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41° 0 1 41° 15' 41° 30 1 41° 45' Lat.

Dep. Lat. | Dep. Lat. Dep. Lat. Dep. 1 0,75 0,66 0,75 0,660 0,75 0,66 0,75 0,67 ) 21,51 1,31 1,50 1,32 1,50 1,33 1,49 1,33 2 32,26 1,97 2,26 1,98 2,25 1,99 2,242,00 3 43,02 2,62 3,01 2,643,00 2,65 2,98 2,66 4 5 3,77 3,28 3,76 3,30 3,75 3,313,73 3,33 5 64,53 3,944,51 3,964,49 3,984,48 4,00 6 75,28 4,595,26 4,625,24 4,645,22 4,66 7 8 6,04 5,25 6,02 5,28 5,99 5,305,97) 5,33 8 9 6979 5,91 6,77 5,93 6,74 5,96 6,72 5,99 9 10 7,55 6,567,52) 6,597,49 6,63 7,46% 6,66 10 11 8,301 7,22 8,277,258,24 7,29 8,21 7,33 11 12 9;06 7,87 9,02 7,91 8,99 7,95 8,95 7,99|12 13 9,81 8,539,77 8,579,74 8,61 9,708,6613 14 10,57| 9,18 10,53 9,28 10,49 9,28 10,45 9,3214 i5 11,32 9,84 11,28 9,89 11,249,94 11,19 9,99 15 16 12,08 10,50 12,03 10,55 11,98 10,60 11,94 10,66 16 17 12,83|11,15 12,78 11,2112,73 11,27 12,6811,3217 18 13,59 11,81 13953|11,8713,48 11,93 13,43 11,9918 1914,34 12,46 14,29 12,53 14,23 12,59 14,1812,65 19 20 15,0913,1215,04|13,19 14,98 13,25 14,92 13,32 20 27 15,85 13,78 15,79 13,85 15,73 13,92 15,67 13,9821 22 16,60 14,43 16 54 14,5 | 16,48 14,58 16,41/14,65 22 23 17,36 15,09,17,30 15,1617,23 15,24 17,16 15,32 23 24 18,11 15,75 18,05 15,82 17,98 15,90j17,91 15,9824 25 18,87 16,39 18,80 16,48 18,73 16,57 18,65 16,65 25 2619,62 17,05 19,55 17,14 19,47 17,23 19,40 17,31 26 27 20,38 17,7020,30 17,80 20,22 17,89 20,14 17,98/27 28 21,1318,3621,05 18,4620,97 18,56:20,8918,65 28 2921,89|19,02 21,81 19,12 21,72|19,22 21,64 19,31 29 30 22,64 19,68 22,56 19,78 22,47 19,88 22,38 19,98 30 3123,39 20,34.23,31 20,44 23,22|20,54 23,13 20,64 31 32 24,15 20,99. 24,0621,10 23,97 21,21 23,8721,31 32 5324,9 121,6524,81 21,7624,72 21,87 24,62 21,97 33 3425,66 22,3125,56 22,42 25,47|22,53,25,37 22,64 34 35/26,42 22,9626,32 23,08 26,21 23, 19:26,1123,31|35 36 27,17|23,62 27,07 23,74 26,96 23,86 26,86 23,97 36 37 27,9324,27 27,82 24,3927,7124,52 27,6024,64 37 38 28,68 24,93 28,57 25,05 28,46 25,18 28,35 25,31 38 3929,44 25,59 29,32 25,71 29,21 25,84f29,10 25,97 39 40 30,19|26,24 30,07 26,37 29,96 26,50 29,8426,64 40 4130,94 26 90 30,83 27,08 30,71 27,17 30,59 27,30 41 4231,70 27 55 31,58|27,69 31,46 27,8331,3327,97 42 43 32,45|282132,33 28,35 32,20 28,49 32,08 28,63 43 4433,21 28 87 33,08 29,01 32,95 29,16 32,83 29,30 44 4533,96 29 52 33,83 29,67 33,70 29,82 33,57 29,9745 4634,72 30 18 34,5930,33 34,45/30,48 34,32 30,63 46 47 35,47 30 83 35,3-130,99 35,20 31,15 35,06 31,30 47 48 36,2331, 49,36,09 31,65 35,95 31,81 35,81|31,96 48 49 36,98|32,15 36,84 32,31 36,7032,47 36,5632,63 49 50 37,74/32,80, 37,5932,97 37,45 33,13 37,3033,29 50 Dep. Lat

° 43' -8° 3u! 48° 15

Dist.

42° 0 42° 15' 43° 3' 42° 45'
Lat. Der

Lat.
Der. Lat.

Dep. Lat. Dep. 1 0,74 0,67 0,74 0,67 0,74 0,68% 0,73 0,68 1 2 1,49 1,34 1,48 1,34 1,47 1,35 1,47 1,36 2 32,23 2,01 2,22 2,02 2,212,03 2,20 2,04 3 42,97 2,68 2,96 2,69 2,95 2,702,94 2,71 4 5 3,72 3,35 3,70 3,36 3,69 3,383,67 3,39 5 6 4,464,01 4,44) 4,034,42 4,05 4,41 4,076 7 5,20 4,68 5,184,715,16 4,735,14 4,757 85,94 5,35 5,92 5,38% 5,90 5,405,87 5,43 8 96,69 6,02 6,66 6,05 6,64 6,08 6,61 6,11] 9 (10 7,43 6,697,40 6,727,37 6,76 7,34 6,79 10 18,177,368,14 7,408,11 7,43 8,08 7,47 11 12 8,92 8,03 8,88 8,07 8,85 8,118,81 8,1512 131 9,66 8,709,62 8,74. 9,58 8,78 9,55 8,82 13 14 10,40 9,37 10,36 9,4110,32 9,4610,28 9,50 14 1511,15 10,04 11,10 10,08 11,06 10,1311,01 10,18 15 16 11,89 10,71|11,84 10,76 11,79 10.81 11,75 10,8616 17|12,63 11,37 12,58|11,43 12,53 11,49 12,48 11,54 17 18 13,38 12,04 13,32 12,10 13,27|12,16 13,22 12,2218 19 14,12 12,71 14,06 12,77 14,01 12,84 13,96 12,90 19 2014,86 13,38 14,80 13,45 14,75 13,51 14,69 13,58 20 21 15,61 14,05 15,5414,12 15,48 14,19 15,42 14,2521 22 16,35 14,72 16,28 14,79 16,22 14,8616,15 14,9322 23/17,09 15,39 17,02 15,40 16,96|15,54 16,89|15,6123 24 17,83|16,06 17,7616,13 17,69 16,22 17,62 16,2924 25 18,58 16,73 18,50 16,80 18,43116,89 18,36 16,97 25 26 19,32 17,40 19,24 17,47 19,17 17,57 19,09 17,65 26 27 20,06 18,07 19,98 18,15119,91 18,24 19,82 18,33 27 28 20,81|18,73 20,72 18,82 20,64 18,92 20,56 19,0128 2921,55 19,40 21,46 19,4921,38|19,6021,29 19,69 29 30122,29 20,07 22,21 20,1722,12 20,27|22,03 20,36 30 3123,0420,74 22,9520,84 22,85 20,94 22,76 21,04 31 3223,78121,41 23,69 21,51 23,5921,62123,50 21,7232 3324,52 22,089 24,4322,1924,3322,30 24,23 22,40133 3425,27 22,75 25,1722,86/25,07 22,97 24,97 23,08 34 35 26,01123,42 25,91|23,53 25,80 23,64 25,70 23,76 35 3626,75 24,09 26,65 24,20 26,54|24,31:26,4324,4436 37|27,49 24,76 27,39 24,8727,28|24,99127,1725,12 37 3828,24 25,43 28,13 25,55|28,01|25,67 27,90 25,8038 39|28,9826,09:28,8726,22 28,75 26,34 28,64 26,48 39 4029,73 26,76 29,61 26,89 29,49|27,02 29,37 27,15 40 41 30,47 27,43 30,3527,57 30,2327,70 30,11|27,83 41 4231,21 28,10 31,0928,24 30,96 29,38 30,8428,5142 4331,95 28,77 31,83 28,91 51,6929,05 31,57 29,19 43 44|32,70 29,4432,5729,38 32,43|29,73,32,3129,87 44 45 33,44 30,11433,31 30,25 33,17 30,40633,04 30,55 45 46 34,18 30,78 34,05 30,9333,90131,08 33,78 31,23 46 47 34,93 31,45 S4,79 31,60-34,64 31,76 34,51 31,90 47 48|35,6732,12 35,53|32,27 35,38 32,43435,24 32,58 48 149 35,41 32,7956,27 52,94136,1133,11 35,98 33,2649 50 37,16133,46 37,01 33,62 36,86 33,7836,72133.94 50

Dep. Lat. Dep. Lat. Dep. I Lat. Dep. 1 1.9t.
48° 0 47° 45' 47° 30' 470 15'

Distil

Dis.

Dist.

Dist. 1

2.77

43° 0'

43° 15' 43° 30 43° 45' Lat. Dep. Lat. Dep. Lat. Dep. Lat.

Dep. il 0.73 0.68 0.73 0.68 0.72 0.69 0.72 0.69 1 2 1.46 1.36 1.461 1.37 1.45 1.38 1.44 1.381 2 3 2.19 2.05 2.18 2.06 2.18 2.06 2.17) 2.07 3 4 2.92 2.73 2.91 2.742.90 2.75 2.89

4 5 3.661 3.41 3.64 3.43 3.63) 3,44 3.61 3.461 5 6 4.39 4,094.37 4.114.35 4.13 4.33 4.151 6 71 5.12 4.77 5.10 4.80) 5,08\ 4,82 5.06 4.841 7 8 5.85 5.46 5.83 5.48) 5.80 5.51 5.78 5.53) 8 9 6.58 6.14

6.55 6.171 6.531 6.19 6,50 6.221 98 101 7.31 6.82 7.28 6.85 7.25 6.88 7.22

6.910 8.047.50 8.01 7.547.981 7.57 7.95

7.6111 12 8.78 8.18 8.74 8.228.70 8.26 8.67 8.30 12 13 9.51 8,87 9.47 8.911 9.43 8.95 9.39) 8.99/13 14 10.24 9.55 10.20 9.59 10.15 9.64 10.11 9.68|14 15 10.97 10.23 10.92 10.28 10.88 10.32 11.83 10.3715 16.11.70 10.91 11.65 10,96 11.60 11.01 11.56 11.07 16 17 12.43|11.59 12.38 11.65 12.3311.70 12.28 11.76 17 18 13.16 12.28.13.11 12.33 13,05/12.39 13.00!12.45 18 1913.89112.96 13.84 13.02 13.78 13.08 13.72 13.14119 2014.63|13.64 14.57|13.70 14.51 13.77 14.45 13.83 20 12115.36 14.32 15.29 14.3915.23 14.45|15.17|14.52 21 22 16.09 15.00 16.02 15.07 15,96 15.14 15.89 15.21 22 23 16.82 15.69.16.75 15.76 16.68 15.83 16.61 15.9 123 24 17.55 16.37 17.48 16.44 17.41 16.52 17.33 16.60 24 25 18.2817.05 18.21.17.13 18.13 17.21.18.06.17.29125 2619.01|17.73 18.94 17.81 18.86 17.90 18.7817.98 26 27 19.74. 18.41 19.66 18.50519.58 18.58 19.50 18.67 27 28|20.47|19.10 20.39 19,1820.31|19.27 20.22 19.36 28 29121.2119.78 21.12 19.87 21.0319.96 20.94 20.0529 30/21.94 20.46 21.8520.55.21.76 20.65 21.67|20.74 30 3122.67 21.14 22.5821.24 22.49|21.34 22.39 21.44 31 32|23.4021.8223.30 21.92 23.2122.03.23.11|22.13 32 33|24.13 22.5 1 24.03 22.61.23.94 22.71 23.84 22.82 35 34 24.86 23.19 24.76 23.2924.66 23.40 24.56 23.51 34 35 25.60 23.87 25.4923.98 25.39 24.09 25.28 24.20135 3626.3324.53 26.22 24.66 26.11 24.78126.00 24.90 36 37 27.06.25.2326.95 25.35 26.84 25.47"26.73 25.5937 38|27.7925.9127.67 26.05 27.5626.16 27.45 26.28|38 39128.5226.66 28.40 26.72.28.29 26.84 28.17|26.97 39 40 29.25 27.28129.13 27.41 29.01 27.5328.89|27.66|40 4129.9827.96 29.86 28.09 29.74 28.2229.62 28.3541 4230.7228.64 30.59 28,78 30,46 28.91 30.34 29.04 42 43 31.45129.30 31.32 29.4631.19 29.60 31.06 29.7443 442.18 30.01 32.05.30.15 31.91130.29 31.78 30.43 44 45 32.9130.69:2.77 30.83 32.64130.97 32,50 31.12|451 46 33.64131.37 33.50131.52 33.3631.66 33.23 31,8146 47/34.37 32.05 34.23 32.20:34.0932.35 33.9532.5047 48 35.10 32.74 34.96 32.89454.8233.04.34.67 33.1948 49 35.8333.42|35.6) 35.57.55.54 33.73.155.39 33.881 4:9 5056,57 34.10236.1254.26136.2734.4236.12 34.58 50 Dep. Lal Dep. Lat. Dep. I

° 43' 46° 30' 46°

. Lat

450

Dist.17

Dist.17

Lat.

44° 0 44° 15' 44° 30' 44° 45' Lat. Dep.

Lat. | Dep. Lat. | Dep. Lat. | Dep. 10,72 0,69 0,72 0,70 0,71 0,70 0,71 0,70 0,71 1 2 1,44 1,39 1,43 1,40 1,43 1,40 1,42 1,41 1,41 2 3 2,16 2,08 2,15 2,09 2,142,10 2,13 2,112,123 42,88 2,782,86 2,79 2,85 2,80 2,842,82 2,83 4 5 3,60 3,473,58 3,493,57 3,50 3,55 3,523,54 5 6 4,32 4,174,30 4,19% 4,28 4,21 4,26 4,224,246 75,03 4,86 5,01| 4,88 4,99 4,91 4,97 4,93 4,95 ? 81 5,75 5,565,73 5,585,71 5,615,68 3,63 5,66 8

9 6,471 6,25 6,45 6,28 6,42 6,31 6,39 6,346,36 9 10 7,19 6,95 7,16 6,98 7,13 7,01 7,10 7,047,07 10 111 7,91 7,647,88 7,687,857,717,81 7,747,7811 12 8,631 8,34 8,60 8,37, 8,568,41 8,52 8,45 8,49|12 13 9,35 9,039,31 9,07 9,27 9,11 9,23 9,159,19 13 14/10,07 9,73|10,03 9,77|9,999,81 9,94 9,869,90 14 1510,79 10,42 10,74 10,47 10,70 10,51 10,65110,56 10,6115 16111,5111,12 11,46 11,1611,41 11,2 11,36 11,26 11,3116 1712,23 11,8112,18|11,8612,1311,92 12,07 11,97 12,02 17 18 12,95 12,51 12,89|12,56 12,84 12,62 12,78 12,67 12,7318 1913,67 13,20 13,61 13,26 13,55 13,32 13,49 13,38, 13,44|19 20 14,39 13,89 14,33 13,9614,26|14,02 14,20 14,08 14,14 20 2115,11|14,59 15,04|i 4,65 14,98|14,72 14,91 14,78 14,85 21 2215,82 15,28.15,7615,35 15,69 15,42 15,62 15,49 15,5622 23 16,54 15,98 16,4716,05 16,40 16,12 16,33|16,19,16,2623 2417,26 16,67 17,1916,75.17,12 16,82 17,04 16,90 16,97 24 25 17,98 17,37 17,91 17,44 17,83 17,52 17,75 17,60 17,68 25 26 18,70 18,06 18,62 18,14 18,5418,22 18,46 18,30 18,38 261 27 19,43 18,76 19,34 18,84 19,2618,92 19,17|19,01 19,0927 28 20,14 19,45 20,06 19,54 19,97 19,63.19,89 19,71 19,80 28 29 20,86 20,15,20,77|20,24 20,68 20,33 20,60 20,42 20,51 29 3031,58|20,84 21,49|20,9321,40 21,0321,3121,12 21,2130 31 22,30 21,53:22,2121,63 22,1121,7322,02 21,82 21,92 31 3223,02 22,23 22,92 22,33 22,8222,43 22,7322,53 22,63 32 33/23,74 22,9223,64 23,03 23,5423,13 23,44 23,23 22,33|33 34 24,46|23,62 24,35|23,72 24,25 23,83 24,15 23,94 24,04 34 35 25,17 24,31 25,07 24,42 24,97 24,53 24,8624,64 24,75 35 3625,8925,01 25,79 25,12 25,68 25,23, 25,57 25,34 25,46 36 37 26,61 25,71.26,50|25,82 26,39 25,93:26,2826,05 26,16 37 3827,33/26,41 27,22 26,52 27,10 26,63 26,99 26,75 26,87 38 39 28,05 27,1027,94 27,21 27,82 27,34 27,7027,4627,58/39 4028,7727,79 28,65 27,91 28,5328,04 28,41 28,16 28,28 40 41 29,49|28,48 29,37 28,61 29,24 28,74129,12 28,86 28,99 41 42 30,21 29,18 30,0829,31 29,96 29,44 29,83 29,57 29,70 42 43 30,93|29,87 30,80 50,01 30,67|30,14:30,54 30,27 30,41 43 4 1 31,65/30,57 31,52 30,70,31,38 30,84 31,25 30,98 31,11 44 45 32,37 31,26 32,23 36,40 32,10131,5431,96 31,68 31,8245 46 33,09 31,96 32,95132,10 32,8132,24 32,67 32,38 32,53 46 4733,81 32,634 33,67|32,80933,52|32,94 33,38|33,09 33,23 47 18 34,53 33,35 34,38 53,49 54,24 33,64, 34,0933,79 33,94 48 49135,25 34904, 35,1034, 19:34,95 34,34 34,80 34,50 34,65 49 5035,97 34,75 5.1,82 34,89 35,66 35,05 35,51 35,20 35,35 50

Dep | Lat. Dep. Lat. Dep. Lat. Dep. 400 o'

4,0 451 49° 30 43° 15' 45°

Dist. I just

Dep. I Liked

Dist.

II. A TABLE of NATURAL Sines, calculated to five places of fig. ures, for every Minute.

NATURAL Sines are Decimals bearing the same proportion to Unity or 1 that the Sine of the corresponding number of Degrees and Minutes bears to Radius or Sine of 90°. That is, 1 is assumed as the Nat. Sine of 90°, and the Table calculated accordingly.

1

Explanation of the Table. To find the Natural Sine of any number of Degrees and Minutes. If the Degrees be less than 45, look for them at the Top of the Columns, and for the Minutes at the left hand ; but if more than 45, look for them at the Bottom, and for the Minutes at the Right hand ; under or over the Degrees and against the Minutes will be the Natural Sine required.

The reverse of this will give the Degrees and Minutes corres-
ponding to any Natural Sine.
Note. As the size of the Type on which this Table is printed

did not admit of putting 60 Minutes on a page, it will be ob-
served that some of the Degrees begin at the Top and some
below the Top of the page ; and the Minutes are placed ac-

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

Find the Nat. Sine and Co-Sine of the Course, and into each of these multiply the Distance ; the Products will be the Latitude and Departure required.

EXAMPLE.
Required the Laiitude and Departure for 6 Chains and 22 Links,
on a Course N. 38° 27' W.
Nat. Sine of 38° 27' 0.62183 Nat. Co-Sine 0.78315

6.22

6.22

[blocks in formation]
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