First, D 107.00 deg. RAW The Geometrical Construction. a Right-line at pleasure, as B A D, and upon any point thereof, as A, protract an Angle of Secondly, The Distance of the two Head-lands being 356.00 Miles enter them between the two fides, at B and C, and joyn BC, making the Triangle B A С. Thirdly, Make A D equal to AC, and joyn CD, so have you conftituted another Triangle ACD. Now in the Triangle A B C, is Given. (1) The Side BC, 356 Co. (2) The Angle BAC 107. 00 deg: And in the Triangle ACD, the Angle BAC being 107. 00 de. the Angle DAC must be 73.00 de. And the Sides A C and A D, being equal (by conftruction) the Angles ADC and ACD, must be also equal, siz. (each of them) 53. 50 deg. And being thus far prepared, you may proceed to find the Angle ACB. By Trigonometrical Calculation. Fig. LXVIII. To a fourth Sine, 73 06 d. 9.980729 This 73. 06 d. should be the quantity of the Angle DCB, but (by the construction) the Angle you fee is Obtuse; and therefore the Complement of 73. 06 deg. to 180, viz. 106. 94 deg. is the quantity of the whole Angle DCB. From which if you substract the Angle ACD, 53. 50 deg. there will remain 53. 44 deg. for the Angle ACB. To the Side B A, 299.00 2.475672 And fo much did the Ship from B, fail to A, and that substracted from 424. 12 there remains 175. 12, and so much did the Ship from C to A Sail. II. Of MERCATOR's Sailing, by the True Sea-Chart. 1 LL. the foregoing Problems are performed by that kind of A Navigation Commonly called Plain Sailing, or Sailing by the Plain Sea-Chart; in which Chart, the Degrees of Longitude and La-titude, in all Places, are supposed to be equal'; which is Erroneous, though most practifed: But there are two other ways of Sailing, both more exact than the former, the one called Mercator's, the other, Sailing by the Middle Latitude. That of Mercator's requires that the Degrees of Latitude in that Chart be inlarged as they go farther from the Equinoctial towards either of the Poles, which is done by Reducing them into Meridional Parts: but the Degrees of Longitudes into Miles and Centesms, as in Plain Sailing: And for the Reducing of Degrees and Minutes of Latitude into Meridional Parts, I have here inferted a Table for the ready performance thereof, to every Degree and Quarter, or 25 Centesms of a Degree. A Degrees Degrees 16 973 988 1004 1020 17 1035 1051 1067 1082 18 1098 1114 1130 1146 19 1161 1177 1193 1209 20 1225 1241 1257 1273 21 1289 1305 1321 1338 22 1354 1370 1386 1402 23 1419 1435 1451 1468 24 1484 1509 1517 1533 25 1550 1567 1583 1600 26 1616 1633 1650 1667 27 1684 1700 1717 1734 28 1751 1768 1785 1802 29 1819 1837 1854 1871 30, 1888 1906 1923 1941 46 3116 3137 3159 3181 47 3203 3225 3247 3269 48 3292 3314 3337 3359 49 3382 3405 3428 3451 50 3475 3498 3522 3545 |