(sin. 2° sec. 30°)2= 0.000065 5.81587 0.000022 4. Find the correction for middle latitude sailing, when the middle latitude is 60°, and the difference of latitude 16°. Ans. 46'. 5. Find the correction for middle latitude sailing, when the middle latitude is 72°, and the difference of latitude 20°. Ans. 124'. 6. Find the correction for middle latitude sailing, when the middle latitude is 50°, and the difference of latitude 8°. Ans. 9'. 7. Find the correction for middle latitude sailing, when the middle latitude is 68°, and the difference of latitude 12° Ans. 34'. Examples. 8. Find the correction for middle latitude sailing, when the middle latitude is 21°, and the difference of latitude 3°. Ans. 1'. 9. Find the correction for middle latitude sailing, when the middle latitude is 24°, and the difference of latitude 6° Ans. 5'. 10. Find the correction for middle latitude sailing, when the middle latitude is 15°, and the difference of latitude 12°. Ans. 26'. 49. Problem. To find the bearing and distance of two given places. [B. p. 79.] Solution. We have by (fig. 20) for the bearing, diff. long. tang. bearing= mer. diff. lat.' (271) and the distance is found by (230). 50. Problem. To find the course, distance, and difference of longitude, when both latitudes and the departure are given. [B. p. 80.] Solution. The course is found by (229), the difference of longitude by (258), and the distance by (230). 51. Problem. To find the distance and difference of longitude, when both latitudes and the course are given. [B. p. 82.] Examples. Solution. The distance is found by (230), and the difference of longitude by (258). 52. Problem. To find the course and difference of longitude, when both latitudes and the distance are given. [B. p. 83.] Solution. The course is found by (233), and the difference of longitude by (258). 53. Problem. To find the distance, the difference of latitude, and the difference of longitude, when one latitude, the course, and departure are given. [B. p. 84.] Solution. The distance is found by (236), the difference of latitude by (235), and the difference of longitude by (258). 54. Problem. To find the course, the difference of latitude, and the difference of longitude, when one latitude, the distance, and the departure are given. [B. p. 85.] Solution. The course is found by (237), the difference of latitude by (238), and the difference of longitude by (258), or by the following proportion deduced from the similar triangles of (fig. 20). : =mer. diff. lat. diff. long. (272) diff. lat. dep. 55. EXAMPLES. 1. A ship sails from Boston a distance of 6747 miles, upon a course S. 46° 59′ E.; to find the place at which it arrives. Diff.lat.= 76°42′ S. 4602', 3.66296 mer.d.l.=5007,3.69958 Lat. in 34°21′ S. 2197 diff. long.=5368/3.72980 89° 28' E. mer. diff. lat. = 5007 long. left =71° 5' W. Ans. The place arrived at is the Cape of Good Hope. 2. Find the bearing and distance from Moscow to St. Helena. course =S. 27° 18′ W. tang. 9.71269 sec. 10.05127 Examples. 3. A ship sails from a position 200 miles to the east of Cape Horn a distance of 3635 miles, upon a course N. N. E.; find the position at which it has arrived. Ans. It has arrived at the equator in the longitude of 33° 18' W. 4. Required the bearing and distance of Botany Bay from London. 5. A ship sails northwesterly from Lima until it arrives in the latitude 23° 7' N., and has made a departure of 9983 miles; find the place at which it has arrived. Ans. Canton. 6. A ship sails from Disappointment Island in the North Pacific Ocean, upon a course S. 61° 41' E., until it has arrived in latitude 14° 7′ S.; find the place at which it has arrived. Ans. The Disappointment Islands in the South Pacific Ocean. 7. A ship sails from Icy Cape (North West Coast of America) a distance of 9138 miles southwesterly, when it has arrived in latitude 62° 30′ S.; find the place at which it has arrived. Ans. Yankee Straits in New South Shetland. 8. A ship sails from Java Head, upon a course S. 68° 53′ W., until it has made a departure of 4749 miles; find the position at which it has arrived. Ans. It has arrived at a position 180 miles south of the Cape of Good Hope. |