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(173.) Aug. 7, 1851, in latitude 50° 48′ N., and longitude 1o 6′ W., the sun had equal altitudes at the following times by chronometer.
9h 3m 428-31
3h 21m 54s.22
Required the error of the chronometer on Greenwich mean time.
For Elements from Nautical Almanac, see preceding example. Ans., 3m 35.48 fast.
(174.) Aug. 21, 1851, in latitude 50° 48' N., and longitude 1o 6' W. the sun had equal altitudes at the following times by chronometer.
10h 49m 15s.4
1h 27m 27$6
Required the error of the chronometer on Greenwich mean Ans., 1m 8.83 fast.
Elements from Nautical Almanac.
Equation of time 3m 15.94 + difference for 1h 0s.606
(175.) Sept. 10, 1851, in latitude 50° 48′ N., and longitude 1° 6′ W., the sun had equal altitudes at the following times by chronometer.
9h 45m 55.2
2h 20m 39.9
Required the error of the chronometer on Greenwich mean time. Ans., 3m 475.28 slow.
Elements from Nautical Almanac.
Equation of time 2m 58.43 + difference in 1h 0.866 + Declination 9th 5° 27′ 27′′ N. 10th 5° 4′ 45′′ N.
(176.) May 14, 1844, in latitude 50° 48′ N., and longitude 15° 0′ W., the sun had equal altitudes at the following times by chronometer.
10h 46m 57.0
1h 39m 42.90
Required the error of the chronometer on the mean time at the place and also on Greenwich mean time.
Ans., Fast on mean time at place 17m 48.7.
Slow on Greenwich m. time 42m 55*3.
Declination 13th 18° 28′ 49′′ N. 14th 18° 43′ 21′′ N.
To find the approximate time by chronometer when the P.M. altitudes should be observed.
After taking the observations in the morning it will often be convenient to estimate nearly at what time by the chronometer the observer should prepare to take the P.M. sights. To do this the error of the chronometer on mean time at the place must be supposed to be known within a few minutes. Thus suppose (as in the last example) a chronometer is known to be about 17 minutes fast of mean time at the place, the time of the A.M. observation was by chronometer at 10h 46m 57, equation of time 4 minutes subtractive from apparent time. It is required to find the time the chronometer will show in the afternoon when the sun has the same altitude.
Let a = estimated error of chronometer on mean time at place (supposed fast).
t = time shown by chronometer at A.M. observation. a = mean time at A.M. observation nearly. equation of time (supposed subtractive from apparent time).
a + E)
.. Mean time of P.M. observation as shown by the chronometer = 12 (t
a + E) ·
E + a
Thus (see ex.) let t = 10h 46m 573, a = 17m, E = 4m ... Time by chronometer = 1h 13m 33 + 26m = 1h 39m. It appears from this that the observer need not prepare to take his P.M. sights until 1h 30m by chronometer.
A similar formula may be made to suit any other case.
RULES FOR FINDING THE LONGITUDE BY CHRONOMETER AND BY LUNAR OBSERVATIONS.
THE two principal methods for finding the longitude at sea, by astronomical observations, are by means of a chronometer, whose error is known on Greenwich mean time; or by observing the distance of the moon from some well known star, and calculating from thence Greenwich mean time: ship mean time is to be obtained in both methods by the same kind of observation. To find the longitude by chronometer, an altitude of a heavenly body is to be taken-an operation requiring very little skill in the observer. To find the longitude by lunar observations, the distance of the moon from some other heavenly body must be observed with considerable accuracy; the skill necessary to do this can only be acquired by practice: for these reasons the method of finding the longitude by chronometer is the one chiefly in use, although the longitude deduced from it depends on the regular going of a time-keeper, whose rate from various causes is continually liable to change, while the other, which in fact is (within certain limits) correct and independent of all errors of chronometer, is rarely applied. Another objection usually urged against the use of the method of finding the longitude by lunar observation, is the labour required in reducing the observations; but we will endeavour to show that this ought not to deter the student; for that the work, although certainly more laborious than that required by the other method, is simple, and no ambiguity or distinction of cases need occur to distract the observer.
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, Nzs the celestial meridian, z the zenith of the spectator, P the pole, and w Q E the celestial equator.
zQ is the latitude, and if x be the place of the sun at the time of the observation x o is its altitude, and zx the zenith distance; draw the circle PXM,
then XM is the sun's declination known from the Nautical Almanac: hence in the triangle ZPX the three sides are known, namely, PX the polar distance, zx the zenith distance, and pz the colatitude, to find the hour angle z PX, from which mean time at the ship is easily found as pointed out in p. 172.