II. A TABLE of NATURAL SINES, calculated to five places of figures, 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. 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 corresponding 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 observed that some of the Degrees begin at the Top and some below the Top of the page; and the Minutes are placed accordingly. 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 Latitude 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 o Deg. 1 Deg. 2 Deg. M 3 Deg. M Nat. N. Co. 000000 Nat. N. Co- Nat. N. Co- Nat. N. Co- Unit 01745 99985 03490 99939 05234 99863 60 30 873 96 618 66 362 05 105 31 00902 99996 02647 99965 04391 99904 06134 99812 29 13 30 46 C1338 99991 03083 99952 04827 99883 06569 99784 14 M M 123. 107005 54 745 N.S. IN.C.S N.S. IN.C.S N.S. IN.C S. 006976 99756 08716 99619 1045399452 12187 99255 60 17 482 49 216 51 59 N.S. N.C.S. 2 4 S3 54 30 53 17 469 21 208 75 945 99399 678 93 43 72 973 96 706 89 42 70 11002 93 735 86 41 67 031 90 764 82 40 21 585 12 324 64 060 86 793 78 39 30 846 92 585 N.C.S. N.S. N.C.S. NS. N.C.S. N.S. 4 Deg. M N.S. N.C.S N.S. N C.S N.S. N.C.S. N.S. IN C.S 107875 99689 0961499537 11349 99354 130819914129 7 Deg. M 87 15 47 339 45 281 57 1001999497 754 07 485 46 08310 99654 1004899494 11783 99303 13514 99083 14 8401992971 572 812 00 543 79 13 7512 7111 M 9 Deg. 10 Deg. 11 Deg. M NS. N.C.S. N.S. IN.C.S. N.S. IN.C.S. NS. IN.C.S 13917 99027 15643 98769 17365 984811908198163 60 64 393 76 109 57 59 60 422 71 138 52 58 7316017 09 737 14 452 9017 481 84 16 7945 M M |