211. But as it is not easy to determine the exact moment either of the beginning or ending of a Lunar Eclipse, because the Earth’s shadow through which the Moon passes is faint and ill defined about the edges; we have recourse to the Eclipses of Jupiter’s Satellites, which disappear so instantaneously as they enter into Jupiter’s shadow, and emerge so suddenly out of it, that we may fix the phenomenon to half a second of time. The first or nearest Satellite to Jupiter is the most advantageous for this purpose, because it’s motion is quicker than the motion of any of the rest, and therefore it’s immersions and emersions are more frequent. [Sidenote: How to solve this important problem. PLATE V.] 212. The _English_ Astronomers have made Tables for shewing the times of the Eclipses of Jupiter’s Satellites to great precision, for the Meridian of _Greenwich_. Now, let an observer, who has these Tables with a good Telescope and a well-regulated Clock at any other place of the Earth, observe the beginning or ending of an Eclipse of one of Jupiter’s Satellites, and note the precise moment of time that he saw the Satellite either immerge into, or emerge out of the shadow, and compare that time with the time shewn by the Tables for _Greenwich_; then, 15 degrees difference of Longitude being allowed for every hour’s difference of time, will give the Longitude of that place from _Greenwich_, as above § 210; and if there be any odd minutes of time, for every minute a quarter of a degree, east or west must be allowed, as the time of observation is before or after the time shewn by the Tables. Such Eclipses are very convenient for this purpose at land, because they happen almost every day; but are of no use at sea, because the rolling of the ship hinders all nice telescopical observations. [Sidenote: Fig. II. Illustrated by an example.] 213. To explain this by a Figure, let _J_ be Jupiter, _K_, _L_, _M_, _N_ his four Satellites in their respective Orbits 1, 2, 3, 4; and let the Earth be at _f_ (suppose in _November_, although that month is no otherways material than to find the Earth readily in this scheme, where it is shewn in eight different parts of it’s Orbit.) Let _Q_ be a place on the Meridian of _Greenwich_, and _R_ a place on some other Meridian. Let a person at _R_ observe the instantaneous vanishing of the first Satellite _K_ into Jupiter’s shadow, suppose at three o’clock in the morning; but by the Tables he finds the immersion of that Satellite to be at midnight at _Greenwich_: he can then immediately determine, that as there are three hours difference of time between _Q_ and _R_, and that _R_ is three hours forwarder in reckoning than _Q_, it must be 45 degrees of east Longitude from the Meridian of _Q_. Were this method as practicable at sea as at land, any sailor might almost as easily, and with equal certainty, find the Longitude as the Latitude. [Sidenote: Fig. II.