And consequently to 15 degrees of Longitude.
Lunar Eclipses useful in finding the Longitude.
210. To every place 15 degrees eastward from any given Meridian, it is noon an hour sooner than on that Meridian; because their Meridian comes to the Sun an hour sooner: and to all places 15 degrees westward it is noon an hour later § [208], because their Meridian comes an hour later to the Sun; and so on: every 15 degrees of motion causing an hour’s difference in time. Therefore they who have noon an hour later than we, have their Meridian, that is, their Longitude 15 degrees westward from us; and they who have noon an hour sooner than we, have their Meridian 15 degrees eastward from ours: and so for every hour’s difference of time 15 degrees difference of Longitude. Consequently, if the beginning or ending of a Lunar Eclipse be observed, suppose at London, to be exactly at mid-night, and in some other place at 11 at night, that place is 15 degrees westward from the Meridian of London: if the same Eclipse be observed at one in the morning at another place, that place is 15 degrees eastward from the said Meridian.
Eclipses of Jupiter’s Satellites much better for that purpose.
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.
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.
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.
Fig. II.
We seldom see the beginning and end of the same Eclipse of
any of Jupiter’s Moons.
214. Whilst the Earth is going from C to F in it’s Orbit, only the immersions of Jupiter’s Satellites into his shadow are generally seen; and their emersions out of it while the Earth goes from G to B. Indeed, both these appearances may be seen of the second, third, and fourth Satellite when eclipsed, whilst the Earth is between D and E, or between G and A; but never of the first Satellite, on account of the smallness of it’s Orbit and the bulk of Jupiter; except only when Jupiter is directly opposite to the Sun; that is, when the Earth is at g: and even then, strictly speaking, we cannot see either the immersions or emersions of any of his Satellites, because his body being directly between us and his conical shadow, his Satellites are hid by his body a few moments before they touch his shadow; and are quite emerged from thence before we can see them, as it were, just dropping from him. And when the Earth is at c, the Sun being between it and Jupiter hides both him and his Moons from us.