Original and Actual Fluidity of the Earth and Planets. 253 



would, by the powerful attraction of the earth, be forced to assume the 

 form of an ellipsoid of unequal axes, having its longest diameter directed 

 towards the earth ; the terrestrial attraction continuing to operate in the same 

 direction, must, according to the theory, have at length, by approximating the 

 movements of revolution and rotation, brought their difference within the limits 

 in which an exact equality would begin to be established ; the libration pro- 

 duced in the greatest axis of the moon in this manner must have been subse- 

 quently destroyed by the internal friction of its particles, and thus the singular ap- 

 pearance produced of an exact equality between the angular motions of revolution 

 and rotation. The illustrious author of the nebular hypothesis having thus ex- 

 plained by means of his theory this remarkable fact, proceeds to apply it to the 

 explanation of the relation which exists between the mean motions of revolution 

 of the first three satellites of Jupiter. Into this further application of the 

 theory it is not my intention to inquire, as the facts may be accounted for by 

 friction ah extra, acting on the satellites, the existence of which may be readily 

 admitted without adopting the nebular hypothesis. But with reference to the 

 explanation offered by Laplace, of the equality of the movements of revolution 

 and rotation of the six satellites whose time of rotation has been observed, it ap- 

 pears to be natural to inquire, whether the explanation does not prove too much, 

 and whether it would not apply equally well to establish the equality of the 

 motions of revolution and rotation of the planets. Unless, in fact, it .can be 

 shown, that the physical cause assigned for the explanation of the fact relating 

 to the satellites operated upon those bodies more powerfully than upon the 

 planets, the explanation cannot be admitted ; for it will be granted, that the 

 attraction of the sun must, on the nebular hypothesis, have operated in the same 

 manner on the planets, as the attraction of the latter on their satellites. The 

 question is therefore one of degree, and not of kind, for the same cause operated 

 in both cases. With the view of ascertaining whether the cause assigned by 

 Laplace acted more powerfully on the satellites than on the planets, I have 

 made the following calculations. 



I shall commence by investigating the figure of a planet, supposed homo- 

 geneous and gaseous, revolving on its axis and round the central body in the 

 same time and in the same plane ; it is easy to prove that the conditions of 

 equilibrium are satisfied by its surface assuming the figure of an ellipsoid with 



2 L 2 



