2 55 J59 L J UC NRLF 1 lllllli llllllii m en $B 2Mfi 323 GIFT OF Prof* R. Tracy Crawford ^.S^Is/i.-^t.'^^y^^J^- FOUR-PLACE i'{ LOGARITHMS BY GEORGE William/ JONES Professor of Mathematics in Cornell University I. Four-place Logarithms of Three-figure XUMBERS. II. The Natural Sines, Cosikes, Tangents, AND Cotangents of Angles differing BY Ten Minutes, and their Four- place Logarithms. A good collection of Mathematical Tables is like a Dictionary : it may lie on the shelf for months, hut ichen it is loanted it is ivanted, and its use for a single hour may he ivorth the iwice of the hook. JONES' FIVE-PLACE LOGARITHMS. PAGES I. LOGARITHMS OF NUMBERS, ... - 2-19 A table of five-place logarithms of four-figure num- bers, with differences for a fifth figure. II. TRIGONOMETRIC FUNCTIONS, ... - 20-64 A table of natural sines, cosines, tangents and co- tangents of angles 0°-180°, to minutes, and of their five-place logarithms, with differences for seconds. III. MINOR TABLES, -. - . . - - 3-19 Natural Logarithms; Ten.Place Logarithms; Weights and Measures; Mathematical Constants; Mei-idionai Parts; Square.Roots; Cube-Roots; Reciprocals; Sines and Tangents of Small Angles. JONES' LOGARITHMIC TABLES. FOUR-PLACE, SIX-PLACE, AND TEN-PLACE. EXPLANATION OF THE TABLES, .... 3-11 I. FOUR-PLACE LOGARITHMS, - - . 12-14 A four-place table of logarithms of the natural num- bers 1, 2, 3,.. 999, with a table of proportional differ- ences in the margin, and of the logarithms of the squares, cubes, squai-e-roots, cube-roots and recip- rocals of the numbers 1, 3, 3,. ,99. IL FOUR-PLACE TRIGONOMETRIC FUNCTIONS, - 15-19 A four-place table of logarithms of the six principal trigonometric functions, Avith differences for min- utes, and of the length of arcs in radians. III. LOGARITHMS OF NUMBERS, - - - 20-37 A six-place table of logarithms of four-figure num- bers, with a table of differences. IV. CONSTANTS OF MATHEMATICS AND OF NATURE —WEIGHTS AND MEASURES, - - 38-41 A table of useful constants, with the logarithms of those in common use. V. ADDITION-SUBTRACTION LOGARITHMS, . 43-58 A six-place table of logarithms so i-elated that, by their use, the logarithm of the sum and of the diff. erence of two numbers may be found from their logarithms without taking o\xt the numbers them- selves. VL SINES AND TANGENTS OF SMALL ANGLES, - 59 A table of the ratios sinA":A, tanA":A for angles 0°-5°, whereby the logarithmic sines and tangents of these small angles are found more exactly than by Table VII. (SEE THE THIRD COVER PAGE.) FOUK-PLACE LOGAEITHMS. -i ^r^ FORM OF A LOGARITHM. ^r^Ji.J(r^ The Logarithm of a number is the exponent of that power to which another number, the base, must be raised to give tlie number first named. The base commonly used is 10 ; and as most numbers are incommensurable powers of 10, a common logarithm, in general, consists of an integer, the charactenstic, and an endless decimal, the mantissa. If a number be resolved into two .factors, of which one is an integer power of 10 and the other lies between 1 and 10, then the exponent of 10 is the characteristic, and the logarithm of the other factor is the mantissa. The characteristic is- positive if the number be larger than 1 , and negative if it be smaller ; the mantissa is always positive. A negative character- istic is indicated by the sign — above it. The logarithms of numbers that differ only by the position of the decimal point have different characteristics but the same mantissa. J&.5'. 7770 = 103x7.77 and log 7770 = 3.8904 ; .0777 = 10-2x7.77, and log .0777 = 2.8904. tables of logarithms. The logarithms of any set of consecutive numbers, arranged in a form convenient for use, constitute a table of logarithms. Such a table to the base 10 need give only the man- tissas ; the characteristics are manifest. This table is arranged upon the common double- entry plan i.e. the mantissa of the logarithm of a three-figure number stands opposite the first two figures and under the third figure. The logarithms are given correct to four places. to take out the logarithm of a number. A three-figure number : Take out the tabular mantissa that lies in line with the first two figures of the number and under the third figure ; the characteristic is the exponent of that integer power of 10 which lies next below the number. E.g. log 677 = 2.8306, log 6.78 = 0.8312, log .0679 = 2.8319, log 676 000 = 5.8299. A number of less than three figures : Make the number a three-figure number by annex- ing zeros, and follow the rale given above. ^.g-. log 700 = 2.8451, log 7 = 0.8451, log .0071 = 3.a513, log 71 000 = 4.8513. A four figure number : Take out the tabular mantissa of the first three figures, and add such part of the difference between this mantissa and the next greater tabular mantissa (the tabular difference)., as the fourth figure is a part of 10 ; and so for a five-figure number. ^.^. •.•log678 =2.8312 and log 679 = 2.8319, .'. log 678.6 = 2.8312 + .0007 x 6/10 = 2.8316, log 6.7875=0.8312 + .0007 x 75/100=0.8317. TO TAKE OUT A NUMBER FROM ITS LOGARITHM. The mantissa found in the table .- Join the figure at the top that lies above the given mantissa to the two figures upon the same line at the extreme left ; in this three-figure number so place the decimal point that the number shall be next above that power of 10 whose exponent is the characteristic of the logarithm. JE-.j/. log-i 2.8312 = 678, log-i 0.8451 = 7, log-i 3.8513 = .0071, log-1 5.8513 = 710000. The mantissa not found in the table ,- Take out the three-figure number of the tabular mantissa next less than the given mantissa, and to these three figures join the quotient of the difference of these two mantissas by the tabular difference. E.g. •.- log 678 = 2.8312 and log 679 = 2.8319, .-. log-i 2.8316 = 678J = 678.6, log-i 2.8317 = .0678f = .06787. The use of trigonometric ratios and their logarithms is explained in works on trigonometry. 1 1 2 3 4 5 6 h i 8 9 0000 0000 3010 4771 6021 6990 7782 8451 9031 9542 1 0000 0414 0792. 1139 1461 1761 2041 2304 2553 2788 2 3010 3222 3424 361.7 3802 3979 4150 4314 4472 4624 3 4771 4914 5051 5185 5315 5441 5563 5682 5798 5911 4 6021 6128 6232 6335 6435 0532 6628 6721 6812 6902 5 6990 7076 7160 7243 7324 7404 7482 7559 7634 7709 6 7782 7853 7924 7993 8062 8129 8195 8261 8325 8388 7 8451 8513 8573 8633 8692 8751 8808 8865 8921 8976 8 9031 9085 9138 9191 9243 9294 9345 9395 9445 9494 9 9542 9590 9638 9685 9731 9777 9823 9868 9912 9956 10 0000 0043 0086' 0128 0170 0212 0253 0294 0334 0374 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 16 2041 2068 2095 2122 2148 2175 2201 2227 225 3 2279 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 31 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 38 5798 5809 5821 5839 5843 5855 5866 5877 5888 5899 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 45 6532 6542 6551 6561 C571 6580 6590 6599 6609 6618 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 50 1 2 3 4 5 6 7 8 9 1 1 50 1 9 3 4 5 6 7 8 9 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 52 7160 7168 7177 7185 7193 7202 7210 7218 7926 7235 53 7243 7351 7259 7267 7275 7284 7292 7300 7308 7316 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 56 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 58 7634 7642 7649 7637 7G64 7672 7679 7686 7694 7701 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 73 8633 8639 8G45 8651 8657 8663 8669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 91 9590 9595 9G00 9605 9609 9614 9619 9624 9628 9638 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 100 1 2 3 4 5 6 7 8 9 ANGLE. SINES. COSINES. TANGENTS. COTANGENTS. ANGLE. Nat. Log. Nat. Log. Nat. Log. Log. Nat. 0°00' .0000 00 1.0000 0.0000 .0000 00 00 00 90°00' 10 .0029 7.4637 1.0000 0000 .0029 7.4637 2.5363 343.77 50 20 .0058 7648 1.0000 0000 .0058 7648 2352 171.89 40 30 .0087 9408 1.0000 0000 .0087 9409 0591 114,59 30 40 .0116 8.0658 .9999 0000 .0116 8.0658 1.9342 85.940 20 50 .0145 1627 .9999 0000 .0145 1627 8373 68,750 10 1°00' .0175 8.2419 .9998 9.9999 .0175 8.2419 1.7581 57.290 89°00' 10 .0204 3088 .9998 9999 .0204 3089 6911 49.104 50 20 .0233 3668 .9997 9999 .0233 3669 6331 42.964 40 30 .0262 4179 .9997 9999 .0262 4181 5819 38.188 30 40 .0291 4637 .9996 9998 .0291 4638 5362 34.368 20 50 .0320 5050 .9995 9998 .0320 5053 4947 31.242 10 2°00' .0349 8.5428 .9994 9.9997 .0349 8.5431 1.4569 28.636 88°00' 10 .0378 5776 .9993 9997 .0378 5779 4221 26.432 50 20 .0407 6097 .9992 9996 .0407 6101 3899 24.542 40 30 .0436 6397 .9990 9996 .0437 6401 3599 22.904 30 40 .0465 6677 .9989 9995 .0466 6682 3318 21.470 20 50 .0494 6940 .9988 9995 .0495 6945 3055 20.206 10 3°00' .0523 8.7188 .9986 9.9994 .0524 8.7194 1.2806 19.081 87°00' 10 .0552 7423 .9985 9993 .0553 7429 2571 18.075 50 20 .0581 7645 .9983 9993 .0582 7652 2348 17.169 40 30 .0610 7857 .9981 9992 .0612 7865 2135 16.350 30 40 .0640 8059 .9980 9991 .0641 8067 1933 15.605 20 50 .0669 8251 .9978 9990 .0670 8261 1739 14.924 10 4°00' .0698 8.8436 .9976 9.9989 .0699 8.8446 1.1554 14.301 86°00' 10 .0727 8613 .9974 9989 .0729 8624 1376 13.727 50 20 .0756 8783 .9971 9988 .0758 8795 1205 13.197 40 30 .0785 8946 .9969 9987 .0787 8960 1040 12.706 30 40 .0814 9104 .9967 9986 .0816 9118 0882 12.251 20 50 .0843 9256 .9964 9985 .0846 9272 0728 11.826 10 50OO' .0872 8.9403 .9962 9.9983 .0875 8.9420 1.0580 11.430 85°00' 10 .0901 9545 .9959 9982 .0904 9563 0437 11.059 50 20 .0929 9682 .9957 9981 ,0934 9701 0299 10.712 40 30 .0958 9816 .9954 9980 ,0963 9836 0164 10.385 30 40 .0987 9945 .9951 9979 .0992 9966 0034 10.078 20 50 .1016 9.0070 .9948 9977 ,1022 9.0093 0.9907 9.7882 10 6 = 00' .1045 9.0192 .9945 9.9976 ,1051 9.0216 0.9784 9.5144 84°00' 10 .1074 0311 .9942 9975 .1080 0336 9664 9.2553 50 20 .1103 0426 .9939 9973 .1110 0453 9547 9.0098 40 30 .1132 0539 .9936 9972 .1139 0567 9433 8.7769 30 40 .1161 0648 .9932 9971 .1169 0678 9322 8.5555 20 50 .1190 0755 ,9929 9969 .1198 0786 9214 8.3450 10 r°oo' .1219 9.0859 .9925 9.9968 .1228 9.0891 0.9109 8.1443 83000' 10 .1248 0961 .9922 9966 .1257 0995 9005 7.9530 50 20 .1276 1060 .9918 9964 .1287 1096 8904 7.7704 40 30 .1305 1157 .9914 9963 .1317 1194 8806 7.5958 30 40 .1334 1252 .9911 9961 ,1346 1291 8709 7.4287 20 50 .1363 1345 .9907 9959 .1376 1385 8615 7.2687 10 8°00' .1392 9.1436 .9903 9.9958 .1405 9.1478 0.8522 7.1154 82°00' 10 .1421 1525 .9899 9956 .1435 1569 8431 6.9682 50 20 .1449 1612 .9894 9954 .1465 1658 8342 6.8269 40 30 .1478 1697 .9890 9952 .1495 1745 8255 6.6912 30 40 .1507 1781 .9886 9950 .1524 1831 8169 6.5606 20 50 .1536 1863 .9881 9948 .1554 1915 8085 6.4348 10 9°00' .1564 9.1943 .9877 9.9946 .1584 9.1997 0.8003 6.3138 81°00' Nat. Log. Nat. Log. Nat. Log. Log. Nat. ANGLE. COSINES. SINES. COTANGENTS. TANGENTS. ANGLE. ANGLE. SINES. COSINES. TANGENTS. COTANGENTS. ANGLE. Nat. Log. Nat, Log. Nat. Log. Log. Nat. 9»00' .1564 9.1943 .9877 9.9946 .1584 9.1997 0.8003 6.3138 81°00' 10 .1593 2022 .9872 9944 .1614 2078 7922 6.1970 50 20 .1622 2100 .9868 9942 .1644 2158 7842 6.0844 40 30 .1650 2176 .9863 9940 .1673 2236 7764 5.9758 30 40 .1679 2251 .9858 9938 .1703 2313 7687 5.8708 20 50 .1708 2324 .9853 9936 .1733 2389 7611 5.7694 10 WOO' .1736 9.2397 .9848 9.9934 .1763 9.2463 0.7537 5.6713 80°00' 10 .1765 2468 .9843 9931 .1793 2536 7464 5.5764 50 20 .1794 2538 .9838 9929 .1823 2609 7391 5.4845 40 30 .1822 2606 .9833 • 9927 .1853 2680 7320 5.3955 30 40 .1851 2674 .9827 9924 .1883 2750 7250 5.3093 20 50 .1880 2740 .9822 9922 .1914 2819 7181 5.2257 10 11°00' .1908 9.2806 .9816 9.9919 .1944 9.2887 0.7113 5.1446 79°00' 10 .1937 2870 .9811 9917 .1974 2953 7047 5.0658 50 20 .1965 2934 .9805 9914 .2004 3020 6980 4.9894 40 30 .1994 2997 .9799 9912 .2035 3085 6915 4.9152 30 40 .2022 3058 .9793 9909 .2065 3149 6851 4.8430 20 50 .2051 3119 .9787 9907 .2095 3212 6788 4.7729 10 12°00' .2079 9.3179 .9781 9.9904 .2126 9,3275 0.6725 4.7046 78°00' 10 .2108 3238 .9775 9901 .2156 3336 6664 4.6382 50 20 .2136 3296 .9769 9899 .2186 3397 6003 4.5736 40 30 .2164 3353 .9763 9896 .2217 3458 6542 4.5107 30 40 .2193 3410 .9757 9893 .2247 3517 6483 4.4494 20 50 .2221 3466 .9750 9890 .2278 3576 6424 4.3897 10 IS'OO' .2250 9.3521 .9744 9.9887 .2309 9.3634 0.6366 4.3315 77°00' '10 .2278 3575 .9737 9884 .2339 3691 6309 4.2747 50 20 .2300 3629 .9730 9881 .2370 3748 6252 4.2193 40 30 .2334 3682 .9724 9878 .2401 3804 6196 4.1653 30 40 .2363 3734 .9717 9875 .2432 3859 6141 4.112 6 20 50 .2391 3786 .9710 9872 .2462 3914 6086 4.0611 10 14000' .2419 9.3837 .9703 9.9869 .2493 9.3968 0.6032 4.0108 76°00/ 10 .2447 3887 .9696 9866 .2524 4021 5979 3.9617 50 20 .2476 3937 .9689 9863 .2555 4074 5926 3.9136 40 30 .2504 3986 .9681 9859 .2586 4127 5873 3.8667 30 40 .2532 4035 .9674 9856 .2617 4178 5822 3.8208 20 50 .2560 4083 .0667 9853 .2648 4230 5770 3.7760 10 15°00' .2588 9.4130 .9659 9.9849 .2679 9.4281 0.5719 3.7321 75°00' 10 .2616 4177 .9653 9846 .2711 4331 5669 3.6891 50 ^ 20 .2644 4223 .9644 9843 .2742 4381 5619 3.6470 40 30 .2672 4269 .9036 9839 .2773 4430 5570 3.6059 30 40 .2700 4314 .9628 9836 .8805 4479 5521 3.5656 20 50 .2728 4359 .9621 9832 .2836 4527 5473 3.5261 10 16000' .2756 9.4403 .9613 9.9828 .2867 9.4575 0.5425 3.4874 74°00' 10 .2784 4447 .9605 9825 .2899 4622 5378 3.4495 50 20 .2818 4491 .9596 9821 .2931 4669 5331 3.4124 40 30 .2840 4533 .9588 9817 .2962 4716 5284 3.3759 30 40 .2868 4576 .9580 9814 .2994 4762 5238 3.3402 20 50 .2896 4618 .9572 9810 .3026 4808 5192 3.3052 10 I70OO' .2924 9.4659 .9563 9.9806 .3057 9.4853 0.5147 3.2709 730OO' 10 .2952 4700 .9555 9802 .3089 4898 5102 3.2371 50 20 .2979 4741 .9546 9798 .3121 4943 5057 3.2041 40 30 .3007 4781 .9537 9794 .3153 4987 5013 3.1716 30 40 .3035 4821 .9528 9790 .3185 5031 4969 3.1397 20 50 .3062 4861 .9520 9786 .3217 5075 4925 3.1084 10 18°00' .3090 9.4900 .9611 9.9782 .3249 9.5118 0.4882 3.0777 72O00' Nat. Log. Nat. Log. Nat. Log. Log. Nat. SENTS. ANGLE. COSINES. SINES. COTANGENTS. TAN ANGLE. ANGLE. SINES. COSINES. TANGENTS. COTANGENTS. ANGLE. Nat. Log. Nat. Log. Nat. Log. Log. Nat. 18°00' .3090 9.4900 .9511 9.9782 .3249 9.5118 0.4882 3.0777 72°00' 10 .3118 4939 .9502 9778 .3281 5J61 4839 3.0475 50 20 .3145 4977 .9492 9774 .3314 5203 4797 3.0178 40 30 .3173 5015 .9483 9770 .3346 5245 4755 2.9887 30 40 .3201 5052 .9474 9765 .3378 5287 4713 2.9600 20 50 .3228 5090 .9465 9761 .3411 5329 4671 2.9319 10 19°00' .3256 9.5126 .9455 9.9757 .3443 9.5370 0.4630 2.9042 71°00' 10 .3283 5163 .9446 9752 .3476 5411 4589 2.8770 50 20 .3311 5199 .9436 9748 .3508 5451 4549 2.8502 40 30 .3338 5235 .9426 9743 .3541 5491 4509 2.8239 30 40 .3365 5270 .9417 9739 .3574 5531 4469 2.7980 20 50 .3393 5306 .9407 9734 .3607 5571 4429 2.7725 10 20000' •3420 9.5341 .9397 9.9730 .3640 9.5611 0.4389 2.7475 70°00' 10 .3448 5375 .9387 9725 .3673 5650 4350 2.7228 50 20 .3475 5409 .9377 9721 .3706 5689 4311 2.6985 40 30 .3502 5443 .9367 9716 .3739 5727 4273 2.6746 30 40 .3529 5477 .9356 9711 .3772 5766 4234 2.6511 20 50 .3557 5510 .9346 9706 .3805 5804 4196 2.6279 10 21°00' .3584 9.5543 .9336 9.9702 .3839 9.5842 0.4158 2.6051 69°00' 10 .3611 5576 .9325 9697 .3872 5879 4121 2.5826 50 20 .3638 5609 .9315 9692 .3906 5917 4083 2.5605 40 30 .3665 5641 .9304 9687 .3939 5954 4046 2.5386 30 40 .3692 5673 .9293 9682 .3973 5991 4009 2.5172 20 50 .3719 5704 .9283 9677 .4006 6028 3972 2.4960 10 22°00' .3746 9.5736 .9272 9.9672 .4040 9.6064 0.3936 2.4751 68°00' 10 .3773 5767 .9261 9667 .4074 6100 3900 2.4545 50 20 .3800 5798 .9250 9661 .4108 6136 3864 2.4342 40 3 .3827 5828 .9239 9656 .4142 6172 3828 2.4142 30 40 .3854 5859 .9228 9651 .4176 6208 3792 2.3945 20 50 .3881 5889 .9216 9646 .4210 6243 3757 2.3750 10 23»00' .3907 9.5919 .9205 9.9640 .4245 9.6279 0.3721 2.3559 67°00' 10 .3934 5948 .9194 9635 .4279 6314 3686 2.3369 50 20 .3961 5978 .9182 9629 .4314 6348 3652 2.3183 40 30 .3987 6007 .9171 9624 .4348 6383 3617 2.2998 30 40 .4014 6036 .9159 9618 .4383 6417 3583 2.2817 20 50 .4041 6065 .9147 9613 .4417 6452 3548 2.2637 10 24°00' .4067 9.6093 .9135 9.9607 .4452 9.6486 0.3514 2.2460 66°00' 10 .4094 6121 .9124 9602 .4487 6520 3480 2.2286 50 20 .4120 6149 .9112 9596 .4522 6553 3447 2.2113 40 30 .4147 6177 .9100 9590 .4557 6587 3413 2.1943 30 40 .4173 6205 .9088 9584 .4592 6620 3380 2.1775 20 50 .4200 6232 .9075 9579 .4628 6654 3346 2.1609 10 25°00' .4226 9.6259 .9063 9.9573 .4663 9.6687 0.3313 2.1445 65°00' 10 .4253 6286 .9051 9567 .4699 6720 3280 2.1283 50 20 .4279 6313 .9038 9561 .4734 6752 3248 2.1123 40 30 .4305 6340 .9026 9555 .4770 6785 3215 2.0965 30 40 .4331 6366 .9013 9549 .4806 6817 3183 2.0809 20 50 .4358 6392 ,9001 9543 .4841 6850 3150 2.0655 10 26«00' .4384 9.6418 .8988 9.9537 .4877 9.6882 0.3118 2.0503 64°00' 10 .4410 6444 .8975 9530 .4913 6914 3086 2.0353 50 20 .4436 6470 .8962 9524 .4950 6946 3054 2.0204 40 30 .4462 6495 .8949 9518 .4986 6977 3023 2.0057 30 40 .4488 6521 .8936 9512 .5022 7009 2991 1.9912 20 50 .4514 6546 .8923 9505 .5059 7040 2960 1.9768 10 27»00' .4540 9.6570 .8910 9.9499 .5095 9.7072 0.2928 1.9626 63°00' Nat. Log. Nat. Log. Nat. Log. Log. Nat. JENTS. ANGLE. COSINES. SINES. COTANGENTS. TANC ANGLE. ANGLE. SINE9. COSINES. TANGENTS. COTANGENTS. ANGLE. Nat. Log. Nat. Log. Nat. Log, Log. Nat. 27»00' .4540 9.6570 .8910 9.9499 .5095 9.7072 0.2928 1.9626 63*00' 10 .4566 6595 .8897 9492 .5132 7103 2897 1.9486 50 20 .4592 6620 .8884 9486 .5169 7134 2866 1.9347 40 30 .4617 6644 .8870 9479 .5206 7165 2835 1.9210 30 40 .4643 6668 .8857 9473 .5243 7196 2804 1.9074 20 50 .4669 6692 .8843 9466 .5280 7226 2774 1.8940 10 28»00' .4695 9.6716 .8829 9.9459 .5317 9.7257 0.2743 1.8807 62°00' 10 .4720 6740 .8816 9453 .5354 7287 2713 1.8676 50 20 .4746 6763 .8802 9446 .5392 7317 2683 1.8546 40 30 .4772 6787 .8788 9439 .5430 7348 2652 1.8418 30 40 .4797 6810 .8774 9432 .5467 7378 2622 1.8291 20 50 .4833 6833 .8760 9425 .5505 7408 2592 1.8165 10 29°00' .4848 9.6856 .8746 9.9418 .5543 9.7438 0.2562 1.8040 61*00' 10 .4874 6878 .8732 9411 .5581 7467 2533 1.7917 50 20 .4899 6901 .8718 9404 .5619 7497 2503 1.7796 40 30 .4924 6923 .8704 9397 .5658 7526 2474 1.7675 30 40 .4950 6946 .8689 9390 .5696 7556 2444 1.7556 20 50 .4975 6968 .8675 9383 .5735 7585 2415 1.7437 10 30«00' .5000 9.6990 .8660 9.9375 .5774 9.7614 0.2386 1.7321 60*00' 10 .5025 7012 .8646 9368 .5812 7644 2356 1.7205 50 20 .5050 7033 .8631 9361 .5851 7673 2327 1.7090 40 30 .5075 7055 .8616 9353 .5890 7701 2299 1.6977 30 40 .5100 7076 .8601 9346 .5930 7730 2270 1.6884 20 50 .5125 7097 .8587 9338 .5969 7759 2241 1.6753 10 31000' .5150 9.7118 .8572 9.9331 .6009 9.7788 0.2212 1.6643 59°00' 10 .5175 7139 .8557 9323 .6048 7816 2184 1.6534 50 20 .5200 7160 .8542 9315 .6088 7845 2155 1.6426 40 30 .5225 7181 .8526 9308 .6128 7873 2127 1.6319 30 40 .5250 7201 .8511 9300 .6168 7902 2098 1.6212 20 50 .5275 7222 .8496 9292 .6208 7930 2070 1.6107 . 10 32»00' .5299 9.7242 .8480 9.9284 .6249 9.7958 0.2042 1.6003 58»00' 10 .5324 7262 .8465 9276 .6289 7986 2014 1.5900 50 20 .5348 7282 .8450 9268 .6330 8014 1986 1.5798 40 30 .5373 7302 .8434 9260 .6371 8042 1958 1.5697 30 40 .5398 7322 .8418 9252 .6412 8070 1930 1.5597 20 50 .5423 7342 .8403 9244 .6453 8097 1903 1.5497 10 33°00' .5446 9.7361 .8387 9.9236 .6494 9.8125 0.1875 1.5399 57*00' 10 .5471 7380 .8371 9228 .6536 8153 1847 1.5301 50 20 .5495 7400 .8355 9219 .6577 8180 1820 1.5204 40 30 .5519 7419 .8339 9211 .6619 8208 1792 1.5108 30 40 .5544 7438 .8323 9203 .6661 8235 1765 1.5013 20 50 .5568 7457 .8307 9194 .6703 8263 1737 1.4919 10 34°00' .5592 9.7476 .8290 9.9186 .6745 9.8290 0.1710 1.4826 56*00' 10 .5616 7494 .8274 9177 .6787 8317 1683 1.4733 50 20 .5640 7513 .8258 9169 .6830 8344 1656 1.4641 40 30 .5664 7531 .8241 9160 .6873 8371 1629 1.4550 30 40 .5688 7550 .8225 9151 .6916 8398 1602 1.4460 20 50 .5712 7568 .8208 9142 .6959 8425 1575 1.4370 10 35»00' .5736 9.7586 .8192 9.9134 .7002 9.8452 0.1548 1.4281 55*00' 10 .5760 7604 .8175 9125 .7046 8479 1521 1.4193 50 20 .5783 7622 .8158 9116 .7089 8506 1494 1.4106 40 30 .5807 7640 .8141 9107 .7133 8533 1467 1.4019 30 40 .5831 7657 .8124 9098 .7177 8559 1441 1.3934 20 50 .5854 7675 .8107 9089 .7221 8586 1414 1.3848 10 36°00' .5873 9.7692 .8090 9.9080 .7265 9.8613 0.1387 1.3764 54*00' Nat. Log. Nat. Log. Nat. Log. Log. Nat. GENTS. ANGLE. COSINES. SINES. COTANGENTS. TAN ANGLE. ANGLE. SINES. COSINES. TANGENTS. COTANGENTS. ANGLE. Nat. Log. Nat. Log. Nat. Log. Log. Nat. 36°00' .5878 9.7692 .8090 9.9080 .7265 9.8613 0.1387 1.3764 54°00' 10 .5901 7710 .8073 9070 .7310 8639 1361 1.3680 50 20 .5925 7727 .8056 9061 .7355 8666 1334 1.3597 40 30 .5948 7744 .8039 9052 .7400 8692 1308 1.3514 30 40 .5972 7761 .8021 9042 .7445 8718 1282 1.3432 20 50 .5995 7778 .8004 9033 .7490 8745 1255 1.3351 10 37°00' .6018 9.7795 .7986 9.9023 .7536 9.8771 0.1229 1.3270 53°00' 10 .6041 7811 .7969 9014 .7581 8797 1203 1.3190 50 20 .6065 7828 .7951 9004 .7627 8824 1176 1.3111 40 30 .6088 7844 .7934 8995 .7673 8850 1150 1.3032 30 40 .6111 7861 .79-16 8985 .7720 8876 1124 1.2954 20 50 .6134 7877 .7898 8975 .7766 8902 1098 1.2876 10 38=00' .6157 9.7893 .7880 9.8965 .7813 9.8928 0.1072 1.2799 52°00' 10 • .6180 7910 .7862 8955 .7860 8954 1046 1.2723 50 20 .6202 79,26 .7844 S^ib .7907 8980 1020 1.2647 40 30 .6225 7941 .7826 8935 .7954 9006 0994 1.2572 30 40 .6248 7957 .7808 8925 .8002 9 32 0968 1.2497 20 50 .6271 7973 .7790 8915 .8050 9058 0942 1.2423 10 39°00' .6293 9.7989 .7771 9.8905 .8098 9.9084 0.0916 1.2349 51°00' 10 .6316 8004 .7753 8895 .8146 9110 0890 1.2276 50 20 .6338 8020 .7735 8884 .8195 9135 0865 1.2203 40 30 .6361 8035 .7716 8874 .8243 9161 0839 1.2131 30 40 .6383 8050 .7698 8864 .8292 9187 0813 1.2059 20 50 .6406 8066 .7679 8853 .8342 9212 0788 1.1988 10 40°00' .6428 9.8081 .7660 9.8843 .8391 9.9238 0.0762 1.1918 50°00' 10 .6450 8096 .7642 8832 .8441 9264 0736 1.1847 50 •20 ,6472 8111 .7623 8821 .8491 9289 0711 1.1778 40 30 .6494 8125 .7604 8810 .8541 9315 0685 1.1708 30 40 .6517 8140 .7585 8800 .8591 9341 0659 1.1640 20 50 .6539 8155 .7566 8789 .8642 9366 0634 1.1571 10 41°00' .6561 9.8169 -.7547 9.8778 .8693 9.9392 0.0608 1.1504 49°00' 10 .6583 8184 .7528 8767 .8744 9417 0583 1.1436 50 20 .6604 8198 .7509 8756 .8796 9443 0557 1.1369 40 30 .6626 8213 .7490 8745 .8847 9468 0532 1.1303 30 40 .6648 8227 .7470 8733 .8899 9494 0506 1.1237 20 50 .6670 8241 .7451 8722 .8952 9519 0481 1.1171 10 42°00' .6691 9.8255 .7431 9.8711 .9004 9.9544 0.0456 1.1106 48°00' 10 .6713 8269 .7412 8699 .9057 9570 0430 1.1041 50 20 .6734 8283 .7392 8688 .9110 9595 0405 1.0977 40 30 .6756 8297 .7373 8676 .9163 9621 0379 1.0913 30 40 .6777 8311 .7353 8665 .9217 9646 0354 1.0850 20 50 .6799 8324 .7333 8653 .9271 9671 0329 1.0786 10 43°00' .6820 9.8338 .7314 9.8641 .9325 9.9697 0.0303 1.0724 47<'00' 10 .6841 8351 .7294 8699 .9380 9722 0278 1.0661 50 20 .6862 8365 .7274 8618 .9435 9747 0253 1.0599 40 30 .6884 8378 .7254 8606 .9490 9772 0228 1.0588 30 40 .6905 8391 .7234 8594 .9545 9798 0202 1.0477 20 50 .6926 8405 .7214 8582 .9601 9823 0177 1.0416 10 44°00' .6947 9.8418 .7193 9.8569 .9657 9.9848 0.0152 1.0355 46°00' 10 .6967 8431 .7173 8557 .9713 9874 0126 1.0295 50 20 .6988 8444 .7153 8545 .9770 9899 0101 1.0235 40 . 30 .7009 8457 .7133 8532 .9827 9924 0076 1.0176 30 40 .7030 8469 .7112 8520 .9884 9949 0051 1.0117 20 50 .7050 8482 .7092 8507 .9942 9975 0025 1.0058 10 45°00' .7071 9.8495 .7071 9.8495 1.0000 0.0000 0.0000 1.0000 45°00' Nat. Log. Nat. Log. Nat. Log. Log. Nat. ANGLE. COSINES. SINES. COTANGENTS. TANGENTS. ANGLE. PAGES VII. TRIGONOMETRIC FUNCTIONS, - - - 60-104 A five-place table of natural sines, cosines, tangents, and cotangents of angles 0°-180°, to minutes, and a six-place table of their logarithms, with differences of logarithms for seconds expressed in units of the sixth decimal place. VIII. NATURAL LOGARITHMS, . - - - 105-117 A six-place table of natural logarithms of the deci- mal numbers, .01, .02, .03,. .9.99, of the natural num- bers 1, 2, 3,. .1218, and of the prime numbers between 1218 and 10000, IX. PRIME AND COMPOSITE NUMBERS, - - 118-13: A table of prime and composite numbers from 1 to 20000, with the factors of the composite numbers that are not divisible by 2 or 5, and ten-place logar- ithms of the primes. X. SQUARES, 138-139 A table of the squares of the natural numbers 1, 2, 3,..999. XI. CUBES, 140-141 A table of the cubes of the decimal numbers .1, .2, .3,..99.9. XII. SQUARE-ROOTS, 142-145 A table of the square-roots, to four decimal places, of the natural numbers 1, 2, 3,. .999, and of the deci- mal numbers .1, .2, .3,.. 99.9. XIII. CUBE-ROOTS, 146-151 A table of the cube-roots, to four decimal places, of the natural numbers 1, 2, 3,. .999 of the decimals .1, .2, .3,..99.9, and of the decimals .01, .02, .03,..9.99. XIV. RECIPROCALS, 152-153 A table of the reciprocals of the decimal numbers .01, .02, .03,.. 9.99. XV. QUARTER-SQUARES, 154-157 A table of the quarter-squares of the natural num- bers 1, 2, 3,..2000. XVI. BESSEL'S COEFFICIENTS, .... 158 A table of BessePs coefficients for second, third, fourth, and fifth differences, for interpolation. XVIT. BINOMIAL COEFFICIENTS, - - - . 159 A table of binomial coefficients for second, third, fourth, and fifth differences, for interpolation. XVIII. ERRORS OF OBSERVATION, - - - . 160 A table of ordinates of the probabilitj--curve, values of probability integrals, and other values. /: Mathematical Text-BooMl PRICE-LIST, OCTOBER i, 1896. I. A DRILL-BOOK IN TRIGONOMETRY. SECOND EDITION. For the elementary and the advanced work of high-school and college classes. i2mo, cloth, xvi + ig2 pp. Single copies by mail, $i.oo. All cash orders (carriage at the buyer's cost), 75 cents. II. A DRILL-BOOK IN ALGEBRA. THIRD EDITION. For the more advanced classes in the high schools and academies and the lo^'-er classes in the colleges. lamo, cloth, xyi + 272 pp. Single copies by mail, $i.oo. All cash orders (carriage at the buyer's cost), 75 cents. AN ANSWER-BOOK, for teachers only, 25 cents. A BOX OF QUESTION-CARDS, for the class-room, 75 cents. III. LOGARITHMIC TABLES. SIXTH EDITION. Eighteen tables, (fouf-place, six-place and ten-place,) with explanations, for use in the class-room, the laboratory, and the office. Large open pages, fine heavy parer. Royal 8vo, cloth, 160 pp. Single copies by mail, $1.00. All cash orders (carriage at the buyer's cost), 75 cents. j » IV. FOUR-PLACE LOGARITHMS. Two tables : one of the logarithms of three-figure numbers, the other of trigo- nometric ratios and their logarithms for angles differing by ten minutes. i2mo, paper, 8 pp. Single copies by mail, 5 cents. All cash orders (carriage at the buyer's cost), 4 cents. V. FIVE-PLACE LOGARITHMS. FIRST EDITION. Eleven tables: one of the logarithms of four-figure numbers, one of trigonome^nc ratios and their logarithms for angles differing by minutes, and nine minor tables, for the use of high-school and college classes. Large open pages, fine heavy pap'^r. Royal 8vo, cloth, 64 pp. Single copies by mail, 60 cents. All cash orders (carriage at the buyer's cost), 45 cents. VI. PROBLEMS IN ALGEBRA, FOR BEGINNERS. IN PREPARATION. VII. HIGHER ALGEBRA. IN PREPARATION. Single copies of these books (except the last) will be sent free to teachers of mathematics, for their inspection. GEORGE W. JONES, Publisher, No Agents. Ithaca, N, '. Syracu**/ N- »• Stockton, Calif. UNIVERSITY OF CALIFORNIA LIBRARY .^ASS BERKELEY U(Jj Return to desk from which borrowed. -J ^ 7 This book is DUE on the last date stamped below. ASTRDNDMY LIBf^ARY LD 21-lOOm-ll, '49(67146816)476