RESEARCHES ON JUPITER'S SATELLITES. 343 



tion ; it will acknowledge the propriety of inscribing in 

 the heavens the name of so great an astronomer beside 

 that of Kepler. 



Let us cite two or three of the laws of Laplace : 



If we add to the mean longitude of the first satellite 

 twice that of the third, and subtract from the sum three 

 times the mean longitude of the second, the result will 

 be exactly equal to 180. 



Would it not be very extraordinary if the three satel- 

 lites had been placed originally at the distances from 

 Jupiter, and in the positions, with respect to each other, 

 adapted for constantly and rigorously maintaining the 

 foregoing relation ? Laplace has replied to this ques- 

 tion by showing that it is not necessary that this relation 

 should have been rigorously true at the origin. The 

 mutual action of the satellites would necessarily have re- 

 duced it to its present mathematical condition, if once 

 the distances and the positions satisfied the Jaw approxi- 

 mately. 



This first law is equally true when we employ the 

 synodical elements. It hence plainly results, that the 

 first three satellites of Jupiter can never be all eclipsed 

 at the same time. Bearing this in mind, we shall have 

 no difficulty in apprehending the import of a celebrated 

 observation of recent times, during which certain astron- 

 omers perceived the planet for a short time without any 

 of his four satellites. This would not by any means 

 authorize us in supposing the satellites to be eclipsed. 

 A satellite disappears when it is projected upon the cen- 

 tral part of the luminous disk of Jupiter, and also when 

 it passes behind the opaque body of the planet. 



The following is another very simple law to which the 

 mean motions of the same satellites of Jupiter are sub- 

 ject : 



