To find the course at Cape of Good Hope, L= 27° 53′. To find the course for the point at which L=37° 53'. To find the course for the point where L = 42° 53′. To find the course for the point where L= 47° 53′. To find the course for the point where L=52° 53′. To find the course for the point where L= 57° 53'. To find the course for the point where L=62° 53′. Log. sin. A Log. cos. 67° 52' = 9.9172900 9.5760680 .. Course S. 67° 52′ E. 281. Since by Art. (276) the course is always directly east or west when L = 90°, and the course is the same for an arc greater than 90° as for one as much less; we may now take in the next 90°, which is greater than 87° 53′ by 2° 7′; hence the course for 92° 7' will be the same as for 87° 53′-namely, N. 88° 15′ E. For L= 97° 7', the same as for 82° 53′ = N. 84° 7′E. == For L= 127° 7', the same as for 52° 53′ = N. 60° 5′ E. Lastly, to find the course for L= 149° 11', Jaffa Cape. Log. cos. 44° 47 = 9.8511876 .. Course N. 44° 47′ E. 282. In finding the courses to be sailed from Cape Jaffa to Cape of Good Hope, taking the same values of L as before, we have only to change N. into S., S. into N., and E. into W., and the courses are all known without any more calculation. As formerly remarked, the courses should be changed midway between the adjacent values of L. To find the distance on a great circle between the Cape of Good Hope and Jaffa Cape. - AP2 AP1 133° 20′ (43° 14′) = 90° 6′ = 5406 miles = distance. Hence the distance by Great-circle Sailing is less than the distance by Mercator's Sailing by 5916.75406 = 510.7 miles. Exercises 31. (367.) In sailing from the Lizard, in latitude 49° 58′ N., longitude 5° 12′ W., to latitude 17° 50' N., longitude 76° 42′ W.; it is required to find x and A, and the courses at the extreme points. (368.) In sailing from the Lizard, in latitude 49° 58′ N., longitude 5° 12' W., to Cape Hatteras, in latitude 35° 14′ N. longitude 75° 34' W.; it is required to find x and A, and the courses at the extreme points. (369.) Find the distance on a great circle from Cape Horn, in latitude 55° 58′ S., longitude 67° 21′ W., to Cape of Good Hope, in latitude 34° 29′ S., longitude 18° 23' E.; find also x and A, and the direction of the great circle at each of these places. (370.) Find the courses to be sailed for each 5° of longitude on the great circle joining St Helena, in latitude 15° 55′ S., longitude 5° 43' W., and Cape Horn, in latitude 55° 58′ S., longitude 67° 21′ W.; and first find x and A. DEMONSTRATION OF THE RULES FOR GREAT-CIRCLE. SAILING. 1 In the spherical triangle, AB1P1 (page 203), we have by Art. (321), Rule II., sin. x cot. A. tan. = (1) (2) Again, from (1) we have tan. A = tan. ↳ cosec. x. And from the spherical triangle ADP, by Art. (321), cos. APD = cos. course cos. AD. sin. A = cos. L. sin. A. .. cos. course cos. L. sin. A. CHAPTER X. NAUTICAL ASTRONOMY. DEFINITIONS AND EXPLANATION OF TERMS. 283. AXIS.-The axis of the heavens is the diameter of the celestial sphere, about which the diurnal rotation of the celestial sphere takes place, and which is due to the real rotation of the earth. The axis of the heavens is only the axis of the earth prolonged; the imaginary extremities of this axis are the poles of the heavens. 284. EQUINOCTIAL.-The celestial great circle, to the plane of which the axis of the heavens is perpendicular, is called the equinoctial, or the celestial equator. It is traced out by extending the plane of the terrestrial equator to the heavens. 285. MERIDIANS.-The celestial meridians are in like manner marked out by extending the planes of the terrestrial meridians; or they are semicircles terminating in the poles of the heavens, and perpendicular to the equinoctial. 286. The Altitude of a celestial body is its distance above the horizon, measured on the vertical circle passing through the body. The complement of the altitude is called the zenith distance. In the case of sun and moon, the true altitude is measured from the rational horizon, and is a little greater than |