CERTAIN HARMONIES OF THE SOLAR SYSTEM. 87 



respectively, the Saturn and the Jupiter of the Minor System of planets ; and 

 there are other curious relations, furnishing subjects for comparison, which are 

 detailed in (101). and (102). 



54^A. It is shown in (16) that the centre of gyration of a thin homogeneous 

 ring is in the circumference of a circle concentric with the edges of the ring, and 

 bisecting its area. Also that R' and r' being the radii of the edges of the ring and 

 G that of the centre of gyration, we shall have 



(a) The same, in (54), is extended to the case in which the equivalent masses are 

 both thin homogeneous rings, one wholly clasping the other; E and »•' representing 

 the respective radii of the centres of gyration of the two clasping rings, and C that 

 of the common centre of gyration. 



ih) The common formula for the centre of gyration will, when reduced, give us 

 the same equation, in the case of any two equal masses, irrespective of the form of 

 either. 



Now although the two systems of bright rings of Saturn can scarcely be presumed 

 to be homogeneous, and although they do not seem to be equal in mass, yet, (55), 

 the equation in question is found to be very nearly applicable to them. 



[Making use of this inductively, as some indication of the ring-like form in 

 revolving masses, (55), we found, that the like equation in the solar system was 

 very nearly justified in the case of the half-planets Earth and Venus ; and, (56), 

 that a similar one was nearly realized in the case of Neptune and Uranus ; the 

 distances being those in the column of Law, in Table (B) of (14).^ 



These results might seem to be consistent with the supposition that the flowing 

 over of the material of the oblate solar atmosphere had given to the masses in 

 question, at some period of their development, a form not unlike that of a thick ring ; 

 and yet the same cannot be regarded as decisive ; and in the case of Uranus and 

 Neptune, there is the other explanation found in (6) of this Consistency; for the 

 masses of Neptune and Uranus are nearly equ,al.'\ 



In another and different instance we have a closer agreement. 



The centre of gyration, (19), of the whole system of Saturn's Bright Rings is at 

 a distance from the planet's centre = 1.9090 ; being just within the outer edge of 

 the Inner Bright Ring (or Rings), which is at the distance 1.9276; as though the 

 division of one great ring had taken place there. 



Some reason why the opening between the system of rings should be permanent, 

 is given in (64); which reason has already been alluded to in Consistency Wth. 



' Before Uranus (Consistency Hth) had perceptibly /aZ/ew in. 



