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 law 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: 
