7^ ss K3 UC-I llllll SIRLF ll llllll III iliii ^B 35 ^03 j > /^ CM ^'^ CM O > FOUR-PLACE LOGARITHMIC AND TRIGONOMETRIC TABLES TOGETHER WITH INTEREST TABLES EDITED BY LOUIS C. KARPINSKI ASSOCIATE PROFESSOR OF MATHEMATICS UNIVERSITY OF MICHIGAN George Wahr, Publisher Ann Arbor, Michigan FOUR-PLACE LOGARITHMIC AND TRIGONOMETRIC TABLES TOGETHER WITH INTEREST TABLES EDITED BY LOUIS c.\karpinski ASSOCIATE PROFESSOR OF MATHEMATICS UNIVERSITY OF MICHIGAN George Wahr, Publisher Ann Arbor, Michigan CAJORl Copyright^ 191 8 BY Louis C. Karpinski All rights reserved Ann Arbor PrKss ann arbor^ mich. QA55 ^3 CONTENTS Explanation of the tables 5-7 I. Constants with their logarithms 9 II. Logarithms of numbers, 100-999 lo-ii III. Logarithms of numbers, 1000-2009 12-13 IV. Logarithms of sines and cosines, 10' intervals. 14-15 V. Logarithms of tangents and cotangents, 10' intervals 16-17 VI. Logarithms of sines and tangents by minutes, 0° to 14° 18-19 Logarithms of cosines and cotangents by min- utes, 76° to 90°. VII. Numerical values of sines and cosines, 10' intervals 20-21 VIII. Numerical values of tangents and cotangents, 10' intervals 22-23 IX. Squares, cubes, square-roots, cube-roots, and reciprocals, i to 100 24 X. Degrees and minutes expressed in radians .... 25 Values of e'' and e"'^. XL Accumulation of i at the end of n years, r«. . . 26 XII. The present value of i in n years, z^" 27 XIII. The accumulation of an annuity of i per annum at the end of n years . . . , 28 XIV. The present value of an annuity of i per annum for n years 29 XV. The annual sinking fund to accumulate to i at the end of n years 30 By addition of i the annuity which i will purchase. — 3 — K Digitized by tine Internet Arcinive in 2007 witin funding from IVIicrosoft Corporation littp://www.arcliive.org/details/fourplacelogaritOOkarpricli EXPLANATION OF THE TABLES I, General. These tables are arranged to give maxi- mum speed in computing which falls within the range of the tables. F.or engineers, physicists, chemists, surveyors, and for statistical experts the tables will be found to be adequate for 90% to 99% of ordinary work. For students of science and mathematics these tables make possible a far greater amount of drill in actual computation than with five-place tables; the use of the four-place table emphasizes the fact that computation should not be carried beyond the places to which measurement is made, and this is. rarely to more than four significant figures. Certain distinct innovations in these tables are to be noted. In the first place both horizontal and vertical inter- polation forms are given in order to afford the variety of experience which will be of service when further and more extensive tables are used. In the second place no lines are used to separate the columns as it is the experience of com- puters that the lines which are commonly found in tables retard the speed of computation, affecting the eye unpleas- antly. In the third place the entry headings, in bold-face type, are repeated in the middle of the tables to reduce to a minimum the necessary movement of the eyes and to elim- inate any uncertainty as to column order, thus increasing both speed and accuracy. 2, Particular. TABLE II Mechanical interpolation, in horizontal form, is introduced. In reading the logarithm of a number re- quiring interpolation, like 232.4, the logarithm of 232 is read — 5 — EXPLANATION OF THE TABLES as 2.3655 and to this 7, the 4/10 of the tabular difference, is added mentally, noting the 7 in column 4 of the difference table. In writing this logarithm 2.36 is written immediately when read ; 55 is noted mentally ; a glance to the right, col- umn 4, shows that 7 is to be added, giving 62 ; then 2.36 is completed to 2.3662, the required logarithm. An error of one unit in the last place is possible, but that is equally true with ordinary interpolation. Mean tabular differences are given. For numbers between 1000 and 2009 it is desirable to use the special table, TABLE III, as errors of one to two units of the last place are common in this interval when the horizontal scheme of interpolation is used. TABLE IV AND TABLE V Mean differences are given and the mechanical scheme of horizontal interpolation is to be employed as in TABLE II. However where the tabular difference is 10 or less inter- polation is to be effected by noting the difference and using the multiphcation table. Thus, log sin 32° 2.(i' is obtained by writing first, 9.72, noting 82 mentally ; then 12 from column 6 is added to 82, making 94; finally 9.7294 is written as the required log- arithm. log cos 32° 26' is obtained by writing 9.92, noting 68 mentally; the tabular difference, a decrease, is noted as 8; then 6/10 of 8 is obtained mentally as 5, since 6x8 = 48 giving here 4.8 or 5 ; finally 63 is written, giving 9.9263 as the required logarithm. Table IV differs from Table V in that the given tabu- lar difference does not apply to the double line. In the lower one of each pair of lines, the interpolation is to be performed mentally, except in the last twelve lines where both tabular differences are given. — 6 — EXPLANATION OF THE TABLES TABLE VI This table can be used for logarithms of cotangents between o° and 14°, and for logarithms of tangents be- tween 76° and 90°, both by minutes, by writing the comple- ment to 10 of the logarithm of the given tangent or cotan- gent. Thus log cot 4° 15' is obtained by noting 8.8699 in the table, and writing 1.1301 as log cot 4° 15'. This same value would be obtained, in a similar manner, for log tan 85° 45'. TABLE VII AND TABLE VIII Vertical interpolation is introduced. Thus, sin 32° 26' is obtained by writing first .53, noting 48 mentally and noting at the right the mean tabular difference, 24; then 6/10 of this difference is read as 14, which added to 48 gives 62; finally, .5362 is the required value. The correct four-place value is .5363, and this would have been obtained by using the actual tabular difference, 25 (.0025), between .5348 and •5373- Were .5362 given as the sine of an angle the angle would be obtained by noting that .5348 is sin 32° 20' ; the tabular difference of 24 is noted, and the actual difference of 14 units of the last place is found to be nearest to 6/10 of 24, giving 32° 26' as the angle. Were 25, the real and not the mean tabular difference used, the 14 would be mid-way between 5/10 and 6/10 of the difference; in this event com- puters make it a rule to take the even digit, giving here again 32° 26'. — 7 TABLE I CONSTANTS WITH THEIR LOGARITHMS Base of natural logarithms Modulus of common logarithms Circumference of a circle in degrees Circumference of a circle in minutes Circumference of a circle in seconds Radius of a circle in degrees or 1 radian Radius of a circle in minutes Radius of a circle in seconds Ratio of a circumference to diameter Volumes and WETGHxa Cubic inches in one gallon (U. S.), Gallons in one cubic foot Cubic inches in one bushel Pounds per cubic foot of water (4 ° C) Pounds per cubic foot of air (0 ° C) Cubic feet in one cubic meter Cubic meters in one cubic yard Cubic inches in one liter Liters in one gallon (U. S.) Pounds in one kilogram 2.2 or Metric ton in pounds Volume of sphere, =4.1888r3 Acceleration gravity, g, at sea level, New York, cm. sec. system Acceleration gravity, g, at sea level, New York, ft. sec. system Lengths and Areas Inches in one meter (By Act of Congress) Feet in 1 rod, 16.5; yds. in 1 rod, 5.5 Square feet in one acre 160 SQUARE R0DS = 1 ACRE; 640 ACRES = 3 .281 FEET = 1 .094 YDS. =1 METER. 1 HORSE POWER =33,000 FT .-LB. Per Min.=550 FT.-LB. Per Sec. 1 KILOWATT =1.341 HORSEPOWER =737.5 FT.-LB. Per Second 1 CUBIC FOOT Per Sec. =448 .9 GAL .Per Min. =1 .9835 ACRE-FT. Per 1 ACRE-FT. Per Day =5.042 CU. FT. Per Sec. 1 BTU. =778.4 FT.-LB. =252 KG.-CAL. 1 REV. Per Min. =6 Per Sec. = .2832 RADIANS Per Min. 1 FT. Per Sec. = .6818 MILES Per Hour. LOGelO =2. 302585, LOGioE = .434234. Number 2.71828183 0.43429448 Logarithm 0.4342945 9.6377843-10 360 21600 1296000 2.5563025 4.3344538 6.1126050 57.29578 3437.7468 206264.806 3.14159265 1.7581226 3.5362739 5.3144251 0.4971499 231 7.48 2150.4 2.3636 .8739 3.3325 62.43 .0807 35.32 .76 61.03 3.786 1.7954 8.9069-10 1.5480 9.8808-10 1.7855 .5782 2.2046 2205 4 . 1888r3- .3434 3.3434 .6221 980.2 2.9913 32.16 1.5073 39.37 1.5952 43560 4.6391 iQ. MILE. Day. — 9 — TABLE II LOGARITHMS OF NUMBERS: 100-549 N 1 2 3 4 5 13 0000 0043 0086 0128 0170 0212 11 0414 0453 0492 0531 0569 0607 12 0792 0828 0864 0899 0934 0969 13 1139 1173 1206 1239 1271 1303 14 1461 1492 1523 1553 1584 1614 6 7 8 9 D1234567S9 0253 0294 0334 0374 41 4 8 12 17 21 25 29 33 37 0645 0682 0719 0755 38 4 8 11 15 19 23 26 30 34 1004 1038 1072 1106 35 3 7 10 14 17 21 24 28 31 1335 1367 1399 1430 32 3 6 10 13 16 19 23 26 29 1644 1673 1703 1732 30 3 6 9 12 15 18 21 24 27 15 1761 1790 1818 1847 1875 1903 16 2041 2068 2095 2122 2148 2175 17 2304 2330 2355 2380 2405 2430 18 2553 2577 2601 2625 2648 2672 19 2788 2810 2833 2856 2878 2900 20 3010 3032 3054 3075 3096 3118 21 3222 3243 3263 3284 3304 3324 22 3424 3444 3464 3483 3502 3522 23 3617 3636 3655 3674 3692 3711 24 3802 3820 3838 3856 3874 3892 25 3979 3997 4014 4031 4048 4065 26 4150 4166 4183 4200 4216 4232 27 4314 4330 4346 4362 4378 4393 28 4472 4487 4502 4518 4533 4548 29 4624 4639 4654 4669 4683 4698 1931 1959 1987 2014 28 3 6 2201 2227 2253 2279 27 3 5 2455 2480 2504 2529 25 2 5 2695 2718 2742 2765 24 2 5 2923 2945 2967 2989 23 2 4 3139 3160 3181 3201 22 2 4 3345 3365 3385 3404 21 2 4 3541 3560 3579 3598 20 2 4 3729 3747 3766 3784 19 2 4 3909 3927 3945 3962 18 2 4 4082 4099 4116 4133 17 2 4 4249 4265 4281 4298 16 2 3 4409 4425 4440 4456 15 2 3 4564 4579 4594 4609 15 2 3 4713 4728 4742 4757 14 1 3 8 11 14 17 20 22 25 8 11 13 16 18 21 24 7 10 12 15 17 20 22 7 9 12 14 16 19 21 7 9 11 13 16 18 20 6 8 11 13 15 17 19 6 8 10 12 14 16 18 6 8 10 12 14 16 17 6 7 9 11 13 15 17 5 7 9 11 12 14 16 5 7 9 10 12 14 16 5 7 8 10 11 13 15 5 6 8 9 11 12 14 5 6 8 9 11 12 14 4 6 7 9 10 12 13 N 9 D 1 2 3 4 5 7 8 30 4771 4786 4800 4814 4829 4843 31 4914 4928 4942 4955 4969 4983 32 5051 5065 5079 5092 5105 5119 33 5185 5198 5211 5224 5237 5250 34 5315 5328 5340 5353 5366 5378 4857 4871 4886 4900 14 1 3 4997 5011 5024 5038 13 1 3 5132 5145 5139 5172 13 1 3 5263 5276 5289 5302 13 1 3 5391 5403 5416 5428 12 1 2 4 6 7 9 10 11 13 4 5 7 8 10 11 12 4 5 7 8 9 11 12 4 5 7 8 9 11 12 4 5 6 7 9 10 11 35 5441 5453 5465 5478 5490 5502 36 5563 5575 5587 5599 5611 5623 37 5682 5694 5705 5717 5729 5740 38 5798 5809 5821 5832 5843 5855 39 5911 5922 5933 5944 5955 5966 40 6021 6031 6042 6053 6064 6075 41 6128 6138 6149 6160 6170 6180 42 6232 6243 6253 6263 6274 6284 43 6335 6345 6355 6365 6375 6385 44 6435 6444 6454 6464 6474 6484 5514 5527 5539 5551 12 1 2 5635 5647 5658 5670 12 1 2 5752 5763 5775 5786 11 1 2 5866 5877 5888 5899 11 1 2 5977 5988 5999 6010 11 1 2 6085 6096 6107 6117 11 1 2 6191 6201 6212 6222 10 1 2 6294 6304 6314 6325 10 1 2 6395 6405 6415 6425 10 1 2 6493 6503 6513 6522 10 1 2 4 5 6 7 9 10 11 4 5 6 7 8 10 11 4 5 6 7 8 9 11 4 5 6 7 8 9 10 3 4 5 7 8 9 10 3 4 5 6 8 9 10 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 45 6532 6542 6551 6561 6571 6580 46 6628 6637 6646 6656 6665 6675 47 6721 6730 6739 6749 6758 6767 48 6812 6821 6830 6839 6848 6857 49 6902 6911 6920 6928 6937 6946 6590 6599 6609 6618 10 1 2 6684 6693 6702 6712 9 12 6776 6785 6794 6803 9 1 2 6866 6875 6884 6893 9 1 2 6955 6964 6972 6981 9 1 2 3 4 5 6 7 8 9 3 4 5 6 7 7 8 3 4 5 6 7 7 8 3 4 5 6 7 7 8 3 4 4 5 6 7 8 50 6990 6998 7007 7016 7024 7033 51 7076 7084 7093 7101 7110 7118 52 7160 7168 7177 7185 7193 7202 53 7243 7251 7259 7267 7275 7284 54 7324 7332 7340 7348 7356 7364 N 1 2 3 4 5 7042 7050 7059 7067 9 1 2 7126 7135 7143 7152 8 12 7210 7218 7226 7235 8 1 2 7292 7300 7308 7316 8 12 7372 7380 7388 7396 8 1 2 6 7 8 9 Dl 2 3 4 4 5 6 7 8 3 3 4 5 6 7 8 3 3 4 5 6 7 7 2 3 4 5 6 6 7 2 3 4 5 6 6 7 3 4 5 6 7 8 9 TABLE II N 1 2 3 55 7404 7412 7419 7427 56 7482 7490 7497 7500 57 7559 7566 7574 7582 58 7634 7642 7649 7657 59 7709 7716 7723 7731 60 7782 7789 7796 7803 61 7853 7860 7868 7875 62 7924 7931 7938 7945 63 7993 8000 8007 8014 64 8062 8069 8075 8082 65 8129 8136 8142 8149 66 8195 8202 8209 8215 67 8261 8267 8274 8280 68 8325 8331 8338 8344 69 8388 8395 8401 8407 70 8451 8457 8463 8470 71 8513 8519 8525 8531 72 8573 8579 8585 8591 73 8633 8639 8645 8651 74 8692 8698 8704 8710 LOGARITHMS OF NUMBERS: 550-999 N 75 8751 8756 8762 8768 76 8808 8814 8820 8825 77 8865 8871 8876 8882 78 8921 8927 8932 8938 79 8976 8982 8987 8993 80 9031 9036 9042 9047 81 9085 9090 9096 9101 82 9138 9143 9149 9154 83 9191 9196 9201 9206 84 9243 9248 9253 9258 85 9294 9299 9304 9309 86 9345 9350 9355 9360 87 9395 9400 9405 9410 88 9445 9450 9455 9460 89 9494 9499 9504 9509 90 9542 9.547 9552 9557 91 9590 9595 9600 9605 92 9638 9643 9647 9652 93 96S5 9689 9694 9699 94 9731 9736 9741 9745 95 9777 9782 9786 9791 96 9823 9827 9832 9836 97 9868 9872 9877 9881 98 9912 9917 9921 9926 99 9956 9961 9965 9969 N 1 2 3 4 5 6 7 8 9 Dl 2 3 4 5 6 7 8 9 7435 7443 7451 7459 7466 7474 8 1 2 2 3 4 5 5 6 7 7513 7520 7528 7536 7543 7551 812 2 3 4 5 5 6 7 7589 7597 7604 7612 7619 7627 8 1 1 2 3 4 5 5 6 7 7664 7672 7679 7686 7694 7701 7 1 1 2 3 4 5 6 7 7738 7745 7752 7760 7767 7774 7 1 1 2 3 4 5 6 7 7810 7818 7825 7832 7839 7846 1 1 1 2 3 4 5 6 6 7882 7889 7896 7903 7910 7917 7 1 1 2 3 3 5 6 6 7952 7959 7966 7973 7980 7987 7 1 1 2 3 3 5 5 6 8021 8028 8035 8041 8048 8055 7 1 1 2 3 3 5 5 6 8089 8096 8102 8109 8116 8122 7 1 1 2 3 3 5 5 6 8156 8162 8169 8176 8182 8189 71 1 2 3 3 5 5 6 8222 8228 8235 8241 8248 8254 7 1 1 2 3 3 5 5 6 8287 8293 8299 8306 8312 8319 6 1 1 2 3 3 5 5 6 8351 8357 8363 8370 8376 8382 6 1 1 2 3 3 4 5 6 8414 8420 8426 8432 8439 8445 6 1 1 2 3 3 4 5 6 8476 8482 8488 8494 8500 8506 6 1 1 2 3 3 4 5 6 8537 8543 8549 8555 8561 8567 6 1 1 2 3 3 4 3 6 8597 8603 8609 8615 8621 8627 6 1 1 2 3 3 4 5 6 8657 8663 8669 8675 8681 8686 6 1 1 2 2 3 4 5 5 8716 8722 8727 8733 8739 8745 61 1 2 2 3 4 5 4 5 6 7 8 9 D12 3 4 5 6 7 8 9 8774 8779 8785 8791 8797 8802 61 1 2 2 3 3 4 5 5 8831 8837 8842 8848 8854 8859 6 1 1 2 2 3 3 4 5 8887 8893 8899 8904 8910 8915 6 1 1 2 2 3 3 4 5 8943 8949 8954 8960 8965 8971 6 1 1 2 2 3 3 4 5 8998 9004 9009 9015 9020 9025 5 1 1 2 2 3 3 4 5 9053 9058 9063 9069 9074 9079 51 1 2 2 3 3 4 5 9106 9112 9117 9122 9128 9133 5 1 1 2 2 3 3 4 5 9159 9165 9170 9175 9180 9186 5 1 1 2 2 3 3 4 5 9212 9217 9222 9227 9232 9238 5 1 1 2 2 3 3 4 5 9263 9269 9274 9279 9284 9289 5 1 1 2 2 3 3 4 5 9315 9320 9325 9330 9335 9340 5 1 1 2 2 3 3 4 5 9365 9370 9375 9380 9385 9390 5 1 1 2 2 3 3 4 5 9415 9420 9425 9430 9435 9440 5 1 1 2 2 3 3 4 5 9465 9469 9474 9479 9484 9489 50 1 2 2 3 3 4 9513 9518 9523 9528 9533 9538 501 2 2 3 3 4 9562 9566 9571 9576 9581 9586 501 2 2 3 3 4 9609 9614 9619 9624 9628 9633 50 1 2 2 3 3 4 9657 9661 9666 9671 9675 9680 50 1 2 2 3 3 4 9703 9708 9713 9717 9722 9727 50 1 2 2 3 3 4 9750 9754 9759 9763 9768 9773 50 1 2 2 3 3 4 9795 9800 9805 9809 9814 9818 50 1 2 2 3 3 4 9841 9845 9850 9854 9859 9863 40 1 2 2 3 3 4 9886 9890 9894 9899 9903 9908 40 1 2 2 3 3 4 9930 9934 9939 9943 9948 9952 40 1 2 2 3 3 3 4 9974 9978 9983 9987 9991 9996 40 1 2 2 3 3 3 4 4 5 6 7 8 9 D 1 2 3 4 5 6 7 8 9 k TABLE III L .OGAR ITHMS ; OF NUMBERS: 1000-1509 No. 1 2 3 4 5 6 7 8 9 100 0000 0004 0009 0013 0017 0022 0026 0030 0035 0039 101 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 102 0086 0090 0095 0099 0103 0107 0111 0116 0120 0124 103 0128 0133 0137 0141 0145 0149 0154 0158 1062 0166 104 0170 0175 0179 0183 0187 0191 0195 0199 0204 0208 105 0212 0216 0220 0224 0228 0233 0237 0241 0245 0249 106 0253 0257 0261 0265 0269 0273 0278 0282 0286 0290 107 0294 0298 0302 0306 0310 0314 0318 0322 0326 0330 108 0334 0338 0342 0346 0350 0354 0358 0362 0366 0370 109 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 110 0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 111 0453 0457 0461 0465 0469 0473 0477 0481 0484 0488 112 0492 0496 0500 0504 0508 0512 0515 0519 0523 0527 113 0531 0535 0538 0542 0546 0550 0554 0558 0561 0565 114 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 115 0607 • 0611 0615 0618 0622 0626 0630 0633 0637 0641 116 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 117 0682 0686 0689 0693 0697 0700 0704 0708 0711 0715 118 0719 0722 0726 0730 0734 0737 0741 0745 0748 0752 119 0755. 0759 0763 0766 0770 0774 0777 0781 0785 0788 120 0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 121 0828 0831 0835 0839 0842 0846 0849 0853 0856 0860 122 0864 0867 0871 0874 0878 0881 0885 0888 0892 0896 123 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 124 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 1 2 3 4 5 6 7 8 9 125 0969 0973 0976 0980 0983 0986 0990 0993 0997 1000 126 1004 1007 1011 1014 1017 1021 1024 1028 1031 1035 127 1038 1041 1045 1048 1052 1055 1059 1062 1065 1069 128 1072 1075 1079 1082 1086 1089 1092 1096 1099 1103 129 1106 1109 1113 1116 1119 1123 1126 1129 1133 1136 130 1139 1143 1146 1149 1153 1156 1159 1163 1166 1169 131 1173 1176 1179 1183 1186 1189 1193 1196 1199 1202 132 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 133 1239 1242 1245 1248 1252 1255 1258 1261 1265 126.S 134 1271 1274 1278 1281 1284 1287 1290 1294 1297 1300 135 1303 1307 1310 1313 1316 1319 1323 1326 1329 1332 136 1335 1339 1342 1345 1348 1351 1355 1358 1361 1364 137 1367 1370 1374 1377 1380 1383 1386 1389 1392 1396 138 1399 1402 1405 1408 1411 1414. 1418 1421 1424 1427 139 1430 1433 1436 1440 1443 1446 1449 1452 1455 1458 140 1461 1464 1467 1471 1474 1477 1480 1483 1486 1489 141 1492 1495 1498 1501 1504 1508 1511 1514 1517 1520 142 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 143 1553 1556 1559 1562 1565 1569 1572 1575 1578 1581 144 1584 1587 1590 1593 1596 1599 1602 1605 1608 1611 145 1614 1617 1C20 1623 1626 1629 1632 1635 1638 1641 146 1644 1647 1649 1652 1655 1658 1661 1664 1667 1670 147 1673 1676 1679 1682 1685 1688 1691 1694 1697 1700 148 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 149 1732 1735 1738 1741 1744 1746 1749 1752 1755 1758 150 1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 No. 1 2 3 4 5 6 7 8 9 12 TABLE III LOGARITHMS OF NUMBERS: 1500-2009 No. 1 2 3 4 5 6 7 8 9 150 1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 151 1790 1793 -1796 1798 1801 1804 1S07 1810 1813 1816 152 1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 153 1847 1850 1853 1855 1858 1861 1864 1867 1870 1872 154 1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 155 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 156 1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 157 1959 1962 1965 1967 1970 1973 1976 1978 1981 1984 158 1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 159 2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 160 2041 2044 2047 2049 2052 2055 2057 2060 2063 2066 161 2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 162 2095 2098 2101 2103 2106 2109 2111 2114 2117 2119 163 2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 164 2148 2151 2154 2156 2159 2162 2164 2167 2170 2172 165 2175 2177 2180 2183 2185 2188 2191 2193 2196 2198 166 2201 2204 2206 2209 2212 2214 2217 2219 2222 2225 167 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 168 2253 2256 2258 2261 2263 2266 2269 2271 2274 2276 169 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 170 2304 2307 2310 2312 2315 2317 2320 2322 2325 2327 171 2330 ?333 2335 2338 2340 2343 2345 2348 2350 2353 172 2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 173 2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 174 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 1 2 3 4 5 6 7 8 9 175 2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 176 2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 177 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 178 2504 2507 2509 2512 2514 2516 2519 2521 2524 2526 179 2529 2531 2533 2536 2538 2541 2543 2545 2548 2550 180 2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 181 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 182 2601 2603 2605 2608 2610 2613 2615 2617 ^620 2622 183 2625 2627 2629 2632 2634 2636 2639 2641 2643 2646 184 2648 2651 ?653 2655 2658 2660 2662 2665 2667 2669 185 2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 186 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 187 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 188 2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 189 2765 2767 2769 2772 2774 2776 2778 2781 2783 2785 190 2788 2790 2792 2794 2797 2799 2801 2804 2806 2808 191 2810 2813 2815 2817 2819 2822 2824 2826 2828 2831 192 2833 2835 2838 2840 2842 2844 2847 2849 2851 2853 193 2856 2858 2860 2862 2865 2867 2869 2871 2874 2876 194 2878 2880 2882 2885 2887 2889 2891 2894 2896 2898 195 2900 2903 2905 2907 2909 2911 2914 2916 2918 2920 196 2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 197 2945 2947 2949 2951 2953 2956 2958 2960 2962 2964 198 2967 2969 2971 2973 2975 2978 2980 2982 2984 2986 199 2989 2991 29?3 2995 2997 2999 3002 3004 3006 3008 200 3010 3012 3015 3017 3019 3021 3023 3025 3028 3030 No. 1 2 3 4 5 6 7 8 9 — 13 — TABLE IV A ° 0' 0° sin '<[% cos sin 8 .2419' log cos 9 .9999 2° sin 8 .5428 log cos 9 .9997 3° sin 8 .7188 log cos 9 .9994 4° sin 8 .8436 log cos 9 .9989 5° sin 8 .9403 '7^ cos 9 .9983 sin 9 .0192 log cos 9976 7" sin 0859 log cos 9968 8° sin 1436 '7^ cos 9958 sin 1943 log cos 9946 10° sin 9 .2397 log cos 9 .9934 11° sin 2806 log cos 9919 A ° 0' 60' 12° sin 3179 log cos 9904 13° sin 3521 log cos 9887 14° sin 3837 log CCS 9869 15° sin 4130 log cos 9849 16° sin 4403 log cos 9828 17° sin 4659 log cos 9806 18° sin 4900 1-,^ cos 9782 sin 5126 log cos 9757 20° sin 9 .5341 leg cos 9 .9730 21° sin 5543 log cos 9702 22° sin 5736 log cos 9672 LOGARITHMS OF SINES AND COSINES 10' 23' 30' 40' 5)' 6d' A° INTERPOLATION 7.4637 7648 9408*0o58*1627*2419 cos 83° Do not interpolate between 10.0000 0000 0000 0000 0000*9999 log sin log sin 0° and log sin 3°. 3088 3668 4179 4637 5059 542S cos 83° In the interval between 9999 9999 9999 9998 9998 9997 leg sin log sin 3° and log sin 14°. interpolation may be used 5776 6097 6397 6677 6940 7188 cos 87° with the actual difference 9997 9996 9996 9995 9995 9994 log sin obtained by subtraction 7423 7645 7857 8059 8251 8436 cos 85° with a possible error 9993 9993 9992 9991 9990 9989 log sin of one unit, fourth place. 8613 8783 8946 9104 92-56 9403 cos 85° Similarity for log cos 87 °-90°, 9989 9988 9987 9986 9985 9983 log sin do not interpolate: between log cos 76° and 87° 9545 9682 9816 9945*0070*0192 cos 84° interpolation may be used. 9982 9981 9980 9979 9977 9976 log sin 0311 0426 0539 0648 0755 0859 cos 83° Separate tables are given 9975 9973 9972 9971 9969 9968 log sin to four places, giving log sines from 0° to 14° . 0961 1060 1157 1252 1345 1436 cos 82° by minutes. 9966 9964 9963 9961 9959 9958 log sin 1525 1612 1697 1781 1863 1943 cos 81 ° Mechanical Interpolation 9956 9954 9952 9950 9948 9946 log sin The following scheme gives 2022 2100 2176 2251 2324 2397 cos 80° tenths of the mean difference 9944 9942 9940 9938 9936 9934 log sin applying throughout the line to which these differences 2468 2538 2606 2674 2740 2806 cos 79° attach. 9931 9929 9927 9924 9922 9919 log sin Regard the differences 2870 2934 2997 3058 3119 3179 cos 78° as units of the fourth place; 9917 9914 9912 9909 9907 9904 log sin they change the last place, 10' 20' 30' 40' 50' 60' A° or two (sometimes more) 50' 40' 30' 20' 10' 0' of the logarithm. 3238 3296 3353 3410 3466 3521 cos 77° An error of one unit 9901 9899 9896 9893 9890 9887 log sin is possible in the last place. 3575 3629 3682 3734 3786 3837 cos 76° 9884 9881 9878 9875 9872 9869 log sin 12 3 4 5 6 7 8 9 3887 3937 3986 4035 4083 4130 cos 75° 49 5 10 15 20 24 29 34 39 44 9866 9863 9859 9856 9853 9849 log sin interpolate mentally 4177 4223 4269 4314 4359 4403 cos 74° 46 5 9 14 18 23 27 32 35 41 9846 9843 9839 9836 9832 9828 log sin using multiplication table 4447 4491 4533 4576 4618 4659 cos 73" 45 4 9 13 17 21 26 30 34 38 9825 9821 9817 9814 9810 9806 log sin , for small differences 4700 4741 4781 4821 4861 4900 cos 72° 40 4 8 12 16 20 24 28 32 36 9802 9798 9794 9790 9786 9782 log sin mentally 4939 4977 5015 5052 5090 5126 cos 71° 38 4 8 11 15 19 23 26 30 34 9778 9774 9770 9765 9761 9757 log sin mentally 5163 5199 5235 5270 5306 5341 cos 70° 36 4 7 11 14 IS 21 25 29 32 9752 9748 9743 9739 9734 9730 log sin 5375 5409 5443 5477 5510 5543 cos 69° 34 3 7 10 13 17 20 24 27 30 9725 9721 9716 9711 9706 9702 sin log 5576 5609 5641 5673 5704 5736 cos 68° 32 3 6 10 13 16 19 22 26 29 9697 9692 9687 9682 9677 9672 log sin 5767 5798 5828 5859 5889 5919 cos 67° 30 3 6 9 12 15 18 21 24 27 9667 9661 96-56 9651 9646 9640 log sin 50' 40' 30' 20' 10' 0' A" 12 3 4 5 6 7 8 9 — 14 — TABLE IV LOGARITHMS OF SINES AND COSINES A" 0' 10' 20' 30' 40' 50' 60' 23° sin 9.5919 5948 5978 6007 6086 6065 6093 cos 66° loff cos 9.9640 9635 9629 9624 9618 9613 9607 log sin 24° sin 6093 6121 6149 6177 6205 6232 6259 cos 65° log cos 9607 9602 9596 9590 9584 9579 9573 log sin 6259 6286 6313 6340 6366 6392 6418 cos 64° 9573 9567 9561 9555 9549 9543 9537 log sin 6418 6444 6470 6495 6521 6546 6570 cos 63° 9537 9530 9524 9518 9512 9505 9499 log sin 6570 6595 6620 6644 6668 6692 6716 cos 62° 9499 9492 9486 9479 9473 9466 9459 log sin 6716 6740 6763 6787 6810 6833 6S56 cos 61° 9459 9453 9446 9439 9432 9425 9418 log sin sm 6856 6878 6901 6923 6946 6968 6990 cos 60° log cos 9418 9411 9404 9397 9390 9383 9375 log sin 30° sin 9.6990 7012 7033 7055 7076 7097 7118 cos 59° log cos 9.9375 9368 9361 9353 9346 9338 9331 log sin 31° sin 7118 7139 7160 7181 7201 7222 7242 cos 58° log cos 9331 9323 9315 9308 9300 9292 9284 log sin 32° sin 7242 7262 7282 7302 7322 7342 7361 cos 57° log cos 9284 9276 9268 8260 9252 9244 9236 sin log 25° sin ^ cos sin log cos 27° sin log cos 28° sin 1.^1 cos 33° sin 7361 7380 7400 7419 7438 7457 7476 cos 56" log cos 9236 9228 9219 9211 9203 9194 9186 log sin 34° sin 7476 7494 7513 7531 7550 7568 7586 cos 55° log cos 9186 9177 9169 9160 9151 9142 9134 log sin A 0' 10' 20' 30' 40' SO' 60' A° 60' 50' 40' 30' 20' 10' 0' 35° sin 7586 7604 7622 7640 7657 7675 7692 cos 54° log cos 9134 9125 9116 9107 9098 9089 9080 log sin 36° sin 7692 7710 7727 7744 7761 7778 7795 cos 53° log cos 9080 9070 9061 9052 9042 9033 9023 log sin 37° sin 7795 7811 782S 7844 7861 7877 7893 cos 52° log cos 9023 9014 9004 8995 8985 8975 8965 log sin 38° sin 7893 7910 7926 7941 7957 7973 7989 cos 51° log cos 8965 8955 8945 8935 8925 8915 8905 log sin 39° sin 7989 8004 8020 8035 8050 8066 8081 cos 50° log cos 8905 8895 8884 8874 8864 8853 8843 log sin 40° sin 9.8081 8096 8111 8125 8140 8155 8169 cos 49° log cos 9.8843 8832 8821 8810 8800 8789 8778 log sin 41° sin 8169 8184 8198 8213 8227 8241 8255 cos 48° i?° cos 8778 8767 8756-8745 8733 8722 8711 log sin sin 8255 8269 8283 8297 8311 8324 8338 cos 47° log cos 8711 8699 8688 8676 8665 8653 8641 log sin 43° sin 8338 8351 8365 8378 8391 8405 8418 cos 46° ^.■^ cos 8641 8629 8618 8606 8594 8582 8569 log sin sin 8418 8431 8444 8457 8469 8482 8495 cos 45° %"' cos 8569 8557 8545 8532 8520 8507 8495 log sin sin 8495 8507 8520 8532 8545 8557 8569 cos 44° log cos 8495 8482 8469 8457 8444 8431 8418 log sin Mean DLferanc-ss d 12345 678 t» 29 3 6 9 12 15 17 20 23 26 interpolate mentally 28 3 6 8 11 14 17 19 22 25 using multiplication table 26 3 5 8 11 13 16 19 21 24 for small differences 25 3 5 8 10 13 15 18 20 23 interpolate mentally 24 2 5 7 10 12 15 17 19 22 for small differences 23 2 5 7 9 12 14 16 19 21 using multiplication table 22 2 4 7 9 11 13 16 18 20 21 2 4 6 9 11 13 15 17 19 21 2 4 6 8 10 12 14 16 19 20 2 4 6 8 10 12 14 16 18 19 2 4 6 8 10 11 13 15 17 18 2 4 6 7 9 11 13 15 17 d 123456789 18 2 4 5 7 9 11 12 14 16 interpolate mentally 17 2 3 5 7 9 10 12 14 15 using multiplication tables 16 2 3 5 7 8 10 12 13 15 for small differences 16 2 3 5 6 8 10 11 13 14 15 2 3 5 6 8 9 11 12 14 15 3 4 6 7 9 10 12 13 11 2 3 4 5 6 8 9 10 14 3 4 6 7 9 10 11 13 11 2 3 4 6 7 8 9 10 14 3 4 4 7 8 10 11 12 12 2 3 5 6 7 8 9 10 13 3 4 5 7 8 9 11 12 12 2 4 5 6 7 8 10 11 13 3 4 5 6 8 9 10 12 12 2 4 5 6 7 9 10 11 12 2 4 5 6 7 9 10 11 13 3 4 5 6 8 9 10 12 d 2 3 4 5 6 7 8 9 TABLE V LOGARITHMS OF TANGENTS AND COTANGENTS 0' 10' 20' 30' 40' 50' CO' A° INTERPOLATION 4637 7648 9409*0658*1627*2419 cot 89 ° Do not interpolate between 5363 2352 0591*9342*8373*7581 log tan log tan 0° and log tan 3°. 3089 3669 4181 4638 5053 5431 cot 8S° or log cot 87° andlog cot 90°. 6911 6331 5819 5362 4947 4569 log tan In the interval between 5779 6101 6401 6682 6945 7194 cot 87° log tan 3° and log tan 14°, or 4221 3899 3599 3318 3055 2806 log tan log cot 76° and log cot 87° 7429 7652 7865 8067 8261 8446 cot 86° interpolation may be used 2571 2348 2135 1933 1739 1554 log tan with the actual difference 8624 8795 8960 9118 9272 9420 cot 85° obtained by subtraction 1376 1205 1040 0882 0728 0580 log tan with a possible error of one unit, fourth place. 9563 9701 9836 9966*0093*0216 cot 84° 0437 0299 0164 0034*9907*9784 lo? tan Separate tables are given 0336 0453 0567 0678 0786 0891 cot 83 ° with four place values 9664 9547 9433 9322 9214 9109 leg tan log tan 0° to log tan 14° log cot 76° to log cot 90° 0995 1096 1194 1291 1385 1478 cot 82° by minutes. 9005 8904 8806 8709 8615 8522 log tan 1569 1658 1745 1831 1915 1997 cot 81 ° Mechanical Interpolation 8431 8342 8255 8169 8085 8003 log tan The following scheme gives 2078 2158 2236 2313 2389 2463 cot 80° tenths of the mean difference 7922 7842 7764 7687 7611 7537 log tan applying throughout the line to which attached. 2536 2609 2680 2750 2819 2887 cot 79° 7464 7391 7320 7250 7181 7113 log tan Regard the differences 2953 3020 3085 3149 3212 3275 cot 78° as units of the fourth place; 7047 6980 6915 6851 6788 6725 log tan they change the last place, 10' 20' 30' 40' 50' 60' A° or two places (or more) 50' 40' 30' 20' 10' 0' of the logarithm. 3336 3397 3458 3517 3576 3634 cot 77° An error of one unit 6664 6603 6542 6483 6424 6366 log tan is possible in the last place. 3691 3748 3804 3859 3914 3968 cot 76° 6309 6252 6196 6141 6086 6032 log tan d 12 3 4 5 6 7 8 9 4021 4074 4127 4178 4230 4281 cot 75° 52 5 10 16 21 26 31 36 42 47 5979 5926 5873 5822 5770 5719 log tan 52 15° tan 9.4281 4331 4381 4430 4479 4527 4575 cot74° 49 5 10 15 20 25 29 34 39 44 log cot 0.5719 5669 5619 5570 5521 5473 5425 log tan 49 16° tan 9.4575 4622 4669 4716 4762 4808 4853 cot 73° 46 5 9 14 19 23 28 33 37 42 log cot 0.5425 5378 5331 5284 5238 5192 5147 log tan 46 17° tan 9.4853 4898 4943 4987 5031 5075 5118 cot 72° 44 4 9 13 18 22 26 31 35 40 log cot 0.5147 5102 5057 5013 4969 4925 4882 log tan 44 18° tan 9.5118 5161 5203 5245 5287 5329 5370 cot 71 ° 42 4 8 13 17 21 25 29 34 38 log cot 0.4882 4839 4797 4755 4713 4671 4630 log tan 42 19° tan 9.5370 5411 5451 5491 5531 5571 5611 cot 70° 40 4 8 12 16 20 24 28 32 36 log cot 0.4630 4589 4549 4509 4469 4429 4389 log tan 40 20° tan 9.5611 5650 5689 5727 5766 5804 5842 cot 69° 39 4 8 12 15 19 23 27 31 35 log cot 0.4389 4350 4311 4273 4234 4196 4158 log tan ^9 21 ° tan 9 .5842 5879 5917 5954 5991 6028 6064 cot 68° 37 4 7 11 15 19 22 26 30 33 log cot 0.4158 4121 4083 4046 4009 3972 3936 log tan 37 22° tan 9.6064 6100 6136 6172 6208 6243 6279 cot 67° 36 4 7 11 14 18 21 25 29 32 log cot 0.3936 3900 3864 3828 3792 3757 3721 loe tan 36 A° CO' 50' 40' 40' 20' 10' 0' ~A° d 1 2 3 4 5 6 7 8 9 i6 0° taT 7 log cot 2 1° tan 8 .2419 log cot 1 .7581 2° tan 8 .5431 log cot 1 .4569 3° tan 8 .7194 ^7^ cot 1 .2806 tan 8 .8446 log cot 1 .1554 5° tan 8.9420 log cot 1 .0580 6° tan 9 .0216 log cot 0.9784 7° tan 9 .0891 "? cotO .9109 tan 9 .1478 log cotO .8522 9° tan 9 .1997 log cot 0.8003 10° tan 9 .2463 17 cot .7537 tan 9 .2887 ^ cot .7113 D 0' 60' 12° tan 9 .3275 log cot . 6725 13° tan 9 .3634 log 14° cotO .6366 tan 9 .3968 log cot .6032 TABLE V LOGARITHMS OF TANGENTS AND COTANGENTS Mean Differences A° 0' 10' 20' 30' 40' 50' 60' A° d 1 2 3 4 5 6 7 8 9 23° tan 9.6279 6314 6348 6383 6417 6452 6486 cot 66° 34 3 7 10 14 17 21 24 28 31 log cot 0.3721 3686 3652 3617 3583 3548 3514 log tan 34 24° tan 9.6486 6520 6553 6587 6620 6654 6687 cot 65° 33 3 7 10 13 17 20 23 27 30 log cot 0.3514 3480 3447 3413 3380 3346 3313 log tan 33 25° tan 9.6687 6720 6752 6785 6817 6850 6882 cot 64° 33 3 7 10 13 16 20 23 26 20 log cot 0.3313 3280 3248 3215 3183 3150 3118 log tan 33 26° tan 9.6882 6914 6946 6977 7009 7040 7072 cot 63° 32 3 6 9 13 16 19 22 25 28 log cot 0.3118 3086 3054 3023 2991 2960 2928 log tan 32 27° tan 9.7072 7103 7134 7165 7196 7226 7257 cot 62° 31 3 6 9 12 15 19 22 25 28 log cot 0.2928 2897 2866 2835 2804 2774 2743 log tan 31 28° tan 9.7257 7287 7317 7348 7378 7408 7438 cot 61 ° 30 3 6 9 12 15 18 21 24 27 log cot 0.2743 2713 2683 2652 2622 2592 2562 log tan 30 29° tan 9.7438 7467 7497 7526 7556 7585 7614 cot 60° 29 3 6 9 12 15 18 21 24 27 log cot 0.2562 2533 2503 2474 2444 2415 2386 log tan 29 30° tan 9.7614 7644 7673 7701 7730 7759 7788 cot 59° 29 3 6 9 12 14 17 20 23 26 leg cot 0.2386 2356 2327 2299 2270 2241 2212 log tan 29 31° can 9.7788 7816 7845 7873 7902 7930 7958 cot 58° 28 3 6 9 11 14 17 20 23 26 log cot 0.2212 2184 2155 2127 2098 2070 2042 log tan 28 32° tan 9.7958 7986 8014 8042 8070 8097 8125 cot 57° 28 log cot 0.2042 2014 1986 1958 1930 1903 1875 log tan 28 33° tan 9.8125 8153 8180 8208 8235 8263 8290 cot 56° 27 log cot 1875 1847 1820 1792 1765 1737 1710 log tan 27 34° tan 9.8290 8317 8344 8371 8398 8425 8452 cot 55° 27 log cot 0.1710 1683 1656 1629 1602 1575 1548 log tan 27 A° 0' 10' 20' 30' 40' 50' 60' A° 60' 50' 40' 30' 20' 10' 0' A° d 35° tan 9.8452 8479 8506 8533 8559 8586 8613 cot 54° 27 leg cot 0.1548 1521 1494 1467 1441 1414 1387 log tan 27 36° tan 9.8613 8639 8666 8692 8718 8745 8771 cot 53° 26 3 5 8 11 13 16 18 21 24 log cot 0.1387 1361 1334 1308 1282 1255 1229 log tan 26 37° tan 9.8771 8797 8824 8850 8876 8902 8928 cot 52° 26 3 5 8 10 13 16 18 21 24 log cot 0.1229 1203 1176 1150 1124 1098 1072 log tan 26 38° tan 9.8928 8954 8980 9006 9032 9058 9084 cot 51° 26 3 5 8 10 13 16 18 21 23 log cot 1072 1046 1020 0994 0968 0942 0916 log tan 26 39° tan 9.9084 9110 9135 9161 9187 9212 9238 cot 50° 26 3 5 8 10 13 15 18 21 23 log cot 0.0916 0890 0865 0839 0813 0788 0762 log tan 26 40° tan 9.9238 9264 9289 9315 9341 0366 9392 cot 49° 26 3 5 8 10 13 15 18 21 23 log cot 0.0762 0736 0711 0685 0659 0634 0608 log tan 26 41° tan 9.9392 9417 9443 9468 9494 9519 9544 cot 48° 25 3 5 8 10 13 15 18 20 23 log cot 0.0608 0583 0557 0532 0506 0481 0456 log tan 25 42° tan 9.9544 9570 9595 9621 9646 9671 9697 cot 47° 25 3 5 8 10 13 15 18 20 23 log cot 0.0456 0430 0405 0379 0354 0329 0303 log tan 25 43° tan 9.9697 9722 9747 9772 9798 9823 9848 cot 46° 25 3 5 8 10 13 15 18 20 23 log cot 0.0303 0278 0253 0228 0202 0177 0152 log tan 25 44° tan 9.9848 9874 9899 9924 9949 9975*0000 cot 45° 25 3 5 8 10 13 15 18 20 23 log cot 0.0152 0126 0101 0076 0051 0025 0000 log tan 25 45° tan 0000 0025 0051 0076 0101 0126 0152 cot 4-1° 25 3 5 8 10 13 15 18 20 23 log cot 0.0000*9975*9949*9924*9899*9874*9848 log tan 25 A° CJ' 5J' 40' 30' 20' 10' 0' A° d 1 2 3 4 5 C 7 8 9 7 — 3 6 8 11 14 17 19 22 25 3 5 8 11 14 16 19 22 25 3 5 8 11 14 16 19 22 24 1 2 3 5 3 4 5 6 7 8 9 8 11 13 16 19 21 24 TABLE VI L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan LSin^ L Tan L Sin L Tan 0' 8.2419 .2419 .5428 .5431 .7188 .7194 .8436 .8446 8.9403 .9420 9.0192 .0216 60' 1' 6.4637 .4637 .2490 .2491 .5484 5467 .7212 .7218 .8454 . 8465 .9417 .9434 9.0204 .0228 59' 2' 6 . 7648 .7648 .2561 .2562 .5500 .5503 .7236 .7242 .8472 .8483 .94.32 .9419 9.0216 .0240 58' 3' 6.9408 .9408 .2630 .2631 .5535 .5538 .7260 .7268 .8490 .8501 .9448 .9133 9.0228 .0253 57' 4' 7.0358 . 0658 .2699 .2700 .5571 .5573 .7283 .7290 .8508 .8518 .9460 .9177 9.0240 .0265 56' 5' 7.1627 .1627 .2766 .2767 .5605 .5308 .7307 .7313 .8525 .8536 .9475 .9192 9.0252 .0277 55' 6' 7.2419 .2419 .2832 .2833 .5640 .5643 .7330 .7337 .8543 .8554 .9189 ,9506 9.0234 .0289 54' 7' 7.3088 .3088 .2898 .2899 .5574 .5677 .7354 .7360 .8580 .8572 .9593 .9520 9.0276 .0300 53' 8' 7.3668 .3668 .2982 .2963 .5708 .5711 .7377 . 7383 ,8578 .8589 .9517 .9534 9.0287 .0312 52' 9' 7.4180 .4180 .3025 .3026 .5742 .5745 .7400 .7406 .8595 .8607 .9531 .9549 9.0299 .0324 51' 10' 7.4637 .4637 .3088 .3089 .5776 .5779 .7423 .7429 .8613 .8624 .9545 .9563 9.0311 .0336 50' 11' 7.5051 .5051 .3150 .3150 .5809 .5812 .7445 .7452 .8630 . 8042 .9559 .9577 9.0323 .0343 49 12' 7.5429 .5429 .3210 .3211 .5842 .5845 .7468 .7475 .8647 .8659 .9573 .9591 9.0334 .0360 48' 13' 7.5777 .5777 .3270 .3271 .5875 .5878 .7491 .7497 .8665 .8676 .9587 .9335 9.0346 .0371 47' 14' 7.6099 .6099 .3329 .3330 .5907 .5911 .7513 .7520 .8682 .8694 .9801 .9319 9.0357 .0383 46' 15' 7.6398 .6398 .3388 .3389 .5939 .5943 .7535 .7542 .8899 .8711 .9814 .9333 9.0370 .0395 45' 16' 7.6678 .6678 .3445 .3446 .5972 .5975 .7557 .7565 .8716 .8728 .9828 .9316 9.0380 .0107 44' 17' 7.6942 .6942 .3502 .3503 .6003 .6007 .7580 .7587 .8733 .8745 .9842 .9880 9.0392 .0418 43' 18' 7.7190 .7190 .3558 ..3559 .6035 .6038 .7602 .7609 .8749 .8762 .9855 .9874 9.0403 .0430 42' 19' 7.7425 .7425 .3613 .3614 .6066 .6070 .7623 .7631 .8766 .8778 .9669 .9688 9.0415 .0441 41' 20' 7.7648 .7648 .3668 .3669 .6097 .6101 .7645 .7652 .8783 .8795 .9682 .9701 9.0426 .0453 40' 21' 7.7859 .7860 .3722 .3723 .6128 .6132 .7667 .7674 .8799 .8812 .9896 .9715 9.0438 .0464 39' 22' 7.8061 .8062 .3775 .3776 .6159 .6163 .7688 .7696 .8816 .8829 .9709 .9729 9.0450 .0476 38' 23' 7.8255 .8255 .3828 .3829 .6189 .6193 .7710 .7717 .8833 .8845 .9723 .9742 9.0460 .0487 37' 24' 7.8439 .8439 .3880 .3881 .6220 .6223 .7731 .7739 .8849 .8862 .9736 .9756 9.0472 .0499 3C' 25' 7.8617 .8617 .3931 .3932 .6250 .6254 .7752 .7760 .8865 .8878 .9750 .9769 9.0483 .0510 35' 26' 7.8787 .8787 .3982 .3983 .6279 .6283 .7773 .7781 .8882 .8895 .9763 .9782 9.0494 .0.521 34' 27' 7.8951 .8951 .4032 .4033 .6309 .6313 .7794 .7802 .8898 .8911 .9776 .9796 9.0505 .0533 33' 28' 7.9109 .9109 .4082 .4083 .6339 .6.343 .7815 .7823 .8914 .8927 .9789 .9809 9.0516 .0544 32' 29' 7.9261 .9261 .4131 .4132 .6368 .6372 .7836 .7844 .8930 . 8944 .9803 .9823 9.0527 .0555 31' L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan 0° 1° 2° 3° 4° 5° 6° 30' 7.9408 9409 .4179 .4181 .6397 .6401 .7857 .7865 .8946 .8960 .9816 .98.36 9.0539 .0567 30' 31' 7-9551 9551 .4227 .4229 .6426 .6430 .7877 .7886 .8932 .8976 .9329 .9349 9.0550 .0578 29' 32' 7.9.389 9689 .4275 .4276 .6454 ,6459 .7898 .7908 .8978 .8992 .9312 .9332 9.0561 .0589 2. 33' 7.9322 9823 .4322 .4323 .6483 .6487 .7918 .7927 .8994 .9008 .9355 .9375 9.0572 .0600 27' 34' 7.9952 .9952 .4368 .4370 .6511 .6515 .7939 .7947 .9010 .9024 .9338 .9338 9.0583 .0611 26' 35' 8.0078 0078 .4414 .4416 .6539 .^544 .7959 .7967 .9026 .9040 .9331 .9931 9.0594 .0622 25' 36' 8.0200 0200 .4459 .4461 .6567 .6571 .7979 .7988 .9042 .9056 .9894 .9915 9.0605 .0633 24' 37' 8.0319 .0319 .4504 .4506 .6595 .6599 .7999 .8008 .9057 .9071 .9907 .9928 9.0616 .0645 23' 38' 8.0435 .0435 .4549 .4551 .6622 .6627 .8019 .8028 .9073 .9087 .9919 .9940 9.0626 .0656 22' 39' 8.0548 .0548 ,4593 .4595 .6650 .6654 .8039 .8048 .9089 .9103 .9932 .9953 9.0637 .0667 21' 40' 8.0658 .0658 .4637 .4638 .6677 .6682 .8059 .8067 .9104 .9118 .9945 .9966 9.0648 .0678 20' 41' 8.0765 .0765 .4680 .4682 .6704 .6709 .8078 .8087 .9119 .9134 .9958 .9979 9.0659 .0688 19' 42' 8.0870 .0870 .4723 .4725 .6731 .6736 .8098 .8107 .9135 .9150 .9970 .9992 9.0670 .0699 18' 43' 8.0972 .0972 .4765 .4767 .6758 .6762 .8117 .8126 .9150 .9165 .9983 .0005 9.0680 .0710 17' 44' 8.1072 .1072 .4807 .4809 .6784 .6789 .8137 .8140 .9166 .9180 .9996 .0017 9.0691 .0721 16' 45' 8.1169 .1170 .4848 .4851 .6810 .6815 .8156 .8165 .9181 .9196 9 .03:)8 .0030 9.0702 .0732 15' 46' 8.1265 .1265 .4890 .4892 .6837 .6842 .8175 .8185 .9196 .9211 9 .0J21 .0313 9.0712 .0743 14' 47' 8.1358 .1359 .49.30 .4933 .6883 .6868 .8194 .8204 .9211 .9226 9 .0333 .0055 9.0723 .0754 13' 48' 8.1450 .1450 .4971 .4973 .6889 .6894 .8213 .8223 .9226 .9211 9 .0046 .0038 r 0734 .0764 12' 49' 8.1539 .1540 .5011 .5013 .6914 .6920 .8232 .8242 .9241 .9256 9.0058 .0080 i .0744 .0775 11' 50' 8.1627 .1627 .5050 .5053 .6940 .6945 .8251 .8261 .9256 .9272 9 .0070 .0093 9.0755 .0786 10' 51' 8.1713 .1713 .5090 .5092 .6935 .6971 .8270 .8280 .9271 .9237 9 .0083 .0105 9.0765 .0796 9' 52' 8.1797 .1798 .5129 .5131 .6991 .6996 .8289 .8299 .9286 .9302 9 .0095 .0118 9.0776 .0807 8' 53' 8.1880 .1880 .5167 .5170 .7016 .7021 .8307 .8317 .9301 .9316 9 .0107 .0130 9.0786 .0818 7' 54' 8.1961 .1962 .5206 .5208 .7041 .7046 .8326 .8336 .9315 .9331 9 .0120 .0143 9.0797 .0828 6' 55' 8.2041 .2041 .5243 .5246 .7066 .7071 .8345 .8355 .9330 .9346 9 .0132 .0155 9.0807 .0839 5' 56' 8.2119 .2120 .5281 .5283 .7090 .7096 .8363 .8373 .9345 .9331 9 .0144 .0167 9.0818 .0849 4' 57' 8.2196 .2196 .5318 .5321 .7115 .7121 .8381 .8392 .9359 .9376 9 .0156 .0180 9.0828 .0860 3' 58' 8.2271 .2272 .5355 .5358 .7140 .7145 .8400 .8410 .9374 .9390 9 .0168 .0192 9.0838 .0871 2' 59' 8.2346 .2346 .5392 .5394 .7164 .7170 .8418 .8428 .9389 .9405 9 .0180 .0204 9.0849 .0881 1' 60' 8.2419 89° .2419 .5428 88° .5431 .7188 87° .7194 .8436 86° .8446 .9403 85° .9420 9 .0192 84' .0216 9.0859 83° .0891 0' L Cos L Cot L Cos L Cot L Cos L Cot L Cop L Cot L Cos L Cot L Co.- L Cot L Cos L Cot i8 — TABLE VI. L Sin L Tan L Sin L Tan „ Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan L Sin L Tan 7° 8 ° 9 ° 10° 1] ° 12 ° 13 ° 0' 9 . 0859 .0891 .1436 .1478 .1943 .1997 .2397 .2463 .2806 .2887 .3179 .3275 .3521 .3634 eC 1' 9.0869 .0902 .1445 .1487 .1951 .2005 .2404 .2471 .2812 .2893 .3185 .3281 .3523 .3639 59' 2' 9.0879 .0912 .1453 .1496 .1959 .2013 .2411 .2478 .2819 .2900 .3191 .3287 .3532 .3845 58' 3' 9.0890 .0923 .1462 A COB . 1 967 .2022 .2418 .2485 .2825 .2907 .3197 .3293 .3337 .3351 57' 4' 9.0900 . 0933 .1471 .1515 .1975 .2030 .2425 .2493 ,2832 .2913 . 3202 ..3300 .3543 .3657 56' 5' 9.0910 .0943 .1480 .1524 .1083 .2038 .2432 .2500 .2838 .2920 .3208 .3308 .3548 .3862 55' 6' 9.0920 .0954 .1489 .1533 .1001 .2046 .2439 .2507 .2845 .2927 .3214 .3312 .3.554 .3668 54' 7' 9.0030 . 0964 .1498 .1542 .1099 . 2054 .2147 .2515 .2851 .2934 .3220 .3?1S .3.559 .3874 53' 8' 9 0940 .0974 .1507 .1551 .2007 .2062 .2454 .2522 .2858 .2940 .3228 .3324 .3534 .3680 52' 9' 9.0951 .0984 .1516 .1560 .2015 .2070 .2461 .2529 .2864 .2947 .3232 .3330 .3570 .3685 51' 0' 9.0961 .0995 . 1525 .1669 .2022 .2078 .2468 .2636 .2870 .2953 .3238 .3336 .3576 .3691 50' 1' 9.0971 .1005 .1533 .1578 .2030 .20S6 .2475 .2544 .2877 .2960 .3244 .3343 .3581 .3897 49' 2' 9.09S1 .1015 .1542 . 1587 .203 5 .2094 .2482 .2551 .2883 .2967 .3253 .3349 .3586 .3702 48' 3' 9.0991 .1025 .1551 .1596 .2046 .2102 .24:9 .2568 .2890 .2973 .3255 . 3355 .3591 .3708 47' 4' 9.1001 .1035 .1560 .1605 .20.'')4 .2110 .2496 .2565 .2898 .2980 .3231 .3361 ..3.597 .3714 46' 5' 9.1011 .1045 .1568 .1613 .2061 .2118 .2503 .2573 .2902 .2987 .3287 .3367 .3802 .3719 45' 6' 9.1020 . 1 056 .1577 .1622 .2069 .2126 .2510 .2580 .2909 .2993 .3273 .3373 .3338 .3725 44' 7' 9.1030 .1066 .1586 .1631 .2077 .2134 .2517 .2587 .2915 .3000 .3279 .3379 .3313 .3731 43' 8' 9.1040 .1076 .1594 .1640 .20.85 .2142 .2-)24 .2594 .2921 ..3006 .32S4 . 3385 .3618 .3736 42' 9' 9.1050 .1086 .1603 .1649 .2092 .2150 .2531 .2801 .2928 .3013 .3290 .3391 .3624 .3742 41' 0' 9.1000 .1096 .1612 .1058 .2100 .2158 .2538 .2809 .2934 .3020 .3296 .3397 .3629 .3748 40' 1' 9.1070 .1106 .1620 . 1667 .2108 .2166 .2545 .2616 .2940 .3026 ..3302 .3403 .3334 .3753 39' ;S' 9.10S0 .1116 . 1629 .1675 .2115 .2174 .2551 .2323 .2947 .3033 .3308 .3409 .3340 .3759 38' 3' 9.1089 .1125 .1637 .1684 .2123 .2181 .2558 .2630 .2953 . 3039 .3313 .3416 .3645 .3764 37' 4' 9.1099 .1135 .1646 .1693 .2131 .2189 .2585 .2637 .2959 .3046 .3319 .3422 .3650 .3770 36' 5' 9.1109 .1145 . 1655 .1702 .2138 .2197 .2572 .2644 .2935 .3052 .3325 .3428 .3655 .3776 35' 6' 9. Ills .1155 . 1663 .1710 .2148 .2205 .2579 .2651 .2972 .3059 .3331 .3434 .3361 .3781 34' 7' 9.1128 .1165 . 1672 .1719 .2153 .2213 .2586 .2658 .2978 .3065 .3336 .3440 .3866 .3787 33' 8' 9.1138 .1175 .1680 .1728 .2181 .2221 .2.593 .2666 .2984 .3072 .3342 .3446 .3871 .3792 32' 9' 9.1147 .1185 .1689 .1736 .2169 .2228 .2800 .2673 .2990 .3078 .3348 .3452 .3677 .3798 31' 7° 8° 9" 10° 11° 12° 13" 0' 9.1157 .1194 .1697 .1745 .2176 .2236 .2606 .2680 .2997 .3085 .3353 .3458 .3882 .3804 30' 1' 9.1167 .1204 .1705 .1754 .2184 .2244 .2613 .2687 .3003 .3091 .3359 .3464 .3687 .3809 29' 2' 9.1176 .1214 .1714 .1762 .2191 .2252 . 2320 . 2694 .3009 .3098 .3365 . 3469 .3092 .3815 28' 3' 9.1186 .1223 .1722 .1771 .2199 .2259 .2327 .2701 .3015 .3104 .3370 .3475 .3698 .3820 27' 4' 9.1195 .1233 .1731 .1779 .2206 .2267 .2634 .2708 .3021 .3110 .3376 .3481 .3703 .3826 26' 5' 9.1205 .1243 .1739 .1788 .2214 .2275 .2640 .2715 .3027 .3117 .3382 .3487 .3708 .3831 25' 6' 9.1214 .1252 .1747 .1797 .2221 .2282 .2647 .2722 .3034 .3123 .3387 .3493 .3713 .3837 24' T 9.1224 .1262 .1756 .1805 .2229 .2290 .2654 .2729 .3040 .3130 .3393 . 3499 .3719 .3842 23' 8' 9.1233 .1272 .1764 .1814 .2236 .2298 .2661 .2736 .3046 .3136 .3399 .3505 .3724 .3848 22' 9' 9.1242 .1281 .1772 .1822 .2243 .2305 .2667 .2743 .3052 .3142 .3404 .3511 .3729 .3853 21' 0' 9.1252 .1291 .1781 .1831 .2251 .2313 .2674 2750 .3058 3149 .3410 .3517 .3734 .3859 20' 1' 9.1261 .1300 .1789 .1839 .2258 .2321 .2681 2757 .3064 3155 .3416 .3523 .3739 .3864 19' 2' 9.1271 .1310 .1797 1848 .2286 .2328 .2887 2764 .3070 3162 .3421 .3529 .3745 .3870 18' 3' 9.1280 .1319 .1806 .1856 .2273 .2336 .2894 .2770 .3077 .3168 .3427 .3535 .3750 .3875 17' 4' 9.1289 .1329 .1814 .1864 .2280 .2343 .2701 .2777 .3083 3174 .3432 .3541 ..3755 .3881 16' 5' 9.1299 .1338 .1822 .1873 .2288 2351 .2707 2784 .3089 3181 .3438 .3546 .3760 .3886 15' 6' 9.1308 .1348 .1830 .1881 .2295 .2359 .2714 2791 .3095 3187 .3444 .3552 .3765 .3892 14' 7' 9.1317 .1357 .1838 .1890 .2333 .2366 .2721 .2798 .3101 .3193 .3449 .3558 .3770 .3897 13' 8' 9.1326 .1367 .1847 .1898 .2310 .2374 .2727 .2805 .3107 .3200 .3455 .3564 .3775 .3903 12' 9' 9.1336 .1376 .1855 .1906 .2317 .2381 .2734 .2812 .3113 .3206 .3460 .3670 .3781 .3908 11' 0' 9.1345 .1385 .1863 1915 .2324 .2389 .2740 2819 .3119 3212 .3466 3576 .3786 .3914 10' r 9.1354 .1395 .1871 1923 .2332 .2396 .2747 2825 .3125 3219 .3471 3581 .3791 .3919 9' 2' 9.1363 .1404 . 1379 .1931 .2339 .2404 .2751 2832 .3131 3225 .3477 3587 .3796 .3924 8' 3' 9.1372 .1413 .1887 1940 .2346 .2411 .2730 2839 .3137 3231 .3482 .3593 .3801 . 3930 7' 4' 9.1381 .1423 .1895 .1948 .2353 .2419 .2767 2846 .3143 3237 .3488 .3599 .3806 .3935 6' 5' 9.1390 .1432 .1933 .1956 .2361 .2426 .2773 2853 .3149 3244 .3493 .3605 .3811 .3941 5' 6' 9.1399 .1441 .1911 .1984 .2338 .2434 .2780 2859 .3155 3250 .3499 3611 ..3816 .3946 4' 7' 9.1409 .1450 .1919 .1973 .2375 .2441 .2786 2866 .3161 3256 .3504 3616 .3822 3952 3' 8' 9.1418 .1460 .1927 1981 .2382 .2448 .2793 .2873 .3167 3262 .3510 3622 .3827 3957 2' 0' 9.1427 .1469 .1935 1989 .2390 .2456 .2799 2880 .3173 .3269 .3515 3628 .3832 .3962 1' 0' 9.1436 .1478 .1943 .1997 .2397 2463 .2806 .2887 .3179 .3275 .3521 .3634 .3837 .3968 tf 82" 81" 80" 79" 78" 77° 76° L Co. L Cot L Co. L Cot L Co. L Cot L Co. L Cot L Co. L Cot L Co. L Cot L Co. L Cot 19 — TABLE VII NUMERICAL VALUES OF SINES A° 0' 10' 20' 30' 40' 50' 60' A° d. P. P 0.0000 0029 0058 0087 0116 0145 0175 89 29 30 29 1 0175 0204 0233 0262 0291 0320 0349 88 29 1 3.0 2.9 2 0349 0378 0407 0436 0465 0494 0523 87 29 2 6.0 5.8 3 0523 0552 0581 0610 0640 0669 0698 86 29 3 9.0 8.7 4 0698 0727 0756 0785 0814 0843 0872 85 29 4 5 12.0 15.0 11.6 14.5 5 0.0872 0901 0929 0958 0987 1016 1045 84 29 6 18.0 17.4 6 1045 1074 1103 1132 1161 1190 1219 83 29 7 21.0 20.3 7 1219 1248 1276 1305 1334 1363 1392 82 29 8 24.0 23.2 8 1392 1421 1449 1478 1507 1536 1564 81 29 9 27.0 26.1 9 1564 1593 1622 1650 1679 1708 1736 80 29 28 2.8 27 2.7 10 0.1736 1765 1794 1822 1851 1880 1908 79 29 1 11 1908 1937 1965 1994 2022 2051 2079 78 28 2 5.6 5.4 12 2079 2108 2136 2164 2193 2221 2250 77 28 3 8.4 8.1 13 2250 2278 2306 2334 2363 2391 2419 76 28 4 11.2 10.8 14 2419 2447 2476 2504 2532 2560 2588 75 28 5 6 14.0 16.8 13.5 16.2 15 0.2588 2616 2644 2672 2700 2728 2756 74 28 7 19.6 18.9 16 2756 2784 2812 2840 2868 2896 2924 73 28 8 22.4 21.6 17 2924 2952 2979 3007 3035 3062 3090 72 28 9 25.2 24.3 18 3090 3118 3145 3173 3201 3228 3256 71 28 19 3256 3283 3311 3338 3365 3393 3420 70 27 26 25 A« 0' 10' 20' 30' 40' 50' 60' d. 1 2.6 2.5 20 0.3420 3448 3475 3502 3529 3557 3584 69 27 2 5.2 5.0 21 3584 3611 3638 3665 3692 3719 3746 68 27 3 7.8 7.5 22 3746 3773 3800 3827 3854 3881 3907 67 27 4 10.4 10.0 23 3907 3934 3961 3987 4014 4041 4067 66 27 5 13.0 12.5 24 4067 4094 4120 4147 4173 4200 4226 65 26 6 7 15.6 18.2 15.0 17.5 25 0.4226 4253 4279 4305 4331 4358 4384 64 26 8 20.8 20.0 26 4384 4410 4436 4462 4488 4514 4540 63 26 9 23.4 22.5 27 4540 4566 4592 4617 4643 4669 4695 62 26 28 4695 4720 4746 4772 4797 4823 4848 61 26 24 23 29 4848 4874 4899 4924 4950 4975 5000 60 25 1 2 2.4 4.8 2.3 4.6 30 0.5000 5025 5050 5075 5100 5125 5150 59 25 3 7.2 6.9 31 5150 5175 5200 5225 5250 5275 5299 58 25 4 9.6 9.2 32 5299 5324 5348 5373 5398 5422 5446 57 24 5 12.0 11.5 33 5446 5471 5495 5519 5544 5568 5592 56 24 6 14.4 13.8 34 5592 5616 5640 5664 5688 5712 5736 .55 24 7 8 16.8 19.2 16.1 18.4 35 0.5736 5760 5783 5807 5831 5854 5878 54 24 9 21.6 20.7 36 5878 5901 5925 5948 5972 5995 6018 53 23 37 6018 6041 6065 6088 6111 6134 6157 52 23 22 21 20 38 6157 6180 6202 6225 6248 6271 6293 51 23 1 2. 2 2.1 2.0 39 6293 6316 6338 6361 6383 6406 6428 50 22 2 3 4. 6. 4 4.2 6 6.3 4.0 6.0' 40 0.6428 6450 6472 6494 6517 6539 6561 49 22. 4 8. 8 8.4 8.0 41 6561 6583 6604 6626 6648 6670 6691 48 22 5 11. 10.5 10.0 42 6691 6713 6734 6756 6777 6799 6820 47 22 6 13. 2 12.6 12.0 43 6820 6841 6862 6884 6905 6926 6947 46 21 7 15. 4 14.7 14.0 44 6947 6967 6988 7009 7030 7050 7071 45 21 8 17.6 16.8 16.0 A° 60' 50' 40' 30' 20' 10' 0' A° d. 9 19. 8 18.9 18.0 NUMERICAL VALUES OF COSINES P. P. TABLE VII NUMERICAL VALUES OF SINES A" 0' 10' 20' 30' 40' 50' 60' A" d. Proporti ional Parts 45 0.7071 7092 7112 7133 7153 7173 7193 44 20 21 20 19 4'5 7193 7214 7234 7254 7274 7294 7314 43 20 1 2.1 2.0 1.9 47 7314 7333 7353 7373 7392 7412 7431 42 20 2 4.2 4.0 3.8 4S 7431 7451 7470 7490 7509 7528 7547 41 19 3 6.3 6.0 5.7 49 7547 7566 7585 7604 7623 7642 7660 40 19 4 5 8.4 10.5 8.0 10.0 7.6 9.5 51 0.7660 7679 7698 7716 7735 7753 7771 39 18 6 12.6 12.0 11. -4 51 7771 7790 7808 7826 7844 7862 7880 38 18 7 14.7 14.0 13.3 5? 7880 7898 7916 7934 7951 7969 7986 37 18 8 16.8 16.0 15.2 51 7986 8004 8021 8039 8056 8073 8090 36 17 9 18.9 18.0 17.1 54 8090 8107 8124 8141 8158 8175 8192 35 17 S5 0.8192 8208 8225 8241 8258 8274 8290 34 16 18 17 16 56 8290 8307 8323 8339 8355 8371 8387 33 16 1 1.8 1.7 1.6 57 8387 8403 8418 8434 8450 8465 8480 32 16 2 3.6 3.4 3.2 58 8480 8496 8511 8526 8.542 8557 8572 31 15 3 5.4 5.1 4.8 59 8572 8587 8601 8616 8631 8646 8660 30 15 4 5 7.2 9.0 6.8 8.5 6.4 8.0 60 0.8660 8675 8689 8704 8778 8732 8746 29 14 6 10.8 10.2 9.6 61 8746 8760 8774 8788 8802 8816 8829 28 It 7 12.6 11.9 11.2 62 8829 8843 8857 8870 8884 8897 8910 27 14 8 14.4 13.6 12.8 63 8910 8923 8936 8949 8962 8975 8988 25 13 9 16.2 15.3 14.4 64 8988 9001 9013 9026 9038 9051 9063 25 12 A" 0' 10' 20' 30' 40' 50' 60' A° d. 65 0.9063 9075 9088 9100 9112 9124 9135 24 12 15 14 13 66 9135 9147 9159 9171 9182 9194 9205 23 12 1 1.5 1.4 1.8 67 9205 9216 9228 9239 9250 9261 9272 22 11 2 3.0 2.8 2.6 68 9272 9283 9293 9304 9315 9325 9336 21 11 3 4.5 4.2 3.9 69 9336 9346 9356 9367 9377 9387 9397 20 10 4 5 6.0 7.5 5.6 7.0 5.2 6.5 70 0.9397 9407 9417 9426 9436 9446 9455 19 10 9.0 8.4 7.8 71 9455 9405 9474 9483 9492 9502 9511 18 9 7 10.5 9.8 9.1 72 9511 9520 9528 9537 9546 9555 9563 17 9 8 12.0 11.2 10.4 73 9.563 9572 9580 9588 9596 9605 9613 16 8 9 13.5 12.6 11.7 74 9613 9621 9628 9636 9644 9652 9659 15 8 75- 0.9659 9667 9674 9681 8689 9696 9703 14 7 12 11 76 9703 9710 9717 9724 9730 9737 9744 13 7 1 1.2 1.1 77 9744 9750 9757 9763 9769 9775 9781 12 6 2 2.4 2.2 78 9781 9787 9793 9799 9805 9811 9816 11 6 3 3.6 3.3 79 9816 9822 9827 9833 9833 9843 9848 10 5 4 5 4.8 6.0 4.4 5.5 80 0.9848 9853 9858 9863 9868 9872 9877 9 5 6 7.2 6.6 81 9877 9S81 9886 9890 9894 9899 9903 8 4 7 8.4 7.7 82 9903 9907 9911 9914 9918 9922 9925 7 4 8 9.6 8.8 83 9925 9029 9932 9936 9939 9942 9945 6 3 9 10.8 9.9 84 9945 9948 9951 9954 9957 9959 9962 5 3 F5 0.9962 9964 9967 9969 9971 9974 9976 4 2 For differences be- 86 9976 9978 9980 9981 9983 9985 9986 3 2 Inw 10 interpolate 87 9986 9988 9989 9990 9992 9993 9994 2 1 mentally. empl< ayinjr 88 9994 9995 9996 9997 9997 9998 9998 1 1 the ordinary multipli- 89 9998 9999 9999 *0900 *0000 *0000 *0000 cation table. A' 60' 50' 40' 30' 20' 10' 0' A° d. NUMERICAL VALUES OF COSINES TABLE VIII NUMERICAL VALUES OF THE TANGENT FUNCTION A" 0' 10' 20' 30' 40' 50' 60' A°d. P.P. 0.0000 0029 0058 0087 0116 0145 0175 89 29 29 30 31 32 33 1 0175 0204 0233 0262 0291 0320 0349 88 29 1 2.9 3.0 3.1 3.2 3.3 2 0349 0378 0407 0437 0465 0495 0524 87 29 2 5.8 6.0 6.2 6.4 6.6 3 0524 0553 0582 0612 0641 0670 06998629 3 8.7 9.0 9.3 9.6 9.9 4 0699 0729 0758 0787 0816 0846 0875 85 29 4 11.6 12.0 12.4 12.8 13.2 5 14.5 15.0 15.5 16.0 16.5 5 0.0875 0904 0934 0963 0992 1022 105184 29 6 17.4 IS.O 18.6 19.2 19.8 6 1051 1080 1110 11-39 1169 1198 1228 83 30 7 20.3 21.0 21.7 22.4 23.1 7 1228 1257 1287 1317 1346 1376 1405 82 30 8 23.2 24.0 24.8 25.6 26.4 8 1405 1435 1465 1495 1564 1554 1.584 81 30 9 26.1 27.0 27.9 28.8 29.7 9 1584 1614 1644 1673 1703 1733 1763 80 30 34 35 36 37 38 10 0.1763 1793 1823 1853 1883 1914 1944 7930 1 3.4 3.5 3.6 3.7 3.8 11 1944 1974 2004 2035 2065 2095 21267830 2 6.8 7.0 7.2 7.4 7.6 12 2126 2156 2186 2217 2247 2278 2309 77 30 3 10.2 10.5 10.8 11.1 11.4 13 2.309 2339 2370 2401 2432 2462 2493 7631 4 13.6 14.0 14.4 14.8 15.2 14 2493 2524 2555 2586 2617 2648 2679 75 31 5 17.0 17.5 18.0 18.5 19.0 6 20.4 21.021.6 22.2 22.8 15 0.2679 2711 2742 2773 2805 2836 2867 74 31 7 23.824.525.225.926.6 16 2867 2899 2931 2962 2994 3026 3057 73 32 8 27.2 28.0 28.8 29.6 30.4 17 3057 3089 3121 3153 3185 3217 3249 72 32 9 30.6 31.5 32.4 33.3 34.2 18 3249 3281 3314 3346 3378 3411 3443 71 32 19 3443 3476 3508 3541 3574 3607 3640 70 33 39 40 41 42 43 1 3.9 4.0 4.1 4.2 4.3 A° 0' 10' 20' 30' 40' 50' 60' A°d. 2 7.8 8.0 8.2 8.4 8.6 3 11.7 12.0 12.3 12.6 12.9 20 1.3640 3673 3706 3/39 3772 3805 38.39 69 33 4 15.6 16.0 16.4 16.8 17.2 21 3839 3872 3906 3939 3973 4006 4040 68 34 5 19.5 20.0 20.5 21.0 21.5 22 4040 4074 4108 4142 4176 4210 4245 67 34 6 23.4 24.0 24.6 25.2 25.8 23 4245 4279 4314 4348 4383 4417 4452 66 34 7 27.3 28.0 28.7 29.4 30.1 24 4452 4487 4522 4557 4592 4628 4663 65 35 8 31.2 32.0 32.8 33.6 34.4 9 35.1 36.0 36.9 37.8 38.7 25 0.4663 4699 4734 4770 4806 4841 4877 64 36 26 4877 4913 4950 4986 5022 5059 5095 63 36 44 45 46 47 48 27 5095 5132 5169 5206 5243 5280 53176237 1 4.4 4.5 4.6 4.7 4.8 28 5317 5354 5392 5430 5467 5505 5543 6138 2 8.8 9.0 9.2 9.4 9.6 29 5543 5581 5619 5658 5696 5735 577460 38 3 13.2 13.5 13.8 14.1 14.4 4 17.6 18.0 18.4 18.8 19.2 30 0.5774 5812 5851 5890 5930 5969 6009 59 39 5 22.0 22.5 23.0 23.5 24.0 31 6009 6048 6088 6128 6168 6208 6249 58 40 6 26.4 27.0 27.6 28.2 28.8 32 6249 6289 6330 6371 6412 6453 6494 5741 7 30.831.532.232.933.6 33 6494 6536 6577 6619 6661 6703 6745 56 42 8 35.2 36.0 36.8 37.6 38.4 34 6745 6787 6830 6873 6916 6959 7002 55 43 9 39.6 40.5 41.4 42.3 43.2 35 .7002 7046 7089 7133 7177 7221 7265 54 44 50 52 54 56 58 36 7265 7310 7355 7400 7445 7490 75365345 1 5.0 5.2 5.4 5.6 5.8 37 7536 7581 7627 7673 7720 7766 781352 46 2 10.0 10.4 10.8 11.2 11.6 38 7813 7860 7907 7954 8002 8050 8098 51 48 3 15.0 15.6 16.2 16.8 17.4 39 8098 8146 8195 8243 8292 8342 839150 49 4 20.0 20.8 21.6 22.4 23.2 5 25.0 26.0 27.0 28.0 29. 40 0.8391 8441 8491 8541 8591 8642 8693 49 50 6 30.0 31.2 32.4 33.6 34.8 41 8693 8744 8796 8847 8899 8952 9004 48 52 7 35.0 36.4 37.8 39.2 40.6 42 9004 9057 9110 9163 9217 9271 932547 54 8 40.0 41.6 43.2 46.8 46.4 43 9325 9380 9435 9490 9545 9601 96.57 46 55 9 45.0 46.8 48.6 50.4 52.2 44 9657 9713 9770 9827 9884 9942 0000 45 57 60' 50' 40' 30' 20' 10' 0' A°d. P.P. NUMERICAL VALUES OF COTANGENTS TABLE VIII NUMERICAL VALUES OF THE TANGENT FUNCTION A° 0' 10' 20' 30' 40' 50' 60' A° d. P. P. 45 1.000 1.006 1.012 1.018 1.024 1.030 1.036 44 6 12 13 14 15 46 1.036 1.042 1.048 1.054 1.060 1.066 1.072 43 6 1 1.2 1.3 1.4 1.5 47 1.072 1.079 1.085 1.091 1.098 1.104 1.111 42 6 2 2.4 2.6 2.8 3.0 48 1.111 1.117 1.124 1.130 1.137 1.144 1.150 41 6 3 3.6 3.9 4.2 4.5 49 1.150 1.157 1.164 1.171 1.178 1.185 1.192 40 7 4 4.8 5.2 5.6 6.0 5 6.0 6.5 7.0 7.5 50 1.192 1.199 1.206 1.213 1.220 1.228 1.235 39 7 6 7.2 7.8 8.4 9.0 51 1.235 1.242 1.250 1.257 1.265 1.272 1.280-38 8 7 8.4 9.1 9.8 10.5 52 1.280 1.288 1.295 1.303 1.311 1.319 1.327 37 8 8 9.6 10.4 11.2 12.0 53 1.327 1.335 1.343 1.351 1.360 1.368 1.376 36 8 9 10.8 11.7 12.6 13.5 54 1.376 1.385 1.393 1.402 1.411 1.419 1.428 35 9 17 18 19 20 55 1.428 1.437 1.446 1.455 1.464 1.473 1.483 34 9 1 1.7 1.8 1.9 2.0 56 1.483 1.492 1.501 1.511 1.520 1.530 1.540 33 10 2 3.4 3.6 3.8 4.0 57 1.540 1.5.50 1.560 1.570 1.580 1.590 1.600 32 10 3 5.1 5.4 5.7 6.0 58 1.600 1.611 1.621 1.632 1.643 1.653 1.664 31 11 4 6.8 7.2 7.6 8.0 59 1.664 1.675 1.686 1.698 1.709 1.720 1.732 30 11 5 8.5 9.0 9.5 10.0 6 10.2 10.8 11.4 12.0 60 1.732 1.744 1.75-) 1.767 1.780 1.792 1.8042912711.912.613.311.0 61 1.804 1.816 1.829 1.842 1.855 1.868 1.88128 13 8 13.6 14.4 15.2 18.0 62 1.881 1.894 1.907 1.921 1.935 1.949 1.963 27 14 9 15.3 16.2 17.118.0 63 1.963 1.977 1.991 2.006 2.020 2.035 2.050 26 14 64 2.050 2.066 2.081 2.097 2.112 2.128 2.145 25 16 22 23 24 25 1 9P'9^ 94. 2*^ A° 0' 10' 20' 30' 40' 50' 60' A° d. 2 4.4 4^6 4^8 5 3 6.6 6.9 7.2 7.5 65 2.145 2.161 2.177 2.194 2.211 2.229 2.246 24 17 4 8.8 9.2 9.6 10.0 66 2.246 2.264 2.282 2.300 2.318 2.337 2.3562318511.011.512.012.5 67 2.356 2.375 2.394 2.414 2.434 2.455 2.475 22 20 6 13.2 13.8 14.4 15.0 68 2.475 2.496 2.517 2.539 2.560 2.583 2.605 2122 7 15.4 16.116.8 17.5 69 2.605 2.628 2.651 2.675 2.699 2.723 2.747 20 24 8 17.6 18.4 19.2 20.0 9 19.8 20.7 21.6 22.5 70 2.747 2.773 2.798 2.824 2.850 2.877 2.904 19 26 71 2.901 2.932 2.960 2.989 3.018 3.047 3.078 18 29 27 28 59 62 72 3.078 3.108 3.140 3.172 3.204 3.237 3.27117 32 1 2.7 2.8 5.9 6.2 73 3.271 3.305 3.340 3.376 3.412 3.450 3.487 16 36 2 5.4 5.6 11.8 12.4 74 3.487 3.526 3.566 3.606 3.647 3.689 3.732 15 41 3 8.1 8.4 17.7 18.6 4 10.8 11.2 23.6 24.8 75 3.732 3.776 3.821 3.867 3.9M 3.962 4.01114 46 5 13.5 14.0 29.5 31.0 76 4.011 4.061 4.113 4.165 4.219 4.275 4.33113 53 6 16.2 16.8 35.4 37.2 77 4.331 4.390 4.449 4.511 4.574 4.638.4.705 12 62 7 18.9 19.6 41.3 43.4 78 4.705 4.773 4.843 4.915 4.989 5.066 5.145 1173 8 21.6 22.4 47.2 49.6 79 5.145 5.226 5.309 5.396 5.485 5.576 5.67110 88 9 24.3 25.2 53.155.8 80 5.671 5.769 5.871 5.976 6.084 6.197 6.314 9 64 67 68 70 81 6.314 6.435 6.561 6.691 6.827 6.968 7.115 8 1 6.4 6.7 6.8 7.0 82 7.115 7.269 7.429 7.596 7.770 7.953 8.144 7 2 12.8 13.4 13.6 14.0 83 8.144 8.345 8.556 8.777 9.010 9.255 9.514 6 3 19.220.120.421.0 84 9.514 9.788 10.078 10.385 10.712 11.059 11.430 5 4 25.6 26.8 27.2 28.0 532.0 33.5 34.0 35.0 85 11.430 11.826 12.251 12.706 13.197 13.727 14.301 4 638.4 40.2 40.8 42.0 86 14.30114.924 15.605 16.350 17.169 18.075 19.081 3 7 44.8 46.9 47.6 49.0 87 19.081 20.206 21.470 22.904 24.542 26.432 28.636 2 8 51.2 53.6 54.4 56.0 88 28.636 31.242 34.368 38.188 42.964 49.104 57.290 1 9 57.660.361.263.0 89 57.290 68.750 85.940 114.59 171.89 343.77 infinit 60' 50' 40' 30' 20' 10' 0' A° d. P. P. NUMERICAL VALUES OF COTANGENTS — 23 — TABLE IX SQUii dlES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS, 1-100 n n2 n3 Vn ^n 1/n n n2 n3 Vn ^n 1/n 1 1 1 1.0000 1.0000 1.00000 51 2601 132651 7.1414 3.7084 .01961 2 4 8 1.4142 1.2599 .50000 52 2704 140608 7.2111 3.7325 .01923 3 9 27 1.7321 1.4422 .33333 53 2809 148877 7.2801 3.7563 .01887 4 16 64 2.0000 1.5874 .25000 54 2916 157464 7.3485 3.7798 .01852 5 25 125 2.2361 1.7100 .20000 55 3025 166375 7.4162 3.8030 .01818 6 36 216 2.4495 1.8171 . 16667 56 3136 175616 7.4833 3.8259 .01786 7 49 343 2.6458 1.9129 . 14288 57 3249 185193 7.5498 3 . 8485 .01754 8 64 512 2.8284 2.0000 . 12500 58 3364 195112 7.6158 3.8709 .01724 9 81 729 3.0000 2.0801 .11111 59 3481 205379 7.6811 3.8930 .01695 10 100 1000 3.1623 2.1544 . 10000 60 3600 216000 7.7460 3.9149 .01667 11 121 1331 3.3166 2.2240 .09091 61 3721 226981 7.8102 3.9365 .0l6a9 12 144 1728 3.4641 2.2894 .08.333 62 3844 238328 7.8740 3.9579 .01613 13 169 2197 3 . 6056 2.3513 . 07692 63 3969 250047 7.9373 3.9791 .01587 14 196 2744 3.7417 2.4101 .07143 64 4096 262144 8.0000 4.0000 .01563 15 225 3375 3.8730 2.4662 .06666 65 4225 274625 8.0623 4.0207 .01538 16 256 4096 4.0000 2.5198 .06250 66 4356 287496 8.1240 4.0412 .01515 17 289 4913 4.1231 2.5713 .05882 67 4489 300763 8.1854 4.0615 .0149 J 18 324 5832 4.2426 2.6207 .05556 68 4624 314432 8.2462 4.0817 .01471 19 361 6859 4.3589 2.6684 .05263 69 4761 328509 8.3066 4.1016 .01449 20 400 8000 4.4721 2.7144 .05000 70 4900 343000 8.3666 4.1213 .01429 21 441 9261 4 . 5826 2.7589 .04762 71 5041 357911 8.4261 4.1408 .01408 22 484 10648 4.6904 2.8020 .04545 72 5184 373248 8.4853 4 . 1602 .01389 23 529 12167 4.7958 2.8439 .04348 73 5329 389017 8.5440 4.1793 .01370 24 576 13824 4.8990 2.8845 .04167 74 5476 405224 8.6023 4.1983 .01351 n n2 n3 Vn ^n 1/n n n2 n3 Vn ^n 1/n 25 625 15625 5.0000 2.9240 .04000 75 5625 421875 8.6603 4.2172 .01333 26 676 17576 5.0990 2.9625 .03846 76 5776 438976 8.7178 4.2358 .01316 27 729 19683 5.1962 3.0000 .03704 77 5929 456533 8.7750 4.2.543 .01299 28 784 21952 5.2915 3.0366 .03571 78 6084 474552 8.8318 4.2727 .01282 29 841 24389 5.3852 3.0723 .03448 79 6241 493039 8.8882 4.2908 .01266 30 900 27000 5.4772 3.1072 .03333 80 6400 512000 8.9443 4.3089 .01250 31 961 29791 5.5678 3.1414 .03226 81 6.561 531441 9.0000 4.3267 .01235 32 1024 32768 5.6569 3.1748 .03125 82 6724 551368 9 . 0554 4.3445 .01220 33 1089 35937 5.7446 3.2075 .03030 83 6889 571787 9.1104 4.3621 .01205 34 1156 39304 5.8310 3.2396 .02941 84 7056 592704 9.1652 4.3795 .01190 35 1225 42875 5.9161 3.2711 .02857 85 7225 614125 9.2195 4.3968 .01176 36 1296 46656 6.0000 3.3019 .02778 86 7396 636056 9.2736 4.4140 .01163 37 1369 50653 6.0828 3.3322 .02703 87 7569 658503 9.3274 4.4310 .01149 38 1444 54872 6.1644 3.3620 .02632 88 7744 681472 9.3808 4.4480 .01136 39 1521 59319 6.2450 3.3912 .02564 89 7921 704969 9.4340 4.4647 .01124 40 1600 64000 6.3246 3.4200 .02500 90 8100 729000 9.4868 4.4814 .01111 41 1681 68921 6.4031 3.4482 .02439 91 8281 753571 9.5.94 4.4979 .01099 42 1764 74088 6.4807 3.4760 .02381 92 8464 778688 9.5917 4.5144 .01087 43 1849 79507 6 . 5574 3.5034 .0232(3 93 8649 804357 9.6437 4.5307 .01075 44 1936 85184 6.6332 3.5303 .02273 94 8836 830584 9.6954 4.5468 .01064 45 2025 91125 6.7082 3 . 5569 .02222 95 9025 857375 9.7468 4.5629 .01053 46 2116 97336 6.7823 3.5830 .02174 96 9216 884736 9.7980 4.5789 .01042 47 2209 103823 6.8557 3.6088 .02128 97 9409 912673 9.8489 4.5917 .01031 48 2304 110592 6.9282 3.6342 .02083 98 9604 911192 970299 9.8995 4.6104 .01020 49 2401 117649 7.0000 3.6593 .02041 99 9801 9.9499 4.6261 .01010 50 2500 125000 7.0711 3.6840 .02000 ; 100 10000 1000000 10.0000 4.6416 .01000 n n^ n3 Vn ^n 1/n n n2 n3 Vn Vn 1/n TABLE X Degrees t to radians Minutes Radians to De- 10° 0.17453 60° 1.04720 10' 0.00291: ^rees and minutes Power Function H°0. 19199 61° 1.06465 11' 0.00320 1 57°17'45" X EX E-" 12° 0.20944 62° 1.08210 12-0.00349 2 114°35'30" 0.0 1.0000 1.0000 13° 0.22689 63° 1.09956 13*0.00378 3 171°53'14" 0.1 1.1052 0.9048 14 ° . 24435 64° 1.11701 14-0.00407 4 229°10'59" 0.2 1.2214 0.8187 15° 0.26180 65° 1.13446 15*0.00436 5 286°28'44" 0.3 1.3499 0.7408 16° 0.27925 66° 1.15192 16' 0.00465 6 343°46'29" 0.4 1.4918 0.6703 17° 0.29671 67° 1.16937 17-0.00495 7 401° 4'14" 0.5 1.6487 0.6065 18° 0.31416 68° 1.18682 18-0.00524 8 458°21'58" 0.6 1.8221 0.5488 19°0. 33161 69° 1.20428 19-0.00553 9 515°39'43" 0.7 0.8 2.0138 0.4966 2.2255 0.4493 20° 0.34907 70° 1.22173 20-0.00582 .1 5°43'47" 0.9 2.4596 0.4066 21° 0.36652 71° 1.23918 21-0.00611 .2 11°27'33" 1.0 2.7183 0.3679 22° 0.38397 72° 1.25664 22-0.00640 .3 17°11'19" 1.1 3.0042 0.3329 23° 0.40143 73° 1.27409 23-0.00669 .4 22°55'06" 1.2 3.3201 0.3012 24° 0.41888 74° 1.29154 24-0.00698 .5 28°38'52" 1.3 3.6693 0.2725 25° 0.43633 75° 1.30900 25-0.00727 .6 34°22'39" 1.4 4.0552 0.2466 26° 0.45379 76° 1.32645 26-0.00756 .7 40° 6'25" 1.5 4.4817 0.2231 27° 0.47124 77° 1.34390 27-0.00785 .8 45°50'12" 1.6 4.9530 0.2019 28° 0.48869 78° 1.36136 28-0.00814 .9 51 °33'58" 1.7 5.4739 0.1827 29° 0.50615 79° 1.37881 29' 0.00844 1.8 6.0496 0.1653 .01 0°34'23" 1.9 6.6859 0.1496 30° 0.52360 80° 1.39626 30-0.00873 .02 1° 8'45" 31° 0.54105 81° 1.41372 31-0.00902 .03 1 °43'08" 2.0 7.3891 0.1353 32 "0.55851 82° 1.43117 32-0.00931 .04 2°17'31" 2.1 8.1662 0.1225 33° 0.57596 83° 1.44862 33-0.00960 .05 2°51'53" 2.2 9.0250 0.1108 34° 0.59341 84° 1.46608 34-0.00989 .06 3°20'16" 2.3 9.9742 0.1003 35° 0.01087 85° 1.48353 35-0.01018 .07 4° 0'39" 2.4 11.023 0.0907 36° 0.62832 86° 1.50098 36-0.01047 .08 4°35'01" 37° 0.64577 87° 1.51844 37-0.01076 .09 5° 9 '24" 2.5 12.182 0.0821 38° 0.66323 88° 1.53589 38-0.01105 2.6 13.464 0.0743 39° 0.68068 89° 1.55334 39-0.01134 .001 0° 3'26" 2.7 14.880 0.0672 .002 0° 6'52" 2.8 16.445 0.0608 40° 0.69813 90° 1.57080 40-0.01164 .003 0°10'18" 2.9 18.174 0.0550 41° 0.71559 91° 1.58825 41-0.01193 .004 0°13'45" 42° 0.73304 92° 1.60570 42-0.01222 .005 0°17'11" 3.0 20.086 .0498 43° 0.75049 93° 1.62316 43-0.01251 .006 0°20'37" 3.0 33.115 .0302 44° 0.76794 94° 1.64061 44-0.01280 .007 0°24'03" 4.0 54.598 .0183 45° 0.78540 95° 1.65806 45-0.01309 .008 0°27'30" 5.0 148.41 .0067 46° 0.80285 96° 1.67552 46-0.01338 .009 0°30'56" 6.0 403.4 .00248 47° 0.82030 97° 1.69297 47-0.01367 7.0 1097 .00091 48° 0.83776 98° 1.71042 48-0.01396 8.0 2981 .00034 49° 0.85521 99° 1.72788 49' 0.01425 9.0 10.0 8103 .00012 22000 .00005 50° 0.87266 100° 1.74533 50-0.01454 51° 0.89012 101° 1.76278 51-0.01484 Degrees and Minutes to Radians 52° 0.90757 102° 1.78024 52-0.01513 1°=. 01745 1' = . 00029 53° 0.92502 103° 1.79769 53' 0.01542 2°= .03491 2' = .00058 54° 0.94248 104° 1.81514 54-0.01571 3°= .05236 3' = .00087 55° 0.95993 105° 1.83260 55-0.01600 4° =.06981 4' =.001 16 56° 0.97738 103° 1.85005 56-0.01629 5°=. .08728 5' =.00145 57° 0.99481 107° 1 86750 57-0.01658 6°=. 10472 6' =.00175 58° 1.01229 103° 1.88496 58-0.01687 7°=. 12217 7'= .00204 59° 1.20974 109° 1.90241 59-0.01716 8° =.13963 8'=, .00233 60° 1.04720 110° 1.91986 60' 0.01745 9°=. 15708 9 = .00262 — 25 — TABLE XI ACCUMULATION OF 1 AT THE END OF n YEARS Yrs. . VA% 2% 2yz7c 3% 4% 5% 6% Yrs. 1 1.01500 1.02000 1.02500 1.03000 1.04000 1.05000 1.06000 1 2 1.03023 1.04040 1.05063 1.06090 1.08160 1 . 10250 1.12360 2 3 1.04568 1.06121 1.07689 1.09273 1 . 12486 1.15763 1.19102 3 4 1.06136 1.08243 1 . 1038 1.12551 1 . 16986 1.21551 1.26248 4 5 1.07728 1 . 10408 1.13141 1 . 15927 1.21665 1.27628 1.33823 5 6 1.09344 1.12616 1.15969 1 . 19405 1.26532 1.34010 1.41852 6 7 1 . 10984 1 . 14869 1.18869 1.22987 1.31593 1.40710 1.50363 7 8 1.12649 1.17166 1.21840 1.26677 1.36857 1.47746 1.59385 8 9 1 . 14339 1 . 19509 1.24886 1.30477 1.42331 1.55133 1.68948 9 10 1 . 16054 1.21900 1.28008 1.34392 1.48024 1.62890 1.79085 10 11 1.17795 1.24337 1.31209 1.38423 1 . 53945 1.71034 1.89831 11 12 1 . 19562 1.26824 1.34489 1.42576 1.60103 1.79586 2.01220 12 13 1.21355 1.29361 1.37851 1.46853 1.66507 1.88565 2 . 13293 13 14 1.23176 1.31948 1.41297 1.51259 1.73168 1.97993 2.26090 14 15 1.25023 1.34587 1.44830 1.55797 1.80094 2.07893 2.39656 15 16 1.26899 1.37279 1.48451 1.60471 1.87298 2.18287 2.54035 16 17 1.28802 1.40024 1.52162 1.65285 1.94730 2.29202 2.69277 17 18 1.30734 1.42825 1.55966 1.70243 2.02582 2.40662 2.85434 18 19 1.32695 1.45681 1.59865 1.75351 2.10685 2.52695 3.02560 19 20 1.34686 1.48595 1.63862 1.80611 2.19112 2.65330 3.20714 20 Yrs. 13^% 2% 2y2% 3% 4% 5% 6% Yrs. 21 1.36706 1.51567 1.67958 1.86029 2.27877 2.78596 3.39956 21 22 1.38756 1.54598 1.72157 1.91610 2.36992 2.92526 3.60354 22 23 1.40838 1.57690 1.76461 1.97359 2.46472 3.07152 3.81975 23 24 1.42950 1.60844 1.80873 2.03279 2.56330 3.22510 4.04893 24 25 1.45095 1.64061 1.85394 2.09378 2.66584 3.38635 4.29187 25 26 1.47271 1.67342 1.90029 2.15659 2.77247 3.55567 4.54938 26 27 1.49480 1 . 70689 1.94780 2.22129 2.88337 3.73346 4.82235 27 28 1.51722 1.74102 1.99650 2.28793 2.99870 3.92013 5.11169 28 29 1 . 53998 1.77584 2.04641 2.35657 3.11865 4.11614 5.41839 29 30 1.56308 1.81136 2.09757 2.42726 3.2434 4.32194 5.74349 30 31 1.58653 1.84759 2.15001 2.50008 3.37313 4.53804 6.08810 31 32 1.61032 1.88454 2.20376 2.57508 3.50806 4.76494 6.45339 32 33 1.63448 1.92223 2.25885 2.65234 3.64838 5.00319 6.84059 33 34 1.65900 1.96068 2.31532 2.73191 3.79432 5.25335 7.25103 34 35 1.68388 1.99989 2.37321 2.81386 3.94609 5.51602 7.68609 35 36 1.70914 2.03989 2.43254 2.89828 4.10393 5.79182 8.14725 36 37 1.73478 2.08069 2.49335 2.98523 4.26809 6.08141 8.63609 37 38 1.76080 2.12230 2.55568 3.07478 4.43881 6.38548 9.15425 38 39 1.78721 2.16474 2.61957 3.16703 4.61637 6.70475 9.70351 39 40 1.81402 2.20804 2.68506 3.26204 4.80102 7.03999 10.28572 40 50 2.10524 2.69159 3.43711 4.38391 7.10668 11.46740 18.42015 50 60 2.44322 3.28103 4.39979 5.89160 10.51963 18.67919 32.98769 60 70 2.83546 3.99956 5.63210 7.91782 15.57162 30.42643 59.07593 70 80 3.29066 4.87544 7.20957 10.64089 23.04980 49.56144 105.79599 80 90 3.81895 5.94313 9.22886 14.30047 34.11933 80.73037 189.46450 90 100 4.43205 7.24465 11.81372 19.21863 50.50495 131.50126 339.30208 100 Yrs. 1M% 2% 2H% 3% 4% 5% 6% Yrs. — 26 — TABLE XII THE PRESENT VALUE OF 1 DUE IN n YEARS Yrs, . VA%. 2%. 2^%. 3%. 4%. 5%. 6%. Yrs. 1 0.98522 0.98039 0.97561 0.97087 0.96154 0.95238 0.94340 1 2 0.97066 0.96117 0.95181 0.94260 0.92456 0.90703 0.89000 2 3 0.95632 0.94232 0.92860 0.91514 0.88900 0.86384 0.83962 3 4 0.94218 0.92.385 0.90595 . 88849 0.85480 0.82270 0.79209 4 5 0.92826 0.90573 0.88385 0.86261 0.82193 0.78353 0.74726 5 6 0.91454 0.88797 0.86230 0.83748 0.79031 0.74622 0.70496 6 7 0.90103 0.87056 0.84127 0.81309 0.7.5992 0.71068 0.66.506 7 8 0.88771 0.85349 0.82075 0.78941 0.73069 0.67684 0.62741 8 9 0.87459 0.83676 0.80073 0.76642 0.70259 0.64461 0.59190 9 10 0.86167 0.82035 0.78120 .0.74409 0.67556 0.61391 0.55839 10 11 0.84893 0.80426 0.76214 0.72242 0.64958 0.58468 0.52679 11 12 0.83639 0.78849 0.74356 0.70138 0.62460 0.55684 0.49697 12 13 0.82403 0.77303 0.72542 0.68095 0.60057 0.53032 0.46884 13 14 0.81185 0.7.5788 0.70773 0.66112 0.57748 0.50507 0.442.30 14 15 0.79985 0.74301 0.69047 0.64186 0.55526 0.48102 0.41727 15 16 0.78803 0.72845 0.67362 0.62317 0.53391 0.45811 0.39365 16 17 0.77639 0.71416 0.65720 0.60502 0.51337 0.43630 0.37136 17 18 0.76491 0.70016 0.64117 0.58739 0.49363 0.41552 0.35034 18 19 0.75361 0.68643 0.62553 0.57029 0.47464 0.39573 0.33051 19 20 0.74247 0.67297 0.61027 0.55368 0.45639 0.37689 0.31180 20 Vrs. 1M%. 2%. 23^%. 3%. 4%. 5%. 6%. Yrs. 21 0.73150 0.65978 . 59539 0.53755 0.43883 0.35894 0.29416 21 22 0.72069 0.64684 0.58086 0.52189 0.42196 0.34185 0.27751 22 23 0.71004 0.63416 0.56670 0.50669 0.40573 0.325.57 0.26180 23 24 0.69954 0.62172 0.55288 0.49193 0.39012 0.31007 0.24698 24 25 0.68921 0.60953 0.53939 0.47761 0.37512 0.29530 0.23300 25 26 0.67902 0.59758 0.52623 0.46369 0.36069 0.28124 0.21981 26 27 0.66899 0.58586 0.51340 0.45019 0.34682 0.26785 0.20737 27 28 0.65910 0.57437 0.50088 0.43708 0.33348 0.25509 0.19563 28 29 0.64936 0.56311 0.48866 0.42435 0.32065 0.24295 0.18456 29 30 0.63976 0.55207 0.47674 0.41199 0.30832 0.23138 0.17411 30 31 0.63031 0.54125 0.46511 0.39999 0.29646 0.22036 0.16425 31 32 0.62099 0.53063 0.45377 0.38834 0.28506 0.20987 0.15496 32 33 0.61182 0.52023 0.44270 0.37703 0.27409 0.19987 0.14619 33 34 0.60277 0.51003 0.43191 0.36604 0.26355 0.19035 0.13791 34 35 0.59387 0.50003 0.42137 0.35538 0.25342 0.18129 0.13011 35 36 0.58509 0.49022 0.41109 0.34503 0.24367 0.17266 0.12274 36 37 0.57644 0.48061 0.40107 0.33498 0.23430 0.16444 0.11579 37 38 0.56792 0.47119 0.39128 0.32523 0.22529 0.15661 0.10924 38 39 0.55953 0.46195 0.38174 0.31575 0.21662 0.14915 0.10306 39 40 0.55126 0.45289 0.37243 0.30656 0.20829 0.14205 0.09722 40 50 0.47500 0.37153 0.29094 0.22811 0.14071 0.08720 0.05429 50 60 0.40930 0.30478 0.22728 0.16973 0.09506 0.05354 0.03031 60 70 0.35268 0.25003 0.17755 0.12630 0.06422 0.03287 0.01693 70 80 0.30389 0.20511 0.13870 0.09398 0.04338 0.02018 0.00945 80 90 0.26185 0.16826 0.10836 0.06993 0.02931 0.01239 0.00527 90 100 0.22563 0.13803 0.08465 0.05203 0.01980 0.00760 0.00295100 frs. 1^%. 2%. 2K%. 3%. 4%. 5%. 6%. Yrs. — 27 — TABLE XIII THE ACCUMULATION OF AN ANNUITY OF 1 PER ANNUM AT THE END OF n YEARS Yrs . 13^%. 2%. 2H%. 3%. 4%. 5%. 6%. Yrs. 1 1.00000 1.00000 1.00000 1.00000 1 00000 1.00000 1.00000 1 2 2.01500 2.02000 2.02500 2.03000 2.04000 z. 05000 2.06000 2 3 3.04523 3.06049 3.07563 3.09090 3.12160 3.15250 3 . 18360 3 4 4.09090 4.12161 4.15252 4.18363 4.24646 4.31013 4.37467 4 5 5.15227 5.20404 5.25633 5.30914 5.41632 5.52563 5.63709 5 6 6.22955 6.30812 6.38774 6.46841 6.63298 6.80191 6.97532 6 7 7.32299 7.43428 7.54743 7.66246 7.89829 8.14201 8.39384 7 8 8.43284 8 . 58297 8.73612 8 . 89234 9.21423 9.54911 9.89747 8 9 9.55933 9.75463 9.95452 10.15911 10.58280 11.02656 11.49132 9 10 10.70272 10.94972 11.20338 11.46388 12.00611 12 . 57789 13.18080 10 11 11.8G326 12.16872 12.48347 12.80780 13.48635 14.20679 14.97164 11 12 13.04121 13.41209 13.79555 14. 19202 15.02581 15.91713 16.86994 12 13 14.23683 14.68033 15.14044 15.61779 16.62684 17.71298 18.88214 13 14 15.45038 15.97394 16.51895 17.08632 18.29191 19.59863 21.01507 14 15 16.68214 17.29342 17.93193 18.59891 20.02359 21.57856 23.27597 15 IS 17.93237 18.63929 19 . 38022 20.15688 21.82453 23.65749 25.67255 16 17 19.20136 20.01207 20.86473 21.76159 23.69751 25.84037 28.21288 17 18 20.48938 21.41231 22.38635 23.41444 25.64541 28.13238 30.90565 18 19 21.79672 22.84056 23.94601 25.11687 27.67123 30.53900 33.75999 19 20 23.12367 24.29737 25.54466 26.87037 29.77808 33.06595 36.78559 20 Yrs. VA%. 2%. 2y2%. 3%. 4%. 5%. 6%. Yrs. 21 24.47052 25.78332 27.18327 28.67649 31.96920 35.71925 39.99273 21 22 25.83758 27.29898 28.86286 30.53678 34.24797 38.50521 43.39229 22 23 27.22514 28.84496 30.58443 32.45288 36.61789 41.43048 46.99583 23 24 28.63352 30.42186 32 . 34904 34.42647 39.08260 44.50200 50.81558 24 25 30.06302 32.03030 34.15776 36.45926 41.64591 47.72710 54.86451 25 26 31.51397 33.67091 36.01171 38.55304 44.31174 51.11345 59.15638 26 27 32.986G8 35.34432 37.91200 40.70963 47.08421 54.66913 63.70577 27 28 34.48148 37.05121 39.85980 42.93092 49.96758 58.40258 68.52811 28 29 35.99870 38.79223 41.85630 45.21885 52.96629 62.32271 73.63980 29 30 37.53868 40.56808 43.90270 47.57542 56.08494 66.43885 79.05819 30 31 39.10176 42.37944 46.00027 50.00268 59.32834 70.76079 84.80168 31 32 40.68829 44.22703 48.15028 52 . 50276 62.70147 75.29883 90.88978 32 33 42.29861 46.11157 50.35403 55.07784 66.20953 80.06377 97.34316 33 34 43.93309 48.03380 52.61289 57.73018 69.85791 85.06696 104.18375 34 35 45 . 59209 49.99448 54.92821 60.46208 73.65222 90.32031 111.43478 35 36 47.27597 51.99437 57.30141 63.27594 77.59831 95.83632 119.12087 36 37 48.98511 54.03425 59.73395 66.17422 81.70225 101.62814 127.26812 37 38 50.71989 56.11494 62.22730 69.15945 85.97034 107.70955 135.90421 38 39 52.48068 58.23724 64.78298 72.23423 90.40915 114.09502 145.05846 39 40 54.26789 60.40198 67.40255 75.40126 95.02552 120.79977 154.76197 40 50 73.68283 84.57940 97.48433 112.79686 152.66703 209.34800 290.33590 50 CO 96.21465 114.05154 135.99159 163.05344 237.99069 353.58372 533.12818 60 70 122.36375 149.97791 185.28411 230.59406 364.29046 588.52851 967.93216 70 00 152. 7108 ■) 193.77195 248.38271 321.36302 551.24498 971.22882 1746.59989 80 90 187. 9299 J 247.15666 329.15425 443.34890 827.98333 1594.60730 3141.07519 90 100 22S. 80304 312.23230 432,54865 607.28773 1237.62370 : 2610.02516 5638.36805100 Yrs. 1>^%. 2%. 2y2%. 3%. 4%. 5%. 6%. Yrs. — 28 — TABLE XIV THE PRESENT VALUE OF AN ANNUITY OF 1 FOR n YEARS Yrs. 1'2%. 2^. 214^. 3%. 4%. 5%. 6%. Yrs. 1 0.98.522 0.98039 0.97561 0.97087 0.96154 0.95238 0.94340 1 2 1 .95588 1.94156 1.92742 1.91347 1.88609 1.85941 1.83339 2 3 2.91220 2.88388 2.8.1002 2.82861 2.77.509 2.72325 2.67301 3 4 3.85438 3.80773 3.76197 3.71710 3.62990 3.54595 3.46511 4 5 4.78265 4.71346 4.64583 4.57971 4.45182 4.32948 4.21236 5 6 5.69719 5.60143 5.50813 5.41719 5.24214 5.07569 4.91732 6 7 6.59821 6.47199 6.34939 6.23028 6.00205 5.78637 5.58238 7 8 7.48593 7.32548 7.17014 7.01969 6.73274 6.46321 6.20979 8 9 8 . 36052 8.16224 7.97087 7.78611 7.43533 7 . 10782 6.80169 9 10 9.22218 8.98259 8.75206 8.53020 8.11090 7.72173 7.36009 10 11 10.07112 9.78685 9.51421 9.25262 8.76048 8.30641 7.88687 11 12 10.90751 10.57534 10.25776 9.95400 9.38507 8.86325 8.38384 12 13 11.73153 11.34837 10.98319 10.63496 9.98565 9.39357 8.85208 13 14 12.54338 12.10625 11.69091 11.29607 10.56312 9.89864 9.29498 14 15 13.34323 12.84926 12.38138 11.93794 11.11839 10.37966 9.71225 15 16 14.13126 13.57771 13.05500 12.56110 11.65230 10.83VVV 10.10.590 16 17 14.90765 14.29187 13.71220 13.16612 12.16567 11.27407 10.47726 17 18 15.67256 14.99203 14.. 3.53.36 13.75351 12.65930 11.68959 10.82760 18 19 16.42617 15.67846 14.97889 14.32380 13.13394 12.08532 11.15812 19 20 17.16864 16.35143 15.58916 14.87747 13.59033 12.46221 11.46992 20 Yrs. 11^%. 2%. 2J^%. 3%. 4%. 5%. 6%. Yrs. 21 17.90014 17.01121 16.184.55 15.41502 14.02916 12.82115 11.76408 21 22 18.f2082 17.65805 16.76541 15.93692 14.45112 13 . 16300 12.04158 22 23 19.33080 18.29220 17.. 33211 16.44361 14.85684 13.48857 12.. 30338 23 24 20.03041 18.91393 17.88499 16.93554 15.24696 13.79864 12.. 5.5036 24 25 20.71961 19.52346 18.42438 17.41315 15.62208 14.09394 12.78336 25 26 21.39863 20.12104 18.95061 17.87684 15.98277 14.37519 13.00317 26 27 22.06762 20.70690 19.46401 18.32703 16.32959 14.64303 13.21053 27 28 22.72672 21.28127 19.96489 18.76411 16.66306 14.89813 13.40016 28 29 23.37608 21.84438 20.45355 19 . 18845 16.98371 15.14017 13.59072 29 30 24.01584 22.39646 20.93029 19.60044 17.29203 15.37245 13.76483 30 31 24.64615 22.93770 21.39541 20.00043 17.58849 15.59281 13.92909 31 32 25.26714 23.46833 21.84918 20.38877 17.87355 15.80268 14.08404 32 33 25.87895 23.98856 22.29188 20.76579 18.14765 16.00255 14.23023 33 34 26.48173 24.49859 22.72379 21.13184 18.41120 16 . 19290 14.36814 34 35 27.07559 24.99862 23.14516 21.48722 18.66461 16.37419 14.49825 35 36 27.66068 25.48884 23.55625 21.83225 18.90828 16.54685 14.62099 36 37 28.23713 25.96945 23.95732 22.16724 19.14258 16.71129 14.73678 37 38 28.80505 26.44064 24.34860 22.49246 19.36786 16.86789 14.84602 38 39 29.36458 26.90259 24.73034 22.80822 19.58448 17.01704 14.94907 39 40 29.91585 27.35548 25.10278 23.11477 19.79277 17.15909 15.04630 40 50 34.99969 31.42361 28.36231 25.72926 21.48218 18.25593 15.76186 SO GO 39.38027 34.76089 30.90866 27.67.556 22.62349 18.92929 16.16143 60 70 43.1.5487 37.49862 32.89786 29.12342 23.39451 19.34268 16.38454 70 80 46.40732 39.74451 34.45182 30.20076 23.91539 19.59646 16.50913 80 90 49.20985 41.58693 35.06577 31.00241 24.26728 19.75226 16.57870 90 190 51.62470 43.09835 36.61411 31.59891 24.50500 19.84791 16.61755100 Yrs. 1H%. 2%. 2>^%. 3%. 4%. s%. 6%. Yrs. 29 TABLE XV THE ANNUAL SINKING FUND TO ACCUMULATE TO 1 AT THE END OF n YEARS, AND, BY ADDITION OF i, THE ANNUITY WHICH 1 WILL PURCHASE Yrs. . 11-^% 2% 21/^% 3% 4% 5% 6% Yrs. 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 2 0.49628 0.49505 0.49383 0.49261 0.49020 0.48780 0.48544 2 3 0.32838 0.32675 0.32514 0.32353 0.32035 0.31721 0.31411 3 4 . 24444 0.24262 0.24082 0.23903 0.23549 0.23201 0.22859 4 5 0.19409 0.19216 0.19025 0.18835 0.18463 0.18097 0.17740 5 6 0.16053 0.15853 0.15655 0.15460 0.15076 0.14702 0.14336 6 7 0.13656 0.13451 0.13250 0.13051 0.12661 0.12282 0.11914 7 8 0.11858 0.11651 0.11447 0.11246 0.10853 0.10472 0.10104 8 9 0.10461 0.10252 0.10046- 0.09843 0.09449 0.09069 0.08702 9 10 0.09343 0.09133 0.08926 0.08723 0.08329 0.07950 0.07587 10 11 0.08429 0.08218 0.08011 0.07808 0.07415 0.07039 0.06679 11 12 0.07668 0.07456 0.07249 0.07046 0.06655 0.06283 0.05928 12 13 0.07024 0.06812 0.06605 0.06403 0.06014 0.05646 0.05296 13 14 0.06472 0.06260 0.06054 0.05853 0.05467 0.05102 0.04758 14 15 0.05994 0.05783 0.05577 0.05377 0.04994 0.04634 0.04296 15 16 0.05577 0.05208 0.05365 0.04997 0.05160 0.04793 0.04961 0.04595 0.04582 0.04220 0.04227 0.03895 16 17 0.03870 0.03544 17 18 0.04881 0.04670 0.04467 04271 0.03899 0.03555 0.03236 18 19 0.04588 0.04378 0.04176 0.03981 0.03614 0.0.3275 0.02962 19 20 0.04325 0.04116 0.03915 0.03722 0.03358 0.03024 0.02718 20 21 0.04087 0.03878 0.03679 0.03487 0.03128 0.02800 0.02500 21 22 0.03870 0.03663 0.03465 0.03275 0.02920 ■ 0.02597 0.02305 22 23 0.03673 0.03467 0.03270 0.03081 0.02731 0.02414 0.02128 23 24 0.03492 0.03287 0.03091 0.02905 0.02559 0.02247 01968 24 25 0.03326 0.03122 0.02928 0.02743 0.02401 0.02095 0.01823 25 VAVo 2% 2H% 3% 4% 5% 6% 26 0.03173 0.02970 0.02777 0.02594 0.02257 0.01956 0.01690 26 27 0.03032 0.02829 0.02638 0.02456 0.02124 0.01829 0.01570 27 28 0.02900 0.02699 0.02509 0.02329 0.02001 0.01712 0.01459 28 29 0.02778 0.02578 0.02389 0.02211 0.01888 0.01605 0.013.58 29 30 0.02664 0.02465 0.02278 0.02102 0.01783 0.01505 0.01265 30 31 0.02557 0.02360 0.02174 0.02000 0.01686 0.01413 0.01179 31 32 0.02458 0.02261 0.02077 0.01905 0.01595 0.01328 0.01100 32 33 0.02364 0.02169 0.01986 0.01816 0.01510 0.01249 0.01027 33 34 0.02276 0.02082 0.01901 0.01732 0.01431 0.01176 0.00960 34 35 0.02193 0.02000 0.01821 0.01654 0.01358 0.01107 0.00897 35 36 0.02115 0.01923 0.01745 0.01580 0.01289 0.01043 0.00839 36 37 0.02041 0.01851 0.01674 0.01511 0.01224 0.00984 0.00786 37 38 0.01972 0.01782 0.01607 0.01446 0.01163 0.00928 0.00736 38 39 0.01905 0.01717 0.01544 0.01384 0.01106 0.00876 0.00689 39 40 0.01842 0.01656 0.01484 0.01326 0.01052 0.00828 0.00646 40 50 0.01357 0.01182 0.01026 0.00887 0.00655 0.00477 0.00344 50 60 0.01039 0.00877 0.00735 0.00613 0.0042:) 0.00283 0.00188 60 70 0.00817 0.00667 0.00540 0.00434 0.00275 0.00170 0.00103 70 80 0.00655 0.00516 0.00403 0.00311 0.00181 0.00103 0.00057 80 90 0.00532 0.00405 0.00304 0.00226 0.00121 0.00063 0.00032 90 100 0.00437 0.00321 0.00231 0.00165 00081 0.00038 0.00018 100 Yrs. iy2% 2% 2y2% 3% 4% 5% 6% y 'rs. 30 UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. l9lup52BsW irn^ ^^^' lu 1111519561^ 5xJul'60HC HfcC*^ '-' wN^nsBO DEAD LD 21-95jtc-11,'50(2877s16)476