VII. On the Extension of Bode's Empirical Law of 

 the Distances of the Planets from the Sun, to the 

 Distances of the Satellites from their respective 

 Primaries. * 



By J. CHALLIS, M.A. 



FELLOW OP TRINITY COLLEGE, AND OP THE CAMBRIDGE 

 PHILOSOPHICAL SOCIETY. 



[Read Dec. 8, 1828.] 



1. More than half a century has elapsed since Bode of 

 Berlin discovered a singular law of the mean distances of the 

 planets from the Sun, according to which if 4 = Mercury's distance, 

 4+3 will = Venus's, 4 + 2.3 = Earth's, 4 + 3.2- = Mars's, &c. No 

 one, I believe, has ever suggested an existing cause of this physical 

 fact ; the theory of universal gravitation points to no such law 

 of the distances at which several small bodies will perform revo- 

 lutions about a much larger ; it has in consequence been customary 

 to ascribe the law of Bode to the original arrangement of the 

 planets at the time they were first set in motion. If however it 

 be owing to a constantly operating cause, a similar phenomenon 

 ought always to be observed under similar circumstances: — the 

 satellites, which revolve round their primaries just as the latter 

 revolve round the Sun, ought to obey the same law of distances. 

 Should this be found to be the case it would afford some reason 

 to think that the cause of the phenomenon is not incidental but 

 I»ermanent. In endeavouring to ascertain whether the satellites 



Y 3 



