HUSSEY'S MATHEMATICAL TABLES ajarneU IniuetBttg Kibcara Jtljara, Jffw fork ALEXANDER GRAY MEMORIAL LIBRARY ELECTRICAL ENGINEERING THE GIFT OF School o f El ectrlcal^ En gineeri ng Cornell University Library QA 55.H97a Logarithmic and other mathematica^^^^^ 3 1924 004 632 513 Cornell University Library The original of tiiis 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/cu31924004632513 LOGARITHMIC AND OTHER MATHEMATICAL TABLES BY WILLIAM J. HUSSEY ASTRONOMER IN THE LICK OBSERVATORY FIFTH EDITION .ALLYN AND BACON ^, %astan \ "" Neto gorfe Cfjicasa Copyright, 1891, By The Register Publishing Company. Copyright, 1895, ■ By/ William J. Htjssey. PREFACE. The extended calculations required by some of the applications of trigonometry are laborious even to experienced computers, and to begin- ners are often a fruitful source of discouragement. Experience in making calculations and familiarity with the formulas employed suggest methods of arrangement by which skilful computers shorten their work and save much of their time. The aim should always be to secure the results to the required degree of accuracy with a minimum expenditure of time and labp;r. So far as the mechanical part of the work is concerned, the principal factors leading, to this end are the proper arrangement of the formulas employed, the use of conveniently arranged tables having the needed helps for facili- tating interpolation, and the use of no more places of .decimals than are necessary to secure the desired accuracy in the results. Orderly arrangement is almost indispensable to correct and rapid com- putation ; on this account the practice of making computations on scraps of paper without systematic arrangement should not be followed. In the beginning, an outline of the entire solution should be made by writing the symbols of the quantities to be used in a vertical column, those to be combined being placed adjacent. In the same solution, turning more than once to the same place in the tables should be avoided, by taking at one opening all the functions of a given angle that may be required, and writing them in their proper places. The tables employed should be conveniently arranged, and, in general, should have auxiliary tables of proportional parts on the margins of the pages, so that the interpolations can easily be made mentally. The number of decimal places to be used in any calculation is governed by the character of the data given, and the degree of accuracy required in the results. When the data have great precision, and the results are required with all attainable accuracy, seven decimal places must be used, or even a larger number. But for nearly all calculations such precision is not required, and the use of logarithms to five places of decimals is suffi- cient, as they afford results which are generally correct to one ten-thousandth iii IV PREFACE. part. In calculations where this degree of accuracy is not necessary, a still smaller number of decimal places may be used. In such cases natural numbers and the natural trigonometric functions are frequently more con- venient than their logarithms. In compiling this book for general use, the needs of computers and of students have been kept in view. The arrangements of the tables are those which have been found the most convenient by experienced computers ; they are at the same time such as are best adapted to the use of stu- dents. All needed helps are given for facilitating interpolation. Aux- iliary tables of proportional parts accompany the logarithmic portions of the book, but are omitted in the table of natural trigonometric functions, "where differences are generally small. Throughout the greater part of the book every tenth line is enclosed by parallel rules, and the other lines are grouped in threes. This gives the pages an open appearance, enabling one to find more readily the numbers sought, and securing in the trigonometric tables a symmetrical arrangement such that the order is the same in reading from the bottom of the page as from the top. The auxiliaries S and T, which are always used in connection with the logarithms of numbers, are conveniently placed at the bottom of pages 2 to 21, instead of in a separate table. Their arithmetical comple- ments, C S and C T, are to be found on pages 62 to 64, adjacent to the logarithmic trigonometric functions with which they are used. The tables of addition and subtraction logarithms are based on those of Zech. The argument in each of these tables is obtained by subtract- ing the smaller logarithm from the larger. The function is always added to the larger logarithm in addition, and always subtracted from it in subtraction. On account of these uniform ways of proceeding, these tables are more convenient than the Gaussian tables. Note to the Fifth Edition. The changes in this edition are as follows : Some of the astronomical constants at the end of the book have been altered to bring them into agreement with the results of recent investigations. The values of log tan 10° 24', log sin 26° 49', and log tan 30° 13' have been corrected. No other errors in the third and fourth editions have come to my notice. W. J. HUSSEY. Mt. Hamilton, California, March, 1907. CONTENTS. PAGE. Introduction, vii Rules for the use of Logarithms, vii Common Logarithms, vii Mantissas of Common Logarithms, ........ viii Characteristics of Common Logarithms, ....... viii Tlie Arithmetical Complement of a Logarithm, ..... viii Explanations of the Tables ix The Logarithms of Numbers . 1-22 Common Logarithms of Numbers from 1 to 1000, . . . . .2-3 " " " " 100 to 10000, . . . . 4-21 Proportional Parts, . 4^ 21 Auxiliaries S and T 2-21 Natural Logarithms of Whole Numbers from 1-200 .... 22 Addition and Subtraction Logarithms, ...... 23- 36 Proportional Parts .......... 24- 36 Explanatory Formulas 24- 36 Logarithms of the Trigonometric Punctions, • . . . . 37-106 Por the Pirst and Last Degrees of all Quadrants, .... 37- 46 Proportional Parts, • . . . . 38- 49 For the next Five Degrees for all Quadrants, ..... 50- 60 Proportional Parts, 50- 60 For the entire Circumference from Minute to Minute, . . . 61-106 Differences and Proportional Parts, ...... 62-106 Auxiliaries C S and C T, . . . . . . . . 62-64 Natural Trigonometric Functions 107-130 Squares, Cubes, Square Roots and Cube Roots, ..... 131-139 Factors for Computing Probable Errors, ...... 140 Trigonometric Formulas, 141-142 General Formulas, 141 Formulas "Relating to Plane Triangles, , 141 " " " Spherical Triangles, ...... 142 Formulas Resulting from the Method of Least Squares, . . 143-145 Formulas for the Combination of Observations and the Determina- tion of Probable Errors, 143 Constants, 146-148 Mathematical and Astronomical Constants 146 Comparison of Linear Measures 146 Dimensions of the Earth according to Bessel, ..... 14? Vl CONTENTS. Dimensions of the Earth according to Clarke, • 147 Constants for Conversion of English Weights and Measures to Metric, and vice versa 147-148 Linear 147 Square, ... 147 Cubic, 147 Capacity, 147 Weight 148 Velocity, 148 Force, 148 Stress, 148 Work, 148 Rate of Doing Work 148 Physical Constants, ....o ,..,,,. 148 INTRODUCTION. Logarithms are used in lengthy numerical calculations to diminish the labor of multiplication, division, involution and evolution, by respectively substituting for them the operations of addition, subtraction, multiplication and division. The rules for their use are as follows: The logarithm of a product is equal to the sum of the logarithms of its factors. The logarithm of a quotient is equal to the logarithm of the dividend, minus the logarithm, of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Or, expressed in formulas, logAXS = logA+logB, log4 =log4— log5, log.4» =wlog.i, log^A = ^-^SA. These rules are true for all systems of logarithms. The Common Logarithm's are the only ones used in numerical calculations and in the following pages they are always meant unless the contrary is stated. The common logarithm of a given number is the index of that power of 10 which is equal to the number. Thus, 2 is the logarithm of 100, because 10' = 100; this equation is usually written log 100 = 2. 10 is the base of the system. A system of logarithms comprises the logarithms of all positive numbers to a given base. Prom the definition of common logarithms it f oUows, that logl = 0, log 0.1 = — 1, log 10 = + 1, log 0.01 = — 2, log 100 =+2, log 0.001 = — 3, log 1000 = + 3, log 0.0001 = — 4, etc., etc., from which it is evident, that logarithms are, in general, not integers. Thus, the logarithm of a number between 0.01 and 0.1 is — 2 + a fraction, 0.1 and 1 is — 1 + a fraction, 1 and 10 is + a fraction, 10 and 100 is 1 + a fraction, 100 and 1000 is 2 + a fraction. The fractional part of a logarithm is usually expressed decimally and is so taken as to be positive. It is then called the mantissa, and the integral part is called the characteristic. Till INTRODUCTION. Changing the decimal point in a number is equivalent to multiplying or dividing it by an integral power of 10; consequently, the logarithms of numbers which are the same, excepting the position of the decimal point, differ by integers. Thus the logarithm of 389.4 is 2,59040, and since 38940 = 100 X 389.4, the first rule for the use of logarithms' gives log 38940 = log 100+ log 389.4 = 2 +2.59040 = 4.59040. Similarly, log 3.8940 = log .01 + log 389.4 = — 2 +2.59040 = 0.59040. Hence, The mantissae of the logarithms of all numbers composed of the same figures in the same order, are the same. The value of the characteristic depends upon the position of the decimal point in the number. An inspection of the above table shows, that The characteristic of the logarithm of a number, partly or wholly integral, is zero or positive, and one less than the number of figures in the integral portion ; The characteristic of the logarithm of a pure decimal is negative, and one more than the number of ciphers preceding the first significant figure. Examples: The mantissae of the logarithms of 349600, 3496, 3.496, .003496 are the same, being .54357; their characteristics are +5, +3,0 and — 3, respectively. Thus, log .003496 = 3.54357, the minus sign being placed over the characteristic to indicate that it only is negative. The rule given above for determining the characteristic of the logarithm of a pure decimal is strictly correct, and so also is the manner of writing the negative characteristic. In computing, however, it is not desirable to use the characteristics in the manner indicated. It is preferable to add 10 to logarithms having negative characteristics and to allow for the increase by a proper interpretation of the results. When so increased the characteristics may, in aU operations, except in some cases in the extraction of roots, be treated as if they were positive. When written in this manner, the rule for their determination is as foUows: The characteristic of the logarithm of a pure decimal is 9, diminished by the number of ciphers preceding^ the first significant figure. Examples: The characteristics of the logarithms of .8437, .02804, .000105 and .000009207 are respectively 9, 8, 6 and 4. The logarithmic trigonometric functions, and the logarithms of constants less than unity contained in these tables, have had their characteristics increased bv 10. In finding the logarithm of a root an apparent difficulty arises when the char- acteristic is negative and is not a multiple of the index of the root. The difficulty disappears by increasing the characteristic negatively by the smallest number which wiU make it such a multiple and by increasing the mantissa positively by the same number. Thus, the logarithm of .003392 is 3.53046. The logarithm of its square root is obtained by writing its logarithm in the form— 4+ 1.53046 and dividing by 2, the index of the root. This gives — 2 + .76523, or 2.76523, or 8.76523. A better way of proceeding is to add 10 times the index of the root to the log- arithm and then divide by the index of the root. Thus, in the example given, adding 20 to the logarithm of .003392 and dividing by 2, gives 8.76523, which is the logarithm of the square root. By adding 30 and dividing by 3, the logarithm of the cube root is obtained. The logarithm of the cube root of .003392 is 9.17682. The arithmetical complement of a logarithm is the difference obtained by subtracting it from 0, or from 10, if it is desired to avoid negative characteristics. INTEODUCTION. H It is easUy obtained by subtracting each figure of the logarithm, except the last significant one, from 9; the last significant figure must be subtracted from 10. Thus, log 2763 = 3.44138, and its arithmetical complement is 6.55862. It is to be noticed, that the logarithm of the reciprocal of a number, is the arithmetical com- plement of the logarithm of the number; for example, log ^^Vf = 6.55862. Since the sine and cosecant, cosine and secant, tangent and cotangent are reciprocals, their logarithms are arithmetical complements. Thus, log sin 22° 18' 24''= 9.57928, and log cosec 22° 18' 24"= 0.42072; log cos 22° 18' 24"= 9.96622, and log sec 22° 18' 24" =0.03378; log tan 22° 18' 24"= 9.61306, and log cot 22° 18' 24"= 0.38694. A dash printed over a terminal 5 indicates that the true value is less than 5. For example the logarithm of 59903 to seven decimal places is 4.7774486; to five decimal places this is written 4.77745. If only four decimal places are required in a computation, the 5 is neglected. Thus, the above logarithm is written 4.7774. When a dash is not printed over a terminal 5, and only four decimal places are required, the fourth decimal figure is increased by one and the 5 neglected. Yot example, the logarithm of 7671 to five decimal places is 3.88485; to four decimal places this is written 3.8849. Table I. Pages 2-3 contain the mantissae of the logarithms of all numbers of one, two and three figures; the characteristics are determined by the rules previously given. If the number has one or two figures, it is given in the first column, headed N, and the mantissa of its logarithm is directly opposite it in the second column, headed L, Thus, log 3 = 0.47712, log 24 = 1.38021, log .067 = 8.82607. If the number has three figures, the first two are given in the first column and the third in the horizontal row at the top or bottom of the page, and the mantissa of its logarithm is at the intersection of the line containing the first two figures and the column containing the third. Thus, log 184 = 2.26482, log 89.1 = 1.94988, log 9.87 = 0.97174. Pages 4-21 contain the mantissae of the logarithms of numbers from 100 to 10009. The arrangement is similar to that just described. The first three figures of the number are given in the first column and the fourth in the horizontal row at the tov or bottom of the page. The last three figures of the mantissae are given in the colunms headed 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the first two, at intervals, in the second column under L. When the first two are not given in any line, they are to be taken from the first line above containing them, except, when the last three are preceded by a *, in which case they are to be taken from the next line. Thus, (p. 13) log 5764 = 3.76072, log 58.35 = 1.76604, log .5889 = 9.77004. When the number has more than four figures, its logarithm is found by inter- polation. For small differences, it is assumed, that differences between numbers are proportional to the differences between their logarithms. For example, required the logarithm of 168.342. The number has three orders of integers, hence the characteristic is 2. Disregarding the decimal point, the number is 168342. The round numbers, having four significant figures, next smaller and next greater than this, are 168300 and 168400, and their mantissae are (p. 5) .22608 and .22634. These numbers differ by 100, their mantissae, by 26. 26, being the difference between two successive values in the table, is the tabular difference. 168342 is 42 greater than 168300, hence its mantissa is -^ of 26 (= 11, to the nearest integer,) greater than that of 168300. Therefore, log 168.342 = 2.22619. SimUarly, log 39.6427 = 1.59816. X INTRODUCTION. To facilitate interpolation, the tentbs of the tabular differences are given under P P, {proportional parts). Thus, from the proportional table for 26, (p. 5), the proportional part for 4 — 10.4 A " « " 2= .52 Therefore, " " " 42 = 10.92, or 11, to the nearest integer, which agrees with the value above. By reversing these operations, the number corresponding to a given logarithm may be found. Por example, find the number of which 1.47384 is the logarithm. The next smaller mantissa (p. 7) is .47378. It corresponds to the number 2977. The difference between it and the next greater mantissa, .47392, is 14, whUe the differ- ence between it and the given mantissa is 6. The figures following 2977 are obtained by dividing 6 by 14, giving 43. Hence, the number is 29.7743. The interpolation is facilitated by using the proportional table for 14. In it, 5.6 is the value next smaller than the given difference 6; 4, the fifth figure of the number, corresponds to 5.6. The difference between 6 and 5.6 is .4, which becomes 4.0 by removing the decimal point one place to the right. Corresponding to 4.0, the nearest value is 3, this is the sixth figure of the number. The interpolations, where proportional parts are given, should be made mentally, the results only being written. The logarithmic sines and tangents of small angles may be found by means of the values of S and T, given at the bottoms of the pages. The formulas for their use are as follows: log sin = log arc + S, log tan = log arc +T, the angle being expressed in seconds of arc. The value of S or T, to be used in any case, is that which corresponds to the angle. Example 1. Find logsin 3".4785. log 3.4785 = 0.54139 p. 8. 8 = 4.68557 p. 2. log sin 3''.4785 =5.22696. Example 2, Find log tan 1° 14' 17".84 =log tan 4457".84. log 4457".84 = 3.64912 p. 10. T = 4.68564 p. 10. log tan 1° 14' 17".84 = 8.33476. Table II. When the logarithms of two numbers are given and the logarithm of their sum or difference is required, it may be found by using the addition or subtraction table The equations at the bottoms of the pages, 24-36 inclusive, indicate the manner of using these tables. In interpolating, it is to be noticed that the function B decreases as the argument A increases; consequently, the proportional parts must be sub- tracted instead of added. Example 1. Given, log a = 0.98519 and log 6 = 0.64834. Eequired log (o + 6) . log a = 0.98519 log 6 = 0.64834 A = log a — log 6 = 0.33685 B = 0.16448 p. 24. log (B + 6) = log a + B = 1.14967. In this case the tabular difference is 31, the proportional table for 31 gives 26 as the proportional part corresponding to 85, the last two figures of A ; subtracting INTBODTJCTION. Xi 26 from 0.16474, the value of B in the table corresponding to a value of A = 0.33600, gives 0.16448. This is the value of B corresponding to A = 0.33685. Example 2. Given, log a and log 6, as in Example 1. Required log (o— 6). In this case x = log a —log 6 is >.3, and, as above, A = log a— log 6 = 0.33685 B= 0.26794 p. 29. log (a — 6) = log a — B = 0.71725. Example 3. Given, log a = 0.74346 and log 6 = 0.59484. Eequired log (a— 6). In this case x = log a — log 6 is <.3, and B = log a— log 6 = 0.14862 A = 0.53790 p. 33. log(a — 6) = loga— A = 0.20556. Tables III and IV. These tables, pp. 37-106, contain the logarithms of the trigonometric functions. The headings of the pages and columns indicate what they contain. The degrees are given at the tops, and bottoms, of the pages. On pp. 37-49, the minutes and each ten seconds are given in columns at the left and right, headed ' ", and the odd seconds are given in a horizontal row at the top and bottom of each page. On Pp. 50-106, the minutes are given in columns at the left and right, headed '' ; and on pp. 50-60, each ten seconds is given in a horizontal row at the top and bottom of each page. The columns of minutes on the left read downward; the horizontal rows at the top, from left to right; these go with the degrees at the tops of the pages. The columns of minutes at the right and the horizontal rows at the bottom, read in the opposite directions, and go with the degrees at the bottoms of the pages. On pp. 62- 106, the tabular differences of the logarithmic sines and cosines are given in the columns headed d {difference), and those of the logarithmic tangents and cotangents in the columns headed c d {common difference). Example 1. Find log sin 0^ 37' 24".37. Page 44. log sin 0° 37' 24" = 8.03659 Tabular difference = 19. proportional part for 3 = 5.7 ft " « " 7= 1.33 log sin 0° 37' 24".37 = 8.03666. The tabular difference is 19 and the proportional table for 19 (p. 45), is used to facilitate the interpolation. The tabular difference is obtained by subtracting log sin 0° 37' 24' = 8.03659 from log sin 0° 37' 25" = 8.03678. In performing this subtrac- tion, only the final figures of the logarithms need be used. Thus, in this case, sub- tract 59 from 78. The interpolation should be made mentally and only the final result written. Example 2. Tind log tan 0° 42' 17".48. Page 47. log tan 0° 42' 17" =8.08992 Tabular difference =17. proportional part for .48 = 8.16 log tan 0° 42' 17".48 = 8.09000. Example 3. Find log cos 0° 57' 19". This is given without interpolation in the first column of page 48, the first figures being given at the top of the column. The value is 9.99994. Example 4. Find log cos 89° 43' 26".4. Page 40. log cos 89° 43' 26" = 7.68296 Tabular difference = 44 proportional part for 4 = 17.6 log cos 89° 43' 26".4 = 7.68278. XU INTEODTJCTION. The proportional part is subtracted, because tlie cosine, here, decreases as the angle increases. Sxample 5. Find log sin 3° 27' 44".6. Page 54. log sin 3° 27' 40" =8.78083 Tabular difference = 35. proportional part for 4 = 14.0 iS " " " 6= 2.1 log sin 3° 27' 44".6 = 8.78099. Also from pages 54 and 55, log cos 3° 27' 44".6 = 9.99920. log tan 3° 27' 44".6 = 8.78178. Example 6. Find log tan 8° 33' 17".4. Page 70. log tan 8° 33' 00" - 9.17708 Tabular difference = 86 proportional part for 10 = 14.3 " " 7 = 10.0 iV " " " 4= .57 log tan 8° 33' 17".4 = 9.17733. Example 7. Pind log cot 56° 43' 24".7. Page 95. log cot 56° 43' 00" =9.81721 Tabular difference = 28. proportional part for 20 = 9.3 " " 4 = 1.9 r\r " " " 1- .33 log cot 56° 43' 24".7 - 9.81709. When the logarithm of a trigonometric function is given, the angle may be found by reversing the above operations. Example 8. Given, log tan x = 9.87258. Find x. In the column of logarithmic tangents on page 98, we find log tan 36° 42' = 9.87238, with the tabular difference 26. The difference between this logarithm and the given one is 20. The proportional table for 26 gives proportional part for 40 = 17.3 " " " 6 = 2.6 ^ " " « 2 = .09 consequently " " " 46.2 = 19.99, or very nearly 20. Hence the number of seconds is 46.2, and the required angle is 36° 42' 46" .2. When a very smaU angle is to be found by means of its logarithmic sine or tangent, and accuracy is desired, the arithmetical complement of S or T, pp. 2-21, should be used. These are given in the columns headed C S and C T, pp. 62-64, The formulas for their use are as follows: log arc = log sin -}- C S, log arc = log tan+ C T, the angle being expressed in seconds of arc. The value of C S or C T to be used in any case, is that which corresponds to the angle. Example 9. Given, log sin x = 6.82973. Find x. The value of x, (see p. 62), lies between 0° 2' and 0° 3', or between 120" and 180", and, corresponding to this, C S = 5.31443 log sin X = 6.82973 log arc = 2.14416. The number corresponding to the logarithm 2.14416 is, (p. 4), 139.368. There- fore, X = 139".368 = 0° 2' 19".368. INTRODUCTION. XIU It is sometimes required to find tlie logarithm of one trigonometric function from that of another, without requiring the angle. To facilitate this, special pro- portional tables, headed with the tabular differences of both functions, are given, (pp. 71-106), wherever the space admits it. Example 10. Given, log tan x = 9.67644. Required log cos x. The difference between the given logarithm and that given in the table, 9.67622, (see p. 87, opposite 25° 23'), is 22. The tabular differences of the two logarithmic functions at this place are 32 and 6. In the proportional table for ^, 22 corresponds to 4; this, subtracted from the tabular logarithmic cosine 9.95591, gives the required log cos x = 9.95587. In the examples already given, the angles have all been less than 90°. The logarithms of trigonometric functions of angles greater than 90° may be obtained by remembering the relations given in the following table: Angle Sine Cosine Tangent Cotangent X + sina; + C0S X + tana! + cota; 90° +03 + cosa! — sin a; — cot X — tana! 180°+ a; — sin a; — cos a; + tana! +cot X 270°+ a; —cos a; + sina; — cot X —tana; For angles greater than 90°, the degrees are given at the tops and bottoms of the pages in smaller type. "Where these have been obtained from the acute angle on the same page, by adding 90° or 270°, they are preceded by a *. This indicates that the co-function is to be taken. Otherwise, the direct function is to be taken. The algebraic signs of the functions, as indicated by the above table, must be attended to. Example 11. Find log sin 112° 15' 17". Page 84. log sin 112° 15' 00" = 9.96640 Tabular difference = 6. proportional part for 17" = 2, nearly, log sin 112° 15' 17" = 9.96638. From the same page, log tan 202° 28' 34" = 9.61671, log cos 202° 28' 34" = 9.96569„, log cot 292° 18' 37" = 9.61314„. In the last two examples the „ following the logarithm indicates that the trigonometric function is negative. This is the usual way of indicating that the number corresponding to a logarithm is negative. Table V. Pages 108-130 contain the natural trigonometric functions for each minute. The arrangement is the same as that of the logarithms of the trigonometric func- tions, pp. 62-106, except that differences and proportional parts are not given. Table VI, Etc. Pages 131-139 contain the squares, cubes, square roots and cube roots of numbers from 1 to 1020. The arrangement of this table, and also of the ones which foUow it, wiU be understood by inspecting them. TABLE OF THE COMMON LOGARITHMS OF NUMBERS WITH THE AUXILIARIES S AND T. 0- -50 N LO 1 2 3 4 5 6 7 8 9 I 2 3 — 00 00000 30103 47712 60 206 69897 77815 84510 90309 95424 00000 30103 47712 04 139 32 222 49136 07 918 34242 50515 II 394 36173 51 851 14 613 38021 53148 17 609 39 794 54407 20412 41497 55630 23045 43136 56820 25527 44716 57978 27875 46240 59 106 4 5 6 60206 69897 77815 61278 70757 78533 62325 71 600 79239 63347 72428 79 934 64345 73239 80618 653!^! 74036 81 291 66276 74819 81954 67210 75587 82607 68 124 76343 83251 69020 77085 83885 7 8 9 10 II •12 13 84510 90309 95424 85 126 90849 95904 85733 91381 96379 86332 91 908 96848 86923 92 428 97313 87506 92942 97772 88081 93450 98227 88649 93952 98677 89 209 94448 99123 89763 94 939 99564 00000 00432 00860 01 284 oi 703 02 119 02531 02938 03342 j)03 743 04139 07918 "394 04532 08 279 II 727 04922 08636 12057 05308 08 991 12385 05 690 09342 12 710 06070 09 691 13033 06446 10037 13 354 06819 10380 13672 07188 10 721 13988 07555 11059 14301 14 14 613 17609 20412 14922 17898 20 683 15 229 18184 20952 15534 18469 21 219 15836 18752 21 484 16 137 19033 21748 16435 19 312 22 on 16732 19590 22 272 17026 19866 22 531 17 319- 20 140, 22 789 17 iS 19 20 21 22 23 23 045 25527 27875 23300 25768 28 103 23553 26007 28330 23805 26 245 28,556 24055 264S2 28780 24304 26717 29003 24551 26951 29 226 24797 27 184 29447 25 042 "*74^^- ■29 667 25285 27646 29885 30 103 30 320 30535 30750 30963 31 175 31387 31597 31 806 32015 32 222 34242 36173 32428 34 439 ^36361 32634 34635. 36549 32 838 34830 36736 33041 35025 36 922 33244 35218 37107 33 445 35 411 37291 33646 35603 37 475 33846 35 793 37658 34044 35984 37840 24 25 26 38021 39 794 41497 38 202 39 9<>7 41 664 38382 40 140 41 830 38561 40312 41996 38739 40483 42 160 38917 40654 42325 39094 40 824 42488 39270 40993 42651 39 445 41 162 42 813 39 620 41330 42975 27 28 29 30 31 32 33 43136 44716 46 240 43297 44871 46389 43457 45025 46538 43 616 45179 46687 43 775 45332 46835 43 933 45484 46982 44091 45637 47129 44248 45788 47276 44404 45 939 47422 44560 46090 47567 47712 47857 48 001 48144 48287 48430 48572 48714 48855 48996 49136 50515 51 851 49276 50651 51983 49415 50786 52 114 49 554 50920 52244 49693 51055 52375 49831 51 188 52504 49969 51322 52634 50 106 51455 52763 50243 51587 52892 50379 51720 53 020 ■ 34 35 36 53148 54407 55630 53275 54531 55751 53403 54654 55871 53529 54 777 55991 53656 54900 56 no 53782 55023 56229 53908 55145 56348 54033 55267 56467 54158 55388 56585 54283 55509 56703 37 38 39 40 |4X 42 ! 43 56820 57978 59106 56937 58 092 59218 57054 58206 -59 329 57171 58320 59 439 57287 58433 59550 57 403 58546 59660 57519 58659 59770 57634 58771 59879 57 749 58883 59988 57864 58995 60097 60 206 60314 ^9423 60531 60638 60 746 60853 60959 61 066 61 172 61 278 62325 63 347 ■61 384 62428 ,63 ^48 61 490 6? 531 •63 548 61595 62 634 63649 61 700 62737 63749 61805 62839 63849 61 909 62 941 •63949 62 014 63043 64048 62 118 63144 64147 62 221 63246 64246 I 44 45 46 6434^ 65321 66276 •64.444 •65418 6^ 379 (64 542 •65 514 ■66464 64 640 65 610 66558 64738 65706 66652 64836 65 801 66745 64933 65 896 66839 65031 65992 66932 65128 66087 67025 65225 66 181 67 117 47 48 49, 50 67 2IO 68 124 69 020 67 302 68215 (69 f 08 6-7 394 168 3.05 •69 ■[97 67486 68395 69285 67578 68485 69373 67 669 68574 69461 67761 68664 69548 67852 68753 69 636 67943 68842 69723 68 034 68931 69 810 6989;7 69 984 -70 070 70157 70243 70329 70415 70501 70586 70672 N LO a 2 3 4 5 G / 8 9 60" =0° ,1' S .4.68.557 T 4.6 i 557 300" =0-5' S 4-68557 T 4.68558 120 =0 ^ .4.68 557 4.6 3 557 360 =06 4.68 557 4.68 558 180 =0 3 it.68557 4-6 5 557 420 = 7 4.68 557 4.68 558 240 =04 4.68 557 4.6i ^^^ ^ - .^-m, i 558 480 =0 8 4.68 557 4.68 558 50— 100 N LO 1 2 3 4 5 6 7 8 9 50 51 52 53 69897 69984 70070 70157 70243 70329 70415 70501 70586 70672 70757 71 600 72428 70842 71684 72509 70927 71767 72591 71 012 71 850 72673 71096 71933 72754 71 i8i 72 oi6 72835 71265 72099 72916 71349 72 181 72997 71433 72263 73078 71517 72346 73159 54 55 56 73239 74036 74819 73320 74 115 74896 73400 74194 74 974 73480 74273 75051 73560 74351 75128 73640 74429 75205 73719 74507 75282 73 799 74586 75358 73878 74663 75 435 73 957 74741 75 511 57 58 59 60 61 62 63 75587 76343 77085 75664 76418 77 159 75740 76492 77232 75815 76567 77305 75891 76641 77 379 75967 76716 77452 76042 1 76 790 77525 76118 76864 77 597 76193 ''76938' 77670 76268 77012 77 743 77815 77887 77960 78032 78 104 78176 78247 78319 78390 78462 78533 79239 79 934 78604 79309 80003 78675 79 379 80072 78746 79 449 80 140 78817^ 79518' So 209 7SS88 79588 80277 78958 79657 80346 79029 79727 So 414 79099 79796 So 482 79169 79865 80550 64 65 66 80618 81 291 81954 80686 81358 82020 80 754 • Si 425 82086 80821 81 491 82 151 80889 81558 S2 217 80956 81 624 82282 81 023 81 690 82347 81 090 81757 82413 81 158 81823 82478 81 224 Si SS9 82543 67 68 69 70 71 72 73 82607 83251 83885 82 672. 83315 83948 82737 83378 84 01 1 82802 83442 84073 82866 83 506 84136 82930 83569 84 198 82995 83 632 84 261 83059 83696 84323 83123 83759 84386 83187 83822 8444S 84510 84572 84634 84696 84757 84819 84880 84942 85 003 85065 83 126 85733 86332 85187 85794 86392 85248 85854 86451 85309 85914 86510 85370 85974 86570 85431 86 034 86629 85491 86094 86 688 85552 86153 86747 85612 86213 86806 85673 86273 86864 74 75 76 86923 87 506 88081 86982 87564 88138 87040 87622 88195 87099 87679 88252 87157 87737 88309 87216 87795 88366 87274 87852 88423 87332 87910 8S4S0 87390 87967 88536 87448 88024 88593 77 78 79 80 81 82 83 88649 89 209 89763 88 705 89265 89818 88762 89321 89873 88818 89376 89927 S8874 89432 89982 88930 89487 90037 88986 89542 go 091 89042 89597 90 146 89098 89653 90200 89154 89 708 90255 90309 90363 90417 90472 90526 90580 90634 90687 90741 90795 90849 91 381 91 908 90 902 91434 91 960 90956 91487 92012 91 009 91 540 92065 91 062 91593 92117 91 116 91645 92 169 91 169 91 698 92 221 91 222 91 751 92273 91275 91 803 92324 91328 91855 92376 84 85 86 92428 92942 93450 92 480 92993 93500 92531 93044 93551 92583 93095 93601 92634 93146 93651 92686 93 197 93 702 92737 93247 93 752 92 788 93298 93 802 92 S40 93 349 93852 92 891 93 399 93902 87 88 89 90 91 92 93 93952 94448 94 939 94002 94498 94988 94052 94 547 95036 94101 94596 95085 94 151 94645 95134 94 201 94694 95182 94250 94 743 95231 94300 94792 95279 94 349 94841 95328 94 399 94890 95376 95424 95472 95521 95569 95617 95665 95 713 95761 95809 95856 95904 96379 96848 95952 96426 96895 95 999 96473 96942 96047 96520 96988 96095 96567 97035 96142 96 614 97081 96 190 96 661 97128 96237 96 708 97174 96 284 96755 97 220 96332 96802 97267 94 95,_. '96 97313 ■97-772 98 227 97 359 9781; 98 272 9-7 j^t-_ 98318 97451 97909 98363 97 497 97 955 98408 97 543 98 000 98453 97589 98 046 98498 97635 98091 98543 976S1 98 137 98588 97727 98 182 98632 97 98 99 100 98677 99123 99564 98 722 99167 99607 98767 99 21 r 99651 98 811 99255 99695 98856 99300 99 739 98 900 99 344 99782 98945 99388 99 826 98989 99432 99870 99034 99476 99913 99078 99520 99957 00000 00043 00087 00 130 00173 00217 00 260 00303 00346 00389 N LO 1 2 3 4 .5 6 7 8 ' 540" =0° 9' S 4-68557 X 4-f>8 558 780" ==o°i3' S 4-68557 T 4.6S 558 600 =010 4-68557 4-68558 840 = 14 4.68 557 4.68 558 660 = II 4-68 557 4.68 558 900 = 15 4.68 557 4.68 558 720 — 12 4-68 557 4-68 558 960 = 16 4.68 557 4.68 558 100—150 K L 1 2 3 1 4 5 6. 7 8 . 9 p r 100 00000 043 087 130 173 217 260 303 346 389 44 43 42 lOI 432 475 518 561 604 647 689 732 775 817 102^ 860 903 945 988 *030 1=072 *iir5 *I57 *i99 *242 I 2 3 4 4-4 8.8 13.2 17.6 4.3 8.6 12.9 17.2 4.2 8.4 12.6 103 01 284 326 368 410 -.452 494 536 578 620 662 104 703 745 787 828 870 912 953 995 *036 *078 16.8 105 02 119 160 202 243 28^ 325 366 407 449 490 106 531 572 612 653 694 735- 776 816 857 898 5 6 22.0 26.4 21.5 25.8 21.0 25.2 107 938 979 *oi9 *o6o »ioo *I4I *i8i *222 *262 *302 7 8 9 30.8 108 03342 383 423 463 503 543 583 623 663 703 30.1 29.4 33.6 37.8 39 3-9 7.8 II. 7 15.6 109 110 III 743 782 822 862. 902 941 981 *02I ^060 HcIOO 35-2 ■^Q.6 34.4 38.7 40 4.0 8.0 12.0 04139 179 218 258 297 336 376 415 454 493 At 532 571 610 650 689 727 766 805 844 883 I 2 4-1 8.2 112 922 961 999 *038 *o77 *ii5 *i54 *192 *23i *269 113 05 308 " 346 385 423 461 500 538 576 614 652 3 4 5 6 12.3 16.4 20.5 24.6 114 690 729 767 805 843 881 918 956 994 *032 16.0 115 06070 108 145 183 221 258 296 333 371 408 116 446 483 521 558 595 633 670 707 744 781 20.0 24.0 19.5 23.4 "7 819 856 893 930 967 *oo4 *04i *078 *II5 *15I 7 8 9 28.7 32.8 36.Q 28.0 27.3 31.2 35-1 . 36 3.6 7-2 10.8 118 119 120 121 07188 , 555 225 591 262 628 298 664 335 700 372 737 408 773 445 8<>9 482 846 518 882 32.0 36.0 37 3.7 7.4 11. 1 918 954 990 *027 *o63 *099 *I35 *i7i *207 »243 Qfi 08279 314 350 386 422 458 493 529 565 600 J tJU 3.8 7.6 II.4 122 636 672 707 743 778 814 849 884 920 955 2 123 991 *026 *o6i #096 *I32 *i67 *202 #237 *272 *307 3 124 09342 377 412 447 482 517 552 587 621 656 4 5 6 15.2 19.0 22.8 14.8 18.5 22.2, 14.4 18.0 125 691 726 760 795 830 864 899 934 968 »003 126 10037 072 106 140 175 209 243 278 312 346 21.6 127 128 129 130 131 380 721 II 059 415 755 093 449- 789 126 483 823 160 517 857 193 551 890 227 585 924 261 619 958 294 653 992 327 687 *025 361 7 8 9 26.6 30.4 34.2 25.9 29.6 33.3 34 3.4 25.2 28.8 32.4 33 3.3 394 428 461 494 528 561 594 628 661 694 .SS 727 760 793 826 860 893 926 959 992 *024 I 3.5 132 12057 090 123 156 189 222 254 287 320 352 2 7.0 6.8 6.6 133 385 418 450 483 516 548 581 613 646 678 3 10.5 10.2 9.9 134 710 743 775 80S 840 872 905 937 969 »ooi 4 14.0 13.6 13.2 135 13033 066 098 130 162 194 226 258 29Q 322 5 17.5 17.0 16.5 136 354 386 418 450 481 513 545 577 609 640 6 21.0 20.4 19.8 137 672 704 735 767 799 830 862 ■893 925 956 7 24.5 23.8 23.1 138 988 *oi9 »05i *o82 *ii4 *I45 ' *i76 if208 *239 »270 8 28.0 27.2 26.4 139 140 141 14 301 333 364 395 426 457 489 520 551 582 9 31.5 30.6 31 3.1 29.7 30 3.0 613 644 675 706 737 768 799 829 860 891 32 922 953 983 *oi4 *o45 *o76 *io6 iti37 *i6S »i98 I 3-2 142 15229 259 290 320 351 381 412 442 473 503 2 6.4 6.2 6.0 143 534 564 594 625 655 685 715 746 776_ 806 3 9.6 9.3 9.0 144 836 866 897 927 957 987 *oi7 it047 *077 . ■-^- , jt T2.8 iM 12.0 --]^^ 145 16 137 167 197 227 256 286 316 346 376 406 5 16.0 i5.5~^ 15.6-. 146 435 465 495 524 554 584 613 643 673. 702 6 19.2 18.6 18.0 147 732 761 791 820 850 879 909 938 967 997 7 22.4 21.7 21.0 148 17026 056 085 114 143 173 202 231 260 289 8 25.6 24.8 24.0 149 150 319 348 377 406 435 464 493 522 551 580 9 28.8 27.9 27.0 17609 638 667 696 725 754 782 811 840 869 N L 1 2 3 4 5 6 7 8 9 P P 960 ' =0° If )' s 4.68557 T 4.68558 1260" =0° 21 'S 4.68557 T 4.68558 1020 =0 ij 4.68557 4.68558 1320 =0 22 4.68 557 4.68 558 1080 =0 I? 4.68557 4-68558 1380 =0 23 4.68 557 4.68 558 1 140 =0 IC 4.68557 4.68558 1440 =0 24 4-68 557 4.68 558 1200 =0 2C 4.68557 4.68558 1500 =0 25 4.68 557 4.68 558 150- -200 jsr L 1 2 3 4 5 6 7 8 j 9 r r 150 151 17609 638 667 696 725 754 782 811 840 869 29 28 898 926 955 984 *oi3 »o4i *o7o »099 *I27 *156- 152 18 184 213 241 270 298 327 355 384 412 441 I 2.9 2.8 153 469 498 526 554 583 611 639 667 696 724 2 5.8 5-6 154 752 780 808 837 865 893 921 949 977 *oo5 3 8.7 8.4 155 19033 061 089 "7 145 173 201 229 257 285 4 11.6 11.2 156 312 340 368 396 424 451 479 507 535 562 5 14-5 14.0 157 590 618 645 673 700 728 756 783 811 838 6 174 16.8 158 866 893 921 948 976 »oo3 *03o *o58 *o85 *II2 7 20.3 19.6 159 20140 167 194 222 249 276 303 330 358 385 8 23.2 26.1 an 22.4 160 161 412 439 466 493 520 548 575 602 629 656 9 25.2 26 2,6 5-2 7.8 683 710 737 763 790 817 844 871 898 925 ^1 162 952 978 »oo5 *032 *o59 »o85 *II2 *I39 *i65 *192 I '^ "* 2 3 5-4 8.1 163 21 219 245 272 299 325 352 378 405 431 458 164 484 5" 537 564 590 617 643 669 696 722 10.8 165 748 775 801 827 854 880 906 932 958 985 4 10.4 166 22011 037 063 089 115 141 167 194 220 246 5 6 13-5 16.2 13.0 15.6 167 272 298 324 350 376 401 427 453 479 505 7 8 9 18.9 21.6 2d.'? 18.2 20.S 23-4 ) 2-5 168 531 557 583 608 634 660 686 712 737 763 169 170 171 789 814 840 866 891 917 943 968 994 *oi9 23045 070 096 121 147 172 198 223 249 274 2. 300 325 350 376 401 426 452 477 502 528 I 172 553 578 603 629 654 679 704 729 754 779 2 3.0 173 805 830 855 880 905 930 955 980 ,005 *o30 3 7-5 174 24055 080 105 130 155 180 204 229 254 279 4 1 0.0 175 304 329 353 378 403 428 452 477 502 527 5 12.5 176 551 576 601 625 650 674 699 724 748 713 6 I ;.o 177 797 822 846 871 895 920 944 969 993 *oi8 7 I 7-5 178 25042 066 091 115 139 164 188 212 237 261 8 20.0 1 179 180 181 285 310 334 358 382 406 431 455 479 503 9 2 2-5 23 2.3 527 551 575 600 624 648 672 696 720. 744 24 768 792 816 840 864 888 912 935 959 983 I 2.4 182 26007 031 055 079 102 126 150 174 198 221 2 4.8 4.6 183 245 269 253 ■52^ 316 340 364 387 411 435 458 3 7-2 6.9 184 482 505 553 576 600 623 647 670 694 4 9.6 9-2 185 717 741 764 788 811 834 858 881 905 928 5 12.0 II-5 186 951 975 998 *02I *o45 it068 #091 *ii4 *I38 #161 6 14.4 13-8 187 27184 207 231 254 277 3PO 323 346 370 393 7 16.8 16.1 ■ 188 416 439 462 485 508 531 554 577 600 623 8 19.2 18.4 189 190 191 646 669 692 715 738 761 784 807 830 852 9 21.6 20.7 21 2.1 875 898 921 944 967 989 *OI2 *035 »o58 »o8i 22 28103 126 149 171 194 217 240 262 285 307 I 2.2 192 330 353 375 398 421 443 466 488 511 533 2 4.4 4.2 193 556 578 601 623 646 668 691 713 735 758 3 6.6 6.3 194 780 803 825 847 870 892 914 937 959 981 4 8.8 8.4 195 29003 026 048 070 092 "5 137 159 181 203 5 II.O 10.5 196 226 248 270 292 314 336 358 380 403 425 6 13-2 12.6 197 447 469 491 513 535 557 579 601 623 645 7 15-4 14.7 198 667 688 710 732 754 776 798 820 842 863 8 17.6 16.8 199 200 885 907 929 951 973 994 *oi6 »038 ^obo ,081 9 19.8 18.9 30103 125 146 168 190 211 233 255- 276 298 N L 1 2 3 4 5 6 7 8 9 P P 1500 • =0° 25' S 4-68 ; ,57 1 C 4.f 8558 18 x>" = 0° 30' S 4 .68557 T 4.68 559 1560 =0 26 4. 68 t 57 4.e 8 558 18 5o = 31 4 -68557 4.68 559 1620 =0 27 4. 68 £ 57 4-i 8558 19 20 = 32 4 .68557 4.68 559 1680 =0 28 4. 68 ; 57 4.t 8558 19 Bo = 33 4 .68557 4.68 559 1740 =0 29 4. 68 I 57 4.t >8 559 20 40 = 34 i t. 68 557 4-68 559 A 200—250 N L I 2 3 4 1 5 6 7 8 9 P P 200 30103 125 146 168 190 211 233 255 276 298 22 21 201 320 341 363 384 406 428 449 471 492 514 202 535 557 578 600 621 643 664 685 707 728 I 2.2 2.1 203 750 771 792 814 835 856 878 899 920 942 2 4.4 4.2 204 963 984 j(Oo6 *027 »048 *o69 *09i »II2 »I33 *i54 3 6.6 6.3 205 31 175 197 218 239 260 281 302 323 345 366 4 8.8 8.4 206 387 408 429 450 471 492 513 534 555 576 5 ii.o 10.5 207 597 618 639 660 68 1 702 723 744 765 785 6 13.2 12.6 208 806 827 848 869 890 9H 931 952 973 994 7 15.4 14.7 209 32015 035 056 077 098 118 139 160 181 201 8 17.6 16.8 19.8 18.9 210 211 222 243 263 284 305 325 346 366 387 408 9 428 449 469 490 510 531 552 572 593 613 212 634 654 675 695 715 736 756 777 797 818 1 2 3 ^,yj 213 838 858 879 899 919 940 960 980 *ooi *02I 4.0 6.0 8.0 214 33041 062 082 102 122 143 163 183 203 224 215 244 264 284 304 325 345 365 385 405 425 4 5 6 216 445 465 486 506 526 546 566 586 606 626 1 0.0 12.0 217 646 666 686 706 726 746 766 786 806 826 218 846/ 866 885 905 925 945 965 985 *005 *025 7 8 9 I4-0 16.0 18.0 2ig 220 221 34044 064 084 104 124 143 163 183 203 223 242 262 282 301 321 341 361 380 400 420 19 439 459 479 498 518 537 557 577 596 616 I 1.9 222 635 655 674 694 713 733 753 772 792 811 2 3.8 223 830 850 869 889 908 928 947 967 986 *oo5 3 5-7 224 35025 044 064 083 102 122 141 160 180 199 4 7.6 225 218 238 257 276 295 315 334 353 372 392 5 9-5 226 411 430 449 468 488 507 526 545 564 583 6 11.4 227 603 622 641 660 679 698 717 736 755 774 7 13.3 228 793 813 832 851 870 889 908 927 946 965 8 15.2 229 230 231 984 »oo3 *02I »040 «059 *078 *097 *"6 *i35 *I54 9 17.1 36173 192 211 229 248 267 286 305 324 342 18 361 380 399 418 436 455 474 493 511 530 I 1.8 232 549 568 586 605 624 642 661 680 698 717 2 3.6 233 736 754 773 791 810 829 847 866 884 903 3 5.4 234 922 940 959 977 996 »oi4 *033 *05i *o70 *o88 . 4 7.2 235 37107 125 144 162 181 199 218 236 254 273 ^ 5 9.0 236 291 310 328. J-^^. 365 383 401 420 438 457 6 10.8 237 475 493 ^ili- _530 548 566 585 603 621 639 7 12.6 238. 658 676 '694 712 731 749 ^767 \)49 785 803 822 8 14.4 239 240 241 840 858 876 894 912 931 967 985 »003 9 16.2 38021 039 057 075 093 112 130 148 166 184 17 — ?02- 220 238 256 274 292 310 328 346 364 I 1-7 242 382 399 417 435 453 471 J39. 507 525 543 2 3-4 243 561 578 596 614 632 650 668 686 763 721 3 5.1 244 739 757 775 792 810 828 846 863 881 899 4 6.8 245 917 934 952 970 9S7 »oo5 *023 *o4i *058 *o76. 5 8.5 246 39094 III 129 146 164 182 199 217 235 252 6 10.2 247 270 287 305 322 340 358 375 393 410 428 7 1 1.9 13.6 248 445 463 480 498 515 533 550 568 585 602 8 249 250 620 637 655 672 690 707 724 742 759 777 9 15.3 794 811 829 846 863 881 89S 915 933 950 N L 1 2 3 4 5 6 7 ? 9 P P 1980 " =o°33' S 4.68557 T 4-68559 2280" =0° 38' S 4.68557- T 4.68559 2040 =0 34 4-68 557 4-68 559 2340 =0 39 4.68557 4.68550 2100 =0 35 4 68 557 4.68 559 2400 =0 40 4.68557 4.68559 2160 =0 36 4-68 557 4-68 559 2460 —0 41 4.68556 4.68560 2220 =0 37 4.68557 4.68 559 2520 =0 42 4.68556 4.68560 250- -300 N L 1 2 3 4 5 6 7 8 9 P P 250 251 39 794 811 829 846 863 881 898 915 933 950 18 967 985 *002 »oi9 »P37 *o54 *o7l »o88 *io6 »I23 252 40140 157 175 192 209 226 243 261 278 295 I 1.8 253 312 329 346 364 381 398 4i§ 432 449 466 2 3-6 254 483 500 518 535 552 569 586 603 620 637- 3 5-4 255 654 671 688 705 722 739 756 773 790 807 4 7-2 256 824 841 858 875 892 909 926 943 960 976 5 9.0 257 993 »oio »027 *044 *o6l »o78 if095 *iii »I28 *145 6 10.8 258 41 162 179 196 212 229 246 263 280 296 313 7 12.6 259 260 261 330 347 363 380 397 414 430 447 464 481 8 9 14.4 16.2 497 £14 531 547 564 581 597 614 631 647 664 681 697 714 731 747 764 780 797 814 . "- 1 262 830 847 863 880 896 913 929 946 963 979 1 J-7 263 996 *0I2 *029 *o45 *o62 »o78 »095 jjili »I27 *I44 2 3 3-4 5.1 6.8 8.5 264 42 160 177 193 210 226 243 259 275 292 308 265 325 341 357 374 390 406 423 439 455 472 4 266 488 504 521 537 553 570 586 602 619 635 5 6 267 651 667 684 700 716 732 749 765 781 797 10.2 268 813 830 846 862 878' 894 911 927 943 959 7 8 9 -.: . 1 1.9 13.6 TC a 269 270 271 975 991 ^008 *024 jf040 »056 *072 »o88 *i04 *I20 43136 152 169 185- 201 217 233 249 265 281 16 1 297 313 329 345 361 377 393 409 ,425 584 441 I 1.6 272 457 473 489 505 521 537 553 569 600 2 3-2 273 616 632 648 664 680 696 712 727 743 759 3 4.8 274 775 791 807 823 838 854 870 886 902 917 4 6.4 275 933 949 965 981 996 »OI2 k028 *044 *o59 »o75 5 8.0 276 44091 107 122 138 154 170 185 201 217 232 6 9.6 277 248 264 279 295 311 326 342 358 373 389 7 11.2 278 404 420 436 451 467 483 498 514 529 545 8- ■12.8 279 280 281 560 576 592 607 623 638 654 669 685 700 9 14.4 716 731 747 762 778 793 809 824 840 855 I 871 886 902 917 932 948 963 979 994 *oio I 1.5 282 45025 040 056 071 086 102 117 133 148 163 2 3.0 283 179 194 209 225 240 255 271 286 301 317 3 4-5 284 332 347 362 378 393 408 423 439 454 469 4 6.0 285 484 500 515 530 545 561 576 591 606 621 5 7.5 286 637 652 667 682 697 712 728 743 758 773 6 9.0 287 . 788 803 818 834 849 864 879 894 909 924 7 10.5 28S_ 939 954 969 984 jfOOO !fOI5 *030 »045 *o6o *o75 8 12.0 289 290 291 46090 105 120 135 150 165- 180 195 210 225 9 13-5 240 255 270 285 300 315 330 345 359 374 1 389 404 419 434 449 464 479 494 509. .523 I 1-4 292 538 553 568 583 598 613 627 642 65r- ■672 2 2.8 293 687 702 716 731 746 761 776 790 805 820 3 4.2 294 -m- 850 864 879 894 909 923 938 953 967 4 5-6 295 982 997 *0I2 *026 *o4i N.056 *°1° *o85 *ioo *ii4 5 7.0 296 47129 144 159 173 188 202 217 232 246 261 6 8.4 297 276 290 305 319 334 349 363 378 392 407 7 9.8 298 422 436 451 465 480 494 509 524 538 553 8 II. 2 299 300 567 582 596 611 625 640 654 669 683 698 9 12.6 712 727 741 756 770 784 799 813 828 842 N L 1 2 3 4 5 6 7 8 9 P P 2460 ' =0° 41' S 4.68556 G ? 4. 68 560 27< 30" = 0° 46' S 4 .68 556 T" 4-68 560 2520 =0 42 4.68 556 4. 68 560 28 20 = 47 4 .68 556 4.68 500 2580 =0 43 4-68 556 4. 68 560 28 3o = 48 4 .68556 4.68560 2640 =0 44 4. 68 556 4. 68 560 29^ ^o = 49 4 .68 556 4.68 560 2700 =0 45 4-68 556 4. 68 560 30( 30 = 50 4 .68 556 4.68 561 300—350 I ^ L 1 2 3 4 5 6 7 8 9 P P 300 301 47712 727 741 756 770 784 799 813 828 842 857 871 885 900 914 929 943 958 972 986 302 48001 015 029 044 058 073 087 lOI 116 130 303 144 159 173 187 202 216 230 244 259 273 15 304 287 302 316 330 344 359 373 387 401 416 I 1-5 305 430 444 458 473 487 501 515 530 544 558 2 3.0 306 572 586 601 615 629 643 657 671 686 700 3 4.5 307 714 728 742 756 770 78! 799 813 827 841 4 6.0 308 855 869 883 897 .911 926 940 954 968 982 5 6 7 S 7-5 309 310 996 *oio *024 ,038 *052 it066 »o8o »094 »io8 »I22 9.0 10.5 12.0 49136 150 164 178 192 206 220 234 248 262 9 13-5 3" 276 290 304 318 332 346 360 374 388 402 312 415 429 443 457 (475 485 499 513 527 541 313 554 568 582 596 ^5o 624 638 651 665 679 314 693 707 721 734 748 762 776 790 803 817 315 831 845 859 872 886 900 914 927 941 955 14 316 969 982. 996 »oio *024 K037 »o5i »o65 »o79 #092 I 1-4 317 50106 120 133 147 161 174 188 202 215 229 2 2.8 318 243 256 270 284 297 3" 325 338 352 365 3 4.2 319 320 321 379 393 406 420 433 447 461 474 488 501 4 5 6 7 8 5-6 7.0 8.4 9.8 1 1.2 515 529 542 556 569 583 596 610 623 637 651 664 678 691 705 718 732 745 759 772 f 522 786 799 813 826 840 853 866 880 893 907 9 12.6 323 920 934 947 961 974 987 «OOI »or4 ,^028 »o4i 324 51055 068 081 095 108 121 135 148 162 17! 325 188 202 215 228 242 ^55 268 282 295 308 326 322 335 348 362 375 388 402 415 428 441 tn 327 455 468 481 495 508 521 534 548 561 574 la 328 587 601 614 627 640 654 667 680 693 706 ' I 1-3 2.6 3-9 5-2 6.5 7.8 329 330 331 720 733 746 759 772 786 799 812 825 838 2 3 4 5 6 851 86§ 878 891 904 917 930 943 957 970 983 996 »009 »022 *035 »048 »o6i »075 ifG88 »ioi 332 52 114 127 140 153 166 179 192 205 218 231 7 9.1 333 244 257 270 284 297 310 323 336 349 362 8 10.4 334 375 388 401 414 427 440 453 466 479 492 9 I.I-7 335 504 517 530 543 556 569 582 '595 608 621 336 634 647 660 673 686 699 711 724 737 750 337 763 776 789 802 815 827 840 853 866 879 338 892 905 917 930 943 956 969 982 994 »oo7 12 339 340 341 53020 033 046 058 071 084 097 no 122 135 I 2 3 4 1.2 2.4 3.6 4.8 148 161 173 186 199 212 224 237 250 263 275 288 301 314 326 339 352- 364 377 390 342 403 415 428 441 453 466 479 491 504 517 5 6.0 343 529 542 555 567 580 593 605 618 631 643 6 7-2 344 656 668 681 694 706 719 732 744 757 769 7 8 81,4 9.6 10.8 345 782 794 807 820 832 845 857 870 882 895 346 908 920 933 945 958 970 983 995 *oo8 »020 9 347 54033 045 058 070 083 095 108 120 133 145 348 158 170 183 195 208 220 233 245 258 270 349 350 283 295 307 320 332 345 357 370 382 394 407 419 .432 444 456 469 481 494 506 5t8 N L 1 2 3 4 5 6 7 8 9 P P 300c >" = 0° 50' S 4.68 556 X 4.68561 3300° = o°55' S 4.68556 T 4.68561 306c > = 51 4.68 556 4.68 561 3360 = 56 4.68 556 4.68 561 312c > =0 52 4.68 556 4.68 561 3420 = 57 4-68 555 4.68 561 318c = 53 4.68 556 4.68 561 3480 = 58 4-68 555 4-68 562 324c ) =0 54 4.68 556 4.68 561 3540 ,= 59 4-68 555 4.68 562 350—400 ,N L 1 2 3 4 5 6 7 8 9 P P 350 351 54407 419 432 444 456 469 481 494 506 518 531 543 555 568 580 593 605 617 630 642 352 654 667 679 691 704 716 728 741 753 765 353 777 790 802 814 827 839 851 864 876 888 13 354 900 913 925 937 949 962 974 986 998 *oii J 1.3 2,6 355 55023 035 047 060 072 084 096 108 121 133 356 145 157 169 182 194 206 218 230 242 255 3 4 5 6 7 8 9 3.9 5.2 6.5 7.8 9.1 10.4 1 1. 7 357 267 279 291 303 315 328 340 352 364 376 358 388 400 413 425 437 449 461 473 485 497 359 360 361 509 522 534 546 558 570 582 594 606 618 630 642 654 666 678 691 703 715 727 739 751 763 775 787 799 811 823 835 847 859 362 871 883 895 907 919 931 943 955 967 979 363 991 »003 »oi5 #027 ,038 »050 ^f062 »o74 »o86 *098 364 56 no 122 134 146 158 170 182 194 205 217 365 229 241 253 265 277 289 301 312 324 336 366 348 360 372 384 396 407 419 431 443- 455 12 367 467 478 490 502 514 526 538 549 561 573 I 1.2 368 585 597 608 620 632 644 656 667 679 6gl 2 2.4 369 370 371 703 714 726 738 75-0 761 773 785 797 808 3 4 5 6 3.6 4.8 6.0 7-2 820 832 844 855 867 879 891 902 914 926 937 949 961 972 984 996 jfOo8 *oi9 »03i *043 372 57054 066 078 089 lOI 113 124 136 148 159 7 8.4 373 171 183 194 206 217 229 241 .252 264 276 8 9.6 374 287 299 310 322 334 345 357 368 380 392 9 10.8 375 403 415 426 438 449 461 473 484 496 507 376 519 530 542 553 565 576 588 600 611 623 377 634 646 657 669 680 692 703 715 726 738 37« 749 761 772 784 795 807 818 830 841 852 11 379 380 381 864 875 887 898 910 921 933 944 955 967 I 2 3 4 I.I 2.2 3-3 4.4 978 990 *ooi *oi3 *024 »o35 *o47 »058 *070 *o8i 58092 104 115 127 138 149 i6i 172 .184 195 382 206 218 229 240 252 263 274 286 297 309 5 5.5 383 320 331 343 354 365 377 388 399 410 422 6 6.6 384 433 444 456 467 478 490 501 512 524 535 7 7.7 385 546 557 569 589 591 6cJ2 614 625 636 647 8 8.8 386 659 670 681 692 704 715 726 737 749 760 9 9.9 387 '771 782 794 805 816 827 838 850 861 872 388 883 894 906 917 928 939 950 961 973 984 389 390 391 995 jfOo6 #017 *028 *040 »05i jt062 *073 *o34 *095 10 59106 n8 129 140 151 162 173 184 195 207 I 2 I.O 2.0 218 229 240- 251 262 273 284 295 306 318 392 329 340 351 362 373 384 395 406 417 428 3 3.0 393 439 450 461 472 483 494 506 517 528 539 4 4.0 394 550 561 572 583 594 605 616 627 638 649 5 6 5.0 6.0 395 660 671 682 693 704 715 726 737 748 759 396 770 780 791 802 813 824 835 846 857 868 7 8 7.0 8.0 9.0 397 879 890 901 912 923 934 945 956 966 977 398 988 999 »oio #021 *032 »043 »054 *o65 *076 ^,086 9 399 400 60097 108 119 130 141 152 163 173 184 195 206 217 228 239 1 249 260 271 282 293 304 N L 1 2 3 4 5 6 7 8 9 P P 3480 ' =0° 58' S 4.68 555 T 4.68 562 3780" =1° 3' S 4 .68555 T 4.68562 3540 =0 59 4.68555 4.68562 3840 = I 4 4 .68555 4.68563 3600 = 1 4.68 555 4.68 562 3900 = I 5 4 .68555 4-68563 3660 =1 I 4.68555 4.68562 3960 = 16 4 .68555 4.68563 3720 = 1 2 4.68555 4.68562 4020 =17 4 68 555 4. 68 563 10 400- -450 N LO 1 2 3 4 5 6 7 8 9 P P 400 401 60206 217 228 239 249 260 271 282 293 304 314 325 336 347 358 369 379 390 401 412 402 423 433 444 455 466 477 487 498 509 520 403 531 541 552 563 574 584 595 606 617 627 404 638 649 660 670 681 692 703 713) 724 735. 405 746 756 767 778 788 799 810 821 831 842 406 853 863 874 885 895 go6 917 927 938 949 11 407 959 970 981 991 »002 »oi3 »023 4.034 *045 *055 I I.I 408 61 066 077 087 098 109 119 130 140 151 162 2 2.2 409 410 411 172 183 194 204 215 225 236 247 257 268 3 4 5 6 3-3 4-4 5-5 6.6 278 289 300 310 321 331' 342 352 363 374 384 395 405 416 426 437 448 45S 469 479 412 490 500 5" 521 532 542 553 563 574 584 7 7-7 413 595 606 616 627 637 648 658 6^9 679 690 8 8.8 414 700 7H 721 731 742 752 763 773 784 794 9 9.9 415 805 815 826 836 847 857 868 878 888 899 416 909 920 930 941 951 962 972 982 993 *oo3 417 62 014 024 034 045 055 066 076s 086 097 107 418 118 128 •138 149 159 170 180 " ige 201 211 419 420 421 221 232 242 252 263 273 284 294" 304 315 10 325 335 346 356 366 377 387 397 408 418 428 439 449 459 469 480 490 500 511 521 422 531 542 552 562 572 583 593 603 613 624 I I.O 423 634 644 655 665 675 685 696 706 716 726 2 2.0 424 737 747 757 767 778 788 798 808 818 829 3 3-0 425 839 849 859 870 880 890 900 910 921 931 4" 5 6 4.0 5-0 6.0 426 941 951 961 972 982 992 ^002 *OI2 *022 *033 427 63043 053 063 073 083 094 104 114 124 134 7 7.0 428 144 155 165 175 185 195 205 215 225 236 8 8.0 429 430 431 246 256 "266 276 286 296 306 317 327 337 9 9.0 347 357 367 377 387 397 407 417 428 438 448 458 468 478 488 498 508 518 528 538 432 548 558 568 579 589 599 609 619 629 639 433 649 659 669 679 689 699 709 719 729 739 434 749 759 769 779 789 799 809 8ig 829 839 435 849 859 869 879 889 899 909 919 929 939 436 949 959 969 979 988 998 *oo8 *oi8 *028 *038 437 64048 058 068 078 088 098 108 118 128 137 %f 438 147 157 167 177 187 197 207 217 227 237 I 0.9 439 440 441 246 256 266 276 286 296 306 316 326 335 2 3 4 5 6 1.8 2.7 3-6 4.5 5-4 6.3 7.2 345 355 365 375 385 395 404 414 424 434 444 454 464 473 483 493 503 513 523 532 442 542 552 562 572 582 591 601 611 621 631 7 8 443' 640 650 660 670 680 689 699 709 719 729 444 738 748 758 768 777 787 797 807 816 826 9 8.1 445 836 846 856 865 875 885 895 904 914 924 446 933 943 953 963 972 982 992 *002 4J.OII *02I 447 65031 040 050 060 070 079 089 099 108 118 448 128 137 147 157 167 176 186 196 205 215 449 450 225 234 244 254 263 273 283 292 302 312 321 331 341 350 360 369 379 389 398 408 N L 1 2 3 4 5 6 7 8 9 P P 3960" = ■1-6' S 4-68 555 T 4.68 563 4260" = 1° 11' S 4.68 554 T 4.6S 564 4020 = I 7 4-68 555 4-68 563 4320 = I 12 4.68 554 4.68 564 4080 = I 8 4-68 555 4-68 563 4380 =1 13 4.68 554 4.68 564 4140 = I 9 4-68 555 4.68 563 4440 =1 14 4.68 554 4.68 564 4200 = I 10 4-68 554 4-68 563 _ 4500 =1 15 4.68 554 4.68 564 11 450- -500 N L 1 2 3 4 5 6 7 8 1 9 r p 450 451 65321 331 341 350 360 369 379 389 398 408 418 427 437 447 456 466 475 485 495 504 452 514 523 533 543 552 562 571 581 591 600 453 610 619 629 639 64S 658 667 67.7 686 696 454 706 715 725 734 744 753 763 772 782 792 455 801 8n 820 ■830 839 849 858 868 877 887 456 896 906 gi6 925 935 944 954 963 973 982 457 992 *ooi *oii *020 *030 *039 *o49 ,058 *o68 *o77 10 458 66087 096 106 115 124 134 143 153 162 172 J I.O 2.0 3-0 4.0 5-0 6.0 459 460 461 181 191 200 210 219 229 238 247 257 266 2 3 4 5 6 276 285 295 304 314 323 332 342 351 361 370 380 389 398 408 417 427 436 445 4.55 ■462 464 474 483 492 502 511 521 530 539 549 463 558 567 577 586 596 605- 614 624 633 642 464 652 661 671 680 689 699 708 717 727 736 7 8 7.0 8.0 465 745 755 764 773 783 792 801 811 820 829 466 839 848 857 867 876 885 894 904 913 922 9 V" 467 932 941 950 960 969 978 987 997 »oo6 *oi5 468 67025 034 043 052 062 071 080 089 099 108 469 470 471 117 127 136 145 154 164 173 182 191 201 9 210 219 228 237 247 256 265 274 284 293 302 311 321 330 339 348 357 367 376 385 472 394 403 413 422 431 440 449 459 468 477 I 0.9 473 486 495 504 514 523 532 541 550 560 569 2 1.8 474 5*78 587 596 605 614 624 633 642 651 660 3 2.7 475 669 679 688 697 706 715 724 733 742 752 4 3-6 476 761 770 779 788 797 806 815 825- 834 843 5 4-5 477 852 861 870 879 888 897 906 916 925 934 6 5-4 478 943 952' 961 970 979 988 997 ^tOo6 *oi5 ,024 7 6-3 479 480 481 68034 043 052 061 070 079 088 097 106 115 8 9 7-2 8.1 124 133 142 151 160 169 178 187 196 205 215 224 233 242 251 260 269 278 287 296 4S2 305 314 323 332 341 350 359 368 377 386 483 395 404 413 422 431 440 449 458 467 476 484 485 494 502 511 520 529 538 547 556 565 485 574 583 592 601 610 619 628 637 646 655 fi 486 664 673 681 690 699 708 717 726 735 744 0.8 1.6 487 753 762 771 780 789 797 806 815 824 833 I 2 488 842 851 860 869 878 886 895 904 913 922 3 4 5 6 2.4 3-2 4.0 4.8 5-6 6.4 ■7 0. 489 490 491 931 940 949 958 966 975 984 993 jf002 *oii 69020 028 037 046 055 064 073 082 090 099 108 117 126 135 144 152 161 170 179 188 492 197 205 214 223 232 241 249 258 267 276 7 8 Q 493 285 294 302 311 320 329 338 346 355 364 494 373 381 390 399 408 417 425 434 443 452 y /■- 495 461 469 478 487 496 504 513 522 531 539 .496 548 557 566 574 583 592 601 609 618 627 497 636 644 653 662 671 679 688 697 705 714 498 723 732 740 749 758 767 775 784 793 801 499 500 810 819 827 836 845 854 862 871 880 888 897 go6 914 923 932 940 949 958 966 975 ]sr L 1 1 2 3 4 5 6 7 8 9 p p 4500' =31° 15' S 4.68554 T 4.68564 4800" =1° 20' S 4 . 68 554 T 4. 68 565 4560 =1 16 ^. 68 554 4. 68 565 4860 =1 21 4 .68553 4-68566 4620 =1 17 i. 68 554 4. 68 565 4920 =1 22 -1 . 68 553 4. 68 566 4680 =1 18 ;.68 554 4-68565 4980 =1 23 4 .68 553 4.68566 4740 =1 19 ^.68 554 ■ 4.68 565 5040 =1 24 4 68553 4.68566 12 500—550 N L 1 2 3 4 5 6 7 8 9 I ' P 500 5or 69897 906 914 923 932 940 949 958 966 975 984 992 *ooi «oio »oi8 *027 *036 »044 »o53 ^^062 502 70070 079 088 096 105 114 122 131 140 148 503 157 165 174 183 191 200 209 217 226 234 504 243 252 260 269 278 286 295 303 312 321 9 505 329 338 346. 355 364 372 38r 389 398 406 I 0.9 506 415 424 432 441 449 458 467 475 484 492 2 1.8 507 501 509 518 526^ 535 544 552 561 569 578 3 2.7 508 586 595 603 612 621 629 638 646 655 663 4 3-6 509 510 5" 672 680 689 697 706 714 723 731 740. 749 5 6 7 8 9 4-5 5-4 6-3 7,2 8.1 757 766 774 783 791 800 808 817 825 S34 842 851 859 868 876 885 893 902 910 gig 512 927 935 944 952 961 969 978 986 995 *003 513 71 012 020 029 037 046 054 063 071 079 088 514 096 105 113 122 130 139 147 155 164 172 515 181 189 198 206 214 223 231 240 248 257 516 265 273 282 290 299 307 315 324 332 341 517 349 357 366 374 383 391 399 408 416 425 518 433 441 450 458 466 475 483 492 500 508 519 520 521 517 525 533 542 550 559 567 575 584 592 I 8 0.8 600 609 617 625 634 642 650 659 667 675 684 692 700 709 717 725 734 742 750 759 522 767 775 784 792 800 809 817 825 834 842 2 1.6 523 850 858 867 875 883 892 900 908 917 925 3 2.4 524 933 941 950 958 966 975 983 991 999 ,008 4 3-2 525 72016 024 032 041 049 057 066 074 082 ogo 5 6 7 8 4.0 4.8 5.6 6.4 526 099 107 "5 123 132 140 148 156 165 173 527 181 189 198 206 214 222 230 239 247 255 528 263 272 280 288 296 304 313 321 329 337 9 7.2 529 530 531 346 354 362 370 378 387 395 403 411 419 428 436 444 452 460 469 477 485 493 501 509 518 526 534 542 550 558 567 575" 583 532 591 599 607 616 624 632 640 648 656 665 533 673 681 689 697 705 713 722 730 738 746 534 754 762 770 779 787 795 803 811 819 827 535 835 843 852 860 868 876 884 892 goo 908 536 916 92r 933 941 949 957 965 973 981 989 537 997 »oo6 *oi4 *022 *030 »038 *o46 *o54 »062 *07o 538 73078 086 094 102 III iig 127 135 143 151 7 539 540 541 159 167 175 183 191 199 207 215 223 231 I 2 3 4 0.7 1.4 2.1 2.8 239 247 255 263 272 280 288 296 304 312 320 328 336 344 352 360 368 376 384 392 542 400 408 416 424 432 440 448 456 464 472 5 6 3-5 543 480 488 496 504 512 520 528 536 544 552 4.2 544 560 568 576 584 592 600 608 616 624 632 7 g 4.9 5-6 6-3 545 640 648 656 664 672 679 687 695 703 711 9 546 719 727 735 743 751 759 767 775 783 791 547 799 807 8i5 823 830 838 846 854 862 870 548 878 886 894 902 910 gi8 926 933 941 949 549 550 957 965 973 981 989 997 *oo5 *oi3 #020 »028 74036 044 052 060 068 076 084 092 099 107 N L 1 2 3 4 5 6 7 8 9 I P 4980" ==I°23 ' S 4-68 553 1 C 4.68566 528 3" = I °28' S A t.6S553 'i C 4.68567 5040 = I 24 4-68 553 4.68 566 534 3 = I 29 ^68 553 4.68 567 5100 = 1 25 4-68 553 4.68 566 540 D = I 30 i t-68 553 4-68 567 5160 = I 26 4-68 553 4-68 567 546 3=1 31 A t.68 552 4.68 568 5220 = 1 27 4-68 553 4-68 567 552< 3 = ] 32 A 1-68 552 4.68 568 13 550—600 N L 1 2 3 4 5 6 7 8 9 P P 550 551 74036 044 052 060 068 076 084 092 099 107 H5 123 131 139 147 155 162 170 178 186 552 194 202 210 218 225 233 241 249 257 265 553 273 280 288 296 304 312 320 327 335 343 554 351 359 367 374 382 390 398 406 414 421 555 429 437 445 453 461 468 476 484 492 500 556 507 515 523 531 539 547 554 562 570 578 557 586 593 601 609 617 624 632 640 648 656 558 663 671 679 687 695 702 710 718 726 733 559 560 561 741 749 757 764 772 780 788 796 803 811 8 819 827 834 842 850 858 865 873 881 889 896 904 912 920 927 935 943 950 958 966 562 974 981 989 997 *oo5 1*012, »020 4^028 »035 *043 .563 75051 059 066 074 082? 159 089 097 105 113 120 I 0.0 1.6 2.4 564 128 136 143 151 166 174 182 189 197 2 3 565 205 2t3 220 228 236 243 251 259 266 274 566 282 289 297 305 312 320 328 335 343 351 4 3-2 567 358 366 374 381 389 397 404 412 420 427 5 5 4.0 4-8 568 435 442 ■450 458 465 473 481 488 496 504 569 570 571 ,511 519 526 534 542 549 557 565 572 580 7 8 9 5-6 6.4 7-2 587 595 603 610 618 626 633 641 648 656 664 671 679 686 694 702 709 717 724 732 572 740 747 755 762 770 778 785 793 800 808 573 815 823 831 833 846 853 861 868 876 884 574 891 899 906 914 921 929. 937 944 952 959 575 967 974 982 989 997 jeoos »0I2 jt020 *027 *035 576 76042 050 057 065 072 080 087 095 103 no 577 118 125 133 140 148 155 163 170 178 185 578 193 200 208 215 223 230 238 245. 253 260 579 580 581 268 275 283 290 298 305 31^- 320 328 335 7 343 350 358 365 373 380 388) 395 403 410 418 425 433 440 448 455 462 470 477 485 582 492 500 507 515 522 530 537 545 552 559 I "•/ 583 567 574 582 589 597 604 612 619 626 634 2 1-4 584 641 649 656 664 671 678 686 693 701 708 3 2.1 2.8 585 716 723 730 738 745 753 760 768 775 782 4 586 790 797 805 812 819 827 834 842 849 856 5 6 3-5 4-2 587 864 871 879 886 B93 901 908 916 923 930 588 938 945 953 960 967 975 982 989 997 *oo4 7 8 Q 4-9 5.6 hi 589 590 591 77012 019 026 034 041 048 056 063 070 078 085 093 100 107 115 122 129 137 144 151 y I — y 159 166 173 l8i 188 195 203 210 217 225 592 232 240 247 254 262 269 276 283 291 298 593 305 313 320 327 335 342 349 357 364 371 594 379 386 393 401 408 415 422 430 437 444 595 452 459 466 474 481 488 495 503 510 517 596 525 532 539 546 554 561 568 576 583 590 597 597 605 612 619 627 634 641 648 656 663 598 670 677 685 692 699 706 714 721 728 735 599 600 743 750 757 764 772 779 786 793 801 808 815 822 830 837 844 851 859 866 873 880 N L 1 2 3 4 5 6 7 8 9 p p 5460 " =1° 31' S 4.68 ,52 T 4.68568 5760" =1° 36 S 4-68552 T 4-68569 5520 = 1 32 4-68 I 52 4. 68 568 5820 =1 37 4.68552 4.68 5fr9 5580 = 1 33 4.68 ; 52 4. 68 568 5880 =1 38 4.68552 4.68569 5640 =1 34 4. 68 ; 52 4. 68 568 5940 =1 39 4.68 551 4-68 569 5700 = 1 35 4-68 ; 52 4. 68 569 6000 =1 40 4.68 551 4-68 570 14 600—650 N L 1 2 3 4 5 6 7 8 9 P I' 600 6oi 77815 822 830 837 844 851 859 866 873 880 887 895 902 909 916 924 931 938 945 952 6o2 960 967 974 981 988 996 *oo3 »oio *oi7 *025 603 78032 039 046 053 061 068 075 082 089 097 604 104 III 118 125 132 140 147 154 161 168 605 176 183 190 197 204 211 219 226 233 240 606 247 254 262 269 276 283 290 297 305 312 8 607 319 326 333 340 347 355 362 .369 376 383 I 0.8 608 390 398 405 412 419 426 433 440 447 455 2 1.6 609 610 611 462 469 476 483 490 497 504 512 519 526 3 4 5 6 2.4 3.2 4.0 4-8, 533 540 547 554 561 569 576 583 590 597 604 611 618 625 633 640 647 654 661 668 612 675 682 689 696 704 711 718 725 732 739 7 5.6 613 746 753 760 767 774 781 789 796 803 810 8 6.4 614 817 824 831 838 845 852 859 866 873 880 9 7.2 615 888 895 902 909 916 923 930 937 944 951 616 958 965^ 972 979 986, 993 *ooo *oo7 *oi4 i02I 617 79029 036 043 050 057 064 071 078 085 092 618 099 106 113 120 127 134 141 148 155 162 619 620 621 169 176 183 190 197 204 2H 218 225 232 7 239 246 253 260 267 274 281 288 295 302 309 316 325 330 337 344 351 35S 365 372 622 379 386 393 400 407 414 421 428 435 442 I 0.7 623 449 456 463 470 477 484 491 498 505 511 2 1-4 624 518 525 532 539 546 553 560 567 574 581 3 2.1 625 588 595 602 609 616 623 630 637 644 650 4 2.8 626 657 664 671 678 685 692 699 706 713 720 5 6 7 8 9 3-5 627 727 734 741 748 754 761 768 775 782 789 4.2 628 796 803 810 817 824 831 837 844 851 858 4-9 5-6 6.3 629 630 631 865 872 879 886 893 900 906 913 920 927 934 941 948 955 962 969 9,75 982 989 996 80003 010 017 024 030 037 044 051 058 065 632 072 079 085 092 099 106 113 120 127 134 633 140 147 154 161 168 175 182 188 195 202 634 209 216 223 229 236 243 250 257 264 271 635 277 284 291 298 305 312 318 325 332 339 636 346 353 359 366 373 380 387 393 400 407 6 637 414 421 428 434 441 448 455 462 468 475 638 482 489 496 502 509 516 523 530 536 543 I 0.6 639 640 641 550 557 564 570 577 584 591 598 604 611 2 3 4 5 6 1.2 1.8 2.4 3-0 3-6 618 625 632 638 645 652 659 665 672 679 686 693 699 706 713 720 726 733 740 747 642 754 760 767 774 781 787 794 801 808 814 643 821 828 835 841 848 855 862 868 875 882 7 9 4.2 4.8 5-4 644 889 895 902 909 gi6 922 929 936 943 949 645 956 963 969 976 983 990 996 *003 *OIO *oi7 646 81023 030 037 043 050 057 064. 070 077 084' 647 090 097 104 III "7 124 131 137 144 151 648 158 164 171 178 184 191 198 204 211 218 649 650 224 231 238 245 251 258 265- 271 278 285 291 298 305 311 318 325 331 338 345 351 N L 1 2 3 4 5 6 7 8 9 P P 6000" = 1° 40' S 4.68 551 T 4.68 570 6- 00" = 1° 45 ' S 4.68 551 T 4.68 571 6060 = I 41 4.68 551 4.68 570 63 60 =1 46 4.68 551 4.68 571 6iao = I 42 4.68 551 4.68 570 64 20 =1 47 4.68 550 4.68 572 6180 - I 43 4.68 551 4.68 570 64 80 = I 48 4.68 550 4.68 572 6240 = I 44 4-68 551 4-68 571 65 40 = I 49 4.68 550 4.68 572 15 650- -700 N L 1 2 3 4 5 6 7 8 9 P P 650 651 81 291 298 305 3" 3i8 325 331 338 345 351 358 365 371 378 385 391 398 405 411 418 652 425 431 438 445 451 458 465 471 478 485- 653 491 498 505 511 518 525 531 538 544 551 "654 558 564 571 578 584 591 598 604 611 617 655 624 631 637 644 651 657 664 671 677 684 656 690 697 704 710 7-17 723 730 737 743 750 657 757 763 770 776 783 790 796 803 809 8i6 658 823 829 836 842 849 856 862 869 875 882 659 660 661 889 895 902 908 915 921 928 935 941 948 954 961 968 974 981 987 994 ;;.000 »oo7 ,014 82020 027 033 040 046 053 060 066 073 079 662 086 092 099 105 112 119 125 132 138 145- 7 663 151 158 164 171 178 184 191 197 204 210 I 0-7 664 217 223 230 236 243 249 256 263 269 276 2 1-4 665 282 289 295 302 308 315 321 328 334 341 3 2.1 666 347 354 360 367 373 380 387 393 400 406 4 2.8 667 413 419 426 432 439 445 452 458 465 471 5 3-5 668 478 484 491 497 504 510 517 523 530 536 6 4.2 669- 670 671 543 549 556 562 569 575 582 588 595 601 7 8 4-9 5-6 fin 607 614 620 627 633 640 646 653 659 666 672 679 685 692 698 705 711 7i8 724 730 y — ^ 672 737 743 750 756 763 769 776 782 789 795 673 802 808 814 821 827 834 840 S47 853 860 674 866 872 ^879 885 892 89S 905 911 918 924 675 930 937 943 950 956 963 969 975 982 988 676 995 *ooi ^^oo8 »oi4 *020 »027 »033 *o4o *046 *052 677 83059 065 072 078 085 091 097 104 no 117 678 123 129 136 142 149 155 161 168 174 181 679 680 681 187 193, 200 206 213 219 225 232 238 245 6 251 257 264 270 276 283 289 296 302 308 315 321 327 334 340 347 353 359 366 372 685 378 385 391 398 404 410 417 423 429 436 I 0.6 683 442 448 455 461 467 474 480 487 493 499 2 1.2 684 506 512 518 525 531 537 544 550 556 563 3 1.8 685 569 575 ■582 588 594 601 607 613 620 626 4 5 2-4 3-0 686 632 639 645 651 658 664 670 677 683 689 687 696 702 708 715 721 727 734 740 746 753 6 3-6 688 759 765 771 778 784 790 797 803 809 816 7 8 9 4.2 68g 690 691 822 828 835 841 847 853 860 866 872 879 4.8 5-4 885 891 897 904 gio gl6 923 929 935 942 948 954 960 967 973 979 985 992 998 *oo4 692 84 01 1 017 023 02g 036 042 048 055 o6i 067 693 073 080 086 092 098 105 m 117 123 130 694 136 142 148 155 161 167 173 180 186 192 695 198 205 211 217 223 230 236 242 248 255 696 261 267 273 280 286 292 298 305 311 317 697 323 330 336 342 348 354 361 367 373 379 6g8 386 392 398 404 410 417 423 429 435 442 699 700 448 454 460 466 473 479 485 491 497 504 510. 516 522 528 535 541 547 553 559 566 N L 1 2 3 4 5 1 6 1 7 8 9 P P 6480* = 1° 48 ' S 4. 68 550 T 4.68 572 b^i 0" =1° 53' S 4.68550 T 4.68573 6540 = 1 49 4. 68 550 4.68 572 684 =1 54 4.68550 4-68573 6600 = 1 50 4-68 550 4-68 572 6gc =1 55 4-68549 4-68574 6660 = 1 51 4-68 550 4- 68 573 696 =1 56 4.68 549 4.68 574 6720 = 1 52 4.68 550 4.68 573 702 =1 57 4-68549 4-68574 16 700- -750 N L 1 2 3 4 5 6 7 8 9 P P 700 701 84510 516 522 528 535 541 547 553 559 566 572 578 584 590 597 603 609 615 621 628 702 634 640 646 652 658 665 671 677 683 689 703 696 702 708 714 720 726 733 739 745 751 704 757 763 770 776 782 788 794 800 807 813 705 819 825 831 837 844 850 856 862 868 874 706 880 887 893 899 905 911 917 924 930 936 707 942 948 954 960 967 973 979 985 991 997 7 708 85003 009 016 022 028 034 040 046 052 058 709 710 711 065 071 077 083 089 095 lOI 107 114 120 I 2 3 4 5 6 0.7 1.4 2.1 2.8 3-5 4.2 4.9 126 132 138 144 i5q 156 163 i6g 175 181 187 193 199 205 211 217 224 230 236 242 712 248 254 260 266 272 278 285 291 297 303 713 309 315 321 327 333 339 345 352 358 364 7 714 370 376 382 388 394 400 406 412 418 425 8 5.6 715 431 437 443 449 455 461 467 473 479 485 9 6.3 716 491 497 503 509 516 522 528 534 540 546 717 552 558 564 570 576 582 588 594 600 606 718 612 618 625 631 637 643 649 655 661 667 719 720 721 673 679 685 691 697 703 709 715 721 727 6 733 739 745 751 757 763 769 775 781 788 794 800 806 812 818 824 830 836 842 848 722 854 860 866 872 878 884 890 896 902 908 I 0.6 723 914 920 926 932 938 944 950 956 962 968 2 1.2 724 974 980 986 992 998 *oo4 *OIO .jOi6 *022 *028 3 1.8 725 86034 040 046 052 058 064 070 076 082 088 4 2.4 726 094 100 106 112 118 124 130 136 141 147 5 3-0 727 153 159 165 171 177 «83 189 195 201 207 6 3-6 728 213 219 225 231 237 243 249 255 261 267 7 8 9 4.2 4.8 54 729 730 731 273 279 285 291 297 303 308 314 320 326 332 338 344 350 356 362 368 374 380 386 392 398 404 410 415 421 427 433 439 445 732 451 457 463 469 475 481 487 493 499 504 • 733 510 516 522 528 534 540 546 552 558 564 734 570 576 581 587 593 599 605 611 617 623 735 629 635 641 646 652 658 664 670 676 682 5 736 688 694 700 705 7" 717 723 729 735 741 737 747 753 759 764 770 776 782 788 794 800 I 0.5 738 806 812 817 823 829 835 841 847 853 859 2 I.O 739 740 741 864 870 876 882 888 894 900 906 911 917 3 4 5 6 7 1-5 2.0 2.5 3.0 3-5 923 929 935 941 947 953 958 964 970 976 982 98S 994 999 *oo5 *OII «oi7 *023 *029 *o35 742 ■ 87040 046 052 058 064 070 075 081 087 093 8 4.0 743 099 105 III 116 122 128 134 140 146 151 9 4-5 744 157 163 169 175 181 186 192 198 204 210 745 216 221 227 233 239 245 251 256 262 268 746 274 280 286 291 297 303 309 315 320 326 747 332 338 344 349 355 361 367 373 379 384 748 390 396 402 408 413 419 425 431 437 442 749 750 448 454 460 466 471 477 483 489 495 500 506 512 51S 523 529 535 54t 547 552 558 N L 1 2 3 4 5 6 7 8 9 P P 696 o" = i°56' S 4.68 549 T 4.68 574 726 0" = ; !° l' S i J.68 549 T 4-68 575 702 =1 57 4.68 549 4-68 574 732 = 2 2 \M 548 4-68 576 708 = I 58 4.68 549 4.68 575 738 = 2 3 \.t% 548 4-68 576 714 3 = I 59 4.68 549 4-68 575 744 = 2 4 1.68 548 4-68 576 7201 0=2 4.68 549 4-68 575 750 = 2 5 t.68 548 4.68 577 17 750—800 N L 1 2 3 4 5 6 7 8 9 P P 750 751 87506 512 518 523 529 535 541 547 552 558 564 570 576 581 587 593 599 604 610 616 752 622 628 633 639 645 651 656 662 668 674 753 679 685 691 697 703 708 714 720 726 731 754 737 743 749 754 760 766 772 777 783 789 755 795 800 806 812 818 823 829 835 841 846 756 852 858 864 869 875 881 887 892 898 904 757 910 915 921 927 933 938 944 950 955 961 758 967 973 978 984 990 996 *ooi #007 *oi3 *oi8 759 760 761 88024 030 036 041 047 053 058 064 070 076 081 087 093 098 104 no 116 121 127 133 138 144 150 156 161 167 173 178 184 190 762 195 201 207 213 218 224 230 235 241 247 R 763 252 258 264 270 275 281 287 292 298 304 I 2 0.6 1.2 764 309 315 321 326 332 338 343 349 355 360 765 366 372 377 383 389 395 400 406 412 417 3 4 1.8 766 423 429 434 440 446 451 457 463 468 474 2-4 767 480 485 491 497 502 508 513 519 525 530 5 3-0 768 536 542 547 553 559 564 570 576 581 587 6 3-6 769 770 77i 593 598 604 610 615 621 627 632 638 643- 7 8 9 4-2 4.8 5-4 649 655 660 666 672 677 683 689 694 700 705 711 717 722 728 734 739 745 750 756 772 762 767 773 779 784 790 795 801 807 812 773 818 824 829 835 840 846 852 857 863 868 774 874 880 885 891 897 902 go8 913 919 925 775 930 936 941 947 953 958 964 969 975 981 776 986 992 997 *oo3 *oo9 !fOI4 *020 *025 *03i *037 777 89.042 048 053 059 064 070 076 081 087 092 778 098 104 109 115 120 126 131 137 143 148* 779 780 781 154 159 165 170 176 182 187 193 198 204 c 209 215 221 226 232 237 243 248 254 260 I 2 u 0.5 I.O 265 271 276 282 287 293 298 304 310 315 782 321 326 332 337 343 348 354 360 365 371 3 1-5 783 376 382 387 393 398 404 409 415 421 426 4 2.0 2.5 3.0 3-5 4.0 784 432 437 443 448 454 459 465 470 476 481 I 785 487 492 498 504 509 515 520 526 531 537 7 592 8 786 542 548 553 559 564 570 575 581 586 787 597 603 609 614 620 625 631 636 642 647 9 4.5 788 653 658 664 669 675 680 686 691 697 702 " 1 789 790 791 708 713 719 724 730 735 741 746 752 757 763 768 774 779 785 790 796 801 807 812 818 823 829 834 840 845 851 856 862 867 792 873 878 883 889 894 900 905 911 916 922 • 793 927 933 938 944 949 955 960 966 971 977 794 982 988 993 998 *0O4 »0O9 »oi5 it020 «026 *03i 795 90037 042 048 053 059 064 069 075 080 086 796 091 097 102 108 "3 119 124 129 135 140 797 146 151 157 162 168 173 179 184 189 195 798 200 206 211 217 222 227 233 238 244 249 799 800 255 260 266 271 276 282 287 293 298 304 309 314 320 325 331 336 342 347 352 358 N L 1 2 3 4 5 6 7 8 9 P P 7500" = 2° 5' S 4-68548 T 4.68 577 7800" = 2° 10' S 4-68 547 T 4-68 578 7560 = 26 4.68548 4.68 577 7860 =211 4.68 547 4.68 579 7620 = 27 4.68548 4.68 577 7920 = 2 12 4.68 547 4.68 579 7680 = 28 4.68 547 4.68 578 7980 =2 13 4-68547 4-68579 7740 = 29 4-68547 4.68 578 8040 = 2 14 4.68546 4.68579 18 800- -850 N L 1 2 3 4 5 6 7 8 9 P P 800 8oi 90309 314 320 325 331 336 342 347 352 358 363 369 374 380 385" 390 396 401 407 412 802 417 423 428 434 439 445 450 455 461 466 803 472 477 482 488 493 499 504 509 515 520 804 526 531 536 542 547 553 558 563 569 574 805 580 585 590 596 601 607 612 617 623 628 806 634 639 644 650 655 660 666 671 677 682 807 687 693 698 703 709 714 720 725 730 736 808 741 747 752 757 763 768 773 779 784 789 809 810 811 795 800 806 811 816 822 827 832 838 843 6 849 854 859 865 870 875 881 886 891 897 902 907 913 918 924 929 934 940 945 950 8l2 956 961 966 972 977 9S2 988 993 998 *004 ■r „ £ 813 91009 014 020 025 030 036 041 046 052 057 I u.u 814 062 068 073 078 084 089 094 100 105 no 2 3 1.2 I.S 8i5 116 121 126 132 137 142 148 153 158 164 816 169 174 180 185 190 196 201 206 212 217 4 5 6 2.4 3.0 3.6 817 222 228 233 238 243 249 254 259 265 270 818 275 281 286 291 297 302 307 312 318 323 819 820 821 328 334 339 344 350 355 360 365 371 376 7 8 9 4.2 4.8 5-4 381 387 392 397 403 408 413 418 424 429 434 440 445 450 455 461 466 471 477 482 822 487 492 498 503 508 514 519 524 529 535 823 540 545 551 556 561 566 572 577 582 587 824 593 598 603 609 614 619 624 630 635 640 825 64^ 651 656 661 666 672 677 682 687 693 826 698 703 709 714 719 724 730 735 740 745 827 751' 756 761 766 772 777 782 787 793 798 828 803 808 814 819 824 829 834 840 845 850 829 830 831 855 86i 866 871 876 882 887 892 897 903 5 r 1 r^ - 908 913 .918 924 929 934 939 944 950 955 960 965 971 976 981 986 991 997 *002 *oo7 832 92012 018 023 028 033 038 044 049 054 059 1 "•S 833 065 070 075 080 085 091 096 lOI 106 III 2 3 T.O 1-5 834 117 122 127 132 137 143 148 153 158 163 835 169 174 179 184 189 195 200 205 210 215 4 2.0 836 221 225 231 236 241 247 252 257 262 267 5 6 2-5 3-0 837 273 278 283 288 293 298 304 309 314 3:9 838 324 330 335 340 345 350 355 361 366 371 7 8 9 3-5 839 840 841 376 381 387 392 397 402 407 412 418 423 4.0 428 433 438 443 449 454 459 464 469 474 480 485 490 495 500 505 511 516 521 526 842 531 536 542 547 552 557 562 567 572 578 843 583 588 593 598 603 609 614 619 624 629 844 634 639 645 650 655- 660 665 670 675 681 845 686 691 696 701 706 711 716 722 727 732 846 737 742 747 752 758 763 768 773 778 783 847 788 793 799 804 809 814 819 824 829 834 848 840 845 850 855 860 865 870 875 881 886 849 850 891 896 901 906 911 916 921 927 932 937 942 947 952 957 962 967 973 978 983 988 N L 1 2 3 4 5 6 7 8 9 P P 7980 " =2" 13' S 4. 68 547 '] C 4.68579 82 3o" =2° 18 S 4. 68 546 T 4. 68 581 8040 =2 14 4. 68 546 4.68 579 83 }o =2 19 4.68 546 4.68 581 8100 =2 15 4. 68 546 4.68 580 84 30 —2 20 4. 68 545 4. 68 582 8160 =2 16 4- 68 546 4.68 580 84 DO =2 21 4.68545 4.68582 8220 =2 17 4. 68 546 4.68 580 85 20 =2 22 4.68 545 4.68 582 19 850- -900 N liO 1 2 3 4 5 6 7 8 9 r p 850 851 92942 947 952 957 962 967 973 978 983 988 993 998 *oo3 «oo8 *oi3 »oi8 «024 *029 *034 *039 852 93044 049 054 059 064 069 075 080 085 090 853 095 100 105 no 115 120 125 131 136 141 854 146 151 156 161 166 171 176 181 186 192 855 197 202 207 212 217 222 227 232 237 242 856 247 252 258 263 268 273 278 283 28S 293 857 298 303 308 313 318 323 328 334 339 344 6 858 349 354 359 364 369 374 379 384 389 394 I 0.6 859 860 861 399 404 409 414 420 425 430 435 440 445 2 3 4 5 6 1.2 1.8 2.4 3.0 3-6 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 526 531 536 541 546 862 551 556 561 566 571 576 581 586 591 596 863 601 606 611 616 621 626 631 636 641 646 7 8 9 4.2 4.8 5.4 864 651 656 661 666 671 676 682 687 692 697 865 702 707 712 717 722 727 732 737 742 747 866 752 757 762 767 772 777 782 787 792 797 867 802 807 812 817 822 827 832 837 842 847 868 852 857 862 867 872 877 882 887 892 897 869 870 871 902 907 912 917 922 927 932 937 942 947 5 952 957 962 967 972 977 982 987 992 997 94002 007 012 017 022 027 032 037 042 047 872 052 057 062 067 072 077 082 086 091 096 I 0.5 873 lOI 106 III 116 121 126 131 136 141. 146 2 I.O 874 151 156 I6i 166 171 176 181 186 191 196 3 1-5 875 201 206 211 216 221 226 231 236 240 245 4 2.0 876 250 255 260 265 270 275 280 285 290 295 5 6 7 8 2.5 3-0 3-5 4.0 4.5 877 300 305 310 315 320 325 330 335 340 345 878 349 354 359 364 369 374 379 384 389 394 879 880 881 309 404 409 414 419 424 429 433 438 443 9 448 453 458 463 468 473 478 4S3 488 493 498 503 507 512 517 522 527 532 537 542 882 547 552 557 562 567 571 576 581 586 591 883 596 60 1 606 611 616 621 626 630 635 640 884 645 650 655 660 665 670 675 680 685 689 885 694 699 704 709 714 719 724 729 734 738 886 743 748 753 758 763 768 773 778 783 787 4 887 792 797 802 807 812 817 822 827 832 836 888 841 846 851 856 861 866 871 876 880 885 I 0.4 889 890 891 890 895 900 905 910 915 919 924 929 934 2 3 4 5 6 0.8 1.2 1.6 2.0 2.4 2.8 939 944 949 954 959 963 968 973 978 983 988 993 998 »002 *007 *OI2 *oi7 *022 *027 »032 892 95 036- 041 046 051 056 06 1 066 071 075 080 7 8 893 085 090 095 100 105 109 114 119 124 129 3.2 894 134 139 143 148 153 158 163 168 173 177 9 1.6 895 182 187 192 197 202 207 211 216 221 226 896 231 236 240 245 250 255 260 265 270 274 897 279 284 289 294 299 303 308 313 318 323 898^ 328- 332 337 342 347 352 357 361 366 371 899 900 376 381 386 390 395 400 405 410 415 419 424 429 434 439 444 448 453 458 463 468 N L 1 2 3 4 5 6 7 8 9 r p 8460" = 2° 21' S 4.68 545 T 4.68 582 8760" = = 2° 26' fc) 4.68544 T 4.68584 8520 = 2 22 4.68 545 4.68 582 8820 = = 2 27 4.68 544 4.68 584 8580 =: 2 23 4.68 545 4.68 583 8880 = = 2 28 4.68 544 4.68 584 8640 = 2 24 4.68 545 4.68 583 8940 = = 2 29 4.68 544 4.68 585 8700 = 2 25 4.68 545 4.68 583 9000 - = 2 30 4.68 544 4.68 585 20 900- -950 N L 1 2 3 4 5 6 7 8 9 r r 900 901 95424 429 434 439 444 448 453 458 463 468 472 477 482 487 492 497 501 506 511 516 902 521 525 530 535 540 545 550 554 559 564 903 569 574 578 583 588 593 598 602 607 612 904 617 622 626 631 636 641 646 650 655 660 905 665 670 674 679 684 689 694 698 703 708 906 713 718 722 727 732 737 742 746 751 756 907 761 766 770 775 780 785 789 794 799 804 908 809 813 818 823 828 832 837 842 847 852 9C9 910 •911 856 861 866 871 875 • 880 885 890 895 899 904 909 914 918 923 928 933 938 942 947 952 957 961 966 971 976 980 985 990 995 912 999 *oo4 ,009 *oi4 *oi9 »023 *028 *033 *038 »042 5 913 96047 052 057 061 066 071 076 080 085 090 I 0.5 914 095 099 104 109 114 118 123 128 133 137 2 I.O 915 142 147 152 156 161 166 171 175 180 185 3 1-5 916 190 194 199 204 209 213 218 223 227 232 4 2.0 917 237 242 246 251 256 261 265 270 275 280 5 2.5 918 284 289 294 298 303 308 313 317 322 327 6 3-0 919 920 921 332 336 341 346 350 355 360 365 369 374 7 8 9 3-5 4.0 4-5 379 384 388 393 398 402 407 412 417 421 426 431 435 440 445 450 454 459 464 468 922 473 478 483 487 492 497 501 506 5" 515 923 520 525 530 534 539 544 548 553 558 562 924 567 572 577 581 586 591 595 600 605 609 925 614 ti9 624 628 633 638 642 647 652 656 926 661 666 670 675 680 685 689 694 699 703 927 708 713 717 722 727 731 736 741 745 750 928 755 759 764 769 774 778 783 788 792 797 929 930 931 802 806 8n 816 820 825 830 834 839 844 4 848 853 858 862 867. 872 876 881 886 890 895 900 904 909 914 918 923 928 932 937 932 942 94,§ 951 956 960 965 970 974 979 984 I 0.4 933 988 993 997 »002 *oo7 »oii *oi6 *02I *025 *030 2 0.8 934 97035 039 044 049 053 058 063 067 072 077 3 1.2 935 081 086 090 095 100 104 109 114 118 123 4 1.6 936 128 132 137 142 146 151 155 160 165 169 5 2.0 937 174 179 183 188 192 197 202 206 211 216 6 2.4 938 220 225 230 234 239 243 248 253 257 262 7 2.8 939 940 941 267 271 276 280 285 290 294 299 304 308 8 9 3-2 3-6 313 317 322 327 331 336 340 345 350 354 359 364 368 373 377 382 387 391 396 400 942 405 410 414 419 424 428 433 437 442 447 943 451 456 460 465 470 474 479 483 488 493 944 497 502 506 511 516 520 525 529 534 539 945 543 548 552 557 562 566 571 575 580 585 946 589 594 598 603 607 612 617 621 626 630 947 635 640 644 649 653 658 663 667 672 676 948 681 685 6go 695 699 704 708 713 717 722 949 950 727 731 736 740 745 749 754 759 763 768 813 772 777 782 786 791 795 800 804 809 N L 1 2 3 4 5 6 7 8 9 P P 9000 " —2° 3< -,' S 4-68 544 " r 4.f )8 585 9300" =2° 35 S 4.68 543 T 4.68 587 9060 = 2 3 [ 4. 68 544 4.f )8 585 9360 =2 36 4.68543 4.68587 9120 = 2 3 2 4- 68 543 4.f )8 586 9420 =2 37 4.68542 4.68588 9180 = 2 3 5 4- 68 543 4.( )8 586 9480 =2 38 4.68542 4.68588 9240 = 2 3. \ 4- 68 543 4.f )8 587 9540 =2 39 4. 68 542 4. 68 588 21 950 —1000 N L 1 2 3 4 5 6 7 8 9 P P 950 951 9777a 777 782 786 791 795 800 804 8og 813 818 823 827 832 836 841 845 850 85§ 859 952 864 868 873 877 882 886 891 8g6 goo 905 953 909 914 gi8 923 928 932 937 941 946 950 954 955 959 964 968 973 978 982 987 ggl 996 955 98000 005 009 014 019 023 028 032 037 041 956 046 050 055 059 064 068 073 078 082 087 957 001 096 100 105 109 114 118 123 127 132 958 137 141 146 150 155 159 164 168 173 177 959 960 g6i 182 18O 191 195 200 204 209 214 218 223 5 227 232 236 241 245 250 254 259 263 268 272 277 281 286 290 295 299 304 308 313 962 318 322 327 331 336 340 345 349 354 358 I 0.5 963 363 367 372 376 381 385 390 394 399 403 2 I.O 964 408 412 417 421 426 430 435 439 444 448 3 1-5 965 453 457 462 466 471 475 480 484 489 493 4 2.0 966 498 502 507 511 516 520 525 529 534 538 5 2.5 967 543 547 552 556 561 565 570 574 579 583 6 3.0 96S 588 592 597 601 605 610 614 619 623 628 7 3-5 969 970 971 632 637 641 646 650 655 659 664 668 673 8 9 4.0 4-5 677 682 GSO 6gl 695 700 704 709 713 717 722 726 731 735 740 744 749 753 758 762 972 767 771 776 780 784 7S9 793 798 802 807 973 811 816 820 825 829 834 838 843 847 851 974 856 860 865 869 874 87S S83 887 892 896 975 900 905 909 914 gi8 923 927 932 936 g4i 970 945 949 954 958 963 967 972 976 g8i 985 977 989. 994 998 *oo3 *007 *OI2 5fOl6 if 02 1 *025 *029 978 99034 038 043 047 052 056 061 065 o6g 074 979 980 981 078 083 087 092 096 100 105 109 114 n8 4 123 127 131 136 140 145 149 154 158 162 167 171 176 180 185 189 193 198 202 207 982 211 216 220 224 229 233 238 242 247 251 I 0.4 983 255 260 264 269 273 277 282 286 291 295 2 0.8 984 300 304 308 313 317 322 326 330 335 339 3 1.2 985 344 348 352 357 361 366 370 374 379 383 4 1.6 986 388 392 396 401 405 410 414 419 423 427 5 2.0 987 432 436 441 445 449 454 458 463 467 471 6 2.4 988 476 480 484 489 493 498 502 506 5" 515 7 2.8 989 990 991 520 524 528 533 537 542 546 550 555 559 8 9 3.2 3.6 564 568 572 577 581 5S5 590 594 599 603 607 612 616 621 625 629 634 63a 642 647 992 651 656 660 664 669 673 677 682 686 6gi 993 695 699 704 708 712 717 721 726 730 734 994 739 743 747 752 756 760 765 769 774 778 995 782 787 791 795 800 804 808 8i3 817 822 996 826 830 835 839 843 848 852 856 861 865 997 870 874 878 883 887 891 896 goo 904 gog 998 913 917 922 926 930 935 939 944 948 952 999 1000 957 961 965 970 974 978 983 987 991. 996 00000 004 009 013 017 022 026 030 035 039 N L 1 2 3 4 5 6 7 8 9 P P 9480 " -2° 38' S 4.68 542 T 4.68 5S8 9780" = 2° 43 S 4. 68 541 T 4. 68 590 9540 =2 39 4-68 E 42 4.68588 9840 = 2 44 4. 68 541 4. 68 590 9600 = 2 40 4.68 5 42 4. 68 589 9900 = 2 45 4. 68 541 4. 68 591 9660 =2 41 4-685 42 4. 68 589 9960 = 2 46 4. 68 541 4. 68 591 9720 =2 42 4.68 5 41 4. 68 590 10020 = 2 47 4. 68 540 4. 68 592 22 THE NATURAL LOGARITHMS WHOLE NUMBERS FROM 1 TO 200. Common logarithms may be converted into natural logarithms hj multi- plying them by 2.3025850930 • Natural log/rithms may be converted i nto common logarithms by multiplying them by 0.4342944819. / > •^"atJtiOg N Nat Log N Nat Log N Nat Log N Nat Log I 2 3 — 00 40 - 41 42 43 3.68 888 80 81 82 83 4-38 203 120 121 122 123 4-78 749 160 161 162 163 5-07517 0.00 000 0.69315 1.09 861 3-71 357 3-73 767 3.76 120 4-39 445 4.40 672 4.41 884 4-79 579 4.80 402 4.81 218 5.08 140 5.08760 5-09 375 4 5 6 i.38'62g 1.60944 1.79 176 44 45 46 3.78419 3.80 666 3.82 864 84 85 86 4.43 082 4-44 265 4-45 435 124 125 126 4.82 028 4.82 831 4.83 628 164 165 166 5-09 987 5-10595 5.11 199 7 8 9 10 II 12 13 1.94 591 2.07 944 2.ig 722 47 48 49 50 51 52 53 3-85015 3.87 120 3.89 182 87 88 89 90 91 92 93 4.46 591 4-47 734 4.48 864 127 128 129 130 131 132 133 4.84419 4.85 203 4.85981 167 168 169 170 171 172 173 5.11 799 5-12 396 5.12 990 2.30 259 3.91 202 4-49 981 4-86 753 5-13 580 2.39 790 2.48 491 2.56495 3-93 183 3-95 124 3-97 029 4.51 086 4-52 179 4-53 260 4-87 520 4.88 280 4-89 035 5.14 166 5.14 749 5-15329 14 15 i6 2.63 906 2.70805 2.77259 54 55 56 3-98 898 4-00 733 4-02 535 94 95 96 4-54 329 4-55 388 4-56435 134 135 136 4-89 784 4.90 527 4.91 265 174 175 176 5-15906 5.16479 5.17048 17 i8 19 20 21 22 23 2.83321 2.89 037 2.94 444 57 58 59 60 61 62 63 4.04 305 4.06 044 4-07 754 97 98 99 100 lOI 102 103 4-57471 4-58497 4.59512 137 138 139 140 141 142 143 4.91 998 4.92 725 4-93 447 177 178 179 180 181 182 183 5-17 615 5.18 178 5-18739 2.99 573 4.09 434 4.60517 4-94 164 5-19296 3.04 452 3.09 104 3.13 549 4.11 087 4-12713 4-14313 4.61 512 4.62497 4-63 473 4-94 876 4-95 583 4.96 284 5:19850 5.20 401 5-20 949 24 25 26 3-17805 3.21 888 3-25 8io 64 65 66 4.15888 4-17439 4-18 965 104 105 106 4.64 439 4-65 396 4-66 344 144 145 146 4.96981 4.97 673 4-98 361 184 185 186 5.21 494 5.22036 5-22 575 27 28 29 30 31 32 33 3.29 584- 3.33 220 3-36 730 67 68 69 70 71 72 73 4.20 469 4-21951 4.23 411 107 108 109 110 III 112 "3 4-67 283 4.68 213 4-69 135 147 148 149 150 151 152 153 4-99 043 4-99 721 5-00 395 187 188 189 190 191 192 193 5-23111 5-23 644 5.24175 3.40 120 4-24 850 4.70048 5.01 064 5-24 702 3-43 399 3.46574 3.49 651 4.26 268 4.27 667 4.29 046 4-70953 4-71 850 4-72 739 5-01 728 5.02 388 5-03 044 5-25 227 5.25 750 5.26 269 34 35 36 3-52 636 3-55 53§ 3-58352 74 75 76 4.30 407 4-31-749 4-33 073 114 115 116 4.73 620 4-74 493 4-75 359 154 155 156 5-03 695 5-04 343 5.04 986 194 195 196 5.26 786 5.27 300 5.27 811 37 38 39 40 3.61 092 3-63 759 3.66356 77 78 79 80 4-34381 4-35 671 4-36 945 117 118 119 120 4.76217 4.77068 4.77912 157 158 159 160 5.05 625 5.06 260 5.06 890 197 198 199 200 5.28 320 5.28 827 5-29 330 3.68888 4.38 203 4.78 749 5-07 517 5.29832 23 II TABLE OF ADDITION AND SUBTRACTION LOGARITHMS FOE THE CALCULATION OF THE LOGARITHMS OF THE SUM AND DirFEEENCE 0¥ TWO NUMBERS WHOSE LOGARITHMS ARE GIVEN. 24 ADDITION. B 6 8 9 r p 0.00 OI 02 03 04 05 06 07 08 09 0.10 11 12 13 14 15 16 17 18 19 0.20 0.30 103 053 003 ^.953 *903 :854 .804 *754 *705 *655 o.2g 606 115 0.2S 629 149 0.27675 207 0.26 744 287 0.25 836 22 23 24 25 26 27 28 29 0.30 31 32 33 34 3-5 36 37 38 39 0.40 41 42 43 44 45 46 47 48 49 0.50 556 066 581 lOI 628 160 698 242 791 507 017 532 054 581 114 652 196 746 458 ,968 484 006 534 067 606 151 701 409 »920 436 »959 487 021 560 106 657 359 »87i 388 *9" 440 »974 515 061 612 310 ,822 340 *864 393 »928 469 016 568 261 *774 292 .817 346 ,882 423 »97o 523 212 163 #726 *677 245 197 *769 *722 300 253 *H36 *790 378 332 *926 *88i 479 434 390 346 302 258 214 170 126 082 038 *994 0.24 950 516 080 0.23 665 247 0.22 836 430 02g 0.21 634 907 473 045 623 206 795 389 f98? 595 863 430 003 581 165 754 349 *949 556 819 387 *96o 539 123 713 309 *9io 516 .776 344 #918 497 082 673 269 ^870 477 733 301 »875 455 041 632 229 ^831 438 689 258 *833 414 000 591 189 *79i 399 646 216 *79i 372 *959 551 149 ^752 361 603 173 .749 330 *9l8 510 log *7I2 322 559 130 t707 2S9 f877 470 069 f673 283 244 206 167 128 090 052 013 *975 *937 21 D.20860 481 108 0.19 740 378 020 0.18 668 322 0.17980 822 444 071 704 342 *985 633 287 946 784 406 034 667 306 *949 599 253 912 746 369 *997 631 270 *9i4 564 218 878 708 331 ♦960 595 234 *879 529 184 845 670 294 1*923 558 198 *844 494 150 811 632 257 *887 522 163 *8o8 460 116 777 594 220 »850 486 127 *773 425 082 744 557 182 *8i3 450 091 .738 390 048 710 519 145 *777 414 056 *703 356 014 677 643 610 577 544 510 477 444 411 378 345 312 0.16 986 665 349 037 10.15 731 430 133 0.14 841 279 954 633 317 007 701 400 104 812 247 g2i 601 286 t976 670 370 074 783 214 88g 56g 255 *945 640 340 045 755 181 857 538 224 *9i4 610 310 016 726 148 825 506 192 ^884 580 281 *986 697 116 793 474 161 *853 550 251 *957 668 083 761 443 130 .822 520 221 *928 640 051 729 411 oog t792 489 192 ,899 611 018 697 380 068 J6i 460 162 ,870 583 554 526 497 469 441 412 384 356 328 300 272 0.13 994 721 452 188 0.12928 673 422 175 244 966 694 425 162 903 648 397 151 216 939 667, 399 136 877 622 372 127 188 gii 640 372 no 851 597 .348 102 160 884 613 346 084 826 572 323 078 132 857 586 319 058 800 547 2g8 054 104 829 559 293 032 775 522 274 030 077 802 532 267 006 749 497 249 005 049 775 505 240 .980 724 472 224 ,981 021 748 479 214 *954 698 447 200 «957 0.11933I 909 885 861 837 814 790 766 742 B 719 50 49 48 5.0 4-9 4.8 1 0.0 g.8 9.6 15.0 14-7 14.4 20.0 19.6 ig.2 25.0 24.5 24.0 30.0 29.4 28.8 35-0 34.3 33-6 40.0 39-2 38.4 45-0 44.1 43-2 46 45 44 4.6 4-5 4.4 9-2 9.0 8.8 13.8 13-5 13.2 18.4 18.0 17.6 23.0 22.5 22.0 27.6 27.0 26.4 32.2 31-5 30.8 36.8 36.0, 35-2 41.4 40.5 39.6 42 41 40 4.2 8.4 4.1 8.2 4.0 8.0 12.6 16.8 12.3 16.4 12.0 16.0 21.0 20.5 20.0 25.2 29.4 33.6 37.8 24.6 28.7 32.8 36.9 24.0 28.0 32.0 36.0 38 37 36 3.8 3-7 3.6 7-6 7-4 7.2 11.4 II. I 10.8 15-2 14.8 144 ig.o 18.5 18.0 22.8 22,2 21.6 26.6 25.9 25.2 30.4 29.6 28.8 34-2 33.3 32.4 34 33 32 3-4 6.8 3.3 6.6 3-2 6.4 10.2 13.6 17.0 9.9 13-2 16.5 9.6 12.8 16.0 20.4 23.8 27.2 30.6 19.8 23.1 26.4 29.7 19.2 22.4 25.6 28.8 p p a>b, A — loga~logb, ]s>g{a + b)=\og a + B. 25 ADDITION. 0.50 51 52 53 54 55 56 57 58 59 0.60 61 62 63 64 65 66 67 68 69 0.70 0.1 1 933 695 461 231 005 o.io 783 565 351 141 0.09 935 77 78 79 0.80 B 732 533 338 146 0.08 958 774 592 415 240 069 0.07 901 909 671 438 208 ^983 761 544 330 120 914 712 514 319 127 940 755 574 397 223 052 736 575, 416 261 108 76 |o.o6 959 812 668 527 81 82 83 84 85 86 87 88 89 0.90 91 . 92 93 94 95 96 97 98 99 1.00 254 121 0.05 991 863 738 616 496 378 263 389 150 039 0.04931 824 720 618 519 421 32f- 231 884 720 559 400 245 093 944 798 654 513 648 415 186 #960 739 522 309 100 894 692 494 299 io8 921 737 557 379 206 035 861 624 392 163 t938 718 501 288 079 874 672 868 376 240 108 978 851 726 604 484 366 251 139 139 028 920 814 710 608 509 411 315 222 130 121 704 543 385 230 078 929 783 640 500 362 227 095 965 838 714 591 472 355 240 127 017 909 803 700 598 499 401 306 213 474 280 090 902 719 539 362 188 018 851 687 671 527 369 215 063 914 769 626 486 837 601 368 140 jt9i6 696 479 267 058 853 814 652 455 261 071 884 701 521 344 171 00 1 435 242 052 865 683 503 327 154 *985 835 348 214 082 952 825 701 579 460 343 229 116 006 898 793 689 588 489 392 297 203 511 354 199 048 900 754 6i2 472 335 200 069 939 8i3 689 567 448 332 217 577 345 118 .894 674 458 246 038 833 632 81S 655 495 338 184 033 885 740 597 458 790 554 323 095 ^872 652 437 225 017 813 531 300 073 *849 630 415 204 .996 793 612 416 223 033 847 664 485 309 137 *968 802 321 105 *995 888 782 679 578 479 382 287 194 112 103. 187 056 927 800 677 555 436 320 206 094 ♦985 877 772 669 568 469 373 278 185 639 479 322 169 018 870 725 583 444 766 742 507 277 050 *827 609 394 183 *976 773 593 396 204 014 829 646 468 292 120 *95l 785 308 174 043 914 788 664 543 425 308 195 083 *974 867 762 659 558 460 363 268 176 094 085 623 463 307 154 003 856 711 569 430 573 377 184 f996 810 628 450 275 103 :934 769 7^9 484 254 028 *8o5 587 373 162 *955 752 553 357 165 *977 792 610 432 257 086 *9i8 294 161 030 901 775 652 531 413 297 183 072 *963 856 751 .649 548 450 353 259 167 076 607 448 291 138 ^988 841 697 555 417 281 147 017 889 763 640 519 401 286 172 061 «952 845 741 639 538 440 344 250 157 067 753 591 432 276 123 *973 827 683 541 403 P P 267 134 004 876 751 628 508 390 274 i6t 050 *94i 835 731 628 528 430 334 240 ■148 058 30 29 28 3-0 2.9 2.8 6.0 5-8 5.6 9.0 8.7 8.4 12.0 11.6 II.2 15.0 14-5 14.0 18.0 17-4 16.8 21.0 20.3 19.6 24.0 23.2 22.4 27.0 26.1 25.2 26 25 24 2.6 2.5 2.4 5-2 5.0 4.8 7.8 7-5 7-2 10.4 1 0.0 9.6 13.0 12.5 12.0 iS.b I5-0 14.4 18.2 17-5 16.8 20.8 20.0 iq.2 23-4 22.5 21.6 22 21 19, 2.2 2.1 i.q 4-4 4.2 3.8 6.6 b-3 5-7 8.8 8.4 7.6 II.O 10.5 9-5 13.2 12.6 11.4 15-4 14-7 13.3 17.6 1 6.8 15-2 19.8 18.9 17.1 17 16 15 1-7 1.6 1-5 3-4 3-2 3-0 5.1 4.8 4-5 6.8 6.4 6.0 8.5 8.0 7-5 10.2 9,6 9.0 1 1.9 n.2 10.5 13.6 12.8 12.0 15-3 14-4 13-5 13 12 11 1-3 1.2 I.I 2.6 2.4 2.2 3.9 3-6 3-3 5.2 4.8 4-4 6-5 6.0 5-5 7.8 7.2 6.6 9.1 8.4 7-7 10.4 9.6 8.8 II. 7 10.8 9.9 B 1 P P a>&, A—loga — log &, log {a-\-b)=loga-\-B. ADDITION. A B 1 2 3 4 5 6 7 8 9 P P 1.00 OI 0.04 139 130 121 112 103 094 085 076 067 058 049 040 032 023 014 005 *996 *987 *979 *970 9 02 0.03 g6i 953 944 935 926 918 909 901 892 883 I 2 3 4 1.8 2.7 3-6 03 875 866 858 849 841 832 824 816 807 799 04 790 782 774 765 757 749 741 732 724 716 05 708 700 691 683 675 667 659 651 643 635 5 4-5 06 627 619 611 603 595 5S7 579 571 563 555 6 5-4 07 548 540 532 524 516 509 501 493 485 478^ 7 6.3 08 470 462 455 447 439 432 424 417 409 401 8 7.2 og 1.10 II 394 3 36 379 371 364 357 349 342 334 327 9 8.1 320 312 305 298 290 283 276 268 261 254 247 240 232 225 218 211 204 197 190 183 8 7 12 175 168 161 154 147 140 133 126 120 113 I 0.8 0.7 13 106 099 092 085 078 071 065 058 051 044 2 1.6 1-4 14 037 031 024 017 on 004 *997 »99i *984 *977 3 4 5 6 2.4 3.2 4.0 4.8 2.1 2.8 15 0.02 971 964 957 951 944 938 931 925 918 912 3-5 4.2 16 905 899 892 886 879 873 867 860 854 848 17 841 835 829 822 816 8x0 803 797 791 785 7 5-6 4.8 18 779 772 766 760 754 748 742 735 729 723 8 6.4 5.6 19 1.20 21- 717 711 705 699 693 687 681 675 669 663 9 7-2 6-3 657 651 645 639 634 628 622 616 610 604 6 599 593 587 581 575 570 564 558 552 547 22 541 535 530 524 518 513 507 502 496 490 [ o.b 23 485 479 474 468 463 457 452 446 441 435 2 1.2 1.8 24 430 424 419 414 408 403 397 392 387 3S1 3 25 376 37^ 365 360 355 350 344 339 334 329 4 2.4 26 323 318 313 308 303 297 292 287 282 277 5 6 3.0 3.6 4.2 27 272 267 262 257 252 246 241 236 231 226 7 28 221 216 211 207 202 197 192 187 182 177 8 4.8 29 1.30 31 172 167 162 158' 153 148 143 138 133 129 9 5-4 124 119 114 110 105 100 095 091 086 o8i 077 072 067 063 058 053 049 044 040 035 5 4 32 030 026 021 017 012 008 003 *999 *994 *99'J I 0.5 0.4 33 o.oi 9S5 981 976 972 967 9&3 959 954 950 945 2 1.0 0.8 34 941 937 932 928 924 919 915 911 906 902 3 1-5 1.2 35 898 894 889 885 881 877 872 868 864 860 4 2.0 1.6 36 856 851 847 843 839 835 831 827 822 818 5 6 7 8 2.5 2.0 37 814 810 806 802 798 794 790 786 782 778 3-0 3-5 40 4.'; 2.4 2.8 38 774 770 766 762 758 754 750 746 742 738 3-2 3.6 39 1.40 41 734 730 726 722 719 715 711 707 703 699 9 695 692 688 684 680 676 673 669 665 661 3 658 654 650 646 643 639 635 632 628 624 42 621 617 613 6io 606 602 599 595 591 588 I 0.3 43 584 581 577 574 570 566 563 559 556 552 2 0.6 44 549 545 542 538 535 531 528 525 521 518 3 0.9 45 514 511 507 504 501 497 494 490 487 484 4 1.2 46 4S0 477 474 470 467 464 460 457 454 450 5 1.5 47 447 444 441 437 .434 431 428 424 421 418 6 1.8 48 415 412 408 405 402 399 396 393 389 386 7 8 Q 2.1 49 1.50 383 380 377 374 371 368 364 361 358 355 2.4 5.-7 0.01 352 349 346 343 340 337 334 331 328 325 V 1 — ' A E 1 2 3 4 5 6 7 8 9 p p a>6, A — log a — log 6 log(a + 6 ) = loga + £. 27 ADDITION. A B 1 2 3 4 5 6 7 8 9 P P 1.50 51 0.01 352 349 346 343 340 337 334 331 328 325 322 319 316 313 310 307 304 301 298 295 52 292 289 286 283 280 278 275 272 269 266 53 263 260 257 255 252 249 246 243 240 238 54 235 232 229 226 224 221 2l8 215 213 210 55 207 204 202 199 196 193 191 188 185 183 56 180 177 175 172 169 167 164 161 159 156 57 153 151 148 146 143 140 138 135 133 130 58 128 125 122 120 117 115 112 no 107 105 59 1.60 6i 102 100 097 095 092 090 087 085 082 080 • o.oi 077 075 073 070 068 065 063 060 058 056 053 051 048 046 044 041 039 037 034 032 62 030 027 025 022 020 018 016 013 on 009 63 006 004 002 *999 *997 *995 «993 »990 *988 ,986 64 0.00 984 981 979 977 975 973 970 968 966 964 65 962 959 957 955 953 951 948 946 944 942 66 940 938 936 933 931 929 927 925 923 921 67 919 917 915 912 910 908 906 904 902 900 a 68 898 896 894 892 890 888 886 884 882 880 69 1.70 71 878 876 -874 872 870 868 866 864 862 860 I 2 3 4 5 0-3 0.6 0.9 1.2 1-5 0.00 858 856 854 852 850 848 846 844 842 841 839 837 835 833 831 829 827 825 823 822 72 820 818 8i6 814 812 810 809 807 805 803 6 1.8 73 801 799 798 796 794 792 790 789 787 785 7 2.1 74 783 781 780 778 776 774 773 771 769 767 8 2.4 75 766 764 762 760 759 757 755 753 752 750 9 2.7 76 748 747 745 , 743 741 740 738 736 735 733 77 731 730 728 726 725 723 721 720 718. 716 78 715 713 712 710 708 707 705 703 702 700 79 1.80 81 699 697 696 694 692 691 689 688 686 684 0.00 683 681 680 678 677 675 674 672 671 669 667 666 664 663 661 660 658 657 655 654 82 652 651 649 648 646 645 644 642 641 639 83 638 636 635- 633 632 630 629 628 626 625 84 623 622 620 619 618 616 615 613 612 611 85 6og 608 606 605 604 602 601 599 598 597 86 595 594 593 591 590 589 587 586 585 583 87 582 581 579 578 577 575 574 573 571 ■■ 570 88 569 567 566 565 564 562 561 560 558 557 89 1.90 91 556 555 553 . 552 551 550 548 547 546 545 0.00 543 542 541 540 538 537 536 535 533 532 531 530 529 527 526 525 524 523 521 520 92 519 518 517 515 514 513 512 511 510 508 93 507 506 5Q5 504 503 502 500 499 498 497 94 496 495 494 492 491 490 489 488 487 486 95 485 483 482 481 480 479 478 477 476 475 96 474 473 471 470 469 468 467 466 465 464 97 463 462 461 460 459 458 457 456 454 453 98 452 451 450 449 448 447 446 445 444 443 99 2.00 442 441 440 439 438 437 436 435 434 433 3.00 432 431 430 429 428 427 426 425 424 423 ABO 1 .2 3 4 1 5 6 7 8 9 P P a>6, A=\oga — log 6, log (a + 6) =loga + .B. ADDITION. A B 1 2 3 4 5 6 7 8 9 P P I 2.0 I 0.00432 422 413 403 394 385 377 368 360 352 9 8 0.8 344 336 328 321 313 306 299 293 286 280 I 0.9 2 273 267 261 25.? 249 244 238 233 227 222 2 1.8 1.6 3 217 212 207 203 198 194 189 185 181 177 3 2.7 3-6 4-5 2.4 4 173 169 165 161 157 154 150 147 144 140 4 5 6 7 8 3-2 4.0 4.8 5.6 6.4 5 137 1.34 131 128 iz.-; 122 liq 117 114 in 6 109 106 104 102 099 097 095 093 091 089 5-4 6.3 7.2 7 087 085 083 081 079 077 075 074 072 070 « 069 067 066 064 063 061 060 059 057 056 g 8.T ■7.2 9 3.0 ' I 055 053 052 051 050 049 "048 047 045 044 9, .. 1 0.00 043 042 041 041 040 039 038 037 036 035 7 r 6 0.6 5 0.5 034 034 033 032 031 031 030 029 029 028 I 0.7 2 027 027 026 026 025 024 024 023 023 022 2 1-4 1.2 I.O 3 022 021 021 020 020 019 019 019 018 018 3 2.1 1.8 1-5 4 017 017 017 016 016 015 015 01 .S 014 014 4 2.8 2.4 2.0 5 014 013 013 013 013 012 OI2 012 on on 5 3-5 3-0 2.S 6 oil on 010 010 010 010 010 009 009 009 6 4.2 3.b 3.0 7 009 008 008 008 008 008 008 007 007 007 7 8 4.9 4.2 4.8 3-5 8 007 007 007 006 006 006 006 006 006 006 6-3 4.0 9 4.0 I 005 005 005 005 005 005 005- 005 005 004 9 S-4 4-5 0.00 004 004 004 004 004 004 004 004 004 004 003 003 003 003 003 003 003 003 003 003. 0.4 0.3 0.6 2 003 003 003 003 002 002 002 002 002 002 3 002 002 002 002 002 002 002 002 002 002 3 4 1.2 0.9 1.2 4 002 002 002 002 002 002 002 001 001 001 1.6 5 001 001 001 001 001 001 001 001 001 001 5 2.0 1-5 6 001 001 001 001 001 001 001 001 001 001 6 2.4 1.8 7 001 001 001 001 001 001 001 001 001 001 7 2.8 2.1 » 001 001 001 001 001 001 001 001 001 001 8 3.2 2.4 9 5.0 001 001 001 001 000 000 000 000 000 000 9 3.6 2.7 0.00 000 000 000 000 000 000 000 000 000 000 A B 1 2 3 4 5 6 7 8 9 P P a>b ) A = log 'a— log&, log (a + &) = loga + B. The abo re ta jle of Adc ition Logarithms is base i on the identity log (a + 6) = loga(l + -^ -) N = loga + log| 1 + - 1) The argi imen t A is log — , and the function B h log , a ], conse- quently 1< Dg(a + 6) = loga + B. Z'd SUBTRACTION. A B 1 2 3 4 5 6 7 8 9 P P 0.300 301 302 303 0.30 206 196 186 176 166 156 146 136 126 116 106 006 a.29 907 096 *996 897 0S6 *986 887 076 *976 S77 066 *966 867 056 if956 ^857 046 *947 848 036 *937 838 026 »927 828 016 *9i7 818 304 305 306 808 710 6l2 798 700 602 788 690 592 778 680 582 769 670 573- 759 661 563 749 651 553 739 641 543 729 631 534 719 621 524 307 308 309 0.310 3" 312 313 514 417 320 504 407 3H 495 398 301 485 388 291 475 378 282 465 369 272 456 359 263 446 349 253 436 340 243 427 330 234 224 215 205 195 186 17b 167 157 147 138 128 033 0.28938 119 024 929 109 014 919 100 005 910 090 *995 900 081 ^986 891 071 *976 881 062 *9f>7 872 052 *957 862 043 *948 853 I 9 0.9 314 315 316 844 750 656 834 740 647 825 731 637 8t5 721 628 806 712 619 797 703 609 787 693 600 778 684 591 768 675 581 759 665 572 2 3 4 1.8 2.7 3-6 317 318 319 0.320 321 '322 323 563 470 377 553 461 368 544 451 359 535 442 350 525 433 341 516 424 331 507 414 322 498 405 313 488 396 304 479 387 295 5 6 7 8 Q 4-5 5-4 6.3 7-2 R.T 285 276 267 258 249 240 230 221 212 203 194 103 012 185 094 003 176 064 *994 166 075 *985 157 066 *976 148 057 !f967 139 048 *958 130 039 *948 I2f 030 *939 112 021 *930 324 325 326 0.27921 831 742 912 822 733 903 813 724 894 804 715 885 796 706 876 787 697 867 778 688 858 769 679 849 760 670 840 751 661 327 328 329 0.330 331 332 333 653 564 475 644 555 466 635 546 458 626 537 449 617 528 440 608 519 431 599 5" 422 590 502 414 581 493 405 573 484 396 387 378 370 361 352 343 335 326 317 308 300 212 125 291 204, 117 2S2 195 108 273 1 86 099 265 177 091 256 169 082 247 160 073 238 151 065 230 143 056 221 134 047 I 2 8 0.8 1.6 334 335 336 039 0.26953 867 030 944 858 021 935 850 013 927 S41 004 918 832 k996 910 824 *987 go I 815 *978 892 807 *970 8S4 798 ^96 1 875 790 3 4 5 2.4 3-2 4.0 337 338 339 0.340 341 342 343 781 696 611 773 688 603 764 679 595 756 671 586 747 662 578 739 654 569 730 645 561 722 637 552 713 628 544 705 620 535 6 7 8 9 4.8 5.6 6.4 7.2 527 519 510 502 493 485 477 468 460 451 443 359 276 435 351 268 426 343 259 418 334 251 410 326 243 401 318 235 393 309 226 384 301 218 376 293 210 368 284 201 344 345 346 193 III • 028 185 102 020 177 094 012 168 086 004 160 078 *995 152 069 *987 144 061 *979 135 053 *97I 127 045 #963 119 036 *955 347 348 349 0.350 0.25 946 865 784 938 857 775 930 849 _767_ 687 922 840 678 914 832 751 906 824 743 897 816 735 8S9 808 727 8Si 800 719 873 792 7" 0.25 703 695 670 662 654 646 638 630 A B 1 2 3 4 5 6 7 8 9 P P It X>.i It x< .i , 1 I > 6 hen hen Put £B = log a — log 6. x = A and log (a — 6) =Ioga — 5. x=B and log (a— 6) = loga— 4. 30 s UBTRAC1 noN. A B 1 2 3 4 5 6 7 8 9 r p 0.350 351 352 353 0.25 703 695 687 678 670 662 654 646 638 630 622 542 462 614 534 454 606 526 446 598 518 438 590 510 430 582 502 422 574 494 414 566 486 406 558 478 398 550 470 390 354 355 356 382 303 224 374 295 216 367 287 209 359 279 201 351 272 193 343 264 185 335 256 177 327 248 169 319 240 161 3" 232 154 I 2 9 0.9 1.8 357 358 359 0.360 361 362 363 146 067 0.24989 138 060 983 130 052 974 122 044 966 114 036 958 106 028 951 099 021 943 091 013 935 083 005 927 075 *997 920 3 4 5 6 7 8 9 2.7 3.6 4-5 5-4 6.3 7.2 8.1 912 904 896 889 881 873 865 858 850 842 835 758 681 827 750 673 819 742 666 811 734 658 804 727 650 796 719 643 788 711 635 781 704 627 773 696 620 765 688 612 364 365 366 604 528 453 597 521 445 589 513 438 582 506 430 574 498 422 566 490 415 559 483 407 551 475 400 544 468 392 536 460 385" 8 367 368 369 0.370 371 372 373 377 302 227 370 295 220 362 287 212 355 280 205 347 272 197 340 265 190 332 257 182 325 250 175 317 242 168 310 235 160 2 3 4 5 6 7 8 9 1.6 2.4 3-2 4.0 4.8 5.6 6.4 7-2 153 145 138 130 123 116 108 lOI 093 086 078 004 0.23 931 071 *997 923 064 *990 916 056 ♦982 gog 049 *975 901 041 *968 894 034 *96o 887 027 *953 879 019 *946 872 012 *938 865 374 375 376 857 784 712 850 777 704 843 770 697 836 763 690 828 755 683 821 748 675 814 741 668 806 733 661 799 726 654 792 719 646 377 378 379 0.380 381 382 383 639 567 495 632 560 488 625 553 481 617 545 474 610 538 466 603 531 459 596 524 452 589 517 445 581 509 438 574 502 431 I 2 3 4 5 6 7 7 0.7 1.4 2.1 2.8 3-5 4.2 4.9 423 416 409 402 395 388 381 373 366 359 352 281 210 345 274 203 338 267 1 96 331 260 189 324 253 182 317 246 175 309 238 168 302 231 161 295 224 154 288 217 147 384 385 386 140 069 000 133 062 *993 126 055 *986 119 048 *979 112 041- *972 105 034 1=965 098 027 *958 091 020 *95i 083 013 «944 076 006 *937 8 9 5.6 6.3 387 388 389 0.390 391 392 393 0.22 930 860 791 923 853 784 916 847 777 909 840 771 902 833 764 895 826 757 888 819 750 881 812 743 874 805 736 867 7q8 729 6 722 716 709 702 695 688 681 674 667 661 I 2 3 4 5 0.6 1.2 1.8 2.4 3-0 654 585 517 647 579 511 640 572 504 633 565 497 626 558 490 620 551 483 613 545 477 606 538 470 599 531 463 592 524 456 394 395 396 450 382 315 443 375 308 436 369 301 429 362 295 422 355 288 416 348 281 409 342 274 402 335 268 395 328 261 389 321 254 6 7 8 3.6 4.2 4.8 397 398 399 0.400 248 i8i 114 241 174 108 234 168 lOI 228 161 094 221 154 088 214 148 081 208 141 075 201 134 068 194 128 061 188 121 055 9 54 0.22048 041 035 028 022 015 008 002 *995 #989 A B 1 2 3 4 5 6 7 8 9 P P If a? > . 3 If !r<.3 t t a>b. I len X = len X = A B = log a — and lo and lo log 6. «(a-b) = g(a — b) = log a — B. log a — A. ai SUBTRAC1 noN. A B 1 2 3 4 5 6 7 1 8 9 P P 0.400 401 402 403 0.22 048 041 035 028 022 015 ooS 002 *995 *989 Q.2I 982 916 851 975 910 844 969 903 838 962 897 831 956 890 825 949 884 818 943 877 812 936 870 805 929 864 799 923 857 792 404 405 406 786 721 656 779 714 649 772 708 643 766 701 636 759 695 630 753 688 623 746 682 617 740 675 6n 733 669 604 727 662 598 407 408 409 0.410 411 412 413 591 527 463 585- 521 456 578 514 450 572 508 444 565 501 437 559 495 431 553 488 425 546 482 418 540 476 412 533 469 405' I 2 3 4 5 6 7 7 0.7 1.4 2.1 2.8 3-5 4.2 4.9 399 393 386 380 374 367 361 355 348 342 336 272 209 329 266 203 323 260 197 317 253 190 310 247 184 304 241 178 298 234 171 291 228 165 285 222 159 279 215 153 414 415 416 146 084 021 140 077 015 134 071 009 127 065 003 121 059 *996 115 052 !t990 109 046 *984 102 040 *978 096 034 *972 090 028 #965 8 9 5.6 6.3 417 418 419 0.420 421 422 423 0.20 959 897 836 953 891 829 947 885 823 941 879 817 934 873 811 928 866 805 922 860 799 916 854 793 910 848 786 903 842 780 774 768 762 756 750 743 737 731 725 719 713 652 591 707 646 585 701 640 579 695 634 573 688 628 567 682 621 561 676 615 555 670 609 549 664 603 543 658 597 537 I 6 0.6 424 425 426 531 470 410 525 464 404 5i8 458 398 512 452 392 506 446 386 500 440 380 494 434 374 488 428 368 482 422 362 476 416 356 2 3 4 1.2 1.8 2.4 427 428 429 0.430 431 432 433 350 291 231 344 285- 225 338 279 219 332 273 213 326 267 207 320 261 201 314 255 196 308 249 190 302 243 184 297 237 178 5 6 7 8 9 3-0 3-6 4.2 4-8 5-4 172 166 160 154 148 142 136 131 125 119 113 054 0.19 996 107 048 990 lOI 042 984 095 037 978 089 031 972 083 025 966 078 019 960 072 013 955 066 007 949 060 001 943 434 435 436 937 879 821 931 873 815 926 867 809 920 862 804 914 856 798 908 850 792 g02 844 786 896 838 781 891 833 775 885 827 769 I 5 0.5 437 438 439 0.440 441 442 443 763 706 648 758 700 643 752 694 637 746 689 631 740 683 626 735 677 620 729 671 614 723 666 608 717 660 603 712 654 597 2 3 4 5 6 7 8 9 I.O 1-5 2.0 2.5 3-0 3-5 4.0 4-5 591 586 580 574 569 563 557 552 546 540 534 478 421 529 472 416 523 466 410 517 461 404 512 455 399 506 450 393 500 444 387 495 438 382 489 433 376 483 427 371 444 445 446 365 309 253 359 303 247 354 298 242 348 292 236 343 297 231 337 281 225 331 275 220 326 270 214 320 264 208 315 259 203 447 448 449 0.450 197 142 087 192 136 081 186 131 076 181 125 070 175 120 064 170 114 059 164 109 053 158 103 048 153 098 042 147 092 037 0.19 031 026 020 015 009 004 *999 *993 *988 *982 A B 1 2 3 4 5 6 7 8 9 P P a>b. Put a If a; > . 3, then x=A It x< .S, then x-B an( an 1 a — log 6. I \og{a—b) = \oga — B. i log(a—b) = \oga — A. 32 SUBTRACTION. A B 1 2 3 4 5 6 7 1 8 1 9 P P 0.450 451 452 453 3.19031 026 020 015 009 004 »999 «993 *988 *982 0.18977 922 867 971 916 862 966 911 856 960 905 851 955 900 846 949 895 840 944 889 835- 938 884 829 933 878 824 927 873 818 454 455 456 813 759 705 808 754 700 802 748 694 797 743 689 791 737 683 786 732 678 781 727 673 775 721 667 770 716 662 764 710 657 6 457 458 459 0.460 461 462. 463 651 598 544 646 592 539 641 .587 534 635 582 528 630 576 523 624 571 518 619 566 512 614 560- 507 608 555 502 603 550 496 I 2 3 4 5 6 7 8 0.6 1.2 1.8 2.4 3-0 3-6 4.2 4.8 491 486 481 475 470 465 459 454 449 443 438 385 333 433 380 328 428 375 322 422 370 317 417 364 312 412 359 307 406 354 301 401 349 296 396 343 291 391 338 286 464 465 466 280 228 176 275 223 171 270 218 166 265 212 160 259 207 155 254 202 150^ 249 197 145 244 192 140 239 186 135 233 181 129 9 5-4 467 468 469 0.470 47i 472 473 124 072 021 119 067 016 114 062 on 109 057 006 103 052 000 098 047 »995 093 042 *990 088 036 *985 083 031 *98o 078 026 *975 Q.17970 964 959 954 949 944 939 934 929 924 918 867 817 913 862 812 908 857 807 903 852 801 898 847 796 893 842 791 888 837 786 883 832 781 878 827 776 873 822 771 I 2 3 4 5 6 0.5 I.O 1.5 2.0 2.5 3-0 474 475 476 766 716 665 761 711 660 756 706 655 751 700 650 746 695 645 741 690 640 736 685 635 731 680 630 726 675 625 721 670 620 477 478 479 0.480 481 482 483 615 565 515 610 560 5" 605 555 506 600 550 501 595 545 496 590 540 491 585 535 486 580 530 481 575 525 476 570 520 471 7 8 9 3-5 4.0 4.5 466 461 456 451 446 441 436 431 426 421 416 367 318 412 ,362 313 407 357 308 402 352 303 397 348 299 392 343 294 387 338 289 382 333 284 377 328 279 372 323 274 484 485 486 269 220 172 264 216 167 259 211 162 255 206 157 250 201 153 245 196 148 240 191 143 235 186 138 230 182 133 325 177 128 4 487 488 489 0.490 49: 492 493 123 075 027 119 070 022 114 066 018 109 06 1 013 104 056 008 099 051 003 095 046 *998 090 042 *994 085 037 «989 080 032 #984 I 2 3 4 5 6 7 8 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3-2 0.16979 974 970 965 960 955 951 946 941 936 931 884 836 927 879 832 922 874 827 917 870 822 912 865 818 908 860 813 903 855 808 898 851 803 893 846 799 889 841 794 494 495 496 789 742 695 784 737 690 780 733 686 775 728 681 770 723 676 766 719 672 761 714 667 756 709 662 751 704 658 747 700 653 9 3-6 . 497 498 499 0.500 648 602 555 644 597 551 639 592 546 634 588 541 630 583 537 625 578 532 620 574 527 616 569 523 611 564 518 472 606 560 513 0.16 509 504 500 495 490 486 481 477 467 A B 1 2 3 4 5 6 7 8 9 P P If: If: 0.3, 1 c<.3, a>b then ;hen Put 33 = log a — log 6. x = A and log (a — 6) = logo— -B. X = J3 and log (a — 6) = loga — A. 33 SUBTRACTION. B P P 0.50 51 52 53 54 55 56 57 58 59 0.60 6i 62 63 64 65 66 67 68 69 0.70 0.16 509 463 417 054 0.15 614 189 0.14777 378 0.13 992 617 255 0.12 903 009 571 147 736 339 954 581 219 860 371 325 563 529 232 o.ii 912 6oi 299 007 o.io 722 446 178 0.09 918 200 880 571 270 ■978 694 419 152 893 665 640 74 75 76 77 78 79 0.80 420 181 73 0.08 949 723 504 2go 083 0.07 881 685 81 82 83 84 85 86 87 0.90 91 92 93 94 95 96 97 98 99 1.00 395 157 926 701 482 269 063 861 666 494 308 127 0.06 951 780 614 451 293 139 0.05 989 844 701 563 428 297 169 044 0.04 922 804 688 475 290 no 934 763 597 435 278 124 975 829 0.04 576 687 549 415 284 156 032 910 792 677 528 105 696 3Q0 916 544 184 834 *92i 485 064 656 261 878 507 148 800 496 463 168 849 540 240 *949 667 392 126 867 135 818 510 211 #921 639 365 100 842 616 591 371 134 903 679 461 248 042 842 646 456 272 092 917 747 581 419 262 109 960 ii5 565 673 536 401 271 143 019 898 780 666 554 347 no 880 657 439 228 022 822 627 438 253 074 900 730 564 403 247 094 945 800 659 522 388 258 131 007 886 769 654 280 234 144 099 ,876 442 022 616 222 840 471 113 766 ,832 400 ,981 576 183 803 435 078 732 *788 357 *940 536 145 766 398 043 698 t745 315 ^899 496 106 728 362 008 664 .701 273 *858 457 068 691 326 *973 630 t057 230 ^817 417 030 654 291 *938 596 429 396 363 330 265 103 786 479 181 *892 611 338 073 8i6 071 755 449 152 *864 583 312 047 791 039 724 419 123 ^835 556 285 021 766 007 693 389 094 *8o7 528 258 ■995 740 *975 663 359 065 ■779 501 231 *970 715 *944 632 329 036 *750 474 205 *944 690 566 323 087 858 635 418 207 002 802 608 419 235 056 882 713 548 387 231 079 931 786 543 646 509 375 245 118 .995 874 757 643 542 517 493 468 444 299 064 835 613 396 186 .981 782 589 401 217 039 865 696 532 372 216 064 916 772 632 495 362 232 106 :983 863 746 632 275 041 8i3 591 375 165 .961 763 570 252 018 790 569 354 145 h94i 743 551 228 *995 768 547 333 124 *92I 724 532 204 *972 745 525 3" 103 *90i 704 513 382 363 345 199 021 848 680 516 356 200 049 901 181 004 831 663 499 340 185 034 163 ,986 814 647 483 324 170 019 872 758 744 730 618 482 349 219 093 f970 851 734 620 604 468 336 590 455 323 207 194 081 069 :958 839 723 609 532 521 I 510 499 *946 827 711 598 488 477 327 145 i.969 797 630 467 309 155 004 858 715 577 441 310 181 056 *934 815 700 587 46 45 44 4.6 4-5 4-4 g.2 9.0 8.8 I3.8 13-5 13.2 18.4 18.0 17.6 23.0 22.5 22.0 27.6 27.0 26.4 32.2 31-5 30.8 36.8 36.0 35-2 41.4 40.5 1 39-6 1 42 41 40 4.2 ■8.4 4.1 8.2 4.0 8.0 12.6 16.8 12.3 16.4 12.0 16.0 21.0 20.5 20.0 25.2 29.4 33-6 37.8 24.6 28.7 32.8 36.9 24.0 28.0 32.0 36.0 38 37 36 3-8 3-7 3-6 7.6 7-4 7.2 11.4 II. I 10.8 15-2 14.8 14.4 19.0 18.5 18.0 22.8 22.2 21.6 26.6 25-9 25.2 30.4 29.6 28.8 34-2 33-3 32.4 34 33 32 3-4 3-3 3-2 6.8 6.6 6.4 10.2 9-9 9.6 13.6 13.2 12.8 17.0 16.5 16.0 20.4 19.8 19.2 23.8 23.1 22.4 27.2 26.4 25.6 30.6 29.7 28.8 30 29 28 3.0 2.9 28 6.0 5-8 =i.6 9.0 8.7 8.4 12.0 11.6 II. 2 15.0 14-5 14.0 18.0 174 16.8 21.0 20.3 19.6 24.0 23.2 22.4 27.0 26.1 25.2 B 1 4 I 5 6 8 9 P P a>b. If a? > . 3, then If aj < . 3, then Put x = loga — log 6. x~A and log(a — 6)=log'a — B. x = B and log (a — fe)=loga — A. 34 SUBTRACTION B p r 1.00 oi 02 03 04 05 06 07 08 09 1.10 II 12 13 14 15 16 17 18 19 1.20 21 22 23 24 25 26 27 28 29 1.30 31 32 33 34 35 36 37 38 39 1.40 41 42 43 44 45 46 47 48 49 1.50 0.04 576 565 554 543 532 521 510 499 488 477 466 359 255 153 054 0.03 958 863 771 682 455 349 245 143 044 948 854 762 673 444 338 234 133 035 938 845 753 664 434 328 224 123 025 929 835 744 655 423 317 214 113 015 920 826 735 647 412 307 204 103 006 910 817 726 638 402 296 194 093 ^996 901 808 717 629 391 286 183 084 *986 891 799 708 620 380 275 173 074 »977 882 790 700 612 370 265 163 064 ^967 873 781 691 603 594 586 577 569 560 552 543 535 526 518 509 426 345 266 189 114 040 0.02 969 899 501 418 337 258 181 106 033 961 492 410 329 250 174 099 026 954 885 484 402 321 243 166 091 018 947 878 476 393 313 235 159 084 on 940 871 467 385 305 227 151 077 004 933 864 459 377 297 219 143 069 *997 926 858 451 369 289 212 136 062 *990 919 851 443 361 282 204 128 055 ♦983 912 844 434 353 274 196 121 047 *976 906 837 830 824 817 810 804 797 790 784 777 771 764 699 636 574 514 455 397 341 286 233 130 080 032 o.oi 985 938 893 849 806 764 723 683 644 606 569 533 497 462 429 0.01 396 B 757 693 629 568 508 449 392 336 281 228 176 125 075 027 980 934 889 845 802 760 719 679 640 602 565 529 494 459 425 392 751 686 623 562 502 443 386 330 276 744 680 617 556 496 437 380 325 270 223 217 171 120 071 022 975 929 884 841 798 166 115 066 018 971 925 880 836 794 756 752 715 675 637 599 562 525 490 456 422 711 672 633 595 558 522 487 452 419 389 386 738 674 611 550 490 432 375 319 265 731 667 605 544 484 426 369 314 260 725 661 598 538 478 420 363 308 254 718 655 592 532 472 414 358 303 249 712 648 586 526 466 409 352 297 244 705 642 580 520 461 403 347 292 238 212 160 no 061 013 966 920 876 832 789 748 707 668 629 591 554 518 483 449 415 383 207 202 196 191 186 155 105 056 008 g6l 916 871 828 785 744 703 664 625 587 551 515 480 445 412 379 150 100 051 003 957 911 867 823 781 740 699 660 621 584 547 511 476 442 409 376 145 095 046 <999 952 907 862 819 777 140 090 042 *994 948 902 858 815 773 736 695 656 618 580 543 508 473 439 405 373 6 135 085 037 »989 943 898 854 811 768 731 727 691 652 614 576 540 504 469 435 402 687 648 610 573 536 501 466 432 399 370 366 8 9 26 25 24 2.6 2.5 2.4 5.2 5.0 4.8 7.8 7-5 7.2 10.4 1 0.0 9.6 13.0 12.5 12.0 15.6 15.0 14.4 18.2 17-5 16.8 20.8 20.0 19.2 23-4 22.5 21.6 22 21 20 2.2 2.1 2.0 4-4 4.2 4.0 6.6 6.3 6.0 8.8 8.4 8.0 II.O 10.5 lO.O 13.2 12.6 12.0 154 14.7 14.0 17.6 16.8 16.0 19.8 18.9 18.0 18 17 16 1.8 1-7 1.6 3-6 ■ 3-4 3-2 5-4 5-1 4.8 7.2 6.8 6.4 9.0 8.5 8.0 10.8 10.2 9.6 12.6 11.9 11.2 14.4 13.6 12.8 16.2 15-3 14.4 14 13 12 1-4 1.3 1.2 2.8 2.6 2.4 4.2 3-9 3-» 5-6 5.2 4.8 7.0 6.5 6.0 8.4 7.8 7.2 9.8 g.l 8.4 II. 2 10.4 9.6 12.6 11.7 10.8 9 8 7 6 0.q 0.8 0.7 0.6 1.8 1.6 1.4 1.2 2.7 2.4 2.1 1.8 3-6 3.2 2.8 2.4 4-5 4.0 3-5 3.0 5-4 4.8 4.2 3-b 6.3 5.6 4.9 4.2 7.2 6.4 5.6 4.8 8.1 7-2 b.3 5.4 23 2.3 4.6 6.9 9.2 "■5 13.8 16.1 18.4 20.7 19 1.9 3-8 5-7 7.6 9-5 11.4 13-3 15.2 17.1 15 1-5 3-0 4-5 6.0- 7-5 9.0 10.5 12.0 13-5 11 I.I 2.2 3-3 4-4 5-5 6.6 7-7 8.8 9.9 5 0;5 i.o 1-5 2.0 2.5 3-0 3-5 4.0 4.5 P P a>b. Put x = loga — log6. I£a5>.3, then x = A and log(a — 6)=:loga — B. lix<.S, then x = B and log (a — 6) = log a — A. 35 SI UBTRACTION. A B 1 2 3 4 5 6 7 8 9 P P 1.50 51 o.oi 396 392 389 386 383 379 j"i_ 373 370 366 363 360 357 354 351 347 344 341 338 335 52 332 329 326 322 319 316 313 310 307 304 53 301 298 295 292 289 286 283 280 277 274 54 271 268 265 262 259 256 253 250 247 244 4 55 242 239 236 233 230 227 224 221 219 216 I 0.4 56 213 210 207 204 202 199 196 193 190 188 2 0.8 57 185 182 179 177 174 171 168 166 163 160 3 1.2 58 158 155 152 150 147 144 142 139 136 134 4 1.6 59 1.60 61 131 128 126 123 120 118 "5 113 no 107 5 6 7 8 9 2.0 2.4 2.8 3-2 3.6 O.OI 105 102 100 097 095 092 089 087 084 082 079 077 074 072 069 067 064 062 059 057 62 054 052 050 047 045 042 040 037 035 033 63 030 028 025 023 02 1 018 016 014 on 009 64 006 004 002 *999 *997 »995 »993 *990 ,988 «986 65 0.00 983 981 979 976 974 972 970 967 965 963 66 961 958 956 954 952 950 947 945 943 941 67 939 936 934 932 930 928 926 923 921 919 68 917 915 913 911 908 906 904 go2 900 898 69 1.70 71 896 894 892 890 888 886 883 881 879 877 3 0.00 87s 873 871 869 867 865 863 861 859 857 855 853 851 849 847 845 843 841 839 837 I 0.3 72 836 834 832 830 828 826 824 822 820 818 2 0.6 73 816 814 813 811 809 807 805 803 801 799 3 0.9 74 798 796 794 792 790 788 787 785 783 781 4 1.2 1-5 1.8 2.1 75 779 777 776 774 772 770 768 767 765 763 5 6 7 8 76 761 760 758 756 754 753 751 749 747 746 77 744 742 740 739 737 735 734 732 730 728 2.4 78 727 725 723 722 720 718 717 715 713 712 Q 2.7 79 1.80 81 710 708 707 705 704 702 700 699 697 695 7 • 0.00 694 692 691 689 687 686 684 683 681 679 678 676 675 673 672 670 669 667 665 664 82 662 661 659 658 656 655 653 652 650 649 83 647 646 644 643 641 640 638 637 635 634 84 632 631 629 628 626 625 624 622 621 619 85 618 616 615 614 612 611 609 608 606 605 86 604 602 601 599 598 597 595 594- 593 591 87 590 588 587 586 584 583 582 580 579 578 88 576 575 574 572 571 570 568 567 566 564 a 89 1.90 91 563 562 561 559 558 557 555 554 553 551 I 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 I.O 1.2 1.4 1.6 0.00 550 549 548 546 545 544 543 541 540 539 538 536 535 534 533 531 530 529 528 527 92 525 524 523 522 520 519 518 517 516 514 93 513 512 5" 510 509 507 506 505 504 503 94 502 500 499 498 497 496 495 493 492 491 95 490 489 488 487 486 484 483 482 481 480 1.8 96 479 478 477 476 474 473 472 471 470 469 y • 97 468 467 466 465 464 462 461 460 459 458 98 457 456 455 454 453 452 451 450 449 448 99 2.00 447 446 445 444 443 442 441 440 439 437 0.00 436 435 434 433 432 431 430 429 428 427 A B 1 2 3 4 5 6 7 8 9 P P a>b. J ?ut a; = log a — log 6 Ifa;>.3, t tien x = = A and Ic g(a- -6)== :log a — B. If » < . 3, t hen X - : B and Ic g(a- -b) = log a — A. 3fi SUBTRACTION. A "2J I 2 3 4 5 6 7 8 9 3.0 I 2 3 4 5 6 7 8 9 4.0 I 2 3 4 5 6 7 8 9 5.0 B P P 0.00 436 426 417 407 398 389 380 371 363 346 275 218 173 138 109 087 069 055 338 269 213 169 134 107 085 067 053 331 262 208 165 131 104 083 066 052 323 256 204 162 128 102 o8i 064 051 3?^ 251 199 158 125 1 00 079 063 050 309 245 194 154 123 097 077 061 049 302 239 190 151 120 095 076 060 048 295 234 186 147 117 093 074 059 047 288 22g 181 144 114 091 072 057 046 0.00043. 042 041 041 040 039 038 037 036 035 027 022 017 014 oil 009 007 005 034 027 021 017 013 on 008 007 005 033 026 021 017 013 010 008 007 005 032 026 020 oi5 013 010 008 006 005 031 025 020 016 013 010 008 006 00§ 031 024 019 015 012 010 008 006 005 030 024 019 015 012 010 008 006 005 029 023 019 015 012 009 007 006 005 029 023 018 014 on 009 007 006 005 0.00 004 004 004 004 004 004 004 004 004 003 003 002 002 001 001 001 001 001 003 003 002 002 001 001 001 001 001 003 003 002 002 001 001 001 001 001 003 003 002 002 001 001 001 001 001 003 002 002 002 001 001 001 001 000 003 002 002 002 001 001 001 001 000 003 002 002 002 001 001 001 001 000 003 002 002 001 001 001 001 001 000 003 002 002 001 001 001 001 001 000 000 000 000 000 000 354 281 223 177 141 112 089 070 056 044 035 028 022 oi8 014 on 009 007 006 004 004 003 002 002 001 001 ooi 001 001 000 9 I o.g 2 1.8 3 2.7 4 3.6 5 4-5 b 5-4 7 6.3 8 7-2 9 8.1 0.8 1.6 2.4 3-2 4.0 4.8 5.6 6.4 7-2 7 6 0.7 0.6 1-4 1.2 2.1 1.8 2.8 2.4 3-5. 3.0 4-2 3-6 4-9 4.2 5-6. 4.8 b.3 5-4 5 0.5 i.o 1-5 2.0 2.5 3-0 3-5 4.0 4-5 4 I 0.4 2 0.8 3 1.2 4 1.6 ■; 2.0 6 2-4 7 2.8 8 3-2 9 3-6 3 0.3 0.6 0.9 1.2 1-5 1.8 2.1 2.4 2.7 B P P a > 6, A = logo — logb, or B = loga — logb, log(a — b) =loga — B. log (a — b) = log a — A. The above table of Subiraction Logarithms is based oa the identity- log (a— &) = log ( X j = loga— log {j^ziJ, where x= -^. b The argTiment is log x, and the function is log! ^J- A is the argument and B the function when log a; > . 3, and B is the argument and A the function when log as < . 3. 37 III TABLE OF THE LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS FEOM 0° TO 1° AND 89° TO 90° FOR EVERY SECOND, AND FROM 1° TO 6<^ AND 84° TO 89° FOR EVERY TEN SECONDS. L Cos *90 L Sin 0° , L Tan 180° *270° o.oo 0" 1" 2" 3" 4" 5" 6- 7" 8" 9" 10" 000 4. _ 68557 98660 ^16270 ^28763 +38454 ♦46373 +53067 +58866 +63982 +68557 50 ooo 10 5. 68557 72697 76476 79952 83170 86167 88969 91602 94085 96433 98660 40 ooo 20 98660 »oo779 ^,02800 *04730 *o6579 *o835i *ioo55 *li694 +13273 +14797 +16270 30 ooo 30 6. 16270 17694 19072 20409 21705 22964 24188 25378 26536 27664 28763 20 ooo 40 28763 29836 30&S2 31904 32903 33879 34833 35767 36682 37577 38454 10 ooo 50 38454 39315 40158 40985 41797 42594 43376 44145 44900 45643 46373 o59 ooo 1 6.4 6373 7090 7797 8492 9175 9849 *05I2 *II65 ^1808 +2442 +3067 50 ooo 10 6.5 3067 3683 4291 4890 5481 6064 6639 7207 7767 8320 8866 40 ooo 20 8866 9406 9939 *0465 ^0985 *I499 *2007 +2509 +3006 +3496 +3982 30 ooo 30 6.6 3982 4462 4936 5406 5870 6330 6785 7235 7680 8121 8557 20 ooo 40 8557 8990 9418 9841 ;f026l ^0676 ;fI088 +1496 +1900 +2300 +2697 10 ooo 50 6.7 2697 3090 3479 3865 4248 4627 5003 5376 5746 6lI2 6476 o58 ooo 2 6476 6836 7193 7548 7900 8248 8595 8938 9278 9616 9952 50 ooo 10 9952 *0285 *o6i5 *0943 *I268 *i59i *i9ii *2230 +2545 +2859 +3170 40 ooo 20 6.83170 3479 3786 4091 4394 4694 4993 5289 5584 5876 6167 30 ooo 30 6167 6455 6742 7027 7310 7591 7870 8147 8423 8697 8969 20 ooc 40 8969 9240 9509 9776 *0042 *03o6 *0568 +0829 ^1088 +1346 :^l602 10 ooc ooc 50 3 6.9 1602 1857 2110 2362 2612 2861 3109 3355 3599 3843 4085 o57 4085 4325 4565 4803 5039 5275 5509 5742 5973 6204 6433 50 ooc 10 6433 6661 6888 7113 7338 7561 7783 8004 8224 8443 8660 40 ooo 20 8660 8877 9093 9307 9520 9733 9944 *oi55 +0364 +0572 +0779 30 ooc 30 7.00779 0986 1191 1395 1599 1 801 2003 2203 2403 2602 2800 20 ooo 40 2800 2997 3193 3388 3582 3776 3968 4160 4351 4541 4730 10 ooo 50 4730 4919 5106 5293 5479 5664 5849 6032 6215 6397 6579 o56 ooo 4 6579 6759 6939 7118 7296 7474 7651 7827 8003 8177 8351 50 ooo 10 8351 8525 8698 8870 9041 921 1 9381 9551 9719 9887 +0055 40 ooo 20 7.1 0055 0222 0388 0553 0718 0882 1046 i2og 1371 1533 1694 30 ooo 30 1694 1854 2014 2174 2333 2491 2648 2805 2962 3118 3273 20 ooo 40 3273 3428 3582 3736 3889 4042 4194 4346 4497 4647 4797 10 ooo 50 4797 4947 5096 5244 5392 5540 5687 5833 59791 6125 6270 o55 o.oc 10' 9' 8' 7' 6" 5" 4" 3" 2' 1' 0" ' L S iu LC OS 89° L( :jot »J79° 269° *359° 38 L Cos L Sin •90° 180° *270° 144 143 142 141 140 139 138 137 136 135 134 133 I 14.4 14-3 14.2 14. 1 14.0 13-9 I 13.8 13-7 13-6 13-5 134 13.3 I 2 28.8 28.6 28.4 28.2 28.0 27.8 2 27.6 27.4 27.2 27.0 26.8 26.6 2 3 43.2 42.9 42.6 42-3 42.0 41.7 3 414 41.1 40.8 40.5 40.2 39-9 3 4 57-6 57-2 56.8 564 56.0 55-6 t 55-2 54-8 544 54-0 53.6 53-2 4 5 72.0 71.5 71.0 70.5 70.0 69.5 ; 69.0 68.5 68.0 67.5 67.0 66.5 5 6 86.4 85.8 85.2 84.6 84.0 83.4 5 82.8 82.2 81.6 81.0 80.4 79.8 6 7 100.8 1 00. 1 99.4 98.7 98.0 97-3 7 96.6 95-9 95-3 94-5 93-8 93.1 7 8 II5-2 114.4 113.6 112.8 II 2.0 111.2 8 110.4 109.6 108.8 108.0 107.2 106.4 8 9 129.6 128.7 127.8 126.9 126.0 125. 1 9 124.2 123-3 122.4 121.5 120.6 119.7 9 132 131 130 129 128 127 126 125 124 123 122 121 1 I 13.2 13.1 13-0 12.9 12.8 12.7 [ 1 12.6 12.5 12.4 12.3 12.2 12.1 I 2 26.4 26.2 26.0 25.8 25.6 25.4 2 25.2 25.0 24.8 24.6 24.4 24.2 2 3 39-6 39-3 39-0 38.7 38.4 38.1 3 37-8 37-5 37-2 36-9 36.6 36.3 3 4 52.8 52.4 52.0 51.6 51.2 50.8 4 50.4 50.0 49.6 49.2 48.8 48.4 4 5 66.0 65.5 65.0 64.5 64.0 63.5 ; 63.0 62.5 62.0 61.5 61.0 60.5. 5 6 79.2 78.6 78.0 77-4 76.8 76.2 6| 75.6 75-0 744 73-8 73-2 72.6 6 7 92.4 91.7 91.0 90-3 89.6 88.g 7 88.2 87.5 86.8 86.1 854 84.7 7 8 105.6 104.8 104.0 103.2 102.4 101.6 5 100.8 1 00.0 99.2 98.4 97.6 96.8 8 9 II8.8 117-9 1 1 7.0 116.1 115.2 114.3 9I1134 112.5 111.6 110.7 109.8 108.9 9 120 119 118 117 116 115 114 113 112 111 110 109 ■ 1 ^ 12.0 11.9 11.8 II. 7 11.6 11.5 I 11.4 "•3 11.2 II. I II.O 10.9 I 24.0 23.8 23.6 23-4 23.2 23.0 2 ! 22.8 22.6 22.4 22.2 22.0 21.8 2 3 V36.0 35-7 35-4 35-1 34-8 34-5 : ! 34-2 33-9 33-6 33-3 33-0 32.7 3 ">. A8.0 47.6 47.2 46.8 46.4 46.0 t i 45-6 45-2 44-8 444 44-0 43.6 4 5 60.0 59-5 59.0 58.5 58.0 57-5 . ) 5-7.0 56.5 56.0 55-5 55-0 54.5 5 6 72.0 71.4 70.8 70.2 69.6 69.0 f ) 68.4 67.8 67.2 66.6 66.0 65.4 6 7 84.0 83-3 82.6 81.9 81.2 80.5 ■ ? 79-8 79.1 78.4 77-7 77.0 76-3 7 8 96.0 95.2 94-4 93-6 92.8 92.0 i i 91.2 90.4 89.6 88.8 88.0 87.2 8 9 108.0 107.1 106.2 105.3 104.4 103.5 < J 102.6 101.7 100.8 99.9 99.0 98.1 9 o.oo / // 0" 1" 2" 3" 4" 5' 6" 7" 8" 9" 10" ooo 5 7.1 6270 6414 6558 6702 6845 6987 7130 7271 7413 755 3 7694 50 ooo 10 7694 7834 7973 8112 8250 8389 8526 8663 8800 893 7 9072 40 ooo 20 9072 9208 9343 9478 9612 9746 9879 *00I2 #0145 *027 7*0409 30 000 30 7.2 0409 0540 0671 0802 0932 1062 1191 1320 1449 157 7 1705 20 ooo 40 1705 1833 i960 2087 2213 2339 2465 259& 2715 284( D 296:1 10 ooo 50 2964 3088 3 212 3335 3458 3580 3702 3824 3946 406 7 4188 54 ooo 6 4188 4308 4 428 4548 4668 4787 4906 5024 5142 5261 3 5378 50 ooo 10 5378 5495 5612 5728 5845 5961 6076 6192 6307 642 [ 6536 40 ooo 20 6536 6650 6764 6877 6991 7104 7216 7329 7441 755 2 7664 30 ooo 30 7664 7775 7886 7997 8107 8217 8327 8437 8546 865 5 8763 20 ooo 40 8763 8872 8980 9088 9196 9303 9410 9517 9623 973< 3 9836 10 ooo 50 9836 9942 *0047 *OI52 *o257 *0362 J, 0467 *057r *o675 *077 3,^0882 53 ooo 7 7.3 0882 0986 1089 1191 1294 1396 1498 1600 1702 180 3 1904 50 ooo 10 1904 2005 2106 2206 2306 2406 2506 2606 2705 280i 1 2903 40 ooo 20 2903 3001 3100 3198 3296 3393 3491 3588 3685 378 2 3879 30 ooo 30 3879 3975 4071 4167 4263 4359 4454 4549 4644 473 3 4833 20 ooo 40 4833 4928 5022 5116 5209 5303 5396 5489 5582 567 5 5767 10 ooo 50 5767 5860 5952 £044 6135 6227 6318 6409 6500 659 I 6682 52 ooo 8 6682 6772 6862 6952 7042 7132 7221 7310 7399 748 3 7577 50' ooo 10 7577 7666 7754 7842 7930 8018 8106 8193 8280 836 7 8454 40 ooo 20 8454 8541 8628 8714 8800 8887 8972 9058 9144 922 J 9314 30 ooo 30 9314 9400 9484 9569 9654 9738 9822 9906 9990 *007' t*oi58 20 ooo 40 7.40158 0241 0324 0408 0491 0573 0656 0739 0821 090 3 0985 10 ooo 50 0985 1067 1 149 1230 1312 1393 1474 1555 1636 171 3 1797 51 ooo 9 1797 1877 1957 2037 2117 2197 2277 2356 2435 251 3 2594 50 000 10 2594 2673 2751 2830 2908 2987 3065 3143 3221 329 5 3376 40 ooo 20 3376 3454 3531 3608 3685 3762 3839 3916 3992 406 J 4145 30 ooo 30 4145 4221 4297 4373 4449 4524 4600 4675 4750 482 ; 4900 20 ooo 40 4900 4975 5050 5124 5199 5273 5347 5421 5495 556 3 5643 10 ooo 50 5643 5716 5790 5863 5936 6009 6082 6155 6228 630 3 6373 50 O.Of 10" 1 9" 8" 7" 6" B" 4" 3" 2" 1" 0" n r L Sin *179° 269° *359° 89" L Cos 39 L Tan 0° *9C ° 180° *270° 108 107 106 105 104 103 102 101 99 98 97 96 I 10.8 10.7 10.6 10.5 10.4 10.3 I 10.2 lO.I 9.9 9.8 9-7 9.6 I 2 21.6 21.4 21.2 21.0 20.8 20.6 2 20.4 20.2 19.8 19.6 19.4 19.2 2 3 32.4 32.1 31.8 31-5 31.2 30.9 3 30.6 30.3 29.7 29.4 29.1 28.8 3 4 43-2 42.8 42.4 42.0 41.6 41.2 4 40.8 40.4 39-6 39-2 38.8 384 4 5 54-0 53-5 53-0 52.5 52.0 51-5 5 51.0 50.5 49-5 49.0 48.5 48.0 5 6 64.8 64.2 63.6 63.0 62.4 61.8 6 61.2 60.6 594 58.8 58.2 57-6 6 7 75.6 74-9 74.2 73-5 72.8 72.1 7 71.4 70.7 69-3 68.6 67.9 67.2 7 8 86.4 85.6 84.8 84.0 83.2 82.4 8 81.6 80.8 79.2 78.4 77.6 76.8 8 9 97.2 96-3 95-4 94-5 93-6 92.7 9 91.8 90.9 89.1 88.2 87.3 86.4 9 95 94 93 92 91 90 89 88 87 86 85 84 1 I 9-5 9-4 9-3 9.2 9.1 9.0 I 8.9 8.8 8.7 a.6 8.5 8.4 I 2 19.0 18.8 18.6 18.4 18.2 18.0 2 17.8 17.6 174 17.2 17.0 16.8 2 3 28.5 28.2 27.9 27.6 27-3 27.0 3 26.7 26.4 26.1 25.8 25-5 25.2 3 4 38.0 37-6 37-2 36.8 364 36-0 4 35-6 35-2 34.8 34-4 34.0 33-6 4 5 47-5 47-0 46.5 46.0 45-5 45.0 5 44-5 44.0 43-5 43.0 42.5 42.0 5 6 57-0 564 55-8 55-2 54-6 54.0 6 534 52.8 52.2 51.6 51.0 50.4 6 7 66.5 65.8 65.1 64.4 63.7 63.0 7 62.3 61.6 60.9 60.2 59-5 58.8 7 8 76.0 75-2 74.4 73.6 72.8 72.0 8 71.2 70.4 69.6 68.8 68.0 67.2 8 9 85.5 84.6 83-7 82.8 81.9 81.0 9 80.1 79.2 78.3 774 76.5 75.6 9 83 82 81 80 79 78 77 76 75 ■74 73 72 1 I 8.3 8.2 8.T 8.0 7-9 7.8 I 7-7 7.6 7-5 74 7-3 7.2 I 2 16.6 16.4 16.2 16.0 15.8 15.6 2 15.4 15.2 15.0 14.8 14.6 14.4 2 3 24.9 24.6 24-3 24.0 23-7 234 3 23.1 22.8 22.5 22.2 21.9 21.6 3 4 33-2 32.8 324 32.0 3r.6 31.2 4 30.8 30.4 30.0 29.6 29.2 28.8 4 5 41.5 41.0 40.5 40.0 39-5 39-0 5 38.5 38.0 37-5 37-0 36.5 36.0 5 6 49.8 49.2 48.6 48.0 474 46.8 6 46.2 45-6 45-0 444 43-8 43-2 6 7 58.1 57.4 56.7 56-0 55-3 54.6 7 53.9 53-2 52.5 51.8 51. 1 50.4 7 8 66.4 65.6 64.8 64.0 63.2 62.4 8 61.6 60.8 60.0 59-2 584 57-6 8 9 74-7 73-8 72.9 72.0 71. 1 70.2 9 69-3 68.4 67.5 66.6 65.7 64.8 9 , 0" 1 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 5 o 7.1 ^7C 7^94 6414 6558 6702 6845 6988 7130 727 7413 7553 7694 50 10 7834 7973 8112 8250 8389 8526 866. 5 8800 8937 9073 40" 20 9073 9208 9343 9478 9612 9746 9879 *ooi: 2*0145 *0277 *0409 30 V 30 7.2 040c ) 0540 0671 0802 0932 1062 iigi 132 1449 1577 1703 20 40 170; 1833 1960 2087 2213 2339 2465 259c 5 2715 2840 2964 10 50 296^ i 3088 3212 3335 3458 3580 3703 382^ ^ 3946 4067 4188 54 6 418J i 4308 4428 4548 4668 4787 4906 502i \ 5142 5260 5378 50 10 537f i 5495 5612 5728 5845 5961 6076 619 2 6307 6421 6536 40 20 653f ) 6650 6764 6877 6991 7104 7216 732( J 7441 7552 7664 30 30 766. I ins 7886 7997 8107 8217 8327 843 7 8546 8655- 8764 20 40 876. \ 8872 8980 9088 9196 9303 9410 951 7 9624 9730 9836 10 50 983' 3 9942 *0047 »0I53 *0258 ^0362 it0467 «057 t«of'75 #0779 »o882 53 7 7.3 088: 2 0986 io8g 1 1 92 1294 1396 1499 i6o( 3 1702 1803 1904 50 10 igoi \ 2005 2106 2206 2307 2406 2506 260 D 2705 2804 2903 40 20 290 J 3001 3100 3198 3296 3394 3491 358 3 3685 3782 3879 30 30 387' } 3975 4071 4167 4263 4359 4454 454 3 4644 4739 4833 20 40 483 ) 4928 5022 5116 5209 5303 5396 548 3 5582 5675 5767 10 50 576 7 5860 5952 6044 6135 6227 6318 640 J 6500 6591 6682 52 8 668 2 6772 6862 6952 7042 7132 7221 731 3 74OQ 7488 7577 50 10 757 7 7666 7754 7842 7930 8018 8106 819 3 8281 8368 8455 40 20 845 ; 8541 8628 8714 8801 8887 8973 905 3 9144 9229 9315 30 30 931 ; 9400 9485 9569 9654 9738 9823 990 7 9991 *oo74 *oi58 20 40 7.4 015 i 0241 0325 0408 0491 0574 0656 073 3 0821 0903 0985 IC 50 098 ; 1067 1149 1230 1312 1393 1474 155 3 1636 1716 1797 51 9 179 7 1877 1958 2038 2117 2197 2277 235 5 2436 2515 2594 50 10 259- \ 2673 2751 2830 2909 2987 3065 314 3 3221 3299 3376 40 20 337 i 3454 3531 3608 3686 3762 3839 391 5 3992 4069 4145 30 30 414 5 4221 4297 4373 4449 4524 4600 467 5 475c 4825 4900 20 40 4900 4975 5050 5124 5199 5273 5347 542 I 5495 5569 5643 10 50 56431 5716 5790 5863 5936 6009 6082 615 5 622S 6300 6373 50 10' 9" 8" V 6" 5" 4" ~F 2" 1" 0" n t *179° 269° *359° 89° L Cot 40 L Cos L Siu 0° •90° 180" #270" o.oo ' " 0' 1" 2' 3" 4" 5' 6' 7" 8' 9" 10" PP ooo 10 o 7-46 373 445 517 589 661 733 805 876 948 *oi9 *090 50 72 ooo lO 7.47 090 162 233 303 374 445 515 586 656 726 797 40 I 7.2 ooo 20 797 867 936 *oo6 #076 »i45 *2I5 *284 *353 *422 »49i 30 2 Itt ooo 30 7.48 491 560 629 698 766 835 903 971 *039 *io8 *I75 20 3 4 28.8 ooo 40 7-49 175 243 3" 379 446 513 581 648 715 782 849 10 5 36.0 ooo 50 849 916 982 *049 *ii5 *l82 »248 *3I4 *38o *446 *5I2 49 6 7 8 43-2 S0.4 57-6 ooo 11 7.50512 578 643 709 774 840 905 970 *035 *ioo *i65 50 ooo 10 7.51 165 230 294 359 423 488 552 616 680 744 808 40 70 ooo 20 808 872 936 999 #063 ^126 »i90 *253 *3i6 *379 *442 30 ooo 30 7.52 442 505 568 631 693 756 818 88l 943 *oo5 *o67 20 I 2 7.0 14.0 ooo 40 7.53067 129 191 253 315 376 438 499 561 622 683 10 3 21.0 ooo 50 683 744 805 866 927 988 »049 *i09 *i7o *230 *29I 48 4 28.0 35 -o 42.0 49.0 56.0 ooo 12 7.54 291 351 411 471 531 591 651 711 771 830 8go 50 ooo 10 890 949 *oo9 *o68 »I27 ^186 »245 *304 *363 *422 *48i 40 I ooo 20 7-55 481 539 598 656 715 773 831 889 948 »oo6 *o64 30 9 63.0 ooo 30 7-56 064 121 179 237 295 352 410 467 524 582 639 20 68 1 ooo 40 639 696 753 810 867 924 980 *037 *094 *i50 *206 :o I 6.8 ooo 50 7.57 206 263 319 375 431 488 544 599 655 711 767 47 2 3 4 13-6 20.4 27.2 ooo 13 767 822 878 934 989 »044 jflOO *i55 *210 *265 *320 50 ooo 10 7.58320 375 430 485 539 594 649 703 758 812 866 40 5 6 34-0 40.8 ooo 20 866 921 975 ,029 *o83 »i37 »i9i *245 *299 *352 *406 30 7 47.6 ooo 30 7.59 406 459 513 566 620 673 726 780 833 886 939 20 8 54.4 61.2 ooo 40 939 992 *o45 »097 »i5o »203 if.255 *3o8 *36o *4I3 *465 10 9 ooo 50 7.60 465 517 570 622 674 726 778 830 882 934 985 46 bo 1 ooo 14 985 »037 *o89 ,140 *I92 »243 *294 «346 «397 «448 *499 50 I 2 13:2 ooo 10 7.61 499 550 601 652 703 754 805 855 906 957 *oo7 +0 3 4 5 19.8 26.4 33.0 ooo 20 7.62 007 058 106 158 209 259 309 359 409 459 509 30 ooo 30 509 559 609 659 708 758 808 857 907 956 ^i,oo6 20 6 39.6 ooo 40 7.63 006 055 104 153 203 252 301 350 399 448 496 10 I 46.2 Co R ooo 50 496 545 594 642 691 740 788 837 885 933 982 45 9 52. 59-4 ooo 15 982 »030 ,078 «^26 *i74 »222 *27o *3i8 *366 *4i4 *46i 50 64 1 ooo 10 7.64 461 509 557 604 652 699 747 794 842 889 936 40 1 6.4 ooo 20 936 983 *030 *078 *I25 »I72 !f2l8 *265 *3I2 *359 *4o6 30 2 12.8 ooo 30 7.65 406 452 499 546 592 638 685 731 778 824 870 20 3 4 19.2 25.6 ooo 40 870 916 962 *009 »055 »ioi ^146 *I92 *238 *284 *330 10 5 32.0 000 50 7.66 330 375 421 467 512 558 603 649 694 739 784 44 6 I 9 38.4 44.8 51.2 •;7.6 ooo 16 784 830 875 920 965 »oio »055 »ioo »i45 *I90 *235 50 000 10 7-67 235 279 324 369 413 458 502 547 591 636 680 +0 pff. 1 *ooo 20 680 724 768 813 857 go I 945 989 *o33 *077 *I2I 30 6 2 *999 30 7.68 121 165 208 252 296 340 383 427 470 514 557 20 2 12.4 999 40 557 601 644 687 731 774 817 85o 903 946 989 10 3 18.6 999 50 989 *032 *075 ijTiS »i6i »204 »247 *289 *332 *375 *4I7 43 4 7 24.8 31.0 37.2 43.4 999 17 7.69417 460 502 545 587 630 672 714 757 799 841 50 999 10 841 883 925 967 #009 »o5i »093 *i35 *I77 *2I9 *26l 40 8 49.6 999 20 7.70 261 302 344 386 427 469 510 552 593 635 676 30 9 55.8 999 30 676 718 759 800 841 883 924 965 »oo6 *047 *o88 20 61 1 999 40 7.71 088 129 170 211 251 292 333 374 414 455 496 10 I 6.1 999 50 496 536 577 617 658 698 739 779 819 859 900 42 2 3 4 12.2 18.3 24.4 999 18 900 940 980 jf020 *o6o »ioo »I40 *i8o *220 *260 *300 50 999 10 7.72 300 340 386 419 459 499 538 578 618 657 697 40 5 30-5 36.6 999 20 697 736 775 815 854 894 933 972 *oii *050 ,090 30 7 42-7 999 30 7.73 090 129 168 207 246 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179 200 220 241 262 282 303 7 3 6.0 53 303 324 344 365 386 406 427 6 4 8.0 54 427 447 468 489 509 530 550 5 5 6 10.0 12.0 55 550 571 591 612 632 653 673 4 56 673 694 714 735 755 776 796 3 7 14.0 57 796 816 837 857 878 898 918 2 8 16.0 58 918 939 959 979 ,000 *020 #040 I 9 iB.o 59 9.02 040 061 081 lOI 121 142 162 60" 50" 40" 30" 20", 10" 0" ' P P *174° 264° *354° 84° L Cot 60 L Cos L Sin 6° *96° 186° *276° 9-99 ' 0" 10' 20' 30" 40" 50" 60" P P 761 9.01 923 943 964 984 *oo4 *024 *043 59 760 760 I 9.02 043 063 083 103 123 143 163 58 759 759 2 163 183 203 223 243 263 283 57 757 21 757 3 283 302 322 342 362 382 402 56 756 I 2.1 756 4 402 421 441 461 481 501 520 55 755 2 3 4.2 6.3 755 5 520 540 560 579 599 619 639 54 753 753 6 639 658 678 698 717 737 757 53 752 4 8.4 752 7 757 776 796 816 835 855 874 52 751 5 10.5 751 8 ■874 894 914 933 953 972 992 51 749 6 12.6 749 9 992 *OII *03i *050 *070 *o89 *io9 50 748 7 8 9 14-7 16.8 18.9 748 10 g.03 109 128 148 167 187 206 226 49 747 747 II 226 245 265 284 303 323 342 48 745 745 12 342 361 381 400 420 439 458 47 744 744 13 458 478 497 516 535 555 574 46 742 on 742 14 574 593 613 632 651 670 690 45 741 I 2 2.0 4.0 741 15 690 709 728 747 766 786 805 44 740 740 16 805 824 843 862 88i 901 920 43 738 3 6.0 738 17 920 939 958 977 996 *oi5 *034 42 737 4 8.0 737 18 9.04 034 053 072 091 no 129 149 41 736 5 1 0.0 736 19 149 168 187 206 225 244 262 40 734 6 7 8 12.0 14.0 16.0 734 20 262 281 300 319 338 357 376 39 733 733 21 376 395 414 433 452 471 490 38 731 9 18.0 731 22 490 508 527 546 565 584 603 37 730 730 23 603 621 640 659 678 697 715 36 728 728 24 715 734 753 772 790 809 828 35 727 -in 727 25 828 847 565 884 903 921 940 34 726 I 2 1.9 3-8 726 26 940 959 977 996 *oi5 *033 *052 33 724 724 27 9.05 052 071 089 108 126 145 164 32 723 723 28 164 182 201 219 238 256 275- 31 721 3 4 5 6 5-7 7.6 9-5 11.4 721 29 275 293 312 330 349 367 386 30 720 720 30 386 404 423 441 460 478 497 29 718 7l8 31 497 515 533 552 570 589 607 28 717 7 13-3 717 32 607 625 644 662 681 699 717 27 716 8 15-2 716 33 717 736 754 772 791 809 827 26 714 9 17.1 714 34 827 845 864 882 900 918 937 25 713 713 35 937 955 973 991 *oio *028 *046 24 711 7" 3b 9.06 046 064 082 lOI 119 137 155 23 710 1» 710 37 155 173 191 210 228 246 264 22 708 708 38 264 282- 300 318 336 354 372 21 707 I 1.8 3-6 5.4 7.2 707 39 372 390 408 426 445 463 481 20 705 2 3 4 705 40 481 499 517 535 553 571 589 19 704 704 41 589 606 624 642 660 678 696 18 702 5 9.0 702 42 696 714 732 750 768 786 804 17 701 6 10.8 701 43 804 821 839 857 875 893 911 16 699 7 12.6 699 44 911 929 946 964 982 4fOOO *oi8 15 698 8 9 144 16.2 698 45 9.07018 035 053 071 089 106 124 14 696 696 46 124 142 160 177 195 213 231 13 695 695 47 231 248 266 284 301 319 337 12 693 693 48 337 354 372 390 407 425 442 II 692 17 692 49 442 460 478 495 513 530 548 10 690 I 2 1.7 3-4 6go 50 548 566 583 601 618 636 653 9 689 689 51 653 671 688 706 723 741 758 8 687 3 5-1 687 52 758 776 793 811 828 846 863 7 686 4 6.8 686 53 863 881 898 915 933 950 968 6 684 5 8.5 684 54 968 985 ^(.002 »020 *o37 *055 *0-2 5 683 6 7 10.2 11.9 683 55 9.08 072 089 107 124 141 159 176 4 681 681 56 176 193 211 228 245 262 280 3 680 8 13-6 680 57 280 297 314 331 349 366 383 2 678 9 15-3 678 58 383 400 418 435 452 469 486 I 677 677 59 486 504 521 538 555 572 589 675 60" 50" 40" 30" 20" 10" 0" ' 9.99 P P *173° 263° *353° 83° L Cos L Sill 61 TABLE OF THE LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS FEOM MINUTE TO MINUTE 62 *90° 180° *270° L Sin C S C T L Tan c d LCot LCos o 60 120 180 —00 6 7 8 9 10 II 12 13 14 15 16 17 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 18 1140 ig 1200 20 1260 21 1320 22 1380 23 1440 24 1500 25 1560 26 1620 27 1680 28 1740 29 1800 30 i86o| 31 1920 19' 2040 2100 2160 2220 2280 2340 2400 2460 2520 2580 2640 2700 2760 2820 2880 2940 3000 3060 32 33 34 35 36 -37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 31201 52 3180 53 3240 54 3300 55 3360 56 3420 57 3480 58 3540 59 3600 60 6.46 373 6.76 476 6.94 085 7.06 579 7.16270 7.24 188 7.30 882 7.36 682 7-41 797 7-46 373 7-50 512 7.54 291 7-57 767 7-6o 985 7.63 982 7.66 784 7.69417 7.71 900 7-74 248 7-76475 7-78 594 7.80615 7-82 545 7-84 393 7.86 166 7.87 870 7.89 509 7.91 088 7.92 612 7-94 084 7.95 508 7.96 887 7.98 223 7-99 520 8.00 779 8.02 002 8.03 192 8.04 350 8.05 478 8.06578 8.07 650 8.08 696 8.09 718 8.10 717 8. 1 1 693 8.12 647 8.13 581 8.14495 8.15391 .16268 8.17 128 8.17 971 8.18 798 8.19 610 8.20 407 8.21 189 8.21 958 8.22 713 8.23 456 8.24186 30103 17609 12494 9691 7918 6694 5800 5115 4576 4139 3779 3476 3218 2997 2802 2633 2483 2348 2227 2119 2021 1930 1848 1773 1704 1639 1579 1524 1472 1424 1379 1336 1297 1259 1223 1 190 1158 1128 1 100 1072 1046 1022 999 976 954 934 914 896 877 860 843 827 812 797 782 769 755 743 730 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5.31 443 5-31 443 5-31 442 5.31442 5-31 442 5.31 442 5-31 442 5-31 442 5-31 443 5-31 442 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 442 5-31 442 5.31 442 5-31 442 5.31 442 5-31 442 5-31 442 5.31442 5-31 442 5-31 443 5-31 442 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31442 5-31 442 5-31 442 5.31 442 5.31 442 5-31 442 5-31 442 5-31 442 5-31 441 5-31 443 5-31 441 L Cos 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 443 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5.31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 444 5-31 445 5-31 445 5-31 445 5-31 445 5-31 441 5.31 441 5.31 441 5-31 441 5-31 441 5-31 441 5-31 441 5-31 441 5-31 441 5-31 441 5.31 440 5.31 440 5.31 440 5.31 440 5.31 440 5.31 440 5-31 440 5-31 440 5-31 440 6.46 373 6.76 476 6.94 085 7.06 579 7.16270 7.24188 7.30 882 7.36 682 7-41 797 7-46 373 7.50512 7-54291 7-57 767 7.60 986 7.63 982 7.66 785 7.69418 7.71 900 7-74 248 7.76476 7-78 595 7.80615 7-82 546 7-84 394 7.86 167 7-87 871 7.89 510 7.91 089 7.92 613 7-94 086 7-95 510 7.96 889 7.9S 225 7-99 522 8.00 781 8.02 004 8.03 194 8.04 353 8.05 481 8.06 581 5-31 439 5-31 439 5.31439 5-31 439 5.31 439 5-31 439 5-31 439 5.31 439 531438 5-31 438 5-31 438 B.07 653 8.08 700 8.09 722 8.10 720 8. 1 1 696 8.12 651 8.13585 8.14 500 8.15395 8.16273 8.17 133 8.17976 8.18 804 8.19 616 8.20413 8.21 195 8.21 964 8.22 720 8.23 462 8.24 192 30103 17609 12494 9691 7918 6694 5800 5115 4576 4139 3779 3476 3219 2996 2803 2633 2482 2348 2228 2119 2020 1931 1848 1773 1704 1639 1579 1524 1473 1424 1379 1336 1297 1259 1223 1 190 1159 1128 1 100 1072 1047 1022 998 976 955 934 915 895 878 860 843 828 812 797 782 769 756 742 730 LCot 0.00 000 3-53627 3-23 524 3-05915 2.93 421 2.83 730 2.75 812 2.69 118 2.63318 2.58 203 0.00 000 0.00 000 0.00 000 0.00 000 0.00 000 0.00000 0.00 000 0.00 000 0.00 000 2.53 627 0.00 000 2.49 488 2.45 709 2.42 233 2.39014 2.36018 2.33 215 2.30 582 2.28 100 2.25 752 0.00000 0.00 000 0.00000 0.00 000 0.00 000 0.00000 9-99 999 9-99 999 9-99 999 2.23 524 9-99 999 2.21 405 2.19385 2.17454 2.15 606 2.13 833 2.12 129 2.10490 2.08 911 2.07 387 9-99 999 9-99 999 9.99 999 9-99 999 9-99 999 9-99 999 9-99 999 9-99 999 9-99998 2.05 914 2.04 490 2.03 III 2.01 775 2.00478 1.99 219 1-97 996 1. 96 806 1-95 647 1-94 519 1-93419 1.92 347 1.91 300 I. go 278 1.89 280 1.88 304 1.87 349 I 86415 1.85 500 1.84 605 1-83 727 1.82 867 1.82 024 1. 81 196 1.80384 1.79587 1.78 80s 1.78036 1.77 280 1.76538 1.75 808 c d 9-99 998 9-99 998 9-99 998 9.99 998 9-99 998 9-99 998 9-99 998 9-99 997 9-99 997 9-99 997 9-99 997 9-99 997 9-99 997 9-99 997 9.99 996 9.99 996 9.99 996 9.99 996 9-99 996 9-99 996 9-99 995 9.99 995 9-99 995 9-99 995 9-99 995 9/99 994 9-99 994 9-99 994 9-99 994 9-99 994 9.99 993 L Tan | L Sm _1 *179° 269° *359° 89° 63 1° *91° 181° *271° • / L Sin d C S C T L Tan cd LCot LCos 3600 3660 I 8.24 186 717 706 5-31 445 5-31 438 8.24 192 718 706 1.75 S08 9-99 993 60 59 8.24 903 5-31 445 5-31 438 8.24 910 1.75 090 9.99 993 3720 2 8.25 609 5-31 445 5-31438 8.25 616 1.74 384 ■9-99 993 58 3780 3 8.26 304 695 684 673 5-31 445 5-31 438 8.26312 696 684 673 1.73 688 9-99 993 57 3840 4 8.26988 5-31 445 5-31437 8.26 996 1.73 004 9-99 992 56 3900 5 8.27661 5-31 445 531437 8.27 669 1-72331 9.99 992 55 3960 6 8.28 324 663 653 5-31445 5-31 437 8.28 332 663 654 643 1.71 668 9-99 992 54 4O20 7 8.28 977 5-31 445 5-31 437 8.28 986 1. 71 014 9.99 992 53 4o8o 8 8.29 621 644 5-31 445 5-31437 8.29 629 1-70371 9-99 992 52 4140 4200 4260 9 10 11 8.30255 634 624 616 5-31 445 5-31437 8.30 263 634 625 617 607 1.69 737 9.99 991 51 50 49 8.30 879 5.31 446 5-31437 8.30888 1.69 112 9-99 991 8.31 495 5.31 446 5-31436 8.31 505 1.68 495 9.99 991 4320 12 8.32 103 608 5-31 446 5.31 436 8.32 112 1.67888 9-99 990 48 4380 13 8.32 702 599 5.31 446 5-31 436 8.32 711 599 1.67 289 9.99 990 47 4440 14 8.33 292 590 5.31 446 5-31 436 8.33 302 591 584 1.66698 9.99 990 46 4500 15 8.33 875 583 5-31 446 5-31 436 8.33 886 1.66 114 9-99 990 45 4560 16 8.34450 575 568 560 5.31 446 5-31435 8.34 461 575 568 561 1.65 539 9-99 989 44 4620 17 8.35018 5.31 446 5-31435 8.35 029 1.64 971 9.99 989 43 468c 18 8.35 578 5-31 446 5-31 435 8.35 590 1.64 410 9-99 989 42 4740 4800 486c 19 20 21 8.36 131 553 547 539 5.31 446 5-31 435 8.36 143 553 546 540 1.63 857 9-99 989 41 40 39 8.36678 5.31 446 5-31 435 8.36 689 1.63 311 9-99 988 8.37217 5-31447 5-31 434 8.37229 1.62 771 9.99 988 492c 22 8.37 750 533 5-31 447 5-31 434 8.37 762 533 1.62 238 9.99 988 38 498c 23 8.38 276 526 5-31447 5-31 434 8.38 289 527 520 1.61 711 9-99 987 37 5040 24 8.38 796 5-31 447 5-31 434 8.38 809 1.61 191 9-99987 36 5100 25 8.39 3-10 514 5-31 447 5-31 434 8.39 323 514 1.60677 9-99 987 35 5160 26 8.39818 508 5-31 447 5-31 433 8.39 832 509 502 496 1.60 168 9.99 986 34 5220 27. 8.40 320 5-31 447 5-31433 8.40 334 1.59 666 9.99 986 33 528c 28 8.40 816 496 5-31 447 5-31 433 8.40 830 1-59 170 9-99 986 32 5340 5400 5460 29 30 31 8.41 307 491 485 480 5-31 447 5-31433 8.41 321 491 486 480 1.58679 9-99 985 31 30 29 8.41 792 5-31 447 5-31 433 8.41 807 1-58 193 9.99985 8.42 272 5-31 448 5-31 432 8.42 287 1-57713 9-99 985 5520 32 8.42 746 474 5.31 448 5.31432 8.42 762 475 1.57238 9-99 984 28 ; 5580 33 8.43 216 470 464 5.31 448 5.31 432 8.43 232 470 464 460 1.56768 9-99 984 27 5640 34 8.43 680 5-31 448 5-31 432 8.43 696 1.56304 9-99 984 26 : 5700 35 8.44 139 459 5.31 448 5-31 431 8.44 156 1-55 844 9-99 983 25 5760 36 8.44 594 455 450 5-31 448 5-31431 8.44 611 455 450 446 1-55389 9-99 983 24 5820 37 8.45 044 5-31 448 5-31 431 8.45 061 1-54 939 9-99 983 23 588c 38 8.45 489 445 5-31 448 5-31 431 8.45 507 1-54 493 9-99 982 22 ■ 5940 6000 . 6060 39 40 41 8.45 930 441 436 433 5-31 449 5-31431 8.45 948 441 437 432 428 1.54052 9-99 982 21 20 19 8.46 366 5.31 449 5-31430 8.46 385 1-53 615 9-99 982 8.46-799 5-31 449 5.31 430 8.46 817 1-53 183 9-99 981 6120 42 8.47 226 427 5-31 449 5.31 430 8.47 245 1-52755 9-99 981 18 6180 43 8.47 650 424 419 416 5-31 449 5-31 430 8.47 669 424 420 416 1-52 331 9-99 981 17 6240 44 8.48 069 5-31 449 5-31 429 8.48 089 1.519" 9-99 980 16 6300 45 8.4S485 5-31 449 5.31 429 8.48 505 I-51 495 9.99 980 15 1 6360 4b 8.48 896 411 408 5-31 449 5.31 429 8.48917 412 408 1. 51 083 9.99 979 14 6420 47 8.49 304 5-31 450 5.31 428 8-49 325 1.50675 9.99 979 13 6480 48 8.49 708 404 5-31 450 5.31 428 8-49 729 404 T. 50 271 9-99 979 12 , 6540 6600 6660 49 50 51 8.50108 396 393 5-31450 5-31 428 8.50 130 397 393 390 386 383 380 376 373 1.49 870 9-99 978 II 10 9 8.50 504 5-31 450 5.31428 8-50527 1-49 473 9.99 978 8.50897 5-31 450 5-31 427 8.50 920 1.49 080 9-99 977 , 6720 52 8.51 287 390 386 382 5-31 450 5.31 427 8.51 310 1.48 690 9-99 977 8 1 6780 53 8.51 673 5-31 450 5.31 427 8.51 696 1.48 304 9-99 977 7 6840 54 8.52055 5-31450 5-31 427 8.52079 1.47 921 9-99 976 6 6900 55 8.52434 379 376 5-31 451 5.31 426 8-52459 1-47 541 9.99 976 5 1 6960 50 8.52810 5-31 451 5.31 426 8.52835 1-47 165 9-99 975 4 ■ 7020 57 8.53 183 373 369 367 363 5-31 451 5.31 426 8.53 208 1.46 792 9-99 975 3 i 7080 58 8.53552 5-31 451 5.31 425 8-53 578 370 367 363 1.46 422 9-99 974 2 , 7140 ' 7200 59 60 8.53919 5-31451 5-31 425 8-53 945 1.46055 9-99 974 I 8.54282 5-31451 5-31 425 8.54 308 1.45 692 9-99 974 i LGos d LCot cd L Tan L Sin ' *17.8' 268° *358° 88° 64 2° *92° 182° *272° « ' L Sin 1 d C S C T L Tan cd L Cot L Cos 7200 7260 I 8.54282 360 357 355 351 349 346 343 341 337 336 332 330 328 325 323 320 318 5-31 451 5-31 425 8.54 30S 361 358 1.45 692 9-99 974 60 59 8.54 642 5-31451 5-31425 8.54 669 1-45331 9-99 973 7320 2 8.54 999 5-31452 5.31 424 8.55 027 1-44 973 9-99 973 58 7380 3 8.55354 5-31452 5-31 424 8.55 382 355 1.44 618 9-99 972 57 7440 4 8.55 705 5-31452 5-31 424 8.55 734 352 1.44 266 9-99 972 56 7500 5 8.56054 5-31 452 5-31 423 8.56083 349 346 1-43 917 9.99 971 55 7560 6 8.56 400 5-31 452 5-31 423 8.56 429 1-43571 9-99 971 54 7620 7 8.56 743 5-31 452 5-31423 8-56773 344 1-43 227 9-99 970 53 7680 8 8.57084 531453 5.31422 8.57114 341 338 336 333 1.42 886 9-99 970 52 7740 78oo 7860 9 10 II 8.57421 5-31453 5.31 422 8.57452 1.42 548 9-99 969 51 50 49 8.57757 5-31 453 5.31422 8.57788 1.42 212 9-99 969 8.58089 5-31 453 5-31 421 S.58 121 1-41 879 9.99 968 7920 12 8.58419 5-31453 5-31421 8.58451 330 328 326 I -41 549 9.99 968 48 7980 13 8.58 747 5-31453 5.31 421 8.58 779 1.41 221 9-99 967 47 8040 14 8.59 072 5-31 454 5.31 421 8.59 105 1-40895 9-99 967 46 8100 15 8.59395 5-31 454 5.31 420 8.59428 323 1.40572 9-99 967 45 8i6o 16 8.59715 5-31 454 5.31 420 8.59 749 321 319 316 1.40 251 9-99 966 44 8220 17 8.60 033 316 313 311 309 307 305 302 5-31 454 5-31 420 8.60 068 1-39932 9-99 966 43 8280 18 8.60 349 5-31 454 5-31419 8.60 384 1.39 616 9-99 965 42 8340 8400 8460 19 20 21 8.60 662 5-31 454 5.31 419 8.60 698 314 311 310 1.39 302 9-99 964 41 40 39 8.60973 5-31455 5.31 418 8.61 009 1-38991 9-99 964 8.61 282 5-31455 5.31 418 8.61 319 1.38681 9-99 963 8520 22 8.61 589 5-31455 5.31418 8.6i 626 307 1.38374 9-99 963 38 8580 23 8.61 894 5-31 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842 9.27 91 1 9.27 980 9.28 049 9.28 117 9.28 186 9.28 254 9.28 323 g.28 3gl 9.28 459 g.28 527 9-28 595 9.28 662 9.28 730 9.28 7g8 g.28 865 74 73 74 73 74 73 73 73 73 73 72 73 72 73 72 72 72 72 72 71 72 71 72 71 71 71 71 70 71 71 70 70 71 70 70 70 70 6g 70 69 70 69 6g 6g 69 69 69 69 68 6g 68 69 68 68 68 68 67 68 68 67 0.75 3f>S 9-99 335 0.75 2y4 0.75 221 0.75 147 0.75 074 0.75 000 0.74927 0.74 854 0-74 781 0.74 708 9-W 333 9-99 33 r 9-99 328 9-99 326 9.99 324 9-99 322 9-99319 9-99317 9-99315 0-74 635 9-99313 0-74 563 0.74 490 0.74418 0.74 345 0.74 273 0.74 201 0.74 129 0.74057 0-73 985 9-99310 9-99 308 9-99 306 9-99 304 9-99 301 9-99 299 9-99 297 9-99 294 9-99 292 0-73 914 0.73 842 0.73 771 0.73 699 0.73 628 0.73 557 0.73 486 0.73415 0.73 345 0-73 274 9-99 290 g.gg 288 9-99 285 g.gg 283 g.gg 281 9-99 278 9-99 276 9-99 274 g.gg 271 9-99 26g 0.73 203 0.73 133 0.73 063 0.72 992 0.72 922 0.72 852 0.72 782 0.72 712 0.72 643 0-72 573 0.72 504 0.72 434 0.72 365 0.72 296 0.72 227 0.72 158 0.72 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634 9.52 669 9-52 705 9-52 740 9-52 775 9.52 811 9.52 846 9.52881 9.52 916 9-52951 g.52986 9-53 021 9-53056 9-53092 9.53 126 9-53 161 9-53 196 9-53 231 9.53 266 9-53 301 9-53 336 9-53 370 9-53 405 LCos 37 37 36 37 36 37 36 37 36 36 37 36 36 36 37 36 36 36 36 36 36 36 36 36 36 36 35' 36 36 36 35 36 35 36 35 36 35 36 35 36 35 35 36 35 35 35 35 35 35 35 36 34 35 35 35 35 35 35 34 35 9-53 697 9-53 738 9-53 779 9-53 820 9-53 861 9-53 902 9-53 943 9-53 984 9.54025 9-54065 9.54 106 9-54 147 9-54 187 9.54228 9.54269 9-54 309 9-54 350 9-54 390 9-54431 9-54471 9-54512 9-54 552 9-54 593 9-54633 9-54673 9-54 714 9-54 754 9-54 794 9-54835 9-54875 9-54915 9-54 955 9-54 995 9-55035 9-55075 9-55 115 9-55 155 9-55 195 9-55 235 9-55275 9-55315 9-55 355 9-55 395 9-55 434 9-55 474 9-55514 9-55 554 9-55 593 9-55 633 9-55673 9-55 712 9-55 752 9-55 791 9-55 831 9-55 870 9.55910 9-55 949 9-55 989 9.56028 9.56067 9.56 107 41 41 41 41 41 41 41 41 40 41 41 40 41 41 40 41 40 41 40 41 40 41 40 40 41 40 40 41 40 40 40 40 40 40 40 40 40 40 40 40 40 40 39 40 40 40 39 40 40 39 40 39 40 39 40 39 40 39 39 40 0.46 303 9-97 567 0.46 262 0.46 221 0.46 180 0.46 139 0.46 098 0.46057 0.46016 0.45 975 0.45 935 9-97 563 9.97558 9-97 554 9-97 550 9-97 545 9-97 541 9-97 536 9-97 532 9-97 528 0-45 894 9-97 523 0.45 853 0.45 813 0.45 772 0.45 731 0.45 691 0.45 650 0.45 610 0.45 569 0.45 529 0.45 488 9.97519 9-97515 9-97 510 9-97 506 9.97 501 9.97497 9-97 492 9-97 488 9-97 484 0.45 448 0.45 407 0.45 367 0.45 327 0.45 286 0.45 246 0.45 206 0.45 165 0.45 125 9-97 479 9-97 475 9-97 470 9-97466 9-97 461 9-97 457 9-97 453 9-97 44S 9-97 444 9-97 439 0-45 085 9-97 435 0.45 045 0.45 005 0.44 965 0.44 925 0.44 885 0.44 845 0.44 805 0.44 765 0.44 725 9-97 430 9-97 426 9.97421 9-97417 9.97412 9-97 408 9-97 403 9-97 399 9-97 394 0.44 685 9-97 390 0.44 645 0.44 605 0.44 566 0.44 526 0.44 486 0.44 446 0.44 407 0.44 367 0.44327 9-97 385 9-97 381 9-97 376 9-97372 9-97 367 9-97 363 9-97358 9-97 353 9-97 349 0.44 288 0.44 248 0.44 209 0.44 169 0.44 130 0.44 090 0.44051 0.44 on 0.43 972 0-43 933 9-97 344 0.43 893 LCot cd LTan 9-97 340 9-97 335 9-97331 9-97 326 9.97322 9.97317 9-97312 9-97 308 9-97 303 9-97 299 L Sin 41 40 I 0.7 0.7 2 1-4 1-3 3 2.0 2.0 4 2.7 2.7 5 3-4 3-3 6 4-1 4.0 7 4.8 4-7 8 .5-5 5.3 9 6.2 6.0 10 6.8 6.7 20 13-7 13.3 30 20.5 20.0 40 27-3 26.7 50 34-2 33-3 37 36 I 0.6 0.6 2 1.2 1.2 3 1.8 1.8 4 2.5 2-4 5 3-1 3-0 6 3-7 3-6 7 4-3 4.2 8 4-9 4-8 9 5-6 5-4 10 6.2 6.0 20 12.3 12.0 30 18.5 18.0 40 24-7 24.0 50 30.8 30.0 34 5 I 0.6 0.1 2 I.I 0.2 3 1-7 0.2 4 2-3 0-3 5 2.8 0.4 6 3-4 0.5 7 4.0 0.6 8 4-5 0.7 9 5-1 0.8 10 5-7 0.8 20 11-3 1-7 30 17.0 2.5 40 22.7 3-3 50 28.3 4-2 5 5 41 40 4.1 4.0 12.3 12.0 20.5 20.0 28.7 28.0 36.9 36.0 4 4 1 39 0.6 1-3 2.0 2.6 3-2 3-9 4.6 5.2 5-8 6.5 13-0 19.5 26.0 32.5 35 0.6 1.2 1.8 2.3 2.9 3.5 4.1 4-7 5-2 5-8 II. 7 17-5 23-3 29.2 4 0.1 0.1 0.2 0.3 0.3 0.4 0.5 0.5 0.6 0.7 1-3 2.0 2.7 3-3 4 4 41 40 51 5-0 15.4 15-0 25.6 25.0 35-9 35-0 36 3.9 II. 7 19-5 27-3 35-1 4 39 4-9 14.6 24-4 34-1 P P »160° 250° *;i40° 70° 82 20° *110° 200° *290° L Sin LTan c d L Cot LCos P P 9 10 II 12 13 14 15 i6 17 i8 ig 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9-53 405 9-53 440 9-53 475 9-53 509 9-53 544 9-53 578 9.53613 9-53 647 9.53 682 9-53716 9-53 751 9-53 785 9-53 819 9-53 854 9-53 888 9.53922 9-53 957 9-53991 9.54025 9-54059 9-54 093 9.54127 9-54 161 9-54 195 9.54229 9-54 263 9-54297 9-54331 9-54 3o 45 I 44 2 43 3 42 4 41 40 b 6 39 7 38 8 37 9 36 10 35 20 34 30 33 40 32 50 31 30 29 28 27 26 25 24 23 22 21 20 36 0.6 1.2 1.8 2.4 3.0 3-6 4.2 4.8 5.4 6.0 12.0 18.0 24.0 30.0 30 0-5 i.o 1-5 2.0 2.5 3.0 3-5 4.0 4-5 5-0 lo.o 15.0 20.0 25.0 35 0.6 1.2 1.8 2.3 2.9 3.5 4.1 4.7 5-2 5.8 II. 7 17-5 23-3 29.2 29 0-5 1.0 1.4 1.9 2.4 2.9 3.4 3.9 4-4 4.8 9-7 14-5 19-3 24.2 34 0.6 I.I 1-7 2.3 2.8 3-4 4.0 4-5 5.1 5-7 11-3 17.0 22.7 28.3 28_ 0.5 o.g 1.4 1.9 2-3 2.8- 3-3 3.7 4.2 4-7 9-3 14.0 18.7 23.3 I 6 0.1 2 0.2 3 0.3 4 0.4 5 0.5 6 0.6 7 0.7 8 0.8 9 0.9 10 1.0 20 2.0 30 3.0 40 4.0 50 5.0 5 0.1 0.2 0.2 0.3 0.4 0-5 0.6 0-7 0.8 0.8 1-7 2.5 3.3 4.2 6 6 36 35" 3.0 2.9 g.o 8.8 3 15.0 14.6 21.0 20.4 4 5 6 27.0 26.2 33-0 32.1 6_ 2.8 8.5 14.2 ig.8 25.5 31.2 5 35 T 3.5 2 10.5 3 4 5 17.5 24.5 31.5 34 3-4 10.2 17.0 23.8 30.6 LCos LCot cd LTan L Sin d P P *156° 246° *336° 66° 86 2i° *U4° 204" *294° L Sin L Tan c d L Cot LOos d P P 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.60 931 5.60 960 5.60 9S8 3.61 016 9- 9- 9- 9.61 045 9.61 073 9.61 lOI 9.61 129 9.61 158 9.61 186 9.61 214 g.6l 242 9.61 270 9.61 298 9.61 326 9.61 354 9.61 J82 9.61 411 9.61 438 9.61 466 9-6i 494 9.61 522 9.61 550 9-6l 578 g.6l 606 9.61 634 9.61 662 9.61 689 9.61 717 9-6l 745 9-fai 773 9.61 800 9.61 828 9.61 856 9.61 883 9.61 911 g.6l 939 9.61 966 g.6l 994 1.62 021 9.62 049 ^.bo. 076 9.62 104 g.62 131 9.62 159 g.62 186 g.62 214 g.62 241 g.62 268 g.62 2g6 9-'^2 323 9.62 350 9.62 377 g.62 405 g.62 432 g,62 45g g.62 486 g.62 513 g.62 541 9.62 568 g.62 595 LCos 29 28 28 29 28 28 28 29 28 28 28 28 28 28 28 28 29 27 28 28 28 28 28 28 28 28 27 28 28 28 27 28 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 27 27 28 27 27 27 27 28 27 27 3.64 858 9.64 892 g.64 926 9.64 g6o g.64 gg4 9.65 028 9.65 062 9.65 096 9.65 130 1.65 164 9-65 197 g.65 231 g.65 265 9.65 29g 9-65 333 g.65 366 g.65 400 9-65 434 9.65 467 9-65 501 9-65 535 9.65 568 9.65 602 g.65 636 g.65 669 9.65 703 9.63 736 9.65 770 g.65 803 9-65 837 9.65 870 9.65 904 9-f'5 937 9.65 971 g.66 004 g.66038 9.66071 9.66 104 g.66 138 g.66 171 g.66 204 J.66 238 g.66 271 g.66 304 9-66 337 g.66 371 9.66 404 9.66 437 9.66 470 9-66 503 9-6& 537 g.66 570 g.66 603 g.66 636 9.66 669 9.66 702 g.66 735 g.66 768 g.66 801 9.66 834 g.66 867 34 34 34 34 34 34 34 34 34 33 34 34 34 34 33 34 34 33 34 34 33 34 34 33 34 33 34 33 34 33 34 33 34 33 34 33 33 34 33 33 34 33 33 33 34 33 33 33 33 34 33 33 33 33 33 33 33 33 33 33 0-35 142 0.35 108 0.35 074 0.35 040 0.35 006 0.34 g72 0.34 938 0.34 904 0.34 870 0.34 836 9-96 °73 9.96 067 9.g6 062 g.96 056 g.g6 050 g.96 045 9.96 039 g.g6 034 g.g6 028 g.g6o22 0.34 803 g.g6oi7 0.34 76g 0.34 735 0.34 701 0.34 667 0.34 634 0.34 600 0.34 566 0-34 533 0-34 499 g.g6oii g.g6 005 g.96 000 9-95 994 9-95 988 9-95 982 9-95 977 9.95 971 9-95 965 0.34465 9-95 9^° 0.34 432 0.34 398 0.34 364 0.34 331 0.34 2g7 0.34 264 0.34 230 0.34 ig7 0.34 163 9-95 954 9-95 948 9-95 942 9-95 937 9-95 931 9-95 925 9-95 920 9-95 9M 9-95 9°8 0-34 130 0.34 og6 0.34 063 0.34 02g 0.33 996 0.33 962 0.33 929 0.33 896 0.33 862 0.33 82g 9-95 902 0-33 796 0.33 762 0.33 729 0.33 696 0.33 663 0.33 629 0.33 596 0.33 563 0.33 530 0-33 497 0-33 463 0.33 430 0.33 397 0.33 364 0.33 331 0.33 2g8 0.33 265 0.33232 0.33 199 0.33 166 0.33 133 L Cot cd LTan 9-95 897 9-95 891 9-95 885 9-95 879 9-95 873 g.gS 868 9.95 862 9-95 356 9-95 850 9-95 844 9-95 839 9-95 833 9.95 827 9.g5 821 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7 6 5 4 3 2 I P P 33 I 0.6 2 I.I 3 1.6 4 2.2 5 2.8 6 3-3 7 3-8 8 4-4 9 5-0 10 5-5 20 II.O 30 16.5 40 22.0 50 27-5 27 I 0.4 2 o.g 3 1.4 4 1.8 5 2.2 6 2.7 7 3-2 8 3-6 9 4-0 10 4-5 20 9.0 30 13-5 40 18.0 50 22.5 32 0-5 I.I 1.6 2.1 2-7 3-2 3-7 4-3 4-8 5-3 10.7 16.0 21.3 26.7 26 0.4 o.g 1-3 1-7 2.2 2.6 3-0 3-5 3-9 4-3 8-7 13-0 17-3 21.7 7 6 I 0.1 0.1 2 0.2 0.2 3 0.4 0-3 4 0.5 0.4 5 0.6 0.5 6 0.7 0.6 7 0.8 0.7 8 0.9 0.8 9 I.O 0.9 10 1.2 1.0 20 2-3 2.0 30 3-5 3-0 40 4-7 4.0 50 5-8 5-0 5 0.1 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 1-7 2-5 3-3 4.2 7 6 32 32 2.3 2-7 6.9 8.0 11.4 13-3 16.0 18.7 20.6 24.0 25.1 29-3 29.7 — 5 33 3-3 9-9 16.5 23.1 29-7 P P *154° 244° *334° 6t° 26° *116° 206° *29fi° L Sin L Tan c d L Cot LCos d P P I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 i6 17 iS 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 g.64 184 9.64 210 9.64 236 9.64 262 9.64 288 9-64313 9.64 339 9.64 365 9.64 391 9-64417 Q.64 442 9.04 468 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g.g5 020 9-95 014 9-95 007 g-g5 001 9-94 995 0.29 283 9-94 988 32 I 0.5 2 I.I 3 1.6 4 2.1 5 2.7 6 3-2 7 3-7 8 4-3 9 4.8 10 5-3 20 10.7 30 16.0 40 21.3 50 26.7 0.5 I.O 1.6 2.1 2.6 3-1 3-6 4.1 4.6 5-2 10.3 15-5 20.7 25.8 26 25 I 0.4 0.4 2 o.g 0.8 3 1-3 1.2 4 1-7 1-7 5 2.2 2.1 6 2.6 2.5 7 3-0 2-9 8 3-5 3-3 9 3-9 3-8 10 4-3 4-2 20 8.7 8.3 30 13-0 12.5 40 17-3 16.7 50 21.7 20.8 24 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3-2 3.6 4.0 8.0 12.0 16.0 20.0 7 I 0.1 2 0.2 3 0.4 4 0.5 5 0.6 6 0.7 7 0.8 8 o.g 9 1.0 10 1.2 20 2.3 30 3-5 40 4-7 50 5-8 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.g I.O 2.0 3-0 4.0 5-0 7 7 32 31 2.3 2.2 6.9 6.6 11.4 II. I 16.0 15-5 20.6 19.9 25.1 24.4 29.7 28.8 6_ 32 2.7 8.0 13-3 18.7 24.0 29-3 L Cos liCot cd L Tan L Sin P P »153° 243° *333° 63° 27° 89 nil 207° *297'' L Sin L Tan c d L Cot L Cos P P 9 10 II 12 '3 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9-65 705 9.65 729 9-65 754 9.65 779 9.65 804 9.65 828 9.65 853 9.65 878 9.65 go2 9-65 927 9-65 9 52 9.65 976 9.66 001 9.66025 9.66 050 9.66075 9.66 099 9.66 124 9.66 148 9.66 173 9.66 197 9.66 221 g.66 246 g. 66 270 g.66 295 9.66 319 9.66 343 9.66 368 g.66 392 g.66 416 9.66 44 1 g.66 465 g.66 489 9.66513 9.66 537 g.66 562 g.66 586 g.66 610 g.66 634 9.66658 ^.66682 9.66 706 9.66 731 9.66 755 g.66 77g g.66 803 9.66 827 g.66 851 g.66 875 g.66 8gg 9.66 922 9.66 946 g.66 g7o 9.66 gg4 9.67018 9.67 042 9.67 066 g.67 ogo g.67113 9-67 137 g.67 161 24 25 25 25 24 25 25 24 25 25 24 25 24 25 25 24 25 24 25 24 24 25 24 25 24 24 25 24 24 25 ■24 24 24 24 25 24 24 24 24 24 24 25 24 24 24 24 24 24 24 23 24 24 24 24 24 24 24 23 24 24 9.70717 9.70 748 9.70 779 9.70 810 g.70 841 9.70873 9.70904 9-70935 g.70 g66 9-70997 g.7l 028 9-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7 059 090 121 153 184 215 246 277 308 339 370 401 431 462 493 524 555 586 617 648 679 7og 740 771 802 833 863 894 925 9-71955 9-7 9-72017 g.72 048 g. 72 078 g.72 log g.72 140 g.72 170 g.72 201 g.72 231 g.72 262 g.72 2g3 g.72 323 9-72 354 g.72 384 9-72415 9-72445 g.72 476 g.72 506 9-72537 9-72 567 31 31 31 31 32 31 31 31 31 31 31 31 31 32 31 31 31 31 31 31 31 31 30 31 31 31 31 31 31 31 31 30 31 31 31 31 30 31 31 30 31 31 31 30 31 31 30 31 30 31 31 30 31 30 31 30 31 30 31 30 0.2g 283 9-94 988 o.2g 252 o.2g 221 o.2g I go 0.29 159 o.2g 127 o.2g og6 0.29 065 o.2g 034 0.2g 003 9-94 982 9-94 975 9-94 969 9-94 962 9-94956 9-94 949 ^-94 943 9-94 936 9-94 930 ,0.28 g72 9-94923 0.28 941 0.28 910 0.28 87g 0.28 847 0.28 816 0.28 785 0.28 754 0.28 723 0.28 6g2 9-94917 9-94 9" 9-94 904 9-94 8g8 9-94 891 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8 3-3 3-2 9 3-3 3-6 10 4-2 4-0 20 8.3 8.0 30 12.5 12.0 40 16.7 16.0 50 20.8 20.0 30 0.5 1.0 1-5 2.0 2.5 3.0 3-5 4.0 4-5 5-0 to.o 15.0 20.0 25.0 23 0.4 0.8 1.2 1-5 1.9 2-3 2-7 3-1 3-4 3-8 7-7 11-5 i.";-3 19.2 7 I 0.1 2 0.2 3 0.4 4 0.5 5 0.6 6 0.7 7 0.8 8 0.9 9 1.0 10 1.2 20 2.3 30 3-5 40 4-7 50 5-8 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5-0 7 6 80 31 2.1 2.6 6.4 7.8 3 4 5 6 10.7 I2.g 15.0 18.1 19-3 23.2 23.6 28.4 7 27-9 30 2-5 7-5 12.5 17-5 22.5 27-5 L Cos LCot cd LTan L Sin P P *152° 242° *b32° 90 28= *118° 208° *298'' I LSin 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Q.67 161 9.67185 9.67 208 9-67 232 9.67256 9.67 280 9.67 303 9.67 327 9.67 350 9-67 374 9-67 398 9.67 421 9-67 445 9.67 468 9.67 492 9-67515 9-67 539 9.67 562 9.67 586 9.67 609 9-67 633 9.67656 9.67 680 9.67 703 9.67 726 g.67 750 9-67 773 9.67 796 9.67 820 9-67 843 9.67 866 9.67 890 9.67913 9.67 936 9-67959 9.67 982 9.68 006 g.6S 029 9.68052 9.68 075 9.6 8 098 9.68 121 9.68 144 9.68 167 9.68 igo 9.68 213 9.68 237 9.68 260 g.68 283 9-68 305 9.68 328 9.68351 9-68374 g.68 397 g.68 420 9-68 443 9.68 466 9.68 489 g.68 512 9-68 534 9-68557 LCos 24 23 24 24 24 23 24 23 24 24 23 24 23 24 23 24 23 24 23 24 23 24 23 23 24 23 23 24 23 23 24 23 23 23 23 24 23 23 23 23 23 23 23 23 23 24 23 23 22 23 23 23 23 23 23 23 23 23 22 23 L Tan cd 9-72 567 9.72 598 g.72 628 9-72 65g g.72 68g g.72 720 9.72 750 9.72 780 g.72 81X 9.72 841 9-72 872 9.72 902 g.72 g32 g.72 g63 9-72 993 9-73 023 9-73054 9-73 084 9-73 "4 9-73 144 9-73175 9-73 205 9-73 235 9-73 265 9-73 295 9 73 326 9-73 356 9-73 386 9-73416 9-73446 9-73 476 9-73 507 9-73 537 9-73 567 9-73 597 9-73 627 9-73 657 9-73 687 9-73 717 9-73 747 9-73 777 9-73 807 9-73837 9-73 867 9-73 8g7 9-73927 9-73 957 9-73 987 9.74017 9-74047 Q- 74 077 9-74 107 9-74137 9.74 166 9-74 196 9.74 226 9-74256 g.74 286 9.74316 9-74 345 9-74 375 31 30 31 30 31 30 30 31 30 31 30 30 31 30 30 31 30 30 30 31 30 30 30 30 31 30 30 30 30 30 31 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 29 30 30 30 30 30 29 30 LCot 0-27433 0.27 402 0.27 372 0.27 341 0.27 311 0.27 280 0.27 250 0.27 220 0.27 i8g 0.27 I5g 0.27 128 0.27 oga 0.27 068 0.27037 0.27 007 0.26977 0.26 946 0.26 916 0.26 886 0.26 856 0.26 825 0.26 7g5 0.26 765 0.26 735 0.26 705 0.26 674 0.26 644 0.26 614 0.26 584 0.26 554 L Cos 9-94 593 9-94 587 9-94 580 9-94 573 9-94 567 9-94 560 9-94 553 9-94 546 9-94 540 9-94 533 9-94 526 9-94 519 9-94 513 9-94 506 9-94 499 9-94 492 9-94 485 9-94 479 9-94 472 9-94 465 9-94 458 0.26 524 L Cot I c d L Tan 0.26 4g3 0.26 463 0.26 433 0.26 403 0.26373 0.26 343 0.26 313 0.26 283 0.26 253 0.26 223 0.26 193 0.26 163 0.26 133 0.26 103 0.26073 0.26 043 0.26013 0.25 983 0.25 g53 0.25 923 0.25 8g3 0.25 863 0.25 834 0.25 804 0.25 774 0.2 5 744 0.25 714 0.25 684 0.25 655 0.25 625 9-94451 9-94 445 9-94 438 9-94 431 9-94 424 9-94417 9.94410 9-94 404 9-94 397 9-94 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22 22 22 22 22 22 L Tan c d L Cot L Cos 9-74 375 9-74405 9-74 435 9-74465 9-74 494 9-74 524 9-74 554 9-74 583 9.74613 9-74 643 9-74 673 9.74 702 9-74 732 9-74 762 9-74 791 9.74 821 9.74851 9.74 880 9.74910 9-74 939 9-74 969 9.74998 9-75 028 9.75058 9-75087 9-75 117 9-75 146 9-75 176 9-75 205 9-75235 9-75 264 9-75 294 9-75 323 9-75 353 9-75 382 9-75 4" 9-75 441 9-75 470 9-75 500 9-75 529 9-75558 9-75 588 9.75617 9-75 647 9.75 676 9-75 705 9-75 735 9-75 764 9-75 793 9.7s 822 9-75 852 9-75 »»i 9.75910 9-75 939 9-75 969 9.75 998 9.76 027 9.76056 9.76086 9-76 115 9.76 144 LCot 30 30 30 29 30 30 29 30 30 30 29 30 30 29 30 30 29 30 29 30 29 30 30 29 30 29 30 29 30 29 30 29 30 29 29 30 29 30 29 29 30 29 30 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 0.25 625 0.25 595 0.25 565 0-25 535 0.25 506 0.25 476 0.25 446 0.25417 0.25 387 0-25 357 0.25 327 0.25 298 0.25 268 0.25 238 0.25 209 0.25 179 0.25 149 0.25 120 0.25 090 0.25 061 0.25 031 0.25 002 0.24972 0.24 942 0.24913 0.24 883 0.24 854 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*lfi2° 252° *342° J *108° 198° *288° 18° /V^ "T Natural ' Sin Tan Cot Cos I 2 3 0.3090 0.3249 3-0777 0.9511 (30 59 58 57 0.3093 0.309b 0.3098 0.3252 0.3256 0.3259 3.0746 3.0716 3.0686 0.9510 0.9509 0.9508 4 5 6 0.3101 0.3104 0.3107 0.3262 0.3265 0.3269 3-0655 3.0625 3-0595 0.9507 0.9506 0.9505 56 55 54 7 8 9 :o II 12 13 0.31 10 0.3112 0.3115 0.3272 0.3275 0.3278 3-0565 3-0535 3-0505 0.9504 0.9503 0.9502 53 52 51 50 49 48 47 0.31 18 0.3281 3-0475 0.9502 0.3121 0.3123 0.3126 0.3285 0.3288 0.3291 3-0445 3.0415 3-0385 0.9501 0.9500 0.9499 M 15 I6 0.3129 0.3132 0.3134 0.3294 0.3298 0.3301 3-0356 3.0326 3.0296 0.9498 0-9497 0.9496 46 45 44 17 i8 19 20 21 22 23 0.3137 0.3140 0.3143 0.3304 0.3307 0.33(0 3.0267 3-0237 3.0208 0.9495 0.9494 0.9493 43 42 41 40 39 38 37 0.3145 0.3314 3.0178 0.9492 0.3148 0.3151 0.3154 0.3317 0.3320 0.3323 3-0149 3.0120 3.0090 0.9492 0.9491 0.9490 24 25 26 03156 03159 0.3162 0.3327 0.3330 0.3333 3.0061 3-0032 3.0003 0.9489 0.9488 0.9487 36 35 34 27 28 29 30 31 32 33 0.3165 0.3168 0.3170 0.3338 0.3339 0.3343 2.9974 2.9945 2.ggl6 '0.9486 0.9485 0.9484 33 32 31 30 29 28 27 0.3173 03346 2.9887 0.9483 0.3176 0.3179 0.3181 0.3349 0.3352 0.3356 2.9858 2.9829 2.9800 0.94S2 0.9481 0.9480 34 35 36 0.3184 0.3187 0.3190 0.3359 0.3362 0.3365 2.9772 2.9743 2-9714 0.9480 0.9479 0.9478 26 25 24 37 38 39 40 41 42 43 0.3192 0.3195 0.3198 0.3369 0.3372 0.3375 2.9680 2.9657 2.9629 0.9477 0.9476 0.9475 23 22 21 20 19 18 17 0.3201 0.3378 2.9600 0-9474 0.3203 0.3206 0.3209 0.3382 0.3385 0.3388 2.9572 2.9544 2.9515 0-9473 0.9472 0.9471 44 45 46 0.3212 0.3214 0.3217 0.3391 0.3395 0.3398 2.9487 2.9459 2.9431 0.9470 0.9469 0.9468 16 15 14 47 43 49 50 51. 52 53 0.3220 0.3223 0.3225 0.3401 0.3404 0.3408 2.9403 2.9375 2-9347 0.9467 0.9466 0.9466 13 12 11 10 9 8 7 0.3228 0.3411 2.9319 0.9465 0.3231 0.3234 0.3236 0.3414 0.3417 0.3421 2.9291 2.9263 2.9235 0.9464 0.9463 0.9462 54 55 56 0.3239 0.3242 0.3245 0.3424 0.3427 0.3430 2.9208 2.9180 2.9152 0.9461 0.9460 0.9459 6 5 4 57 58 59 60 0.3247 0.3250 0-3253 0.3434 0-3437 0.3440 2.9125 2.9097 2.9070 0.9458 0.9457 0-9456 3 2 1 0.3256 0-3443 2.9042 0-9455 Cos Cot Tan Sin ' 19° *109° 199° 117 »289° Sin Tan Cot Cos I 2 3 0.3256 0.3443 2.9042 0.9455 60 59 58 57 0.3258 0.3261 0.3264 0.3447 0.3450 0.3453 2.9015 2.8987 2.8960 0.9454 0.9453 0.9452 4 5 6 0.3267 0.3269 0.3272 0-3456 0.3460 0.3463 2.8933 2.8905 2.8878 0-9451 0.9450 0.9449 56 55 54 7 8 9 10 11 12 13 0.3275 0.327S 0.3280 0.3466 0.3469 0.3473 2.8S51 2.S824 2.8797 0.9449 0.9448 0.9447 53 52 51 50 49 48 47 0.3283 0.3476 2.8770 0.9446, 0.3286 0.3289 0.3291 0.3479 0.3482 0.3486 2.8743 2.8716 2.8689 0.9445 0-9444 0-9443 14 15 16 0.3294 0.3297 0.3300 0.3489 0.3492 0.3495 2.8662 2.8636 2.8609 0-9442 0.9441 0.9440 46 45 44 17 18 19 20 21 22 23 0.3302 0.3305 0.3308 0-3499 0.3502 0-3505 2.8582 2.8556 2.8529 0.9439 0.9438 0.9437 43 42 41 40 39 38 37- 0.3311 0.3508 2.S502 0.9436 0.3313 0.3316 0.3319 0.3512 0.3515 0.3518 2.6476 2.8449 2.8423 0.9435 0.9434 0.9433 24 25 26 0.3322 0.3324 0.3327 0.3522 0.3525 0.3528 2.8397 2^8370 2r8344 0.9432 0.9431 0.9430 36 35 34 27 28 29 30 31 32 33 0.3330 0.3333 0.3335 0.3531 0.3535 0.3538 2.831S 2.S291 2.8265 0.9429 0.9428 0.9427 33 32 31 30 29 28 . 27 0.3338 0.3541 2.8239 0.9426 0.3341 0.3344 0.3346 0.3544 0.3548 0.3551 2.8213 2.8187 2.8161 0.9425 0.9424 0.9423 34 35 36 0.3349 0.3352 0-3355 0.3554 0.3558 0.3561 2.8135 2.8109 2.8083 0.9423 0.9422 0.942 1 26 25 24 37 38 39 40 41 42 43 0.3357 0.3360 0.3363 0.3564 0.3567 0-3571 2.8057 2.8032 2.8006 0.94C0 0.9419 0.9418 23 22 21 20 19 iS 17 0.3365 0-3574 2.7980 0.9417 0.3368 0.3371 0-3374 0-3577 0.3581 0-3584 2.7955 2.7929 2.7903 0.9416 0-9415 0.9414 44 45 46 0.3376 0.3379 0.3382 0.3587 0.3590 0-3594 2.7878 2.7852 2.7827 0.9413 0.9412 0.941 1 16 15 14 47 48 49 50 51 52 53 0.3385 0.3387 0.3390 0-3597 0.3600 0.3604 2.7801 2.7776 2.7751 0.9410 0.9409 0.9408 13 12 1 1 10 9 8 7 0.3393 0.3607 2-77:5 0.9407 ■ 0.3396 0.3398 0.3401 0.3610 0.3613 0.3617 2.7700 2.7675 2.7650 0.9406 0.9405 0.9404 54 55 S6 0.3404 0.3407 0.3409 0.3620 0.3623 0.3627 2.7625 2.7600 2.7575 0.9403 0.9402 0.9401 6 5 4 57 58 59 60 0.3412 0.3415 0-3417 0.3630 0.3633 0.3636 2.7550 2.7525 2.7500 0.9400 0-9399 0.9398 3 2 I 0.3420 0.3640 27475 0-9397 Cos Cot Tan Sin ' *161° 251° *341° 71° Natural 70° *160° 250° »340° 118 *110° 200° *290° 20° Natural 21"' *111° 201° *291° Sin Tan Cot Cos ' Sin Tan Cot Cos I 2 3 0.3420 0.3640 2.7475 0.9397 60 59 58 57 I 2 3 0.3584 0-3839 2.6051 0-9336 60 59 58 57 0.3423 0.3426 0.3428 0.3643 0.3646 0.3650 2.7450 2.7425 2.7400 0.9396 0-9395 0.9394 0.3586 0-3589 0-3592 0.3842 0.3845 0.3849 2.6028 2-6006 2.5983 0.9335 0-9334 0-9333 4 5 6 0.3431 0.3434 0-3437 0.3653 0.3656 0.3659 2.7376 2.7351 2.7326 0.9393 0.9392 0.9391 56 55 54 4 5 6 0.3595 0.3597 0.3600 0.3852 0.3855 0.3859 2.5961 2.5938 2.5916 0-9332 0.9331 0.9330 56 55 54 7 8 9 10 II 12 13 0.3439 0.3442 0.3445 0.3663 0.3666 0.3669 2.7302 2.7277 2.7^53 0.9390 0.93^9 0.9388 53 52 51 50 49 48 47 7 8 9 10 II 12 13 0-3603 0.3605 0.3608 0-3862 0-3S65 0.38&9 2.5893 2.5871 2.5848 0.9328 0.9327 0.9326 53 52 51 50 '49 48 47 0.3448 0.3673 2.7228 0.9387 0.361 r 0.3872 2.5826 0-9325 0.3450 0.3453 0.3456 0.3676 0.3679 0.3683 2.7204 2.7179 2.7155 0.9386 0.9385 0.9384 0.3614 0.3616 0.3619 0.3875 0.3879 0.3882 2.5804 2.5782 2.5759 0.9324 0.9323 0.9322 14 15 i6 0.3458 0.3461 0.3464 0.3686 0.3689 0.3693 2.7130 2.7106 2.7082 0.9383 0.9382 0.9381 46 45 44 14 15 16 0.3622 0.3624 0.3627 0.3885 0.3889 0.3892 2.5737 2.5715 2.5693 0.9321 0.9320 0.9319 46 45 44 17 i8 19 20 21 22 23 0.3467 0.3469 0.3472 0.3696 0.3699 0.3702 2.7058 2.7034 2.7009 0.9380 0.9379 0.9378 43 42 41 40 39 38 37 17 18 19 20 21 22 23 0.3630 0.3633 0.3635 0.3895 0.3899 0.3902 2.5671 2.5649 2.5627 0.9318 0-9317 0.9316 43 42 41 40 39 38 37 0-3475 0.3706 2.6985 0.9377 0:3638 0.3906 2.5605 0-9315 0.3478 0.3480 0.3483 0.3709 0.3712 0.3716 2.6961 2.6937 2.6913 0.9376 0.9375 0.9374 0.3641 0.3643 0.3646 0.3909 0.3912 0.3916 2.5583 2.5561 2.5539 0.9314 0.9313 0.9312 24 25 26 0.3486 0.3488 0.3491 0.3719 0.3722 0.3726 2.6889 2.6865 Z.6841 0.9373 0.9372 0.9371 36 35 34 24 25 26 0.3649 0.3651 0-3654 0.3919 0.3922 0.3926 2-5517 2-5495 2-5473 0.9311 0.9309 0.9308 36 35 34 27 28 29 30 31 32 33 0.3494 0.3497 0.3499 0.3729 0.3732 0.3736 2.68x8 2.6794 2.6770 0.9370 0.9369 0.9368 33 32 31 30 29 28 27 27 28 29 30 31 32 33 0-3657 0-3660 0.3662 0.3929 0.3932 0.3936 2.5452 2.5430 2.5408 0-9307 0.9306 0.9305 33 32 31 30 29 28 27 0.3502 0.3739 2.6746 0.9367 0.3665 0.3939 2.5386 0-9304 0.3505 0.3508 0.3510 0.3742 0.3745 0.3749 2.6723 2.6699 2.6675 0.9366 0.9365 0.9364 0.3668 0.3670 0-3673 0.3942 0.3946 0-3949 2.5365 2-5343 2.5322 0.9303 0.9302 0.9301 34 35 36 0.3513 0.3516 0.3518 0.3752 0.3755 0.3759 2.6652 2.6628 2.6605 0.9363 -0.9362 0.9361 26 25 24 34 35 36 0.3676 0.3679 0.3681 0-3953 0.3956 0.3959 2.5300 2.5279 2.5257 0.9300 0.9299 0.9298 26 25 24 37 38 39 40 41 42 43- 0.3521 0.3524 0.3527 0.3762 0.3765 0.3769 2.6581 2.6558 2.6534 0.9360 0.9359 0.9358 23 22 21 20 19 18 17 37 38 39 40 41 42 43 0-3684 0-3687 0.3689 0.3963 0.3966 0.3969 2.5236 2.5214 2.5193 0.9297 0.9296 0-9295 23 22 21 20 19 18 17 0.3529 0-3772 2.65 1 1 0-9356 0.3692 0-3973 2.5172 0-9293 0.3532 0.3535 0.3537 0-377.5 0.3779 0.3782 2.6488 2.6464 2.6441 0-9355 0.9354 0.9353 0.3695 0.3697 0.3700 0.3976 ■ 0.3979 0-3983 2-5150 2-5129 2.5108 0.9292 0.9291 0.9290 44 45 46 0.3540 0.3543 0.3546 0.3785 0.3789 0-3792 2.6418 2.6395 2.6371 0.9352 0.9351 0.9350 16 15 14 44 45 46 0.3703- 0.3706 0.3708 0.3986 0.3990 0-3993 2.50S6 2.5065 2-5044 0.9289 0.928S 0.9287 i6' 15 14 47 48 49 50 51 52 53 0.3548 0.3551 0.3554 0.3795 0.3799 0-3802 2.6348 2.6325. 2.6302 0.9349 0-9348 0-9347 13 12 II 10 9 8 7 47 48 49 50 51 52 53 0.3711 0.3714 0.3716 0.3996 0.4000 0.4003 2.5023 2.5002 2.4981 0.92S6 0.9285 0.9284 13 12 n 10 9 8 7 0-3557 0.3805 2.6279 0.9346 0.3719 0.4006 2.4960 0.9283 0.3559 0.3562 0.3565 0.3809 0.3812 0.3815 2.6256 2.6233 2.6210 0-9345 0.9344 0.9343 0-3722 0-3724 0.3727 0.4010 0.4013 0.4017 2.4939 2.4918 2.4897 0.9282 0.9281 0.9279 54 55 56 0.3567 0.3570 0.3573 0.3819 0.3822 0.3825 2.6187 2.6165 2.6142 0.9342 0.9341 0.9340 6 5 4 54 55 56 0.3730 0.3733 0.3735 0.4020 0.4023 0.4027 2.4876 2.4855 2.4834 0.9278 0.9277 0.9276 6 5 4 57 58 59 60 0.3576 0.3578 0.3581 0.3829 0.3832 0-3835 2.6119 2.6096 2.6074 0.9339 0.9338 0.9337 3 2 I 57 58 59 60 0.3738 0.3741 0-3743 0.4030 0.4033 0.4037 2.4813 2.4792 2.4772 0.9275 0-9274 0-9273 3 2 I 0.3584 0.3839 2.6051 0.9336 0.3746 0-4040 2-4751 0.9272 Cos Uot Tan Sin Cos Cot Tan Sin ' *159° 249° *339° 69° Natural 68° *158° 248° *338° *112° 202° *292° ■22° Natural 23° 119 *113° 203° *293'' ' Sin Tan Cot Cos I 2 3 0.3746 0.4040 2.4751 0.9272 60 59 58 .57 0-3749 0.3751 0.3754 0.4044 0.4047 0.4050 2.4730 2.4709 2.4689 0.9271 0.9270 0.9269 4 5 6 0.3757 0.3760 0.3762 0.4054 0.4057 0.4061 2.4668 2.4648 2.4627 0.9267 0.9266 0.9265 56 55 54 7 8 9 10 II 12 13 0.3765 0.3768 0.3770 0.4064 0.4067 0.4071 2.4606 2.4586 2.4566 0.9264 0.9263 0.9262 53 52 51 50 49 48 47 0.3773 0.4074 2-4545 0.9261 0.3776 0.3778 0.3781 0.4078 0.4081 0.4084 2.4525 2.4504 2.4484 0.9260 0.9259 0.9258 14 15 i6 0.3784 0.3786 0.3789 0.4088 0.4091 0.4095 2.4464 2.4443 2.4423 0.9257 0.9255 0.9254 46 45 44 17 i8 19 20 21 22 23 0.3792 0.3795 0.3797 0.4098 0.4 1 01 0.4105 2.4403 2.4383 2.4362 0.9253 0.9252 0.9251 43 42 41 40 39 38 37 0.3800 0.4108 2.4342 0.9250 0.3803 0.3805 0.3808 0.41 1 1 0.41 1 5 0.4118 2.4322 2.4302 2.4282 0.9249 0.9248 0.9247 24 25 26 0.3811 0.3813 0.3816 0.4122 0.4125 0.4129 2.4262 2.4242 2.4222 0.9245 0.9244 0.9243 36 35 34 27 28 29 30 31 32 33 0.3819 0.3821 0.3824 0.4132 0.4135 0.4139 2.4202 2.4182 2.4162 0.9242 0.9241 0.9240 33 32 • 31 30 29 28 27 .0.3827 0.4142 2.4142 0.9239 0.3830 0.3832 0.3835 0.4146 0.4149 0.4152 2.4122 2.4102 2.4083 0.9238 0.9237 0.9235 34 35 36 0.3838 0.3840 0.3843 0.4156 0.4159 0.4163 2.4063 2.4043 2.4023 0.9234 0.9233 0.9232 26 25 24 37 38 39 40 41 42 43 0.3846 0.3S48 0.3851 0.4166 0.4169 0.4173 2.4004 2.39S4 2.3964 0.9231 0.9230 0.9229 23 22 21 20 19 18 17 0.3854 0.4176 2.3945 0.922S 0.3856 0.3859 0.3862 0.4180 0.4183 0.41S7 2.3925 2.3906 2.3886 0.9227 0.9225 0.9224 44 45 46 0.3864 0.3867 0.3870 0.4190 0.4193 0.4197 2.3867 2.3847 2.3828 0.9223 0.9222 0.9221 16 15 14 47 48 49 50 51 52 53 0.3872 0.3875 0.3878 0.4200 0.4204 0.4207 2.3808 2.3789 2.3770 0.9220 0.9219 0.9218 13 12 II 10 9 8 7 0.3881 0.4210 2.3750 0.9216 0.3883 0.3886 0.3889 0.4214 0.4217 0.4221 2.3731 2.3712 2.3693 0.9215 0.9214 0.9213 54 55 56 0.3891 0.3894 0.3897 0.4224 0.4228 0.4231 2.3673 2.3654 2.3635 0.9212 0.92 1 1 0.9210 6 5 4 57 58 59 60 0.3899 0.3902 0.3905 0.4234 0.4238 0.4241 2.3616 2.3597 2.3578 0.9208 0.9207 0.9206 3 2 I 0.3907 0.4245 2.3559 0.9205 Cos Cot Tan Sin ' ' Sin Tan Cot Cos I 2 3 0.3907 0.4245 2.3559 0.9205 60 59 58 57 0.3910 0.3913 0.3915 0.4248 0.4252 0.4255 2.3539 2.3520 2.3501 0.9204 0.9203 0.9202 4 5 6 0.3918 0.3921 0.3923 0.4258 0.4262 0.4265 2.3483 2.3464 2.3445 0.9200 0.9199 0.9198 56 55 54 7 8 9 10 II 12 13 0.3926 0.3929 0.3931 0.4269 0.4272 0.4276 2.3426 2.3407 2.3388 0.9197 0.9196 0.919s 53 52 51 50 49 48- 47 0.3934 0.4279 2.3369 0.9194 0.3937 0.3939 0.3942 0.4283 0.4286 0.4289 2.3351 2.3332 2.3313 0.9192 0.9191 0.9190 14 15 16 0.3945 0.3947 0.3950 0.4293 0.4296 0.4300 2.3294 2.3276 2.3257 0.9189 0.9188 0.9187 46 45 44 17 18 19 20 21 22 23 0.3953 0.3955 0.3958 0.4303 0.4307 0.4310 2.3238 2.3220 2.3201 0.9186 0.9184 0.9183 43 42 41 40 39 38 37 0.3961 0.4314 2.3183 0.9182 0.3963 0.3966 0.3969 0.4317 0.4320 0.4324 2.3164 2.3146 2.3127 0.9181 0.9180 0.9179 24 25 26 0.3971 0.3974 0.3977 0.4327 0.4331 0.4334 2.3109 2.3090 2.3072 0.9178 0.9176 0.9175 36 35 34 27 28 29 30 31 32 33 0.3979 0.3982 0.3985 0.4338 0.4341 0.4345 2.3053 2.3035 2.3017 0.9174 0.9173 0.9172 33 32 31 30 29 28 27 0.3987 0.4348 2.2998 0.91 71 0.3990 0.3993 0.3995 0.4352 0.4355 0.4359 2.2980 2.2962 2.2944 0.9169 0.9168 0.9167 34 35 36 0.3998 0.4001 0.4003 0.4362 0.4365 0.4369 2.2925 2.2907 2.2889 0.9166 0.9165 0.9164 26 25 24 37 38 39 40 41 42 43 0.4006 0.4009 0.401 1 0.4372 0.4376 0-4379 2.2871 2.2853 2.2835 0.9162 0.9161 0.9160 23 22 21 20 19 18 17 0.4014 0-4383 2.2817 0.9159 0.4017 0.4019 0.4022 0.4386 0.4390 0.4393 2.2709 2.2781 2.2763 0.9158 0.9157 0.9155 44 45 46. 0.4025 0.4027 0.4030 0.4397 0.4400 0.4404 2.2745 2.2727 2.2709 0.9154 0.9153 0.9152 16 15 14 47 48 49 50 51 52 53 0.4033 0.4035 0.4038 0.4407 0.441 1 0.4414 2.2691 2.2673 2.2655 0.9151 0.9150 0.9148 13 12 II 10 9 8 7 0.4041 0.4417 2.2637 0.9147 0.4043 0.4046 0.4049 0.4421 0.4424 0.4428 2.2620 2.2602 2.2584 0.9146 0.9145 0.9144 54 55 56 0.4051 0.4054 0.4057 0.4431 0.4435 0.4438 2.2566 2.2549 2.2531 0.9143 0.9141 0.9140 6 5 4 57 58 59 60 0.4059 0.4062 0.4065 0.4442 0.4445 0.4449 2.2513 2.2496 2.2478 0.9139 0.9138 0.9137, 3 2 I 0.4067 0.4452 2.2460 0.9135 Cos Cot Tan Sin ' «157° 247° *337° 67° Natural 66° *156° 246° *336° 120 *114° 204° *294° 2i° Natueal *115° 205° *2m° ' Sin Tan Cot Cos I 2 3 0.4067 0.4452 2.2460 0.9135 60 59 58 57 0.4070 0.4073 0.4075 0.4456 0.4459 0.4463 2.2443 2.2425 2.2408 0.9134 0.9133 0.9132 4 5 6 0.4078 0.4081 0.4083 0.4466 0.4470 0.4473 2.2390 2.2373 2.2355 0.9131 0.91.30 0.9128 56 55 54 7 8 9 10 II 12 13 0.4086 0.4089 0.4091 0.4477 0.4480 0.4484 2.2338 2.2320 2.2303 0.9127 0.9126 0.9125 53 52 51 50 49 48 47 0.4094 0.4487 2.2286 0.9124 0.4097 0.4099 0.4102 0.4491, 0.4494 0.4498 2.2268 2.22^1 2.2234 o.gi22 0.9121 0.9120 14 15 i6 0.4105 0.4107 0.41 10 0.4501 0.4505 0.4508 2.2216 2.2199 2.2182 0.9119 0.91 1 8 0.9116 46 45 44 17 i8 19 20 21 22 23 0.4112 U.4115 0.41 1 8 0.4512 0.4515 0.4519 2'.2l65 2.2148 2.2130 0.91 1 5 0.91 14 0.91 13 43 42 41 40 39 38 37 0.4120 0.4522 2.2II3 0.91 12 0.4123 0.4126 0.4128 0.4526 0.4529 0-4533 2.2og6 2.2079 2.2062 0.91 10 0.9109 0.9108 24 25 26 0.4131 0.4134 0.4136 0.4536 0.4540 0.4543 2.2045 2.2028 2.2011 0.9107 0.9106 0.9104 36 35 34 27 28 29 30 31 32 33 0.4139 0.4142 0.4144 0.4547 0.4550 0.4554 2.1994 2.1977 2.1.960 0.9103 0.9102 0.9101 33 32 31 30 29 28 27 0.4147 0.4557 2.1943 0.9100 0.4150 0.4152 0.4155 0.4561 0.4564 0.4568 2.1926 2.1909 2.1892 0.9098 0.9097 0.9096 34 35 36 0.4158 0.4160 0.4163 0.4571 0.4575 0.4578 2.1876 2.1859 2.1842 0.9095 0.9094 0.9092 26 25 24 37 38 39 40 41 42 43 0.4165 0.4168 0.41 71 0.4582 0.4585 0.4589 2.1825 2.1808 2.1792 0.9091 0.9090 0.9089 23 '22 21 20 19 18 17 0.4173 0.4592 2.1775 0.9088 0.4176 0.4179 0.41 81 0.4596 0.4599 0.4603 2.1758 2.1742 2.1725 0.9086 0.9085 0.9084 44 45 46 0.4184 0.4187 0.4189 0.4607 0.4610 0.4614 2.1708 2.1692 2.1675 0.9083 0.9081 0.9080 16 15 14 47 48 49 50 51 52 53 0.4192 0.4195 0.4197 0.4617 0.4621 0.4624 2.1659 2.1642 2.1625 0.9079 0.9078 0.9077 13 12 11 10 9 8 7 0.4200 0.4628 2.1609 0.9075 0.4202 0.4205 0.4208 0.4631 0.4635 0.4638 2.1592 2.1576 2.1560 0.9074 0.9073 0.9072 54 55 56 0.4210 0.4213 0.4216 0.4642 0.4645 0.4649 2.1543 2.1527 2.1510 0.9070 0.9069 0.9068 6 5 4 57 58 59 60 0.4218 0.4221 0.4224 0.4652 0.4656 0.4660 2.1494 2.1478 2.1461 0.9067 0.9066 0.9064 3 2 I 0.4226 0.4663 2.1445 0.9063 Cos Cot Tan Sin *155° 245° *335° 6:.° ' Sin Tan Cot Cos I 2 3 0.4226 0.4663 2.1445 0.9063 60 59 58 57 0.4229 0.4231 0.4234 0.4667 0.4670 0.4674 2.1429 2.1413 2.1396 0.9062 0.9061 0.9059 4 5 6 0.4237 0.4239 0.4242 0.4677 0.4681 0.4684 2.1380 2.1364 2.1348 0.9058 0.9057 0.9056 56 55 54 7 8 9 10 II 12 13 0.4245 0.4247 0.4250 ■ 0.4688 0.4691 0.4695 2.1332 2.1315 2.1299 0.9054 0.9053 0.9052 53 52 51 50 49 48 47 0.4253 0.4699 2.1283 0.9051 0.4255 0.4258 0.4260 0.4702 0.4706 04709 2.1267 2.1251 2.123 s 0.9050 0.9048 0.9047 15 16 0.4263 0.4266 0.4268 04713 04716 0.4720 2.1219 2.1203 2.1187 0.9046 0.9P45 0.9043 46 45 44 17 18 19 2U 21 22 2^ 0.4271 0.4274 0.4276 04723 U4727 0.4731 2.1171 2.1 1 55 2.1139 0.9042 0.9041 0.9040 43 42 41 40 39 38 37 0.4279 04734 2.1123 0.9038 0.4281 0.4284 0.4287 04738 0.4741 04745 2.1107 2.1092 2.1076 0.9037 0.9036 0.9035 24 25 26 0.4289 0.4292 0.4295 04748 04752 04755 2.1060 2.1044 2.1028 0.9033 0.9032 0.9031 36 35 34 27 28 29 30 31 32 33 0.4297 0.4300 0.4302 04759 0.4763 0.4766 2.1013 2.0997 2.0981 0.9030 0.9028 0.9027 33 32 31 30 29 28 27 0.4305 0.4770 2.0965 0.9026 0.4308 0.4310 0.4313 0.4773 04777 0.4780 2.0950 2.0934 2.0918. 0.9025 '0.9023 0.9022 34 35 36 0.4316 0.43 1 8 0.4321 0.4784 0.4788 0.4791 2.0903 2.0887 2.0872 0.9021 0.9020 0.9018 26 25 24 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 0.4323 0.4326 0.4329 04795 U.4798 0.4S02 2.0856 2.0840 2.0825 0.9017 o.goi6 0.9015 23 22 21 20 19 18 17 0.4331 0.4806 2.0809 0.9013 0.4334 0.4337 0.4339 0.4S09 0.4S13 0.4816 2.0794 2.0778 2.0763 0.9012 o.goii 0.9010 0.4342 0.4344 0.4347 0.4350 0.4352 0.4355 0.4820 04823 0.4827 0.4831 04834 04838 2.0748 2.0732 2.0717 2.0701 2.0686 2.0671 0.9008 0.9007 0.9006 0.9004 0.9003 0.9002 16 15 14 13 12 II 10 9 8 7 0.4358 0.4841 2.0655 0.9001 0.4360 0.4363 0.4365 04845 0.4849 0.4852 2.0640 2.0625 2.0609 o.8g99 0.8gg8 o.8g97 0.4368 0-4371 0.4373 0.4376 0.4378 0.4381 0.4856 0.4859 04863 0.4867 0.4870 0.4874 2.0594 2.0579 2.0564 2.0549 2.0533 2.0518 0.8996 0.8994 0.8993 0.8992 o.8g90 0.8989 6 5 4 3 2 I 0.4384 04877 2.0503 0.8988 Cos Cot Tan, Sin t Natural 64^' *154° 244° *334° *116° 206° *^%° 26° Natxjeal 27= 121 *117° 207° *297'' ' Sin Tan Cot Cos ' Sin Tan Cot Cos I 2 3 0.4384 0.4877 2.0503 0.8988 60 59 58 57 1 2 3 0.4540 0.5095 1.9626 0.8910 60 59 58 57 0.4386 o.43ii9 0.4392 0.4881 0.4885 0.4888 2.0488 2.0473 2.0458 0.8987 0.8985 0.8984 0.4542 0.4545 0.4548 0.5099 0.5103 0.5106 1.9612 1.9598 19584 0.8909 0.8907 0.8906 4 5 6 0.4394 0.4397 0.4399 0.4892 0.4895 0.4899 2.0443 2.0428 2.0413 0.8983 0.8982 0.8980 56 55 54 4 5 6 0.4550 0.4553 0.4555 0.5110 0.5114 0.5117 1.9570 19556 1.9542 0.8905 0.8903 0.8902 56 55 54 7 8 9 10 II 12 13 0.4402 0.4405 0.4407 0.4903 0.4906 0.4910 2.0398 2.0383 2.0368 0.8979 0.8978 0.8976 53 52 51 50 49 48 .47 7 8 9 10 II 12 13 0.4558 0.4561 0.4563 0.5121 0.5125 0.5128 19528 1.9514 1.9500 0.8901 0.8899 0.8898 53 52 51 50 49 48 47 0.4410 0.4913 2.0353 0.8975 0.4566 0.5132 1.9486 0.8897 0.4412 0.4415 0.4418 0.4917 0.4921 0.4924 2.0338 2.0323 2.0308 0.8974 0.8973 0.8971 0.4568 0.4571 0.4574 0.5136 0-5139 0.5143 1.9472 1.9458 1.9444 0.S895 0.8894 0.8893 14 15 i6 0.4420 0.4423 0.4425 0.4928 0.4931 0.4935 2.0293 2.0278 2.0263 0.8970 0.8969 0.8967 46 45 4-4 14 15 16 0.4576 0.4579 0.4581 0.5147 0.5150 0.5154 1.9430 1 9416 1.9402 0.8892 0.8890 0.8889 46 45 44 17 i8 19 20 21 22 23 0.4428 0.4431 0.4433 0.4939 0.4942 0.4946 2.0248 2.0233 2.0219 0.8966 0.8965 0.8964 43 42 41 40 39 38 37 17 18 19 20 21 22 23 0.4584 0.4586 0.4589 0.5158 0.5161 0.5165 1.9388 1-9375 1.9361 0.8888 0.8886 0.8885 43 42 41 40 39 38 37 0.4436 0.4950 2.0204 0.8962 0.4592 0.5169 1-9347 0.8884 0.4439 0.4441 0.4444 0-4953 0.4957 0.4960 2.0189 2.0174 2.0160 0.8961 0.8960 0.8958 0.4594 0-4597 0.4599 0.5172 0.5176 0.5180 1-9333 1.9319 1.9306 0.8882 0.8881 0.8879 24 25 26 0.4446 0.4449 0.4452 0.4964 0.4968 0.4971 2.0145 2.0130 2.01 1 5 0.8957 0.8956 0.8955 36 35 34 24 25 ,26 0.4602 0.4605 0.4607 0.5184 0.5187 0.5191 1.9292 1.9278 1.9265 0.8878 0.8877 0.8875 36 35 34 27 28 29 30 31 32 33 0.4454 0.4457 0.4459 0.4975 0.4979 0.4982 2.0101 2.0086 2.0072 0.8953 0.8952 0.8951 33 32 31 30 29 28 27 27 28 29 80 31 32 33 0.4610 0.4612 0.4615 0.5195 0.5198 0.5202 1.9251 1.9237 1.9223 0.8874 0.8873 0.8871 33 32 31 30 29 28 27 0.4462 0.4986 2.0057 0.8949 0.4617 0.5206 j.g2io 0.8870 0.4465 0.4467 0.4470 0.4989 0.4993 04957 2.0042 2.0028 2.0013 0.8948 0.89.17 0-89^5 0.4620 0.4623 0.4625 0.5209 0.5213 0.5217 1.9196 1.9183 1.9169 0.8869 0.8867 0.8866 34 35 36 0.4472 0.4475 0.4478 0.5000 0.5004 0.5008 1-9999 1.9984 1.9970 0.8944 0.8943 0.8942 26 25 24 34 35 36 0.4628 0.4630 ■0.4633 0.5220 0.5224 0.5228 1.9155 1.9142 1. 9128 0.8865 0.8863 0.8862 26 25 24 37 38 39 40 41 42 43 0.4480 0.4483 0.4485 0.5011 0.5015 0.5019 1-9955 1.9941 1.9926 0.8940 0.8939 0.8938 23 22 21 20 19 18 17 37 38 39 40 41 42 43 0.4636 0.4638 0.4641 0.5232 0.5235 0.5239 1.9115 1.9101 l.go88 0.8861 0.8859 0.8858 23 22 21 20 19 18 17 0.4488 0.5022 1.9912 0.8936 0.4643 0-5243 1.9074 0.8857 0.4491 0.4493 0.4496 0.5026 0.5029 0.5033 1.9897 1.9883 1.9868 0.8935 0.8934 0.8932 0.4646 0.4648 0.4J651 0.5246 0.5250 0.5254 1. 9061 1.9047 1.9034 0.8855 0.8854 0.8853 44 45 46 0.4498 0.4501 0.4504 0.5037 0.5040 0.5044 1.9854 1.9840 1.9825 0.8931 0.8930 0.8928 16 15 14 44 45 46 0.4654 0.4656 0.4659 0.5258 0.5261 0.5265 1.9020 1.9007 1.8993 0.8851 0.8850 0.8849 16 15 14 47 48 49 50 51 52 53 0.4506 0.4509 0.4511 0.5048 0.5051 0.5055 1.9811 1-9797 1.9782 0.8927 0.8926 0.8925 13 12 11 10 9 8 7 47 48 49 50 51 52 53 0.4661 0.4664 0.4666 0.5269 0.5272 0.5276 1.8980 1.8967 1-8953 0.8847 0.S846 0.8844 13 12 II 10 9 8 7 0.4514 0.5059 1.9768 0.8923 0.4669 0.5280 1.8940 0.8843 0.4517 0.4519 0.4522 0.5062 0.5066 0.5070 1-9754 1.9740 1.9725 0.8922 0.8921 0.8919 0.4672 0.4674 0.4677 0.5284 0.5287 0.5291 1.8927 1.8913 1.8900 0.8842 0.8840 0.8839 54 55 56 0.4524 0.4527 0.4530 0.5073 0.5077 0.5081 1.9711 1.9697 1.9683 0.8918 0.8917 0.8915 6 5 4 54 55 56 0.4679 0.4682 0.4684 0.5295 0.5298 0.5302 1.8887 1.8873 1.8860 0.8838 0.8836 0.8835 6 5 4 57 58 59 60 0.4532 0.4535 0.4537 0.5084 0.5088 0.5092 1.9669 1.9654 1.9640 0.8914 0.8913 0.8911 3 2 I 57 58 59 60 0.4687 0.4690 0.4692 0.5306 0.5310 0.5313 1.8847 1.8834 1.8820 0.8834 0.8832 0.8831 3 2 I 0.4540 0.5095 1.9626 0.8910 0.4695 0.5317 1.8807 0.8829 Cos Cot Tan 1 Sin ' Cos Cot Tan Sin ' *153° 243° *333° 63° Natural *152° 242° *332° 122 *118° 208° *298° 28° Natukal 29° *119° 209° *a99° ' Sin Tan Cot Cos I 2 3 0.4695 0-5317 1.8807 0.8829 60 59 58 57 0.4697 0.4700 0.4702 0.5321 0.5325 0.5328 1.8794 1.8781 1.8768 0.8828 0.8827 0.8825 4 5 6 0.4705 0.4708 0.4710 0.5332 0.5336 0.5340 1.8755 1.8741 1.8728 0.8824 0.8823 0.8821 56 55 54 7 8 9 10 II 12 13 0.4713 0.4715 0.4718 0.5343 0.5347 0.5351 1-8715 1.8702 1.8689 0.8820 0.8819 0.8817 53 52 51 50 49 48 47 0.4720 0.5354 1.8676 0.8816 0.4723 0.4726 0.4728 0.5358 0.5362 0.5366 1.8663 1.8650 1.8637 0.8814 0.8813 0.8812 14 15 i6 0.4731 0.4733 0.4736 0.5369 0.5373 0.5377 1.8624 1.8611 1.8598 0.8810 0.8809 0.8808 46 45 44 17 i8 19 20 21 22 23 0.4738 0.4741 0.4743 0.5381 0.5384 0.5388 1.8585 1.8572 1.8559 0.8806 0.8805 0.8803 43 42 41 40 39 38 37 0.4746 0.5392 1.8546 0.8802 0.4749 0.4751 0.4754 0.5396 0.5399 0.5403 1.8533 1.8520 1.8507 0.8801 0.8799 0.8798 24 25 26 0.4756 0.4759 0.4761 0.5407 0.5411 0.5415 1-8495 1.8482 1.8469 0.8796 0.8795 0.8794 36 35 34 27 28 zg 30 31 32 33 0.4764 0.4766 0.4769 0.5418 0.5422 0.5426 1.8456 1.8443 1.8430 0.8792 0.8791 0.8790 33 32 31 30 29 28 27 0.4772 0.5430 1. 8418 0.8788 0.4774 0.4777 0.4779 0.5433 0.5437 0.5441 1.8405 1.8392 1.8379 0.8787 0.8785 0.8784 34 35 36 0.4782 0.4784 0.4787 0.5445 0.5448 0.5452 1.8367 1.8354 1.8341 0.8783 0.8781 0.8780 26 25 24 37 38 39 40 41 42 43 0.4789 0.4792 0.4795 0.5456 0.5460 0.5464 1.8329 1. 8316 1.8303 0.8778 0.8777 0.8776 23 22 21 20 19 18 17 0.4797 0.5467 1.8291 0.8774 0.4800 0.4802 0.4805 0.5471 0.5475 0.5479 1.8278 1.8265 1.8253 0.8773 0.8771 0.8770 44 45 46 0.4807 0.4810 0.4812 0.5482 0.5486 0.5490 1.8240 1.8228 1. 8215 0.8769 0.8767 0.8766 16 15 14 47 48 49 50 51 52 53 0.4815 0.4818 0.4820 0.5494 0.5498 0.5501 1.8202 1. 8190 1.8177 0.8764 0.8763 0.8762 13 12 II 10 9 8 7 0.4823 0.5505 1. 8165 0.8760 0.4825 0.4828 0.4830 0.5509 0.5513 0.5517 1. 8152 1. 8140 1. 8127 0.8759 0.8757 0.8756 54 55 56 0.4833 0.4835 0.4838 0.5520 0.5524 0.5528 1.8115 1. 8103 1.8090 0.8755 0.8753 0.8752 6 5 4 57 58 59 60 0.4840 0.4843 0.4846 0.5532 0.5535 0.5539 1.8078 1.8065 1.8053 0.8750 0.8749 0.8748 3 2 I 0.4848 0.5543 1.8040 0.8746 Cos Cot Tan Sin ' *151° 241° *331° 61 Natural 1 Sin Tan Cot Cos I 2 3 0.4848 0.5543 1.8040 0.8746 60 59 58 57 0.4851 0.4853 0.4856 0.5547 0.5551 0.5555 1.8028 1. 8016 1.8003 0.8745 0.8743 0.8742 4 5 6 0.4858 0.4861 0.4863 0.5558 0.5562 0.5566 1-7991 1-7979 1.7966 0.8741 0.8739 0.8738 56 55 54 7 8 9 10 II 12 13 0.4866 0.4868 0.4871 0.5570 0.5574 0.5577 1-7954 1.7942 1.7930 0.8736 0.8735 0.8733 53 52 51 50 49 48 47 0.4874, 0.5581 1.7917 0.8732 0.4876 0.4879 0.4881 0.5585 0.5589 0.5593 1.7905 1-7893 1.7881 0.8731 0.8729 0.8728 14 15 16 0.4884 0.4886 0.4889 0.5596 0.5600 0.5604 1.7868 1.7856 1.7844 0.8726 0.8725 0.8724 46 45 44 17 18 19 20 21 22 23 0.4891 0.4894 0.4896 0.5608 0.5612 0.5616 1.7832 1.7820 1.7808 0.8722 0.8721 0.8719 43 42 41 40 39 38 37 0.4899 0.5619 1-7796 0.8718 0.4901 0.4904 0.4907 0.5623 0.5627 0.5631 1-7783 I-777I 1-7759 0.8716 0.8715 0.8714 24 25 26 0.4909 0.4912 0.4914 0.5635 0.5639 0.5642 1-7747 1-7735 1-7723 0.8712 0.8711 0.8709 36 35 34 27 28 29. 30 31 32 33 0.4917 0.4919 0.4922 0.5646 0.5650 0.5654 1.7711 1.7699 1.7687 0.8708 0.8706 0.8705 33 32 31 30 29 28 27 0.4924 0.5658 1-7675 0.8704 0.4927 0.4929 0.4932, 0.5662 0.5665 0.5669 1.7663 1. 7651 1-7639 0.8702 0.8701 0.8699 34 35 36 0.4934 0.4937 0.4939 0.5673 0.5677 0.5681 1.7627 1. 7615 1.7603 o.86g8 0.8696 0.8695 26 25 24 37 38 39 40 41 42 43 0.4942 0.4944 0.4947 0.5685 0.5688 0.5692 I-7591 1-7579 1-7567 0.8694 0.8692 0.S691 23 22 21 20 19 18 17 0.4950 0.5696 1-7556 0.86S9 , 0.4952 0.4955 0.4957 0.5700 0.5704 0.5708 1-7544 1.7532 1-7520 0.8688 0.8686 0.8685 44 45 46 0.4960 0.4962 0.4965 0.5712 0.5715 0.5719 1.7508 1.7496 1.7485 0.8683 0.8682 0.8681 16 15 14 47 48 49 50 51 52 53 0.4967 0.4970 0.4972 0.5723 0-5727 0.5731 1-7473 1.7461 1-7449 0.8679 0.8678 0.8676 13 12 11 10 9 8 7 0.4975 0.5735 1-7437 0.8675 0.4977 0.4980 0.4982 0.5739 0.5743 0.5746 1.7426 1.7414 1.7402 0.8673 0.8672 0.8670 54 55 56 0.4985 0.4987 0.4990 0.5750 0.5754 0.5758 1-7391 1-7379 1-7367 0.8669 0.8668 0.8666 6 5 4 57 58 59 60 0.4992 0.4995 0.4997 0.5762 0.5766 0.5770 1-7355 1-7344 1.7332 0.8665 0.8663 0.8662 3 2 I 0.5000 0.5774 1. 732 1 0.8660 Cos Cot Tan Sin ' 60° *150° 240° *330° *120° 210° *300° 30° Natural 31° 123 *121° 211° *301° Sin Tan Cot Cos 1 2 3 0.5000 0.5774 1. 7321 0.8660 60 59 58 57 0.5003 0.5005 0.5008 0.5777 0.5781 0.5785 1-7309 1.7297 1.7286 0.8659 0.8657 0.8656 4 5 6 0.5010 0.5013 0.5015 0.57S9 0.5793 0.5797 1.7274 1.7262 1-7251 0.8654 0.8653 0.8652 56 55 54 7 8 9 10 II 12 13 0.5018 0.5020 0.5023 0.5801 0.5805 0.5808 1-7239 1.7228 1. 7216 0.8650 0.8649 0.8647 53 52 51 50 49 48 47 0.5025 0.5812 1.7205 0.8646 0.5028 0.5030 0.5033 0.5816 0.5820 0.5824 1. 7193 1. 7182 1-7170 0.8644 0.8643 0.8641 14 15 i6 0.5035 0.5038 0.5040 0.5828 0.5832 0.5836 1-7159 1-7147 1. 7136 0.8640 0.8638 0.8637 46 45 44 17 i8 19 20 21 22 23 0.5043 0.5045 0.5048 0.5840 0.5844 0.5847 1. 7124 1-7113 1.7102 0.8635 0.8634 0.8632 43 42 41 40 39 38 37 0.5650 0.5851 1.7090 0.8631 0.5053 0.5055 0.5058 0.5855 0.5859 0.5863 1.7079 1. 706 J 1.7056 0.8630 0.8628 0.8627 24 25 26 0.5060 0.5063 0.5065 0.5867 0.5871 0.5875 1.7045 1-7033 1.7022 0.8625 0.8624 0.8622 36 35 34 27 28 29 30 31 32 33 0.5068 0.5070 0.5073 0.5879 0.5883 0.5887 t.7011 1.6999 1.6988 0.8621 0.8619 0.8618 33 32 31 30 29 28 27 0.5075 0.5890 1.6977 0.8616 0.5078 0.5080 0.5083 0.5894 0.5898 0.5902 1.6965 1-6954 1.6943 0.8615 0.8613 0.8612 34 35 36 0.5085 0.5088 0.5090 0.5906 0.5910 0.5914 1.6932 1.6920 1.6909 0.8610 0.8609 0.8607 26 25 24 37 38 39 40 41 42 43 0.5093 0.5095 0.5098 0.5918 0.5922 0.5926 1.6898 1.6887 1.6875 0.8606 0.8604 0.8603 23 22 21 20 19 18 17 0.5100 0.5930 1.6864 0.8601 0.5103 0.5105 0.5108 0.5934 0.5938 0.5942 1-6853 1.6842 1.6831 0.8600 0.8599 0.8597 44 45 46 0.5110 0.5113 0.5115 0.5945 0.5949 0.5953 1.6820 1.6808 1.6797 0.8596 0-8594 0.8593 16 15 14 47 48 49 50 S- 52 53 0.5118 0.5120 0.5123 0.5957 0.5961 0.5965 1.6786 1-6775 1.6764 0.8591 0.8590 0.8588 13 12 II 10 9 8 7 0.5125 0.5969 1-6753 0.8587 C.5128 0.513c 0.5133 0.5973 0.5977 asgSi 1.6742 1-6731 1.6720 0,8585 0.8584 0.8582 54 55 56 0.5135 0.5138 0.5140 0.5985 0.5989 0.5993 1.6709 1.6698 1.6687 0.8581 0.8579 0.S578 6 5 4 57 58 59 60 0.5143 0.5145 0.5148 0.5997 0.6001 0.6005 1.6676 1.6665 1.6654 0.S576 0.8575 0-8573 3 2 . I 0.5150 0.6009 1.6643 0.8572 Cos Cot Tan Sin ' ' Sin Tan Cot Cos 60 59 58 57 I 2 3 0.5150 0.6009 1.6643 0.8572 0-5153 0-5155 0.5158 0.6013 0.6017 0.6020 1.6632 1. 662 1 1.6610 0.8570 0.8569 0.8567 4 5 6 0.5160 0.5163 0.5165 0.6024 0.6028 0.6032 1.6599 1.6588 1.6577 0.8566 0.8564 0.8563 56 55 54 7 8 9 10 II 12 13 0.5168 0.5170 0.5173 0.6036 0.6040 0.6044 1.6566 1.6555 1.6545 0.8561 0.8560 0.8558 53 52 51 50 49 48 47 0.5175 0.6048 1.6534 0-8557 0.5178 0.5180 0.5183 0.6052 0.6056 0.6060 1.6523 1.6512 1.6501 0.8555 0-8554 0.8552 14 15 16 0.5185 0.5188 0.5190 0.6064 0.6068 0.6072 1.6490 1.6479 1.6469 0.8551 0-8549 0.8548 46 45 44 17 18 19 20 21 22 23- 0.5193 0.5195 0.5198 0.6076 0.6080 0.6084 1.6458 1.6447 1.6436 0.8546 0-8545 0.8543 43 42 41 40 39 38 37 0.5200 0.6088 1.6426 0.8542 0.5203 0.5205 0.5208 0.6092 o.6og6 0.6100 I. 641 5 1.6404 1.6393 0.8540 0-8539 0-8537 24 25 26 0.5210 0.5213 0.5215 0.6104 0.6108 0.6112 1.6383 1.6372 1.6361 0.8536 0.8534 0.8532 36 35 34 27 28 29 30 31 32 33 0.5218 0.5220 0.5223 0.61 1 6 0.6120 0.6124 1.6351 1.6340 1.6329 0.8531 0.8529 0.8528 33 32 31 30 29 28 27 0.5225 0.6128 1.6319 0.8526 0.5227 0.5230 0.5232 0.6132 0.6136 0.6140 1.6308 1.6297 1.6287 0.8525 0.8523 0.8522 34 35 36 0-5235 0-5237 0.5240 0.6144 0.6148 0.6152 1.6276 1.6265 1.6255 0.8520 0.8519 0.8517 26 25 24 37 38 39 40 41 42 43 0.5242 0.5245 0-5247 0.6156 0.6160 0.6164 1.6244 1.6234 1.6223 0.8516 0.8514 0.8513 23 22 21 20 19 18 17 0.5250 0.6168 1. 6212 0.8511 0.5252 0-5255 0.5257 0.6172 0.6176 0.61S0 1.6202 1.6191 1.6181 0.8510 0.8508 0.8507 44 45 46 0.5260 0.5262 0.5265 0.6184 0.6188 0.6192 1.6170 1.6160 1.6149 0.8505 0.8504 0.8502 16 15 14 47 48 49 50 51 52 53 0.5267 0.5270 0.5272 0.6196 0.6200 0.6204 1-6139 1.6128, 1.6118 0.8500 0.8499 0.8497 13 12 II 10 9 8 7 0.5275 0.6208 1.6107 0.8496 0.5277 0.5279 0.5282 0.6212 0.6216 0.6220 1.6097 1.6087 1.6076 0.8494 0-8493 0.8491 54 55 56 0.5284 0.5287 0.5289 0.6224 0.6228 0.6233 1.6066 1.6055 1.6045 0.8490 0.8488 0.8487 6 5 4 57 58 59 60 0.5292 0.5294 0.5297 0.6237 0.6241 0.6245 1.6034 1.6024 1.6014 0.8485 . 0.8484 0.8482 3 2 I 0-5299 0.6249 1.6003 0.8480 Cos Cot Tan Sin ' *149° 239° *329° 59° Natural 58° *148° 238° *328° 124 *122° 212° *302'' 32° Natural 33° *123° 213° *303° ' Sin Tan Cot Cos I 2 3 0.5299 0.6249 I 6003 0.8480 60 59 58 57 0.5302 0.5304 0.5307 0.6253 I 0.6257 I 0.6261 I 5993 5983 5972 0.8479 0.8477 0.8476 4 5 6 0.5309 0.5312 0.5314 0.6265 I 0.6269 I 0.6273 I 5962 5952 5941 0.8474 0.8473 0.8471 56 55 54 7 8 9 10 11 12 13 0.5316 0.5319 0.5321 0.6277 I 0.6281 I 0.6285 I 5931 5921 591 1 0.8470 0.8468 0.8467 53 52 51 50 49 48 47 0.5324 0.6289 I 5900 0.8465 0.5326 0.5329 0.5331 0.6293 I 0.6297 I 0.6301 I 5890 5880 5869 0.8463 0.8462 0.8460 14 15 i6 0.5334 0.5336 0.5339 0.6305 I 0.6310 I 0.6314 I 5859 5849 5839 0.8459 0.8457 0.8456 46 45 44 17 i8 19 20 21 22 23 0.5341 0.5344 0.5346 0.6318 I 0.6322 I 0.6326 I 5829 5818 5808 0.8454 0.8453 0.8451 43 42 41 40 39 38 37 0.5348 0.6330 I 5798 0.8450 0.5351 0.5353 0.5356 0.6334 I 0.6338 I 0.6342 I 5788 5778 5768 0:8448 0.8446 0.8445 24 25 26 0.5358 0.5361 0.5363 0.6346 I 0.6350 I 0.6354 I 5757 5747 5737 0.8443 0.8442 0.8440 36 35 34 27 28 29 30 31 32 33 0.5366 0.5368 0.5371 0.6358 I 0.6363 I 0.6367 I 5727 5717 5707 0.8439 0.8437 0.8435 33 32 31 30 29 28 27 0.5373 0.6371 I 5697 0.8434 0.5375 0.5378 0.5380 0.6375 I 0.6379 I 0.6383 I 5687 5677 5667 0.8432 0.8431 0.8429 34 35 3& 0.5383 0.5385 0.5388 0.6387 I 0.6391 I 0.6395 I 5657 5647 5637 0.8428 0.8426 0.8425 26 25 24 37 38 39 40 41 42 43 0.5390 0.5393 0.5395 0.6399 I 0.6403 I 0.6408 I 5627 5617 5607 0.8423 0.8421 0.8420 23 22 21 20 19 18 17 0.5398 0.6412 I 5597 0.8418 0.5400 0.5402 0.5405 0.6416 1 0.6420 I 0.6424 I 55S7 5577 5567 0.8417 0.8415 0.8414 44 45 46 0.5407 0.5410 0.5412 0.6428 I 0.6432 I 0.6436 r 5557 5547 5537 0.8412 0.8410 0.8409 16 15 14 47 48 49 50 51 52 53 0.5415 0.5417 0.5420 0.6440 I 0.6445 I 0.6449 I 5527 5517 5507 0.8407 0.8406 0.8404 13 12 11 10 9 8 7 0.5422 0.6453 I 5497 0.8403 0.5424 0.5427 0.5429 0.6457 I 0.6461 I 0.6465 I 5487 5477 5468 0.8401 0.8399 0.8398 54 55 56 0.5432 0.5434 0.5437 0.6469 I 0.6473 I 0.6478 I 5458 5448 5438 0.8396 0.8395 0.8393 6 5 4 57 58 59 60 0.5439 0.5442 0.5444 0.6482 I 0.6486 I 0.6490 I 5428 5418 5408 0.8391 0.8390 0.8388 3 2 I 0.5446 0.6494 I 5399 0.8387 Cos Cot ran Sin ' t Sin Tan Cot Cos I 2 3 0.5446 0.6494 I 5399 0.8387 60 59 58 ■ 57 0.5449 0.5451 0.5454 0.6498 1 0.6502 1 0.6506 1 5389 5379 5369 0.8385 0.8384 0.8382 4 5 6 0.5456 0.5459 0.5461 0.6511 I 0.6515 I 0.6519 1 5359 5350 5340 0.8380 0.8379 0.8377 56 55 54 7 8 9 10 11 12 13 0.5463 0.5466 0.5468 0.6523 1 0.6527 1 0.6531 1 5330 5320 5311 0.8376 0.8374 0.8372 53 52 51 50 49 48 47 0.5471 0.6536 1 5301 0.8371 0.5473 0.5476 0.5478 0.6540 I 0.6544 I 0.6548 I 5291 5282 5272 0.8369 0.8368 0.8366 14 15 16 0.5480 0.5483 0.5485 0.6552 I 0.6556 I 0.6560 1 5262 5253 5243 0.8364 0.8363 0.8361 46 45 44 17 18 19 20 21 22 23 6.5488 0.5490 0.5493 0.6565 1 0.6569 1 0.6573 I 5233 5224 5214 0.8360 0.8358 0.8356 43 42 41 40 39 38 37 0.5495 0.6577 1 5204 0.8355 0.5498 0.5500 0.5502 0.6581 I 0.6585 I 0.6590 I 5195 5185 5175 0.8353 0.8352 0.8350 24 25 26 0.5505 0.5507 ' 0.5510 0.6594 I 0.6598 I 0.6602 I 5166 5156 5147 0.8348 0.8347 0.8345 36 35 34 27 28 29 30 31 32 33 0.5512 0.5515 0.5517 0.6606 I 0.6610 1 '0.6615 I 5137 5127 5118 0.8344 0.8342 0.8340 33 32 31 30 29 28 27 0.5519 0.6619 I 5108 0.8339 0.5522 0.5524 0.5527 0.6623 I 0.6627 I 0.6631 I 5099 5089 5080 0.8337 0.8336 0.8334 34 35 36 0.5529 0.5531 0.5534 0.6636 1 0.6640 1 0.6644 I 5070 5061 5051 0.8332 0.8331 0.8329 26 25 24 37 38 39 40 41 42 43 0.5536 0.5539 0.5541 0.6648 I 0.6652 I 0.6657 I 5042 5032 5023 0.8328 0.8326 0.8324 23 22 21 20 19 18 17 0-5544 0.6661 I 5013 0.8323 0.5546 0.5548 0.5551 0.6665 I o.666g 1 0.6673 I 5004 4994 4985 0.8321 0.8320 0.8318 44 45 46 0.5553 0.5556 0.5558 0.6678 1 0.6682 I 0.6686 I 4975 4966 4957 0.8316 0.8315 0.8313 16 15 14 47 48 49 50 51 52 53 0.5561 0.5563 0.5565 0.6690 1 0.6694 I 0.6699 I 4947 4938 4928 0.8311 0.8310 0.8308 13 12 II 10 9 8 7 0.5568 0.6703 I 4919 0.8307 0.5570 0.5573 0.5575 0.6707 1 0.6711 1 0.6715 1 4910 4900 4891 0.8305 .0.8303 .0.8302 54 55 56 0.5577 0.5580 0.5582 0.6720 1 0.6724 I 0.6728 I 4882 4872 4863 .0.8300 0.8298 0.8297 6 5 4 57 58, 59 60 0.5585 0.5587 0.5590 0.6732 I 0.6737 I 0.6741 I 4854 4844 4835 0.8295 0.8294 0.8292 3 2 1 0.5592 0.6745 I 4826 0.8290 Cos Cot ran Sin t *147° 237° *327° 57° Natural 56° *146° 236° *326° 125 *124° 214° *304° 34° Natural 35° *125° 215° *305° ' Sin Tan Cot Cos I 2 3 0.5592 0.6745 1.4826 0.8290 60 59 58 57 "•5594 0.5597 0.5599 0.6749 0.6754 0.6758 1.4816 1.4807 1.4798 0.S289 0.8287 0.8285 4 5 6 0.5602 0.5604 0.5606 0.6762 0.6766 0.6771 1.4788 1-4779 1.4770 0.8284 0.8282 0.8281 56 55 54 7 8 9 10 11 12 13 0.5609 0.5611 0.5614 0.6775 0.6779 0.6783 1.4761 1.4751 1.4742 0.8279 0.8277 0.8276 53 52 51 50 49 48 47 0.5616 0.6787 1.4733 0.8274 0.5618 0.5621 0.5623 0.6792 0.6796 0.6800 1.4724 1-4715 1.4705 0.S272 0.8271 0.8269 14 15 i6 0.5626 0.5628 0.5630 0.6805 0.6809 0.6813 1.4696 1.4687 1.4678 0.S268 0.8266 0.8264 46 45 44 '7 i8 '9 20 21 22 23 0.5633 0.5635 0.5638 0.6817 0.6822 0.6826 1.4669 1.4659 1.4650 0.S263 0.8261 0.8259 43 42 41 40 39 38 37 0.5640 0.6830 1.4641 0.8258 0.5642 0.5645 0.5647 0.6834 0.6839 0.6843 1.4632 1.4623 1.4614 0.8256 0.8254 0.8253 24 25 26 0.5650 0.5652 0.5654 0.6847 0.6851 0.6856 1.4605 1.4596 1.4586 .0.8251 0.8249 0.8248 36 35 34 27 28 29 30 31 32 33 0.5657 0.5659 0.5662 0.6S60 0.6864 0.6869 1.4577 1.4568 1-4559 0.8246 0.8245 0.8243 33 32 31 30 29 28 27 0.5O64 0.6S73 1.4550 0.8241 0.5666 0.5669 0.5671 0.68 7 7 0.6S81 0.6886 1.4541 1.4532 1.4523 0.8240 0.8238 0.8236 34 35 36 0.5674 0.5&76 0.5678 0.6890 0.6S94 0.6899 1.4514 1.4505 1.4496 0.8235 0.8233 0.8231 26 25 24 37 38 39 40 41 42 43 0.5681 0.5683 0.5680 0.6903 0.6907 0.69 1 1 1.4487 1.4478 1.4469 0.8230 08228 0.8226 23 22 21 20 19 18 17 0.5688 0.6gi6 1.4460 0.8225 0.5690 0.5693 0.5695 0.6920 0.6924 0.6929 1.445 1 1.4442 1-4433 0.8223 0.8221 0.8220 44 45 46 0.5698 0.5700 0.5702 0.6933 0.6937 0.6942 1.4424 I-4415 1.4406. 0.8218 0.8216 0.8215 16 15 14 47 48 49 50 51 52 53 0.5.705 0.5707 0.5710 0.6946 0.6950 0.6954 1-4397 1.4388 1-4379 0.8213 0.82 1 1 0.8210 13 12 ir 10 9 8 7 0.5712 0.6959 1.4370 0.8208 0.5714 0.5717 0.5719 0.6963 0.6967 0.6972 1. 4361 1.4352 1.4344 0.8207 0.8205 0.8203 54 55 56 0.5721 0.5724 0.5726 0.6976 0.6980 0.6985 1.4335 1.4326 1.4317 0,8202 0.8200 0.8198 6 . 5 4 57 58 59 60 •0.5729 0.5731 0.5733 0.6989 0.6993 0.6998 1.4308 1.4299 1.4290 0.8197 0.8195 0.8193 3 2 I 0.5736 0.7002 1.4281 0.8192 Cos Cot Tan Sin ■ ' Sin Tan Cot Cos I 2 3 0.5736 0.7002 1.4281 0.8192 60 59 58 57 0.5738 0.5741 0.5743 0.7006 0.7011 0.7015 1.4273 1.4264 1-4255 0.8190 0.8188 0.8187 4 5 6 0-5745 0.5748 0.5750 0.7019 0.7024 0.7028 1.4246 1.4237 1.4229 0.8185 0.8183 0.8181 56 55 54 7 8 9 10 11 12 13 0.5752 0.5755 0.5757 0.7032 0.7037 0.7041 1.4220 1.4211 1.4202 0.8180 0.8178 0.S176 53 52 51 50 49 48 47 0.5760 0.7046 1.4193 0.S175 0.5762 0.5764 0.5767 0.7050 0.7054 0.7059 1.4185 1.4176 1.4167 0.8173 0.8171 0.8170 14 15 16 0.5769 0.5771 0.5774 0.7063 0.7067 0.7072 1.4158 1.4150 1.4141 0.S168 0.8166 0.8165 46 45 44 17 18 19 20 21 22 23 0.5776 0.5779 0.5781 0.7076 0.7080 0.7085 1.4132 1.4124 1.4115 0.8163 0.8161 0.8160 43 42 41 40 39 38 37 0.5783 0.7089 1.4106 0.S158 0.5786 0.5788 0.5790 0.7094 0.7098 0.7102 1.4097 1.4089 1.4080 0.S156 0.8155 0.8153 24 25 26 0.5793 0.5795 0.5798 0.7107 0.71 1 1 0.7115 1.4071 1 .4063 1.4054 0.8151 0.S150 0.8148 36 35 34 27 28 29 30 31 32 33 0.5800 0.5802 0.5805 0.7120 0.7124 0.7129 1.4045 1.4037 1.4028 0.8146 0.8145 0.8143 33 32 31 30 29 28 27 0.5807 0.7133 1.4019 0.8141 0.5809 0.5812 0.5814 0.7137 0.7142 0.7146 1.4011 1.4002 1.3994 0.8139 0.8138 0.8136 34 35 36 0.5&16 0.5819 0.5821 0.7151 0.7155 0.7159 1.3985 1.3976 1.3968 0.8134 0.8133 0.8131 26 25 24 37 38 39 40 41 42 43 0.5824 0.5826 0.5828 0.7164 0.7168 0.7173 1.3959 1.3951 1.3942 0.8129 0.8128 0.8126 23 22 21 20 19 18 17 0.5831 0.7177 1.3934 0.8124 0.5833 0.5835 0.5838 o.7i»i 0.7186 0.7190 1.3925 1.3916 1.3908 0.8123 0.8121 0.8119 44 45 46 0.5840 0.5842 0.5845 0.7195 0.7199 0.7203 1.3899 1.3891 1.3882 0.8117 0.8116 0.8114 16 15 14 47 48 49 50 51 52 53 0.5847 0.5850 0.5852 0.7208 ■0.7212 0.7217 1.3874 1.3865 1.3857 0.8112 0.8111 0.8109 13 12 II 10 9 8 7 0.5854 0.7221 1.3848 0.8 107 0.5857 0.5859 0.5861 0.7226 0.7230 0.7234 1.3840 1.3831 1.3823 0.8106 0.8104 0.8102 54 55 56 0.5864 0.5866 0.5868 0.7239 0.7243 0.7248 1.3814 1.3806 1.3798 0.8100 0.S099 0.8097 6 5 4 57 58 59 60 0.5871 0.5873 0.5875 0.7252 0.7257 0.7261 1.3789 1.3781 1.3772 0.8095 0.8094 0.8092 3 2 I 0.5878 0.7265 1.3764 0.8090 Cos Cot Tan Sin ' *145° 235° *325° 55° Natural 54° *144° 234° *324° 126 *126° 216° *306° 36° Natural 37^ »127° 217° *307° ' Sin Tan Cot Cos I 2 3 0.5878 0.7265 1.3764 0.8090 60 59 58 57 0.5880 0.5883 0.5885 0.7270 0.7274 0.7279 1-3755 1-3747 1-3739 0.8088 0.8087 0.8085 4 5 6 0.5887 0.5890 0.5892 0.7283 0.7288 0.7292 I-3730 1.3722 1-3713 0.8083 0.8082 0.8080 56 55 54 7 8 9 10 II 12 13 0.5894 0.5897 0.5899 0.7297 0.7301 0.7306 1-3705 1.3697 1.3688 0.8078 0.8076 0.8075 53 52 51 50 49 48 47 0.5901 0.7310 1.3680 0.8073 0.5904 0.5906 0.5908 0.7314 0.7319 0.7323 1.3672 1.3663 1-3655 0.8071 0.8070 0.8068 14 15 i6 0.5911 0.5913 0.5915 0.7328 0.7332 0.7337 1.3647 1.3638 1.3630 0.8066 0.8064 0.8063 46 45 44 17 i8 19 20 21 22 23 0.5918 0.5920 0.5922 0.7341 0.7346 0.7350 1.3622 1.3613 1.3605 0.8061 0.8059 0.8058 43 42 41 ■ 40 39 38 37 0.5925 0.7355 1-3597 0.8056 0.5927 0.5930 0.5932 0-7359 0.7364 0.7368 1.3588 1.3580 1-3572 0.8054 0.8052 0.8051 24 25 26 0.5934 0.5937 0.5939 0.7373 0.7377 0.7382 1.3564 1-3555 1-3547 0.8049 0.8047 0.8045 36 35 34 27 28 29 30 31 32 33 0.5941 0.5944 0.5946 0.7386 0.7391 0-7395 1-3539 1-3531 1.3522 0.8044 0.8042 0.8040 33 32 31 30 29 28 27 0.5948 0.7400 1-3514 0.8039 0.5951 0.5953 0.5955 0.7404 0.7409 0.7413 1-3506 1.3498 1.3490 0.8037 0.8035 0.8033 34 35 36 0.5958 0.5960 0.5962 0.7418 0.7422 0.7427 1.3481 1-3473 1-3465 0.8032 0.8030 0.8028 26 25 24 37 38 39 40 41 42 43 0.5965 0.5967 0.5969 0-7431 0.7436 0.7440 1-3457 1.3449 1.3440 0.8026 0.8025 0.8023 23 22 21 20 19 18 17 0.5972 0.7445 1.3432 o.8o2i 0.5974 0.5976 0.5979 0.7449 0.7454 0.7458 1.3424 1.3416 1.3408 0.8019 0.8018 0.8016 44 45 46 0.5981 0.5983 0.5986 0.7463 0.7467 0.7472 1.3400 1-3392 1-3384 0.8014 0.8013 0.80H 16 15 14 47 48 49 50 51 52 53 0.5988 0.5990 0.5993 0.7476 0.7481 0.7485 1.3375 1-3367 1-3359 0.8009 0.8007 0.8006 13 12 II 10 9 8 7 0.5995 0.7490 1-3351 0.8004 0.5997 0.6000 0.6002 0-7495 0-7499 0-7504 1-3343 1-3335 1-3327 0.8002 0.8000 0.7999 54 55 56 0.6004 0.6007 0.6009 0-7508 0-7513 0.7517 1-3319 1-33" 1-3303 0.7997 0.7995 0.7993 6 5 4 57 58 59 60 0.6011 0.6014 0.6016 0.7522 0.7526 0.7531 1-3295 1-3287 1-3278 0.7992 0.7990 0.7988 3 2 1 0.6018 0.7536 1.3270 0.7986 Cos 1 Cot Tan 1 Sin ' r Sin Tan Cot Cos I 2 3 0.6018 0.7536 1.3270 0.7986 60 59 58 57 0.6020 0.6023 0.6025 0.7540 0.7545 0.7549 1.3262 1.3254 1.3246 0.7985 0-7983 0.7981 4 5 6 0.6027 0.6030 0.6032 0.7554 0.7558 0.7563 1.3238 1.3230 1.3222 0.7979 0.7978 0.7976 56 55 54 7 8 9 10 11 12 13 0.6034 0.6037 0.6039 0.7568 0.7572 0-7577 1.3214 1.3206 1.3198 0.7974 0.7972 0.7971 53 52 51 50 49 48 47 0.6041 0.7581 1.3190 0.7969 0.6044 0.6046 0.6048 0.7586 0.7590 0.7595 1.3182 1-3175 1-3167 0.7967 0.7965 0.7964 14 15 16 0.6051 0.6053 0.6055 0.7600 0.7604 0.7609 1-3159 1-3151 1-3143 0.7962 0.7960 0.7958 46 45 44 17 18 19 20 21 22 23 0.6058 0.6060 0.6062 0.7613 0.7618 0.7623 1-3135 1-3127 1.3119 0.7956 0.7955 0.7953 43 42 41 40 39 38 37 0.6065 0.7627 1.3111 0.7951 0.6067 0.6069 0.6071 0.7632 0.7636 0.7641 1.3103 1-3095 1-3087 0.7949 0.7948 0.7946 24 25 26 0.6074 0.6076 0.6078 0.7646 0.7650 0.7655 1.3079 1.3072 1.3064 0.7944 0.7942 0.7941 36 35 34 27 28 29 30 31 32 33 0.6081 0.6083 0.6085 0.6088 0.7659 0.7664 0.7669 1.3056 1.3048 1.3040 0.7939 0.7937 0.7935 33 32 31 30 29 28> 27 0-7673 1.3032 0.7934 0.6090 0.6092 0.6095 0.7678 0.7683 0.7687 1.3024 1-3017 1-3009 0.7932 0.7930 0.7928 34 35 36 0.6097 0.6099 0.6101 0.7692 0.7696 0.7701 1. 3001 1.2993 1.2985 0.7926 0.7925 0.7923 26 25 24 37 38 39 40 41 42 43 0.6104 0.6106 0.6108 0.7706 0.7710 0.7715 1.2977 1.2970 1.2962 0.7921 0.7919 0.7918 23 22 21 20 19 18 17 0.61 1 1 0.7720 1-2954 0.7916 0.6113 0.6115 0.6118 0.7724 0.7729 0.7734 1-2946 1-2938 1.2931 0.7914 0.7912 0.7910 44 45 46 0.6120 0.6122 0.6124 0.7738 0.7743 0.7747 1.2923 1.2915 1.2907 0.7909 0.7907 0-7905 16 15 14 47 48 49 50 51 52 53 0.6127 0.6129 0.6131 0.7752 0.7757 0.7761 1.2900 1.2892 1.2884 0.7903 0.7902 0.7900 13 12 11 10 9 8 7 0.6134 0.7766 1.2876 0.7898 0.6136 0.6138 0.6141 0.7771 0.7775 0.7780 1.2869 1.2861 1.2853 0.7896 0.7894 0.7893 54 55 56 0.6143 0.6145 0.6147 0.7785 0.7789 0.7794 1.2846 1.2838 1.2830 0.7891 0.7889 0.7887 6 5 4 57 58 59 60 0.6150 0.6152 0.6154 0.7799 0.7803 0.7808 1.2822 1.2815 1.2807 0.7885 0.7884 0.7882 3 2 I 0.6157 0.7813 1.2799 0.7880 Cos Cot 1 Tan Sin ' »143° 233° *323° 53° Natural 52° *142° 232° *322° »128° 218° *308° 38° Natural 39° 127 *129° 219° *309° / Sin Tan Cot Cos I 2 3 0.6157 0.7813 1.2799 0.7880 60 59 58 57 0.6159 0.6161 0.6163 0.7818 0.7822 0.7827 1.2792 1.2784 1.2776 0.7878 0.7877 0.7875 4 5 6 0.6166 0.6168 0.6170 0.7832 0.7S36 0.7841 1.2769 1.2761 1.2753 0.7873 0.7871 0.7869 56 55 54 7 8 9 10 II 12 13 0.6173 0.6175 0.6177 0.7846 0.7850 0.7855 1.2746 1.2738 1-2731 0.7868 0.7866 0.7864 53 52 51 50 49 48 47 0.61 Bo 0.7860 1.2723 0.7862 0.6182 0.6184 0.6186 0.7865 0.7869 0.7874 1-2715 1.2708 1.2700 0.7860 0.7859 0.7857 14 15 i6 0.6189 0.6191 0.6193 0.7879 0.7883 0.7888 1.2693 1.2685 1.2677 0.7855 0.7853 0.7851 46 45 44 17 i8 19 20 21 22 23 0.6196 0.6198 0.6200 0.7893 0.7898 0.7902 1.2670 1.2662 1.2655 0.7850 0.7848 0.7846 43 42 41 40 39 38 37 0.6202 0.7907 1.2647 0.7S44 0.6205 0.6207 0.6209 0.7912 0.7916 0.7921 1.2640 1.2632 1.2624 0.7842 0.7841 0.7839 24 25 26 0.62 II 0.6214 0.6216 0.7926 0.7931 0.7935 1. 2617 1.2609 1.2602 0.7837 0.7835 0.7833 36 35 34 27 28 29 30 31 32 33 0.6218 0.6221 0.6223 0.7940 0.7945 0.7950 1.2594 1.2587 1-2579 0.7832 0.7830 0.7828 33 32 31 30 29 28 27 0.6225 0.7954 1.2572 0.7826 0.6227 0.6230 0.6232 0.7959 0.7964 0.7969 1.2564 1-2557 1.2549 0.7824 0.7822 0.7821 34 35 36 0.6234 0.6237 0.6239 0.7973 0.7978 0.7983 1.2542 1.2534 1.2527 0.7819 0.7817 0.7815 26 25 24 37 38 39 40 41 42 43 0.6241 0.6243 0.6246 0.7988 0.7992 0.7997 1.2519 1.2512 1.2504 0.7813 0.7812 0.7810 23 22 21 20 19 18 17 0.6248 0.8002 1.2497 0.7808 0.6250 0.6252 0.6255 0.8007 0.8012 0.8016 1.2489 1.2482 1.2475 0.7806 0.7804 0.7802 44 45 46 0.6257 0.6259 0.6262 0.8021 0.8026 0.8031 1.2467 1.2460 1.2452 0.7801 0.7799 0.7797 16 15 14 47 48 49 50 51 52 53 0.6264 0.6266 0.6268 0.8035 0.8040 0.8045 1.2445 1.2437 1.2430 0.7795 0-7793 0.7792 13 12 II 10 9 8 7 0.6271 0.8050 1.2423 0-7790 0.6273 0.6275 0.6277 0.8055 0.8059 0.8064 1.2415 1.2408 1.2401 0.7788 0.7786 0.7784 54 55 56 0.6280 0.6282 0.6284 0.8069 0.8074 0.8079 1.2393 1.2386 1.2378 0.7782 0.7781 0.7779 6 5 4 57 58 59 60 0.6286 0.6289 0.6291 0.8083 0.8088 0.8093 1-2371 1.2364 1.2356 0.7777 0.7775 0.7773 3 2 I 0.6293 0.8098 1.2349 0.7771 Cos Cot Tan Sin ' ' Sin Tan Cot Cos 1 2 3 0.6293 0.8098 1.2349 0.7771 60 59 58 57 0.6295 0.6298 0.6300 0.8103 0.8107 0.8112 1.2342 1.2334 1.2327 0.7770 0.7768 0.7766 4 5 6 0.6302 0.6305 0.6307 0.S117 0.8122 0.8127 1.2320 1. 2312 1.2305 0.7764 0.7762 0.7760 56 55 54 7 8 9 10 II 12 13 0.6309 0.63 1 1 0.6314 0.8132 0.8136 d.8141 1.2298 1.2290 1.2283 0.7759 0.7757 0.7755 53 52 51 50 49 48 47 0.6316 0.8146 1.2276 0.7753 0.6318 0.6320 0.6323 0.8151 0.8156 0.8161 1.2268 1.2261 1.2254 0.7751 0.7749 0.7748 14 15 16 0.6325 0.6327 0.6329 0.8165 0.8170 0.8175 1.2247 1.2239 1.2232 0.7746 0.7744 0.7742 46 45 44 17 18 19 20 21 22 23 0.6332 0.6334 0.6336 0.8180 0.8185 0.8190 1.2225 1. 2218 1. 2210 0.7740 0.7738 0.7737 43 42 41 40 39 38 37 0.6338 0.8195 1.2203 0.7735 0.6341 0.6343 0-6345 0.8199 0.8204 0.8209 1.2196 1.2189 1.2181 0.7733 0.7731 0.7729 24 25 26 0.6347 0.6350 0.6352 0.8214 0.8219 0.8224 1.2174 1.2167 1.2160 0.7727 0.7725 0.7724 36 35 34 27 28 29 30 31 32 33 0.6354 0.6356 0.6359 0.8229 0.8234 0.8238 1.2153 1.2145 1.2138 0.7722 0.7720 0.7718 33 32 31 30 29 28 27 0.6361 0.8243 1.2131 0.7716 0.6363 0.6365 0.6368 0.8248 0.8253 0.8258 1.2124 1.2117 1. 2109 0.7714 0-7713 0.7711 34 35 36 0.6370 0.637.2 0-6374 0.8263 0.8268 0.8273 1.2102 1.2095 1.2088 0.7709 0.7707 0.7705 26 25 24 37 38 39 40 41 42 43' 0.6376 0.6379 0.6381 0.8278 0.8283 0.8287 1.2081 1.2074 1.2066 0.7703 0.7701 0.7700 23 22 21 20 19 18 17 0.6383 0.8292 1.2059 0.7698 0.6385 0.6388 0.6390 0.8297 0.8302 0.8307 1.2052 1.2045 1.2038 0.7696 0.7694 0.7692 44 45 46 0.6392 0.6394 0.6397 0.8312 0.8317 0.8322 1.2031 1.2024 1. 2017 0.7690 0.7688 0.7687 16 15 14 47 48 49 50 51 52 53 0.6399 0.6401 0.6403 0.8327 0.8332 0.8337 1.2009 1.2002 1.1995 0.7685 0.7683 0.7681 13 12 II 10 9 8 7 0.6406 0.8342 1.1988 0.7679 0.6408 0.6410 0.6412 0.8346 6.8351 0.8356 1.1981 1.1974 1.1967 0.7677 0.7675 0.7674 54 55 ■56 0.6414 0.6417 0.6419 0.8361 0.8366 0.8371 1.1960 1-1953 1. 1946 0.7672 0.7670 0.7668 6 5 4 57 58 59 60 0.6421 0.6423 0.6426 0.8376 0.8381 0.8386 1-1939 1.1932 1. 1925 0.7666 0.7664 0.7662 3 2 I 0.6428 0.8391 1. 1918 0.7660 Cos 1 Cot Tan Sin ' *141° 231° *321° 51° Natural 50° *140° 230° *320° 128 *130° 220° »310° 40° Natubal 4:1° *131° 221° »311° ' Sin Tan Cot Cos I 2 3 0.6428 0.8391 i.igiS 0.7660 60 59 58 57 0.6430 0.6432 0.6435 0.8396 0.8401 0.8406 1.1910 1.1903 I.l8g6 0.7659 0-7657 0-7655 4 5 6 0.6437 0.6439 0.6441 0.841 1 0.S416 0.8421 1. 1889 1. 1882 1-1875 0-7653 0.7651 0.7649 56 55 54 7 8 9 10 II 12 '3 0.6443 0.6446 0.6448 0.8426 0.8431 0.8436 1.1868 i.i86i 1.1854 0.7647 0-7645 0.7644 53 52 51 50 49 48 47 0.6450 0.8441 1. 1847 0.7642 0.6452 0.6455 0.6457 0.8446 0.8451 0.8456 1. 1840 1-1833 1. 1826 0.7640 0.7638 0.7636 14 15. i6 0.6459 0.6461 0.6463 0.8461 0.8466 0.8471 1.1819 1.1812 1. 1806 0.7634 0.7632 0.7630 46 45 44 17 i8 19 20 21 22 23 0.6466 0.6468 0.6470 0.8476 0.8481 0.8486 I.I 799 1. 1792 1. 1785 0.7629 0.7627 0.7625 43 42 41 40 39 38 37 0.6472 0.8491 1.1778 0.7623 0.6475 0.6477 0.6479 0.8496 0.8501 0.8506 I.I77I 1. 1764 I-1757 0.7621 0.7619 0.7617 24 25 26 0.6481 0.6483 0.6486 0.8511 0.8516 0.8521 1. 1750 1.1743 1-1736 0.7615 0.7613 0.7612 36 35 34 27 28 29 30 31 32 33 0.6488 0.6490 0.6492 0.8526 0.8531 0.8536 1.1729 1. 1722 1.1715 0.7610 0.7608 0.7606 33 32 31 30 29 •28 27 0.6494 0.8541 1-1708. 0.7604 0.6497 0.6499 0.6501 0.8546 0.8551 0.8556 1.1702 1. 1695 1. 1688 0.7602 0.7600 0.7598 34 35 36 0.6503 0.6506 0.6508 0.8561 0.8566 0.8571 I.l68i 1-1674 1. 1 667 0.7596 0-7595 0-7593 26 25 24 37 38 39 40 41 42 43 0.6510 0.6512 0.6514 0.8576 .0.8581 ^^8586 1. 1660 ;-i653 1. 1647 0.7591 0.7589 0.7587 23 22 21 20 19 18 17 0.6517 0.8591 1.1640 0.7585 0.6519 0.6521 0.6523 0.8596 0.8601 0.8606 1. 1633 1. 1626 1.1619 0.7583 0.7581 0.7579 44 45 46 0.6525 0.6528 0.6530 0.86II 0.8617 0.8622 1.1612 1. 1606 1-1599 0.7578 0.7576 0-7574 16 15 14 47 48 49 50 51 52 53 0.6532 0.6534 0.6536 0.8627 0.8632 0.8637 1-1592 1.1585 1. 1578 0.7572 0-7570 0.7568 13 12 11 10 9 8 7 0.6539 0.8642 1-1571 0.7566 0.0541 0.6543 0.6545 0.8647 0.8652 0.8657 1. 1565 1.1558 1-1551 0.7564 0.7562 0.7560 54 55 56 0.6547 0.6550 0.6552 0.8662 0.8667 0.8672 1.1544 1-1538 1-1531 0-7559 0-7557 0-7555 6 5 4 57 58 59 60 0.6554 0.6556 0.6558 0.8678 0.8683 0.8688 1. 1524 I-1517 1.1510 0-7553 0.7551 0.7549 3 2 I 0.6561 0.8693 1-1504 0.7547 Cos Cot Tan Sin ' ' Sin Tan Cot Cos I 2 3 0.6561 0.8693 1. 1504 0-7547 60 59 58 57 0.6563 0.6565 0.6567 0.8698 0.8703 0.8708 1.1497 1.1490 1.1483 0-7545 0-7543 0-754I 4 5 6 0.6569 0.6572 0.6574 0.8713 0.8718 0.8724 1-1477 1. 1470 1. 1463 0-7539 0.7538 0.7536 56 55 54 7 8 9 10 II 12 13 0.6576 0.6578 0.6580 0.8729 0.8734 0.8739 1.1456 1. 1450 1-1443 0-7534 0-7532 0.7530 53 52 51 50 49 48 47 0.6583 0.8744 1.1436 0.7528 0.6585 0.6587 0.6589 0.8749 0.8754 0-8759 1. 1430 1.1423 1.1416 0.7526 0-7524 0.7522 14 15 i6 0.6591 0-6593 0.6596 0.8765 0.8770 0-8775 1.1410 1. 1403 1-1396 0.7520 0.7518 0.7516 46- 45 44 17 18 19 20 21 22 23 0.6598 0.6600 0.6602 0.8780 0.8785 0.8790 1. 1389 1-1383 1. 1376 07515 0.7513 0.7511 43 42 41 40 39 38 37 0.6604 0.8796 1.1369 0.7509 0.6607 0.6609 0.661 1 0.8S01 0.8806 o.88n 1.1363 1.1356 1-1349 0.7507 0.7505 0-7503 24 25 26 0.6613 0.6615 0.6617 0.8816 0.8821 0.8827 1.1343 1.1336 1. 1329 0.7501 0.7499 0-7497 36 35 34 27 28 29 30 31 32 33 0.6620 0.6622 0.6624 0.8832 0.8837 0.8842 I;I323 1.1316 1.1310 0.7495 0.7493 0.7491 33 32 31 30 29 28 27 0.6626 0.8847 1.1303 0.7490 0.6628 0.6631 0.6633 0.8852 0.8858 0.8863 1.1296 1 . 1 290 1. 1283 0.7488 0.7486 0.7484 34 35 36 0.6635 0.6637 0.6639 0.8S68 0.8873 0.8878 1. 1276 1.1270 1.1263 0.7482 0.7480 0.7478 26 25 24 37 38 39 40 41 42 43 0.6641 0.6644 0.6646 0.8884 0.8889 0.8894 1.1257 1.1250 1.1243 0.7476 0.7474 0.7472 23 22 21 20 19 18 17 0.6648 0.S899 1. 1237 0.7470 0.6650 0.6652 0.6654 0.8904 0.8910 0.8915 1.1230 1. 1224 1.1217 0.7468 0.7466 0.7464 44 45 46 0.6657 0.6659 0.6661 0.8920 0.8925 0.8931 1.1211 1. 1204 1. 1197 0.7463 0.7461 0-7459 16 15 14 47 48 49 50 51 52 53 0.6663 0.6665 0.6667 0.8936 0.8941 0.8946 1.1191 1.1184 1.1178 0-7457 0.7455 0.7453 13 12 II 10 9 8 7 0.6670 0.8952 1.1171 0.7451 0.6672 0.6674 0.6676 0.8957 0.8962 0.8967 1.1165 1.1158 1.1152 0.7449 0.7447 0-7445 54 55 56 0.6678 0.6680 0.6683 0.8972 0.8978 0.8983 1.1145 1.1139 1.1132 0-7443 .0.7441 0-7439 6 5 4 57 58 59 60 0.6685 0.6687 0.6689 0.8988 0.8994 0.S999 1.1126 1.1119 1.1113 0-7437 0.7435 0.7433 3 2 I .0.6691 0.9004 i.i 106 0.7431 Cos Cot Tan Sin ' *139° 229° *319° 49° Natukal 48° *138° 228° *318° n32° 222° *312° 42° Natukal 43° »133° 223° 129 »313'' ' Sin Tan Cot Cos I 2 3 0.6691 0.9004 1.1106 0-7431 60 59 58 57 0.6693 0.6696 0.6698 0.9009 0.9015 o.go2o I.IIOO I.I093 1. 1087 0.7430 0.7428 0.7426 4 5 6 0.6700 0.6702 0.6704 0.9025 0.9030 0.9036 1. 1080 1.1074 1. 1067 0.7424 0.7422 0.7420 56 55 54 7 8 9 10 II 12 13 0.6706 0.6709 0.671 1 0.9041 " 0.9046 0.9052 i.io6i 1. 1054 1. 1048 0.7418 0.7416 0.7414 53 52 51 50 49 48 47 0.6713 0.9057 1.1041 0.7412 0.6715 0.6717 0.6719 0.9062 0.9067 0.9073 1-1035 1. 1028 1. 1022 0.7410 0.7408 0.7406 14 i6 0.6722 0.6724 0.6726 0.9078 0.9083 0.9089 1.1016 1. 1009 1. 1003 0.7404 0.7402 0.7400 46 45 44 17 i8 19 20 21 22 2_ 0.6728 0.6730 0.6732 0.9094 0.9099 0.9105 1.0996 1.0990 1.0983 0.7398 0.7396 0.7394 43 42 41 40 39 38 37 0.6734 0.91 10 1.0977 0.7392 0.6737 0.6739 0.6741 0.9115 0.9121 0.9126 1.0971 1.0964 1.0958 0.7390 0.7388 0-7387 24 25 26 0-6743 0.6745 0.6747 0.9131 0.9137 0.9142 1.0951 1-0945 1.0939 0.7385 0.73S3 0.7381 36 35 34 27 28 29 30 3' 32 33 0.6749 0.6752 0-6754 0.9147 0.9153 0.9158 1.0932 1.0926 1.0919 0.7379 0-7377 0-7375 33 32 31 30 29 28 27 0.6756 0.9163 1.0913 0-7373 0.6758 0.6760 0.6762 0.9169 0.9174 0.9179 1.0907 1 .0900 1.0894 0.7371 0.7369 0.7367 34 35 36 0.6764 0.6767 0.6769 0.9185 0.9190 0.9195 1.08S8 1.0881 1.0875 0.7365 0.7363 0.7361 26 25 24 37 38 39 40 41 42 43 0.6771 0.6773 0.6775 0.9201 0.9206 0.9212 1.0869 1.0S62 1.0856 0.7359 0-7357 0-7355 23 22 21 20 19 18 17 0.6777 0.9217 1.0S50 0-7353 0.6779 0.67S2 0.6784 0.9222 0.9228 0.9233 1.0843 1.0S37 1.0831 0-735I 0.7349 0-7347 44 45 46 0.6786 0.67SS 0.6790 0.9239 0.9244 0.9249 1.0824 1.0818 1.0812 0-7345 0.7343 0.7341 16 15 14 47 48 49 50 51 52 53 0.6792 0.6794 0.6797 0.9255 0.9260 0.9266 1.0S05 1-0799 1.0793 0.7339 0.7337 0-7335 13 12 II 10 9 8 7 0.6799 0.9271 1.0786 0.7333 0.6801 0.6803 0.6805 0.9276 0.9282 0.9287 1.0780 1.0774 1.0768 0-7331 0.7329 0.7327 54 55 56 0.6807 0.6809 . 0.6811 0.9293 0.9298 0.9303 1.0761 1-0755 1. 0749 0.7325 0.7323 0.7321 6 5 4 57 58 59 fiO 0.6814 o.68r6 0.6818 0.9309 0.9314 0.9320 1.0742 1.0736 1.0730 0.7319 0.7318 0.7316 3 2 I 0.6820 0.9325 1.0724 0.7314 Cos Cot Tan Sin ' ' Sin Tan Cot Cos I 2 3 0.6820 0.9325 1.0724 0.7314 60 59 58 57 0.6822 0.6824 0.6826 0.9331 0.9336 0.9341 1.0717 1.0711 1.0705 0.7312 0.7310 0.7308 4 5 6 0.6828 0.6831 0.6833 0.9347 0.9352 0.9358 1.0699 1.0692 1.0686 0.7306 0.7304 0.7302 56 55 54 7 8 9 10 II 12 13 0.6835 0.6837 0.6839 0.9363 0.9369 0.9374 1.0680 1.0674 1.0668 0.7300 0.7298 0.7296 53 52 51 50 49 48 47 0.6841 0.9380 1. 066 1 0.7294 0-6843 0.6845 0.6848 0.93 8 5 0.9391 0.9396 1-0655 1 .0649 1.0643 0.7292 0.7290 0.7288 '4 15 16 0.6850 0.6852 0.6854 0.9402 0.9407 0.9413 1-0637 1.0630 1.0624 0.7286 0.7284 0.7282 46 45 44 17 18 19 20 21 22 23 0.6856 0.6858 0.6S60 0.9418 0.9424 0.9429 1.0618 1. 061 2 1 .0606 0.7280 0.7278 0.7276 43 42 41 40 39 38 37 0.6862 0.9435 1.0599 0.7274 0.6865 0.6867 0.6869 0.9440 0.9446 0.9451 1-0593 1.0587 1.0581 0.7272 0.7270 0.7268 24 25 26 0.6871 0.6S73 0.6875 0.9457 0.9462 0.9468 1-0575 1.0569 1.0562 0.7266 0.7264 0.7262 36 35 34 27 28 29 30 31 32 33 0.6877 0.6879 0.6S8I 0.9473 0.9479 0.9484 1.0556 1.0550 1.0544 0.7260 0.7258 0.7256 33 32 31 30 29 28 27 0.6884 0.9490 1.0538 0.7254 0.6886 0.6888 0.6890 , 0.9495 0.9501 0.9506 1.0532 1.0526 1.0519. 0.7252 0.7250 0.7248 34 35 36 0.6892 0.6894 0.6896 0.9512 0.9517 0.9523 1.0513 1.0507 1.0501 0.7246 0.7244 0.7242 26 25 24 37 38 39 40 41 42 43 0.6898 0.6900 0.6903 0.9528 0.9534 0.9540 1.0495 1.0489 1.0483 0.7240 0.7238 0.7236 23 22 21 20 19 18 17 0.6905 0.9545 1.0477 0.7234 0.6907 0.6909 o.6qii 0.9551 0.9556 0.9562 1.0470 1.0464 1-0458 0.7232 0.7230 0.7228 44 45 46 0.6913 0.6915 0.6917 0-9567 0.9573 0.9578 1.0452 1.0446 1.0440 0.7226 0.7224 0.7222 16 15 14 47 48 49 50 51 52 53 0.6919 0.6921 0.6924 0.9584 0.9590 0.9595 1.0434 1.0428 1.0422 0.7220 0.7218 0.7216 13 12 11 10 9 8 7 0.6926 0.9601 1.0416 0.7214 0.6928 0.6930 0.6932 0.9606 0.9612 0.9618 1.0410 1.0404 1.0398 0.7212 0.7210 0.7208 54 55 56 0.6934 0.6936 0.6938 0.9623 0.9629 0.9634 1.0392 1.0385 1-0379 0.7206 0.7203 0.7201 6 5 4 57 58 59 60 0.6940 0.6942 0.6944 0.9640 0.9646 0.9651 1-0373 1-0367 1.0361 0.7199 0.7197 0.7195 3 2 I 0.6947 0.9657 1-0355 0.7193 Cos Cot Tan Sin ' *137- 227° *317° 47° Natural 46° *136° 226° *316° 130 Natural 44° *134° 224° *314° ' Sin Tan Cot Cos , I 2 3 0.6^47 0.9657 I.0355 0.7193 60 59 58 57 0.6949 0.6951 0.6953 0.9663 0.9668 0.9674 1.0349 I -0343 I-0337 0.7191 0.7189 0.7187 4 5 6 0.6955 0.6957 0.6959 0.9679 0.9685 0.9691 1.0331 1.0325 1.0319 0.7185 0.7183 0.7181 56 55 54 7 8 9 10 II 12 13 0.6961 0.6963 0.6965 0.9696 0.9702 0.9708 1.0313 1.0307 1. 030 1 0.7179 0.7177 0.7175 53 52 51 50 49 48 47 0.6967 0.9713 1.0295 0.7173 0.6970 0.6972 0.6974 C.9719 0.9725 0.9730 1.0289 1.0283 1.0277 0.7171 0.7169 0.7167 14 15 i6 0.6976 0.6978 0.69S0 0.9736 0.9742 0.9747 1.0271 1.0265 1.0259 0.7165 0.7163 0.7x61 46 45 44 17 i8 19 20 21 22 23 0.6982 0.6984 0.6986 0.9753 0.9759 0.9764 1.0253 1.0247 1.024 1 0.7159 0.7157 0.7155 43 42 41 40 39 38 37 0.O988 0.9770 I-0235 0.7153 0.6990 0.6992 0.6995 0.9776 0.9781 0.9787 1.0230 1.0224 1.0218 0.7151 0.7149 0.7147 24 25 26 0.6997 6999 0.7001 0-9793 0.9798 0.9804 1.0212 1.0206 1.0200 0.7145 0.7143 0.7141 36 35 34 27 28 29 30 31 32 33 0.7003 0.7005 0.7007 0.9810 0.9816 0.9821 1.0194 1.0188 1.0182 0.7139 0.7137 0.7135 33 32 31 30 29 28 27 0.7009 0.9827 1.0176 0.7x33 0.7011 0.70x3 0.7015 0.9833 0.9838 0.9844 1.0170 1.0104 1.0158 0.7130 0.7x28 0.7126 34 35 36 0.7017 0.7019 0.7022 0.9850 0.9856 0.9861 1-0152 1.0147 1.0141 0.7124 0.7x22 0.7x20 26 25 24 37 38 39 40 41 42 43 0.7024 0.7026 0.7028 0.9867 0.9873 0.9879 I-0135 1.0129 1.0123 0.7118 0.7116 0.71x4 23 , 22 2X 20 19 18 17 0.7030 0.9884 1.0117 0.7112 0.7032 0.7034 0.7036 0.9890 0.9896 0.9902 I.OIII 1.0105 1.0099 0.71x0 0.7108 0.7106 44 45 46 0.7038 0.7040 0.7042 0.9907 0.9913 0.9919 1.0094 1.0088 1.0082 0.7104 0.7102 0.7100 16 15 14 47 48 49 50 51 52 53 0.7044 0.7046 0.7048 0.9925 0.9930 0.9936 1.0076 1.0070 1.0064 0.7098 0.7096 0.7094 13 13 II 10 9 8 7 0.7050 0.9942 1.0058 0.7092 0.7053 0.7055 0.7057 0.9948 0.9954 0-9959 1.0052 1.0047 1.0041 0.7090 0.7088 0.7085 54 55 56 0.7059 0.7061 0.7063 0.9965 0.9971 0.9977 1.0035 1.0029 1.0023 0.7083 0.7081 0.7079 6 5 4 57 58 59 60 0.7065 0.7067 0.7069 0.9983 0.9988 0.9994 1.0017 I.00I2 I.COO6 0.7077 0.7075 0.7073 3 2 I 0.7071 1 .0000 1.0000 0.7071 • Cos Cot Tan ; Sin ' *135- 225° *315° 45° Natural 131 / VI \ TABLE OF SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS WHOLE NUMBERS FROM 1 TO 1020. The numbers are given in the columns headed N, their squares, cubes, square roots and cube roots respectively in the columns headed W, N >. t/n and f n 60 X N» N3 l/N f^ N N' N' /N #'N I 2 3' 0.0000 0.0000 30 31 32 33 900 27000 5-4772 3.1072 I 4 9 I 8 27 1.0000 I.4142 1.7321 1. 0000 1.2599 1.4422 961 1024 1089 29791 32768 35937 5-5678 5-6569 5-7446 3-1414 3-1748 3-2075 4 5 6 i6 25 36 64 125 216 2.0000 2.2361 2-4495 1.5874 1.7100 I.8I71 34 35 36 1156 1225 1296 39304 42875 46656 5.8310 5-9161 6.0000 3.2396 3.2711 3-3019 7 8 9 10 II 12 13 49 64 81 343 512 729 2.6458 2.8284 3.0000 1.9129 2.0000 2.0801 37 38 39 40 41 42 43 1369 1444 1521 50653 54872 59319 6.0828 6.1644 6.2450 3-3322 3.3620 3-3912 100 1000 3.1623 2.1544 1600 64000 6.3246 3.4200 121 144 169 1331 1728 2197 3.3166 3.4641 3-6056 2.2240 2.2894 2.3513 1681 1764 1849 68921 74088 79507 6.4031 6.4807 6.5574 3-4482 3.4760 3-5034 14 15 i6 196 225 256 2744 3375 4096 3-7417 3-8730 4.0000 2.4101 2.4662 2.5198 44 45 46 1936 2025 2116 85184 91125 97336 6.6332 6.7082 6.7823 3-5303 3-5569 3-5830 17 i8 19 20 21 22 23 289 324 361 4913 5832 6859 4.1231 4.2426 4-3589 2.5713 2.6207 2.6684 47 48 49 50 51 52 53 2209 2304 2401 103823 I 10592 1 1 7649 6-8557 6.9282 7.0000 3.6088 3-6342 3-6593 400 8000 4.4721 2.7144 2500 125000 7.0711 3-6840 441 484 529 9261 10648 12167 4.5826 4.6904 4-7958 2-7589 2.8020 2.8439 2601 2704 ■2809 132651 140608 148877 7.1414 7.2111 7.2801 3-7084 3-7325 3-7563 24 25 26 576 625 676 13824 15625 17576 4.8990 5.0000 5.0990 2.8845 2.9240 2.9625 54 55 56 2916 3025 3136 157464 166375 175616 7-3485 7.4162 7.4833 3-7798 3.8030 3-8259 27 28 29 30 729 784 841 19683 21952 24389 5.1962 5-2915 5-3852 3.0000 3.0366 3.0723 57 58 59 60 3249 3364 3481 185193 195112 205379 7-5498 7-6158 7.6811 3-8485 3.8709 3.8930 900 27000 5-4772 3.1072 3600 216000 7-7460 3-9149 K N' N» V'N ^/N N W N' V/N fN 132 60—180 N N» N' l/N fN N N» N' l/N fN 60 6i 3600 216000 7.7460 3.9149 120 121 14400 1728000 10.9545 4.9324 3721 226981 7.8102 3-9365 14641 1771561 11.0000 4.9461 62 3844 238328 7.8740 3-9579 122 14884 1815848 11.0454 4.9597 63 3969 250047 7-9373 3-9791 123 15129 1860867 11.0905 4.9732 64 4096 262144 8.0000 4.0000 124 15376 1906624 11.1355 4.9866 ' 63 4225 274625 8.0623 4.0207 125 15625 1953125 11.1803 5.0000 66 4356 287496 8.1240 4.0412 126 15876 2000376 11.2250 5.0133 67 4489 300763 8.1854 4.0615 127 16129 2048383 11.2694 5.0265 68 4624 314432 8.2462 4.0817 128 16384 2097152 11.3137 5.0397 69 70 71 4761 328509 8.3066 4.1016 129 130 131 16641 2146689 11.3578 5.0528 4900 343000 8.3666 4.1213 16900 2197000 11.4018 5.0658 5041 3579" 8.4261 4.1408 17161 2248091 11.4455 5.0788 72 5184 373248 8.4853 4.1602 132 17424 2299968 11.4891 5.0916 73 5329 389017 8.5440 4-1793 133 17689 2352637 11.5326 5.1045 74 5476 405224 8.6023 4.1983 134 17956 2406104 11.5758 5-1172 75 5625 421875 8.6603 4.2172 135 18225 2460375 11.6190 5.1299 76 5776 438976 8.7178 4.2358 136 18496 2515456 11.6619 5.1426 77 5929 456533 8.7750 4.2543 137 18769 2571353 11.7047 5.1551 78 6084 474552 8.8318 4.2727 138 19044 2628072 11.7473 5.1676 79 80 8i 6241 493039 8.8882 4.2908 139 140 141 19321 2685619 11.7898 5.1801 6400 512000 8.9443 4.3089 19600 2744000 11.8322 5.1925 6561 531441 9.0000 4.3267 19881 2803221 11.8743 5.2048 82 6724 551368 9.0554 4-3445 142 20164 2863288 11.9164 5.2171 83 6889 571787 9.1 104 4.3621 143 20449 2924207 11.9583 5.2293 84 7056 592704 9.1652 4.3795 144 20736 2985984 12.0000 5.2415 85 7225 614125 9-2195 4.3968 145 21025 3048625 12.0416 5.2536 86 7396 636056 9.2736 4.4140 146 21316 3112136 12.0830 5.2656 87 7569 658503 9.3274 4.4310 147 21609 3176523 12.1244 5.2776 88 7744 681472 9.3808 4.4480 148 21904 3241792 12.1655 5.2896 89 90 .91 7921 704969 9.4340 4.4647 149 150 151 22201 3307949 12.2066 5.3015 8100 729000 9.4868 4.4814 22500 3375000 12.2474 5.3133 8281 753571 9.5394 4.4979 22801 3442951 12.2882 5.3251 92 8464 778688 9-5917 4.5144 152 23104 3511808 12.3288 5.3368 93 8649 804357 9-6437 4.5307 153 23409 3581577 12.3693 5.3485 94 8836 830584 9-6954 4.5468 154 23716 3652264 12.4097 5.3601 95 9025 857375 9-7468 4.5629 155 24025 3723875 12.4499 5.3717 96 9216 884736 9-7980 4.5789 156 24336 3796416 12.4900 5.3832 97 9409 912673 9.8489 4.5947 157 24649 3869893 12.5300 5.3947 98 9604 941 192 9.8995 4.6104 158 24964 3944312 12.5698 5.4061 99 100 lOI 9801 970299 9.9499 4.6261 159 160 161 25281 4019679 12.6095 5.4175 1 0000 I 000000 10.0000 4.6416 25600 4096000 12.6491 5.4288 ■ I020I 1030301 10.0499 4.6570 25921 4173281 12.6886 5.4401 102 10404 1061208 10.0995 4.6723 162 26244 4251528 12.7279 5-4514 103 10609 1092727 10.1489 4.6875 163 26569 4330747 12.7671 5.4626 104 I0816 I 124864 10.1980 4.7027 164 26896 4410944 12.8062 5-4737 105 IIO25 1157625 10.2470 4.7177 165 27225 4492125 12.8452 5.4848 106 1 1236 1191016 10.2956 4.7326 166 27556 4574296 12.8841 5.4959 107 1 1449 1225043 10.3441 4-7475 ■ 167 27889 4657463 12.9228 5.5069 108 1 1 664 1259712 10.3923 4.7622 168 28224 4741632 12.9615 5.5178 109 110 III I1881 1295029 10.4403 4.7769 169 170 171 28561 4826809 13.0000 5.5288 I2I00 1331000 10.4881 4.7914 28900 4913000 13.0384 5-5397 I232I 1367631 10.5357 4.8059 29241 5000211 13.0767 5-5505 H2 12544 1404928 10.5830 4.8203 172 29584 5088448 13.1149 5-5613 113 12769 1442897 10.6301 4-8346 173 29929 5177717 13.1529 5-5721 114 12996 148 1 544 10.6771 4.8488 174 30276 5268024 13.1909 5.5828 115 13225 1520875 10.7238 4.8629 175 30625 5359375 13.2288 5.5934 116 13456 1560896 10.7703 4-8770 176 30976 5451776 13-2665 5.6041 117 13689 1601613 10.8167 4.8910 177 31329 5545233 13-3041 5.6147 118 13924 1643032 10.8628 4-9049 178 31684 5639752 13.3417 5.6252 119 120 I4161 1685159 10.9087 4.9187 179 ISO 32041 5735339 13.3791 5.6357 14400 1728000 10.9545 4.9324 32400 5832000 13.4164 5.6462 N, N» N' 1 V/N ifN N m N» >/N fN 133 180—300 N N^ N» i/N ^N N' N» N» Vn #'.N 180 i8i 182 1S3 32400 5832000 13.4164 5.6462 240 241 242 243 57600 13824000 15.4919 6.2145 32761 33124 33489 5929741 6028568 6128487 134536 13.4907 13-5277 5-6567 5.6671 5-6774 58081 58564 59049 13997521 14172488 14348907 15.5242 15-5563 15.5885 6.2231 6.2317 6.2403 184 185 186 33856 34225 34596 6229504 6331625 6434856 IJ.564T 13.6015 13.6382 -5:6877 5.6980 5-7083 244 245 246 59536 60025 60516 14526784 14706125 14886936 15.6205 15-6525 15.6844 6.2488 6.2573 6.2658 187 188 189 190 191 192 193 34969 35344 35721 6539203 6644672 6751269 13.6748 13.7113 13-7477 5-7185 5-7287 5-7388 247 248 249 250 251 252 253 61009 61504 62001 15069223 15252992 15438249 15.7162 15.7480 15-7797 6-2743 6.2828 6.2912 36100 6859000 13-7840 5.7489 62500 15625000 15.8114 6.2996 36481 36864 37249 6967871 7077888 7189057 13.8203 13-8564 13-8924 5-7590 5.7690 5-7790 '\63001 63504 64009 15813251 16003008 16194277 15.8430 15.8745 15.9060 6.3080 6.3164 6.3247 194 195 196 37636 38025 38416 7301384 7414875 7529536 13.9284 13.9642 14.0000 5.7890 5-7989 5.8088 254 255 256 64516 65025 65536 16387064 16581375 16777216 15-9374 15.9687 16.0000 6.3330 6-3413 6.3496 197 198 199 200 201 202 203 38809 39204 39601 7645373 7762392 7880599 14-0357 14.0712 14.T067 5.8186 5-8285 5-8383 257 258 259 260 261 262 263 66049 66564 67081 16974593 17173512 17373979 16.0312 16.0624 16.0935 6-3579 6.3661 6-3743 40000 8000000 14.1421 5.8480 67600 17576000 16.1245 6.3825 40401 40804 41209 8 I 2060 I 8242408 8365427 14-1774 14.2127 14.2478 5-8578 5-8675 5.8771 68121 68644 69169 17779581 17984728 18191447 16.1555 16.1864 16.2173 6.3907 6.3988 6.4070 204 205 206 41616 42025 42436 8489664 8615125 8741816 14.2829 14.3178 14-3527 5.8868 5-8964 5-9059 264 265 266 69696 70225 70756 18399744 18609625 18821096 16.2481 16.2788 16.3095 6.4151 6.4232 6.4312 207 208 2og 210 211 212 213 42849 43264 43681 8869743 8998912 9129329 14-3875 14.4222 14.4568 5-9155 5.9250 5-9345 267 268 269 270 271 272 273 71289 71824 72361 19034163 19248832 19465109 16.3401 16.3707 16.4012 6.4393 6-4473 6-4553 44100 9261000 14.4914 5-9439 72900 19683000 16.4317 6.4633 44521 44944 45369 9393931 9528128 9663597 14.5258 14.5602 14-5945 5-9533 5.9627 5-9721 73441 73984 74529 19902511 20123648 20346417 16.4621 16.4924 16.5227 6.4713 6.4792 6.4872 214 215 216 45796 46225 46656 9800344 9938375 10077696 14.6287 14.6629 14.6969 5.9814 5-9907 6.0000 274 275 276 75076 75625 76176 20570824 20796875 21024576 16.5529 16.5831 16.6132 6.4951 6.5030 6.5108 217 218 219 220 221 222 223 47089 47524 47961 10218313 10360232 10503459 14.7309 14.7648 14.7986 6.0092 6.0185 6.0277 277 278 279 280 281 282 283 76729 77284 77841 21253933 21484952 21717639 16.6433 16.6733 16.7033 6.5187 6.5265 6.5343 48400 10648000 14.8324 6.0368 78400 21952000 16.7332 6.5421 48841 49284 49729 10793861 10941048 H089567 14.8661 14.8997 14.9332 6.0459 6.0550 6.0641 78961 79524 80089 22188041 22425768 22665187 16.7631 16.7929 16.8226 6.5499 6.5577 6.5654 224 225 226 50176 50625 51076 11239424 I 1390625 11543176 14.9666 15.0000 15-0333 6.0732 6.0822 6.0912 284 285 286 80656 81225 81796 22906304 23149125 23393656 16.8523 16.8819 16.9115 6.5731 6.5808 6.5885 227 228 229 230 231 232 233 51529 51984 52441 I I 697083 I1852352 12008989 15.0665 15-0997 15-1327 6.1002 6.1091 6.1180 287 288 289 290 291 292 293 82369 82944 83521 23639903 23887872 24137569 16.9411 16.9706 17.0000 6.5962 6.6039 6.6115 52900 12167000 15.1658 6.1269 84100 24389000 17.0294 6.6191 53361 53824 54289 12326391 12487168 12649337 15.1987 15-2315 15-2643 6.1358 6.1446 6-1534 84681 85264 85849 24642171 24897088 25153757 17-0587 17.0880 17.1172 6.6267 6.6343 6.6419 234 235 236 54756 55225 55696 12812904 12977875 13144256 15-2971 15-3297 15.3623 6.1622 6.1710 6-1797 294 295 296 86436 87025 87616 25412184 25672375 25934336 17.1464 17.1756 17.2047 6.6494 6.6569 6.6644 237 238 239 240 56169 56644 57121 13312053 13481272 13651919 15-3948 15-4272 15.4596 6.1885 6.1972 6.2058 297 298 299 300 88209 88804 89401 26198073 26463592 26730899 17-2337 17.2627 17.2916 6.6719 6.6794 6.6869 57600. 13824000 15.4919 6.2145 90000 27000000 17.3205 6.6943 J^ ]sr^ ■ N^ l/N ifN N N' N' t/n ifN 134 300—420 N N= N' T/N fN N N« N' V^ fN 300 301 302 303 90000 27000000 17.3205 6.6943 360 361 362 363 129600 46656000 18.9737 7-II38 90601 91204 91809 27270901 27543608 27818127 17.3494 17-3781 17.4069 6.7018 6.7092 6.7166 I 3032 I I 3 1044 131769 47045881 47437928 47832147 19.0000 19.0263 19.0526 7-1204 7.1269 7.1335 304 305 306 92416 93025 93636 28094464 28372625 28652616 17.4356 17.4642 17.4929 6.7240 6-7313 6.7387 364 365 366 132496 133225 133956 48228544 48627125 49027896 19.0788 19.1050 I9-I31I 7.1400 7.1466 7.1531 307 308 309 310 3" 312 313 94249 94864 95481 28934443 29218112 29503629 17.5214 17-5499 17-5784 6.7460 6.7533 6.7606 367 368 369 370 371 372 373 134689 135424 136161 49430863 49836032 50243409 19.1572 19.1833 19.2094 7.1596 7.1661 7.1726 96100 29791000 17.6068 6.7679 136900 50653000 19-2354 7-1791 96721 97344 97969 30080231 30371328 30664297 17.6352 17-6635 17.6918 6.7752 6.7824 6.7897 137641 138384 139129 510648U 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8.8023 8.8066 549081 550564 552049 406869021 408518488 410172407 27.2213 27.2397 27.2580 9.0491 9.0532 9.0572 684 685 686 467856 469225 470596 320013504 321419125 322828856 26.1534 26.1725 26.1916 8.8109 8.8152 8.8194 744 745 746 553536 555025 556516 411830784 413493625 4I5I60936 27.2764 27.2947 27.3130 9-0613 9-0654 9.0694 687 688 689 690 691 692 693 471969 473344 474721 324242703 325660672 327082769 26.2107 26.2298 26.2488 8.8237 8.8280 8.8323 747 748 749 750 751 752 753 558009 559504 561001 416832723 418508992 420189749 27.3313 27.3496 27.3679 9-0735 9-0775 9.0816 476100 328509000 26.2679 8.8366 562500 421875000 27.3861 9.0856 477481 478864 480249 329939371 331373888 332812557 26.2869 26.3059 26.3249 8.8408 8.8451 8.8493 564001 565504 567009 423564751 425259008 426957777 27.4044 27.4226 27.4408 9.0896 9.0937 9.0977 694 695 696 481636 483025 484416 334255384 335702373 337153536 26.3439 26.3629 26.3818 8.8536 8.8578 8.8621 754 755 756 568516 570025 571536 428661064 430368875 43208I2I6 27.4591 27-4773 27.4955 9.1017 9.1057 9.1098 697 698 699 700 701 702 703 485809 487204 488601 338608873 340068392 341532099 26.4008 26.4197 26.4386 8.8663 8.8706 8.8748 757 758 759 760 761 762 763 573049 574564 576081 433798093 4355I95I2 437245479 27.5136 27.5318 27.5500 9.1138 9.1178 9.1218 490000 343000000 26.4575 8.8790 577600 438976000 27.5681 9.1258 491401 492804 494209 344472101 345948408 347428927 26.4764 26.4953 26.5141 8.8833 8.8875 8.8917 579121 580644 582169 440711081 442450728 444194947 27.5862 27.6043 27.6225 9.1298 9.1338 9-1378 704 705 706 495616 497025 498436 348913664 350402625 351895816 26.5330 26.5518 26.5707 8.8959 8.9001 8.9043 764 765 766 583696 585225 586756 445943744 447697125 449455096 27.6405 27.6586 27.6767 9.1418 9.1458 9.1498 707 708 709 710 711 712 713 499849 501264 502681 353393243 354894912 356400829 26.5895 26.6083 26.6271 8.9085 8.9127 8.9169 767 768 769 770 771 772 773 588289 589824 591361 451217663 452984832 454756609 27.6948 27.7128 27.7308 9-1537 9.1577 9.1617 504100 357911000 26.6458 8.9211 592900 456533000 27.7489 9.1657 505521 506944 508369 359425431 360944128 362467097 26.6646 26.6833 26.7021 8.9253 8.9295 8.9337 594441 595984 597529 458314011 460099648 461889917 27.7669 27.7849 27.8029 9.1696 9.1736 9.1775 714 715 716 509796 511225 512656 363994344 365525875 367061696 26.7208 26.7395 26.7582 8.9378 8.9420 8.9462 774 775 776 599076 600625 602176 463684824 465484375 467288576 27.8209 27.8388 27.8568 9.1815 9-1855 9.1894 717 718 719 720 514089 515524 516961 368601813 370146232 371694959 26.7769 26.7955 26.8142 8.9503 8.9545 8.9587 777 778 779 780 603729 605284 606841 469097433 470910952 472729139 27.8747 27.8927 27.9106 9.1933 9.1973 9.2012 5 I 8400 373248000 26.8328 8.9628 608400 474552000 27.9285 9.2052 N 'N' N= V'N ^N N W N» l/N fN 138 780—900 N N» N» i/if fN N N« N' t/n fN 780 781 782 783 608400 474552000 27.9285 9-2052 840 841 842 843 705600 592704000 28.9828 9-4354 609961 611524 613089 476379541 478211768 480048687 27.9464 27.9643 27.9821 9.2091 9.2130 9.2170 707281 708964 710649 594823321 596947688 599077107 29.0000 29.0172 29.0345 9-4391 9-4429 9.4466 784 785 786 614656 616225 617796 481890304 483736625 485587656 28.0000 28.0179 28.0357 9.2209 9.2248 9.2287 844 845 846 712336 714025 715716 601211584 603351125 605495736 29-0517 29.0689 29.0861 9-4503 9.4541 9.4578 787 788 789 790 791 792 793 619369 620944 622521 487443403 489303872 491 169069 28.0535 28.0713 28.0891 9.2326 9.2365 9.2404 847 848 849 850 851 852 853 717409 719104 720801 607645423 609800192 611960049- 29.1033 29.1204 29.1376 9.4615 9.4652 9.4690 624100 493039000 28.1069 9.2443 722500 614125000 29.1548 9.4727 625681 627264 628849 494913671 496793088 498677257 28.1247 28.1425 28.1603 9.2482 9.2521 9.2560 724201 725904 727609 616295051 618470208 620650477 29.1719 29.1890 29.2062 9.4764 9.4801 9-4838 794 795 796 630436 632025 633616 500566184 502459875 504358336 28.1780 28.1957 28.2135 9.2599 9.2638 9.2677 854 855 856 729316 731025 732736 622835864 625026375 627222016 29.2233 29.2404 29-2575 9.4875 9.4912 9-4949 797 798 799 800 801 802 803 635209 636804 638401 506261573 508169592 510082399 28.2312 28.2489 28.2666 9.2716 9.2754 9-2793 857 858 859 860 861 862 863 734449 736164 737881 629422793 631628712 633839779 29.2746 29.2916 29.3087 g.4986 9.5023 9.5060 640000 512000000 28.2843 9.2832 739600 636056000 29.3258 9.5097 641601 643204 644809 513922401 515849608 517781627 28.3019 28.3196 28.3373 .9.2870 9.2909 9.2948 741321 743044 744769 638277381 640503928 642735647 29.3428 29.3598 29.3769 9-5134 9-5171 9.5207 804 805 806 646416 648025 649636 519718464 521660125 523606616 28.3549 28.3725 28,3901 9.2986 9-3025 9.3063 864 865 866 746496 748225 749956 644972544 647214625 649461896 29.3939 29.4109 29.4279 9.5244 9.5281 9-5317 807 808 809 810 811 812 813 651249 652864 654481 525557943 527514112 529475129 28.4077 28.4253 28.4429 9.3102 9.3140 9.3179 867 868 869 870 871 872 873 751689 753424 755161 651714363 653972032 65623490^ 29.4449 29.4618 29.4788 9-5354 9-5391 9-5427 656100 531441000 28.4605 9-3217 756900 658503000 29.4958 9-5464 657721 659344 660969 533411731 535387328 537367797 28.4781 28.4956 28.5132 9-3255 9-3294 9'3332 758641 760384 762129 660776311 663054848 665338617 29.5127 29.5296 29.5466 9-5501 9-5537 9-5574 814 8i5 816 662596 664225 665856 539353144 541343375 543338496 28.5307 28.5482 28.5657 9-3370 9.3408 9-3447 874 875 876 763876 765625 767376 667627624 669921875 672221376 29.5635 29.5804 29.5973 9.5610 9-5647 9.5683 817 818 819 820 821 822 823 667489 669124 670761 545338513 547343432 549353259 28.5832 28.6007 28.6182 9-3485 9-3523 9-3561 877 878 879 880 881 882 883 769129 770884 772641 674526133 676836152 679151439 29.6142 29.6311 29.6479 9-5719 9-5756 9-5792 672400 674041 675684 677329 551368000 28.6356 9-3599 774400 681472000 29.6648 9.5828 553387661 555412248 557441767 28.6531 28.6705 28.6880 9-3637 9-3675 9-3713 776161 777924 779689 683797841 686128968 688465387 29.6816 29.6985 29-7153 9.5865 9.5901 9-5937 824 825 826 678976 680625 682276 559476224 561515625 563559976 28.7054 28.7228 28.7402 9-3751 9-3789 9.3827 884 885 886 781456 783225 784996 690807104 693154125 695506456 29-7321 29-7489 29.7658 9-5973 9.6010 9.6046 827 828 829 830 831 832 833 683929 685584 687241 565609283 567663552 569722789 28.7576 28.7750 2S.7924 9-3865 9.3902 9.3940 887 888 889 890 891 892 893 786769 788544 790321 697864103 700227072 702595369 29.7825 29-7993 29.8161 9.6082 9.6118 9.6154 688900 571787000 28.8097 9.3978 792100 704969000 29.8329 9.6190 690561 692224 693889 573856191 575930368 578009537 28.8271 28.8444 28.8617 9.4016 9.4053 9.4091 793881 795664 797449 707347971 709732288 712121957 29.8496 29.8664 29.8831 9.6226 9.6262 9.6298 834 835 836 695556 697225 698896 580093704 582182875 584277056 28.8791 28.8964 28.9137 9.4129 9.4166 9.4204 894 895 896 799236 801025 802816 714516984 716917375 719323136 29.8998 29.9166 29-9333 9.6334 9.6370 9.6406 837 838 839 840 700569 702244 703921 586376253 588480472 590589719 28.9310 28.9482 28.9655 9.4241 9.4279 9.4316 897 898 899 900 804609 806404 808201 721734273 724150792 726572699 29-9500 29.9666 29-9833 9.6442 9-6477 9-6513 705600 592704000 28.9828 9-4354 810000 729000000 30.0000 9.6549 JS" N' N' /n fN N N» N' Vn fN 139 900- -102 N N^ N» •n fN N N» W t/n fN 900 90 1 902 903 810000 729000000 30.0000 9-6549 960 961 962 963 921600 884736000 30.9839 9.8648 811801 813604 815409 731432701 733870808 736314327 30.0167 30.0333 30.0500 9.6585 9.6620 9.6656 923521 925444 927369 887503681 890277128 893056347 31.0000 31.0161 31.0322 9.8683 9.8717 9.8751 904 903 906 817216 819025 820836 738763264 741217625 743677416 30.0666 30.0832 30.0998 9.6692 9.6727 9.6763 964 965 966 929296 931225 933156 895841344 898632125 901428696 31.0483 31-0644 31.0805 9-8785 9.8819 9.8854 . 907 908 909 910 911 912 913 822649 824464 826281 746142643 748613312 751089429 30.1164 30.1330 30.1496 9.6799 9.6834 9.6870 967 968 969 970 971 972 973 935089 937024 938961 904231063 907039232 909853209 31.0966 31.1127 31.1288 9.8888 9.8922 9.8956 828100 753571000 30.1662 9.6905 940900 912673000 31.1448 9.8990 829921 831744 833569 756058031 758550528 761048497 30.1828 30.1993 30.2159 9.6941 9.6976 9.70x2 942841 944784 946729 915498611 918330048 921167317 31.1609 31.1769 31.1929 9.9024 9.9058 9.9092 914 915 916 835396 837225 839056 763551944 766060875 768575296 30.2324 30.2490 30.2655 9.7047 9.7082 9.7118 974 975 976 948676 950625 952576 924010424 926859375 929714176 31.2090 31.2256 31.2410 9.9126 9.9160 9.9194 917 918 919 920 921 922 923 840889 842724 844561 771095213 773620632 776151559 30.2820 30.2985 30.3150 9-7153 9.7188 9.7224 977 978 979 980 981 982 983 954529 956484 958441 932574833 935441352 938313739 31.2570 31.2730 31.2890 9.9227 9.9261 9-9295 846400 778688000 30.3315 9-7259 960400 941 192000 31-3050 9-9329 848241 850084 851929 781229961 783777448 786330467 30.3480 30.3645 30.3809 9.7294 9.7329 9-7364 962361 964324 966289 944076141 946966168 949862087 31-3209 31-3369 31-3528 9.9363 9.9396 9-9430 924 925 926 853776 855625 857476 788889024 791453125 794022776 30.3974 30.4138 30.4302 9.7400 9-7435 9-7470 984 985 986 968256 970225 972196 952763904 955671625 958585256 31.3688 31-3847 31.4006 9-9464 9.9497 9-9531 927 928 929 930 931 932 933 859329 861 1 84 863041 796597983 799178752 801765089 30.4467 30.4631 30.4795 9-7505 9-7540 9-7575 987 988 989 990 991 992 993 974169 976144 978121 961504803 964430272 967361669 31.4166 31-4325 31.4484 9-9565 9-9598 9.9632 864900 804357000 30.4959 9.7610 980100 970299000 31-4643 9.9666 866761 868624 870489 806954491 809557568 812166237 30.5123 30.5287 30.5450 9-7645 g.7680 9-7715 982081 984064 986049 973242271 976191488 979146657 31.4802 31.4960 31-5119 9.9699 9-9733 9.9766 934 935 936 872356 874225 876096 814780504 817400375 820025856 30.5614 30.5778 30.5941 9-7750 9-7785 9.7819 994 995 996 988036 990025 992016 982107784 985074875 988047936 31-5278 31-5436 31-5595 9.9800 9-9833 9.9866 937 938 939 940 941 942 943 877969 879844 881721 822656953 825293672 827936019 30.6105 30.6268 30.6431 9-7854 9.7889 9.7924 997 998 999 1000 1001 1002 1003 994009 996004 998001 991026973 994011992 997002999 31-5753 31-5911 31.6070 9.9900 9-9933 9-9967 883600 830584000 30.6594 9-7959 I 000000 I 000000000 31.6228 10.0000 885481 887364 889249 833237621 835896888 838561807 30.6757 30.6920 30.7083 9-7993 9.8028 9.8063 1002001 1004004 1006009 1003003001 1006012008 1009027027 31.6386 31.6544 31.6702 10.0033 10.0067 10.0100 944 945 946 891136 893025 894916 841232384 843908625 846590536 30.7246 30.7409 30.7571 9.8097 9.8132 9.8167 1004 1005 1006 1008016 1010025 1012036 1012048064 1015075125 1018108216 31.6860 31-7017 31-7175 10.0133 10.0166 10.0200 947 948 949 950 951 952 953 896809 898704 900601 849278123 851971392 854670349 30.7734 30.7896 30.8058 9.8201 9.8236 9.8270 1007 1008 1009 1010 1011 1012 1013 1014049 1016064 101 808 I 1021147343 1024192512 1027243729 31-7333 31.7490 31.7648 10.0233 10.0266 10.0299 902500 857375000 30.8221 9-8305 1020T00 1030301000 31.7805 10.0332 904401 906304 908209 860085351 862801408 865523177 30.8383 30.8545 30.8707 9-8339 9-8374 9.8408 1022121 1024144 1026169 1033364331 1036433728 1039509197 31.7962 31.8119 31.8277 10.0365 10.0398 10.0431 ' 954 955 956 910116 912025 913936 868250664 870983875 873722816 30.8869 30.9031 30.9192 9-8443 9-8477 9.8511 1014 1015 1016 1028196 1030225 1032256 1042590744 1045678375 1048772096 31-8434 31-8591 31.8748 10.0465 10.0498 10.0531 957 958 959 960 915849 917764 919681 876467493 879217912 881974079 30.9354 30.9516 30.9677 9.8546 9.8580 9.8614 1017 1018 1019 1020 1034289 1036324 1038361 1051871913 1054977832 1058089859 31.8904 31.9061 31.9218 10.0563 10.0596 10.0629 921600 884736000 30.9839 9.8648 1040400 1061208000 31-9374 10.0662 N W N» i/n fN ]sr m N» Vn fN ■VII TABLE OF FACTORS COMPUTING PROBABLE ERRORS. n .6745 J -6745 .6745 J .6745 n .6745 J .6745 .6745 I .6745 l/ji— 1 \/'n(n—l) Vnn-l) r run—l) Vn{n-l) 2 3 40 41 42 43 0.0171 8.23241 0.1080 9.03344 0.4769 0.2754 9.67846 9.43990 0.6745 0.4769 9.82898 9.67846 0.0167 0.0163 0.0159 8.22155 8.21096 8.20062 0.1066 01053 0.1041 9.02795 9.02258 9.01735 4 5 6 0.1947 0.1508 0.1231 9.28938 9.17846 9.09041 0.3894 0.3372 0.3016 9.59041 9.52795 9-47949 44 45 46 0.0155 0.0152 0.0148 8.19051 8.18064 8.17099 0.1029 0.1017 0.1005 9.01224 9.00725 9.00237 7 8 9 10 II 12 13 0.1041 0.0901 0.0795 9.01735 8.95488 8.90031 0.2754 0.2549 0.2385 9.43990 9.40643 9-37743 47 48 49 50 51 52 53 0.0145 0.0142 0.0139 8.16155 8.15231 8.14326 0.0994 0.0984 0.0974 8.99760 8.99283 8.98835 0.071 1 8.85185 0.2248 9.35185 0.0136 8.13439 0.0964 8.98388 0.0643 0.0587 0.0540 8.8082B 8.76869 8.73241 0.2133 0.2029 0.1947 9.32898 9.30828 9.28938 0.0134 0.013 1 0.0128 8.12571 8.11719 8.10884 0.0954 0.0944 0.0935 8.97949 8.97519 8.97097 14 15 i6 0.0500 0.0465 0.0435 8.69894 8.66787 8.63887 0.1871 0.1803 0.1742 9.27200 9.25591 9.24093 54 55 56 0.0126 0.0124 0.0122 8.10064 8.09260 8.08470 0.0926 0.0918 0.0900 8.96684 8.96278 8.95879 17 l8 19 20 21 22 23 0.0409 0.0386 0.0365 8.6II69 8.586II 8.56196 0.1686 0.1636 0.1590 9.22692 9.21375 9.20134 57 58 59 60 61 62 63 0.0119 0.0117 0.0115 8.07694 8.06932 8.06184 0.0901 0.0893 0.0886 8.95488 8.95104, 8.94726 0.0346 8.53908 0.1547 9.18960 0.0113 8.05447 0.0878 8.94355 0.0329 0.0314 0.0300 8.51735 8.49665 8.47690 0.1508 0.1472 0.1438 9.17846 9.16787 9.15776 O.OIII O.OIIO o.oioS 8.04723 8.0401 1 8.03311 0.0871 0.0864 0.0857 8.93990 8.93631 8.93278 24 25 26 0.0287 0.0275 0.0265 8.45801 8.43990 8.42252 0.1406 0.1377 0.1349 9.14811 9.13887 9.13001 64 65 66 0.0106 O.OIC5 0.0103 8.02622 8.01943 8.01275 0.0850 0.0843 0.0837 8.92931 ' 8.92589 8.92252 27 28 29 30 31 32 33- 0.0255 00245 0.0237 8.40581 8.38971 8.37420 0.1323 0.1298 0.1275 9.12149 9.11329 9.10540 67 68 69 70 71 72 73 O.OIOI O.OIOO 0.0098 8.00617 7.99968 7.99330 0.0830 0.0824 0.0818 8.91920 8.91594 8.91272 0.0229 8.35922 0.1252 9.09778 0.0097 7.98700 0.0812 8.90955 0.0221 0.0214 0.0208 8.34473 8.33072 8.3I7I4 0.1231 0.1211 0.1192 9.09041 9.08329 9.07640 0.0096 0.0094 0.0093 7.98080 7.97468 7.96865 0.0806 0.0800 0.0795 8.90643 8.90335 8.90031 34 ■35 36 0.0201 0.0196 0.0190 8.30398 8.29120 8.27879 0.1174 0.1157 0.1 140 9.06972 9.06324 9.05694 74 75 76 0.0092 0.0091 0.0089 7.96270 7.95683 7.95104 0.0789 0.0784 0.0779 8.89731 8.89436 8.89144 37 38 39 4O 0.0185 0.0180 O.OI75 8.26672 8.25498 8.24355 0.1124 0.1 109 0.1094 9.05082 9.04487 9.03908 77 78 79 80 0.0088 0.0087 0.0086 7-94532 7.93968 7-93411 0.0774 0.0769 0.0764 8.88857 8.88573 8.88293 ^ 0.0171 8.23241 0.1080 9.03344 0.0085 7.92962 0.0759 8.88016 I n ■6745 J .6745 ■6745 Vn—1 J .6745 /n— 1 n .6745 1 -6745 .6745 Vn — l 1 .6745 , ' Vn—l V'n(n-l) l/n(n-l) l/n(n— 1) y n n— 1)