(149.) Sept. 17, 1844, in latitude by account 36° 45′ N., the following altitudes were observed at the same time. The index correction was + 55" and height of eye was 8 feet, required the true latitude. Ans., 36° 44' N. (150.) Feb. 20, 1846, in latitude by account 36° 40′ N., the following altitudes were observed at the same time. The index correction was + 1' and height of eye above the sea 10 feet, required the true latitude. Ans., 36° 37' N. (151.) May 1, 1845, in latitude by account 41° 20 N. the following altitudes of stars were taken at the same instant, required the true latitude. True alt. a Pegasi. Bearing. Bearing. E. True alt. a Tauri. (152.) March 2, 1845, in latitude by account 41° 20′ N. long., 60° E., the altitudes of the two following stars were observed at the same time, required the true latitude. True alt. a Andromedæ. 73° 14' Bearing. True alt. a Tauri. Bearing. Ans., 41° 23' N. (153.) January 2, 1847, in latitude by account 38° 10' N., the following altitudes of the stars a Pegasi and a Aquilæ were observed at the same instant. The index correction 15" and height of eye sea 41 feet, required the true latitude. Ans., 32° 43' N. (154.) Dec. 27, 1847, the following altitudes were observed at the same instant, in latitude by account 37° 10' N., required Third. When the objects are two heavenly bodies observed at different times. Let x, figs. (a) and (b), be the place of the heavenly body first observed, and y the place of the second body when its altitude was taken, and let y be the place of the second body when the first altitude was taken. Then in the elapsed time (t) between the observations (which measures the angle y Py'), the second heavenly body has moved from y' to y, and the polar angle between the two observed places of the bodies, namely, XPy is equal, in fig. (a), to APX-APY + t = (APX + t) - A Py', and, in fig. (b), to APY-APX-tAPy' (APX+t) (t the elapsed time being expressed in sidereal time). rule for finding the latitude may be Hence the preceding adapted to this case, using the angle XPy (the polar angle between the two places observed) instead of x Py' the difference of the right ascensions of the heavenly bodies. The polar angle x Py may be found by the following Rule XXXVIII. 1. Subtract the time shown by the chronometer at the first observation (increased if necessary by 12 hours) from the time shown at the second observation, and thus find the elapsed time. 2. * Correct the elapsed time for rate of chronometer, if any, either by proportional logs. or by the common rule of proportion. 3. Add to the elapsed time so corrected, the acceleration of sidereal on mean solar time (taken from table in Nautical Almanac or elsewhere). The result is the elapsed time expressed in sidereal time. 4. Add this elapsed time to the right ascension of the heavenly body first observed, and take the difference between the sum and the right ascension of the second heavenly body; the remainder (subtracted from 24 hours if greater than 12 hours) will be the polar angle required. EXAMPLES. 1. The altitude of a Pegasi was observed when the chronometer showed 6h 42m 10s, and the altitude of * When great accuracy is not required, and the elapsed time is small, these two corrections in 2 and 3 for rate of chronometer and acceleration may be omitted. a Aquila was observed when the chronometer showed 8h 32m 5s, required the polar angle between the two places observed; the rate of the chronometer being 12.5 gaining. 2. The altitude of Sirius was observed when the chronometer showed 2h 10m 20s, and the altitude of Spica was observed when the chronometer showed 3h 20m 15s, required the polar angle between the two places observed; the rate of chronometer being 25 losing. |