iMATICAL i ABL NEW AND ENLARGED EDITION CARGILL G. KNOTT, U.Sc., F.R.S.E, UC-NRLF fl40 6d, 00 OQ CONTENTS. I. Useful Numbers with their Logarithms ... 1 II. Four-Figure Logarithms of Numbers, with Differences, from 100 to 999, and from 1000 to 1109 . . . 2, 3 Anti-logarithmic Table, with Differences, from log *000 to log '999 4, 5 Napierian Logarithms of Numbers from 0*1 to 5 '09; with Subsidiary Table ...... 6 III. Logarithms of Sines and Tangents of Small Arcs up to 8, increasing by Minutes ..... 7 Logarithms of the Circular Functions (Sine, Cosine, Tangent), and the Functions themselves, of Angles or Arcs increasing by 0*1 of a Degree or 6 Minutes, with Differences to Minutes : Logarithms of Sines, Cosines, Tangents . . 8-13 Natural Sines, Cosines, Tangents, Cotangents, Secants, Cosecants . . . . . . 14-25 IV. Chords to everyD^reS^iljSm^fej^a Degree from V. Circular Functions, wiCM^tliEHELogaritliMis, of Arcs measured in RadiaU^ffi7>ER6i3T!>f a Raflian to 1'57 of a Radian^-that is, forOfe First Quadrant. (Equi- valents in De^^e^Sj^jft^^^^^m^^rgin) . . 27, 28, 29 VI. Numbers from 1 t^tflfl-AvitTu t)ie-JRt*ni pvnnn.l 1 Square, Cube, Square-Root, and Cube-Root of each number, and the Cube-Root of ten times each number . . 30, 31 Reciprocals of Numbers to the first four figures . . 32, 33 Prime Numbers from 101 to 2011 33 Squares of Numbers to the first four figures . . 34, 35 Cubes of Numbers to the first four figures . . . 36, 37 VII. Compound Interest Table showing 'Amount ' of 1 . 38 Compound Interest Table showing ' Present Value ' ofl 39 VIII. Positive and Negative Powers of the Exponential Constant e ( = 271828...), with the closely related Hyperbolic Sines, Cosines, and Tangents (sinh, cosh, tanli), and the Logarithms of the Sines and Cosines (log sinh and log cosh) ...... 40 A special feature of the Tables of the Circular Functions is the promi- nence given to the true scientific unit of angle namely, the Radian. The pupil cannot be introduced too soon to this conception ; and most of the Tables included in Parts III. and V. give the angles in both the natural and conventional units. Table V., which, so far as the compiler knows, is now (1905) published, for the first time, will be found of great service in graphical construction and in the graphical solution of equa- tions involving the circular functions. pros USEFUL NUMBERS WITH THEIR LOGARITHMS. METRIC SYSTEM. Loo. LOG. 1 metre = 39-370113 in. 1-59517 1 in. = 2'54 cm. 40483 = 3-280843 ft. 51599 1 ft. = 30-48 cm. 1-48401 = 1-0936 yd. 03886 1 yd. = .0-9144 in. 1-96114 IKm. = 0-62137 ml. 1-79335 1 ml. = 1-6093 Km. 20665 l(m.)2 = 10 7639 (ft. )2 1-03197 1 (in.)2 = 6-4516 (cm.)2 80967 = 1196 (yd.)2 07773 1 ( y d.)2 r= 0-8361 (m.) 2 1-92227 1 (Km.)2 = 0-3861 (ml.)2 1-58670 l(ml.)2 = 2'59(Km.)2 41330 1 hectare = 2-4716 acres 39298 1 acre = 0'4046 hectare 1-60702 1 (m.p = l'308(yd.)3 11659 1 (yd.)3 = 07646 (m.)3 1-88341 1 litre = 61-0238(in.)3 1-78550 l(in.)3 = 16-387 (cm.)3 1-21450 = 176 pint 24546 1 pint = 0-568 1. 1-75454 = 22 gallon 1-34237 1 gallon = 4-5461. 65703 1 gram = 15 -43236 gr. 118843 1 gr. = 0-0648 g. "2-81157 IKg. = 2-20462 Ib. 34333 1 lb. t = 0-4536 Kg. 1-65667 MATHEMATICAL, CONSTANTS. LoQ JT = 3-14159265... =3-1416 or 22/7 nearly. 49715 180/<3 6982 6998 7015 7031 7047 7063 235 6 8 10 11 13 15 85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 2 o 5 7 8 10 12 13 15 86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 235 7 8 10 12 13 15 87 7413 7430 7447 7464 7482 7499 7516 7534 7551 7568 235 7 9 10 12 14 16 88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 245 7 9 11 12 14 16 89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 245 7 9 11 13 14 16 90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 246 7 9 11 13 15 17 91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 246 8 9 11 13 15 17 92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 246 8 10 12 14 15 17 93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 246 8 10 12 14 16 18 94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 246 8 10 12 14 16 18 95 8913 8933 8954 8974 8995 9016 9036 9057 9078 90S):) 246 8 10 12 15 17 19 96 9120 9141 9162 9183 9204 9226 9247 9268 9290 9311 246 8 11 13 15 17 19 97 9.'M3 9354 9376 9397 9419 9441 9462 9484 9506 9528 247 9 11 13 15 17 20 98 9550 9572 9594 9616 9638 90(51 0083 9705 9727 9750 247 9 11 13 16 18 20 99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 257 9 11 14 16 18 20 NAPIERIAN LOGARITHMS of Numbers from 01 to 5 "09; with Subsidiary Table. Number. 1 2 3 4 5 6 7 8 9 Subsidiary Table. No. Nap. Log. No. Nap. Log. 6 1-7918 40 3-6889 7 1-9459 50 3-9120 01 0-2 3-0974 2-3906 7927 4393 8797 4859 9598 5303 0339 5729 1029 6137 1674 6529 2280 6907 2852 7270 3393 7621 8 9 10 2-0794 2-1972 2-3026 60 70 80 4-0943 4-2485 4-3820 0-3 7960 8288 ; 8606 8913 9212 9502 9783 0057 0324 0584 20 2-9957 90 4-4998 0-4 n.c 1-0837 3068 1084 3267 1325 3461 1560 3651 1790 OQ-JQ 2015 4022 2235 4202 2450 266012866 4379 /lfiKy ; AT*IA 30 3-4012 100 4-0052 u o 0-6 4892 5057 5220 5380 OOOO 5537 5692 5845 5995 6143 6289 Mean Differences. 0-7 6433 6575 6715 6853 69^9 7123 7256 7386 7515 7043 0-8 7769 7893 8015 8137 8256 8375 8492 8607 8722 8835 1 2 3 456 0-9 8946 9057 9166 9274 9381 9487 9592 9695 9798 9899 789 1-0 o-oooo 0100 0198 0296 0392 0488 0583 0677 0770 0862 11 0953 1044 1133 1222 1310 1398 1484 1570 1655 1740 9 17 26 35 44 52 61 70 78 1-2 1823 1906 1989 2070 2151 2231 2311 2390 2469 2546 8 16 24 32 40 48 56 64 72 1-3 2624 2700 2776 2852 2927 3001 3075 3148 3221 3293 7 1, j 22 30 3 7 45 52 59 67 3365 3436 3o07 3577 3646 3716 3784 3853 3920 ! 3988 7 14 21 28 35 41 48 55 62 1-5 4055 4121 4187 4253 4318 4383 4447 4511 4574 4637 6 13 19 26 32 39 45 52 58 1-6 4700 4762 4824 4886 4947 5008 1 5068 5128 5188 5247 6 12 18 24 30 36 42 48 55 1-7 5306 5365 5423 5481 5539 5596 '< 5053 5710 5766 5822 6 1 L 17 24 2 9 34 40 46 52 1-8 5878 5933 5988 6043 6098 6152 ! 6206 6259 6313 0366 5 11 16 22 27 32 38 43 49 19 6419 6471 6523 6575 6627 6678 I 6729 6780 6831 6881 5 1( ) 15 20 2 6 31 36 41 46 20 6931 6981 7031 7080 7129 7178 7227 7275 7324 7372 5 10 15 20 24 29 34 39 44 21 7419 7467 7514 7561 7608 7655 7701 7747 7793 7839 5 9 14 19 23 28 33 37 42 2-2 7885 7930 7975 8020 8065 8109 8154 8198 8242 8286 4 ( ) 13 18 2 2 27 31 36 40 2-3 8329 8372 8416 8459 8502 8544 8587 8629 8671 8713 4 9 13 17 21 26 30 34 38 2-4 8755 8796 8838 8879 8920 8961 9002 9042 9083 j 9123 4 i * 12 16 20 24 29 33 37 2-5 9163 9203 9243 9282 9322 9361 9400 9439 9478 9517 4 i * 12 16 20 24 27 31 35 2-6 9555 9594 9632 9670 9708 9746 9783 9821 9858 9895 4 I 3 11 15 19 23 26 30 34 2-7 9933 9969 0006 0043 0080 0116 0152 0188 0225 0260 4 ' r 11 lf> 18 22 26 29 33 2-8 1-0296 0332 0367 0403 0438 0473 0508 0543 0578 ! 0613 4 r 11 14 1 8 21 25 28 32 2-9 0647 0682 0716 0750 0784 I 0818 ! 0852 0880 0919 0953 3 7 10 14 17 20 24 27 31 30 0986 1019 1053 1086 1119 1151 1184 1217 1249 1282 3 7 10 13 16 20 23 26 30 31 1314 1346 1378 1410 1442 1474 1 1506 15S7 1569 1600 3 6 10 13 16 19 22 25 29 3-2 1632 1063 1694 1725 1750 17S7 1817 1848 1878 1909 3 ( 5 9 12 1 5 18 21 25 28 3-3 1 1939 1909 2000 2030 2060 2090 2119 2149 2179 2208 369 12 15 18 21 24 27 3-4 2238 2267 2296 2326 2355 2384 2413 2442 2470 2499 3 3 9 12 1 4 17 20 23 26 35 2528 2556 2585 2613 2641 2669 2698 2726 2754 2782 368 11 14 17 20 22 25 3-6 2809 2837 2865 2892 2920 2947 2975 3002 3029 3056 358 11 14 16 19 22 25 3-7 3083 3110 3137 3164 3191 3218 3244 3271 3297 3324 358 11 13 16 19 21 24 3-8 3350 3376 3403 3429 3455 3481 3507 3533 3558 3584 3 5 8 10 1 3 16 18 21 23 3-9 3610 3635 3661 3686 3712 3737 3762 3788 3813 3838 3 3 8 10 13 15 18 20 23 4-0 3863 3888 3913 3938 3962 3987 4012 4030 4061 4085 257 10 12 15 17 20 22 41 4110 4134 4159 4183 4207 4231 4255 4279 4303 4327 257 10 12 14 17 19 22 4-2 4351 4375 4398 4422 4446 4409 4493 4516 4540 4563 257 9 12 14 16 19 21 4-3 4586 4609 4633 4656 4679 4702 4725 4748 4770 4793 2 5 7 9 1 1 14 16 18 21 4-4 4816 4839 4861 4884 4907 4929 I 4951 4974 4990 5019 247 9 11 13 16 18 20 4-5 5041 5063 5085 5107 5129 5151 5173 5195 1 5217 5239 247 9 11 13 15 18 20 4-6 5261 5282 5304 5326 5347 5369 5390 5412 5433 5454 246 9 11 13 15 17 19 1-7 5476 5497 5518 5539 5560 5581 5602 5623 ! 5044 5665 2 t 6 8 1 1 13 15 17 19 4-8 5686 5707 5728 5748 5769 5790 5810 5831 5851 5872 246 8 10 12 14 16 19 4-9 5892 5913 5933 5953 5974 5994 6014 6034 6054 6074 246 8 10 12 14 16 18 5-0 6094 6114 6134 6154 6174 6194 6214 6233 6253 6273 246 8 10 12 14 16 18 LOGARITHMS OF SINES OF SMALL ARCS. Arc 0' 1' 2' 3' 4' 5' 6' T 8' 9' Cd c rt Table of Addition to be made to Logs, of bines to get corresponding Logs, of Tangents. i4 9518 9522 9525 9529 9538 1233 1117 64 .f 9537 9540 9544 9548 9551 9555 9558 9562 9560 9569 1223 1-134 65 ,.-9573 9576 9580 9583 9587 9590 9594 9597 9601 9604 1223 1-152 66 ,,-9607 9611 9614 9617 9621 9624 9627 9631 9634 9637 11223 1169 67 I.-9040 9643 9647 9650 9653 9(55(5 9659 9662 96632 0547 0502 0578 0593 3 5 8 10 13 49 0608 0024 0039 0654 0670 0685 0700 0716 0731 0746 3 5 8 10 13 50 '0702 0777 0793 0808 0824 0839 0854 0870 0885 0901 3 5 S 10 13 51 0016 0932 OJ47 0963 0978 0994 1010 1025 1041 1056 35 8 10 13 52 1072 1U88 1103 1119 1135 1150 1166 1182 1197 1213 3 5 8 10 13 53 1229 1245 1-^60 1276 1292 1308 1324 1340 1356 1371 3 5 8 11 33 54 1387 1403 1419 1435 1451 1467 1483 1499 1516 1532 3 5 8 11 13 55 1548 1564 1580 1596 1612 1629 1645 1661 1677 1694 3 5 8 11 14 56 1710 1726 1743 1759 1776 1792 1809 1825 1842 1858 3 5 8 11 14 57 1875 1891 1908 1925 1941 1958 1975 1992 2008 2025 3 6 8 11 14 58 2042 2059 2076 2093 2110 2127 2144 2161 2178 2195 3 6 9 11 14 59 2212 i229 2247 2264 2281 2299 2316 2333 2351 2368 3 6 9 12 14 60 2386 2403 2421 2438 2456 2474 2491 2509 2527 2545 3 6 9 12 15 61 2562 2580 2598 2616 2634 2652 2670 2689 2707 27-25 3 6 9 12 15 62 2743 2762 2780 2798 2817 2835 2854 2872 2891 2910 3 6 9 12 15 63 2928 2947 2966 2985 3004 3023 3042 3061 3080 3099 3 6 9 13 16 64 3118 3137 3157 3176 3196 3215 3235 3254 3274 3294 3 6 10 13 16 65 3313 3333 3353 3373 3393 3413 3433 3453 3473 3494 3 7 10 13 17 66 '3514 3535 3555 3576 3596 3617 3638 3659 3679 3700 3 7 10 14 17 67 3721 3743 3764 3785 3806 3828 3849 3871 3892 3914 4 7 11 14 18 68 3936 3958 3980 4002 4024 4046 4068 4091 4113 4136 4 7 11 15 19 69 4158 4181 4204 4227 4250 4273 4296 4319 4342 4366 4 8 12 15 19 70 4389 4413 4437 4461 4484 4509 4533 4557 4581 4606 4 8 12 16 20 71 4630 4655 4680 4705 4730 4755 4780 4805 4831 4857 4 8 13 17 21 72 4882 4908 4934 4960 4986 5013 5039 5066 6093 5120 4 9 13 18 22 73 5147 5174 5201 5229 5256 5284 5312 5340 5368 5397 5 9 14 19 23 74 5425 5454 5483 5512 5541 5570 5600 5629 5659 56b9 5 10 15 20 25 75 5719 5750 5780 5811 5842 5873 5905 5936 5968 6000 5 10 16 21 26 76 6032 6065 6097 6130 6163 6196 6230 6264 6298 6332 6 11 17 22 28 77 6366 6401 6436 6471 6507 6542 6578 6615 6651 66fe8 6 12 18 24 30 78 6725 (.763 6800 6838 6877 6915 6954 6994 7033 7073 6 13 19 26 32 79 7113 7154 7195 7236 7278 7320 7363 7406 7449 7493 7 14 21 28 35 80 7537 7581 7626 7672 7718 77g4 7811 7858 7906 7954 8 16 23 31 39 81 8003 8052 8102 8152 8203 8255 8307 8360 8413 8467 9 17 26 35 43 82 8522 8577 8633 8690 8748 8806 8865 8924 8985 9046 10 20 29 39 49 83 9109 9172 9236 9301 9367 9433 9501 9570 9640 9711 11 12 34 45 56 84 9784 9857 9932 0008 0085 0164 0244 0326 0409 0494 13 26 40 53 66 85 1-0580 0669 0759 0850 0944 1040 1138 1238 1341 1446 16 32 48 64 81 86 1-1 554 1664 1777 1893 2012 2135 2261 2391 2525 2663 87 1-2806 2954 3106 3264 3429 3599 3777 3962 4155 4357 88 1-4569 4792 5027 5275 5539 5819 6119 6441 0789 7167 89 1-7581 8038 8550 9130 9800 0591 1561 2810 4571 7581 90 + ao Radian =0017 1 0035 0052 1 0070 1 0087 | 0105 1 0122 1 0140 j-0157 1 14 NATURAL SINES. d d Mean Differences. rt g 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' at K - 8 '0 o-i. 0^2 0'3 0'4 0-5 0'6 V? 0'8 0-9 1' 2' 3' 4' 5' oooo oooo 0017 0035 0052 0070 0087 0105 0122 0140 0157 3 6 9 12 15 0175 1 0175 0192 0209 0227 0244 0262 0279 0297 0314 0332 3 6 9 12 15 0349 2 0349 0366 03b4 0401 0419 0436 0454 0471 0488 0506 3 6 9 12 15 0524 3 0523 0541 0558 0576 0593 0610 0628 0645 0663 0680 3 6 9 12 15 0698 4 0698 0715 0732 0750 0767 0785 0802 0819 0837 0854 3 6 9 12 14 0873 5 0872 0889 0906 0924 0941 0958 0976 U993 1011 1028 3 6 9 12 14 1047 6 1045 1063 1080 1097 1115 1132 1149 1167 1184 1201 3 6 9 12 14 1222 7 1219 1236 1253 | 1271 1288 1305 1323 1340 1357 1374 3 6 9 12 14 1396 8 1392 1409 1426 1444 1461 1478 1495 1513 1530 1547 3 6 9 12 14 1571 9 1564 1582 1599 1616 1633 1650 1668 1685 1702 1719 3 6 9 12 14 1745 10 1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 3 6 9 11 14 1920 11 1908 1925 1942 1959 1977 1994 2011 2028 2045 2062 3 6 9 11 14 2004 12 2079 2096 2113 2130 2147 2164 2181 2198 2215 2233 3 6 9 11 14 2269 13 2250 2267 2284 2300 2317 2334 2351 2368 2385 2402 3 6 8 11 14 2443 14 2419 2436 2453 2470 2487 2504 2521 2538 2554 2571 3 6 8 11 14 2618 15 2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 3 6 8 11 14 2793 16 2756 2773 2790 2807 2823 2840 2857 2874 2890 2907 3 6 8 11 14 2967 17 2924 2940 2957 2974 2990 3007 3024 3040 3057 3074 3 6 8 11 14 3142 18 3090 3107 3123 3140 3156 3173 3190 3206 3223 3239 3 6 8 11 14 3316 19 '3256 3272 3289 3305 3322 3338 3355 3371 3387 3404 3 5 8 11 14 3491 20 3420 3437 3453 3469 3486 3502 3518 3535 3551 3567 3 5 8 11 14 3665 21 3584 3600 3616 3633 3649 3665 3681 3697 3714 3730 3 5 8 11 14 3840 22 3746 3762 3778 3795 3811 3827 3843 3859 3875 3891 3 5 8 11 14 4014 23 3907 3923 3939 3955 3971 3987 4003 4019 4035 4051 3 5 8 11 14 4189 24 4067 40S3 4099 4115 4131 4147 4163 4179 4195 4210 3 5 8 11 13 4363 25 4226 4242 4258 4274 4289 4305 4321 4337 4352 4368 3 5 8 11 13 4538 26 4384 4399 4415 4431 4446 4462 4478 4493 4509 4524 3 5 8 10 13 4712 27 4540 4555 4571 4586 4602 4617 4633 4648 4664 4679 3 5 8 10 13 4887 28 4695 4710 4726 4741 4756 4772 4787 4802 4818 4833 3 5 8 10 13 5061 29 4848 4863 4879 4894 4909 4924 4939 4955 4970 4985 3 5 8 10 13 5236 30 5000 5015 5030 5045 5060 5075 5090 5105 5120 5135 3 5 8 10 13 5411 31 5150 5165 5180 5195 5210 5225 5240 5255 5270 5284 2 5 7 10 12 '5585 32 5299 5314 5329 5344 5358 5373 5388 5402 5417 5432 2 5 7 10 12 5760 33 5446 5461 5476 5490 5505 5519 5534 5548 5563 5577 2 5 7 10 12 5934 34 5592 5606 5621 5635 5650 5664 5678 5693 5707 5721 2 5 7 10 12 6109 35 5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 2 5 7 9 12 6283 36 5878 5892 5906 5920 5934 5948 5962 5976 5990 6004 2 5 7 9 12 6458 37 6018 6032 6046 6060 6074 6088 6101 6115 6129 6143 2 5 7 9 12 6632 38 6157 6170 6184 6198 6211 6225 6239 6252 6266 6280 2 5 7 9 11 6807 39 6293 6307 6320 6334 6347 6361 6374 6388 6401 6414 2 4 7 9 11 6981 40 6428 6441 6455 646S 6481 6494 6508 6521 6534 6547 2 4 7 9 11 7156 41 6561 6574 6587 6600 6613 6626 6639 6652 6665 6678 24 7 9 11 7330 42 6691 6704 6717 6730 6743 6756 6769 6782 6794 6807 2 4 6 9 11 7505 43 6820 6833 6845 6858 6871 6884 6896 6909 6921 6934 2 4 6 8 11 7679 44 6947 6959 6972 6984 6997 7009 7022 7034 7046 7059 2 4 6 8 10 7854 45 7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 2 4 6 8 10 Radian =001710035 10052 0070] 0087 0105 1 0122 0140 0157 NATURAL SINES. 15 Mean Differences. .2 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1 Q o-o 0-2 0'3 0'4 i 5 0'6 0-7 0'8 0-9 1' 2' 3' 4' 5' 785 45 7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 2 4 6 8 10 803 46 7193 7206 7218 7230 7242 7254 7266 7278 7290 7302 2 4 6 8 10 820 47 7314 7325 7337 7349 7361 7373 7385 7396 7408 7420 2 4 6 8 10 838 48 7431 7443 7455 7466 7478 7490 7501 7513 7524 7536 2 4 6 8 10 855 49 7547 7559 7570 7581 7593 7604 7615 7627 7638 7649 24689 873 50 7660 7672 7683 7694 7705 7716 7727 7738 7749 7760 24679 890 51 7771 7782 7793 7804 7815 7826 7837 7848 7859 7869 24579 908 52 7880 7891 7902 7912 7923 7934 7944 7955 7965 7976 24579 925 53 7986 7997 8007 8018 80-28 8039 8049 8059 8070 SOiSO 23579 942 54 8090 8100 8111 8121 8131 8141 8151 8161 8171 8181 23578 960 55 8192 8202 8211 8221 8231 8241 8251 8261 8271 8281 23578 977 56 8290 8300 8310 8320 8329 8339 8348 8358 8368 8377 23568 995 57 8387 8396 8406 8415 8425 8434 8443 8453 8462 8471 23568 1-012 58 8480 8490 8499 8508 8517 8526 8536 8545 8554 8563 23568 1-030 59 8572 8581 8590 8599 8607 8616 8625 8634 8643 8652 13467 1-047 60 8660 8669 8678 8686 8695 8704 8712 8721 8729 8738 13467 1-065 61 -8746 8755 8763 8771 8780 8788 8796 8805 8813 8821 13467 1-082 62 8829 8838 8846 8854 8862 8870 SS'JP 8886 8894 8902 13457 1100 63 8910 8918 8926 8934 8942 8949 8957 8965 8973 8980 13456 1-117 64 8988 8996 9003 9011 9018 9026 9033 9041 9048 9056 13456 1-134 65 9063 9070 9078 9085 9092 9100 9107 9114 9121 9128 12456 1-152 66 9135 9143 9150 9157 9164 9171 9178 9184 9191 9198 12356 1-169 67 9205 9212 9219 9225 9232 9239 9245 9252 9259 9265 12346 1-187 68 9272 9278 9-285 9291 9298 9304 9311 9317 9323 9330 12345 1-204 69 9336 9342 9348 9354 9361 9367 9373 9379 9385 9391 12345 1-222 70 9397 9403 9409 9415 9421 9426 9432 9438 9444 9449 12345 1-239 71 9455 9461 9466 9472 9478 9483 9489 9494 9500 9505 12345 1-257 72 9511 9516 9521 9527 9532 9537 9542 9548 9553 9558 12334 1-274 73 9563 9568 9573 9578 9583 9588 9593 9598 9603 9608 12234 1-292 74 9613 9617 9622 9627 963-2 9636 9641 9646 9650 9655 12234 1-309 75 9659 9664 9668 9673 9677 9681 9686 9690 9694 9699 11234 1-326 76 9703 9707 9711 9715 9720 9724 9728 9732 9736 9740 11233 1-344 77 9744 9748 9751 9755 9759 9763 9767 9770 9774 9778 11233 1-361 78 9781 9785 9789 9792 9798 9799 9803 9806 9810 9813 1 223 1-379 79 9816 9820 9823 9826 9829 9833 9836 9839 9842 9845 1 223 1-396 80 9848 9851 9854 9857 9860 9863 9866 9869 9871 9874 122 1-414 81 9877 9880 9882 9885 9888 9S90 9893 9895 9898 9900 122 1-431 82 9903 9905 9907 9910 9912 9914 9917 9919 9921 9923 122 1-449 83 9925 9928 9930 9932 9934 9936 9938 9940 9942 9943 112 1-466 84 9945 9947 9949 9951 9952 9954 9956 9957 9959 9960 112 1-484 85 9962 9963 9965 9966 9968 9969 9971 9972 9973 9974 00111 1-501 86 9976 9977 9978 9979 9980 9981 9982 99S3 9984 9985 00111 1-518 87 9986 9987 9988 9989 9990 9990 9991 9992 9993 9993 00011 1-536 88 9994 9995 9995 9996 9996 9997 9997 9997 9998 9998 00000 1-553 89 9998 9999 9999 9999 9999 1-000 i-ooo 1-000 I'OOO i-ooo 00000 1-571 90 1-000 Radian =0017 0035 1 0052 0070 1 0087 0105 0122 0140 0157 16 NATURAL COSINES. (3 X Mean Differences. .1 1 0' 6 12' 18' 24' 30' 36' 42' 48' 54' 1 tc q o-o 0'l O n '2 (T3 0-4 0-5 0-6 0-7 0'8 0-9 1' 2' 3' 4' 5' 0000 i-ooo i-ooo i-ooo i-ooo i-ooo i-ooo 9999 9999 9090 9999 00000 0175 i 9998 9998 9998 9997 9997 9997 9996 9996 9995 9995 00000 0349 2 9994 9993 9993 9992 9991 999 J 9990 9:*89 9983 9987 00011 0524 3 9986 9935 9.JS4 9983 9982 9981 9980 9979 9978 9977 00111 0698 4 9976 9974 9971 9372 9971 9969 9968 9966 9965 9963 00111 0873 5 9962 996 J 9959 9957 9956 9954 9952 9951 9949 9947 01112 1047 6 9945 9943 9942 9940 9938 9936 9934 5)932 9930 9928 01112 1222 7 9925 9923 9921 9919 9917 9914 9912 9910 9907 9905 01122 1896 8 9903 99 JO 9898 9S95 9893 9S90 9888 9885 9882 9880 01122 1571 9 9877 9374 9871 9869 9606 9863 98(50 9857 98 >4 9351 01122 -1745 10 9848 9845 9842 9339 9836 9633 9829 9826 9823 9620 11223 1920 11 9816 9313 9810 9806 9803 9799 9790 9792 9780 9785 11223 2094 12 9781 9778 9774 1)770 9767 9763 9759 9755 9751 9748 11233 2269 13 9744 9740 9736 9732 9728 9724 8720 9715 9711 9707 11233 2443 14 9703 9099 9J94 969 j 9686 9681 9677 9673 9668 90(54 11234 2618 15 9059 9655 9050 9640 9641 9636 9632 9627 9622 9617 12234 2793 16 9613 9608 9603 9598 9593 9588 9583 9578 9573 9568 12234 2937 17 9563 9558 9553 9548 9542 9537 9532 9527 9.321 9516 12334 3142 18 9511 9505 9500 9494 94S9 9483 9478 9472 9466 9461 12345 3316 19 9455 9449 9444 9438 9432 9426 9421 9415 9409 9403 12345 3491 20 9397 9391 9385 9379 9373 9367 9361 9354 9348 9342 12345 3665 21 9336 9330 9323 9317 9311 9304 9298 9291 9285 9278 12345 3840 22 9272 9265 9259 9252 9245 9239 9232 9225 9219 9212 12346 4014 23 9205 9198 9191 9184 "9178 9171 9164 9157 9150 9143 12356 4189 24 9135 9128 9121 9114 9107 9100 9092 9085 9078 9070 12456 4363 25 9063 9056 9048 9041 9033 9026 9018 9011 9003 8990 13456 4538 26 8988 8980 8973 8965. 8957 8149 8942 8934 8926 8918 13456 4712 27 8910 8902 8S94 8886 8878 8870 8862 8854 8346 8838 13457 4387 28 8829 8821 8313 8305 8796 8788 8780 8771 8763 8755 13467 5061 29 8746 8738 8729 8721 8712 8704 8695 8686 8678 8669 13467 5236 30 8660 8652 8643 8034 8625 8616 8607 8509 8590 8581 13467 5411 31 8572 85G3 8554 8545 8536 8526 8517 8508 8499 8490 23568 5585 32 8480 8471 8462 8453 8443 8434 8425 8415 8406 8396 23568 5760 33 8387 8377 8363 8358 8348 8:,39 8329 832 J 8310 b3uO 23568 5934 34 8290 8281 8271 8261 8251 8241 8231 8221 8211 8202 23578 6109 35 8192 8181 8171 8161 8151 8141 8131 8121 8111 8100 23578 6283 36 8090 8080 8070 8059 8049 8039 8028 8018 8007 7997 23579 6458 37 7986 7976 7965 7955 7944 7934 7923 7912 7902 7891 24579 6632 33 7880 7869 785!) 7848 7837 7826 7815 7804 7793 7782 24579 6807 39 7771 7760 7749 7738 7727 7716 7705 7694 7683 7672 24679 6981 40 7660 7649 7638 7627 7615 7604 7593 7581 7570 7559 24689 7156 41 7547 7536 75 ^ 7513 7501 7490 7478 7466 7455 7443 2 4 6 8 10 7330 42 7431 7420 7408 7396 7385 7373 7361 7349 7337 7325 2 4 6 8 10 7.505 43 7314 7302 7290 7278 7266 7254 7242 7230 7218 7206 2 4 6 8 10 7679 44 7193 7181 7169 7157 7145 7133 7120 7108 7096 7083 2 4 6 8 10 7854 45 7071 7059 7046 7034 7022 7009 6997 6984 6972 6951) 2 4 6 8 10 Radian = 0017 0035 ' 0052 0070 0087 0105 0122^0140 0157 NATURAL COSINES. 17 d 3 Mean Differences. 1 E 0' 6 12' 18' 24 30' 36' 42' 48' 54' i I o-o o-i 0'2 0-3 0'4 05 0-6 0-7 0'8 0-9 1' 2' 3' 4' 5' 785 45 7071 7059 7046 7034 7022 7009 6997 6984 6972 6959 2 4 6 8 10 803 46 6947 6934 6921 6909 6896 6884 6871 6858 6845 6833 2 4 6 8 11 820 47 6820 6807 6794 6782 6769 6756 6743 6730 6717 6704 2 4 6 9 11 838 48 6691 6678 6665 6652 6639 6626 6613 6600 6587 6574 2 4 7 9 11 855 49 6561 6547 6534 6521 6508 6494 6481 6468 6455 6441 2 4 7 9 11 873 50 6428 6414 6401 6388 6374 6361 6347 6334 6320 6307 2 4 7 9 11 890 51 6293 6280 6266 6252 6239 6225 6211 6198 6184 6170 2 5 7 9 11 90S 52 6157 6143 6129 6115 6101 6088 6074 6060 6046 6032 2 5 7 9 12 925 53 6018 6004 5990 5976 5962 5948 5934 5920 5906 5892 2 5 7 9 12 942 54 5878 5864 5850 5835 5821 5807 5793 5779 5764 5750 2 5 7 9 12 960 55 5736 5721 5707 5693 5678 5664 5650 5635 5621 5606 2 5 7 10 12 977 56 5592 5577 5563 5548 5534 5519 5505 5490 5476 5461 2 5 7 10 12 995 57 5446 5432 5417 5402 5388 5373 5358 5344 5329 5314 2 5 7 10 12 1-012 58 5299 5284 5270 5255 5240 5225 5210 5195 5180 5165 2 5 7 10 12 1-030 59 5150 5135 5120 5105 5090 5075 5060 5045 5030 5015 3 5 8 10 13 1-047 60 5000 4985 4970 4955 4939 4924 4909 4894 4879 4863 3 5 8 10 13 1-065 61 4848 4833 4818 4802 4787 4772 4756 4741 4726 4710 3 5 8 10 13 1-082 62 4695 4679 4664 4648 4633 4617 4602 4586 4571 4555 3 5 8 10 13 1-100 63 4540 4524 4509 4493 4478 4462 4446 4431 4415 4399 3 5 8 10 13 1-117 64 4384 4368 4352 4337 4321 4305 4289 4274 4258 4242 3 5 8 11 13 1-134 65 4226 4210 4195 4179 4163 4147 4131 4115 4099 4083 3 5 8 11 13 1-152 66 4067 4051 4035 4019 4003 3987 3971 3955 3939 3923 3 5 8 11 14 1-169 67 3907 3891 3875 3859 3843 3827 3811 3795 3778 3762 3 5 8 11 14 1-187 68 3746 3730 3714 3697 3681 3665 3649 3633 3616 3600 3 5 8 11 14 1-204 69 3584 3567 3551 3535 3518 3502 3486 3469 3453 3437 3 5 8 11 14 1-222 70 3420 3404 3387 3371 3355 3338 3322 3305 3289 3272 3 5 8 11 14 1-239 71 3256 3239 3223 3206 3190 3173 3156 3140 3123 3107 3 6 8 11 14 1-257 72 3090 3074 3057 3040 3024 3007 2990 2974 2957 2940 3 6 8 11 14 1-274 73 2924 2907 2890 2874 2857 2840 2823 2807 2790 2773 3 6 8 11 14 1-292 74 2756 2740 2723 2706 2689 2672 2656 2639 2622 2605 3 6 8 11 14 1*309 75 2588 2571 2554 2538 2521 2504 2487 2470 2453 2436 3 6 8 11 14 1-326 76 2419 2402 2385 2368 2351 2334 2317 2300 2284 2267 3 6 8 11 14 1-344 77 2250 2233 2215 2198 2181 2164 2147 2130 2113 2096 3 6 9 11 14 1-361 78 2079 2062 2045 2028 2011 1994 1977 1959 1942 1925 3 6 9 11 14 1-379 79 1908 1891 1874 1857 1840 1822 1805 1788 17-71 1754 3 6 9 11 14 1-396 80 1736 1719 1702 1685 1668 1650 1633 1616 1599 1582 3 6 9 12 14 1-414 81 1564 1547 1530 1513 1495 1478 1461 1444 1426 1409 3 6 9 12 14 1-431 82 1392 1374 1357 1340 1323 1305 1288 1271 1253 1236 3 6 9 12 14 1-449 83 1219 1201 1184 1167 1149 1132 1115 1097 1080 1063 3 6 9 12 14 1-466 84 1045 1028 1011 0993 0976 0958 0941 0924 0906 0889 3 6 9 12 14 1-484 85 0872 0854 0837 0819 0802 0785 0767 0750 0732 0715 3 6 9 12 14 1-501 86 0698 0680 0663 0645 0628 0610 0593 0576 0558 0541 3 6 9 12 15 1-518 87 0523 0506 0488 0471 0454 0436 0419 0401 0384 0366 3 6 9 12 15 1-536 88 0349 0332 0314 0297 0279 0262 0244 0227 0209 0192 3 6 9 12 15 1-553 89 0175 0157 0140 0122 0105 0087 0070 0052 0035 0017 3 6 9 12 15 1-571 90 oooo Radian =0017 0035 0052 0070 0087 0105 0122 0140 0157 C 18 NATURAL TANGENTS. a; Mean Differences. a (y 6' ' 12' 18' 24' 30' 36' 42' 48' 54' I I o-o o-i 0'2 03 0'4 0-5 0-6 0-7 9 70 1-1472 1-1519 1-1567 130 1-8126 1-8151 1-8175 11 0-1917 01975 0-2033 71 1-1614 1-1661 1-1709 131 1-8199 1-8223 1-8247 12 0-2091 0-2148 0'2206 72 1-1756 1-1803 1-1850 132 1-8271 1-8294 1-8318 13 0-2264 0-2322 0-2380 73 1-1896 1-1943 11990 133 1-8341 1-8364 1-8387 14 0-2437 0-2495 0-2553 74 1-2036 1-2083 1-2129 134 1-8410 1-8433 1-8455 15 0-2611 0-2668 0-2726 75 1-2175 1-2221 1-2267 135 1-8478 1-8500 1-8522 16 0-2783 0-2841 0-2899 76 1-2313 1-2359 1-2405 136 1-8544 1-8565 1-8587 17 0-2956 0-3014 0-3071 77 1-2450 1-2490 1-2541 137 1-8608 1-8630 1-8651 18 0-3129 0-3186 0-3244 78 1-2586 1-2632 1-2677 138 1-8672 1-8692 1-8713 19 0-3301 0-3358 0-3416 79 1-2722 1-2766 1-2811 139 1-8733 1'8754 1-8774 20 0-3473 0-3530 0-3587 80 1-2856 1-2900 1-2945 140 1-8794 1-8814 1-8833 21 0-3645 0-3702 0-3759 81 1-2989 1-3033 1-3077 141 1-8853 1-8872 1-8891 22 0-3816 0-3873 0-3930 82 1-3121 1-3165 1-3209 142 1-8910 1-8929 1-8948 23 0-3987 0-4044 0-4101 83 1-3252 1-3296 1-3339 143 1-8966 1-8985 1-9003 24 0-4158 0-4215 0-4272 84 1-3383 1-3426 1-3469 144 1-9021 1-9039 1 -9057 25 0-4329 0-4386 0-4442 85 1-3512 1-3555 1-3597 145 1-9074 1-9092 1-9109 26 0-4499 0-4556 0-4612 86 1-3640 1-3682 1-3725 146 1-9126 1-9143 1-9160 27 0-4669 0-4725 0-4782 87 1-3767 1-3809 1-3851 147 1-9176 1-9193 1-9209 28 0-4838 0-4895 0-4951 88 1-3893 1-3935 1-3977 148 1-9225 1-9241 1-9257 29 0-5008 0-5064 0-5120 89 1-4018 1-4060 1-4101 149 1-9273 1-9288 1-9303 30 0-5176 0-5233 0-5289 90 1-4142 1-4183 1-4224 150 1-9319 1-9333 1-9348 31 0-5345 0-5401 0-5457 91 1-4265 1-4306 1-4346 151 1-9363 1-9377 1-9392 32 0-5513 0-5569 0-5625 92 1-4387 1-4427 1-4467 152 1-9406 1-9420 1-9434 33 0-5680 0-5736 0-5792 93 1-4507 1-4547 1-4587 153 1-9447 1-9461 1-9474 34 0-5847 0-5903 0-5959 94 1-4627 1-4667 1-4706 154 1-9487 1-9500 1-9513 35 0-6014 0-6070 0-6125 95 1-4746 1-4785 1-4824 155 1-9526 1-9538 1-9551 36 0-6180 0-6236 0-6291 96 1-4863 1-4902 1-4941 156 1-9563 1-9575 1-9587 37 0-6346 0-6401 06456 97 1-4979 1-5018 1-5056 157 1-9598 1-9^10 1-9621 38 0-6511 0-6566 0-6621 98 1-5094 1-5132 1-5170 158 1-9633 1-9644 1-9654 39 0-6676 0-6731 0-6786 99 1-5208 1-5246 1-5283 1J59 1-9665 1 -9676 1-9686 40 0-6840 0-6895 0-6950 100 1-5321 1-5358 1-5395 160 1-9696 1-9706 1-9716 41 0-7004 0-7059 0-7113 101 1-5432 1-5469 1-5506 161 1-9726 1-9735 1-9745 42 0-7167 0-7222 0-7276 102 1-5543 1-5579 1-5616 162 1-9754 1-9763 1-9772 43 0-7330 0-7384 0-7438 103 1-5652 1-5688 1-5724 163 1-9780 1-9789 1 '9797 44 0-7492 07546 0-7600 104 1-5760 1-5796 1-5832 164 1-9806 1-9813 1-9821 45 0-7654 0-7707 0-7761 105 1-5867 1-5902 1-5938 165 1-9829 1-9836 1-9844 46 0-7815 0-7868 07922 106 1-5973 1-6008 1-6042 166 1-9851 1-9858 1-9865 47 0-7975 0-8028 0-8082 107 1-6077 1-6112 1-6146 167 1-9871 1-9878 1-9884 48 0-8135 0-8188 0-8241 108 1-6180 1-6214 1-6248 168 1-9890 1-9896 1-9902 49 0-8294 0-8347 0*8400 109 1-6282 1-6316 1-6350 169 1-9908 1-9913 1-9919 50 0-8452 0-8505 0-8558 110 1-6383 1-6416 1-6450 170 1-9924 1-9929 1-9934 51 0-8610 0-8663 0-8715 111 1-6483 1-6515 16548 171 1-9938 1-9943 1-9947 52 0-8767 0-8820 0-8872 112 1-6581 1-6613 1-6640 172 1-9951 1-9955 1-9959 53 0-8924 0-8976 0-9028 113 1-6678 1-6710 1-6742 173 1-9963 1-9966 1 -9969 54 0-9080 0-9132 0-9183 114 1-6773 1-6805 1-6836 174 1-9973 1-9976 1-9978 55 0-9235 0-9287 0-9338 115 1-6868 1-6899 1-0930 175 1-9981 1-9983 1-9986 56 0-9389 0-9441 0-9492 116 1-6961 1-6992 1-7022 176 1-9988 1-9990 1-9992 57 0-9543 0-9594 0-9645 117 1-7053 1-7083 17113 177 1-9993 1-9995 1-9996 58 0-9696 0-9747 0-9798 118 1-7143 1-7173 1-7203 178 1-9997 1-9998 1-9999 59 C-9848 0-9899 0-9950 119 1-7233 1-7262 1-7291 179 1-9999 2-0000 2-0000 60 1-0000 1-0050 1-0101 120 1-7321 1-7350 1-7378 180 2-0000 2-0000 2-0000 CIRCULAR FUNCTIONS TO RADIANS. 27 Degree. Radian. Sine. Tangent. Cosine. Logarithm of Sine. Tangent. Cosine. 573 10 0998 1003 9973 2-9993 f-0015 1-9978 6'30 11 1098 1104 9940 f-0405 ,,'0431 ,,9974 6-88 12 1197 1206 9928 n-0781 ,,'0813 ,,'9969 7'45 13 1296 1307 9916 u-1127 ,,'1164 ,,'9963 8-02 14 1395 1409 9902 ,,'1447 ,,-&90 ,,-9957 8-59 15 1494 1511 9888 u-1745 ,,'1794 ,,'9951 9-17 16 1593 1614 9872 .,-2023 ,,'2078 ,,'9944 9-74 17 1692 1717 9856 n-2284 ,,2347 ,,'9937 10-31 18 1790 1820 9839 u-2529 ,,'2600 ,,'9929 10-89 19 1889 1923 98-20 .,'2761 ti*2840 ,,9921 11-46 20 1987 2027 9801 ,,'2981 ,,-3069 ,,'9913 12-03 21 2085 2131 9780 ,,'3190 ,,-3287 ,,'9904 12-61 22 2182 2236 9759 ,.-3389 ,,-3495 ,,'9894 13-18 23 2280 2341 9737 ,,-3579 ,,-3695 ,,'9884 1375 24 2377 2447 9713 ,,-3760 ,,-3887 ,,'9874 14-32 25 2474 2553 9689 n-3934 ,,'4071 ,,'9863 14-90 26 2571 2660 9664 ,,'4101 ,,'4249 ,,-9S52 15-47 27 2667 2768 9638 ,,-4261 ,,-4421 ,,9840 16-04 28 2764 2876 9611 ,,4415 ,,4587 ,,'9827 16-62 29 2859 2984 9583 ,,'4563 ,,'4748 ,,'9815 17*19 30 2955 3093 9553 ,,4706 ,,-4904 ,,'9802 17-76 31 3051 3203 9523 ,,'4844 ,,-5056 ,,'9788 18-33 32 3146 3314 9492 ,,'4977 ,,'6203 ,,'9774 18-91 33 3240 3425 9460 ,,-5106 ,,'5347 ,,9759 19-48 34 3335 3537 9428 ,,-5231 ,5487 ,,'9744 20-05 35 3429 3650 9394 ,,-5352 n'5623 ,,9728 20-63 36 3523 3764 9359 ,,-5469 ,,'5757 ,,9712 21-20 37 3616 3879 9323 ,,-5582 ,,'5887 i,-9696 2177 38 3709 3994 9287 ,,-5693 ,,'6014 ,,'9679 22-34 39 3802 4111 9249 n '5800 ,,-6139 ,,-9661 22-92 40 3894 4228 9211 ,,-5904 n'6261 ,,'9643 23-49 41 3986 4346 9171 ,,-6005 ,,'6381 ,,-9624 24-06 42 4078 4466 9131 ,,-6104 ,,'6499 ,,-9605 24-64 43 4169 4586 9090 i. -6200 ,,'6615 ,,-9586 25-21 44 4259 4708 9048 ,,-6293 ,,'6728 ,,-9565 25-78 45 4350 4831 9005 ,,'6385 ,,'6840 ,,-9545 26-36 46 4439 4954 8961 ,,'6473 ,,-6950 ,,'9523 26-93 47 4529 5080 8916 ,,'6560 ,,7058 ,,-9502 27-50 48 4618 5206 8870 ,,-6644 ,,7165 ,,'9479 28-07 49 4706 5334 8823 ,,-6727 ,,7270 ,,'9456 28-65 50 4794 5463 8776 ,,-6807 ,,7374 ,,-9433 29-22 51 4882 5594 8727 ,,-6886 ,,7477 ,,'9409 29-79 52 4969 5726 8678 ,,-6962 ,,7578 ,,'9384 30-37 53 5055 5859 8628 ,,'7037 ,,7678 ,,-9359 30-94 54 5141 5994 8577 ,,-7111 ,,7777 ,,'9333 31-51 55 5227 6131 8525 ,,-7182 ,,7875 ,,'9307 32-09 56 5312 6269 8473 ,,'7253 ,,7972 ,,'9280 32-66 57 5396 6410 8419 ,,'7321 ,,'8068 ,,'9253 33-23 58 5480 6552 8365 ,,'7388 ,,'8164 ,,9224 33-80 59 5564 6696 8309 ,,'7454 ,,'8258 ,,-9196 34-37 60 5646 6841 8253 1,7518 ,,'8351 ,,-9166 28 CIRCULAR FUNCTIONS TO RADIANS, Degree. Radian. Sine. Tangent. Cosine. Logarithms of Sine. Tangent. Cosine. 34-38 60 5646 0-6841 8253 1-7518 f-8351 T-9166 34-9.V 61 572:) 0-6989 8196 H 7681 ,,-8444 ,,-9136 35-52 62 5810 0-7139 8139 M -7642 i,-8536 ,,-9106 36-10 63 5891 0-7291 8080 i,7767 1664 1661 1658 165u ' 1653 1650 1647 1645 1642 3 127 449 823 1217 1613 61 1039 1637 1634 1631 1629 ! 1626 1623 1621 1618 !(>!<; 3 131 457 827 1223 1619 62 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 3 137 461 829 1229 1621 63 1587 1585 1582 1580 1577 1575 1572 1570 1567 1565 3 139 463 839 1231 1627 64 1563 1560 1558 1555 1553 1550 1548 1546 1543 1541 3 149 467 853 1237 1637 65 1538 1536 1534 1531 1529 1527 1524 1522 1520 1517 2 151 479 857 1249 1657 66 1515 1513 1511 1508 1506 1504 1502 1499 1497 1495 2 157 487 859 1259 1663 67 1493 1490 1488 1486 1484 1481 1479 1477 1475 1473 2 163 491 863 1277 1667 68 1471 1468 1466 1464 146-2 1460 1458 1456 1453 1451 2 167 499 877 1279 1669 69 1449 1447 1445 1443 1441 1439 1437 1435 1433 1431 2 173 503 881 1283 1693 70 1429 1427 1425 1422 1420 1418 1416 1414 1412 1410 2 179 509 883 12b9 1697 71 1408 1406 1404 1403 1401 1399 1397 1395 1393 1391 2 181 521 887 1291 1699 72 1389 1387 1385 1383 1881 1379 1377 1376 1374 1372 2 191 523 907 1297 1709 73 1370 1368 1366 1364 1362 1361 1359 1357 1355 1353 2 193 541 911 1301 1721 74 1351 1350 1348 1346 1344 1 1342 1340 1339 1337 1335 2 197 547 919 Ib03 1723 75 1333 1332 1330 1328 1326 1325 1323 1321 1319 1318 2 199 557 Oi 1307 1733 76 1316 1314 1312 1311 1309 1307 1305 1304 1302 1300 2 211 563 937 1319 1741 77 1299 1297 1295 1294 1292 1290 1289 1287 1285 1284 2 223 569 941 1321 1747 78 1282 1280 1279 1277 1276 1274 1272 1271 1269 1267 2 227 571 947 1327 1753 79 1266 1264 1263 1261 1259 1258 1256 1255 1253 1252 2 229 577 953 1361 1759 80 1250 1248 1247 1245 1244 1242 1241 1239 1238 1236 2 233 5b7 907 1367 1777 81 1235 1233 1232 1230 1229 1227 1225 1224 1222 1221 2 239 593 971 1373 1783 82 1220 1218 1217 1215 1214 1212 1211 1209 1208 1206 2 241 599 977 1381 1787 83 1205 1203 1202 1200 1199 1198 1196 1195 1193 1192 1 251 6ul 983 1399 1789 84 1190 1189 1188 1186 1185 1183 1182 1181 1179 1178 1 257 007 991 1409 1801 85 1176 1175 1174 1172 1171 1170 1168 1167 1166 1164 I 263 613 997 1423 1811 86 1163 1161 1160 1159 1157 1156 1155 1153 1152 1151 1 269 617 1009 1427 1823 87 1149 1148 1147 1145 1144 1143 1142 1140 1139 1138 1 271 619 1013 1429 1831 88 1136 1135 1134 1133 1131 1130 1129 1127 1126 1125 1 277 631 1019 1433 1847 89 1124 1122 1121 1120 1119 1117 1116 1115 1114 1112 1 281 641 1021 1439 1861 90 1111 1110 1109 1107 1106 1105 1104 1103 1101 1100 1 283 643 lOol 1447 1867 91 1099 1098 1096 1095 1094 1093 1092 1091 1089 1088 1 293 647 1033 1451 1871 92 1087 1086 1085 1083 1082 1081 1080 1079 1078 1076 1 307 653 1039 1453 1873 93 1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 1 311 659 H'49 1459 1877 94 1064 1063 1062 1060 1059 1058 1057 1056 1055 1054 1 313 661 1051 1471 1879 95 1053 1052 1050 1049 1048 1047 1046 1045 1044 1043 1 317 673 1061 1481 1889 96 1042 1041 1040 1038 1037 1036 1035 1034 1033 1032 1 331 677 1003 1483 1901 97 1031 1030 1029 1028 1027 1026 1025 1024 1022 1021 1 337 6b3 1069 1487 1907 98 1020 1019 1018 ' 1017 1016 1015 1014 1013 1012 1011 1 347 691 1087 1489 1913 99 1010 1009 1008 1007 1006 1005 1004 1003 1002 1001 1 349 701 1091 1493 1931 100 1000 9990 99bO 9970 9960 9950 9940 9930 9921 9911 10 353 709 1093 1499 1933 101 9901 9891 9881 9872 9862 9852 9843 9833 9823 9814 10 359 719 1097 1511 1949 102 9804 9794 9785 9775 9766 9756 9747 9737 9728 9718 10 367 727 1103 1523 1951 103 9709 9699 9690 9681 9671 9662 9653 9643 9634 9625 9 373 733 1109 1531 1973 104 9615 9606 9597 9588 9579 9569 9560 9551 9542 9533 5) 379 739 1117 1543 1979" 105 9524 9515 9506 9497 9488 9479 9470 9461 9452 9443 9 383 743 1123 1549 1987 106 9434 9425 9416 9407 9398 9390 9381 9372 9363 9355 9 389 751 1129 1553 1993 107 5)346 9337 9328 9320 ( )311 9302 9294 9285 9276 5)268 5) 397 757 1151 1569 1997 108 5)259 9251 9242 9234 9225 9217 9208 1)200 9191 9183 9 401 761 1153 1567 1999 109 9174 9166 9158 9149 9141 9132 9124 9116 9107 9099 S 409 769 1163 1571 2003 110 9091 9083 9074 9006 9058 9050 9042 9033 9025 9017 8 419 773 1171 1579 2011 34 SQUARES OF NUMBERS. The squares are given to the first four figures, no account being taken of ' place-value. 1 1 Number. 1 2 3 4 5 6 7 8 9 Mean Differences. 1 2 3 456 789 10 1000 1020 1040 1061 1082 1103 1124 1145 1166 1188 246 8 11 13 15 17 19 11 1210 1232 1254 1277 1300 1323 1346 1369 1392 1416 257 9 12 14 16 18 21 12 1440 1464 1488 1513 1538 1563 158S 1613 1638 1664 358 10 13 15 18 20 23 13 1690 1716 1742 1769 1796 1823 1850 1877 1904 1932 358 11 14 16 1 19 22 24 14 1960 1988 2016 2045 2074 2103 2132 2161 2190 2220 369 12 15 17 JO 23 26 15 2250 2280 2310 2341 2372 2403 2434 2465 2496 2528 369 12 16 19 22 25 28 16 2560 2592 2624 2657 2690 2723 2756 2789 2822 2856 3 7 10 13 17 20 23 26 30 17 2390 2924 2958 2993 3028 3063 3098 3133 3168 3204 4 7 11 14 18 21 25 28 32 18 3240 3276 3312 3349 3386 3423 3460 3497 3534 3572 4 7 11 15 19 22 26 30 33 19 3610 3648 3636 3725 3764 3803 3842 3881 3920 3960 4 8 12 16 20 23 27 31 35 20 4000 4040 4080 4121 4162 4203 4244 4285 4326 4368 4 8 12 16 21 25 29 33 37 21 4410 4452 4494 4537 4580 4623 4666 4709 4752 4796 4 9 13 17 22 26 30 34 39 22 4840 4834 4928 4973 5018 5063 5108 5153 5198 5244 5 9 14 18 23 27 32 36 41 23 5290 5336 5382 5429 5476 5523 5570 5617 5664 5712 5 9 14 19 24 28 33 38 42 24 5760 5808 5856 5905 5954 6003 6052 6101 6150 6200 5 10 15 20 25 29 34 39 44 25 6250 6300 6350 6401 6452 6503 6554 6605 6656 6708 5 10 15 20 26 31 36 41 46 26 6760 6812 6864 6917 6970 7023 7076 7129 7182 7236 5 11 16 21 27 32 37 42 48 27 7290 7344 7398 7453 7508 7563 7618 7673 7728 7784 6 11 17 22 28 33 39 44 50 28 7840 7896 7952 8009 8066 8123 8180 8237 8294 8352 6 11 17 23 29 34 40 46 51 29 8410 8468 8526 8585 8644 8703 8762 8821 8880 8940 6 12 18 24 30 35 41 47 53 30 9000 9060 9120 9181 9242 9303 9364 9425 9486 9548 6 12 18 24 31 37 43 49 55 31 9610 9672 9734 9797 9860 9923 9986 6 13 19 25 32 38 44 50 56 31 1005 1011 1018 112 334 456 32 1024 1030 1037 1043 1050 1056 1063 1069 1076 1082 112 334 556 33 1089 1096 1102 1109 1116 1122 1129 1136 1142 1149 112 334 556 34 1156 1163 1170 1176 1183 1190 1197 1204 1211 1218 112 334 566 35 1225 1232 1239 1246 1253 1260 1267 1274 1282 1289 112 344 566 36 1296 1303 1310 1318 1325 1332 1340 1347 1354 1362 112 344 566 37 1369 1376 1384 1391 1399 1406 1414 1421 1429 1436 122 345 567 38 1444 1452 1459 1467 1475 1482 1490 1498 1505 1513 122 345 567 39 1521 1529 1537 1544 1552 1560 1568 1576 1584 1592 122 345 667 40 1600 1608 1616 1624 1632 1640 1648 1656 1665 1673 122 345 667 41 1681 1689 1697 1706 1714 1722 1731 1739 1747 1756 122 345 677 42 1764 1772 1781 1789 1798 1806 1815 1823 1832 1840 123 345 678 43 1849 1858 1866 1875 1884 1892 1901 1910 1918 1927 123 345 678 44 1936 1945 195'4 1962 1971 1980 1989 1998 2007 2016 123 4 4 5 678 45 2025 2034 2043 2052 2061 2070 2079 2088 2098 2107 123 455 678 46 2116 2125 2134 2144 2153 2162 2172 2181 2190 2200 123 456 778 47 2209 2218 2228 2237 2247 2256 2266 2275 2285 2294 123 456 789 48 2304 2314 2323 2333 2343 2352 2362 2372 2381 2391 123 456 789 49 2401 2411 2421 2430 2440 2450 2460 2470 2480 2490 123 456 789 50 2500 2510 2520 2530 2540 2550 2560 2570 2581 2591 123 456 789 51 2601 2611 2621 2632 2642 2652 2663 2673 2683 2694 123 456 789 52 2704 2714 2725 2735 2746 2756 2767 2777 2788 2798 123 456 789 53 2809 2820 2830 2841 2852 2862 2873 2884 2894 2905 123 456 7 9 10 54 2916 2927 2938 2948 2959 2970 2981 2992 3003 3014 123 457 8 9 10 55 3025 3036 3047 3058 3069 3080 3091 3102 3114 3125 123 467 8 9 10 SQUARES OF NUMBERS. 35 The squares are given to the first four figures, no account being taken of ' place-value.' 1 4" Mean Differences. s & __ 1 2 3 456 789 55 3025 3036 3047 3058 3069 3080 3091 3102 3114 3125 123 467 8 9 10 56 3136 3147 3158 3170 3181 3192 3204 3215 3226 3238 123 567 8 9 10 57 3249 3260 3272 3283 3295 3306 3318 3329 3341 3352 123 567 8 9 10 58 3364 3376 3387 3399 3411 3422 3434 3446 3457 3469 124 567 8 9 11 59 3481 3493 3505 3516 3528 3540 3552 3564 3576 3588 124 567 8 10 11 60 3600 3612 3624 3636 3648 3660 3672 3684 3697 3709 124 567 8 10 11 61 3721 3733 3745 3758 3770 3782 3795 3807 3819 3832 124 567 9 10 11 62 3844 3856 3869 3881 3894 3906 3919 3931 3944 3956 134 568 9 10 11 63 3969 3982 3994 4007 4020 4032 4045 4058 4070 4083 134 568 9 10 11 64 4096 4109 4122 4134 4147 4160 4173 4186 4199 4212 134 568 9 10 12 65 4225 4238 4251 4264 4277 4290 4303 4316 4330 4343 134 578 9 10 12 66 4356 4369 4382 4396 4409 4422 4436 4449 4462 4476 134 578 9 11 12 67 4489 4502 4516 4529 4543 4556 4570 4583 4597 4610 134 578 9 11 12 68 4624 4638 4651 4665 4679 4692 4706 4720 4733 4747 134 578 10 11 12 69 4761 4775 4789 4802 4816 4830 4844 4858 4872 4886 134 678 10 11 13 70 4900 4914 4928 4942 4956 4970 4984 4998 5013 5027 134 678 10 11 13 71 5041 5055 5069 5084 5098 5112 5127 5141 5155 5170 134 679 10 11 13 72 5184 5198 5213 5227 5242 5256 5271 5285 5300 5314 134 679 10 12 13 73 5329 5344 5358 5373 5388 5402 5417 5432 5446 5461 134 679 10 12 13 74 5476 5491 5506 5520 5535 5550 5565 5580 5595 5610 134 679 10 12 13 75 5625 5640 5655 5670 5685 5700 5715 5730 5746 5761 235 689 11 12 14 76 5776 5791 5806 5822 5837 5852 5868 5883 5898 5914 235 689 11 12 14 77 5929 5944 5960 5975 5991 6006 6022 6037 6053 6068 235 689 11 12 14 78 6084 6100 6115 6131 6147 6162 6178 6194 6209 6225 235 689 11 13 14 79 6241 6257 6273 6288 6304 6320 6336 6352 6368 6384 235 6 8 10 11 13 14 80 6400 6416 6432 6448 6464 6480 6496 6512 6529 6545 235 6 8 10 11 13 14 81 6561 6577 6593 6610 6626 6642 6659 6675 6691 6708 235 7 8 10 11 13 15 82 6724 6740 6757 6773 6790 6806 6823 6839 6856 6872 235 7 8 10 12 13 15 83 6889 6906 6922 6934) 6956 6972 6989 7006 7022 7039 235 7 8 10 12 13 15 84 7056 7073 7090 7106 7123 7140 7157 7174 7191 7208 235 7 8 10 12 14 15 85 7225 7242 7259 7276 7293 7310 7327 7344 7362 7379 235 7 9 10 12 14 15 86 7396 7413 7430 7448 7465 7482 7500 7517 7534 7552 235 7 9 10 12 14 16 87 7569 7586 7604 7621 7639 7656 7674 7691 7709 7726 245 7 9 11 12 14 16 88 7744 7762 7779 7797 7815 7832 7850 7868 7885 7903 245 7 9 11 12 14 16 89 7921 7939 7957 7974 7992 8010 8028 8046 8064 8082 245 7 9 11 13 14 16 90 8100 8118 8136 8154 8172 8190 8208 8226 8245 8263 245 7 9 11 13 14 16 91 8281 8299 8317 8336 8354 8372 8391 8409 8427 8446 245 7 9 11 13 15 16 92 8464 8482 8501 8519 8538 8556 8575 8593 8612 8630 4 6 7 9 11 13 15 17 93 8649 8668 8686 8705 8724 8742 8761 8780 8798 8817 4 6 7 9 11 13 15 17 94 883G 8855 8874 8892 8911 8930 8949 8968 8987 9006 4 6 8 9 11 13 15 17 95 9025 9044 9063 9082 9101 9120 9139 9158* 9178 9197 4 6 8 10 11 13 15 17 96 9216 9235 9254 9274 9293 9312 9332 9351 9370 9390 4 6 8 10 12 14 15 17 97 9409 9428 9448 9467 9487 9506 9526 9545 9565 9584 4 6 8 10 12 14 16 18 98 9604 9624 9643 9663 96S3 9702 9722 9742 9761 9781 4 6 8 10 12 14 16 18 99 9801 9821 9841 9860 9880 9900 9920 9940 9960 9980 4 6 8 10 12 14 16 18 36 CUBES OF NUMBERS. The cubes are given to tlie first four figures, no account being taken of 'place- value.' tJ Mean Differences. 3 j 5 5 i 123 456 789 10 1000 1030 1061 1093 1125 1158 1191 1225 1260 1295 3 7 10 13 17 20 23 26 30 11 1331 1308 1405 1443 1482 1521 1561 1602 1643 1685 4 8 12 16 20 24 28 32 36 12 1723 1772 1816 1801 1907 1953 2000 2048 2097 2147 5 9 14 19 23 28 33 38 42 13 2197 2248 2300 2353 2406 24GO 2515 2571 2628 2686 5 11 16 22 27 33 38 44 49 14 2744 2803 2863 2924 2986 3049 3112 3177 3242 3308 6 13 19 25 32 38 44 50 57 15 3375 3443 3512 3582 3652 3724 3796 3870 3944 4020 7 14 22 29 36 43 50 58 65 16 4096 4173 4252 4331 4411 4492 4574 4657 4742 4827 8 16 25 33 41 49 57 65 74 17 4913 5000 5088 5178 5268 5359 5452 5545 5640 5735 9 18 28 37 46 55 64 74 83 18 5832 5930 6029 6126 6230 6332 6435 6539 6645 6751 10 20 31 41 52 62 72 82 92 19 6859 0968 7078 1 7189 7301 7415 7530 7645 7762 7881 11 23 34 46 57 68 80 91 103 20 8000 8121 8242 8365 8490 8615 8742 8870 8999 9129 13 25 38 50 63 76 88 101 113 21 9261 9394 9528 9604 9800 9938 14 27 41 54 68 82 95 109 122 21 1008 1022 1036 1050 135 679 10 12 13 22 1065 1079 1094 1109 1124 1139 1154 1170 1185 1201 235 689 11 12 14 23 1217 1233 1219 1265 12ol 1296 1314 1331 1348 1365 235 7 8 10 12 13 15 24 1382 1400 141 i 14J5 1453 1471 1489 1507 1525 1544 245 7 9 11 13 14 16 25 1563 1581 1600 1619 1639 1658 1678 1697 1717 1737 246 8 10 12 14 16 18 26 1758 1778 1798 181s) 1840 1861 1882 1903 1925 1947 246 8 11 13 15 17 19 27 196S 1990 2012 2035 2057 2080 2102 2125 2148 2172 257 9 11 14 16 18 20 28 2195 2219 2243 2267 2291 2315 2339 2364 2389 2414 257 10 12 15 17 20 22 29 2439 2464 2490 2515 2541 2567 2593 2620 2646 2673 358 10 13 16 18 21 23 30 2700 2727 2754 2/ 82 2809 2837 2865 2893 2922 2950 368 11 14 17 20 22 25 31 2979 3008 3037 3066 3096 3126 3155 3186 3216 3246 369 12 15 18 21 24 27 32 3277 3308 3339 3370 3401 3433 3465 3497 3529 3561 3 6 10 13 16 19 22 25 29 33 3594 3626 3659 361)3 M726 3760 3793 3827 3861 3896 3 7 10 13 17 20 24 27 30 34 3930 3965 4000 40J5 4071 4106 4142 4178 4214 4251 4 7 11 14 18 21 25 29 32 35 4288 4324 4361 4399 4436 4474 4512 4550 4588 4627 4 8 11 15 19 23 26 30 34 36 4666 4705 4744 4783 4S23 4863 4903 4943 4984 5024 4 8 12 16 20 24 28 32 36 37 5065 5106 5148 j 5190 5231 5273 5316 5358 5401 5444 4 8 13 17 21 25 30 34 38 38 5487 5531 5574 5618 5662 5707 5751 5796 5841 5886 4 9 13 18 22 27 31 36 40 39 5932 5978 6024 j 6070 6116 6163 (5210 6257 6304 6352 5 9 14 19 23 28 33 37 42 40 6400 6448 6496 6545 6594 6643 6692 6742 6792 6842 5 10 15 20 25 30 34 39 44 41 6892 6943 6993 7044 7096 7147 7199 7251 7303 7356 5 10 16 21 26 31 36 41 47 42 7409 7462 7515 7569 7623 7677 7731 7785 7840 7895 5 11 16 22 27 33 38 43 49 43 7951 8006 8062 j 8118 8175 8231 ! 8288 8345 8403 84(50 (3 11 17 23 28 34 40 45 51 44 8518 8577 8635 8694 8753 8812 8872 8931 8992 9052 6 12 18 24 30 36 42 48 54 45 9113 9173 9235 9296 9358 9420 9482 9544 9607 9670 6 12 19 25 31 37 43 50 56 46 9734 9797 9861 9925 9990 6 13 19 26 32 38 45 51 58 46 1005 1012 1018 1025 1032 112 334 556 47 1038 1045 1052 1058 1065 1072 1079 1085 1092 1099 1 1 2 334 556 48 1106 1113 1120 1127 1134 1141 1148 1155 1162 1169 112 344 566 49 1176 1184 1191 1198 1206 1213 1220 1223 1235 1243 112 344 567 50 1250 1258 1265 1273 12^0 1288 129^5 1303 1311 1319 122 345 567 51 1327 1334 1342 1350 1358 1366 1374 1382 1390 1398 122 345 667 52 1406 1414 1 1422 1431 1439 1447 1455 1464 1472 1480 122 345 677 53 1489 1497 i 1506 1514 1523 1531 1540 1549 1557 1566 123 345 678 54 1575 1583 1592 ! 1601 1610 1619 1628 1637 1646 1655 123 445 678 55 1. 1664 1673 j 1682 1691 1700 1710 1719 1728 1737 1747 123 456 678 CUBES OF NUMBERS. 37 The cubes are given to the first four figures, no account being taken of 'place- value.' s Mean Differences. X) o 1 2 3 4 5 Q 7 g q 1 2 3 456 789 55 1664 1673 1682 1691 1700 1710 1719 1728 1737 1747 1 2 3 456 678 56 1756 1766 1775 1785 1794 1804 1813 1823 1833 1842 123 456 789 57 1852 1862 1871 1881 1891 1901 1911 1921 1931 1941 123 456 789 58 1951 1961 1971 1982 1992 2002 2012 2023 2033 2043 123 456 789 59 2054 2064 2075 2085 2096 2106 2117 2128 2138 2149 123 456 7 8 10 60 2160 2171 2182 2193 2203 2214 2225 2236 2248 2259 123 4 6 7 8 9 10 61 2270 2281 2292 2303 2315 2326 2337 2349 2360 2372 124 567 8 9 10 62 2383 2395 2406 2418 2430 2441 2453 2465 2477 2489 124 567 8 9 11 63 2500 2512 2524 2536 2548 2560 2573 2585 2597 2G09 124 567 8 10 11 64 2621 2634 2646 2658 2671 2683 2696 2708 2721 2734 134 568 9 10 11 65 2746 2759 2772 2784 2797 2810 2823 2836 2849 2862 134 568 9 10 12 66 2875 2888 2901 2914 2928 2941 2954 2967 2981 2994 134 578 9 11 12 67 3008 3021 3035 3048 3062 3075 3089 3103 3117 3130 134 578 10 11 12 68 3144 3158 3172 3186 3200 3214 3228 3242 3257 3271 134 678 10 11 13 69 3285 3299 3314 3328 3343 3357 3372 3386 3401 3415 134 679 10 12 13 70 3430 3445 3459 3474 3489 3504 3519 3534 3549 3564 134 679 10 12 13 71 3579 3594 3609 3625 3640 3655 3671 3686 3701 3717 2 3 5 679 11 12 14 72 3732 3748 3764 3779 3795 3811 3827 3842 3858 3874 2 3 5 689 11 13 14 73 3890 3906 3922 3938 3954 3971 3987 4003 4019 4036 235 6 8 10 11 13 15 74 4052 4069 4085 4102 4118 4135 4152 4168 4185 4202 235 7 8 10 12 13 15 75 4219 4236 4253 4270 4287 4304 4321 4338 4355 4372 235 7 9 10 12 14 15 76 4390 4407 4425 4442 4459 4477 4495 4512 4530 4548 245 7 9 11 12 14 16 77 4565 4583 4601 4619 4637 4655 4673 4691 4709 4727 245 7 9 11 13 14 16 78 4746 4764 4782 4800 4819 4837 4856 4874 4893 4912 246 7 9 11 13 15 17 79 4930 4949 4968 4987 5006 5025 5044 5063 5082 5101 246 8 10 11 13 15 17 80 5120 5139 5158 5178 5197 5217 5236 5256 5275 5295 246 8 10 12 14 16 17 81 5314 5334 5354 5374 5394 5413 5433 5453 5473 5494 246 8 10 12 14 16 18 82 5514 5534 5554 5574 5595 5615 5636 5656 5677 5697 246 8 10 12 14 16 18 83 5718 5739 5759 5780 5801 5822 5843 5864 5885 5906 246 8 10 13 15 17 19 84 5927 5948 5969 5991 6012 6034 6055 6076 6098 6120 246 9 11 13 15 17 19 85 6141 6163 6185 6207 6228 6250 6272 6294 6316 6338 247 9 11 13 15 18 20 86 6361 6383 6405 6427 6450 6472 6495 6517 6540 6562 257 9 11 13 16 18 20 87 6585 6608 6631 6653 6676 G699 6722 6745 G7G8 6792 257 9 12 14 16 18 21 88 6815 6838 6S61 6885 6908 G932 6955 6979 7002 7026 257 9 12 14 16 19 21 89 7050 7073 7097 7121 7145 7169 7193 7217 7242 72GG 257 10 12 14 17 19 22 90 7290 7314 7339 7363 7388 7412 7437 7461 7486 7511 257 10 12 15 17 20 22 91 7536 7561 7586 7610 7636 7661 7686 7711 7736 7762 358 10 13 15 18 20 23 92 7787 7812 7838 7863 7889 7915 7940 7966 7992 8018 358 10 13 15 18 21 23 93 8044 8070 8096 8122 8148 8174 8200 8227 8253 8279 358 10 13 16 18 21 24 94 8306 8332 8359 8386 8412 8439 8466 8493 8520 8547 358 11 13 16 19 21 24 95 8574 8601 8628 8655 8683 8710 8737 8765 8792 8820 358 11 14 16 19 22 25 96 8847 8875 8903 8931 8958 8986 9014 9042 9070 9099 368 11 14 17 20 22 26 97 9127 9155 9183 9212 9240 9209 9297 9326 >3f)4 93S3 369 11 14 17 20 23 26 98 9412 9441 9470 9499 9528 9557 9586 9615 9G44 9G74 369 12 15 17 20 23 26 99 9703 9732 J762 9791 9821 9851 9880 9910 9940 J970 369 12 15 18 21 24 27 . i COMPOUND INTEREST TABLE, Showing 'Amount' of 1, after from 1 to 50 years (or other equal periods), at N ,81 IV. I* y. 2V. 2-5 % 3V. 35 /. 4% 4'5 % 5V. 1 1 -01 000 1-01500 1-02000 1-02500 1-03000 1-03500 1-04000 1-04500 1-05000 2 1-02010 1-03023 1-04040 1-05063 1-06090 1-07123 1-08160 1-09203 1-10250 3 1-03030 1-04568 1-06121 1-07689 1-09273 1-10872 1-12486 1-14117 115763 4 1-04060 1-06136 1-08243 1-10381 1-12551 1-14752 1-16986 1-19252 1-21551 5 1-05101 1-07728 1-10408 1-13141 1-15927 1-18769 1-21665 1-24618 1-27628 6 1-06152 1-09344 1-12616 1-15969 1 19405 1-22926 1-26532 1-30226 1-34010 7 1-07214 1-10984 1-14869 1-18869 1-22987 1-27228 1-31593 1-36086 1-40710 8 1-08286 1-12649 1-17166 1-21840 1-26677 1-31681 1-36857 1-42210 1-47746 9 1-09369 1-14339 1-19509 1-24886 1-30477 1-36290 1-42331 1-48610 1-55133 10 1-10462 1-16054 1-21899 1-28008 1-34392 1-41060 1-48024 1-55297 1-62889 11 1-11567 1-17795 1-24337 1-31209 1-38423 1-45997 1-53945 1-62285 1-71034 12 1-12683 1-19562 1-26824 1-34489 1-42576 1-51107 1-60103 1-69588 1-79586 13 1-13809 1-21355 1-29361 1-37851 1-46853 1-56396 1-66507 1-77220 1-88565 14 1-14947 1-23176 1-31948 1-41297 1-51259 1-61869 1-73168 1-85194 1-97993 15 1-16097 1-25023 1-34587 1-44830 1-55797 1-67535 1-80094 1-93528 2-07893 16 1-17258 1-26899 1-37279 1-48451 1-60471 1-73399 1-87298 2-02237 2-18287 17 1-18430 1-28802 1-40024 1-52162 1-65285 1-79468 1-94790 2-11338 2-29202 18 1-19615 1-30734 1-42S25 1-55966 1-70243 1-85749 2*02582 2-20848 2-40662 19 1-20811 1-32695 1 -45681 1-59865 1-75351 1-92250 2-10685 2-30786 2-52695 20 1-22019 1-34686 1-48595 1-63862 1-80611 1-98979 219112 2-41171 2-65330 21 1-23239 1-36706 1-51567 1-67958 1 -86029 2-05943 2-27877 2-52024 2-78596 22 1-24472 1-38756 1-54598 1-72157 1-91610 2-13151 2-36992 2-63365 2-92526 23 1-25716 1-40838 1-57690 1-76461 1-97359 2-20611 2-46472 2-75217 3-07152 24 1-26973 1-42950 1-60844 1-80873 2-03279 2-28333 2-56330 2-87601 3-22510 25 1-28243 1-45095 1-64061 1-85394 2-09378 2-36324 2-66584 3-00543 3-38635 26 1-29526 1-47271 1-67342 1-90029 2-15659 2-44596 277247 3-14068 3-55567 27 1-30821 1-49480 1-70689 1-94780 2-22129 2-53157 2-88337 3-28201 3-73346 28 1-32129 1-51722 1-74102 1-99650 2-28793 2-62017 2-99870 3-42970 3-92013 29 1-33450 1-53998 1-77584 2-04641 2-35657 271188 311865 3-58404 4-11614 30 1-34785 1-56308 1-81136 2-09757 2-42726 2-80679 3-24340 3-74532 4-32194 31 1-36133 1-58653 1-84759 2-15001 2-50008 2-90503 3-37313 3-91386 4-53804 32 1-37494 1-61032 1-88454 2-20376 2-57508 3-00671 3-50806 4 -0^998 4-76494 33 1-38869 1-63448 1-92223 2-25885 2-65234 3-11194 3-64838 4-27403 5-00319 34 1-40258 1-65900 1-96068 2-31532 2-73191 3-22086 3-79432 4-46636 5-25335 35 1-41660 1-68388 1-99989 2-37321 2-81386 3-33359 3-94609 4-66735 5-51602 36 1-43077 1-70914 2-03989 2-43254 2-89828 3-45027 4-10393 4-87738 5-79182 37 1-44508 1-73478 2-08069 2-49335 2-98523 3-57103 4-2(5809 5-09686 6-08141 38 1-45953 1-76080 2-12230 2-55568 3-07478 3-69601 4-43881 5-32622 6-35848 39 1-47412 1-78721 2-16474 2-61957 3-16703 3'b2537 4-61637 5-56590 6-70475 40 1-48886 1-81402 2-20804 2-68506 3-26204 3-95926 4-80102 5-81636 7-03999 41 1-50375 1-84123 2-25220 275219 3-35990 4-09783 4-99306 6-07810 7-39199 42 1-51879 1-86885 2-29724 2-82100 3-46070 4-24126 5-19278 6-35162 7-76159 43 1-53398 1-89688 2-34319 2-89152 3-56452 4-38970 5-40050 6-63744 8-14967 44 1-54932 1-92533 2'b9005 2-96381 3-67145 4-54334 5-61652 6-93612 8-55715 45 1-56481 1-95421 2-43785 3-03790 3-78160 4-70236 5-84118 7-24825 8-98501 46 1-58046 1-98353 2-48661 3-11385 3-89504 4-86694 6-07482 7*57442 9-43426 47 1-59626 2-01328 2-53634 3-19170 4-01190 5-03728 6-31782 7-91527 9-90597 48 1-61223 2-04348 2-58707 3-27149 4-13225 5-21359 6-57053 8-27146 10-40127 49 1-62835 2-07413 2-63881 3-35328 4-25622 5-39606 6-83335 8-64367 10-92133 50 1-64463 2-10524 2-69159 3-43711 4-38391 5-58493 7-10668 9-03264 11-46740 COMPOUND INTEREST TABLE. Present Value of 1 due 1 to 50 years (or other equal periods) hence, at 39 Year or Period. IV. 1-5 % 2V. 2'5 V. 3V. 3'5 /. 4V. 4'5 V. 5V. 1 99010 98522 98039 97561 97087 96618 96154 95694 95238 2 9S030 97066 96117 95181 94260 93351 92456 91573 90703 3 97059 95632 94232 92860 91514 90194 88900 87630 86384 4 96098 94218 92385 90595 88849 87144 85480 83856 82270 5 95147 92826 90573 88385 86261 84197 82193 80245 78353 6 94205 91454 88797 86230 83748 81350 79031 76790 74622 7 93272 90103 87056 84127 81309 78599 75992 73483 71068 8 92348 88771 85349 82075 78941 75941 73069 70319 67684 9 91434 87459 83676 80073 76642 73373 70259 67290 64461 10 90529 86167 82035 78120 74409 70692 67556 64393 61391 11 89632 84893 80426 76214 72242 68495 64958 61620 58468 12 88745 83639 78849 74356 70138 66178 62460 58966 55684 13 87866 82403 77303 72542 68095 63940 60057 56427 53032 14 86996 81185 75788 70773 66112 61778 57748 53997 50507 15 66135 79985 74301 69047 64186 59689 55526 51672 48102 16 85282 78803 72845 67363 62317 57671 53391 49447 45811 17 84438 77639 71416 65720 60502 55720 51337 47318 43630 18 83602 76491 70016 64117 58739 53836 49363 452hO 41552 19 82774 75361 68643 62553 57029 52016 47464 43330 39573 20 81954 74247 67297 61027 55368 50257 45639 41464 37689 21 -81143 73150 65978 59539 53755 48557 43883 39679 35894 22 80340 72069 64684 58086 52169 46915 42196 37970 34185 23 79544 71004 63416 56670 50669 45329 40573 36335 32557 24 78757 69954 62172 55288 49193 43796 39012 34770 31007 25 77977 68921 60953 53939 47761 42315 37512 33273 29530 26 77205 67902 59758 52623 46369 40884 36069 31840 28124 27 76440 66899 58586 51340 45019 39501 34682 30469 26785 28 75684 65910 57437 50088 43708 38165 33348 29157 25509 29 74934 64936 56311 48866 42435 36875 32065 27902 24295 30 74192 63976 55207 47674 41199 35628 30832 26700 23138 31 73458 63031 54125 46511 39999 34423 29646 25550 22036 32 72730 62099 53063 45377 38834 33259 28506 24450 20987 33 72010 61182 52023 44270 37703 32134 27409 23397 19987 34 71297 60277 51003 43191 36604 31048 26355 22390 19035 35 70591 59387 50003 42137 35538 29998 25342 21425 18129 36 69892 58509 49022 41109 34503 28983 24367 20503 17266 37 69200 57644 48061 40107 33498 28003 23430 19620 16444 38 -68515 56792 47119 39128 32523 27056 22529 18775 15661 39 67837 55953 46195 38174 31575 26141 21662 17967 14915 40 67165 55126 45289 37243 30656 25257 20829 17193 14205 41 66500 54312 44401 36335 29763 24403 20028 16453 13528 42 65842 53509 43530 35448 28896 23578 19257 15744 12884 43 65190 52718 42677 34584 28054 22781 18517 15066 12270 44 04545 51939 41840 33740 27237 22010 17805 14417 11686 45 63900 51171 41020 32917 26444 21266 17120 13796 11130 46 63273 50415 40215 32115 25674 20547 16461 13202 10600 47 62646 49670 39427 31331 24926 19852 15828 12634 10095 48 62026 48936 38654 30567 24200 19181 15219 12090 09614 49 61412 48213 37896 29822 23495 18532 14634 11569 09156 50 60804 47500 37153 29094 22811 17905 14071 11071 08720 40 EXPONENTIALS 6- HYPERBOLIC FUNCTIONS. X e* e-* cosh x sinh x tanhz log cosh x log sinh x 1 1-1052 9048 1-0050 1002 0997 0-0022 f-0007 2 1-2214 8187 1-0201 2013 1974 0086 n-3039 3 1-3499 7408 1 -0453 3045 2913 0193 n'4836 4 1-4918 6703 1-0811 4108 3799 0339 ..-6136 5 1-6487 6065 11276 5211 4621 0522 n-7169 6 1-8221 5488 1-1855 6367 5370 07S9 ,,-8039 7 2-0138 4966 1-2552 7586 6044 0987 M-8800 8 2-2255 4493 1-3374 8881 6640 1263 ,,9485 9 2-4596 4066 1-4331 1-0265 7163 1563 0-0114 i-o 27183 3679 1-6431 11752 7616 1884 0-0701 1-1 3-0042 3329 1-6685 1-3357 8005 2223 0-1257 1-2 33201 3012 1-8107 1-5095 8337 2578 0-1788 1-3 3-6693 2725 1-9709 1-6984 SC17 2947 0-2300 1-4 4-0552 2466 2-1509 1-9043 8854 3326 0-2797 1-5 4-4817 2231 2-3524 2-1293 9051 3715 0-3282 1-6 4-9530 2019 2-5775 2'3756 9217 4112 0-3758 1-7 5-4739 1827 2-8283 2 -6456 9354 4515 0-4225 1-8 6-0496 1653 3-1075 2-9422 9468 4924 0-4687 1-9 6-6859 1496 3-4177 3-2682 9563 5337 0-5143 2-0 7-3891 1353 37622 S'6269 9640 5754 0-5595 21 8-1662 1225 41443 4-0219 9704 6175 0-6044 22 9-0251 1108 4-5679 4-4571 9758 6597 0-6491 23 9-9742 1003 5-0372 4-9370 9801 7022 0-6935 2-4 11-0232 0907 5-5570 5-4662 9837 . . '7448 ;, 0-7377 2-5 12-1825 0821 6-1323 6-0502 9866 7876 07S18 2-6 13-4638 0743 6-7690 6-6947 9890 8305 0-82*7 27 148797 .'0672 7 '4 7 35 7-4063 9910 8735 0-8696 2-8 16-4446 0608 8-2527 8-1919 9926 9166 0-9134 2-9 18-1741 0550 9-1146 9-0596 9940 9597 0-9571 3-0 20-0855 0498 10-068 10-018 9951 1-0029 1-0008 3-1 22-1980 0450 11-122 11-076 9959 1 '0462 1 -0444 3-2 24-5325 0408 12-287 12-246 9967 1-0894 1 '0880 3-3 27-1126 0369 13-575 13-538 9973 1-1327 1-1316 3-4 29-9641 0334 14-999 14-965 9978 1-1761 1-1751 3-5 331155 0302 16-573 16-543 9982 1-2194 1-2186 36 36-5982 0273 18-313 18-285 9985 1-2628 1 -2621 3-7 40-4473 0247 20-236 20-211 9988 1 -3061 1 -3056 3-8 44-7012 0224 22-362 22-339 9990 1-3495 1 -3491 39 49-4024 0202 24:711 24-691 9992 1-3929 1 '3925 4-0 54-5982 0183 27 '308 27-190 9993 1-4363 1-4360 4-1 60-3403 0166 30-178 30-162 9995 1-4797 1-4795 4-2 66-6863 0150 33-351 33-336 9996 1-5231 1-5229 4-3 73-6998 0136 36-857 36-843 9996 1 '5665 1-5664 4-4 81-4509 0123 40-732 40719 9997 1-6099 1-6098 4-5 90-0171 0111 45-014 45-003 9997 1-6533 1-6532 4-6 99-4843 0101 49-747 49737 9998 1 '6968 1-6967 4-7 109-9472 0091 54-978 54-969 9998 1-7402 1-7401 4'8 121-5104 0082 60-759 60-751 9999 1-7836 1-7836 4-9 134-2898 0074 67-149 67141 9999 1 -8270 1-8270 5-0 148-4132 0067 74-210 74-203 9999 1-8705 1-8704 YB I734T Books \ E J. S. M/ Descript Trigonoi Mensura Mensura Land Su Mensura GEOMETRIES ON THE NEW LINES. 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. iensuratio Fables of \ dtci ^NovS9PW REC" '3 flOV l b 1959 ftEC'D CD JAK 251960 120d'6S$F REC'D LD SEP 2 8 '3 -1PM c T,n 91 A f^Ow A 'so General Library ^ '(AimuOm'BB 9 UniVerS &k!lef ^^ and Cheapness Journal & WEHTiETH CENTURY DICTIONARY OF TH_BfGUSH LANGUAGE. Edited by the Rev, THOMAS DAVIDSON, Editor of " Cham!>ers ! s English Dictionary/' 1224 pages, STO, Price 1224 pages, demy Svo* Price 3/6 Also, quarter bound, s, ; half morocco, 8s. 6d, net T&is awrveUousiy Cfeeap Book, Svs. ~ Supersedes aSi othtr ohaap Dictionaries " I ! -W, ROBERTSON NiCOLL in British