3927 2 88 4158 4389 4620 4850 5081 5311 5542 5772 6002 6232 8 68 68 67 67- 89 6462 6692 6921 7151 7380 7609 7838 8067 8296 8525 4 5 91 lU 90 113 90 89 112 111 190 191 27 8754 28 1033 8982 1261 9211 1488 9439 1715 9667 1942 9895 2169 *0123 2396 *0351 *0578 *0806 2622 2849 3075 6 7 8 187 160 182 136 158 181 134. 183 167 t 155 179 178 92 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 9 205 203 202 200 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 21 ,48 48 95 29 0035 0257 0480 0702 0925 1147 1369 1591 1813 2034 8 4 5 66 88 110 65 87 109 65 W 86 86 108 107 96 2256 2478 2699 2920 3141 3363 3584 3804 4025 4246 97 4466 4687 4907 5127 5347 5567 ' 5787 6007 . 6226 6446 6 132 131 130 128 98 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 7 8 9 154 176 198 153 174 196 161 150 173 171 194 198 99 8853 9071 9289 9507 9725 9943 *0161 *0378 *0595 *0813 200 1 2 3 4 5 6 7 8 9', DiiFerences. -- . ■ 1 oo III. LOGARITHMS OF NUMBERS. , 200 1 2 3 4 5 6 7 8 9 Differences. 200 30 1030 1247 1464 1681 1898 2114 2331 2547 2764 2980 220 22 44 218 22 44 210 43 214 01 3196 3412 3628 3844 4059 4275 4491 4706 4921 5136 1 2 21 48 02 5351 5566 5781 5996 6211 6425 6639 6854 7068 7282 8 66 66 65 64 03 7496 7710 7924 8137 8351 8564 8778 8991 9204 9417 4 5 C 8S 110 182 67 109 131 86 106 180 66 107 123 04 9630 9843 *0056 *0268 *0481 *0693 *0906 *1118 *1330 *1542 05 31 1754 1966 2177 2389 2600 2812 3023 3234 3445 3656 7' 8 154 176 168 174 151 178 160 171 06 3867 4078 4289 4499 4710 4920 5130 5340 5551 5760 9 198 190 194 198 01 5970 6180 6390 6599 6809 7018 7227 7436 7646 7854 212 210 208 206 08 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 1 2 8 21 42 64 21 42 63 21 21 09 32 0146 0354 0562 0769 0977 1184 1391 1598 1805 2012 42 62 41 62 210 11 32 2219 4282 2426 4488 2633 4694 2839 4899 3046 5105 3252 5310 3458 5516 3665 5721 3871 5926 4077 6131 4 S 6 85 106 127 64 105 126 68 104 126 62 108 124 12 6336 6541 6745 6950 7155 7359 7563 7767 7972 8176 T 148 147 146 144 13 8380 8583 8787 8991 9194 9398 9601 9805 *0008 *0211 8 9 170 191 168 189 166 187 165 185 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 6260 2 8 41 61 40 61 40 60 40 69 17 6460 6660 6860 7060 7260 7459 7659 7858 8058 8257 4 82 81 80 79 18 8456 8656 8855 9054 9253 9451 9650 9849 *0047 *0246 6 6 T 102 122 143 101 100 99 19 34 0444 0642 0841 1039 1237 1435 1632 1830 2028 2225 121 141 120 140 119 139 220 34 2423 2620 2817 3014 3212 3409 ' 3606 3802 3999 4196 8 9 163 184 162 162 160 180 158 178 ' 21 4392 4589 4785 4981 5178 5374 5570 5766 5962 6157 196 20 194 19 192 19 190 19 22 6353 6549 6744 6939 7135 7330 7525 7720 7915 8110 1 23 8305 8500 8694 8889 9083 9278 9472 9666 9860 *0054 2 89 39 86 86 24 35 0248 0442 0636 0829 1023 1216 1410 1603 1796 1989 3 4 69 78 68 78 8S 77 57 76 25 2183 2375 2568 2761 2954 3147 3339 ^3532 3724 3916 5 G 7 98 118 187 97 116 186 96 116. 184 96 114 183 26 4108 4301 4493 4685 4876 5068 5260 5452 5643 5834 27 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 8 157 166 154 162 28 7935 8125 8316 8506 8696 8886 9076 9266 9456 9646 9 176 176 173 171 29 9835 *0025 *0215 *0404 *0593 *0783 *0972 *1161 *1360 *1539 1 188 19 186 19 184 18 182 16 230 36 1728 1917 2105 2294 2482 2671 2859 3048 3236 3424 2 3 4 33 B6 75 87 66 74 37 65 ■74 86 66 78 31 3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 '^,3.2 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 6 94 98 92 91 33 7356 7542 7729 7915 8101 8287 8473 8659 8845 9030 6 7 8 113 182 150 112 1«0 149 110 129 147 109 127 146 34 9216 9401 9587 9772 9958 *0143 *0328 *0513 *0698 *0883 35 37 1068 1253 1437 1622 1806 1991 ■2175 2360 2544 2728 9 169 167 166 164 36 2912 3096 3280 3464 3647 3831 4015 4198 4382 4565 1 180 18 178 18 86 176 16. 38 175 18 86 37 4748 4932 5115 5298 5481 5664 5846 6029 6212 6394 2 86 38 6577 6769 6942 7124 7306 7488 7670 7852 8034 8216 8 64 72 90 63 68 68 39 8398 8580 8761 8943 9124 9306 9487 9668 9849 *0030 4 6 71 89 70 86 70 88 240 38 0211 0392 0573 0754 0934 1115 1296 1476 1656 1837 6 7 8 108 126 144 107 125 142 106 128 141 106 128 140 41 2017 2197 2377 2557 2737 2917 3097 3277 3456 3636 42 3815 3995 4174 4353 4533 4712 4891 5070 5249 5428 9 162 160 168 168 43 5606 5785 5964 6142 6321 6499 6677 C856 7034 7212 174 173 172 171 44 7390 7568 7746 7923 8101 8279 8456 8634 8811 8989 1 2 17 35 17 36 17 84 17 34 45 9166 9343 9520 9698 9875 *0051 *0228 *0405 *0582 *0759 3 4 5 52 70 87 62 69 87 62 69 86 61 68 66 46 39 0935 1112 1288 1464 1641 1817 1993 2169 2345 2521 47 2697 2873 3048 3224 3400 3575 3751 3926 4101 4277 104 104 108 108 48 4452 4627 4802 4977 5152 5326 5501 5676 5850 6025 7 8 9 122 189 167 121 188 166 120 188 165 120 187 164 49 6199 6374 6548 '6722 6896 7071 7245 7419 7592 7766 250 1 2 3 4 5 6 7 8 9 Differences. 1 _ ZJ lii. -LUtiARiTHMS OF NUMBERS. 23 250 1 2 3 4 5 6 7 8 9 a . Differences. 250 39 7040 8114 8287 8461 8634 8808 8981 9154 9328 9501 1 2 no 17 84 169 17 34 168 167 17 17 84 88 51 9674 9847 *0020 *0192 *0365 *0538 *0711 *0883 *1056 *1228 52 40 1401 1573 1745 1917 2089 2261 2433 2605 2777 2949 8 51 51 50 50 53 54 3121 4834 3292 3464 5005 5176 3635 5346 3807 5517 3978 5688 4149 5858 4320 6029 4492 6199 4663 6370 4 5 6 68 85 102 68 86 101 67 67 84 84 101 100 55 65 40 6710 6881 7051 7221 7391 7561 7731 7901 8070 7 8 119 186 118 185 118 117 134 184 56, 8240 8410 8579 8749 8918 9087 9257 9426 9595 9764 9 158 152 151 150 57 9933 *0102 *0271 *0440 *0609 *0777 *0946 *1114 *lg83 *1451 166 165 164 163 58 59 41 1620 3300 1788 1956 3467 3635 2124 3803 2293 3970 2461 4137 2629 4305 2796 447 2 2964 4639 3132 4806 1 2 8 IT 83 50 17 88 50 16 16 83 88 49 49 260 414973 5140 5307 5474 5641 5808 5974 6141 6308 6474 4 5 66 88 66 83 66 65 82 82 61 6641 6807 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 9 116 188 149 116 132 149 115 114 131 180 148 147 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 65 3246 3410 3574 3737 3901 4065 4228 4392 4555 4718 1 2 16 82 16 32 16 16 82 32 66 4882 5045 5208 5371 5534 5697 5860 6023 6186 6349 8 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 894^ 9106 9268 9429 9591 6 6 81 97 81 97 80 80 96 95 69 9752 9914 *0075 *0236 *0398 *0559 *0720 *0881 *1042 *1203 7 113 113 112 111 270 43 1364 1525 1685 1846 2007 2167 2328 2488 2649 2809 8 9 180 ,146 129 146 128 127 144 148 71 2969 3130 3290 3450 3610 3770 3930 4090 4249 4409 158 157 156 155 72 4569 4729 4888 5048 5207 5367 5526 5685 5844 6004 1 16 16 16 16 73 6163 6322 6481 6640 6799 6957 7116 7275 7433 7592 2 8 4 32 47 68 31 47 68 81 31 47 47 62 62 74 7751 7909 8067 8226 8384 8542 8701 8859 9017 9175 75 9333 9491 9648 9806 9964 *0122 *0279 *0437 *0594 *0752 5 6 79 95 79 94 78 78 94 98 76 44 0909 1066 1224 1381 1538 1695 1852 2009 2166 2323 7 111 110 109 109 77 2480 2637 2793 2950 3106 3263 3419 3576 3732 3889 S 9 126 142 126 141 125 124 140 140 78 4045 4201 4357 4513 4669 4825 4981 5137 5293 5449 79 5604 5760 5915 6071 6226 6382 6537 6692 6848 7003 1 151 15 153 15 152 151 15 15 280 44 7158 7313 7468 7623 7778 7933 8088 8242 8397 8552 2 s 81 46 81 46 30 30 46 45 81 8706 8861 9015 9170 9324 9478 9633 9787 9941 *0095 4 62 61 61 60 82 45 0249 0403 0557 0711 0865 1018 1172 1326 1479 1633 5 77 77 76 76 83 1786 1940 2093 2247 2400 2553 2706 2859 3012 3165 6 7 92 108 92 107 91 91 10A 1(16 84 3318 3471 3624 3777 3930 4082 423,5 4387 4540 4692 8 128 122 122 121 85 4845 4997 5150 5302 5454 5606 5758 5910 6062 6214 9 189 138 187 136 86 6366 6518 6670 6821 6973 7125 7276 7428 7579 7731 1 150 15 149 15 148 147 16 16 87 7882 8033 8184 8336 8487 8638 8789 8940 9091 9242 2 80 80 80 29 88 9392 9543 i 9694 9845 9995 *0146 *0296 *0447 *0597 *0748 8 4 5 45 60 76 45 60 75 44 44 69 59 74 74 89 46 0898 1048 1198 1348 1499 1649 1799 1948 2098 2248 290 46 2398 2548 2697 2847 2997 3146 3296 3445 3594 3744 6 1 90 105 89 104 , 89 88 104 108 91 3893 4042 4191 4340 4490 4639 4788 4936 5085 5234 8 120 119 118 118 92 5383 5532 5680 5829 5977 6126 6274 6423 6571 6719 9 135 184 133 182 93 6868 7016 7164 7312 7460 7608 7756 7904 8052 8200 146 145 144 1 94 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675 1 2 15 29 15 14 29 29 95 9822 9969 *0116 *0263 *0410 *0557 *0704 *0851 *0998 *1145 8 4 44 58 44 4S 58 58 73 72 96 47 1292 1438 1585 1732 1878 2025 2171 2318 2464 2610 5 18 97 2756 2903 3049 3195 3341 3487 3633 3779 3925 4071 6 88 87 86 98 4216 4362 4508 4653 4799 4944 5090 5235 5381 5526 7 102 102 101 8 117 116 115 9 181 181 ISO 99 5671 5816 5962 6107 6252 6397 6542 6687 6832 6970 300 1 2 3 4 5 6 7 8 9 Differences. 1 , -,^ 24 m. 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 145 144 148 142 02 48 0007 0151 0294 0438 0582 0725 0869 1012 1156 1299 1 2 16 14 14 14 29 29 29 28 03 1443 1586 1729 1872 2016 2159 2302 2445 2588 2731 3 44 43 48 48 04 05 2874 4300 3016 4442 3159 4585 3302 4727 3445 4869 3687 5011 3730 5153 3872 5295 4015 4157 5437 5579 4 5 6 68 58 67 67 78 72 72 71 87 86 86 86 06 5721 5863 6005 6147 6289 6430 6572 6714 6855 6997 7 8 9 102 101 100 , 99 116 115 114 114 181 180 129 128 07 7138 7280 7421 7663 7704 7845 7986 81,27 8269 8410 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 1782 1922 2062 2201 2341 2481 2621 1 2 8 14 14 14 14 28 28 28 28 42 42 42 41 11 2760 2900 3040 3179 3319 3458 3697 3737 3876 4016 12 4155 4294 4433 4572 4711 4850 4989 5128 5267 5406 4 66 66 56 66 13 6544 5683 5822 5960 6099 6238 6376 6515 6653 6791 6 6 7 71 70 70 69 86 84 88 88 99 98 97 97 14 6930 7068 7206 7344 7483 7621 7759 7897 8035 8173 15 8311 844S 8586 8724 8862 8999 9137 9275 9412 9560 8 9 118 112 111 110 127 126 126 124 16 9687 9824 9962 *0099 *0236 *0374 *0511 *0648 *0785 *0922 17 18 60 1059 2427 1196 2664 1333 2700 1470 2837 1607 2973 1744 3109 1880 3246 2017 3382 2154 2291 3518 3655 1 187 136 186 184 14 14 14 18 19 320 3791 50 5160 3927 5286 4063 5421 4199 5567 4335 5693 4471 5828 4607 5964 4743 6099 4878 5014 6234 6370 2 8 4 27 27 27 27 41 41 41 40 55 64 54 64 21 6505 6640 6776 6911 7046 7181 7316 7451 7586 7721 5 6 7 69 68 68 67 82 82 81 80 96 96 95 94 22 7856 7991 8126 8260 8395 8530 8664 8799 8934 9068 23 9203 9337 9471 9606 9740 9874 *0009 *0143 *0277 *0411 8 110 109 108 107 24 51 0545 0679 0813 0947 1081 1215 1349 1482 1616 1760 9 128 122 122 121 25 1883 2017 2151 2284 2418 2551 2684 2818 2951 3084 188 182 181 180 18 18 18 18 26 3218 3351 3484 3617 3750 3883 4016 4149 4282 4415 1 27 4548 4681 4813 4946 6079 5211 5344 5476 5609 5741 2 27 26 26 26 28 5874 6006 6139 6271 6403 6535 6668 6800 6932 7064 8 4 40 40 89 89 68 58 52 62 67 66 66 66 29 7196 7328 7460 7592 7724 7855 7987 8119 8261 8382 6 330 518514 8646 8777 8909 9040 9171 9303 9434 9566 9697 6 7 80 79 79 78 93 92 92 91 31 9828 9959 *0090 *0221 *0353 *0484 *0615 *0745 *0876 +1007 8 106 106 105 104 32 52 1138 1269 1400 1630 1661 1792 1922 2063 2183 2314 9 120 119 118 117 33 2444 2575 2705 2835 2966 3096 3226 3366 3486 3616 34 35 3746 5045 3876 5174 4006 5304 4136 5434 4266 6563 4396 5693 4526 6822 4656 5951 4785 4915 6081 6210 129 128 127 1 18 18 18 2 26 26 28 36 6339 6469 6598 6727 6856 6985 7114 7243 7372 7501 8 89 88 88 4 52 61 61 5 65 64 64 37 7630 7759 7888 8016 8145 8274 8402 8531 8660 8788 38 8917 9045 9174 9302 9430 9559 9687 9815 9943 *0072 6 77 77 76 39 53 0200 0328 0456 0584 0712 0840 0968 1096 1223 1351 7 90 90 89 8 103 102 102 340 53 1479 1607 1734 1862 1990 2117 2246 2372 2500 2627 9 116 115 114 41 2754 2882 3009 3136 3264 3391 3618 3645 3772 3899 42 4026 4153 4280 4407 4634 4661 4787 4914 5041 5167 126 126 124 43 5294 5421 5547 5674 5800 5927 6053 6180 6306 6432 1 18 18 12 2 28 28 25 3 88 88 87 44 6558 6685 6811 6937 7063 •7189 7315 7441 7567 7693 45 7819 7945 8071 8197 8322 8448 8674 8699 8825 8961 4 50 50 60 8 68 63 62 6 76 75 74 46 9076 9202 9327 9452 9578 9703 9829 9954 *0079 *0204 47 54 0329 0455 0580 0705 0830 0955 1080 1205 1330 1464 7 88 88 87 48 1579 1704 1829 1953 2078 2203 2327 2452 2576 2701 8 101 100 99 9 113 118 112 49 2825 2950 3074 3199 3323 3447 3671 3696 3820 3944 350 1 2 3 4 5 6 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 1 2. 12 25 12 25 12 24 53 7775 7898 8021 8144 8267 8389 8512 8635 8758 8881 3 87 87 87 54 9003 9126 9249 9371 9494 9616 9739 9861 9984 *0106 4 5 50 62 49 62 49 61 55 55 0228 0351 0473 0595 0717 0840 0962 1084 1206 1328 6 74 74 78 56 1450 1572 1694 1816 1938 2060 2181 2303 2425 2547 7 8 87 99 86 98 85 98 51 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 24 12 24 12 24 61 7507 7627 7748 7868 7988 8108 8228 8349 8469 8589 8 36 36 86 . 62 8789 8829 8948 9068 9188 9308 9428 9548 9667 9787 4 48 48 48 63 9907 *0026 *0146 *0265 *0385 *0504 *0624 *P743 *0863 *0982 5 6 61 73 60 72 60 71 64 56 1101 1221 1340 1459 1578 1698 1817 1936 2055 2174 7 85 84 88 65 2293 2412 2531 2650 2769 2887 3006 3125 3244 3362 8 9 97 109 96 108 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 8 24 85 23 85 23 85 370 56 8202 8319 8436 8554 8671 8788 8905 9023 9140 9257 i 4T 4T 46" 71 9374 9491 9608 9725 9842 9959 *0076 *0193 *0309 *0426 5 g 59 71 59 70 58 70 72 57 0543 0660 0776 0893 1010 1126 1243 1359 1476 1592 T 83 82 81 73 , 1709 1825 1942 2058 2174 2291 2407 2523 2639 2755 8 94 94 98 74 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 9 106 105 104 75 4031 4147 4263 4379 4494 4610 4726 4841 4957 5072 115 12 114 118 11 76 5188 5303 5419 5534 5650 5765 6880 5996 6111 6226 1 11 77 6341 6457 6572 6687 6802 6917 7032 7147 7262 7377 2 28 28 28 78 7492 7607 7722 7836 7951 8066 8181 8295 8410 8525 8 4 35 46 84 46 84 45 79 380 8639 57 9784 8754 9898 8868 8983 9097 *0241 9212 *0355 9326 *0469 9441 9555 *0583 *0697 9669 *0811 5 6 7 58 69 81 57 68 80 57 68 79 *0012 *0126 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 IM 108 102 83 3199 3312 3426 3539 3652 3765 3879 3992 4105 4218 84 4331 4444 4557 4670 4783 4896 5009 5122 5235 5348 1 112 11 111 11 110 11 85 5461 55.74 5686 57,99 5912 6024 6137 6250 6362 6475 2 22 22 22 86 6587 6700 6812- 6925 7037 7149 7262 7374 7486 7599 3 4 34 45 38 44 38 44 87 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 B 56 56 65 88 8832 8944 9056 9167 9279 9391 9503 9615 9726 9838 6 67 67 66 89 9950 *0061 *0173 *0284 *0396 *0507 *0619 *0730 *0842 *0953 7 8 78 90 78 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 22 11 22 94 5496 5606 5717 5827 5937 6047 6157 6267 6377 6487 3 33 82 95 6597 6707 68^' 6927 7037 7146 7256 7366 7476 7586 4 5 44 55 43 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 9 76 87 98 76 86 97 98 9883 9992 *0101 *0210 *0319 *0428 *0537 *0646*0755 *0864 99 60 0973 1082 1191 1299 1408 1517 1625 1734 1843 1951 400 1 2 3 4 5 6 7 8 9 Differences. ■2G HI. LOGARITHMS OF NUMBERS. 1 400 1 2 3 4 5 6 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 1 2 11 22 11 22 11 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 6 44 66 48 54 48 64 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 86 76 86 07 9594 9701 9808 9914 *0021 *0128 *0234 *0341 *0447 *0554 9 98 97 96 08 610660 0767 0873 0979 1086 U92 1298 1405 1511 1617 09 1723 1829 1936 2042 2148 2264 2360 2466 2572 2678 106 106 104 410 01 2784 2890 2996 3102 3207 3313 "3419 3525 3630 3736 1 2 11 21 11 21 10 21 11 3842 3947 4053 4159 4264 4370 4475 4581 4686 4792 3 82 82 81 12 4897 5003 5108 5213 5319 5424 5629 5634 5740 5845 4 42 42 42 13 5950 6055 6160 6265 6370 6476 6681 6686 6790 6896 5 6 63 64 63 68 74 62 62 78 14 7000 7105 7210 7315 7420 7526 7629 7734 7839 7943 7 74 15 8048 8153 8257 8362 8460 8571 8676 8780 8884 8989 8 9 88 96 84 96 88 94 16 9093 9198 9302 9406 9511 9615 9719 9824 9928 *0032 17 18 62 0136 1176 0240 1280 0344 13^4 0448 1488 0552 1592 0656 1695 0760 1799 0864 1903 0968 2007 1072 2110 1 108 10 102 10 19 2214 2318 2421 2525 2628 2732 2836 2939 3042 3146 2 8 21 81 20 81 420 62 3249 3353 3456 3559 3663 3766 3869 3973 4076 4179 4 41 41 21 4282 4385 4488 4591 4695 4798 4901 5004 5107 5210 6 6 7 62 62 72 61 61 71 22 5312 5415 5518 5621 5724 5827 5929 6032 6135 6238 23 6340 6443 6546 6648 6751 6853 6956 7058 7161 7263 8 82 82 24 7366 7468 7571 7673 7775 7878 7980 8082 8185 8287 9 98 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 2265 2356 8 4 80 40 80 40 29 2457 2559 2660 2761 2862 2963 3064 3165 3266 3367 6 61 60 430 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 6182 5283 6383 8 81 SO 32 5484 5584 5685 5785 6886 5986 6087 6187 6287 6388 9 91 90 33 6488 6588 6688 6789 6889 6989 7089 7189 7290 7390 34 35 7490 8489 7590 8589 7690 8689 7790 8789 7890 8888 7990 8988 8090 9088 8190 9188 8290 9287 8389 9387 1 2 99 10 20 98 10 20 36 9486 9586 9686 9785 9886 9984 *0084 *0183- *0283 *0382 8 4 S 80 40 60 29 89 49 37 64 0481 0581 0680 0779 0879 0978 1077 1177 1276 1375 38 1474 1573 1672 1771 1871 1970 2069 2168 2267 2366 6 69 69 39 2465 2563 2662 2761 2860 2959 3058 3166 3255 3364 7 8 69 79 69 78 440 64 3453 3551 3650 3749 3847 3946 4044 4143 4242 4340 9 89 88 41 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 42 5422 5521 5619 5717 6816 5913 6011 6110 6208 6306 97 96 43 6404 6502 6600 6698 6796 6894 6992 7089 7187 7285 1 2 8 10 19 29 10 19 29 44 7383 7481 7579 7676 7774 7872 7969 8067 8165 8262 45 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 4 B 89 49 88 48 46 9335 9432 9530 9627 9724 9821 9919 *0016 *0113 *0210 6 68 63 47 65 0308 0405 0502 0599 0696 0793 0890 0987 1084 1181 7 8 9 68 78 87 67 77 86 48 1278 1375 1472 1569 1666 1762 1869 1966 2063 2160 49 2246 2343 2440 2536 2633 2730 2826 2923 3019 3116 450 1 2 3 , 4 6 6 7 8 9 Diiferences, _11 III. LOGAEITHMS OF NUMBERS. 27 450 1 2 3 4 5 6 7 8 9 Differences. 450 C5 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 6619 5715 5810 5906 6002 1 2 10 19 10 19 53 6098 6194 6290 6386 6482 6577 6673 6769 6864 6960 8 29 29 54 55 7056 8011 7152 8107 7247 8202 7343 8298 7438 8393 7534 8488 7629 8584 7725 8679 7820 8774 7916 8870 4 b 89 49 58 88 48 58 5G 8965 9060 9155 9250 9346 9441 9536 9631 9726 9821 T s 68 78 67 77 51 9916 *0011 *0106 *0201 *0296 *0391 *0486 *0581 *0676 *0771 9 87 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 8 29 28 62 4642 4736 4830 4924 5018 5112 5206 5299 5393 5487 4 88 38 63 5581 5675 5769 5862 5956 6050 6143 6237 6331 6424 5 48 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 98 9 92 9 68 67 0246 0339 0431 0524 0617 0710 0802 0895 0988 1080 1 69 470 1173 67 2098 1265 2190 1358 2283 1451 2375 1543 2467 1636 2560 1728 2652 1821 2744 1913 2836 2005 2929 2 8 19 28 87 18 28 87 71 72 3021 3942 3113 4034 3205 4126 3297 4218 3390 4310 3482 4402 3574 4494 3666 4586. 3758 4677 3850 4769 5 6 7 47 56 65 46 85 64 .73 4861 4953 5045 5137 5228 5320 5412 5503 5595 5687 3 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 86 27 36 79 68 0336 0426 0517 0607 0698 0789 0879 0970 1060 1151 5 46 45 480 6'8 1241 1332 1422 1513 1603 1693 1784 1874 1964 2055 6 7 55 64 54 63 81 2145 2235 2326 2416 2506 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 4436 4576 4666 4756 84 4845 4935 5025 5114 5204 5294 5383 5473 5563 5652 1 2 89 9 18 88 9 18 85 5742 5831 5921 6010 6100 6189 6279 6368 6458 6547 86 6636 6726- 6815- 6904 6994 7083 7172 7261 7351 7440 3 4 27 86 45 26 85 44 87 7529 7618 7707 7796 7886 7975 8064 8153 8242 8331 5 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 SO 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 ] 2 9 17 26 9 17 26 , 94 3727 3815 3903 3991 4078 4166 4254 4342 4430 4517 8 95 4605 4693 4781- 4868 4956 5044 5131 5219 5307 5394 4 5 85 44 84 48 96 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 6 52 62 -97 6356 6444 6531 6618 6706 6793 6880 6968 7055 7142 7 8 9 61 70 78 60 69 7T .98 7229 7317 7404 7491 7578 7665 7752 7839 7926 8014 99 8101 8188 8275 8362 8449 8535 8622 8709 8796 8883 ( 500 1 2 3 4 5 6 7 8 9 Differences. i 28 m. LOGARKTHMS OF NUMBERS. 1 500 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 *O0U *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 1 9 » 04 2431 2517 2603 2689 2775 2861 2947 3033 3119 3205 2 3 IT 26 17 26 05 3291 3377 3463 3549 3635 3721 3807 3893 3979 4065 i 86 84 06 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 5 6 44 52 43 62 07 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 7 61 60 08 5864 5949 6035 0120 6206 6291 6376 6462 6547 6632 8 9 70 7S 69 77 09 6718 6803 6888 6974 7059 7144 7229 7315 7400 7485 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 88 84 13 710117 0202 0287 0371 0456 0540 0625 0710 0794 0879 1 2 9 17 8 , 17 14 15 0963 1807 1048 1892 1132 1976 1217 2060 1301 2144 1385 2229 1470 2313 1554 2397 1639 2481 1723 2566 8 4 5 26 ■84 43 26 34 42 16 2650 2734 2818 2902 2986 3070 3154 3238 3323 3407 6 51 60 n 3491 3575 3659 3742 3826 3910 3994 4078 4162 4246 7 3 60 63 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 716003 6087 6170 6254 6337 6421 6504 6588 6671 6754 21 6838 0921 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 8 4 17 25 88 16 25 33 24 9331 9414 9497 9580 9663 9745 9828 9911 9994 *O077 25 72 0159 0242 0325 0407 0490 0573 0655 0738 0821 0903 5 6 7 42 50 68 41 49 67 26 0986 1068 1151 1233 1310 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 6340 5422 5503 5585 5667 5748 5830 81 30 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 3 24 24 34 35 7541 8354 7623 8435 7704 8516 7785 8597 7866 8678 7948 8759 8029 8841 8110 8922 8191 9003 8273 9084 4 6 6 82 41 49 82 40 48 36 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 7 8 9 57 65 73 56 64 72 37 9974 *0055 *0136 ♦0217 *0298 *0378 *0459 *0540 *0621 *0702 38 73 0782 0863 0944 1024 1105 1186 1266 1347 1428 1508 39 1589 1669 1750 1830 1911 1991 2072 2152 2233 2313 1 540 73 2394 2474 2555 2635 2715 2796 2876 2956 3037 3117 7!» 8 41 3197 3278 3358 3438 3518 3598 3679 3759 3839 3919 1 42 3999 4079 4160 4240 4320 4400 4480 4560 4640 4720 2 16 43 4800 4880 4960 5040 5120 5200 5279 5359 5439 5519 3 4 24 32 44 5599 5679 5759 5838 5918 5998 6078 6157 6237 6317 5 40 45 6397 6476 6556 6635 6715 6795 6874 6954 7034 7113 6 7 47 55 46 7193 7272 7352 7431 7511 7590 7670 7749 7829 7908 8 68 47 7987 8067 814g 8225 8305 8384 8463 8543 8622 8701 9 71 48 8781 8860 8939 9018 9097 9177 9256 9335 9414 9493 49 9572 9651 9731 9810 9889 9968 *0047 *0126 *0205 *0284 .350 1 2 3 4 5 6 7 8 9 Differences. 1 III. LOGARITHMS OF NUMBERS. 29 ■ ■ — — ■ ~ 550 1 2 3 4 5 G 7 8 9 Differences. 5&0 74 0363 0442 0521 0600 0678 0757 0836 0915 0994 1073 51 1152 1230 1309 1388 1467 1540 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 1 8 8 54 3510 3588 3667 3745 3823 3902 3980 4058 4136 4215 2 3 16 24 16 28 ■55 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 4 82 81 56 5075 5153 5231 5309 5387 5465 5543 5621 5699 5777 5 6 40 47 89 47 57 5855 5933 6011 6089 6167 6245 6323 6401 6479 6556 T 55 55 58 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 S 9 68 71 62 70 59 ,7412 7489 7567 7645 7722 7800 7878 7955 8033 8110 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 8 15 63 75 0508 0586 0663 0740 0817 0894 0971 1048 1125 1202 1 2 8 15 64 1279 1356 1433 1510 1587 1664 1741 1818 1895 1972 8 4 28 31 28 30 . 65 2048 2125 2202 2279 2356 2433 2509 2586 2663 »740 5 39 38 66 2816 2893 2970 3047 3123 3200 3277 3353 3^30 3506 6 46 46 67 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 T 8 54 62 S3 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 6940 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 3 4 15 23 30 15 22 80 74 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 75 9668 9743 9819 9894 9970 *0045 *0121 *0196 *0272 *0347 5 6 T 38 45 S3 87 44 S2 76 76 0422 0498 0573 0649 0724 0799 0875 0950 1025 1101 77 1176 1251 1326 1402 1477 1552 1627 1702 1778 1853 S 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 78 82 4923 4998 5072 5147 5221 5296 5370 6445 5520 5594 1 2 7 15 83 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 8 22 84 6413 6487 6562 6636 6710 6785 6859 6933 7007 7082 4 5 29 87 44 85 7156 7230 7304 7379 7453 7527 7601 7675 7749 7823 6 86 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 3 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 86 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 9 58 65 97 5974 6047 6120 6193 6265 6338 6411 6483 6556 6629 98 6701 6774 6846 6919 6992 7064 7137 7209 7282 7354 99 7427 7499 7572 7644 7717 77S9 7862 7934 8006 8079 600 1 2 3 4 5 6 7 8 9 Differences. ,j— Z — ' 30 HI. LOGARITHMS OF NUMBERS. 1 — ■ — — 1 600 1 2 3 i 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 78 72 03 78 0317 0389 0461 0533 0605 0677 0749 0821 0893 0965 1 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 6 G 29 87 44 29 86 48 06 2473 2544 2616 2688 2759 2831 2902 2974 3046 3117 07 3189 3260 3332 3403 3475 3546 3618 3689 3761 3832 7 51 60 08 3904 3975 4046 4118 4189 4261 4332 4403 4475 4546 S g 58 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 86 85 16 9581 9651 9722 9792 9863 9933 *0004 *0074 *0144 *02]5 6 7 48 50 42 49 n 79 0285 0356 0426 0496 0567 0637 0707 0778 0848 0918 8 67 56 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 3790 3860 3930 4000 4070 4139 4209 .4279 4349 4418 1 7 7 23 4488 4558 4627 4697 4767 4836 4906 4976 5045 5115 2 3 14 21 14 20 24 5185 5254 5324 5393 5463 5632 5602 5672 5741 5811 4 28 27 25 5880 5949 6019 6088 6158 6227 6297 6366 6436 6505 6 6 85 41 84 41 26 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 7 48 48 27 7268 7337 7406 7475 7545 7614 7683 7752 7821 7890 8 9 65 62 64 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 2 18 33 1404 1472 1541 1609 1678 1747 1815 1884 1952 2021 8 4 5 20 27 84 34 2089 2158 2226 2295 2363 2432 2500 2568 2637 2705 35 2774 2842 2910 2979 3047 3110 3184 3252 3321 3389 6 7 8 40 47 54 36 3457 3525 3594 3662 3730 3798 3867 3935 4003 4071 37 4139 4208 4276 4344 4412 4480 4548 4616 4685 4753 9 60 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 2 8 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 6 7 38 40 46 45 9560 9627 9694 9762 9829 9896 9964 *0031 *0098 *0165 46 810233 0300 0367 0434 0501 0569 0636 0703 0770 0837 8 9 58 69 ■47 0904 0971 1039 1106 1173 1240 1307 1374 1441 1508 48 1575 1642 1709 1776 1843 1910 1977 2044 2111 2178 49 2245 2312 2379 2445 2512 2579 2646 2713 2780 2847 650 1 2 3 4 5 6 7 8 9 Differences. TTT LOGARITHMS OF NUMBERS. « 31 650 1 2 3 4 5 6 .7 8 9 Differences. ' 1 1 650 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 1 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 2T 84 55 6241 6308 6374 6440 6506 6573 6639 6705 6771 6838 6 40 56 6904 6970 7036 7102 7169 7235 7301 7367 7433 7499 T g 4T 54 57 7565 7631 7698 7764 7830 7896 7962 8028 ,8094 8160 9 V> 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 T 18 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 83 40 64 2168 2233 2299 2364 2430 2495 2560 2626 2691 2756 T 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 7 68 4776 4841 4906 4971 5036 5101 5166 5231 5296 5361 1 69 5426 5491 5556 5621 5686 5751 5815 5880 5945 6010 2 8 18 20 670 82 6075 6140 6204 6269 6334 6399 6464 6528 6593 6658 4 26 71 6723 6787 0852 6917 6981 7046 7111 7175 7240 7305 5 6 T 38 39 46 72 7369 7434 7499 7563 7628. 7692 7757 7821 7886 7951 73 8015 8080 8144 8209 8273 8338 8402 8467 8531 8595 S 52 74 8660 8724 8789 8853 8918 8982 9046 9111 9175 9239 J) 59 75 9304 9308 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 0717 0781 0845 0909 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 32 680 83 2509 2573 2637 2700 2764 2828 2892 2956 3020 3083 6, T 88 45 81 3147 3211 3275 3338 3402 3466 3530 3593 3657 3721 S 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 2 63 6 13 85 5691 5754 5817 5881 5944 6007 6071 6134 6197 6261 86 6324 6387 6451 6514 6577 6641 6704 6767 6830 6894 3 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 44 50 690 83 8849 8912 8975 9038 9101 9164 9227 9289 9352 9415 9 67 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 8 6 12 19' 94 1359 1422 1485 .1547 1610 1672 1735 1797 1860 1922 95 1985 2047 2110 2172 2235 2297 2360 2422 2484 2547 4 5 25 31 96 2609 2672 2734 2796 2859 2921 2983 3046 3108 3170 6 8T 97 3233 3295 3357 3420 3482 3544 3606 3669 3731 3793 7 8 9 43 SO S6 98 3855 3918 3980 4042 4104 4166 4229 4291 4353 4415 99 4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 " 1 700 1 2 3 4 5 6 7 8 9 Differences. 32 III. LOGAEITHMS OF NIBIBERS. 700 1 '2 3 4 5 6 7 8 9 Differences. TOO 84 5098 5160 5222 5284 5346 5408 5470 5532 5594 5656 01 0718 5780 5842 5904 5966 6028 6090 0151 6213 0275 02 6337 6399 6461 6523 6585 6646 6708 6770 6832 6894 62 61 03 0n5.> 7017 7079 7141 7202 7264 7326 7388 7449 7511 1 6 6 04 7573 7634 7696 7758 7819 7881 7943 8004 806G 8128 2 12 3 19 12 18 05 8189 8251 8312 8374 8435 8497 8559 8620 8682 8743 4 25 24 00 8805 8866 8928 8989 9051 9112 9174 9235 9297 9358 6 81 G 87 81 87 07 9419 9481 9542 9604 9665 9726 9788 9849 9911 9972 7 48 48 08 85 0033 0095 0156 0217 0279 0340 0401 0462 0524 0585 8 SO 9 66 49 66 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 2291^ 2358 2419 12 2480 2541 2602 2663 2724 2785 2846 2907' 2968 3029 60 6 12 13 3090 3150 3211 3272 3333 3394 3455 3516 3577 3637 1 2 14 3698 3759 3820 3881 3941 4002 4063 4124 4185 4245 8 4 8 18 24 80 15 4306 4367 4428 4488 4549 4610 4670 4731 ,4792 4852 16 4913 4974 5034 5095 5156 5216 5277 5337 5398 5459 6 86 n 5519 5580 5640 5701 5761 5822 5882 5943 6003 6064 7 8 42 48 18 6124 6185 6245 6306 6366 6427 6487 6548 6608 6668 9 64 19 6729 6789 6850 6910 6970 7031 7091 7152 7212 7272 720 85 7332 7393 7453 7513 7574 7634 7694 7755 7815 7875 21 7935 7995 8056 8116 8176 8236 8297 8357 8417 8477 69 22 .8537 8597 8657 8718 8778 8838 8898 8958 9018 9078 1 6 23 9138 9198 9258 9318 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 0757 0817 08T7- 6 6 7 80 85 41 26 0937 0996 1056 1116 1176 1236 1295 1355 141-^ 1475 27 1534 1594 1654 1714 1773 1833 1893 1952 2012 2072 8 47 68 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 68 32 4511 457,0 4630 4689 4748 4808 4867 4926 4985 5045 1 2 6 12 33 5104 5163 5222 5282 5341 5400 5459 5519 5578 5637 8 17 34 5696 5755 5814 5874 5933 5992 6051 6110 6169 6228 4 5 23 29 35 6287 6346 6405 6465 6524 6583 6642 6701 6760 6819 6 86 36 6878 6937 6996 7055 7114 7173 7232 7291 7350 7409 7 8 41 46 37 7467 7526 7585 7644 7703 7762 7821 7880 7939 ^7998 9 82 38 8056 8115 8174 8233 8292 8350 8409 8468 8527 8586 39 8644 8703 8762 8821 8879 8938 8997 9056 9114 9173 740 86 9232 9290 9349 9408 9466 9525 9584 9642 9701 9760 57 41 9818 9877 9935 9994 *0053 *0111 *0170 *0228 *0287 *0345 1 6 42 87 0404 0462 0521 0579 0638 0696 0755 0813 0872 0930 2 3 4 11 17 23 43 0989 1047 1106 1164 1223 1281 1339 1398 1456 1515 44 1573 1631 1690 1748 1806 1865 1923 1981 2040' 2098 5 29 45 2156 2215 2273 2331 2389 2448 2506 2564 2622 2681 6 7 34 40 4G 2739 2797 2855 2913 2972 3030 3088 3146 3204 3262 8 46 47 3321 3379 3437 3495 3553 3611 3669 3727 3785 3844 9 61 48 3902 3960 4018 4076 4134 4192 4250 4308 4366 4424 49 4482 4540 4598 4656 4714 4772 4830 4888 4945 5003 750 1 2' 3 4 5 6 7 8 9 Differences. III. LOGARITHMS OP NUMBERS. 33 750 1 2 3 4 5 6 7 8 9. Differences. 150 87 5061 5119 5177 5235 5293 5351 5409 6466 5524 5582 51 5640 5698 5756 5813 ■5871 5929 5987 6045 6102 6160 52 6218 6276 6333 6391 6449 6507 6564 6622 66§0 6737 5S 53 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314 1 6 54 7371 7429 7487 7544 7602 7659 7717 7774 7832 7889 2 3 12 IT 55 7947 8004 8062 8119 8177 8234 8292 8349 8407 8464 4 23 5G 8522 8579 8637 ^694 8752 8809 8866 8924 8981 9039 5 6 29 85 57 9096 9153 9211 9268 9325 9383 9440 9497 9555 9612 T 41 58 9669 9726 9784 9841 9898 9956 *0013 *P070 *0127 *0185 3 9 46 52 59 88 0242 0299 0356 0413 0471 0528 0585 0642 0699 0756 T60 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 5T 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 S 4 5 17 28 29 65 3661 3718 3775 3832 3888 3945 4002 4059 4115 4172 66 4229 4285 4342 4399 4455 4512 4569 4625 4682 4739 6 84 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 110 88 6491 6547 6604 6660 6716 6773 6829 6885 6942 6998 71 7054 7111 7167 7223 7280 7336 7392 7449 7505 7561 56 72 7617 7674 7730 7786 7842 7898 7955 8011 8067 8123 1 6 73 8179 8236 8292 8348 8404 8460 8516 8573 8629 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 6 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 9 45 50 78 0980 1035 1091 1147 1203 1259 1314 1370 1426 1482 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 83 86 5423 5478 5533 5588 5644 5699 5754 5809 5864 5920 T 3 89 44 87 5975 6030 6085 6140 6195 6251 6306 6361 6416 6471 9 60 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 S4 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 8 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 2T 95 90 0367 0422 0476 0531 0586 0640 0695 0749 0804 0859 6 7 32 88 96 0913 0968 1022 1077 1131 1186 1240 1295 1349 1404 8 48 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 m. LOGARITHMS OF NUMBERS. 1 — 1 800 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 41?0 02 4174 4229 4283 4337 4391 4445 4499 4653 4607 4661 55 03 4716 4770 4824 4878 4932 4986 5040 5094 5148 5202 1 6 04 5256 5310 5364 5418 5472 5526 5580 5634 5688 5742 2 8 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 83 07 6874 6927 6981 7035 7089 7143 7196 7250 7304 7358 7 89 08 7411 7465 7519 7573 7626 7680 7734 7787 7841 7895 8 9 44 60 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 1 2 54 6 11 13 910091 0144 0197 0251 0304 0358 0411 0464 0518 0571 14 0624 0678 0731 0784 0838 0891 0944 0998 1051 1104 8 4 6 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 83 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 22 487 2 4925 4977 5030 5083 5136 5189 5241 5294 5347 1 6 23 5400 5453 5505 5558 5611 5664 5716 5769 5822 6875 2 3 4 11 16 21 24 5927 5980 6033 6085 6138 6191 6243 6296 6349 6401 25 6454 6507 6559 6612 6664 6'717 6770 6822 6875 6927 5 27 82 26 6980 7033 7085 7138 7190 7243 7295 .7348 7400 7463 7 87 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 919078 9130 91S3 9235 9287 9340 9392 9444 9496 9549 31 9601 9653 9706 9758 9810 9862 9914 9967 *0019 *007l 1 2 B2 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 3 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 T 8 81 86 42 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 4744 61 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 10 16 43 5828 5879 5931 5982 6034 6085 6137 6188 6240 6291 4 20 44 6342 6394 6445 6497 6548 6600 6651 6702 6754 6805 .6 6 7 26 81 36 45 6857 6908 6959 7011 7062 7114 7165 7216 7268 7319 46 7370 7422 7473 7524 7576 7627 7678 7730 7781 7832 8 9 41 46 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 2 3 4 5 6 7 8 ' 9 DiiFerences. ,1 m. LOGAEITHMS 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 *0O32 *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 1 5 54 1458 1509 1560 1610 1661 1712 1763 1814 1865 1915 2 8 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 6 6 26 81 57 2981 3031 3082 3133 3183 3234 3285 3335 3386 3437 T 86 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 61 5 10 63 6011. 6061 6111 6162 6212 6262 esis 6363 6413 6463 64 6514 6564 6614 6665 6715 6765 6815 6865 6916 6966 3 4 6 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 86 41 68 8520 8570 8620 8670 8720 8770 8820 8870 8920 8970 9 46 i 69 9020 9070 91,20 9170 9^20 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 10 15 74 1511 1561 1611 1660 1710 1760 1809 1859 1909 1958 4 20 75 2008 2058 2107 2157 2207 2256 2306 2355 2405 2455 5 6 25 80 76 2504 2554 2603 2653 2702 2752 2801 2851 2901 2950 T 85 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 1 2 49 5 10 82 5469 5518 5567 5616 5665 571'5 5764 5813 5862 5912 83 5961 6010 6059 6108 6157 6207 6256 63.05 6354 6403 8 15 84 6452 6501 6551 6600 6649 6698 6747 6,796 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 78'75 7 8 84 89 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 46 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 J677 1726 1775 6 6 T 24 29 84 95 1823 1872 1920 1969 2017 2066 2114 2l53 2211 2260 96 2308 2356 2405 2453 2502 2550 2599 2647 2696 2744 8 9 88 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 in. LOGARITHMS OF NUMBERS. ' 900 1 2 3 4 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 6062 5110 5158 02 5207 6265 6303 5351 6399 5447 6495 5543 5692 5640 49 03 5688 6736 6784 6832 5880 5928 6976 6024 6072 6120 1 6 04 6168 6216 6265 6313 6361 6409 6467 6505 6553 6601 2 8 10 IB 05 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 4 20 06 7128 7176 7224 7272 7320 7368 7416 7464 7512 7559 6 e 25 29 07 7607 7655 7703 7751 7799 7847 7894 7942 7990 8038 7 84 08 8086 8134 8181 8229 8277 8326 8373 8421 8468 8516 8 9 89 44 09 8564 8612 8669 8707 8755 8803 8860 8898 8946 8994 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 1 2 48 S 10 13 96 0471 0518 0566 0613 0661 0709 0756 0804 0851 0899 14 0946 0994 1041 1089 1136 1184 1231 1279 1326 1374 8 4 6 14 19 24 15 1421 1469 1516 1563 1611 1658 1706 1753 1801 1848 16 1896 1943 1990 2038 2085 2132 2180 2227 2275 2322 6 29 17 2369 2417 2464 2511 2659 2606 2653 2701 2748 2795 7 8 84 88 18 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 9 48 19 3316 3363 3410 3457 3604 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 4590 4637 4684 47 22 4731 4778 4825 4872 4919 4966 5013 5061 5108 6155 1 8 23 5202 6249 ■5296 5343 5390 5437 6484 6631 6678 6625 2 8 4 9 14 19 24 6672 5719 5766 5813 5860 5907 6964 6001 6048 6096 25' 6142 6189 6236 6283 6329 6376 6423 6470 6517 6564 6 24 28 26 6611 6668 6705 6752 6799 6845 6892 6939 6986 7033 7 88 27 7080 7127 7173 7220 7267 7314 7361 7408 7454 7501 8 S3 28 7548 7695 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 8960 8996 9043 9090 9136 9183 9229 9276 9323 9369 46 32 9416 9463 9509 9556 9602 9649 9696 9742 9789 9835 1 2 5 9 33 9882 9928 9975 *0021 *0068 *0114 *0161 *0207 *0254 *0300 8- 14 34 97 0347 0393 0440 0486 0633 0579 0626 0672 0719 0765 4 5 18 28 36 0812 0858 0904 0951 0997 1044 1090 1137 1183 .1229 6 28 36 1276 1322 1369 1416 1461 1608 1554 1601 1647 1693 7 8 82 87 37 1740 1786 1832 1879 1925 1971 2018 2064 2110 2167 9 41 38 2203 2249 2295 2342 2388 2434 2481 2527 2673 2619 39 2666 2712 2758 2804 2861 2897 2943 2989 3036 3082 940 97 3128 3174 3220 3266 3313 3369 3406 3461 3497 3643 45 B 41 3690 3636 3682 3728 3774 3820 3866 3913 3969 4005 1 42 4051 4097 4143 4189 4235 4281 4327 4374 4420 4466 2 9 43 4512 4568 4604 4650 4696 4742 4788 4834 4880 4926 8 4 14 18 44 4972 6018 5064 5110 6156 5202 6248 5294 6340 5386 6 28 45 6432 5478 5624 5570 5616 5662 5707 5753 6799 5845 6 7 27 82 46 6891 5937 6983 6029 6075 6121 6167 6212 6258 6304 8 86 47 6350 6396 6442 6488 6533 6579 6625 6671 6717 6763 9 41 48 6808 6864 6900 6946 6992 7037 7083 7129 7175 7220 49 7266 7312 7368 7403 7449 7495 7541 7586 7632 7678 950 L — . 1 2 3 4 5 6 7 8 9 Differences. 111. LOGARITHMS OF NUMBERS. 37 — -J 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 1 2 5 9 56 0458 0503 0549 0594 0640 0685 0730 0776 0821 0867 8 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 6 6 28 23 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 87 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 4S 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 8 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 I 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 8 i 9 91 6074 6117 6161 6205 6249 6293 6337 6380 6424 6468 18 17 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 80 84 95 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 9 39 96 8259 8303 8347 8390 8434 8477 8621 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. 1 38 IV. MATHEMATICAL CONSTANTS. BERNOULLI'S NUMBERS. Theae numbers are defined by the equation x/(elc-r)-a/[ai + a'/2i+a'/S'.-\ ] =l-Ja; + Bja!V2 !-B.irV* I + B.iuVe ! and found, in succession, by iho formula B,„=B„^C,„„/3- B,„_.C,„„/5+. ■ -iB.n T}±l/(2n+l) B Num. Log. 2 1/6 .16666 6667 9.221S4 87496 4 1/80 .08883 8888 8.S2287 874S8 6 1/42 .02880 9624 8.8767507096 8 1/80 .08888 8888 8.52287 874B8 10 S/66 .07675 7576 8.87942 60688 12 691/2780 .258118558 9.4088164008 14 7/6 1.1666 6667 0.06694 67896 16 8617/510 7.09215686 0.86077 88827 18 48867/798 64.9711779 1.74018 60488 20 174611/880 529.12 4242 2.72856 76597 22 854518/188 61^2.12819 8.7918896878 24 286864091/2780 86580.2531 4.98741 88S11 26 8558108/6 1426617.17 6.16897 24616 28 27298281.1 7.4861846066 80 601680874. 8.77929 40208 EULER'S NUMBERS. These numbers are defined by the equation 1/(1 -'eV2 1 -Ho*/* I-a!V6 I +)=1+E, x'/2 I+E'ibV* H and found, in succession, by the formula ^>n=*^Ji.'>^ln-J-^».4E»„-4+-'- + C,„,«E4TC,„,, Ea±li then Ej=1, £4=6, E,=61, Es=1886, E,„=60621, E„=27 02766, E,. =1998 60981, E,j=l 98916 12145. r-FUNCTI0N8— LOG r p. EcLBB's OOHSTAKT, y, 0.67721 56649 01632 8fe061. p 1284 6 6789 1.0 9.99758 618 280 068 9.98884 621 416 215 021 1.1 9.97884 668 478 810 147 9.96990 889 694 664 421 1.2 9.96292 169 052 *940 *884 9.95782 686 646 469 878 1.8 9.96302 281 166 104 047 9.94995 948 905 868 884 1.4 9.94806 781 761 745 784 727 724 726 781 741 1.6 764 772 794 820 860 884 921 968 *008 *067 1.6 9.96110 167 227 291 359 9.96430 505 588 606 760 1.7 889 981 *027 •126 *229 9.96886 444 566 672 791 1.8 9.96918 *088 *167 •298 •483 9.97571 712 856 *004 *164 1.9 9.98807 468 622 784 949 9.99117 288 462 688 818 HYPERBOLIC FUNCTIONS. «* = l+iB+a>V21+fl!V8l+«1899 (1»)*/41.0»88 06828 85156 29987 1' =.0!>29 08882 08665 72160 (1°)»= .0"16 19521 94779 59060 (l')» = .0'846 1594994076 (1°)V6 ! .0'" 1849601628 16826 (l')V2 1= .0'428 0797497088 (1<')»= .0" 2826699029 78608 {1')" = .0'»24618 78210 (1<')V6:= .0' =89 2.5831 98574 (l')V8 ! = .0>'410229702 (1°)'= .0"49338469 70266 (!')* = .0"71.'5936 (1'>)V7:=> .0"978S38486 (!')*/*!= .0"29S88 (l'')«= .0»*861031 8082094988 (1')' = .0"208 (1°)V8!= .0' =21 85494 80869 (r)V5!= .0"2 (1°)"= .0" 16027 8S120 87484 1° =.01745829251994329577 (1»)>°= .0"262 28513 39893 (1°)»= .0^80 46174 19786 70860 (1°)"= .0"4 67778 91668 8inl''=- .017452406487284 log sin 1° = - 8.2418668184 8inl'= .00029 0888204568 log sin 1' = - 6.46872 61111 8lnl"= .000004848186811 log sin 1" = - 4.6866748668 lY. CHEMISTRY, ENGINEERING, AND PHYSIOS. 39 CHEMISTRY. Weight of 1 liter of hydrogen in grams, ■ . . - - of 1 liter of air, at sea level, under pressure of 760 mm., lat. 45", - ■ - - l.i Ratio of atomic weight of gases to specihc heat, - - 6.25 Expansion of gases for 1 degree centigrade, - - .00867 Aluminium, Antimony, Arsenic, Barium, Bismuthji Boron, Bromine, Cadmium, Calcium, Carbon, Chlorine, Chromium, Cobalt, Copper, Fluorine, Gold, Hydrogen, Iodine, Iron, Lead, Lithium, Magnesium, Al.. Sb., As., Ba., Bi., B., Br., Cd., Ca., 0., 01., Or., Oo., Oa., I'., Au., H., I-, Pe., Pb., Li., Mg., ATOMIC 27 120 75 187 208.9 11 79.95 112 40 12 85.43 52.1 59 63.4 19 197.8 1.007 126.85 56 206.95 7.02 24.8 WEIGHTS. Manganese, Mercury, Molybdenum, Nickel, Nitrogen, Oxygen, Phosphorus, Platinum, Potassium, Selenium, Silicon Silver, Sodium, Strontium, Sulphur, Tellurium, Tin, Titanium, Tungsten, Tlranlmn, Zinc, Zirconium. Mn., Hg., Mo., Ni.. N., C, P-. Pt., K., Be., Si., Ag., Na., Sr., S., Te., Sn., Ti., W., V; Zn., Zr., 65 200. 96 68.T 14.08 16 81 195 89.11 79 28.4 107.92 28.05 87.6 82.06 125 119 48 184 289.6 65.8 90.6 ENGINEEEINS. FRICTION. Let F. B. be the coefficient^ of friclion if the body be at rest, F. M, if in motion, and A the angle of repose. P. E. F. M, Clay, dry, .... .88-. 65 wet, - . .25-.S1 Gravel, - . - .70-1.00 Iron on iron, or brass, .16-.25 .1&..20 [oiled, on wood, - .40-, 60 .25-.40 [oiled. Masonry, dry, - .60-. 70 on clay, . . . .80-.50 Sand, .68-.84 Wood on stone, - ,18- .58 on wood, . . 25-.50 .25-.50 [oiled. A. 21-88° 14-17 85^5 9-14 22-81 81^5 17-27 80-40 10.80 .06-.08] 14-27 .05-.08] .06-.D8] MODin.UB OF BLASTIOITT. Let \ be the elongation, p the force in tons, I length,/ the cross section in square inches, e the elasticity ; then \=pl//6. ' e. Brass, ... - ■ 5500 Iron, steel, . - wire, . . 6400 wrought, . Copper, cast, - . 7000 Lead, .... wire, hard drawn, 8000 Phosphor-bronze, Gun metal, - . 4500-6000 Timber, . Iron, cast, . . 5000-6000 Zinc, rolled, STBENQTH OF UATEBtALS. Let T be the ultimate tenacity in pounds and L the crushing load, per square inch, for T. Brick, ordinary, . . - the original modulus of 12000-13000 12000-13000 1000 6000 600-9S0 5500 Copper, cast, rolled, . - wire, ... Iron, cast, .... steel, - ... wrought; ... Hope, hemp, . • - - manilla, .... Timber, oak and pine. 18000-25000 80000-50000 45000-60000 18000-28000 56000-175000 45000-60000 11000-13000 7000-10000 5000-15000 per square inch short blocks. L. 1500-6000 8000-15000 9000-12000 65000-110000 60000-176000 40000-65000 4000-12000 WEIOHT OP HATESIALS IN POtlNDS PER CUBIC FOOT. Aluminium, Brass, - - . . Brick, common. Clay, compact. Copper, . . Earth, loose. Glass, - - Gravel and sand. 160-170 . 476-626 - 110-130 . 120-185 535-660 73-90 - 150-180 90-120 Iron, cast. - . steel, wrought. Platinum, Stone, . Tim"ber, - . "Water, pure, at Zinc, 485-433 485-495 . 475-490 - 1300-1375 180-170 80-05 ' F., 62.42 425-450 PHYSICS. DENSITY OP AIR. Let t Stand for the temperature centigrade, k for the height of the barometer column expressed in millimeters, M for the mass in grams of one cubic centimeter of air ; then M=.0O1298/(l-|-.00S67 if) •A/760. DENSITY AND VOLUME OP WATER. Let C be the temperature In centigrade degrees ; B, the density ; V, the volume of 1 gram in cubic centimeters ; then : C. D. V. 0. D. V. C. D. T. 0° 0.99987 1.00013 13°0.99943 1.00057 26''0.99712 1.00289 9998 9997 9999 1.00000 0.99999 9997 14 16 16 17 18 19 9975 9965 9933 0007 0003 0001 0000 0001 0003 0007 20 0011 21 0018 22 0023 28 0084 24 0046 9930 9916 9900 9884 9863 9846 9826 9805 9783 9760 9787 0070 26 0084 27 0100-28 0116 29 0135 80 0164 40 0174 50 0196 60 0218 70 0240 80 0264 90 100 9687 0314 0341 9603 0896 9577 0425 9235 0770 8819 1198 8838 1691 7794 2256 7194 2887 6566 8567 3866 4312 ELECTEICITT. 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 13.5° C, 1.483 volts. Loss by hysteresis for wrought iron, .0023^'^ ergs per cycle per cubic centimeter. PRACTICAL UNITS EXPRESSED IN O. G. S. UNITS. Let V be the velocity of light, about 8.10**' cm. per sec. Electrostatic. Electromagnetic. Practical. C.G.S. Quantity, - - ■ Current, - Potential, - Resistance, Capacity, - Self induction. C.G.S. T/lOi.e., 8-10» T/10 3-10» lO'/V 1/(3.10') 10»/V« 1/(9-10") VV10» 9-10". 1 coulomb. 1/10, 1 ampere, 1/10, 1 volt, 10", 1 ohm, 10», 1 farad, tl/W, 1 henry, 10". UNITS OF RESISTANCE. Let L be the length of a mercui'y column, 1 millimeter square, at 0° C, and R the resistance in true ohms. L. E. L. E. True ohm, 106.8 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*1088 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. 846. Let the specific resistance at 0° 0. in 0. G. S. units be R ; the resistance at 0° 0. in legal ohms of a wire 1 mm. in di- ameter and 1 m. long, E'. If R^ be the resistance of a wire at 0° C, and a the temperature coefficient ; then the resis- tance at ^° 0, is found by the formula Et=R„(l-|-a*). E. R'. a. Aluminium, annealed, - . . 2913 .0871 Antimony, pressed, - - 83300 .4314 Bismuth, pressed, ... Copper, annealed, . - . - hard drawn, - . . . . German Silver, ... Gold, annealed, hard drawn, - . - - . Iron, annealed, • - Lead, pressed. Mercury, . - - Nickel, annealed. Platinum, annealed. Silver, annealed, hard drawn. Tin, pressed. Zinc, pressed, - ■ . 13114 1.6680 .00864 1698 .0203 .00383 1684 .0208 20940 .2662 .00044 2069 .0262 .00863 2095 .0267 9718 .1286 .004-.005 19636 .2494 .00887 95114 1.2098 00072 12457 .1684 9056 .1151 .0014^.0086 1603 .0191 .00877 1684 .0203 18215 .1680 .oasos 3628 .0716 .01)865 40 IV. PHYSICS. GRAVITT. Length of the seconds pendulum at height h above sea level : In Inches, - - -39.012640+.20S26S slnMat.-3 A/10' In feet, - - - - S.2S1W5+ .017866 sin» lat.-S A/W in meters, - - 0.990910+ .005290 sin" lat. -8 A/10' Acceleration by gravity, per second of mean solar time : in feet, 82.086628+.171298 sin" lat.-8 A/10" In meters, .... 9.7798S6-i-.052210 sin" lat.-8 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 iVom 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 =.289 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^ arc expressed in terms of the lengths at 0° by the formula ?t= ?o (1 + <» Oi "id volumes by the formula Vt=V„(l+SaO. If the Fahrenheit scale bo used, these formulae become '■ = '31 [l + o' («-82)], Vt=V3j [1 +3a' (*-82)]. Aluminium, . • Bismuth, - - - Brass, Brick, Cadmium, Carbon, gas coke, graphite, - ■ Copper, Glass, Gold, - - . Iron, cast, . steel, wrought, - • Lead, - . . - Magnesium, Nickel, Platinum, Silver, Stone, . - Tin, . . . . Wood, - - Zinc, . . .0*231-.0«235 182 133 .0»128-.0*180 073 074 134 051 307 054 079 167 070 144 117 110 108 280 269 128 088 192 045 223 036 290 816 055 172 092 147 144 122 117 312 276 091 194 117 233 063 298 102 030 170 030 044 093 039 080 0G5 061 060 155 149 071 049 107 025 125 020 160 106 050 175 106 051 081 080 068 065 160 158 051 108 065 160 035 165 CONDUCTIVITIES FOR UEAT. 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 9,°, flj° C, and Q the quantity of heat in minor calories that flows through the plate in t seconds ; then : Q = K • A • « ■ (fli -0^)/]). K. K. Brass, .... .802 Ice, ..... .0067 Copper, .... 1.108 Iron, .164 Fire-brick, - - . .00174 Paratfine, - - . .00014 German silver, . .109 Water, .... .0014 Glass, - - .0006-.002 Zinc, .... .807 IIEAT8 OP FUSION. Cal. B.T.U. per kg. per lb. Bismuth, Cadmium, - Ice, Lead, Mercury, 12.6 13.6 80 5.4 22.7 Nickel, 24.6 Platinum, 144 Silver, - 9.7 Tin, - . 5.08 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 50.6 MELTING POINTS. C. F. Aluminium, about 600° 1100° Bismuth, 260 500 Cadmium, - - - 815 600 Copper, .... 1054 1930 Gold, - . - 1W6 1910 Ice, - - 32 Iridium, - - 1950 8540 Iron, pig, about 1075 1970 pure, about 1600 2900 Iron, cast steel, Lead, Mercury, Nickel, . Faraffine, Platinum, Silver, Tin, - Zinc, C. F. ■ 1870° 2500° 826 620 ■ -40 -40 ■ 1450 2640 54 129 1775 8230 ■ 954 1750 ' 280 446 • 412 774 Aluminium, 16-97° Bismuth, 20-48 Brass, - . 14-98 Cadmium, . 0-100 Carbon, charcoal, 20 diamond, 20 graphite, 20 Copper, - - 15-100 Gold, . . 0-100 Ice, . . . -20-0 Iron, pure, 0-100 SPECIFIC IIEA18. 3., .212 Iron, steel, ord. tem., .116-.119 .0805 wrought, ord. temp., .108 .086 Lead, - - 19-48° C, .0816 .056 Magnesium, 20-60 .245 .164 Mercury, - 5-86 .088 .121 Nickel, . 14-97 .109 .167 Platinum, . 0-100 .033 .098 Sliver, - . 0-100 .066 .082 Steam, at constant press. ,.478 .504 Tin, - - 0-100° C, .066 .113 Zinc, . - 0-100 .0936 LIGHT. Units op Lianx : one candle power, British, Is the light f^oni a spermaceti candle burning 120 grains an hour ; 1 carcel is 9.....■•. 7.92 .8987 25 89.87 1.595165 6 2.3622 15.240 19.685 1.3283 6.5617 5.4864 8.7232 9.6661 1 III 1 uiocur, ..•.•*.. ' Kilometers in 1 mile, .... 8/5 7 2.7559 17.780 22.966 2.1886 7.6563 6.4008 4.8496 11.266 1.60935 .2066 50 8 3.1496 20.320 26.247 2.4884 8.7489 7.8152 4.9710 12.875 in 1 nautical mile, ...... 1.85.327 .267989 9 8.6483 22.860 29.528 2.7482 9.8426 8.2296 5.6928 14.484 1 Meters in 1 chain, ....... 20.1168 1.8035 60 in 1 foot, 4/18 .304801 9.484016 MEASURES OF AREA. inl yard, 12/18 .914402 9.961137 S.q. in. Sq.cm. fn 1 inl Sq. ft. Sq. m. Sq.yds. Sq. m. Acres Hectar i Miles in 1 kilometer, .... 6/8 .621870 9.7938 50 inl inl inl inl inl inl Yards in 1 meter, .... - 13/12 1.09861 .0888 68 sq.cm. sq. in. sq. m. sq. ft. sq. m. sq. yd. hectar. acre. inl mile, 1760 8.245518 1 .16600 6.4616 10.764 .09290 1.1960 .88618 2.4710 .40469 2 .31000 12.903 21.528 .18681 2.8920 1.6723 4.9421 .80937 8 .46600 19.866 32.292 .27871 8.6880 2.6084 7.4181 1.2141 Acres in 1 heotar, ...... 5/2 2.47104 .8928 80 4 .62000 28.807 48.065 .87161 4.7889 3.8445 9.8842 1.6187 in 1 square mile, .----- 640 2.806180 5 .77500 82.268 63.819 .46462 5.9799 4.1807 12.855 2.0234 Ars in 1 acre, ......... 40.4687 1.607120 6 .98000 88.710 64.688 .66742 7.1759 6.0163 14,326 2.4281 Square centimeters in 1 square inch, - ■ 6.45168 .8096 69 7 1.0850 45.161 76.847 .66082 8.8719 6.8529 17.297 2.8323 Square feet in 1 square chain, ... 4356 3.6390 88 8 1.2400 51.618 86.111 .74823 9.5679 6.6390 19.768 3.2375 in 1 square meter, - * . - . . ■ 10.7639 1.0819 68 9 1.3950 58.066 96.875 .38613 10.764 7.5252 22.239 3.6422 Hectars in 1 square mile, ..... - 269.000 2.4138 00 Square inches in 1 square meter, . . - 1560.00 8.1908 81 MEASURES OF VOLUME. Square meters in 1 square foot, - 1/11 in 1 square yard, - - . . 5/6 .092908 8.968082 .886131 9.9222 74 Cu. in. Cu. cm. inl inl ' cu.cm. cu. in. Cu. ft. Cu. m. Cu.yds. Cu. m. inl inl nl inl cu. m. cu. ft. cu. m. cu. yd. Square yards in 1 acre, - - ' in 1 square meter, - .... 6/5 4840 8.634845 1.19599 .0777 26 1 .06102 16.887 2 .12205 82.774 85.314 .02982 1.8079 .76456 70.629 .06663 2.6159 1.5291 MEASURES or VOLUME. 3 .18307 49.161 105.94 .08496 3.9238 2.2937 Cubic centimeters in 1 cubic inch, . - 16.3872 1.2145 04 4 .24409 65.549 141.26 .11827 5.2318 8.0582 Cubic feet in 1 cubic meter, .... 85.8145 1.6479 53 5 .80612 81.986 176.57 .14159 6.5897 8.3228 Cubic meters in 1 cubic yard, - - 3/4 .764659 9.883411 6 .86614 98.828 211.89 .16990 7.S477 4.5374 ! Cubic yards in 1 cubic meter, - . - 4/8 1.30794 .1165 89 7 .42716 114.71 8 .48819 181.10 247.20 .19822 9.1556 5.8519 282.62 .22664 10.464 6.1166 MEASURES OF CAPACITY. 9 .64921 147.48 817.83 .25435 11.771 6.8810 Bushels imperial in 1 liter, . ■ .027610 8.4894 97 MEASURES OF OAPACTTY. United States in 1 liter, .... ■ .028377 8.4529 73 Gallons imperial in 1 liter, . . - - United States in 1 liter, .... .220083 9.3426 87 • .264170 9.4218 84 Flu. oz. Cu.cm. inl inl- cu.cm. flu. oz. U.S. Liters Imp. Liters U.S. H.lits. gals, in in 1 gals, in in 1 bu. in in 1 1 lit. U.S.gal. 1 lit. imp.gal. 1 h.litU.S.bu. Cubie inches in 1 bushel imperial, - . 2218.19 3.8469 99 1 .03381 29.674 .26417 8.7854 .22008 4.6487 2.8377 .85289 , in 1 bushel United States, ... • 2150.42 8.8325 28 2 .06763 69.147 .528.34 7.5709 .44017 9.0876 5.6765 .70479 in 1 gallon imperial, - . . . - ■ 277.274 2.4429 09 8 .10144 88.721 .79251 11.356 .66026 13.631 8.5132 1.0572 in 1 gallon United States, ... 281 2.8686 12 4 .18526 118.29 1.0667 16.142 .88083 13.175 11.351 1.4096 in 1 liter, 61.0234 1.7864 96 ; Liters in 1 bushel imperial, .... 86.8499 1.6606 03 5 .16907 147.87 1.8209 18.927 1.1004 22.719 14.189 1.7620 In 1 bushel United States, . . - . 85.2393 1.5470 27 6 .20288 177.44 1.5S50 22.718 1.8205 27.262 17.026 2.1144 in 1 gallon imperial, ..... 4.54378 .6574 13 7 .23670 207.02 1.8492 26.498 1.5406 31.806 19.864 2.4667 in 1 gallon United States, ... 8.78648 .678116 8 .27051 286.59 2.1134 80.283 1.7607 86.850 22.702 2.8191 in 1 cubic inch, - . .... .016887 8.214504 9 .80432 266.16 2.8775 34.069 1.9807 40.894 25.540 WEIGHTS. 8.1715 WEIGHTS. ^...ntna 1*\ 1 irrtam __.._.. 15.4824 1.188482 Grains Grams in 1 in 1 Oz. Grams Oz. av. Grams Lb.av. Kilog. ^ urains m l gram, ........ Troy in in 1 in 1 in 1 in 1 in 1 ' /^nnivio in 1 n) . ' 46 V. ADDITION-SUBTRACTION LOGARITHMS. A B 1 2 3 4 5 6 7 8 9 Differences. :i.oo 0.04 1393 1484 lo75 1666 1758 1850 1942 2034 2126 2219 95 100 105 110 01 2311 2404 2497 2591 2684 2778 2872 2966 3060 3155 1 2 10 19 10 20 U 21 11 22 02 3249 3344 3439 3535 3630 3726 3822 3918 4014 4111 8 29 80 82 88 03 4207 4304 4401 4498 4596 4694 4792 4890 4988 5086 4 88 40 42 44 04 5185 5284 5383 5483 5582 5682 5782 5882 5982 6083 5 G 48 57 60 60 68 63 65 60 05 6184 6285 6386 6487 6589 6691 6793 6895 0997 7100 7 S D 67 70 80 70 80 90 74 84 95 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 115 120 126 180 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 8 28 85 24 86 25 88 20 89 9.10 0.05 1497 1609 1721 1833 1946 2059 2172 2285 2399 2513 4 40 48 80 52 n 2627 2741 2855 2970 3085 3200 3316 3431 3547 3663 5 G 58 69 60 72 68 75 06 78 12 3780 3896 4013 4130 4247 4365 4483 4601 4719 4837 ' 7 81 84 88 91 13 4956 5075 5194 5314 5434 5554 5674 5794 5915 6036 8 9 92 104 90 108 100 118 104 117 160 14 6157 6278 6400 6522 6644 6766 6889 7012 7135 7259 185 140 145 15 7382 7506 7630 7755* 7879 8004 8129 8255 8380 8506 I 14 14 16 16 16 8632 8759 8886 9012 9140 9267 9395 9523 9651 9779 2 3 27 41 28 42 29 44 80 46 17 9908 *0037 *0166 *0296 *0426 *0556 *0686 *0816 *0947 *1078 4 54 66 68 00 18 0.06 1210 1341 1473 1605 1738 1870 2003 2136 2270 2404 5 68 70 78 75 19 2537 2672 2806 2941 3076 3211 3347 3483 3619 3755 6 7 81 95 84 98 87 102 90 105 9.20 0.06 3892 4029 4166 4304 4441 4579 4718 4856 4995 5134 8 9 108 122 112 120 116 181 120 135 ' 21 5274 5413 5553 5694 5834 5975 6116 6257 6399 6541 165 16 160 16 166 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 88 84 24 9587 9735 9883 *0032 *0181 *0331 *0480 *0630 *0780 *0931 3 4 47 62 48 64 50 06 61 08 25 0.07 1082 1233 1384 1536 1688 1840 1993 2146 2299 2453 5 6 7 78 98 109 80 96 112 83 99 116 85 102 119 26 2606 2761 2915 30T0 3225 3380 3536 3692 3848 4004 27 4161 4318 4476 4633 4791 4950 5108 5267 5427 5586 8 124 128 182 186 28 5746 5906 6067 6228 6389 6550 6712 6874 7037 7199 9 140 144 149 163 29 7362 7526 7689 7853 8017 8182 8347 8512 8678 8844 1 17S 18 180 18 185 19 190 19 9.30 0.07 9010 9176 9343 9510 9678 9845 *0014 *0182 *035l *0520 2 3 4 85 53 70 86 54 72 87 56 74 83 67 70 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 93 95 33 4146 4322 4499 4676 4853 5031 5209 5387 5566 5745 G 7 8 105 123 140 108 126 144 111 130 148 114 133 152 34 5924 6104 6284 6464 6645 6826 7007 7189 7371 7553 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 *L2T4 1 195 20 200 20 205 21 210 21 37 0.09 1464 1654 1844 2035 2226 2418 2610 2802 2995 3188 2 39 40 41 42 38 39 3381 5334 3574 5531 3768 5728 3963 5926 4158 6125 4353 6324 4548 6523 4744 6722 4940 6922 5137 7122 3 4 5 59 78 98 00 80 100 62 82 103 03 84 105 9.40 0.09 7323 7524 7725 7927 8129 8331 8534 8737 8941 9145 6 7 117 137 120 140 123 144 120 147 41 9349 9554 9759 9964 *0170 *0376 *0583 *0790 *0997 *1205 8 150 160 164 108 42 0.10 1413 1621 1830 2039 2249 2459 2669 2880 3091 3302 9 176 180 185 189 43 3514 3726 3939 4152 4366 4579 4794 5008 5223 5438 21S 220 230 240 44 5654 5870 6087 6304 6521 6739 6957 7175 7394 7614 1 2 22 43 22 44 28 46 24 48 45 7033 8053 8274 . ^95 8716 8938 9160 9382 9605 9828 3 4 5 65 86 108 06 88 110 69 92 115 72 96 120 46 0.110052 0276 0500 0725 0950 1176 1402 1629 1855 ^ 2083 47 2310 2538 2767 2996 3225 3455 3685 3915 4146 4378 6 129 182 138 144 48 4609 4842 6074 5307 6540 5774 6008 6243 6478 6714 7 8 9 151 172 194 154 170 198 161 184 207 168 192 210 49 6949 7186 7422 7660 7897 8135 8373 8612 8851 9091 A = log(5- log a, log a + B^ log (a + b). B=:log« — log^, log 3 f A = log (a -b) ' Y. ADDiTION-SUBTEACTION LOaARITPIJ\|S. 47 A B 1 2 3 4 5 6 7 8 9 , Differences. 9.60 0.119331 9572 9812 *0054 *0295 *0538 *0780 *1023 *1267 *15i0 245 260 255 260 51 0.12 1755 1999 2244 2490 2736' 2982 3229 3476 3724 3972 1 2 25 49 25 50 26 26 61 62 52 4221 4470 4719 4969 5219 5470 5721 5973 6225 6477 3 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 6 6 123 147 125 150 128 180 153 166 55 56 0.13 1879 4521 2142 4787 2404 5054 2667 2931 5322 5590 3195 5858 3459 6127 3724 3989 4255 6396 6666 6936 7 8 9 172 196 221 176 200 226 179 182 204 208 . 280 284 57 7207 7478 7750 8022 8294 8567 8841 9114 9389 9663 270 280 290 300 58 9939 *0214 *0491 *0767 *1044 *1322 *1600 *1878 *2157 *2437 1 27 28 29 80 59 0.14 2716 2997 3277 3559 3840 4123 4405 4688 4972 5256 2 3 54 81 66 84 68 60 87 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 6 135 162 140 168 145 150 174 180 62 0.15,1330 1624 1919 2215 2511 2807 3104 3401 3699 3997 7 189 196 208 210 63 64 4296 7310 4595 • 7-615 4895 7919 5195 5496 8224 8530 5797 8836 6099 9142 6401 6704 7007 9449 9757 *0065 8 9 216 243 310 224 252 320 282 240 261 270 830 340 65 0.16 0374 0683 0992 1302 1613 1924 2235 2547 2859 3172 1 81 32 38 84 66 3486 3800 4114 4429 4745 5061 5377 5^94 6011 6329 2 S 62 93 64 96 66 68 99 102 61 6648 6967 7286 7606 7926 8247 8569 8891 9213 9536 4 124 128 182 136 68 9860 *0183 *0508 *0833 *1158 *1484 *1811 *2138 *2465 *2793 S 155 160 165 170 69 0.17 3122 3451 3780 4110 4441 4772 5104 5436 5768 6101 6 7 186 217 192 224 198 204 281 288 9.'70 0.17 6435 6769 7104 7439 7774 8111 8447 8784 9122 9460 8 9 24S 279 256 288 264 272 n 9799 *0138 *0478 *0818 *1159 *1501 *1842 *2185 *2528 *2871 850 85 360 36 370 380 87 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 2 70 72 74 76 74 0.19 0203 0558 0913 1269 1626 1983 2340 2699 3057 3416 3 4 105- 140 108 144 111 114 148 152 75 3776 4136 4497 4858 5220 5582 5945 6308 6672 7037 5 G 7 175 210 245 180 216 252 185 190 76 7402 7767 8133 8500 8867 9235 9603 9972 *0341 *0711 222 228 259 266 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 9 316 824 883 342 79 8601 8983 9365 9748 *0131 *0515 *0900 *1284 *1670 *2056 1 890 39 400 40 410 420 41 42 9.80 0.21 2443 2830 3217 3606 3994 4384 4774 5164 5555 5947 2 3 4 78 117 156 SO 120 160 82 84 123 126 164 168 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 8 234 278 312 240 280 320 246 262 84 8357 8766 9176 9586 9997 *0409 *0821 *1233 *1646 *2060 287 294 828 836 85 0.23 2474 2889 3304 3720 4137 4554 4971 ^389 5808 6227 9 351 860 869 878 86 6647 7067 7488 7910 8332 8755 9178 9602 *0026 *0451 1 480 43 440 44 450 460 45 46 90 92 87 0.24 0876 1302 1729 2156 2584 3012 3441 3870 4300 4730 2 86 88 88 89 5162 9503 5593 9941 6025 *0379 6458 6891 *0817 *1256 7325 *1696 7760 *2136 8195 8630 9067 *2576 *3018 *3459 3 4 5 129 172 215 132 176 220 135 138 180 184 225 230 9.90 91 0.25 3902 8357 4345 8806 4788 9255 5233 5677 9705 *0155 6122 *0606 6568 *1058 7015 7462 7909 *1510 *1962 *2416 6 7 3 268 801 844 264 308 852 270 276 816 822 360 868 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 470 480 490 600 94 0.27 2065 2531 2998 3464 3932 4400 4869 5338 5808 6278 1 2 47 94 48 96 49 60 98 100 95 96 6749 0.28 1490 7221 1968 7693 2445 8165 8639 2924 3403 9113 3882 9587 4363 *0062 *0538 *1014 4843 5325 5807 8 4 5 141 188 286 144 192 240 147 150 196 200 245 250 97 6289 67'^2 7256 7740 8225 8710 9196 9682 '*0169 *0657 6 282 288 294 300 98 99 0.29 1145 6059 1634 65^3 2123 7048 2613 3104 7544 8040 3595 8537 4086 9035 4579 5071 5565 9533 *0031 *0530 7 8 9 329 876 423 886 884 482 843 , ,350 892 41)0 441 45(1 A = log 6-\oga, log a + B = log(a + (5). B = loga-log^, logi5 + A = log (a -b). ' -- — --...._ 1 •is j 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 BO 003 2533 2583 2633 2683 2733 2784 2834 2884 2934 298f 1 6 004 3035 3085 3135 3185 3236 3286 3336 3386 3437 3487 2 3 10 IB 005 3537 3587 3638 3688 3738 3789 3839 3889 3940 3990 i 20 006 4040 4091 4141 4191 4242 4292 4343 4393 4443 4494 5 6 7 26 80 85 007 4544 4595 4G45 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 46 0.010 0.30 6059 6109 6160 6211 6261 6312 6362 6413 6464 6514 Oil 0565 6615 6666 6717 6767 6818 6869 6919 6970 7021 012 7071 7122 7173 7224 7274 7325 7376 7426 7477 7528 61 013 7579 7629 7680 7731 7782 7832 7883 7934 7985 8036 1 2 6 10 014 8086 8137 8188 8239 8290 8341 8391 8442 8493 8544 8 IB 015 8595 8646 8696 8747 8798 8849 8900 8951 9002 9053 4 S 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 86 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 62 6 022 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 S 4 16 21 025 3710 3761 3813 3864 3916 3967 4019 4070 4122 4173 B 6 7 26 81 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 6410 5462 5514 5565 5617 5669 5720 9 47 029 5772 5824 5875 5927 5979 6030 6082 6134 6186 6237 0.030 0.316289 6341 6392 6444 6496 6548 6599 6651 6703 6755 031 6807 G858 6910 6962 7014 7066 7117 7169 7221 7273 68 032 7325 7377 7428 7480 7532 7584 7636 7688 7740 7791 1 2 6 51 033 7843 7895 7947 7999 8051 8103 8155 8207 8259 8311 8 16 034 8363 8415 8467 8519 8571 8622 8674 8726 8778 8830 4 B 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 T 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 041 2014 2066 2118 2171 2223 2276 2328 2380 2433 2485 1 54 S 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 5 27 045 4113 4165 4218 4270 4323 4376 4428 4481 4533 4586 8 7 82 88 046 4639 4691 4744 4797 4849 4902 4955 5007 5060 5113 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 = loga- log (5, \ogd + 'B = log(a + ^). B = log a - log 5, log^H f-A=log( a-b). 'ti.r-..^ ■,- - V. ADX)ITION-SUBTRACTION LOGARITHM^. 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 1 58 6 056 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 8 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 T 8 82 87 42 0.060 0.33 2065 2119 2172 2226 2279 2333 2386 2440 2493 2547 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 6 068 6360 6413 6467 6521 6575 6629 6683 6737 6791 6845 11 16 069 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 56 078 1779 1833 1888 1942 1997 2051 2106 2160 2215 2269 1 6 079 2324 2378 2433 2487 2542 2597 2651 2706 2760 2815 2 8 11 17 0.080 0.34 2869 2924 2979 3033 3088 3142 3197 3252 3306 3361 i 5 6 22 28 S3 081 3416 3470 3525 3580 3634 3689 3744 3798 3853 3908 082 3962 4017 4072 4127 4181 4236 4291 4346 4400 4455 7 89 083 4510 4565 4619 4674 4729 4784 4838 4893 4948 5003 8 9 44 60 084 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 7585 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 8 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 0513 5 28 093 0.35 0015 0070 0125 0181 0236 0291 0347 0402 0457 6 7 8 84 89 45 094 0568 0624 0679 0734 0790 0845 0901 0956 1012 1067 095 1122 1178 1233 1289 1344 1400 1455 1511 1566 1622 9 60 096 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 1 A = log « - log I), logd f B = log(a + ^). B = log a - log 5, log (54 -A = log( a-b). 1 L . . - . 1 ^0 V. ADDITION-SUBTRACTION LOGARITHMS. T 1 1 — \ A B 1 2 3 4 5 6 7 8 9 Differences. 1 b.ioo 0.35 3902 3958 4013 4069 4126 4181 4236 4292 4348 4404 101 4459 4515 4571 4627 4683 4738 4794 4860 4906 4962 102 5018 5073 5129 6185 6241 5297 6363 6409 5466 6520 103 5576 5632 5688 6744 6800 5856 5912 5968 6024 6080 104 6136 6192 6248 6304 6360 6416 6472 6528 6684 6640 65 105 6696 6752 6808 6864 6920 6976 7032 7088 7144 7200 1 2 8 6 11 17 106 7256 7312 7368 7424 7480 7636 7593 7649 7705 7761 107 7817 7873 7929 7985 8042 8098 8154 8210 8266 8322 4 22 108 8379 8435 8491 8547 8603 8660 8716 8772 8828 8884 6 6 7 28 83 89 109 8941 8997 9053 9109 9166 9222 9278 9336 9391 9447 0.110 0.35 9503 9560 9616 9672 9729 9785 9841 9898 9964 *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 66 6 m 3458 3515 3572 3628 3685 3742 3798 3856 3912 3969 2 11 118 4025 4082 4139 4196 4252 4309 4366 4423 4480 4536 8 4 6 17 22 28 119 4593 4650 4707 4764 4820 4877 4934 4991 6048 5105 0.120 0.36 5162 5218 5275 5332 5389 5446 6603 6560 5617 5674 6 7 84 89 121 5730 5787 5844 6901 5958 6016 6072 6129 6186 6243 8 45 122 6300 6357 6414 6471 6528 6685 6642 6699 6756 6813 9 50 123 6870 6927 6984 7041 7098 7156 7212 7269 7326 7384 124 7441 7498 7555 7612 7669 7726 7783 7840 7898 7965 125 8012 8069 8126 8183 8240 8298 8365 8412 8469 8526 120 8584 8641 8698 8755 8812 8870 8927 8984 9041 9099 127 9156 9213 9270 9328 9385 9442 9500 9557 9614 9671 B7 128 9729 9786 9843 9901 9958 *0015 *0073 *0130 *0187 *0246 1 6 129 0.37 0302 0360 0417 0474 0532 0589 0646 0704 0761 0819 3 8 11 17 0.130 0.37 0876 0934 0991 1048 1106 1163 1221 1278 1336 1393 4 5 6 28 29 84 131 1451 1508 1566 1623 1681 1738 1796 1853 1911 1968 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 61 134 3178 3235 3293 3361 3408 3466 3524 3681 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 6778 6836 5894 5952 6010 139 6067 6125 6183 6241 6299 6357 6416 6473 6531 6589 1 68 6 0.140 0.37 6647 6705 6763 6821 6879 6937 6995 7063 7111 7169 2 8 4 12 17 23 141 7227 7285 7343 7401 7459 7618 7576 7634 7692 7750 142 7808 7866 7924 7982 8040 8099 8167 8215 8273 8331 5 29 143 8389 8447 8506 8564 8622 8680 8738 8797 8865 8913 6 7 8 85 41 46 144 8971 9029 9088 9146 9204 9262 9321 9379 9437 9496 145 9554 9612 9670 9728 9787 9845 9903 9962 *0020 *0078 9 62 146 0.38 0137 0195 0253 0312 0370 0428 0487 0545 0603 0662 147 0720 0778 0837 0896 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 + 3). B=::loga-log d, log^^ -A = log( a-i). V. ADDITION-SUBTRACTION LOGARITHMB. 51 . ^_ 1 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 1 2 8 6 12 18 156 5997 6056 6115 6174 6233 6292 6351 6409 6468 65'27 151 6586 6645 6704 6763 6822 6881 6940 6999 7058 7117 4 24 158 7176 7235 7294 7353 7412 7471 7530 7589 7648 7707 6 30 159 7766 7825 7884 7943 8002 8062 8121 8180 8239 8298 6 7 85 41 0.160 0.38 8357 8416 8475 8534 8593 8653 8712 8771 8830 8889 8 9 47 58 161 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 6 167 2508 2568 2627 2687 2746 2806 2865 2925 2984 3044 2 12 168 3103 3163 3222 3282 3342 3401 3461 3520 3580 3640 8 4 5 18 24 80 169 3699 3759 3818 3878 3938 3997 4057 4117 4176 4236 o.no 0.39 4296 4355 4415 4475 4534 4594 4654 4713 4773 4833 6 7 86 42 m 4892 4952 5012 5072 5131 5191 5251 5311 5370 5430 8 48 ■ 172 5490 5550 5609 5669 5729 5789 5849 5908 5968 6028 9 54 173 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 8 12 18 0.180 0.40 0289 0350 0410 0470 0530 0591 0651 0711 0771 0832 4 5 6 24 81 87 181 0892 0952 1012 1073 1133 1193 1254 1314 1374 1435 182 1495 1555 1616 1676 1736 1797 185f 1917 1978 2038 7 48 183 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 12 19 25 191 6947 7007 7068 7129 7190 7251 7312 7372 7433 7494 4 192 7555 7616 7677 7738 7799 7859 7920 7981 8042 8103 6 31 193 8164 8225 8286 8347 8408 8469 8530 8591 8652 8713 7 8 87 48 60 194 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 = loga- log 6, log i + B = log (a + 6). B = log a - log 3, log 5 4-A = log( a-d). 52 V. ADDITION-SUBTRACTION LOGARITHMS. 1 — — 1 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 0608 0574 0640 0706 0771 67 66 402 0837 0903 0968 1034 1099 1165 1230 1296 1361 1427 1 2 7 18 20 7 13 403 1492 1557 1623 1688 1753 1819 1884 1949 2014 2080 3 20 404 2145 2210 2275 2340 2405 247,0 2535 2600 2666 2730 4 27 26 405 2795 2860 2925 2990 3054 3119 3184 3249 3313 3378 6 e 34 40 83 40 406 3443 3507 3572 3636 3701 3766 3830 3895 3959 4024 7 8 9 47 54 60' 46 53 69 407 4088 4152 4217 4281 4346 4410 4474 4538 4602 4667 408 4731 4795 4859 4923 4987 5051 5115 5179 5243 5307 409 5371 5435 5499 5563 5627 5690 6764 5818 5882 5945 65 64 0.410 9.78 6009 6073 61§6 6200 6264 6327 6391 6454 6518 6581 1 2 7 18 6 13 411 6645 6708 6772 6835 6898 6962 7025 7088 7151 7215 8 20 19 412 7278 7341 7404 7467 7531 7594 7657 7720 7783 7846 4 26 26 413 7909 7972 8035 8098 8160 8223 8286 8349 8412 8474 6 6 83 89 32 88 414 8537 8600 8663 8725 8788 8861 8913 8976 9038 9101 7 46 45 415 9163 9226 9288 9351 9413 9475 9638 9600 9662 9725 8 9 62 69 61 68 416 9787 9849 9912 9974 *0036 *0098 *0160 *0222 *0284 *0346 417 9.79 0409 0471 0533 0594 0656 0718 0780 0842 0904 0966 68 62 418 1028 1089 1151 1213 1275 1336 1398 1460 1521 1683 1 6 6 419 1644 1706 1768 1829 1891 1952 2013 2075 2136 2198 2 8 18 19 12 19 0.420 9.79 2259 2320 2382 2443 2504 2565 2627 2688 2749 2810 4 26 25 421 2871 2932 2993 3064 3116 3177 3238 3298 3359 3420 5 6 32 38 81 87 422 3481 3542 3603 3664 3725 3786 3846 3907 3968 4028 7 44 48 423 4089 4150 4210 4271 4331 4392 4453 4613 4574 4634 8 9 50 57 60 66 424 4694 4765 4815 4876 4936 4996 6057 6117 5177 5238 425 5298 5358 5418 5478 5538 5599 5659 5719 5779 6839 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 8 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 81 37 80 86 0.430 9.79 8281 8340 8399 8458 8517 8576 8636 8694 8753 8812 7 48 42 431 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 0396 0454 0512 0670 434 0628 0687 0745 0803 0861 0919 0978 1036 1094 1162 1 59 6 58 6 435 1210 1268 1326 1384 1442 1500 1558 1616 1674 1732 2 3 • 12 18 12 17 436 1789 1847 1905 1963 2021 2078 2136 2194 2251 2309 4 24 23 437 2367 2424 2482 2640 2597 2665 2712 2770 2827 2885 5 80 29 438 2942 2999 3057 3114 3171 3229 3286 3343 3401 3458 6 1 85 41 85 41 439 3515 3572 3630 3687 3744 3801 3858 3915 3972 4029 8 47 46 0.440 9.80 4086 4143 4200 4257 4314 4371 4428 4485 4542 4698 9 53 62 441 4655 4712 4769 4826 4882 4939 4996 5052 5109 5166 442 5222 5279 5335 5392 5448 5505 6561 5618 5674 5731 1 2 67 6 11 66 6 11 443 5787 5844 5900 5956 6013 6069 6126 6181 6238 6294 444 6350 6406 6462 6619 6576 6631 6687 6743 6799 6855 8 4 17 23 17 22 445 6911 5967 7023 7079 7135 7191 7246 7302 7358 7414 5 29 28 446 7470 7526 7581 7637 7693 7748 7804 7860 7915 7971 6 7 8 84 40 46 34 39 45 447 8027 8082 8138 8193 8249 8304 8360 8415 8471 8626 448 8582 8637 8692 8748 8803 8858 8914 8969 9024 9079 9 61 60 449 9134 9190 9245 9300 9355 9410 9465 9620 9575 9630 B = log a -log b. log « + 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 9.810234 0289 0344 0399 0453 0508 0563 0617 0672 0727 452 0781 0836 0890 0945 1000 1054 1109 1163 1218 1272 55 54 453 1326 1381 1435 1490 1544 1598 1652 1707 1761 1815 1 6 5 454 1870 1924 1978 2032 2086 2140 2194 2249 2303 2357 2 8 11 IT 11 16 455 2411 2465 2519 2573 2627 2681 2735 2788 2842 2896 4 22 22 456 2950 3004 3058 3111 3165 3219 3273 3326 3380 3434 5 6 7 28 83 89 27 82 88 461 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 5 11 62 5 10 463 6672 6725 6777 6830 6882 6934 6987 7039^ 7092 7144 464 7196 7249 7301 7353 7406 7458 7510 7562 7614 7667 8 4 16 21 16 21 465 7719 7771 7823 7875 7927 7979 8031 8083 8135 8187 5 2T 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 43 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 8 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 6 6 26 31 25 30 476 3347 3397 3447 3498 3548 3598 3648 3698 3748 3798 7 36 35 477 3848 3898 3948 3998 4048 4098 4148 4198 4248 4298 3 9 41 46 40 46 478 4347 4397 4447 4497 4547 4596 4646 4696 4746 4795 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 7308 7357 7405 7454 7503 7552 7600 7649 7698 7746 4 6 20 25 19 24 485 7795 7844 7892 7941 7990 8038 8087 8135 8184 8232 '6 29 29 486 8281 8329 8378 8426 8475 8523 8572 8620 8668 8717 T 3 84 39 84 38 487 8765 8813 8862 8910 8958 9007 9055 9103 9151 9199 9 44 48 488 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 2108 2156 2203 2250 2297 2344 2391 2438 2485 2532 5 24 28 495 2579 2626 2674 2721 2767 2814 2861 2908 2955 3002 6 7 28 33 28 82 496 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( a-V). 54 V. ADDITION-SUBTRACTION LOGARITHMS. B C 1 2 3 4 5 6 7 8 9 Differences. 0.50 9.83 4911 5373 5833 6292 6749 7205 7659 8111 8562 9011 400 450 440 480 51 9459 9906 *0351 *0795 *1237 *1677 *2116 *2554 *2990 *3425 1 2 40 92 46 90 41 48 33 86 52 9.84 3858 4290 4721 5150 5578 6004 6429 6852 7275 7695 3 183 186 182 129 53 8115 8533 8949 9365 9778 *0191 0602 *1012 *1421 *1828 4 134 180 176 172 54 9.85 2234 2639 3042 3444 3845 4244 4642 5039 5435 5829 B 280 276 226 270 220 216 264 258 55 6222 6614 7005 7394 7782 8169 8554 8939 9322 9704 T 3 822 868 818 860 80S 801 852 344 56 9.86 0085 0464 0842 1220 1595 1970 2344 2716 3087 3457 9 414 405 896 337 57 3826 4194 4560 4926 5290 5653 6015 6376 6736 7094 420 410 400 890 58 7452 7808 8163 8517 8870 9222 9573 9923 *0272 *0619 1 42 41 40 89 59 9.87 0966 1311 1655 1999 2341 2682 3022 3361 3699 4036 2 8 34 126 32 128 80 78 120 117 0.60 9.87 4372 4707 5041 5374 5706 6037 6367 6696 7023 7350 4 5 6 163 210 262 164 205 246 100 156 200 196 240 284 61 7676 8001 8325 8648 8969 9290 9610 9929 *0247 *0564 62 9.88 0880 1195 1510 1823 2135 2446 2757 3066 3375 3682 T 294 237 280 278 63 3989 4295 4600 4903 5206 5509 5810 6110 6409 6708 8 9 886 878 828 869 820 312 860 851 64 7006 7302 7598 7893 8187 8480 8773 9064 9355 9644 880 870 860 860 65 9933 *0221 *0608 *0795 *1080 *1365 *1649 *1932 *2214 *2495 1 2 8 88 76 114 87 74 lU 86 86 72 70 108 105 66 9.89 2775 3055 3334 3612 3889 4165 4441 4710 4990 5263 67 . 5535 5807 6077 6347 6617 6885 7153 7419 7685 7951 4 162 148 144 140 68 8215 8479 8742 9004 9265 9526 9786 *0045 *0304 *0561 5 6 7 190 223 266 136 222 269 180 176 216 210 262 246 69 9.90 0818 1074 1330 1585 1839 2092 2344 2596 2847 3097 0.70 9.90 3347 3596 3844 4092 4338 4584 483b 5074 5318 5562 3 9 804 842 296 888 283 280 824 815 71 5804 6046 6287 6528 6768 7007 7245 7483 7720 7956 840 830 820 810 72 8192 8427 8662 8895 9128 9361 9593 9824 *0054 *0284 1 84 83 82 31 73 9.910513 0742 0969 1197 1423 1649 1874 2099 2323 2546 2 8 4 68 102 186 60 99 182 64 62 90 98 128 124 74 2769 2991 3213 3434 3654 3874 4093 4311 4529 4746 75 4963 5179 5394 5609 5823 6037 6250 6462 6674 6885 5 170 204 165 198 160 166 192 186 76 7096 7306 7515 7724 7932 8140 8347 8554 8760 8965 7 288 231 224 217 77 9170 9374 9578 9781 9984 *0186 *0387 *0588 *0788 *0988 8 9 272 306 264 297 256 243 288 279 78 9.92 1188 1386 1584 1782 1979 2176 2372 2567 2762 2956 79 3150 3344 3536 3729 3920 4111 4302 4492 4682 4871 1 800 80 290 29 280 270 28 27 0.80 9.92 5060 5248 5435 5622 5809 5995 6180 6365 6550 6734 2 8 60 90 63 87 56 64 84 31 81 6918 7101 7283 7465 7647 7828 8008 8188 8368 8547 4 120 110 112 108 82 8725 8904 9081 9258 9435 9611 9787 9962 *0137 *0311 5 160 145' 140 186 83 9.93 0485 0658 0831 1004 1176 1347 1518 1689 1859 2028 6 7 180 210 174 208 168 162 196 189 84 2198 2366 2535 2703 2870 3037 3203 3369 3535 3700 8 240 232 224 216 85 3865 4029 4193 4356 4619 4682 4844 5006 5167 5328 9 270 260 26 261 260 25 262 248 240 280 24 28 86 5488 5648 5807 5966 6125 6283 6441 6599 6755 6912 1 87 7068 7224 7379 7534 7689 7843 7996 8150 8302 8455 2 62 60 48 46 88 8607 8759 8910 9061 9211 9361 9511 9660 9809 9957 8 4 78 104 75 100 72 69 96 92 89 9.94 0105 0253 0400 0547 0694 0840 0986 1131 1276 1421 5 180 126 120 115 0.90 9.94 1565 1709 1852 1995 2138 2280 2422 2564 2705 2846 6 T 156 182 160 175 144 138 168 161 91 2986 3126 3266 3405 3544 3683 3821 3959 4097 4234 8 208 200 192 184 92 4371 4507 4644 4779 4915 5050 5184 5319 5453 5586 9 284 225 210 207 93 5720 5853 5985 6118 6250 6381 6512 6643 6774 6904 220 210 200 190 94 7034 7163 7293 7421 7550 7678 7806 7934 8061 8188 1 2 22 44 21 42 20 19 40 33 95 8314 8440 8566 8692 8817 8942 9067 9191 9315 9439 8 4 66 88 68 S4 60 57 80 76 96 9562 9685 9807 9930 *0052 *0174 *0295 *0416 *0537 *0657 5 110 105 100 96 97 9.96 0778 0897 ion 1136 1255 1374 1492 1610 1728 1845 C 182 126 120 114 98 1962 2079 2196 2312 2428 2543 2659 2774 2888 3003 7 8 154 176 147 168 140 188 160 152 99 3117 3231 3344 3458 3571 3683 3796 3908 4020 4131 9 198 189 180 171 B = log a - log b. log « + C = log( a- -^)- ■■ 1 V. AUJJiTiON-SUBTIlACTION LOGAEITHMS. 55 , 1 B C 1 2 3 4 5 6 7 8 9 Differences. ) 1.00 9.95 4243 4353 4464 4575 4085 4795 4904 5013 5122 5231 180 170 160 150 01 02 5340 6409 5448 6514 5556 6620 5663 6724 5771 6829 5878 6933 5984 7038 6091 7141 6197 7245 6303 7348 1 3 8 18 86 54 17 34 51 ' 16 82 48 15 80 46 03 7451 7554 7657 7759 7861 7963 8064 8166 8267 8367 4 T2 68 64 60 04 8468 8568 8668 8768 8867 8966 9065 9164 9263 9361 5 G 90 108 85 102 80 96 75 90 05 9459 9556 9654 9751 9848 9945 *0041 *0138 *0234 *0329 T 8 9 126 144 162 119 186 153 112 128 144 105 ' 120 135 06 9.96 0425 0520 0615 0710 0805 0899 0993 1087 1181 1274 01 1367 1460 1553 1645 1737 ' 1829 1921 2013 2104 2195 140 180 120 110 08 2286 237G 2467 2557 2647 2737 2826 2915 3004 3093 1 14 18 12 11 09 3182 3270 3358 3446 3534 3621 3709 3796 3882 3969 2 3 28 42 26 89 24 86 22 88 1.10 9.96 4055 4142 4228 4313 4399 4484 4569 4654 4739 4823 4 G 66 70 84 52 65 78 48 60 72 44 65 66 11 4908 4992 5076 5159 5243 5326 5409 5492 5574 5657 12 5739 5821 5903 5984 6066 6147 6228 6308 6389 6469 7 98 91 34 77 13 6550 6629 6709 6789 6868 6947 7026 7105 7184 7262 8 9 112 126 104 117 96 108 88 99 14 7340 7418 7496 7574 7651 7728 7805 7882 7959 8035 100 90 86 80 75 15 8112 8188 8264 8339 8415 8490 8565 8640 8715 8790 1 2 8 10 20 30 9 9 18 17 27 26 8 16 24 8 15 28 16 8864 8938 9013 9086 9160 9234 9307 9380 9453 9526 I'Z 9598 9671 9743 9815 9887 9959 *0030 *0102 *0173 *0244 4 40 86 34 82 30 18 9.97 0315 0385 0456 0526 0596 0666 0736 0806 0875 0944 5 G T 50 60 70 45 43 54 61 63 60 40 48 56 38 46 58 19 1013 1082 1151 1220 1288 1356 1425 1492 1560 1628 1.20 9.97 1695 1762 1830 1897 1963 2030 2096 2163 2229 2295 3 9 80 90 72 63 81 77 64 72 60 63 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 6 23 3643 3705 3768 3830 3892 3954 4016 4077 4139 4200 2 3 4 14 22 29 14 14 21 20 23 27 13 20 26 13 19 20 24 4261 4322 4383 4444 4504 4565 4625 4685 4745 4805 25 4864 4924 4983 5042 5101 5160 5219 5278 5336 5395 5 G 7 86 48 50 85 34 42 41 49 48 88 40 46 83 88 45 26 5453 5511 5569 5627 5684 5742 5799 5857 5914 5971 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 68 61 63 59 61 53 29 7135 7189 7243 7297 7350 7404 7457 7510 7564 7617 1 62 6 60 58 6 6 66 6 54 5 1.30 9.97 7669 7722 7775 7827 7879 7932 7984 8036 8087 8139 2 8 12 19 12 12 18 17 11 17 11 16 31 8191 8242 8293 8345 8396 8447 8497 8548 8599 8649 4 25 24 28 22 22 32 8699 8750 8800 8850 8900 8949 8999 9048 9098 9147 5 31 30 29 23 27 33 9196 9245 9294 9343 9391 9440 9488 9537 9585 9633 6 7 87 43 36 85 42 41 34 39 32 88 34 35 9681 9.98 0154 9729 0201 9776 0247 9824 0294 9872 0340 9919 0387 9966 0433. *O013 0479 *0060 0525 *0107 0570 8 9 50 56 52 5 48 46 54 52 50 48 5 5 45 50 46 6 43 49 44 4 36 0616 0662 0707 0753 0798 0843 0888 0933 0978 1023 1 31 1067 1112 1156 1200 1245 1289 1333 1376 1420 1464 2 10 10 10 9 9 38 1507 1551 1594 1637 1681 1724 1767 1809 1852 1895 8 4 16 21 15 14 20 19 14 18 13 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 T 81 86 30 29 85 84 28 32 26 31 41 42 2767 3167 2807 3206 2847 3245 2888 3285 2928 3324 2968 3363 3008 3402 3048 3441 3087 3480 3127 3518 8 9 42 4T 40 33 43 43 37 41 85 40 43 3557 3596 3634 3672 3711 3749 3787 3825 3863 3901 1 2 42 4 8 40 38 4 4 8 3 86 4 7 34 3 7 44 3938 3976 4014 4051 4088 4126 4163 4200 4237 4274 45 4311 4347 4384 4421 4457 4493 4530 4566 4602 4638 8 4 18 17 12 11 16 15 11 14 10 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 G 7 8 25 29 34 24 28 28 27 82 SO 22 25 29 20 24 27 49 5714 5747 5781 5814 5847 5880 5913 5946 5979 6012 9 88 86 34 32 81 '-— 1 B = log a — log i>- log a + G = log( a- -d). .")(_) V. ADDITION-SUBTRACTION LOGARITHMS. ' " -1 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 6336 51 6367 6399 6431 6463 6494 6526 6657 6689 6620 6661 33 32 81 30 52 6682 6713 6745 6775 6806 6837 6868 6899 6929 6960 1 2 3 T 8 6 3 G 6 53 6990 7021 7051 7081 7111 7141 7171 7201 7231 7261 3 10 10 9 9 54 7291 7320 7350 7379 7409 7438 7468 7497 7526 7665 4 5 13 . IT 13 16 12 16 12 IS 55 7584 7613 7642 7671 7700 7728 7757 7785 7814 7842 6 20 19 19 18 56 7871 7899 7927 7965 7983 8012 8039 8067 8095 8123 7 s 28 26 22 26 22 25 21 24 57 8151 8178 8206 8233 8261 8288 8315 8343 8370 8397 9 SO 29 28 27 58 8424 8451 8478 8605 8532 8558 8685 8612 8638 8665 59 8691 8717 8744 8770 8796 8822 8848 8874 8900 8926 29 28 2T 26 1.60 9.98 8952 8977 9003 9029 9054 9080 9105 9131 9156 9181 1 2 3 6 8 6 3 B 3 5 61 9206 9231 9257 9282 9306' 9331 9356 9381 9406 9430 3 9 S 8 S 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 5 15 17 20 14 17 20 14 16 19 13 16 IS 64 9935 9959 9982 *0005 *0028 *0052 *0075 *0098 *0121 *0144 1 3 28 22 22 21 65 9.99 0167 0190 0213 0235 0258 0281 0303 0326 0348 0371 9 26 2S 24 ,28 66 0393 0416 0438 0460 0482 0504 0526 0548 0570 0692 67 0614 0636 0668 0680 0701 0723 0744 0766 0787 0809 25 8 24 2 83 2 22 2 68 0830 0851 0873 0894 0916 0936 0957 0978 0999 1020 1 ^ 1041 1062 1083 1103 1124 1145 1165 1186 1206 1227 2 8 5 8 6 7 6 7 4 7 1.70 9.99 1247 1267 1288 1308 1328 1348 1368 1388 1408 1428 4 10 10 9 9 71 1448 1468 1488 1508 1627 1547 1567 1586 1606 1625 5 6 7 18 IS 18 12 14 17 12 14 16 11 18 15 72 1645 1664 1684 1703 1722 1741 1761 1780 1799 1818 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 9 23 22 21 20 75 2208 2226 2244 2262 2280 2298 2315 2333 2351 2369 21 2 20 2 19 2 18 2 76 2386 2404 2422 2439 2457 2474 2492 2509 2527 2544 1 77 2561 2579 2596 2613 2630 2647 2664 2681 2698 2715 2 4 4 4 4 78 2732 2749 2766 2782 2799 2816 2833 2849 2866 2882 3 4 6 g 6 8 6 g 5 7 79 2899 2915 2932 2948 2964 2981 2997 3013 3029 3046 S 11 10 10 9 1.80 9.99 3062 3078 3094 3110 3126 3142 3158 3174 3189 3205 6 7 18 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 9 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 2 8 8 8 8 86 3963 3977 3991 4005 4019 4033 4047 4060 4074 4088 8 4 5 5 7 9 5 6 8 5 6 8 4 6 1 87 4102 4115 4129 4143 4156 4170 4183 4197 4210 4223 88 4237 4250 4263 4277 4290 4303 4316 4330 4343 4356 6 10 10 9 8 89 4369 4382 4395 4408 4421 4434 4447 4469 4472 4485 7 8 12 14 11 13 11 12 10 11 1.90 9.99 4498 4511 4523 4536 4549 4561 4674 4586 4599 4611 9 15 14 14 13 91 4624 4636 4649 4661 4673 4686 4698 4710 4723 4735 92 4747 4759 4771 4783 4795 4807 4819 4831 4843 4855 18 12 11 10 93 4867 4879 4891 4903 4915 4926 4938 4950 4962 4973 1 1 1 1 1 94 4985 4996 5008 6020 5031 6043 5054 5066 5077 5088 1 8 8 4 2 4 2 8 2 8 95 5100 5111 .3122 5134 5145 5156 5167 5178 5190 6201 4 5 6 7 6 6 4 6 4 6 96 5212 5223 5234 5245 6266 5267 5278 5289 6300 5310 8 7 7 6 97 5321 5332 5343 5354 5364 5375 6386 5397 6407 5418 7 9 8 8 7 98 5428 5439 5450 5460 5471 6481 5491 5602 6512 5523 8 9 10 12 10 11 9 -10 8 9 99 5533 5543 5554 5564 5574 5584 5696 5605 6615 5625 B = log a - log d. log « + C = log( a- -b). 1 Y . ADDITION-SUBTRACTION LOGARITHM^ 5T 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 6984 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 1 2 1 2 1 2 06 6201 6210 6218 6227 6236 6245 6253 6262 6271 6279 3 3 8 07 6288 6296 6305 6313 6322 6330 6339 6347 6356 6364 5 6 4 5 6 4 08 6373 6381 6389 6398 6406 6414 6423 6431 6439 6447 5 6 09 6455 6464 6472 6480 6488 6496 6504 6512 6520 6528 7 8 9 7 8 9 6 7 8 2.10 9.99 6537 6544 6552 6560 6568 6576 6584 6592 6600 6608 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 5 18 7121 7128 7134 7141 7148 7154 7161 7167 7174 7180 4 8 8 19 7187 7193 7200 7206 7213 7219 7226 7232 7238 7245 6 5 4 4 2.20 9.99 7251 7257 7264 7270 7276 7283 7289 7295 7301 7308 7 6 6 21 7314 7320 7326 7332 7339 7345 7351 7357 7363 7369 8 9 6 1 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 1 5 1 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 8 31 7868 7873 7878 7882 7887 7892 7897 7902 7907 7912 6 7 4 4 8 4 32 7916 7921 7926 7931 7935 7940 7945 7950 7954 7959 8 5 4 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 8 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 8 1 2 2 1 1 2 41 8307 8311 8315 8319 8323 8327 8330 8334 8338 8342 4 5 42 8346 8350 8353 8357 8361 8365 8368 8372 8376 8380 6 2 2 43 8383 8387 8391 8395 8398 8402 8406 8409 8413 8417 7 8 9 8 8 4 2 2 B 44 8420 8424 8428 8431 8435 8438 8442 8446 8449 8453 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 « — log b- log ffl + C = log ( a-b). 58 V. ADDITION-SUBTRACTION LOGARITHMS. B C 1 2 3 4 5 6 7 8 9 Differences. 2.50 9.99 8624 8628 8631 8634 8637 8640 8643 8646 8650 8653 51 8656 8659 8662 8665 S668 8671 8674 8677 8680 8683 52 8686 8689 8693 8696 8699 8702 8705 8708 8710 8713 16 15 14 18 53 8716 8719 8722 8725 8728 8731 8734 8737 8740 8743 1 2 2 1 1 54 55 8746 8774 8749 8777 8751 8730 8754 8783 8757 8786 8760 8788 8763 8791 8766 8794 8769 8797 8771 8799 2 S S 5 4 6 8 5 8 8 4 4 6 S 56 8802 8805 8808 8810 8813 8816 8819 8821 8824 8827 9 8 8 7 7 57 8830 8832 8835 ■8838 8840 8843 8846 8848 8851 8854 10 7 11 S 18 9 11 12 8 8 10 9 11 10 58 8856 8859 8861 886t 8867 8869 8872 8874 8877 8880 59 8882 8885 8887 8890 8893 8895 8898 8900 8903 8905 9 14 . 14 18 12 2.60 9.99 8908 8910 8913 8915 8918 8920 8923 8925 8928 8930 Gl 8933 8935 8938 8940 8942 8945 8947 8950 8952 8955 62 8957 8959 8962 8964 8967 8969 8971 8974 8976 8978 63 8981 8983 8985 8988 8990 8992 8995 8997 8999 9002 \ 12 1 2 11 1 2 10 1 2 64 9004 9006 9009 9011 9013 9015 9018 9020 9022 9024 2 65 9027 9029 9031 9033 9036 9038 9040 9042 9044 9047 8 4 6 4 6 6 8 4 c 8 4 5 66 9049 9051 9053 9055 9058 9060 9062 9064 9066 9068 67 9071 9073 9075 9077 9079 9081 9083 9085 9087 9090 6 7 7 6 68 9092 9094 9096 9098 9100 9102 9104 9106 9108 9110 7 8 8 7 69 9112 9114 9116 9118 9121 9123 9125 9127 9129 9131 8 9 10 11 9 10 8 9 2.70 9.99 9133 9135 9137 9139 9141 9143 9145 9146 9148 9150 71 9152 9154 9156 9158 9160 9162 9164 9166 9168 9170 72 9172 9174 9175 9177 9179 9181 9183 9185 9187 9189 73 9191 9192 9194 9196 9198 9200 9202 9204 9205 9207 9 8 7 74 9209 9211 9213 9214 9216 9218 9220 9222 9223 9225 1 2 1 2 1 2 1 1 75 9227 9229 9231 9232 9234 9236 9238 9239 9241 9243 8 a 2 2 76 9245 9246 9248 9250 9252 9253 9255 9257 9258 9260 4 4 8 8 77 9262 9264 9265 9267 9269 9270 9272 9274 9275 9277 5 6 7 6 6 6 4 6 6 4 4 6 78 9279 9280 9282 9284 9285 9287 9289 9290 9292 9293 79 9295 9297 9298 9300 9302 9303 9305 9306 9308 9310 8 7 6 6 2.8 9.99 9311 9327 9342 9357 9372 9386 9400 9414 9427 9440 9 8 7 6 9 9453 9465 9478 9489 9501 9512 9524 9534 9545 9555 3.0 9.99 9565 9575 9585 9595 9604 9613 9622 9630 9639 9647 1 9655 9663 9670 9678 9685 9692 9699 9706 9713 9720 ,6 5 4 2 9726 9732 9738 9744 9750 9756 9761 9767 9772 9777 1 2 8 1 1 2 1 1 2 1 1 3 9782 9787 9792 9797 9801 9806 9810 9815 9819 9823 4 9827 9831 9835 9839 9842 9846 9849 9853 9856 9859 4 2 2 2 5 9863 9866 9869 9872 9875 9878 9880 9883 9886 9888 5- a 4 8 8 2 2 6 9891 9893 9896 9898 9900 9903 9905 9907 9909 9911 7 4 4 8 7 9913 9915 9917 9919 9921 9923 9925 9926 9928 9930 8 6 4 8 8 9931 9933 9934 9936 9937 9939 9940 9941 9943 9944 9 5 5 4 9 9945 9947 9948 9949 9950 9951 9952 9953 9955 9956 4.0 9.99 9957 9958 9959 9959 9960 9961 9962 9963 9964 9965 1 9966 9966 9967 9968 9969 9969 9970 9971 9971 9972 8 2 I 2 9973 9973 9974 9974 9975 9976 9976 9977 9977 9978 1 3 9978 9979 9979 9980 9980 9981 9981 9981 9982 9982 2 8 4 1 1 1 4 9983 9983 9983 9984 9984 9985 9985 9985 9986 9986 5 9986 9987 9987 9987 9987 9988 9988 9988 9989 9989 6 2 1 6 9989 9989 9990 9990 9990 9990 9990 9991 9991 9991 6' 1 2 2 " 1 1 7 9991 9992 9992 9992 9992 9992 9992 9993 9993 9993 8 2 2 1 8 9993 9993 9993 9994 9994 9994 9994 9994 9994 9994 9 8 2 1 9 9995 9995 9995 9995 9995 9995 9995 9995 9995 9996 5. 9,99 9996 9997 9997 9998 9998 9999 9999 9999 9999 9999 B = log a - log b. -/ log a + C: = logC %-b). vx. si^JiJS ANIJ TANGENTS OF SMALL ANGL|:S. 59 1 1 10 + LOO (BIN A" : A) 10 + tOG ( TAK A" : A) ' Mm. Seo. 0° 1° 2° 3° 4° 0° 1° 2° 3° 40 0' 4.68 5575 5553 5487 5376 5222 4.68 5575 5619 5761 5972 6281 0" 1 / 5575 5552 5485 5374 5219 5575 5620 5754 6976 6287 60 2 5575 5551 5484 5372 5216 5575 5622 5757 5981 6293 120 3 5575 5551 5482 5370 5213 5575 5623 5760 6985 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 6776 6008 6329 480 9 5574 5546 5473 5356 5195^ 5576 5633 5779 6013 6335 540 10 4.68 5574 5545 5471 5364 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 6795 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 17 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 6661 5829 6085 6430 1440 25 5571 5531 5446 5317 5145 5583 5663 6833 6090 6436 1500 26 5571 5530 5444 5315 5141 5583 6665 5836 6095 6443 1560 27 5570 5529 5443 5312 5138 5584 5668 5840 6100 6449 1620 28 5570 5527 5441 5310 5135 5584 6670 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 6869 6142 6503 2100 36 5567 5518 5426 5289 5108 5591 5688 5873 6147 6509 2160 37 5566 5517 5424 5286 5105 5592 5690 5877 6162 6516 2220 38 ■ 5566 5516 5422 5284 5101 5593 5693 5881 6168 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 6644 2460 42 5564 5511 5414 5273 5088 5596 5702 5897 6179 6651 2620 43 5564 5510 5412 5270 5084 5597 5706 6900 6185 6557 2580 44 5563 5509 5410 5268 5081 5599 5707 6905 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 6262 6643 3300 56 5556 5492 5385 5234 5038 5613 6740 5965 6258 6650 3360 57 5555 5491 5383 5231 5034 5615 6743 6959 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 Mill. 0" 3600" 7200" 10800" 14400" 0" 3600" 7 200" 10800' 14400" Sec. 60 VII. TRIGONOMETRIC FUNCTIONS. 0° Sines, Cosines. Tamoekts. Cotangents. 179° Nat. Log. Dif. Nat. Log. DIf. Nnt. Ldff. DIf. Log. Nat. 0' .00 000 00 X 1.0000 0.00 0000 .00 .00 000 X CO 00 00 60' 1 029 G.4G3726 5017. 000 0000 029 6.46 3726 6017. 3.63 6274 8487.7 59 2 088 6.76 4756 2985. 000 0000 058 G.76 4756 2935. 3.23 5244 1718.9 58 3 0S7 C.!)4 0847 2082. 000 0000 087 6.94 0847 2082. 3.05 9153 1146.9 57 4 116 7.06 5786 1615. 000 0000 116 7.06 5786 1615. 2.93 4214 889.44 66 5 145 7.16 2696 1320. 000 0000 .02 145 7.16 2696 1820. 2.83 7304 637.85 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 853. 000 9999 233 7.36 6817 858. 2.63 3183 429.72 52 9 2G2 7.41 7968 768. 000 9999 .02 262 7.41 7970 763. 2.58 2030 881.97 51 10 .00 291 7.46 37 26 690. 1.0000 9.99 9998 .00 .00 291 7.46 3727 690. 2.53 0273 848.77 50 11 820 7.50 5118 680. .99 999 9998 .02 320 7.50 5120 680. 2.49 4880 812.52 49 12 849 7.54 2906 579. 999 9997 .00 349 7.54 2909 5T9. 2.45 7091 286.48 48 13 878 7.57 7668 586. 999 9997 .02 378 7.57 7672 686. 2.42 2328 264.44 47 14 407 7.60 9853 499. 999 9996 .00 407 7.60 9857 499. 2.39 0143 246.65 46 15 436 7.63 9816 467. 999 9996 .02 486 7.03 9820 467. 2.36 0180 229.18 45 16 465 7.66 7845 489. 999 9995 .00 465 7.66 7849 489. 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 891. 999 9994 524 7.71 9003 891. 2.28 0997 190.98 42 19 653 7.74 2478 871. 993 9993 .00 553 7.74 2484 371. 2.25 7516 180.98 41 20 .00 532 7.76 4754 858. .99 993 9.99 9993 .02 .00 582 7.76 4761' 858. 2.23 5239 171.89 40 21 611 7.78 5943 837. 993 9992 611 7.78 5951 337. 2.214049 168.70 39 22 640 7.80 6146 322. 993 D99L 640 7.80 6155 322. 2.19 3845 156.26 38 23 669 7.82 5451 803. 993 9990 669 7.82 5460 808. 2.17 4540 149.47 37 24 693 7.84 3934 295. 998 9989 .00 698 7.84-3944 296. 2.15 6056 143.24' 36 25 727 7.,86 1662 284. 997 9989 .02 727 7.86 1674 284. 2.13 8326 187.51 35 26 786 7.87 8695 278. 997 9988 756 7.87 8708 278. 2.12 1292 182.22 34 27 735 7.89 5085 268. 997 9987 785 7.89 5099 268. 2.10 4901 127.32 33 28 814 7.91 0879 254. 997 9986 816 7.91 0894 254. 2.08 9106 122.77 32 29 844 7.92 6119 248. 996 9985 .08 844 7.92 6134 245. 2.07 3866 118.54 31 30 .00 878 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 280. 2.04 4900 110.89 29 32 981 7.96 8870 223. 996 9981 931 7.96 8889 223. 2.03 nil 107.48 28 33 960 7.98-2233 216. 995 9980 960 7.98 2253 216. 2.01 7747 104.17 27 34 989 7.99 5198 210. 995 9979 .08 989 7.99 5219 210. 2.00 4781 101.11 26 35 .01 013 8.00 7787 204. 995 9977 .02 .01 018 8.00 7809 204. 1.99 2191 93.218 25 ' 36 (147 8.02 0021 198. 995 9976 047 8.02 0044 198. 1.97 9956 98.439 24 37 076 8.03 1919 198. 994 9975 .03 076 8.03 1945 193. 1.96 8055 92.908 23 38 108 8.04 3501 188. 994 9973 .02 106 8.04 3527 183. 1.95 6473 90.463 22 39 184 8.05 4781 183. 994 9972 135 8.05 4809 188. 1.945191 88.144 21 40 .01164 8.06 5776 179. .99 993 9.99 9971 .03 .01164 8.06 5806 179. 1.93 4194 85.940 20 41 193 8.07 6500 174. 993 9969 .02 198 8.07 6531 174. 1.92 3469 38.844 19 42 222 8.08 6965 170. 993 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 168. 992 9964 .02 280 8.10 7203 163. 1.89 2797 78.126 16 45 809 8.11 6926 159. 991 9963 .08 309 8.11 6963 169. 1.88 3037 70.890 15 46 888 8.12 6471 156. 991 • 9961 388 8.12 6510 156. 1.87 3490 74.729 14 f 47 867 8.13 5810 152. 991 9959 .02 367 8.13 5851 152. 1.86 4149- 78.189 13 48 396 8.14 4953 149. 990 9958 .03 396 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 0048 70.158 11 50 01454 8.16 2681 143. .99 989 9.99 9954 .08 .01 458 8.16 2727 143. 1.83 7273 68.750 10 51 463 8.17 1280 141. 939 9952 484 8.17 1328 141. 1.82 8672 67,402 9 52 613 9713 138. ■ 939 9950 813 9763 I3S.' 0237 m.105 8 53 642 8.18 7985 135. 988 9948 842 8.18 8036 185. 1.81 1964 64.358 7 54 671 8.19 6102 133. 983 9946 671 8.19 6156 183. 1.80 3844 68.687 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 123. 1.78 8047 61.383 4 57 658 9581 12o. 986 9940 688 9641 126. 0359 60.306 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 68.261 1 60 01746 8.24 1855 .99 985 9.99 9934 .01 746 8.24 1921 1.75 8079 67.290 90° Nat Log. DIf. Nat. Log. DIf. Nat. Log. CoTABororis. Dif. Log. Nat. Tanoehis. 89° COSIKKS. Sines. VII. TRIGONOMETRIC FUNCTIONS. 61 1° SiHES. 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 118. 0898 56.361 59 2 ■ 808 8.25 6094 116. 984 9929 .03 804 8.25 6165 116. 1.74 3835 65442 58 3 882 8.26 3042 114. 988 9927 833 8.26 3115 114. 1.73 6885 54.561 57 4. 862 9881 112. 988 9925 .05 862 9956 112. 0044 58.709 56 5 891 8.27 6614 110, 982 9922 .08 891 8.27 6691 111. 1.72 3309 52,882 56 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 51.308 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 0.36 8.30 8794 103. .99 979 9.99 9910 .05 .02 036 8.30 8884 108. 1.69 1116 49.104 50 11 065 8.31 4954 101. 979 9907 .08 066 8.31 5046 101. 1.68 4964 48.412 49 12 094 8.32 1027 99.8 978 9905 .06 095 8.32 1122 99.9 1.67 8878 47.740 48 13 123 7016 98.5 977 9902 124 7114 98.5 2886 .035 47 14 152 8.33 2924 97.2 977^ 9899 .08 163 8.33 3025 97.2 1.06 6975 46.449 46 15 181 8753 959 976 989'r .06 182 8866 959 1144 45.829 45 16 211 8.34 4504 94.6 976 9894 211 8.34 4610 94.7 1.65 5390 .226 44 11 240 8.35 0181 9S.4 975 9891 240 8.35 0289 98.4 1.64 9711 44.689 43 18 269 5783 92.2 974 9888 269 5895 92.3 4105 .066 42 19 298 8.30 1315 91.0 9T4 9885 298 8.36 1430 91.1 1.63 8570 43,508 41 20 .02 827 8.36 6777 89.9 .99 973 9.99 9882 .05 .02 828 8.36 6895 90.0 1.63 3105 42,964 40 21 866 8.37 2171 88.8 972 9879 367 8.37 2292 88.8 1.62 7708 .433 39 22 385 7499 87.7 972 9876 836 7622 87.8 2378 41.916 38 23 414 8.38 2762 86.7 971 9873 415 8.38 2889 86.7 1.01 7111 .411 37 24 443 7962 85.7 970 9870 444 8092 857 1908 40.917 36 25 472 8.39 3101 84.6 969 9867 473 8.39 3234 84.7 1.60 6766 .486 35 . 26 501 8179 88.7 969 9864 502 8315 88.7 1685 89.965 34 27 530 8.40 3199 82.7 968 9861 531 8.40 3338 82.8 1.59 6662 .606 33 28 560 8161 81.8 967 9858 .07 560 8304 81.8 1696 .067 32 29 689 8.41 3068 80.9 966 9864 .06 589 8.41 3213 80.9 1.58 6787 83.618 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 38.188 30 31 647 8.42 2717 79.1 965 9848 .07 648 8.42 2869 79.2 1.57 7131 87.769 29 32 676 7462 78.2 964 9844 .06 677 7618 78.3 2382 .358 28 33 705 8.43 2156 77.4 963 9841 706 8.43 2315 77.5 1.56 7685 86.956 27 34 734 6800 76.0 968 9838 .07 785 6962 76.6 3038 .563 26 35 763 8.44 1394 758 962 9834 .05 764 8.44 1560 758 1.55 8440 .178 25 36 792 5941 75.0 961 9831 .07 793 6110 751 3890 85801 24 37 821 8.45 0440 74.2 960 9827 .06 822 8.45 0613 74.3 1.54 9387 .431 23 38 860 4893 78.5 969 9824 .07 851 5070 73.6 4930 .070 22 39 879 9301 72.7 959 9820 881 9481 72.3 0519 34.715 21 40 .02 908 8.46 3665 72.0 .99 968 9.99 9816 .05 .02 910 8.46 3849 72.1 1.53 6151 84.868 20 41 938 7985 71.8 957 9813 .07 989 8172 71.4 , 1828 .027 19 42 967 8.47 2263 70.6 966 9809 963 8.47 2454 70.7 1.52 7646 88.694 18 43 996 6498 69.9 955 9805 997 6693 70.0 3307 .866 17 44 .03 025 8.48 0693 69.8 954 -9801 .03 026 8.48 0892 69.8 1.519108 .046 16 > 45 .08 054 4848 68.6 953 9797 .05 056 5050 03.7 4950 82.730 15 46 083 8963 63.0 952 9794 .07 034 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 148 7293 66.8 2707 81.821 12 49 170 8.50 1080 66.1 960 9782 172 8.50 1298 66.2 1.49 8702 .528 11 50 .03199 8.50 5045 65.5 .99 949 9.99 9778 .07 .03 201 8.50 5267 656 1.49 4733 81.242 10 51 228 8974 64.9 943 9774 .08 280 9200 65.0 0800 30,960 9 52 257 8.51 2867 64.8 947 9769 .07 259 8.513098 64.4 1.48 6902 .688 8 53 286 6726 63.8 940 9765 288 6961 63.8 3039 .412 7 54 816 8.52 0551 68.2 945 9761 817 8.52 0790 68.8 1.47 9210 .145 6 55 845 4343 62.7 944 9757 846 4586 62.7 5414 29.382 5 56 874 8102 62.1 943 9753 .08 876 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 .371 3 58^ 432 5523 61.1 941 9744 434 5779 61.1 4221 .122 2 59 461 9186 60.6 940 9740 .03 468 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 28.636 91° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. Tangents. 88° COSINKS. Sines. Cotangents. 1 62 YJI. TEIGONOMETRIC FUNCTIONS. 2° StHSS. Cosines. TANoionra. Cotangents. 177° Nat Log. Dif. Nat. Log. Dif. Nat._ Log. Dif. Log. Nat. 0' .03 490 8.54 2819 60.1 .99 989 9.99 9735 .07 .03 402 8.54 3084 60.1 1.45 0916 28.686 60' 1 519 6422 59.6 983 9731 .08 521 6691 59.6 3309 .899 59 2 5*3 9995 69.1 937 9726 .0- 550 8.55 0268 69.2 1.44 9732 .166 58 3 677 8.55 3539 58.0 986 9722 .08 579 3817 68.7 6183 27.987 57 4 606 7054 58.1 985 9717 .07 609 7336 68.2 2664 .712 .56 5 635 8.56 0540 57.7 ' 984 9713 .03 688 8.56 0828 67.7 1.43 9172 .490 55 6 664 3999 67.2 988 9708 .07 667 4291 57.8 5709 .271 54 7 693 7431 66.8 982 9704 .08 696 7727 56.8 2273 .057 53 8 728 8.57 0836 56.8 981 9699 725 8.57 1137 66.4 1.42 8863 26.845 52 9 752 4214 65.9 980 9694 754 4520 66.0 5480 .687 51 10 .03 781 8.57 7566 55.4 .99 929 9.99 9689 .OT .03 788 8.67 7877 65.5 1.42 2123 26.482 50 11 810 8.58 0892 55.0 927 9685 .08 812 8.58 1208 66.1 1.41 8792 .280 49 12 889 4193 54.6 926 9680 842 4514 64.7 5486 .081 48 13 868 7469 54.2 925 9675 871 7795 54.3 2205 25.885 47 14 897 8.59 0721 58.8 924 9670 900 8.59 1051 58.9 1.40 8949 .642 46 15 926 3948 68.4 923 9665 929 4283 58.5 5717 .462 46 16 955 7152 58.0 922 9660 958 7492 63.1 2508 .264 44 17 9St 8.60 0332 52.6 921 9655 987 8.60 0677 62.7 1.39 9323 .080 43 18 .04 018 3489 62.2 919 9650 .04 016 3839 52.8 6161 24.898 42 19 W2 6623 61.9 918 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 61.6 1.38 9906 24.542 40 21 100 8.61 2823 51.1 916 9635 .10 104 3189 61.2 6811 .868 39 22 129 5891 60.8 915 9629 .08 133 6262 60.9 3738 .196 38 23 159 8937 50.4 918 9624 162 9313 60.5 0687 .026 37 24 ISS 8.62 1962 50.1 912 9619 * 191 8.62 2343 50.2 1.37 7657 28.859 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 49.6 1660 .532 34 27 275 8.63 0911 49.1 909 9603 .10 279 8.63 1308 49.1 1.36 8692 .872 33 28 804 3854 48.7 907 9597 .08 808 4256 48.8 5744 .214 32 29 888 6776 48.4 906 9592 .10 887 7184 48.6 2816 .053 31 30 .04 862 8.63 9680 48.1 .99 90S 9.99 9586 .08 .04 866 8.64 0093 48.2 1.35 9907 22.904 30 31 891 8.64 2563 47.8 904 9581 .10 895 2982 47.9 7018 .762 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 483 8.65 1537 46.9 1.34 8463 .808 26 35 S07 3911 46.6 898 9558 .08 512 4352 46.6 5648 .164 25 36 586 6702 46.2 897 9553 .10 641 7149 46.8 2851 .022 24 37 565 9475 45.9 896 9547 670 9928 46.0 0072 21.881 23 38 594 8.66 2230 45.6 894 9541 699 8.66 2689 45.7 1.33 7311 .748 22 39 628 4968 45.4 898 9535 628 5433 45.5 4567 .606 21 40 .04 668 8.66 7689 45.1 .99 892 9.99 9529 .08 .04 668 8.66 8160 46.2 1.33 1840 21.470 20 41 682 8.67 0393 44.8 890 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 .206 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 .12 808 8.68 1544 48.8 1.31 8456 .819 15 46 627 3665 43.5 883 9493 .10 838 4172 48.5 5828 .693 14 47 856 6272 43.2 882 9487 862 6784 43.8 3216 .569 13 48 885 8863 42.9 881 9481 891 9381 43.0 0619 .446 12 49 914 8.69 1438 42.7 879 9475 920 8.69 1963 42.8 1.30 8037 .825 11 50 .04 943 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 41.8 1.29 7861 .856 7 ' 54 059 4090 41.6 872 9443 .10 066 4646 41.6 5354 .740 6 55 088 6577 41.2 870 9437 095 7140 41.3 2860 .627 6 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 2 59 205 6383 40.8 864 9411 212 6972 40.4 3028 .188 1 60 .05 284 8.71 8800 .99 863 9.99 9404 .05 241 8.71 9396 1.28 0604 19.081 92° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Cotangents. Log. Nat. 87° CosrsES. Snres. Tangents. TJI. TRIGONOMETRIC FUNCTIONS. 63 3° BiNXS. Cosines. Tangents. Dif. Cotangents. 176° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .05 234 8.71 8800 48.1 .99 863 9.99 9404 .10 .06 241 8.719396 40.2 1.28 0604 19.081 60' 1 268 8.72 1204 39.9 861 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 89.4 868 9384 .10 828 6588, 39.5 3412 .768 57 4 850 8337 89.2 857 9378 .12 367 8959 39.3 1041 .666 56 5 879 8.73 0688 89.0 855 9371 887 8.73 1317 39.1 1.26 8683 .664 55 6 408 3027 88.8 854 9364 416 3663 88.9 6337 .464 54 7 487 5354 38.6 852 9357 445 5996 88.7 4004 .366 53 8 466 7667 38.4 851 9350 474 8317 88.5 1683 .268 52 9 495 9969 88.2 849 9343 603 8.74 0626 88.8 1.25 9374 .171 51 10 .05 524 8.74 2259 38.0 .99 847 9.99 9336 .12 .05 588 8.74 2922 88.1 1.25 7078 18.075 50 11 553 4536 87.8 846 9329 562 5207 37.9 4793 17.980 49 12 682 6802 87.6 844 9322 591 7479 37.7 2521 .886 48 13 611 9055 37.4 842 ^315 620 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 37.0 889 9301 678 4227 37.1 5773 .611 45 16 698 5747 36.8 888 9294 708 6453 86.9 3547 .521 44 17 727 7955 86.6 886 9287 .18 787 8668 86.7 1332 .431 43 18 756 8.76 0151 86.4 834 9279 .12 766 8.76 0872 86.6 1.23 91^8. .848 42 19 785 2337 86.2 883 9272 795 "S'065 36.4 " 6933 .256 41 20 .05 814 8.76 4511 86.1 .99 831 9.99 9265 .18 .05 824 8.76 5246 36.2 1.23 4754 17.169 40 21 844 6675 35.9 829 9257 .12 864 7417 36.0 2583 .084 39 22 878 8828 35.7 827 9250 .13 888 9578 36.8 0422 16.999 38 23 902 8.77 0970 35.5 826 9242 .12 912 8.77 1727 36.7 1.22 8273 .915 37 24 981 3101 85.4 824 9235 -.18 941 3866 85.5 6134 .832 36 25 960 5223 35.2 822 9227 .12 970 5995 85.3 4005 .760 35 26 989 7333 85.0 821 9220 .13 .06 999 8114 35.1 1886 .'668 34 27 .06 018 9434 34.8 819 9212 .12 .06 029 8.78 0222 35.0 1.219778 .587 33 28 047 8.78 1524 34.7 817 9205 .13 058 2320 84,8 7680 .607 32 29 076 3605 84.5 815 9197 087 4408 84.0 5592 .428 31 30 .06105 8.78 5675 84.4 .99 818 9.99 9189 .13 .06 116 8.78 6486 84.5 1.21 3514 16.350 30 31 134 7736 84.2 812 9181 .12 145 8554 34.3 1446 .272 29 32 168 9787 34.0 810 9174 .18 175 8.79 5613 34.2 1.20 9387 .195 28 33 192 8.79 1828 33.9 808 9166 204 2662 84.0 7338 .119 27 34 221 3859 38.7 806 9158 238 4701 88.8 5299 .043 26 35 250 5881 88.6 804 9150 262 6731 83.7 3269 16.969 25 36 279 7894 88.4 808 9142 391 8752 33.5 1248 .895 ■24 37 808 9897 33.8 801 9134 821 8.80 0763 83.4 1.19 9237 .821 23 38 837 8.80 1892 88.1 799 9126 850 2765 33.2 7235 .748 22 39 866 3876 82.9 797 9118 379 4758 33.1 5242 .676 21 40 .06 895 8.80 5852 32.8 .99 795 9.99 9110 .13 .06 408 8.80 6742 32.9 1.19 3258 15.606 20 41 424 7819 32.6 793 9102 438 8717 32.8 1283 .534 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 .394 17 . 44 611 3667 82.2 788 9077 .18 525 4589 32.3 5411 .325 16 45 540 5599 32.1 786 9069 664 6529 32.2 3471 .257 15 46 569 7522 81.9 784 9061 684 8461 82.1 1539 .189 14 47 598 9436 81.8 782 9053 .15 618 8.82 0384 31.9 1.17 9616 .122 13 48 627 8.82 1343 81.6 780 9044 .18 642 2298 81.S 77Q2 .066 12 49 656 3240 81.5 778 9036 .15 671 4205 81.6 5795 14.990 11 50 .06 685 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 31.2 774 9019 .16 730 7992 81.4 2008 .860 9 52 748 8884 81.1 772 9010 .18 759 9874 31.2 0126 .796 8 53 778 8.83 0749 81.0 770 9002' .15 788 8.83 1748 81.1 1.16 8252 .732 7 54 802 2607 80.8 768 8993 817 3613 31.0 6387 .669 6 55 881 4456 80.7 766 8984 .13 847 5471 80.8 4529 .606 5 56 860 6297 80.6 764 8976 .15 876 7321 30.7 2679 .544 4 57 889 8180 80.4 762 8967 905 9163 80.6 0837 .482 3 58 918 9956 30.8 760 8958 .18 934 8.84 0998 30.5 1.15 9002 .421 2 S9 947 8.84 1774 80.2 ^58 8950 .15 968 2825 30.3 7175 .861 1 60 .06 976 8.84 3585 .99 756 9.99 8941 .06 993 8.84 4644 1.15 5356 14.301 93° Nat. , Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 86° Cosines. Sines. Tangents. 64 Vn. TRIGONOMETRIC FUNCTIONS. 4° SlKES. Cosines. Tangents. Cotangents. Dif. Log. Nat. 175° Nat Log. Dif. Nat. Log. Dlf. Nat. Log. 0' .06 976 8.84 3585 80.0 .99 756 9.99 8941 .15 .06 993 8.84 4644 80.2 1.15 5356 14.801 60' 1 .07 005 5387 29.9 754 8932 .07 022 6455 80.1 3545 .241 59 2 084 7183 29.8 762 8923 051 8260 80.0 1740 .182 58 3 063 8971 29.7 760 8914 080 8.85 0057 29.8 1.14 9943 .124 57 4 092 8.85 0751 29.6 748 8905 110 1846 29.7 8154 .066 56 5 121 2525 29.4 746 8896 139 3628 29.6 • 6372 .008 55 6 150 4291 29.8 744 8887 168 5403 29.6 4597 18.951 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 9 237 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 28.7 784 8841 .16 814 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 T29 8823 .17 378 7632 28.7 2368 .568 47 14 882 8165 28.4 72T 8813 .16 402 9351 28.6 ' 0649 .510 46 15 411 9868 28.8 726 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 7 230 .404 44 17 469 3255 28.1 721 8785 .15 490 4469 28.2 5531 .862 43 18 498 4938 28.11 719 8776 .17 519 6162 28.1 3838 .800 42 19 527 6615 27.8 716 8766 .15 548 7849 28.0 2151 .243 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 .16 607 8.88 1202 27.8 1.11 8798 .146 39 22 614 8.88 1607 27.6 710 8738 .17 036 2869 27.7 7131 .096 38 23 643 3258 27.4 708 8728 665 4530 27.6 5470 .046 37 24 672 4903 27.8 705 8718 695 6185 27.5 3815 12.996 36 25 701 6542 27.2 708 8708 .15 724 7833 27.4 2167. .947 35 26 780 8174 27.1 701 8699 .17 7.'» 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 26.8 094 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 33 983 9432 26.4 685 8629 958 8.90 0803 26.6 1.09 9197 .666 27 34 962 8.90 1017 26.3 683 8619 987 2398 26.6 7602 .520 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 24 37 049 5736 26.0 676 8589 .18 075 7147 26.2 2853 .884 23 38 078 7297 26.9 678 8578 .17 104 8719 26.1 1281 .839 22 39 107 8853 671 8568 184 8.910285 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 25.0 664 8537 .17 221 4951 25.7 5049 .168 18 43 223 5022 25.6 661 8527 .18 251 6495 3505 .120 17 44 252 6550 25.4 669 8516 .17 280 8034 25.6 1966 .077 16 45 281 8073 25.8 65T 8506 .18 809 9568 26.6 0432 .085 15 46 810 9591 26.2 664 8495 .17 389 8.92 1096 25.4 1.07 8904 11.992 14 47 839 8.92 1103 26.1 662 8485 .18 368 2619 26.8 7381 .950 13 48 . 868 2610 26.0 649 8474 .17 397 4136 25.2 5864 .909 12 49 897 4112 647 8464 .18 427- 5649 26.1 4351 .867 U 50 .08 426 8.92 5609 24.9 .99 644 9.99 8453 .18 .08 466 8.92 7156 25.0 1.07 2844 11.826 10 51 455 7100 24.8 642 8442 486 8658 1342 .786 9 52 484 8587 24.7 639 8431 .17 614 8.93 0155 24.9 1.06 9845 .745 8 53 513 8.93 0068 24.6 687 8421 .18 544 1647 24.8 8353 .705 7 54 542 1544 24.6 686 8410 578 3134 24.7 6866 .664 6 55 571 3015 24.4 632 8399 602 4616 24.6 5394 .626 5 56 600 4481 680 8388 682 6093 24.6 3907 .665 4 57 629 5942 24.8 627 8377 661 7565 2435 .546 3 58 658 7398 24.2 626 8366 690 9032 24.4 0968 .507 2 59 687 8850 24.1 622 8355 720 8.94 0#l 24.8 1.05 9506 .468 1 60 .08 T16 8.94 0296 .99 619 9.99 8344 .08 749 8.94 1952 1.05 8048 11.430 94° Xat. Log. Dlf. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 85° Cosines. Sl.NES. Cotangents. Tangents. VII. TRIGONOMETRIC FUNCTIONS. 65 5° SiNEB. Cosines. Tangents. Cotangekts. 174° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .08 Tie 8.94 0296 24.0 .99 619 9.99 8344 .18 .08 749 8.94 1952 24.2 1.05 8048 11.430 60' 1 745 1738 28.9 617 8333 773 3404 24.1 6596 .392 59 2 774 3174 614 8322 807 4852 5148 .854 58 3 808 4606 28.8 612 8311 837 6295 24.0 3705 .316 57 4 881 6034 28.T 609 8300 866 7734 23.9 2266 .279 56 5 860 7456 23.6 607 8289 .20 895 9168 28.8 0832 .242 55 6 889 8874 604 8277 .18 925 8.95 0597 28.7 1.04 9403 .205 54 1 918 8.95 0287 28.5 602 8266 954 2021 7979 .168 63 S 947 1696 28.4 699 8255 .20 983 3441 23.6 6559 .132 52 . 9 976 3100 23.3 696 8243 .18 .09 013 4856 23.5 5144 .095 51 10 .09 006 8.95 4499 28.8 .99 694 9.99 8232 .20 .09 042 8.95 6267 23.5 1.04 3733 11.059 50 11 084 5894 28.2 691 8220 .18 071 7674 28.4 2326 .024 49 12 068 7284 28.1 688 8209 .20 101 9075 28.8 0925 10.988 48 13 092 8670 23.0 686 8197 .18 180 8.96 0473 28.2 1.03 9527 .953 47 14 121 8.96 0052 583 8186 .20 159 1866 8134 .918 46 15 150 ' 1429 22.9 680 8174 .18 189 3255 23.1 6745 .883 45 16 179 2801 22.8 578 8163 .20 218 4639 28.0 5361 .848 44 It 208 4170 22.7 575 8151 247 6019 22,9 3981 .814 43 18 287 5534 672 8139 .18 277 7394 2606 .780 42 19 266 6893 22.6 570 8128 .20 806 8766 22.8 1234 .746 41 20 .09 295 8.96 8249 22.6 .99 567 9.99 8116 .20 .09 385 8.97 0133 22.7 1.02 9867 10.712 40 21 824 9600 564 8104 365 1496 8504 .678 39 22 858 8.97 0947 22.4 562 8092 894 2855 22.6 7145 .645 38 23 882 2289 22.3 569 8080 428 4209 22.5 5791 .612' 37 24 411 3628 22.2 556 8068 458 5560 22.4 4440 .679 36 25 440 4962 588 8056 482 6906 3094 .546 35 ' 26 469 6293 22.1 551 8044 511 8248 22.3 1752 • .514 34 27 498 7619 22.0 548 8032 541 9586. 0414 .481 33 28 627 8941 545 8020 570 8.98 0921 22.2 1.019079 .449 32 29 556 8.98 0259 21.9 542 8008 600 2251 22.1 7749 .417 31 30 .09 585 8.98 1573 21.8 .99 540 9.99 7996 .20 .09 629 8.98 3577 22.0 1.01 6423 10.885 30 31 614 2883 537 7984 658 4899 5101 .854 29 32 642 4189 21.7 534 7972 .22 688 6217 21.9 3783 .322 28 33 671 5491 21.6 681 7959 .20 717 7532 21.8 2468 .291- 27 34 700 6789 628 7947 , 746 8842 1158 .260 2B 35 729 8083 21.6 526 7935 .22 776 8.99 0149 21.7 1.00 9851 .229 25 36 768 9374 21.4 523 7922 .20 805 1451 8549 .199 24 37 787 8.99 0660 620 7910 .22 884 2750 21.6 7250 .168 23 38 816 1943 21.8 617 7897 .20 864 4045 21.5 5955 .138 22 39 845 3222 514 7885 .22 893 5337 4663 .108 21 40 .09 874 8.99 4497 21.2 .99 511 9.99 7872 .20 .09 923 8.99 6624 21.4 1.00 3376 10.078 20 41 90S 5768 21.1 508 7860 .22 962 7908 21.8 2092 .048 19 42 982 7036 606 7847 .20 981 9188 0812 .019 18 43 961 8299 21.0 508 7835 .22 .10 Oil 9.00 0465 21.2 0.99 9535 9.9898 17 44 990 9560 20.9 500 7822 040 1738 8262 601 16 45 .10 019 9.00 0816 497 7809 .20 069 3007 21.1 6993 810 15 46 048 2069 20.8 494 7797 .22 099 4272 21.0 5728 021 14 ' 47 07T 3318 491 7784 128 5534 4466 9.8734 13 48 106 4563 20.7 488 7771 158 6792 20.9 3208 448 12 49 136 5805 485 7758 187 8047 1953 164 11 50 .10164 9.00 7044 20.6 .99 482 9.99 7745 .22 .10 216 9.00 9298 20.8 0.99 0702 9.7882 10 51 192 8278 20.5 479 7732 246 9.01 0546 20.7 0.98 9454 , 601 9 52 221 9510 476 7719 275 1790 8210 "322 8 53 250 9.01 0737- 20.4 478 7706 805 3031 20.6 6969 044 7 54 ■ 279 1962 20.3 470 7693 834 4268 5732 9.6768 6 55 308 3182 467 7680 868 5502 20.5 4498 498 5 56 837 4400 20.2 464 7667 898 6732 3268 220 4 57 866 5613 461 7654 422 7959 20.4 2041 9.5949 3 58 896 6824 20.1 458 7641 462 9183 20.8 0817 679 2 59 424 8031 456 7628 .28 481 9.02 0403 0.97 9597 411 1 60 10 468 9.01 9235 99 452 9.99 7614 .10 610 9.02 1620 0.97 8380 9.5144 95° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. JNat. Cotangents. Tangents. 84° Cosines. SnjES. _ . . 1 66 Vn. TRIGONOMETRIC FUNCTIONS. 1 1 6° StKKfl. COSIHBS. Tangents. Dif. Cotangents. 173° Nat. log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat, 0' .10 458 9.019235 20.0 .99 452 9.99 7614 .22 .10 610 9.02 1620 20.2 0.97 8380 9,6144 60' 1 4S3 9.02 0435 449 7601 640 2834 7166 9.487S 69 2 611 1632 19.9 446 7588 .28 569 4044 20.1 5956 614 58 3 540 2825 448 7574 .22 699 5251 4749 852 57 4 569 4016 19.8 440 7561 .28 628 6455 20.0 3545 090 56 5 69T 5203 19.7 487 7547 .22 657 7655 2345 9.8881 55 6 626 6386 484 7534 .23 687 8852 19.9 1148 572 54 1 655 7567 19.6 481 7520 .22 716 9.03 0046 0.96 9954 816 53 . 8 684 8744 428 7507 .23 746 1237 19.8 8763 060 52 9 718 9918 19.6 424 7493 .22 775 2425 19.7 7575 9.2806 51 10 .10 742 9.03 1089 19.5 .99 421 9.99 7480 .28 .10 805 9.03 3609 19.7 0.96 6391 9,2668 50 H 771 2257 19.4 413 7466 834 4791 19.6 5209 302 49 12 800 3421 416 •7452 .22 868 5969 4031 082 48 13 829 4582 19.8 412 7439 .23 898 7144 19.8 2856 9.1803 47 14 868 5741 409 7425 922 8316 1684 656 46 15 887 6896 19.2 406 7411 952 9485 19.4 0515 809 45 16 916 8048 402 7397 981 9.04 0651 0.95 9349 066 44 17 945 9197 19.1 899 7383 .11 Oil 1813 19.8 8187 9.0821 43 18 978 9.04 0342 896 7369 040 2973 7027 679 42 19 .11 002 1485 19.0 898 7355 070 4130 19.2 5870 838 41 20 .11081 9.04 2625 19.0 .99 890 9.99 7341 .28 .11 099 9.04 5284 19.2 0.95 4716 9.0098 40 21 060 3762 18.9 886 7327 128 6434 19.1 3566 8.9860 39 22 089 4895 838 7313 168 7582 2418 628 38 23 lis 6026 18.8 880 7299 187 8727 19.0 1273 887 37 24 147 7154 877 7285 217 9869 0131 162 36 25 176 8279 18.7 874 7271 246 9.05 1008 18.9 0.94 8992 8.3919 35 26 205 9400 870 7257 .25 276 2144 7856 686 34 27 284 9.05 0519 18.6 867 7242 .23 805 3277 18.8 6723 456 33 28 268 1635 364 7228 885 4407 5593 228 32 29 291 2749 18.5 860 7214 .26 864 5535 18.7 4465 8.7996 31 30 .11820 9.05 38.>;9 18.6 .99 867 9.99 7199 .28 .11 894 9.05 6659 18.7 0.94 3341 8.7769 30 31 849 4966 18.4 354 7185 .25 428 7781 2219 642 29 32 878 6071 851 7170 .28 452 8900 18.6 1100 817 28 33 407 7172 18.8 847 7156 .25 482 9.06 0016 0,93 9984 098 27 34 486 8271 844 7141 .28 611 1130 18.5 8870 8.6370 26 35 465 9367 18.2 341 7127 .26 541 2240 7760 648 25 36 494 9.06 0460 887 7112 .23 570 3348 18.4 6652 427 24 37 523 1551 18.1 884 7098 .25 600 4453 5547 208 23 38 652 2639 881 7083 629 5556 18.8 4444 8.6989 22 39 680 3724 18.0 827 7068 659 6655 3345 772 ■ 21 40 .11609 9.06 4806 18.0 .99 824 9.99 7053 .28 .11688 9.06 7752 18 2 0.93 2248 8.6566 20 41 688 5885 820 7039 .25 718 8846 1154 840 19 42 667 6962 17.9 817 7024 747 9938 0062 126 18 43 696 8036 814 7009 777 9.07 1027 18.1 0.92 8973 8.4913 17 ■ 44 726 9107 17.8 810 6994 806 2113 7887 701 16 45 764 9.07 0176 307 6979 886 3197 18.0 6803 490 15 46 788 1242 17.7 803 6964 866 4278 5722 280 14 47 812 2306 800 6949 895 5356 17.9 4644 071 13 48 840 3366 17.6 297 6934 924 6432 3568 8.8868 12 49 869 4424 298 6919 964 7505 2495 656 11 50 .11 898 9.07 5480 17.6 .99 290 9.99 6904 .25 .11988 9.07 8576 17.8 0.92 1424 8.3460 10 51 927 6533 17.6 286 6889 .12 018 9644 0356 245 9 52 956 7583 283 6874 .27 042 9.08 0710 17.7 0.91 9290 041 8 53 985 8631 17.4 279 6858 .25 072 1773 8227 8.2838 7 54 .12 014 9676 276 6843 101 2833 17.6 7167 686 6 55 043 9.08 0719 17.8 272 6828 .27 131 3891 6109 434 5 56 071 1759 269 6812 .25 160 4947 5053 284 4 57 100 2797 265 6797 190 6000 17.5 4000 035 3 58 129 3832 17.2 262 6782 .27 219 7050 2950 8.1887 2 59 158 4864 258 6766 .25 249 8098 17.4 1902 640 1 60 .12 1S7 9.98 5894 .99 255 9.99 6751 .12 278 9.08 9144 0.91 0856 8.1443 96° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log, Nat, Tangento, 83° Cosines, Sinks. Vn. TRIGONOMETRIC FUNCTIONS. 67 ' 1 70 Sines. COBIKES. Tangents. Dif. Cotangents. 172° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .12 18T 9.08 5894 17.1 .99 255 9.99 6751 .27 .12 278 9.08 9144 17.4 0.91 0856 8.1448 60' 1 216 6922 251 6735 .25 808 9.09 0187 0.90 9813 248 59 2 245 7947 248 6720 .27 888 1228 17.8 8772 064 58 3 274 8970 17.0 244 6704 867 2266 7734 8.0860 57 4 802 9990 240 6688 .25 397 3302 17.2 6698 667 56 5 SSI 9.09 1008 16.9 287 6673 .27 426 4336 5664 476 55 6 S60 2024 288 6657 466 5367 17.1 4633 285 54 7 S89 3037 16.8 280 6641 486 6395 3605 095 53 8 . 418 4047 226 6625 .25 515 7422 2578 7.9906 52 9 44T 5056 222 6610 .27 544 8446 17.0 1554 718 51 10 .12 476 9.09 6062 16.7 .99 219 9.99 6594 .27 .12 574 9.09 9468 17.0 0.90 0532 7.9580 50 11 504 7065 215 6578 603 9.10 0487 0.89 9513 844 49 12 588 8066 211 6562 633 1504 16.9 8496 158 48 13 562 9065 16.6 208 6546 662 2519 7481 7.8978 47 14 591 9.10 0062 204 6530 692 3532 16.8 6468 789 46 15 620 1056 16.5 200 6514 722 4542 5458 606 45 16 649 2048 197 6498 761 5550 4450 424 44 17 678 3037 198 6482 .28 781 6556 16.7 3444 248 43 18 706 4025 16.4 189 6465 .27 810 7559 2441 062 42 19 735 5010 186 6449 840 8560 1440 7.7882 41 20 .12 764 9.10 5992 16.4 .99 182 9.99 6433 .27 .12 869 9.10 9559 16.6 0.89 0441 7.7704 40 21 793 6973 16.8 178 6417 .28 899 9.110556 0.88 9444 625 39 22 822 7951 175 6400 .27 929 1551 16.6 8449 843 38 23 851 8927 16.2 171 6384 968 2543 7457 171 37 24 880 9901 167 6368 .28 988 3533 6467 7.6996 36 25 908 9.11 0873 163 6351 .27 .18 017 4521 16.4 5479 821 35 26 937 1842 16.1 160 6335 .28 047 5507 4493 647 34 27 966 2809 156 6318 .27 076 6491 3509 473 33 - 28 995 3774 162 6302 .28 106 .7472 16.8 2528 801 32 29 .18 024 4737 16.0 148 6285 .27 186 8452 1548 129 31 30 .18 058 9.115698 16.0 .99 144 9.99 6269 .28 .18 165 9.11 9429 16.8 0.88 0571 7.6953 30 31 081 6656 141 6252 195 9.12 0404 16.2 0.87 9596 787 29 32 110 7613 15.9 187 6235 .27 224 1377 8623 613 28 33 189 8567 188 6219 .28 254 2348 7652 449 27 34 168 9519 15.8 129 6202 284 3317 16.1 6683 281 .26 35 197 9.12 0469 125 6185 818 4284 5716 113 25 36 226' 1417 122 6168 1 843 5249 16.0 4751 7.4947 24 37 2S4 2362 15.7 118 6151 872 6211 3789 781 23 38 288 3306 114 6134 402 7172 2828 615 22 39 812 4248 110 '6117 432 8130 1870 451 21 40 .18 841 9.12 5187 15.6 .99 106 9.99 6100 .23 .13 461 9.12 9087 15.9 0.87 0913 7.4287 20 41 870 6125 102 6083 491 9.13 0041 0.86 9959 124 19 42 899 7060 098 6066 621 0994 16.8 9006 7.3962 18 43 427 7993 15.5 094 6049 650 1944 8056 800 17 44 456 8925 091 6032 580 2893 7107 639 16 45 485 9854 087 6015 609 3839 6161 479 15 46 614 9.13 0781 15.4 088 ' 5998 .30 639 4784 16.7 5216 819 14 47 543 1706 079 5980 .28 669 5726 4274 160 13 48 572 2630 075 5963 693 6667 15.6 3333 002 12 49 600 3551 15.8 071 5946 .80 723 7605 2395 7.2844 11 50 .18 629 9.13 4470 16.8 .99 067 9.99 5928 .28 .13 753 9.13 8542 16.6 0.86 1458 7.2637 10 51 658 5387 063 5911 787 9476 0524 531 9 52 687 6303 15.2 059 5894 .80 817 9.14 0409 15.5 0.85 9591 875 8 53 716 7216 055 5876 .28 846 1340 8660 220 7 54 744 8128 061 5859 .80 876 2269 7731 066 6 55 773 9037 15.1 047 5841 906 3196 15.4 6804 7.1912 5 56 802 9944 043 5823 .28 985 4121 5879 759 4 57 831 9.14 0850 089 5806 .80 965 5044 4956 607 3 58 860 1754 15.0 085 5788 .28 995 5966 15.8 4034 465 2 59 889 2655 031 5771 .30 .14 024 6885 3115 804 1 60 .13 917 9.14 3555 .99 027 9.99 5753 .14 064 9.14 7803 0.85 2197 7.1154 , 97° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 82° Cosines. SlKES. _ _ _ ;-, 1 J 68 Vn. TRIGONOMETRIC FUNCTIONS. 8° SiBES. Cosines. Tangents. COTANOENTS. 171° Nat. Log. Dlf. Nat. Log. Dlf. Nat. Log. Dlf. Log. Nat. 0' .18 917 9.14 3555 15.0 .99 027 9.99 5753 .80 .14 054 9.14 7803 18.8 0.85 2197 7.1154 60' 1 D46 4453 14.9 023 5735 084 8718 18.2 1282 004 69 2 (ITS 5349 019 5717 118 9632 0368 7.0S66 58 3 .14 004 6243 016 5699 143 9.15 0644 0.84 9466 706 57 4 083 7136 14.8 Oil 5681 .28 178 1454 8546 558 66 5 061 8026 006 5664 .80 202 2363 16.1 7637 410 55 6 090 8915 002 5646 282 3269 6731 264 54 7 119 9802 14.7 .98 998 5628 262 4174 5826 117 53 8 148 9.15 0686 994 5610 .82 291 5077 16.0 4923 6.9972 52 9 177 1569 990 5591 .80 821 5978 4022 827 51 10 .14 205 9.15 2451 14.7 .93 986 9.99 5573 .80 .14 861 9.15 6877 15.0 0.84 3123 6.9682 50 11 284 3330 14.6 982 5555 381 7775 14.9 2225 683 49 12 268 4208 973 5537 410 8671 1329 898 48 13 292 5083 978 5519 440 9565 0435 252 47 14 820 5957 969 5501 .82 470 9.16 0457 14.8 0.83 9543 110 46 15 349 6830 14.6 965 5482 .80 499 1347 8663 6.8969 46 16 878 7700 961 5464 629 2236 7764 823 44 n 407 8569 14.4 987 5446 .82 689 3123 6877 687 43 18 486 9435 968 5427 .80 588 4008 14.7 5992 848 42 19 464 9.16 0301 948 5409 .82 618 4892 5108 408 41 20 .14 498 9.16 1164 14.4 .98 944 9.99 5390 .80 .14 648 9.16 5774 14.7 0.83 4226 6.8269 40 21 522 2025 14.3 940 5372 .82 678 6654 14.6 3346 131 39 22 661 2885 986 5353 707 7632 2468 6.7994 38 23 680 3743 981 5334 .80 787 8409 1591 866 37 24 603 4600 14.2 927 5316 .82 767 9284 0716 720 36 25 687 6454 923 5297 796 9.17 0157 14.6 0.82 9843 684 36 26 666 6307 919 5278 .80 326 1029 8971 448 34 21 695 7159 914 5260 .82 856 1899 8101 313 33 28 723 8008 14.1 910 5241 886 2767 7233 179 32 29 752 8856 906 5222 916 3634 14.4 6366 046 31 30 .14 781 9.16 9702 14.1 .98 902 9.99 5203 .82 .14 946 9.17 4499 14.4 0.82 5501 6.6912 30 31 810 9.17 0547 14.0 897 5184 976 6362 4638 779 29 32 888 1389 898 5165 .16 008 6224 14.3 3776 646 28 33 867 2230 889 5146 084 7084 2916 814 27 34 396 3070 884 5127 064 7942 2058 333 26 35 926 3908 13.9 880 5108 094 8799 1201 282 25 36 964 4744 876 5089 124 9656 14.2 0345 122 24 37 982 5578 871 5070 158 9.18 0508 0.81 9492 0.6992 23 38 .16 Oil 6411 367 5051 138 1360 8640 868 22 39 040 7242 18.8 868 6032 218 2211 14.1 7789 784 21 40 .15 069 9.17 8072 18.8 .98 853 9.99 5013 .88 .15 248 9.18 3059 14.1 0.81 6941 6.5606 20 41 007 8900 854 4993 .82 272 3907 6093 478 19 42 126 9726 849 4974 8»2 4752 5248 350 18 43 155 9.18 0551 18.7 845 4955 .88 882 6697 14.0 4403 228 n . 44 184 1374 841 4935 .82 862 6439 3561 097 16 45 212 2196 886 4916 .88 891 7280 2720 6.4971 15 46 241 3016 18.6 832 4896 .82 421 8120 1880 846 14 47 270 3834 827 4877 .83 451 8958 18.9 1042 721 13 48 299 4651 823 4857 .32 481 9794 0206 696 12 49 827 5466 818 4838 .88 511 9.19 0629 0.80 9371 472 11 50 .15 856 9.18 6280 13.5 .98 814 9.99 4818 .83 .16 640 9.19 1462 18.9 0.80 8538 6.4843 10 51 885 7092 809 4798 .82 670 2294 18.8 7706 226 9 52 414 7903 805 4779 .38 600 3124 6876 108 8 53 «2 8712 800 4759 630 3953 6047 6.8930 7 54 471 9519 18.4 796 4739 .32 660 4780 6220 869 6 55 500 9.19 0325 791 4720 .83 689 5606 18.7 4394 787 S 56 529 1130 787 4700 719 6430 3570 617 4 57 667 a933 782 4680 749 7253 2747 496 3 58 586 2734 13.8 778 4660 779 8074 1926 376 2 59 616 3534 778 4640 809 8894 1106 267 1 60 .15 643 9.19 4332 .98 769 9.99 4620 .16 888 9.19 9713 0.80 0287 6.8188 98° Nat Log. Dlf. Nat. Log. Dlf. Nat. Log. Dlf. COTAKOEKTS. Log. Nat. Tangents. 81° COSIMKS. Bines. 1 __ — __ --' ■■■a yn. TRIGONOMETRIC FUNCTIONS. 69 _ — . 1 9° Sines. . Cosines. Tahsknts. Cotangents. 170° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .15 648 9.19 4332 18.8 .98 769 9.99 4620 .83 .15 888 9.19 9713 18.6 0.80 0287 6.8188 60' 1 6T2 5129 764 4600 868 9.20 0529 0.79 9471 019 59 2 TOl 5925 18.2 760 4580 898 1345 8666 6.2901 58 3 780 6719 766 4560 928 2159 18.5 7841 788 57 4 768 7511 761 4540 .86 958 2971 7029 666 56 5 787 8302 746 4519 .83 988 3782 6218 649 56 6 816 9091 18.1 741 4499 .16 017 4592 5408 432 54 1 . 845 9879 787 4479 047 5400 4600 816 53 8 878 9.20 0666 732 4459 .86 077 6207 18.4 3793 200 52 9 902 1451 728 4438 .83 107 7013 2987 085 51 10 .16 981 9.20 2234 18.1 .98 723 9.99 4418 .33 .16 187 9.20 7817 18.4 0.79 2183 6.1970 50 11 969 3017 18.0 718 4398 .36 187 8619 1381 856 49 12 988 3797 714 4377 .33 198 9420 18.8 0680 742 48 13 .16 017 4577 709 4357 .36 226 9.210220 0.78 9780 628 47 14 046 6354 704 4336 .88 256 1018 8982 615 46 15 074 6131 12.9 700 4316 .86 286 1815 8185 402 45 16 103 6906 695 4295 816 2611 18.2 7389 290 44 If 182 7679 690 4274 .83 846 3406 6696 178 43 . 18 160 8452 12.8 636 4254 .35 876 4198 5802 066 42 19 189 9222 681 4233 405 4989 5011 6.0965 41 20 .16 218 9.20 9992 12.8 .98 676 9.99 4212 .88 •16 436 9.215780 18.1 0.78 4220 6.0844 40 21 246 9.21 0760 671 4191 .88 466 6568 3432 734 39 22 276 1526 667 4171 .36 495 7356 2644 624 38 23 804 2291 12.7 662 4150 526 8142 1858 614 37 24 888 3055 657 4129 665 8926 1074 406 36 25 861 3818 652 4108 685 9710 13.0 0290 298 36 26 890 4579 648 4087 615 9.22 0492 0.77 9508 188 34 27 419 5338 648 4066 646 1272 8728 080 33 28 447 6097 12.6 638 4045 674 2052 7948 6.9972 32 29 476 6854 638 4024 704 2830 7170 865 31, 30 .16 505 9.21 7609 12.6 .98 629 9.99 4003 .35 .16 784 9.22 3607 12.9 0.77 6393 5.9768 30 ■ 31 583 8363 624 3982 .87 764 4382 5618 861 29 32 562 9116 12.5 619 3960 .85 794 5156 4844 546 28 33 591 9868 614 3939 824 5929 4071 439 27 34 620 9.22 0618 609 3918 864 6700 3300 338 26 35 648 1367 604 3897 .87 834 7471 12.8 2529 228 25 36 677 2115 12.4 600 3875 .36 914 8239 1761 124 24 37 706 2861 595 3854 .87 944 9007 0993 019 23 38 734 3606 590 3832 .86 974 9773 0227 6.8916 22 39 768 4349 686 3811 .37 .17 004 9.23 0539 12.7 0.76 9461 811 21 40 .16 792 9.22 5092 12.4 .9S 680 9.99 3789 .85 •n 038 9.23 1302 12.7 0.76 8698 6.8708 20 41 820 5833 12.8 575 3768 .87 083 2066 7935 606 19 42 849 6573 570 3746 .35 093 2826 7174 • 502 18 43 878 7311 666 3725 .37 128 3586 6414 400 17 44 906 8048 661 3703 153 4345 12.6 5665 298 16 45 986 •8784 12.2 666 3681 .86 183 5103 4897 197 15 46 964 9518 661 3660 .87 218 6859 4141 096 14 47 992 9.23 0252 646 3638" 248 6614 3386 6.7994 13 48 .17 021 0984 541 3616 278 7368 12.5 2632 894 12 49 050 1715 586 3594 303 8120 1880 794 11 50 .17 078 9.23 2444 12.1 .98 581 9.99 3572 .87 .17 833 9.23 8872 12.6 0.76 1128 5.7894 10 51 107 3172 526 3550 383 9622 0378 694 9 52 136 3899 621 3528 898 9.24 0371 0.76 9629 495 8 53 164 4625 516 3506 428 1118 8882 896 7 54 193 5349 611 3484 458 1866 12.4 8136 297 6 55 222 6073 12.0 506 3462 488 2610 7390 199 6 56 250 6795 601 3440 613 3354 6646 101 4 ■57 279 7515 496 3418 548 4097 5903 004 3 58 808 8235 491 3396 573 4839 12.3 ' 5161 5.6906 2 59 888 8953 486 3374 .88 608 5679 4421 809 1 60 .17 865 9.23 9670 .98 481 9.99 3351 .17 883 9.24 6319 0.75 3681 6.6718 99° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. Tangents. 80° C03IHKB. SiKBS. Cotangents. 1 70 Vn. TRIGONOMETRIC FUNCTIONS. 10° Sinks. COSIMBS. Tangents. Cotangents. 169° Nat Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .17 865 9.23 9G70 11.9 .98 481 9.99 3351 .87 .17 688 9.24 6319 12.8 0.76 3681 6.6718 60' 1 898 9.24 0386 476 3329 668 7067 2943 617 69 2 42-2 1101 471 3307 .83 698 7794 2206 621 68 3 451 1814 466 3284 .87 728 8530 12.2 1470 426 57 4 479 2526 461 3262 768 9264 0736 329 56 5 508 3237 11.8 465 3240 .88 783 9998 0002 284 66 6 687 3947 460 3217 .87 318 9.25 0730 0.74 9270 140 64 7 565 4656 446 3195 .88 348 1461 8539 04& 63 8 694 5363 440 3172 378 2191 7809 6.6951 62 9 628 6069 485 3149 .87 908 2920 12.1 7080 867 51 10 .17 651 9.24 6775 11.7 .93 480 9.99 3127 .88 .17 938 9.25 3648 12.1 0.74 6352 6.6764 60 11 680 7478 426 3104 963 4374 5626 671 49 12 708 8181 420 3081 .87 998 6100 4900 •> 878 48 13 787 8883 414 3059 .88 .18 028 6824 4176 485 47 14 766 9583 409 3036 068 6647 12.0 3453 393 46 15 794 9.25 0282 11.6 404 3013 088 7269 2731 301 46 16- 828 0980 899 2990 113 7990 2010 209 44 n 862 1677 894 2967 143 8710 1290 118 43 18 880 2373 889 2944 1T3 9429 0671 026 42 19 909 3067 888 2921 208 9.26 0146 0.73 9864 5.4986 41 20 .17 987 9.25 3761 11.5 .98 878 9.99 2898 .88 .18 233 9.26 0863 11.9 0.73 9137 6.4845 40 21 966 4453 878 2875 268 1678 8422 755 39 22 995 5144 868 2862 293 2292 7708 665 38 23 .18 028 5834 862 2829 828 3006 6995 676 37 24 052 6523 857 2806 368 3717 6283 486 36 26 081 7211 862 2783 .40 884 4428 11.8 5572 897 36 26 109 7898 11.4 847 2759 .88 414 5138 4862 808 34 27 188 8583 841 2736 444 5847 4153 219 33 28 166 9268 836 2713 474 6555 3445 181 32 29 195 9961 881 2690 .40 604 7261 2739 048 31 30 .18 224 9.26 0633 11.4 .98 825 9.99 2666 .88 .18 534 9.26 7967 11.7 0.73 2033 6.8968 30 31 252 1314 11.8 820 2643 .40 564 8671 1329 868 29 32 281 1994 816 2619 .38 594 9375 0625 781 28 33 809 2673 810 2596 ..40 624 9.27 0077 0.72 9923 694 27 34 888 3361 804 2672 .38 684 0779 9221 607 26 35 867 4027 299 2549 .40 634 1479 8521 621 25 36 896 4703 11.2 294 2525 714 2178 11.6 7822 486 24 37 424 6377 288 2501 .88 745 2876 7124 849 23 38 462 6061 288 2478 .40 776 3573 6427 268 22 39 481 6723 277 2454 806 4269 5731 178 21 40 .18 609 9.26 7395 11.2 .98 272 9.99 2430 .40 .18 886 9.27 4964 11.6 0.72 5036 6.8098 20 41 688 8066 267 2406 865 5658 4342 008 19 42 667" 8734 11.1 261 2382 .88 896 6351 11.5 3649 6.2924 18 43 595 9402 266 2359 .40 926 7043 2967 889 17 44 624 9.27 0069 260 2336 965 7734 2266 765 16 45 652 0735 246 2311 986 8424 1576 672 15 46 681 1400 240 2287 .19 016 9113 0887 688 14 47 710 2064 11.0 284 2263 046 9801 0199 606 13 48 788 2726 229 2239 .42 076 9.28 0488 11.4 0.71 9612 422 12 49 767 3388 228 2214 .40 106 1174 8826 839 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 6.2267 10 61 824 4708 212 2166 166 2542 7458 174 9 52 862 5367 207 2142 197 3226 6776 092 8 63 881 6025 10.9 201 2118 .42 227 3907 6093 on 7 64 910 6681 196 2093 .40 267 4588 11.8 5412 8.1929 6 65 988 7337 190 2069 .42 287 6268 4732 848 5 . 56 967 7991 186 2044 .40 817 5947 4053 767 4 57 996 8645 179 2020 847 6624 3376 636 3 58 .19 024 9297 174 1996 .42 878 7301 2699 606 2 59 062. 9948 163 1971 .40 408 7977 2023 526 1 60 .19 081 9.28 0699 .93168 9.99 1947 .19 438 9.28 8662 0.71 1348 6.1446 100° Nat. Log. Dlf. Nat. Log. Dlf. Nat. Log. Dlf. COTAlfOENTS. Log. Nat. Tangbwts. 79° CosraES. Sines. 1 — Z J VII. TRIGONOMETRIO FUNCTIONS. n 11° Sines. C08IIIB8. Tabgenis. Cotangents. 168° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .19 081 9.28 0599 10.8 .98163 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 866 59 2 188 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 5 234 3836 10.7 135 1823 .40 689 2013 7987 049 55 6 252 4480 129 1799 .42 619 2682 11.1 7318 5.0970 54 1 231 5124 124 1774 649 3350 6650 892 53 8 809 5766 118 1749 680 4017 5983 814 52 9 838 6408 112 1724 710 4684 5316 786 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 881 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 16 588 0870 073 1549 921 9322 0678 197 44 n 566 1504 067 1524 .48 952 9980 0020 121 43 18 695 2137 10.5 061 1498 .42 982 9.30 0638 0.69 9362 045 42 19 628 2768 056 1473 .20 012 1295. 10.9 8705 4.9969 41 20 .19 652 9.29 3399 10.5 .98 060 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 089 1397 103 3261 6739 744 38 23 787 5286 088 1372 .48 188 3914 6086 669 37 24 766 5913 10.4 027 1346 .42 164 4567 5433 594 36 25 794 6539 021 1321 .48 194 5218 4782 520 35 26 823 7164 016 1295 .42 224 5869 10.8 4131 446 34 27 851 7788 010 1270 .48 254 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 .20 346 9.30 8463 10.8 0.69 1537 4.9152 30 31 965 9.30 0276 10.8 987 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 4.8988 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 968 1038 527 2327 7673 716 24 37 186 3979 10.2 952 1012 557 2968 7032 644 23 38 165 4593 946 0986 588 3608 6392 578 22 39, 198 5207 940 0960 618 4247 10.6 5753 601 21 40 .20 222 9.30 5819 10.2 .97 934 9.99 0934 .48 .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 43 807 7650 916 0855 .43 739 6795 3205 218 17 M 836 8259 10.1 910 0829 770 7430 2570 147 16 45 364 8867 905 0803 800 8064 1936 077 15 46 898 9474 899 a777 .45 880 8697 1303 007 14 47 421 9.31 0080 898 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 .48 921 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 52 568 3097 863 0618 .21013 2479 7521 591 8 53 592 3698 9.98 867 '0591 .48 048 3106 6894 522 7 54 620 4297 10.0 851 0565 .45 078 3733 10.4 6267 453 6 55 649 4897 9.97 845 0538 104 4358 5642 386 5 56 677 5495 9.95 889 0511 .48 134 4983 5017 817 4 57 706 6092 883 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. COTANQENTS. Log. Nat. Tasoents. 78° COSIHES. Sines. Vn. TRIGONOMETRIC FUNCTIONS. 1 SDflB. Cosines. Tahoentb. Cotangents. 167° Nat. Log. Dlf. Nat Log. Dlf. Nat. Log. Dif. Log. Nat. 0' .20 791 9.31 7879 9.90 .97 815 9.99 0404 .43 .21256 9.32 7475 10.8 0.67 2525 4.7046 60' 1 820 8473 9.8S 809 0378 .45 286 8095 1905 4.6979 59 '2 S4S 9066 9.87 603 0351 316 8715 1285 912 58 3 87T 9658 9.85 797 0324 847 9334 0666 845 57 i 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 .47 488 1187 8813 646 54 7 990 2019 9.80 772 0215 .46 469 1803 8197 680 53 8 .21 019 2607 9.78 766 0188 499 2418 7582 514 52 9 047 3194 9.77 760 0161 529 3033 10.2 6967 448 51 10 .21 076 9.32 3780 9.77 .97 764 9.99 0134 .45 .21 560 9.33 3646 10.2 0.66 6354 46382 50 11 104 4366 9.78 748 0107 .47 590 4259 5741 817 49 12 182 4950 742 0079 .46 621 4871 5129 252 48 13 161 5534 9.72 785 0052 651 5482 4518 187 47 14 189 6117 729 0025 .47 682 6093 3907 122 46 15 218 6700 9.68 728 9.98 9997 .45 712 6702 3298 057 45 16 246 7281 717 9970 .47 743 7311 10.1 2689 4.5993 44 n 276 7862 9.67 711 9942 .46 778 7919 2081 928 43 18 808 8442 9.66 705 9915 .47 804 8527 1473 864 42 19 881 9021 9.63 698 9887 .45 884 9133 0867 800 41 20 .21860 9.32 9599 9.62 .97 692 9.98 9860 .47 .21 864 9.33 9739 10.1 0.66 0261 46736 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 9.67 678 9777 .47 956 1552 8448 646 37 24 474 1903 9.58 667 9749 986 2155 10.0 7845 483 36 25 502 2478 9.65 661 9721 .22 017 2757 7243 420 35 26 680 3051 655 9693 . 047 3358 6642 867 34 27 659 3624 9.52 648 9665 078 3958 6042 294 33 28 587 4195 9.68 642 9637 .45 108 4558 9.98 5442 282 32" 29 616 4767 9.60 686 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 231 6949 3051 4.4988 28 33 729 7043 9.48 611 9497 261 7545 2455 922 27 34 768 7610 9.43 604 9469 292 8141 9.90 1859 860 26 35 786 8176 598 9441 322 8735 1265 799 25 36 814 8742 9.42 592 9413 353 9329 9.88 0671 787 24 37 843 9307 9.40 585 9385 .48 888 9922 9.87 0078 676 23. 38 871 9871 9.38 679 9356 .47 414 9.35 0514 0.64 9486 615 22 39 899 9.34 0434 9.37 578 9328 444 1106 9.85 8894 565 21 40 .21 928 9.34 0996 9.87 .97 666 9.98 9300 .48 .22 475 9.35 1697 9.83 0.64 8303 4.4494 20 41 956 1558 9.86 660 9271 .47 505 2287 9.82 7713 484 19 42 986 2119 9.88 563 9243 .48 536 2876 7124 878 18 43 .22 018 2679 647 9214 .47 567 3465 9.80 6535 818 17 44 041 3239 9.80 541 9186 .48 597 4053 9.78 5947 253 16 45 070 3797 584 9157 628 4640 5360 194 15 46 098 4355 9.28 528 9128 .47 668 5227 9.77 4773 184 14 47 126 4912 521 9100 .48 689 5813 9.75 4187 075 13 48 166 5469 9.25 616 9071 719 6398 9.73 3602 015 12 49 188 6024 508 9042 .47 750 6982 3018 4.8956 11 50 .22 212 9.34 6579 9.25 .97 602 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 54 826 8792 9.18 476 8898 908 9893 9.68 0107 662 6 55 868 9343 9.17 470 8869 984 9.36 0474 9.66 0.63 9526 604 6 56 882 9893 463 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 9.13 460 8782 .23 026 2210 9.62 7790 480 2 59 467 1540 444 8753 056 2787 7213 872 1 60 .22 496 9.35 2088 .97 437 9.98 8724 .23 087 9.36 3364 0.63 6636 4.8815 102° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tahgbhtb, 77° COSIMES. Sines. — ■ 1 VII. TRIGONOMETRIC FUNCTIONS. 73 - -1 13° SiNEB. COBIKES. Tahgekts. Cotangents. 166° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .22 495 9.35 2088 9.12 .97 437 9.98 8724 .48 28 087 9.36 3364 9.60 0.63 6636 4.8815 60' 1 523 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 148 57 4 603 4271 9.07 411 8607 209 5664 9.56 4336 086 56 6 637 4815 9.05 404 8578 .50 240 6237 3763 029 55 6 665 5358 898 8548 .48 271 6810 9.53 3190 4.2972 54 7 693 5901 9.08 891 8519 .50 801 7382 9.52 2618 916 53 8 722 6443 9.02 884 8489 .48 882 7953 2047 869 52 9 750 6984 9.00 378 8460 .50 868 8524 9.60 1476 6C8 51 10 .22 778 9.35 7524 9.00 .97 371 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 12 885 8603 8.97 358 8371 .48 456 9.37 0232 9.45 0.62 9768 635 48 13 863 9141 8.95 851 8342 .50 486 0799 9.47 9201 680 47 li 892 9678 345 8312 616 1367 9.43 8633 521 46 15 920 9.36 0215 888 8282 547 1933 8067 468 45 16 949 0752 8.92 881 8262 .48 678 2499 9.42 7501 418 44 17 977 1287 325 8223 .50 608 3064 6936 358 43 18 .28 005 1822 8.90 818 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 .28 700 9.37 4756 9.88 0.62 5244 4.2198 40 21 090 3422 8.87 298 8103 731 5319 9.87 4681 139 39 22 ,118 3954 8.85 291 8073 762 5881 9.35 4119 084 38 23 146 4485 284 8043 798 6442 3558 080 37 24 1T5 5016 8.88 278 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 .62 885 8122 1878 868 34 27 260 6604 8.78 257 7922 .50 916 8681 9.30 1319 814 33 28 288 7131 8.80 251 7892 946 9239 0761 760 32 29 816 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 4.1668 30 31 373 8711 8.75 230 7801 .60 089 0910 9090 600 29 32 401 9236 223 7771 .62 069 1466 9.23 8534 547 28 33 429 9761 8.78 217 7740 .50 100 2020 9.25 7980 493 27 ■ 34 458 9.37 0285 8.72 210 7710 .62 181 2575 9.28 7425 441 26 35 486 ^--^OSOS 8.70 203 7679 .50 162 3129 9.22 6871 388 25 36 514 ~ 1330 196 7649 .62 193 3682 9.20 6318 336 24- 37 542 1852 8.68 189 7618 .60 223 4234 5766 282 23 38 571 2373 182 7588 .62 254 4786 9.18 5214 280 22 39 599 2894 .23 627 9.37 3414 8.67 176 7557 285 5337 4663 178 21 40 8.65 .97 169 9.98 7526 .50 .24 816 9.38 5888 9.17 0.614112 4.1120 20 41 656 3933 162 7496 .62 847 6438 9.15 3562 074 19 42 684 4452 8.68 155 7465 877 6987 3013 022 18 43 712 4970 8.62 148 7434 408 7536 9:18 2464 4.0970 17 44 740 5487 8.60 141 7403 489 8084 9.12 1916 918 16 45 769 6003 134 7372 470 8631 1369 867 15 46 797 6519 127 7341 601 9178 9.10 0822 815 14 47 825 7035 8.57 120 7310 832 9724 0276 764 13 48 858 7549 118 7279 562 9.39 0270 9.08 0.60 9730 713 12 49 882 8063 106 7248 693 0815 9185 662 11 50 .28 910 9.37-8577 8.53 .97 100 9.98 7217 .52 .24 624 9.39 1360 9.05 0.60 8640 4.0611 10 51 988 9089 098 7186 665 1903 9.07 8097 560 9 52^ 966S=^ 9601 -—086 7155 686 2447 9.03 7553 509 8 53 995 9.38 0113 8.52 079 7124 .63 717 2989 7011 459 7 54 .24 028 0624 8.50 072 7092 .52 747 3531 6469 408 6 55 051 yll34 8.48 065 7061 778 4073 9.02 5927 368 5 56 079 1643 058 7030 .63 809 4614 9.00 5386 808 4 57 108 2152 051 6998 .52 840 5154 4846 257 3 58 186 2661 8.45 044- ^ 6967 871 5694 8.98 4306 207 2 59 164 3168 037 ^ 6936 .53 902 6233 8.97 3767 158 ] 60 .24192 9.38 3675 .97 080 9.98 6904 .24 98.3 9.39"6771 0.60 3229 4.0108 103° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. TaNGH!NI«. 76° Cosines. Sines. 74 Vn. TEIGONOMETRIC FUNCTIONS. 1 14° SiHKS. Cosiszs. TA^fGENTS. Dlf. 165° Xat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .24 192 9.38 3675 8.45 .97 080 9.98 6904 .62 .24 988 9.39 6771 8.97 0.60 3229 4.0108 60' 1 220 4182 8.42 028 6873 .53 964 7309 8.95 2691 058 59 2 249 4687 015 6841 995 7846 2154 009 58 3 27" 5192 008 6809 .62 .25 026 8383 8.93 1617 8.9959 57 4 805 5697 8.40 001 6778 .53 056 8919 1081 910 56 5 883 6201 8.88 .96 994 6746 087 9455 8.92 0545 861 55 6 862 6704 987 6714 .52 lis 9990 8.90 0010 812 54 7 890 7207 8.37 980 6683 .53 149 9.40 0524 0.59 9476 763 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 4T4 9.38 8711 8.88 .96 969 9.98 6587 .58 .26 243 9.40 2124 8.87 0.59 7876 8.9617 50 11 503 9211 952 6555 273 2656 8.85 7344 568 49 12 581' 9711 8.82 945 6523 304 3187 6813 520 48 13 559 9.39 0210 8.80 987 6491 336 3718 6282 471 47 14 68T 0708 980 6459 866 4249 8.82 5751 428 46 15 615 1206 8.28 923 6427 397 4778 8.88 5222 876 45 16 644 1703 8.27 916 6395 428 5308 8.80 4692 827 44 n 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 .56 621 ■ 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 S.77 0.59 2581 3.9186 40 21 784 4179 880 6234 588 7945 2055 089 39 22 813 4673 8.22 878 6202 .65 614 8471 8!75 1529 04^ 38 23 841 5166 8.20 860 6169 .68 645 8996 1004 8.8996 37 24 869 5658 - 858 6137 .66 676 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 .56 738 0569 8.72 9431 854 34 27 954 7132 8.15 887 6039 .58 769 1092 8908 807 33 28 982 7621 8.17 829 6007 ..56 800 1615 8.70 8385 760 32 29 .26 010 8111 8.15 822 5974 .53 831 2137 8.68 7863 714 31 30 .26 088 9.39 8600 8.18 4tffi? 9.98 5942 .55 .25 862 9.41 2658 8.68 0.58 7342 8.8667 3Q. 31 066 9088 8.12 807 5909 898 -3179 8.67 6821 621 29 32 094 9575 800 5876 924 3699 6301 575 28 33 122 9.40 0062 798 5843 .53 956 4219 8.65 5781 528 27 34 ISl 0549 8.10 786 5811 .56 986 4738 5262 482 26 35 179 1035 8.08 778 5778 .26 017 5257 8.68 4743 436 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 31£U> 299 22 39 291 2972 749 5646 141 7326 2674 254 21 40 .26 820 9.40 3455 8.05 .96 742 9.98 5613 .55 .26172 9.417842 8.60 0.58 2158 8.8208 20 41 848 3938 8.08 784 5580 208 8358 8.58 1642 163 19 42 876 4420 8.02 727 5547 286 8873 8.67 1127 118 18 43 404 4901 t 719 5514 .67 266 9387 0613 078 17 44 482 5382 8.00 712 5480 .65 297 9901 0099 028 16 45 460 5862 7.98 705 5447 828 9.42 0415 8.68 0.57 9585 3.7983 15 46 488 6341 697 5414 359 0927 8.65 9073 988 14 47 616 6820 690 5381 .67 390 1440 8.58 8560 893 13 48 545 7299 7.97 682 5347 .65 421 1952 8.52 8048 848 12 49 578 7777 7.95 678 5314 .57 452 2463 7537 804 11 •50 .26 601 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 7.93 660 5247 .57 515 3484 8.48 6516 716 9 52 657 9207 7.92 668 5213 .56 546 3993 8.50 6007 671 8 • 53 685 9682 645 5180 .57 577 4503 8.47 5497 627 7 54 718 9.41 0157 638 5146 .55 608 5011 4989 588 6 55 741 0632 7.90 630 5113 .67 689 5519 4481 689 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 .56 788 7041 8.48 2959 408 2 59 864 2524 600 4978 .57 764 7547 8.42 2453 364 1 60 .25 882 9.41 2996 .96 698 9.98 4944 .26 795 9.42 8052 0.57 1948 8.7821 104° N»t. Log. Dlf. Nat. Log. Dlf. Hat. Log. COTAMGKKTS. Dif. Log. Nat. Tahgehts. 75° Cosines. SlSE6. 1 _ — _ - , Yn.. TRIGONOMETRIC rimCTIONS. 75 — ■ 1 15° SiHBS. COSIHJIS. Takqehts. Dif. Cotangents. 164° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .25 883 9.41 2996 7.85 .96 698 9.98 4944 .57 .26 795 9.42 8052 8.43 0.57 1948 8.7821 60' 1 910 3467 585 4910 826 8558 8.40 1442 277 59 2 988 3938 7.88 578 4876 867 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 640 4706 .27 013 1577 8423 019 53 8 lOT 6751 7.77 582 4672 044 2079 8.85 7921 3.6976 52 9 185 7217 7.78 524 4638 .58 076 2580 8.83 7420 983 51 10 .26163 9.41 7684 7.77 .96 517 9.98 4603 .67 .27 107 9.43 3080 8.33 0.56 6920 8.6891 50 11 191 8150 7.75 509 4569 188 3580 6420 848 49 12 219 8615 7.78 502 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 282 5078 8.80 4922 72^ 46 15 803 9.42 0007 479 4432 .58 268 5576 8.28 4424 680 45 ■ 16 831 0470 471 4397 .57 294 6073 3927 688 44 17 859 0933 7.70 463 4,363 .68 326 6570 3430 596 43 18 887 1395 466 4328 .67 857 7067 8.27 2933 664 42 19 415 1857 7.68 448 4294 .68 888 V 7563 2437 512 41 20 .26 443 9.42 2318 7.67 .96 440 9.98 4259 .68 .27 419 9.43 8059 8.25 0.56 1941 8.6470 40 21 471 2778 488 4224 .67 451 8554 8.28 1446 429 39 22 500 3238 7.65 425 4190 .68 482 9048 8.25 0952 887 38 23 628 3697 417 4155 618 9543 8.22 0457 346 37 24 656 4156 410 '4120 645 9.44 0036 0.55 9964 305 36 25 584 4615 7.68 402 4085 676 0529 9471 264 35 26 612- 5073 7.62 894 4050 607 1022 8.20 8978 222 34 27 640 5530 386 4015 .57 688 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 .96 368 9.98 3911 .60 .27 782 9.44 2988 818 0.55 7012 8.6059 30 31 752 7354 35^ 3875 .58 764 3479 8.15 6521 018 29 32 780 7809 7.57 . 347 3840 795 3968 8.17 603a 8.5978 28 33 808 8263 340 3805 826 4458 8.15 5542 987 27 34 886 8717 7.55 382 3770 858 4947 8.18 5053 897 26 35 864 9170 824 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 V 0527 7.52 301 3629 988 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 8.5656 20 41 082 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 586 17 44 116 3226 7.48 253 3416 .68 172 9810 0190 497 16 45 144 3675 7.46 246 3381 .60 203 9.45 0294 8.05 0.54 9706 467 15 46 172 4122 238 3345 284 0777 9223 418 14 47 200 4569 230 3309 266 1260 8740- 379 13 48 228 5016 7.48 222 3273 .68 297 , 1743 8.08 8257 889 12 49 256 5462 214 3238 .60 829 '2225 8.02 7775 800 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 8.5261 10 51 812 6353 198 3166 891 3187 6813 222 9 52 840 6798 7.40 190 3130 428 3668 8.00 6332 188 8 53 868 7242 182 3094 454 4148 5852 144 •7 54 396 7686 7.88 17^ 3058 480 4628 7.98 5372 105 6 55 424 8129 166 3022 617 5107 4893 067 5 56 452 8572 7.87 158 2986 549 5586 7.97 4414 028 , 4 3 57 480- 9014 150 2950 580 6064 3936 8.4989 58 508 9456 7.35 ■ 142 2914 612 6542 7.96 3458 951 2 59 686 9897 184 2878 643 7019 2981 912 1 60 .27 564 9.44 0338 .96 126 9.98 2842 .23 675 9.45 7496 0.54 2504 8.4874 105° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat.. 74° Cosines. Sines. Tangents. 76 VII. TRIGONOMETRIC FUNCTIONS. r — -1 16° Suns. COSINBS. Tahgents. Dif. COTAKSlUraS. 163° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .27 664 9.44 0338 7.88 .96 126 9.98 2842 .62 .28 675 9.45 7496 7.96 0.54 2504 8.4874 60' 1 S92 0778 118 2805 .60 706 7973 7.98 2027 886 59 2 620 1218 110 2769 788 8449 1651 798 58 3 648 1658 7.80 102 2733 .62 769 8925 7.92 1075 760 57 4 6T6 2096 7.82 094 2696 .60 801 9400 0600 722 56 5 704 2536 7.80 086 2660 882 9875 7.90 0125 684 55 6 781 2973 7.28 078 2624 .62 864 9.46 0349 0.53 9661 646 54 7 769 3410 070 2587 .60 895 0823 9177 608 53 8 787 3847 062 2551 .62 927 1297 7.88 8703 570 62 9 815 4284 7.27 054 2514 968 1770 7.87 8230 588 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 8.449$ 50 11 871 5155 087 2441 .62 .29 021 2715 7.85 7286 458 49 12 899 5590 029 2404 058 3186 7.87 6814 420 48 13 927 6025 7.2S 021 2367 .60 084 3658 7.88 6342 888 47 14 965 6459 018 2331 .62 116 U128 7.85 6872 846 46 15 983 6893 7.22 005 2294 147 4599 7.88 5401 808 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 .28128 9.44 9054 7.18 .95 964 9.98 2109 .62 .29 805 9.46 6945 7.80 0.53 3055 8.4124 40 21 150 9485 7.17 956 2072 837 7413 7.78 2587 087 39 22 178 9915 948 2035 868 7880 2120 050 38 23 206 9.45 0345 940 1998 400 8347 1653 014 37 24 234 0775 7.15 981 1961 482 8814 7.77 1186 3.8977 36 25 262 1204 7.18 928 1924 .68 463 9280 0720 941 35 26 290 1632 915 1886 .62 496 9746 7.75 0254 904 34 27 818 2060 907 1849 626 9.47 0211 0.52 9789 868 33 28 846 2488 7.12 898 1812 .63 558 0676 9324 832 32 29 874 2915 890 1774 .62 590 1141 7.78 8859 796 31 30 .28 402 9.45 3342 7.10 .95 882 9.98 1737 .62 .29 621 9.47 1605 7.73 0.62 8395 8.8769 30 31 429 3768 874 1700 .63 658 2069 7.72 7931 723 29 32 457 4194 7.08 865 1662 .62 686 2532 7468 687 28 33 485 4619 857 1625 .63 716 2995 7.70 7006 652 27 34 618 5044 849 1587 748 3457 6543 616 26 35 541 5469 r.DT 841 1549 .62 780 3919 6081 580 25 36 569 5893 7.05 882 1512 .68 811 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 39 662 7162 7.03 807 1399 .68 906 5763 4237 488 21 40 .28 680 9.45 7584 7.03 .96 799 9.98 1361 .68 .29 988 9.47 6223 7.67 0.62 3777 8.3402 20 41 708 8006 7.02 791 1323 970 6683 7.66 3317 867 19 42 786 8427 782 1285 .80 001 7 142 2868 882 18 43 764 8848 7.00 774 1247 083 7601 7.68 2399 297 17 44 792 9268 766 1209 066 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 47 878 0527 740 1095 160 9432 0568 156 13 48 908 0946 6.97 782 1057 192 9889 7.60 01.11 122 12 49 981 1364 724 1019 224 9.48 0345 0.51 9655 087 11 50 .28 959 9.46 1782 6.95 .95 715 9.98 0981 .65 .30 255 9.48 0801 7.60 0.51 9199 8.8062 10 51 987 2199 707 0942 .68 287 1257 7.58 8743 017 9 52 .29 015 2616 6.98 698 0904 319 1712 8288 8.2988 8 53 042 3032 690 0866 .65 851 2167 7.67 7833 948 7 54 070 3448 681 0827 .68 382 2621 7379 914 6 55 098 3864 6.92 678 0789 .65 414 3075 6925 879 5 56 126 4279 664 0750 .63 446 3529 7.65 6471 845 4 57 154 4694 6.90 656 0712 .66 478 3982 6018 811 3 58 182 5108 647 0673 .68 509 4435 7.68 5565 777 2 59 209 5522 6.88 689 0635 .66 641 4887 5113 743 1 60 .29 287 9.46 5935 .95 630 9.98 0596 .80 573 9.48 5339 0.51 4661 8.2709 106° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. COTAKGENTO. Dif. Log. Nat. 73° COSIKES. Sines. Takoests. 1 YII. TRIGONOMETRIC FUNCTIONS. rr 17° SiHBB. Cosines. Tangents. Dif. Cotangents. 162° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .29 23T 9.46 5935 6.38 .96 686 9.98 0596 .68 .30 678 9.48 5339 7.58 0.514661 3.2709 GO' . 1 266 6348 622 0558 .65 605 5791 7.52 4209 675 59 2 293 6761 6.87 613 0519 687 6242 3758 641 58 ' 3 821 7173 605 0480 .68 669 6693 7.50 330T 607 57 4 843 7585 6.85 59G 0442 .65 700 7143 2857 678 56 5 876 7996 688 0403 782 7593 2407 539 55 6 404 8407 6.83 679 0364 764 8043 7.48 1957 506 54 1 482 8817 671 0325 796 8492 1508 472 53 8 460 9227 562 0,286 828 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 .96 545 9.98 0208 .65 .30 891 9.48 9838 7.47 0.51 0162 3.2871 50 11 648 0455 6.80 586 0169 923 9.49 0286 7.45 0.50 9714 888 49 12 571 0863 628 0130 955 0733 9267 805 48 13 599 1271 619 0091 987 1180 8820 272 47 14 626 1679 fi.78 611 0052 .67 .81 019 1627 7.48 8373 238 46 15 654 2086 6.77 602 0012 .65 051 2073 7927 205 45 16 682 2492 498 9.97 9973 088 25'19 7481 172 44 n 710 2898 485 9934 115 2965 7.42 7035 139 43 18 787 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 .29 798 9.47 4115 6.78 .95 459 9.97 9816 .67 .81 210 9.49 4299 7.40 0.50 5701 3.2041 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 8.1975 38 23 876 5327 6.72 488 9697 .65 806 5630 7.38 4370 943 37 24 904 5730 424 9658 .67 888 6073 7.87 3927 910 36 25 932 6133 415 9618 .65 870 6515 3485 878 35 26 960 6536 6.70 407 9579 .67 ■ 402 6957 3043 845 34 27 987 6938 398 9539 484 7399 2601 818 33 28 .30 015 7340 6.68 889 9499 466 7841 7.86 2159 780 32 29 043 7741 880 9459 .65 498 8282 7.83 1718 748 31 30 .80 071 9.47 8142 6.67 .95 872 9.97 9420 .67 .81680 9.49 8722 7.85 0.50 1278 8.1716 30 31 098 8542 868 9380 562 9163 7.83 0837 684 29 32 126 8942 854 9340 594 9603 7.32 0397 652 28 33 154 9342 6.65 816 9300 626 9.50 0042 0.49 9958 620 27 34 182 9741 837 9260 653 0481 9519 588 26 35 209 9.48 0140 328 9220 690 0920 9080 556 25 36 237 0539 6.68 819 9180 722 1359 7.80 8641 624 24 37 265 0937 6.62 810 9140 754 1797 8203 492 23 38 292 1334 801 9100 .68 786 2235 7.28 7765 460 22 39 820 1731 293 9059 .67 818 2672 7328 429 21 40 .30 848 9.48 2128 6.62 .95 284 9.97 9019 .67 .81 860 9.50 3109 7.28 0.49 6891 3.1897 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 308 17 44 459 3712 6.58 248 8858 .68 978 4854 7.25 5146 271 16 45 486 4107 6.67 240 8817 .67 .32 010 5289 4711 240 15 46 514 4501 231 8777 042 5724 4276 209 14 47 642 4895 222 8737 .68 074 6159 7.28 3841 178 13 48 570 5289 6.55 218 8696 106 6593 3407 146 12 49 597 5682 204 8655 .67 139 7027 7.22 2973 115 11 50 .30 626 9.48 6075 6.58 .96 195 9.97 8615 .68 .32 171 9.50 7460 7.22 0.49 2540 3.1084 10 51 653 6467 6.55 186 8574 203 7893 2107 058 9 52 680 6860 6.52 177 8533 .67 286 8326 , 1674 022 8 53 708 7251 6.68 168 8493 .68 267. 8759 7.20 1241 8.0991 7 54 786 7643 6.52 169 8452 299 9191 7.18 0809 961 6 55 768 8084 6.50 160 8411 881 9622 7.20 0378 930 5 56 791 8424 142 8370 368 9.51 0054 7.18 0.48 9946 899 4 57 819 8814 188 8329 896 0485 9515 863 3 58 846 9204 6.48 124 8288 428 0916 7.17 9084 888 2 59 874 9593 116 8247 460 1346 8654 807 1 60 .80 902 . 9.48 9982 .96 106 ' 9.97 8206 • :82 492 9.5i 1776 0.48 8224 8.0777 107° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 72° COSINEB. Sines. _ 78 Vn. TRIGONOMETRIC FUNCTIONS. 18° Sixes. COSUiKS. Tasgknts. Dif. COTABOEHTO. 161° Nat Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .30 902 9.48 9982 G.4S .95 106 9.97 8206 .68 .32 492 9.51 1776 7.17 0.48 8224 8.0777 60' 1 929 9.49 0371 6.47 097 8165 524 2206 7.16 7794 746 59. 2 957 0759 088 8124 656 2635 7365 716 58 3 985 1147 079 8083 588 3064 6936 686 57 4 .81 012 1535 6.46 070 8042 621 3493 7.18 6507 655 56 5 040 1922 6.43 061 8001 .70 663 3921 6079 625 55 6 068 2308 6.45 052 7959 .68 686 4349 5651 595 54 7 095 2695 6.48 048 7918 717 4777 7.12 5223 566 53 8 123 3081 6.42 038 7877 .70 749 5204 4796 635 52 9 161 3466 024 7835 .68 782 5631 7.10 4369 606 51 10 .81 178 9.49 3851 6.42 .96 015 9.97 7794 .70 .32 814 9.51 6057 7.12 0.48 3943 8.0476 50 11 206 4236 006 7752 .68 846 6484 7.10 3516 446 49 12 ■> 283 '4621 6.40 .94 997 7711 .70 878 6910 7.08 3090 415 48 13 261 5005 6.88 988 7669 .68 911 7335 7.10 2665 888 47 14 289 538'8 6.40 979 7628 .70 943 7761 7.08 2239 856 46 15 816 5772 6.37 970 7586 975 8186 7.07 1814 826 45 16 844 6154 6.38 "961 7544 .68 .88 007 8610 1390 296 44 n 872 6537 6.87 952 7503 .70 040 9034 0966 267 43 18 399 6919 948 7461 072 9458 0542 287 42 . 19 427 7301 6.85 938 7419 104 9882 7.05 0118 208 41 20 .31454 9.49 7682 6.87 .94 924 9.97 7377 .70 .33136 9.52 0305 7.05 0.47 9695 8.0178 40 21 482 8064 6.33 916 7335 169 0728 9272 149 39 22 610 8444 6.86 906 7293 201 1151 7.08 8849 120 38 23 687 8825 6.82 897 7251 288 1573 8427 090 37 24 665 9204 6.33 888 7209 266 1995 8005 061 36 25 593 9584 6.82 878 7167 298 2417 7.02 7583 082 35 26 620 9963 869 7125 330 • — 2838 7162 003 34 27 648 9.50 0342 860 7083 363 3259 6741 2.9974 33 28 676 0721 6.80 851 7041 896 3680 7.00 6320 945 32 29 708 1099 6.28 842 6999 427 4100 5900 916 31 30 .31 780 9.50 1476 6.80 .94 882 9.97 6957 .72 .38 460 9.52 4520 7.00 0.47 5480 2.9887 30 31 768 1854 6.28 823 6914 .70 492 4940 6.98 5060 868 29 32 ;«6 2231 6.27 814 6872 624 5359 4641 829 28 33 818 2607 6.28 805 6830 .72 657 5778 4222 800 27 34 841 2984 6.27 795 6787 .70 689 6197 6.97 3803 772 26 35 868 3360 6.25 786 6745 .72 621 6615 3385 743 26 36 896 3735 777 6702 .70 654 7033 2967 714 24 37 923 4110 768 6660 .72 ' 686 7451 6.96 2549 686 23 38 961 4485 768 6617 718 7868 2132 657 22 39 979 4860 6.28 749 6574 .70 751 8285 1715 629 21 40 .82 006 9.50 5234 6.23 .94 740 9.97 6532 .72 .83 783 9.52 8702 6.95 0.47 1298 2.9600 20 41 034 5608 6.22 780 6489 816 9119 6.98 0881 672 19 42 061 5981 721 6446 .70 848 9535 0465 544 18 43 089 6354 712 6404 .72 881 9951 6.92 0049 615 17 44 116 6727 6.20 702 6361 913 9.53 0366 0.46 9634 487 16 45 144 7099 698 6318 945 0781 9219 459* 15 46 171 7471 684 6275 978 1196 8804 431 14 47 199 7843 6.18 674 6232 .84 010 1611 6.90 8389 408 13 48 227 8214 665 6189 043 2025 7975 875 12 49 254 8585 666 6146 075 2439 7561 847 11 50 .82 282 9.50 8956 6.17 .94 646 9.97 6103 .72 .84108 9.53 2853 6.88 0.46 7147 2.9819 10 • 51 809 9326 687 6060 140 3266 6734 291 9 52 337 9696 6.15 627 6017 178 3679 6321 263 8 53 864 9.510065 618 5974 .73 205 4092 6.87 5908 236 7 54 392 0434 609 5930 .72 238 4504 5496 208 6 55 419 0803 699 5887 270 4916 5084 180 5 56 447 1172 6.13 690 5844 .73 303 5328 6.86 4672 162 4 57 474 1540 6.12 680 5800 .72 836 5739 4261 125 3 58 602 1907 6.18 571 5757 368 6150 3850 097 2' 59 629- 2275 6.12 561 5714 .78 400 6561 3439 070 1 60 .82 657 9.51 2642 .94 552 9.97 5670 .34 438 9.53 6972 0.46 3028 2.9042 108° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. COTANGBNTO. Dif. Log. Nat. Tangents. 71° Cosines. SiKES. YJl. TRIGONOMETRIC FUNCTIONS. 79 r "T.-^" s 19° Sines. Cosines. TiKQENTS. Cotangents. 160° Nat.- Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .32 55T 9.512642 6.12 .94 662 9.97 5670 .72 .84483 9.53 6972 6.88 0.46 3028 2.9042 60' 1 584 3009 6.10 642 6627 .78 465 7382 2618 015 59 2 • 612 3375 538 5583 498 7792 2208 2.8987 58 3 689 3741 528 5539 .72 530 8202 6.82 1798 960 57 4 667 4107 6.08 514 5496 .78 668 8611 1389 938 56 5 694 4472 504 5452 696 9020 0980 905 65 6 722 4837 495 5408 .72 628 9429 6.80 0571 878 54 1 749 5202 6.07 485 5365 .78 661 9837 0163 851 53 8 777 5566 476 5321 693 9.64 0245 0.45 9755 824 52 9 804 5930 466 5277 726 0653 9,347 797 51 10 .32 882 9.51 6294 6.06 .94 457 9.97 5233 .78 .84 768 9.54 1061 6.78 0.45 8939 2.8770 50 11 869 6657 447 5189 791 1468 8532 748 49 12 887 7020 6.03 488 5145 824 1875 6.77 8125 716 48 13 914 ^ 7382 6.06 428 5101 866 2281 6.78 7719 689 47 14 ' 942 7745 6.08 418 5057 889 2688 6.77 7312 662 46 15 969 8107 6.02 409 5013 922 3094 6.75 6906 686 45 16 997 8468 899 4969 954 3499 6.77 6501 609 44 IT .33 024 8829 890 4925 .75 987 3905 6.75 6095 582 43 18 051 9190 880 4880 .78 .85 020 4310 5690 656 42 19 079 9551 6.00 870 4836 052 4715 6.78 5285 629 41 20 .88106 9.51 9911 6.00 .94 861 9.97 4792 .73 .85 085 9.54 5119 6.76 0.45 4881 '2.8502' 40 21 134 9.52 0271 851 4748 .75 118 5524 6.78 4476 476 39 22 161 0631 5.98 842 4703 .78 150 5928 6.72 4072 449 38 23 189 0990 882 4659 .76 188 6331 6.78 3669 428 37 24 216 1349 5.97 822 4614 .78 216 6735 6.72 3265 897 36 25 244 1707 5.98 818 4570 .75 248 7138 6.70 2862 870 35 26 271 2066 5.97 303 • 4525 .78 281 7540 6.72 2460 344 U 27 298 2424 595 2781 •298 4481 .75 814 7943 6.70 2057 318 33 28 826 284 4436 846 8345 1655 291 32 29 858 3138 274 4391 .73 879 8747 1253 266 31 30 .83 881 9.52 3495 5.95 .94 264 9.97 4347 .76 .85 412 9.54 9149 6.68 0.45 0851 2.8239 30 31 408 3852 8.93 254 4302 445 9550 0450 218 29 32 486 4208 246 4257 477 9951 0049 187 28 33 463 4564 285 4212 510 9.55 0352 6.67 0.44 9648 161 27 34 490 4920 5.92 225 4167 548 0752 6.68 9248 186 26 35 518 5275 215 4122 676 1153 6.65 8847 109 25 36 546 5630 6.90 206 4077 608 1552 6.67 8448 083 24 37 573 5984 5.92 196 4032 641 1952 6.66 8048 057 23 38 600 6339 5.90 186 3987 674 2351 7649 082 22 39 627 6693 6.88 176 3942 707 2750 7250 006 ■21 40 .83 655 9.52 7046 6.90 .94 167 9.97 3897 .76 .35 740 9.55 3149 6.65 0.44 6851 2.7980 20 41 682 7400 5.88 157 3852 772 3548 0.68 6452 956 19 42 710 7753 5.87 147 3807 .77 805 3946 6054 929 18 43 787 8105 5.88 187 3761 .75 888 4344 6.62 5656 908 17 44 764 8458 6.87 127 3716 871 4741 6.63 5259 878 16 45 792 8810 6.86 118 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 6.86 098 3580 969 -5933 6.60 4067 801 13 48 874 9864 088 3535 .77 .86 002 6329 3671 776 12 49 901 9.53 0215 5.83 ^ 078 3489 .75 085 6725 3275 751 11 50 .38 929 9.53 0565 5.83 .94 068 9.97 3444 .77 .36 068 9.56 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 .75 134 7913 6.58 2087 675 8 53 .34 Oil 1614 089 3307 .77 167 8308 1692 650 7 54 038 1963 029 3261 199 8703 6.57 1297 625 6 55 065 2312 019 3215 282 9097 0903 600 5 56 098 2661 5.80 009 3169 .75 266 9491 0509 575 4 57 .120 3009 .98 999 3124 .77 298 9885 0115 550 3 58 147 3357 5.78 989 3078 881 9.66 0279 0.43 9721 525 2 59 175 3704 6.80 979 3032 864 0673 6.55 9327 500 1 60 .34 202 9.53 4052 .93 969 9.97 2986 .86 397 9.56 1066 0.43 8934 2.7475 109° Nat. Log; Dif. 1 Nat. Log. Dif. Nat. Log. Dif. ■COTANSENTS. Log. Nat. 70° COSIHES. Sinks. Tangents. 1 80 VH. TRIGONOMETRIC FUNCTIONS. . — J 20° Sinks. Cosines. Tasokkts. Dlf. COTANOENIB. 159° Nat. Log. Dlf. Nat. Log. Dlf. Nat. Log. Log. Nat. 0' .84 202 9.53 4052 6.78 .93 969 9.97 2986 .77 .86 897 9.56 1066 6.66 0.43 8934 2.7476 60' 1 229 4399 5.77 959 2940 480 1459 6.68 8541 460 69 2 267 4745 8.78 949 2894 468 1851 6.65 8149 425 58 3 2*4 5092 5.77 989 2848 496 2244 6.53 7756 400 57 4 811 5438 8.75 929 2802 .78 529 2636 7364 876 56 5 889 5783 6.77 919 2755 .77 662 3028 6.62 6972 861 55 6 866 6129 5.76 909 2709 595 3419 6.53 6581 826 54 7 898 6474 6.78 899 2663 628 3811 6.82 6189 802 53 8 421 6818 6.78 889 2617 .78 661 4202 5798 277 52 9 448 7163 6.78 879 2570 .77 694 4593 6.60 5407 268 51 10 .84 476 9.53 7507 6.73 .98 869 9.97 2524 .77 .86 727 9.56 4983 6.60 0.43 5017 2.7228 50 11 608 7851 5.72 889 2478 .78 760 5373 4627 204 49 12 680 8194 5.78 849 2431 .77 798 5763 4237 179 48 13 687 8538 6.70 889 2385 .78 826 6153 6.48 3847 165 47 14 684 8880 5.72 829 2338 869 6542 6.80 3458 180 46 15 612 9223 6.70 819 2291 .77 892 6932 6.47 3068 106 45 16 689 9565 809 2245 .78 926 7320 6.48 2680 082 44 17 666 9907 799 2198 988 7709 2291 068 43 18 694 9.54 0249 6.68 789 2151 .77 991 8098 6.47 1902 084 42 19 721 0590 779 2105 .78 .87 024 8486 6.48 1514 009 41. 20 .84 748 9.54 0931 8.68 .93 769 9.97 2058 .78 .87 087 9.56 8873 6.47 0.43 1127 2.6985 40 21 775 1272 789 2011 090 9261 6.48 0739 961 39 22 808 1613 8.67 748 1964 128 9648 0352 987 38 23 880 , 1953 788 1917 167 9.57 0035 0.42 9965 918 37 24 887 2293 6.68 728 1870 190 0422 9678 889 36 25 884 2632 718 1823 228 0809 6.43 9191 865 35 26 912 2971 708 1776 2S6 1195 8805 841 34 27 989 3310 698' 1729 289 1581 8419 818 33 28 966 3649 6.68 638 1682 S?2 1967 6.42 8033 794 32 29 998 3987 677 1635 386 2352 6.48 7648 770 31 30 .85 021 9.54 4325 8.68 .98 667 9.97 1588 .80 .87 888 9.57 2738 6.42 0.42 7262 2.6746 30 31 048 4663 5.62 667 1540 .78 422 3123 6.40 6877 728 29 32 076 5000 8.63 647 1493 465' 3507 6.42 6493 699 28 33 102 5338 8.60 687 1446 .80 488 3892 6.40 6108 676 27 34 180 5674 6.62 626 1398 .78 621 4276 5724 652 26 35 157 6011 8.60 616 1351 .80 684., 4660 ^ 5340 628 25 36 184 6347 606 1303 .78 688 5044 6.88 " 4956 608 24 37 211 6683 596 1256 .80 621 5427 4573 681 23 38 289 7019 8.68 585 ' 1208 .78 664 5810 4190 663 22 39 266 7354 678 1161 .80 687 6193 3807 684 21 40 .38 293 9.54 7689 8.88 .98 866 9.97 1113 .78 .87 720 9.57 6576 6.88 0.42 3424 2.6511 20 41 320 8024 568 1066 .80 754 6959 6.87 3041 488 19 42 847 8359 8.87 544 1018 787 7341 2659 464 18 43 878 • 8693 584 0970 820 7723 6.88 2277 441 17 44 402 9027 8.88 524 0922 868 8104 6.87 1896 418 16 45 429 9360 614 0874 .78 887 8486 6.88 1614 895 15 46 456 9693 503 0827 .80 • 920 8867 1133 871 14 47 484 9.55 0026 498 0779 963 9248 0762 348 13 48 811 0359 488 0731 986 9629 6.88 0371 825 12 49 588 0692 8.63 472 0683 .88 020 9.68 0009 0.41 9991 802 11 50 .36 668 9.55 1024 8.58 .93 462 9.97 0635 .82 .88 053 9.58 0389 6.88 0.419611 2.6279 10 51 892 1356 6.62 452 0586 .80 086 0769 9231 266 9 52 619 1687 441 0638 120 1149 6.82 8851 288 8 53 647 2018 481 0490 158 1528 8472 . 210 7 54 674 2349 420 0442 186 1907 8093 187 6 , 55 701 2680 6.80 410 0394 .82 220 2286 7714 165 6 56 728 3010 6.52 400 0345 .80 268 2666 7335 142 4 57 758 3341 8.48 889 0297 N 286 3044 6.80 6956 119 3 58 782 3670 8.80 379 0249 .82 820 3422 6578 096 2 59 810 4000 8.48 868 0200 .80 868 3800 6.28 6200 074 1 60 .86 887 9.55 4329 .93 868 9.97 0152 .88 886 9.58 4177 0.41 5823 2.6061 110° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. CoTAKSEK-re. Dif. Log. Nat. Tangents. 69° COSIMEB. Sines. 1 VII. TEIGONOMETKIC FUNCTION'S. 81 21° SiHES. Cosines. Tangents. COTAN&ENTS. 158° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .85 837 9.55 4329 5.48 .98 358 9.97 0152 .82 .88 886 9.58 4177 6.30 0.41 5823 2.6051 60' 1 864 4658 348 0103 .80 420 4555 6.28 5445 028 59 2 891 4987 5.47 887 0055 .82 453 4932 5068 006 58 3 918 5315 827 0006 487 5309 4691 2.6988 57 4 945 5643 816 9.96 9957 .80 520 5686 6.27 4314 961 56 5 973 5971 806 9909 .82 558 6062 6.28 3938 988 55 6 .86 000 6299 5.45 296 9860 587 6439 6.27 3561 916 54 7 027 6626 286 9811 620 6815 6.25 3185 893 53 8 054 6953 274 9762 .80 654 7190 6.27 '2?T7r 871 52 9 081 7280 5.48 264 9714 .82 687 7566 6.25 2434 848 51 10 .36 108 9.55 7606 5.48 .93 258 9.96 9665 .82 .88 721 9.58 7941 6.26 0.41 2059 2.6826 50 11 135 7932 243 9616 754 8316 1684 804 49 12 162 8258 5.42 282 9567 787 8691 1309 782 48 13 190 8583 5.48 222 9518 821 9066 6.28 0934 759 47 14 217 8909 5.42 211 9469 854 9440 0560 737 46 15 244 9234 5.40 201 9420 .83 888 9814 0186 715 45 16 271 9558 6.42 190 9370 .82 921 9.59 0188 0.40 9812 693 44 17 298 9883 6.40 180 9321 955 0562 6.22 9438 071 43 18 325 9.56 0207 169 9272 988 0935 9065 649 42 19 352 0531 159 9223 .83 .39 022 1308 8692 627 41 20 .86 879 9.56 0855 5.88 .93 148 9.96 9173 .82 .89 065 9.59 1681 6.22 0.40 8319 2.6605 40 21 406 1178 187 9124 089 2054 6.20 7946 583 39 22 484 1501 127 9075 .83 122 2426 6.22 7574 561 38 23 461 1824 5.37 116 9025 .82 156 2799 6.20 7201 689 37 24 488 2146 106 8976 .88 190 3171 6.18 6829 617 36 25 515 2468 095 8926 .82 223 3542 6.20 6458 495 35 26 542 2790 084 8877 .fe8 257 3914 6.18 6086 478 34 27 569 3112 5.85 074 8827 290 4285 5715 462 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 .86 650 9.56 4075 5.85 .93 042 9.96 8678 .83 .39 891 9.59 5398 6.17 0.40 4602 2.5886 30 31 677 4396 5.88 081 8628 425 5768 4232 365 29 32 704 4716 020 8578 458 6138 .3862 843 28 33 731 5036 010 8528 ..82 492 6508 3492 822 27 34 758 5356 .92 999- 8479 .88 526 6878 6.16 3-122 300 26 35 • 785 5676 5.82 988 8429 569 7247 2753 279 25 36 812 5995. 978 8379 593 7616 2384 257 24 37. 889 6314 5.30 967 8329 .85 626 7985 2015 236 23 38 867 6632 5.32 956 8278 .88 660 8354 6.13 1646 214 22 39 894 6951 6.80 945 8228 694 8722 6.15 1278 193 21 40 .86 921 9.56 7269 6.80 .92 935 9.96 8178 .83 .89 727 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 5.80 913 8078 .85 795 9827 6.12 " -0173 129 18 43 .37 002 8222 5.28 902 8027 .88 829 9.60 0194 6.18 0.39 9806 108 17 44 029 8539 892 7977 862 0562 6.12 9438 086 16 45 056 8856 6.27 881 7927 .85 896 0929 9071 065 15 46 088 9172 870 7876 .88 980 1296 8704 044 14 47 110 9488 859 7826 .86 968 1663 6.10 8337 028 13 48 187 9804 849 7775 .83 997 2029 7971 002 12 49 164 9.57 0120 6.25 838 7725 .88 .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 7239 2.4960 10 51 218 0751 5.26 816 7624 .85 098 3127 6873 939 9 52 245 1066 5.28 805 '7573 132 3493 6.08 6507 918 8 53 272 1380 5.25 794 7522 166 3858 6142 897 7 54 299 1695 5.28 784 7471 .83 200 4223 5777 876 6 , 55 326 2009 778 7421 .85 234 4588 5412 855 5 56 853 2323 5.22 762 7370 267 4953 6.07 5047 834 4 57 380 2636 5.28 751 7319 801 5317 6.08 4683 813 3 58 407 2950 6.22 740 7268 885 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 .40 408 9.60 6410 0.39 3590 2.4751 111° Nat. Log. Dif. Nat Log. Dif. Nat. Log. Dif. Log. Nat. Tangents. 68° Cosines. Sines. COTAHSENTS. 82 VII. TRIGONOMETRIC FUNCTIONS. 22° SlHKB. Cosnras. Takqbnts. COTANSEHTS. 157° Nat. Jvog. Dlf. Nat. Log. Dif. Nat Log. Dlf. Log. Nat. 0' .87 461 9 51 3515 5.22 .92 718 9.96 1166 .85 .40 408 9.60 6410 6.05 0.39 3690 2.4751 60' 1 4SS 3888 6.20 707 7115 486 .6113 6.07 3227 780 69 2 515 4200 697 1064 470 7131 6.05 2863 709 68 3 M2 4612 686 1013 .87 504 1500 2600 689 67 4 S69 4824 676 6961 .85 588 1863 6.08 2137 668 66 5 695 5136 6.18 664 6910 572 8225 6.06 1115 648 65 6 622 5441 653 6859 ■■ 606 8588 6.08 1412 627 54 1 649 5158 642 6808 .87 640 8950 1060 606 63 8 676 6069 6.17 681 6156 .85 674 9312 0688 636 52 9 708 6319 620 6105 .87 707 9614 0326 666 51 10 .87 780 9.51 6689 6.17 .92 609 9.96 6653 .35 .40 741 9.610036 6.02 0.38 9964 2.4546 50 11 757 6999 698 6602 .87 776 0391 6.08 9603 525 49 12 784 1309 6.15 687 6550 .86 309 0159 6.02 9241 504 48 13 811 1618 676 6499 .87 348 1120 6.00 8880 484 41 14 883 1921 666 6441 377 1480 6.02 8520 464 46 15 865 8236 664 6395 .35 911 1841 6.00 8159 448 46 16 892 8545 5.18 543 6344 .87 945 2201 1199 428 44 11 T19 8853 6.15 • 682 6292 979 2561 1439 408 43 18 946 9162 6.18 621 6240 .41013 2921 1019 888 42 19 978 9410 6.12 610 6188 047 3281 6119 862 41 20 .87 999 9.51 9111 6.18 .92 499 9.96 6136 .35 .41 081 9.61 3641 5.98 0.38 6359 2.4842 40 21 .88 026 9.58 0085 6.12 438 6085 .87 115 4000 6000 822 39 22 088 0392 477 6033 149 4359 5641 802 38 23 080 0699 5.10 466 5981 138 4118 5282 232 31 24 107 1005 6.12 465 5929 .88 217 5011 6.97 4923 262 36 25 184 1312 6.10 444 5816 .87 261 5435 4565 ?42 35 26 161 1618 482 5824 285 6193 4201 222 34 2t 188 1924 6.08 421 5112 819 6151 ■ 3849 202 33 28 215 2229 6.10 410 5120 858 6509 3491 182 32 29 241 2535 6.03 '899 5668 .88 887 6861 6.95 3133 162 31 30 .88 263 9.58 2840 6.08 .92 888 9.96 5615 .37 .41421 9.61 1224 5.97 0.38 2116 2.4142 30 31 295 3145 6.07 377 5563 455 1582 5.95 2418 122 29 32 822 3449 6.08 866 5511 .83 490 1939 6.93 2061 102 28 33 349 3154 5.07 865 5458 .87 624 8295 6.95 1105 088 21 34 876 4058 6.05 848 5406 .88 658 8652 6.93 1348 068 26 35 408 4361 6.07 382 5353 .37 592 9008 0992 043 25 36 480 4665 5.06 821 5301 .88 626 9364 0636 028 24 31 456 4968 5.07 810 5248 660 9120 0280 004 23 38 483 5212 5.08 299 5195 .87 694 9.62 0016 0.31 9924 2.8984 22 39 510 5514 6.05 237 5143 .88 723 0432 5.92 9568 964 21 40 .88 687 9.58 5811 6.03 .92 276 9.96 5090 .88 .41 768 9.62 0181 6.92 0.31 9213 2.8946 : 20 41 664 6119 6.06 265 5031 797 1142 8858 925 ■ 19 42 691 6482 6.02 264 4984 331 1491 8503 906 '■ 18 43 617- 6183 5.08 248 4931 .87 866 1852 8148 336 11 44 644 1085 6.02 231 4819 .38 399 2201 6.90 7193 867 16 45 671 1386 5.03 220 4826 933 2561 1439 847 16 46 693 1688 6.02 209 4113 968 2916 1086 823 14 41 725 1989 5.00 198 4120 .90 .42 002 3269 6731 808 13 48 752 8289 5.02 186 4666 .38 036 3623 5.33 6311 789 12 49 778 8590 5.00 176 4613 070 3916 6.90 6024 770 11 50 .38 305 9.58 8890 6.00 .92 164 9.96 4560 .38 .42 105 9.62 4330 6.38 0.31 6610 2.3750 10 51 832 9190 4.98 162 4501 139 4683 6311 131 9 52 359 9489 6.00 141 4454 .90 178 5036 6.87 4964 712 8 53 886 9189 4.98 130 4400 .38 207 5388 6.88 4612 693 1 54 912 9.59 0088 119 4341 242 6141 ■ 6.87 4259 673 6 55 989 0381 107 4294 .90 276 6093 ' 3901 654 5 56 966 0686 4.97 096 4240 .38 810 6445 3655 685 4 51 993 0984 085 4187 .90 845 6197 3203 616 3 58 .89 020 1282 073 4133 .83 879 1149 2851 597 2 59 046 1580 062 4080 .90 418 1601 5.85 2499 578 1 60 .89 078 9.59 1818 .92 060 9.96 4026 .42 447 9.62 1852 0.31 2148 2.8559 112° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Dlf. Cotangents. Log; Nat. Tangents. 67° Cosines. SOTES. Yll. TRIGONOMETRIC FUNCTIONS. 83 23° Sines. Cosines. Tangents. ^ Cotangents. 156° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .89 078 9.59 1878 4.97 .92 060 9.96 4026 90 .42 447 9.62 7852 6.85 0.37 2148 2.3559 60' 1 100 2176 4.95 089 3972 88 482 8203 1797 539 59 2 127 2473 028 3919 90 516 8554 144^ 520 58 3 153 2770 016 3865 551 8905 6.88 1095 501 57 4 180 3067 4.98 006 3811 585 9255 6.85 0745 483 56 5 207 3363 .91 994 3757 88 619 9606 5.83 0394 464 55 6 234 3659 982 3704 90 664 9956 0044 446 .54 7 260 3955 971 3650 688 9.63 0306 0.36 9694 426 53 8 287 4251 969 3596 722 0656 5.82 9344 407 52 9 314 4547 4.92 948 3542 757 1005 6.83 8995 888 51 10 .39 841 9.59 4842 4.92 .91 936 9.96 3488 90 .42 791 9.63 1355 5.82 0.36 8645 2.8869 50 11 367 5137 925 3434 92 826 1704 8296 351 49 12 894 5432 914 3379 90 860 2053 7947 832 48 13 421 5727 4.90 902 •3325 894- 2402 5.80 7598 818 47 14 448 6021 891 3271 929 2750 6.82 7250 294 46 15 474 6315 879 3217 968 3099 6.80 6901 276 45 16 501 6609 868 3163 92 998 3447 6553 257 44 n 628 6903 4.88 866 3108 90 .48 032 3795 6205 238 43 18 555 7196 4.90 845 3054 92 067 4143 6.78 5857 220 42 19 681 7490 4.88 833 2999 90 101 4490 6.80 5510 201 41 20 .89 608 9.59 7783 4.87 .91 822 9.96 2945 92 .48 136 9.63 4838 6.78 0.36 5162 2.8183 40 21 685 8075 4.88 810 2890 90 170 5185 4815 ' 164 39 22 661 8368 4.87 799 2836 92 206 5532 4468 146 38 23 688 8660 787 2781 90 289 5879 4121 127 37 24 716 8952 776 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 848 6919 5.77 3081 072 34 27 796 9827 741 2562 90 878 7265 2735 053 33 28 822 9.60 0118 729 2508 92 412 7611 5.76 2389 085 32 29 848 0409 718 2453 447 7956 5.77 2044 017 31 30 .89 876 9.60 0700 4.83 .91 706 9.96 2398 92 .48 481 9.63 8302 5.75 0.36 1698 2.2998 ' 30 31 902 0990 694 2343 616 8647 1353 980 29 32 928 L280 688 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 5.78 0.35 9973 907 25 36 085 2439 686 2067 92 689, 0371 5.75 9629 889 24 37 062 2728 625 2012 724 0716 5.73 9284 871 23 38 088 3017 4.80 618 1957 758 1060 8940 868 22 39 116 3305 4.82 601 1902 98 793 1404 6.72 8596 885 21 40 .40 141 9.60 3594 4.80 .91 590 9.96 1846 92 .43 828 9.64 1747 5.78 0.35 8253 2.2817 20 41 168 3882 578 1791 93 862 2091 5.72 7909 799 19 42 196 4170 4.78 566 1735 92 897 2434 7566 781 18 43 221 4457 4.80 556 1680t 98 982 2777: 7223 , 763 17 44 248 4745 4.78 643 1624 92 966 3120, 6880 745 16 45 276 5032 681 1569 98 .44 001 3463: 6537 727 15 46 301 5319 519 1513 92 036 3806 6.70 6194 709 14 47 828 5606 4.77 508 1458 98 071 4148; 5852 691 13 48 356 5892 4.78 496 1402- 105 4490 5510 678 12 49 881 6179 4.77 484 1346 140 4832 5168 666 11 50 .40 408 9.60 6465 4.77 .91 472 9.96 1290 92 .44175 9.64 5174 6.70 0.35 4826 2.2687 10 51 484 6751 4.75 461 1235 98 210 5516 5.68 4484 620 9 52 . 461 7036 4.77 449 1179 244 5857; 6.70 4143 602 8 53 488 7322 4.76 487 1123 279 '6199 5.68 3801 684 7 54 614 7607 425 1067 814 65401 3460 566 6 55 641 7892 414 1011 349 6881' 3119 549 5 56 567 8177 4.78 402 0955 884 7222 5.67 2778 681 4 57 594 8461 390 0899 418 7562, 5.68 , 2438 518 3 58 621 8745 878 0843> 95 453 7903. 5.67 2097 496 2 59 647 9029 366 0786 98 488 8243, 1757 478 1 60 .40 674 9.60 9313 .91 855 9.9G0730 .44 623 9.64 8583 0.35 1417 2.2460 113° Nat. Log. Dif. Nat. Log. D if. Nat. Log. Dif. Log. Nat. Tangunts. 66° Cosines. Sines. Cotangents. 84 Vn. TRIGONOMETRIC FUNCTIONS. 24° Srass. COSIHKS. Tahqentb. Ootahokhts. 155° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .40 674 9.60 9313 4.78 .91858 9.96 0730 .93 .44828 9.64 8583 6.67 0.35 1417 2.2460 60' 1 700 9597 4.72 848 0674 858 8923 1077 448 59 2 72T 9880 4.78 881 0618 .96 698 9263 8.68 0737 426 58 3 768 9.61 0164 4.72 819 0561 .98 627 9602 6.67 0398 408 57 4 780 0447 4.70 807 0505 .95 662 9942 6.65 0058 890 66 5 806 0729 4.72 295 0448 .98 697 9.65 0281 0.34 9719 878 65 6 883 1012 4.70 283 0392 .96 782 0620 9380 866 54 7 860 1294 272 0335 .98 767 0959 6.68 9041 888 53 8 886 1576 260 0279 .95 802 1297 5.66 8703 820 52 9 918 1858 243 0222 837 1636 5.63 8364 808 51 10 .40 989 9.61 2140 4.68 .91286 9.96 0165 .98 .44 872 9.65 1974 5.68 0.34 8026 2.2286 60 11 966 2421 224 010« .96 907 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 284 47 14 045 3264 188 9938 .98 .45 012 3326 6.62 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 n 125 4105 152 9768 117 4337 5663 165 43 18 151 4385 140 9711 152 4674 5326 148 42 19 178 4665 4.66 128 9654 .97 187 5011 4989 180 41 20 .41204 9.614944 4.65 .91 116 9.95 9596 .96 .45 222 9.65 5348 6.60 0.34 4652 2.2118 40 21 281 "5223 104 9539 287 5684 4316 096 39 22 257 6502 , 092 9482 292 6020 3980 079 38 23 284 5781 080 9425 327 6356 3644 062 37 24 810 6060 4.68 008 9368 .97 862 6692 3308 046 36 25 887 6338 056 9310 .96 397 7028 2972 028 35 26 868 6616 044 9253 .97 432 7364 8.88 2636 Oil 34 27 890 6894 082 9195 .95 467 7699 2301 2.1994 33 28 416 7172 020 9138 .97 602 8034 1966 977 32 29 448 7450 4.62 008 9080 .95 688 8369 1631 960 31 30 .41 469 9.61 7727 4.62 .90 996 9.95 9023 .97 .48 678 9.65 8704 6.58 0.34 1296 2.1948 30 31 496 8004 «84 8965 .96 608 9039 6.67 0961 926 29 32 S22 8281 972 8908 .97 648 9373 6.68 0627 909 28 33 B49 8558 4.60 960 8850 678 9708 5.87 0292 892 27 34 678 8834 948 8792 718 9.66 0042 0.33 9958 876 26 35 602 9110 986 8734 .98 748 0376 9624 869 26 36 628 9386 924 8677 .97 784 0710 5.88 9290 842 24 37 666 9662 911 8619 819 1043 6.67 8967 828 23 38 681 9938- 4.58 899 8561 864 1377 6.85 8623 808 22 39 707 9.62 021? 887 8503 889 1710 8290 792 21 40 .41784 9.62 0488 4.68 .90 875 9.95 8445 .97 .46-924 9.66 2043 8.88 0.33 7957 2.1776 20 41 760 0763 868 8387 960 2376 7624 768 19 42 787 1038 861 8329 995 2709 7291 742 18 43 818 1313 4.67 889 8271 46 080 3042 6958 725 17 44 840 1587 826 8213 .98 066 3375 6.68 6625 708 16 45 866 1861 814 8154 .97 101 3707 6293 692 15 46 892 2135 802 8096 186 4039 5961 676 14 47 919 2409 4.66 790 8038 .98 171 4371 5629 669 13 48 946 2682 4.67 778 7979 .97 206 4703 5297 642 12 49 972 2956 4.86 766 7921 242 5035 5.52 4965 626 11 50 41998 9.62 3229 4.65 90 758 9.95 7863 .98 46 277 9.66 5366 6.68 0.33 4634 2.1609 10 51 42 024 3502 4.68 741 7804 .97 812 5698 6.62 4302 592 9 52 061 3774 4.58 729 7746 .98 848 6029 3971 676 8 53 077 4047 4.68 717 7687 388 6360 3640 560 7 54 104 4319 704 7628 .97 418 6691 6.80 3309 848 6 55 180 4591 692 7570 .98 464 7021 6.62 2979 627 6 56 1S6 4863 680 7511 489 7352 6.60 2648 610 4 57 188 5135 4.82 668 7452 525 7682 6.62 2318 494 3 58 209 5406 655 7393 .97 560 8013 6.60 1987 478 2 59 286 5677 643 7335 .98 696 8343 1657 461 1 60 42 262 9.62 5948 90 681 9.95 7276 46 681 9.66 8673 0.33 1327 2.1446 114° Nat Log. Dif. Nat. Log. Dif. 1 Nat. Log. Dif. Log. Nat. 65° CosniES. Sines. COTAWGENTB. TaNSESTO. Yn. TEIGOlSrOMETRIC FUNCTIONS. 85 • 25° Sinks. Cosines. Taboents. Dif. Cotangents. 154° Nat. Log. Dif. Nat. Log. Bif. Nat. Log. Log. Nat. 0' .42 262 9.62 5948 4.62 .90 681 9.95 7276 .98 .46 681 9.66 8673 6.48 0.33 1327 2.1445 60' 1 2S8 6219 618 7217 666 9002 5.50 0998 429 59 2 815 6490 4.50 606 7158 702 9332 5.48 0668 418 58 3 841 6J60 694 7099 787 9661 5.50 0339 896 57 4 867 7030 682 7040 772 9991 5.48 0009 880 56 5 894 7300 569 6981 1.00 808 9.67 0320 0.32 9680 864 55 6 420 7570 657 6921 .98 848 0649 5.47 9351 848 64 T . 446 7840 4.48 545 6862 879 0977 6.48 9023 832 53 8 478 8109 582 6803 914 1306 8694 815 52 9 499 8378 520 6744 1.00 960 1635 6.47 8365 299 51 10 .42 626 9.62 8647 4.48 .90 507 9.95 6684 .98 .46 985 9.67 1963 6.47 0.32 8037 2.1288 50 11 552 8916 495 6625 .47 021 2291 7709 267 49 12 678 9185 4.47 483 6566 1.00 056 2619 7381 251 48 13 604 9453 470 6506 .98 092 2947 6.45 7053 286 47 14 681 9721 468 ■6447 1.00 128 3274 6.47 6726 219 46 15 667 9989 446 6387 168 3602 5.45 6398 208 45 16 688 9.63 0257 4.45 488 6327 .98 199 3929 6.47 6071 187 44 n 709 0524 4.47 421 6268 1.00 234 4257 5.46 5743 171 43 18 786 0792 4.45 408 6208 270 4584 5416 155 42 19 762 1059 396 6148 .98 305 4911 5.48 5089 139 41 20 .42 788 9.63 1326 4.45 .90 383 9.95 6089 1.00 .47 841 9.67 5237 6.45 0.32 4763 2.1128 40 21 81S 1593 4.48 871 6029 377 5564 5.43 4436 107 39 22 841 1859 368 5969 412 5890 5.45 4110 092 38 23 867 2125 4.46 846 5909 448 6217 6.48 3783 076 37 24 894 2392 4.48 384 5849 483 6543 3457 060 36 25 920 2658 4.42 821 5789 519 6869 5.42 3131 044 35 26 946 2923 4.48 809 5729 565 7194 6.43 2806 028 34 27 972 3189 4.42 296 5669 690 7520 2480 018 33 28 999 3454 284 5609 1.02 626 7846 6.42 2154 2.0997 32 29 .48 025 3719 271 5548 1.00 662 8171 1829 981 31 30 .48 051 9.63 3984 4.42 .90 269 9.95 5488 1.00 .47 698 9.67 8496 5.42 0.32 1504 2.0965 30 31 077 4249 246 5428 783 8821 1179 950 29 32 104 4514 4.40 238 5368 1.02 769 9146 0854 934 28 33 180 4778 221 5307 1.00 806 9471 5.40 0529 918 27 34 166 5042 208 5247 1.02 840 9795 5.42 0205 908 26 35 182 5306 196 5186 1.00 876 9.68 0120 5.40 0.31 9880 887 25 36 209 5570 188 5126 1.02 912 0444 9556 872 24 37 285 5834 4.88 171 5065 1.00 948 0768 9232 866 23 38 261 6097 168 5005 1.02 984 1092 8908 840 22 39 287 6360 146 4944 .48 019 1416 8584 826 21 40 .43 818 9.63 6623 4.88 .90 133 9.95 4883 1.00 .48 055 9.68 1740 5.38 0.31 8260 2.0809 20 41 840 6886 4.87 120 4823 1.02 '091 2063 6.40 7937 794 19 42 866 7148 4.38 108 4762 127 2387 6.88 7613 778 18 43 892 7411 4.87 095 4701 168 2710 7290 763 17 44 418 7673 082 4640 198 3033 6967 748 16 45 445 7935 070 4579 284 3356 6644 732 15 46 471 8197 4.85 057 4518 270 3679 6.87 6321 717 14 47 497 8458 4.87 045 4457 306 4001 6.88 5999 701 13 48 628 8720 4.85 082 4396 842 4324 6.37 5676 686 12 49 549 8981 019 4335 878 4646 5354 671 11 50 .48 575 9.63 9242 4.85 .90 007 9.95 4274 1.02 .48 414 9.68 4968 5.37 0.315032 2.0665 10 51 602 9503 .89 994 4213 460 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 1.02 621 5934 5.85 4066 609 7 54 680 0284 956 4029 567 6255 6.87 3745 694 6 55 706 0544 948 3968 1.03 698 6577 6.85 3423 679 5 56 783 0804 930 3906 1.02 629 6898 3102 564 4 57 759 1064 918 3845 1.08 665 7219 2781 549 3 58 785 1324 4.32 905 3783 1.02 701 7540 2460 588 2 59 811 1583 892 3722 1.03 787 7861 2139 618 1 60 48 887 9.64 1842 89 879 9.95 3660 48 773 9.68 8182 0.31 1818 2.0603 115° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 64° Cosines. Sines. Cotangents. ^ Tangents. 1 J 86 Vn. TRIGONOMETRIC FUNCTIONS. 1 ' ' — 1 26° Snras. Cosrara. Tangents. COTANOENTS. 153° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .48 887 9.64 1842 4.82 .89 879 9.95 3660 1.02 .48 773 9.68 8182 6.88 0.31 1818 2.0508 60' 1 868 2101 867 3599 1.08 809 8502 6.86 1498 488 59 2 889 2360 4.80 864 3537 845 8823 6.83 1177 478 58 3 916 2618 4.82 841 3475 881 9143 ,0857 468 57 4 942 2877 4.80 828 3413 i.oa 917 9463 0537 448 66 5 968 3135 816 3352 1.08 953 9783 0217 428 65 6 994 3393 4.28 803 3290 989 9.69 0103 0.30 9897 413 64 1 .44 020 3650 4.80 790 3228 .49 026 0423 6.82 9577 898 63 8 046 3908 4.28 777 3166 062 0742 6.88 9258 883 52 9 072 4165 4.80 764 3104 098 1062 5.82 8938 868 61 10 .44 098 9.64 4423 4.28 .89 752 9.96 3042 1.08 .49 134 9.69 1381 5.82 0.30 8619 2.0868 50 11 124 4680 4.27 789 2980 170 1700 8300 888 49 12 181 4936 4.28 726 2918 1.06 206 2019 7981 828 48 13 177 5193 718 2855 1.03 242 2338 5.80 7662 808 47 14 208 5450 4.27 700 2793 278- 2656 5.82 7344 298 46 15 229 5706 687 2731 815 2975 5.80 7025 278 45 16 255 5962 674 2669 1.05 851 3293 6.82 6707 268 44 11 281 6218 662 2606 1.08 887 3612 5.80 6388 248 43 18 807 6474 4.25 649 2544 1.06 423 3930 6070 288 42 19 888 6729 636 2481 1.08 459 4248 6762 219 41 20 .44 859 9.64 6984 4.27 .89 623 9.95 2419 1.06 .49 495 9.69 4666 6.28 0.30 6434 2.0204 40 21 885 7240 4.28 610 2356 1.03 582 4883 6.80 5117 189 39 22 411 7494 4.25 697 2294 1.06 568 5201 6.28 4799 174 38 23 487 7749 684 2231 604 5518 5.80 4482 160 37 24 464 8004 4.28 571 2168 1.03 640 6836 6.28 4164 146 36 25 490 8258 668 2106 1.06 677 6153 3847 180 35 26 616 8512 545 2043 718 6470 3630 116 34 21 542 8766 582 1980 749 6787 5.27 3213 101 33 28 568 9020 619 1917 786 7103 6.28 2897 036 32 29 594 9274 4.22 506 1864 822 7420 6.27 2580 072 31 30 .44 620 9.64 9627 4.28 .89 498 9.95 1791 1.06 .49 858 9.69 7736 5.28 0.30 2264 2.0057 30 31 646 9781 4.22 480 1728 894 8053 6.27 1947 042 29 32 672 9.65 0034 467 1665 981 8369 1631 023 28 33 698 0287 4.20 464 1602 967 8685 1315 013 27 34 724 0539 4.22 441 1639 .50 004 9001 5.25 0999 1.9999 26 35 750 0792 4.20 428 1476 1.07 040 9316 5.27 0684 984 25 36 776 1044 4.22 416 1412 1.05 076 9632 6.26 0368 970 24 37 802 1297 4.20 402 1349 113 9947 5.27 0053 956 23 38 828 1549 4.18 889 1286 1.07 149 9.70 0263 6.26 0.29 9737 941 22 39 854 1800 4.20 876 1222 1.06 185 0578 9422 926 21 40 .44 880 9.65 2052 4.20 .89 868 9.96 1169 1.05 .50 222 9.70 0893 6.25 0.29 9107 1.9912 20 41 906 2304 4.18 860 1096 1.07 268 1208 8792 897 19 42 982 2555 887 1032 295 1523 5.28 8477 388 18 43 953 2806 824 0968 1.05 881 1837 5.26 8163 863 17 44 984 3057 ■ 811, 0905 1.07 868 2152 5.28 7848 354 16 45 .45 010 3308 4.17 298 0841 1.06 404 2466 5.25 7534 840 16 46 036 3558 286 0778 1.07 441 2781 6.23 7219 826 14 47 062 3808 4.18 272 0714 477 3096 6905 811 13 48 088 4059 4.17 259 0650 514 3409 6.22 6591 797 12 49 114 4309 4.16 246 0586 660 3722 6.23 6278 782 11 50 .46140 9.65 4568 4.17 .89 282 9.95 0522 1.07 .50 587 9.70 4036 6.28 0.29 5964 1.9768 10 51 166 4808 219 0468 628 4350 6.22 5650 784 9 52 192 5068 4.15 ...m. 0394 660 4663 5337 740 8 53 218 5307 193 0330 696 4976 6.28 5024 726 7 54 248 5566 180 0266 738 5290 6.22 4710 711 6 56 269 5805 167 0202 769 5603 4397 697 6 56 296 6054 4.18 158 0138 806 5916 6.20 4084 683 4 57 821 6302 4.15 140 0074 843 6228 6.22 3772 669 3 58 847 6551 4.18 127 0010 1.08 879 6541 3469 664 2 59 878 6799 114 9.94 9946 1.07 016 6854 6.20 3146 640 1 60 .45 899 9.65 7047 .89 101 9.94 9881 .50 968 9.70 7166 0.29 2834 1.9626 116° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. TAHaEHTS. 63° Cosines. SiNEB. Vii. TRIGONOMETRIC FUNCTIONS. 87 B 1 27° Sines. CoaiNES. Tangents. Dif. Cotangents. 152° Nat. Log-. Djf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .45 899 9.65 7047 4.18 .89 101 9.94 9881 1.08 .50 963 9.70 7166 5.20 0.29 2834 1.9626 60' 1 425 7295 4.12 087 9816 1.07 989 7478 2522 612 59 2 451 7542 4.18 074 9752 .51026 7790 2210 698 58 3 477 7790 4.12 061 9688 1.08 068 8102 1898 584 57 4 503 8037 048 9623 099 8414 1586 570 56 5 . 629 8284 035 9558 1.07 186 8726 5.18 1274 666 55 6 654 8531 021 9494 1.08 178 9037 5.20 0963 642 54 7 630 8778 008 9429 209 9349 5.18 0651 628 53 8 60G 9025 4.10 .88 995 9364 1.07 246 9660 0340 514 52 9 682 9271 981 9300 1.08 283 9971 0029 500 51 10 .45 668 9.65 9517 4.10 .88 968 9.94 9235 1.08 .51819 9.710282 6.18 0.28 9718 1.9486 50 H 684 9763 955 9170 866 0593 9407 472 49 12 710 9.66 0009 942 9105 893 0904 9096 458 48 13 786 0255 928 9040 480 1215 6.17 8785 444 47 14 762 0501 4.08 915 8975 467 1525 5.18 8475 430 46 15 ' 787 0746 902 8910 508 1836 5.17 8164 416 45 16 818 0991 888 8845 540 2146 7854 402 44 17 839 1236 875 8780 577 2456 7544 888 43 18 865 1481 862 8715 614 2766 7234 875 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 .51688 9.713386 6.17 0.28 6614 L9847 40 21 942 2214 4.08 822 8519 724 3696 6.15 6304 338 39 22 968 2459 4.07 808 8454 1.10 761 4005 5995 819 38 23 994 2703 4.05 795 8388 1.08 798 4314 5.17 5686 806 37 24 .46 020 2946 4.07 782 8323 1.10 835 4624 5.15 5376 292 36 25 046 3190 4.06 768 8257 1.08 872 4933 5067 278 35 26 072 3433 4.07 756 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 6.18 4140 287 32 29 149 4163 715 7995 1.10 .52 020 6168 5.15 3832 228 31 80 .46 175 9.66 4406 4.08 .88 701 9.94 7929 1.10 .62 057 9.716477 5.18 0.28 3523 1.9210 30 31 201 4648 4.05 638 7863 094 6785 3215 196 29 32 226 4891 4.08 674 7797 181 7093 2907 138 28 33 252 5133 661 7731 168 7401 2599 169 27 34 278 5375 647 7665 1.08 205 7709 2291 185 26 35 804 5617 684 7600 1.12 242 8017 1983 142 25 36, 880 5859 4.02 620 7533 1.10 279 8325 1675 128 24 37 855 6100 4.08 607 7467 816 8633 6.12 1367 115 23 38 881 6342 4.02 593 7401 853 8940 5.18 1060 101 22 39 407 6583 580 7335 390 9248 5.12 0752 088 21 40 .46 483 9.66 6824 4.02 .88 566 9.94 7269 1.10 .62 427 9.719555 5.12 0.28 0445 1.9074 20 41 468 7065 4.00 558 7203 1.12 464 9862 0138 061 19 42 484 7305 4.02 589 7136 1.10 601 9.72 0169 0.27 9831 047 18 43 510 7546 4.00 526 7070 588 0476 9524 034 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 8.98 485 6871 1.12 650 1396 5.10 8604 1.8998 14 47 613 8506 4.00 472 6804 1.10 687 1702 6.12 8298 980 13 48 689 8746 463 6738 1.12 724 2009 6.10 7991 967 12 49 664 8986 8.98 445 6671 761 2315 7685 968 11 50 .46 690 9.66 9225 8.98 .88 481 9.94 6604 1.10 .52 793 9.72 2621 5.10 0.27 7379 1.8940 10 51 716 9464 417 6538 1.12 836 2927 5.08 7073 927 9 52 742 9703 404 6471 873 3232 6.10 6768 918 8 53 767 9942 890 6404 910 3538 6462 900 7 54 798 9.67 0181 8.97 377 6337 947 3844 5.08 6156 887 6 55 819 0419 8.98- 363 6270 985 4149 5851 878 5 56 844 0658 3.97 849 6203 53 022 4454 5.10 5546 860 4 57 870 0896 836 6136 059 4760 6.08 5240 847 3 58 896 1134 822 6069 096 5065 4935 834 2 59 921 1372 8.95 308 6002 134 5370 5.07 4630 820 1 60 .46 947 9.67 1609 .88 295 9.94 5935 53171 9.72 5674 0.27 4326 1.8307 117° Nat. Log. Dif. Nat. Log. , Dif. Nat. Log. Cotangents. Dif. Log. Nat. 62° COSIHES. SiSES. Tangents. . — _ 1 88 Vn. TRIGONOMETRIC FUNCTIONS. 28° Suiss. 1 COSIBES. Takgbnts. COTAKOENXe. 151° Nat Log. DIf. Nat. Log. Dif. Nat. Log. Dlf. Log. Nat. 0' .46 947 9.67 1609 3.97 .88 296 9.94 5935 1.12 .83 171 9.72 5674 6.08 0.27 4326 1.8807 60' 1 973 1847 8.95 281 5868 1.18 203 5979 4021 794 59 2 999 2084 267 5800 1.12 246 6284 6.07 3716 781 58 3 .47 024 2321 254 5733 288 6588 3412 768 57 4 050 2558 240 5666 1.18 820 6892 6.08 3108 765 56 5 076 2795 226 5598 1.12 868 7197 6.07 2803 741 56 6 101 3032 8.98 218 5531 896 7501 2499 728 54 7 127 3268 8.96 199 5464 1.13 482 7805 2195 716 53 8 158 3505 8.98 186 5396 470 8109 5.05 1891 702 52 9 178 3741 172 5328 1.12 807 8412 8.07 1688 689 51 10 .47 204 9.67 3977 8.98 .88 168 9.94 5261 1.18 .68 645 9.72 8716 6.07 0.27 1284 1.8676 50 . 11 229 4213 8.92 144 5193 682 9020 6.05 0980 663 49 12 26S 4448 8.98 180 5125 1.12 620 9323 0677 660 48 13 281 4684 8.92 117 5058 1.18 657 9626 0374 637 47 14 806 4919 8.98 108 4990 694 9929 5.07 0071 624 46 15 882 5155 8.92 089 4922 732 9.73 0233 6.08 0.26 9767 611 46 16 858 5390 8.90 076 4854 769 0535 8.08 9465 598 44 n 888 5624 8.92 062 4786 807 0838 9162 888 43 18 409 5859 048 4718 844 1141 8859 872 42 19 484 6094 8.90 084 4650 882 1444 6.08 8556 869 41 20 .47 460 9.67 6328 8.90 .88 020 9.94 4582 1.18 .63 920 9.73 1746 6.03 0.26 8254 1.8546 40 21 486 6562 006 4514 957 2048 6.06 7952 888 39 22 SU 6796 .87 998 4446 1.16 998 2351 6.08 7649 820 38 23 587 7030 979 4377 1.18 .64 032 2653 7347 ' 807 37 24 562 7264 966 4309 070 2955 7045 496 36 25 588 7498 8.88 951 4241 1.16 107 3257 6.02 6743 482 36 26 e.U 7731 987 4172 1.18 146 3558 6.03 6442 469 34 27 689 7964 928 4104 188 3860 6140 486 33 28 665 8197 909 4036 1.16 220 4162 6.02 5838 443 32 29 690 8430 896 3967 1.18 268 4463 553,7 480 31 30 .47 716 9.67 8663 8.87 .87 882 9.94 3899 1.16 .64 296 9.73 4764 6.03 0.26 5236 1.8418 30 31 741 8895 8.88 866 3830 . 888 5066 6.02 4934 408 29 32 767 9128 8.87 854 3761 1.18 871 5367 4633 892 28 33 798 9360 840 3693 1.16 409 5668 4332 379 27 34 818 9592 826 3624 446 5969 8.00 4031 867 26 35 844 9824 812 3555 484 6269 6,02 3731 854 26 36 869 9.68 0056 798 3486 622 6570 8.00 3430 841 24 37 895 0288 8.8S 784 3417 660 6870 6.02 3130 829 23 38 920 0519 770 3348 597 7171 6.00 2829 816 22 39 946 0750 8.87 766 3279 688 7471 2529 803 21 40 .47 971 9.68 0982 8.85 .87 748 9.94 3210 1.16 .64 678 9.73 7771 8.00 0.26 2229 1.8291 20 41 997 1213 3.88 729 3141 711 8071 1929 278 19 42 .48 022 1443 8.86 715 3072 748 8371 1629 268 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 678 2864 1.18 862 9271 4.98 0729 228 15 46 124 2365 659 2790 900 9570 6.00 0430 215 14 47 160 2595 645 2726 1.17 938 9870 4.98 0130 202 13 48 175 2825 681 2656 1.16 976 9.74 0169 0.25 9831 190 12 49 201 3055 8.82 617 2587 1.17 .66 018 0468 9532 177 11 50 .48 226 9.68 3284 8.88 .87 608 9.94 2517 1.16 .56 061 9.74 0767 4.98 0.26 9233 1.8166 10 61 252 3514 3.82 589 2448 1.17 089 1066 8934 182 9 52 277 3743 676 2378 127 1365 8636 140 8 53 808 3972 561 2308 1.16 168 1664 4.97 8336 127 7 54 828 4201 546 2239 1.17 208 1962 4.98 8038 118 6 55 854 4430 8.80 632 2169 241 2261 4.97 7739 108 5 56 879 4658 8.82 618 2099 279 2559 4.98 7441 090 4 57 405 4887 8.80 604 2029 817 2858 4.97 7142 078 3 58 480 5115 490 1959 865 3156 6844 068 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. Dlf. Nat. Log. Dlf. Nat. Log. GOTAHOBNTS. Dlf. Log. Nat. TANOEirrs. 61° COSINBS. SiNIiS. Vn. TRiaONOMETKIO FUNCTIONS. 89 29° Sinks. , Cosines. Tangents. Cotangents. 150° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .48 481 9.68 5571 3.80 .87 462 9.94 1819 1.17 .55 481 9.74 3752 4.97 0.25 6248 1.8040 60' 1 506 . 5799 443 1749 469 4050 5950 028 59 2 532 6027 8.78 434 1679 507 4348 4.95 5652 016 58 3 55T 6254 8.80 420 1609 545 4645 4.97 5355 003 57 4 583 6482 8.78 406 1539 583 4943 4.95 5057 1.7991 56 5 60S 6709 891 1469 1.18 621 • 5240 4.97 4760 979 55 6 634 6936 877 1398 1.17 659 5538 4.95 4462 966 54 7 659 7163 8.77 868 1328 697 5835 4165 954 53 8 684 7389 8.78 349 1258 1.18 736 6132 3868 942 52 9 TIO 7616 835 1187 1.17 774 6429 3571 930 51 10 .48 T85 9.68 7843 8.77 .87 821 9.94 1117 1.18 .55 812 9.74 6726 4.95 0.25.3274 1.7917 50 11 761 8069 806 1046 850 7023 4.98 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 11 918 9423 221 0622 079 8801 1199 882 43 18 983 9648 207 0551 117 9097 0903 820 42 19 964 9873 193 0480 156 9393 0607 808 41 20 .48 989 9.69 0098 8.75 .87 178 9.94 0409 1.18 .56194 9.74 9689 4.93 0.25 0311 1.7796 40 21 ,49 014 0323 164 0338 232 9985 0015 788 39 22 040 0548 3.78 150 0267 270 9.75 0281 4.92 0.24 9719 771 38 23 065 0772 136 0196 809 0576 4.93 9424 759 37 24 090 0996 121 0125 847 0872 4.92 9128 747 36 25 116 1220 107 0054 1.20 885 1167 8833 785 35 26 141 1444 098 9.93.9982 1.18 424 1462 8538 723 34 21 166 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 33 818 3008 .86 993 9482 693 3526 4.90 6474 639 27 34 844 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 8.70 949 9267 SOS 4409 5591 603 24 31 419 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 1.20 928 5291 4709 567 21 40 .49 493 9.69 4564 8.70 .86 892 9.93 8980 1.20 .56 962 9.75 5585 4.8S 0.24 4415 1.7556 20 41 521 4786 8.68 878 • 8908 .57 000 5878 4.90 4122 544 19 42 546 5007 3.70 868 8836 1.22 039 6172 4.38 3828 532 18 43 571 5229 3.68 849 8763 1.20 078 6465 4.90 3535 520 17 44 596 5450 884 8691 116 6759 4.88 3241 508 16 45 622 567,1 820 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 478 13 48 697 6334 3.67 .777 8402 1.20 271 7931 2069 461 12 • 49 723 6554 8.68 762 8330 809 8224 1776 449 11 50 .49 748 9.69 6775 3.67 .86 748 9.93 8258 1.22 .57 848 9.75 8517 4.88 0.24 1483 1.7437 10 51 778 6995 788 8185 1.20 886 ' 8810 4.87 1190 426 9 52 798 7215 719 8113 1.22 42? 9102 4.8S 0898 414 8 53 824 7435 8.65 704 8040 464 9395 4.87 0605 402 7 54 849 7654 8.67 690 7967 1.20 603 9687 0313 391 6 55 874 7874 675 7895 1.22 541 9979 4.88 0021 879 5 56 899 8094 3.65 661 7822 580 9.76 0272 4.87 0.23 9728 867 4 57 924 8313 646 7749 619 0564 9436 855 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 832 1 60 ,50 000 9.69 8970 .86 608 9.93 7531 .57 785 9.76 1439 0.23 8561 1.7321 o' 119° Nat. Log. Dif. Nat. Log. Dif. - Nat. Log. Cotangents. Dif. Log. Nat. Tangents. 60° Cosines. Sines. 90 Vn. TRIGONOMETRIC FUNCTIONS. .. ... \ 30° Srass. Cosines. Tasoknts. Dif. COTANGBHTO. 149° Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .50 000 9.69 8970 8.65 .86 608 9.93 7531 1.22 .57 786 9.76 1439 4.87 0.23 8561 1.7821 60' 1 025 9189 8.68 688 7458 774 1731 8269 809 59 2 050 9407 8.65 578 7385 818 2023 4.86 7977 297 58 3 076 9626 8.68 569 7312 1.28 851 2314 4.87 7686 286 67 4 lo: 9844 644 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 261 54 7 176 0498 601 7019 .58 007 3479 6521 289 53 8 201 0716 8.62 486 6946 1.28 046 3770 6230 228 52 9 227 0933 8.68 471 6872 1.22 085 4061 5939 216 61 10 .50 252 9.70 1151 8.62 .86 457 9.93 6799 1.28 .58124 9.76 4352 4.85 0.23 5648 1.7206 50 11 277 1368 442 6725 1.22 162 4643 4.83 5357 198 49 12 802 1585 427 6652 1.28 201 4933 4.85 5067 182 48 13 827 1802 418 6578 1.22 240 5224 4.88 4776 170 47 14 852 2019 898 6505 1.28 279 5514 4.86 4486 169 46 15 877 2236 8.60 884 6431 818 5805 4.88 4195 147 45 16 408 2452 8.62 869 6357 1.22 867 6095 3905 186 44 17 423 2669 8.60 854 6284 1.28 896 6385 3615 124 43 18 458 2885 840 6210 486 6675 3325 118 42 19 478 3101 826 6136 474 6965 3035 102 41 20 .60 608 9.70 3317 8.60 .86 810 9.93 6062 1.28 .68 518 9.76 7255 4.88 0.23 2745 1.7090 40 21 628 3533 295 5988 652 7545 4.82 2455 079 39 22 658 3749 8.58 281 5914 691 7834 4.88 2166 067 38 23 678 3964 266 5840 681 8124 1876 066 37 24 608 4179 8.60 251 5766 670 8414 4.82 1586 045 36 25 628 4395 8.68 287 5692 709 8703 1297 088 35 26 664 4610 222 5618 1.26 748 8992 1008 022 34 27 679 4825 207 5543 1.28 787 9281 4.88 0719 Oil 33 28 704 5040 8.57 192 5469 -^26 9571 4.82 -— 0429 1.6999 33— 29 729 5254 8.68 178 5395 1.26 ^"4 865 9860 4.80 ' 0140 988 31 30 .50 754 9.70 5469 8.67 .86 168 9.93 5320 1.28 .68.906 9.77 0148 4.82 0.22 9852 1.6977 30 31 779 5683 8.58 148 5246 1.26 944 0437 9563 965 29 32 804 5898 8.67 188 5171 1.28 983 0726 9274 964 28 33 829 6112 119 5097 1.25 .69 022 1015 4.80 8985 948 27 34 854 6326 8.55 104 5022 1.28 061 1303 4.82 8697 982 26 35 879 6539 8.57 089 4948 1.25 101 1592 4.80 8408 920 25 36 904 6753 074 4873 140 1880 8120 909 24 37 929 6967 8.56 069 4798 179 2168 4.82 7832 898 23 38 954 7180 046 4723 1.28 218 2457 4.80 7543 887 22 39 979 7393 080 4649 1.25 258 2745 7255 876 21 40 .61004 9.70 7606 8.55 .86 015 9.93 4574 1.26 .59 297 9.77 3033 4.80 0.22 6967 1.6864 20 41 029 7819 000 4499 886 3321 4.78 6679 858 19 42 054 8032 .85 985 4424 876 3608 4.80 6392 842 18 43 079 8245 970 4349 416 3896 6104 881 17 44 104 8458 8.58 966 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 1.25 688 4759 4.78 5241 797 14 47 179 9094 911 4048 678 5046 4954 786 13 48 204 9306 896 3973 612 5333 4.80 4667 776 12 49 229 9518 881 3898 1.27 651 5621 4.78 4379 764 11 50 .61254 9.70 9730 8.62 .85 866 9.93 3822 1.26 .89 691 9.77 5908 4.78 0.22 4092 1.6758 10 51 279 9941 8.68 851 3747 1.27 780 6195 3805 742 9 52 804 9.71 0153 8.62 886 3671 1.25 770 6482 4.77 3518 781 8 53 829 0364 821 3596 1.27 809 6768 4.78 3232 720 7 54 854 0575 806 3520 1.26 849 7055 2945 709 6 55 879 0786 792 3445 1.27 888 7342 4.77 2658 698 5 56 404 0997 777 3369 928 7628 4.78 2372 687 4 57 429 1208 762 3293 967 7915 4.7T 2085 676 3 58 454 1419 8.60 747 3217 .60 007 8201 4.78 1799 665 2 59 479 1629 782 3141 1.26 046 8488 4.77- 1512 664 1 ' 60 .51 604 9.71 1839 .85 717 9.93 3066 .60 086 9.77 8774 0.22 1226 1.6643 120° Nat. Log. Dif. Nat. Log. Dlf. Nat. Log. Dif. Log. Nat. 59° (JOBIHES. SiKBS. COTAHGBNTB. Tangeh™. ■ - ■ - ' ' ■■- ■ ■ 1 Vn. TRIGONOMETRIC FUNCTIONS. 91 1 ■ «F 1 31° SmES. COSIKES. Tangents. Dif. Cotangents. 148° Nat. Log. Dif. Nat. Log. Dif. Nat. -Log. Log. Nat. 0' .51 504 9.711889 8.62 .85 717 9.93 3066 1.27 .60 086 9.77 8774 4.77 0.22 1226 1.6648 60' 1 529 2050 8.60 702 2990 126 9060 0940 682 59 2 554 2260 8.48 687 2914 165 9346 0654 621 58 3 579 2469 8.50 672 2838 206 9632 0368 610 57 4 ,604 2679 657 2762 1.28 245 9918 4.76 0082 599 56 5 628 2889 8.43 642 2685 1.27 284 9.78 0203 4.77 0.219797 588 55 6 653 3098 8.50 627 2609 824 0489 9511 577 54 T 678 3308 8.48 612 2533 864 0775 4.75 9225 566 53 8 708 3517 697 2457 1.28 408 1060 4.77 8940 565 52 9 728 3726 682 2380 1.27 448 1346 4.75 8654 545 51 10 .61768 9.713935 8.48 .85 567 9.93 2304 1.27 .60 488 9.78 1631 4.78 0.218369 1.6684 50 11 778 4144 8.47 651 2228 1.28 522 1916 8084 623 49 12 SOB 4352 8.48 586 2151 1.27 562 2201 7799 612 48 13 828 4561 8.47 621 2075 1.28 . 602 2486 7514 601 47 14 852 4769 3.48 606 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 11 927 5394 481 1768 761 3626 4.78 6374 458 43 18 962 5602 3.45 446 1691 801 3910 4.76 6090 447 42 19 977 5809 8.47 481 1614 841 4195 4.78 5805 486 41 20 ."52 002 9.716017 8.45 .86 416 9.93 1537 1.28 .60 881 9.78 4479 4.75 0.215521 1.6426 40 21 026 6224 3.47 401 1460 921 4764 4.78 5236 416 39 22 051 6432 3.45 385 1383 960 5048 4952 404 38 23 076 6639 370 1306 .61 000 5332 4668 898 37 24 101 6846 355 1229 040 5616 4384 383 36 25 126 7053 8.43 840 1152 080 5900 410.0 872 35 26 151 7259 3.45 325 1075 120 6184 3816 861 34 27 175 7466 810 0998 160 6468 3532 851 33 28 200 7673 3.48 294 0921 1.80 200 6752 3248 340 32 29 225 7879 279 0843 1.28 240 7036 4.72 2964 829 31 30 .52 250 9.718085 8.43 .85 264 9.93 0766 1.80 .61280 9.78 7319 4.73 0.21 2681 1.6819 30 31 275 8291 249 0688 1.28 820 7603 4.72 2397 308 29 32 299 8497 284 0611 1.80 360 7886 4.78 2114 297 28 33 824 8703 218 0533 1.28 400 8170 4.72 1830 287 27 34 349 8909 8.42 203 0456 1.80 440 8453 1547 276 26 35 374 9114 8.43 188 0378 480 8736 1264 265 25 36 899 9320 8.42 178 0300 1.28 620 9019 0981 256 24 37 423 9525 167 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 228 21 40 .52 498 9.72 0140 8.42 .85 112 9.92 9989 1.30 .61681 9.79 0151 4.72 0.20 9849 1.6212 20 41 622 0345 8.40 096 9911 721 0434 4.70 9566 202 19 42,- 647 0549 8.42 081- 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 061 9677 842 1281 8719 170 16 45' 621 1162 035 9599 882 1563 4.72 8437 160 15 46 646 1366 020 ■ 9521 1.82 922 1846 4.70 8154 149 14 - 47 671 1570 005 9442 1.80 962 2128 7872 139 13 48 696 1774 .84 989 9364 .62 008 2410 7590 128 12 49 720 1978 8.88 974 9286 1.82 043 2692 7308 118 11 50 .52 745 9.72 2181 8.40 .84 969 9.92 9207 1.80 .62 088 9.79 2974 4.70 0.20 7026 1.6107 10 51 770" 2385 8.88 943 9129 1.82 124 3256 6744 097 9 52 794 2588 928 9050 1.80 164 3538 4.68 6462 087 8 53 819 2791 913 8972 1.82 204 3819 4.70 6181 076 7 54 344 2994 897 8893 1.80 245 4101 5899 066 6 65 869 3197 882 88.15 1.82 285 4383 4.68 5617 055 5 56 898 3400 866 8736 825 4664 4.70 5336 045 4 57 918 3603 3.87 851 8657 366 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 .82 992 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. Dif. Log. Nat. Tangents. 58° CosnTEB. Sines. Cotangents. 9:2 Vn. TRIGONOMETRIC FUNCTIONS. :vi° SniES. Cosines. Tangents. COTANQENTS. 147° Nat. Log. Dif. Nat. Log. Dif. Nnt. Loff. Dir. Log. Nat. 0' .52 992 9.72 4210 8.37 .84 805 9.92 8420 1.80 .62 4ST 9.79 5789 4.68 0.20 4211 1.6008 60' 1 .58 017 4412 789 8342 1.32 52T 6070 3930 1.6998 59 2 041 4614 774 82G3 1.88 668 6351 3649 988 58 3 066 4816 8.85 759 8183 1.82 608 6632 3368 972 57 4 091 ' 5017 3.37 748 8104 649 6913 3087 962 56 5 115 5219 8.35 728 8025 689 7194 4.67 2806 952 65 6 140 5420 8.87 712 7946 780 7474 4.68 2626 941 64 7 164 5622 8.85 697 7867 1.83 770 7755 2245 981 53 8 189 5823 681 7787 1.82 811 8036 467 1964 921 52 9 214 6024 666 7708 862 8316 1684 911 51 10 .58 288 9.72 6225 8.36 .84 650 9.92 7629 1.83 .62 892 9.79 8596 4.68 0.20 1404 1.6900 50 11 268 6426 8.88 686 7549 1.82 938 8877 4.67 1123 890 49 12 288 6626 8.85 619 7470 1.88 978 9167 0843 880 48 13 812 6827 8.83 604 7390 .68 014 9437 0663 869 47 14 887 7027 8.85 688 7310 1.82 055 9717 0283 859 46 15 861 7228 8.88 578 7231 1.88 096 9997 0003 849 45 16 386 7428 657 7151 186 9.80 0277 0.19 9723 889 44 n 411 7628 842 7071 177 0557 4.66 9443 829 43 18 486 7828 8.82 526 6991 217 0836 4.67 9164 818 42 19 460 8027 3.38 611 6911 268 1116 8884 808 41 20 .53 484 9.72 8227 8.88 .84 496 9.92 6831 1.88 .68 299 9.80 1396 4.66 0.19 8604 1.5798 40 21 509 8427 3.32 480 6761 840 1675 4.67 8326 788 39 22 584 8626 464 6671 880 1956 466 8045 778 38 23 558 8825 448 6591 421 2234 7766 768 37 24 688 9024 483 6511 462 2613 7487 757 36 25 607 9223 417 6431 503 2792 467 7208 747 35 26 682 ^ 9422 402 6351 1.35 644 3072 4.66 6928 787 34 27 666 9621 886 6270 1.88 684 3351 6649 727 33 28 681 9820 8.80 870 6190 '625 3630 6370 717 32 29 706 9.73 0018 8.82 855 6il0 1.35 666 3909 4.68 6091 707 31 30 .68 780 9.73 0217 8.30 .84 389 9.92 6029 1.88 .68 707 9.80 4187 4.65 0.19 5813 1.6697 30 31 764 0415 824 6949 1.85 748 4466 6634 687 29 32 779 0613 808 5868 1.88 789 4745 4.68 6255 677 , 28 33 804 0811 292 5788 1.85 830 5023 4.66 4977 667' 27 34 828 1009 8.28 277 5707 871 5302 468 4698 667 26 36 868 1206 8.80 261 6626 912 6580 466 4420 647 25 36 877 1404 245 5545 1.38 953 5859 468 4141 687 24 37 902 1602 3.28 280 6466 1.86 994 6137 3863 627 23 38 926 1799 214 6384 .64 085 6415 3586 617 22 39 961 1996 198 5303 078 6693 3307 607 21 40 .58 975 9.73 2193 8.28 .84182 9.92 6222 1.35 .64117 9.80 6971 4.68 0.19 3029 1.6597 20 41 .64 000 2390 167 5141 168 7249 2751 687 19 42 024 2587 161 5060 199 7527 2473 577 18 43 049 2784 8.27 186 4979 1.87 240 7805 2196 667 17 44 078 2980 3.28 120 4897 1.36 281 8083 1917 567 16 45 097 3177 8.27 104 4816 822 8361 462 1639 647 15 46 122 3373 088 4736 368 8638 4.68 1362 537 14 47 146 3569 072 4664 1.37 404 8916 462 1084 627 13 48 171 3765 067 4572 1.35 446 9193 468 0807 517 12 49 196 3961 041 4491 1.87 487 9471 462 0529 507 11 50 .64 220 9.73 4157 8.27 .84 025 9.92 4409 1.85 .64 528 9.80 9748 462 0.19 0262 1.5497 10 51 244 4353 009 4328 1.37 669 9.81 0025 0.18 9976 487 9 52 269 4549 3.26 .88 994 4246 610 0302 4.68 9698 477 ,8 53 293 4744 978 4164 1.86 662 0680 462 9420 468 7 54 817 4939 8.27 962 4083 1.87 698 0867 9143 468 6 55 842 5135 8.25 946 4001 784 1134 460 8866 448 5 56 866 6330 930 3919 \ 775 1410 462 8590 438 4 57 891 5525 8.28 915 3837 817 1687 8313 428 3 58 415 5719 8.26 899 3765 858 1964 8036 418 2 69 440 5914 888 3673 899 2241 4.60 7759 408 1 60 .64 464 9.73 6109 .88 867 9.92 3691 .64 941 9.81 2517 0.18 7483 1.6899 122° Nat Log. Dlf. Nat. Log. Dif. Nat. Log. COTAHOENTS. Dif. Log. Nat. • 57° Cobdhs. SnfES. Vil. i'KIGONOMETRIC FUNCTIONS. • 93 33° Sines. Cosines. Tangents. Cotangents. 146° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .54 464 9.73 6109 3.23 .83 867 9.92 3591 1.37 .04 941 9.81 2517 4.62 0.18 7483 1.5899 60' 1 483 6303 3.25 851 3509 982 2794 4.60 7206 889 59 2 518 6498 3.23 885 3427 .65 024 3070 4.62 6930 879 58 3 587 6692 819 3345 065 3347 4.60 6653 369 57 4 561 6886 804 3263 106 3623 6377 359 56 5 686 7080 788 3181 1.88 148 3899 4.62 6101 350 55 6 610 7274 8.22 772 3098 1.87 189 4176 4.60 5824 340 54 1 635 7467 3.23 766 3016 1.88 231 4452 5548 380 53 8 659 7661 740 2933 1.37 272 4728 5272 820 52 9 683 7855 3.22 724 2851 1.38 814 5004 4996 811 51 10 .54 708 9.73 8048 8.22 .88 708 9.92 2768 1.87 .65 855 9.81 5280 4.68 0.18 4720 1.5801 50 11 782 8241 692 2686 1.88 897 5555 4.60. 4445 291 49 12 7S6 8434 676 2603 488 5831 4169 282 48 13 781 8627 660 2520 1.87 480 6107 4.58 3893 272 47 14 805 8820 646 2438 1.88 621 —6382 4.60 3618 262 46 15 829 9013 629 2355 563 -^658 4.68 3342 253 45 16 854 9206 3:20 618 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 8.20 .88 549 9.92 1940 1.38 .68 771 9.818035 4.58 0.18 1965 1.5204 40 21 975 9.74 0167 683 i857 813 8310 1690 195 39 22 999 0359 8.18 617 1774 854 8585 1415 186 38 23 .55 024 0550 3.20 601 1691 1.40 896 8860 1140 176 37 24 048 0742 486 1607 1.88 988 9135 0865 166 36 25 072 0934 8.18 469 1524 980 9410 4.57 0590 156 35 26 097 1125 468 1441 1.40 .66 021 • 9684 4.58 0316 147 34 27 121 1316 8.20 487 1357 1.88 063 9959 0041 137 33 28 , 145 1508 8.18 421 1274 1.40 105 9.82 0234 4.67 0.17 9766 127 32 29 169 1699 3.17 406 1190 1.88 147 0508 4.58 9492 118 31 30 .55 194 9.74 1889 3.18 .88 889 9.92 1107 1.40 .66189 9.82 0783 4.57 0.17 9217 1.5108 30 31 218 2080 878 1023 230 1057 4.58 8943 099 29 32 242 2271 856 0939 1.88 272 1332 4.67 8668 089 28 33 266 2462 8.17 840 0856 1.40 814 1606 8394 080 27 34 291 2652 824 0772 856 1880 8120 070 26 35 816 2842 8.18 308 0688 898 2154 4.58 7846 061 25 36 839 3033 8.17 292 0604 440 2429 4.57 7571 051 24 37 863 3223 276 0520 482 2703 '7297 042 23 38 888 3413 8.15 260 0436 624 2977 7023 082 22 39 412 3602 8.17 244 0352 566 3251 4.56 6749 028 21 40 .55 436 9.74 3792 8.17 .83 228 9.92 0268 1.40 .66 608 9.82 3524 4.57. 0.17 6476 1.5018 20 41 460 3982 8.15 212 0184 1.42 650 3798 6202 004 19 42 434 4171 8.17 195 0099 1.40 692 4072 4.55 5928 1.4994 18 43 609 4361 8.16 179 0015 784 4345 4.57 5655 985 17 44 683 4550 163 9.91 9931 1.42 776 4619 5.381 975 16 45 657 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 116 9677 1.40 902 5439 4.67 4561 947 13 48 630 5306 8.13 098 9593 1.42 944 5713 4.55 4287 988 12 49 654 5494 8.15 082 9508 1.40 986 5986 4014 928 11 50 .55 678 9.74 5683 8.13 .83 066 9.91 9424 1.42 .67028 9.82 6259 4.65 0.17 3741 1.4919 10 - 51 702 5871 8.15 050 9339 071 6532 3468 910 9 52 726 6060 8.13 084 9254 118 6805 3195 900 8 53 760 6248 017 9169 1.40 156 7078 2922 891 7 54 775 6436 001 9085 1.42 197 7351 2649 882 6 55 799 6624 82 985 9000 239 7624 2376 ,872 5 56 823 6812 8.12 969 8915 282 7897 ■2103 868 4 57 847 6999 3.13 963 8830 324 8170 4.68 1830 854 3 58 871 7187 8.12 936 8745 1.43 866 8442 4.55 1558 844 2 59 895 7374 8.18 920 8659 1.42 409 8715 4.68 1285 835 1 60 55 919 9.74 7562 83 904 9.91 8574 67 461 9.82 8987 0.17 1013 1.4826 123° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Cotangents. Dif. Log. Nat. 56° Cosines. Sines. Tangents. 94 VII. TRIGONOMETRIC FUNCTIONS. 1 1 34° Sixes. CosniES. Tanoshts. CoTANOENTe. 145= Nat. Log. Dlf. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .65 919 9.74 7562 3.12 .82 904 9.91 8574 1.43 .67 451 9.82 8987 455 0.17 1013 1.4826 60' .1 948 7749 SS7 8489 498 9260 4.58 0740 816 59 2 968 7930 871 8404 1.48 636 9532 4.55 0468 807 58 3 992 8123 855 8318 1.42 578 9805 4.68 0195 798 57 4 .66 016 8310 889 8233 1.48 620 9.83 0077 0.16 9923 788 56 5 040 8497 8.10 822 8147 1.42 668 0349 9651 779 55 6 064 8683 8.12 806 8062 1.48 705 0621 9379 770 64 1 088 8870 8.10 790 7976 1.42 748 0893 9107 761 53 8 112 9056 3.12 778 7891 1.48 790 1165 8835 751 52 9 136 9243 8.10 767 7805 882 1437 8563 742 51 10 .56 160 9.74 9429 8.10 .82 741 9.91 7719 1.42 .67 876 9.83 1709 458 0.16 8291 1.4788 50 11 184 9615 724 7634 1.48 917 1981 8019 724 49 12 203 9801 708 7548 960 2253 7T47 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 468 7204 696 46 15 280 0358 3.08 659 7290 088 3068 4.62 6932 687 45 16 805 0543 8.10 643 7204 180 3339 458 6661 678 44 17 829 0729 8.08 626 7118 178 3611 4.52 6389 669 43 18 358 0914 610 7032 215 3882 4.58 6118 659 42 19 87T 1099 598 6946 1.45 268 4154 452 5846 650 41 20 .56 401 9.75 1284 8.08 .82 577 9.91 6859 1.48 .68 801 9.83 4425 4.62 0.16 5575 1.4641 40 21 - 425 1469 561 6773 848 4696 5304 682 39 22 449 1654 544 6687 1.45 886 4967 5033 628 38 23 473 1839 8.07 628 6600 1.48 429 5238 4762 614 37 24 497 2023 8.08 611 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 450 3136 569 31 30 .56 641 9.75 3128 8.07 .82 413 9.91 5994 1.45 .68 728 9.83 7134 452 0.16 2866 1.4560 30 31 665 3312 8.05 896 5907 771 7405 450 2595 541 29 32 689 3495 8.07 880 5820 814 7675 4.62 2325 582 28 33 713 3679 8.05 868 5733 867 7946 450 2054 528 27 34 786 3862 8.07 847 5646 900 8216 452 1784 614 26 35 760 4046 8.05 330 5559 942 8487 460 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 452 0703 478 22 39 856 4778 3.08 264 5210 114 9568 450 0432 469 21 40 .56 880 9.75 4960 3.05 .82 248 9.915123 1.47 .69 167 9.83 9838 4.60 0.16 0162 1.4460 20 41 904 5143 281 5035 1.45 200 9.84 0108 /' 0.15 9892 461 19 42 928 5326 3.08 214 4948 1.47 243 0378 9622 442 18 43 952 5508 • 198 4860 1.45 286 0648 4.48 9352 488 17 44 976 5690 181 4773 1.47 329 0917 4.60 9083 424 16 45 .57 000 5872 165 4685 1.45 872 1187 8813 416 15 46 024 6054 148 4598 1.47 416 1457 8543 406 14 47 047 6236 132 4510 459 1727 4.48 8273 397 13 48 071 6418 115 4422 602 1996 450 8004 888 12 49 095 6600 098 4334 645 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 450 0.15 7465 1.4870 10 51 143 6963 065 .4158 681 2805 4.48 7195 861 9 52 167 7144 3.03 048 4070 675 3074 6926 852 8 53 191 7326 8.02 082 3982 718 3343 6657 344 7 ■ 54 215 7507 015 3894 761 3612 450 6388 385 6 55 238 7688 .81 999 3806 804 3882 4.48 6118 826 5 56 262 7869 982 3718 847 4151 5849 817 4 57 286 8050 3.00 965 3630 1.48 891 4420 5580 808 3 58 810 8230 8.02 949 3541 1.47 934 4689 5311 299 2 59 884 8411 3.00 932 3453 977 4958 5042 290 1 60 .57 358 9.75 8591 .81 915 9.91 3365 .70 021 9.84 5227 0.154773 1.4281 124° 1 .. 1 Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Cotangents. Log. Nat. Tangents. 55= ■ Cosines. Sines. VII. TRIGONOMETRIC FUNCTIONS. 95 1 35° SiNEB. Cosines. Tangents. Cotangents. 144° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .67 858 9.75 8591 8.02 .81 915 9.91 3365 1.48 .70 021 9.84 5227 4.48 0.15 4773 1.4281 60' 1 881 8772 8.00 ■ 899 3276 064 5496 4.47 4504 278 59 2 405 8952 882 3187 1.47 107 5764 4.48 4236 264 58 3 429 9132 866 3099 1.48 161 6033 3967 255 57 4 458 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 T 524 9852 2.98 798 2744 825 7108 4.47 2892 220 53 8 548 9.76 0031 8.00 782 2655 868 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 16 788 1464 2.97 647 1942 717 9522 0478 141 44 11 '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 1.60 848 0325 9675 115 41 20 .57 888 9.76 2177 2.98 .81 680 9.91 1584 1.48 .70 891 9.85 0593 4.47 0.14 9407 1.4106 40 21 857 2356 2.97 568 1495 1.50 985 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 2.97 518 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 064 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 037 32 29 047 3777 428 0776 285 3001 4.45 6999 028 31 30 .58 070 9.76 3954 2.96 .81 412 9.910686 1.60 .71829 9.85,3268 4.46 0.14 6732 1.4019 30 31 094 4131 895 0596 373 3535 6465 Oil 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 2.98 344 0325 505 4336 5664 985 26 35 189 4838 2.95 827 0235 1.52 649 4603 5397 976 25 36 212 5015 2.93 810 0144 1.50 698 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 961 22 39 283 5544 2.93 269 9873 1.52 726 5671 4329 942 21 40 .58 807 9.76 5720 2.98 .81242 9.90 9782 1.52 .71 769 9.85 5938 4.48 0.14 4062 1.8984 20 41 880 5896 ' 225 9691 1.50 813 6204 4.46 3796 926 19 42 854 6072 2.92 208 9601 1.52 857 / 6471 4.48 3529 916 18 ' 43 378 6247 2.98 191 9510 901 6737 4.45 3263 908 17 44 401 6423 2.92 174 9419 946 7004 4.43 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 128 9146 078 7803, 2197 874 13 48 496 7124 2.98 106 9055 122 8069 4.45 1931 865 12 49 619 7300 2.92 089 8964 167 8336 4.43 1664 857 11 50 .68 548. 9.76 7475 2.90 .81 072 9.90 8873 1.58 .72 211 9.85 8602 4.43 0.14 1398 1.8848 10 51 567 7649 2.92 055 8781 1.52 255 , 8868 1132 840 9 52 590 7824 088 8690 299 9134 0866 831 8 53 614 7999 2.90 021 8599 1.68 844 9400 0600 828 7 54 687 8173 2.92 004 8507 1.52 888 9666 0334 814 6 55 661 8348 2.90 .80 987 8416 1.58 482 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 2.90 958 8233 1.58 621 0464' 9536 789 3 58 781 8871 986 8141 565 0730 4.42 9270 781 2 59 755 9045 919 8049 1.52 610 0995 4.48 9005 772 1 60 .58 779 9.76 9219 .80 902 9.90 7958 .72 654 9.86 1261 0.13 8739 1.8764 125° Nat. < Log. Dif. Nat. Log. Dif., Nat. Log. Cotangents. Dif. Log. Nat. 54° i GOBIVES. Sines. . Tangents. 96 Vn. TRIGONOMETRIC FUNCTIONS. 36° SiKES. Cosnras. Tangents. Cotangents. 143° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat, 0' .SS779 9.76 9219 2.90 .80 902 9.90 7958 1.58 .72 664 9.86 1261 4.48 0.13 8739 1.8764 60' 1 802 9393 2.88 885 7866 699 1527 4.42 8473 765 59 2 8-20 9566 2.90 867 7774 748 1792 4.48 8208 747 58 3 849 9740 2.88 850 7682 788 2058 4.42 7942 789 57 4 878 9913 2.90 833 7590 882 2323 4.48 7677 780 50 5 896 9.77 0087 2.88 816 7498 877 2589 4.42 7411 722 56 6 920 0260 799 7406 921 2854 7146 718 54 7 943 0433 782 7314 960 3119 4.48 6881 705 53 8 967 0606 765 7222 1.65 .78 010 3385 4.42 6615 697 52 9 990 0779 748 7129 1.58 055 3660 6360 688 51 10 .59 014 9.77 0962 2.83 .80 780 9.90 7037 1.63 .78 100 9.86 3915 4.42 0.13 6085 1.8680 60 11 087 1125 718 6945 1.55 144 4180 5820 672 49 12 061 1298 2.87 696 6852 1.53 189 4445 5556 668 48 13 084 1470 2.88 679 6760 1.55 234 4710 6290 666 47 14 108 1643 2.87 662 6667 1.53 278 4975 5025 647 46 15 181 1815 644 6575 1.55 328 5240 4760 688 45 16 164 1987 627 6482 368 5505 4495 630 44 17 178 2159 610 6389 413 5770 4230 622 43 18 201 2331 S98 6296 1.58 467 6035 3965 613 42 19 225 2503 576 6204 1.55 502 6300 4.40 3700 606 41 20 .59 248 9.77 2675 2.87 .80 558 9.90 6111 1.66 .73 547 9.86 6564 4.42 0.13 3436 1.8597 40 21 272 2847 2.86 641 6018 592 6829 3171 688 39 22 295 3018 2.87 524 5926 687 7094 4.40 2906 680 38 23 818 3190 2.86 507 5832 681 7358 4.42 2642 672 37 24 842 3361 2.87 489 5739 1.67 726 7623 4.40 2377 564 36 25 865 3533 2.85 472 6645 1.65 771 7887 4.42 2113 666 35 26 889 3704 465 5552 816 8152 4.40 1848 647 34 27 412 3875 488 5459 861 8416 1584 539 33 28 436 4046 420 5366 1.57 906 8680 4.42 1320 681 32 29 459 4217 403 6272 1.55 961 8945 4.40 1056 622 31 30 .59 482 9.77 4388 2.88 .80 386 9.90 6179 1.57 .78 996 9.86 9209 4.40 0.13 0791 1.8614 30 31 506 4558 2.85 868 5085 1.55 .74 041 9473 0527 506 29 32 529 4729 2.88 851 4992 1.67 086 9737 0263 498 28 33 662 4899 2.85 884 4898 181 9.87 0001 0.12 9999 490 27 34 676 5070 2.S8 816 4804 1.66 176 0265 9736 481 26 35 699 5240 299 4711 1.67 221 0529 947 1 478 25 36 622 5410 282 4617 267 0793 9207 466 24 37 646 5580 ■ 264 4523 812 1057 8943 457 23 38 669 5750 247 4429 357 1321 8679 449 22 39 693 6920 280 4335 402 1585 8415 440 21 40 .59 716 9.77 6090 2.82 .80 212 9.90 4241 1.67 .74 447 9.87 1849 4.88 0.12 8151 1.8432 20 41 789 6269 2.83 196 4147 492 2112 4.40 7888 424 19 42 763 6429 2.82 178 4053 588 2376 7624 416 18 43 786 6598 2.83 160 3959 1.68 688 2640 4.88 7360 408 17 44 809 6768 2.82 148 3864 1.57 628 2903 4.40 7097 400 16 45 832 6937 125 3770 674 3167 4.88 6833 892 16 46 856 7106 108 3676 1.68 719 3430 4.40 6570 384 14 47 879 7275 091 3581 1.57 764 3694 4.38 6306 375 13 48 902 7444 078 3487 1.58 810 3957 6043 867 12 49 926 7613 2.80 056 3392 1.57 866 4220 4.40 5780 869 11 50 .59 949 9.77 7781 2.82 .80 088 9.90 3298 1.68 .74 900 9.87 4484 4.88 0.12 5516 1.8851 10 51 972 7950 021 3203 946 4747 5253 348 9 52 995 8119 2.80 008 3108 1.67 991 5010 4990 835 8 53 .60 019 8287 .79 986 3014 1.58 .75 087 5273 4.40 4727 327 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 934 2729 173 6063 3937 808 4 57 112 8960 916 2634 219 6326 3674 296 3 58 185 9128 2.78 899 2539 264 6589 3411 287 2 59 158 9296 2.80 881 2444 810 6852 4.87 3148 278 1 60 .60 182 9.77 9463 .79 864 9.90 2349 ' .76 866 9.87 7114 0.12 2886 1.8270 126° Nat. Log. Dtf. Nat. Log. Dif. Nat. Log. COTAHGEHTB. Dif. Log. Nat. 1 Tangents. 53° COSIKES. SnfES. Vn. TRIGONOMETRIC FUNCTIONS. 9T 1 37° SiHZS. OOSIHEB. Tangents. Dif. Cotangents. 142° Nnt. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .60 182 9.7> 9463 2.80 .79 864 9.90 2349. 1.60 .75 855 9.87 7114 4.88 0.12 2886 1.8270 60' 1 205 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 437 2097 246 57 4 274, 9.78 0133 793 1967 1.58 638 8165 438 1835 288 56 5 298 0300 776 1872 1.60 584 8428 1572 280 55 6 821 0467 7S8 1776 1.58 629 8691 487 1309 222 54 7 344 0634 741 1681 1.60 675 8953 483 1047 214 53 8 367 0801 728 1585 1.68 721 9216 4.87 0784 206 52 9 890 0968 2.T7 706 1490 1.60 767 9478 488 0522 198 51 10 .60 414 9.78 1134 2.78 .79 688 9.90 1394 1.60 .75 812 9.87 9741 487 0.12 0259 1.8190 50 11 437 1301 671 1298 868 9.88 0003 0.11 9997 182 49 12 460 1468 2.77 658 1202 904 0265 4.38 9735 175 48 13 483 1634 635 1106 950 0528 4.87 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 438 8686 148 44 17 576 2298 665 0722 184 1577 487 8423 185 43 18 599 2464 547 0626 1.62 180 1839 8161 127 42 19 622 2630 580 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 487 0.11 7637 1.8111 40 21 668 2961 2.77 494 0337 1.62 818 2625 7375 103 39 22 691 3127 2.75 477 0240 1.60 864 2887 485 7113 095 38 23 714 3292 2.77 459 0144 1.62 410 3148 437 6852 087 37 24 788 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 888 9757 594 4196 4.85 5804 056 33 28 880 4118 2.78 871 9660 1.60 640 4457 487 5543 048 32 29 853 4^82 2.75 363 9564 1.62 686 4719 485 5281 040 31 30 .60 876 9.78 4447 2.75 .79 835 9.89 9467 1.62 .76 788 9.88 4980 4.87 0.115020 1.8082 30 31 899 4612 2.73 818 9370 779 5242 4758 024 29 32 922 4776 2.75 800 9273 825 5504 485 4496 017 28 33 945 4941 2.78 282 9176 1.68 871 5765 4235 009 27 34 968 5105 264 9078 1.62 918 6026 487 3974 001 26 35 991 5269 247 8981 964 6288 4.85 3712 1.2993 25 36 .61 015 5433 229 8884 .77 010 6549 487 3451 985 24 37 088 5597 211 8787 1.68 057 6811 4.85 3189 977 23 38 061 5761 198 8689 1.62 108 7072 2928 970 22 39 081 5925 176 8592 1.68 149 7333 2667 962 21 40 .61 107 9.78 6089 2.72 .79 158 9.89 8494 1.62 .77196 9.88 7594 4.85 0.11 2406 1.2964 20 41 180 6252 2.73 140 8397 1.68 242 7855 1 2145 946 19 42 158 6416 2.72 122 8299 1.62 289 8116 437 1884 988 18 43 176 6579 105 8202 1.68, 885 8378 485 1622 981 17 44 199 6742 2.78 087 8104 882 8639 1361 923 16 45 222 6906 2.72 069 8006 428 8900 1100 91S 15 46 245 7069 051 7908 475 . 9161 4.88 0839 907 14 ■47 ,268 7232 033 7810 521 9421 485 0579 900 13 48 291 7395 2.70 016 7712 668 9682 0318 892 12 49 814 7557 2.72 .78 998 7614 615 9943 0057 884 11 50 .61 387 9.78 7720 2.72 .78 980 9.89 7516 1.63 .77 661 9.89 0204 485 0.10 9796 1.287S 10 51 360 7883 2.70 962 7418 708 0465 488 9535 869 9 52 888 8045 2.72 944 7320 754 0725 4.35 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 488 8753 846 6 ■ 55 ,451 8532 891 7025 1.65 895 1507 435 8493 888 5 56 474 8694 878 6926 1.68 941 1768 438 8232 880 4 57 497 8856 855 6828 1.65 988 2028 435 7972 822 3 58 520 9018 887 6729 1.68 .78 035 2289 488 7711 815 2 59 548 9180 ,819 6631 1.65 082 2549 435 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. Dif. Log. Nat. Tangents. 52° Cosines. Snras. COTAMGENTS. . L — — - 1 98 Vn. TRIGONOMETRIC FUNCTIONS. 38° Snras. 1 CosrNES. Tanobittb. COTAHGENTS. 141° Not. Log. Dif. Nat. Log. Dif. Not. Log. Dif. Log. Nat. 0' 61666 9.78 9342 2.70 .78 801 9.89 6532 1.66 .78129 9.89 2810 4.88 0.10 7190 1.2799 60' 1 689 9504 2.68 783 6433 1.68 176 3070 4.86 ■ 6930 792 69 2 612 9665 2.70 766 6335 1.66 222 3331 438 6669 784 58 3 635 9827 2.68 747 6236 269 3691 6409 776 57 4 668 9988 729 6137 816 3861 6149 769 56 5 681 9.79 0149 711 6038 868 4111 4.36 5889 761 56 G 704 0310 694 5939 410 4372 4.88 5628 768 64 726 0471 676 5840 467 4632 5368 746 63 8 749 0632 658 5741 1.67 604 4892 5108 788 62 9 772 0798 640 5641 1.65 661 5152 4848 781 61 10 .61 795 9.79 0954 2.68 .78 622 9.89 5542 1.65 .78 698 9.89 5412 4.88 0.10 4588 1.2728 50 11 818 1115 2.67 604 5443 1.67 646 5672 4328 716 49 12 841 1275 2.68 686 5343 1.66 692 5932 4068 708 48 13 864 1436 2.67 668 5244 789 6192 3808 700 47 14 887 1596 2.68 650 5145 1.67 786 6452 3548 698 46 15 909 1757 2.67 532 5045 884 6712 4.82 3288 686 45 16 982 1917 614 4945 1.66 881 6971 4.33 3029 677 44 n 956 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 775V 4.32 2249 656 41 20 .62 024 9.79 2557 2.66 .78 442 9.89 4546 1.67 .79 070 9.89 8010 4.88 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 8630 4.82 1470 682 38 23 092 3035 2.67 887 4246 212 8789 438 1211 624 37 24 118 3195 2.65 869 4146 269 9049 482 0951 617 36 25 188 3354 2.67 351 4046 806 9308 4.88 0692 609 35 26 160 3514 2.65 383 3946 854 9568 4.82 0432 602 34 27 188 3673 815 3846 1.68 401 9827 4.88 0173 694 33 28 206 3832 297 3745 1.67 449 9.90 0087 4.32 0.09 9913 587 32 29 229 3991 . 279 3645 1.68 496 0346 9664 579 31 30 .62 261 9.79 4160 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 2.66 248 3444 1.68 591 0864 488 9136 564 29 32 297 4467 225 3343 1.67 689 1124 482 8876 ' 657 28 33 820 4626 2.63 206 3243 1.68 686 1383 8617 649 27 34 842 4784 188 3142 784 1642 8358 642 26 35 366 4942 2.65 170 3041 781 1901 8099 584 25 36 388 5101 2.63 152 2940 829 2160 4.88 7840 527 24 37 411 5259 184 2839 1.67 877 2420 482 7680 519 23 38 488 5417 116 2739 1.68 924 2679 7321 612 22 39 466 5575 098 2638 1.70 972 2938 7062 604 21 40 .62 479 9.79 5733 2.68 .78 079 9.89 2536 1.68 .80 020 9.90 3197 482 0.09 6803 1.2497 20 41 602 5891 061 2435 067 3456 4.80 6544 489 19 42 624 6049 2.62 048 2334 115 3714 482 6286 482 18 43 547 6206 2.68 025 2233,, 168 3973 6027 476 17 44 570 6364 2.62 007 2132 1.70 211 4232 5768 467 16 45 692 6521 2.68 .77 988 2030 1.68 268 4491 5609 460 16 46 615 6679 2.62 970 1929 1.70 306 4750 4.80 5250 452 14 47 688 6836 962 1827 1.68 854 5008 4.82 4992 445 13 43 660 6993 934 1726 1.70 402 5267 4733 437 12 49 688 7150 916 1624 1.68 460 5526 4474 480 11 50 .62 706 9.79 7307 "*.62 .77 897 9.89 1523 1.70 .80 498 9.90 5785 4.80 0.09 4215 1.2428 10 51 728 7464 879 1421 646 6043 432 3957 416 9 52 761 7621 2.60 861 1319 694 6302 480 3698 408 8 53 774 7777 2.62 848 1217 642 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 482 2923 886 6 56 842 8247 788 0911 786 7336 480 2664 878 4 58 ' 864 8403 2.62 769 0809 884 7594 4.32 2406 871 3 887 8560 2.60 751 0707 882 7853 4.80 2147 864 2 59 909 8716 788 0605 980 8111 1889 356 1 60 .62 982 9.79 8872 .77 716 9.89 0603 .80 978 9.90 8369 0.09 1631 1.2849 i 128° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. COTAHQEMTS. Dif. Log. Nat. Tangents. 51° CosniES. SiSES. Til. TRIGONOMETRIC- FUNCTIONS. 99 1 39° Sines. COSIKEB. Tangents. Cotangents. 140° Nat. Log. Dif. Hat. Log. Dif. Nat. Log. Dif. Log. Nat. 1 0' .62 983 9.79 8872 2.60 .77 716 9.89 0503 1.72 .80 978 9.90 8369 4.82 0.09 1631 1.2849 60' 1 955 9028 696 0400 1.70 .81 027 8628 480 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 1.70 128 9144 0856 827 57 4 022 9495 641 0093 1.72 171 9402 0598 820 56 5 04,5 9651 2.58 628 9.88 9990 1.70 220 9660 0340 812 55 6 068 9806 2.60 605 9888 1.72 268 9918 4.82 0082 806 54 1 090 9962 2.58 586 9785 816 9.91 0177 480 0.08 9823 298 53 8 118 9.80 0117 568 9682 .864 0435 9565 290 52 9 185 0272 550 9579 1.70 418 0693 9307 288 51 10 .68 158 9.80 0427 2.58 .77 581 9.88 9477 1.72 .81461 9.91 0951 4.80 0.08 9049 1.2276 50 11 ISO 0582 518 9374 510 1209 8791 268 49 12 203 0737 494 9271 558 1467 8533 261 48 13 225 0892 476 9168 1.78 606 1725 4.28 8275 254 47 14 248 1047 2.57 458 9064 1.72 655 1982 4.80 8018 247 46 15 271 1201 2.58 489 89GJ. 708 2240 7760 289 45 16 293 1356 421 8858 752 2498 7502 282 44 17 816> 1511 2.57 402 8755 1.78 800 2756 7244 225 43 18 838 1665 884 8651 1.72 849 3014 428 6986 218. 42 19 861 1819 866 8548 1.78 898 3271 4.80 6729 210 41 20 .68 888 9.80 1973 2.68 .77 847 9.88 8444 1.72 .81946 9.91 3529 4.80 0.08 6471 1.2208 40 21 406 2128 2.57 829 8341 1.78 995 3787 428 6213 196 39 22 428 2282 810 8237 1.72 .82 044 4044 4.80 5956 189 38 23 461 2436 2.55 292 8134 1.78 092 4302 5698 181 37 24 478 2689 2.67 278 8030 141 4560 4.28 5440 174 36 25 496 2743 255 7926 190 4817 480 5183 167 35 26 518 2897 2.55 286 7822 288 5075 428 4925 160 34 27 540 3050 2.57 218 7718 287 5332 4.80 4668 158 33 28 563 3204 2.55 199 7614 886 5590 428 4410 145 32 29 685 3357 2.57 181 7510 885 5847 4153 188 31 30 .68 608 9.80 3511 2.56 .77 162 9.88 7406 1.78 .82 484 9.91 6104 4.80 0.08 3896 1.2181 30 31 630 3664 144 7302 488 6362 428 3638 124 29 32 668 3817 125 7198 1.75 681 6619 4.80 3381 117 28 33 676 3970 107 7093 1.78 580 6877 428 3123 109 27 34 698 4123 088 6989 629 7134 2866 102 26 35 720 4276 2.58 070 6885 1.75 678 7391 2609 095 25 36 742 4428 2.65 051 6780 1.78 727 7648 480 2352 088 24 37 765 4581 038 6676 1.75 776 7906 4.28 2094 081 23 38 787 4734 2.58 014 6571 825 8163 1837 074 22 39 810 4886 2.55 .76 996 6466 1.78 874 8420 1580 066 21 . 40 .68 882 9.80 5039 2.68 .76 977 9.88 6362 1.75 .82 928 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 .88 022 9191 0809 045 18 43 899 5495 921 6047 071 9448 0552 088 17 44 922 5647 903 5942 120 9705 0295 081 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 2.58 828 5522 1.77 817 0733 9267 002 12 49 088 6406 2.62 810' 5416 1.75 866 0990 9010 1.1995 11 50 .64 056 9.80 6557 2.53 .76 791 9.88 5311 1.77 .88 415 9.92 1247 4.27 0.07 8753 1.1988 10 51 078 6709 2.52 . 772 5205 1.75 465 1503 428 8497 981 9 52 100 6860 764 5100 1.77 514 1760 8240 974 8 53 128 7011 2.68 785 4994 1.76 564 2017 7983 967 7 54 145 7163 2.52 717 4889 1.77 618 2274" 427 7726 960 6 55 167 7314 698 4783 662 2530 428 7470 958 5 56 190 7465 2.50 679 4677, 1.75 712 2787 7213 946 4 57 212 7615 2.52 661 4572 i.77 761 3044 427 6956 989 3 58 284 7766 642 4466 811 3300 4.28 6700 982 2 59 256 7917 2.60 628 4360 860 3557 6443 925 1 60 .64 279 9.80 8067' .76 604 9.88 4254 .88 910 9.92 3814 0.07 6186 1.1918 .129° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Cotangents. Log. Nat. 50° Cosines. Sines. 100 Vn. TRIGONOMETRIC FUNCTIONS. 40° Sines. Cosines. TANGENra. Dif. Cotangents. 139° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .64 279 9.80 8067 2.62 .76 604 9.88 4254 1.77 .88 910 9.92 3814 4.27 0.07 6186 1.1918 60' 1 801 8218 2.50 586 4148 960 4070 4.28 6930 910 59 2 823 8368 2.52 567 4042 .84 009 4327 4.27 5673 908 58 3 846 8519 2.50 648 3936 1.78 069 4583 4.28 5417 896 57 4 868 8669 680 3829 1.77 108 . 4840 4.27 5160 889 56 5 890 8819 611 3723 168 5096 4904 882 55 6 «2 8969 492 3617 1.78 208 5352 4.28 4648 876 54 1 485 9119 478 3510 1.77 258 5609 "4.27 4391 868 53 8 467 9269 465 3404 1.78 807 5865 4.28 4135 861 52 9 479 9419 436 3297 1.77 857 6122 4.27 3878 884 51 10 .64 601 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 11 624 9718 2.60 898 3084 467 6634 3366 840 49 12 646 9868 2.48 880 2977 1.77 507 6890 4.28 3110 833 48 13 668 9.810017 2.50 361 2871 1.78 656 7147 4.27 2853 826 47 14 690 0167 2.48 842 2764 606 7403 2597 819 46 15 612 0316 823 2657 656 7659 2341 -812 45 16 685 0465 304 2550 706 7915 2085 806 44 n 667 0614 286 2443 756 8171 1829 799 43 18 679 0763 267 2336 806 8427 4.23 1573 792 42 19 701 0912 248 2229 1.80 856 8684 4.27 1316 786 41 20 .64 728 9.81 1061 2.48 .76 229 9.88 2121 1.78 .84 906 9.92 8940 427 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 1.78 067 9708 0292 767 37 24 812 1655 2.48 154 1692 1.80 107 9964 0036 750 36 25 884 1804 2.47 185 1584 1.78 167 9.93 0220 4.26 0.06-9780 748 35 26 866 1952 116 1477 1.80 207 0475 427 9525 736 34 21 878 2100 097 1369 257 0731 9269 729 33 28 901 2248 078 1261 808 0987 9013 722 32 29 928 2396 059 1153 1.78 858 1243 8757 716 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 2695 022 0938 468 1755 4.26 8245 702 29 32 989 2840 003 0830 509 2010 4.27 7990 695 28 33 .66 Oil 2988 2.45 .75 984 0722 1.82 859 2266 7734 688 27 • 34 088 3135 2.47 965 0613 1.80 609 2522 7478 , 681 26 35 066 3283 2.45 946 0505 660 2778 4.26 7222 674 25 36 077 3430 2.47 927 0397 710 3033 4.27 6967 667 24 37 100 3578 2.46 908 0289 1.82 761 3289 6711 660 23 38 122 3725 889 0180 1.80 811 3545 4.25 6455 668 22 39 144 3872 870 0072 1.82 862 3800 427 6200 647 21 40 .65166 9.814019 2.46 .76 861 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 683 19 42 210 4313 81^ 9746 .86 014 4567 4.25 5433 626 18. 43 282 4460 794 9637 1.80 064 4822 4.27 5178 619 ■17 44 254 4607 2.48 775 9529 1.82 116 5078 4.25 4922 612 16 45 276 4753 2.45 756 9420 166 5333 4.27 4667 606 15 46 298 4900 2.48 788 9311 216 5589 4.25 4411 509 14 47 820 5046 2.45 719 9202 267 5844 4.27 4156 692 13 48 842 5193 2.48 700 9093 818 6100 4.28 3900 586 12 49 864 5339 680 8984 868 6355 4.27 3645 578 11 50 .66 886 9.81 5485 2.46 .76 661 9.87 8875 1.82 .86 419 9.93 6611 425 0.06 3389 1.1571 10 51 408 5632 2.48 642 8766 1.88 470 6866 3134 568 9 52 480 5778 628 8656 J.82 521 7121 4.27 2879 588 8 53 462 5924 2.42 604 8547 672 7377 425 2623 581 7 54 474 6069 2.43 585 8438 1.83 623 7632 2368 844 6 55 496 6215 666 8328 1.82 674 7887 2113 688 5 56 618 6361 847 8219 1.83 725 8142 427 1858 681 4 57 510 6507 2.42 528 8109 776 8398 425 1602 624 3 58 562 6652 2.48 609 7999 1.82 827 8653 1347 517 2 59 ;m 6798 2.42 490 7890 1.83 878 8908 1092 510 1 60 .65 606 9.81 6943 .76 471 9.87 7780 .86 929 9.93 9163 0.06 0837 1.1804 130° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 49° COSIHES. Sines. COTANGENTB. Tangents. MATH. DEPT. TH. TRIGONOMETRIC FUNCTIONS. 101 41° SiKIB. Cosines. Tangents. Dif. Cotangents. 138° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Log. Nat. 0' .65 606 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' 1 628 7088 452 7670 980 9418 0582 497 59 2 650 7233 2.48 433 7560 .87 081 9673 0327 490 58 3 672 7379 2.42 414 7450 082 . 9928 0072 483 57 4 694 7524 2.40 396 7340 188 9.94 0183 4.27 0.05 9817 477 56 , 5 716 7668 '2.42 876 7230 184 0439 4.25 9561 470 55 6 788 7813 856 7120 236 0694 9306 463 54 1 759 7958 887 7010 1.85 287 0949 9051 456 53 8 781 8103 2.40 818 6899 1.83 888 1.204 8796 450 52 9 803 8247 2.42 299 6789 1.85 889 1459 4.28 8541 448 51 10 .66 826 9.81 8392 2.40 .75 280 9.87 6678 1.88 .87 441 9.94 1713 4.26 0.05 8287 1.1486 50 11 847 8536 2.42 261 6568 1.86 492 1968 8032 480 49 12 869 8681 2.40 241 6457 1.88 643 2223 7777 423 48 13 891 8825 222 6347 1.86 695 2478 7522 416 47 14 913 8969 208 6236 646 2733 7267 410 46 15 936 9113 184 6125 698 2988 7012 408 45 16 956 9257 165 6014 1.88 749 3243 6757 896 44 IT 978 9401 146 5904 1.86 801 3498 4.28 6502 889 43 18 .66 000 9545 126 5793 852 3752 4.25 6248 883 42 19 022 9689 2.88 107 5682 904 4007 5993 376 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 1.86 .88 007 4517 4.23 5483 363 39 22 088 9.82 0120 2.88 050 5348 069 4771 4.25 5229 366 38 23 109 0263 030 5237 110 5026 4974 349 37 24 131 0406 2.40 Oil 5126 1.87 162 5281 4.28 4719 343 36 25 163 0550 2.88 .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 1.85 817 6045 4.28 3955 828 33 28 • 218 0979 984 4680 1.87 869 6299 4.25 3701 816 32 29 240 1122 916 4568 421 6554 4.28 3446 810 31 30 .66 262 9.82 1265 2.37 .74 896 9.87 4456 1.87 .88 478 9.94 6808 4.25 0.05 3192 1.1808 30 31 284 1407 2.88 876 4344 624 7063 2937 296 29 32 806 1550 857 4232 1.85 576 7318 4.23 2682 290 28 33 827 1693 2.37 838 4121 1.87 628 7572 4.25 2428 288 27 34 849 1835 818 4009 1.88 680 7827 4.28 2173 276 26 35 871 1977 2.88 799 3896 1.87 732 8081 1919 270 25 36 893 2120 2.87 780 3784 784 8335 4.25 1665 263 24 37 414 2262 760 3672 836 8590 4.28 1410 267 23 38 486 2404 741 3560 888 8844 4.25 1156 250 22 39 458 2546 722 3448 1.88 940 9099 4.23 0901 248 21 40 .66 480 9.82 2688 2.87 .74 708 9.87 3335 1.87 .88 992 9.94 9353 4.26 0.05 0647 1.1287 20 41 501 2830 683 3223 1.88 .89 045 9608 4.28 0392 230 19 42 528 2972 664 3110 1.87 097 9862 0138 224 18 43 645 3114 2.85 644 2998 1.88 149 9.95 0116 4.25 0.04 9884 217 17 44 566 3255 2.37 625 2885 201 0371 4.23 9629 211 16 45 588 3397 606 2772 258 0625 9375 204 15 46 610 3539 2.35 686 2659 1.87 806 0879 9121 197 14 47 682 3680 667 2547 1.88 868 1133 4.25 8867 191 13 48' 658 3821 2.87 548 2434 410 1388 4.28 8612 184 12 49 676 3963 2.85 528 2321 468 1642 8358 178 11 50 .66 697 9.82 4104 2.85 .74 609 9.87 2208 1.88 .89 516 9.95 1896 4.28 0.04 8104 1.1171 10 51 718 4245 489 2095 1.90 667 2150 4.25 7850 165 9 52 740 .4386 ■ 470 1981 1.88 620 2405 4.28 7595 158 8 53 762 4527 461 1868 672 2659 7341 152 7 54 788 4668 2.88 431 1755 1.90 725 2913 7087 146 6 55 805 4808 2.85 412 1641 1.88 777 3167 6833 189 5 56 827 4949 892 1528 1.90 880 3421 6579 182 4 57 848 5090 2.88 878 1414 1.88 888 3675 6325 126 3 58 870 5230 2.85 858 1301 1.90 985 3929 6071 119 2 59 891 5371 2.88 884 1187 988 4183 5817 113 1 60 .66 918 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° Cosiiira. Sines. Tangents. 10 i Vn. TRIGONOMETRIC FUNCTIONS. 42° SiSES. Cosines. Tanobnto. COTANOESra. 137° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. 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' 1 985 5651 295 0960 1.90 098 4691 4.25 5309 100 59 2 950 5791 276 0846 146 4946 4.23 6054 098 58 3 978 5931 266 0732 199 5200 4800 087 57 4 999 6071 287 0618 251 5454 4546 080 56 5 .67 021 6211 , 217 0504 304 5708 4.22 4292 074 55 6 043 6351 198 O390 867 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 1.90 468 6469 3531 064 52 9 107 6770 2.88 189 0047 616 6723 3277 048 51 10 .67 129 9.82 6910 2.82 .74 120 9.86 9933 1.92 .90 669 9.95 6977 4.28 0.04 3023 1.1041 50 11 161 7049 2.83 100 9818 1.90 621 7231 2769- 085 49 12 1T2 7189 2.32 080 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 15 287 7606 022 9360 1.92 884 8247 4.22 1753 009 ' 45 16 263 7745 002 9245 887 8500 4.28 1500 003 44 17 280 7884 .78 988 9130 940 8754 1246 1.0996 43 18 801 8023 963 9015 998 9008 0992 990 42 19 323 8162 944 8900 91046 9262 0738 983 41 20 .67 844 9.82 8301 2.80 .78 924 9.86 8785 1.92 91099 9.95 9516 4.22 0.04 0484 1.0977 40 21 866 8439 2.82 904 8670 .168 9769 4.23 0231 971 39 22 387 8578 2.80 '885 8555 206 9.96 0023 0.03 9977 964 38 23 409 8716 2.82 865 8440 1,93 259 0277 4.22 972;3 968 37 24 430 8855 2.80 846 8324 1.92 318 0530 4.28 9470 951 36 25 462 8993 826 8209 1.93 806 0784 9216 946 35 26 4T8 9131 806 8093 1.92 419 1038 8962 989 34 27 495 9269 787 7978 1.98 473 1292 4.22 8708 982 33 28 616 9407 767 7862 1.92 626 1545 4.28 8455 926 32 29 538 9545 747 7747 1.98 680 1799 4.22 8201 919 31 30 .67 659 9.82 9683 2.80 .73 728 9.86 7631 1.98 .91633 9.96^052 4.28 0.03 7948 1.0918 30 31 680 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 34 646 0234 2.80 649 7167 847 3067 4.22 6933 888 26 35 666 0372 2.28 629 7051 901 3320 4.28 6680 881 25 36 6S8 0509 610 6935 965 3574 6426 875' ' 24 37 709 0646 2.80 590 6819 .92 008 3828 4.22 6172 869 23 38 780 0784 2.28 670 6703 1.95 062 4081 4.23 5919 862 22 39 762 0921 561 6586 1.98 116 4335 4.22 5665 856 21 40 .67 778 9.83 1058 2.28 .73 531 9.86 6470 1.95 .92 170 9.96 4588 4.28 0.03 5412 1.0850 20 41 795 1195 611 6353 1.93 224 4842 4.22 5158 843 19 42 816 1332 491 6237 1.95 277 5095 4.28 4905 887 18 43 887 1469 472 6120 1.98 331 5349 4.22 4651 881 17 44 859 1606 2.27 462 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 2.27 418 5770 493 6109 4.22 3891 .812 14 47 923 2015 2.28 393 5653 . 547 6362 4.28 3638 805 • 13 48 944 2152 2.27 878 5536 601 6616 4.22 3384 799 12 49 965 2288 2.28 858 5419 666 6869 4.23 3131 793 11 50 .67 987 9.83 2425 2.27 .73 333 9.86 5302 1.95 .92 709 9.96 7123 4.22 0.03 2877 1.0786 10 51 .68 008 2561 314 5185 763 7'376- 2624 780 9 52 029 2697 294 5068 1.97 817 7629 4.23 2371 774 8 53 051 2833 274 4950 1.96 872 7883 4.22 2117 768 7 54 072 2969 254 4833 926 813S 1864 761 6 ; 55 093 3105 284 4716 1.97 980 8389 4.23 1611 1.0755 5 56 116 3241 215 4598 1.95 .93 034 8643 4.22 1357 749 4 57 136 3377 2.26 195 4481 1.97 088 8896 1104 742 : 3 58 167 3512 2.27 175 4363 143 9149 4.28 0851 786 2 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 .98 262 9.96 9656 0.03 0344 1.0724 132° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. COTAMGEHTS. Log. Nat. Tasgesm. 47° COSISES. SlHES. VII. TRIGONOMETKIC FUISrCTIONS. 103 1 43° Sines, COBINEB. Taksentb. Cotangentb. 136° Nat. Log. Dif. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 0' .68 200 9.83 3783 2.27 .78 186 9.86 4127 1.95 .98 252 9.96 9656 4.22 0.03 0344 1.0724 60' 1 221 3919 2.25 116 4010 1.97 806 "9909 0091 717 59 2 242 4054 096 3892 860 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 5 806 4460 086 3538 1.98 524 0922 9078 692 55 6 327 4595 016 3419 1.97 578 1175 4.28 8825 686 , 54 7 849 4730 .72 996 3301 688 1429 4.22 8571 680 53 8 870 4865 2.28 976 3183 1.98 683 1682 8318 674 52 9 891 4999 2.25 967 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 J,-rS661 50 11 484 5269 2.28 917 2827 1.97 862 2441 4.28 75^ 655 49 12 455 5403 2.25 897 2709 1.98 906 2695 4.22 ^05 649 48 13 476 5538 2.23 877 2590 961 2948 %062 643 47 M ■497 5672 2.25 857 2471 1.97 .94 016 3201 6799 637 46 15 518 5807 2.28 887 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 285 4213 5787 612 42 19 603 ^343 767 1877 290 4466 4.2S 5534 606 41 20 .68 624 9.83 6477 2.23 .72 737 9.86 1758 2.00 .94 846 9.97 4720 4.22 0.02 5280 1.0599 40 21 645 6611 717 1638 1.98 400 4973 5027 693 39 22 666 6745 2.22 697 1519 465 -5226 4774 687 38 23 688 6878 2,23 677 1400 2.00 610 5479 4521 581 37 24 709 7012 667 1280 1.98 565 5732 4268 675 36 25 780 7146 2.22 687 .1161 2.00 620 5985 4015 569 35 26 761 7279 617 1041 1.98 676 6238 3762 562 34 27 772 7412 2.23 597 0922 2.00 731 6491, 3509 656 33 28 798 7546 2.22 577 0802 786 6744 3256 650 32 29 814 7679 567 0682 841 6997 3003 644 31 30 .68 835 9.83 7812 2.22 .72 587 9.86 0562 2.00 .94896 9.97 7250 4.22 0.02 2750 1.0538 30 31 857 7945 617 0442 952 7503 2497 582 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 467 0082 118 8262 1738 613 26 35 941 8477 437 9.85 9962 178 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 483 21 40 .69 046 9.83 9140 2.20 .72 887 9.85 9360 2.02, .96 461 9.97 9780 4.22 0.02 0220 1.0477 20 41 067 9272 817 9239 2.00 506 9.98 0033 0.01 9967 470 19 42 08S 9404 297 9119 2.02 562 0286 4.20 9714 464 18 " 43 109 9536 277 8998 618 0538' 4.22 9462 468 17 44 ISO 9668 257 8877 678 0791 9209 462 16 45 151 9800 236 8756 729 1044 8956 446 15 46 172 9932 216 8635 785 1297 8703 440 14 47 198 9.84 0064 196 8514 841 1550 8450 484 13 48 214 0196 176 8393 897 1803 8197 428 12 49 285 0328 2.18 156 8272 962 2056 7944 422 11 50 .69 266 9.84 0459 2.20 .72 186 9.85 8151 2.08 .96 008 9.98 2309 4.22 0.017691 1.0416 10 51 277 0591 2.18 116 8029 2.02 064 2562 4.20 7438 410 9 52 298 0722 2.20 096 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 066 7665 2.08 282 3320 6680 392 6 55 861 1116 086 7543 2.02 288 3573 6427 885 5 56 882 1247 015 7422 2.08 344 3826' 6174 379 4 57 403 1378 .71 995 7300 400 4079 5921 873 3 58 424 1509 .974 7178 457 4332 4.20 5668 867 2 59 445 1640 / 951 7056 518 4584 4.22 5416 361 1 60 .69 466 9.84 1771 \ .71 934 9.85 6934 .96669 9.98 4837 0.015163 1.0855 133° Nat. Log. L. Nat. Log. Dif. Nat. Log. Dif. Log. Nat. 46° COBIHES. SlWES. C9TAK6ENT8. Tahgehts. 104 Vn. TRIGONOMETRIC FUNCTIONS. 1 44° 0' Sinks. CkMIHKS. Tan&ents. Dif. COTANaKNTC. 135° Nat Log. Dif. Nat Log. Dlf. Nat. Log. Log. Nat .69 466 9.84 1771 2.18 .71934 9.85 6934 2.08 .96 669 9.98 4837 4.22 0.01 5163 i.o?b;} 60' 1 487 1902 914 6812 625 5090 4910 849 59 2 BOS 2033 2.17 894 6690 681 5343 4657 848 58 3 629 2163 2.18 8T8 6568 738 5596 4.20 4404 887 57 •i 549 2294 2.17 853 6446 2.05 794 5848 4.22 4152 831 56 5 670 2424 2.18 \888 6323 2.08 860 6101 3899 826 65 6 591 2555 2.17 818 6201 2.05 907 6354 3646 819 54 7 612 2685 792 6078 2.08 963 6607 3393 313 53 8 683 2815 2.18 772 5956 2.05 .97 020 6860 4.20 3140 807 62 9 664 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 .97 188 9.98 7365 422 0.01 2636 1.0295 60 11 696 3206 711 5588 189 7618 2382 239 49 12 717 3336 691 5465 246 7871 4.20 2129' 283 48 13 787 3466 2.16 671 5342 302 8123 422 1877 277 47 14 758 3595 2.17 650 5219 369 8376 1624 271 46 15 779 3725 680 5096 416 8629 1371 265 45 16 800 3855 2.15 610 4973 472 8882 4.20 1118 259 44 17 821 3984 2.17 690 4850 629 9134 422 0866 258 43 18 842 4114 2.15 669 4727 2.07 686 9387 0613 247 42 19 862 4243 649 4603 2.05 648 9640 0360 241 41 20 .69 883 9.84 4372 2.17 .71 629 9.85 4480 2.07 .97 700 9.98 9893 420 0.01 0107 1.0286 ■ 40 21 904 4502 2.16 508 4356 2.05 766 9.99 0145 4.22 0.00 9855 280 39 22 926 4631 488 4233 2.07 813 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 36 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 2.13 866 3490 165 1914 4.22 8086 188 32 29 070 5533 2.15 845 3366 218 2167 7833 182 31 30 .70 091 9.84 5662 2.18 .71 825 9.85 3242 2.07 .98 270 9.99 2420 4.20 0.00 7580 1.0176 ,30 31 112 5790 2.15 308 3118 827 2672 422 7328 170 29 32 182 5919 2.18 284 2994 2.08 884 2925 7075 164 28 33 158 6047 264 2869 2.07 441 3178 6822 158 27 34 174 6175 2.15 248 2745 2.08 499 3431 4.20 6569 152 26 35 195 6304 2.13 228 2620 2.07 656 3683 422 .6317 147 26 36 218 6432 208 2496 2.08 618 3936 6064 141 24 37 236 6560 182 2371 2.07 671 4189 420 5811 186 23 38 267 6688 162 2247 2.08 728 4441 422 5559 ■ 129 22 39 277 6816 141 2122 786 4694 5306 123 21 40 .70 298 9.84 6944 2.12 .71 121 9.85 1997 2.08 .98 848 9.99 4947 420 0.00 5053 1.0117 20 41 819 7071 2.13 100 1872 901 5199 4.22 4801 111 19 42 889 7199 080 1747 968 5452 4548 105 18 43 860 7327 2.12 069 1622 .99 016 5705 420 4295 090 17 44 881 7454 2.13 039 1497 078 5957 422 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 646S 4.20 3537 082 14 47 448 7836 2.18 978 1121 247 6715 4.22 3285 076 13 48 463 7964 2.12 967 0996 2.10 804 6968 3032 . 070 12 49 484 8091 937 0870 2.08 362 7221 4.20 2779 064 11 50 .70 605 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 062 9 52 546 8472 875 0493 2.08 586 7979 420 2021 047 8 53 567 8599 856 0368 2.10 594 8231 422 1769 041 7 54 687 8726 2.10 834 0242 652 8484 1516 085 6 55 608 8852 2.12 818 0116 -■H* 8737 420 1263 029 6-' 56 628 8979 798 9.84 9990 768 8989 422 1011 023 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 012 2 59 690 9359 2.10 781 9611 2.10 942 9747 422 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. I-og. Dlf. Nat Log. Dif. Nat Log. C!OTANGENTS. Dlf. Log. Nat Tangents. 45° Cosines. SlIfES. Vin. NATURAL LOGARITHMS. 105 Num. Log. Num. Log. Num. Loo. Num. Log. Num. Log. s 1 .00 00 .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 6055 .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 .0,'3 6.49 3442 .53 9 36 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 0.113329 .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 §.16 7419 .66 9.58 4485 .16 0.14 8420 .66 6818 .16 0.77 0108 .n 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;i7 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 .73 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 9.813670 .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 .88 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. Loo. Num. Log. Num. Log. Num. Loo. Num. Loo. 106 Vin. NATURAL LOGARITHMS. Ndm. Log. Num. Loo. Num. Log. Num. Loo. Num. Loo. 2.60* 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 7405 .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 1.68 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 8400 .93 5339 .94 8410 .44 5471 .94 1.37 1181 .44 1.49 0654 .94 7366 .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 Nn«. Loo. NOM. Log. Num. Loa. Num. Log. Num. Log. Ym. NATURAL LOGARITHMS. 107 NrM. Log. Num. Log. NCM. . 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 1.710188 .03 6747 i .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 1 .05 3028 .06 1.62 1366 .56 5598 .06 1710 .56 1.88 0991 '■ .06 4445 .07 3341 .57 7395 : .07 3359 i .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 1.811562 : .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 .n 2873 .67 5189 .17 9699 .67 7620 .17 9906 .18 4805 .68 6951 '■ .18 1.82 1318 .68 9118 .18 1.97 1299 .19 S734 .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 .21 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 1 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 i .32 3719 .82 9859 .32 1.99 0610 .33 3351 .83 3017 ; .33 5300 .83 1.92 1325 .33 1976 .34 5226 .84 4731 1 .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 i .92 4416 , .42 4179 ; .43 1939 .93 1.78 0024 .43 1.86 0975 1 .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 95.55 ■ .47 9279 .97 6747 .47 7176 I .97 1615 .47 2.01 0895 ! -^S - ,1.70 1105 ': .98 8421 ' .48 8721 ' .98 3049 .48 2233 ' , .49 * 29,28 i i .99 1.79 0091 .49 1.87 0263 .99 4481 .49 3569 Ndm. Log. Num. Log. Nmi. Loo. Num. Log. Num. LCKl. - -■■ 108 vm. naturaij logarithms. I — 1 Num. Loo. Num. Loo. Ndm. Loo. NlTM. Loo. Num. Loo. 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 .61 1242 .01 8335 .61 2344 .52 7566 .02 1938 .52 2416 .02 9444 .52 3395 .53 8895 .03 3185 .53 3589 .03 2.20 0552 .63 4445 .54 2.02 0222 .04 4429 .54 4761 .04 1659 .64 6493 .65 1548 .05 5672 .55 5931 .05 2765 .55 6541 .56 2871 .06 6914 .66 7100 .06 3869 .56 7588 .57 4193 .07 8153 .67 8268 .07 4972 .67 8633 .58 5513 .08 9392 .68 9434 .08 6074 .58 9678 .59 6832 .09 2.09 0629 .69 2.16 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 2.210470 .62 3844 .63 2088 .13 5561 .63 6245 .13 1566 .63 4883 .64 3398 .14 6790 .64 6403 .14 2660 .64 6921 .65 4706 .15 8018 .65 7659 .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 6353 .71 4472 .21 2.22 0290 .71 3166 .72 3814 .22 6670 .72 5619 .22 1375 .72 4186 .73 5109 .23 7786 .73 6765 .23 2459 .73 6214 .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 3616 .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 3236 .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 6376 .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 6848 .88 3802 .38 8680 .88 2.29 0513 .89 5596 .39 7041 .89 4927 .39 9646 .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 2536 .91 8128 .41 9421 .91 7174, .41 1773 .91 3544 .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 1664 .45 6015 .95 7573 .96 4429 .46 5349 .96 2770 .46 7072 .96 8577 .97 5684 .47 6631 .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 0239 .99 1685 Nun. L06. NtTM. Loo. NUH. Loo. Num. Loo. Num. Loo. 1 VIII. NATURAL LOGARITHMS. •> 109 1 Num. Log. Num. Loo. 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 4.615121 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 1 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 4.7,2 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 0B38 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 4-522 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 3.218876 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 5.241747 39 6464 40 3.68 8879 90 4.49 9810 140 4.94 1642 190 5.24 7024 240 6.48 0639 41 3.713572 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 6.49 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 6.27 3000 45 6.50 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 6.513429 49 3.89 1820 99 4.59 5120 49 5.00 3946 99 5.29 3305 49 7453 Num. Loa. Num. Log, Num. Log. Num. Log. Num. Log. 110 Vin. NATURAL LOGARITHMS. h Nan. i Loo. Num. Loo. Num. Loo. Num. Loo. Num. Loo. •^50 5.52 1461 300 5.70 3782 350 5.85 7933 400 5.99 1465 450 6.10 9248 51 545 S 01 7110 51 5.86 0786 01 3961 51 6.11 1467 i 52 9429 02 5.71 0427 52 3631 02 6452 62 3682 : 53 5.53 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 66 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 66 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 8468 69 4711 19 5191 69 5.910797 19 7871 69 6.16 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 6.92 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 0401 26 6897 76 9589 26 4439 76 5418 77 4018 27 9960 77 5.93 2245 27 67.84 77 7616 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 6.66 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 8479 93 5.68 0173 43 7730 93 3810 43 3570 93 6.20 0509 94 3580 44 5.84 0642 94 6351 44 6825 94 2536 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 6676 97 3732 47 9325 97 3936 47 2559 97 8690. 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. Log. Num. Log. Num. Loo. Num. Loo. Num. Loo. YIII. NATURAL LOGARITHMS. Ill Num. Log. Num. too. Num. Loo. 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 05 5228 55 4635 05 8198 06 6537 56 6.32 ores 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 6.510258 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 6030 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. Loa. Num. Loo. Num. Log. Num. Loo. Num. Log. 112 Vin. NATURAL LOGARITHMS. ■ ' — ■ - ■ » NOM. Loo, NOM. Loo. Num. Loo. Num. LOQ, Num. Loo. 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 6.829 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 f> 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 6,813445 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 63 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 6.710523 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 Nl-M. ■ Loo. NOH. Loo. NXJM. Loo. Num. Loo. Num. Loo, VIII. NATURAL LOGARITHMS. 113 — " ■■ 1 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 65 1856 05 4235 06 3737 56 2243 06 8505 66 2721 06 6064 Ot 4731 57 3190 "< 07 9409 57 3586 07 6893 08 5723 58 4136 08 7.01 0312 58 4450 08 6721 09 6715 59 5080 09 1214 59 5313 09 7549 lOlO 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 6712 "'64 9618 14 1676 15 2644 65 6.97 0730 15 6610 66 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 7.113956 21 8538 71 6348 21 1976 71 5613 31 5682 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 69 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 21 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 7.215975 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 il 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. Loo. Num. Log. Num. Log. Num. Log. Num. Log. 114 Vin. NATURAL LOGARITHMS. NlM. Log. NrM. Log. Num. Log. Num. Log. Num. Log. U53 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 33 1822 67 7.53 2088 51 9130 59 5705 37 8625 S7 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 6268 53 7944 33 6828 33 7.75 4910 11 5073 21 6909 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 7.918992 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 0303 91 4155 21 7447 21 7.39 0799 27 7.614312 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 0427 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 8.114624 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 NrM. Log. NCM. Log. Num. Log. Num. Log. Num. Log. Vni. NATURAL LOGARITHMS. 115 1 Num. Log. n™. Log. Nmu. Log. Num. Log. n™. Log. 3483 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 6D88 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 4-743 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 8.410276 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 8.510571 13 6559 91 8.21 3653 99 8498 23 6931 69 0974 17 7297 97 6277 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. Loo. Ndm. Log. Num. Log. n™. Log. 116 YrH. NATURAL LOGARITHMS. < Ndh. Log. Nra. Log. Ndm. Log. Num. Log. Num. Loo. 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 63 3893 6007 8.70 0681 97 3584 69 4774 31 9867 79 4971 11 1346 6421 7329 71 6065 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 2692 91 8913 43 6656 51 1990 6907 8.84 0291 69 5037 6623 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 8.710620 6481 8.77 6630 6947 8.84 6065 7417 8.91 1530 47 8880 73 1608 91 8172 49 6363 33 3685 51 9588 79 2696 6621 8.78 2783 69 7791 51 6104 53 9942 89 4239 29 4009 61 8078 57 6908 57 8.64 0649 91 4668 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 5886 27 7515 29 6518 41 5389 97 8.73 1821 19 7700 39 9^21 37 7580 43 6737 99 2143 37 8.80 0415 43 9789 41 8110 49 6781 6203 2788 63 2823 57 8.86 1776 47 8905 79 8.66 1986 11 4077 69 3725 69 3474 49 9170 83 2678 17 6043 61 4025 79 4888 59 8.93 0494 91 4060 21 5686 73 6825 " 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 9867 89 • 8220 21 8.87 0803 77 2873 13 7862 57 8.74 1456 91 8519 27 1646 83 3664 21 9227 63 2415 6701 8.810012 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 6370 93 0864 39 8.94 1022 57 5393 6301 8464 61 8926 7207 2808 43 1545 5861 8.67 6076 6311 8.75 0049 6763 8.819222 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 3363 29 6866 81 6505 81 9482 37 4161 93 3648 37 6962 87 7286 97 8.68 2199 43 6107 6803 6119 43 7791 91 7806 5903 3216 63 6682 23 8055 47 8343 99 8846 23 6598 59 7626 27 8641 53 9170 7703 9366 27 7273 61 7941 29 8934 83 8.89 3298 17 8.95 1181 39 9296 67 8884 33 9519 97 5219 23 1958 Num. Loo. Num. Log. Num. Log. Num. Loo. Num. Log. Vm. NATURAL LOGARITHMS. m Ndm. Loo. NlTM. Log. Num. Loa. Ndm. Log. Num. Log. 772'? 8.95 2476 8221 9.01 4447 8681 9.06 8892 9127 9.118992 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 63 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 i6373 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 9.01 0791 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 leooo 9.21 0340 If DM. Los. Num. Los. 1 NtTM. Log. Num. Log. Num. Loo. 118 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 7 9 NOM. 1 3 7 9 000 000 0000 477 121 2647 846 098 0400 32 50 3-167 701 567 9861 3-132 706 717 7828 1 041 892 6862 118 948 3623 230 448 9214 278 768 6010 51 7-73 38-19 11-47 3.173 2 3-7 861 727 8360 3' 462 897 9979 52 716 887 7288 7186016889 17-31 232 3 491 861 6988 3-11 668 201 7241 3-13 53 32-59 13-41 3- 179' 7«-ll i 612 783 8667 688 468 4666 672 097 8679 72 54 783 197 2661 3. 181 787987 8268 32-6I 5 3-17 724 276 8696 319 770 852 0116 55 19-29 7.79 746 8661962 13-43 6 785 829 8860 3«-7 826 074 8027 3-23 56 3-11.17 760 608 8949 3^-7 755 112 2664 7 861 268 8487 868 822 8601 7-11 897 627 0913 57 756 636 1082 3-191 761 176 8182 3-193 8 3* 919 078 0924 3-29 949 890 0066 58 7-83 11-53 768 688 1012 19-31 9 7-13 3-31 986 7717848 32.11 59 3-197 778 064 6984 3-199 777 426 8224 10 004 821 8788 012 837 2247 029 888 7777 087426 4979 60 778 8744720 32-67 788 188 6911 3-7.29 11 3-37 068 078 4435 3* -13 7-17 61 13-47 787 460 4745 790 286 1640 791 690 6490 12 112 3-41 108 803 7210 3-43 62 33.23 7-89 3-11-19 17-37 13 117 271 2067 7-19 186 720 6672 143 014 8008 63 800 029 8692 3.211 72-13 32-71 14 3-47 11-13 3-72 178 186 2684 64 806 868 0296 808 210 9729 810 904 2807 11-59 15 178 976 9478 3«-17 195 899 6524 3-53 65 3-7-31 8149181818 32-73 818 8864146 16 7-23 212 187 6044 222 7164711 132 66 820 201 4695 3-13-17 23-29 3-223 n 3*. 19 238 046 1031 3-59 262 853 0810 67 11-61 828 016 0642 880 688 6687 7-97 18 257 678 5749 3-61 11-17 3'. 7 68 3.227 884 420 7087 3-229 13-53 19 281 088 8672 286 567 8090 294 466 2262 298 853 0764 69 889 478 0474 32.7-11 17-41 3-233 20 3-67 7-29 3'-23 11-19 70 846 718 0180 19-37 7-101 850 646 2852 21 824 282 4868 3-71 7-31 3-73 71 32.79 23.31 3.239 856 728 8904 22 13-17 848 804 8680 856 026 8572 359 8864828 72 7-103 3.241 8616844109 3» 23 3.7.11 867 8659210 3.79 378 397 9009 73 17-43 866 108 9746 11.67 868 644 4834 24 882 017 0426 3> 13-19 3-83 74 3-13-19 870 988 8138 32.83 7.107 25 899 678 7215 11-23 409 938 1288 7-37 75 876 689 9870 3-251 879 095 8796 3.11.23 26 34.29 419 956 7485 3-89 429 752 2800 76 881 884 6668 7-109 13.59 886 926 8398 27 432 969 2909 3-7-13 442479 7691 32.31 77 3-257 888179 4939 3-7-37 19-41 28 448 7068199 461786 4355 7-41 172 78 11-71 38-29 896 974 7824 3.263 29 3-97 466 867 6204 32-11 13-23 79 7-113 13-61 901468 8214 17-47 30 7-43 3-101 487188 8756 3-103 80 32-89 11.73 3-269 907948 6216 31 492 760 8890 495 5448875 601 069 2622 11.29 81 909 020 8542 3.271 19-43 32.7-13 32 3-107 17-19 3-109 7.47 82 914 8431671 915 899 8362 917 605 5096 918 664 6806 33 619 827 9988 3»-37 627 629 9009 3-113 83 3-277 72.17 38-31 928 761 9608 34 11-31 7» 640 829 4748 642 826 4270 84 292 3.281 7-112 3-283 35 38-13 547 774 7054 3-7-17 555 094 4486 85 23-37 980 949 0812 982 980 8219 983 998 1638 36 19» S-IP 564 666 0648 32-41 86 3-7-41 986 010 7957 3-172 11-79 37 7-63 571 70S 8318 13-29 678 639 2100 87 13-67 32-97 942 999 6984 3-293 38 3-127 5881987740 32-43 689 949 6013 88 944 976 9084 946 960 7086 947 923 6198 7-127 39 17-23 3-131 698 790 6068 3-7-19 89 S'l-ll 19-47 3-13-23 29-31 40 6031448726 13-31 11-37 611723 3080 90 17-53 3-7-43 967 607 2871 32-101 41 3-137 7-59 3-139 622 214 0280 91 969 5188770 11-83 7-131 968 816 6114 42 624282 0958 32-47 7.61 3-11-13 92 3-307 13-71 32-103 968 016 7140 43 684 477 2702 636487 8964 19-23 642 464 6202 93 72-19 3-311 971 789 6909 3-313 44 y.V 646 403 7262 3-149 662 246 8410 94 978 589 6234 23-41 976849 9790 13-73 45 11-41 3-151 669 916 2001 38-17 95 3-317 979 092 9006 3-11-29 7-137 46 668 700 9254 665 630 9910 669-816 8806 7-67 96 312 32.107 986426 4741 3-17-19 47 3-157 11-43 32-53 680 335 6134 97 987 219 2299 7-139 989 8945687 11-89 48 13-37 3-7-23 687 628 9612 3.163 98 32.109 992 658 6178 3.7.47 23-43 49 691 081 4921 17-29 7-71 698 100 5456 99 996 078 6546 3-331 998 6961588 38.37 Nun. log 2=::. 301 029 9957. Num. log 5 = .698 970 0043. iX. PRIME A^D 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 32-167 11-137/ 3-503 01 3-337 005 609 4454 32-113 008 174 1840 51 179 264 4643 17-89 37.41 72-31 02 009 025 7421 3-11-31 13-79 3-73 52 32-132 182 699 9088 3-509 11-139 03 013 258 665S .014100 8215 17-61 016 615 5476 53 184 9751907 3-7.73 29-53 3-'-19 - ■ 04 3-347 7-149 3-349 020 775 4882 54 23.'67 188865 9261 7.13-17 190 061 4178 05 021 602 7160 3*- 13 7-151 3-353 55 3-11-47 191 171 4567 32.173 192 846 1152 06 025 715 3889 026 583 2645 11-97 028 977 7052 56 7-223 3.521 ^195 068 9965 3-523 Of 3^-7-17 29-37 3-359 13-83 57 196 176 1850 112.13 19.83 198 882 1800 08 23-47 3-192 036 229 5441 32-112 58 3-17-31 199 480 9149 3-232 7-227 09 087 824 7606 088 620 1619 040 206 6276 7-157 59 37-43 33.59 208 804 9161 3-13-41 110 3-367 042 575 5124 33-41 044 9315461 160 204 8913819 7.229 206 015 8768 206 556 0441 11 11-101 3-7-53 0480581781 3.373 61 32-179 207 684 3674 3-72.11 209 246 8488 12 19-59 060 379 7663 72.23 052 698 9419 62 209 783 0148 3-541 211 387 5529 32. 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^-127 31.37 3.383 64 3-547 31-53 33. 61 17-97 15 0610758236 061 829 8078 13-89 19.61 65 13-127 3-19-29 219 822 5084 3-7-79 16 33-43 065 679 7147 3-389 7-167 66 11-151 220 892 2492 221935 6998 222 456 8867 17 068 556 8951 3-17-23 11.107 32-131 67 3-557 7-239 3.13.43 23-73 18 072 249 8976 7-13^ 074450 7190 29-41 68 412 32-11-17 7-241 3-563 19 3-397 076 640 4487 32.7-19 11-109 69 19-89 228 666 9681 229 681 8423 230 193 3789 120 079 548 0074 3-401 17-71 3-13-31 170 35.7 13-131 3-569 232 742 0627 21 7-173 088 860 8009 085 290 6782 23-53 71 29-59 3.571 17-101 32-191 22 3-11-37 087426 4570 3-409 089 551 8829 72 235 780 8703 236 285 2774 11-157 7-13-19 23 090 258 0529 3^-137 092 869 6996 3-7-59 73 3-577 238 798 5627 32-193 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 32-139 7-179 3-419 100 026 7301 75 17-103 243 781 9161 7-251 246 266 8395 26 13-97 3-421 7-181 33-47 76 3-587 41-43 3-19-31 29-61 27 31-41 19-67 106 190 8978 106 870 5445 77 7-11-23 32-197 249 687 4278 3-593 28 3-7-61 108 226 6564 32- 11:. 13 110 252 9174 78 13-137 251 161 3482 252124 5525 252 610 8406 29 110 926 2428 3-431 112 939 9761 3-433 79 32-199 11-163 3-599 7-257 130 114 277 2966 114 944 4167 116 276 6876 7-11-17 180 255 518 7128 3-601 13-139 33-67 31 3-19-23 13-101 3-439 120 244 7955 81 257 918 4608 72.37 23-79 17-107 32 120 902 8176 33-7' 122 870 9229 3.443 82 3-607 260 786 6687 32.7.29 31-59 33 113 31-43 7-191 13.103 83 262 688 3443 3.13.47 11.167 3-613 34 3= -149 17-79 3-449 19-71 84 7.-263 19.97 266 466 8964 432 35 7-193 3-11-41 23-59 32-151 85 3-617 17-109 3-619 11-132 36 188 858 1252 29-47 135 768 5146 372 86 269 746 8731 3*-23 271144 8179 3-7-89 37 3-457 187 670 6372 3*-- 17 7-197 87 272 078 7875 272 537 7774 278 464 2726 273 926 7801 38 140 198 6786 3-461 19-73 3-463 88 32-11.19 7-269 3-17-37 276 2319579 39 13-107 7-199 11.127 145 817 7145 89 31-61 3-631 7-271 32-211 140 3-467 23.61 3.7.67 148 910 9931 190 278 982 1169 11.173 280 350 6980 23-83 41 17-83 3i'-157 13.109 3.11.43 91 3-72-13 281714 9700 33.71 19-101 . 42 7«.29 153 204 9001 154423 9731 155 032 2288 92 17-113 3-641 41-47 3-643 43 33-53 166 2461904 3.479 158 060 7989 93 286 782 2738 286 281 8540 13-149 7-277 44 11-131 3-13-37 160 468 5311 32.7-23 94 3-647 29-67 3-11-59 289 811 8391 45 1616674124 162 265 6148 31.47 164 055 2919 95 290 267 2694 32.7-31 19-103 3-653 46 3-487 7-11-19 32.163 13-113 96 37-53 13-151 7-281 11-179 47 167 612 6727 3-491 7-211 3-17-29 97 33-73 295 127 0858 3-659 296 446 7942 48 170 555 0685 171 141 1510 172810 9685 172 894 6978 98 7-283 3-661 298 197 8671 32-13-17 49 3-7-71 174 059 8077 3.499 175 801 6328 99 11-181 299 5072987 800878 0649 300 812 7941 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 120 IX. PRLME AKD COMPOSITE NUMBERS. 1 XUM. 1 3 7 9 Num. 1 3 7 9 200 3-23.29 801 680 9493 3«-223 7S-41 250 41.61 898 460 8496 23-109 13-193 01 808 412 0706 3-11-61 804 7058982 3-673 51 3^.31 7-369 3.839 11-229 02 43-47 7.17« 806 868 7487 807 282 0470 52 401 672 8467 3-292 7.192 38.281 03 3-677 19-107 3-7.97 809 4172258 53 403 292 1452 17-149 43-59 404 662 7009 04 13-157 3«-227 23-89 3-683 64 3-7-ll« 406846 8602 32-283 406 369 8355 05 7-293 812 388 9494 11«-17 29-71 65 406 710 4686 3.23.37 407 730 7280 3-853 06 3«.229 814 499 2280 3.13.53 315 760 4907 56 13-197 11-233 17-151 7-367 01 19-109 3-691 31.67 3«.7.11 57 3-857 31-83 3-859 4114518421 08 818 272 0802 318 689 2699 819 622 4491 819 988 4400 58 29-89 32.7-41 13-199 3-863 09 3.17-41 7-13-23 3«.233 822 012 4886 69 413 467 4130 413 802 6168 72-53 23-113 210 11-191 3-701 7«-43 3.19-37 260 32.172 19.137 3-11-79 4164740791 11 8244882338 824 899 4971 29.73 13-163 61 7-373 3-13-67 417 803 7226 3^-97 12 3-7-101 11-193 3.709 828 176 6614 62 4184670209 43-61 37-71 11-239 13 828 588 4497 3«.79 329 804 5222 3-23-31 63 3.877 420 450 8591 32.293 7.13.29 14 880 616 6678 381 022 1710 19.113 7-307 64 19-139 3-881 422 763 9418 3.883 15 3»-239 833 044 0298 3-719 17-127 65 11.241 7.379 424 8916544 424 718 3878 16 884 654 7669 3.7.103 11-197 3i'-241 66 3.887 426 3711664 3-7-127 17-157 n 13-167 41-53 7-311 888 257 2302 67 426 673 8880 3'. 11 427 648 3712 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» 3-733 69 32.13.23 480 236 3684 3-29-31 4312028846 220 31-71 848 0144972 843 802 8832 47« 270 37-73 3.17-53 482 488 25,58 32-7-43 21 3-11-67 844 981 4189 3-739 7-317 71 488 129 5176 438449 7938 11 -13 -19 484 409 2076 22 846 648 6586 3M3-19 17-131 3.743 72 3-907 7-389 3'-101 4360085857 23 23-97 7.11-29 349 665 9841 850 054 0986 73 486 8217001 3.911 7-17-23 3-11-83 24 3*. 83 850 829 2786 3-7.107 13.173 74 487 909 035S 13.211 41-67 489174 7398 25 862 876 4960 3.751 37-61 32.251 75 3-7-131 489 806 2114 3-919 31-89 26 7.17-19 31.73 855 451 5201 366 8344969 76 11-261 32.307 4420091591 3-13-71 21 3.'757 866699 4367 3«. 11-23 43.53 77 17-163 47.59 443 675 8798 7-397 28 868125 2868 3.761 859 266 1646 3.7.109 78 38-103 112.23 3-929 4464486148 29 29-79 860 404 0547 361 160 9962 11^.19 79 446 759 8866 3.72.19 446 692 4664 32-311 230 3.13.59 7«.47 3-769 868 423 9329 280 447 813 1088 447 628 0978 7.401 532 31 868 799 9455 3«.257 7-331 3.773 81 3.937 29-97 32.313 460 0950769 32 11.211 23.101 13-179 17-137 82 7.13-31 3-941 11.257 3.23-41 33 32.7.37 867 914 7888 3-19-41 869 080 2218 83 19-149 462 246 6746 452 869 8868 17-167 34 869 401 4187 3.11.71 370 513 0896 3*. 29 84 3-947 463 776 8597 3.13-73 7-11-37 35 871 252 6291 13.181 872 369 5825 7.337 85 464 997 2178 32.317 456 910 2404 3-963 36 3.787 17.139 3«-263 23.103 86 456 517 8578 7-409 47-61 19-151 37 874 9815640 3.7.113 876 0291817 3-13.61 87 32.11.29 132.17 3-7.137 469 241 6649 38 376 759 8954 377 124 0428 7-11-31 878 2161497 88 43-67 3-312 460446 7889 3*- 107 39 3.797 878 942 6986 3-17-47 880 080^80 89 72-69 11-263 461948 4952 13.223 240 74 32-89 29-83 3.11-73 290 3.967 462 847 0858 32-17-19 463 748 7212 . 41 382 197 2104 19-127 888 276 6504 41.69 91 41.71 3-971 464986 4291 3-7.139 42 3«.269 884 853 4141 3.809 7-347 92 23.127 37-79 466 422 7224 29.101 43 11.13.17 3-811 886 856 6292 3»-271 93 3-977 7-419 3.11-89 468199 6861 44 887 567 7794 7-349 888 683 9694 31-79 94 17-173 38.109 7-421 3-983 45 3-19.43 11-223 3'. 7. 13 390 768 6287 95 13-227 470 268 4470 470 8618245 11-269 46 23.107 3-821 892 169 1495 3-823 96 32-7-47 471 781 6516 3-23-43 4726101976 47 7-353 893 224 1164 398 926 0066 37-67 97 472 902 6518 3-991 13-229 32-331 48 3-827 13-191 3-829 19-131 98 11-271 19-157 29-103 72-6I 49 47.53 3^277 11-227 3-72.17 99 3-997 41-73 3^-37 476 9764658 Num. log 2 = ..301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBER^. 121 1 Num. ] 3 7 9 Num. 1 3 7 9 300 477 265 9954 3-7-11.1331.97 3-17-59 350 32-389 31-113 3.7:167 112.29 01 478 710 7555 23-131 7-431 479 8681130 51 545 430 8295 3-1171 546 172 3683 32.17.23 02 3.19-53 480 4381472 3.1009 13.233 52 7-503 13-271 547 4054597 647 651 6584 ■^ 03 7-433 32.337 482444 7919 3-1013 53 3-11-107 648 143 6874 33.131 548 880 6626 04 488 016 4201 17-179 11-277 484157 4244 54 649125 9268 3-1181 649 861 1886 3.7-132 05 3»-113 43-71 3-1019 7-19-23 55 53-67 11.17-19 551 088 8652 551 827 9880 06 485 8638296 3-1021 4867187760 32-11-31 56 3-1187 7.509 3-29-41 43-83 07 37-83 7.439 17-181 4884096889 57 662 789 8602 32.397 72-73 3-1193 08 3-13-79 488 978 5247 32 . 7' 489 817 9083 58 654 0048210 554 246 8082 17-211 37-97 09 11-281 3.1031 19.163 3.1033 59 33-7-19 865467 2172 3-11-109 59-61 310 7-443 29-107 13.239 492 620 7220 360 13-277 3.1201 557 146 1428 32-401 11 3-17-61 11-283 3.1039 494 015 3748 61 23-157 667 8679616 658 348 5088 7-11-47 12 494298 7687 32 - 347 53.59 3.7.149 62 3-17-71 559 0683840 32.13-31 19-191 13 31-101 13-241 496 514 5187 43.73 63 660 026 2489 3.7.173 660 748 3011 3-1213 14 3!'-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!'.13 65 3-1217 13.281 3.23-53 563862 4095 16 29-109 500 099 1919 500 648 0634 500 922 2392 66 7-523 32.11.37 19-193 3-1223 IT 3-7-151 19-167 32.353 11.172 67 664 7848846 665 020 9283 666498 6299 13-283 18 502 568 6691 3-1061 608 382 0636 3-1063 68 ,32.409 29.127 3-1229 7-17-31 19 603 926 8042 31-103 23-139 7-457 69 567144 0452 3.1231 567 849 4506 33.137 320 3-11-97 606 556 9887 3-1069 506 369 7171 370 568819 0^1 7.232 11-337 569 266 8383 21- 13^-19 33-7-17 5074610609 3-29-37 71 3.1237 47.79 32-7-59 570 426 1784 22 507990 7248 11-298 7-461 609 068 0460 72 612 3.17.73 671 869 3928 3.11.113 23 32-359 53-61 3-13-83 41-79 73 7.13.41 572 057 9899 37-101 572 7654652 24 7-463 3-23-47 17-191 32-192 74 3.29.43 19.197 3-1249 23.163 25 6i2 016 9695 512 284 0683 512 817 7686 613 0848606 75 112.31 33.139 13-172 3.7-179 26 3-1087 13-251 3'-112 7-467 76 576808 8384 53.71 676 996 6202 676 226 1374 27 514 630 5441 3-1091 29-113 3-1093 77 32-419 73.11 3-1259 677 376 8919 28 17-193 7^-67 19-173 11-13-23 78 19-199 3-13-97 7-541 32-421 29 3-1097 37-89 3-7-157 5188828166 79 17-223 678 982 8427 679 440 6971 29-131 330 518 645 5243 32-367 5194341949 3-1103 380 3-7-181 5801263254 34-47 13.293 31 7-11-43 520 221 4859 31-107 521007 2524 81 37-103 3-31-41 11-347 3-19-67 32 3* -41 621630 3413 3-1109 622 813 7962 82 682 177 0377 682 404 2980 43-89 7-547 33 522 674 6327 3-11-101 47-71 32-7-53 83 3-1277 583 538 8198 3-1279 11-349 34 13-257 624136 3766 5246567124 17-197 84 23-167 32. 7. 61 685 122 1863 3-1283 35 3-1117 7.479 32-373 6262100038 85 686573 6186 685 799 0090 7-19-29 17-227 36 526 468 5125 3-19.59 7-13-37 3-1123 86 3«-ll-13 586 924 7081 3-1289 53-73 37 527 768 7525 528 0168412 11.-307 31-109 87 72.79 3.1291 588 495 8010 32-431 38 3.7«-23 17.199 3-1129 630 0716688 88 588 943 6427 11.353 132-23 589 887 9431 39 630 827 7898 32-13-29 43.79 3-11.103 89 3.1297 17-229 32-433 7-557 340 19-179 41-83 532 3721336 7.487 390 47.83 3.1301 691843 4112 3-1303 41 3»-379 583186 2883 3-17-67 13-263 91 692 287 8160 7.13.43 592 958 5715 693176 2685 '42 11-311 3-7-163 23-149 33-127 92 3.1307 593 618 8081 3-7-11-17 594 2820288 | 43 47-73 685 678 8034 7-491 19-181 93 694603 0488 32.19.23 31-127 3-13-101 44 3-31-37 11-313 32-383 687 6931944 94 7-563 595 826 7771 596 2671264 11-359 45 7-17-29 3-1151 638 699 8795 3-1153 95 32-439 59-67 3-1319 37-107 46 539 201 5993 639 462 4916 639 963 8417 540 204 2998 96 17-233 3.1321 598 4622005 34-72 47 3-13-89 23-151 3-19-61 72-71 97 11-192 29.137 41.97 23-173 48 592 > , 3* -43 11-317 3-1163 98 3-1327 7.569 32.443 600 864 0368 49 542 949 8483 7-499 13-269 543 948 9426 99 13-307 3.113 7.571 3.31.43 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 1 122 IX. PRIME AND COMPOSITE NUMBERS. Num. 1 3 T 9 Num. 1 3 7 9 400 602168 5514 6U2 386 6901 602 819 8424 19-211 450 7-643 3-19-79 658 387 6681 33-167 01 3-7.191 603 469 U'Jl 3-13-103 604118 0062 51 13-347 654 466 3386 664850 0906 656 042 8418 02 604 834 0731 3^-149 604 981 6296 3-17-79 52 3-11-137 656 426 6877 32.503 7-647 03 29.139 37-109 11-367 7-577 53 23-197 3-1511 13-349 3-17-89 04 32.449 13-311 3-19-71 607 847 7768 54 19-239 7-11-59 657 724 9642 667 916 9808 05 607 562 2432 3- 7 193 608 205 0077 32.11-41 55 3-37-41 29-157 3-72-31 47-97 06 31-131 17-239 72-83 13-313 56 659 060 0722 33-132 669 681 0116 3-1523 07 3-23.59 609 9144101 33-151 610 558 7063 57 7-653 17-269 23-199 19.241 08 7-11-53 3-1361 61-67 3-29-47 58 32-509 661 149 8572 3-11-139 13-353 09 611829 4795 612 041 7446 17-241 612 677 9188 59 661 907 2928 3-1531 662 474 5038 32.7-73 410 3-1367 11-373 3-372 7-587 460 43-107 663 040 9749 17-271 11-419 11 618 947 476S 32-457 23-179 3-1373 61 3-29-53 7-659 35-19 31-149 12 13-317 7.19-31 615 634 4689 616 844 8829 62 664 736 9685 3-23-67 7-661 3-1543 13 3'-17 616 2654068 3-7-197 616 895 4264 63 11-421 41-113 666 287 0959 666 424 8725 14 41-101 3-1381 11-13-29 32-461 64 3-7-13-17 666 798 6837 3-1549 667 359 5462 15 7.593 6188619811 618 780 0245 613 983 9204 65 667 646 3896 32-11.47 663106 2879 3-1553 16 3-19.73 23-181 32-463 11-379 66 59-79 668 6654155 13-359 7-23-29 n 43-97 3-13-107 620 864 4758 3.7-199 67 33-173 669 595 7310 3-1559 670 158 0462 18 37-113 47-89 53-79 59-71 68 31-151 3.7-223 43-109 32.521 19 3-11-127 7-599 3-1399 13-17-19 ■ 69 671 265 4829 13-192 7-11-61 37-127 420 623 862 6816 32-467 7-601 3-23-61 470 3-1567 672 874 9787 32.523 17-277 21 624886 2414 11-383 625008 6010 625 209 5254 71 7-673 3-1571 53-89 3-112-13 22 32-7-67 41-103 3-1409 626 287 6851 72 674 084 0004 674 217 9456 29-163 674 769 8140 23 626448 0258 3-17-83 19-223 33.157 73 3-19-83 676186 6046 3-1579 7-677 24 627 468 2725 627 678 0818 31-137 7-607 74 11-431 32-17-31 47-101 3-1583^ 25 3-13-109 028 696 8827 3»-ll-43 629807 6401 75 676 735 0804 72-97 67-71 677616 7048 26 629 5115842 3-7'-29 17-251 3-1423 76 32-232 11-433 3-7-227 19-251 27 680 529 5714 680 732 8928 7-13-47 11.389 77 13-367 3-37-43 17-281 3''-59 28 3-1427 681 748 0744 3-1429 632 856 0462 78 7-683 679 700 8809 680 068 4275 680 244 8870 29 7-613 3''-53 688165 8887 3-1433 79 3.1597 680 607 4290 32.13-41 681160 7499 430 11-17-23 13-331 59-73 31-139 480 6813317060 3-1601 11-19-23 3-7-229 31 32-479 19-227 3-1439 7-617 81 17-283 682 415 8617 682 776 6468 61-79 32 29-149 3-11-131 686 186 8952 32.13-37 82 3-1607 7-13-53 3-1609 11-439 33 61-71 7-619 637189 4221 687 889 6501 83 684 087 0875 33-179 7-691 3-1613 34 3-1447 43-101 3'' • 7 - 23 638 389 4077 84 47-103 29-167 37-131 13-373 35 19" -229 3-1451 639 187 5599 3-1453 85 32-72-11 23-211 3-1619 43.113 36 72-89 039 786 2180 11-397 17-257 86 636 725 6211 3-1621 31-157 32-541 37 3-31.47 640 779 4773 3-1459 29-151 87 687 618 1296 11-443 688 152 7856 7-17-41 38 13-337 32-487 41-107 3-7-11-19 88 3-1627 19-257 33. 181 689 220 0878 39 642 563 4371 23-191 6481564666 53-83 89 67-73 3-7-233 59-83 3-23-71 440 3^-163 7-17-37 3-13-113 644 840 0988 490 132.29 690 461 8982 7-701 690 998 0821 41 11-401 3-1471 7-631 32-491 91 3-1637 173 3-11-149 691 876 8226 42 648 520 6149 645 716 9894 19-233 43-103 92 7-19-37 32.547 13-379 3-31-53 43 3-7-211 11-13-31 32-17-29 23-193 93 6929860025 6981111155 698 463 1272 11-449 44 f47 4S0 7732 3-1481 648 067 1294 3-1483 94 31-61 693 990 6105 3-17-97 72.101 45 048 457 5948 61-73 649 042 6841 78-13 95 694 692 9263 3-13-127 695218 9189 32-19-29 46 3-1487 649 626 8868 3-1489 41-109 96 112-41 7-709 696 0941600 696268 9967 47 17-263 32-7-71 ll'-37 3-1493 97 3-1657 696 618 4592 32-7.79 13-383 48 651 874 9489 661 668 7889 7-641 672 98 17-293 3-11-151 697 839 8682 3-1663 49 3«-499 662 ■886 4186 3-1499 11-409 99 7.23-31 693 3615661 19-263 698 888 1368 Num. log 2 z=. 301 029 9957. Nob. log 5 = .698 970 0043. IX. PRIME AWD 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 1416460 740599 5128 740 915 0765 7-787 01 699 9244027 32-557 29-173 3-7-239 51 3-11.167 37-149 32-6I3 741 860 3941 02 700 790 2214 700 963 1782 11-457 47-107 52 742 017 7471 3-7-263 742 489 4646 3-19-97 03 32.13-43 7-719 3-23-73 702 344 8584 53 742 808 6586 11-503 72.113 29-191 04 71= 3-412 72-103 33-11-17 54 3-1847 23-241 3-432 31-179 05 708 8778685 31-163 13-389 704 064 6794 55 7-13-61 32-6I7 744 840 3968 3-17-109 06 3-7-241 61-83 32-563 37-137 56 67-83 745 309 0699 19-293 748 777 2179 07 11-461 3.19-89 705 607 1634 3-1693 57 32-619 746 089 0481 3.11.132 7-797 08 706 949 1949 13-17-23 706 4617876 7-727 58 746 712 0225 3-1861 37-151 35-23 09 3-1697 11-463 3-1699 707485 0120 59 747 489 4928 7-17-47 29-193 11-509 510 ^07 655 3285 3«-7 708165 8579 3-13-131 560 3-1867 13.431 32-7-89 71-79 11 19-269 708 675 7927 7.17-43 709 185 1296 61 31-181 3-1871 41-137 3-1873 12 32-569 47-109 3-1709 23-223 62 7-11-73 749 9680885 17-331 13-433 13 7-733 3-29-59 11-467 32.571 63 3-1877 43-131 3-1879 751 202 0946 14 53-97 37-139 711 564 1683 19-271 64 751356 0997 33-11-19 751 817 7877 3-7-269 15 3-17-101 712 0601425 33-191 7-11-67 65 7621258078 752 278 9855 752 5861787 752 789 6989 16 13-397 3-1721 713 238 4615 3-1723 66 32-17-37 7-809 3-1889 768 506 4670 17 713 574 5378 7-739 31-167 714 245 9110 67 53-107 3-31-61 7-811 32-631 18 3-11-157 71-73 3-7-13-19715 083 6707 68 13-19-23 764 677 6560 112-47 765 036 9838 19 29-179 32-577 • 715 752 7168 3-1733 69 3-7-271 756 3411888 33-211 41-139 520 7-743 112.43 41-127 716 754 8574 570 756 951 0410 3-1901 13-439 3-11.173 21 33.193 13-401 3.37-47 17-307 71 756 7121602 29-197 7571681922 7-19-43 22 23-227 3-1741 718 262 5001 32-7-83 72 3-1907 59-97 3-23-83 17-337 23 718 584 7200 718 750 7347 719 082 5739 132.31 73 11-521 32-72.13 758 684 8499 3-1913 24 3-1747 72-107 32.11-53 29-181 74 758 9875469 759138 8168 7-821 769 592 3086 25 59-89 3-17-103 7-751 3-1753 75 .3«-7l 11-523 3-19-101 13-443 26 721068 8018 19-277 23-229 11-479 76 7-823 3-17-113 73-79 32-641 27 3-7-251 722 067 7718 3-1759 722 551 6620 77 . 29-199 23-251 53-109 761852 6945 28 722 7161675 32-587 17-311 3-41-43 78 3-41-47 762 163 1928 32-643 7-827 29 11-13.37 67-79 724 029 9729 7.757 79 763 753 5649 3-1931 11-17-31 3-1933 530 32-19-31 724 5216271 3-29-61 725 012 7253 580 768 502 8655 7-829 768 9518260 37-157 31 47-113 3-7-11-23 13-409 33.197 81 3-13-149 764 4008280 3-7-277 11-232 1 ' 32 17-313 726 156 4662 7-761 732 82 764 9975998 32-647 765445 0181 3-29-67 33 3-1777 726 9T1 6887 32.593 19-281 83 73-17 19-307 13-449 766 838 4753 34 7-2-109 3-13-137 728 110 1841 3-1783 84 32-11-59 766 685 8868 3-1949 767 081 6214 35 728 434 9510 53-101 11-487 23-233 85 767 230 0981 3-1951 767 675 2240 33.7-31 36 3-1787 31-173 3-1789 7-13-59 86 767 971 7214 11-13-41 768 416 0882 7685641096 37 41-131 33-199 19-283 3-11-163 87 3-19-103 7-839 32 - 653 769 308 4602 38 730 862 9920 7-769 781846 9755 17-317 88 769 4511794 3-37-53 7-292 3-13-151 39 32-599 781830 4208 3-7-257 782 318 3275 89 43-137 71-83 770 631 1278 17-347 540 11-491 3-1801 732 956 3696 32-6OI 590 3-7.281 771 072 7882 3-11-179 19-311 41 7-773 788 438 0271 788 758 8856 733 919 1510 91 23-257 3-'-73 61-97 3-1973 42 3-13.139 11-17-29 31-67 61-89 92 31-191 772 541 7826 772 884 9272 72.112 43 784 879 8028 3-1811 735 359 8330 3-72-37 93 32-659 17-349 3.1979 778 713 3258 44 735 678 72S9 786 838 8343 13-419 736 816 8079 94 13-457 3-7-283 19.313 32. 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 32. 607 7-11-71 3-1823 96 3-1987 67-89 33-13-17 47-127 47 788 066 7148 13-421 788 542 7409 738 7018004 97 7-853 3-11-181 43-139 3-1993 48 33.7.29 789 018 2459 3.31-59 11-499 98 776 778 8024 31-193 777 209 2581 53-113 49 172.19 3-1831 23-239 32-13.47 99 3-1997 13-461 3-1999 7-857 Ndm. log 2=^.301 029 9957. NOM. log 5 = .698 970 0043. ■ 124 IX. PRIME AND COMPOSITE NUMBERS. 1 Nr.M. 1 3 7 9 NnM. 1 3 7 9 600 17-353 3^-23-29 778 657 6819 3 - 2003 650 3-11-197 7-929 3»-241 23-283 01 778 946 7280 7-859 11-547 13-463 51 17-383 3-13-167 7«-19 3-41-53 02 3»-223 19-317 3-7*-41 7802462889 52 814 814 2002 11-593 61-107 814 846 6686 03 37-163 3-2011 780 8211759 3»-ll-61 53 3-7-311 47-139 3-2179 13-603 04 7-863 781252 5942 781689 9686 23-263 54 31-211 32-727 816 042 8409 3-37-69 05 3-2017 781 970 6789 3«-673 73-83 55 816 807 5994 8164401680 79-83 7-937 06 11-19-29 3-43-47 782 978 9949 3-7-17= 56 38' 817 102 4048 3-11-199 817499 2619 07 13-467 788 408 2811 59-103 788 8821484 67 817 6314672 3-7-313 818 0278419 32-17-43 08 3-2027 7-11-79 3-2029 784646 9741 58 8182918908 29-227 7-941 11-599 09 784 688 6995 3»-677 7-13-67 3-19-107 59 3-138 19-347 32-733 819 4781284 610 786 4010250 17-359 31-197 41-149 660 7-23-41 3-31-71 820 0043068 3-2203 11 3«.7-97 786 264 8958 3-2039 29-211 61 11-601 17-389 13-509 820 792 38U 12 786 822 8T96 3-13-157 11-557 33-227 62 3-2207 37-179 3-472 7-947 13 7876818161 787 672 9647 17-19' 7-877 63 19-349 32-11-67 8219718176 3-2213 14 3-23-89 788 880 5153 3«-683 11-13-43 64 29-229 7-13-73 172-23 61-109 15 788 946 7270 3-7-293 47-131 3-2053 65 32-739 823 017 6284 3-7-317 828 409 0149 16 61-101 789 792 1677 7-881 31-199 66 828 589 4337 3-2221 59-113 3'-13-19 17 3-ll«17 790 496 2770 3-29-71 37-167 67 7-953 824 8211249 11-607 824 7114486 18 7-883 3'- 229 23-269 3-2063 68 3-17-131 41-163 32-743 8258611960 19 41-151 11-563 792 181 4961 792 821 6864 69 8254910299 3-23-97 37-181 3-7-11-29 620 S^'-IS-SS 792 601 7812 3-2069 7-887 670 826 189 6179 826269 2194 19-353 826 657 7919 21 798 161 5292 3-19-109 798 680 8674 32-691 71 3-2237 72-137 3-2239 827 304 6411 22 798 860 2018 7«-127 13-479 794 4188809 72 11-13-47 3^-83 7-312 3-2243 23 3-31-67 23-271 3*-7-ll 17-367 73 53-127 8282086146 828 466 6474 23-293 24 79« 3-2081 795 6715069 3-2083 74 32-7-107 11-613 3-13-173 17-397 25 7-19-47 132-37 796 8661550 11-569 75 43-157 3-2251 29-233 32-751 26 3-2087 796 782 4117 3-2089 7971982698 76 830 0109869 830189 3874 67-101 7-967 27 797 886 8008 ■32-17-41 7977521287 3-7-13-23 77 3-37-61 13-521 33-251 881 166 6889 28 11-571 61-103 798 448 4604 19-331 78 881 298 7444 3-7-17-19 11-617 3-31-73 29 3'- 233 7-29-31 3-2099 799 2716088 79 831 988 7806 882 0616146 7-971 13-523 630 799 409 4796 3-11-191 7-17-53 32.701 680 3-2267 832 7004710 3-2269 11-619 31 800 0981802 59-107 800 510 8769 71-89 81 72-139 32-757 17-401 3-2273 32 3-7»-43 800 928 1818 32-19-37 801885 0967 82 19-359 888 976 3713 884 229 9029 8848571127 33 13-487 3-2111 8018887071 3-2113 83 3«-ll-23 834 611 4207 3-43-63 7-977 34 17-373 802 294 71U 11-577 7-907 84 886119 5904 3-2281 41-167 32-761 35 3-29-73 802 978 8558 3-13-163 8088888260 85 13-17-31 7-11-89 836 184 1496 198 36 808 6258956 3»-7-101 808 984 8499 3-11-193 86 3-2287 836 518 9989 32-7-109 886 893 5164 37 23-277 804 843 9186 7-911 8047626022 87 887 019 9485 3-29-79 13-232 3-2293 38 3«-709 13-491 3-2129 8064328881 88 7-983 887777 7696 71-97 832 39 7-11-83 3-2131 805 976 8507 3* -79 89 3-2297 61-113 3-112-19 888 7861449 640 37-173 19-337 43-149 13-17-29 690 67-103 32-13-59 889 289 4560 3-72-47 41 3-2137 11^-53 32-23-31 72.131 91 839 640 8980 31-223 889 917 7757 11-17-37 42 807 602 6699 3-2141 808 008 2999 3-2143 92 32-769 7-23-43 3-2309 132-41 43 59-109 7-919 41-157 47-137 93 29-239 3-2311 7-991 38-257 44 3-19-113 17-379 3-7-307 809 492 8769 94 11-631 53-131 8417972989 8419228117 45 809 627 0419 3'- 239 11-587 3-2153 95 3-7-331 17-409 32.773 842 546 8865 46 7-13-71 23-281 29-223 810 8371511 96 842 671 6338 3-11-211 843 0458105 3-23-101 47 3»-7l9 811 106 6070 3-17-127 11-19-31 97 843 296 0827 19-367 848 668 7230 7-997 48 811 642 0215 3-2161 13-499 3«-7-103 98 3-13-179 844 042 0420 3-17-137 29-241 49 812 SU 6091 43-151 73-89 67-97 99 844 539 3021 3»-7-37 844 9118789 3-2333 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043 • IX. PRIME AND COMPOSITE NUMBERS. 125 Num. VOO 01 02 03 04 05 0.6 01 08 09 110 11 12 13 14 15 16 17 18 19 120 21 22 23 24 25 26 21 28 29 130 31 32 33 34 35 36 31 38 39 140 41 42 43 '44 45 46 41 48 49 9 845160 0m 41-149 1S.11.13 43-163 3^.19-41 845 908 8389 3-2339 846 2T5 2424 1-11-59 3-2341 8461699635 32-11.11 19-89 13-541 31-221 84T5109652 3-2341 8477516884 3^-29 1-19-53 11-641 3-2351 23-301 1-1009 3-2351 11-643 13-91 32-181 1-1013 41-113 3^-263 8614418147 13-541 3-2311 852 540 9858 11-419 3-2311 1-1019 31-193 3-2381 854866 7780 23-311 3-1-11-31 13-19-29 11-101 3'-191 43-161 11-653 3'- 11 -41 856 910 0608 19-319 3-1* 857 995 4966 868115 9822 3-29-83 31-233 1-1033 3-2411 13-551 859 918 4862 848 6201174 3-13-181 31-191 8498579817 3-1-331 849 9719128 19-313 3-11-139 41-151 31-229 3-23-103 8518086142 11-641 3«-1-113 852 906 7588 858 028 6147 3»-13-61 ll=-59 1-1021 3-2383 11-421 864 862 3624 3-2389 61-101 865 942 9462 3-2393 856 547 6449 1-13-19 3-2399 23-313 867 754 5221 3'' -89 1-1031 868 4770418 3''-ll-13 8590782247 8596586726 3-19-121 860158 2618 11-659 Num. 3-2411 53-131 11-661 3^-809 23-311 1«.149 3-2431 864 570 4069 865 168 2195 3 - 2441 866846 4227 11-433 Si-l-lS 112-61 19-389 3-2461 869 876 8188 41-181 3-2411 1-1063 8605176775 3-41-59 1-11-61 33-269 132-43 3-2423 1-1039 19-383 29-251 862 810 8100 3-1-341 31-191 3-11-13.118681448468 S'-Sll 61-109 868 789 1078 868 867 9619 11-103 38.211 13-563 3-2441 11-431 3-1-349 865 2816850 11-23-29 41-119 1-1049 3-31-19 8662282474 32-19.43 1-1051 3-11-223 31-199 53-139 867408 5565 13-101 3-2459 41-151 3-23-101 83-89 32-821 868 820 7062 13-569 12-151 11-613 32-823 31-239 3-1-353 8702282790 3-2413 13-511 1-1061 11-19-23 8711641828 3-31-61 43-113 32-821 11-611 3-13-191 872 214 5684 29-251 32.829 11-439 31-241 3-41-53 878 959 6547 1-1069 3-11-221 59-121 872 664 1481 872 680 6072 3-19-131 1-11-91 878 727 8806 35-211 874 807 8331 874 428 8806 32.75.17 875 003 3636 150 51" 52 53 54 55 56 51 58 59 160 61 62 63 64 65 66 61 68 69 110 11 12 13 14 15 16 11 18 19 180 81 82 83 84 85 86 81 88 89 190 91 92 93 94 95 96 91 98 99 1 13-511 3-41-61 8754664159 3-2503 1-29-31 11-683 8760445602 13-103 3-23-109 8763910618 3-13-193 8767872971 11-443 ' 36-31 877198 5168 3-1-359 877428 9408 19-391 S77 774 8600 877 889 4254 32-839 1-13-83 3-11-229 8784648458 8786792881 3-2521 1-23-41 32-29' 61-113 879 267 9668 879 497 2872 11-13-53 3-I-I92 8798410560 3^-281 880184 5528 88029899t4 3-2531 11-101 3-11-149 11-691 8809849905 881213 4168 1-1081 3-43-59 23-331 3-2539 19-401 882 0119616 32.1.112 29-263 3-2543 13-581 11-449 1-1091 8880866100 3^-283 8882688596 3-2549 8886046609 1-1093 3-2551 41-163 19-91 3-2551 8849651982 885 417 7651 3-13-191 885 982 8114 12-151 13-19-31 32-23-31 11-11-41 8847387378 32-853 1-1091 885756 8811 3-11-233 43-119 886 434 8196 3-11-151 886 659 8979 3-1-361 13-593 11-101 32-851 8874486002 3-31-83 1-1103 887 786 0848 888 010 9122 59-131 32-859 11-19-31 3-2519 11-109 8887970678 3-29-89 61-121 3^-1-41 23-331 889 469 7840 889 693 7914 889 8067519 3-13-199 1-1109 19-409 3-2591 31-251 43-181 3-12-53 8917046762 29-269 3'-112 13-101 13-601 32.11-19 8988788802 41-191 3-1-313 8948714539 11-23-31 32-863 11-451 l-ll-lOl 3-2593 13-599 8914817088 3-23-113 11-109 31-211 3-19-131 8980401120 1-1111 3 - 2609 898 706 2981 11-461 32. 13-61 1-19-59 41-161 3-2611 895 035 5975 3''. 91 29-211 1-1123 3-2621 8958091502 3-43-61 11-463 8961402614 8963608455 8964711005 3-31-11 8966915266 3-11-239 73-23 13-601 32-8II 53-149 3-2633 897 6820618 1-1129 8980117888 11-119 3'- 293 41-193 3-1-13-29 8986708430 892 3-19-139 899108 8682 32-881 1-11-103 8994874543 8996563808 11-461 3-2641 132-41 32-883 9008124970 900 4217585 3-11-241 19-419 901076 7157 3-2651 1-11-61 23-341 32 -881 61-131 902 709 8180 13-109 3-1--319 31-251 13-613 3-2659 19-101 12-163 3-2663 11-121 19-421 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. 1-2G IX. PRIME AND COMPOSITE NUMBERS. >JrM. 1 3 T 9 NlTM. 1 3 7 9 800 3'.7.127 53-151 3-17-157 908 6782987 850 929 4T0 0162 11-773 47-181 67-127 01 908 6S6 7817 3-2671 904 Oil 8886 3«.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 5668 3»-947 930 796 2680 3-2843 03 3-2677 29-277 3«-19-47 905 202 0287 53 19.449 7-23-53 981 805 2814 981407 0136 04 11-17-43 3-7-383 13-619 3-2683 54 32-13.73 981610 4064 3-7-11.37 83-103 05 83.97 906 957 6991 7-1161 906 281 1558 55 17.503 3-2851 43-199 38.317 06 3-2687 11-733 3-2689 906 819 7155 56 7-1223 982 626 9440 13-659 11-19.41 07 7-1153 33-13-23 41-197 3-2693 57 3-2857 938 182 8287 32-953 23.373 08 907 4651068 59-137 907 787 4431 907 894 8354 58 983 537 9020 3-2861 31-277 3-7-409 09 3*-29-31 908109 6404 3-2699 7-13-89 59 112-71 13-661 934846 9267 984 447 9489 810 90S 588 6822 3-37-73 ll'-67 32-17-53 860 3-47-61 7-1229 3-19-151 934962 7078 11 909 0744014 7-19-61 909 895 5460 23-353 61 79-109 38.11-29 7-1231 3-132-17 12 3-2707 909 716 4632 38-7-43 11-739 62 37-233 986 668 8861 935 859 7980 935 960 4690 13 47-173 3-2711 79-103 3-2713 63 32.7-137 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 4690 32.312 15 3-11-13-1931-263 3-2719 41-199 65 41-211 17.509 11-787 7-1237 16 911 748 8779 3^-907 912 062 5556 3-7-389 66 3-2887 937 668 8144 3''- 107 987 969 0080 17 912 276 2105 11-743 13-17-37 912 700 2082 67 13-23-29 3.72.59 938 869 6976 3-11-263 18 S'l-lOl 7^-167 3-2729 19-431 68 988 669 7562 19-457 7.17.73 988 969 7972 19 918 886 9269 3-2731 7-1171 32.911 69 3-2897 989 169 6796 3.13.223 989 469 8808 820 59-139 13-631 29-283 914 290 2557 870 7-11-113 32.967 939 8686445 3-2903 21 3-7-17-23 43-191 3^-11-83 914 818 9804 71 31-281 040 167 7140 23.379 940 466 6777 22 914 924 6482 3-2741 19-433 3-13-211 72 3'-17-19 11.13.61 3.2909 7.29.43 23 915452 6017 915 6681164 915 769 0660 7-11-107 73 941068 9882 3.41.71 941862 8857 32.971 24 3-41-67 916 086 2998 3-2749 73-113 74 941 661 1202 7.1249 941 869 1265 13-673 25 37-223 32-7-131 23-359 3.2753 75 3-2917 942 156 9285 32.7-139 19-461 26 11-751 917 187 7528 7-1181 917 462 9919 76 942 568 6808 3.23-127 11-797 3-37-79 27 3»-919 917 668 0248 3-31-89 17.487 77 72-179 31-283 67.131 948 445 0490 28 7^-13^ 3-11-251 918 897 8888 3'. 307 78 3-2927 948 642 8828 3-29.101 11-17-47 29 918 606 9161 918 7116654 918 9210901 43.193 79 59.149 32-977 19.463 3-7-419 830 3-2767 19«-23 3^-13-71 7.1187 880 13-677 944 680 7019 944 827 9963 23-383 31 919 658 2823 3-17-163 919 966 7015 3-47.59 81 32-11-89 7-1259 3-2939 946 419 3426 32 53-157 7-29-41 11-757 920 592 8621 82 945 617 8221 3.17.173 7.13.97 3''-109 33 3-2777 13-641 3-7-397 31.269 83 946009 8848 112.73 946 804 8660 946 4031389 34 19-439 3^-103 17-491 3.112-23 84 3-7-421 37-239 32.983 946 8941961 35 7-1193 9218424814 61-137 13-643 85 53-167 3-13-227 17.521 3-2953 36 3^-929 922 862 0968 3-2789 922 678 6679 86 947482 7366 947680 7498 947 776 7086 72-I8I 37 11-761 3-2791 928 088 5164 32.72.19 8T 3-2957 19-467 3.11.269 13-683 38 17'-29 83-101 923 606 6480 928 710 1944 88 83.107 38-7-47 948 7661802 3-2963 39 3-2797 7-11-109 32.311 37.227 89 17-523 949 048 2928 7-31-41 11-809 840 31-271 3-2801 7.1201 3.2803 890 32.23.43 29-307 3-2969 59-151 41 13-647 47-179 19-443 926 260 6095 91 7.19-67 3-2971 37-241 32-991 42 3-7-401 925 466 8007 3-532 925 776 0688 92 11.811 950 510 8980 79-113 960 802 8230 43 925 879 0893 32-937 11-13-59 3.29.97 93 3-13-229 960 997 8840 38-331 7-1277 44 23-367 926 496 7898 926 702 4942 7.17-71 94 961886 0949 3-11-271 23-389 3-19-157 45 3».313 79-107 3.2819 11.769 95 951 871 6571 7-1279 132-53 172.31 46 927 4216951 3-7-13-319277295598 32.941 96 3-29.103 962 458 8964 3-72. 61 962744 0240 47 43-197 37-229 72.173 61.139 97 952 840 8667 32.997 47-191 3.41.73 48 3-11-257 17-499 32.23-41 13.653 98 7-1283 13.691 11-19-43 89.101 49 7-1213 3-19-149 29-293 3.2833 99 3S-37 17-232 3-2999 954194 2618 Num. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. .LX. PRIME AKD COMPOSITE NTJMBE:^S. 127 1 Num. 1 3 7 9 n™. 1 3 7 9 900 954 290 7617 3-3001 9545801627 32-7-11-13 950' 3-3167 13-17-43 3-3169 37-257 01 954 772 9897 954 869S711 71-127 29-311 51 978 226 181- 32.7-151 31-307 3-19-167 02 3-31.97 7-1289 32-17-59 955 639 6530 52 978 682 5652 89-107 7-1361 13-733 03 11-821 3-3011 7-1291 3-23-131 53 33-353 979 229 5980 3-11-172 979 502 8488 04 956 2164692 956S12 6S08 83-109- 966 600 5882 54 7-29-47 3-3181 979 866 9226 32-IO6I 05 3-7-431 11-823 3-3019 967 080 2597 55 980 048 8451 41-233 19-503 112-79 06 13-17-41 3^-19-53 957 463 6157 3-3023 56 3-3187 73-131 32-1063 7-1367 07 47-193 43-211 29-313 7-1297 57 17-563 3-3191 61-157 3-31-103 08 3= -1009 31-293 3-13-233 61-149 58 11-13-67 7-372 981 682 7274 43-223 09 958 6116578 3-7-433 11-827 33-337 59 3-23-139 53-181 3.7-457 29-331 910 19-479 9591845427 7-1301 959 470 7021 960 982 816 4697 32.11.97 13-739 3-3203 ; 11 3-3037 13-701 32-1013 11-829 61 7-1373 982 858 9428 59-163 983129 9247 12 7-1303 3-3041 960 828 0605 3-17-179 62 32-1069 983 810 4858 3-3209 988 581 1867 13 23-397 960 613 4576 960 803 6249 13-19-37 63 983 671 3829 3.132.19 23-419 3''-7-17 ,14 3-11-277 41-223 3-3049 7-1307 64 31-311 984 2121668 11-877 984 482 8064 15 9614685564 3*-113 961 753 2142 3-43-71 65 3-3217 72.197 32-29-37 13-743 16 961942 8881 7-ll 168 071 8820 3-23-211 06 3.43.109 7»-41 33-521 11-1279 56 168 191 2019 168 260 8496 7. 2081 17-857 Ot 148 824 9680 3-4691 7-2011 3.13-192 57 32. 1619 13-19-59 3.43.113 61-239 08 148 688 498S 148 6951798 148 818 6146 73-193 58 7.2083 3-4861 29.503 3»-1621 09 3.7.11-61 17.829 3-37-127 23-613 59 164 088 0575 164144 6825 11.1327 13-1123 1410 59.239 3i'-1567 149 484 6668 3-4703 1460 3.31.157 17-859 3».541 7-2087 11 103.137 11-1283 19-743 7-2017 61 19.769 3-4871 47.311 3-11-443 12 38.523 29-487 3.17.277 71-199 62 164 977 0771 7-2089 165165 2614 166 214 6899 13 13-1087 3-7-673 67.211 32-1571 63 3.4877 165 883 8726 3.7.17.411655114108 | 14 79.179 160 6416414 7-43.47 150 725 7466 64 U* 3i'-1627 97.151 3-19-257 15 3-53-89 150 848 6067 32-112-13 161 082 5818 65 72.13.23 165 926 6496 166 046 0879 107-137 16 7'-17» 3-4721 31-457 3-4723 66 3<.181 11-31-43 3.4889 166 400 8086 17 37-383 151 461 7871 1516848394 11-1289 67 17.863 3-67-73 13.1129 3''-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 32-19-83 152 196 6828 3.4733 69 3-59-83 7-2099 32.23.71 167 287 7899 1420 11-1291 7-2029 162 502 8S05 13.1093 1470 61-241 3.132-29 7.11.191 3.4903 21 3S-I579 61-233 3.7.677 59.241 71 47-313 1677012860 167 819 2899 41-359 22 182 980 1864 3-11-431 41.347 35.17.31 72 3-7-701 167 996 8121 3.4909 11-13-103 23 7-19-107 43-331 23-619 29.491 73 168 282 2296 32-1637 168409 0886 3-178 24 3.47-101 158 601 4748 32-1583 158 784 8865 74 168 626 9462 23-641 168708 6802 78.43 25 168 8458401 3-4751 53-269 3.72.97 75 3''-ll-149 168 830 8424 3-4919 169 066 9327 26 13-1097 17-839 11-1297 19.751 76 29-509 3-7-19-37 169 292 2749 38-547 27 3-67.71 7-2039 3-4759 109.131 77 169 409 8981 11-17-79 7-2111 169 648 0491 28 1S4 7S8 6192 3»-232 7-13-157 3.11.433 78 3-13-379 169 762 6769 32-31-53 23-643 29 31.461 155128 8987 17-292 79.181 79 7-2113 3-4931 170 178 6788 3-4933 1430 32.7-227 155 4271886 3-19-251 41.349 1480 192.41 113-131 13-17.67 59-251 31 11-1301 3-13-367 103-139 32.37.43 81 3-4937 170 643 0228 3-11-449 7-29-73 32 1S5 978 8447 156 088 9919 166166 2609 7.23.89 82 170 877 5073 3S-61 171 068 2876 3-4943 33 3-17-281 11-1303 3»-59 13.1103 83 171170 4849 7-13-163 37-401 11-19-71 34 156 579 4858 3-7-683 156 7610988 3.4783 84 32.17.97 171 821 6875 3-7^101 31.479 35 113-127 31-463 72-293 83-173 85 171 755 6981 3-4951 83-179 32-13-127 36 3-4787 53-271 3-4789 157 426 8448 86 7.11.193 89-167 172 223 3414 172 2817615 37 7-2053 32-1597 11-1307 3-4793 87 3.4957 107-139 38-19-29 172 578 7488 38 73-197 19-757 167 970 2486 158 080 6126 88 23.647 3-112-41 172 8071884 3-7-709 39 3»-13-41 37-389 3-4799 7-112-17 89 172 928 8686 53-281 178 098 8178 47-317 1440 158 892 6504 3-4801 158 578 5662 32. 1601 1490 3.4967 7-2129 3-4969 17-877 41 168 694 1182 7-29-71 13-1109 158 «85 1418 91 13.31-37 32-1657 7-2131 3-4973 42 3-11-19.23 159 055 6085 32-7-229 47-307 92 43-347 178 8561890 11-23-59 174 080 7180 43 159 296 426T 3-17-283 159 476 9565 3-4813 93 3«-7-79 109-137 3-13-383 174 3215278 44 7-2063 11-13-101 159 777 6728 169 887 7911 94 67-223 3-17.293 174 654 0845 3^-11.151 45 3-4817 97-149 3-61-79 19-761 95 174 670 2418 19.787 174 844 4987 .7.2137 46 1601988261 32-I6O7 17-23-37 3-7.13-53 96 3.4987 13-1151 3^-1663 175 192 7884 47 29-499 41-353 31-467 1«0 738 5681 97 11.1361 3-7-23-31 17-881 3-4993 48 3«.1609 7-2069 3-11-439 161038 4124 98 71-211 178 898 7795 7-2141 13-1153 49 43.337 3-4831 7-19-109 3^-179 99 3-19-263 11-29-47 3-4999 58-283 Noil. log 2 = .301 029 9957. Ndm. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBEI^S. 133 1 Num. 1 3 7 9 Num. 1 3 7 9 1500 7-2143 32-1667 43 - 349 3-5003 1550 3-5167 37-419 32.1723 13-1193 01 17.883 176467 4846 176 6881608 23.653 51 190 689 7978 3-5171 59.263 3-7-739 02 32.1669 83-181 3-5009 7.19.113 52 11.17-83 192-43 191 087 5630 53-293 03 176 987 8748 3-5011 11-1367 3'. 557 53 3.31.167 72-317 3-5179 41-379 04 132.89 72-307 41-367 101.149 54 191478 9604 32-11.157 7-2221 3-71-73 05 3.29.173 177 628 0616 32-7-239 11.372 55 191768 8214 103.151 47.331 191 981 6808 06 177 868 8086 3.5021 13-19-61 3.5023 56 32.7-13-19 79-197 3.5189 192 260 7186 07 7-2153 178199 6991 178 814 9348 17.887 57 23-677 3.29.179 37.421 33.577 08 3.11.457 178 4877810 3-47.107 79.191 58 192 6958276 192,6510707 11.13.109 7.17.131 09 178718 0191 3s.i3.43 31.487 3.7.719 59 3-5197 31.503 32.1733 19.821 ' 1510 179 006 7076 11.1373 1791782292 29.521 1560 193152 4869 3.7.743 198 319 4804 3.112.43 11 32.23-73 7.17.127 3.5039 13.1163 61 67-233 13.1201 7-23.97 193 683 2249 12 179 6806184 3.712 7. 2161 32.412 62 3.41.127 17.919 3.5209 198 931 1912 13 179 867 6818 37-409 180 039 8109 180 097 1890 63 72.11.29 3*. 193 19.823 3.13.401 14 3-72-103 19.797 3". 11. 17 180 888 9656 64 194264 5160 194820 0458 194 4810826 194 486 5905 15 109-139 3.5051 23-659 3.31.163 65 32.37.47 11.1423 3.17.307 7.2237 ' 16 180 727 8477 59.257 29-523 7.11.197 66 194 819 4896 3.23.227 194 986 8484 32.1741 17 3-13-389 181 071 4578 3-5059 43.353 67 195 096 7106 7.2239 61.257 195318 8601 18 17.19-47 32.7.241 181 471 9929 3-61.83 68 3.5227 195 4291425 33.7.83 29.541 19 11.1381 181 648 5378 7-13.167 181 815 0150 69 13.17.71 3.5231 11.1427 3.5233 1520. 33.563 23.661 3.37-137 67.227 1570 7.2243 41.383 113-139 23.683 21 7.41.53- 3.11.461 182 829 0406 32.19.89 71 3.5237 19.827 3-132-31 11.1429 22 31.491 13.1171 182 6148477 97.157 72 79.199 32.1747 196 645 8868 3.72.107 23 3-5077 182785 4421 32-1693 72.311 73 196766 8811 196 811 6427 196 9219448 196 977 1884 24 188 013 4681 3. 5081 79-193 3-13-17-23 74 33.11.53. 7.13.173 3-29-181 197 252 9830 25 101-151 7-2179 11-19-73 183 826 0780 75 19.829 3.59.89 7-2251 32.17-103 26 3-5087 183 639 9042 3-7-727 183 810 5961 76 197688 7690 11.1433 197 749 0676 13-1213 27 188 867 4772 32-1697 184 088 0786 3-11.463 77 3.7.751 197 914 8038 32.1753 31-509 28 7-37-59 17-29-31 184822 2656 184379 0807 78 43.367 3.5261 198299 6090 3-19-277 29 32-1699 41-373 3-5099 184 663 0446 79 198 409 6835 17.929 198 674 6181 7-37-61 1530 11-13-107 3-5101 134 890 0822 3'-7 1580 3.23.229 198 789 6401 3-11-479 198 904 8995 31 61-251 186 060 2825 172-53 185 280 4162 81 97.163 32.7.251 1991241146 3-5273 32 3-5107 7-11-199 32-13.131 186 513 8242 82 13-1217 199 288 8281 72-17-19 11-1439 33 185 570 4886 3-19-269 72.313 3-5113 83 32-1759 71.223 3-5279 47-337 34 232-29 67-229 103.149 186 080 0861 84 7-31-73 3.5281 13-23-53 33-587 35 3-7-17-43 13-1181 3.5119 186 362 9404 85 112-131 83.191 101-157 200 276 7991 36 186 419 4892 3^-569 112.127 3-47-109 86 3-17-311 29.547 32-41-43 7-2267 37 19-809 186 758 6272 186 871 6144 7-13= 87 59-269 3.11.13.37 200 7684448 3-67-79 38 32-1709 187 041 0400 3.23.223 11-1399 88 200 877 8457 7.2269 201 041 8955 201096 8650 39 187 266 8382 3-7.733 89.173 32-29-59 89 3-5297 23.691 3-7-757 13-1223 1540 187 548 9209 73.211 7-31-71 19-811 1590 201 424 4876 33.19.31 201688 2811 3-5303 41 3-11-467 187 887 1784 38.571 17-907 91 7-2273 2017520628 11-1447 201 915 7827 42 7-2203 3.53-97 188 2814795 3-37-139 92 32-29-6I 202 024 8951 3-5309 17-937 43 13-1187 11-23-61 43.359 188 619 1672 93 89-179, 3.47-113 202 406 5726 32-7.11-23 | 44 3-5147 188 781 6714 3-19.271 7-2207 94 19-839 107-149 37-431 41.389 45 188 956 5925 32-17.101 13.29.41 3-5153 95 3^13-409 7-43-53 3''-197 203 005 6747 46 189 237 6802 7.472 189 406 0855 31-499 96 11-1451 3-17-313 7-2281 3.5323 47 3^.191 189 674 5256 3.7.11.67 23-673 97 208 8821097 208 386 4917 13-1229 19.292 48 118-137 3.13.397 17-911 32-1721 98 3-7-761 11-1453 3.732 59.271 49 7-2213 190 185 5209 190 247 6880 11-1409 99 203 875 6283 32.1777 17.941 3.5333 Num. log2 = .301 029 9957. Num. log5 = .698 970 0043. 134 IX. PRIME AND COMPOSITE NUMBERS. ... ... ,_l Num. 1 3 7 9 Num. 1 3 7 9 1600 204 147 1262 13-1231 204809 9449 7-2287 '1650 29-569 3-6501 17-971 3-5503 01 3».593 67-239 3-19-281 83-193 51 11-19.79 72-337 83-199 217 988 7682 02 37-433 3-7«-109 11-31-47 32-13-137 52 3.6507 13-31-41 3-7-787 218 246 5797 03 17 •23-41 206 014 7926 7-29-79 43-373 53 61.271 32-11.167 23-719 3-37-149 04 3-5347 61-263 3«-1783 11-1459 64 7.17.139 71-233 218 719 2669 13.19-67 05 7-2293 3-5351 205 664 4074 3-53-101 55 33. 613 218 876 7151 3-5519 29-571 06 205 772 5821 205 826 6694 205 984 7987 205988 8608 56 219 086 5572 3-5521 219 248 8722 32-7-263 OT 3-11-487 206 096 944T 3-23-233 7-2297 67 73-227 219 401 1804 112-137 59v281 08 13-1237 3M787 206 476 0618 3-31-173 58 3-5527 7-23-103 32.19.97 63-313 ' 09 206 688 0848 7-11M9 206 744 9441 17-947 69 47-353 3-5531 7.2371 3-11.503 1610 3«-1789 206 906 7929 3-7-13-59 89-181 1660 13-1277 220186 6679 220 291 1857 17-977 11 207122 4977 3-41-131 71-227 3*- 199 61 3-72-113 J7-449 3-29.191 220 604 8878 12 78-47 23-701 207 558 5859 1272 62 11-1611 32-1847 13.1279 3-23-241 13 3-19-283 13-17-73 3=.11.163 207 876 6216 63 220 918 8686 220 970 5876 127.131 7-2377 14 207 980 4876 3-5381 67-241 3-7-769 64 32-4.32 11-17^89 3.31.179 221 888 1588 15 31-521 29-557 107-151 11-13-113 65 221440 8208 3-7-13-61 221696 7867 33-617 16 3-5387 7-2309 3-17-317 19-23-37 66 221 701 0644 19-877 7.2381 79-211 17 103-157 33-599 7-2311 3-5393 67 3-6557 222 018 7602 32.17-109 13-1283 18 11-1471 209 069 0841 209 166 8667 209 220 0281 68 7-2383 3-67-83 11-37-41 3-5663 19 S«-7-257 209 8278159 3-5399 97-167 69 222 482 8571 222 584 8984 59-283 222 690 4647 1620 17-953 3.11-491 19-853 32. 1801 1670 3-19-293 222 7944811 3-6569 72.11.31 21 13-29-43 31-523 209 970 5167' 72-331 71 17-983 33-6I9 73-229 3.5673 22 3-5407 210 181 1682 33-601 210 291 7608 72 23-727 7-2389 43-389 228 469 9812 23 210 845 2778 3-7-773 13-1249 3-5413 73 32-11-132 29-677 3-7-797 19-881 24 109-149 37-439 7-11-211 210 826 6887 74 228 781 8964 3-6581 228 987 0208 32-I86I 25 3-5417 210 988 6864 3-5419 71-229 75 7-2393 11-1523 13-1289 224 248 1010 26 7-23-101 3«-13-]39 211807 4667 i -11-17-29 76 3-37-161 224 8517460 3»-23 41-409 27 53-307 211 467 6244 41-397 73-223 77 31-641 3-6591 19-883 3.7.17.47 28 3»-67 19-857 3-61-89 7-13-179 78 97-173 13-1291 224 978 0904 103.163 29 11-1481 3-5431 43-379 32-I8II 79 3-29-193 7-2399 3-11-509 107.157 1630 212214 2474 7-17-137 23-709 47-347 1680 53-317 32-1867 76 3-13.431 31 3-5437 11-1483 32-72-37 212 693 5424 81 225 693 6482 17-23-43 67-261 112-139 32 19-859 3-5441 29-563 3 - 5443 82 33-7-89 225 908 4449 3-71-79 226 058 8104 33 7-2333 218 066 9621 17-312 218 225 4728 83 226 109 9200 3-31.181 113-149 32.1871 34 3-13-419 59-277 3-5449 213 491 1988 84 11-1631 226419 4486 17-991 7.29.83 35 83-197 3^23-79 11-1487 3-7-19-41 85 3-41-137 19-887 32-1873 23.733 36 218 809 8446 218 862 9804 13-1259 214 0221487 86 13-1297 3-7-11-73 101-167 3.5623 37 3«. 17-107 7-2339 3-53-103 11-1489 87 227 140 8264 47-359 7-2411 227 846 7182 38 2148404108 3-43-127 7-2341 33-6O7 88 3-17-331 227 449 6205 3-13-433 227 608 9857 39 37-443 132-97 19-863 232.31 89 7-19-127 32-1877 61-277 3.43-131 1640 3-7-11-71 47-349 32-1823 61-269 1690 227 912 4018 227 968 7915 11-29-53 37.457 41 216 185 0465 3-5471 216298 7982 3-13-421 91 32-1879 13.1301 3-6639 7-2417 42 216899 6011 11-1493 216 568 2671 7-2347 92 228426 0255 3.5641 228 679 9942 3''-ll-19 43 3-5477 215 T16 8.5.52 3-5479 17-967 93 228 682 6097 7-41-59 228 886 4875 13-1303 44 41-401 3^-7-29 216 086 6924 3-5483 94 3-5647 228 990 8108 32-7-269 17.997 45 216192 8024 216 2450977 7-2351 109-161 95 11-23-67 3-5651 31-647 3.6653 46 3«-31.59 101-163 3-11-499 43-383 96 7-2423 229 502 6621 192.47 71.239 47 7-13-181 3-172-19 216 878 1417 32-1831 97 3-5657 11-1543 3-5659 229 9121088 48 216 988 5594 53-311 217 141 6879 11-1499 98 229 963 2620 33-17-37 230 116 6868 3-7-809 49 3-23-239 217 299 6590 33-13-47 7-2357 99 13-1307 280270 0574 23-739 89-191 XI-.V1. log 2 = . 301 029 9957. Num. log 5 = .698 970 0043, IX. PRIME AND COMPOSITE NUMBERS. 135 1 1 NlTM. 1 3 7 9 Num. 1 3 7 9 noo 32.1889 72-347 3-5669 73-233 1750 11-37-43 23-761 7-41-61 2482618427 01 230 729 8446 3-53-107 7-11-13-17 32-3I-6I 51 3-13-449 83-211 3-5839 243 509 8126 02 230 988 0717 29-587 2311881360 2811891455 52 7-2503 33-11-59 17-1031 3-5843 03 3-7.811 281 291 1464 33-631 11-1549 53 47-373 89-197 13-19.71 2440048281 04 2314950764 3-13-19-23 2816479612 3-5683 54 32-1949 53.331 3-5849 7-23-109 05 17'. 59 231 800 7921 37,-461 7-2437 55 2448018662 3-5851 97.181 32.1951 06 3-112.47 113-151 3-5689 132.101 56 17-1033 7.13-193 11-1597 244 747 0428 07 43-397 32-7-271 232 411B784 3-5693 57 3-5857 244 845 9090 3''.7.31 2449941661 , 08 19-29-31 11-1553 7-2441 23.743 58 245 048 6789 3-5861 43-409 3-11-13-41 09 3^-211 282 818 2926 3-41-139 282 970 7128 59 72-359 73-241 245 438 6340 246 487 9913 nio 72-349 3-5701 2331738554 32-1901 1760 3-5867 29-607 3-5869 246 734 6985 11 71-241 109-157 233 427 6507 17-19-53 61 11,-1601 32-19-103 79-223 3-7-839 12 3-13-439 288 579 8567 32.11-173 7-2447 62 67-263 246 079 8412 2461784045 172 -61 13 37-463 3-5711 238 984 7967 3-29-197 63 33-653 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 32-37-53 15 3-5717 17-1009 3-7-19-43 2844919742 65 19-929 127-139 246 916 9170 246 966 1066 16 1312 32-1907 234 694 4071, 3-59-97 66 3-7-292 17-1039 32-13-151 247 2119707 17 7-11-223 13-1321 89-193 41-419 67 41-431 3-43-137 11-1607 3-71-83 18 32-23-83 235 098 9901 3-17-337 235250 6116 68 247 5068241 247665 9469 23-769 72-192 19 235 8011408 3-11-521 29-593 33-72-13 69 3-5897 13-1361 3-17-347 11-1609 1720 103-167 285 604 1898 235 7051587' 235 755 6346 1770 31-571 32-7-28I 248144 9873 3-5903 21 3-5737 7-2459 32-1913 67-257 71 89-199 248 2921226 7-2531 13-29-47 22 17-1013 3-5741 7-23-107 3-5743 72 32-11.179 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 8801660 3^-73 24 3-7-821 43-401 3-5749 47-367 74 113-157 11-1613 249124 9493 249178 8894 25 13-1327 36-71 2369652991 3-11-523 75 3-61-97 41-433 32-1973 7.43-59 26 41-421 61-283 31-557 7-2467 76 249 467 4148 3-31-191 109-163 3-5923 27 32.19-101 23-751 3-13-443 37-467 77 13-1367 7-2539 29-613 23.773 28 11-1571 3-7-823 59-293 32.17-113 78 3-5927 260 005 0285 3-72.112 2601616361 29 237 820 1108 287 8708415 72-353 238 020 9987 '79 250 200 8597 33-659 13.372 3-17-349 1730 3-73-79 113-13 33-641 19-911 1780 7-2543 19-937 250 590 7587 11-1619 31 7-2473 3-29-199 288 472 6569 3-23-251 81 32-1979 47-379 3-5939 103-173 32 238 572 9617 17-1019 2387238754 13-31-43 82 71-251 3-13-457 2610782645 32-7-283 33 3-53-109 288 873 7870 3-5779 7-2477 83 11-1621 17-1049 2518218128 261870 5055 34 239 074 1882 32-41-47 11-19-83 3-5783 84 3-19-313 7-2549 33-66I 13-1373 35 289 824 5098 7-37-67 17-1021 239 524 7082 85 251 662 5500 3-11-541 7-2551 3-5953 36 33-643 97-179 3-7-827 11-1579 86 53-337 2519648982 17-1051 107-167 37 29-599 3-5791 2399748011 32-1931 87 3-7-23-37 61-293 3-59-101 19-941 38 7-13-191 2401247302 240 224 6541 240 274 6076 88 2528918032 32-1987 31-577 3-67-89 39 3 -11 -17 -31 240 3744970 32-1933 127-137 89 262 684 6167 29-617 11-1627 7-2557 1740 240 674 2070 3-5801 132-103 3-7-829 1790 3''. 13-17 252 926 8117 3-47-127 2530718865 41 23-757 11-1583 240 973 3518 241023 2192 91 258 119 8839 3-7-853 19-23.41 32-II-I8I 42 3-5807 7-19-131 3-37-157 29-601 92 253 862 2398 268 410 7048 7-13-197 258 566 0672 43 241 322 8029 32-13-149 7-47-53 3-5813 93 3-43-139 79-227 32-1993 2587982299 ' 44 107-163 241 621 1808 73-239 241770 5426 94 7-11-233 3-5981 131-137 3-3;-193 45 32-7-277 31-563 3-11-232 13.17.79 95 29-619 13-1381 254288 7827 254 2821605 46 19-919 3-5821 242 218 8202 33-647 96 3-59te7 11-23-71 3-53-113 7-17-151 47 242 817 7687 101-173 2424668862 7-11-227 97 254 572 2442 32.1997 254 717 2184 3-13-461 48 3-5827 242 6159576 32-29-67 242 764 9778 98 264 813 8410 72-367 264968 7347 255 007 0218 49 242 814 6898 3-73-17 242 963 5918 3-19-307 99 32-1999 19-947 3-7-857 41-439 Num. , log 2 = .301 029 9957. Num. log 5 = .698 970 0043. . 136 IX. PKLME AND COMPOSITE NUMBERS. " Sim. 1 3 7 9 Num. 1 3 7 9 1800 47-383 3-17-353 11-1637 3'- 23 -29 1850 3-7-881 267 242 1488 3-31-199 83-223 01 7-31.83 2S6 586 0490 43-419 37-487 51 107-173 32-ll»-17 267670 6266 3-6173 02 3-6007 67-269 3»-2003 112-149 62 267 6644817 267 711 8267 97.191 7-2647 03 13.19-73 3-6011 17-1061 3-7-859 53 3«. 29-71 43-431 3-37-167 268 086 3044 04 256 260 6065 2B6 803 7491 266 405 0188 256 4681449 54 268 188 1589 3-7-883 17.1091 3^-229 05 3-11-547 7-2579 3-13-463 266 698 6980 55 13-1427 268 4141446 7-11-241 67-277 06 266141 7926 3^-223 7-29-89 3-19-317 66 3-23-269 19-977 32-2063 31-599 07 17-1063 11-31-53 2671268530 101-179 67 72-379 3-41-151 13-1429 3-11.563 08 3^-7^-41 13«-107 3-6029 257414 6588 58 17-1093 269 116 8269 269 209 2989 29-641 09 79-229 3-37-163 257 606 6864 32-2011 69 3-6197 269849 4698 3-6199 7-2657 1810 23-787 43-421 19-953 7-13-199 1860 11-19-89 3'-13-53 23-809 3-6203 11 3-6037 59-307 33-11-61 258 184 2250 61 37-503 7-2659 269 909 6987 43-433 12 268 182 1604 3-7-863 253 825 9847 3-6043 62 32-2069 11-1693 3-7-887 13-1433 13 253 4217579 253 469 6616 7-2591 11-17-97 63 31-601 3-6211 270 876 0052 32-19-109 14 3-6047 268 7091006 3-23-263 258 852 7006 64 7-2663 103-181 29-643 17-1097 15 7-2593 3=-2017 67-271 3-6053 65 3-6217 23-811 3»-691 47.397 16 11-13-127 41-443 37-491 259 8810249 66 270 934 9129 3-6221 11-1697 3-72-127 17 3'-673 17-1069 3-73-83 7'-53 67 2711675789 71-263 19-983 271 868 6221 18 259 617 7668 3-11-19-29 13-1399 32-43-47 68 3-13-479 7-17-157 3-6229 11-1699 19 259 866 5789 7-23-113 31-587 260 047 5260 69 271 682 6876 32-31-67 7-2671 3-23-271 1820 3-6067 109-167 32-7-17= 131-139 1870 271 864 8802 59-317 13-1439 53-363 21 260 888 7944 3-13-467 260 476 8588 3-6073 71 3»-7-ll 272 143 4176 3-17-367 272 282 6448 22 7-19-137 200 619 8752 11-1657 260 762 8449 72 97-193 3-792 61-307 32-2O8I 23 3-69-103 260 858 1820 3-6079 13-23-61 73 272 660 9689 11-13-13141-467 7-2677 24 17-29-37 3' -2027 71-257 3-7-11-79 74 3-6247 272 889 1062 32-2083 2729781091 25 261 286 6651 261 884 2533 261 429 4166 19-312 75 17-1103 3-7-19-47 278 168 8784 3-132.37 26 3«-2029 7-2609 3-6089 261 714 7768 76 73-257 29-647 72-383 1372 27 ll^'-lSl 3-6091 72-373 3»-677 77 3-6257 273 638 6802 3-11-569 89-211 28 101-181 47-389 262 142 4649 262 189 9599 78 7-2683 32-2087 278 857 4354 3-6263 29 3-7-13-67 11-1663 32-19-107 29-631 79 19-23-43 278 996 1188 274 088 5414 11-1709 1830 262 474 8210 3-6101 262 617 1816 3-17-359 1880 32-2089 274 227 1460. 3-6269 7-2687 31 263 712 0626 262 759 4954 13-1409 7-2617 81 13-1447 3-6271 31-607 - 33-17-41 32 3-31-197 73-251 3-41-149 268183 7712 82 11-29-59 7-2689 67-281 19-991 33 23-797 33-7-97 11-1667 3-6113 83 3-6277 37-509 32-7-13-23 276 067 8461 | 34 263 423 0109 13-17-83 7-2621 59-311 84 83-227 3-11.571 47-401 3-61-103 35 3«-2039 268 707 0646 3-29-211 11-1669 85 7-2693 17-1109 109-173 276 513 6605 36 7-43-61 3-6121 264 088 2260 32-13-157 86 3-6287 13-1451 3-19-331 275 743 8846 37 2G4 132 7972 19-967 17-23-47 264 8218778 87 113-167 3''- 233 43-439 3-7-29-31 38 3-11-557 31-593 3*. 227 7-37-71 88 79-239 23-821 11-17-10113-1453 1 39 53-347 3-6131 264 747 0084 3-6133 89 32-2099 7-2699 3-6299 276 483 8260 1840 264 841 4258 7-11-239 79-233 41-449 1890 41-461 3-6301 7-37-73 32-11-191 41 3-17-19' 265124 5582 3-7-877 113-163 91 276 714 4946 276 760 4226 276 852 2683 276 8981772 42 13i>.109 3'-23-89 266 454 6858 3-6143 92 3-7-17-53 127-149 3'-701 23-823 43 7-2633 266 596 0281 103-179 265 7878648 93 11-1721 3-6311 29-653 3-59-107 44 3^-683 265 881 5668 3-11-13-43 19-971 94 13-31-47 19-997 277640 4561 7-2707 45 266 019 9089 3-6151 266 161 1122 32-7-293 95 3-6317 11-1723 3-71-89 277 816 4266 46 266 266 2228 37-499 59-313 11-23-73 96 67-283 32-72-43 13-1459 3-6323 47 3 -47 -131 7^-13-29 32-2053 17-1087 97 61-311 278 130 0067 7-2711 278278 8268 4S 266 725 4670 3-61-101 7-19-139 3-6163 98 3»-19-37 41--JG3 3-6329 17-1117 49 11-412 267 007 3697 53-349 13-1423 99 7-2713 3-13-487 112-157 32-2111 XlM. log 2 = .301 029 9957. Num. log 5 = .698 970 0043. IX. PRIME AND COMPOSITE NUMBERS. 137 NCM. 1 / 3 7 9 Num. 1 3 7 9 1900 278 776 4580 31-613 83-229 278 959 2707 1950 290 056 8823 32-11-197 290 190 4840 3-7-929 01 3-6337 279 050 6482 32.2113 7 -11-13-19 51 109-179 13-19.79 29-673 181-149 02 23-827 3-17-373 53-359 3-6343 52 3^-241 7.2789 8-23-283 59-381 03 279 461 6098 7-2719 27? 698 6099 79-241 58 290724 4800 3.17-383 7-2791 32-13-167 04 3-11-577 137-139 3-7-907 43.448 54 290 946 7847 290 9912320 11-1777 113-173 05 279 917 7770 32-29.73 17-19-59 3.6853 55 3-73-19 291 218 4003 32-41-58 291 846 6467 06 72.389 11-1733 23-829 280 827 9187 56 31-681 3.6521 17-1151 3-11-593 07 38-13.163 280 419 0088 3-6359 280 555 6080 57 291 613 0169 282-37 - 2917461408 7-2797 08 280 601 1S15 3-6361 280 787 6735 33-7.101 58 8-61-107 291 879 2289 8-6529 19-1081 09 17-1123 61-313 132-113 71.269 59 11-13-137 32.7-311 292 189 6926 3-47-189 1910 3-6367 7-2729 82-11.193 97.197 1960 17.1153 292 822 5899 7-2801 292 465 4465 11 29-659 3-23-277 7.2731 3.6373 61 32.2179 11-1788 8-13-503 28-853 12 281 510 6015 13-1471 31-617 11.87.47 62 7-2803 3-31-211 19-1033 •33-727 IS 3-7-911 192-53 3-6379 281 919 2424 63 67-293 29-677 73-269 41-479 14 281 964 6288 3^-709 41-467 3.13-491 64 8-6547 13-1511 32.37-59 72-401 15 11-1741 107-179 282 327 4992 72-17-23 65 43-457 8-6551 11-1787 3-6553 16 32-2129 282 463 4996 3-6389 29-661 66 293 605 6032 7-532 71-277 13-17-89 17 19-1009 3-7-11-83 127-151 32-2131 67 3-'79-83 103-191 3-7-937 11-1789 18 282 8T1 2453 282 916 6268 7-2741 31-619 68 294 047 1613 39 294 179 5418 3-6563 19 3-6397 17-1129 35-79 73-263 69 7-29-97 47-419 294400 0849 294 444 1802 1920 7-13-211 3-37-173 288 469 5864 3-19-387 1970 82-11-199 17-19-61 3-6569 294 664 5895 21 288 649 9720 283 596 1828 11-1747 283 730 7868 71 23-857 3-6571 294 840 8364 32-7-313 22 3-43-149 47-409 £ -13-17-29 7-41-67 72 13-37-41 112-1,63 295 0610446 109-181 23 284 001 8679 32-2137 284187 3450 3-112-53 73 3-6577 • 7-2819 33.17.48 295 8251470 24 71-271 7-2749 19-1013 2844081725 74 19-1039 3-6581 72.18-31 3-29-227 25 33-23-31 18-1481 3-72-131 284 633 7382 75 295 689 0890 295 638 0687 23-859 295 764 9612 26 11-17-103 3-6421 284 814 0974 32-2141 76 3-7-941 295 852 8706 3-11-599 58-873 27 7-2753 284 949 3214 37-521 13-1483 77 17-1163 32-183 296 160 4185 8-19-347 28 3-6427 11-1753 32-2143 286 309 7181 78 181-151 73-271 47-421 7-11-257 29 101-191 3-59-109 23-839 3-7-919 79 33.733 296 511 6247 3-6599 13-1528 1930 285 579 8107 97-199 43.449 285 769 7825 1980 296 687 1238 3-7-23-41 29-683 32-31.71 31 3-41-157 7-31-89 3-47-137 286 984 6425 81 11-1801 296 950 2895 7-19-149 297 081 7377 32 1392 82-19-113 7-11-251 8-17-879 82 3-6607 48-461 32-2203 79-251 33 13-1487 286 299 2509 61-317 83-233 83 7-2838 8-11-601 83-239 3-17-389 34 3^-7-307 23-292 3-6449 11-1759 84 297 563 5571 297 607 8324 89-223 23-863 35 37-523 3-6451 13-1489 3"- 239 85 3-13-509 297 826 1426 3-6619 7-2837 86 19-1019 172-67 107-181 7-2767 86 298 001 1114 32.2207 298132 2918 3-37-179 37 3-11-587 237196 8785 82-2153 287 331 3627 87 3,1-641 7-17-167 11-13.189 103-193 1 38 287 8761816 3-7-18-71287 510 6108 3.23-281 88 32.472 59-837 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 33-11-67 1940 3-29-223 287868 8837 8-6469 18-1498 1990 7-2843 13-1531 17-1171 43-463 41 7-47-59 33-719 288 1S2 1806 3-6473 91 3-6637 299 186 6987 32-2213 299 267 5316 42 288 271 5883 288 316 8102 288 405 7402 288460 4483 92 11-1811 3-29.229 299 441 9208 3-7-13-73 43 3M7.127 288 639,8507 3-11-19-81 7-2777 93 19-1049 31.643 299 659 8089 127-157 44 288 718 6008 3-6481 288 852 6142 32-2I6I 94 3-172-23 72-11-37 8.61.109 299 921 1303 45 53-367 72-897 289 075 8789 11-29-61 95 71-281 83-739 7.2851 3-6658 46 3-13-499 289 209 7826 33-7-IO8 289 843 6451 96 800 182 2946 800 225 8068 41.487 19-1051 47 289 388 2568 3-6491 289 522 0648 8-43-151 97 82-7-317 800 448 8020 3.6659 300 573 7469 48 7-112-23 289 655 8805 13-1499 289 789 5656 98' 13-29-53 3-6661 11.23-79 32-2221 49 3-73-89 101-193 3-67.97 17-81-37 99 300 884 5192 300 877 9660 300 964 8466 7-2857 Num. 1 , log 2 = .301 029 9957. Ndm. log 5 = .698 970 0043. 138 X. SQUARES. " 1 1 2 3 4 5 6 7 8 9 1 4 9 16 25 36 49 64 81 1 100 121 144 169 196 225 256 289 324 361 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 10000 10201 10404 10609 10816 1 1025 1 1^36 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 n 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 113569 114244 114921 34 115600 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 7609 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 0909 19 1844 19 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 21 0681 46 21 1600 21 2521 213444 214369 215296 21 6225 217156 218089 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 ;30 1 1 2 3 4 5 6 7 8 9 X. SQITAEES. • 13( 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 8524 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 3024 28 4089 28 5150 38 6225 28 7296 28 8369 28 9'444 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 310249 311364 312481 56 31 3600 314721 31 5844 31 6969 318096 319225 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 61921 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 33'21 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 417316 418609 419904 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 512656 6l4089 515524 516961 72 51 8400 519841 52 1284 52 2729 52 4176 52 5625 52 7076 52 8529 52 9984 53 1441 73 ~ "^^900 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 613089 614656 61 6225 017796 619369 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 48Q9 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 715716 717409 719104 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 7,9 2100 79 3881 79 5664 79 7449 79 9236 80 1025 80 2816 80 4609 80 6404 80 8201 90 81 0000 81 1801 813604 81 5409 817216 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 91 0116 91 2025 913936 915849 917764 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 XI. CUBES. 1 — — — — 1 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0.000 .001 .008 .027 .064 .126 .216 .343 .512 .729 1 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 1061.21 1092.73 1 124.86 1 157.63 1 191.02 1 225.04 1 259.71 1 2^5.03 1.1 331.00 367.63 404.93 442.90 481.54 520.88 560.90 601.61 643.03 685.16 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 11390.6 11543.2 11697.1 11852.4 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 17 374.0 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 21024.6 21253.9 21485.0 21717.6 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 31255.9 31554.5 31855.0 32 157.4 32 461.8 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 41063.6 41421.7 41781.9 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 51478.8 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 58 411.1 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 62 670.8 63 044.8 63 821.2 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 71991.3 72 511,7 73 034.6 73 560.1 42 74 088.0 74618.5 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 84 027.7 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 99 897,3 100 546 101196 101848 102 603 103 162 47 103 823 104 487 105 154 105 824 106 496 107 172 107 850 108 531 109 215 109 902 4S 110 592 111 285 111 980 112 679 113 380 114 084 114 791 116 501 116 214 116 930 49 117 649 118 371 119 095 119 823 120 554 121287 122 024 122 763 123 506 124 251 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 XI. CUBES. 141 ... ... ., . 1 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 151419 152 273 153 130 153 991 154 854 155 721 156 591 54 157 464 158 340 159 220 160 103 160 989 161879 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 181321 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 201230 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 221445 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 24^ 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 291434 292 755 294 080 295 408 296 741 298 078 299 418 6T 300 763 302 112 303 464 304 821 306 182 307 547 308 916 310 289 311666 313 047 68 314 432 315 821 317 215 318 612 320 014 321419 322 829 324 243 325 661 327 083 69 328 509 329 939 331374 332 813 334 255 335 702 337 154 338 609 340 068 341 532 10 343 000 344 472 345 948 347 429 348 914 350 403 351 896 353 393 354 895 356 401 11 357 911 359 425 360 944 362 467 363 994 365 526 367 062 368 602 370 146 371695 72 373 248 374 805 376 367 377 933 379 503 381078 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 3S0 478 212 480 049 481890 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 521660 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 561516 563 560 565 609 567 664 569 723 88 571787 573 856 575 930 578 010 580094 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 1704 969 707 348 709 732 712 122 714 517 716 917 719 323 721734 724 151 726 573 90 \ 729 000 731433 733 871 736 314 738 763 741218 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 881974 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 Xn. SQUARE ROOTS. 1 8 Differences. 0.0000 1.0000 1.4142 1.7321 2.0000 1 3.1625 3166 4641 5056 7417 2 4.4721 5826 6904 7958 8990 3 5.4772 5678 0569 7446 8310 * 6.3246 4031 ^807 5574 6332 5 7.0711 1414 2111 2801 3485 6 7460 8102 8740 9373 *0000 7 8.3666 4261 4853 5440 6023 8 9443 *0000 *0554 *1104 *1652 9 9.4868 5394 5917 6437 6954 10 lo.ooao 0499 0995 1489 1980 11 4881 5357 5830 6301 6771 12 9545 *0000 *0454 *0905 *1355 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 11.4018 4455 4891 5326 5758 8322 8743 9164 9583 *0000 12.2474 2882 3288 3693 4097 6491 6886 7279 7671 8062 13.0384 0767 1149 1529 1909 4164 4536 4907 5277 5647 7840 8203 8564 8924 9284 14.1421 4914 8324 15.1658 4919 8114 16.1245 4317 7332 17.0294 1774 5258 8661 1987 5242 8430 1555 4621 7631 0587 2127 5602 8997 2315 5563 8745 1864 4924 7929 0880 2478 5945 9332 2643 5885 9060 2173 5227 8226 1172 2829 6287 9666 2971 6205 9374 2481 5529 8523, 1464 17.3205 3494 3781 4069 4356 6068 6352 6635 6918 7200 8885 9165 9444 9722 *0000 18.1659 1934 2209 2483 2757 4391 4662 4932 5203 5472 7083 7350 7617 7883 8149 9737 *0000 *0263 *0526 *0788 19.2354 2614 2873 3132 3391 4936 5192 5448 5704 5959 7484 7737 7990 8242 8494 20.0000 0250 0499 0749 0998 2485 2731 2978 3224 3470 4939 5183 5426 5670 5913 7364 7605 7846 8087 8327 9762 *0000 *0238 *0476 *0713 21.2132 2368 2603 2838 3073 4476 4709 4942 5174 5407 6795 7025 7256 7486 7715 9089 9317 9545 9773 *0000 22.1359 1585 1811 2036 2261 2.2361 2.4495 2.6458 2.8284 3.0000 8730 *0000 *1231 *2426 *3589 *0000 *0990 *1962 *2915 *3852 9161 *0000 *0828 *1644 *2450 7082 7823 8557 9282 *0000 4162 4833 5498 6158 6811 *0623 *1240 *1854 *2462 *3066 6603' 7178 7750 8318 8882 *2195 *2736 *3274 *3808 *4340 7468 7980 8489 8995 9499 2470 2956 3441 3923 4403 7238 7703 8167 8628 9087 *1803 *2250 *2694 *3137 *3578 6190 6619 7047 7473 7898 *0416 *0830 *1244 *1655 *20^6 4499 4900 5300 5698 6095 8452 8841 9228 9615 *0000 2288 2665 3041 3417 3791 6015 6382 6748 7113 7477 9642 *0000 *0357 *0712 *1067 3178 3527 3875 4222 4568 6629 6969 7309 7648 7986 *0000 *0333 *0665 *0997 *1327 3297 3623 3948 4272 4596 6525 68,44 7162 7480 7797 9687 *0000 *0312 *0624 *0935 2788 3095 3401 3707 4012, 5831 6132 64a3 6733 7033 8819 9115 9411 9706 *0000 1756 2047 2337 2627 2916 4642 4929 5214 5499 5784 7482 7764 8045 8326 8606 *0278 *0555 *0831 *1108 *1384 3030 3303 3576 3848 4120 5742 6011 6279 6548 6815 8414 8680 8944 9209 9473 *1050 *1311 *1572 *1833 *2094 3649 3907 4165 4422 4679 6214 6469 6723 6977 7231 8746 8997 9249 9499 9750 1246 1494 1742 1990 2237 3715 3961 4206 4450 4695 6155 6398 6640 6882 7123 8567 8806 9045 9284 9523 *0950 *1187 *1424 *1660 *1896 3307 3542 3776 4009 4243 5639 5870 6102 6333 6564 7945 8174 8403 8632 8861 *0227 *0454 *0681 *0097 *n33 2486 2711 2935 3159 3383 soo 490 480 470 1 60 49 .48 47 2 100 96 96 94 3 150 147 144 141 4 200 196 192 188 S 260 24S 240 235 6 SOO 294 2S8 282 7 850 84& 336 329 8 400 892 884 376 9 450 441 482 423 460 480 440 480 1 46 45 44 43 2 92 90 88 86 8 188 185 182 129 4 184 180 176 172 6 280 225 220 215 6 276 270 264 268 7 822 816 808 801 8 868 860 352 344 9 414 406 896 887 420 410 400 890 1 42 41 40 39 2 84 82 80 78 8 126 128 120 117 4 168 164 160 156 5 210 205 200 195 6 252 246 240 284 7 294 287 280 278 8 836 828 820 812 9 878 869 360 851 8S0 370 360 860 1 88 87 86 36 2 76 74 72 70 8 114 111 108 106 4 1S2 148 144 140 5 190 189 ISO 176 (i 228 222 216 210 7 266, 2,'59 252 245 8 804 296 288 280 9 842 833 824 315 840 830 820 810 1 34 83 82 81 2 68 66 64 62 8 102 99 96 93 4 186 132 128 124 5 170 166 160 169 6 204 198 192 186 7 288 281 224 217 8 272 264 266 248 9 806 297 288 279 800 290 280 270 1 80 29 28 27 2 60 iiS 56 54 3 90 87 84 81 4 120 116 112 108 5 150 145 140 185 6 180 174 168 162 7 210 208 196 189 8 240 232 224 216 9 270 261 252 248 260 260 240 230 1 26 25 24 28 2 52 50 48 46 8 78 75 72 69 4 104 100 96 92 5 180 125 120 116 6 156 150 144 188 7 182 175 168 161 8 208 200 192 184 9 284 225 216 207 Differences. XII. SQUAEE ROOTS. 143 f 50 1 2 f i' 4 5 6 7 8 9' Differences. 50 22.3607 3830 4054 4277 4499 4722 4944 5167 5389 5610 1 2 220 22 44 215 22 48 210 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 8 66 66 68 62 53 23.0217 0434 0651 0868 1084 . 1301 1517 1733 1948 2164 4 5 e 88 110 182 86 108 129 84 105 126 83 104 125 54 2379 2594 2809 3024 3238 3452 3666 3880 4094 4307 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 3926 2074 4131 2281 2487 2693 4336 4540 4745 1 2 8 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 82 102 81 101 80 100 61 6982 7184 7386 7588 7790 7992 8193 8395 8596 8797 6 124 122 121 120 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 9 165 185 163 184 162 182 160 180 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 2 3 20 40 69 20 89 59 19 89 58 19 38 58 66 6905 7099 7294 7488 7682 7876 8070 8263 8457 8650 67 8844 9037 9230 9422 9615 9808 *0000 *0192 *0384 *0576 4 79 78 78 77 68 69 26.0768 2679 0960 2869 1151 3059 1343 3249 1534 3439 1725 3629 1916 3818 2107 2298 2488 4008 4197 4386 5 6 7 99 119 189 98 118 18T 97 116 186 96 115 134 70 26.4575 4764 4953 5141 5330 5518 5707 5895 6083 6271 8 9 158 178 15T 176 ■165 175 154 178 71 72 6458 8328 6646 8514 6833 8701 7021 8887 7208 9072 7395 9258 7582 9444 7769 7955 8142 9629 9815 *0000 1 190 19 188 19 186^ 19 184 18 73 ■27.0185 0370 0555 0740 0924 1109 1293 1477 1662 1846 2 88 88 87 37 74 2029 2213 2397 2580 2764 2947 3130 3313 3496 3679 8 4, 57 76 56 75 56 74 55 74 75 76 3861 5681 4044 5862 4226 6043 4408 ^225 4591 6405 4773 6586 4955 6767 5136 5318 5500 6948 7128 7308 5 6 7 95 114 188 94 118 132 98 112 130 92 110 129 77 7489 7669 7849 8029 8209 8388 8568 8747 8927 9106 8 152 160 149 147 78 9285 9464 9643 9821 ="0000 *0179 *0357 *0555 *0713 *0891 9 171 169 167 166 79 28.1069 1247 1425 1603 1780 1957 2135 2312 2489 2666 1 182 18 180 18 178 18 176 18 80 81 28.2843 4605 3019 4781 3,196 4956 3373 5132 3549 5307 3725 5482 3901 5657 4077 4253 4429 5832 6007 6182 2 8 4 86 56 78 86 64 72 86 63 71 -36 58 70 82 6S56 6531 6705 6880 7054 7228 7402 7576 7750 7924 5 91 90 89 88 83 8097 8271 8444 8617 8791 8964 9137 9310 9482 9655 6 109 108 107 106 84 9828 *0000 *0172 *0345 *0517 *0689 *0861 *1033 *1204 *1376 7 8 127 146 126 144 125 142 123 141 85 29.1548 1719 1890 2062 2233 2404 2575 2746 2916 3087 9 164 162 160 158 86 87 3258 4958 3428 5127 3598 5296 3769 54.66 3939 5635 4109 5804 4279 5973 4449 4618 4788 6142 '6311 6479 1 2 174 17 85 1T2 17 34 170 17 84 168 17 34 88 6648 6816 6985 7153 7321 7489 7658 7825 7993 8161 3 52 52 61 50 89 8329 8496 8664 8831 8998 9166 9333 9500 9666 9833 4 5 70 87 69 86 68 85 67 84 90 91 30.0000 1662 0167 1828 0333 1993 0500 2159 0666 2324 0832 2490 0998 2655 1164 1330 1496 2820 2985 3150 6 7 8 104 122 189 108 120 138 102 119 186 101 lis 184 92 3315 3480 3645 3809 3974 4138 4302 4467 4631 4795 9 157 166 158 151 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 88 16 88 16 82 .16 82 95 8221 8383 8545 8707 8869 9031 9192 9354 9516 9677 8 4 5 50 66 83 49 66 82 49 66 81 48 64 SO 96 9839 *0000 ♦0161 *0322 *0483 *0644 *0805 *0966 *1127 *1288 97 31.1448 1609 1769 1929 2090 2250 2410 2570 2730 2890 6 100 98 97 96 98 99 3050 4643 3209 4802 3369 4960 3528 5119 3688 5278 3847 5436 4006 5595 4166 4325 4484 5753 &911 6070 7 8 9 116 188 149 115 181 148 118 180 146 112 128 144 100 1 2 3 4 5 6 7 8 9 Differences. 144 Xn. SQUARE ROOTS. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 1 0.0000 1.0000 3162 0488 4472 0954 5477 1402 6325 1832 7071 2247 7746 2649 8367 3038 8944 3416 9487 3784 1 2 2S0 26 80 246 26 49 240 24 48 285 24 4T 2 4142 4491 4832 5166 5492 6811 6125 6432 6733 7029 8 75 74 72 96 120 71 94 118 3 7321 7607 7889 8166 8439 8708 8974 9235 9494 9748 4 5 100 125 160 98 128 4 2.0000 0248 0494 0736 0976 1213 1448 1679 1909 2136 6 147 144 141 6 2361 2583 2804 3022 3238 3452 3664 3875 4083 4290 7 8 175 200 172 196 168 192 166 188 6 44 95 4698 4900 5100 5298 5495 5690 5884 6077 6268 9 226 221 216 212 1 6458 6646 6833 7019 7203 7386 7568 7749. 7928 8107 2.30 225 220 216 8 8284 8460 8636 8810 8983 9155 9326 9496 9665 9833 1 2 8 28 46 69 28 46 68 22 44 66 22 43 66 9 3.0000 0166 0332 0496 0659 0822 0984 1145 1305 1464 10 3.1623 1780 1937 2094 2249 2404 2558 2711 2863 3015 4 6 6 92 116 90 118 88 110 86 108 11 3166 3317 3466 3615 3764 3912 4059 4205 4351 4496 138 135 182 129 12 4641 4785 4928 5071 5214 5355 5496 5637 5777 5917 7 161 168 164 151 13 6056 6194 6332 6469 6606 6742 6878 7014 7148 7283 8 9 184 207 180 203 176 198 172 194 14 7417 7550 7683 7815 7947 8079 8210 8341 8471 8601 210 20S 200 196 15 8730 8859 8987 9115 9243 9370 9497 9623 9749 9875 1 2 8 21 42 68 21 41 62 20 40 60 20 89 69 16 4.0000 0125 0249 0373 0497 0620 0743 0866 0988 1110 n 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 5 6 7 105 126 147 108 128 144 100 120 140 98 117 187 19 3589 3704 3818 3932 4045 4159 4272 4385 4497 4609 20 4.4721 4833 4944 5056 5166 5277 5387 5497 5607 5717 8 9 168 189 164 185 160 180 156 176 21 5826 5935 6043 6152 6260 6368 6476 6583 6690 6797 190 19 186 19 180 18 176 18 22 6904 7011 7117 7223 7329 7434 7539 7645 7749 7854 1 23 7958 8062 8166 8270 8374 8477 8580 8683 8785 8888 2 88 87 86 86 24 8990 9092 9193 9295 9396 9497 9598 9699 9800 9900 8 4 67 76 56 74 54 72 53 70 25 26 5.0000 0990 0100 1088 0200 1186 0299 1284 0398 1381 0498 1478 0596 1575 0695 1672 0794 1769 0892 1865 5 6 7 95 114 133 98 111 130 90 108 126 88 106 128 27 1962 2058 2154 2249 2345 2440 2536 2631 2726 2820 8 162 148 144 140 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 17 166 17 160 16 155 16 30 5.4772 4863 4955 5045 5136 5227 5317 5408 5498 5588 2 84 83 82 81 31 5678 5767 5857 5946 6036 6125 6214 6303 6391 6480 8 4 51 68 50 66 48 64 47 62 32 6569 6657 6745 6833 6921 7009 7096 7184 7271 7359 6 86 88 80 78 33 7446 7533 7619 7706 7793 7879 7966 8052 8138 8224 6 102 99 96 98 34 8310 8395 8481 8566 8652 8737 8822 8907 8992 9076 7 8 119 186 116 132 112 128 109 124 35 9161 9245 9330 9414 9498 9582 9666 9749 9833 9917 9 168 149 144 140 36 6.0000 0083 0166 0249 0332 0415 0498 0581 0663 0745 1 160 15 145 15 140 14 185 14 37 0828 0910 0992 1074 1156 1237 1319 1400 1482 1563 2 80 29 28 27 38 1644 1725 1806 1887 1968 2048 2129 2209 2290 2370 8 45 41 42 70 41 39 2450 2530 2610 2690 2769 2849 2929 3008 3087 3166 4 6 60 75 58 78 64 68 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 81 95 108 42 4807 4885 4962 5038 5115 5192 5269 5345 5422 5498 9 185 131 126 122 43 5574 5651 5727 5803 5879 5955 6030 6106 6182 6257 180 125 120 116 44 6332 6408 6483 6558 6633 6708 6783 6858 6933 7007 1 2 18 26 18 26 12 24 12 28 45 7082 7157 7231 7305 7380 7454' 7528 7602 7676 7750 8 89 88 86 85 46 7823 7897 7971 8044 8118 8191 8264 8337 8411 8484 4 5 6 52 65 78 60 63 75 48 60 72 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 9 104 117 100 113 96 108 92 104 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Diiferences. -A.J.JL. d(^ iUAI IE B „00T S. 1 /I R 140 - 1 I 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Diiferences. ; 50 7.0711 0781 0852 0922 0993 1063 1134 1204 1274 1344 114 1 11 2 23 112 110 108 11 11 11 22 22 22 51 1414 1484 1554 1624 1694 1764 1833 1903 1972 2042 52 2111 2180 2250 2319 2388 2457 2526 2595 2664 2732 3 84 84 88 82 53 2801 2870 2938 3007 3075 3144 3212 3280 3348 3417 4 46 5 67 6 68 45 66 67 44 43 65 54 66 66 54 3485 3553 3621 3689 3756 3824 3892 3959 4027 4095 55 4162 4229 4297 4364 4431 4498 4565 4632 4699 4766 7 80 8 91 78 90 77 76 88 86 56 4833 4900 4967 5033 5100 5166 5233 5299 5366 5432 9 103 101 99 97 51 5498 5565 5631 5697 .5763 5829 5895 5961 6026 6092 106 104 102 100 1 1 58 6158 6223 6289 6354 6420 6485 6551 6616 6681 6746 1 11 2 21 3 82 10 21 81 10 10 20 20 81 80 59 6811 6877 6942 7006 7071 7136 7201 7266 7330 7395 60 7.7460 7524 7589 7653 7717 7782 7846 7910 7974 8038 4 42 5 53 42 52 41 40 61 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 T 74 8 85 9 95 78 88 94 71 70 82 80 92 90 63 9373 9436 9498 9561 9624 9687 9750 9812 9875 9937 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 2 20 8 29 10 9 19 19 29 28 9 9 18 18 -66 1240 1302 1363 1425 1486 1548 1609 1670 1731 1792 28 27 67 1854 1915 1976 2037 2098 2158 2219 2280 2341 2401 4 89 88 88 37 86 68 2462 2523 2583 2644 2704 2765 2825 2885 2946 3006 5 49 6 59 7 69 48 47 68 66 67 66 46 45 65 54 69 3066 3126 3187 3247 3307 3367 3427 3487 3546 3606 64 63 70 8.3666 3726 3785 3845 3905 3964 4024 4083 4143 4202 8 78 9 88 77 75 86 85 74 72 88 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 74 5440 6023 5499 6081 5557 6139 5615 6197 5674 6255 5732 6313 5790 6371 5849 6429 5907 6487 5965 6545 2 18 8 26 4 85 17 17 26 25 84 84 16 16 26 24 83 32 ■js 6603 6660 6718 6776 6833 6891 6948 7006 7063 7121 5 44 6 58 48 42 52 60 41 40 49 48 76 7178 7235 7293 7350 7407 7464 7521 7579 7636 7693 T 62 60 59 57 56 77 78 7750 8318 7807 8374 7864 8431 7920 8487 7977 8544 8034 8600 8091 8657 8148 8713 8204 8769 8261 8826 8 70 9 79 69 67 77 76 66 64 74 72 79 8882 8938 8994 9051 9107 9163 9219 9275 9331 9387 78 1 8 76 74 8 7 72 70 7 7 80 8.9443 9499 9554 9610 9666 9722 9778 9833 9889 9944 2 16 3 23 4 81 15 16 28 22 80 80 14 14 22 21 29 28 81 9.0000 0056 0111 0167 0222 0277 0333 0388 0443 0499 82 0554 0609 0664 0719 0774 0830 0885 0940 0995 1049 5 39 88 87 36 85 83 ,84 1104 1652 1159 1706 1214 1761 1269 1815 1324 1869 1378 1924 1433 1978 1488 2033 1542 2087 1597 2141 6 47 7 65 8 62 46 44 58 62 61 59 43 42 50 49 58 56 85 2195 2250 2304 2358 2412 2466 2520 2574 2628 2682 9 70 68 67 66 68 86 2736 2790 2844 2898 2952 3005 3059 3113 3167 3220 68 1 7 66 64 7 6 62 60 6 6 87 3274 3327 3381 3434 3488 3541 3595 3648 3702 3755 2 14 18 13 12 12 88 89 3808 4340 3862 4393 3915 4446 3968 4499 4021 4552 4074 4604 4128 4657 4181 4710 4234 4763 4287 4816 8 20 4 27 5 84 20 19 26 26 33 82 19 18 25 24 81 80 90 9.4868 4921 4974 5026 5079 5131 5184 5237 5289 5341 6 41 7 48 40 88 46 45 87 86 4R 42 91 5394 5446 5499 5551 5603 5656, 5708 5760 5812 5864 8 54 68 61 50 48 92 5917 5969 6021 6073 6125 6177 6229 6281 6333 6385 9 61 69 58 56 54 93 6437 6488 6540 6592 6644 6695 6747 6799 6850 6902 68 66 64 52 50 94 6954 7005 ^7057 7108 7160 7211 7263 7314 7365 7417 1 6 2 12 6 5 11 11 5 5 10 10 95 96 7468 7980- 7519 8031 7570 8082 7622 8133 7673 8184 7724 8234 7775 8285 7826 8336 7877 8387 7929 8438 8 17 4 23 5 29 17 16 22 22 28 27 16 15 21 20 26 25 97 8489 8539 8590 8641 8691 8742 8793 8843 8894 8944 6 85 84 82 81 30 98 8995 9045 9096 9146 9197 9247 9298 9348 9398 9448 7 41 8 46 9 52 89 88 46 48 50 49 36 85 42 40 47 45 99 9499 9549 9599 9649 9700 9750 9800 9850 9900 9950 100 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. .146 Xm. CUBE ROOTS. 1 2 3 4 5 6 7 8 9 Differences. 1 0.0000 1.0000 2.1544 2240 1.2599 1.4422 2894 3513 1.5874 4101 1.7100 4662 1.8171 5198 1.9129 5713 »0000 6207 *0801 6684 1 2 250 2B 50 246 26 49 240 24 48 285 24 47 2 7144 7589 8020 8439 8845 9240 9625 *0000 *0366 *0723 3 4 5 75 100 125 74 98 128 72 96 120 71 94 lis 3 3.1072 1414 1748 2075 2396 2711 3019 3322 3620 3912 4 4200 4482 4760 5034 5303 5569 5830 6088 6342 6593 6 160 147 144 141 5 6840 7084 7325 7563 7798 8030 8259 8485 8709 8930 7 8 175 200 172 196 168 192 165 IBS 6 9149 9365 9579 9791 *0000 *0207 *0412 *0615 *0817 *1016 9 225 221 216 212 1 4.1213 1408 1602 1793 1983 2172 2358 2543 2727 2908 280 226 220 216 8 3089 3267 3445 3621 3795 3968 4140 4310 4480 4647 1 2 23 46 28 46 22 44 22 43 9 4814 4979 5144 5307 5468 5629 5789 5947 6104 6261 3 69 68 66 66 10 4.6416 6570 6723 6875 7027 7177 7326 7475 7622 7769 i 5 92 116 90 113 88 110 86 108 U 7914 8059 8203 8346 8488 8629 8770 8910 9049 9187 6 138 136 182 129 12 9324 9461 9597 9732 9866 *0000 *0133 *0265 *0397 *0528 7 8 9 161 184 207 158 180 208 154 176 198 181 172 194 13 5.0658 0788 0916 1045 1172 1299 1426 1551 1676 1801 14 1925 2048 2171 2293 2415 2536 2656 2776 2896 3015 210 205 200 195 15 3133 3251 3368 3485 3601 3717 3832 3947 4061 4175 1 2 a 21 42 68 21 41 62 20 40 60 20 89 69 16 4288 4401 4514 4626 4737 4848 4959 5069 5178 5288 17 5397 5505 5613 5721 5828 5934 6041 6147 6252 6357 4 84 82 80 78 18 6462 6567 6671 6774 6877 6980 7083 7185 7287 7388 5 6 7 105 126 147 108 128 100 120 140 98 117 187 19 7489 7590 7690 7790 7890 7989 8088 8186 8285 8383 20 5.8480 8578 8675 8771 8868 8964 9059 9155 9250 9345 8 9 168 189 164 185 160 180 156 176 21 9439 9533 9627 9721 9814 9907 *0000 *0092 *0185 *0277 190 185 180 175 22 6.0368 0459 0550 0641 0732 0822 0912 1002 1091 1180 1 19 19 18 18 23 1269 1358 1446 1534 1622 1710 1797 1885 1972 2058 2 8 4 88 67 76 87 66 74 86 64 72 86 58 70 24 2145 2231 2317 2403 2488 2573 2658 2743 2828 2912 25 2996 3080 3164 3247 3330 3413 3496 3579 3661 3743 5 6 7 96 114 183 93 111 130 90 108 126 88 106 128 26 3825 3907 3988 4070 4151 4232 4312 4393 4473 4553 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 17 166 17 160 16 165 16 30 31 6.6943 7679 7018 7752 7092 7824 7166 7897 7240 7969 7313 8041 7387 8113 7460 8185 7533 8256 7606 8328 2 8 4 34 61 68 38 60 66 82 48 64 31 47 62 32 839'9 8470 8541 8612 8683 8753 8824 8894 8964 9034 6 85 83 80 78 33 9104 9174 9244 9313 9382 9451 9521 9589 9658 9727 6 7 8 102 119 186 99 116 182 96 112 128 98 109 124 34 9795 9864 9932 *0000 *0068 *0136 *0203 *0271 *0338 *0406 35 7.0473 0540 0607 0674 0740 0807 0873 0940 1006 1072 9 168 149 144 140 36 1138 1204 1269 1335 1400 1466 1531 1596 1661 1726 1 2 160 16 80 145 15 29 140 14 28 135 14 27 37 1791 1855 1920 1984 2048 2112 2177 2240 2304 2368 38 39 2432 3061 2495 3124 2558 3186 2622 3248 2685 3310 2748 3372 2811 3434 2874 3496 2936 3558 2999 3619 8 4 5 45 60 76 44 68 78 42 66 70 41 54 68 40 7.3681 3742 3803 3864 3925 3986 4047 4108 4169 4229 6 7 8 90 105 120 87 102 116 84 98 112 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 9 136 181 120 122 43 5478 5537 5595 5654 5712 5770 5828 5886 5944 6001 180 126 120 116 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 88 36 35 46 47 7194 7750 7250 7805 7306 7860 7362 7915 7418 7970 7473 8025 7529 8079 7584 8134 7639 8188 7695 8243 4 5 6 52 65 78 60 63 76 48 60 72 46 53 69 48 8297 8352 8406 8460 8514 8568 8622 8676 8730 8784 7 91 88 84 81 49 8837 8891 8944 8998 9051 9105 9158 9211 9264 9317 8 9 104 117 100 118 96 108 92 104 50 1 2 3 4 5 6 7 8 9 Differences. 1 XIII. CUBE BOOTS. 14T 50 1 2 , 3 4 5 6 7 8 9 Differences. 50 7.9370 9423 9476 9528- 9581 9634 9686 9739 9791 9843 1 2 110 11 22 105 100 95 10 lo' 20 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 88 !2 80 29 53 0927 0978 1028 1079 1130 1180 1231 1281 1332 1382 4 6 & 44 55 66 12 58 68 40 38 60 48 60 57 54 1433 1483 1533 1583 1633 1683 1733 1783 1833 1882 55 1932 1982 2031 2081 2130 2180 2229 2278 2327 2377 7 8 77 88 14 34 70 67 80 76 56 2426 2475 2524 2573 2621 2670 2719 2768 2816 2865 9 99 »5 90 86 57 2913 2962 3010 305a^ 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 8 9 18 28 9 18 27 9 18 26 9 8 IT 17 26 25 60 8.4343 4390 4437 4484 4530 4577 4623 4670 4716 4763 4 5 87 46 36 45 85 44 84 34 43 42 52 60 61 4809 4856 4902 4948 4994 5040 5086 5132 5178 ■5224 6 65 54 S3 62 5270 5316 5362 5408 5453 5499 5544 5590 5635 5681 7 8 9 64 74 88 68 72 81 62 70 79 60 59 69 67 77 76 63 5726 5772 5817 5862 5907 5952 5997 6043 6088 6132 64 6177 6222 6267 6312 6357 6401 6446 6490 6535 6579 82 80 78 76 T4 65 6624 6668 6713 6757 6801 6845 6890 6934 6978 7022 1 2 8 8 16 25 8 16 24 8 16 23 8 T 15 15 28 22 66 7066 7110 7154 7198 7241 7285 7329 7373 7416 7460 67 7503 7547 7590 7634 7677 7721 7764 7807 7850 7893 4 88 32 81 80 30 68 7937 79,80 8023 8066 8109 8152 8194 8237 8280 8323 6 6 41 49 40 48 89 47 88 3T 46 44 69 8366 8408 8451 8493 8536 8578 8621 8663 8706 8748 7 57 56 56 68 52 70 8.8790 8833 8875 8917 8959 9001 9043 9085 9127 9169 8 9 66 74 64 72 62 TO 61 59 68 67 71 9211 9253 9295 9337 9378 9420 9462 9503 9545 9587 72 TO 68 66 64 72 9628 9670 9711 9752 9794 9835 9876 9918 9959 *0000 1 7 7 7 T 6 73 9.0041 0082 0123 0164 0205 0246 0287 0328 0369 0410 2 3 4 14 22 29 14 21 28 14 20 27 13 13 20 19 26 26 74 0450 0491 0532 0572 0613 0654 0694 0735 0775 0816 75 0856 0896 0937 0977 1017 1057 1098 1138 1178 1218 5 6 86 43 35 42 84 41 83 32 40 88 76 1258 1298 1338 1378 1418 1458 1498 1537 1577 1617 7 50 49 48 46 46 77 1657 1696 1736 1775 .1815 1855 1894 1933 1973 2012 S 58 56 54 68 51 59 68 78 2052 2091 2130 2170 2209 2248 2287 2326 2365 2404 9 65 63 61 79 2443 2482 2521 2560 2599 2638 2677 2716 2754 2793 1. 62 6 60 6 58 6 56 54 6 5 80 81 9.2832 3217 2870 3255 2909 3294 2948 3332 2986 3370 3025 3408 3063 3447 3102 3485 3140 3523 3179 3561 2 8 4 12 19 25 12 18 24 12 17 23 11 11 17 16 22 22 82 3599 3637 3675 3713 3751 3789 3827 3865 3902 3940 5 81 80 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 3 37 43 50 36 42 48 85 41 46 34 32 39 88 46 43 85 4727 4764 4801 4838 4875 4912 4949 4986 5023 5060 9 56 54 52 60 49 86 5097 5134 5171 5207 5244 5281 5317 5354 5391 5427 1 52 5 50 5 48 5 46 44 5 4 87 5464 5501 5537 5574 5610 5647 5683 5719 5756 5792 2 10 10 10 9 9 88 5828 5865 5901 5937 6973 6010 6046 6082 6118 6154 8 4 5 16 21 26 15 20 25 14 19 24 14 13 18 18 23 22 89 6190 6226 6262 6298 6334 6370 6406 6442 6477 6513 90 9.6549 6585 6620 6656 6692 6727 6763 6799 6834 6870 6 7 8 31 86 42 30 35 40 29 84 88 28 26 32 81 87 86 91 6905 6941 6976 7012 7047 7082 7118 7153 7188 7224 92 7259 7294 7329 7364 7400 7435 7470 750.5 7540 7575 9 47 45 48 41 40 93 7610 7645 7680 7715 7750 7785 7819 7854 7889 7924 42 40 88 86 84 94 7959 7993 8028 8063 8097 8132 8167 8201 8236 8270 1 2 4 8 4 8 4 8 4 3 7 7 95 8305 8339 8374 8408 8443 8477 8511 8546 8580 8614 3 4 5 18 17 21 12 16 20 11 15 19 11 10 14 14 13 17 96 8648 8683 8717 8751 8785 8819 8854 8888 8922 8956 97 8990 9024 9058 9092 9126 9160 9194 9227 9261 9295 6 25 24 23 22 , 20 98 9329 9363 9396 9430 9464 9497 9531 9565 9598 9632 7 8 9 29 84 38 23 82 86 27 SO 84 25 24 29 27 82 81 99 9666 9699 9733 9766 9800 9833 9866 9900 9933 9967 100 1 2 3 4 5 6 7 8 9 Differences. 148 XTTT. CUBE ROOTS. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. 0.0000 4642 5848 6694 7368 7937 8434 8879 9283 9655 1 84 8 88 g 82 8 81 80 8 8 1 1.0000 0323 0627 0914 1187 1447 1696 1935 2164 2386 2 17 17 16 16 16 2 2599 2806 3006 3200 3389 3672 3751 3925 4095 4260 8 i 5 26 84 42 25 88 42 26 88 41 24 24 82 82 41 40 3 4422 4581 4736 4888 5037 5183 5326 5467 5606 •6741 4 5874 6005 6134 6261 6386 6510 6631 6751 6869 6986 ■G 50 SO 49 49 48 6 7100 7213 7325 7435 7544 7652 7758 7863 7967 8070 7 8 59 07 68 66 57 '66 57 56 65 64 6 8171 8272 8371 8469 8566 8663 8758 8852 8945 9038 9 76 76 74 78 72 1 • 9129 9220 9310 9399 9487 9574 9661 9747 9832 9916 79 78 77 76 76 8 2.0000 0083 0165 0247 0328 0408 0488 0567 0646 0724 1 2 8 8 18 24 8 16 28 8 16 28 8 8 15 16 28 28 9 0801 0878 0954 1029 1105 1179 1253 1327 14Q0 1472 10 2.1544 1616 1687 1758 1828 1898 1967 2036 2104 2172 4 5 82 40 81 89 81 89 80 80 88 88 11 2240 2307 2374- 2440 2506 2572 2637 2702 2766 2831 6 47 47 46 46 45 12 2894 2958 3021 3084 3146 3208 3270 3331 3392 3453 7 8 9 66 68 71 65 62 70 64 62 69 58 58 61 60 63 68 13 3513 3573 3633 3693 3752- 3811 3870 3928 3986 4044 14 4101 4159 4216 4272 4329 4385 4441 4497 4662 4607 74 78 72 71 70 15 4662 4717 4771 4825 4879 4933 4987 5040 5093 5146 1 2 8 7 16 22 7 15 22 7 14 22 7 7 14 14 21 21 16 6198 5251 5303 5355 5407 5458 5610 5561 5612 5662 17 5713, 5763 6813 6863 5913 5962 6012 6061 6110 6159 4 80 29 29 28 28 18 19 6207 6684 6256 6731 6304 6777 6352 6824 6400 6870 6448 6916 6496 6962 6543 7008 6590 7053 6637 7099 5 6 7 87 44 62 87 ■ 44 61 86 43 60 36 86 48 42 60 49 20 2.7144 7189 7234 7279 7324 7369 7413 7457 7501 7545 8 9 69 67 68 66 58 65 67 66 64 68 21 7589 7633 7677 7720 7763 7806 7860 7892 7935 7978 69 68 67 66 65 22 8020 8063 8105 8147 8189 8231 8273 8314 8356 8397 1 7 7 7 7 7 23 8439 8480 8521, 8562 8603 8643 8684 8724 8765 8805 2 3 4 14 21 23 14 20 2T 18 20 27 18 13 20 20 26 26 24 8845 8885 8925 8965 9004 9044 90,83 9123 9162 9201 25 9240 9279 9318 9357 9395 9434 9472 9611 9549 9687 5 6 7 85 41 48 84 41 43 84 40 47 83 83 40 39 46 46 26 9625 9663 9701 9738 9776 9814 9851 9888 9926 9963 27 3.0000 0037 0074 0111 0147 0184 0221 0257 0293 0330 8 65 64 54 53 62 '28 0366 0402 0438 0474 0510 0646 0581 0617 0652 0688 9 62 •61 60 69 69 29 0723 0758 0794 0829 0864 0899 0934 0968 1003 1038 1 64 6 68 6 62 6 61 60 6 6 30 3.1072 1107 1141 1176 1210 1244 1278 1312 1346 1380 2 8 4 18 19 26 18 19 26 12 19 26 12 12 18 18 24 24 31 1414 1448 1481 1515 1648 1582 1615 1648 1682 1715 32 1748 1781 1814 1847 1880 1913 1945 1978 2010 2043 5 82 82 81 81 80 33 2075 2108 2140 2172 2204 2237 2269 2301 2332 2364 6 as 88 37 87 86 34 2396 2428 2460 2491 2523 2554 2686 2617 2648 2679 7 8 46 61 44 60 48 60 48 42 49 48 35 2711 2742 2773 2804 2836 2866 2897 2927 2958 2989 9 68 67 66 56 54 36 3019 3050 3080 3111 3141 3171 3202 3232 3262 3292 1 2 69 6 12 68 6 12 57 6 11 66 66 6 6 11 11 37 3322 3352 3382 3412 3442 3472 3601 3531 3561 3590 38 3620 3649 3679 3708 3737 3767 3796 3825 3854 3883 8 18 17 17 17 17 39 3912 3941 3970 3999 4028 4056 4086 4114 4142 4171 4 S 24 80 28 29 28 29 22 22 28 28- 40 3.4200 4228 4256 4285 4313 4341 4370 4398 4426 4454 6 T 8 85 41 47 86 41 46 84 40 46 84 83 89 89 46 44 41 4482 4510 4538 4566 4594 4622 4650 4677 4705 4733 42 4760 4788 4815 4843 4870 4898 4925 4952 4980 5007 9 58 62 51 50 60 43 5034 5061 5088 5115 6142 5169 5196 5223 5250 6277 64 68 62 51 60 44 5303 5330 6357 5384 5410 5437 5463 5490 5516 5543 1 2 6 11 5 11 6 10 6 6 10 10 45 5569 5595 5622 6648 6674 5700 5726 5752 5778 5804 8 4 5 16 22 27 16 21 27 16 21 26 16 16 20 20 26 26 46 5830 5856 5882 5908 5934 6960 5986 6011 6037 6063 47 6088 6114 6139 6165 6190 6216 6241 6267 6292 6317 6 82 82 •81 31 30 48 6342 6368 6393 6418 6443 6468 6493 6518 6543 6568 7 8 9 38 43 49 87 42 48 86 42 47 86 85 41 40 46 46 49 6593 6618 6643 6668 6692 6717 6742 6766 6791 6816 50 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Differences. Xni. CUBE ROOTS. 149 ■ - -- - -1 50 .0 .1 2 .3 .4 .5 .6 .7 .8 .9 Differences. 50 3.6840 6865 6889 6914 6938 6963 6987 7011 7036 7060 1 2 49 5 10 48 5 10 47 5 9 46 5 9 46 6 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 7563 7586 7610 7634 7657 7681 7704 7728 7751 7774 4 6 6 20 25 29 19 24 29 19 24 28 18 23 28 18 23 27 54 7798 7821 7844 7867 7891 7914 7937 7960 7983 8006 55 8030 8053 8076 8099 8121 8144 8167 8190 8213 8236 7 8 84 39 84 88 83 88 82 87 32 86 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 2 3 4 9 18 4 9 18 4 4 4 59 8930 89^2 8974 8996 9018 9040 9061 9083 9105 9127 8 18 8 12 8 12 60 3.9149 9170 9192 9214 9235 9257 9279 9300 ■9322 9343 "4 6 6 18 22 26 17 22 26 17 21 25 16 21 25 16 20 24 61 9365 9386 9408 9429 9451 9472 9494 9515 9536 9558 62 9579 9600 9621 9643 9664 9685 9706 9727 9748 9770 T 81 30 29 29 28 63 9791 9812 9833 9854 9875 9896 9916 9937 9958 9979 8 9 85 40 34 89 84 88 38 87 82 86 64 4.0000 0021 0042 0062 0083 0104 0125 0145 0166 0187 89 88 87 86 86 65 0207 0228 0248 0269 0290 0310 0331 0351 0372 0392 1 2 8 4 8 12 4 8 11 4 7 11 4 7 11 4 7 11 66 0412 0433 0453 0474 0494 0514 0534 0555 0575 0595 67 0615 0636 0656 0676 0696 0716 0736 0756 0776 0797 4 16 .16 15 14 14 68 0817 0837 0857 0876 0896 0916 0936 0956 0976 0996 5 6 7 20 28 27 19 28 27 19 22 26 18 22 2.5 18 21 26 69 1016 1035 1055 1075 1095 1114 1134 1154 1174 1193 70 4.1213 1232 1252 1272 1291 1311 1330 1350 1369 1389 ' 8 9 81 85 30 34 30 83 29 32 28 32 71 1408 1428 1447 1466 1486 1505 1524 1544 1563 1582 34 3 88 8 82 8 81 8 30 8 72 1602 1621 1640 1659 1679 1698 1717 1736 1755 1774 1 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 4 10 14 10 13 10 18 9 12 9 12 75 2172 2190 2209 2228 2246 2265 2284 2302 2321 2340 5 6 7 17 20 24 17 20 28 16 19 22 16 19 22 15 18 21 76 2358 2377 2395 2414 2432 2451 2469 2488 2506 2525 77 2543 2562 2580 2598 2617 2635 2653 2672 2690 2708 8 2T 26 26 25 24 78 2727 2745 2763 2781 2799 2818 2836 2854 2872 2890 9 81 80 29 28 27 79 2908 2927 2945 2963 2981 2999 3017 3035 3053 3071 1 29 8 28 8 27 8 26 8 25 3 80 4.3089 3107 3125 3142 3160 3178 3196 3214 3232 3260 2 3 4 6 9 12 6 8 11 5 8 11 5 8 10 5 S 10 81 3267 3285 3303 3321 3339 3356 3374 3392 3409 3427 82 3445 .3462 3480 3498 3515 3533 3551 3568 3586 3603 6 15 14 14 18 13 83 3621 3638 3656 3673 3691 3708 3726 3743 3760 3778 6 7 8 17 20 23 17 20 22 16 19 22 16 18 21 15 18 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 1 2 24 2 5 23 2 5 22 2 4 21 2 4 20 2 ■ 4 87 4310 4327 4344 4361 4378 4395 4412 4429 4446 4463 88 89 4480 4647 4496 4664 ^513 4681 4530 4698 4547 4714 4564 4731 4580 4748 4597 4764 4614 4781 4631 4797 3 4 6 7 10 12 7 9 12 7 9 11 6 8 11 6 8 10 90 4.4814 4831 4847 4864 4880 4897 4913 4930 4946 4963 6 1 8 14 17 19 14 16 18 IS 15 18 18 15 17 12 14 16 91 4979 4996 5012 5029 5045 5062 5078 5094 5111 6127 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 s 2 8 2 3 95 5629 5645 5661 5677 6693 5709 5725 5741 5757 6773 8 4 5 6 8 10 6 7 g 5 7 9 5 6 s 5 6 8 96 5789 5804 5820 5836 5852 5868 5884 5900 5915 5931 97 5947 5963 5979 5994 6010 6026 6042 6057 6073 6089 6 11 11 10 10 9 98 6104 6120 6136 6151 6167 6183 6198 6214 6229 6246 7 13 15 17 18 14 16 12 14 15 11 13 14 11 12 14 99 6261 6276 6292 6307 6323 6338 6354 6369 6385 6400 8 9 100 .0 .1 .i .3 .4 .5 .6 .7 .8 .9 Differences. " " " 1 150 Xm. CITBE ROOTS. 1 2 3 4 ~ 5 6 7 8 9 Differences. .0 .1 0.0000 4642 2154 4791 2714 4932 3107 5066 3420 5192 3684 5313 3915 5429 4121 5540 4309 5646 4481 5749 1 2 140 185 U 14 28 27 180 13 26 125 18 • 26 .2 5848 5944 6037 6127 6214 6300 6383 6463 6642 6619 8 42 41 89 88 .3 6694 6768 6840 6910 6980 7047 7114 7179 7243 7306 4 5 G 56 84 70 OS 84 81 62 65 78 60 68 75 .4 7368 7429 7489 7548 7606 7663 7719 7775 7830 7884 .5 7937 7990 8041 8093 8143 8193 8243 8291 8340 8387 7 8 98 95 112 108 91 104 88 100 .6 8434 8481 8627 8573 8618 8662 8707 8750 8794 8837 9 126 122 117 118 .1 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 1 2 8. 12 12 24 28 86 35 11 11 .9 9655 9691 9726 9761 9796 9830 9865 9899 9933 9967 22 88 21 82 1.0 1.0000 0033* 0066 0099 0132 0164 0196 0228 0260 0291 4 6 6 48 46 60 68 72 69 44 66 66 42 58 63 1.1 0323 0354 0385 0416 0446 0477 0507 0537 0567 0597 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 S4 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 10 10 9 9 1.6 1696 1720 1745 1769 1793 1817 1840 1864 1888 1911 2 8 20 19 80 29 18 27 17 26 1.7 1935 1958 1981 2005 2028 2051 2074 2096 2119 2142 4 40 88 86 84 1.8 2164 2187 2209 2232 2264 2276 2298 2320 2342 2364 5 50 48 45 43 1.9 2386 2407 2429 2450 2472 2493 2515 2536 2557 2578 6 7 60 57 70 67 54 63 61 60 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 8 8 7 65 7 60 6 2.2 3006 3026 3046 3065 3084 3104 3123 3142 3162 3181 1 2.3 3200 3219 3238 3257 3276 3295 3314 3333 3351 3370 2 16 19 14 18 12 2.4 3389 3407 3426 3444 3463 3481 3499 3518 3636 3554 8 4 24 28 21 32 80 28 20 26 18 24 2.5 3572 3590 3608 3626 3644 3662 3680 3698 3715 3733 5 40 88 8S 88 30 2.6 3751 3768 3786 3803 3821 3838 3856 3873 3890 3908 T 48 45 42 56 A3 49 89 46 86 42 2.7 3925 3942 3959 3976 3993 4010 4027 4U44 4061 4078 8 64 60 56 52 48 2.8 4095 4111 4128 4145 4161 4178 4195 4211 4228 4244 9 72 68 68 59 64 2.9 4260 4277 4293 4309 4326 4342 4358 4374 4390 4406 1 66 56 64 6 6 6 63 6 62 6 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 3 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 28 27 27 26 3.3 4888 4903 4918 4933 4948 4963 4978 4993 5007 5022 C 84 88 32 82 81 3.4 5037 5052 5066 5081 6096 5110 5126 5139 5154 5168 7 8 89 89 38 45 44 43 87 42 86 42 3.5 5183 6197 5212 5226 5241 5255 5269 5283 6298 5312 9 60 60 49 48 47 3.6 3.7 5326 5467 5340 6481 5355 6495 5369 5508 5383 5522 5397 5536 5411 5550 5425 5564 6439 5677 5453 5591 1 2 51 50 49 6 5 6 10 10 10 48 5 10 47 6 9 3.8 5605 5619 5632 5646 5659 5673 5687 5700 5714 5727 8 16 15 15 14 14 3.9 5741 5754 5767 5781 5794 6808 5821 5834 5848 5861 4 5 20 20 20 26 25 25 19 24 19 24 4.0 1.5874 5887 5900 6914 5927 5940 5953 69fi6 5979 5992 6 81 30 29 29 28 4.1 6005 6018 6031 6044 6057 6070 6083 6096 6109 6121 7 8 86 35 84 41 40 89 84 88 38 38 4.2 6134 6147 6160 6173 6185 6198 6211 6223 6236 6249 9 46 45 44 48 42 4.3 6261 6274 6287 6299 6312 6324 6337 6349 6362 6374 46 45 44 43 42 4.4 6386 6399 6411 6424 6436 6448 6461 6473 6485 6497 1 2 5 5 4 9 9 9 4 9 4 8 4.5 6510 6522 6534 6546 6568 6571 6583 6595 6607 6619 8 14 14 18 18 18 46 6631 6643 6655 6667 6679 6691 6703 6715 6727 6739 4 18 18 18 17 17 4.7 6751 6763 6774 6786 6798 6810 6822 6833 6845 6857 6 C 28 28 22 28 27 26 22 26 21 26 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 7064 7065 7077 7088 8 9 87 86 85 41 41 40 84 39 34 3S 5.0 1 2 3 4 5 6 7 8 9 Differences. JLill. CUBE ROOTS. 151 5.0 1 2 • 3 4 5 G 7 8 9 Differences. 6.0 1.7100 7111 7123 7134 7145 7167 7108 7179 7190 7202 1 41 4 40 4 89 4 38 3T 4 4 5.1 7213 7224 7235 7247 7268 7269 7280 7291 7303 7314 2 8 8 8 S 7 5.2 7325 7336 7347 7358 7369 7380 7391 7402 7413 7424 3 i 5 12 16 21 12 16 20 12 16 20 11 11 15 15 19 19 5.3 7435 7446 7457 7468 7479 7490 7501 7512 7522 7533 5.4 7544 7555 7666 7577 7587 7698 7609 7620 7630 7641 6 25 24 23 28 22 5.5 7652 7662 7673 7684 7694 7705 7716 7726 7737 7748 T 8 29 88 28 82 27 81 27 26 80 80 5.6 7758 -7769 7779 7790 7800 7811 7821 7832 7842 7863 9 87 86 85 84 88 5.7 7863 7874 7884 7894 7906 7915 7926 7936 7946 7967 36 35 34 83 82 5.8 7967 7977 7988 7998 8008 8018 8029 8039 8049^ 8069 1 2 8 4 7 U 4 7 11 8 7 10 8 8 7 6 10 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 18 13 17 16 6.1 8272 8282 8292 8302 8311 8321 8331 8341 8351 8361 6 22 21 20 20 19 6.2 6.3 8371 8469 8381 8479 8391 8489 8400 8498 8410 8608 8420 8618 8430 8528 8440 8537 8460 8547 8459 8557 7 8 9 25 29 82 25 28 82 24 27 81 28 22 26 26 30 29 6.4 8566 8576 8586 8595 8605 8616 8624 8634 8643 8653 81 80 29 2S 27 6.5 8668 8672 8682 8691 8701 8710 8720 8729 8739 8748 1 2 8 6 8 6 8 6 8 3 6 5 6.6 8758 8767 8777 8786 8796 8805 8814 8824 8833 8843 3 9 9 9 8 8 6.7 8852 8861 8871 8880 8889 8899 8908 8917 8927 8936 i 12 12 12 11 11 6.8 8945 8955 8964 8973 8982 8992 9001 9010 9019 9029 6 6 16 19 15 18 15 17 14 14 17 16 6.9 9038 9047 9056 9065 9074 9084 9093 9102 9111 9120 7 22 21 20 20 19 7.0 1.9129 9138 9148 9157 91G6 9175 9184 9193 9202 9211 8 9 25 28 24 27 28 26 22 22 25 24 7.1 9220 9229 9238 9247 9266 9265 9274 9283 9292 9301 26 25 24 23 22 7.2 9310 9319 9328 9337 9346 9354 9363 9372 9381 9390 1 3 8 2 2 2 7.3 9399 9408 9416 9425 9434 9443 9462 9461 9469 9478 2 8 i 6 8 10 5 8 10 5 7 10 5 4 7 7 9 9 7.4 9487 9496 9604 9513 9522 9531 9539 9548 9667 9566 7.5 9574 9583 9592 9600 9609 9618 9626 9635 9644 9652 5 6 18 16 18 15 12 14 12 11 14 18 7.6 9661 9670 9678 9687 9695 9704 9713 9721 9730 9738 7 18 18 17 16 15 7.7 7.8 9747 9832 9755 9840 9764 9849 9772 9857 9781 9866 9789 9874 9798 9883 9806 9891 9815 9899 9823 9908 8 9 21 23 20 23 19 22 18 IS 21 20 7.9 9916 9925 9933 9941 9950 9958 9967 9975 9983 9992 1 21 2 20 2 19 2 18 17 2 2 8.0 8.1 2.0000 0083 0008 0091 0017 0100 0025 0108 0033 0116 0042 0124 0050 0132 0068 0141 0066 0149 0075 0157 2 3 4 4 6 8 4 6 8 4 6 S 4 8 5 5 7 7 8.2 0165 0173 0182 0190 0198 0206 0214 0223 0231 0239 6 11 10 10 9 9 8.3 0247 0255 0263 0271 0279 0288 0296 0304 0312 0320 6 7 18 15 12 14. 11 IS 11 10 18 12 8.4 0328 0336 0344 0352 0360 0368 0376 0384 0392 0400 8 17~-T6" 15 14 14 8.5 0408 0416 0424 0432 0440 0448 0466 0464 0472 0480 9 19 18 17 16 15 8.6 0488 0496 0504 0512 0620 0528 0536 0643 0561 0569 1 16 2 15 2 14 1 18 12 1 1 8.7 0567 0575 0583 0691 0699 0606 0614 0622 0630 0638 2 8 8 8 8 2 8.8 0646 0653 0661 0669 0677 0685 0692 0700 0708 0716 8 4 S 6 6 8 5 6 8 4 6 7 4 4 5 6 7 6 8.9 0724 0731 0739 0747 0756 0762 0770 0778 0785 0793 9.0 2.0801 0809 0816 0824 0832 0839 0847 0855 0862 0870 6 10 11 9 11 8 10 8 7 9 S 9.1 0878 0885 0893 0901 0908 0916 0923 0931 0939 0946 8 18 12 11 10 10 9.2 0954 0961 0969 0977 0984 0992 0999 1007 1014 1022 9 14 14 18 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 1 2 1 9.5 1179 1187 1194 1201 1209 1216 1224 1231 1238 1246 3 4 6 3 4 6 3 1 5 8 4 5 2 2 8 3 4 4 9.6 1253 1261 1268 1275 1283 1290 1297 1305 1312 1319 9.7 1327 1334 1341 1349 1356 1363 1371 1378 1385 1392 6 7 6 5 5 4 9.8 1400 1407 1414 1422 1429 1436 1443 1451 1468 1465 7 8 9 8 9 7 3 6 7 8 6 5 6 6 9.9 1472 1480 1487 1494 1501 1508 1516 1523 1530 1537 10 9 7 6 10.0 1 2 3 4 5 6 7 8 9 Differences. 152 XIV. RECrPROOALS. 1 2 3 4 5 6 7 8 9 Differences. .0 00 100.0 50.00 33.33 26.00 20.00 16.67 14.29 12.50 11.11 1 93 10 96~ 10 94 9 92 90 9 <9 .1 10.0000 9.091 8.333 7.692 7.143 6.667 6.250 5.882 5.556 5.263 2 '20 19 19 18 18 . .2 5.0000 4.762 4.545 4.348 4.167 4.000 3.846 3.704 3.671 3.448 8 29 29 28 28 '27 .3 3.3333 3.226 3.125 3.030 2.941 2.857 2.778 2.703 2.632 2.564 4 6 6 89 49 59 88 48 58 88 47 66 87 86 46 46 56 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 8 69 78 67 77 66 76 64 63 74 72 .6 1.6667 6393 6129 5873 5625 5385 5152 4925 4706 4493 9 88 86 86 88 81 .1 . 4286 4085 3889 3699 3514 3333 3168 2987 2821 2658 88 86 84 82 80 .8 2500 2346 2195 2048 1906 1765 1628 1494 1364 1236 1 2 8 9 18 26 9 17 26 8 17 26 8 8 16 16 26 24 .9 1111 0989 0870 0753 0638 0526 0417 0309 0204 0101 1.0 1.0000 ♦9901 *9804 *9709 *9616 *9524 *9434 *9346 *9259 ♦9174 4 8 6 85 44 88' 84 48 62 84 42 60 38 32 41 40 49 48 1.1 , 0.9091 9009 8929 8850 8772 8696 8621 8547 8476 8403 1.2 8333 8264 8197 8130 8065 8000 7937 7874 7813 7752 7 62 60 69 67 66 1.3 7692 7634 7576 7519 '7463 7407 7353 7299 7246 7194 8 9 70 79 69 77 67 76 66 64 74 72 1.4 7143 7092 7042 6993 6944 6897 6849 6803 6757 6711 78 76 74 72 70 1.6 6667 6623 6579 6536 6494 6452 6410 6369 6329 6289 1 2 3 8 16 23 8 16 28 7 15 22 7 7 14 14 22 21 1.6 6250 6211 6173 6135 6098 6061 6024 6988 6962 6917 1.7 5882 5848 6814 6780 5747 6714 6682 5650 5618 5587 4 81 80 80 29 28 1.8 5566 6525 5496 5464 5436 5405 5376 5348 5319 5291 5 6 7 89 47 65 88 46 63 87 44 62 86 85 43 42 60 49 1.9 6263 5236 5208 5181 5155 5128 5102 5076 5051 5025 2.0 0.5000 4975 4950 4926 4902 4878 4854 4831 4808 4786 8 9 62 70 61 68 69 67 68 66 65 68 2.1 4762 4739 4717 4696 4673 4661 4630 4608 4587 4666 68 7 66 7 64 6 62 60 6 6 2.2 4646 4625 4506 4484 4464 4444 4425 4405 4386 4367 1 2.3 4348 4329 4310 4292 4274 4255 4237 4219 4202 4184 2 14 13 13 12 12 2.4 4167 4149 4132 4115 4098 4082 4065 4049 4032 4016 8 4 20 27 20 26 19 26 19 18 25 24 2.6 4000 3984 3968 3953 3937 3922 3906 3891 3876 3861 5 6 7 84 41 48 88 40 46 82 88 46 81 80 37 36 48 42 2.6 3846 3831 3817 3802 3788 3774 3759 3745 3731 3717 2.7 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 8 54 58 51 60 48 2.8 3571 3559 3646 3534 3521 3509 3497 3484 3472 3460 9 61 69 58 66 64 2.9 3448 3436 3425 3413 3401 3390 3378 3367 3366 3344 1 58 6 66 6 54 6 62 50 6 6 3.0 0.3333 3322 3311 3300 3289 3279 3268 3257 3247 3236 2 8 4 12 17 28 11 17 22 11 10 10 3.1 3226 3215 3205 3195 3185 3175 3165 3155 3145 3135 16 22 16 15 21 20 3.2 3125 3116 3106. 3096 3086 3077 '3067 3058 ,3049 3040 6 29 28 27 26 26 3.3 3030 3021 3012 3003 2994 2985 2976 2967 2959 2950 6 85 84 82 81 80 3.4 2941 2933v 2924 2916 2907 2899 2890 2882 2874 2865 7 8 41 46 89 46 88 48 36 86 42 40 3.5 2857 2849 2841 2833 2826 2817 2809 2801 2793 2786 9 62 60 49 47 46 3.6 2778 2770 2762 2766 2747 2740 2732 2725 2717 2710 ; 48 S 10 46 6 9 44 4 9 48 . 42 4 4 9 8 3.7 2703 2695 2688 2681 2674 2667 2660 2663 2646 2639 3.8 2632 2625 2618 2611 2604 2597 2591 2584 2677 2571 8 14 14 18 18 18 3.9 2564 2568 2551 2546 2538 2532 2526 2619 2513 2506 4 5 19 24 18 28 18 22 17 ,17 22 21 4.0 0.2500 2494 2488 2481 2475 2469 2463 2457 2451 2445 6 29 28 26 26 26 4.1 2439 2433 2427 2421 2415 2410 2404 2398 2392 2387 7 8 34 88 82 87 81 86 80 29 84 84 4.2 2381 2375 2370 2364 2358 2353 2347 2342 2336 2331 9 48 41 40 39 88 4.3 2326 2320 2315 2309 2304 2299 2294 2288 2283 2278 41 40 89 88 87 4.4 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 1 2 4 8 4 8 4 8 4 4 8 7 4.6 2222 2217 2212 2208 2203 2198 2193 2188 2183 2179 3 12 12 12 11 11 4.6 2174 2169 2165 2160 2155 2151 2146 2141 2137 2132 4 5 6 16 21 25 16 20 24 16 20 23 15 16 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 8 9 88 87 82 86 81 85 30 80 84 33 5.0 1 2 3 4 5 6 7 8 9 Differences. XIY. RECIPROCALS. 153 ' ■ - ■ ■ - - -■■■ 1 5.0 1 2 3 4 5 6 7 8 9 Differences. 5.0 0.2000 1990 1992 1988 1984 1980 1976 1972 1969 1965 36 1 4 2 7 35 4 7 84 8 7 33 82 8 8' 7 6 5.1 1961 1957 1953 1949 1946 1942 1938 1934 1931 1927 5.2 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 S 11 4 14 5 18 11 14 18 10 10 10 18 13 IT 16 5.3 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 14 17 5.4 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 C 22 21 20 20 19 5.5 1818 1815 1812 1808 1805 1802 1799 1795 1792 1789 7 25 8 29 25 23 24 2T 23 22 26 26 5.6 1786 1783 1779 1776 1773 1770 1767 1764 1761 1757 9 82 82 81 80 29 5.7 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 81 30 29 28 2T ' 5.8 1724 1721 1718 1715 1712 1709 1706 1704 1701 1698 1 3 2 6 3 9 8 6 9 3 6 9 3 3 6 5 8 8 5.9 1695 1692 1689 1686 1684 1681 1678 1675 1672 1669 6.0 1667 1664 1661 1658 1656 1653 1650 1647 1645 1642 4 12 5 16 12 16 12 15 11 11 14 14 6.1 1639 1637 1634 1631 1629 ■ 1626 1623 1621 1618 1616 6 19 18 17 IT 16 6.2 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 7 22 8 26 9 2S 21 24 27 20 23 26 20 19 22 22 26 24 6.3 1587 1585 1582 1580 1577 1575 1572 1570 1567 1565 6.4 1563 1560 1558 1555 1553 1550 1548 1546 1543 1541 26 25 24 23 22 6.5 1538 1536 1534 1531 1529 1527 1524 1522 1520 1517 1 8 2 6 8 8 8 6 8 2 5 7 2 2 6 4 7 7 6.6 1515 1513 1511 1508 1506 1504 1502 1499 1497 1495 6.7 1493 1490 1488 1486 1484 1481 1479 1477 1475 1473 4 10 10 10 9 9 6.8 1471 1468 1466 1464 1462 1460 1458 1456 1453 1451 5 18 6 16 7 IB 18 15 18 12 14 IT 12 11 14 13 16 15 6.9 1449 1447 1445 1443 1441 1439 1437 1435 1433 1431 7.0 1429 1427 1425 1422 1420 1418 1416 1414 1412 1410 8 21 9 23 20 28 19 22 18 18 21 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 2 4 8 6 4 8 4 6 8 4 6 8 4 3 5 6 T 7 7.4 1351 1350 1348 1346 1344 1342 1340 1339 1337 1335 7.5 1333 1332 1330 1328 1326 1325 1323 1321 1319 1318 5 11 6 IS 10 12 10 11 9 9 11 10 ' 7.6 1316 1314 1312 1311 1309 1307 1305 1304 1302 1300 7 15 14 13 18 12 '7.7 7.8 1299 1282 1297 1280 1295 1279 1294 1277 1292 1276 1290 1274 1289 1272 1287 1271 1285 1269 1284 1267 8 17 9 19 16 18 15 IT 14 14 16 16 7.9 1266 1264 1263 1261 1259 1258 1256 1255 1253 1252 16 1 2 15 2 U 1 13 12 1 1 8.0 1250 1248 1247 1245 1244 1242 1241 1239 1238 1236 2 8 3 5 4 6 3 5 6 8 4 6 3 2 4 4 5 5 8.1 1235 1233 1232 1230 1229 1227 1225 1224 1222 1221 8.2 1220 1218 1217 1215 1214 1212 1211 1209 1208 1206 5 8 8 T 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 6 10 7 11 8 18 9 11 12 8 10 11 8 T 9 8 10 10 8.5 1176 11J75 1174 1172 1171 1170 1168 1167 1166 1164 9 14 14 13 12 11 8.6 1163 1161 1160 1159 1157 1156 1155 1153 1152 1151 11 1 1 10 1 9 1 8 T 1 1 8.7 1149 1148 1147 1145 1144 1143 1142 1140 1139 1138 9 2 2 2 2 1 8.8 1136 1135 1134 1133 1131 1130 1129 1127 1126 1125 3 3 4 4 5 6 3 4 5 3 4 5 2 2 3 8 4 4 8.9 1124 1122 1121 1120 1119 1117 1116 1115 1114 1112 9.0 1111 1110 1109 1107 1106 1105 1104 1103 1101 1100 6 7 7 8 8 9 6 7 S 5 6 T 6 4 6 5 6 6 9.1 1099 1098 1096 1095 1094 1093 1092 1091 1089 1088 9.2 1087 1086 1085 1083 1082 1081 1080 1079 1078 1076 9 10 9 8 T 6 9.3 - 1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 6 6 4 8 2 9.4 1064 1063 1062 1060 1059 1058 1057 1056 1055 1054 1 1 2 1 1 1 1 1 9.5 1053 1052 1050 1049 1048 1047 1046 1045 1044 1043 8 2 4 2 5 3 2 .2 3 1 2 2 1 1 1 1 2 1 9.6 1042 1041 1040 1038 1037 1036 1035 1.034 1033 1032 9.7 1031 1030 1029' 1028 1027 L026 1025 1024 1022 1021 6 4 S 2 2 1 9.8 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 7 4 8 5 9 5 4 4 5 8 3 4 2 1 2 2 8 2 9.9 1010 1009 1008 1007 1006 1005 1004 1003 1002 1001 10.0 1 2 3 4 5 6 7 8 9 Differences. 154 XV. QUARTER-SQUARES. 1 1 1 2 3 4 5 6 7 8 9 1 2 4 6 9 12 16 20 : 1 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 1190 ■? 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 n 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 10000 10100 10201 1 0302 10404 1.0506 10609 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 1766 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 41-80 4336 4492 4649 4806 4964 5122 5281 5440 32 5600 5760 5921 6082 6244 6406 6569 673i 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 ?7 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 46 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 ii'^ + i] ^-i(« -dy = ab XV. QUARTER-SQUARES. 155 1 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 9«96 9960 S3 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 51 8 1225 8 1510 8 1796 8 2082 8 2369 8 2656 2944 3232 3521 3810 58 4100 4390 4681 4972 5264 6556 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 2ll2 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 110224 11 0556 110889 11 1222 11 1556 11 1890 67 112225 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 10 12 2500 12 2850 12 3201 12 3552 12 3904 12 4256 12 4609 12 4962 12 5316 12 5670 11 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 73 6025 6420 6816 7212 7609 8006 8404 8802 9201 9600 80 16 0000 16 0400 16 0801 16 1202 16 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 210222 210681 21 1140 92 21 1600 212060 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 i(fl + 6r-i(a -bf^ab. i 156 XV. QUARTER-SQUAEES. — 1 100 1 2 3 4 5 6 7 8 9 100 25 0000 26 0500 25 1001 25 1602 25 2004 25 2506 25 3009 26 3512 26 4016 26 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 8?42 9361 9880 04 27 0400 27 0920 27 1441 27 1962 27 2484 27 3006 27 3529 27 4052 27 4576 27 6100 05 6625 6150 6676 7202 7729 8256 8784 9312 9841 28 0370 06 28 0900 28 1430 28 1961 28 2492 28 3024 28 3556 2S 4089 28 4622 28 5166 6690 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 4162 30 4704 30 5256 30 5809 30 6362 30 6916 30 7470 11 8025 8580 9136 9692 310249 310806 31 1364 31 1922 31 2481 31 3040 12 313600 314160 314721 31 5282 5844 6406 6969 7532 8096 8660 13 9225 9790 32 0366 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 15 33 0626 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 7610 18 8100 8690 9281 9872 35 0464 35 1056 35 1649 35 2242 35 2836 35 3430 19 35 4025 35 4620 35 6216 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 6420 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 5166 37 5769 6382 6996 7610 23 8225 8840 "9456 38 0072 38 0689 38 1306 38 1924 38 2642 38 3161 38 3780 24 38 4400 38 5020 38 5641 6262 6884 7606 8129 8762 9376 39 0000 25 39 0626 39 1250 39 1876 39 2502 39 3129 39 3766 39 4384 39 5012 39 6641 6270 26 6900 7630 8161 8792 9424 40 0056 40 0689 40 1322 40 1966 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 416380 29 41 6025 6670 7316 7962 8609 9256 99D4 42 0552 42 1201 42 1860 130 42 2600 42 3150 42 3801 42 4452 42 6104 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 6600 43 6260 6921 7582 8244 8906 9569 44 0232 44 0896 44 1660 33 44 2225 44 2890 44 3556 44 4222 44 4889 44 5556 44 6224 6892 7561 8230 34 8900 9670 45 0241 46 0912 45 1584 45 2256 46 2929 45 3602 46 4276 46 4960 35 45 5626 46 6300 6976 7652 8329 9006 9684 46 0362 46 1041 46 1720 36 46 2400 46 3080 46 3761 46 4442 46 5124 46 6806 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 9656 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 0656 50 1264 50 1972 50 2681 50 339'0 42 50 4100 50 4810 50 6521 50 6232 60 6944 7656 8369 9082 9796 510510 43 51 1225 51 1940 512656 61 3372 514089 514806 515524 616242 51 6961 7680 44 8400 9120 9841 62 0662 52 1284 , 62 2006 62 2729 62 3462 52 4176 52 4900 45 52 5625 52 6350 52 7076 7802 8629 9266 9984 53 0712 63 1441 63 2170 46 53 2900 53 3630 53 4361 53 5092 53 5824 53 6556 63 7289 8022 8756 9490 47 64 0225 54 0960 64 1696 54 2432 64 3169 54 3906 54 4644 54 6382 64 6121 54 6860 48 7600 8340 9081 9822 66 0564 66 1306 55 2049 55 2792 55 3536 55 4280 49 55 5025 55 5770 55 6516 55 7262 8009 8756 9604 66 0252 56 1001 66 1760 i{a + by-Ua- -bf = ab. I l_l XY. QUARTER-SQUARES. 157 150 1 2 3 4 5 6 7 8 9 150 56 2500 56 3250 56 4001 56 4152 56 5504 56 6256 56 1009 56 1162 56 8516 56 9210 51 51 0025 51 0180 51 1536 51 2292 51 3049 51 3806 51 4564 51 5322 51 6081 51 6840 52 1600 8360 9121 9882 58 0644 58 1406 58 2169 58 2932 58 3696 58 4460 53 58 5225 58 5990 58 6156 58 1522 8289 9056 9824 59 0592 59 1361 59 2130 64 59 2900 59 3610 59 4441 59 5212 59 5984 59 6156 59 1529 8302 9016 9850 55 60 0625 60 1400 60 2116 60 2952 60 3129 60 4506 60 5284 60 6062 60 6841 60 1620 56 8400 9180 9961 61 0142 61 1524 612306 613089 613812 614656 615440 51 61 6225 61 1010 61 1196 8582 9369 62 0156 62 0944 62,1132 62 2521 62 3310 58 62 4100 62 4890 62 5681 62 6412 62 1264 8056 8849 9642 63 0436 63 1230 59 «3 2025 63 2820 63 3616 63 4412 63 5209 63 6006 63 6804 63 1602 8401 9200 160 64 0000 64 0800 641601 64 2402 64 3204 64 4006 ,64 4809 64 5612 64 6416 64 1220 61 8025 8830 9636 65 0442 65 1249 65 2056 65 2864 65 3612 65 4481 65 5290 62 65 6100 65 6910 65 1121 8532 9344 66 0156 66 0969 66 1182 66 2596 66 3410 63 66 4225 66 5040 66 5856 66 6612 66 1489 8306 9124 9942 61 0161 61 1580 64 61 2400 61 3220 61 4041 61 4862 61 5684 61 6506 61 1329 61 8152 8916 9800 65 68 0625 68 1450 68 2216 68 3102 68 3929 68 4156 68 5584 68 6412 68 1241 68 8070 66 8900 9.130 69 0561 69 1392 69 2224 69 3056 69 3889 69 4122 69 5556 69 6390 61 69 1225 69 8060 8896 9132 10 0569 10 1406 10 2244 10 3082 70 3921 10 4160 68 10 5600 10 6440 10 1281 10 8122 8964 9806 110649 111492 112336 113180 69 114025 114810 115116 116562 111409 118256 9104 9952 12 0801 12 1650 110 12 2500 12 3350 12 4201 12 5052- 12 5904 12 6156 12 1609 12 8462 72 9316 73 0110 11 13 1025 13 1880 13 2136 13 3592 13 4449 13 5306 13 6164 13 1022 73 1881 8140 12 9600 14 0460 14 1321 14 2182 14 3044 14 3906 144169 14 5632 14 6496 14 1360 13 14 8225 9090 9956 15 0822 15 1689 15 2556 15 3424 15 4292 15 5161 15 6030 14 15 6900 15 1110 15 8641 9512 16 0384 16 1256 16 2129 16 3002 76 3876 16 4150 15 16 5625 16 6500 16 1316 16 8252 9129 11 0006 11 0884 11 1162 11 2641 11 3520 16 11 4400 11 5280 11 6161 11 1042 11 1924 8806 9689 18 0512 18 1456 18 2340 n 18 3225 18 4110 18 4996 18 5882 18 6169 18 1656 18 8544 9432 19 0321 19 1210 18 19 2100 19 2990 19 3881 19 4112 19 5664 19 6556 19 1449 19 8342 9236 80 0130 19 80 1025 80 1920 80 2816 80 3112 80 4609 80 5506 80 6404 80 1302 80 8201 9100 180 81 0000 81 0900 811801 812102 813604 81 4506 81 5409 81 6312 811216 818120 81 9025 9930 82 0836 82 1142 82 2649 82 3556 82 4464 82 5312 82 6281 82 1190 82 82 8100 82 9010 9921 ■ 83 0832 83 1144 83 2656 83 3569 83 4482 83 5396 83 6310 88 83 1225 83 8140 83 9056 9912 84 0889 84 1806 84 2124 84 3642 84 4561 84 5480 84 84 6400 84 1320 84 8241 84 9162 85 0084 85 1006 85 1929 85 2852 85 3116 85 4100 85 85 5625 85 6550 85 1416 85 8402 9329 86 0256 86 1184 86 2112 86 3041 86 3910 86 86 4900 86 5830 86 6161 86 1692 86 8624 9556 81 0489 81 1422 81 2356 81 3290 81 814225 81 5160 81 6096 81 1032 81 1969 81 8906 9844 88 0182 88 1121 88 2660 88 88 3600 88 4540 88 5481 88 6422 88 1364 88 8306 88 9249 89 0192 89 1136 89 2080 89 89 3025 89 3910 89 4916 89 5862 89 6809 89 1156 89 8104 9652 90 0601 90 1550 \190 90 2500 90 3450 90 4401 90 5352 90 6304 90 1256 90 8209 90 9162 910116 911010 91 91 2025 91 2980 913936 914892 915849 916806 911164 918122 9681 92 0640 92 92 1600 92 2560 92 3521 92 4482 92 5444 92 6406 92 1369 92 8332 92 9296 93 0260 93 93 1225 93 2190 93 3156 93 4122 93 5089 93 6056 93 1024 93 1992 93 8961 9930 94 94 0900 94 1810 94 2841 94 3812 94 4184 94 5156 94 6129 94 7102 94 8616 94 9650 95 95 0625 95 1600 95 2516 95 3552 95 4529 95 5506 95 6484 95 1462 95 8441 95 9420 96 96 0400 96 1380 96 2361 96 3342 96 4324 96 5306 96 6289 96 1212 ^6 8256 96 9240 91 91 0225 91 1210 912196 913182 914169 91 5156 91 6144 91 1132 91 8121 91 9110 98 98 0100 98 1090 98 2081 98 3012 98 4064 98 5056 98 6049 98 1042 98 8036 98 9030 99 99 0025 99 1020 99 2016 99 3012 99 4009 99 5006 99 6004 99 1002 99 8001 99 9000 \(a + 6r-\(a -6y = a b. 158 XVI. BESSEL'S COEFFICIENTS. 1 1 c, c, Cs C4 Cb c, c. Ca C4 Ce .00 0.00000 0.00000 0.00000 0.00000 .50 O.12500 0.00000 0.02344 0.00000 .01 0495 0081 0083 0008 .51 2495 0042 2343 0006 .02 0980 0157 0165 0016 .52 2480 0083 2340 0009 .03 1455 0228 0246 0023 .63 2455 0125 2334 0014 .04 1920 0294 0326 0030 .54 2420 0166 2327 0019 .05 2375 0366 0405 0036 .55 2375 0206 2318 0023 .06 2820 0414 0483 0043 .66 2320 0246 2306 0028 .07 3255 0467 0560 0048 .57 2255 0286 2293 0032 .08 3680 0515 0636 0053 .68 2180 0326 2277 0036 .09 4095 0560 0710 0058 .69 2096 0363 2260 0041 .10 0.04500 0.00600 0.00784 0.00063 .60 0.12000 0.00400 0.02240 0.00046 .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 1656 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 1066 0626 2046 0070 .18 7380 0787 1321 0085 .68 0880 0653 2011 0072 .19 7695 0795 1381 0086 .69 0696 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 0766 1804 0083 .24 9120 0790 1659 0086 .74 9620 0770 1758 0084 .25 9375 0781 1709 0085 .75 9376 0781 1709 0086 .26 9620 0770 1758 0084 .76 9120 0790 1659 0086 .27 9855 0756 1804 0083 .77 8856 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 0075 .81 7695 0796 1381 0086 .32 0880 0653 2011 0072 .82 7380 0787 1321 0086 .33 1055 0626 2046 0070 .83 7056 0776 1259 0083 .34 1220 0598 2080 0067 .84 6720 0762 1196 0081 .35 1375 0569 2111 0063 .86 6375 0744 1130 0079 .36 1520 0538 2141 0060 .86 6020 0722 1064 0077 .37 1655 0505 2169 0056 .87 6656 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 0063 43 2255 0286 2293 0032 .93 3266 0467 0560 0048 .44 2320 0246 2306 0028 .94 2820 0414 0483 0043 .45 2375 0206 2318 0023 .95 2375 0356 0406 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 0167 0166 0016 .49 2495 0042 2343 0005 .99 0496 0081 0083 0008 C „ C,, Negative. c ,, C,, Negative. .... , X^ ^TT, BINOMIAL COEFFICIENTS. 159 i I ' c. c, Cs . a Ce Ci c, Cs C4^ c» . .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 .62 2480 6157 3817 2657 j .03 1455 0955 0709 0563 .53 2455 6103 3769 2615 .04 1920 1254 0928 0735 .54 2420 6044 3717 2572 1 .05 2375 1544 1139 0899 .55 2375 6981 3664 2528 .06 2820 1824 1340 1056 .56. 2320 6914 3607 2482 .07 3255 2094 1534 1206 .57 2255 6842 3549 2434 1 .08 3680 2355 1719 1348 .58 2180 6765 3488 2386 .09 4095 2607 1897 1483 .59 2095 5685 3425 2336 I .10 0.04500 0.02850 0.02066 0.01612 .60 0.12000 0.05600 0.03360 0.02285 J .11 4895 3084 2228 1733 .61 1895 6511 3293 2233 .12 5280 3309 2382 1849 .62 1780 6419 3224 2180 I .13 5655 3525 2529 19>58 .63 1655 5322 3154 2125 i -1* 6020 3732 2669 2060 .64 1520 6222 3081 2071 ! ■!» 6375 3931 2801 • 2157 .65 1375 5119 3007 2015 1 .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 1 -^^ 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 C„ C., JN egative. 160 XVnX ERRORS OF OBSERVATION. , , t. t .4769 n. 0.6746 V^»-l) 0.6745 Vn(n-l) 0.8463 Vn(n-1) 0.8468 »V(»-1) 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 1608 1890 0845 6 3016 1231 1643 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 7412101 . 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 0^12 1.1 .16824 880206 1.1 5419 13 1947 0540 0677 0188 1.2 .13367 910314 1.2 5817 14 1871 0500 0627 0167 1.3 .10410 934003 1.3 6194 1.4 .07947 952285 1.4 6550 15 1803 0465 0683 0151 16 1742 0435 0646 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 1608 0329 0412 0090 2.0 .01033 0.995322 2.0 0.8227 22 1472 0314 0393 0084 2.1 .0«6858 997020 2.1 8433 23 1438 0300 0376 0078 2.2 .0«4461 998137 2.2 8622 24 1406 0287 0360 0073 2.3 .0*2845 998857 2.3 8792 2.4 .021778 999310 2.4 8945 25 1377 0275 0345 0069 26 1349 0265 0332 0066 2.5 .ono89 999593 2.5 9082 27 1323 0265 0319 0061 2.6 .0^6540 999764 2.6 9205 28 1298 0245 0307 0058 2.7 .0'3850 999866 2.7 9314 29 1275 0237 0297 0055 2.8 .082221 999925 2.8 9411 , 2.9 .0n256 999959 2.9 9495 30 0.1252 0.0229 0.0287 0.0052 31 1231 0221 0277 0050 3.0 .0*6963 0.9999779 3.0 0.9570 32 1211 0214 0268 0047 3.1 .0*3783 9999884 3.1 9635. 33 1192 0208 0260 0045 3.2 .0*2015 9999940 3.2 9691 34 1174 0201 0262 0043 3.3 .0*1052 9999969 3.3 9740 3.4 .0»5382 9999985 3.4 9782 35 1157 0196 0245 0041 36 1140 0190 0238 0040 3.5 .0*2700 9999993 3.5 9818 37 1124 0185 0232 0038 3.6 .0n327 9999996 3.6 9848 38 1109 0180 0225 0037 3.7 .0«6396 9999998 3.7 9874 39 1094 0175 0220 0035 3.8 .0«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 .0'1232 4.2 9954 44 1029 0165 0194 0029 4.3 .0*5264 4.3 9963 4.4 .0"2205 4.4 9970 45 1017 0152 0190 0028 46 1005 0148 0186 0027 4.5 .0»9057 4.5 9976 47 0994 0145 0182 0027 4.6 .0»3645 4.6 9981 48 0984 0142 0178 0026 4.7 .0n438 4.7 9985 49 0974 0139 0174 0026 4.8 .0'