82 STATEMENT AND EXPOSITION OF 



IStJi. We have Kirkwood's Analogy; already discussed [(106) to (108) inclusive]. 



19th. It is consistent with Laplace's Nebular Hypothesis that the large planets 

 should be furnished with satellites, while the small planets are not so attended, 

 with the bare exception of the Earth; which, even, has but one, unless some small 

 bodies, not wholly unlike aerolites, are to be added to the number. The " aban- 

 donment" of nebulous rings, etc., could more readily proceed and be carried to the 

 result of condensed rings, or of satellites, in the case of the larger bodies. 



20th. The greater density of the smaller planets in clsmparison with the larger ; 

 and the tendency to a law of increase from without inward, in the whole series ; 

 as manifested in Table (A) in (3). The decidedly abnormal deviations from, this 

 are specially accounted for. [See references in exposition of Consistencies 22d 

 and S9th respectively.] 



2lst. The Nebular Hypothesis furnishes M. Laplace with an explanation of the 

 exact commensurability of the angular motions, and thus of the periodic times, 

 etc., of Jupiter's satellites ; they having " immediately after their formation not 

 moved in a perfect vacuum." The action, in this case, of a resisting medium, 

 itself consistent with his hypothesis, is illustrated by M. Laplace in the way already 

 indicated in (67). 



The farther summation of consistencies will have special reference to other 

 phenomena and relations discussed in this paper. 



22d. In addition to Consistency 2lst, we have an approximate commensurability 

 of periodic times of some of the satellites of Saturn, and also of those of tJie four 

 outer 2)lanets of the Solar System ; as detailed in (67). 



23cZ. The modification of the Laplace Nebular Hypothesis, (37), providing. for 

 spheroidal shells, provides, also, for a conservative force for the holding together 

 of great masses ; and so prevents the indefinite multiplication of asteroids in all 

 regions of the system. 



24<7i. As if in consistency with a common origin and mode of development, we 

 have the three laws of distances of planets and half-planets, as stated in (10); and 

 the arrangement in accordance with these, in Table (B), in (14). 



2bth. We have also the prevalence of similar laws in the System of Saturn ; 

 the arrangement in accordance with which is exhibited in Table (C) in (18 

 Then, moreover, we have the arrangement in so far as a more restricted systen^ 

 would admit (viz., in accordance with two such laws) in the System of Jupiter ; as 

 shown in Table (D) in (20); and in the approximate arrangement of the System 

 of Uranus in Table (E) in (21). 



2Qth. The gradual and systematic increase or diminution, as the case may be, 

 of the leading ratio, and its powers in these several systems, would seem again to 

 indicate that the arrangement had a physical origin, not unlike that under discus- 

 sion. [See the Summing up of these relations in (22).] 



27;;7i. The consistency of the results obtained in so many connexions by a reference 

 of positions to the centres of gyration of the revolving masses, together with other 



