From our own impression of the utility of lunars we feel it right to devote more than usual space to this method of finding the longitude, and we shall therefore give a variety of distinct rules to suit such cases as most commonly occur. Longitude by chronometer. When a chronometer is taken to sea, the error on Greenwich mean time, and its daily rate are supposed to accompany it knowing then the error and rate, it is easy to determine the Greenwich mean time at any instant afterwards by applying its original error and the accumulated rate in the interval: the corresponding mean time at the ship may be found by observing the altitude of the sun, or any other heavenly body, when it bears as nearly east or west as possible. The difference between the two times is the longitude of ship. To find the longitude by an observed altitude of the sun. Let NWSE represent the horizon, N zs the celestial meridian, z the zenith of the spectator, p the pole, and wQ E the celestial equator. Then zą is the latitude, and if x be the place of the sun at the time of the observation xo is its altitude, and zx the zenith distance; draw the circle PXM, W M N then XM is the sun's declination known from the Nautical Almanac: hence in the triangle z PX the three sides are known, namely, Px the polar distance, zx the zenith distance, and PZ the colatitude, to find the hour angle ZPX, from which mean time at the ship is easily found as pointed out in P. 172. Rule XLVII. 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. EXAMPLES. 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 45.5 and its daily rate was 5-7 losing. Or the mean time at Greenwich when the observation was taken. 0 455 fast 12 1 55-4 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. On April 1, the chronometer was fast 1m 58s7 on Greenwich mean time, and its mean daily rate was 11-2 gaining. Greenwich, April 17.. 21 22 Interval from April 1 to Greenwich date, 16a 211⁄21. |