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First. When the object observed is the sun.
1. Get a Greenwich date.
2. Find Greenwich mean time at the instant of the observation, by bringing up the error of the chronometer by Rule XLII. p. 167.
3. Take out of the Nautical Almanac both the declination of the sun and the equation of time, for the noon before and the noon after the Greenwich date; take out also the sun's semidiameter.
4. Correct the declination and equation of time for the Greenwich date (or rather for the Greenwich mean time as shown by the chronometer), either by proportional logarithms or otherwise.
5. Correct the observed altitude for index correction, dip, semi., correction in alt., and thus get the true altitude, which subtract from 90° to obtain the zenith distance.
6. To find apparent time at ship (using log. haversines).* Under the latitude put the sun's declination, and, if the names be alike, take the difference; but if unlike take the sum. Under the result put the zenith distance, and find the sum and difference. Add together the log. secants of the two first terms in this form (omitting the tens in each index) and the halves of the log. haversines of the two last, and (rejecting the ten 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 the meridian; the result is apparent time at the ship at the instant of observation.
7. To find ship mean time. To the apparent time just
* If the student have no table of haversines he may proceed as pointed out in the note, p. 171, and example, p. 174, to find ship apparent time.
obtained, apply the equation of time, with its proper sign as directed in the Nautical Almanac: the result is mean time at the ship or place of observation.
8. To find the longitude. Under ship mean time put Greenwich mean time as known by the chronometer; the difference is the longitude in time, west, if the Greenwich time is greater than ship time, otherwise east.
1. Sept. 23, 1845, at 4h 45m P.M. mean time nearly, in latitude 50° 30' N., and longitude by account 110° 0′ W., when a chronometer showed 11h 59m 30s, the observed altitude of the sun's lower limb was 11° 0′ 50′′, the index correction 3' 20" and the height of the eye above the sea 20 feet; required the longitude.
On August 21 the chronometer was fast on Greenwich mean time 0m 45s.5 and its daily rate was 55.7 losing.
Or the mean time at Greenwich when the observation was taken.
2. April 18, 1844, at 9h 18m A.M. mean time nearly, in latitude 50° 48′ N., and longitude by account 1° 0′ W., when a chronometer showed 9h 27m 48s, the observed altitude of
the sun's lower limb was 76° 16′ 46′′ (in artificial horizon), index correction 3′ 46′′-; required the longitude. April 1, the chronometer was fast 1m 58s.7 on Greenwich mean time, and its mean daily rate was 11-2 gaining.
Interval from April 1 to Greenwich date, 16a 211.
(177.) Sept. 25, 1845, at 4h 20m P.M., mean time nearly, in latitude 59° 30' N., and longitude by account 112° 30' W., when a chronometer showed 11h 44m 20s, the observed altitude of the sun's lower limb was 10° 50' 10", the index correction + 6′ 10′′ and height of eye above the sea 18 feet, required the longitude. On Sept. 20, the chronometer was fast on Greenwich mean time 0m 30s.7 and its daily rate was 10s 5 losing. Ans., 112° 33' W.
(178.) May 30, 1845, at 3h 10m P.M., mean time nearly, in latitude 30° 12′ 0′′ S., and longitude by account 156° 0' E., the observed altitude of the sun's lower limb was 21° S′ 40′′ when a chronometer showed 4h 44m 56; the