QA 53 ?4 UC-NRLF I'l ill Ml ii[{ 1 1 III 1 N 1 : 1 1 i 1 II mil II 111111 *<: IbS 775 4 THREE AND FOUR PLACE TABLES ct LOGAEITHMTC AND TRIGONOMETRIC FUNCTIONS BT JAMES MILLS PEIRCE mnVEESITT PEOFESSOR OF MATHEMATICS IN HARVARD UNITERSITY ■v-.,. ^,, ^/6^ = ^J BOSTON GINN BROTHERS 1871 Entered according to Act of Congress, in the year 1871, by James Mills Pubob, in the Office of the Librarian of Congress, at Washington. ^fitli PBOPORTIONAL PARTS. S lO 15 30 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1,6 1.7 1.8 1.9 2.0 1 2 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 2 3 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5,4 5.7 6.0 3 4 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 6.4 6.8 7.2 7.6 8.0 4 5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 5 6 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2 7.8 8.4 9.0 9.6 10,2 10.8 11.4 12.0 6 7 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7.0 7.7 8.4 9.1 9.8 10.5 11.2 11.9 12.6 13.3 14,0 7 8 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 8.8 9.6 10.4 11.2 12.0 12.8 13.6 14.4 15.2 16.0 8 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 9.0 9.9 10.8 11.7 12.6 13.5 14.4 15.3 16.2 17.1 18.0 9 35 30 35 40 1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 1 2 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 2 3 6.3 6.6 6.9 7.2 7.5 7.8 8.1 8.4 8.7 9.0 9.3 9.6 9.9 10.2 10.5 10.8 11.1 11.4 11.7 12.0 3 4 8.4 8.8 9.2 9.6 10.0 10.4 10.8 11.2 11.6 12.0 12.4 12.8 13.2 13.6 14.0 14.4 14.8 15.2 15.6 16.0 4 5 10.5 11.0 11,5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 5 6 12.6 13.2 13.8 14.4 15.0 15.6 16.2 16.8 17.4 18.0 18.6 19.2 19.8 20.4 21.0 21.6 22.2 22.8 23.4 24.0 6 7 14.7 15.4 16.1 16.8 17.5 18.2 18.9 19.6 20.3 21.0 21.7 22.4 23.1 23.8 24.5 25.2 25.9 26.6 27.3 28.0 7 8 16.8 17.6 18.4 19.2 20.0 20.8 21.6 22.4 23.2 24.0 24.8 25.6 26.4 27.2 28.0 28.8 29.6 30.4 31.2 32.0 8 9 18.9 19.8 20.7 21.6 22.5 23.4 24.3 25.2 26.1 27.0 27.9 28.8 29.7 30.6 31.5 32,4 33.3 34.2 35.1 36.0 9 45 SO 55 60 1 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 1 2 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 2 3 12.3 12.6 12.9 13.2 13.5 13.8 14.1 14.4 14.7 15.0 15.3 15.6 15.9 16.2 16.5 16.8 17.1 17.4 17.7 18.0 3 4 16.4 16.8 17.2 17.6 18.0 18.4 18.8 19.2 19.6 20.0 20.4 20.8 21.2 21.6 22.0 22.4 22.8 23.2 23.6 24.0 4 5 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 5 6 24.6 25.2 25.8 26.4 27.0 27.6 28.2 28.8 29.4 30.0 30.6 31.2 31.8 32.4 33.0 33.6 34,2 34.8 35.4 30.0 6 7 28.7 29.4 30.1 30.8 31.5 32.2 32.9 33.6 34.3 35.0 35.7 36.4 37.1 37.8 38.5 39.2 39.9 40.6 41.3 42.0 7 8 32.8 33.6 34.4 35.2 36.0 36.8 37.6 38.4 39.2 40.0 40.8 41.6 42.4 43.2 44.0 44.8 45.6 46.4 47.2 48.0 8 9 36.9 37.8 38.7 39.6 40.5 41.4 42.3 43.2 44.1 45.0 45.9 46.8 47.7 48.6 49.5 50.4 51.3 52.2 53.1 54.0 9 65 yo 75 SO 1 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 1 2 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.8 16.0 2 3 18.3 18.6 18.9 19.2 19.5 19.8 20.1 20.4 20.7 21.0 21.3 21.6 21.9 22.2 22.5 22.8 23.1 23.4 23.7 24.0 3 4 24.4 24.8 25.2 25.6 26.0 26.4 26.8 27.2 27.6 28.0 28.4 28.8 29.2 29.6 30.0 30.4 30.8 31.2 31.6 32.0 4 5 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 5 6 36.6 37.2 37.8 38.4 39.0 39.6 40.2 40.8 41.4 42.0 42.6 43.2 43.8 44.4 45.0 45.6 46.2 46.8 47.4 48.0 6 7 42.7 43.4 44.1 44.8 45.5 46.2 46.9 47.6 48.3 49.0 49.7 50.4 51.1 51.8 52.5 53.2 53.9 54.6 55.3 56.0 7 8 48.8 49.6 50.4 51.2 52.0 52.8 53.6 54.4 55.2 56.0 56.8 57.6 58.4 59.2 60.0 60.8 61.6 62.4 63.2 64.0 8 9 54.9 55.8 56.7 57.6 58.J5 59.4 60.3 61.2 62.1 63.0 .... • • 63.9 64.8 65.7 66.6 67.5 68.4 69.3 70.2 71.1 72.0 9 05 lOO 1 8.1 8.2 8.3 8A\ S|5>" : §j;:*»*.7jf8.8: M k-o 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0 1 2 16.2 16.4 16.6 16.8 "iVIo f7.S'l7.4"ir.6* 17.8*16.0 18.2 18.4 18.6 18.8 19.0 19.2 19.4 19.6 19.8 20.0 2 3 24.3 24.6 24.9 25.2 25.5 25.8 26.1 26.4 26.7 27.0 27.3 27.6 27.9 28.2 28.5 28.8 29.1 29.4 29.7 30.0 3 4 32.4 32.8 33.2 33.6 34.0 34.4 34.8 35.2 35.6 36.0 36.4 36.8 37.2 37.6 38.0 38.4 38,8 39.2 39.0 40.0 4 5 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 5 6 48.6 49.2 49.8 50.4 51.0 51.0 52.2 52.8 53.4 54.0 54.6 55.2 55.8 56.4 57.0 57.6 58.2 58.8 59.4 00.0 6 7 56.7 57.4 58.1 58.8 59.5 60.2 60.9 61.6 62.3 63.0 63.7 64.4 65.1 65.8 66.5 67.2 67.9 68.6 69.3 70.0 / 8 64.8 65.6 66.4 67.2 68.0 68.8 69.6 70.4 71.2 72.0 72.8 73.6 74.4 75.2 76.0 76.8 77.6 78.4 79.2 80.0 8 9 72.9 73.8 74.7 75.6 76.5 77.4 78.3 79.2 80.1 81.0 81.9 82.8 83.7 84.6 85.5 86.4 87.3 88.2 89.1 90.0 9 THREE-PLACE TABLES. LOGAKITUMS OF Numbers. lo gsinqp = l0g((jp in degrees) -|- S log tan (f 9 "~~" log (9 5 IQ degrees) -f- T qp T O 1 3 3 4 9 « 7 8 9 lO 1 000 041 079 114 i 146 176 204 230 255 279 301 3 301 322 342 362 380 398 415 431 447 462 477 8.242 3 477 491 505 519 531 544 556 568 580 591 602 3° .82 4 602 613 623 633 643 653 663 672 681 690 699 4° .01 S e 699 708 716 724 732 740 748 756 763 771 778 8.-241 6°.12 8.243 8.244 778 785 792 799 806 813 820 826 833 839 845 T 845 851 857 863 869 875 881 886 892 898 903 7°. 83 7°. 70 8 903 908 914 919 924 929 934 940 944 949 954 8.245 9 954 959 964 968 973 978 982 987 991 996 000 9 .04 8.246 lO 000 004 009 013 017 021 025 029 033 037 041 10 .3S 0°.20 LOGAKITIIXIIC Natural sin CSC tan ctn sec cos sin CSC tan ctn sec COS 1 8.242 1.758 8.242 1.758 1 0.000 0.000 0.017 57.30 0.017 57.29 1.000 1.000 1 89 f .543 .457 .543 .457 .000 0.000 .035 '* 28.65 .035 28.64 .001 0.999 88 8 .719 .281 .719 .281 .001 9.999 .052 " 19.11 .052 19.08 .001 .999 1 87 4 .844 .156 .845 .155 .001 .999 .070 '* 14.34 .070 14.30 .002 .998 86 5 8.940 1.060 8.942 1.058 .002 .998 .087 " 11.47 .087 -18 11.43 .004 2 .996 1 86. 84 9.019 0.981 9.022 0.978 .002 .998 .105 9.57 .105 9.51 .006 .995 7 .086 .914 .089 .911 .003 .997 .122 " 8.21 .123 8.14' .008 .993 83 8 .144 .856 .148 .852 .004 .996 .139 " 7.19 .141 7.12 .010 .990 82 9 .194 .806 .200 .800 .005 .995 .156-" 6.39 .158 6.31 .012 .988 81 10 .240 .760 .246 .754 .007 .993 .174 " 5.76 .176 5.67 .015 .985 80 11 .281 .719 .289 .711 .008 .992 .191 5.24 .194 5.14 .019 .982 79 12 .318 " .682 .327 ^ .673 .010 .990 .208 " 4.81 .213 4.70 .022 .978 78 1ft .352 '•* .648 .363 '* .637 .011 .989 .225 " 4.45 aa .231 4.33 3; .026 4 .974 4 77 14 .384 ^ .616 .397 ^ .603 .013 .987 .242 '■' 4.13 »a .249 4.01 .031 .970 76 15 .413 ^' .587 .428 " .572 .015 .985 .259 " 3.80 ai .268 -10 3.73 ■^1 .035 4 . 5 .966 "i 75 16 .440 .560 .457 .543 .017 .983 .276 3.G3 .287 3.49 .040 .961 74 17 .466 ^* .534 .485 ** .515 .019 .981 .292 '" 3.42 ai .306 3.27 .046 6 .956 5 73 IS .490 ^ .510 .512 " .488 .022 .978 .309 '" 3.24 18 .325 19 3.08 19 .051 b .951 5 72 19 .513 *' .487 .537 ^ .403 .024 .976 .326 " 3.07 I'i .344 la 2.90 18 .058 ■I .946 6 71 20 .534 ^' .466 .561 ** .439 .027 .973 .342 " 2.92 15 .364 2.75 15 11 .064 6 .940 6 70 21 .554 .446 .584 .416 .030 .970 .358 2.79 .384 2.61 .071 .934 69 22 .574 ^ .426 .606 ^^ .394 .033 .967 .375 " 2.67 .404 2.48 .079 .927 '; 68 23 .592 '* .408 .628 ^* .372 .036 .964 .391 '" 2.56 11 .424 'M 2.36 I'J .086 7 .921 6 67 24 .609 " .391 .649 ^' .351 .039 .961 .407 '' 2.46 10 .445 !il 2.25 11 .095 9 .914 7 66 25 .026 " .374 .669 ^ .331 .043 .957 .423 "* 2.37 9 .466 iil 2.14 11 .103 8 .906 8 65 26 .642 .358 .688 .312 .046 .954 .438 2.28 .488 2.05 .113 .899 64 27 .657 '^ .343 .707 " .293 .050 .950 .454 " 2.20 .510 1.96 .122 .891 8 63 28 .672 '* .328 .726 '* .274 .054 .946 .469 '' 2.13 7 .532 W 1.88 8 .133 11 .883 8 62 29 .686 '* .314 .744 '* .256 .058 .942 .485 " 2.06 J .554 1.80 .143 .875 8 61 30 .699 " .301 .761 " .239 .062 .938 .500 " 2.00 .577 1.73 .155 .866 • 9 60 31 .712 .288 .779 ° .221 .067 .933 .515 1.94 .601 1.66 .167 .857 59 32 .724 " .276 .796 " .204 .072 .928 .530 '^ 1.89 b .625 •2i 1.60 .179 12 .848 9 58 33 .730 '* .264 .813 " .187 .076 .924 .545 '= 1.84 b .649 1.54 ii .192 13 .839 9 57 34 35 .748 " .252 .7.59 " .241 .829 '* .171 .081 .919 .559 " . 15 1.79 5 .675 2.1 1.48 A .206 Mi .829 m 56 55 .845 '^ .155 .087 .913 .574 1.74 .700 1.43 .221 .819 36 .769 .231 .861 .139 .092 .908 .588- 1.70 .727 1.38 .236 .809 54 37 .779 '» .221 .877 '* .123 .098 .902 .602 " 1.66 .754 1.33 S .252 IB .799 10 53 38 .789 '" .211 .893 '* .107 .103 .897 .616 '" 1.62 .781 '■ti 1.28 6 .269 11 .788 11 52 39 .799 '" .201 .908 '* .092 .109 .891 .629 '^ 1.59 .810 1.23 6 .287 18 .777 11 51 40 41 .808 ^ .192 .924 '* .076 .116 .884 .043 " 1.56 . 4 .839 ..30 1.19 4 4 .305 18 -20 .766 11 11 50 49 .817 .183 .939 .061 .122 .878 .656 1.52 .869 1.15 .325 .755 42 .826 " .174 .954 '* .046 .129 .871 .669 " 1.49 .900 31 1.11 4 .346 21 .743 12 48 43 .834 * .166 .970 '* .030 .136 .864 .682 " 1.47 .933 33 1.07 4 .367 21 .731 12 47 44 .842 * .158 9.985 " .015 .143 .857 .695 " 1.44 0.966 1.04 3 .390 23 .719 12 46 45 9.849 ' 0.151 0.000 '* 0.000 0.151 9.849 0.707 '^ 1.41 1.000 1.00 4 1.414 24 0.707 12 45 cos sec ctn tan CSC sin cos sec Ctn tan CSC sin Logarithmic Nati JRAL 4273«4 LOGARITHMS OF NUMBERS. Proportional Parts. t O 1 2 3 4 s 6 7 8 9 •< ^g 1 3 3 4 s 6 7 8 » lO 1 40 ~io 0000 043 086 128 170 212 253 294 334 374 4.1 8.3 12.4 10.6 20.7 34.8 29.0 33.1 37.3 41.4 50 11 414 453 492 531 569 607 645 682 719 755 3.8 7.6 11.3 16.1 18.9 32.7 26.5 30.3 34.0 37.8 2 00 12 792 828 864 899 934 969 o04 o38 o72 i06 3.5 7.0 10.4 13.9 17.4 20.9 34.3 37.8 31.3 34.8 10 13 1139 173 206 239 271 303 335 367 399 430 3.3 6.4 9.7 13.9 16.1 19.3 22.5 36.7 39.0 33.2 20 30 14 15 461 492 523 553 584 614 644 673 703 732 3.0 6.0 9.0 12.0 15.0 18.0 31.0 34.0 37.0 30.0 1761 790 818 847 875 903 931 959 987 014 3.8 6.6 8.4 11.2 14.0 16.8 19.6 33.4 25.2 28.0 40 16 2041 068 095 122 148 175 201 227 253 279 3.8 6.3 7.9 10.5 13.3 16.8 18.4 31.1 23.7 96.3 50 17 304 330 355 380 405 430 455 480 504 529 3.S 6.0 7.4 9.9 13.4 14.9 17.4 19.9 23.3 24.8 3 00 18 553 577 601 625 648 672 695 718 742 765 3.3 4.7 7.0 9.4 11.7 14.1 16.4 18.8 21.1 23.5 10 80 19 20 788 810 833 856 878 900 923 945 967 989 3.3 4.5 6.7 8.9 11.1 13.4 15.6 17.8 20.0 23.3 3010 032 054 075 096 118 139 160 181 201 3.1 4,2 6.4 8.6 10.6 12.7 14.8 17.0 19.1 21.2 30 21 222 243 263 284 304 324 345 365 385 404 3.0 4.0 6.1 8.1 10.1 13.1 14.1 16.3 18.2 20.2 40 22 424 444 464 483 502 522 541 560 579 598 1.9 3.9 6.8 7.7 9.7 11.6 13.5 15.4 17.4 19.3 50 23 617 636 655 674 692 711 729 747 766 784 1.8 3.7 6.6 7.4 9.3 11.1 13.9 14.8 16.6 18.5 4 00 10 24 25 802 820 838 856 874 892 909 927 945 962 1.8 3.5 5.3 7.1 8.9 10.6 12.4 14.3 16.0 17.7 3979 997 ol4 o31 o48 o65 o82 o99 il6 i33 1.7 3.4 6.1 6.8 8.6 10.3 11.9 13.6 16.3 17.0 20 26 4150 166 183 200 216 232 249 865 281 298 1.6 3.3 4.9 6.6 8.3 9.8 11.5 13.1 14.8 16.4 30 27 314 330 346 362 378 393 409 425 440 456 1.6 8.3 4.7 6.3 7.9 9.6 11.1 13.6 14.2 15.8 40 28 472 487 502 518 533 548 564 579 594 609 1.6 3.0 4.6 6.1 7.6 9.1 10.7 12.2 13.7 16.2 50 5 00 29 30 624 639 654 669 683 698 713 728 748 757 1.5 3.9 4.4 5.9 7.4 8.8 10.3 11.8 13.3 14.7 4771 786 800 814 829 843 857 871 886 900 1.4 2.8 4.3 5.7 7.1 8.6 10.0 11.4 13.8 14.2 10 31 914 928 942 955 969 983 997 oil o24 o38 1.4 3.8 4.1 6.5 6.9 8.3 9.7 11.0 13.4 13.8 20 32 5051 065 079 092 105 119 132 145 159 172 1.3 2.7 4.0 5.3 6.7 8.0 9.4 10.7 13.0 13.4 30 33 185 198 211 224 237 250 863 276 889 302 1.3 2.6 3.9 6.3 6.5 7.8 9.1 10.4 11.7 13.0 40 50 34 35 315 328 340 353 366 378 391 403 416 428 1.3 3.5 3.8 5.0 6.3 7.6 8.8 10.1 11.3 12.6 5441 453 465 478 490 502 514 587 539 551 1.2 3.4 3.7 4.9 6.1 7.3 8.6 9.8 11.0 12.2 6 00 36 563 575 587 599 611 623 635 647 658 670 1.3 3.4 3.6 4.8 5.9 7.1 8.3 9.6 10.7 11.9 10 37 682 694 705 717 729 740 752 763 775 786 1.2 3.3 3.6 4.6 5.8 6.9 8.1 9.3 10.4 11.6 20 38 798 809 821 838 843 855 866 877 888 899 1.1 3.3 3.4 4.6 5.6 6.8 7.9 9.0 10.3 11.3 30 40 39 40 911 922 933 944 955 966 977 988 999 olO I.l 3.3 3.3 4.4 5.6 6.6 7.7 8.8 9.9 11.0 6021 031 042 053 064 075 085 096 107 117 1.1 3.1 3.3 4.3 5.4 6.4 7.6 8.6 9.7 10.7 50 41 128 138 149 160 170 180 191 801 812 822 1.0 3.1 3.1 4.3 5.3 6.3 7.3 8.4 9.4 10.5 7 00 42 232 243 853 263 274 284 294 304 314 385 1.0 3.0 3.1 4.1 5.1 6.1 7.9 8.2 9.2 10.2 10 43 335 345 355 365 375 385 395 405 415 425 1.0 3.0 a.o 4.0 6.0 6.0 7.0 8.0 9.0 10.0 20 30 44 45 435 444 454 464 474 484 493 503 513 522 1.0 2.0 3.9 3.9 4.9 5.9 6.8 7.8 8.8 9.8 6532 542 551 561 571 580 590 599 609 618 I.O 1.9 2.9 3.8 4.8 6.7 6.7 7.6 8.6 9.5 40 46 628 637 646 656 665 675 684 693 708 712 0.9 1.9 3.8 8.7 4.7 6.6 6.6 7.5 8.4 9.3 50 47 721 730 739 749 758 767 776 785 794 803 0.9 1.8 3.7 3.7 4.6 6.5 6.4 7.3 8.2 9.1 8 00 48 612 821 830 839 848 857 866 875 884 893 0.9 1.8 2.7 3.6 4.6 8.4 6.3 7.3 8.1 9.0 10 20 49 50 902 911 920 928 937 946 955 964 972 981 0.9 1 8 3.6 3.5 4.4 5.3 6.1 7.0 7.9 8.8 6990 998 o07 ol6 o24 o33 o42 o50 o59 o67 0.9 1.7 2.6 3.4 4.3 6.2 6.0 6.9 7.7 8.6 30 51 7076 084 093 101 110 118 126 135 143 152 0.8 1.7 2.6 3.4 4.3 6.1 6.9 6.7 7.6 8.4 40 52 160 168 177 185 193 202 210 218 226 235 0.8 1.7 2.6 3.3 4.1 6.0 6.8 6.6 7.4 8.3 50 53 243 251 259 267 275 284 292 300 308 316 0.8 1.6 2.4 3.3 4.1 4.9 6.7 6.8 7.3 8.1 9 00 54 324 332 340 348 356 364 372 380 388 396 0.8 1.6 3.4 3.2 4.0 4.8 6.6 6.4 7.2 8.0 log arc (f = log (ip in minut es) + 6.4637 + lo g radius. log 9 o (X 1 8 9 4 3 3< 4 0" sin (f = log (()p in D linut es) + S. CD 1.5 "■■'«" 6.4636 ).6 6.4634 r.8 O 1 4 07.8 4 38.8 6 06.7 6 33.3 5 56.0 S 6. 4633 6.4633 6.4631 6.4630 LOGARITHMS OF NUMBERS. J II Proportional Parts. 1 3 3 4 S 6 7 8 9 ■< '^i t 3 3 4 s 6 7 8 » lO 9 10 55 7404 412 419 427 435 443 451 459 466 474 0.8 1.6 2.3 3.1 3.9 4.7 5.5 t%3 7.0 7.8 20 56 482 490 497 505 513 520 528 536 543 551 0.8 1.5 2.3 3.1 3.8 4.6 5.4 6.1 6.9 7.7 30 57 559 5C6 574 582 589 597 604 612 619 627 0.8 1.6 2.3 3.0 3.8 4.5 6.3 6.0 6.8 7.6 40 58 G34 642 649 657 664 672 679 686 694 701 0.7 1.6 2.2 3.0 3.7 4.5 5.2 5.9 6.7 7.4 50 10 00 59 60 709 716 723 731 738 745 752 760 767 774 0.7 1.5 2.2 2.9 3.6 4.4 5.1 5.9 6.6 7.3 7782 789 796 803 810 818 825 832 839 846 0.7 1.4 2.2 2.9 3.6 4.3 5.0 6.7 6.6 7.2 10 61 853 860 868 875 882 889 896 903 910 917 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.4 7.1 20 62 924 931 938 945 952 959 966 973 980 987 0.7 1.4 2.1 2.8 3.5 4.2 4,9 5.6 6.3 6.9 30 63 993 oOO o07 ul4 o21 o28 o35 o41 o48 o55 0.7 1.4 2.1 2.7 3.4 4.1 4.8 6.5 6.2 6.6 40 50 64 65 80G2 069 075 082 089 096 102 109 116 122 0.7 1.3 2.0 2.7 3.4 4.0 4.7 5.4 6.1 0.7 8129 136 142 149 156 162 169 176 182 189 0.7 1.3 2.0 2.7 3.3 4.0 4.6 5.3 6.0 6.6 1100 66 195 202 209 215 222 228 235 241 248 254 0.7 1.3 2.0 2.6 3.3 3.9 4.6 5.2 5.9 6.5 10 67 2G1 267 274 280 287 293 299 306 312 319 0.6 1.3 1.9 2.6 3.2 3.9 4.5 5.1 5.8 6.4 20 68 325 331 338 344 351 357 363 370 376 382 0.6 1.3 1.9 2.5 3.2 3.6 4.4 5.1 6.7 6.3 30 40 69 70 388 395 401 407 414 420 426 432 439 445 0.6 1.2 1.9 2.6 3.1 3.7 4.4 5.0 5.6 6.2 8451 457 463 470 476 482 488 494 500 506 0.6 1.2 1.8 2.5 3.1 3.7 4.3 4.9 6.5 6.2 50 71 513 519 525 531 537 543 549 555 561 567 0.6 1.2 1.8 2.4 3.0 3.6 4.3 4.9 6.6 6.1 12 00 72 573 579 585 591 597 603 609 615 621 627 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 10 73 633 639 645 651 657 663 669 675 681 686 0.6 1.2 1.8 2.4 3.0 3.6 4.1 4.7 5.3 6.9 20 30 74 75 692 698 704 710 716 722 727 733 739 745 0.6 1.2 1.7 2.3 2.9 3.5 4.1 4.7 5.2 5.8 8751 756 762 ,768 774 779 785 791 797 802 0.6 1.2 1.7 2.3 2.9 3.6 4.0 4.6 5.2 5.8 40 76 808 814 820 825 831 837 842 848 854 859 0.6 1.1 1.7 2.3 2.3 3.4 4.0 4.5 6.1 5.7 50 77 865 871 876 882 887 893 899 904 910 915 0.6 1.1 1.7 2.2 2.8 3.4 3.9 4.5 5.0 5.6 13 00 78 921 927 932 938 943 949 954 960 965 971 0.6 1.1 1.7 2.2 2.3 3.3 3.9 4.4 6.0 5.5 10 20 79 80 976 982 987 993 998 o04 o09 ol5 o20 o25 0.6 1.1 1.6 2.2 2.7 3.3 3.8 4.4 4.9 5.5 9031 036 042 047 053 058 063 069 074 079 0.5 1.1 1.6 2.2 2.7 3.2 3.8 4.3 4.9 6.4 30 81 oa5 090 096 101 106 112 117 122 128 133 0.5 1.1 1.6 2.1 2.7 3.2 3.7 4.3 4.8 5.3 1 40 82 138 143 149 154 159 165 170 175 180 186 0.5 l.I 1.6 2.1 2.6 3.2 3.7 4.2 4.7 8.3 ! 50 83 191 196 201 206 212 217 222 227 232 238 0.5 1.0 1.6 2.1 2.6 3.1 3.6 4.2 4.7 5.2 14 00 1 1" 84 85 243 248 253 258 263 269 274 279 284 289 0.4 1.0 1.5 2.1 2.6 3.1 3.6 4.1 4.6 6.1 9294 299 304 309 315 320 325 330 335 340 0.5 1.0 1.6 2.0 2.5 3.0 3.6 4.1 4.6 5.1 i 20 86 345 350 355 360 365 370 375 380 385 390 0.5 1.0 1.6 2.0 2.5 3.0 3.5 4.0 4.6 5.0 30 87 395 400 405 410 415 420 425 430 435 440 0.5 I.O l.S 2.0 2.5 3.0 3.5 4.0 4.5 6.0 40 88 445 450 455 460 465 469 474 479 484 489 0.5 1.0 1.6 2.0 2.5 2.9 3.4 3.9 4.4 4.9 50 15 00 89 90 494 499 504 509 513 518 523 528 533 538 0.5 1.0 1.6 1.9 2.4 2.9 3.4 3.9 4.4 4.9 9542 547 552 557 562 566 571 576 581 5t-6 0.5 1.0 1.4 1.9 2.4 2.9 3.4 3.8 4.3 4.8 10 91 590 595 600 605 609 614 619 624 628 633 0.5 0.9 1.4 1.9 2.4 2.8 3.3 3.8 4.3 4.7 20 92 638 643 647 652 657 661 666 671 675 680 0.5 0.9 1.4 1.9 2.3 2.6 3.3 3.8 4.2 4.7 30 93 685 689 694 699 703 708 713 717 722 727 0.5 0.9 1.4 1.9 2.3 2.S 3.3 3.7 4.2 4.6 40 50 94 95 731 736 741 745 750 754 759 763 768 773 O.S 0.9 1.4 1.8 2.3 2.S 3.2 3.7 4.1 4.6 9777 782 786 791 795 800 805 809 814 818 0.5 0.9 1.4 1.8 2.3 2.7 3.2 3.6 4.1 4.5 IfiOO 96 82:} 827 832 836 841 845 850 854 859 863 0.5 0.9 1.4 1.8 2.3 2.7 3.2 3.6 4.1 4.6 10 97 868 872 877 881 886 890 894 899 903 908 0.4 0.9 1.3 1.8 2.2 2.7 3.1 3.6 4.0 4.5 20 98 912 917 921 926 930 934 939 943 948 952 0.4 0.9 1.3 1.8 2.2 2.6 3.1 3.5 4.0 4.4 30 99 956 961 965 969 974 978 983 987 9!) I 996 0.4 0.9 1.3 1.7 2.3 2.6 3.1 8.5 3.9 4.4 log tan qp ; = log ((jp in mi nutes) -(- r. 1 ° '»! oo.li" 6. 44.2 1 40.6 6. 9 15. -i 6. 5 42.6 6. 8 06.0 • r LOGABITHMIC TRIGONOMETRIC FUNCTIONS , Angles in All QUADKANTS. Names. -qp 0° qi so°—

Tod +CSC D t 1 3 3 4 3 6 7 8 2"=3C 1' I" 4 =0'. 25 60' 50' 40' m 20' 10' 0' ^ Proportional Parts. 10 r LOGARITH mC TRIGONOMETRIC FUNCTIONS. Points of tue Compass. Namoi. sin Oi 3J OJ 1 li n IJ 2 2i 2i 2} 3 3i 3J 3i 4 8.6908 8.9913 9.16e5 9.390-2 9.3856 9.4628 9.6275 9.5828 9.6310 9.6734 9.7110 9.7447 9.7750 9.8024 9.8271 9.8495 cos CSC 1.3092 1.0087 0.8335 0.7098 0.6144 0.5372 0.4725 0.4172 0.3690 0.3366 0.289C 0.3553 0.3350 0.1976 0.1729 0.1505 sec tan 8.6913 8.9934 9.1712 9.3987 9.3988 9.4819 9.5536 9.6173 9.6748 9.7280 9.7777 9.8349 9.8702 9.9142 9.9573 0.0000 etn etn 1.3087 1.0066 0.8388 0.7013 0.6013 0.6181 0.4464 0.3828 0.3252 0.2720 0.3233 0.1751 0.1298 0.0858 0.0427 0.0000 tan sec 0.0005 0.0021 0.0047 0.0084 0.0132 0.0191 0.0263 0.0344 0.0438 0.0546 0.0667 0.0803 0.0952 0.1118 0.1302 0.1505 CSC cos 9.9995 9.9979 9.99S3 9.9916 9.9868 9.9809 9.9738 9.9656 9.9562 9,9454 9.9333 9.9198 9.9048 9.8883 9.8698 9.8495 sm 7* ri 7i 7 tii 6i 6i 6 5i 5.i 5i 5 4J 4i 4i 4 Names. Points of the Compass. 3 t 0' IC 20' 30' 40' 50' 60' ' m 8 ' m 8 10=0 40 40=2 40 20=120 50=3 20 Proportional Parts. si 30=2 00 60=4 00 1 » 3 4 5 « 7 8 • sin 9.7586 604 622 640 657 675 9.7692 cos 1.8 3.6 6.3 7.1 8.9 10.6 12.4 14.2 15.9 35° 2'' 20-" tan etn 9.8452 479 506 0.1548 521 494 533 467 559 586 9.8613 441 414 0.1387 etn tan 3" 36" 54° 3.7 6.3 8.0 10.7 13.4 16.0 18.7 21.4 24.1 cos sin 9.9134 125 116 107 098 089 9.9080 sm cos 0.9 1.8 2.7 3.6 4.5 6.4 6.3 7.2 8.1 9.7692 710 727 744 761 778 9.7795 1.7 3.4 6.1 6.8 8.5 10.2 12.0 13.7 15.4 36° 2" 24"" tan etn 9.8613 639 666 0.1387 361 334 692 308 718 745 9.8771 282 255 0.1229 etn tan 3" 32" 53° 2.6 6.3 7.9 10.6 13.2 15.9 18.6 21. 1 33.8 cos sin 9.9080 070 061 052 042 033 9.9023 sm cos 0.9 1.9 2.8 3.7 4.7 6.6 ] 6.5 7.5 8.4 9.7795 811 828 844 861 877 9.7893 1.6 3.3 4.9 6.6 8.2 9.9 11.6 13.2 14.8 37° 2" 28"- tan etn 9.8771 797 824 0.1229 203 176 850 150 876 902 9.8928 124 098 0.1072 etn tan 3" 28" 52° 3.6 6.2 7.8 10.6 13.1 15.7 18.3 20.9 23.5 cos sin 9.9023 014 004 895 985 o75 9. 8065 sin cos I.O 1.9 3.9 3.9 4.8 5.8 6.8 7.8 8.7 9.7893 910 926 941 957 973 9.7989 1.6 3.3 4.8 6.4 7.9 9.5 11.1 12.7 14.3 38° 2'' 32™ tan etn 9.8928 954 980 0.1072 046 020 a06 994 o32 o58 9. 9084 !)68 942 0.0016 etn tan 3" 24" 51° 3.6 6.3 7.8 10.4 13.0 15.6 18.2 30.7 23.3 cos sin 9.8965 955 945 935 925 915 9.8905 sm cos 1.0 2.0 3.0 4.0 6.0 6.0 7.0 8.0 9.0 9.7989 o04 o20 <^5 o50 o66 9. 8o81 1.5 3.1 4.6 6.1 7.7 9.2 10.7 12.3 13.8 39° 2" 36" tan etn 9.9084 110 135 0.0916 890 865 161 339 187 212 9.9238 813 788 0.0762 etn tan 3'> 20" 50° 2.6 6.1 7.7 10.3 12.9 15.4 18.0 20.6 23.2 cos sin 9.8905 895 884 874 864 853 9.8843 sm cos 1.0 3.1 3.1 4.3 5.2 6.3 7.3 8.3 fl.4 9.8081 096 111 125 140 155 9.8169 1.0 3.0 4.4 6.9 7.4 8.9 10.4 11.8 13.3 40° 2'' 40"" tan etn 9.9238 264 289 0.0762 736 711 315 685 341 366 9.9392 659 634 0.0608 etn tan 3» 1 6-" 49° 2.6 5.1 7.7 10.3 12.8 15.3 17.9 20.5 23.0 cos sin 9.8843 832 821 810 800 789 9.8778 sin cos 1.1 2.2 3.2 4.3 6.4 6.5 7.6 8.6 9.7 9.8169 184 198 213 227 241 9.8255 1.4 2.9 4.3 5.7 7.1 8.6 JO.O 11.4 12.9 41° 2'' 44" tan etn 9.9392 417 443 468 0.0608 583 557 532 494 519 9.9544 506 481 0.0456 etn tan 3" I2» 48° 2.5 6.1 7.6 10.2 12.7 15.3 17.8 20.4 22.9 cos sin 9.8778 767 756 745 733 722 9.8711 sin cos i.i 2.2 3.4 4.5 5.6 6.7 7.8 8.9 10. 1 9.8255 269 283 297 311 324 9.8338 1.4 2.8 4.1 5.5 6.9 8.3 9.7 11. D 12.4 II 42° 2'" 48"' tan etn 9.9544 570 595 0.0456 430 405 621 379 646 671 9.9697 354 329 0.0303 etn tan 3>' o8"> 47° 2.3 6.1 7.6 10.1 12.7 15.2 17.8 30.3 33.8 cos sin 9.8711 699 688 676 665 653 9.8641 sm cos 1.2 3.3 3.6 4.6 6.8 6.9 8.1 9.3 10.4 9.8338 351 365 378 391 405 9.8418 1.3 3.7 4.0 6.3 6.7 8.0 9.3 10.7 12.0 43° tan etn 9.9697 722 747 0.0303 278 253 772 228 798 823 9.9848 202 177 0.0152 etn tan 3" 04'" 46° 2.5 6.1 7.6 10.1 12.7 15.2 17.7 20.2 22.8 cos sin 9.8641 629 618 606 594 582 9.8569 sin cos 1.3 3.4 3.6 4.8 6.0 7.2 8.4 9.6 10.8 9.8418 431 444 457 469 482 9.8495 1.3 2.6 3.9 5.1 6.4 7.7 9.0 10.3 11.6 44° 2" 56" tan etn 9.9848 874 899 0.0152 126 101 924 076 949 975 0. ooOO 051 025 0.0000 etn tan 3" 00" 45° 2.8 6.1 7.6 10.1 13.6 15.2 17.7 90.2 22.7 cos 9.8569 557 545 532 520 507 9.8495 sin 1.3 2.5 3.7 6.0 6.2 7.4 8.7 9.9 11.3 f=W 8"=45' GA/ fan J A/ 9AJ a/\l tAI At Si t 1 » 3 4 9 6 T S 9 2"=3(y - 1'= 4 =0'. -=60' 25 W av W «»w itV IV V ' Proportional Parts • 11 INVERSE TRIGONOMETRIC FUNCTIONS. log^ sin"'^ cos"M tati"^^ ctn-'^ s m + 3 ii "cfi '11 1) 3 C 's _c 8- o i V log^ sin"M cos"'^ tair'^ ctn-M 8.50 .51 .52 .53 .54 8.55 .56 .57 .58 .59 8.60 .61 .62 .63 .64 8.65 .66 .67 .68 .69 8.70 .71 .72 .73 .74 8.75 .76 .77 .78 .79 8.80 .81 .82 .83 .84 8.85 .86 .87 .88 .89 8.90 .91 .92 .93 .94 8.95 .96 .97 .98 .99 9.00 O / t o * 1 48.7 0.35 88 11.3 1 t 1 48.7 0.25 o r 88 11.3 1.50 .49 .48 .47 .46 1.45 .44 .43 .42 .41 1.40 .39 .38 .37 .36 1.35 .34 .33 .32 .31 1.30 .29 .28 .27 .26 1.25 .24 .23 .22 .21 1.20 .19 .18 .17 .16 1.15 .14 .13 .12 .11 1.10 .09 .08 .07 .06 1.05 .04 .03 .02 .01 1.00 9.00 .01 .02 .03 .04 9.05 .06 .07 .08 .09 9.10 .11 .12 .13 .14 9.15 .16 .17 .18 .19 9.20 .21 .22 .23 .24 9.25 .26 .27 .28 .29 9.30 .31 .32 .33 .34 9.35 .36 .37 .38 .39 9.40 .41 .42 .43 .44 9.45 .46 .47 .48 .49 9.50 Of/ O i 5 44 0.8 84 16 o / / 5 43 0.8 f 84 17 1.00 0.99 .98 .97 .96 0.95 .94 .93 .92 .91 0.90 .89 .88 .87 .86 0.85 .84 .83 .82 .81 0.80 .79 .78 .77 .76 0.75 .74 .73 .72 .71 0.70 .69 .68 .67 .66 0.65 .64 .63 .62 .61 0.60 .59 .58 .57 .56 0.55 .54 .53 .52 .51 0.50 1 51.3 0.26 88 08.7 1 53.9 0.26 88 06.1 1 56.5 0.27 88 03.5 1 59.2 27 88 00.8 1 51.2 0.26 1 53.8 0.26 1 56.4 0.27 1 59.2 0.27 88 08.8 88 06.2 88 03.6 88 00.8 5 52 0.8 84 08 6 01 0.8 83 59 6 09 0.9 83 51 6 18 0.9 83 42 5 51 0.8 5 59 0.8 6 07 0.8 6 15 0.9 84 09 84 01 83 .53 83 45 2 02.0 0.28 87 58.0 2 01.9 0.28 87 58.1 6 27 0.9 83 33 6 24 o.n 83 30 2 04.8 0.29 87 55.2 2 07.8 0.29 87 52.2 2 10.7 0.30 87 49.3 2 13.8 0.31 87 46.2 2 04.8 0.29 2 07.7 0.29 2 10.6 0.30 2 13.7 0.31 87 55.2 87 52.3 87 49.4 87 46.3 6 36 0.9 83 24 6 45 0.9 83 15 6 54 1.0 83 06 7 04 1.0 82 56 6 33 0.9 6 42 0.9 6 51 0.9 7 01 1.0 83 27 83 18 83 09 82 59 2 16.9 0.32 87 43.1 2 16.8 0.31 87 43.2 7 14 1.0 82 46 7 11 1.0 82 49 2 20.1 0.32 87 39.9 2 23.4 0.33 87 36.6 2 26.7 0.34 87 33.3 2 30.1 0.35 87 29.9 2 20.0 0.32 2 23.2 0.33 2 26.6 0.34 2 30.0 0.34 87 40.0 87 36.8 87 33.4 87 30.0 7 24 1.0 62 36 7 35 1.1 82 25 7 45 1.1 82 15 7 56 11 82 04 7 20 1.0 7 31 i.o 7 41 1.0 7 52 1.1 82 40 82 29 82 19 82 08 2 33.6 oM 87 26.4 2 33.5 0.35 87 26.5 8 07 1.1 81 53 8 02 1.1 81 58 2 37.2 0.36 87 22.8 2 40.9 0.37 87 19.1 2 44.6 0.38 87 15.4 2 48.4 0.39 87 11.6 2 37.0 0.36 2 40.7 0.37 2 44.4 0.38 2 48.2 0.39 87 23.0 87 19.3 87 15.6 87 11.8 8 19 1.2 81 41 8 30 1.2 81 30 8 42 1.2 81 18 8 55 1 2 81 05 8 13 1.1 8 25 1.1 8 36 1.2 8 48 12 81 47 81 35 81 24 81 12 2 52.4 0.40 87 07.6 2 52.2 n.40 87 07.8 9 07 1.:) 80 53 9 00 12 81 00 2 56.4 0.41 87 03.6 3 00.5 0.42 86 59.5 3 04.7 0.43 86 55.3 3 09.0 0.44 86 51.0 2 56.2 0.40 3 00.3 0.41 3 04.4 0.42 3 08.7 0.43 87 03.8 86 .59.7 86 55.6 86 51.3 9 20 1.3 80 40 9 33 1.3 80 27 9 47 1.4 80 13 10 00 1.4 80 00 9 13 1.3 9 25 1.3 9 38 1.3 9 52 13 80 47 80 35" 80 22 80 08 3 13.4 0.4.5 86 46.6 3 13.1 0.44 86 46.9 10 15 1.4 79 45 10 05 14 79 55 3 17.9 0.46 86 42.1 3 22.5 0.47 86 37.5 3 27.3 0.48 86 32.7 3 32.1 0.49 86 27.9 3 17.6 0.45 3 22.2 0.46 3 36.9 0.48 3 31.7 0.49 86 42.4 86 37.8 86 33.1 86 28.3 10 2<) 1.6 79 31 10 44 1,5 79 16 10 59 1.5 79 01 11 15 1.6 78 45 10 19 1.4 10 33 1.4 10 47 1.6 11 02 1 5 79 41 79 27 79 13 78 58 3 37.1 0.50 86 22.9 3 36.6 0.50 86 23.4 11 31 1.6 78 29 11 17 15 78 43 3 42.1 0.51 86 17.9 3 47.3 0.52 86 12.7 3 52.6 0.54 86 07.4 3 58.0 0.O-, 86 02.0 3 41.7 0.51 3 46.8 0.62 3 52.1 0.53 3 57.5 0.55 86 18.3 86 13.2 86 07.9 86 02.5 11 47 1.7 78 13 12 04 1.7 77 56 12 21 1.7 77 39 12 38 1.8 77 22 11 32 1.6 11 48 1.6 12 04 1.6 12 20 1.7 78 28 78 12 77 56 77 40 4 03.6 0.56 85 56.4 4 03.0 0.56 85 57.0 12 56 1.8 77 04 12 37 17 77 23 4 09.3 0.57 85 50.7 4 15.1 0.59 85 44.9 4 21.0 0.60 85 39.0 4 27.1 0.62 85 32.9 4 08.6 0.67 4 14.4 0.58 4 20.3 0.60 4 26.3 0.61 85 51.4 85 45.6 85 39.7 85 33.7 13 15 1.9 76 45 13 33 1.9 76 27 13 53 2.0 76 07 14 13 2.0 75 47 12 54 1.7 13 12 1.8 13 29 1.8 13 48 1.8 77 00 76 48 70 31 76 12 4 33.4 0.63 85 26.6 4 32.5 62 85 27.5 14 33 2.1 75 27 14 06 19 75 54 4 39.7 0.65 85 20.3 4 46.3 0.66 85 13.7 4 53.0 0.68 85 07.0 4 59.8 0.69 85 00.2 4 38.8 0.64 4 45.3 0.65 4 51.9 0.67 4 58.7 0.68 85 21.2 85 14.7 85 08.1 85 01.3 14 54 2.1 75 00 15 15 2.2 74 45 15 37 2.2 74 23 15 59 2.3 74 01 14 25 1.9 14 44 1.9 15 04 2.0 15 24 2.0 75 35 75 16 74 56 74 30 5 06.8 0.71 84 53.2 5 05.6 0.70 84 54.4 16 22 2.3 73 38 15 44 2.1 74 16 5 14.0 0.72 84 46.0 5 21.3 0.74 84 38.7 5 28.8 0.76 84 31.2 5 36.5 0.78 84 23.5 5 12.7 0.72 5 19.9 0.73 5 27.3 0.75 5 34.9 0.77 84 47.3 84 40.1 84 32.7 84 25.1 16 46 2.4 73 14 17 10 2.4 72 50 17 35 2.5 72 25 18 00 i.6 72 00 10 05 2.1 16 27 2.1 16 48 2.2 17 10 2.2 73 55 73 33 73 12 72 50 5 44.4 0.80 84 15.6 off Of 5 42.6 0.78 ' / 84 17.4 O 1 18 26 a.6 71 34 off of 17 33 2.3 o f f 72 27 o ' CSC" '.4 sec'M ctn"M tan-'^ log -4 csc'^ sec' 'J ctn-M tan"M log^ 12 INVERSE TRIGONOMETBIC FUNCTIONS. log ^ sin" M cos"'^ tan'M ctn"M log A sin'^^ loj; A sin-M | log A sin-M 9.50 .51 .52 .53 .54 9.55 .56 .57 .58 .59 9.60 .61 .62 .63 .64 9.65 .66 .67 .68 .69 9.70 .71 .72 .73 .74 9.75 .76 .77 .78 .79 9.80 .81 .82 .83 .84 9.85 .86 .87 .88 .89 9.90 .91 .92 .93 .94 9.95 .96 .97 .98 .99 0.00 O / / Of 18 26 2.6 71 34 o / / 17 33 2.3 O 1 72 27 0.50 .49 .48 .47 .46 0.45 .44 .43 .42 .41 0.40 .39 .38 .37 .36 0.35 .34 .33 .32 .31 0.30 .29 .28 .27 .26 0.25 .24 .23 .22 .21 0.20 .19 .18 .17 .16 0.15 .14 .13 .12 .11 0.10 .09 .08 .07 .06 0.05 .04 .03 .02 .01 0.00 9.750 .755 .760 .765 .770 9.775 .780 .785 .790 .795 9.800 .805 .810 .815 .820 9.825 .830 .835 .840 .845 9.850 .852 .854 .856 .858 9.860 .862 .864 .866 .868 9.870 .872 .874 .876 .878 9.880 .882 .884 .886 .888 9.890 .891 .892 .893 .894 9.895 .896 .897 .898 .899 9.900 34 13 1 5.4 9.900 .901 .902 .903 .904 9.905 .906 .907 .908 .909 9.910 .911 .912 .913 .914 9.915 .916 .917 .918 .919 9.920 .921 .922 .923 .924 9.925 .926 .927 .928 .929 9.930 .931 .932 .933 .934 9.935 .936 .937 .938 .939 9.940 .941 .942 .943 .944 9.945 .946 .947 .948 .949 9.950 O ( 1 52 36 10 9.950 .951 .952 .953 .954 9.955 .956 .957 .958 .959 9.960 .961 .962 .963 .964 9.965 .966 .967 .968 .969 9.970 .971 .972 .973 .974 9.975 .976 .977 .978 .979 9.980 .981 .982 .983 .984 9.985 .986 .987 .988 .989 9.990 .991 .992 .993 .994 9.995 .996 .997 .998 .999 0.000 O 1 / 63 02 16 18 53 2.7 71 07 19 20 2.8 70 40 19 48 2.9 70 12 20 17 a.p 69 43 17 56 2.3 18 19 2.4 18 43 2.4 19 07 2.5 72 04 71 41 71 17 70 53 34 40 35 08 35 36 36 04 6.6 6.6 6.7 5,8 52 46 10 52 56 10 53 07 11 53 17 11 63 17 16 63 33 16 63 49 16 64 06 IB 20 47 3.0 69 13 19 32 2.5 70 28 30 34 5.9 53 28 u 64 22 16 21 17 3.1 68 43 21 49 3.2 68 11 22 21 3.3 67 39 22 54 3.3 67 06 19 57 2.5 20 23 2.6 20 49 2.6 21 15 2.7 70 03 69 37 69 11 68 45 37 03 37 33 38 04 38 35 6.0 6.1 6.2 6.3 53 39 11 53 50 11 54 00 11 54 11 11 04 39 17 64 55 17 65 12 17 65 30 17 23 28 3.4 66 32 21 42 2.7 68 18 39 07 6.4 .54 22 11 65 47 IS 24 02 3.5 65 58 24 38 3.6 65 22 25 15 3.7 64 45 25 53 3.8 64 07 22 10 2.8 22 38 2.8 23 06 2.9 23 35 2.9 67 50 67 22 66 54 66 25 39 40 40 13 40 47 41 21 6.6 6.7 6.8 7.0 54 33 11 54 45 11 54 56 11 55 07 11 66 05 18 66 23 18 66 41 18 67 00 19 26 32 4.0 63 28 24 04 2.9 65 56 41 56 -.1 55 19 11 67 18 19 27 12 4.1 62 48 27 53 4.2 62 07 28 36 4.3 61 24 29 20 4.4 60 40 24 34 3.0 25 04 3.0 25 35 3.1 26 06 3.1 65 26 64 56 64 25 63 54 42 32 43 09 43 47 44 25 7.3 7.4 7.6 7.8 55 30 12 55 42 12 55 53 12 56 05 12 67 37 19 67 57 20 68 16 20 68 36 20 30 05 4.6 59 55 26 37 3.2 63 23 45 04 7.9 56 17 12 68 57 21 30 51 4.7 59 09 31 39 4.9 58 21 32 29 6.0 57 31 33 20 ,1.2 56 40 27 09 3.2 27 41 3.3 28 14 3.3 28 47 3.3 62 51 62 19 61 46 61 13 45 20 45 36 45 52 46 09 8.0 8.1 8.2 8.2 56 29 12 56 41 12 56 53 12 57 05 12 69 18 21 69 39 SI 70 00 22 70 22 22 34 13 r,.i 55 47 29 21 3.4 60 39 46 25 8 3 57 17 12 70 45 23 35 08 54 52 36 04 53 56 37 03 52 57 38 04 51 56 29 55 3.4 30 29 3.5 31 04 3.5 31 39 3.5 60 05 59 31 58 56 58 21 46 42 46 59 47 16 47 33 3.4 8.5 8.6 8.7 57 30 12 57 42 13 57 55 13 58 07 13 71 08 23 71 31 24 71 55 94 72 20 25 39 07 50 53 32 15 3.6 57 45 47 51 8.7 58 20 13 72 45 25 40 13 49 47 41 21 48 39 42 32 47 28 43 47 46 13 32 51 3.6 33 27 3.6 34 04 3.7 34 41 3 7 57 09 56 33 55 56 55 19 48 08 48 26 48 44 49 02 8.8 8.9 9.0 9.1 58 33 13 58 46 13 58 59 13 59 12 13 73 U 26 73 37 27 74 04 28 74 33 29 45 04 44 56 35 18 3.7 54 42 49 20 9.2 59 26 13 75 02 30 46 25 43 35 47 51 42 09 49 20 40 40 50 55 39 05 35 55 3.8 36 33 3.8 37 11 3.8 37 49 3 8 54 05 53 27 52 49 52 11 49 39 49 58 50 17 50 36 9.3 9.4 9.5 9.6 59 39 14 59 53 14 60 06 14 60 20 u 75 32 31 70 03 32 76 36 33 77 10 35 52 36 37 24 :$8 28 3.9 51 32 50 55 9.7 60 34 14 77 45 36 54 22 35 38 56 17 33 43 58 20 31 40 60 34 29 26 39 06 3.9 39 45 3.9 40 24 3.9 41 03 3.9 50 54 50 15 49 36 48 .57 51 05 9.8 51 15 9.n 51 25 9.9 51 .35»io.o 60 48 14 61 03 14 01 17 14 61 31 n 78 23 38 79 02 41 79 44 44 80 30 47 63 02 26 58 41 43 .19 48 17 51 45 in 61 46 1.5 81 19 65 47 24 13 68 57 21 03 72 45 17 15 77 45 12 15 42 22 3.9 43 01 3.9 43 41 4.0 44 20 4.0 47 38 46 59 46 19 45 40 51 55 52 05 52 15 52 25 10.1 10.2 10.2 10.3 62 01 15 02 16 15 62 31 15 62 46 15 82 14 83 16 84 30 86 07 90 00 00 oil o t 45 00 4.0 O 1 1 45 00 O ' 52 36 o / 10.4 1 63 02 16 90 00 ' ' cac'^A see 'A ctur'A tan" '.4 log^ * Beyond this point the uncertainty i imounts to ± 0'.5. 13 TRAVERSE TABLE. 1 2 3 4 5' 6 7 8 9 10" 11 12 13 14 15' 16 17 18 19 20^ 21 22 23 24 25° 26 27 28 29 30 31 32 33 34 35° 36 37 38 39 40 41 42 43 44 45° diff lat = dist . cos course. 12 3 4 5 6 7 8 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 1.00 2.00 3.00 4.00 1.00 2.00 1 3.00 4.00 1.00 2.00 3.00 3.99 1.00 2.00 2.99 3.99 5.00 5.00 4.99 4.99 1.00 1.99 I 2.99 3.98 |4. 98 0.99 1.9912.98 3.98 0.99 1.9912.98 3.97 0.99 1.98 2.97 3.96 0.99 1.98 2.96 3.95 0.98 1.97 1 2.95 3.94 h'' 0.98 0.98 0.97 0.97 1.96 1.96 1.95 1.94 2.94 2.93 2.92 2.91 3.93 3.91 3.90 3.88 0.97 1.93 0.96 0.96 0.95 0.95 1.92 1 91 1.90 1.89 2.90 3.86 2.88 2.87 2.85 2.84 3.85 3.83 3.80 3.78 0.94 1.: 0.93 0.93 0.92 0.91 1.87 1.85 1.84 1.83 0.91 1.81 0.90 0.89 0.88 0.87 air 1.80 1.78 1.77 1.75 1.73 0.86 0.85 0.84 0.83 0.82 1.71 1.70 1.68 1.66 2.82 3.76 2.80 2.78 2.76 2.74 3.73 3.71 3.68 3.65 2.72 3.63 2.70 2.67 2.65 2.62 3.60 3.56 3.53 3.50 2.60 3.46 2.57 2.54 2.52 2.49 3.43 3.39 3.35 3.32 4.97 4.96 4.95 4.94 4.92 4.91 4.89 4.87 4.85 6.00 7.00 6.00 7.00 5.99 6.99 5.99 6.98 5.98 6.97 8.00 9.00 8.00 8.99 7.99 8.99 7.98 8.98 7.97 8.97 5.97 6.96 7.96 8.95 5.96 6.95 7.94 8.93 5.94 6.93 7.92 8.91 5.93 6.91 7.90 8.89 1.91 6.89 5.89 5.87 5.85 5.82 6.87 6.85 6.82 6.79 4.83 4.81 4.78 4.76 4.73 4.70 4.67 4.64 4.60 4.57 4.53 4.49 4.46 4.41 4.37 4.33 29 4.24 4.19 4.15 l.C4|2.46 3.28 I 4.10 5.80 6.76 5.77 5.74 5.71 5.67 6.73 6.69 6.66 6,62 5.64 6.58 5.60 5.56 5.52 5.48 6.54 6.49 6.44 6.39 5.44 6.34 5.39 5.35 5.30 5.25 6.29 6.24 6.18 6.12 5.20 6.06 5.14 5.09 5.03 4.97 6.00 5.94 5.87 5.80 7.88 8.86 7.85 7.83 7.79 7.76 8.83 8.80 8.77 8.73 dep = dist . sin course. 12 3 4 5 6 7 8 9 0.00 0.00 0.00 0.00 0.00 0.00 0.0010.00 0.00 0.02 0.03 0.03 0.07 0.05 0.10 0.07 0.14 0.09 0.17 0.10 0.21 0.12 0.24 0.14 0.28 0.16 0.31 0.17 0.35 7.73 8.69 7.69 7.65 7.61 7.56 8.65 8.61 8.56 8.51 7.52 8.46 7.47 7.42 7.36 7.31 8.40 8.34 8.28 8.22 7.25 8.16 7.19 7.13 7.06 7.00 8.09 8.02 7.95 7.87 6.93 7.79 6.86 6.78 6.71 6.63 7.71 7.63 7..55 7.46 4.91 5.7;s 6.55 7.31 0.81 0.80 0.79 0.78 ojt" 1.62 1.60 1.58 1.55 1.53 0.75 0.74 0.73 0.72 1.51 1.49 1.46 1.44 0.71 1.41 2.43 2.40 2.36 2.33 3.24 3.19 3.15 3.11 2.30 3.06 2.26 2.23 2.19 2.16 3.02 2.97 2.93 2.88 4.05 3.99 3.94 3.89 3.83 3.77 3.72 3.66 3.60 2.12 2.83 3.54 4.24 4.95 4.85 4.79 4.73 4.66 5.66 5.59 5.52 5.44 4.60 5.36 4..53 4.46 4.39 4.32 5.28 5.20 5.12 5.04 6.47 6.39 6.30 6.22 7.28 7.19 7 09 6.99 6.13 6.89 6.04 5.95 5.85 5.75 6.79 6.69 6.58 6.47 5.66 6.36 1.00 1.00 0.99 2.00 1.99 1.98 3.00 2.99 2.97 4.00U.99I5.99 6.99 3.98 4.98 5.97 6.97 3.96 4.95 5.94 6.92 0.98 1.96 0.97 0.96 0.94 1.94 1.91 1.88 0.92 1.85 0.90 0.88 0.86 0.83 1.81 1.76 1.72 1.66 0.80 0.77 0.74 1.61 1.55 1.48 2.94 3.92 2.91 2.87 2.82 3.88 3.83 3.77 2.77 3.70 2.71 2.65 2.57 3.62 3.53 3.43 2.49 3.33 2.41 2.32 2.22 3.21 3.09 2.96 4.90 4.85 4.78 4.71 4.62 4.52 4.41 4.29 4.16 4.02 3.87 3.70 5.88 6.87 5.82 6.79 5.74 6.70 5.65 6.59 5..54 6.47 5.42 6.33 5.29 6.17 5.15 6.00 4.99 5.82 4.82 5.62 4.64 5.41 4.45 5.19 7.99 7.96 7.91 8.99 8.96 8.90 7.85 8.83 7.76 7.66 7.53 8.73 8.61 8.47 7.39 8.31 7^3 7.06 6.86 8.14 7.94 7.72 6.65 7.48 6.43 6.18 5.93 7.23 6.96 6.67 123456789 dep = dist . sin course. 0.19 0.21 0.22 0.24 0.38 0.42 0.45 0.48 0.26 0.52 0.28 0.29 0.31 0.33 0.55 0.58 0.62 0.65 0.34 0.68 0.36 0.37 0.39 0.41 0.72 0.75 0.78 0.81 0.42 0.85 0.44 0.45 0.47 0.48 0.88 0.91 0.94 0.97 0.50 1.00 0.52 53 0.54 0.56 1.03 1.06 1.09 1.12 0,05 0.07 0.10 0.14 0.16 0.21 0.21 0.28 0,09 0.17 0.26 0.35 0.10 0.12 0.21 0.24 0.31 0.37 0.42 0.49 0.26 0.35 1 0.44 1 0.52 0.61 0.31 0.42 0.37 0.49 0.42 0.56 0.47 0.63 0.52 0.61 1 0.70 0.78 0.63 0.73 0.73 0.85 0.84 0.97 0.94 1.10 0.52 0.69 0.57 0.76 0.62 0.83 0.67 0.90 0.73 0.97 0.78 1.04 0.83 1.10 0.88 1.17 0.93 1.24 0.98 1.30 1.03 1.37 1.08 1.43 1.12 1.50 1.17 1.56 1.22 1.63 1.27 1.69 1.32 1,75 1.36 1.82 1.41 1.88 1.45 1.94 1.50 2.00 1.55 2.06 1.59 2.12 1.63 2.18 1.68 2.24 0,57 1,15 0.59 0.60 0.62 0.63 1.18 1.20 1.23 1.26 0.64 1.29 Me 0.67 0.68 0.69 1.31 1.34 1.36 1.39 0.71 1.41 1.72 2.29 1.76 2.35 1.81 2.41 1.85 2.46 1.89 2.52 1.93 2.57 1.97 2.62 2.01 2.68 2.05 2.73 2.08 2.78 2.12 2.83 0.8; 0.95 1.04 1.12 1.21 1.29 1.38 1.46 1.55 1.63 1.71 1.79 1.87 1.95 2.03 2.11 2.19 2.27 2.35 2.42 2.50 2.58 2.65 2.72 2.80 2.87 2.94 3.01 3.08 3.15 3.21 3.28 3.35 3.41 3.47 3.54 1.04 1.22 1.14 1.34 1.25 1.46 1.35 1.57 1.45 1.69 1.55 1.81 1.65 1.93 1.75 2.05 1.85 2.16 1,95 2.28 2.05 2.39 2.15 2.51 2.25 2.62 2.34 2.74 2.44 2.85 2.54 2.96 2.63 3.07 2.72 3.18 2.82 3.29 2.91 3.39 3.00 3.50 3.09 3.61 3.18 3.71 3.27 3.81 3.36 3.91 3.44 4.02 3.53 4.11 3.61 4.21 3.69 4.31 3.78 4.41 3.86 4.50 3.94 4.59 4.01 4.68 4.09 4.77 4.17 4.86 4.24 4.95 0.14 0.16 0.28 0.31 0.42 0.47 0.56 0.63 0.70 0.78 0.84 0.94 0.97 1.10 1.11 1.25 1.25 1.41 1..39 1.56 1.53 1 72 1.66 1.87 1 80 2.02 1.94 2.18 2.07 2.33 2.21 2.48 2.34 2.63 2.47 2.78 2.60 2.93 2.74 3,08 2.87 3.23 3.00 3.37 3.13 3.52 3.25 3.66 3.38 3.80 3.51 3.95 3.63 4.09 3.76 4.23 3.88 4.36 4.00 4.50 4.12 4.64 4.24 4.77 4.36 4.90 4.47 5.03 4.59 5.1G 4.70 5.29 4.81 5.42 4.93 5..54 5.03 5,66 5.14 5.79 5.25 5.90 5.35 6.02 5.46 6.14 5.56 6.25 5.66 6.36 0.05 0.10 0.10 0.20 0.15 0.29 0.20 0.39 0.24 0.4d 0.29 0.58 0.34 0.67 0.38 0.77 0.43 0.86 0.47 0.94 0.51 1.03 0.56 1.11 0.60 1.19 0.63 1.27 0.67 1.34 0.15 0.20 0.29 0.39 0.44 0.59 0.59 0.78 0.73 0.97 0.87 1.01 1.16 1.35 1,15 1.53 1.28 1.71 1.41 1.89 1.54 2.06 1.67 2.22 1.79 2.38 1.90 2.54 2.01 2.69 0.25 0.49 0.73 0.98 1.21 1.45 1.68 1.91 2.14 2.36 2.57 2!Y8 2.98 3.17 3.36 0.29 0.59 0.88 0.34 0.69 1.03 1.17 1.37 1.46 1.74 2.02 1.70 2.03 2.36 2.30 2.68 2.57 2.83 3.08 2.99 3.30 3.60 3.33 3.89 3.57 3.81 4.03 4.17 4.44 4.70 0.39 0.44 0.78 0.88 1.17 1.32 1.56 1.76 1.94 2.19 2.32 2.61 2.70 3.03 3.06 3.44 3.42 3.85 3.77 4.24 4.11 4.63 4.44 5.00 4.77 5..36 5.08 5.71 5.37 6.04 123456789 diflf lat = dist . cos course. 14 w 89 88 87 86 85* 84 83 82 81 80° 79 78 77 76 75° 74 73 72 71 70° 69 68 67 66 65° 64 63 62 61 60° 59 58 57 56 55° 54 53 52 51 50° 49 48 47 46 45° CoaaECTioN op Middle Latitude S.\iLiNa. •a 3 0° 5 10 15 20 25 26° 27 28 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 47 48 49 50 51° 52 53 54 55 56° 57 58 59 60 61° 62 63 64 65 66° 67 68 69 70 71° 72 73 74 75 Add to log sec, or sub- tract from tog cos, of mid lat, if diff lat o 10». 0.00055 56 59 63 70 79 0.00082 84 86 89 92 0.00095 098 102 106 110 0.00114 118 123 128 133 0.00139 145 152 159 166 0.00174 183 192 202 213 0.00225 238 251 266 283 0.00300 320 341 365 391 0.00419 451 487 527 572 0.00623 681 747 823 912 0.01016 1138 1284 1459 1673 For a given mid lat, the correction nearly propor- tional to the square o/the diff lat. 1 MERIDIONAL PARTS. 1 0° 10° 20° 30° 40° 50° 60° 70° 80° 85° 87° 89° 0°oo' 603 1225 1888 2623 3474 4527 5966 80° 00' 8375 85° 00' 10765 87° 00' 12522 89° 00' 16300 10 10 613 1236 1900 36 90 47 95 05 8404 02 788 02 561 01 357 20 20 623 46 12 49 3506 68 6025 10 33 04 811 04 599 02 416 30 30 634 57 23 62 21 88 55 15 63 06 834 06 639 03 476 40 40 644 68 35 75 37 4608 85 20 92 08 858 08 678 04 537 50 I'OO' 50 654 78 46 88 53 29 6115 25 30' 8522 8552 10' 12 10881 905 10' 12 12719 759 05' 06 16599 662 60 664 1289 1958 2702 3569 4649 6146 ^H^ 10 70 674 1300 70 15 85 70 77 35 83 14 929 14 801 07 726 ^^Bl 20 80 684 11 81 28 3601 91 6208 40 8614 16 953 16 842 08 792 ^^hI 30 90 695 21 93 42 17 4712 39 45 44 18 978 18 884 09 858 ■1 40 100 705 32 2005 55 33 33 71 50 76 20' 11002 20' 12927 10' 16926 50 2«oo' 110 715 43 17 68 49 54 6303 55 81° 00' 8707 22 24 027 052 22 24 970 13014 11 12 996 17067 120 725 1354 2028 2782 3665 4775 6335 8739 10 130 736 64 40 95 81 96 67 05 71 26 077 26 059 13 139 20 140 746 75 52 2809 98 4818 6400 10 8804 28 102 28 104 14 213 30 150 756 86 64 22 3714 39 33 15 36 30' 11127 30 13149 15 17289 40 160 766 97 76 36 31 61 67 20 69 32 153 32 195 16 366 50 3° 00' 170 777 1408 88 49 47 83 6500 25 30' 8903 8936 34 36 179 205 34 36 242 290 17 18 445 526 180 787 1419 2100 2863 3764 4905 6534 10 190 797 30 11 77 80 27 69 35 70 38 231 38 338 19 609 20 200 807 40 23 91 97 49 6603 40 9005 40' 11257 40' 13386 20' 17693 30 210 818 51 35 2904 3814 72 39 45 39 42 284 42 436 21 781 40 220 828 62 47 18 31 94 74 50 74 44 310 44 486 22 870 50 4° 00' 230 838 73 59 32 48 5017 6710 55 82° 00' 9110 46 48 337 365 46 48 537 589 23 24 962 18056 240 848 1484 2171 2946 3865 5039 6746 9145 10 250 859 95 84 60 82 62 82 05 82 50' 11392 50' 13641 25' 18153 20 260 869 1506 96 74 99 85 6819 10 9218 52 420 52 695 26 252 30 270 879 17 2208 88 3916 5108 56 15 55 54 448 64 749 27 355 40 280 890 28 20 3002 33 32 94 20 92 56 476 66 804 28 461 50 5' 00' 290 900 39 32 16 51 55 6932 25 30' 9330 9368 58 86° 00' 504 58 88° 00' 860 29 30' 570 18682 300 910 1550 2244 3030 3968 5179 6970 11533 13916 10 310 921 61 57 44 85 5203 7009 35 9407 02 561 02 974 31 799 20 320 931 72 69 58 4003 26 48 40 45 04 590 04 14033 32 920 30 331 942 83 81 73 21 50 88 45 85 06 620 06 093 33 19045 40 341 952 94 93 87 38 75 7128 50 9525 08 649 08 154 34 174 50 6° 00' 351 962 1605 2306 3101 56 99 69 55 83° 00' 65 10' 12 11679 709 10' 12 14216 279 35' 36 19309 450 361 973 1616 2318 3116 4074 5324 7210 9606 10 371 983 28 30 30 92 48 52 05 47 14 739 14 343 37 596 20 381 994 39 43 44 4110 73 94 10 89 16 770 16 408 38 749 30 391 1004 50 55 59 28 98 7336 15 9731 18 801 18 475 39 909 40 401 1014 61 68 73 46 5423 79 20 74 20' 11832 20' 14543 40' 20076 50 7" 00' 411 1025 72 80 88 64 48 7423 25 30' 9817 9861 22 24 863 895 22 24 €13 684 41 42 253 439 421 1035 1684 2393 3203 4183 5474 7467 10 431 1046 95 2405 17 4201 5500 7512 35 9906 26 927 26 756 43 635 20 441 1056 1706 18 32 20 26 57 40 51 28 959 28 830 44 843 30 451 1067 17 30 47 38 52 7603 45 96 30' 11992 30' 14906 45' 21065 40 461 1077 29 43 62 57 78 50 50 10043 32 12025 32 983 46 303 50 8° 00' 471 1088 40 56 77 75 5604 97 55 84° 00' 89 34 36 058 092 34 36 15062 143 47 48 557 832 482 1098 1751 2468 3292 4294 5631 7745 10137 10 492 1109 62 81 3306 4313 58 93 05 85 38 125 38 226 49 22132 20 502 1119 74 94 22 32 85 7842 10 10234 40' 12160 40' 15311 50' 22459 30 512 1130 85 2506 37 51 5712 92 15 83 42 194 42 398 51 821 40 522 1140 97 19 52 70 39 7942 20 10334 44 229 44 487 52 23226 50 90 00' 532 1151 1808 32 67 90 67 94 25 30' 85 10437 46 48 264 300 46 48 579 673 53 54 685 24215 542 1161 1819 2545 3382 4409 5795 8046 10 552 1172 31 58 97 29 6823 99 35 89 60' 12336 50' 15770 55' 24842 20 562 1183 42 71 3413 48 51 8152 40 10542 52 373 52 869 56 25609 30 573 1193 54 84 28 68 79 8207 45 97 54 409 54 972 57 26598 40 583 1204 65 97 43 88 5908 62 50 10652 56 447 56 16078 58 27992 50 59.3 1215 77 2610 59 4507 37 8318 55 85° 00' 10708 58 87° 00' 484 58 89° 00' 187 59 90° 00' 30375 16° 00- 603 1225 1888 2623 3474 4527 5966 8375 10765 12522 16300 00 ^HM^Hi ^^■HH ^^■^^ 15 University Press, Cambridge : Printed by Welch, Bigelow, & Co. I UNIVERSITY OF CALIFORNIA LIBRARY This book is DUE on the last date stamped below. 50 cents on fourth day ovft^ .. One dollar on seventh day overdue^,. OCT 20 134/ .-■-IT .^/l^^'i MAY 1 2 1955 LD 21-100m-12,'46(A2012sl6)4120 Stcckton, C«l»- T.l«''«« US. pat. Off 4??364 UNIVERSITY OF CALIFORNIA LIBRARY y-^ vf -:0;:^i?t!x y }mii:M:M^'mmMmm^