Though Galileo had discovered the satellites of Jupiter, their times of revolution, and even some of their inequalities, it yet remained to define their motions with precision, and to construct tables for calculating their places. This task was performed by the elder Cassini, who was invited from Italy, his native country, by Louis the Fourteenth, and settled in France in 1669. His tables of the satellites had been published at Bologna three years before, and he continued to improve them, by a series of observations made in the observa tory at Paris, with great diligence and accuracy.
The theory of the motions of these small bodies is a research of great difficulty, and had been attempted by many astronomers before Cassini, with very little success. The planes of the orbits, their inclinations to the orbit of Jupiter, and the lines in which they inter sected that orbit, were all to be determined, as well as the times of revolution, and the dis tances of each from its primary. Add to this, that it is only in a few points of their orbits that they can be observed with advantage. The best are at the times of immersion into the shadow of Jupiter, and emersion from it. The same excellent astronomer discovered four satellites of Saturn, in addition to that already observed by Huygens. He also dis covered the rotation of Jupiter and of Mars upon their axes.
The constant attention bestowed on the eclipses of the satellites of Jupiter, made an 11 inequality be remarked in the periods of their return, which seemed to depend on the position of the earth relatively to Jupiter and the sun, and not, as the inequalities of that sort might have been expected to do, on the place of Jupiter in his orbit. From the opposition of Jupiter to the sun, till the conjunction, it was found, that the observed emersion of the satellites from the shadow fell more and more behind the computed ; the differences amounting near the conjunction to about fourteen minutes. When, after the conjunction, the immersions were observed, an acceleration was remarked just equal to the former retardation, so that, at the opposition, the eclipse happened fourteen minutes sooner than by the calculation.
The first person who 'offered an explanation of these facts was Olaus Roemer, a , Danish astronomer. He observed that the increase of the retardation corresponded nearly to the increase of the earth's distance from Jupiter, and conversely, the acceleration to the diminution of that distance. Hence it occurred to him, that it was to the time which light requires to traverse those distances that the whole series of phenomena was to be as cribed. This explanation was so simple and satisfactory, that it was readily received.
Though Roemer was the first who communicated this explanation to the world, yet it seems certain that it had before occurred to Cassini, and that he was prevented from making it known by a consideration which does him great honour. The explanation. which the motion of light afforded, seemed not to be consistent with two circumstances involved in the phenomenon. If such was the cause of the alternate acceleration and re tardation above described, why was it observed only in the eclipses of the first satellite, and not in those of the other three ? This difficulty appeared so great to Cassini, that he suppressed the explanation which he would otherwise have given.
The other difficulty occurred to Maraldi. Why did not an equation or allowance of the same kind arise from the position of Jupiter, with respect to his aphelion, for, all other things being the same, his distance from the earth must be greater, as he was nearer to that point of his orbit ? Both these difficulties have since been completely removed. If the aforesaid inequality was not for sometime observed in any satellite but the first, it was only because the motions of the first are the most regular, and were the soonest un derstood, but it now appears that the same equation belongs to all the satellites. The solution of Maraldi's difficulty is similar ; for the quantity of what is called the equation of the light, is now known to be affected by Jupiter's place in his orbit.
Thus, every thing- conspires to prove the reality of the motion of light, so singular on account of the immensity of the velocity, and the smallness of the bodies to which it is communicated.