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EXAMPLE. Required the Degrees and Minutes corresponding to the Logan rithmic Tangent 9.73597. Given Log

9.73597 Next greater Log. 9.73627 Next less 9.73476 Next less

9.73476

Difference

121

Difference

151

As 151 : 5 ::: 121 : 4 The Degrees and Minutes for the Log. next less than the given one are 28° 30', to which add t' and it makes 28° 34' Note. As after the most careful attention of the Printers, some

figures in the Table may be wrong ; and as some may be so blurred as to be illegible, let it be observed, that the Sines and Co-Secants, the Co-Sines and Secants, and the Tangents and Co-Tangents, standing against each other respectively, being added together, will amount to 20.00000, if the Tables are accurate. Thus against 28° 20' the Sine 9.67633 added to the Co-Secant 10.32367 their Sum is 20.00000; 80 also is the Sum of the Co-Sine 9.94458 and the Secant 10. 05542, and likewise the Sum of the Tangent 9.73175 and the Co-Tangent 10.26825. An error may consequently be easily detected, or any defaced figure be supplied.

To calculate the Northing or Southing, &c. for any Course and Distance by Logarithms.

This is done by the first Case of RIGAT ANGJED TRIGONOM.ETRY, as follows:

Find the Log. Sine and Co-Sine of the Course ; to each of these add the Log. of the Distance ; subtract Radius or 10.00000 from their Sums, and the Remainders will be the required Latitude and Departure. Note. When the Angle is very small or very large, and the

Distance short, the Sum of the Log. Sine or Co-Sine and the Log. of the Distance may be less than 10.00000 or Radius, which cannot therefore be subtracted. In such cases look for the Log, without regard to the Index, and the corresponding Number will be a Decimal, the first Figure of which will be Tenths if the Index be 9, and Hundredths if the Index be 8.

Bb

No

0 1 | 2 | 3 4

No 1 0.00000 0.04139 0.07918 0.11394 0.14613 1 2 30103 32222 34242 36173 38021 2 3 47712 49136 505151 51851 531481 3

60206 61278 62325 63347 643451 4 5 69897 70757 71600) 72428 73239 5 6 77815 78533 792391 79934 80618 6 7 84510 85126 85733 86332 86923 7 8 90309 90848 91381 91908 92428 8 9 95424 95904 96379 96848 973139 101.00000 1.00432 1.008601 1.01284) 1.01703 10 11 1.04139 1.04532 1.04922 1,05308 1,05690 11 12 07918 08279 086361 08991 09342/12 13 11394 11727 12057 12385 12710/13 14 14613 14922 15229 15534 15836 14 15 17609 17898 18184 18469 18752 15 16 20412 20683 20951 21219 21484/16 17 23045 23300 23553 23805 24055 17 18 25527 25768 26007 26245 26482/18 19 27875

28103 28330 28556 28780119 20 30103 30320 30535 30750 30963/20 21 1.32222 1.32428 1.32634 1.32838 1.33041121 22 34242 34439 34635 34830 3502522 23 36173 36361 36549 36736 36922 23 24

38021 38202 38382 38561 38739124 25 39794 39967 40140 40312 4048325 26 41497 41664

41830 419961 42160/26 27 43136 43297 43457 43616) 43775127 28 44716

44871

4502 45179 4533228 29 46240 46389 46538 46687 46835/29 30 47712 47857 48001 48144

4828730 31 1.49136 1.49276 1.49415 1.49554) 1,4969331 32 50515 50650 50786 50920 51054132 33 51851 51985 52114 52244

52375133 34 53148 53275 53403 53529 53656/34 35 54407 54531 546541 54777 54900135 36 55630 55751 55871 55991 561 1036 37 56820 56957 57054 57171 5728737 38 57978 58092 58206 58320 5843338 39 59106 59218 59329 59439 5955039 40 60206 60314 60423 60530 60638 40 41 1.61278 1.61384 7.61490 1.61595 1.61700 41 42 62325 62428 62531 62634 6273742 43 63347 63448 63548 63649 637 49143 44 64345 64444 64542 64640 64738 44

65321 65418 65514 65610 6570645 46 66276 66370 66464 66558 6665246

67210 67302 67394 67486 67578 47 48 68124 682 15 68305 68395 6848448 49

69020 691081 69197 69285 69373149

5 | 6 | 7 | 8 8 9 Nol

No 10.17609 0.20412 0.23045 0.25527 0.27875 1 2 39794 41497 43136 44716 462401 2 3 54407 55630 56820 57978 59106 3 4 65321 662761 67210 68124 6902014 5 74036 748191 75587 76343 77085 5 6 81291

81954 82607 83251 83885) 6 7 87506 88081 88649 89209 897637 8 92942 93450 93952 944481 94939| 8 9 97772 98227 98677 99123 995641 9 101 1,02119 1.02531/ 1.02938 1.03342) 1.0374310 11 1.06070 1.06446) 1.068191 1.07188 1.07555 11 12 09691 10037 10380 10721 1105912 13 13033 13354 13672 13988 14302 13 14 16137 16435 16733 17026 17319114 15

19033 19312 19590 198661 20140115 16

21748 22011 22272 22531 22789/16 17 24304 24551 24797 25042 25285 17 18

26717 26951 27184 27 416 27646118 19 29003 29226 29447 29667 29885/19 20

31175 31387 31597 31806 32015/20 21) 1.33244 1.33445/ 1.336461 1.33846 1.3404421 22 35218 35411 35603 35793 35984 22 23 37107 37291 37475 37658 37840123 24 38917 39093 39270 39445 39620|24 25 40654

40824) 40993 41162) 41330125 42325 42488 42651 42813 42975 26 27 43933 44091 44248 44404 44560/27 28 45484

45637 45788 45939 46090128 29 46982 47129 47276 47422 4756729 30 48430 48572 48714 48855 4.899630 31) 1.49831 1.49969 1.501061 1.50243 7.5037931

51188 51322 51455) 51587 51720:32 33 52504 52634 52763 52892 53020133 34 53782 53908 54033 54158 5428334 35 55023 55145 55267 55388 5550935 36 56229 56348 56467 56585 5670336 37 57403 57519

57634 57749 5786437 38 58546 58659

58771 58883 58995/38 39 59660 59770 59879 59988 60097 39 40 60746 60853 60959 61066 61172 40 4111.61805 1.61909 1.62014 1.62118 1.62221 41 42 62839 62941 63043 63144 63246/42 43 63849 63949 64048 64147 6424643 44 64836 64933 65031 65128 65225/44 45 65801 65896 65992 66087 66181/45 46 66745 66839

66932

67025 67117 46 47 67669 67761 67852 67943 68034 47 48 685741 68664 68753 .68842 6893148 49 69461 69548 69636 69723 69810119

26

8

32

86392

O 1 2 3 4 No.

No. 51 1.70757| 1.70842 1.70927 1,71012 1.71096 51 52 71600 71684 71767) 71850 71933 52 53 72428 72509 72591 72673 7275453 54 73239 73320 73400 73480 73560 54 55 74036 74115 74194 74273 74351 55 56 74819 74896 74974) 75051 751281 56 57

75587 75664 75740 75815 75891 57 58 76343) 76418! 76492 76567 76641| 58 59 77085 77159 77232 77305 77379 59 601 77815 77887 77960 78032 78104601 61) 1.78533 1.78604 1.78675 1.78746) 1.788171 61 62 79239 79309 79379 79449 795181 62 63

79934 80003 80072 80140 80209 63 64 806181

80686 80754 80821 80889 64 65

81291 81358 81425 81491 815581 65 66

81954) 82020 82086 82151 82217) 66 67

82607 82672 82737 82802 82866 67 68

83251) 83315 83378 83442 83506 68 69

83885 83948 84011 84073 84136 69 701

84510 84572 84634 84696 84757 70 711 1.85126 1.85187 1.85248) 1.85309 1.85370 71 72 85733 85794

85854 85914 859741 72 73 86332

86451 86510 865701 73 74 86923

86982 87040 87099 87157| 74 75 87506 87564

87622 87679 87737| 75 76 88081

88195 88252 88309 76 77 88649 88705

88762 88818 888741 77 78 89209

89265 89321) 89376 89432 78 79 89763 89818

898731 89927 899821 79 80 90309

90417 90472 90526 80 81/ 1.90849) 1.90902 1.90956 1.91009 1.91062 81 82 91381

91434 91487 91540 915931 82 83 91908

91960 92012 92065 92117 83 84 92428

92480 92531 92583 92634 84 85 92942

92993 93044 93095 931461 85 86 93450

93500 93551 93601 936511 86 87 93952

94002 94052 94101 94151) 87 88 94448

94498 94547 94596 946451 88 89 94939

94988 95036 95085 95134 89 90 95424

954721 95521 95569 95617 901 91| 1.95904) 1.95952 1.95999 1.96047 1.96095) 91 92

96379 96426) 964731 96520 96567 92

96848 96895 96942 96988 97035 93 94!

97313) 97359 97405 974511 97497] 94 95 97772 97818) 978641 97909 979551 95 96 98227) 98272 98318 98363 984081 96 97 986771 98722 98767 98811 98856 97 98 991231 99167 992111 99255

99300 98 99 995641 996071 996511 99695

99739) 991

88138

90363

93

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5 6 7 No.

No. 51 1.711811.71265 1.7 1349 1.7 14331 1.71517 51 52 72016 7209.9 72181 72263 723461 52 53 72835 72916 72997 73078 731591 53 54 73640 73719 73799 73878 739571 54 55 74429) 74507 74586 74663 74741 55 56 75205 75282 75358 75435 75511 56 57 75967 76042 76118 76193 76268 57 58 767 161 76790 76864 76938 7701258 59 77452 77525 77597 77671)

7774359 60 78176 78247 78319 78390 78462 60 611.78888 1.78958) 1.79029 1.79099) 1.79169 61 62 79588 79657 79727

79796 798651 62 63 80277 80346

80414

80482 803501 63 64 80956 81023 81090

81158 812241 64 65 81624 81690 81757

81823 81889 65 66 82282 82347 82413 82478 82543 66 67 82930 82995

83059

83123 831871 67 68 83569 836321 83696 83759 83822 68 69 84198 84261 84323

84386 84448 69 70 84819 84880

84942

85003 850651 70 71 1.85431| 1.854911 1.85552 1.85612 1.8567371 72 86034 86094 86153

86213 86273 72 73 86629 86688 86747

86806 86864 73 74 87216 87274 87332

87390 87448 74 75 87795 87852 87910

87967 88024 7 76 88366 88423

88480 88536 88593 76 77 88930 88986 89042 89398 89154 77 78 89487 89542 89597 89653 89708) 73 79 90037 9009] 90146 90200 902551 79 80 90580 90634 90687 90741 907951 80 811 1.911161.1.91169 1.91222 1.91271 1.9:328 81 82 91645 91698 91751 91803 91855 82 83 92169

92221

92273 92324 92376 83 84 92686 92737 92788

92840 92891 84 85 93197 93247 93298 93349 93399/ 85 86 93702 93752

93802 93852 93902) 86 87 94201 94250

94300

94349 94399 87 88 94694 94743

94792 94841 948901 88 89 95182 95231 95279 95328

95376 89 90 95665 95713

95761

95808 958,61 9 911.96142 1.961901 1.96237| 1.96284 1.90332 91 92 96614 96661 96708 96755 96802 92 93 97081 97128 97174 97220 97267 93 94 97543 97589 97635 9768 977271 94 95 98000 98046 980 9813: 98182 95 96 98453 98498 98543 98588 98632 96 97 989001 98345 98989 9903 99078/ 97 98 99344 99388 99432 99470 99520 98

99782 99826 9987, 9991: 999571 99

1

99

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