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1591

M 70° 710 72° 73° 74° 75° 76° 77° 78" 790 0939693 945519 951057 956305 961262 965926 970296 974370 978148 981627 60 1939792 945613 951146 956390 961342 966001 970366 974435 978208 981683 2939891 945708 951236 956475 961422 966076 970436 974501 978268 9817385 3 939991 945802 951326 9,6560 961502 966151 970506 974566 978329 9817937 4 940090 945897 951415 956644 961582 966226 970577 974631 978389 981849 36 5940189 945991951505 956729 961662 966301 970647 974696 978449 98190455

940288 946085 951594 956814 961741 966376 970716 974761 978509/98195954 7 940387 946180 95 1684 956898 961821 966451 970786 974826 978569 982014 8 940486 946274 951773 956983 961901 966526 970856 974891 978629 982069 9940585 946368 951862 57067 961980 966600 970926 974956 978689 9811235 101940684 946462 951951 957151 962059 966675 970995 975020 978748 983178 11940782 946555 952040 957235 962139 966749 971565 975085 978808 982233 12940881 946649 952129 957319 962218 966823 971134 975149 978867 982287 13/940979 946743 952218 957404 962297 966898 971204 975214 978927 982342 14,941078 946837 952307 957487 962376 966972 971273 975278 978986 982396 15 941176 946930 952396 957571 962455 967046 971342 975342 979045 98245045 16 941274 947024 952484 957655 962534 967120 971411 975406 979105 9825054 17 941372 947117 952573 957739 962613 967194 971480 975471 979164 98255945 18 941471 947210 952661 957822 962692 967268 971549 975535 979223 982613 19 941569 947304 952750 957906 962770 967342 971618 975598 979282 982 20 941666 947397 952838 957990 962849 967415 971687 975662 979341 21 941764 947490 952926 958073 962928 967489 971755 975726 979399 9827743 22 941862 947583 953015 958156 963006 967 562 971824 975790 97945 23 941960 947676 953103 958234 963084 967636 971893 975853 979517 24 942057 947768 953191 958323 963163 967709 971961 975917 979575 25 942555 947861 953279 958436 963241 967782 972030 975980 979634 9889893 26 942252 947954 953366 958489 963319 967856 972098 976044 979692 983041 34 27 942350 948046 953454 958572 963397 967929 972166 976107 979750 98309633 28 942447 948139 953542 958654 963475 968002 972234 976170 979809 983149 29 942544 948231 953629 958737 963553 968075 972302 976233 979867 983202 30 942641 948324 953717 958820 963630 968148 972370 976296 979925 9832553 31,942739 948416953804 958902 963708 968220 972438 976359 979983 983308 329428369-8508953892 958985 963786 968293 972506 976422 980041 9833613 33 942932 948600 953979 959067 963863 968366 972573 976485 980098 983414 34 943029 948692954066 959150 963941 968438 972641 976547 980156 9834665 35 943126 948784954153 959232 964018 968511 972708 976610 980214983519 36 943223 948876 954240 959314 964095 968583 972776 976672 9802719835740 37 943319 948968954327 959396 964173 968656 972843 976735 980319 983624 38 943416 949059 954414 959478 964250 968728 972911 976797 980386 9836763 39 943512 949151 954501 959560 964327 968800 972978 976859980443 98379 943609 949243 954588 959643 964404 968872 973045 976921980500983 4943705 949334 954674 959724 964481 968944 973112 976984 980558983833 42 943801 949425 954761 959805 964557 969016 973 179 977046 98061598388 43 943897 949517 954847 959887 964634 969088 973246 977108 980672 983937 44 943993 949608 954934 959968 964711 969159 973313 977169 980728 983959 45.944089 949699 955020 960050 964787 969231 973379 977231 98078598404 46 944185 949790 955106 960131 464864 969302 973446 977293 980841 984092 47 944281 949881 955192 960212 964940 969374 973512 9773549808999 48 944376 949972 955278 960294 965016 969445 973579 977416 980955 984156 49 944472 950063 955364 960375 965093 9695 17 973645 977477 981012 98424 50 944568950154 955450 960456 965 169 969588 973712 977539 981068984398 5944663 950244 955536 960537 965245 969659 973778 977600981124984330 52:944758 950335 955622 960618 965321969730 973844 977661 981181 984401 53 944854 950425 955707 960698 965397 969801 973910 977722 981237 984453 54 944949 950516 955793 960779 965473 969872 973976 977783 981293 984503 55 945044 950606 955879 960860 965548969943 974042 977844 981349 9845 36 945139 950696 955964 96094 965624 970014974108 977905 981405 984605 57.945234 950786 956049 961021 965700 970084 974173 977966 981460 98465 58 945329 950877 956134 961101 965775 970155 974239 978026 981516 984707 59 945424 950967 956220 961181965850970225 974305 978087 9815729347 60 945519 951057 956305 961262 965926 970296 974370 978148 98162798480

M 19° 18° 17° 16°

129

150 140 13° Natural Co-sines.

Diff. to 100"

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Diff. to 100"

84°

86°

88° 89° M

M Bu $19 82° 859 0984808 987688 9.0268 99-546 994522 996195 997564 9986-999391 999-48-60 1984858-987734 9-0309 991582994552 996220 997584998645999401, 9998559 2984909 987779 9 0349 992617 994583 996245 997604 998660 999411 99985258) 3984959 987824 9389,992652994613 996270 997625 998675999421 999863 57 4985009 987870 990429 992687 994643 996295 997645 998690 999431 99986736 5985059.987915 990469 992722/994673/996320997664: 998705 999441 99987aiss 5985109 987960 990509 992757/994703 996345 997684 998719 999450 99987715+ 2985159988005 990549 992792994733 996370 997704/998734 999460 99988;3 $985209988050 990589-9928371994762 996395 997724 998749 999469 999886) 9985259 98804990629992862/994792996419/997743 948763 999479 9998905) 10985309 988139 990669 991896 094822996444 997763 998778 9994881 99980450 11985358 988184 990708 992931 994851 996468 997782998792 999497 999898 49 12985408 988128 990748 992966 994881 996493 997801 998306 999507 999903 48 3985457 988273 990787 993000 994910 996517 997821 998820 999;16 99990747 14985507 988317 990827 993034 994939 996541 997840 998834 999525 999910|46| 15985556 988362 990866 993068 994969 996566 997859 998848 999534 999914 45 16985605 988406 990905 993103 994998 996589 997878 998862 9995421 999918 44 17985654 988450 990944 993137 995027 996614 997897 998876 999551 999922 43 18985703 988494 990983 993171 995056 996637 997916 998890 999560 999925 42 19985752 988538 99 1022 993205 995084 996661 997934 998904 999568 999929|41| 20 985801 988582 99106143238 995113 996685 997953 998917 999577 99993240 11985850 988626 991100 993272 995142 096709 997972 99893 999585 999936393 22 985899 988669 991138 993306 995170996732 997990 998944 999594 999939 38 23 985947 988713 991177 993339 995 199 9967 56 998008 998957 999602 999942 37 24985996 988756991216 993373 995227 996779 998027 998971 999610 999945 36 25 986045 988800 991254 993406 995256 996802 998045 998984 999618 999948 35 26 986093 988843 991292 993439 995284 996825 998063 998997999626 99995134 27 986141 988886 991331 993473 995312 996848 998081 999010999634 9999541331 28986189 988930 991369 993506 995340996872 998099 999023 999642 999957 32 29986238 988973 991407 993539 995368 996894 998117 999035 999650 99995931 30986286 989016 991445 993572 995396 996917 998135 999048099657 999962 30 31 986334 989059 991483 993605 995424 996940 998153 999061 999665 999964 29 32986381 989102 991521 993638, 995452996963 998170 499073 999672 999967|22|| 33986429 989145 991558 993670 995479 996985 998188 999086 999680 99996927 34986477 989187 991596 993703 995507 997008 998205 999098 999687 99997146 35 986535 989230 991634:993735 995535 997030 998223 999111 999694 999974 25 36986572:989272 991671,993768 995562 997053 998240999123 999701 99996 37 986620 989315 991709 993800 995589 997075 995257 999135 999709 999978 23 38986667 989357 991746 993833 995617997097 998274999147 999716 999980 22 39 986714 989399 991783993865 995644 997119 998291999159 999722 999981 21 40986762 989442 991820 993897 995671997 141 998308 999179 999729 999983 20 41 986809 989484 991857 993929 995698 997163 998325999183.999736 999985 19 42 986856 989 26 991894 993961 995725 997185 998 42 999194 999743 999986 18 43936903 989568 991931 993993:995752 997207 998359 999 206 999749 999988 17 44986950 989610 991968 994025 995778 997229 998375 999218 999756 999989.16 45986996 989651 992005 994056 995805 997250 99892 999229 999762|| 999990:15| 46 987043 989693 992042 994088 995832 997272 998408 999240 999768 99999214 47987090 989735 992078 994120 995858 997293 998425 999252 999775 999993 13 48987136 989776 992115994151 995884 997314 998441 999263 999781 99999412 49487183 989818 992151 994182.995911 997336 99845799927A 999787 999995 50987229 989859 992187 994214 995937 997357 998473 999285 999793 999996 51 987275 989900 992224 994245, 995963 997378 998489 999296 999799999997 52987322 989942 992260 994276 995989 997399 998505999307 999804) 999997 53987368989983 992296 994307 996015 997420 998521 999318 99980 999998 54987414 990024 992332 994338 996041 997441 998537999328 999816 999998 15 987460 990065 992368 994369 996067 997462 998552999339 999821 999999 > 987506 990105992404 994400 996095 997482998568 999350999827 999999 17987551 990146 992439 994430 996118 997503 998583 999360 999832 1000000 3 8987597 990187 992475 994461 996144 997523 998599 999370 999837 1000000 2 9987643 990228 992511 994491 9961691997544 998614 999381 9998431000000 987688 990268 992546 994522 096105 997564 998630 999391 9994810000000

4o

1° M

Natural Co-sines.

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TABLE V.

A TRAVERSE TABLE,

To overy Degree and Quarter Degree of the Compass or Horizon.

EXPLANATION.

This Table is calculated for the easy and expeditious solution of je several cases of Right-angled Plane Trigonometry. It is generalresteemed a useful and requisite assistant to the Surveyor, the Tavigator, and to every one, who has any concern with trigonometry

the exercise of his profession. The manner of using it must be very bvious to all, who are acquainted with the principles of that excellent Tanch of geometry ; but to those, who have only a superficial knowedge of the subject, the following description and examples will be ecessary.

In this Table, one of the acute angles whether given, or required fless than 45o, is found, to the nearest 15'at the top of the page ; but f more than 45o, it must be sought at the bottom, where the numbers Te found in a retrograde order. And whether the angle under considration, be at the top, or bottom, the Hypothenuse, if less than 120, is dways in a Distance column ; against which, in a column marked Latia ude, is found the side contiguous to the angle ; and in a column, narked Departure, the side opposite the angle.

When the given numbers exceed the limits of the table, any aliquot parts, such as a half, one third, &c. may be taken ; and those found corresponding are to be doubled, trebled &c. that is, multiplied by the same figure, that the given number is divided by.

EXAMPLES

1. Let the Hypothenuse of a right angled triangle=96 and one of he acute angles=330 45'; required the sides.

Under 330 45' at the top of the table, and against 96 in a Distance column, are found 79.84 in a Latitude column for the side contiguous o the given angle, and 53.34 in a Departure column for the side oppo. site the given angle.

2. Let the sides of a right angled triangle be=89.23 and 66.02 ; required the angles and Hypothenuse.

By inspecting this table, till these two sides are found against each Other in adjoining columns of Latitude and Departure, the angle opposite the longest side is found to be 53° 30', the other, 36° 30' and he Hypothenuse, 111.

In this manner all the cases of Righl-angled Plane Trigonometry can be readily solved ; but for more particular directions, books on this ubject shogle be consulted,

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15
30

45'
Lat. Dep

Lat. | Dep.
1.00
0.00
1.00 0.01

1.00 0.01 2.00 0.01

2 2.00 0.02 2 2.00 3.00 0.01 3 3.00

0.03 3 3.00 0.04 0.02 4 4.00 0.03 4 4.00 0.05 5.00 0.02

5.00

0.04 5 5.00 0.07 6.00 0.03

6
6 00
0.05

6 6.00 0.08 7.00 0.03 7

0.06

7.00 0.09 0.03 8 8.00 0.07

8.00 0.10 9.00 0.04

9.00
0.08

9.00 0.12
10.00 0.04
10 10.00

10 0.09

10.00

0.13 11.00

11
00%
11.00 Q.10

11.00 0.14 12.00 0.05

12 I 2.00 0.10

12.00

0.16 13.00 0.06 13 13.00

O.IT 13 13.00 0.17 14.00 0.06 14

14.00

0.12 14 14.00 0.18 15.00 0.07 19 15.00 0.13 15

15.00 0.20 26.00

16.00 0.14

16 16.00 0.21 17.00 0.07 17 17.00

0.15

17 17.00 0,22 18.00 0.08

18.00
0.16 18

18.00 0.24
19.00
0.08

19 19.00 0.17 19 19.00 0.25 20.00 0.09 20 20.co

20 0.17

20.00 0.26 21.CO 0.09

21 21.00

0.18 21 21.00 22.00 0.10 22 22.00 0.19 22 22.00

0.29 23.00 O, 10 23 23.00

0 20 23 23.00 0.30 24.00 0.10 24 24.00

0.21 24 24.00 0.31 25.00 0.11 25 25.00

0.22 25 25.00 0.33 26.00 O.IT 26 26.00 0.23

26 26.00 27.00 0.12 27 27.00

27 27.00 0.35 28.00 0,12 28

28.00 0.24

28 28.00

0.37 29.00 0.13 29 29.00 0.25 29 29.00 0.38 30.00 0.13

30 30.00 0.26 30 30.00 0.39 31.00 0.14

31

31.00 0.27 31 31.00 0.41 32.00 0.14 32 32.00

0.28

32 32.00 0.42 33.00 0.14

33 33.00 0.29 33 33.00 0.43 34.00 0.15

34 34.00 0.30 34 34.00 0.44 35.00 0.15 | 35 35.00 0.31 35 35.00

0.46
36 00
0.16
36 36.00

0.31
36 36.00

0.47 37.00 0.16 37 37.00

0.32 37

37.00 0.48 38.00 0.17 38 38.00 0.33 38 38.00 0.50 39.00 0,17 39 39.00 0.34 39

39.00

051 40.00 0.17 40 40.00 0.35 40 40.00

0.52 41 00 0.18

41
41.00 0.36 41 41.00

0.54 42.00

0.18 42 42.00 0.37 42 42.00 0.55 43.00

43 43.00 0.38 43 43.00 0.56 44.00

44 44.00 0.38 44 44.00 0.58 4500 0.20 45 45.00 0.39 45 45.00

C.59 46.00 0,20

46 46.00

0.40 46 46.00 0.60 47.00 0.21

47 47.00 0.41 47 47.00 0.62 48.00 0.21

48
48 00 0.42

48 48.00 0.63
49.00
0,21
49 49.00

0:43

49

49.00 0.64 50.00 0.22

50.00

0.44 50 50.00 0.65 51.00 0.22

51 51.00
0.45 ST 51.00

0.67 52.00 0.23

52.06
52
0.45 52

0.68

52.00
53.00
0.23
53
0.46 53 53.00

0.99
S4.00
54 54.00

54

54.00
55.00
55 55.00

55.00 0.72
56.00
0.24

56.00
0.49 56 56.00

0.73 57.00

57 57.00
3.50 57

57.00

0.75
58.00
0.25
58 58.00

0.5"
58 57.99

0.76 59.00

59

59.00 0.51 59 58.99 0.77 60.00 0.26

60

59.99 0.79 Dep. Lat. Dep. Lat.

32 33 34 35 36 37 38 39 40

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60
60.00 0.52

Dep. Lat.
45'
301

15' 89 Degrees.

Dist.

Dist.

Dist.

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