In this Diagram, the Orbits of Jupiter’s Moons are drawn in true proportion to his diameter; but, in proportion to the Earth’s Orbit they are drawn 81 times too large.
[PLATE VI].
Jupiter’s conjunctions with the Sun, or oppositions to him,
are every year in different parts of the Heavens.
215. In whatever month of the year Jupiter is in conjunction with the Sun, or in opposition to him, in the next year it will be a month later at least. For whilst the Earth goes once round the Sun, Jupiter describes a twelfth part of his Orbit. And therefore, when the Earth has finished it’s 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.
The surprising velocity of light.
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 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 161⁄2 minutes of time to go through a space equal to the diameter of the Earth’s Orbit, which is 162 millions of miles in length: and consequently the particles of light fly about 164 thousand 494 miles every second of time, which is above a million of times swifter than the motion of a cannon bullet. And as light is 161⁄2 minutes in travelling across the Earth’s Orbit, it must be 81⁄4 minutes in coming from the Sun to us: therefore, if the Sun were annihilated we should see him for 81⁄4 minutes after; and if he were again created he would be 81⁄4 minutes old before we could see him.
Fig. V.
Illustrated by a Figure.
217. To illustrate this progressive motion of light, let A and B be the Earth in two different parts of it’s Orbit, whose distance is 81 millions 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 81⁄4 minutes sooner when the Earth is at B, than when it is at A. And so, as Mr. Romer 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 Semidiameter of that Circle; and as the Earth goes through all the 360 degrees of it’s 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 is 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 it’s distance from the Sun.
218. As the Earth moves from D to C, through the side AB of it’s 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 it’s 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 ere it overtakes the Earth.
219. That these accelerations of the immersions of Jupiter’s Satellites into his shadow, as the Earth approaches towards 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 excentric 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.
220. TABLES for converting mean solar Time into Degrees and Parts of the terrestrial Equator; and also for converting Degrees and Parts of the Equator into mean solar Time.