CERTAIN HARMONIES OF THE SOLAR SYSTEM. 41 



in which case (C)^ is the greater because of the superior density of the Earth. 

 [And the great relative distance of our own sateUite (nearly 60 radii of the 

 Earth) as, in the similar instance in Saturn's system, is also [6 of (43)] indicative 

 of a great oblateness of the nebulous material at some stage of its progress.] 



(56) Again, a like relation is found in the case of the mean distance and centre 

 of (simultaneous) gyration of Uranihs and Neptune. 



In the instance of these we have an approximation to equality in the masses;^ the 

 ratio of the mass of Neptune to that of Uranus being 



'^ = 1.11678. 



m'S 



Moreover (C), the centre of gyration of the two planets is at the distance 

 25.4457-; and while 



l{mean dist. q?)^ + ^{mean dist. ^f= 635.704 

 (C)'= (25.4457-)^ =647.481 



This is consistent with a ring-like form of the two masses in question, after the 

 "abandonment" of the material of which they were constituted; the flowing over 

 of material in this outer portion of the 



oblate solar atmosphere having given to ^'S- ^- 



the whole, or, at least, to both the parts of 

 the masses in question, a form not unlike 

 that of a thick ring. 



All this is consistent with that form, yet 

 does not require the masses to have had 

 such a form; since, (17), the equation here 

 in question would, accuxately, exist in the case of any equal masses. 



(57) The state of things arrived at (perhaps later) in the case of Jupiter and 

 Saturn, (63), seems to be inconsistent with a mere ring-like form for both masses; 

 but to be a consequence of the accession of material from regions of the sun's 

 atmosphere extra-equatorial. Accordingly we shall find that the equation here in 

 question does not obtain in that instance. 



But under the conditions approximated to in the case of planets exterior to 

 them, and at length attained in the instance of those two great masses, viz. 



ma"^ = m'a'^, 

 we have the masses inversely as the squares of the radii of gyration; so that the 

 resulting planets must increase in mass, in the progress inward, until we come to 

 the instance of Jupiter, the greatest of all f the ring-like masses, or the shells, 

 though successively decreasing in volume, yet increasing more rapidly in density, 



' The mass of Neptune is the greater; Uranus having just possibly lost somewhat in the process, 

 (43), which carried away the mass of the now missing planet. 



" Mr. Trowbridge, in his investigation ah-eady referred to (Note to 38), [in 1864], shows that this 

 would be true of the " abandoned" rings. But the increase of the mass of the great planets, in the 

 progress inward, would seem to be too rapid to be explained by that alone. The other changes and 

 relations in question may, as it would seem, have been even more efficient; and the most of these 

 were indicated by the author of this paper in ISSt, as heretofore stated in the same Note to Article (38). 

 6 January, 1875. 



