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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 And con- hour's difference of time. Therefore they who have sequently noon an hour later than we, have their meridian, that is their longitude, 15 degrees westward from us; longitude. and they who have noon an hour sooner than we, have their meridian 15 degrees eastward from ours;
to 15 de
and so for every hour's difference of time, 15 deLunar e grees difference of longitude. Consequently, if the useful in beginning or ending of a lunar eclipse be observed, finding the suppose at London, to be exactly at midnight, and longitude. 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.
211. But as it is not easy to determine the exact of Jupi. moment either of the beginning or ending of a lunar lites much eclipse, because the Earth's shadow through which better for the Moon passes is faint and ill-defined about the
edges, we have recourse to the eclipses of Jupiter's satellites, which disappear much more quickly as they enter into Jupiter's shadow, and emerge more suddenly out of it. The first or nearest satellite to Jupiter is the most advantageous for this purpose, because its motion is quicker than the motion of any the rest, and therefore its immersions and emersions are more frequent and more sudden than those of the others are.
212 The English astronomers have calculated 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 How to satellites, and note the precise moment of time that solve this he saw the satellite either immerge into, or emerge important out of the shadow, and compare that time with the problem. 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 later or earlier than the time shewn by the tables. Such eclipses are very convenient for this purpose on 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.
213. To explain this by a figure, let J be Jupiter, Fig. II. K, L, M, N, his four satellites in their respective Illustraorbits, 1, 2, 3, 4; and let the Earth be at f, sup- ted by an pose in November, although that month is no other. example. wise material than to find the Earth readily in this scheme, where it is shewn in eight different parts of its orbit. Let. Q be a place on the meridian of Greenwich, and R a place on some other meridian eastward from Greenwich. Let a person at Robserve the instantaneous vanishing of the first satellite Kinto Jupiter's shadow, suppose at three 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 Ris three hours forwarder in reckoning than Q, it must be in 45 degrees of east longitude from the meridian of Q. Were this method as practicable at sea as on land, any sailor might almost as easily, and with almost equal certainty, find the longitude as the latitude.
214. While the Earth is going from C to F in Fig. II. its orbit, only the immersion of Jupiter's satellites
We sel- into his shadow are generally seen; and their emerthe begin- sions out of it while the Earth goes from G to B.ning and Indeed, both these appearances may be seen of the end of the second, third and fourth satellite when eclipsed,
clipse of while the Earth is between D and E, or between any of Ju-G and A; but never of the first satellite, on account piter's of the smallness of its 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 immer. sions 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 behind him. And when the Earth is at c, the Sun, being between it and Jupiter, hides both him and his moons from us.
In this diagram, the orbits of Jupiter's moons are drawn in true proportion to his diameter; but in Jupiter's proportion to the Earth's orbit, they are drawn 81 conjunc- times too large.
tions with 215. In whatever month of the year Jupiter is in or opposi- conjunction with the Sun, or in opposition to him, in the next year it will be a month later at least. For every year while the earth goes once round the Sun, Jupiter dein differ- scribes a twelfth part of his orbit. And, therefore, of the hea- when the Earth has finished its annual period from being in a line with the Sun and Jupiter, it must go as much forwarder as Jupiter has moved in that time, to overtake him again: just like the minute-hand of a watch, which must, from any conjunction with the hour-hand, go once round the dial-plate and somewhat above a twelfth part more, to overtake the hour-hand again.
216. It is found by observation, that when the Earth is between the Sun and Jupiter, as at g, his
satellites are eclipsed about 8 minutes sooner than Plate IV. they should be according to the tables; and when the Earth is at B or C, these eclipses happen about 8 minutes later than the tables predict them.* Hence it is undeniably certain, that the motion of light is not instantaneous, since it takes about 16-1 minutes of time to go through a space equal to the diameter of the Earth's orbit which is 190 millions of miles in length; and consequently the particles of light fly about 193 thousand 939 miles every second of time, which is above a million of times swifter than the mo. tion of a cannon ball. And as light is 164 minutes The surin travelling across the Earth's orbit, it must be 84 prising ve minutes coming from the Sun to us; therefore, if light. locity of the Sun were annihilated, we should see him for 81 minutes after; and if he were again created, he would be 84 minutes old before we could see him.
217. To explain the progressive motion of light, Fig. V. let A and B be the Earth, in two different parts of Illustrat its orbit, whose distance from each other is 95 mil. ed by a filions of miles, equal to the Earth's distance from the Sun S. It is plain that if the motion of light , were instantaneous, the satellite 1 would appear to enter into Jupiter's shadow FF at the same moment of time to a spectator in A as to another in B. But by many years observations it has been found, that the immersion of the satellite into the shadow is seen 84 minutes sooner when the Earth is at B, than when it is at A. And so, as Mr. ROEMER first discovered, the motion of Light is thereby proved to be progressive, and not instantaneous, as was formerly believed. It is easy to compute in what time the Earth moves from A to B; for the chord of 60 degrees of any circle is equal to the semi-diameter of that circle; and as the Earth goes through
* In the tables which have been published in the nautical almanaos, &c. a proper allowance for the progress of light is made.
all the 360 degrees of its orbit in a year, it goes through 60 of those degrees in about 61 days.Therefore, if on any given day, suppose the first of June, the Earth be at A, on the first of August it will be at B: the chord, or straight line AB, being equal to DS, the radius of the Earth's orbit, the same with AS, its distance from the Sun.
218. As the Earth moves from D to C, through the side AB of its orbit, it is constantly meeting the light of Jupiter's satellites sooner, which occasions an apparent acceleration of their eclipses: and as it moves through the other half H of its orbit from C to D, it is receding from their light, which occasions an apparent retardation of their eclipses; because their light is then longer before it overtakes the Earth.
219. That these accelerations of the immersions of Jupiter's satellites into his shadow, as the Earth approaches toward Jupiter, and the retardations of their emersions out of his shadow, as the Earth is going from him, are not occasioned by any inequality arising from the motions of the satellites in eccentric orbits, is plain, because it affects them all alike, in whatever parts of their orbits they are eclipsed. Besides, they go often round their orbits every year, and their motions are no way commensurate to the Earth's. Therefore, a phenomenon, not to be accounted for from the real motions of the satellites, but so easily deducible from the Earth's motion, and so answerable thereto, must be allowed to result from it. This affords one very good proof of the Earth's annual motion.