Under the latitude put the sun's declination, and, if the names be alike, take the difference; but if unlike, take their sum. Under the result put the zenith distance, and find their sum and difference. Add together the log. secants of the two first terms in this form, and the halves of the log. haversines of the two last; and (rejecting the tens in the index) look out the sum as a log. haversine, to be taken out at the top of the page if the sun is west of the meridian, but at the bottom of the page if the sun is east of meridian. The result is apparent solar time at the instant of observation. 5. To find mean time. To apparent solar time apply the equation of time with its proper sign, as directed in the Nautical Almanac; the result is mean time at the place. 6. The difference between mean time thus found, and the time shown by chronometer at the observation, will be the error of the chronometer on mean time at the place.* Rule XLIV. To find the error of a chronometer on mean time at Greenwich by a single altitude of the sun. Find mean time at the place of observation as directed in preceding Rule. See 1, 2, 3, 4, and 5. 6. To the mean time at the place thus found apply the longitude in time; adding if west, and subtracting if east (rejecting or adding 24 hours if necessary): the result will be mean time at Greenwich at the time of the observation. Reduce the angle thus found into time, and if the sun is west of meridian, the same will be apparent time; but if east of meridian, subtract the angle from 24 hours; the remainder will then be apparent solar time at the instant of observation. * A similar observation being taken a few days afterwards, the mean daily rate may be found as pointed out in p. 167. 7. The difference between which and the time shown by chronometer will be the error of the chronometer on Greenwich mean time. EXAMPLE. May 10, 1842, at 8h 44m A.M., mean time nearly, in latitude 50° 48' N., and long. 1° 6′ W., when a chronometer showed 8h 26m 59s-7, the observed altitude of the sun's lower limb was 39° 14′ 30′′, index correction + 4' 24" and height of eye above the sea 20 feet, required the error of the chronometer on mean time at the place, and also its error on Greenwich mean time. To find ship apparent time (using haversines). To find ship apparent time (using the common tables of If the computed ship mean time differ several minutes from the estimated ship mean time, it will be advisable, when great accuracy is required, to recalculate the sun's declination and the hour angle; using the approximate ship time just found to determine the Greenwich date; the following example will illustrate the mode of proceeding : March 16, 1844, at 10h 10m A.M, mean time nearly, in lat. 50° 48′ N., and long. 1° 6' W., when a chronometer showed 10h 15m 47.2, the observed altitude of the sun's lower limb was 58° 46′ 30′′ (in artificial horizon), the index correction + 1' 20", required the error of chronometer on Greenwich mean time. The mean time at the place is found to be 21h 47m 59s.7, but the mean time used for computing the declination and equation of time was 22h 10m. Now this has rendered the declination slightly incorrect, and therefore the time computed from it. When it is desirable to obtain mean time at the place as correctly as possible, we must recalculate the declination and apparent time, using the approximate mean time for finding a more correct Greenwich date; thus the mean time at the place is found above to be 21h 47m 52s-7, assuming therefore the mean time to be 21h 48m, obtain a second Greenwich date, and recompute the sun's declination and hour angle as follows: |