Now, if at this reduced time Jupiter be not less than 6 degrees above the horizon of the given place, and the sun be as many below it, or stars of the third magnitude be visible to the naked eye, the eclipse may be observed at that place: this, it is presumed, does not require to be illustrated by an example. SECOND, To find the Longitude of the Place of Observation of an Eclipse. RULE. Reduce the mean time of the eclipse at Greenwich into apparent time, by Problem II., page 416. Then, to the observed time of the eclipse, at the given place, apply the error of the watch for apparent time, deduced from observations of the sun's altitude, or from those of a fixed star, a planet, or the moon: hence the apparent time at the place of observation will be known. Now, the difference between this time and the apparent time at Greenwich will be the longitude of the place of observation in time; which will be east or west, according as the former is greater or less than the latter. Example 1. January 8th, 1825, in latitude 39:5 N., and longitude 28:3 W., by account, an immersion of the first satellite of Jupiter was observed at 8:12:59, by a watch which was 146: fast for apparent time; required the true longitude of the place of observation? Mean time of the eclipse at Greenwich 10:10" 29: 7.16 Apparent time of the eclipse at Greenwich-10: 313: Note. If Jupiter be far enough from the meridian at the time of observing an immersion or an emersion of one of his satellites, the apparent time of observation may be inferred directly from his altitude; and, if the altitude be taken at the same instant of observing the immersion or emersion of the satellite, the use of a watch will then become unnecessary. Example 2. January 2d, 1825, in latitude 39:51:10" N., and longitude 4:15. E., by account, an emersion of the first satellite of Jupiter was observed; and, at the same instant, the altitude of that planet's centre, east of the meridian, was found to be 28:49:30"; the height of the eye above the level of the sea was 20 feet; required the true longitude of the place of observation ? Mean time of the emersion at Greenwich = Equation of time = Apparent time at Greenwich = 7 3:50: 28:45:13" = 064902 = 519385 454483 Log. 5. 657518 Jupiter's horary dist., east of the merid.=432" 16: Log. rising=5. 79691.3 Jupiter's reduced right ascension = Right ascension of the meridian = Apparent time at the place of observ, Apparent time at Greenwich = S. 43.39 4:11 23: . 21. 4.52 7 6:31: 6.49. 19 Longitude of the place of obs., in time=017 12:4:18:0" east. Remarks. An immersion of a satellite is, the instant of its entrance into the shadow of Jupiter; and an emersion is that of its re-appearance out of the shadow. The instant of an immersion is known by the last appearance of the satellite; that of an emersion, by its first appearance. The eclipses of Jupiter's satellites afford the readiest, and, for general practice, the best method of determining the true longitudes of places on shore: but, since those eclipses cannot be distinctly observed except by means of telescopes of a high magnifying power,—and since these cannot possibly be used at sea, on account of the incessant motion of the vessel, which continually throws the object out of the field of view,-this method, therefore, though the very best at land, will be but of little, if any advantage to the mariner. It is to be observed, however, that this method of finding the longitude is not always available; because Jupiter passes so apparently close to the sun at certain intervals, that, for about six weeks in every year, both himself and his satellites are entirely lost in the superior splendour of the solar rays. PROBLEM XII. To find the Longitude of a Place by an Eclipse of the Moon. RULE. Observe the times, per watch, (regulated to apparent time,) of the beginning and the end of the eclipse: the mean of these times will be the apparent time of the middle of the eclipse; the difference between which and that given in the Nautical Almanac, will be the longitude of the place of observation in time; which will be east or west, according as it is greater or less than the time at Greenwich. Note. If only the beginning or the end of the eclipse be observed, the apparent time of observation must be compared with the time answering to the corresponding phase in the Nautical Almanac ; but, it must be remembered, that it will always be conducive to greater accuracy to observe the instants of both phases. Example 1. May 31st, 1825, in latitude 38:24. N., and longitude 26:0: E., by account, the beginning of the lunar eclipse was observed at 13:35:32: per watch, and the end at 14:447; the error of the watch was 2:13: slow for apparent time; required the true longitude of the place of observation? Example 2. November 25th, 1825, in latitude 16:40. N., and longitude 54:40 E., by account, the beginning of the lunar eclipse was observed at 7:640, and the end at 9:0755; per watch, not regulated. In order to find the error of the watch, the altitude of Aldebaran, east of the meridian, was taken at 8:730, and found to be 28:42:30"; the height of the eye above the level of the horizon was 22 feet; required the true longitude of the place of observation ? Time, per watch, of observing the star's altitude = 8 7:30: 3.38.40 0:30:55" Nat.V. S.=000040 28. 36. 16 N. co-V. S. 521240 = Remainder 521200 Log. 5.717004 Star's horary distance, east of the mer. 4:17 13: Log, rising 5, 75313.2 Apparent time of obs. the star's alt. = 8 415! Time of observation, per watch, = 8. 7.30 Beginning of the eclipse, per watch, = 7 6:40: Longitude of the place of obs., in time=3:38"32 = 54:3817 east. Remarks. From the two preceding examples, it is evident that the beginning and the end of the eclipse are the principal phases from which the longitude is to be found. If the observer be provided with a sextant, those phases may be observed to a tolerable degree of accuracy, by means of the largest telescope belonging to that instrument; or they may be observed with a good night telescope. This method of finding the longitude at sea is evidently the most simple of any of the astronomical methods that have been proposed for that purpose; however, since the lunar eclipses happen so very seldom, there are but few opportunities of carrying it into practice: nevertheless, whenever such eclipses take place, the prudent mariner will do well to avail himself thereof, and to determine his longitude by them accordingly. SOLUTION OF PROBLEMS RELATIVE TO THE VARIATION OF THE COMPASS. Definitions. The variation of the compass is the deviation of the points of the mariner's compass from the corresponding points of the horizon, and is denominated east or west variation accordingly. East variation is, when the north point of the compass is to the eastward of the true north point of the horizon; west variation is, when the north point of the compass is to the westward of the true north point of the horizon. The variation of the compass may be found by various methods, such as amplitudes, azimuths, transits, equal altitudes, rising and setting of the celestial objects, &c. |