CERTAIN HARMONIES OF THE SOLAR SYSTEM. 85 



4:5th. A like effect may be more distinctly traced in the system of Saturn, in 

 the instance of the satellite Hyperion, which is just outside of Titan, the Jupiter 

 of the system ; as may be made apparent by a comparison of the columns of Fact 

 and of Law in Table (C) in (18); which is withal explained in (66). That Mars 

 also seems to have perGe2)tibly fallen in by the acquisition of material from the aste- 

 roid mass is discussed in (65). 



4i6th. The subsidiary hypothesis of the transference of the half-planet mass, is 

 still farther and very remarkably confirmed by the ratios due to the Ancient State 

 exhibited in Table (F) in (45), the Uranus-Saturn ratio of which is 7iot justified, 

 unless we also restore Saturn to its ancient state, by restoring also the missing planet 

 to its legitimate place ; and then combine that, the mass of Uranus, and also that 

 of the ancient Saturn \^, all at their common centre of gyration; and then the 

 appropriate ratio in Table (F) is very scrupulously jxhstified} 



i:lth. The conformity of the ratios of the Ancient State is itself a justification 

 of the mass of the missing half-planet ; that mass being independently determined 

 in conformity to the condition, that the centre of gyration of that half-planet and 

 Uranus should be the same with the whole-planet limit (U) in Table (B) in (14). 



This value of the mass is still farther confirmed, in so far as may be, by the 

 curious relations developed in (104); in which the mass of the ancient Saturn i^ 

 (Saturn deprived of the mass of the now-missing planet) enters in one connexion, 

 and the mass of the existing Saturn in another. 



48(!7i. The justification of the ratios of the Ancient State, as the same are exhi- 

 bited in Table (F) in (45), itself demands a special value of the asteroid-mass ; and 

 the value thus ascertained, with the data which we have, agrees closely with that 

 signified by M. Le Verrier (in one of his investigations of the subject), as being 

 required by the perturbations of the planet Mars. [See explanations and quotations 

 in (47) and Note.l 



4:9th. The arrangements of the Ancient State exhibited in Table (F) in (45), 

 into which combinations of planetary masses alternately enter, justify the posi- 

 tion of Mercury in their own series. Then withal the aphelion of Mercury's 

 orbit has a whole-planet place in Table (B) in (14), while the perihelion of the 

 same has a half-planet place. The arrangements of both tables thus consistently 

 indicate that Mercury has accumulated in itself the material appropriate for a planet 

 and a half planet, and that its position justifies that. 



50^7i. The arrangements now specified, also serve to account for the great eccen- 

 tricity of Mercury's orbit ; the planet having absorbed into itself the ring-like 

 or shell-like masses, one due to the whole-planet position at the aphelion of the 

 orbit, and the other to the half-planet position at the perihelion. 



■ As the annual aberration of the sun, planets, and fixed stars is without explanation, if we do 

 not admit the doctrine of the eartli's motion ; but the whole explanation is adequate in mode and 

 in measure with that motion first admitted. There is certainly an approximation to a parallelism 

 here. 



