Sum of two last terms-117.52.34 Nat. ver. sine Difference of ditto= Diff. of true alts.. True central dist.. 2.56. 4 Nat. ver. sine 10.10.26 Nat. ver. sine 57:13:12′′Nat. ver. sine Near.precd.dist. at6=57. 12. 47 Prop. log. 3037.-Diff. 18 increasing ; Difference of ditto= 0: 0:25 P. log. 2.6355 Portion of time. 0 050: P. log. 2.3318 sce Rule, p. 383. Mean time at Greenw.-6 0:50:; which is to be considered as the correct mean time, because the portion of time is so small that the equation in Table A vanishes, or becomes nearly insensible. Now, the right ascensions and declinations of the objects being reduced to the correct mean time at Greenwich, thus found, the results will be as follows, viz. : Difference of R. A.= 346 39:12 Log. half elapsed time =0.078078 True lat. of the place 43: 9:38" Nat.co-V.S. 315955; which is South. To find the Mean Time and the Longitude. Sun's true central altitude = Sum = Half sum = Apparent time = = 40:48:49" 70. 13.41 Log. co-secant = 0.026389 .. 43. 9.38 Log, secant = 0.137010 Mean time at ship Long. of the ship, in time = 2420" 50:35:12:30 West. Hence the latitude of the place of observation is 43:9:38" south; the correct mean time 3:40:0!, and the true longitude 35: 12:30" west; as required. Note. From the above Example the Method of deducing the latitude, the mean time, and the longitude, from the same set of observations, when a fixed star, or a planet, is one of the objects, will appear obvious. In taking leave of the lunar observations, I am desirous of intimating to the young navigator that, whenever it can be conveniently done, the longitude should be inferred from two distances on opposite sides of the principal object, viz., from an observed angular distance between the moon's enlightened limb and a star east of her; and, also, from one to the westward of her: for, in this instance, as the imperceptible errors of the sextant (and the very best is not perfect), and the unavoidable errors in its use, would have a mutual tendency to correct each other; half the sum of the two longitudes would be more entitled to confidence than either longitude considered singly. PROBLEM XII. To find the Longitude of a Place by the Eclipses of Jupiter's The eclipses of Jupiter's satellites are distinguished by the appellations of immersions, or emersions. An immersion of a satellite signifies the instant of its entrance into the shadow of Jupiter; and an emersion, that of its re-appearance out of the shadow. The instant of an immersion is known by the last appearance of the satellite; and that of an emersion, by its first appearance out of the shadow of the planet. FIRST, To know if an Eclipse will be visible at a given Place. RULE. Reduce the mean time of the eclipse at Greenwich (as given in page XX. of the month in the Nautical Almanac) to the meridian of the place of observation, by Problem IV., page 343. Then, if at this reduced time Jupiter be not less than 8 degrees above the horizon of the given place, and the sun about as many degrees below it, or stars of the third magnitude, to be visible to the naked eye, the eclipse will be visible at such place: this, it is presumed, does not require to be illustrated by an example. M M SECOND, To find the Longitude of the Place of Observation. RULE. To the observed time of the eclipse per watch, at the given place, apply the error of the machine for mean time, deduced from observations of the sun's altitude, or from those of the moon, a planet, or a fixed star: hence the correct mean time at the place of observation will be known.-Now, the difference between this and the mean time of immersion or emersion at Greenwich, will be the longitude of the place of observation, in time:—east, if the time at the given place be the greatest; otherwise, west. Example. January 7th, 1836, at Trincomalee, in latitude 8:33 north, and longitude, by account, 81:22: east, an emersion of the first satellite of Jupiter was observed to take place at 131854 per watch, the error of which was 1:16 slow for mean time; required the true longitude of the place of observation? Remarks.-1. If Jupiter be far enough from the meridian at the time of observing an immersion or an emersion of one of his satellites, and his altitude to be taken at the exact moment of the satellite's disappearance or re-appearance; the correct mean time of observation may be inferred therefrom by Problem IV., page 439; and thus any irregularity in the going of the watch, betwixt the time of finding its error and the moment of observation, will be provided against or obviated. 2. The eclipses of Jupiter's satellites afford the readiest means of determining the longitudes of places on shore; but, since those eclipses cannot be distinctly seen, except through telescopes of a high magnifying power, and since glasses of this description cannot be used at sea, on account of the incessant motion of the vessel, which continually throws the planet out of the field of view; the above method of find ing the longitude is, therefore, of little use, if any, to the practical navigator :—moreover, it is not always available; because Jupiter passes so apparently close to the sun at certain intervals, that, for about six weeks in every year, that planet and its satellites are entirely lost in the refulgent splendour of the solar rays. PROBLEM XIII. To find the Longitude of a Place by an Eclipse of the Moon. RULE. Observe the moments, per watch (duly regulated to mean time), of the beginning and the end of the eclipse: then, half the sum of the observed times will be the mean 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: east, if the time at such place be the greatest; otherwise, west. Note. If only the beginning or the end of the eclipse be observed, the mean time of observation must be compared with the time answer-、 ing 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. April 30th, 1836, in latitude 38:24 north, and longitude, by account, 99:12 west, the beginning of a lunar eclipse was observed at 12:28 33, and the end thereof at 14:33 21; the error of the watch was 113 fast for mean time; required the true longitude of the place of observation? Obs. beginning of the eclipse, per watch = 122833! |