CERTAIN HARMONIES OP TEE SOLAR SYSTEM. 83 



facts in the same connexion, all but insist upon and require that the masses in 

 question must have turned around together. [See especially the application of 

 this in (39) and (41); also (44) with Table (F) in (45); and (53), (54), (56) and 

 (104).] 



2'Sth. The conditions involved in connexion with what is stated in Consistency 

 27<7i, also show that the law or laws of apportionment of the masses are not inde- 

 pendent of the laws of the distances ; but that they are functions, one sort of the 

 other. [See, again, last Note to (44) ; also quotations in (99), and its last Note hut one.] 



29th. It is in perfect agreement with Consistency 26th and 21th, if not also with 

 Consistency 28th, that the rings of Saturn referred to their respective centres of 

 gyration have, in Table (C), in (18), the places oi satellites. 



SOth. We have, besides, the commensurability of the periodic times of the two 

 great satellites of Saturn with those due to some of the limits of Table (C) in (18), 

 at which satellites are now missing, as that commensurability is exhibited in (66), 

 and in consequence of which (in view of the Laplace Hypothesis, or of that hypo- 

 thesis as modified) the existence of satellites may have been prevented there; and 

 thus also possibly may have been occasioned the space between the two systems 

 of Saturn's bright rings; all, as explained in (64). 



31st. Again we have the commensurability of the periodic time of Jupiter, and 

 some of the periodic times due to certain of the asteroid limits, and also that of 

 Mars ; which may have been the means of breaking up former planets or asteroids, 

 as is also explained in (64). With respect to the special relations of the half- 

 planets. Earth and Venus — in accordance with the Laplace Nebular Hypothesis, 

 or else with the same modified as in (37), we have: — 



C . Z2d. The abnormal density of the Earth accounted for (a density too great 

 for the Earth's place in the system). [See 1 of (39).] 



33cZ. In connexion with that, we have the great inclination of the equator 

 of the other half-planet Venus to the plane of its orbit ; apparently accounted 

 for in 2 of (39). 



34i;7i. We have the approximate agreement of the neutral point (the Kirk- 

 wood limit of the Earth's sphere of attraction between the two half-planets on 

 that side) with the lohole-planet limit for the combination of the two masses ; 

 as exhibited in 4 of (39). [The approximation to an agreement also of this 

 last with the centre of gyration of the two half-planets has already been adverted 

 to in the exposition of Consistency 21th, and its reference.] 



35*;^. The great ohlateness of the nebulous Earth (with its accumulated dense 

 material) is, (96), recorded in the great distance of the moon, = to full sixty 

 equatorial radii of its primary planet. 



36<A. That the ascertained density of the moon should be but 0.55654 of that 

 of the Earth is another fact in place in this discussion, in view of Consistency 35th. 



In consistency tvith the rest, and in confirmation of our subsidiary hypotliesis 

 accounting for the disappearance of the noiv-missing half planet, lohich shoidd, be 



