sict. ir.j DISSERTATION SECOND. 157 



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 intersected that orbit, 

 were all to be determined, as well as the times of revolution, 

 and the distances 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 satel- 

 lites of Saturn, in addition to that already observed by 

 Huygens. He also discovered the rotation of Jupiter and 

 of Mars upon their axes. 



The constant attention bestowed on the eclipses of the 

 satellites of Jupiter, made an 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 expect- 

 ed 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 diffe- 

 rences amounting, near the conjunction, to about fourteen 

 minutes. When, after the conjunction, the immersions 

 were observed, an acceleration was remarked jus( equal 

 to the former retardation, so that, at the opposition, the 

 eclipse happened fourteen minutes sooner than by the cal- 

 culation. 



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 con- 

 versely, the acceleration to the diminution of that distance* 



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