386 



SPECIAL RESULTS IN THE URANOLOGICAL 



Bd. m. S. 463; English edit. Yol. i. p. 89, and Vol. iii. 

 p. 340) of the relative magnitudes and distances in this 

 system of satellites. The periods of revolution and mean 

 distances, the latter expressed in parts of the equatorial 

 semi-diameter of Saturn, according to the observations 

 of Sir John Herschel at the Cape of Good Hope ( 63 ) 

 between 1835 and 1837, are as follows : 



Between the four first or nearest satellites, we find a re- 

 markable relation in the commensurability of their periods 

 of revolution. Ths period of the 3d satellite (Tethys), is 

 double that of the 1st (Mimas) ; and that of the 4th satel- 

 lite (Dione), is double that of the 2d (Enceladus). The 

 exactness of these proportions amounts to -g-i-g- of the longer 

 periods. This result, which has not been much attended to, 

 was communicated to me as early as November 1845, in 

 letters from Sir John Herschel. The four satellites of Ju- 

 piter shew also a certain degree of regularity in their dis- 

 tances, the intervals between them presenting with tolerable 

 approximation the series 3, 6, 12. The 2d satellite is dis- 



