In each of the following examples it is required to find the true azimuth, also the error of compass and deviation for the position of the ship's head at the time of observation.

302. The latitude of a place is most simply determined by observation of the meridian altitude of a known heavenly body. When such an observation cannot be obtained by reason of the state of the weather, the altitude of the body may often be obtained a little before or a little after its meridian passage. And if at the time of observing such an altitude near the meridian, the hour-angle of the body is known, we may find by computation very nearly the difference of altitude by which to reduce the observed to the Meridian altitude. The correction is called the "Reduction to the meridian." This method, in point of simplicity, is little inferior to the meridian altitude, to which it is next in importance. The altitude may also be determined by a direct process, deduced from spherical trigonometry. The former is the method used in the following pages. The Term "" near the meridian" implies a meridian distance limited according to the latitude and declination, and also the degree of precision with which the time is known (see Raper, Table 47).

Ex 2. 1876, February 6th, A.M. at ship, lat. acct. 51° 50' N., long. 105° 41' W., obs. alt. sun's L.L. South of observer 22° 10' 30", index corr. + 56", height of eye 22 feet, time by watch 6a ob 4TM 4a, found to be 28m 47% fast on app. time at ship, diff. of long. made to East 19.8 miles since error of watch on app. time at ship was determined: required the latitude by reduction to meridian.

Ex. 3. 1876, April 7th, A.M. at ship, lat. by acct. 58° 50' N., long. 51° 42′ W., obs. alt. sun's L.L. South of observer 37° 42′ 15", index corr. '6, height of eye 10 feet, time by watch 74 ob 59m 50s, found to be 1h 22m fast on app. time at ship, the diff. of long. made to East was 207 miles after the error on apparent time at ship was determined: required the latitude by reduction to meridian.

Time by watch, April

Watch fast

April

Diff. log. 20'7 × 4

623 39 13
24

0

92

6,0)17,4'065

37 38 7
I 7

00

254

Decl. apparent noon

37 37
+ 16

37 53

Ex. 4. 1876, August 7th, A.M. at ship, lat. acct. 40° 52' N., long. 36° 47′ W., obs. alt. sun's L.L. South of observer 65° 1′, index corr. + 17, eye 14 feet, time by watch 11h 15m 46a, found to be 26m 16s slow of app. time at ship, the diff. of long. made to East was 17 miles after the error on app. time at ship was determined: required the latitude.

Ex. 5. 1876, March 9th, A.M. at ship, lat. acct. 30° 21′ S., long. 16° 45′ W., obs. alt. sun's L.L. North of observer was 63° 37′, index corr. - 1' 57", eye 21 feet, time by watch, March 8 21h 49m 25" (being 9h 49m 25 A.M. on 9th), found to be 1h 59m 10 slow of apparent time at ship, the diff. of long. made to East was 23 miles after the error on apparent time at ship was determined: required the latitude.