« r CHAUNCEY WETMORE WELLS 1872-1933 This book belonged to Chauncey Wetmore Wells. He taught in Yale College, of which he was a graduate, from 1897 to 1901, and from 1 90 1 to 1933 at this University. Chauncey Wells was, essentially, a scholar. The range of his read- ing was wide, the breadth of his literary sympathy as uncommon as the breadth of his human sympathy. He was less concerned with the collection of facts than with meditation upon their sig- nificance. His distinctive power lay in his ability to give to his students a subtle perception of the inner implications of form, of manners, of taste, of the really disciplined and discriminating mind. And this perception appeared not only in his thinking and teaching but also in all his relations with books and with men. FIVE-PLACE LOGARITHMIC AND TRIGO NOMETRIC TABLES EDITED BY JAMES M. TAYLOR, A.M., LL.D. Colgate University • • ••••••. ••• •• • • GINN AND COMPANY BOSTON • NEW YORK • CHICAGO • LONDON ATLANTA • DALLAS • COLUMBUS • SAN FRANCISCO COPYKIGHT, 1905 By JAMES M. TAYLOR ALL BIGHTS RESEKVED 521.6 « e ccr* •«• IN MEMORIAM GINN AND COMPANY* PRO- PRIETORS • BOSTON • U.S.A. PEEFACE The editor's aim in these tables has been to secure an open and attractive page, an arrangement easily understood but not involving needless repetitions, and some simple device by which any required data in the table can be quickly found. By lessening the time and weariness involved in using logarithmic tables, it is hoped that log- arithmic computation will be encouraged and made more attractive to the beginner. These tables are intended primarily for those who use logarith- mic and trigonometric tables for the first time. The editor believes that clearness of comprehension of the tables by beginners is pro- moted by retaining the decimal point before mantissas and by tabu- lating the exact characteristics of the trigonometric functions. In § 6, simple rules are given for the characteristics of the logarithmic functions of angles between 6° and 84°. The computer should apply these fundamental rules so that when the given angle is between these limits he will seek only the mantissas of its func- tions in thQ table, and will know at once the relation of an angle to 45° from the characteristic of its logarithmic tangent or cotan- gent. Moreover, these rules are useful as simple checks. In Tables III and IV characteristics are written only at the top and the bottom of each column of mantissas. Even these are superfluous when the angle is between 6° and 84°. In Tables I, III, and IV the first two figures of a mantissa are written only in the first mantissa having these figures and in the first mantissa of each group of five m^antissas. This plan makes the printed figures stand out clear and distinct in an open page, greatly aids the eye in following either rows or columns, and practically reduces groups of five mantissas to groups of four. In using such tables the student is not fatigued through the strain and confusion incident to con- sulting pages crowded with needlessly repeated figures. To enable the computer to find at once the page or the part of a page on which any given datum is tabulated, each table is provided with a system of tabs. The explanation of these tabs in §§ 10-13 will contribute to the better understanding of the tables themselves, and their use will lead the student to a method in his work and enable him to find any desired data in the tables in less than half the time usually required. j^^^^^^ ^ ^^^^^^^^ Colgate University, December, 1905 iii 863f7y3 CONTENTS Tables Pages Explanation of tables v-xvi I. Five-place mantissas of the logarithms of the entire numbers from 1 to 11,000 1-21 II. The values and logarithms of important constants .... 22 III. Five-place logarithms of the sines, cosines, tangents, and cotan- gents of angles from 1° to 89° for each minute 23-45 IV. Five-place logarithms of sines, cosines, tangents, cotangents Of angles from 0' to 3' for each second 46 Of angles from 3' to 2° for every ten seconds .... 47-52 V. Four-place values of the sines, cosines, tangents, and cotan- gents of angles from 0° to 90° for each minute 53-71 VI. The logarithms S and T for angles less than 2° 72 EXPLANATION OF TABLES Table I 1. Table I contains five-place mantissas of the common loga- rithms of all entire numbers from 1 to 11,000. Mantissas can be expressed only approximately, and in a five-place table all the fig- ures which follow the fifth are rejected, the fifth being increased by 1 whenever the sixth figure is 5 or more. When, after the fifth figure has been increased, the last signifi- cant figure in a mantissa is 5, it is printed with a bar under it. Hence in the fifth place 5 indicates that the fifth figure was 4 and the sixth 5 or more ; in the fourth place 5 indicates that the fourth figure was 4, the fifth 9, and the sixth 5 or more ; and so on. When their place is blank the first two figures of any mantissa are the two figures first above the blank space. Note. For brevity in the following pages we shall call the decimal part of the logarithm of a number the mantissa of the number, and the integral part of the logarithm the characteristic of the number. 2. To find from the table the mantissa of any whole number. We have the two following cases. (a) When the given number is less than 11,000, that is, when the number is in the table. E.g.^ let the number be 7423. On page 14, in the column headed "N," we find the first three figures, 742 ; passing along this line or row to the column with the fourth figure, 3, at its top, we find .87058, which is the mantissa of 7423. Thus the first three figures of a number of four figures give the rotv, and the fourth figure gives the column in which the mantissa is found. When the number is one of less than four figures, by adding one or more ciphers we obtain a number of four figures whose mantissa is the same as that of the given number. E.g.^ the mantissa of 59 = the mantissa of 5900 = .77085. To save time in finding the mantissa of a number of one or two figures, the mantissa of each whole number from 1 to 100 is given on page 1 in the column headed "M," at the right of the number itself in the column headed " N." vi EXP^NATIO^OF TABLES Ex. 1. Find log 8300 and log O.obdsi' The characteristic of 8300 is +3, and that of 0.00083 is -4, or 6 - 10. The mantissa of 8300 or 0.00083 is the same as the mantissa of 83. The mantissa of 83 = .91908. Hence log 8300 = 3.91908, and log 0.00083 = 4.91908, or 6.91908 - 10. If the number lies between 10,000 and 11,000, its mantissa will be found on page 20 or 21. Here the first fotir figures of the num- ber give the row, and ilnQ fifth figure gives the column in which the mantissa is found. E.g., the mantissa of 10315 = .01347. Note. For the explanation of the marginal tabs of Table I see § 10. Ex, 2. Verify each of the following identities : log 4354 = 3.63889 ; log 62.81 = 1.79803 ; log 37.96 = 1.57933 ; log 945.8 = 2.97580 ; log 0.749 = 1.87448 ; log 10.327 = 1.01397. (h') When the given number is greater than 11,000, that is, when the number is not in the table. In this case we assume that any small increase in a number is proportional to the corresponding increase in its mantissa. This assumption, though not mathematically exact, is sufficiently correct for interpolation within narrow limits. E.g.., let the number be 54376. The mantissa of 54370 = the mantissa of 5437.0. For convenience we put, or conceive, a decimal point after the fourth figure. The mantissa of 5438 =.73544 The mantissa of 5437 = .73536 Hence the tabular difference = .00008 That is, for an increase of 1 in the number 5437 there is an increase in the mantissa of 8 hundred-thousandths, or 8 points, as we may say for brevity. Hence for an increase of .6 in the number there will be an increase in the man- tissa of .6 of 8 points, or 5 points nearly. Hence the mantissa of 5437.6 = .73536 + .00005 = .73541. Therefore the mantissa of 54376 = .73541. Ex. 3. Find log 27.583. The characteristic is 1, and the mantissa is that of 2758.3. The mantissa of 2758 = .44059 The increase for .3 = .3 of 16 points = 5 .-.log 27. 583 = 1.44064 The increase for .3 is often called the correction for ,3. EXPLANATION OF TABLE I vii By aid of the marginal difference table this computation can easily be made mentally. E.g.^ the mantissa of 2758 is .44059, and the tabular difference is 16 points. In the marginal table headed 16, in line 3, we find 5, which is .3 of 16. Ex. 4. Verify each of the following identities : log 92.378 = 1.96557 ; log 0.034796 = 2.54153 ; log 23.804 = 1.37665 ; log 0.0030975 = 3.49101 ; log0.67857 = 1.83159; log 0.075809 =2.87972. 3. To find a number lolien its logarithm is given. Keep in mind that the mantissa determines the figures and their order in the expression of a number, while the characteristic deter- mines unifs place. Observe that the least and greatest mantissa on each page is written at the bottom of the page. We have the two following cases. (a) When the given mantissa is in the table. Ex. 1. Given \ogx = 2.68269, to find the value of x. On page 9 we find the mantissa .68269 in row 481 and in column 6; hence .68269 is the mantissa of 4816. Since the characteristic is 2, we have X = 481.6. Similarly if \ogx = 2.68269, x = 0.04816. Observe that the first mantissa which is .68 + or .69 + has its first two figures in black type ; this is to aid in locating on the page any mantissa which is between .68 and .69. Ex. 2. Find the value of x in each of the following equations : log X = 3.63889 ; log x = 1. 79803 ; log x = 1.57933 ; log X = 2.97580 ; log x = 1.87448 ; log x = 1.01397. For the answers see example 2 in § 2. (b) When the given mantissa is not in the table. Ex. 3. Given log x = 2.28250, to find the value of x. On page 3 we find that of tabulated mantissas the next less than .28250 is .28240, which is the mantissa of 1916. The tabular difference is 22 points. The given mantissa exceeds the next less mantissa by 10 points. Hence 1916 should be increased by ^f of 1, or 0.5 approximately. That is, .28250 is the mantissa of 1916.5 or 19165. Since the characteristic is 2, we have x = 191.65. Ex. 4. Given logx = 1.03720, to find x to six places. When the mantissa is less than .04175, we use pages 20 and 21. The next less mantissa is .03719, mantissa of 10894. viii EXPLANATION OF TABLES The tabular difference is 4 ; hence the correction is ^ of 1, or .3. Hence X = 0.108943. If only five places were required, interpolation would be unnecessary. Ex. 5. Given logx = - 1.23457, to find x. Here log x is not in the type form ; — 1 is not the characteristic nor is — .23457 the mantissa. To put log x in the type form we add in the form — 1 + 1 ; we thus obtain logx = - 2 + (1 - .23457) = 2.76543, or 8.76543 - 10. .-. X = 0.058268. Ex. 6. Find the value of x in each of the following equations : log X = 1.96557 ; log x = 1.83159 ; log x = 3.49101 ; log X = 1.37665 ; log x = 2.54153 ; log x = 2.87972. For the answers see example 4 in § 2. Ex. 7. Given x = 432/5271, to find x by logarithms. Here log x = log 432 - log 5271. log 432 = 2.63548 = 12.63548 - 10 log 5271= 3.72189 .-. logx= 8.91359-10 .-. X = 0.08196. Observe that before we subtract we write the characteristic 2 in the form 12 — 10, and thus make the positive part of the minuend greater than the positive part of the subtrahend. Ex. 8. Given x = \/32.17 x .00271, to find x by logarithms. Here log x = (log 32. 17 + log .00271)/4. log 32.17 = 1.50745 log .00271 = 3.43297 .-. logx = 2.94042/4 = (38.94042 -40)/4 = 9.73511-10, or L 73511. .-. X = 0.54339. Note that before dividing by 4 we write the characteristic — 2 in the form 38 — 40, so that the negative part, — 40, when divided by 4 gives — 10 as a quotient. Table II 4. This table contains the values and logarithms of some impor- tant constants and their combinations which most frequently occur. The table needs no explanation. EXPLANATION OF TABLE IH ix Table III 5. This table contains the logarithms of the sines, cosines, tan- gents, and cotangents of angles from 1° to 89° at intervals of 1'. When the angle is less than 45°, the number of degrees is found at the top of the page, the number of minutes in the left-hand minute column, and the name of the function at the top of the column of mantissas. When the angle is greater than 45°, the number of degrees is found at the bottom of the page, the number of minutes in the right-hand minute column, and the name of the function at the bottom of the column of* mantissas. The mantissa is in the same row as the number of minutes, and the characteristic is at the top or bottom of the column of mantissas. The characteristic at the top of any column is usually the same as that at the bottom ; the only exceptions are found on pages 26 and 45, where the characteristic at the top of the column is to be taken with any mantissa above the bar, and the characteristic at the bottom, is to be taken with any mantissa below the bar. 6. To find the logarithm of the sine, cosine, tangent, or cotangent of a given angle. The following rules for characteristics should be used when applicable. (a) The characteristic of the sine of an angle between 6° and 90°, or of the cosine of an angle between 0° and 84°, is 9 — 10. For sin 6° = cos 84° > 0.1, sin 90° = cos 0° = 1, and the characteristic of a number between 0.1 and 1 is — 1, or 9 — 10. (b) The characteristic of the tangent of an angle between 6° and 45°, or of the cotangent of an angle between 45° and 84°, is 9 — 10. For tan 6° = cot 84° > 0.1, tan 45° = cot 45° = 1, and the characteristic of a number between 0.1 and 1 is — 1, or 9 — 10. (c) The characteristic of the tangent of an angle between 45° and 84°, or of the cotangent of an angle between 6° and 45°, is 0. For tan 45° = cot 45° = 1, tan 84° = cot 6° < 10, and the characteristic of a number between 1 and 10 is 0. By the rules above what is the characteristic of sin 7° ? sin 88° ? cos 4° ? cos 83°? tan6°? tan 44°? cot 46°? cot 83°? tan 47°? cot7°? tan 78°? cot 41°? Ex. 1. Find log sin 35° 42', i.e., the logarithm of the sine of 35° 42'. By (a), the characteristic is 9 — 10. On page 41, under 35°, in the mantissa column headed "log sin " and in the row 42' we find the mantissa .76607. Hence log sin 35° 42' = 9.76607 - 10. Note. For an explanation of the marginal tabs of Table III, see § 11. X EXPLANATION OF TABLES Ex. 2. Verify each of the following identities : log tan 41° 32' = 9.94732 - 10 ; log cos 29° 18' = 9.94055 - 10 ; log sin 68° 21' = 9.96823 - 10 ; log cot 28° 35' = 0.26373 ; log tan 88° 35' = 1.60677; log cos 61° 27' = 9.67936 - 10 Ex. 3. Find log tan 32° 24' 33". To interpolate for seconds, we assume that any S7nall increase in an angle is proportional to the corresponding increase or decrease in the logarithm of any function of the angle. log tan 32° 24' = 9.80251 - 10. The tabular difference for 1', or 60", is 28 points. Hence, if an increase of 60" in the angle causes an increase of 28 points in the mantissa, an increase of 33" in the angle will cause an increase of 33/60 of 28, or 15, points in the mantissa. .-. log tan 32° 24' 33" = 9.80266 - 10. Ex. 4. Find log tan 81° 32' 14". logtan 81° 32' = 0.82723. The tabular difference for 60" is 87 points. Hence the correction for 14" is ^^ of 87, or 20, points. .-. log tan 81° 32' 14" = 0.82743. Ex. 5. Find log cos 38° 25' 17". log cos 38° 25' = 9.89405 - 10. The tabular difference for 60" is 10 points. Hence the correction for 17" is ^^ of 10, or 3, points. Since the cosine decreases as the angle increases, this correction is to be subtracted. .-. log cos 38° 25' 17" = 9.89402 - 10. Ex. 6. Find log cot 84° 38' 13". log cot 84° 38' = 8.97285 - 10. Here we take the characteristic at the top of the page, since the mantissa is above the bar. The tabular difference for 60" is 135 points. Hence the correction for 13" is J§ of 135, or 29, points. .-. log cot 84° 38' 13" = 9.97256 - 10. It must be kept in mind that when the angle increases the cosine or the cotangent decreases; hence the correction for seconds must be subtracted in finding the logarithm of the cosine or cotangent of an angle. If an angle is less than 2° or greater than 88°, and involves seconds, consult Table IV. EXPLANATION OF TABLE III xi Ex. 7. Verify each of the following identities : log sin 34° 9' 17'' = 9.74929 - 10 ; log sin 61° 56' 43" = 9.94671 - 10 ; log tan 42° 16' 41" = 9.95867 - 10 ; log tan 78° 19' 31" = 0.68481 ; log cos 26° 17' 13" = 9.95260 - 10 ; log cos 81° 51' 35" = 9.15106 - 10 ; log cot 25° 50' 20" = 0.31492 ; log cot 84° 25' 30" = 8.98950 - 10. 7. To find the value of an angle when the logarithm of its sine, cosine, tangent, or cotangent is given. Ex. 1. Given log sin A = 9.48213 - 10, to find a value of A. On page 32, in column headed "log sin," under 17°, in row 40', we Snd the given mantissa, the given characteristic being at the top of this column. .-. A = 17° 40'. Observe that when the characteristic of sin A or cos ^ is — 1, a mantissa less than .84949 is in a column headed " log sin," while a mantissa greater than .84949 is in a column footed " log sin." When the characteristic of tan A or cot A is — 1, the mantissa is in a column headed " log tan " ; when the characteristic is 0, the mantissa is in a column footed " log tan." When the characteristic of any function is + 1 or — 2, the angle is less than 6° or greater than 84° ; hence we consult one of ihe first three pages of the table. Ex. 2. Find the value of A in each of the following equations : log sin A = 9.96823 - 10 ; log tan A = 9.94732 - 10 ; log cos A = 9.94055 - 10 ; log cot A = 0.26373. For the answers see example 2 in § 6. Ex. 3. Given log sin A - 9.93422 - 10, to find the value of A. The given mantissa is not found in the table. The next less mantissa is .93420, mantissa of sin 59° 15'. The tabular difference for 60" is 7 points. The given mantissa exceeds the next less by 2 points. Hence the correction is f of 60", or 17". .-. A = 59° 15' 17". Ex. 4. Given log tan ^ = 0.46940, to find the value of A. The next less mantissa is .46922, mantissa of tan 71° 15'. The tabular difference for 60" is 41 points. The given mantissa exceeds the next less by 18 points. Hence the correction is ^f of 60", or 26". .-. A = 71° 15' 26". Ex. 5. Given log cos A = 9.56871 — 10, to find the value of A. The next less mantissa is .56854, mantissa of cos 68° 16'. The tabular difference for 60" is 32 points. xii EXPLANATION OF TABLES The given mantissa exceeds the next less by 17 points. Hence the correction is ^^ of 60", or 32''. Since the angle decreases when the cosine increases, we subtract this correc- tion from 68° 16' and obtain A = 68° 15' 28". Ex. 6. Find the value of A in each of the following equations : log sin ^ = 9.74929- 10 log tan J. = 9.95867 - 10 log cos ^ =9.95260-10 log cot A = 0.31492 ; log cot A = 8.98950 - 10. For the answers see example 7 in § 6. log sin J. = 9.94571 - 10; log tan ^ =0.68481 ; log cos ^ =9.15106 - 10; Table IV S. The first page of this table contains the logarithms of the sines of angles from 0° to 0° 3' at intervals of 1", or the logarithms of cosines of angles from 89° 57' to 90°. Since within the limits of 0° and 3', to five places of decimals, log tan A = log sin A, and within the limits of 89° 57' and 90° log cot A = log cos A, any log sin on this page can be taken as log tan, and any log cos as log cot. E.g., log tan 0° 1' 52" = log sin 0° 1' 52" = 6.73479 - 10 ; and log cot 89° 58' 37" = log cos 89° 58' 37" = 6.60465 - 10. The other pages of this table contain the logarithms of the sines, cosines, and tangents of angles from 3' to 2° at intervals of 10"; also the logarithms of the sines, cosines, and cotangents of angles from 88° to 89° 57' at intervals of 10". For the explanation of the marginal tabs see § 12. Ex. Find log sin 0° 50' 25". log sin 0° 50' 20" = 8.16557 - 10. The tabular difference for 10" is 143 points. Hence the correction for 5" is j% of 143, or 72, points. .-. log sin 0° 50' 25" = 8.16629 - 10. Similarly log cos 1° 48' 35" = 9.99978 - 10. Also log tan 0° 46' 32" = 8.13152 - 10. log cot 88° 32' 43" = 8.40475 - 10. Any logarithmic tangent or cotangent found in this. table is nega- tive. Hence when log tan A or log cot A is positive, we use the relation log cot A = — log tan A before consulting the table. E.g. , log cot 0° 2' 15" = - log tan 0° 2' 15" = (10 - 10) - (6.81591 - 10) = 3.18409. Again, if log tan A = 2.35063, log cot ^ = 10 - 2.35063 - 10 = 7.64937 - 10. .-.^ = 89° 44' 40". EXPLANATION OF TABS xiii Table V 9. This four-place table contains the natural sines, cosines, tan- gents, and cotangents of angles from 0° to 90° at intervals of 1'. For the explanation of the marginal tabs see § 13. ' Ex. 1, Verify each of the following identities : sin 27° 42' = 0.4648 ; tan 72° 21' = 3.1429 ; sin 22° 3' 22'' = 0.3755 •, cos 68° 43' = 0.3630 ; cot 82° 28' = 0.1322 ; tan 60° 4' 38" = 1.7375. Ex. 2. Find the value of A in each of the following equations : sin ^ 1=0.4648 ; tan ^ = 3.1429; sin ^ = 0.3755; cos A = 0.3630 ; cot A = 0. 1322 ; tan ^ = 1.7375. Ex. 3. The bearing of a course is N. 25° 42' E., and its length is 9.32 chains ; find its latitude and departure to two decimal places. Latitude == 9.32 sin 25° 42' = 9.32 x 0.434 = 4.04 chains. Departure = 9.32 cos 25° 42' = 9.32 x 0.901 = 8.40 chains. Explanation of Marginal Tabs 10. Table I. The pupil should place his book of tables on his desk at his left, and in manipulating them use only his left hand. If he opens the tables with the projecting tab B, all the marginal tabs of Table I can be seen in the left-hand margin. Using the projecting tab A, he puts his forefinger under the first pages of the table, and placing his thmPxb on any marginal tab, as tab 5, he turns to the right the leaves not held between his thumb and finger, thus opening the table at the pages marked by the marginal tab 5. When thus opened it is found that the first figure on the marginal ta,b used is the first figure of every number found on the pages opened, that the mantissa on this tab is the least mantissa on these pages, and that the greatest mantissa on these pages is a little greater than the mantissa on the next tab below. Hence, to find the pages needed when the number is given, use the tab which has on it the first figure of the given number. To find the pages needed when the logarithm is given, use the tab which has on it the matitissa next less than the given one. 11. Table III. Open the book of tables with tab C, so that all the marginal tabs of Table III can be seen in the left-hand margin. Opening this table with any marginal tab, as tab 17° — 20°, we find that the number of degrees at the top of this tab are those at the tops of the pages opened, and that the numbers of degrees at the xiv EXPLANATION OF TABLES bottom of tnis tab are those at the bottoms of these pages. The first mantissa on this tab is the least mantissa on these pages, in the columns headed " log sin," and the greatest mantissa in these columns is the first mantissa on the next tab below. The second mantissa on this tab is the least mantissa on these pages, in the columns headed ^' log tan," and the greatest mantissa in these col- umns is the second mantissa on the next tab below. The last mantissa on this tab is the least mantissa on these pages, in the columns /oo^ec^ "log sin," and the greatest mantissa in these columns is the last mantissa on the next tab above. The mantissa next to the last is the least mantissa on these pages in the columns footed '< log tan," and the greatest mantissa in these columns is the corresponding mantissa on the next tab above. Hence: To find the pages needed when the angle is given, use the tab on which the number of degrees is written or included. To find the pages needed when log sin or log cos is given, and the characteristic is 9 — 10, use the tab whose first or last mantissa is the next less than the given one. To find the pages needed when log tan or log cot is given : When the characteristic is 9 — 10, use the tab whose second man- tissa is the next less than the given one. When the characteristic is 0, use the tab whose mantissa next to the last is the next less than the given one. When the characteristic of any function is — 2 or + 1, look for the logarithm on one of the first three pages of the table. On tab 41°-44° observe that the last mantissa is the greatest in the columns headed ''log sin," as well as the least in the columns footed "log sin"; and that the mantissa next to the last is the greatest logarithm in the columns headed " log tan," as well as the least in the columns footed " log tan." Where no characteristic is written before a mantissa on any tab, 1 is understood with the first, second, or fourth mantissa, and with the third. 12. Table IV. To open the tables, use the projecting tab D. The first, the second, and the last logarithm on any marginal tab have the same meaning and use respectively as the first, the second, and the last logarithm on a tab in Table III. Since the logarithmic tangents of angles between 88° and 90° are not recorded in this table, its tabs have no logarithm corresponding to the third logarithm on a tab in Table III. EXPLANATION OF TABS XV 13. Table V. To open t,he tables, use the projecting tab E. To find the pages needed when the angle is given, use the mar- ginal tab on which the name of the required function is written and the given number of degrees is written or included. To find the pages needed when a function is given, use a tab on which the name of the given function is written and on which the first or the last function is the next less than the given one. If this next less function is the first on the tab, the given func- tion will be found in a column headed "sin " or " tan " ; if it is the last on the tab, the given function will be found in a column footed "sin" or "tan." 14. Table VI. This table is to be used when greater accuracy- is required than can be secured by interpolation in Table IV. In it a = the number of seconds in an angle less than 2° 2', S = log (sin a" /a) = log sin a" — log «r, (1) T = log (tan a" /a) = log tan a" — log a. (2) From (1), log sin a" can be obtained from S and a, or a can be found from S and log sin a". From (2), log tan a" can be obtained from T and a, or a can be found from T and log tan a". Ex. 1. Find log sin 0° 42' 13". 0° 42' 13" = 2533" = a", .-.log a = 3.40364 S = 4.68556 - 10 .-. log sin a" = 8.08920 - 10 Ex. 3. Find log tan 0° 58' 32.7' 0° 58' 32.7" = 3512.7" = a". log a: = 3.54564 r= 4.68562 - 10 .-. log tan a" = 8.23126 - 10 Find A when there is given : Ex. 5. logsin^ = 6.67237- 10. Here ^ < 2° ; hence we put log sin <3:" = 6.67237 - 10 S = 4.68557 - 10 .'. log a = 1.98680 .-. a" = 97.006" = r 37.006". Ex. 2. Find log cos 88° 18' 21.2". cos 88° 18' 21.2" = sin 1° 41' 38.8". 1°41'38.8" = 6098.8" = a", .-.log a = 3.78525 S = 4.68551 - 10 .-. log cos 88° 18' 21.2" = 8.47076 - 10 Ex. 4. Find log tan 89° 13' 34.22". cot 89° 13' 34.22" = tan 46' 25.78". 46' 25.78" = 2785.78" = a". .-. log a = 3.44495 T= 4.68560- 10 .-. log cot 89° 13' 34.22" = 8. 13055 - 10 .-.log tan 89° 13' 34.22" = 1.86945. Ex. 6. log tan A = 2.35427. Let log tan a" = log cot A ; then log tan a" = 7.64573-10 r= 4.68558 - 10 .-. log a = 2.96015 .-. a" = 912.32" = 15' 12.32". .-. ^ = 90° - a" = 89° 44' 47.68". : : \'^\ V\. ; ••• :•* TABLE I : i ^;r • * • • *i *: • ; i .;. • •• •• • FIVE-PLACE MANTISSAS OF THE commojn" logarithms OF THE ENTIRE NUMBERS From 1 to 11000 1-100 N M N M N M N M N ' M 1 .00 000 21 .32 222 41 .61 278 61 .78 533 81 .90 849 2 30103 22 34 242 42 62 325 62 79 239 82 91381 3 47 712 23 36 173 43 63 347 63 79 934 83 91908 4 60 206 24 38 021 44 64 345 64 80 618 84 92 428 5 69 897 25 39 794 45 65 321 65 81291 85 92 942 6 .77 815 26 .41 497 46 .66 276 66 .81 954 86 .93 450 7 84 510 27 43 136 47 67 210 67 82 607 87 93 952 8 90 309 28 44 716 48 68 124 68 83 251 88 94 448 9 95 424 29 46 240 49 69 020 69 83 885 89 94 939 10 00 000 30 47 712 . 50 69 897 70 84 510 90 95 424 11 .04 139 31 .49136 51 .70 757 71 .85 126 91 .95 904 12 07 918 32 50 515 52 71600 72 85 733 92 96 379 13 11394 33 51851 53 72 428 73 86 332 93 96 848 14 14 613 34 53 148 54 73 239 74 86 923 94 97 313 15 17 609 35 54 407 55 74 036 75 87 506 95 97 772 16 .20 412 36 .55 630 56 .74 819 76 .88 081 96 .98 227 17 23 045 37 56 820 57 75 587 77 88 649 97 98 677 18 25 527 38 57 978 58 76 343 78 89 209 98 99 123 19 27 875 39 59 106 59 77 085 79 89 763 99 99 564 20 30103 40 60 206 60 77 815 80 90 309 100 00 000 1000-1500 N^ .^^.^^ ^i^^^ :» ; ; 3 4 5 6 7 8 9 Dif. 100 .QC QGG ,0Q a43 .00 087 .00 130 .00 173 .00 217 .00 260 .00 303 .00 346 .00 389 40 39 1(51^ ^ U3^; :475: £13 561 604 647 689 732 775 817 4 4 l02 ^ ^^60 903^ 945 988.01030 01 072 01 115 01 157 01 199 01 242 8 8 103 01 284 01 326 01 368 01 410 452 494 536 578 620 662 12 12 104 703 745 787 828 870 912 953 995 02 036 02 078 16 16 105 .02 119 .02 160 .02 202 .02 243 .02 284 .02 325 .02 366 .02 407 .02 449 .02 490 20 20 106 531 572 612 653 694 735 776 816 857 898 24 23 107 938 979 03 019 03 060 03 100 03 141 03 181 03 222 03 262 03 302 28 27 108 03 342 03 383 423 463 503 543 583 623 663 703 32 31 109 743 782 822 862 902 941 981 04 021 04 060 04 100 36. 35 110 .04 139 .04 179 .04 218 .04 258 .04 297 .04 336 .04 376 .04 415 .04 454 .04 493 38 86 111 532 571 610 650 689 727 766 805 844 883 4 4 112 922 961 999 05 038 05 077 05 115 05 154 05 192 05 231 05 269 8 7 113 : 05 308 05 346 05 385 423 461 500 538 576 614 652 11 11 114 690 729 767 805 843 881 918 956 994 06 032 15 14 115 .06 070 .06 108 .06 145 .06 183 .06 221 .06 258 .06 296 .06 333 .06 371 .06 408 19 18 116 446 483 521 558 595 633 670 707 744 781 23 22 117 819 856 893 930 967 07 004 07 041 07 078 07115 07151 27 25 118 07 188 07 225 07 262 07 298 07 335 372 408 445 482 518 30 29 119 555 591 628 664 700 737 773 809 846 882 34 32 120 .07 918 .07 954 .07 990 .08 027 .08 063 .08 099 .08 135 .08 171 .08 207 .08 243 34 33 121 08 279 08 314 08 350 386 422 458 493 529 565 600 3 3 122 636 672 707 743 778 814 849 884 920 955 7 7 123 991 09 026 09 061 09 096 09 132 09 167 09 202 09 237 09 272 09 307 10 10 124 09 342 377 412 447 482 517 552 587 621 656 14 13 125 .09 691 .09 726 .09 760 .09 795 .09 830 .09 864 .09 899 .09 934 .09 968 .10 003 17 17 126 10 037 10 072 10106 10140 10175 10 209 10 243 10 278 10 312 346 20 20 127 380 415 449 483 517 551 585 619 653 687 24 23 128 721 755 789 823 857 890 924 958 992 11025 27 26 129 11059 11093 11126 11160 11193 11227 11261 11294 11327 361 31 30 130 .11 394 .11 428 .11 461 .11 494 .11 528 .11 561 .11 594 .11 628 .11 661 .11 694 32 31 131 727 760 793 826 860 893 926 959 992 12 024 3 3 132 12 057 12 090 12 123 12 156 12 189 12 222 12 254 12 287 12 320 352 6 6 133 385 418 450 483 516 548 581 613 646 678 10 9 134 710 743 775 808 840 872 905 937 969 13 001 13 12 135 .13 033 .13 066 .13 098 .13 130 .13 162 .13 194 .13 226 .13 258 .13 290 .13 322 16 16 136 354 386 418 450 481 513 545 577 609 640 19 19 137 672 704 735 767 799 830 862 893 925 956 22 22 138 988 14 019 14 051 14 082 14 1,14 14 145 14 176 14 208 14 239 14 270 26 25 139 14 301 333 364 395 426 457 489 520 551 582 29 28 140 .14 613 .14 644 .14 675 .14 706 .14 737 .14 768 .14 799 .14 829 .14 860 .14 891 30 29 141 922 953 983 15 014 15 045 15 076 15 106 15 137 15 168 15 198 3 3 142 15 229 15 259 15 290 320 351 381 412 442 473 503 6 6 143 534 564 594 625 655 685 715 746 776 806 9 9 144 836 866 897 927 957 987 16 017 16 047 16 077 16107 12 12 145 .16 137 .16 167 .16 197 .16 227 .16 256 .16 286 .16 316 .16 346 .16 376 .16 406 15. 15 146 435 465 495 524 554 584 613 643 673 702 18 17 147 732 761 791 820 850 879 909 938 967 997 21 20 148 17 026 17 056 17 085 17114 17143 17173 17 202 17 231 17 260 17 289 24 23 149 319 348 377 406 435 464 493 522 551 580 27 26 150 N .17 609 .17 638 .17 667 .17 696 .17 725 .17 754 .17 782 .17 811 .17 840 .17 869 12 3 4 5 6 7 8 9 .00 000 -.17 869 1500 -2000 3 N 150 12 3 4 5 6 7 8 9 Dif. .17 609 .17 638 .17 667 .17 696 .17 725 .17 754 .17 782 .17 811 .17 840 .17 869 29 27 151 898 926 955 984 18 013 18 041 18 070 18 099 18 127 18156 3 3 152 18 184' 18 213 18 241 18 270 298 327 355 384 412 441 6 5 153 469 498 526 554 583 611 639 667 696 724 9 8 154 752 780 808 837 865 893 921 949 977 19 005 12 11 155 .19 033 .19 061 .19 089 .19 117 .19 145 .19 173 .19 201 .19 229 .19 257 A9 285 15 14 156 312 340 368 396 424 451 479 507 t35 ' 562 17 16 157 590 618 645 673 700 728 756 783 811 838 20 19 158 866 893 921 948 976 20 003 20 030 20 058 20 085 20112 23 22 159 20 140 20 167 20 194 20 222 20 249 276 303 330 358 385 26 24 160 .20 412 .20 439 .20 466 .20 493 .20 520 .20 548 .20 575 .20 602 .20 629 .20 656 26 25 161 683 710 737 763 790 817 844 871 898 925 3 3 162 952 978 21 005 21 032 21 059 21 085 21 112 21 139 21 165 21 192 5 5 163 21 219 21 245 272 299 325 352 378 405 431 458 8 8 164 484 511 537 564 590 617 643 669 696 722 10 10 165 .21 748 .21 775 .21 801 .21 827 .21 854 .21 880 .21 906 .21 932 .21 958 .21 985 13 13 166 22 011 22 037 22 063 22 089 22 115 22 141 22 167 22 194 22 220 22 246 16 15 167 272 298 324 350 376 401 427 453 479 505 18 18 168 531 557 583 608 634 660 686 712 737 763 21 20 169 789 814 840 866 891 917 943 968 994 23 019 23 23 170 .23 045 .23 070 .23 096 .23 121 .23 147 .23 172 .23 198 .23 223 .23 249 .23 274 25 24 171 300 325 350 376 401 426 452 477 502 528 3 2 172 553 578 603 629 654 679 704 729 754 779 5 5 173 805 830 855 880 905 930 955 980 24 005 24 030 8 7 174 24 055 24 080 24 105 24 130 24 155 24 180 24 204 24 229 254 279 10 10 175 .24 304 .24 329 .24 353 .24 378 .24 403 .24 428 .24 452 .24 477 .24 502 .24 527 13 12 176 551 576 601 625 650 674 699 724 748 773 15 14 177 797 822 8+6 871 895 920 944 969 993 25 018 18 17 178 25 042 25 066 25 091 25 115 25 139 25 164 25 188 25 212 25 237 261 20 19 179 285 310 334 358 382 406 431 455 479 503 23 22 180 .25 527 .25 551 .25 575 .25 600 .25 624 .25 648 .25 672 .25 696 .25 720 .25 744 24 23 181 768 792 816 840 864 888 912 935 959 983 2 2 182 26 007 26 031 26 055 26 079 26 102 26126 26 150 26 174 26198 26 221* 5 5 183 245 269 293 316 340 364 387 411 435 458 7 7 184 482 505 529 553 576 600 623 647 670 694 10 9 185 .26 717 .26 741 .26 764 .26 788 .26 811 .26 834 .26 858 .26 881 .26 905 .26 928 12 12 186 951 975 998 27 021 27 045 27 068 27 091 27 114 27 138 27 161 14 14 187 27 184 27 207 27 231 254 277 300 323 346 370 393 17 16 188 416 439 462 485 508 531 554 577 600 623 19 18 189 646 669 692 715 738 761 784 807 830 852 22 21 190 .27 875 .27 898 .27 921 .27 944 .27 967 .27 989 .28 012 .28 035 .28 058 .28 081 22 21 191 28 103 28 126 28 149 28 171 28 194 28 217 240 262 285 307 2 2 192 330 353 375 398 421 443 466 488 511 533 4 4 193 - 556 578 601 623 646 668 691 713 735 758 7 6 780 80a 825 847 870 892 914 937 959 981 9 8 195 .29 003 .29 026 .29 048 .29 070 .29 092 .29 115 .29 137 .29 159 .29 181 .29 203 11 11 196 226 248 270 292 314 336 358 380 403 425 13 13 197 447 469 • 491 513 535 557 579 601 623 645 15 15 198 667 688 710 732 754 776 798 820 842 863 18 17 199 885 907 929 951 973 994 30 016 30 038 30 060 30 081 20 19 200 N .30 103 .30 125 .30 146 .30 168 .30 190 .30 211 .30 233 .30 255 .30 276 .30 298 12 3 4 5 6 7 8 9 17 609 -.30 298 2000-2500 N 200 12 3 4 5 6 7 8 9 Dif. 21 .30 103 .30 125 .30 146 .30 168 .30 190 .30 211 .30 233 .30 255 .30 276 .30 298 201 320 341 363 384 406 428 449 471 492 514 2 202 535 557 578 600 621 643 664 685 707 728 4 203 750 771 792 814 835 856 878 899 920 942 6 204 963 984 31006 31027 31048 31069 31091 31112 31133 31154 8 205 .31 175 .31 197 .31 218 .31 239 .31 260 .31 281 .31 302 .31 323 .31 345 .31 366 11 206 387 408 429 450 471 492 513 534 . 555 576 13 207 597 618 639 660 681 702 723 744 765 785 15 208 806 827 848 869 890 911 931 952 973 994 17 209 32 015 32 035 32 056 32 077 32 098 32 118 32 139 32 160 32181 32 201 19 210 .32 222 .32 243 .32 263 .32 284 .32 305 .32 325 .32 346 .32 366 .32 387 .32 408 20 211 428 449 4^9 490 510 531 552 572 593 613 2 212 634 654 675 695 715 736 756 777 797 818 4 213- 838 858 879 899 919 940 960 980 33 001 33 021 6 214 33 041 33 062 33 082 33 102 33 122 33143 33 163 33 183 203 224 8 215 .33 244 .33 264 .33 284 .33 304 .33 325 .33 345 .33 365 .33 385 .33 405 .33 425 10 216 445 465 . 486 506 526 546 566 586 606 626 12 217 646 666 686 706 726 746 766 786 806 826 14 218 846 866 885 905 925 945 965 985 34 005 34 025 16 219 34 044 34 064 34 084 34104 34 124 34 143 34 163 34183 203 223 18 220 .34 242 .34 262 .34 282 .34 301 .34 321 .34 341 .34 361 .34 380 .34 400 .34 420 19 221 439 459 479 498 518 537 557 577 596 616 2 222 635 655 674 694 713 733 753 772 792 811 4 223 830 850 869 889 908 928 947 967 986 35 005 6 224 35 025 35 044 35 064 35 083 35 102 35 122 35 141 35 160 35 180 199 8 225 .35 218 .35 238 .35 257 .35 276 .35 295 .35 315 .35 334 .35 353 .35 372 .35 392 10 226 411 430 449 468 488 507 526 545 564 583 11 227 603 622 641 660 679 698 717 736 755 774 13 228 793 813 832 851 870 889 908 927 946 965 15 229 984 36 003 36 021 36 040 36 059 36 078 36 097 36 116 36135 36154 17 230 .36 173 .36192 .36 211 .36 229 .36 248 .36 267 .36 286 .36 305 .36 324 .36 342 18 231 361 380 399 418 436 455 474 493 511 530 2 232 549 568 586 605 624 642 661 680 698 717 4 233 736 754 773 791 810 829 847 866 884 903 5 234 922 940 959 977 996 37 014 37 033 37 051 37 070 37 088 7 235 .37 107 .37 125 .37 144 .37 162 .37 181 .37 199 .37 218 .37 236 .37 254 .37 273 9 236 291 310 328 346 365 383 401 420 438 457 11 237 475 493 511 530 548 566 585 603 621 639 13 238 658 676 694 712 731 749 767 XS5 803 822 14 239 840 858 876 894 912 931 949 967 985 38 003 16 240 .38 021 .38 039 .38 057 .38 075 .38 093 .38 112 .38 130 .38 148 .38 166 .38 184 17 241 202 220 238 256 274 292 310 328 346 364 2 242 382 399 417 435 453 471 489 507 525 543 3 243 561 578 596 614 632 650 668 686 703 '"1 ~5 244 739 757 775 792 810 828 846 863 881 89. 7 245 .38 917 .38 934 .38 952 .38 970 .38 987 .39 005 .39 023 .39 041 .39 058 .39 076 9 246 39 094 39 111 39129 39 146 39164 182 199 217 235 252 10 247 270 287 305 322 340 358 375 393 410 428 12 248 445 463 480 498 .515 533 550 568 585 602 14 249 620 637 655 672 690 707 724 742 759 777 15 250 N .39 794 .39 811 .39 829 .39 846 .39 863 .39 881 .39 898 .39 915 .39 933 .39 950 12 3 4 5 6 7 8 9 .30 103 -.39 950 2500-3000 N 250 1 2 3 4 5 .39 881 6 7 8 9 Dif. 18 .39 794 .39 811 .39 829 .39 846 .39 863 .39 898 .39 915 .39 933 .39 950 251 967 985 40 002 40 019 40 037 40 054 40 071 40088 40 106 40123 2 252 40140 40157 175 192 209 226 243 261 278 295 4 253 312 329 346 364 381 398 415 432 449 466 5 254 483 500 518 535 552 569 586 603 620 637 7 255 .40 654 .40 671 .40 688 .40 705 .40 722 .40 739 .40 756 .40 773 .40 790 .40 807 9 256 824 841 858 875 892 909 926 943 960 976 11 257 993 41010 41027 41044 41061 41078 41095 41111 41128 41145 13 258 41162 179 196 212 229 246 263 280 296 313 14 259 330 347 363 380 397 414 430 447 464 48] 16 260 .41 497 .41 514 .41 531 .41 547 .41 564 .41 581 .41 597 .41 614 .41 631 .41 647 171 261 664 681 697 714 731 747 764 780 797 814 2; 262 830 847 863 880 896 913 929 946 963 979 3' ^ 263 996 42012 42 029 42 045 42 062 42 078 42 095 42 111 42 127 42 144 5' 264 42160 177 193 210 226 243 259 275 292 308 7i 265 .42 325 .42 341 .42 357 .42 374 .42 390 .42 406 .42 423 .42 439 .42 455 .42 472 9 266 488 504 521 537 553 570 586 602 619 635 10 267 651 667 684 700 716 732 749 765 781 797 12 268 813 830 846 862 878 894 911 927 943 959 14 269 . 975 991 43 008 43 024 43 040 43 056 43 072 43 088 43 104 43 120 15 270 .43 136 .43 152 .43 169 .43185 .43 201 .43 217 .43 233 .43 249 .43 265 .43 281 16 271 297 313 329 345 361 377 393 409 425 441 2 272 457 473 489 505 521 537 553 569 584 600 3 273 616 632 648 664 680 696 712 727 743 759 5 274 775 791 807 823 838 854 870 886 902 917 6 275 .43 933 .43 949 .43 965 .43 981 .43 996 .44 012 .44 028 .44 044 .44 059 .44 075 8 276 44 091 44 107 44 122 44 138 44154 170 185 201 217 232 10 277 248 . 264 279 295 311 326 342 358 373 389 11 278 404 420 436 451 467 483 498 514 529 545 13 279 560 576 592 607 623 638 654 669 685 700 14 280 .44 716 .44 731 .44 747 .44 762 .44 778 .44 793 .44 809 .44 824 .44 840 .44 855 16 281 871 886 902 917 932 948 963 979 994 45 010 2 282 45 025 45 040 45 056 4S071 45 086 45 102 45 117 45 133 45 148 163 3 283 179 194 209 225 240 255 271 286 301 317 5 284 332 347 362 378 393 408 423 439 454 469 6 285 .45 484 .45 500 .45 515 .45 530 .45 545 .45 561 .45 576 .45 591 .45 606 .45 621 8 286 637 652 667 682 697 712 728 743 758 773 9 287 788 803 818 834 849 864 879 894 909 92f 11 288 939 954 969 984- 46 000 46 015 46 030 46 045 46 060 46 075 12 289 46 090 46105 46120 46 135 150 165 180 195 210 225 14 290 .46 240 .46 255 .46 270 .46 285 .46 300 .46 315 .46 330 .46 345 .46 359 .46 374 14 291 389 404 419 434 449 464 479 494 509 523 1 292 538 553 568 583 598 613 627 642 657 672 3 293 687 702 716 731 746 761 776 790 805 820 4 294 835 850 864 879 894 909 923 938 953 967 6 295 .46 982 .46 997 .47 012 .47 026 .47 041 .47 056 .47 070 .47 085 .47 100 .47 114 7 296 47 129 47 144 159 173 188 202 217 232 246 261 8 297 276 290 305 319 334 349 363 378 392 407 10 298 422 436 451 465 480 494 509 524 538 553 11 299 567 582 596 611 625 640 654 669 683 698 13 300 N .47 712 .47 727 .47 741 .47 756 .47 770 .47 784 .47 799 .47 813 .47 828 .47 842 1 2 3 4 5 6 7 8 9 .39 794 -.47 842 3000-3500 N 12 3 4 5 6 7 8 9 Dif. 15 300 .47 7l5 .47 727 .47 741 .47 756 .47 770 .47 784 .47 799 .47 813 .47 828 .47 842 301 857 871 885 900 914 929 943 958 972 986 2 302 48 001 48 015 48 029 48 044 48 058 48 073 48 087 48 101 48 116 48 130 3 303 144 159 173 187 202 216 230 244 259 273 5 304 287 302 316 330 344 359 373 387 401 416 6 305 .48 430 .48 444 .48 458 .48 473 .48 487 .48 501 .48 515 .48 530 .48 544 .48 558 8 306 572 586 601 615 629 643 657 671 686 700 9 307 714 728 742 756 770 785 799 813 827 841 11 308 855 869 883 897 911 926 940 954 968 982 12 309 996 49 010 49 024 49 038 49 052 49 066 49 080 49 094 49108 49 122 14 310 .49 136 .49 150 .49 164 .49 178 .49 192 .49 206 .49 220 .49 234 .49 248 .49 262 14 311 276 290 304 318 332 346 360 374 388 402 1 312 415 429 443 457 471 485 499 513 527 541 3 313 554 568 582 596 610 624 638 651 665 679 4 314 693 707 721 734 748 762 776 790 803 817 6 315 .49 831 .49 845 .49 859 .49 872 .49 886 .49 900 .49 914 .49 927 .49 941 .49 955 7 316 969 982 996 50 010 50 024 50037 50 051 50 065 50 079 50 092 8 317 50106 50120 50 133 147 161 174 188 202 215 229 10 318 243 256 270 284 297 311 325 338 352 365 11 319 379 393 406 420 433 447 461 474 488 501 13 320 .50 515 .50 529 .50 542 .50 556 .50 569 .50 583 .50 596 .50 610 .50 623 .50 637 13 321 651 654 678 691 705 718 732 745 759 772 1 322 786 799 813 826 840 853 866 880 893 907 3 323 920 934 947 961 974 987 61001 51014 51028 51041 4 324 51055 51068 51081 51095 51108 51121 135 148 162 175 5 325 .51188 .51202 .51215 .51228 .51242 .51 255 .51268 .51282 .51295 .51308 7 326 322 335 348 362 375 388 ^02 415 428 441 8 327 455 458 481 495 508 521 534 548 561 574 9 328 587 601 614 627 640 654 667 680 693 706 10 329 720 733 746 759 772 786 799 812 825 838 12 330 .51851 .51865 .51878 .51891 .51904 .51917 .51930 .51943 .51957 .51970 13 331 983 996 52 009 52 022 52 035 52 048 52 061 52 075 52 088 52101 1 332 52 114 52 127 140 153 166 179 192 205 218 231' 3 333 244 257 270 284 297 310 323 336 349- 362 4 334 375 388 401 414 427 440 453 466 479 492 5 335 .52 504 .52 517 .52 530 .52 543 .52 556 .52 569 .52 582 .52 595 .52 608 .52 621 7 336 634 647 650 673 686 699 711 724 737 750 8 337 763 776 789 802 815 827 840 853 866 879 9 338 892 905 917 930 943 956 969 982 994 53 007 10 339 53 020 53 033 53 046 53 058 53 071 53 084 53 097 53 110 53 122 135 12 340 .53148 .53 161 .53173 .53 186 .53 199 .53 212 .53 224 .53 237 .53 250 .53 263 12 341 275 . 288 301 314 326 339 352 364 377 390 1 342 403 415 428 441 453 466 479 491 504 517 2 343 529 542 555 567 580 593 605 618 631 643 4 344 656 668 681 694 706 719 732 744 757 769 5 345 .53 782 .53 794 .53 807 .53 820 .53 832 .53 845 .53 857 .53 870 .53 882 .53 895 6 346 908 920 933 945 958 970 983 995 54 008 54 020 7 347 54 033 54 045 54 058 54 070 54 083 54 095 54 108 54 120 133 145 8 348 158 170 183 195 208 220 233 . 245 258 270 10 349 283 295 307 320 332 345 357 370 382 394 11 350 N .54 407 .54 419 .54 432 .54 444 .54 456 .54 469 .54 481 .54 494 .54 506 .54 518 12 3 4 5 6 7 8 9 ,47712 — .54 518 3500-4000 N 350 1 .54 419 2 3 4 5 6 7 8 9 Dif. 13 .54 407 .54 432 .54 444 .54 456 .54 469 .54 481 .54 494 .54 506 .54 518 351 531 543 555 568 580 593 605 617 630 642 1 352 654 667 679 691 704 716 728 741 753 765 3 353 777 790 802 814 827 839 851 864 876 888 4 354 900 913 925 937 949 962 974 986 998 55 011 5 355 .55 023 .55 035 .55 047 .55 060 .55 072 .55 084 .55 096 .55 108 .55 121 .55 133 7 356 145 157 169 182 194 206 218 230 242 255 8 357 267 279 291 303 315 328 340 352 364 376 9 358 388 400 413 425 437 449 461 473 485 497 10 359 509 522 534 546 558 570 582 594 606 618 12 360 .55 630 .55 642 .55 654 .55 666 .55 678 .55 691 .55 703 .55 715 .55 727 .55 739 12 361 751 763 775 787 799 811 823 835 847 859 1 362 871 883 895 907 919 931 943 955 967 979 2 363 991 66 003 56 015 56 027 56 038 56 050 56 062 56 074 56 086 56 098 4 36+ 56110 122 134 146 158 170 182 194 205 217 5 365 .56 229 .56 241 .56 253 .56 265 .56 277 .56 289 .56 301 .56 312 .56 324 .56 336 6 366 348 360 372 384 396 407 419 431 443 455 7 367 467 478 490 502 514 526 538 549 561 573 8 368 585 597 608 620 632 644 656 667 679 691 10 369 703 714 726 738 750 761 773 785 797 808 11 370 .56 820 .56 832 .56 844 .56 855 .56 867 .56 879 .56 891 .56 902 .56 914 .56 926 12 371 937 949 961 972 984 996 57 008 57 019 57 031 57 043 1 372 57 054 57 066 57 078 57 089 57101 57 113 124 136 148 159 2 373 171 183 194 206 217 229 241 252 264 276 4 374 287 299 310 322 334 345 357 368 380 392 5 375 .57 403 .57 415 .57 426 .57 438 .57 449 .57 461 .57 473 .57 484 .57 496 .57 507 6 376 519 530 542 553 565 576 588 600 611 623 7 377 634 646 657 669 680 692 703 715 726 738 8 378 749 761 772 784 795 807 818 830 841 852 10 379 864 875 887 898 910 921 933 944 955 967 11 380 .57 978 .57 990 .58 001 .58 013 .58 024 .58 035 .58 047 .58 058 .58 070 .58 081 11 381 58 092 58104 115 127 138 149 161 172 184 195 1 382 206 218 229 240 252 263 274 286 297 309 2 383 320 331 343 354 365 377 388 399 410 422 3 384 433 444 456 467 478 490 501 512 524 535 4 385 .58 546 .58 557 .58 569 .58580 .58 591 .58 602 .58 614 .58 625 .58 636 .58 647 6 386 659 670 681 692 704 715 726 737 749 760 7 387 771 782 794 805 816 827 838 850 861 872 8 388 883 894 906 917 928 939 950 961 973 984 9 389 995 59 006 59 017 59 028 59 040 59 051 59 062 59 073 59 084 59 095 10 390 .59 106 .59118 .59 129 .59 140 .59 151 .59162 .59173 .59 184 .59 195 .59 207 11 391 218 229 240 251 262 273' 284 295 306 318 1 392 329 340 351 362 373 384 395 406 417 428 2 393 439 450 461 472 483 494 506 517 528 539 3 394 550 561 572 583 594 605 616 627 638 649 4 395 .59 660 .59 671 .59 682 .59 693 .59 704 .59 715 .59 726 .59 737 .59 748 .59 759 6 396 770 780 791 802 813 824 835 846 857 868 7 397 879 890 901 912 923 934 945 956 966 977 8 398 988 999 60 010 60 021 60 032 60 043 60 054 60065 60 076 60 086 9 399 60 097 60 108 119 130 141 152 163 173 184 195 10 400 N .60 206 .60 217 .60 228 .60 239 .60 249 .60 260 .60 271 .60 282 .60 293 .60 304 1 2 3 4 5 6 7 8 9 .54 407 -.60 304 4000-4500 N 12 3 4 5 6 7 8 9 Dif. 11 1 2 3 4 400 401 402 403 404 .60 206 .60 217 .60 228 .60 239 .60 249 314 325 336 347 358 423 433 444 455 466 531 541 552 563 574 638 649 660 670 681 .60 260 .60 271 .60 282 .60 293 .60 304 369 379 390 401 412 477 487 498 509 520 584 595 606 617 627 692 703 713 724 735 405 406 407 408 409 .60 746 .60 756 .60 767 .60 778 .60 788 853 863 874 885 895 959 970 981 991 61002 61066 61077 61087 61098 109 172 183 194 204 215 .60 799 .60 810 .60 821 .60 831 .60 842 906 917 927 938 949 61013 61023 61034 61045 61055 119 130 140 151 162 225 236 247 257 268 6 7 8 9 10 410 411 412 413 414 .61 278 .61 289 .61 300 .61 310 .61 321 384 395 405 416 426 490 500 511 521 532 595 606 616 627 637 700 711 721 731 742 .61 331 .61 342 .61 352 .61 363 .61 374 437 448 458 469 479 542 553 563 574 584 648 658 669 679 690 752 763 773 784 794 11 1 2 3 4 415 416 417 418 419 .61 805 .61 815 .61 826 .61 836 .61 847 909 920 930 941 951 62 014 62 024 62 034 62 045 62 055 118 128 138 149 159 221 232 242 252 263 .61857 .61868 .61878 .61888 .61899 962 972 982 993 62 003 62 066 62 076 62 086 62 097 107 170 180 190 201 211 273 284 294 304 315 6 7 8 9 10 420 421 422 423 424 .62 325 .62 335 .62 346 .62 356 .62 366 428 439 449 459 469 531 542 552 562 572 634 644 655 665 675 737 747 757 767 778 .62 377 .62 387 .62 397 .62 408 .62 418 480 490 500 511 521 583 593 603 613 624 685 696 706 716 726 788 798 808 818 829 10 1 2 3 4 425 426 427 428 429 .62 839 .62 849 .62 859 .62 870 .62 880 941 951 961 972 982 63 043 63 053 63 063 63 073 63 083 144 155 165 175 185 246 256 266 276 286 .62 890 .62 900 .62 910 .62 921 .62 931 992 63 002 63 012 63 022 63 033 63 094 104 114 124 134 195 205 215 225 236 296 306 317 327 337 5 6 7 8 9 430 431 432 433 434 .63 347 .63 357 .63 367 .63 377 .63 387 448 458 468 478 488 548 558 568 579 589 649 659 669 679 689 749 759 769 779 789 .63 397 .63 407 .63 417 .63 428 .63 438 498 508 518 528 538 599 609 619 629 639 699 709 719 729 739 799 809 819 829 839 10 1 2 3 4 435 436 437 438 439 .63 849 .63 859 .63 869 .63 879 .63 889 949 959 969 979 988 64 048 64 058 64 058 64 078 64 088 147 157 167 177 187 246 256 266 276 286 .63 899 .63 909 .63 919 .63 929 .63 939 998 64 008 64 018 64 028 64 038 64 098 108 118 128 137 197 207 217 227 237 296 306 316 326 335 5 6 7 8 9 440 441 442 443 444 .64 345 .64 355 .64 365 .64 375 .64 385 444 454 464 473 483 542 552 562 572 582 640 650 660 670 680 738 748 758 768 777 .64 395 .64 404 .64 414 .64 424 .64 434 493 503 513 523 532 591 601 611 621 631 689 699 709 719 729 787 797 807 816 826 9 1 2 3 4 445 446 447 448 449 .64 836 .64 846 .64 856 .64 865 .64 875 933 943 953 963 972 65 031 65 040 65 050 65 060 65 070 128 137 147 157 167 225 234 244 254 263 .64 885 .64 895 .64 904 .64 914 .64 924 982 992 65 002 65 011 65 021 65 079 65 089 099 108 118 176 186 196 205 215 273 283 292 302 312 5 5 6 7 8 450 N .65 321 .65 331 .65 341 .65 350 .65 360 .65 369 .65 379 .65 389 .65 398 .65 408 _ 12 3 4 5 6 7 8 9 .60 206 -.65 408 4500-5000 N 12 3 4 5 6 7 8 9 Dif. 10 1 2 3 4 450 451 452 453 454 .65 321 .65 331 .65 341 .65 350 .65 360 418 427 437 447 456 514 523 533 543 552 610 619 629 639 648 706 715 725 734 744 .65 369 .65 379 .65 389 .65 398 .65 408 466 475 485 495 504 562 571 581 591 600 658 667 677 686 696 753 763 772 782 792 455 456 457 458 459 .65 801 .65 811 .65 820 .65 830 .65 839 896 906 916 925 935 992 66 001 66 011 66 020 66 030 66 087 096 106 115 124 181 191 200 210 219 .65 849 .65 858 .65 868 .65 877 .65 887 944 954 963 973 982 66 039 66 049 66 058 66 068 66 077 134 143 153 162 172 229 238 247 257 266 5 6 7 8 9 460 461 462 463 464 .66 276 .66 285 .66 295 .66 304 .66 314 370 380 389 398 408 464' 474 483 492 502 558 567 577 586 596 652 661 671 680 689 .66 323 .66 332 .66 342 .66 351 .66 361 417 427 436 445 455 511 521 530 539 549 605 614 624 633 642 699 708 717 727 736 9 1 2 3 4 465 466 467 468 469 .66 745 .66 755 .66 764 .66 773 .66 783 839 848 857 867 876 932 941 950 960 969 67 025 67 034 67 043 67 052 67 062 117 127 136 145 . 154 .66 792 .66 801 .66 811 .66 820 .66 829 885 894 904 913 922 978 987 997 67 006 67 015 67 071 67 080 67 089 099 108 164 173 182 191 201 I 6 7 8 470 471 472 473 474 .67 210 .67 219 .67 228 .67 237 .67 247 302 311 321 330 339 394 403 413 422 431 486 495 504 514 523 578 587 596 605 614 .67 256 .67 265 .67 274 .67 284 .67 293 348 357 367 376 385 440 449 459 468 477 532 541 550 560 569 624 633 642 651 660 9 1 2 3 4 475 476 477 478 479 .67 669 .67 679 .67 688 .67 697 .67 706 761 770 779 788 797 852 861 870 879 888 943 952 961 970 979 68 034 68 043 68 052 68 061 68 070 .67 715 .67 724 .67 733 .67 742 .67 752 806 815 825 834 843 897 906 916 925 934 988 997 68 006 68 015 68 024 68 079 68 088 097 106 115 5 5 6 7 8 480 481 482 483 484 .68 124 .68 133 .68 142 .68 151 .68 160 215 224 233 242 251 305 314 323 332 341 395 404 413 422 431 485 494 502 511 520 .68 169 .68 178 .68 187 .68 196 .68 205 260 269 278 287 296 350 359 368 377 386 440 449 458 467 476 529 538 547 556 565 9 1 2 3 4 485 486 487 488 489 .68 574 .68 583 .68 592 .68 601 .68 610 664 673 681 690 699 753 762 771 780 789 842 851 860 869 878 931 940 949 958 966 .68 619 .68 628 .68 637 .68 646 .68 655 708 717 726 735 744 797 806 815 824 833 886 895 904 913 922 975 984 993 69 002 69 011 5 5 6 7 8 490 491 492 493 494 .69 020 .69 028 .69 037 .69 046 .69 055 108 117 126 135 144 197 205 214 223 232 285 294 302 311 320 373 381 390 399 408 .69 064 .69 073 .69 082 .69 090 .69 099 152 161 170 179 188 241 249 258 267 276 329 338 346 355 364 417 . 425 434 443 452 8 1 2 2 3 495 496 497 498 499 .69 461 .69 469 .69 478 .69 487 .69 496 548 557 566 574 583 636 644 653 662 671 723 732 740 749 758 810 819 827 . 836 845 .69 504 .69 513 .69 522 .69 531 .69 539 592 601 609 618 627 679 688 697 705 714 767 775 784 793 801 854 862 871 880 888 4 5 6 6 7 500 N .69 897 .69 906 .69 914 .69 923 .69 932 .69 940 .69 949 .69 958 .69 966 .69 975 1 2 3 4 5 6 7 8 9 .65 321 -.69 975 10 5000-5500 N 500 501 502 503 504 12 3 4 5 6 7 8 9 Dif. 9 1 2 3 4 .69 897 .69 906 .69 914 .69 923 .69 932 984 992 70 001 70 010 70 018 70 070 70 079 088 096 105 157 165 174 183 191 243 252 260 269 278 .69 940 .69 949 .69 958 .69 966 .69 975 70 027 70 036 70 044 70 053 70 062 114 122 131 140 148 200 209 217 226 234 286 295 303 312 321 505 506 507 508 509 .70 329 .70 338 .70 346 .70 355 .70 364 415 424 432 441 449 501 509 518 526 535 586 595 603 612 621 672 680 689 697 706 .70 372 .70 381 .70 389 .70 398 .70 406 458 467 475 484 492 544 552 561 569 578 629 638 646 655 663 714 723 731 740 749 5 5 6 7 8 510 511 512 513 514 .70 757 .70 766 .70.774 .70 783 .70 791 842 851 859 868 876 927 935 944 952 - 961 71012 71020 71029 71037 71046 096 105 113 122 130 .70 800 .70 808 .70 817 .70 825 .70 834 885 893 902 910 919 969 978 986 995 71003 71054 71063 71071 71079 088 139 147 155 164 172 8 1 2 2 3 515 516 517 518 519 .71 181 .71 189 .71 198 .71 206 .71 214 265 273 282 290 299 349 357. 366 374 383 433 441 450 458 466 517 525 533 542 550 .71 223 .71 231 .71 240 .71 248 .71 257 307 315 324 332 341 391 >399 408 416 425 475 483 492 500 508 559 567 575 584 592 4 5 6 6 7 520 521 522 523 524 .71 600 .71 609 .71 617 .71 625 .71 634 684 692 700 709 717 767 775 784 792 800 850 858 867 875 883 933 941 950 958 966 .71 642 .71 650 .71 659 .71 667 .71 675 725 734 742 750 759 809 817 825 834 842 892 900 908 917 925 975 983 991 999 72 008 8 1 2 2 3 525 526 527 528 529 .72 016 .72 024 .72 032 .72 041 .72 049 099 107 115 123 132 181 189 198 206 214 263 272 280 288 296 346 354 362 370 378 .72 057 .72 066 .72 074 .72 082 .72 090 140 148 156 165 173 222 230 239 247 255 304 313 321 329 337 387 395 403 411 419 4 5 6 6 7 530 531 532 533 534 .72 428 .72 436 .72 444 .72 452 .72 460 509 518 526 534 "542 591 599 607 616 624 673 681 689 697 705 754 762 770 779 787 .72 469 .72 477 .72 485 .72 493 .72 501 550 558 567 575 583 632 640 648 656 665 713 722 730 738 746 795 803 811 819 827 8 1 2 2 3 535 536 537 538 539 .72 835 .72 843 .72 852 .72 860 .72 868 916 925 933 941 949 997 73 006 73 014 73 022 73 030 73 078 086 094 102 . Ill 159 167 175 183 191 .72 876 .72 884 .72 892 .72 900 .72 908 957 965 973 981 989 73 038 73 046 73 054 73 062 73 070 119 127 135 143 151 199 207 215 223 231 4 5 6 6 7 540 541 542 543 544 .73 239 .73 247 .73 255 .73 263 .73 272 320 328 336 344 352 400 408 416 424 432 480 488 496 504 512 560 568 576 584 592 .73 280 .73 288 .73 296 .73 304 .73 312 360 368 376 384 392 440 448 456 464 472 520 528 536 544 552 600 608 616 624 632 7 1 1 2 3 545 546 547 548 549 .73 640 .73 648 .73 656 .73 664 .73 672 719 727 735 743 751 799 807 815 823 830 878 886 894 902 910 957 965 973 981 989 .73 679 .73 687 .73 695 .73 703 .73 711 759 767 775 783 791 838 846 854 862 870 918 926 933 941 949 997 74 005 74 013 74 020 74 028 4 4 5 6 6 550 N .74 036 .74 044 .74 052 .74 060 .74 068 .74 076 .74 084 .74 092 .74 099 .74 107 --- 12 3 4 5 6 7 8 9 .69 897 -.74 107 5500-6000 11 N 12 3 4 5 6 7 8 9 Dif. 650 551 552 553 554 .74 036 .74 044 .74 052 .74 060 .74 068 115 123 131 139 147 194 202 210 218 225 273 280 288 296 304 351 359 367 374 382 .74 076 .74 084 .74 092 .74 099' .74 107 155 162 170 178 186 233 241 249 257 265 312 320 327 335 343 390 398 406 414 421 8 1 2 2 3 555 556 557 55S 559 < 660 561 562 563 564 .74 429 .74 437 .74 445 .74 453 .74 461 507 515 523 531 539 586 593 601 609 617 663 671 679 687 695 741 749 757 764 772 .74 468 .74 476 .74 484 .74 492 .74 500 547 554 562 570 578 624 632 640 648 656 702 710 718 726 733 780 788 796 803 811 4 5 6 6 7 .74 819 .74 827 .74 834 .74 842 .74 850 896 904 912 920 927 974 981 989 997 75 005 75 051 75 059 75 066 75 074 082 128 136 143 151 159 .74 858 .74 865 .74 873 .74 881 .74 889 935 943 950 958 966 75 012 75 020 75 028 75 035 75 043 089 097 105 113 120 166 174 182 189 197 7 1 1 2 3 565 566 567 568 569 .75 205 .75 213 .75 220 .75 228 .75 236 282 289 297 305 312 358 366 374 381 389 435 442 450 458 465 511 519 526 534 542 .75 243 .75 251 .75 259 .75 266 .75 274 320 328 335 343 351 397 404 412 420 427 473 481 488 496 504 549 557 565 572 580 4 4 5 6 6 570 571 572 573 574 .75 587 .75 595 .75 603 .75 610 .75 618 664 671 679 686 694 740 747 755 762 770 815 823 831 838 846 891 899 906 914 921 .75 626 .75 633 .75 641 .75 648 .75 656 702 709 717 724 732 778 785 793 800 808 853 861 868 876 884 929 937 944 952 959 8 1 2 2 3 575 576 577 578 579 .75 967 .75 974 .75 982 .75 989 .75 997 76 042 76 050 76 057 76 065 76 072 118. 125 133 140 148 193 200 -208 215 223 268 275 283 290 298 .76 005 .76 012 .76 020 .76 027 .76 035 080 087 095 103 110 155 163 170 178 185 230 238 245 253 260 305 313 320 328 335 4 5 6 6 7 680 581 582 583 584 .76 343 .76 350 .76 358 .76 365 .76 373 418 425 433 +40 448 492 500 507 515 522 567 574 582 589 597 641 649 jbl^ 664 671 .76 380 .76 388 .76 395 .76 403 .76 410 455 462 470 477 485 530 537 545 552 559 604 612 619 626 634 678 686 693 701 708 7 1 1 2 3 585 586 587 588 589 .76 716 .76 723 .76 730 .76 738 .76 745 790 797 805 812 819 864 871 879 886 893 938 945 953 960 967 77 012 77 019 77 026 77 034 77 041 .76 753 .76 760 .76 768 .76 775 .76 782 827 834 842 849 856 901 908 916 923 930 975 982 989 997 77 004 77 048 77 056 77 063 77 070 073 4 4 5 6 6 590 591 592 593 594 .77 085 .77 093 .77100 .77 107 .77115 159 166 173 181 188 232 240 247 254 262 305 313 320 327 335 379 386 393 401 408 .77 122 .77 129 .77 137 .77 144 .77 151 195 203 210 217 225 269 276 283 291 298 342 349 357 364 371 415 422 430 437 444 7 1 1 2 3 595 596 597 598 599 .77 452 .77 459 .77 466 .77 474 .77 481 525 532 539 546 554 597 605 612 619 627 670 677 685 692 699 743 750 757 764 772 .77 488 .77 495 .77 503 .77 510 .77 517 561 568 576 583 590 634 641 648 656 663 706 714 721 728 735 779 786*0 793 d 801 808 4 4 5 6 6 600 .77 815 .77 822 .77 830 .77 837 .77 844 .77 851 .77 859 .77 866 .77 873 .77 880 N 12 3 4 5 6 7 8 9 74 036 -,77 880 12 6000-6500 N 600 1 2 3 4 5 6 7 8 9 Dif. 8 .77 815 .77 822 .77 830 .77 837 .77 844 .77 851 .77 859 .77 866 .77 873 .77 880 601 887 895 902 909 916 924 931 938 945 952 1 602 960 967 974 981 988 996 78 003 78 010 78 017 78 025 2 603 78 032 78 039 78 046 78 053 78 061 78 068 075 082 089 097 2 604 104 111 118 125 132 140 147 154 161 168 3 60S .78 176 .78 183 .78 190 .78 197 .78 204 .78 211 .78 219 .78 226 .78 233 .78 240 4 606 247 254 262 269 276 283 290 297 305 312 5 607 319 326 333 340 347 355 362 369 376 38'3 6 608 390 398 405 412 419 426 433 440 447 455 6 609 462 469 476 483 490 497 504 512 519 526 ^ 7 610 .78 533 .78 540 .78 547 .78 554 .78 561 .78 569 .78 576 .78 583 .78 590 .78 597 7 611 604 611 618 625 633 640 647 654 661 668 1 612 675 682 689 696 704 711 718 725 732 739 1 613 746 753 760 767 774 781 789 796 803 810 2 614 817 824 831 838 845 852 859 866 873 880 3 615 .78 888 .78 895 .78 902 .78 909 .78 916 .78 923 .78 930 .78 937 .78 944 .78 951 4 616 958 965 972 979 986 993 79 000 79 007 79 014 79 021 4 617 79 029 79 036 79 043 79 050 79 057 79 064 071 078 085 092 5 618 099 106 113 120 127 134 141 148 155 162 6 619 169 176 183 190 197 204 211 218 225 232 6 620 .79 239 .79 246 .79 253 .79 260 .79 267 .79 274 .79 281 .79 288 .79 295 .79 302 7 621 309 316 323 330 337 344 351 358 365 372 1 622 379 386 393 400 407 414 421 428 435 442 1 623 449 456 463 470 477 484 491 498 505 511 2 624 518 525 532 539 546 553 560 567 574 581 3 625 .79 588 .79 595 .79 602 .79 609 .79 616 .79 623 .79 630 .79 637 .79 644 .79 650 4 626 657 664 671 678 685 692 699 706 713 720 4 627 727 734 741 748 754 761 768 775 782 789 5 628 796 803 810 817 824 831 837 844 851 858 6 629 865 872 879 886 893 900 906 913 920 927 6 630 .79 934 .79 941 .79 948 .79 955 .79 962 .79 969 .79 975 .79 982 .79 989 .79 996 7 631 80 003 80 010 80 017 80 024 80 030 80 037 80 044 80 051 80 058 80 065 1 632 072 079 085 092 099 106 113 120 127 134 1 633 140 147 154 161 168 175 182 188 195 202 2 634 209 216 223 229 236 243 250 257 264 271 3 635 .80 277 .80 284 .80 291 .80 298 .80 305 .80 312 .80318 .80 325 .80 332 .80 339 4 636 346 353 359 366 373 380 387 393 400 407 4 637 414 421 428 434 441 448 455 462 468 475 5 638 482 489 496 502 509 516 523 530 536 543 6 639 550 557 564 570 577 584 591 598 604 611 6 640 .80 618 .80 625 .80 632 .80 638 .80 645 .80 652 .80 659 .80 665 .80 672^.80 679 6 641 686 693 699 706 713 720 726 733 740 747 1 642 754 760 767 774 781 787 794 801 808 814 1 643 821 828 835 841 848 855 862 868 875 882 2 644 889 895 902 909 916 922 929 936 943 949 2 645 .80 956 .80 963 .80 969 .80 976 .80 983 .80 990 .80 996 .81003 .81010 .81017 3 646 81023 81030 81037 81043 81 050 81057 81064 070 077 084 4 647 090 097 104 111 117 124 131 137 144 151 4 648 158 164 171 178 184 191 198 204 211 218 5 649 224 231 238 245 251 258 265 271 278 285 5 650 N .81 291 .81298 .81305 .81311 .81318 .81 325 .81 331 .81 338 .81 345 .81 351 1 2 3 4 5 6 7 8 9 .77 815 — .81351 6500-7000 13 650 651 652 653 654 655 656 657 658 659 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 N .81 291 .81 298 .81 305 .81 311 .81 318 358 365 371 378 385 425 431 438 445 451 491 498 505 511 518 558 564 571 578 584 .81 624 .81 631 .81 637 .81 644 .81 651 690 697 704 710 717 757 763 770 776 783 823 829 836 842 849 889 895 902 908 915 .81 954 .81 961 .81 968 .81 974 .81 981 82 020 82 027 82 033 82 040 82 046 086 092 099 105 112 151 158 164 171 178 217 223 230 236 243 .82 282 .82 289 .82 295 .82 302 ,82 308 347 354 360 367 373 413 419 426 432 439 478 484 491 497 504 543 549 556 562 569 .82 607 .82 614 .82 620 .82 627 .82 633 672 679 685 692 698 737 743 750 756 763 802 808 814 821 827 866 872 879 885 892 .82 930 .82 937 .82 943 .82 950 .82 956 995 83 001 83 008 83 014 83 020 83 059 065 072 078 085 123 129 136 142 149 187 193 200 206 213 .83 251 .83 257 .83 264 .83 270 .83 276 315 321 327 334 340 378 385 391 398 404 442 448 455 461 467 506 512 518 525 531 .83 569 .83 575 .83 582 .83 588 .83 594 632 639 645 651 658 696 702 708 715 721 .759 765 771 778 784 ^,822 828 835 841 847 .83 885 .83 891 .83 897 .83 904 .83 910 948 954 960 967 973 84 011 84 017 8-1023 84 029 84 036 073 080 086 092 098 136 142 148 155 161 .84198 .84 205 .84 211 .84 217 .84 223 261 267 273 280 286 323 330 336 342 348 386 392 398 404 410 448 454 460 466 473 .81 325 .81 331 .81 338 .81 345 .81 351 391 398 405 411 418 458 465 471 478 485 525 531 538 544 551 591 598 604 611 617 .81 657 .81 664 .81 671 .81 677 .81 684 723 730 737 743 750 790 796 803 809 816 856 862 869 875 882 921 928 935 941 948 .81 987 .81 994 .82 000 .82 007 .82 014 82 053 82 060 066 073 079 119 125 132 138 145 184 191 197 204 210 249 256 263 269 276 .82 315 .82 321 .82 328 .82 334 .82 341 380 387 393 400 406 445 452 458 465 471 510 517 523 530 536 575 582 588 595 601 .82 640 .82 646 .82 653 .82 659 .82 666 705 711 718 724 730 769 776 782 789 795 834 840 847 853 860 898 905 911 918 924 .82 963 .82 969 .82 975 .82 982 .82 988 83 027 83 033 83 040 83 046 83 052 091 097 104 110 117 155 161 168 174 181 219 225 232 238 245 .83 283 .83 289 .83 296 .83 302 .83 308 347 353 359 366 372 410 417 423 429 436 474 480 487 493 499 537 544 550 556 563 .83 601 .83 607 .83 613 .83 620 .83 626 664 670 677 683 689 727 734 740 746 753 790 797 803 809 816 853 860 866 872 879 .83 916 .83 923 .83 929 .83 935 .83 942 979 985 992 998 84 004 84 042 84 048 84 055 84 061 067 105 111 117 123 130 167 173 180 186 192 .84 230 .84 236 .84 242 .84 248 .84 255 292 298 305 311 317 354 361 367 373 379 417 423 429 435 442 479 485 491 497 504 .84 510 .84 516 -.84 522 .84 528 .84 535 .84 541 .84 547 .84 553 .84 559 .84 566 Dif. 6 1 1 2 2 3 4 4 5 5 7 1 1 2 3 4 4 5 6 6 6 1 1 2 2 3 4 4 5 5 7 1 1 2 3 4 4 5 6 6 6 1 1 2 2 3 4 4 5 5 .81291 — .84 566 14 7000-7500 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 7]7 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 .84 510 .84 516 .84 522 .84 528 .84 535 572 578 584 590 597 634 640 646 652 658 696 702 708 714 720 757 763 770 776 782 .84 819 .84 825 .84 831 .84 837 .84 844 880 887 893 899 905 942 948 954 960 967 85 003 85 009 85 016 85 022 85 028 065 071 077 083 089 .85 126 .85 132 .85 138 .85 144 .85 150 187 193 199 205 211 248 254 260 266 272 309 315 321 327 333 370 376 382 388 394 .85 431 .85 437 .85 443 .85 449 .85 455 491 497 503 509 516 552 558 564 570 576 612 618 625 631 637 673 679 685 691 697 .85 733 .85 739 .85 745 .85 751 .85 757 794 800 806 812 818 854 860 866 872 878 914 920 926 932 938 974 980 986 992 998 .86 034 .86 040 .86 046 .86 052 .86 058 094 100 106 112 118 153 159 165 171 177 213 219 225 231 237 273 279 285 291 297 .86 332 .86 338 .86 344 .86 350 .86 356 392 398 404 410 415 451 457 463 469 475 510 516 522 528 534 570 576 581 587 593 .86 629 .86 635 .86 641 .86 646 .86 652 688 694 700 705 711 747 753 759 764 770 806 812 817 823 829 864 870 876 882 888 .86 923 .86 929 .86 935 .86 941 .86 947 982 988 994 999 87 005 87 040 87 046 87 052 87 058 064 099 105 111 116 122 157 163 169 175 181 .87 216 .87 221 .87 227 .87 233 .87 239 274 280 286 291 297 332 338 344 349 355 390 396 402* 408 413 448 454 460 466 471 .84 541 .84 547 .84 553 .84 559 .84 566 603 609 615 621 628 665 671 677 683 689 726 733 739 745 751 788 794 800 807 813 .84 850 .84 856 .84 862 .84 868 .84 874 911 917 924 930 936 973 979 985 991 997 85 034 85 040 85 046 85 052 85 058 095 101 107 114 120 .85 156 .85 163 .85 169 .85 175 .85 181 217 224 230 236 242 278 285 291 297 303 339 345 352 358 364 400 406 412 418 425 .85 461 .85 467 .85 473 .85 479 .85 485 522 528 534 540 546 582 588 594 600 606 643 649 655 661 667 703 709 715 721 727 .85 763 .85 769 .85 775 .85 781 .85 788 824 830 836 842 848 884 890 896 902 908 944 950 956 962 968 86 004 86 010 86 016 86 022 86 028 .86 064 .86 070 .86 076 .86 082 .86 088 124 130 136 141 147 183 189 195 201 207 243 249 255 261 267 303 308 314 320 326 .86 362 .86 368 .86 374 .86 380 .86 386 421 427 433 439 445 481 487 493 499 504 540 546 552 558 564 599 605 611 ■ 617 623 .86 658 .86 664 .86 670 .86 676 .86 682 717 723 729 735 741 776 782 788 794 800 835 841 847 853 859 894 900 906 911 917 .86 953 .86 958 .86 964 .86 970 .86 976 87 011 87 017 87 023 87 029 87 035 070 075 081 087 093 128 134 140 146 151 186 192 198 204 210 .87 245 .87 251 .87 256 .87 262 .87 268 303 309 315 320 326 361 367 373 379 384 419 425 431 437 442 477 483 489 495 500 .87 506 .87 512 .87 518 .87 523 .87 529 .87 535 .87 541 .87 547 .87 552 .87 558 Dif. .84 510 -.87 558 7500-8000 15 N 750 1 2 .87 518 3 4 5 6 7 8 9 Dif. 6 .87 506 .87 512 .87 523 .87 529 .87 535 .87 541 .87 547 .87 552 .87 558 751 564 570 576 581 587 593 599 604 610 616 1 752 622 628 633 639 645 651 656 662 668 674 1 753 679 685 691 697 703 708 714 720 726 731 2 754 737 743 749 754 760 766 772 777 783 789 2 755 .87 795 .87 800 .87 806 .87 812 .87 818 .87 823 .87 829 .87 835 .87 841 .87 846 3 756 852 858 864 869 875 881 887 892 898 904 4 757 910 915 921 927 933 938 944 950 955 961 4 758 967 973 978 984 990 996 88 001 88 007 88 013 88 018 5 759 88 024 88 030 88 036 88 041 88 047 88 053 058 064 070 076 5 760 .88 081 .88 087 .88 093 .88 098 .88 104 .88 110 .88116 .88121 .88127 .88 133 5 761 138 144 150 156 161 167 173 178 184 190 1 762 195 201 207 213 218 224 230 235 241 247 1 763 252 258 264 270 275 281 287 292 298 304 2 764 309 315 321 326 332 338 343 349 355 360 2 765 .88 366 .88 372 .88 377 .88 383 .88 389 .88 395 .88 400 .88 406 .88 412 .88 417 3 766 423 429 434 440 446 451 457 463 468 474 3 767 480 485 491 497 502 508 513 519 525 530 4 768 536 542 547 553 559 564 570 576 581 587 4 769 593 598 604 610 615 621 627 632 638 643 5 770 .88 649 .88 655 .88 660 .88 666 .88 672 .88 677 .88 683 .88 689 .88 694 .88 700 6 771 705 711 717 722 728 734 739 745 750 756 1 772 762 767 773 779 784 790 795 801 • 807 812 1 773 818 824 829 835 840 846 852 857 863 868 2 774 874 880 885 891 897 902 908 913 919 925 2 775 .88 930 .88 936 .88 941 .88 947 .88 953 .88 958 .88 964 .88 969 .88 975 .88 981 3 776 986 992 997 89 003 89 009 89 014 89 020 89 025 89 031 89 037 4 777 89 042 89 048 89 053 059 064 070 076 081 087 092 4 778 098 104 109 115 120 126 131 137 143 148 5 779 154 159 165 170 176 182 187 193 198 204 5 780 .89 209 .89 215 .89 221 .89 226 .89 232 .89 237 .89 243 .89 248 .89 254 .89 260 5 781 265 271 276 282 287 293 298 304 310 315 1 782 321 326 332 337 343 348 354 360 365 371 1 783 376 382 387 393 398 404 409 415 421 426 2 784 432 437 443 448 454 459 465 470 476 481 2 785 .89 487 .89 492 .89 498 .89 504 .89 509 .89 515 .89 520 .89 526 .89 531 .89 537 3 786 542 548 553 559 564 570 575 581 586 592 3 787 597 603 609 614 620 625 631 636 642 647 4 788 653 658 664 669 675 680 686 691 697 702 4 789 708 713 719 724 730 735 741 746 752 757 5 790 .89 763 .89 768 .89 774 .89 779 .89 785 .89 790 .89 796 .89 801 .89 807 .89 812 6 791 818 823 829 834 840 845 851 856 862 867 1 792 873 878 883 889 894 900 905 911 916 922 1 793 927 933 938 944 949 955 960 966 971 977 2 794 982 988 993 998 90 004 90 009 90 015 90 020 90 026 90 031 2 795 .90 037 .90 042 .90 048 .90 053 .90 059 .90 064 .90 069 .90 075 .90 080 .90 086 3 796 091 097 102 108 113 119 124 129 135 140 4 797 146 151 157 162 168 173 179 184 189 195 4 798 200 206 211 217 222 227 233 238 244 249 5 799 255 260 266 271 276 282 287 293 298 304 5 800 N .90 309 .90 314 .90 320 .90 325 3 .90 331 .90 336 .90 342 .90 347 .90 352 .90 358 1 2 4 5 6 7 8 9 .87 506 -.90 358 16 8000-8500 N 800 SOI 802 803 804 12 3 4 5 6 7 8 9 Dif. 5 1 1 2 2 .90 309 .90 314 .90 320 363 369 374 417 423 428 472 477 482 526 531 536 .90 325 .90 331 380 385 434 439 488 493 542 547 .90 336 390 445 499 553 .90 342 .90 347 .90 352 .90 358 396 401 407 412 450 455 461 466 504 509 515 520 558 563 569 574 805 806 807 808 809 .90 580 .90 585 .90 590 634 639 644 687 693 698 741 747 752 795 800 806 .90 596 .90 601 650 655 703 709 757 763 811 816 .90 607 660 714 768 822 .90 612 .90 617 .90 623 .90 628 666 671 677 682 720 725 730 736 773 779 784 789 827 832 838 843 3 3 4 4 5 810 811 812 813 814 .90 849 .90 854 .90 859 902 907 913 956 961 966 91009 91014 91020 062 068 073 .90 865 .90 870 918 924 972 977 91025 91030 078 084 .90 875 929 982 91036 089 .90 881 .90 886 .90 891 .90 897 934 940 945 950 988 993 998 91004 91041 91046 91052 057 094 100 105 110 6 1 1 2 2 815 816 817 818 819 .91 116 .91 121 .91 126 169 174 180 222 228 233 275 281 286 328 334 339 .91 132 .91 137 185 190 238 243 291 297 344 350 .91 142 196 249 302 355 .91 148 .91 153 .91 158 .91 164 201 206 212 217 254 259 265 270 307 312 318 323 360 365 371 376 3 4 4 5 5 820 821 822 823 824 .91 381 .91 387 .91 392 434 440 445 487 492 498 540 545 551 593 598 603 .91 397 .91 403 450 455 503 508 556 561 609 614 .91 408 461 514 566 619 .91 413 .91 418 .91 424 .91 429 466 471 477 482 519 524 529 535 572 577 582 587 624 630 635 640 5 1 1 2 2 825 826 827 828 829 .91645 .91651 .91656 698 703 709 751 756 761 803 808 814 855 861 866 .91661 .91666 714 719 766 772 819 824 871 876 .91 672 724 777 829 882 .91 677 .91 682 .91 687 .91 693 730 735 740 745 782 787 793 798 834 840 845 850 887 892 897 903 3 3 4 4 5 830 831 832 833 834 .91 908 .91 913 .91 918 960 965 971 92 012 92 018 92 023 065 070 075 117 122 127 .91 924 .91 929 976 981 92 028 92 033 080 085 132 137 .91 934 986 92 038 091 143 .91 939 .91 944 .91 950 .91 955 991 997 92 002 92 007 92 044 92 049 054 059 096 101 106 111 148 153 158 163 6 1 1 2 2 835 836 837 838 839 .92 169 .92 174 .92 179 221 226 231 273 278 283 324 330 335 376 381 387 .92 184 .92 189 236 241 288 293 340 345 392 397 .92 195 247 298 350 402 .92 200 .92 205 .92 210 .92 215 252 257 262 267 304 309 314 319 355 361 366 371 407 412 418 423 3 4 4 5 5 840 841 842 843 844 .92 428 .92 433 .92 438 480 485 490 531 536 542 583 588 593 634 639 645 .92 443 .92 449 495 500 547 552 598 603 650 655 .92 454 505 557 609 660 .92 459 .92 464 .92 469 .92 474 511 516 521 526 562 567 572 578 614 619 624 629 665 670 675 681 5 1 1 2 2 845 846 847 848 849 .92 686 .92 691 .92 696 737 742 747 788 793 799 840 «45 850 891 896 901 .92 701 .92 706 752 758 804 809 855 860 906 911 .92 711 763 814 865 916 .92 716 .92 722 .92 727 .92 732 768 773 778 783 819 824 829 834 870 875 881 886 921 927 932 937 3 3 4 4 5 850 N .92 942 .92 947 .92 952 .92 957 .92 962 .92 967 .92 973 .92 978 .92 983 .92 988 1 2 3 4 5 6 7 8 9 .90 309 -.92 988 8500-9000 17 830 851 852 853 854 855 856 857 858 859 830 861 862 863 86+ 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 891 892 893 894 895 896 897 898 899 900 N .92 942 .92 947 .92 952 .92 957 .92 962 993 998 93 003 93 008 93 013 93 044 93 049 054 059 064 095 100 105 110 115 146 151 156 161 166 ,93 197 .93 202 .93 207 .93 212 .93 217 247 252 258 263 268 298 303 308 313 318 349 354 359 364 369 399 404 409 414 420 .93 450 500 551 601 651 .93 702 752 802 852 902 .93 455 505 556 606 656 .93 707 757 807 857 907 .93 460 510 561 611 651 .93 712 762 812 862 912 .93 465 515 566 616 666 .93 717 767 817 867 917 .93 470 520 571 621 671 .93 722 772 822 872 922 .93 952 .93 957 .93 962 .93 967 .93 972 94 002 94 007 94 012 94 017 94 022 052 057 052 067 072 101 106 111 116 121 151 156 161 166 171 .94 201 .94 206 .94 211 .94 216 .94 221 250 255 260 265 270 300 305 310 315 320 349 354 359 364 369 399 404 409 414 419 .94 448 .94 453 .94 458 .94 463 .94 468 498 503 507 512 517 547 552 557 562 567 596 601 606 611 616 645 650 655 660 665 .94 694 .94 699 .94 704 .94 709 .94 714 743 748 753 758 763 792 797 802 807 812 841 846 851 856 861 890 895 900 905 910 .94 939 .94 944 .94 949 .94 954 .94 959 988 993 998 95 002 95 007 95 036 95 041 95 0+6 051 056 085 090 095 100 105 134 139 143 148 153 .95 182 .95 187 .95 192 .95 197 .95 202 231 236 240 245 250 279 284 289 294 299 328 332 337 342 347 376 381 386 390 395 .92 967 .92 973 .92 978 .92 983 .92 988 93 018 93 024 93 029 93 034 93 039 069 075 080 085 090 120 125 131 136 141 171 176 181 186 192 .93 222 .93 227 .93 232 .93 237 .93 242 273 278 283 288 293 323 328 334 339 344 374 379 384 389 394 425 430 435 440 445 .93 475 .93 480 .93 485 .93 490 .93 495 526 531 536 541 546 576 581 586 591 596 626 631 636 641 646 676 682 687 692 697 .93 727 .93 732 .93 737 .93 742 .93 747 777 782 787 792 797 827 832 837 842 847 877 882 887 892 897 927 932 937 942 947 .93 977 .93 982 .93 987 .93 992 .93 997 94 027 94 032 94 037 94 042 94 047 077 082 086 091 096 126 131 136 141 146 176 181 186 191 196 .94 226 .94 231 .94 236 .94 240 .94 245 275 280 285 290 295 325 330 335 340 345 374 379 384 389 394 424 429 433 438 443 .94 473 .94 478 .94 483 .94 488 .94 493 522 527 532 537 542 571 576 581 586 591 621 626 630 635 640 670 675 680 685 689 .94 719 .94 724 .94 729 .94 734 .94 738 768 773 778 783 787 817 822 827 832 836 866 871 876 880 885 915 919 924 929 934 .94 963 .94 968 .94 973 .94 978 .94 983 95 012 95 017 95 022 95 027 95 032 061 066 071 075 080 109 114 119 124 129 158 163 168 173 177 .95 207 .95 211 .95 216 .95 221 .95 226 255 260 265 270 274 303 308 313 318 323 352 357 361 366 371 400 405 410 415 419 .95 424 .95 429 .95 434 .95 439 .95 444 .95 448 .95 453 .95 458 .95 463 .95 468 Dif. 6 1 1 2 2 3 4 4 5 5 5 1 1 2 2 3 3 4 4 5 4 1 1 2 2 2 3 3 4 5 1 1 2 2 3 3 4 4 5 4 1 1 2 2 2 3 3 4 .92 942 -.95 468 18 9000-9500 N 900 12 3 4 5 6 7 8 9 Dif. 5 .95 424 .95 429 .95 434 .95 439 .95 444 .95 448 .95 453 .95 458 .95 463 .95 468 901 472 477 482 487 492 497 501 506 511 516 1 902 521 525 530 535 540 545 550 554 559 564 1 903 569 574 578 583 588 593 598 602 607 612 2 904 617 622 626 631 636 641 646 650 655 660 2 905 .95 665 .95 670 .95 674 .95 679 .95 684 .95 689 .95 694 .95 698 .95 703 .95 708 3 906 713 718 722 727 732 737 742 746 751 756 3 907 761 766 770 775 780 785 789 794 799 804 4 908 809 813 818 823 828 832 837 842 847 852 4 909 856 861 866 871 875 880 885 890 895 899 5 910 .95 904 .95 909 .95 914 .95 918 .95 923 .95 928 .95 933 .95 938 .95 942 .95 947 4 911 952 957 961 966 971 976 980 985 990 995 912 999 96 004 96 009 96 014 96 019 96 023 96 028 96 033 96 038 96 042 1 913 96 047 052 057 061 066 071 076 080 085 090 1 914 095 099 104 109 114 118 123 128 133 137 2 915 .96 142 .96 147 .96 152 .96 156 .96 161 .96 166 .96 171 .96 175 ..96 180 .96 185 2 916 190 194 199 204 209 213 218 223 227 232 2 917 237 242 246 251 256 261 265 270 275 280 3 918 284 289 294 298 303 308 313 317 322 327 3 919 332 336 341 346 350 355 360 365 369 374 4 920 .96 379 .96 384 .96 388 .96 393 .96 398 .96 402 .96 407 .96 412 .96 417 .96 421 5 921 426 431 435 440 445 450 454 459 464 468 1 922 473 478 483 487 492 497 501 506 511 515 1 923 520 525 530 534 539 544 548 553 558 562 2 924 567 572 577 '581 586 591 595 600 605 609 2 925 .96 614 .96 619 .96 624 .96 628 .96 633 .96 638 .96 642 .96 647 .96 652 .96 656 3 926 661 666 670 675 680 685 689 694 699 703 3 927 708 713 717 722 727 731 736 741 745 750 4 928 755 759 764 769 774 778 783 788 792 797 4 929 802 806 811 816 820 825 830 834 839 844 5 930 .96 848 .96 853 .96 858 .96 862 .96 867 .96 872 .96 876 .96 881 .96 886 .96 890 4 931 895 900 904 909 914 918 923 928 932 937 932 942 946 951 956 960 965 970 974 979 984 1 933 988 993 997 97 002 97 007 97 011 97 016 97 021 97 025 97 030 1 934 97 035 97 039 97 044 049 053 058 063 067 072 077 2 935 .97 081 .97 086 .97 090 .97 095 .97 100 .97104 .97 109 .97 114 .97 118 .97 123 2 936 128 132 137 142 146 151 155 160 165 169 2 937 174 179 183 188 192 197 202 206 211 216 3 938 220 225 230 234 239 243 248 253 257 262 3 939 267 271 270 280 285 290 294 299 304 308 4 940 .97 313 .97 317 .97 322 .97 327 .97 331 .97 336 .97 340 .97 345 .97 350 .97 354 5 941 359 364 368 373 377 382 387 391 396 400 1 942 405 410 414 419 424 428 433 437 442 447 1 943 451 456 460 465 470 474 479 483 488 493 2 944 497 502 506 511 516 520 525 529 534 539 2 945 .97 543 .97 548 .97 552 .97 557 .97 562 .97 566 .97 571 .97 575 .97 580 .97 585 3 946 589 594 598 603 607 612 617 621 626 630 3 947 635 640 644 649 653 658 663 667 672 676 4 948 681 685 690 695 699 704 708 713 717 722 4 949 727 731 736 740 745 749 754 759 763 768 5 950 N .97 772 .97 777 .97 782 .97 786 .97 791 .97 795 .97 800 .97 804 .97 809 .97 813 1 2 3 4 5 6 7 8 9 .95 424 — .97 813 9500-10000 19 N 950 951 952 953 954 955 956 957 958 959 930 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 N Dif. .97 772 .97 777 .97 782 .97 786 .97 791 818 823 827 832 836 864 868 873 877 882 909 914 918 923 928 955 959 964 968 973 .98 000. .98 005 .98 009 .98 014 .98 019 046 050 055 059 064 091 096 100 105 109 137 141 146 1.50 . 155 182 186 191 195 200 .98 227 .98 232 .98 236 .98 241 .98 245 272 277 281 286 290 318 322 327 331 336 363 367 372 376 381 408 412 417 421 426 .98 453 .98 457 .98 462 .98 466 .98 471 498 502 507 511 516 "543 547 552 556 561 588 592 597 601 605 632 637 641 646 650 .98677 .98 682 .98 686 .98 691 .98 695 722 726 731 735 740 767 771 776 780 784 811 816 820 825 829 856 860 865 869 874 .98 900 .98 905 .98 909 .98 914 .98 918 945 949 954 958 963 989 994 998 99 003 99 007 99 034 99 038 99 043 047 052 078 083 087 092 096 .99 123 .99 127 .99 131 .99 136 .99 140 167 171 176 180 185 211 216 220 224 229 255 260 264 269 273 300 ■ 304 308 313 317 .99 344 .99 348 .99 352 .99 357 .99 361 388 392 396 401 405 432 436 441 445 449 476 480 484 489 493 520 524 528 533 537 .99 564 .99 568 .99 572 .99 577 .99 581 607 612 616 621 625 651 656 660 664 669 695 699 704 708 712 739 743 747 752 756 .99 782 .99 787 .99 791 .99 795 .99 800 826 870 913 957 830 874 917 961 835 839 843 878 883 887 922 926 930 965 970 974 .97 795 .97 800 .97 804 .97 809 .97 813 841 845 850 855 859 886 891 896 900 905 932 937 941 946 950 978 982 987 991 996 .98 023 .98 028 .98 032 .98 037 .98 041 068 073 078 082 087 114 118 123 127 132 159 164 168 173 177 204 209 214 218 223 .98 250 .98 254 .98 259 .98 263 .98 268 295 299 304 308 313 340 345 349 354 358 385 390 394 399 403 430 435 439 444 448 .98 475 .98480 .98 484 .98 489 .98 493 520 525 529 534 538 565 570 574 579 583 610 614 619 623 628 655 659 664 668 673 .98 700 .98 704 .98 709 .98 713 .98 717 744 749 753 758 762 789 793 798 802 807 834 . 838 843 847 851 878 883 887 892 896 .98 923 .98 927 .98 932 .98 936 .98 941 967 972 976 981 985 99 012 99 016 99 021 99 025 99 029 056 061 065 069 074 100 105 109 114 118 .99 145 .99 149 .99 154 .99 158 .99 162 189 193 198' 202 207 233 238 242 247 251 277 282 286 291 295 322 326 330 335 339 .99 366 .99 370 .99 374 .99 379 .99 383 410 414 419 423 427 454 458 463 467 471 498 502 506 511 515 542- 546 550 555 559 .99 585 .99 590 .99 594 .99 599 .99 603 629 634 638 642 647 673 677 682 686 691 717 721 726 730 734 760 765 769 774 778 .99 804 .99 808 .99 813 .99 817 .99 822 848 852 856 861 865 891 896 900 904 909 935 939 944 948 952 978 983 987 991 996 .00 000 .00 004 .00 009 .00 013 .00 017 .00 022 .00 026 .00 030 .00 035 .00 039 .97 772 -.99 996 20 10000-10500 N 12 3 4 5 6 7 8 9 1000 .00 000 .00 004 .00 009 .00 013 .00 017 .00 022 .00 026 .00 030 .00 035 .00 039 01 043 048 052 056 061 065 069 074 078 082 02 087 091 095 100 104 108 113 117 121 126 03 130 134 139 143 147 152 156 160 165 169 04 173 178 182 186 191 195 199 204 208 212 05 .00 217 .00 221 .00 225 .00 230 .00 234 .00 238 .00 243 .00 247 .00 251 .00 255 06 260 264 268 273 277 281 286 290 294 299 07 303 307 312 316 320 325 329 333 337 342 OS 346 350 355 359 363 368 372 376 381 385 09 389 393 398 402 406 411 415 419 424 428 1010 .00 432 .00 436 .00 441 .00 445 .00 449 .00 454 .00 458 .00 462 .00 467 .00 471 11 475 479 484 488 492 497 501 505 509 514 12 518 522 527 531 535 540 544 548 552 557 13 561 565 570 574 578 582 587 591 595 600 H 604 608 612 617 621 625 629 634 638 642 15 .00 647 .00 651 .00 655 .00 659 .00 664 .00 668 .00 672 .00 677 .00 681 .00 685 16 689 694 698 702 706 711 715 719 724 728 17 732 736 741 745 749 753 758 762 766 771 18 775 779 783 788 792 796 800 805 809 813 19 817 822 826 830 834 839 843 847 852 856 1020 .00 860 .00 864 .00 869 .00 873 .00 877 .00 881 .00 886 .00 890 .00 894 .00 898 21 903 907 911 915 920 924 928 932 937 941 22 945 949 954 958 962 966 971 975 979 983 23 988 992 996 01000 01005 01009 01013 01017 01022 01026 24 01030 01034 01038 043 047 051 055 060 064 068 25 .01072 .01077 .01081 .01085 .01089 .01 094 .01 098 .01 102 .01 106 .01 111 26 115 119 123 127 132 136 140 144 149 153 27 157 161 166 170 174 178 182 187 191 195 28 199 204 208 212 216 220 225 229 233 237 29 242 246 250 254 258 263 267 271 275 280 1030 .01 284 .01 288 .01 292 .01 296 .01 301 .01 305 .01 309 .01 313 .01 317 .01 322 31 326 330 334 339 343 347 351 355 360 364 32 368 372 376 381 385 389 393 397 402 406 33 410 414 418 423 427 431 435 439 444 448 34 452 456 460 465 469 473 477 481 486 490 35 .01 494 .01 498 .01 502 .01 507 .01 511 .01 515 .01 519 .01 523 .01 528 .01 532 36 536 540 544 549 553 557 561 565 569 574 37 578 582 586 590 595 599 603 607 611 616 38 620 624 628 632 636, 641 645 649 653 657 39 662 666 670 674 678 682 687 691 695 699 1040 .01 703 .01 708 .01 712 .01 716 .01 720 .01 724 .01 728 .01 733 .01 737 .01 741 41 745 749 753 758 762 766 770 774 778 783 42 787 791 795 799 803 808 812 816 820 824 43 828 833 837 841 845 849 853 858 862 866 44 870 874 878 883 887 891 895 899 903 907 45 .01 912 .01 916 .01 920 .01 924 .01 928 .01 932 .01 937 .01 941 .01 945 .01 949 46 953 957 961 966 970 974 978 982 986 991 47 995 999 02 003 02 007 02 011 02 015 02 020 02 024 02 028 02 032 48 .02 036 02 040 044 049 053 057 061 065 069 073 49 078 082 086 090 094 098 102 107 111 115 1050 .02 119 .02 123 .02 127 .02 131 .02 135 .02 140 .02 144 .02 148 .02 152 .02 156 N 12 3 4 5 6^7 8 9 .00 000 — .02156 10500-11000 21 N 1 2 3 4 5 6 7 8 9 1050 .02 119 .02123 .02 127 .02 131 .02 135 .02 140 .02144 .02 148 .02 152 .02 156 51 160 164 169 173 177 181 185 189 193 197 52 202 206 210 214 218 222 226 230 235 239 53 243 247 251 255 259 263 268 272 276 280 54 284 288 292 296 301 305 309 313 317 321 55 .02 325 .02 329 .02 333 .02 338 .02 342 .02 346 .02 350 .02 354 .02 358 .02 362 56 366 371 375 379 383 387 391 395 399 403 57 407 412 416 420 424 428 432 436 440 444 58 449 453 457 461 465 469 473 477 481 485 59 490 494 498 502 506 510 514 518 522 526 1060 .02 531 .02 535 .02 539 .02 543 .02 547 .02 551 .02 555 .02 559 .02 563 .02 567 61 572 576 580 584 588 592 596 600 604 608 62 612 617 621 625 629 633 637 641 645 649 63 653 657 661 666 670 674 678 682 686 690 64 694 698 702 706 710 715 719 723 727 731 65 .02 735 .02 739 .02 743 .02 747 .02 751 .02 755 .02 759 .02 763 .02 768 .02 772 66 776 780 784 788 792 796 800 804 808 812 67 816 821 825 829 833 837 841 845 849 853 68 857 861 865 869 873 877 882 886 890 894 69 898 902 906 910 914 918 922 926 930 934 1070 .02 938 .02 942 .02 946 .02 951 .02 955 .02 959 .02 963 .02 967 .02 971 .02 975 71 979 983 987 991 995 999 03 003 03 007 03 011 03 015 72 03 019 03 024 03 028 03 032 03 036 03 040 044 048 052 056 73 060 064 068 072 076 080 084 088 092 096 74 100 104 109 113 117 121 125 129 133 137 75 .03 141 .03 145 .03 149 .03 153 .03 157 .03 161 .03 165 .03 169 .03 173 .03 177 76 181 185 189 193 197 201 205 209 214 218 77 222 226 230 234 238 242 246 250 254 258 78 262 266 270 274 278 282 286 290 294 298 79 302 306 310 314 318 322 326 330 334 338 1080 .03 342 .03 346 .03 350 .03 354 .03 358 .03 362 .03 366 .03 371 .03 375 .03 379 81 383 387 391 395 399 403 407 411 415 419 82 423 427 431 435 439 443 447 451 455 459 83 463 467 471 475 479. 483 487 491 495 499 84 503 507 511 515 519 523 527 531 535 539 85 .03 543 .03 547 .03 551 .03 555 .03 559 .03 563 .03 567 .03 571 .03 575 .03 579 86 583 587 591 595 599 603 607 611 615 619 87 623 627 631 635 639 643 647 651 655 659 88 663 667 671 675 679 683 687 691 695 699 89 703 707 711 715 719 723 727 731 735 739 1090 .03 743 .03 747 .03 751 .03 755 .03 759 .03 763 .03 767 .03 771 .03 775 .03 778 91 782 786 790 794 798 802 806 810 814 818 92 822 826 830 834 838 842 846 850 854 858 93 862 866 870 874 878 882 886 890 894 898 94 902 906 910 914 918 922 926 930 933 937 95 .03 941 .03 945 .03 949 .03 953 .03 957 .03 961 .03 965 .03 969 .03 973 .03 977 96 981 985 989 993 997 04 001 04 005 04 009 04 013 04 017 97 04 021 04 025 04 029 04 033 04 036 040 044 048 052 056 98 060 064 068 072 076 080 084 088 092 096 99 100 104 108 112 116 120 123 127 131 135 1100 .04 139 .04 143 .04147 .04 151 .04 155 .04 159 .04 163 .04 167 .04 171 .04175 9 . N 1 2 3 4 5 6 7 8 ,02 119 -.04 175 22 TABLE II IMPORTANT CONSTANTS AND THEIR COMMON LOGARITHMS The circumference of a circle . . . . = 360° . . = 21600' . . = 1 296 000" . . 7r = 3. 14 159 265 358 979 323 846 264 338 328 7r2 =9. 86 960 440 . I/tt ■. . =0.31830 989 . l/7r2 =0.10132 118 . Vtt = 1. 77 245 385 . I/Vtt =0.56 418 958 . \/(3/7r) =0.97 720 502 . y(4/7r) = 1.12 837 917 . ^TT =1.46 459189 . I/a^tt =0.68 278 406 . 1 radian = ISOVtt = 57. 29 577 951° = 3 437.74 677' . = 206 264. 806" . = 0. 01 745 329 . = 0. 00 029 089 . = 0. 00 000 485 . = 2. 71 828 183 . = 0.43 429 448 . = 2.30 258 5 . . = 39.37 inches . = 1.09 361 1 yard = 3.28 083 3 feet = 0.62 137 mile In terms of a radian 1° V V Base of natural logarithms = e . . . . Modulus of common logarithms = logioe . Factor by which to multiply common logs, to obtain natural logs, or 1/logio e . . 1 meter . 1 kilometer 1 mile = 1.60 934 7 kilom. 1 yard = 0.91 440 2 metre 1 foot = 0.30 480 1 metre 1 inch = 25.40 005 mm. 1 pound Av. . = 7000 grains = 453.59 242 77 grammes 1 ounce Av = 28.34 953 grammes 1 ounce Troy = 31.10 348 grammes 1 grain " = 0.06 479 892 gramme 2.20 462 2 pounds Av. 15.43 235 639 grains 1 kilogramme 1 gramme 1 litre = 1.05 668 U. S. quart = 0.26417 U. S. gallon = 33.814 U. S. fluid oz 1 quart, U. S = 0.94 636 litre 1 gallon, U. S. 1 fluid ounce . 1 gallon U. S. 1 British gallon 1 British bushel = 3.78 544 litres . = 0.02 957 3 litre = 231 cu. inches = 4.54 346 litres . = 36.34 77 litres . Common Logarithms 2. 55 630 250 4. ZZ 445 375 6. 11 260 500 0. 49 714 987 0. 99 429 975 1. 50 285 013 1.00 570 025 0. 24 857 494 1. 75 142 506 1.98 998 569 0. 05 245 506 0. 16 571 662 1.83 428 338 1. 75 812 263 3. SZ e>l1 388 5.31442 513 2. 24 187 737 6.68 557 487 0. 43 429 448 1.63 778 431 0.36 22157 1.59 516 54 0. 03 886 29 0.51598 42 1. 79 335 03 0. 20 664 97 1.96113 71 1. 48 401 58 1. 40 483 46 3. 84 509 80 2. 65 666 58 1.45 254 59 1. 49 280 91 2.81 156 78 0. 34 ZZZ 42 1. 18 843 22 0. 02 394 4 1.42 188 4 1.52 910 1.97 605 6 0.57 8116 2. 47 090 2. 36 361 20 0. 65 738 67 1. 56 047 69 23 TABLE m THE COMMOI^ LOaARITHMS OF THE TRIGONOMETRIC FUNCTIONS OF ANGLES From 1° to 89° FOR EVERY MINUTE FIVE-PLACE MANTISSAS 24 1° f log sin log tan log cot log cos 1 8-10 8-10 1 9-10 .24 186 .24 192 .75 808 .99 993 60 1 903 910 090 993 59 2 25 609 25 616 74 384 993 58 3 26 304 26 312 73 688 993 57 4 988 996 004 992 56 5 .27 661 .27 669 .72 331 .99 992 55 6 28 324 28 332 71668 992 54 7 977 986 014 992 53 8 29 621 29 629 70 371 992 52 9 30 255 30 263 69 737 991 51 10 .30 879 .30 888 .69112 .99 991 50 11 31495 31505 68 495 991 49 12 32 103 32 112 67 888 990 48 13 702 711 289 990 47 14 33 292 33 302 66 698 990 46 15 .33 875 .33 886 .66 114 .99 990 45 16 34 450 34 461 65 539 989 44 17 35 018 35 029 64 971 989 43 18 578 590 410 989 42 19 36131 36143 63 857 989 41 20 .36 678 .36 689 .63 311 .99 988 40 21 37 217 37 229 62 771 988 39 22 750 762 238 988 38 23 38 276 38 289 61711 987 37 24 796 809 191 987 36 25 .39 310 .39 323 .60 677 .99 987 35 26 818 832 168 986 34 27 40 320 40 334 59 666 986 33 28 816 830 170 986 32 29 41307 41321 58 679 985 31 30 .41 792 .41 807 .58 193 .99 985 30 31 42 272 42 287 57 713 985 29 32 746 762 238 984 28 33 43 216 43 232 56 768 984 27 34 680 696 304 984 26 35 .44 139 .44 156 .55 844 .99 983 25 36 594 611 389 983 24 37 45 044 45 061 54 939 983 23 38 489 507 493 982 22 39 930 948 052 982 21 40 .46 366 .46 385 .53 615 .99 982 20 41 799 817 183 981 19 42 47 226 47 245 52 755 981 18 43 650 669 331 981 17 44 48 069 48 089 51911 980 16 45 .48 485 .48 505 .51495 .99 980 15 46 896 917 083 979 14 47 49 304 49 325 50 675 979 13 48 708 729 271 979 12 49 50108 50130 49 870 978 11 50 .50 504 .50 527 .49 473 .99 978 10 51 897 920 080 977 9 52 51287 51310 48 690 977 8 53 673 696 304 977 7 54 52 055 52 079 47 921 976 6 55 .52 434 .52 459 .47 541 .99 976 5 56 810 835 165 975 4 57 53 183 53 208 46 792 975 3 58 552 578 422 974 2 59 919 945 055 974 1 60 .54 282 .54 308 .45 692 .99 974 8-10 8-10 1 9-10 f log cos log cot log tan log sin f 2° f log sin log tan log cot log cos f 8-10 8-10 1 9-10 .54 282 .54 308 .45 692 .99 974 60 1 642 669 331 973 59 2 999 55 027 44 973 973 58 3 55 354 382 618 972 57 4 705 734 266 972 56 5 .56 054 .56 083 .43 917 .99 971 55 6 400 429 571 971 54 7 743 773 227 970 53 8 57 084 57 114 42 886 970 52 9 421 452 548 969 51 10 .57 757 .57 788 .42 212 .99 969 50 11 58 089 58121 41879 968 49 12 419 451 549 968 48 13 747 779 221 967 47 14 59 072 59 105 40 895 967 46 15 .59 395 .59 428 .40 572 .99 967 45 16 715 749 251 966 44 17 60 033 60 068 39 932 966 43 18 349 384 616 965 42 19 662 698 302 964 41 20 .60 973 .61 009 .38 991 .99 %4 40 21 61282 319 681 963 39 22 589 626 374 963 38 23 894 931 069 962 37 24 62 196 62 234 37 766 962 36 25 .62 497 .62 535 .37 465 .99 961 35 26 795 834 166 961 34 27 63 091 63 131 36 869 960 33 28 385 426 574 .960 32 29 678 718 282 959 31 30 .63 968 .64 009 .35 991 .99 959 30 31 64 256 298 702 958 29 32 543 585 415 958 28 33 827 870 130 957 27 34 65 110 65 154 34 846 956 26 35 .65 391 .65 435 .34 565 .99 956 25 36 670 715 285 955 24 37 947 993 007 955 23 38 66 223 66 269 33 731 954 22 39 497 543 457 954 21 40 .66 769 .66 816 .33 184 .99 953 20 41 67 039 67 087 32 913 952 19 42 308 356 644 952 18 43 575 624 376 951 17 44 841 890 110 951 16 45 .68104 .68154 .31846 .99 950 15 46 367 417 583 949 14 47 627 678 322 949 13 48 886 938 062 948 12 49 69144 69196 30 804 948 11 50 .69 400 .69 453 .30 547 .99 947 10 51 654 708 292 946 9 52 907 962 038 946 8 53 70159 70 214 29 786 945 7 54 409 465 535 944 6 55 .70 658 .70 714 .29 286 .99 944 5 56 905 962 038 943 4 57 71151 71208 28 792 942 3 58 395 453 547 942 2 59 638 697 303 941 1 60 t .71880 .71940 .28 060 .99 940 8-10 8-10 1 9-10 log cos log cot log tan log sin t 88' 87° 3° t log sin log tan log cot log cos f 8-10 8-10 1 9-10 .71880 .71940 .28 060 .99 940 60 1 72 120 72 181 27 819 940 59 2 359 420 580 939 58 3 597 659 341 938 57 4 834 896 104 938 56 5 .73 069 .73 132 .26 868 .99 937 55 6 303 366 634 936 54 7 535 600 400 936 53 8 767 832 168 935 52 9 997 74 063 25 937 934 51 10 .74 226 .74 292 .25 708 .99 934 50 11 454 521 479 933 49 12 680 748 252 932 48 13 906 974 026 932 47 14 75 130 75 199 24 801 931 46 15 .75 353 .75 423 .24 577 .99 930 45 16 575 645 355 929 44 17 795 867 133 929 43 18 76 015 76 087 23 913 928 42 19 231 306 694 927 41 20 .76 451 .76 525 .23 475 .99 926 40 21 667 742 258 926 39 22 883 958 042 925 38 23 77 097 77 173 22 827 924 37 24 310 387 613 923 36 25 .77 522 .77 600 .22 400 .99 923 35 26 733 811 189 922 34 27 943 78 022 21978 921 33 28 78152 232 768 920 32 29 360 441 559 920 31 30 .78 568 .78 649 .21351 .99 919 30 31 774 855 145 918 29 32 979 79 061 20 939 917 28 33 79183 266 734 917 27 34 386 470 530 916 26 35 .79 588 .79 673 .20 327 .99 915 25 36 789 875 125 914 24 37 990 80 076 19 924 913 23 38 80 189 277 723 913 22 39 388 476 524 912 21 40 .80 585 .80 674 .19 326 .99 911 20 41 782 872 128 910 19 42 978 81068 18 932 909 18 43 81173 264 736 909 17 44 367 459 541 908 16 45 .81 560 .81 653 .18 347 .99 907 15 46 752 846 154 906 14 47 944 82 038 17 962 905 13 48 82 134 230 770 904 12 49 324 420 580 904 11 50 .82 513 .82 610 .17 390 .99 903 10 51 701 799 201 902 9 52 888 987 013 901 8 53 83 075 83 175 16 825 900 7 54 261 361 639 899 6 55 .83 446 .83 547 .16 453 .99 898 5 56 630 732 268 898 4 57 813 916 084 897 3 58 996 84 100 15 900 896 2 59 84 177 282 718 895 1 60 f .84 358 .84 464 .15 536 .99 894 8-10 8-10 1 9-10 log cos log cot log tan log sin f 25 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 .60 log sin log tan log cot log cos 8-10 8-10 .84 358 .84 464 539 718 646 826 897 85 006 85 075 .85 252 429 605 780 955 .86 128 301 474 645 816 .86 987 87 156 325 494 661 .87 829 995 88161 326 490 .88 654 817 980 89142 304 .89 464 625 784 943 90102 .90 260 417 574 730 885 .91 040 195 349 502 655 .91 807 959 92 110 261 411 .92 561 710 859 93 007 154 .93 301 448 594 740 885 .94 030 8-10 log cos 185 .85 363 540 717 893 86 069 .86 243 417 591 763 935 .87 106 277 447 616 785 .87 953 88 120 287 453 618 .88 783 948 89111 274 437 .89 598 760 920 90 080 240 .90 399 557 715 872 91029 .91 185 340 495 650 803 .91 957 92 110 262 414 565 .92 716 866 93 016 165 313 .93 462 609 756 903 94 049 .94 195 8-10 log cot 1 9-10 .15 536 .99 894 354 893 174 892 14 994 891 815 891 .14 637 .99 890 460 889 283 888 107 887 13 931 886 .13 757 .99 885 583 884 409 883 237 882 065 881 12 894 , 723 553 384 215 .12 047 11880 713 547 382 .11217 052 10 889 726 563 .10 402 240 080 09 920 760 .09 601 443 285 128 08 971 .08 815 660 505 350 197 .08 043 07 890 738 586 435 .07 284 134 06 984 835 687 .06 538 391 244 097 05 951 .05 805 1 log tan .99 880 879 879 878 877 .99 876 875 874 873 872 .99 871 870 869 868 867 .99 866 865 864 863 862 .99 861 860 859 858 857 .99 856 855 854 853 852 .99 851 850 848 847 846 .99 845 844 843 842 841 .99 840 839 838 837 836 .99 834 9-10 log sin 86< 85' 26 5° r log sin log tan log cot log cos f 8-10 8-10 1 9-10 .94 030 .94 195 .05 805 .99 834 60 1 174 340 660 833 59 2 317 485 515 832 58 3 461 630 370 831 57 4 603 773 227 830 56 5 .94 746 .94 917 .05 083 .99 829 55 6 887 95 060 04 940 828 54 7 95 029 202 798 827 53 8 170 344 656 825 52 9 310 486 514 824 51 10 .95 450 .95 627 .04 373 .99 823 50 11 589 767 233 822 49 12 728 908 092 821 48 13 867 96 047 03 953 820 47 14 96 005 187 813 819 46 15 .96 143 .96 325 .03 675 .99 817 45 16 280 464 536 816 44 17 417 602 398 815 43 18 553 739 261 814 42 19 689 877 123 813 41 20 .96 825 .97 013 .02 987 .99 812 40 21 960 150 850 810 39 22 97 095 285 715 809 38 23 229 421 579 808 37 24 363 556 444 807 36 25 .97 496 .97 691 .02 309 .99 806 35 26 629 825 175 804 34 27 762 959 04] 803 33 28 894 98 092 01908 802 32 29 98 026 225 775 801 31 30 .98 157 .98 358 .01 642 .99 800 30 31 288 490 510 798 29 32 419 622 378 797 28 33 549 753 247 796 27 34 679 884 116 795 26 35 .98 808 .99 015 .00 985 .99 793 25 36 937 145 855 792 24 37 99 066 275 725 791 23 38 194 405 595 790 22 39 322 534 466 788 21 40 .99 450 .99 662 .00 338 .99 787 20 41 577 791 209 786 19 42 704 919 081 785 18 43 830 00 046 99 954 783 17 44 956 174 826 782 16 45 .00 082 .00 301 .99 699 .99 781 15 46 207 427 573 780 14 47 332 553 447 778 13 48 456 679 321 777 12 49 581 805 195 776 11 50 .00 704 .00 930 .99 070 .99 775 10 51 828 0105i 98 945 773 9 52 951 179 821 772 8 53 01074 303 697 771 7 54 196 427 573 769 6 55 .01318 .01550 .98 450 .99 768 5 56 440 673 327 767 4 57 561 796 204 765 3 58 682 918 082 764 2 59 803 02 040 97 960 763 1 60 .01923 .02 162 .97 838 .99 761 9-10 9-10 9-10 log cos log cot log tan log sin t 6° f log sin log tan log cot log cos t 9-10 9-10 9-10 .01 923 .02 162 .97 838 .99 761 60 1 02 043 283 717 760 59 2 163 404 596 759 58 3 283 525 475 757 57 4 402 645 355 756 56 5 .02 520 .02 766 .97 234 .99 755 55 6 639 885 115 753 54 7 757 03 005 96 995 752 53 8 874 124 876 751 52 9 992 242 758 749 51 10 .03 109 .03 361 .96 639 .99 748 50 11 226 479 521 747 49 12 342 597 403 745 48 13 458 714 286 744 47 14 574 832 168 742 46 15 .03 690 .03 948 .96 052 .99 741 45 16 805 04 065 95 935 740 44 17 920 181 819 738 43 18 04 034 297 703 737 42 19 149 413 587 736 41 20 .04 262 .04 528 .95 472 .99 734 40 21 376 643 357 733 39 22 490 758 242 731 38 23 603 873 127 730 37 24 715 987 013 728 36 25 .04 828 .05 101 .94 899 .99 727 35 26 940 214 786 726 34 27 05 052 328 672 724 33 28 164 441 559 723 32 29 275 553 447 721 31 30 .05 386 .05 666 .94 334 .99 720 30 31 497 778 222 718 29 32 607 890 110 717 28 33 717 06 002 93 998 716 27 34 827 113 887 714 26 35 .05 937 .06 224 .93 776 .99 713 25 36 06 046 335 665 711 24 37 155 445 555 710 23 38 264 556 444 708 22 39 372 666 334 707 21 40 .06 481 .06 775 .93 225 .99 705 20 41 589 885 115 704 19 42 696 994 006 702 18 43 804 07103 92 897 701 17 44 911 211 789 699 16 45 .07 018 .07 320 .92 680 .99 698 15 46 124 428 572 696 14 47 231 536 464 695 13 48 337 643 357 693 12 49 442 751 249 692 11 50 .07 548 .07 858 .92 142 .99 690 10 51 653 964 036 689 9 52 758 08 071 91929 687 8 53 863 177 823 686 7 54 968 283 717 684 6 55 .08 072 .08 389 .91611 .99 683 5 56 176 495 505 681 4 57 280 600 400 680 3 58 383 705 295 678 2 59 486 810 190 677 1 60 .08 589 .08 914 .91 086 .99 675 9-10 9-10 9-10 f log cos log cot log tan log sin t 84< 83° n" log sin log tan log cot log cos 1 9-10 9-10 9-10 .08 589 .08 914 .91 086 .99 675 60 1 692 09 019 90 981 674 59 2 795 123 877 672 58 3 897 227 773 670 57 4 999 330 670 669 56 5 .09 101 .09 434 .90 566 .99 667 55 6 202 537 463 666 54 7 304 640 360 664 53 8 405 742 258 663 52 9 506 845 155 661 51 10 .09 606 .09 947 .90 053 .99 659 50 11 707 10 049 89 951 658 49 12 807 150 850 656 48 13 907 252 748 655 47 14 10 006 353 647 653 46 15 .10106 .10 454 .89 546 .99 651 45 16 205 555 445 650 44 17 304 656 344 648 43 18 402 756 244 647 42 19 501 856 144 645 41 20 .10 599 .10 956 .89 044 .99 643 40 21 697 11056 88 944 642 39 22 795 155 845 640 38 23 893 254 746 638 37 24 990 353 647 637 36 25 .11087 .11452 .88 548 .99 635 35 26 184 551 449 633 34 27 281 649 351 632 33 28 377 747 253 630 32 29 474 845 155 629 31 30 .11570 .11943 .88 057 .99 627 30 31 666 12 040 87 960 625 29 32 761 138 862 624 28 33 857 235 765 622 27 34 952 332 668 620 26 35 .12 047 .12 428 .87 572 .99 618 25 36 142 525 475 617 24 37 236 621 379 615 23 38 331 717 283 613 22 39 425 813 187 612 21 40 .12 519 .12 909 .87 091 .99 610 20 41 612 13 004 86 996 608 19 42 706 099 901 607 18 43 799 194 806 605 17 44 892 289 711 603 16 45 .12 985 .13 384 .86 616 .99 601 15 46 13 078 478 522 600 14 47 171 573 427 598 13 48 263 667 333 596 12 49 355 761 239 595 11 50 .13 447 .13 854 .86 146 .99 593 10 51 539 948 052 591 9 52 630 14 041 85 959 589 8 53 722 134 866 588 7 54 813 227 773 586 6 55 .13 904 .14 320 .85 680 .99 584 5 56 994 412 588 582 4 57 14 085 504 496 581 3 58 175 597 403 579 2 59 266 688 312 577 1 60 .14 356 .14 780 .85 220 .99 575 9-10 9-10 9-10 t log cos log cot log tan log sin t 8° 27 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .14 356 .14 780 .85 220 .99 575 60 1 445 872 128 574 59 2 535 963 037 572 58 3 624 15 054 84 946 570 57 4 714 145 855 568 56 5 .14 803 .15 236 .84 764 .99 566 55 6 891 327 673 565 54 7 980 417 583 563 53 8 15 069 508 492 561 52 9 157 598 402 559 51 10 .15 245 .15 688 .84 312 .99 557 50 11 333 777 223 556 49 12 421 867 133 554 48 13 508 956 044 552 47 14 596 16 046 83 954 550 46 15 .15 683 .16 135 .83 865 .99 548 45 16 770 224 776 546 44 17 857 312 688 545 43 18 944 401 599 543 42 19 16 030 489 511 541 41 20 .16116 .16 577 .83 423 .99 539 40 21 203 665 335 537 39 22 289 753 247 535 38 23 374 841 159 533 37 24 460 928 072 532 36 25 .16 545 .17 016 .82 984 .99 530 35 26 631 103 897 528 34 27 716 190 810 526 33 28 801 277 723 524 32 29 886 363 637 522 31 30 .16 970 .17 450 .82 5.50 .99 520 30 31 17 055 536 464 518 29 32 139 622 378 517 28 33 223 708 292 515 27 34 307 794 206 513 26 35 .17 391 .17 880 .82 120 .99 511 25 36 474 965 035 509 24 37 558 18 051 81949 507 23 38 641 136 864 505 22 39 724 221 779 503 21 40 .17 807 .18 306 .81694 .99 501 20 41 890 391 609 499 19 42 973 475 525 497 18 43 18 055 560 440 495 17 44 137 644 356 494 16 45 .18 220 .18 728 .81272 .99 492 15 46 302 812 188 490 14 47 383 896 104 488 13 48 465 979 021 486 12 49 547 19 063 80 937 484 11 50 .18 628 .19 146 .80 854 .99 482 10 51 709 229 771 480 9 52 790 312 688 478 8 53 871 395 605 476 7 54 952 478 522 474 6 55 .19 033 .19 561 .80 439 .99 472 5 56 113 643 357 470 4 57 193 725 275 468 3 58 273 807 193 466 2 59 353 889 111 464 1 60 .19 433 .19 971 .80 029 .99 462 9-10 9-10 9-10 f log cos log cot log tan log sin t 82< 8V 28 9° 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .19 433 .19 971 .80 029 .99 462 60 1 513 20 053 79 947 460 59 2 592 134 866 458 58 3 672 216 784 456 57 4 751 297 703 454 56 6 .19 830 .20 378 .79 622 .99 452 55 6 909 459 541 450 54 7 988 540 460 448 53 8 20 067 621 379 446 52 9 145 701 299 444 51 10 .20 223 .20 782 .79 218 .99 442 50 11 302 862 138 440 49 12 380 942 058 438 48 13 458 21022 78 978 436 47 14 535 102 898 434 46 15 .20 613 .21182 .78 818 .99 432 45 16 691 261 739 429 44 17 768 341 659 427 43 18 845 420 580 425 42 19 922 499 501 423 41 20 .20 999 .21578 .78 422 .99 421 40 21 21076 657 343 419 39 22 153 736 264 417 38 23 229 814 186 415 37 24 306 893 107 413 36 25 .21 382 .21971 .78 029 .99 411 35 26 458 22 049 77 951 409 34 27 534 127 873 407 33 28 610 205 795 404 31 29 685 283 717 402 31 30 .21 761 .22 361 .77 639 .99 400 30 31 836 438 562 398 29 32 912 516 484 396 28 33 987 593 407 394 27 34 22 062 670 330 392 26 35 .22 137 .22 747 .77 253 .99 390 25 36 211 824 176 388 24 37 286 901 099 385 23 38 361 977 023 383 22 39 435 23 054 76 946 381 21 40 .22 509 .23 130 .76 870 .99 379 20 41 583 206 794 377 19 42 657 283 717 375 18 43 731 359- 641 372 17 44 805 435 565 370 16 45 .22 878 .23 510 .76 490 .99 368 15 46 952 586 414 366 14 47 23 025 661 339 364 13 48 098 737 263 362 12 49 171 812 188 359 11 50 .23 244 .23 887 .76113 .99 357 10 51 317 962 038 355 9 52 390 24 037 75 963 353 8 53 462 112 888 351 7 54 535 186 814 348 6 55 .23 607 .24 261 .75 739 .99 346 5 56 679 335 665 344 4 57 752 410 590 342 3 58 823 484 516 340 2 59 895 558 442 337 1 60 .23 967 .24 632 .75 368 .99 335 9-10 9-10 9-10 1 log cos log cot log tan log sin f 10° f log sin log tan log cot log cos f 9-10 9-10 9-10 .23 967 .24 632 .75 368 .99 335 60 1 24 039 706 294 333 59 2 110 779 221 331 58 3 181 853 147' 328 57 4 253 926 074 326 56 5 .24 324 .25 000 .75 000 .99 324 55 6 395 073 74 927 322 54 7 466 146 854 319 53 8 536 219 781 317 52 9 607 292 708 315 51 10 .24 677 .25 365 .74 635 .99 313 50 11 748 437 563 310 49 12 818 510 490 308 48 13 888 582 418 306 47 14 958 655 345 304 46 15 .25 028 .25 727 .74 273 .99 301 45 16 098 799 201 299 44 17 168 871 129 297 43 18 237 943 057 294 42 19 307 26 015 73 985 292 41 20 .25 376 .26 086 .73 914 .99 290 40 21 445 158 842 288 39 22 514 229 771 285 38 23 583 301 699 283 37 24 652 372 628 281 36 25 .25 721 .26 443 .73 557 .99 278 35 26 790 514 486 276 34 27 858 585 415 274 33 28 927 655 345 271 31 29 995 726 274 269 31 30 .26 063 .26 797 .73 203 .99 267 30 31 131 867 133 264 29 32 199 937 063 262 28 33 267 27 008 72 992 260 27 34 335 078 922 257 26 35 .26 403 .27 148 .72 852 .99 255 25 36 470 218 782 252 24 37 538 288 712 250 23 38 605 357 643 248 22 39 672 427 573 245 21 40 .26 739 .27 496 .72 504 .99 243 20 41 806 566 434 241 19 42 873 635 365 238 18 43 940 704 296 236 17 44 27 007 773 227 233 16 45 .27 073 .27 842 .72 158 .99 231 15 46 140 911 089 229 14 47 206 980 020 226 13 48 273 28 049 71951 224 12 49 339 117 883 221 11 50 .27 405 .28 186 .71 814 .99 219 10 51 471 254 746 217 9 52 537 323 677 214 8 53 602 391 609 212 7 54 668 459 541 209 6 55 .27 734 .28 527 .71 473 .99 207 5 56 799 595 405 204 4 57 864 662 338 202 3 58 930 730 270 200 2 59 995 798 202 197 1 60 .28 060 .28 865 .71 135 .99 195 9-10 9-10 9-10 f log cos log cot log tan log sin f 80< 79< 11° t log sin log tan log cot log cos 1 9-10 9-10 9-10 .28 060 .28 865 .71 135 .99 195 60 1 125 933 067 192 59 2 190 29 000 000 190 58 3 254 067 70 933 187 57 4 319 134 866 185 56 5 .28 384 .29 201 .70 799 .99 182 55 6 448 268 732 180 54 7 512 335 665 177 53 8 577 402 598 175 52 9 641 468 532 172 51 10 .28 705 .29 535 .70 465 .99170 50 11 769 601 399 167 49 12 833 668 332 165 48 13 896 734 266 162 47 14 960 800 200 160 46 15 .29 024 .29 866 .70 134 .99 157 45 16 087 932 068 155 44 17 150 998 002 152 43 18 214 30 064 69 936 150 42 19 277 130 870 147 41 20 .29 340 .30 195 .69 805 .99 145 40 21 403 261 739 142 39 22 466 326 674 140 38 23 529 391 609 137 37 24 591 457 543 135 36 25 .29 6.54 .30 522 .69 478 .99 132 35 26 716 587 413 130 34 27 779 652 348 127 33 •28 841 717 283 124 32 29 903 782 218 122 31 30 .29 966 .30 846 .69 154 .99119 30 31 30 028 911 089 117 29 32 090 975 025 114 28 33 151 31040 68 960 112 27 34 213 104 896 109 26 35 .30 275 .31 168 .68 832 .99 106 25 36 336 233 767 104 24 37 398 297 703 101 23 38 459 361 639 099 22 39 521 425 575 096 21 40 .30 582 .31489 .68 511 .99 093 20 41 643 552 448 091 19 42 704 616 384 088 18 43 765 679 321 086 17 44 826 743 257 083 16 45 .30 887 .31 806 .68 194 .99 080 15 46 947 870 130 078 14 47 31 008 933 067 075 13 48 068 996 004 072 12 49 129 32 059 67 941 070 11 50 .31 189 .32 122 .67 878 .99 067 10 51 250 185 815 064 9 52 310 248 752 062 8 53 370 311 689 059 7 54 430 373 627 056 6 55 .31 490 .32 436 .67 564 .99 054 5 56 549 498 502 051 4 57 609 561 439 048 3 58 669 623 377 046 2 59 728 685 315 043 1 60 .31 788 .32 747 .67 253 .99 040 9-10 9-10 9-10 f log cos log cot log tan log sin f 12° 29 f log sin log tan log cot log cos f 9-10 9-10 9-10 .31 788 .32 747 .67 253 .99 040 60 1 847 810 190 038 59 2 907 872 128 035 58 3 966 933 067 032 57 4 32 025 995 005 030 56 5 .32 084 .33 057 .66 943 .99 027 55 6 143 119 881 024 54 7 202 180 820 022 53 8 261 242 758 019 52 9 319 303 697 016 51 10 .32 378 .33 365 .66 635 .99 013 50 11 437 426 574 Oil 49 12 495 ' 487 513 008 48 13 553 548 452 005 47 14 612 609 391 002 46 15 .32 670 .33 670 .66 330 .99 000 45 16 728 731 269 98 997 44 17 786 792 208 994 43 18 844 853 147 991 42 19 902 913 087 989 41 20 .32 960 .33 974 .66 026 .98 986 40 21 33 018 34 034 65 966 983 39 22 075 095 905 980 38 23 133 155 845 978 37 24 190 215 785 975 36 25 .33 248 .34 276 .65 724 .98 972 35 26 305 336 664 969 34 27 362 396 604 967 33 28 420 456 544 964 32 29 477 516 484 961 31 30 .33 534 .34 576 .65 424 .98 958 30 31 591 635 365 955 29 32 647 695 305 953 28 33 704 755 245 950 27 34 761 814 186 947 26 35 .33 818 .34 874 .65 126 .98 944 25 36 874 933 067 941 24 37 931 992 008 938 23 38 987 35 051 64 949 936 22 39 34 043 111 889 933 21 40 .34 100 .35 170 .64 830 .98 930 20 41 156 229 771 927 19 42 212 288 712 924 18 43 268 347 653 921 17 44 324 405 595 919 16 45 .34 380 .35 464 .64 536 .98 916 15 46 436 523 477 913 14 47 491 581 419 910 13 48 547 640 360 907 12 49 602 698 302 904 11 50 .34 658 .35 757 .64 243 .98 901 10 51 713 815 185 898 9 52 769 873 127 896 8 53 824 931 069 893 7 54 879 989 Oil 890 6 55 .34 934 .36 047 .63 953 .98 887 5 56 989 105 895 884 4 57 35 044 163 837 881 3 58 099 221 779 878 2 59 154 279 721 875 1 60 .35 209 .36 336 .63 664 .98 872 9-10 9-10 9-10 t log cos log cot log tan log sin r 78° 77° 30 13 o 1 log sin log tan log cot log cos ! 1 9-10 9-10 9-10 .35 209 .36 336 .63 664 .98 872 60 1 263 394 606 869 59 2 318 452 548 867 58 3 373 509 491 864 57 4 427 566 434 861 56 5 .35 481 .36 624 .63 376 .98 858 55 6 536 681 319 855 54 7 590 738 262 852 53 8 644 795 205 849 52 9 698 852 148 846 51 10 .35 752 .36 909 .63 091 .98 843 50 11 806 966 034 840 49 12 860 37 023 62 977 837 48 13 914 080 920 834 47 14 968 137 863 831 46 15 .36 022 .37 193 .62 807 .98 828 45 16 075 250 750 825 44 17 129 306 694 822 43 18 182 363 637 819 42 19 236 419 581 816 41 20 .36 289 .37 476 .62 524 .98 813 40 21 342 532 468 810 39 22 395 588 412 807 38 23 449 644 356 804 37 24 502 700 300 801 36 25 .36 555 .37 756 .62 244 .98 798 35 26 608 812 188 795 34 27 660 868 132 792 33 28 713 924 076 789 32 29 766 980 020 786 31 30 .36 819 .38 035 .61 965 .98 783 30 31 871 091 909 780 29 32 924 147 853 777 28 33 976 202 798 774 27 34 37 028 257 743 771 26 35 .37 081 .38 313 .61 687 .98 768 25 36 133 368 632 765 24 37 185 423 577 762 23 38 237 479 521 759 22 39 289 534 466 756 21 40 .37 341 .38 589 .61411 .98 753 20 41 393 644 356 750 19 42 445 699 301 746 18 43 497 754 246 743 17 44 549 808 192 740 16 45 .37 600 .38 863 .61 137 .98 737 15 46 652 918 082 734 14 47 703 972 028 731 13 48 755 39 027 60 973 728 12 49 806 082 918 725 11 50 .37 858 .39 136 .60 864 .98 722 10 51 909 190 810 719 9 52 960 245 755 715 8 53 38 011 299 701 712 7 54 062 353 647 709 6 55 .38 113 .39 407 .60 593 .98 706 5 56 164 461 539 703 4 57 215 515 485 700 3 58 266 569 431 697 2 59 317 623 377 694 1 60 .38 368 .39 677 .60 323 .98 690 9-10 9-10 9-10 1 log cos log cot log tan log sin f 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 14^ log sin log tan log cot 9-10 9-10 .38 368 .39 677 .60 323 418 731 269 469 785 215 519 838 162 570 892 108 .38 620 .39 945 .60 055 670 999 001 721 40 052 59 948 771 106 894 821 159 841 .38 871 .40 212 .59 788 921 266 734 971 319 681 39 021 372 628 071 425 575 .39 121 170 220 270 319 .39 369 418 467 517 566 .39 615 664 713 762 811 .39 860 909 958 40 006 055 .40 103 152 200 249 297 .40 346 394 442 490 538 .40 586 634 682 730 778 .40 825 873 921 968 41016 .41 063 111 158 205 252 .41 300 9-10 log cos .40 478 531 584 636 689 .40 742 795 847 900 952 .41 005 057 109 161 214 .41 266 318 370 422 474 .41 526 578 629 681 733 .41 784 836 887 939 990 .42 041 093 144 195 246 .42 297 348 399 450 501 .42 552 603 653 704 755 .42 805 9-10 log cot .59 522 469 416 364 311 .59 258 205 153 100 048 .58 995 943 891 839 786 .58 734 682 630 578 526 .58 474 422 371 319 267 .58 216 164 113 061 010 .57 959 907 856 805 754 .57 703 652 601 550 499 .57 448 397 347 296 245 .57 195 log tan log COS f 9-10 .98 690 60 687 59 684 58 681 57 678 56 .98 675 55 671 54 668 53 665 52 662 51 .98 659 50 656 49 652 48 649 47 646 46 .98 643 45 640 44 636 43 633 42 630 41 .98 627 40 623 39 620 38 617 37 614 36 .98 610 35 607 34 6(H 33 601 32 597 31 .98 594 30 591 29 588 28 584 27 581 26 .98 578 25 574 24 571 23 568 22 565 21 .98 561 20 558 19 555 18 551 17 548 16 .98 545 15 541 14 538 13 535 12 531 11 .98 528 10 525 9 521 8 518 7 515 6 .98 511 5 508 4 505 3 501 2 498 1 .98 494 9-10 log sin f 76< 75° 15° 1 log sin log tan log cot log cos 1 9-10 9-10 9-10 .41 300 .42 805 .57 195 .98 494 60 1 347 856 144 491 59 2 394 906 094 488 58 3 441 957 043 484 57 4 488 43 007 56 993 481 56 .5 .41535 .43 057 .56 943 .98 477 55 6 582 108 892 474 54 7 628 158 842 471 53 8 675 208 792 467 52 9 722 258 742 464 51 10 .41 768 .43 308 .56 692 .98 460 50 11 815 358 642 457 49 12 861 408 592 453 48 13 908 458 542 450 47 14 954 508 492 447 46 15 .42 001 .43 558 .56 442 .98 443 45 16 047 607 393 440 44 17 093 657 343 436 43 18 140 707 293 433 42 19 186 756 244 429 41 20 .42 232 .43 806 .56 194 .98 426 40 21 278 855 145 422 39 22 324 905 095 419 38 23 370 954 046 415 37 24 416 44 004 55 996 412 36 25 .42 461 .44 053 .55 947 .98 409 35 26 507 102 898 405 34 27 553 151 849 402 33 28 599 201 799 398 32 29 644 250 750 395 31 30 .42 690 .44 299 .55 701 .98 391 30 31 735 348 652 388 29 32 781 397 603 384 28 33 826 446 554 381 27 34 872 495 505 377 26 35 .42 917 .44 544 .55 456 .98 373 25 36 962 592 408 370 24 37 43 008 641 359 366 23 38 053 690 310 363 22 39 098 738 262 359 21 40 .43 143 .44 787 .55 213 .98 356 20 41 188 836 164 352 19 42 233 884 116 349 18 43 278 933 067 345 17 44 323 981 019 342 16 45 .43 367 .45 029 .54 971 .98 338 15 46 412 078 922 334 14 47 457 126 874 331 13 48 502 174 826 327 12 49 546 222 778 324 11 50 .43 591 .45 271 .54 729 .98 320 10 51 635 319 681 317 9 52 680 367 633 313 8 53 724 415 585 309 7 54 769 463 537 306 6 55 .43 813 .45 511 .54 489 .98 302 5 56 857 559 441 299 4 57 901 606 394 295 3 58 946 654 346 291 2 59 990 702 298 288 1 60 .44 034 .45 750 .54 250 .98 284 9-10 9-10 9-10 f log cos log cot log tan log sin f 16° 31 t log sin log tan log cot log cos 9-10 9-10 9-10 1 .44 034 .45 750 .54 250 .98 284 60 1 078 797 203 281 59 2 122 845 155 277 58 3 166 892 108 273 57 4 210 940 060 270 56 5 .44 253 .45 987 .54 013 .98 266 55 6 297 46 035 53 965 262 54 7 341 082 918 259 53 8 385 130 870 255 52 9 428 177 823 251 51 10 .44 472 .46 224 .53 776 .98 248 50 11 516 271 729 244 49 12 559 319 681 240 48 13 602 366 634 237 47 14 646 413 587 233 46 15 .44 689 .46 460 .53 540 .98 229 45 16 733 507 493 226 44 17 776 554 446 222 43 18 819 601 399 218 42 19 862 648 352 215 41 20 .44 905 .46 694 .53 306 .98 211 40 21 948 741 259 207 39 22 992 788 212 204 38 23 45 035 835 165 200 37 24 077 881 119 196 36 25 .45 120 .46 928 .53 072 .98 192 35 26 163 975 025 189 34 27 206 47 021 52 979 185 33 28 249 068 932 181 32 29 292 114 886 177 31 30 .45 334 .47 160 .52 840 .98 174 30 31 377 207 793 170 29 32 419 253 747 166 28 33 462 299 701 162 27 34 504 346 654 159 26 35 .45 547 .47 392 .52 608 .98155 25 36 589 438 562 151 24 37 632 484 516 147 23 38 674 530 470 144 22 39 716 576 424 140 21 40 .45 758 .47 622 .52 378 .98136 20 41 801 668 332 132 19 42 843 714 286 129 18 43 885 760 240 125 17 44 927 806 194 121 16 45 .45 969 .47 852 .52 148 .98117 15 46 46011 897 103 113 14 47 053 943 057 110 13 48 095 989 on 106 12 49 136 48 035 51965 102 11 50 .46178 .48 080 .51920 .98 098 10 51 220 126 874 094 9 52 262 171 829 090 8 53 303 217 783 087 7 54 345 262 738 083 6 55 .46 386 .48 307 .51693 .98 079 5 56 428 353 647 075 4 57 469 398 602 071 3 58 511 443 557 067 2 59 552 489 511 063 1 60 .46 594 .48 534 .51 466 .98 060 9-10 9-10 9-10 1 log cos log cot log tan log sin f 74c 73° 32 17° f log sin log tan log cot log cos f 9-10 9-10 9-10 .46 594 .48 534 .51466 .98 060 60 1 635 579 421 056 59 2 676 624 376 052 58 3 717 669 331 048 57 4 758 714 286 044 56 5 .46 800 .48 759 .51 241 .98 040 55 6 841 804 196 036 54 7 882 849, 151 032 53 8 923 894 106 029 52 9 964 939 061 025 51 10 .47 005 .48 984 .51016 .98 021 50 11 045 49 029 50 971 017 49 12 086- 073 927 013 48 13 127 118 882 009 47 14 168 163 837 005 46 15 .47 209 .49 207 .50 793 .98 001 45 16 249 252 748 97 997 44 17 290 296 704 993 43 18 330 341 659 989 42 19 371 9 385 615 986 41 20 .47 411 .49 430 .50 570 .97 982 40 21 452 474 526 978 39 22 492 519 481 974 38 23 533 563 437 970 37 24 573 607 393 966 36 25 .47 613 .49 652 .50 348 .97 962 35 26 654 696 304 958 34 27 694 740 260 954 33 28 734 784 216 950 32 29 774 828 172 946 31 30 .47 814 .49 872 .50 128 .97 942 30 31 854 916 084 938 29 32 894 960 040 934 28 33 934 50 004 49 996 930 27 34 974 048 952 926 26 35 .48 014 .50 092 .49 908 .97 922 25 36 054 136 864 918 24 37 094 ISO 820 914 23 38 133 223 777 910 22 39 173 267 733 906 21 40 .48 213 .50 311 .49 689 .97 902 20 41 252 355 645 898 19 42 292 398 602 894 18 43 332 442 558 890 17 44 371 485 515 886 16 45 .48 411 .50 529 .49 471 .97 882 15 46 450 572 428 878 14 47 490 616 384 874 13 48 529 659 341 870 12 49 568 703 297 866 11 50 .48 607 .50 746 .49 254 .97 861 10 51 647 789 211 857 9 52 686 833 167 853 8 53 725 876 124 849 7 54 764 919 081 845 6 56 .48 803 .50 962 .49 038 .97 841 5 56 842 51005 48 995 837 4 57 881 048 952 833 3 58 920 092 908 829 2 59 959 135 865 825 1 60 .48 998 .51178 .48 822 .97 821 9-10 9-10 9-10 f log cos log cot log tan log sin f 18' 1 log sin log tan log cot log cos t 9-10 9-10 9-10 .48 998 .51178 .48 822 .97 821 60 1 49 037 221 779 817 59 2 076 264 736 812 58 3 115 306 694 808 57 4 153 349 651 804 56 5 .49 192 .51392 .48 608 .97 800 55 6 231 435 565 796 54 7 269 478 522 792 53 8 308 520 480 788 52 9 347 563 437 784 51 10 .49 385 .51606 .48 394 .97 779 50 11 424 648 352 775 49 12 462 691 309 771 48 13 500 734 266 767 47 14 539 776 224 763 46 15 .49 577 .51 819 .48 181 .97 759 45 16 615 861 139 754 44 17 654 903 097 750 43 18 692 946 054 746 42 19 730 988 012 742 41 20 .49 768 .52 031 .47 969 .97 738 40 21 806 073 927 734 39 22 844 115 885 729 38 23 882 157 843 725 37 24 920 200 800 721 36 25 .49 958 .52 242 .47 758 .97 717 35 26 996 284 716 713 34 27 50 034 326 674 708 33 28 072 368 632 704 32 29 110 410 590 700 31 30 .50 148 .52 452 .47 548 .97 696 30 31 185 494 506 691 29 32 223 536 464 687 28 33 261 578 422 683 27 34 298 620 380 679 26 35 .50 336 .52 661 .47 339 .97 674 25 36 374 703 297 670 24 37 411 745 255 666 23 38 449 787 213 662 22 39 486 829 171 657 21 40 .50 523 .52 870 .47 130 .97 653 20 41 561 912 088 649 19 42 598 953 047 645 18 43 635 995 005 640 17 44 673 53 037 46 963 636 16 45 .50 710 .53 078 .46 922 .97 632 15 46 747 120 880 628 14 47 784 161 839 623 13 48 821 202 798 619 12 49 858 244 756 615 11 50 .50 896 .53 285 .46 715 .97 610 10 51 933 327 673 606 9 52 970 368 632 602 8 53 51007 409 591 597 7 54 043 450 550 593 6 55 .51 080 .53 492 .46 508 .97 589 6 56 117 533 467 584 4 57 154 574 426 580 3 58 191 615 385 576 2 59 227 656 344 571 1 60 .51 264 .53 697 .46 303 .97 567 9-10 9-10 9-10 1 log cos log cot log tan log sin t 72° 7r 19^ f log sin log tan log cot log cos t 9-10 9-10 9-10 .51 264 .53 697 .46 303 .97 567 60 1 301 738 262 563 59 2 338 779 221 558 58 3 374 820 180 554 57 4 411 861 139 550 56 6 .51447 .53 902 .46 098 .97 545 55 6 484 943 057 541 54 7 520 984 016 536 53 8 557 54 025 45 975 532 52 9 593 065 935 528 51 10 .51629 .54 106 .45 894 .97 523 50 11 666 147 853 519 49 12 702 187 813 515 48 13 738 228 772 510 47 14 774 269 731 506 46 15 .51811 .54 309 .45 691 .97 501 45 16 847 350 650 497 44 17 883 390 610 492 43 18 919 431 569 488 42 19 955 471 529 484 41 20 .51 991 .54 512 .45 488 .97 479 40 21 52 027 552 448 475 39 22 063 593 407 470 38 23 099 633 367 466 37 24 135 673 327 461 36 25 .52 171 .54 714 .45 286 .97 457 35 26 207 754 246 453 34 27 242 794 206 448 33 28 278 835 165 444 32 29 314 875 125 439 31 30 .52 350 .54 915 .45 085 .97 435 30 31 385 955 045 430 29 32 421 995 005 426 28 33 456 55 035 44 965 421 27 34 492 075 925 417 26 35 .52 527 .55 115 .44 885 .97 412 25 36 563 155 845 408 24 37 598 195 805 403 23 38 634 235 765 399 22 39 669 275 725 394 21 40 .52 705 .55 315 .44 685 .97 390 20 41 740 355 645 385 19 42 775 395 605 381 18 43 811 434 566 376 17 44 846 474 526 372 16 45 .52 881 .55 514 .44 486 .97 367 15 46 916 554 446 363 14 47 951 593 407 358 13 48 986 633 367 353 12 49 53 021 673 327 349 11 50 .53 056 .55 712 .44 288 .97 344 10 51 092 752 248 340 9 52 126 791 209 335 8 53 161 . 831 169 331 7 54 196 870 130 326 6 55 .53 231 .55 910 .44 090 .97 322 5 56 266 949 051 317 4 57 301 989 Oil 312 3 58 336 56 028 43 972 308 2 59 370 067 933 303 1 60 .53 405 .56 107 .43 893 .97 299 9-10 9-10 9-10 r log cos log cot log tan log sin f 20 33 t log sin log tan log cot log cos f 9-10 9-10 9-10 .53 405 .56 107 .43 893 .97 299 60 1 440 146 854 294 59 2 475 185 815 289 58 3 509 224 776 285 57 4 544 264 736 280 56 5 .53 578 .56 303 .43 697 .97 276 55 6 613 342 658 271 54 7 647 381 619 266 53 8 682 420 580 262 52 9 716 459 541 257 51 10 .53 751 .56 498 .43 502 .97 252 50 11 785 537 463 248 49 12 819 576 424 243 48 13 854 615 385 238 47 14 888 654 346 234 46 15 .53 922 .56 693 .43 307 .97 229 45 16 957 732 268 224 44 17 991 771 229 220 43 18 54 025 810 190 215 42 19 059 849 151 210 41 20 .54 093 .56 887 .43 113 .97 206 40 21 127 926 074 201 39 22 161 965 035 196 38 23 195 57 004 42 996 192 37 24 229 042 958 187 36 25 .54 263 .57 081 .42 919 .97 182 35 26 297 120 880 178 34 27 331 158 842 173 33 28 365 197 803 168 32 29 399 235 765 163 31 30 .54 433 .57 274 .42 726 .97 159 30 31 466 312 688 154 29 32 500 351 649 149 28 33 534 389 611 145 27 34 567 428 572 140 26 35 .54 601 .57 466 .42 534 .97 135 25 36 635 504 496 130 24 37 668 543 457 126 23 38 702 581 419 121 22 39 735 619 381 116 21 40 .54 769 .57 658 .42 342 .97 111 20 41 802 696 304 107 19 42 836 734 266 102 18 43 869 772 228 097 17 44 903 810 190 092 16 45 .54 936 .57 849 .42 151 .97 087 15 46 969 887 113 083 14 47 55 003 925 075 078 13 48 036 963 037 073 12 49 069 58 001 41999 068 11 50 .55 102 .58 039 .41 961 .97 063 10 51 136 077 923 059 9 52 169 115 885 054 8 53 202 153 847 049 7 54 235 191 809 044 6 55 .55 268 .58 229 .41 771 .97 039 5 56 301 267 733 035 4 57 334 304 696 030 3 58 367 342 658 025 2 59 400 380 620 020 1 60 .55 433 .58 418 .41 582 .97 015 9-10 9-10 9-10 f log cos log cot log tan log sin 1 70° 69° 34 21° f log sin log tan log cot log cos f 9-10 .55 433 9-10 .58 418 .41582 9-10 .97 015 60 1 466 455 545 010 59 2 499 493 507 005 58 3 532 531 469 001 57 4 564 569 431 96 996 56 5 .55 597 .58 606 .41 394 .96 991 55 6 630 644 356 986 54 7 663 681 319 981 53 8 695 719 281 976 52 9 728 757 243 971 51 10 .55 761 .58 794 .41 206 .96 966 50 11 793 832 168 962 49 12 826 869 131 957 48 13 858 907 093 952 47 14 891 944 056 947 46 15 .55 923 .58 981 .41019 .96 942 45 16 956 59 019 40 981 937 44 17 988 056 944 932 43 18 56 021 094 906 927 42 19 053 131 869 922 41 20 .56 085 .59 168 .40 832 .96 917 40 21 118 205 795 912 39 22 150 243 757 907 38 23 182 280 720 903 37 24 215 317 683 898 36 25 .56 247 .59 354 .40 646 .96 893 . 35 26 279 391 609 888 34 27 311 429 571 883 33 28 343 466 534 878 31 29 375 503 497 873 31 30 ..%408 .59 540 .40 460 .96 868 30 31 440 577 423 863 29 32 472 614 386 858 28 33 504 651 349 853 27 34 536 688 312 848 26 35 .56 568 .59 725 .40 275 .96 843 25 36 599 762 238 838 24 37 631 799 201 833 23 38 663 835 165 828 22 39 695 872 128 823 21 40 .56 727 .59 909 .40 091 .96 818 20 41 759 946 054 813 19 42 790 983 017 808 18 43 822 60 019 39 981 803 17 44 854 056 944 798 16 45 .56 886 .60 093 .39 907 .96 793 15 46 917 130 870 788 14 47 949 166 834 783 13 48 980 203 797 778 12 49 57 012 240 760 772 11 50 .57 044 .60 276 .39 724 .96 767 10 51 075 ■ 313 687 762 9 52 107 349 651 757 8 53 138 386 614 752 7 54 169 422 578 747 6 55 .57 201 .60 459 .39 541 .96 742 5 56 232 495 505 737 4 57 264 532 468 732 3 58 295 568 432 727 2 59 326 605 395 722 1 60 .57 358 .60 641 .39 359 .96 717 9-10 9-10 9-10 f log cos log cot log tan log sin f 22° f log sin log tan log cot log cos r 9-10 9-10 9-10 .57 358 .60 641 .39 359 .96 717 60 1 389 677 323 711 59 2 420 714 286 706 58 3 451 750 250 701 57 4 482 786 214 696 56 5 .57 514 .60 823 .39 177 .96 691 55 6 545 859 141 686 54 7 576 895 105 681 53 8 607 931 069 676 52 9 638 967 033 670 51 10 .57 669 .61004 .38 996 .96 665 50 11 700 040 960 660 49 12 731 076 924 655 48 13 762 112 888 650 47 14 793 148 852 645 46 15 .57 824 .61 184 .38 816 .96 640 45 16 855 220 780 634 44 17 885 256 744 629 43 18 916 292 708 624 42 19 947 328 672 619 41 20 .57 978 .61 364 .38 636 .96 614 40 21 58 008 400 600 608 39 22 039 436 564 603 38 23 070 472 528 598 37 24 101 508 492 593 36 25 .58 131 .61 544 .38 456 .96 588 35 26 162 579 421 582 34 27 192 615 385 577 33 28 223 651 349 572 32 29 253 687 313 567 31 30 .58 284 .61 722 .38 278 .96 562 30 31 314 758 242 556 29 32 345 794 206 551 28 33 375 830 170 546 27 34 406 865 135 541 26 35 .58 436 .61 901 .38 099 .96 535 25 36 467 936 064 530 24 37 497 972 028 525 23 38 527 62 008 37 992 520 22 39 557 043 957 514 21 40 .58 588 .62 079 .37 921 .96 509 20 41 618 114 886 504 19 42 648 150 850 498 18 43 678 185 815 493 17 44 709 221 779 488 16 45 .58 739 .62 256 .37 744 .96 483 15 46 769 292 708 477 14 47 799 327 673 472 13 48 829 362 638 467 12 49 859 398 602 461 11 50 .58 889 .62 433 .37 567 .96456 10 51 919 468 532 451 9 52 949 504 496 445 8 53 979 539 461 440 7 54 59 009 574 426 435 6 55 .59 039 .62 609 .37 391 .96 429 5 56 069 645 355 424 4 57 098 680 320 419 3 58 128 715 285 413 2 59 158 750 250 408 1 60 .59 188 .62 785 .37 215 .96 403 9-10 log cos 9-10 log cot log tan 9-10 log sin f f 68' 67° 23^ f log sin log tan log cot log cos f 9-10 9-10 9-10 .59 188 .62 785 .37 215 .96 403 60 1 218 820 180 397 59 2 247 855 145 392 58 3 277 890 110 387 57 4 307 926 074 381 56 6 .59 336 .62 961 .37 039 .96 376 55 6 366 996 004 370 54 7 396 63 031 36 969 365 53 8 425 066 934 360 52 9 455 101 899 354 51. 10 .59 484 .63 135 .36 865 .96 349 50 11 514 170 830 343 49 12 543 205 795 338 48 13 573 240 760 333 47 14 602 275 725 327 46 15 .59 632 .63 310 .36 690 .96 322 45 16 661 345 655 316 44 17 690 379 621 311 43 18 720 414 586 305 42 19 749 449 551 300 41 20 .59 778 .63 484 .36 516 .96 294 40 21 808 519 481 289 39 22 837 553 447 284 38 23 866 588 412 278 37 24 895 623 377 273 36 25 .59 924 .63 657 .36 343 .96 267 35 26 954 692 308 262 34 27 983 726 274 256 33 28 60 012 761 239 251 32 29 041 796 204 245 31 30 .60 070 .63 830 .36 170 .96 240 30 31 099 865 135 234 29 32 128 899 101 229 28 33 157 934 066 223 27 34 186 968 032 218 26 35 .60 215 .64 003 .35 997 .96 212 25 36 244 037 963 207 24 37 273 072 928 201 23 38 302 106 894 196 22 .39 331 140 860 190 21 40 .60 359 .64 175 .35 825 .96 185 20 41 388 209 791 179 19 42 417 243 757 174 18 43 446 278 722 168 17 44 474 312 688 162 16 45 .60 503 .64 346 .35 654 .96157 15 46 532 381 619 151 14 47 561 415 585 146 13 48 589 449 551 140 12 49 618 483 517 135 11 50 .60 646 .64 517 .35 483 .96 129 10 51 675 552 448 123 9 52 704 586 414 118 8 53 732 620 380 112 7 54 761 654 346 107 6 55 .60 789 .64 688 .35 312 .96 101 5 56 818 722 278 095 4 57 846 756 244 090 3 58 875 790 210 084 2 59 903 824 176 079 1 60 .60 931 .64 858 .35 142 .96 073 9-10 9-10 9-10 f log cos log cot log tan log sin f 24° 35 f log sin log tan log cot log cos 1 9-10 9-10 9-10 .60 931 .64 858 35 142 .96 073 60 1 960 892 108 067 59 2 988 926 074 062 58 3 61016 960 040 056 57 4 045 994 006 050 56 5 .61 073 .65 028 .34 972 .96 045 55 6 101 062 938 039 54 7 129 096 904 034 53 8 158 130 870 028 52 9 186 164 836 022 51 10 .61 214 .65 197 .34 803 .96 017 50 11 242 231 769 Oil 49 12 270 265 735 005 48 13 298 299 701 000 47 14 326 333 667 95 994 46 15 .61 354 .65 366 .34 634 .95 988 45 16 382 400 600 982 44 17 411 434 566 977 43 18 438 467 533 971 42 19 466 501 499 965 41 20 .61 494 .65 535 .34 465 .95 960 40 21 522 568 432 954 39 22 550 602 398 948 38 23 578 636 364 942 37 24 606 669 331 937 36 25 .61 634 .65 703 .34 297 .95 931 35 26 662 736 264 925 34 27 689 770 230 920 33 28 717 803 197 914 32 29 745 837 163 908 31 30 .61 773 .65 870 .34 130 .95 902 30 31 800 904 096 897 29 32 828 937 063 891 28 33 856 971 029 885 27 34 883 66 004 33 996 879 26 35 .61911 .66 038 .33 962 .95 873 25 36 939 071 929 868 24 37 966 104 896 862 23 38 994 138 862 856 22 39 62 021 171 829 850 21 40 .62 049 .66 204 .33 796 .95 844 20 41 076 238 762 839 19 42 104 271 729 833 18 43 131 304 696 827 17 44 159 337 663 821 16 45 .62 186 .66 371 .33 629 .95 815 15 46 214 404 596 810 14 47 241 437 563 804 13 48 268 470 530 798 12 49 296 503 497 792 11 50 .62 323 .66 537 .33 463 .95 786 10 51 350 570 430 780 9 52 377 603 397 775 8 53 405 636 364 769 7 54 432 669 331 763 6 55 .62 459 .66 702 .33 298 .95 757 5 56 486 735 265 751 4 57 513 768 232 745 3 58 541 801 199 739 2 59 568 834 166 733 1 60 .62 595 .66 867 .33 133 .95 728 9-10 9-10 9-10 1 log cos log cot log tan log sin r 66° 65^ 36 25° 1 log sin log tan log cot log cos t 9-10 9-10 9-10 .62 595 .66 867 .33 133 .95 728 60 1 622 900 100 722 59 2 649 933 067 716 58 3 676 966 034 710 57 4 703 999 001 704 56 5 .62 730 .67 032 .32 968' .95 698 55 6 757 065 935 692 54 7 784 098 902 686 53 8 811 131 869 680 52 9 838 163 837 674 51 10 .62 865 .67 196 .32 804 .95 668 50 11 892 229 771 663 49 12 918 262 738 657 48 13 945 295 705 651 47 14 972 327 673 645 46 15 .62 999 .67 360 .32 640 .95 639 45 16 63 026 393 607 633 44 17 052 426 574 627 43 18 079 458 542 621 42 19 106 491 509 615 41 20 .63 133 .67 524 .32 476 .95 609 40 21 159 556 444 603 39 22 186 589 411 597 38 23 213 622 378 591 37 24 239 654 346 585 36 25 .63 266 .67 687 .32 313 .95 579 35 26 292 719 281 573 34 27 319 752 248 567 33 28 345 785 215 561 32 29 372 817 183 555 31 80 .63 398 .67 850 .32 150 .95 549 30 31 425 882 118 543 29 32 451 915 085 537 28 33 478 947 053 531 27 34 504 980 020 525 26 35 .63 531 .68 012 .31988 .95 519 25 36 557 044 956 513 24 37 583 077 923 507 23 38 610 109 891 500 22 39 636 142 858 494 21 40 .63 662 .68 174 .31 826 .95 488 20 41 689 206 794 482 19 42 715 239 761 476 18 43 741 271 729 470 17 44 767 303 697 464 16 45 .63 794 .68 336 .31 664 .95 458 15 46 820 368 632 452 14 47 846 400 600 446 13 48 872 432 568 440 12 49 898 465 535 434 11 60 .63 924 .68 497 .31 503 .95 427 10 51 950 529 471 421 9 52 976 561 439 415 8 53 64 002 593 407 409 7 54 028 626 374 403 6 55 .64 054 .68 658 .31342 .95 397 5 56 080 690 310 391 4 57 106 722 278 384 3 58 132 754 246 378 2 59 158 786 214 372 1 60 .64 184 .68 818 .31 182 .95 366 9-10 9-10 9-10 t log cos log cot log tan log sin f 26° 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .64 184 .68 818 .31 182 .95 366 60 1 210 850 150 360 59 2 236 882 118 354 58 3 262 914 086 348 57 4 288 946 054 341 56 5 .64 313 .68 978 .31022 .95 335 55 6 339 69 010 30 990 329 54 7 365 042 958 323 53 8 391 074 926 317 52 9 417 106 894 310 51 10 .64 442 .69 138 .30 862 .95 304 50 11 468 170 830 298 49 12 494 202 798 292 48 13 519 234 766 286 47 14 545 266 734 279 46 15 .64 571 .69 298 .30 702 .95 273 45 16 596 329 671 267 44 17 622 361 639 261 43 18 647 393 607 254 42 19 673 425 575 248 41 20 .64 698 .69 457 .30 543 .95 242 40 21 724 488 512 236 39 22 749 520 480 229 38 23 775 552 448 223 37 24 800 584 416 217 36 25 .64 826 .69 615 .30 385 .95 211 35 26 851 647 353 204 34 27 877 679 321 198 33 28 902 710 290 192 32 29 927 742 258 185 31 30 .64 953 .69 774 .30 226 .95 179 30 31 978 805 195 173 29 32 65 003 837 163 167 28 33 029 868 132 160 27 34 054 900 100 154 26 35 .65 079 .69 932 .30 068 .95 148 25 36 104 963 037 141 24 37 130 995 005 135 23 38 155 70 026 29 974 129 22 39 180 058 942 122 21 40 .65 205 .70 089 .29 911 .95 116 20 41 230 121 879 110 19 42 255 152 848 103 18 43 281 184 816 097 17 44 306 215 785 090 16 45 .65 331 .70 247 .29 753 .95 084 16 46 356 278 722 078 14 47 381 309 691 071 13 48 406 341 659 065 12 49 431 372 628 059 U 50 .65 456 .70 404 .29 596 .95 052 10 51 481 435 565 046 9 52 506 466 534 039 8 53 531 498 502 033 7 54 556 529 471 . 027 6 55 .65 580 .70 560 .29 440 .95 020 6 56 605 592 408 014 4 57 630 623 377 007 3 58 655 654 346 001 2 59 680 685 315 94 995 1 60 .65 705 .70 717 .29 283 .94 988 9-10 9-10 9-10 t log cos log cot log tan log sin f 64° 63^ 2T ) log sin log tan log cot log cos 9-10 9-10 9-10 1 .65 705 .70 717 .29 283 .94 988 60 1 729 748 252 982 59 2 754 779 221 975 58 3 779 810 190 969 57 4 804 841 159 962 56 5 .65 828 .70 873 .29 127 .94 956 55 6 853 904 096 949 54 7 878 935 065 943 53 8 902 966 034 936 52 9 927 997 003 930 51 10 .65 952 .71028 .28 972 .94 923 50 11 976 059 941 917 49 12 66 001 090 910 911 48 13 025 121 879 904 47 14 050 153 847 898 46 15 .66 075 .71 184 .28 816 .94 891 45 16 099 215 785 885 44 17 124 246 754 878 43 18 148 277 723 871 42 19 173 308 692 865 41 20 .66 197 .71 339 .28 661 .94 858 40 21 221 370 630 852 39 22 246 401 599 845 38 23 270 431 569 839 37 24 295 462 538 832 36 25 .66 319 .71493 .28 507 .94 826 35 26 343 524 476 819 34 27 368 555 445 813 33 28 392 586 414 806 32 29 416 617 383 799 31 30 .66 441 .71 648 .28 352 .94 793 30 31 465 679 321 786 29 32 489 709 291 780 28 33 513 740 260 773 27 34 537 771 229 767 26 35 .66 562 .71 802 .28 198 .94 760 25 36 586 833 167 753 24 37 610 863 137 747 23 38 634 894 106 740 22 39 658 925 075 734 21 40 .66 682 .71 955 .28 045 .94 727 20 41 706 986 014 720 19 42 731 72 017 27 983 714 18 43 755 048 952 707 17 44 779 078 922 700 16 45 .66 803 .72 109 .27 891 .94 694 15 46 827 140 860 687 14 47 851 170 830 680 13 48 875 201 799 674 12 49 899 231 769 667 11 50 .66 922 .72 262 .27 738 .94 660 10 51 946 293 707 654 9 52 970 323 677 647 8 53 994 354 646 640 7 54 67 018 384 616 634 6 55 .67 042 .72 415 .27 585 .94 627 5 56 066 445 555 620 4- 57 090 476 524 614 3 58 113 506 494 607 2 59 137 537 463 600 1 60 f .67 161 .72 567 .27 433 .94 593 9-10 9-10 9-10 log cos log cot log tan log sin 1 28° 37 t log sin log tan log cot log cos 1 9-10 9-10 9-10 .67 161 .72 567 .27 433 .94 593 60 1 185 598 402 587 59 2 208 628 372 580 58 3 232 659 341 573 57 4 256 689 311 567 56 5 .67 280 .72 720 .27 280 .94 560 55 6 303 750 250 553 54 7 327 780 220 546 53 8 350 811 189 540 52 9 374 841 159 533 51 10 .67 398 .72 872 .27 128 .94 526 50 11 421 902 098 519 49 12 445 932 068 513 48 13 468 963 037 506 47 14 492 993 007 499 46 15 .67 515 .73 023 .26 977 .94 492 45 16 539 054 946 485 44 17 562 084 916 479 43 18 586 114 886 472 42 19 609 144 856 465 41 20 .67 633 .73 175 .26 825 .94 458 40 21 656 205 795 451 39 22 680 235 765 445 38 23 703 265 735 438 37 24 726 295 705 431 36 25 .67 750 .73 326 .26 674 .94 424 35 26 773 356 644 417 34 27 796 386 614 410 33 28 820 416 584 404 32 29 843 446 554 397 31 30 .67 866 .73 476 .26 524 .94 390 30 31 890 507 493 383 29 32 913 537 463 376 28 33 936 567 433 369 27 34 959 597 403 362 26 35 .67 982 .73 627 .26 373 .94 355 25 36 68 006 657 343 349 24 37 029 687 313 342 23 38 052 717 283 335 22 39 075 747 253 328 21 40 .68 098 .73 777 .26 223 .94 321 20 41 121 807 193 314 19 42 144 837 163 307 18 43 167 867 133 300 17 44 190 897 103 293 16 45 .68 213 .73 927 .26 073 .94 286 15 46 237 957 043 279 14 47 260 987 013 273 13 48 283 74 017 25 983 266 12 49 305 047 953 259 11 50 .68 328 .74 077 .25 923 .94 252 10 51 351 107 893 245 9 52 374 137 863 238 8 53 397 166 834 231 7 54 420 196 804 224 6 55 .68 443 .74 226 .25 774 .94 217 5 56 466 256 744 210 4 57 489 286 714 203 3 58 512 316 684 196 2 59 534 345 655 189 1 60 .68 557 .74 375 .25 625 .94 182 9-10 9-10 9-10 1 log cos log cot log tan log sin f 63° 61' 38 29° t log sin log tan log cot log cos f 9-10 9-10 9-10 .68 557 .74 375 .25 625 .94 182 60 1 580 405 595 175 59 2 603 435 565 168 58 3 625 465 535 161 57 4 648 494 506 154 56 5 .68 671 .74 524 .25 476 .94 147 55 6 694 554 446 140 54 7 716 583 417 133 53 8 739 613 387 126 52 9 762 643 357 119 51 10 .68 784 .74 673 .25 327 .94112 50 11 807 702 298 105 49 12 829 732 268 098 48 13 852 762 238 090 47 14 875 791 209 083 46 15 .68 897 .74 821 .25 179 .94 076 45 16 920 851 149 069 44 17 942 880 120 062 43 18 965 910 090 055 42 19 987 939 061 048 41 20 .69 010 .74 969 .25 031 .94 041 40 21 032 998 002 034 39 22 055 75 028 24 972 027 38 23 077 058 942 020 37 24 100 087 913 012 36 25 .69122 .75 117 .24 883 .94 005 35 26 144 146 854 93 998 34 27 167 176 824 991 33 28 189 205 795 984 32 29 212 235 765 977 31 30 .69 234 .75 264 .24 736 .93 970 30 31 256 294 706 963 29 32 279 323 677 955 28 33 301 353 647 948 27 34 323 382 618 941 26 35 .69 345 .75 411 .24 589 .93 934 25 36 368 441 559 927 24 37 • 390 470 530 920 23 38 412 500 500 912 22 39 434 529 471 905 21 40 .69 456 .75 558 .24 442 .93 898 20 41 479 588 412 891 19 42 501 617 383 884 18 43 523 647 353 876 17 44 545 676 324 869 16 45 .69 567 .75 705 .24 295 .93 862 15 46 589 735 265 855 14 47 611 764 236 847 13 48 633 793 207 840 12 49 655 822 178 833 11 50 .69 677 .75 852 .24 148 .93 826 10 51 699 881 119 819 9 52 721 910 090 811 8 53 743 939 061 804 7 54 765 969 031 797 6 55 .69 787 .75 998 .24 002 .93 789 5 56 809 76 027 23 973 782 4 57 831 056 944 775 3 58 853 086 914 768 2 59 875 115 885 760 1 60 .69 897 .76 144 .23 856 .93 753 9-10 9-10 9-10 t log cos log cot log tan log sin f 30' f log sin log tan log cot log cos t 9-10 9-10 9-10 .69 897 .76 144 .23 856 .93 753 60 1 919 173 827 746 59 2 941 202 798 738 58 3 963 231 769 731 57 4 984 261 739 724 56 5 .70 006 .76 290 .23 710 .93 717 55 6 028 319 681 709 54 7 050 348 652 702 53 8 072 377 623 695 52 9 093 406 594 687 51 10 .70115 .76 435 .23 565 .93 680 50 11 137 464 536 673 49 12 159 493 507 665 48 13 180 522 478 658 47 14 202 551 449 650 46 15 .70 224 .76 580 .23 420 .93 643 45 16 245 609 391 636 44 17 267 639 361 628 43 18 288 668 332 621 42 19 310 697 303 614 41 20 .70 332 .76 725 .23 275 .93 606 40 21 353 754 246 599 39 22 375 783 217 591 38 23 396 812 188 584 37 24 418 841 159 577 36 25 .70 439 .76 870 .23 130 .93 569 35 26 461 899 101 562 34 27 482 928 072 554 33 28 504 957 043 547 32 29 525 986 014 539 31 30 .70 547 .77 015 .22 985 .93 532 30 31 568 044 956 525 29 32 590 073 927 517 28 33 611 101 899 510 27 34 633 130 870 502 26 35 .70 654 .77 159 .22 841 .93 495 25 36 675 188 812 487 24 37 697 217 783 480 23 38 718 246 754 472 22 39 739 274 726 465 21 40 .70 761 .77 303 .22 697 .93 457 20 41 782 332 668 450 19 42 803 361 639 442 18 43 824 390 . 610 435 17 44 846 418 582 427 16 45 .70 867 .77 447 .22 553 .93 420 15 46 888 476 524 412 14 47 909 505 495 405 13 48 931 533 467 397 12 49 952 562 438 390 11 50 .70 973 .77 591 .22 409 .93 382 10 51 994 619 381 375 9 52 71015 648 352 367 8 53 036 677 323 360 7 54 058 706 294 352 6 55 .71 079 .77 734 .22 266 .93 344 5 56 100 763 237 337 4 57 121 791 209 329 3 58 142 820 180 322 2 59 163 849 151 314 1 60 .71 184 .77 877 .22 123 .93 307 9-10 9-10 9-10 t log cos log cot log tan log sin t 60^ 59° 31° t log sin log tan log cot log cos t f 9-10 9-10 9-10 .71 184 .77 877 .22 123 .93 307 60 1 205 906 094 299 59 2 226 935 065 291 58 3 247 963 037 284 57 4 268 992 008 276 56 5 .71289 .78 020 .21980 .93 269 65 6 310 049 951 261 54 7 331 077 923 253 53 8 352 106 894 246 52 9 373 135 865 238 51 10 .71 393 .78 163 .21 837 .93 230 60 11 414 192 808 223 49 12 435 220 780 215 48 13 456 249 751 207 47 14 477 277 723 200 46 16 .71 498 .78 306 .21 694 .93 192 46 16 519 334 666 184 44 17 539 363 637 177 43 18 560 391 609 169 42 19 581 419 581 161 41 20 .71602 .78 448 .21552 .93 154 40 21 622 476 524 146 39 22 643 505 495 138 38 23 664 533 467 131 37 24 685 562 438 123 36 25 .71705 .78 590 .21410 .93 115 36 26 726 618 382. 108 34 27 747 647 353 100 33 28 767 675 325 092 32 29 788 704 296 084 31 30 .71 809 .78 732 .21 268 .93 077 30 31 829 760 240 069 29 32 850 789 211 061 28 33 870 817 183 053 27 34 891 845 155 046 26 35 .71911 .78 874 .21126 .93 038 26 36 932 902 098 030 24 37 952 930 070 022 23 38 973 959 041 014 22 39 994 987 013 007 21 40 .72 014 .79 015 .20 985 .92 999 20 41 034 043 957 991 19 42 055 072 928 983 18 43 075 100 900 976 17 44 096 128 872 968 16 45 .72 116 .79156 .20 844 .92 960 16 46 137 185 815 952 14 47 157 213 787 944 13 48 177 241 759 936 12 49 198 269 731 929 11 50 .72 218 .79 297 .20 703 .92 921 10 51 238 326 674 913 9 52 259 354 646 905 8 53 279 382 618 897 7 54 299 410 590 889 6 55 .72 320 .79 438 .20 562 .92 881 5 56 340 466 534 874 4 57 360 495 505 866 3 58 381 523 477 858 2 59 401 551 449 850 1 60 .72 421 .79 579 .20 421 .92 842 9-10 9-10 9-10 f log cos log cot log tan log sin t 32° 39 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .72 421 .79 579 .20 421 .92 842 60 1 441 607 393 834 59 2 461 635 365 826 58 3 482 663 337 818 57 4 502 691 309 810 56 6 .72 522 .79 719 .20 281 .92 803 66 6 542 747 253 795 54 7 562 776 224 787 53 8 582 804 196 779 52 9 602 832 168 771 51 10 .72 622 .79 860 .20 140 .92 763 60 11 643 888 112 755 49 12 663 916 084 747 48 13 683 944 056 739 47 14 703 972 028 731 46 15 .72 723 .80 000 .20000 .92 723 45 16 743 028 19 972 715 44 17 763 056 944 707 43 18 783 084 916 699 42 19 803 112 888 691 41 20 .72 823 .80140 .19 860 .92 683 40 21 843 168 832 675 39 22 863 195 805 667 38 23 883 223 777 659 37 24 902 251 749 651 36 26 .72 922 .80 279 .19 721 .92 643 36 26 942 307 693 635 34 27 962 335 665 627 33 28 982 363 637 619 32 29 73 002 391 609 611 31 30 .73 022 .80 419 .19 581 .92 603 30 31 041 447 553 595 29 32 061 474 526 587 28 33 081 502 498 579 27 34 101 530 470 571 26 36 .73 121 .80 558 .19 442 .92 563 26 36 140 586 414 555 24 37 160 614 386 546 23 38 180 642 358 538 22 39 200 669 331 530 21 40 .73 219 .80 697 .19 303 .92 522 20 41 239 725 275 514 19 42 259 753 247 506 18 43 278 781 219 498 17 44 298 808 192 490 16 46 .73 318 .80 836 .19 164 .92 482 16 46 337 864 136 473 14 47 357 892 108 465 13 48 377 919 081 457 12 49 396 947 053 449 11 60 .73 416 .80 975 .19 025 .92 441 10 51 435 81003 18 997 433 9 52 455 030 970 425 8 53 474 058 942 416 7 54 494 086 914 408 6 65 .73 513 .81113 .18 887 .92 400 6 56 533 141 859 392 4 57 552 169 831 384 3 58 572 196 804 376 2 59 591 224 776 367 1 60 .73 611 .81 252 .18 748 .92 359 9-10 9-10 9-10 1 log cos log cot log tan log sin 1 58' 57< 40 33° f log sin log tan log cot log cos 1 9-10 9-10 9-10 .73 611 .81252 .18 748 .92 359 60 1 630 279 721 351 59 2 650 307 693 343 58 3 669 335 665 335 57 4 689 362 638 326 56 5 .73 708 .81390 .18 610 .92 318 55 6 727 418 582 310 54 7 747 445 555 302 53 8 766 473 527 293 52 9 785 500 500 285 51 10 .73 805 .81528 .18 472 .92 277 50 11 824 556 444 269 49 12 843 583 417 260 48 13 863 611 389 252 47 14 882 638 362 244 46 15 .73 901 .81666 .18 334 .92 235 45 16 921 693 307 227 44 17 940 721 279 219 43 18 959 748 252 211 42 19 978 776 224 202 41 20 .73 997 .81 803 .18 197 .92 194 40 21 74 017 831 169 186 39 22 036 858 142 177 38 23 055 886 114 169 37 24 074 913 087 161 36 25 .74 093 .81 941 .18 059 .92 152 35 26 113 968 032 144 34 27 132 996 004 136 33 28 151 82 023 17 977 127 32 29 170 051 949 119 31 30 .74 189 .82 078 .17 922 .92 111 30 31 208 106 894 102 29 32 227 133 867 094 28 33 246 161 839 086 27 34 265 188 812 077 26 35 .74 284 .82 215 .17 785 .92 069 25 36 303 243 757 060 24 37 322 270 730 052 23 38 341 298 702 044 22 39 360 325 675 035 21 40 .74 379 .82 352 .17 648 .92 027 20 41 398 380 620 018 19 42 417 407 593 010 18 43 436 435 565 002 17 44 455 462 538 91993 16 45 .74 474 .82 489 .17 511 .91985 15 46 493 517 483 976 14 47 512 544 456 968 13 48 531 571 429 959 12 49 549 599 401 951 11 50 .74 568 .82 626 .17 374 .91942 10 51 587 653 347 934 9 52 606 681 319 925 8 53 625 708 292 917 7 54 644 735 265 908 6 55 .74 662 .82 762 .17 238 .91 900 5 56 681 790 210 891 4 57 700 817 183 883 3 58 719 844 156 874 2 59 737 871 129 866 1 60 .74 756 .82 899 .17 101 .91857 9-10 9-10 9-10 1 log cos log cot log tan log sin f 34^ t log sin log tan log cot log cos 1 9-10 9-10 9-10 .74 756 .82 899 .17101 .91 857 60 1 775 926 074 849 59 2 794 953 047 840 58 3 812 980 020 832 57 4 831 83 008 16 992 823 56 5 .74 850 .83 035 .16 965 .91 815 55 6 868 062 938 806 54 7 887 089 911 798 53 8 906 117 883 789 52 9 924 144 856 781 51 10 .74 943 .83 171 .16 829 .91 772 50 11 961 198 802 763 49 12 980 225 775 755 48 13 999 252 748 746 47 14 75 017 280 720 738 46 15 .75 036 .83 307 .16 693 .91 729 45 16 054 334 666 720 44 17 073 361 639 712 43 18 091 388 612 703 42 19 110 415 585 695 41 20 .75 128 .83 442 .16 558 .91 686 40 21 147 470 530 677 39 22 165 497 503 669 38 23 184 524 476 660 37 24 202 551 449 651 36 25 .75 221 .83 578 .16 422 .91 643 35 26 239 605 395 634 34 27 258 632 368 625 33 28 276 659 341 617 32 29 294 686 314 608 31 30 .75 313 .83 713 .16 287 .91 599 30 31 331 740 260 591 29 32 350 768 232 582 28 33 368 795 205 573 27 34 386 822 178 565 26 35 .75 405 .83 849 .16151 .91 556 25 36 423 876 124 547 24 37 441 903 097 538 23 38 '459 930 070 530 22 39 478 957 043 521 21 40 .75 496 .83 984 .16 016 .91 512 20 41 514 84 011 15 989 504 19 42 533 038 962 495 18 43 551 065 935 486 17 44 569 092 908 477 16 45 .75 587 .84 119 .15 881 .91 469 15 46 605 146 854 460 14 47 624 173 827 451 13 48 642 200 800 442 12 49 660 227 773 433 11 50 .75 678 .84 254 .15 746 .91 425 10 51 696 280 720 416 9 52 714 307 693 407 8 53 733 334 666 398 7 54 751 361 639 389 6 55 .75 769 .84 388 .15 612 .91 381 5 56 787 415 585 372 4 57 805 442 558 363 3 58 823 469 531 354 2 59 841 496 504 345 1 60 .75 859 .84 523 .15 477 .91 336 9-10 9-10 9-10 t log cos log cot log tan log sin 1 56° dd"" 35° 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .75 859 .84 523 .15 477 .91 336 60 1 877 550 450 328 59 2 895 576 424 319 58 3 913 603 397 310 57 4 931 630 370 301 56 5 .75 949 .84 657 .15 343 .91 292 55 6 967 684 316 283 54 7 985 711 289 274 53 8 76 003 738 262 266 52 9 021 764 236 257 51 10 .76 039 .84 791 .15 209 .91 248 50 11 057 818 182 239 49 12 075 845 155 230 48 13 093 872 128 221 47 14 111 899 101 212 46 15 .76 129 .84 925 .15 075 .91 203 45 16 146 952 048 194 44 17 164 979 021 185 43 18 182 85 006 14 994 176 42 19 200 033 967 167 41 20 .76 218 .85 059 .14 941 .91 158 40 21 236 086 914 149 39 22 253 113 887 141 38 23 271 140 860 132 37 24 289 166 834 123 36 25 .76 307 .85 193 .14 807 .91 114 35 26 324 220 780 105 34 27 342 247 753 096 33 28 360 273 727 087 32 29 378 300 700 078 31 30 .76 395 .85 327 .14 673 .91 069 30 31 413 354 646 060 29 32 431 380 620 051 28 33 448 407 593 042 27 34 466 434 566 033 26 35 .76 484 .85 460 .14 540 .91 023 25 36 501 487 513 014 24 37 519 514 486 005 23 38 537 540 460 90 996 22 39 554 567 433 987 21 40 .76 572 .85 594 .14 406 .90 978 20 41 590 620 380 969 19 42 607 647 353 960 18 43 625 674 326 951 17 44 642 700 300 942 16 45 .76 660 .85 727 .14 273 .90 933 15 46 677 754 246 924 14 47 695 780 220 915 13 48 712 807 193 906 12 49 730 834 166 896 11 50 .76 747 .85 860 .14 140 .90 887 10 51 765 887 113 878 9 52 782 913 087 869 8 53 800 940 060 860 7 54 817 967 033 851 6 55 .76 835 .85 993 .14 007 .90 842 5 56 852 86 020 13 980 832 4 57 870 046 954 823 3 58 887 073 927 814 2 59 904 100 900 805 1 60 .76 922 .86 126 .13 874 .90 796 9-10 9-10 Q_in t log cos log cot log tan log sin f 36° 41 t log sin log tan log cot log cos 1 9-10 9-10 9-10 .76 922 .86 126 .13 874 .90 796 60 1 939 153 847 787 59 2 957 179 821 777 58 3 974 206 794 768 57 4 991 232 768 759 56 5 .77 009 .86 259 .13 741 .90 750 55 6 026 285 715 741 54 7 043 312 688 731 53 8 061 338 662 722 52 9 078 365 635 713 51 10 .77 095 .86 392 .13 608 .90 704 50 11 112 418 582 694 49 12 130 445 555 685 48 13 147 471 529 676 47 14 164 498 502 667 46 15 .77 181 .86 524 .13 476 .90 657 45 16 199 551 449 648 44 17 216 577 423 639 43 18 233 603 397 630 42 19 250 630 370 620 41 20 .77 268 .86 656 .13 344 .90 611 40 21 285 683 317 602 39 22 302 709 291 592 38 23 319 736 264 583 37 24 336 762 238 574 36 25 .77 353 .86 789 .13 211 .90 565 35 26 370 815 185 555 34 27 387 842 158 546 33 28 405 868 132 537 32 29 422 894 106 527 31 30 .77 439 .86 921 .13 079 .90 518 30 31 456 947 053 509 29 32 473 974 026 499 28 33 490 87 000 000 490 27 34 507 027 12 973 480 26 35 .77 524 .87 053 .12 947 .90 471 25 36 541 079 921 462 24 37 558 106 894 452 23 38 575 132 868 443 22 39 592 158 842 434 21 40 .77 609 .87185 .12 815 .90 424 20 41 626 211 789 415 19 42 643 238 762 405 18 43 660 264 736 396 17 44 677 290 710 386 16 45 .77 694 .87 317 .12 683 .90 377 15 46 711 343 657 368 14 47 728 369 631 358 13 48 744 396 604 349 12 49 761 422 578 339 11. 50 .77 778 .87 448 .12 552 .90 330 10 51 795 475 525 320 9 52 812 501 499 311 8 53 829 527 473 301 7 54 846 554 446 292 6 55 .77 862 .87 580 .12 420 .90 282 5 56 879 606 394 273 4 57 896 633 367 263 3 58 913 659 341 254 2 59 930 685 315 244 1 60 .77 946 .87 711 .12 289 .90 235 9-10 9-10 9-10 f log cos log cot log tan log sin f 5¥ 53' 42 37° f log sin log tan log cot log cos ' 9-10 9-10 9-10* .77 946 .87 711 .12 289 .90 235 60 1 963 738 262 225 59 2 980 764 236 216 58 3 997 790 210 206 57 4 78 013 817 183 197 56 5 .78 030 .87 843 .12 157 .90 187 55 6 047 869 131 178 54 7 063 895 105 168 53 8 080 922 078 159 52 9 097 948 052 149 51 10 .78113 .87 974 .12 026 .90139 50 11 130 88 000 000 130 49 12 147 027 11973 120 48 13 163 053 947 111 47 14 180 079 921 101 46 15 .78197 .88105 .11895 .90 091 45 16 213 131 869 082 44 17 230 158 842 072 43 18 246 184 816 063 42 19 263 210 790 053 41 20 .78 280 .88 236 .11764 .90 043 40 21 296 262 738 034 39 22 313 289 711 024 38 23 329 315 685 014 37 24 346 341 659 005 36 25 .78 362 .88 367 .11633 .89 995 35 26 379 393 607 985 34 27 395 420 580 976 33 28 412 446 554 966 32 29 428 472 528 956 31 30 .78 445 .88 498 .11502 .89 947 30 31 461 524 476 937 29 32 478 550 450 927 28 33 494 577 423 918 27 34 510 603 397 908 26 35 .78 527 .88 629 .11371 .89 898 25 36 543 655 345 888 24 37 560 681 319 879 23 38 576 707 293 869 22 39 592 733 267 859 21 40 .78 609 .88 759 .11241 .89 849 20 41 625 786 214 840 19 42 642 812 188 830 18 43 658 838 162 820 17 44 674 864 136 810 16 45 .78 691 .88 890 .11110 .89 801 15 46 707 916 084 791 14 47 723 942 058 781 13 48 739 968 032 771 12 49 756 994 006 761 11 50 .78 772 .89 020 .10 980 .89 752 10 51 788 046 954 742 9 52 805 073 927 732 8 53 821 099 901 722 7 54 837 125 875 712 6 55 .78 853 .89151 .10 849 .89 702 5 56 869 177 823 693 4 57 886 203 797 683 3 58 902 229 771 673 2 59 918 255 745 663 1 60 1 .78 934 .89 281 .10 719 .89 653 9-10 9-10 9-10 log cos log cot log tan log sin f 38^ f log sin log tan log cot log cos f 9-10 9-10 9-10 .78 934 .89 281 .10 719 .89 653 60 1 950 307 693 643 59 2 967 333 667 633 58 3 983 359 641 624 57 4 999 385 615 614 56 5 .79 015 .89 411 .10 589 .89 604 55 6 031 437 563 594 54 7 047 463 537 584 53 8 063 489 511 574 52 9 079 515 485 564 51 10 .79 095 .89 541 .10 459 .89 554 50 11 111 567 433 544 49 12 128 593 407 534 48 13 144 619 381 524 47 14 160 645 355 514 46 15 .79176 .89 671 .10 329 .89 504 45 16 192 697 303 495 44 17 208 723 277 485 43 18 224 749 251 475 42 19 240 775 225 465 41 20 .79 256 .89 801 .10199 .89 455 40 21 272 827 173 445 39 22 288 853 147 435 38 23 304 879 121 425 37 24 319 905 095 415 36 25 .79 335 .89 931 .10 069 .89 405 35 26 351 957 043 395 34 27 367 983 017 385 33 28 383 90 009 09 991 375 32 29 399 035 965 364 31 30 .79 415 .90 061 .09 939 .89 354 30 31 431 086 914 344 29 32 447 112 888 334 28 33 463 138 862 324 27 34 478 164 836 314 26 35 .79 494 .90 190 .09 810 .89 304 25 36 510 216 784 294 24 37 526 242 758 284 23 38 542 268 732 274 22 39 558 294 706 264 21 40 .79 573 .90 320 .09 680 .89 254 20 41 589 346 654 244 19 42 605 371 629 233 18 43 621 397 603 223 17 44 636 423 577 213 16 45 .79 652 .90 449 .09 551 .89 203 15 46 668 475 525 193 14 47 684 501 499 183 13 48 699 527 473 173 12 49 715 553 447 162 11 50 .79 731 .90 578 .09 422 .89152 10 51 746 604 396 142 9 52 762 630 370 132 8 53 778 656 344 122 7 54 793 682 318 112 6 55 .79 809 .90 708 .09 292 .89 101 5 56 825 734 266 091 4 57 840 759 241 081 3 58 856 785 215 071 2 59 872 811 189 060 1 60 .79 887 .90 837 .09163 .89 050 9-10 9-10 9-10 1 log cos log cot log tan log sin f 52° 51° 39° f log sin log tan log cot log cos 9-10 9-10 9-10 ! .79 887 .90 837 .09 163 .89 050 60 1 903 863 137 040 59 2 918 889 111 030 58 3 934 914 086 020 57 4 950 940 060 009 56 5 .79 965 .90 966 .09 034 .88 999 55 6 981 992 008 989 54 7 996 91018 08 982 978 53 8 80 012 043 957 968 52 9 027 069 931 958 51 10 .80 043 .91095 .08 905 .88 948 50 11 058 121 879 937 49 12 074 147 853 927 48 13 089 172 828 917 47 14 105 198 802 906 46 15 .80 120 .91 224 .08 776 .88 896 45 16 136 250 750 886 44 17 151 276 724 875 43 18 166 301 699 865 42 19 182 327 673 855 41 20 .80 197 .91 353 .08 647 .88 844 40 21 213 379 621 834 39 22 228 404 596 824 38 23 244 430 570 813 37 24 259 456 544 803 36 25 .80 274 .91482 .08 518 .88 793 35 26 290 507 493 782 34 27 305 533 467 772 33 28 320 559 441 761 32 29 336 585 415 751 31 30 .80 351 .91610 .08 390 .88 741 30 31 366 636 364 730 29 32 382 662 338 720 28 33 397 688 312 709 27 34 412 713 287 699 26 35 .80 428 .91 739 .08 261 .88 688 25 36 443 765 235 678 24 37 458 791 209 668 23 38 473 816 184 657 22 39 489 842 158 647 21 40 .80 504 .91 868 .08 132 .88 636 20 41 519 893 107 626 19 42 534 919 081 615 18 43 550 945 055 605 17 44 565 971 029 594 16 45 .80 580 .91996 .08 004 .88 584 15 46 595 92 022 07 978 573 14 47 610 048 952 563 13 48 625 073 927 552 12 49 641 099 901 542 11 50 .80 656 .92 125 .07 875 .88 531 10 51 671 150 850 521 9 52 686 176 824 510 8 53 701 202 798 499 7 54 716 227 773 489 6 55 .80 731 .92 253 .07 747 .88 478 5 56 746 279 721 468 4 57 762 304 696 457 3 58 777 330 670 447 2 59 792 356 644 436 1 60 .80 807 .92 381 .07 619 .88 425 9-10 9-10 9-10 1 log cos log cot log tan log sin t 40° 43 t log sin log tan log cot log cos 1 **9-10 9-10 9-10 .80 807 .92 381 .07 619 .88 425 60 1 822 407 593 415 59 2 837 433 567 404 58 3 852 458 542 394 57 4 867 484 516 383 56 5 .80 882 .92 510 .07 490 .88 372 55 6 897 535 465 362 54 7 912 561 439 351 53 8 927 587 413 340 52 9 942 612 388 330 51 10 .80 957 .92 638 .07 362 .88 319 50 11 972 663 337 308 49 12 987 689 311 298 48 13 81002 715 285 287 47 14 017 740 260 276 46 15 .81 032 .92 766 .07 234 .88 266 45 16 047 792 208 255 44 17 061 817 183 244 43 18 076 843 157 234 42 19 091 868 132 223 41 20 .81 106 .92 894 .07 106 .88 212 40 21 121 920 080 201 39 22 136 945 055 191 38 23 151 971 029 180 37 24 166 996 004 169 36 25 .81 180 .93 022 .06 978 .88 158 35 26 195 048 952 148 34 27 210 073 927 137 33 28 225 099 901 126 32 29 240 124 876 115 31 30 .81 254 .93 150 .06 850 .88 105 30 31 269 175 825 094 29 32 284 201 799 083 28 33 299 227 773 072 27 34 314 252 748 061 26 35 .81328 .93 278 .06 722 .88 051 25 36 343 303 697 040 24 37 358 329 671 029 23 38 372 354 646 018 22 39 387 380 620 007 21 40 .81402 .93 406 .06 594 .87 996 20 41 417 431 569 985 19 42 431 457 543 975 18 43 446 482 518 964 17 44 461 508 492 953 16 45 .81 475 .93 533 .06 467 .87 942 15 46 490 559 441 931 14 47 505 584 416 920 13 48 519 610 390 909 12 49 534 636 364 898 11 50 .81 549 .93 661 .06 339 .87 887 10 51 563 687 313 877 9 52 578 712 288 866 8 53 592 738 262 855 7 54 607 763 237 844 6 55 .81622 .93 789 .06 211 .87 833 5 56 636 814 186 822 4 57 651 840 160 811 3 58 665 865 135 800 2 59 680 891 109 789 1 60 .81 694 .93 916 .06 084 .87 778 9-10 9-10 9-10 t log cos log cot log tan log sin f 50< 49< 44 41^ 42° o_4.o 2418 f log sin log tan log cot log cos f f log sin log tan log cot log cos f .2419 9-10 9-10 9-10 9-10 9-10 9-10 0580 .81 694 .93 916 .06 084 .87 778 60 .82 551 .95 444 .04 556 .87107 60 )9 834 1 709 942 058 767 59 1 565 469 531 096 59 50-88° 2 723 967 033 756 58 2 579 495 505 085 58 o_8o 940*^ 3 738 993 007 745 57 3 593 520 480 073 57 4 752 94 018 05 982 734 56 4 607 545 455 062 56 9419 5 .81 767 .94 044 .05 956 .87 723 55 5 .82 621 .95 571 .04 429 .87 050 55 JO 029 6 781 069 931 712 54 6 635 596 404 039 54 )9 462 7 796 095 905 701 53 7 649 622 378 028 53 l°-84° 8 810 120 880 690 52 8 663 647 353 016 52 9 825 146 854 679 51 9 677 672 328 005 51 °-12° 10 .81839 .94 171 .05 829 .87 668 50 10 .82 691 .95 698 .04 302 .86 993 50 1.9 433 19 971 33 664 11 854 197 803 657 49 11 705 723 277 982 49 12 868 222 778 646 48 12 719 748 252 970 48 )8 872 13 882 248 752 635 47 13 733 774 226 959 47 70-80'^ 14 897 273 727 624 46 14 747 799 201 947 46 15 .81911 .94 299 .05 701 .87 613 45 15 .82 761 .95 825 .04 175 .§6 936 45 13°-1( 16 926 324 676 601 44 16 775 850 150 924 44 .35 201 .36 33. .51 46< .98 06< 17 940 350 650 590 43 17 788 875 125 913 43 18 955 375 625 579 42 18 802 901 099 902 42 19 969 401 599 568 41 19 816 926 074 890 41 j^o-'y 20 .81983 .94 426 .05 574 .87 557 40 20 .82 830 .95 952 .04 048 .86 879 40 21 998 452 548 546 39 21 844 977 023 867 39 0-20° 22 82 012 477 523 535 38 22 858 96 002 03 998 855 38 5 594 23 026 503 497 524 37 23 872 028 972 844 37 J 534 24 041 528 472 513 36 24 885 053 947 832 36 582 015 25 .82 055 .94 554 .05 446 .87 501 35 25 .82 899 .96 078 .03 922 .86 821 35 0-720 26 069 579 421 490 34 26 913 104 896 809 34 27 084 604 396 479 33 27 927 129 871 798 33 210-24° 28 098 630 370 468 31 28 941 155 845 786 32 .55 433 29 112 655 345 457 31 29 955 180 820 775 31 .58 418 .33 133 .95 728 65°-68'^ 30 .82 126 .94 681 .05 319 .87 446 30 30 .82 968 .96 205 .03 795 .86 763 30 31 141 706 294 434 29 31 982 231 769 752 29 32 155 732 268 423 28 32 996 256 744 740 28 33 169 757 243 412 27 33 83 010 281 719 728 27 25°-28= 34 184 783 217 401 26 34 023 307 693 717 26 .62 595 .66 867 .25 625 .94 182 35 .82 198 .94 808 .05 192 .87 390 25 35 .83 037 .96 332 .03 668 .86 705 25 36 212 834 166 378 24 36 051 357 643 694 24 37 226 859 141 367 23 37 065 383 617 682 23 61o-64^ 38 240 884 116 356 22 38 078 408 592 670 22 39 255 910 090 345 21 39 092 433 567 659 21 9°-32° 40 .82 269 .94 935 .05 065 .87 334 20 40 .83 106 .96 459 .03 541 .86 647 20 38 557 41 283 961 039 322 19 41 120 484 516 635 19 '4 375 18 748 32 359 42 297 986 014 311 18 42 133 510 490 624 18 43 311 95 012 04 988 300 17 43 147 535 465 612 17 7°-60° 44 326 037 963 288 16 44 161 560 440 600 16 °-36° 45 .82 340 .95 062 .04 938 .87 277 16 45 .83 174 .96 586 .03 414 .86 589 15 5 611 46 354 088 912 266 14 46 188 611 389 577 14 252 47 368 113 887 255 13 47 202 636 364 565 13 5 289 48 382 139 861 243 12 48 215 662 338 554 12 )235 °-56° 49 396 164 836 232 11 49 229 687 313 542 11 50 .82 410 .95 190 .04 810 .87 221 10 50 .83 242 .96 712 .03 288 .86 530 10 51 424 215 785 209 9 51 256 738 262 518 9 370-40° 52 439 240 760 198 8 52 270 763 237 507 8 .77 946 53 453 266 734 187 7 53 283 788 212 495 7 .87 711 .06 084 .87 778 54 467 291 709 175 6 54 297 814 186 483 6 55 .82 481 .95 317 .04 683 .87164 5 55 .83 310 .96 839 .03 161 .86 472 5 4qo ftP^ 56 495 342 658 153 4 56 324 864 136 460 4 57 509 368 632 141 3 57 338 890 110 448 3 41°-44o 58 523 393 607 130 2 58 351 915 085 436 2 .81 694 .93 916 .00 000 59 537 418 582 119 1 59 365 940 060 425 1 60 .82 551 .95 444 .04 556 .87107 60 .83 378 .96 966 .03 034 .86 413 .84 949 9-10 9-10 9-10 9-10 9-10 9-10 45°-48° t log cos log cot log tan log sin f F log cos log cot log tan log sin f 48< 47< 1 log sin log tan log cot log COS f 9-10 9-10 9-10 .83 378 .96 966 .03 034 .86 413 60 1 392 991 009 401 59 2 405 97 016 02 984 389 58 3 419 042 958 377 57 4 432 067 933 366 56 5 .83 446 .97 092 .02 908 .86 354 55 6 459 118 882 342 54 7 473 143 857 330 53 8 486 168 832 318 52 9 500 193 807 306 51 10 .83 513 .97 219 .02 781 .86 295 50 11 527 244 756 283 49 12 540 269 731 271 48 13 554 295 705 259 47 14 567 320 680 247 46 15 .83 581 .97 345 .02 655 .86 235 45 16 594 371 629 223 44 17 608 396 604 211 43 18 621 421 579 200 42 19 634 447 553 188 41 20 .83 648 .97 472 .02 528 .86 176 40 21 661 497 503 164 39 22 674 523 477 152 38 23 688 548 452 140 37 24 701 573 427 128 36 25 .83 715 .97 598 .02 402 .86116 35 26 728 624 376 104 34 27 741 649 351 092 33 28 755 674 326 080 32 29 768 700 300 068 31 30 .83 781 .97 725 .02 275 .86 056 30 31 795 750 250 044 29 32 808 776 224 032 28 33 821 801 199 020 27 34 834 826 174 008 26 35 .83 848 .97 851 .02 149 .85 996 25 36 861 877 123 984 24 37 874 902 098 972 23 38 887 927 073 960 22 39 901 953 047 948 21 40 .83 914 .97 978 .02 022 .85 936 20 41 927 98 003 01997 924 19 42 940 029 971 912 18 43 954 054 946 900 17 44 967 079 921 888 16 45 .83 980 .98 104 .01 896 .85 876 15 46 993 130 870 864 14 47 84 006 155 845 851 13 48 020 180 820 839 12 49 033 206 794 827 11 50 .84 046 .98 231 .01 769 .85 815 10 51 059 256 744 803 9 52 072 281 719 791 8 53 085 307 693 779 7 54 098 332 668 766 6 55 .84 112 .98 357 .01 643 .85 754 5 56 125 383 617 742 4 57 138 408 592 730 3 58 151 433 567 718 2 59 164 458 542 706 1 60 .84 177 .98 484 .01 516 .85 693 9-10 9-10 9-10 r log cos log cot log tan log sin 1 440 45 1 log sin log tan log cot log cos f 9-10 9-10 9-10 .84 177 .98 484 .01516 .85 693 60 1 190 509 491 681 59 2 203 534 466 669 58 3 216 560 440 657 57 4 229 585 415 645 56 5 .84 242 .98 610 .01 390 .85 632 55 6 255 635 365 620 54 7 269 661 339 608 53 8 282 686 314 596 52 9 295 711 289 583 51 10 .84 308 .98 737 .01 263 .85 571 50 11 321 762 238 559 49 12 334 787 213 547 48 13 347 812 188 534 47 14 360 838 162 522 46 15 .84 373 .98 863 .01137 .85 510 45 16 385 888 112 497 44 17 398 913 087 485 43 18 411 939 061 473 42 19 424 964 036 460 41 20 .84 437 .98 989 .01011 .85 448 40 21 450 99 015 00 985 436 39 22 463 040 960 423 38 23 476 065 935 411 37 24 489 090 910 399 36 25 .84 502 .99 116 .00 884 .85 386 35 26 515 141 859 374 34 27 528 166 834 361 33 28 540 191 809 349 32 29 553 217 783 337 31 30 .84 566 .99 242 .00 758 .85 324 30 31 579 267 733 312 29 32 592 293 707 299 28 33 605 318 682 287 27 34 618 343 657 274 26 35 .84 630 .99 368 .00 632 .85 262 25 36 643 394 606 250 24 37 656 419 581 237 23 38 669 444 556 225 22 39 682 469 531 212 21 40 .84 694 .99 495 .00 505 .85 200 20 41 707 520 480 187 19 42 720 545 455 175 18 43 733 570 430 162 17 44 745 596 404 150 16 45 .84 758 .99 621 .00 379 .85 137 15 46 771 646 354 125 14 47 784 672 328 112 13 48 796 697 303 100 12 49 809 722 278 087 11 50 .84 822 .99 747 .00 253 .85 074 10 51 835 773 227 062 9 52 847 798 202 049 8 53 860 823 177 037 7 54 873 848 152 024- 6 55 .84 885 .99 874 .00126 .85 012 5 56 898 899 101 84 999 4 57 911 924 076 986 3 58 923 949 051 974 2 59 936 975 025 961 1 60 F .84 949 .00 000 .00 000 .84 949 9-10 9-10 log cos log cot log tan log sin r 46^ 45° 46 TABLE IV THE LOGARITHMS OF THE TEIGONOMETRIC FUNCTIONS OF ANGLES From 0' to 3' and 89° 57' to 90°, for every second From 3' to 2° and 88° to 89° 57', for every ' ten seconds log cos A = 0.00 000, when 0' < ^ < 16' log sin A = 0.00 000, when 89° W 88°, when log sin A or log cos A < 2.54282 or > 1.99974, or when log tan A or log cot A < 2.54308 or > 1.45692. a S log sin a" a T log tan a" a T log tan a" 5 146 2.39 713 2 409 6.68 557 _ 2.06 740 6.68 557 _ 200 4.98 660 5 424 6.68 567 2.41 999 3 417 6.68 556 _ 2.21 920 6.68 558 _ 1 726 3.92 263 5 689 6.6S 568 2.44 072 3 823 6.68 555 _ 2.26 795 6.68 559 _ 2 432 2.07 156 5 941 6.68 569 2.45 955 4 190 6.68 555 _ 2.30 776 6.68 560 2 976 2.15 924 6184 6.68 570 2.47 697 4 840 6.68 554 _ 2.37 038 6.68 561 3 434 2.22 142 6417 6.68 571 2.49 305 5 414 6.68 553 _ 2.41 904 6.68 562 3 838 2.26 973 6 642 6.68 572 2.50 802 5 932 6.68 552 _ 2.45 872 6.68 563 _ 4 204 2.30 930 6 859 6.68 573 2.52 200 6 408 6.6S 551 _ 2.49 223 6.68 564 _ 4 540 2.34 270 7 070 6.68 574 2.53 516 6 633 6.68 550 _ 2.50 721 6.68 565 _ 4 699 2.35 766 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