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EXAMPLE 2. At a place in long. 5h. 0m. 42sec. W., and lat. 39° 57′ 8" N. On the 7th of September, 1838, the following observations were made:-Time by a mean solar clock, 11h. 20m. 26.2; altitude of a Arietis (east of the meridian), 39° 48′ 38′′; barom., 30.2 inches; therm., 75°. From the Nautical Almanac, the right ascension and declination of a Arietis were, 1h. 58m. 6.2 and + 22° 41′ 55′′.3; and the sidereal time at Greenwich mean noon was, 11h. 4m. 28.07. Required the error of the clock. Ans. 14m. 43.1sec. too fast.
EXAMPLE 3. The date, place, and instruments being the same as in the last example, the observed altitude of a Lyra (west of the meridian) was, 38° 44′ 49′′ and clock time 12h. 10m. 45.2. The right ascension and declination of a Lyra were, 18h. 31m. 29.06 and + 38° 38′ 20′′.5. Required the error of the clock. Ans. 14m. 39.9sec. too fast.
Note. The mean of the results obtained by east and by west observations, (like those of the last two examples,) will be nearly independent of any error in the instrument used in measuring the altitudes; for, the hour angles will be both too great or both too small, and since, in one case the hour angle is subtracted and in the other added, to obtain the sidereal time, it follows that one of the resulting times will be too great and the other too small.