When one of the satellites is passing between Jupiter and the sun, it casts its shadow on the primary, as the moon casts its shadow on the earth in a solar eclipse. We see with the telescope the shadow traversing the disk. Sometimes, the satellite itself is seen projected on the disk; but, being illuminated as well as the primary, it is not so easily distinguished as Venus or Mercury, when seen on the sun's disk in one of their transits, since these bodies have their dark sides turned towards us; but the satellite is illuminated by the sun, as well as the primary, and therefore is not easily distinguishable from it. The eclipses of Jupiter's satellites have been studied with great attention by astronomers, on account of their affording one of the easiest methods of determining the _longitude_. On this subject, Sir John Herschel remarks: "The discovery of Jupiter's satellites by Galileo, which was one of the first fruits of the invention of the telescope, forms one of the most memorable epochs in the history of astronomy. The first astronomical solution of the problem of 'the longitude,'--the most important problem for the interests of mankind that has ever been brought under the dominion of strict scientific principles,--dates immediately from this discovery. The final and conclusive establishment of the Copernican system of astronomy may also be considered as referable to the discovery and study of this exquisite miniature system, in which the laws of the planetary motions, as ascertained by Kepler, and especially that which connects their periods and distances, were speedily traced, and found to be satisfactorily maintained." The entrance of one of Jupiter's satellites into the shadow of the primary, being seen like the entrance of the moon into the earth's shadow at the same moment of absolute time, at all places where the planet is visible, and being wholly independent of parallax, that is, presenting the same phenomenon to places remote from each other; being, moreover, predicted beforehand, with great accuracy, for the instant of its occurrence at Greenwich, and given in the Nautical Almanac; this would seem to be one of those events which are peculiarly adapted for finding the longitude. For you will recollect, that "any instantaneous appearance in the heavens, visible at the same moment of absolute time at any two places, may be employed for determining the difference of longitude between those places; for the difference in their local times, as indicated by clocks or chronometers, allowing fifteen degrees for every hour, will show their difference of longitude."