Original and Actual Fluidity of the Earth and Planets. 257 



its times of rotation and revolution at the period of separation will be nearly 

 equal ; and since we have no reason to assume any difference in the mode 

 in which the planets and satellites were thrown off from the central mass, we 

 may suppose, in order to render our calculations possible, that at the period 

 of separation, the movements of rotation and revolution were so nearly equal 

 as to justify us in using equations (3) instead of (4). Equations (4) might be 

 used as well as ( 3 ), but require an additional hypothesis as to the time of ro- 

 tation of the planet ; but as this hypothesis should be the same for the planets 

 and satellites, the generality of the reasoning is not affected by the use of equa- 

 tions (3). In these equations, the only quantity which is unknown is a, the 

 radius of the planet or satellite at the time of its separation. We may obtain a 

 value for a, in terms of the actual radius of the planet and its past and present 

 moments of inertia, by the ordinary principles of mechanics ; and if we as- 

 sume as the measure of contraction of each planet the ratio which its original 

 time of rotation bears to its actual time of rotation, we can calculate the value 

 of e and e' for each planet and satellite. It will be shown afterwards, that the 

 amount of contraction thus assumed is much too small for the planets which 

 are attended with satellites, and probably for all the planets ; but it ■vvill be 

 useful to make the calculation upon this supposition in the first instance. 



Let i, I denote the former and present moment of inertia of the planet, sup- 

 posed homogeneous; a, a, its former and present radius, and n the number of 

 rotations contained in one revolution; then 



a^ : a^ :: i : /:: n : 1, 

 therefore, 



a : a :: ^n : 1, 

 or, 



a' = a' ^?i' ; 



and substituting this value in (3), we find 



-S^^v'"'. (5) 



The data from which I have calculated the values of e corresponding to each 

 planet and satellite are contained in the following Tables. 



