3. The same mode of observing equal altitudes might be applied to stars, hut the observations would be extended to very inconvenient hours, and it is nearly as accurate to observe two bright stars, one to the cast and the other to the west, and if possible at about the same altitudes. Each star will then give an error of the chronometer, and if the altitudes are rightly observed, the same error of the chrono meter. If the errors do not agree, a mean will come nearer to the truth than either of them separately; but if the stars have not the same polar distance, the effect of a given error in altitude upon the hour angle must be computed for each, and the difference between the chronometer's errors divided in this ratio. Thus, sup pose,the eastern star gives a chronometer error of fast, and the western star an error of 28..0 fast, while an error of 1' in the altitude of the eastern star causes twice the error in the deduced hour angle that a similar error of 1' does in the western star; the concluded true error should be 27'.0, instead of the mean error The reader will see that if the observations are made at exactly the same altitude, any mistake as to the index error, refraction, or any instrumental defect, is thus got rid of without much trouble. But, as has been mentioned before, very perfect observations of stars with reflecting instruments can scarcely be made unless the instru ment is mounted on a stand. From good sets of observations of a star east and a star west, the time may be determined to 0'.3 or The time is required to reduce circum-meridian observations to the meridian for finding the latitude, and again the latitude is required in order to deduce the time from altitudes. An approximate latitude, such as results from the largest observed altitude about the meri dian, will give the time near enough for the reduction to the meridian, and then the time may be computed rigorously with the exact latitude. Provision may be made for this revision by taking out the differ ences of the logarithms at each step of the first computation ; but generally speaking, when the altitudes for time are taken nrr the prime vertical, as they ought to be, a small error in the latitude has so little effect on the hour angle, that the approximate latitude is near enough.
Determination of Greenwich Time astronomically.-1. There are two phenomena which are seen at the same moment from whatever part of the earth they are visible, namely, a lunar eclipse and the eclipses of Jupiter's satellites. The first was the only phenomenon from which longitudes were derived previous to the invention of telescopes, but it is not of frequent occurrence, and unfortunately cannot be noted very exactly. It has been proposed to measure equal .quantities of the eclipse on each side of the middle, and formerly astronomers were very careful to note the moments when the Umbra touched or covered well defined spots. But at present, lunar eclipses are scarcely regarded, as there are many more accurate means of determining the longitude, and of more frequent occurrence ; and lunar eclipses are of uo value in the theory of the moon's motions. The eclipses of the satellites of Jupiter, especially of the first satellite, are much more common, and have been of great use in modern geography. The time at which the eclipses take place, that is, when the satellite, passing into the shadow of Jupiter, is lost (immerges), or passing out of the shadow, becomes visible (emerges), arc set down in the Nautical Almanac' at the time they would be seen at Greenwich if visible. The observer at any other place notes when this phenomenon does actually happen at the place of observation, and the difference between the two times is the longitude of the place from Greenwich ; east if the time of the eclipse is later than at Greenwich, and west if it be earlier. Unfortunately this method, so easy in practice, is by no means as accurate as it might at first sight appear. The theory of the satellites is scarcely to be con
sidered as perfect, but this objection might be obviated by comparing corresponding observations, and might be very much diminished by correcting the predictions of the ' Nautical Almanac' by observations made at Greenwich, or any other well known place, about the aline time. But the phenomenon is a gradual and not an instantaneous one, and the appearance or disappearance of the satellite varies greatly with the goodness of the telescope, the aye or mood of the observer, the atmosphere at the place of observation, &c., so that a longitude deduced from an eclipse of the first satellite may be considerably wide of the truth. With ordinary telescopes we believe that eclipses of the second satellite are more than twice as uncertain as the first, and that the third and fourth satellites are not worth observing for this pur pose, being much inferior to good lunar distances. A large mass of eclipses of Jupiter's satellites made by the same telescope and the same observer, and where the immersions are nearly as numerous as the emersions, will however yield a satisfactory result. The aperture of the object-glass employed, and also the sight of the observer, should correspond as nearly as possible with the telescope and observer at Greenwich, or whatever place is adopted as a standard of comparison. It is not considered advisable to use a smaller telescope than an achromatic of 21 inches aperture for this purpose, or one larger than of 3i aperture.
2. The -time at Greenwich is most accurately determined by solar eclipses or occultations of fixed stars by the moon. The computations are rather long, but not very difficult or abstruse. The beginning and end of the solar eclipse should be observed ; the latter is the better marked phenomenon, and if the eclipse be annular, the commencement and breaking up of the annulus. Recent observations have shown that these appearances are not instantaneous, and therefore that longitudes deduced from them are not free from uncertainty. The occultation of a fixed star by the moon is not liable to this objection; and when the star is bright, and both immersion and emersion can be carefully observed, the longitude from an occultation affords perhaps the best determination possible of the longitude between two distant places. Yet even here doubts may arise, at least in some cases. The star may be occulted too early by a lunar mountain, or disappear too late in a lunar valley. The occultation should be observed at both places, which is not often possible, and the star should pass not far from the centre of the moon. If the solar eclipse or the occultation be not observed at Greenwich, or at any well determined observatory, the data of the Nautical Almanac' must be corrected by the meridian observations of the moon about the time. The tables of the sun are at present nearly as perfect as observation can make them, but the moon may be out or even 20", which might occasion an error of 30' or 40' iu the deduced longitude, or from an eighth to a sixth of 1°. The solar eclipses, &c., with a map showing in what parts of the globe they are visible, are given in the NauticarAlmanac, and the occulta tions by the moon of all fixed stars to the sixth magnitude inclusive, visible at Greenwich, are also predicted to the nearest minute, with such a description of the relative situation of moon and star as will enable any one to observe them without difficulty. All possible occultations of fixed stars to the fifth magnitude inclusive, visible any where, arc also set down in that valuable work, with the data neces sary for determining whether they arc visible at any specified place. We cannot press too earnestly on all persons interested in perfecting geography, the absolute necessity of learning to observe an occultation, and to take altitudes methodically with a circle or sextant. The com putations may be made at home.