of the Satellites from their Primaries. 183 



cases the ratio - admits of being expressed approximately by 



very simple numbers. This circumstance is Avorthy of remark, 

 as it appears not to be accidental. 



11. The following conclusions may I think, be fairly derived 

 from the preceding investigations : — 



1st. The planets and satellites arrange themselves about their 

 primaries at mean distances, which observe with more or less 

 accuracy the following progression : — 



a, a + b, a + rb, a + r'b, &c. ; 



with the exception of the satellites of Saturn which assume a 

 twofold progression of the same kind. 



2d. It is probable that the value of r must necessarily be 

 one of the terms of the series l, l^, 2, 2\, 3, &c. 



3d. There is some degree of probability that the ratio of h 

 to a may always be expressed by very simple numbers. 



4th. It is probable that the deviations from exact conformity 

 to the law are depending on the masses and mutual actions of 

 the revolving bodies, or, as in the case of Saturn, on the action 

 of contiguous bodies. 



J. CHALLIS. 



Trinity College, 

 Nov. 10, 1828. 



