CERTAIN HARMONIES OF THE SOLAR SYSTEM 45 



Then also, in view, (62), of the very small exterior half-planetary mass, in this 

 instance, and the close approximation of Jupiter's o'ermastering influence; and 

 the much larger, (62), interior half-planetary mass, and its special relations to 

 Mars as here specified, we discern, at last, how the formation of half-planets in 

 this region may have been prevented; also, why the range of the asteroids should 

 be so extensive; why the eccentricity of their orbits should be so great; why so 

 many have been discovered at distances approaching to that of the interior half- 

 planetary mass, and even on the side toward Mars ; and why so few have been 

 found at distances approaching to that of the exterior half-planetary mass.' 



Besides all this, we have the fact, that the actual distance of Mars [as seen in 

 Table (B), in (14)], is appreciably less than the distance registered in the column 

 of Law; Mars, like Uranus [see 5 of (43)], having seemingly /aZZew w; though 

 not, like Uranus, influenced, to a proportionate extent, by a large planet interior 

 to itself; yet the acquisition of sufiicient material fi-om the interior half-planetary 

 mass, with the inferior velocity of revolution appertaining to that mass, would pro- 

 duce just such an efi"ect.^ 



And the Earth-Venus mass, while it endured (if at all), would have had a periodic 

 time iths of that of Mars; and might, with the other influences in question, con- 

 tribute to the very considerable eccentricity of the orbit of Mars ; — on which, how- 

 ever, it does not seem to be justifiable to insist. 



(66) In the System of Saturn there are withal vacuities, (64), in the series of satel- 

 lites, under the conditions already specified in the other cases. Thus, in the large 

 interval from Japetus to Titan, if the places for intei'polated terms as indicated in 

 Table (C), in (18), be compared with those which would be due to satellites with 

 periodic times commensurable with the periodic time of Japetus, or with that of 

 Titan, we shall have the following results: — 



' Then, among things gupposable, but not as yet fortified by groups of coincidences, and which 

 cannot now be used in the way of induction, are these: If either of tlie half-planets were after all 

 formed, the oblateness of the nebulous material must have been so great that it might be questioned 

 whether of the two possible forms of a rotating spheroid of equilibrium — the density and the time of 

 rotation being given — the one usually differing but little from a sphere, the other, with the equatorial 

 diameter enormous in comparison with the axis, the latter might not be the form of the spheroid here 

 produced; it being such as the ring of Saturn might become if the body of the planet were removed, 

 and the ring filled up so as to be imperforate. Such a form would be eminently unstable ; and if it 

 were broken up, the fragments would all be small; as the asteroids indeed are. 



Then two such half-planets (with orbits, as has been seen, very eccentric) might all the more 

 readily have realized the ingenious conjecture advanced by Prof. Vaughan at the meeting of the 

 American Association for the Advancement of Science, in 1857; viz. that the asteroids were the 

 fragments resulting from the collision of two planetary bodies, in that region of the solar system ; 

 thus presenting a new phase of the hypothesis of Olbers. 



In the same category, as to not furnishing any induction as yet, may be included the fact that 

 the orbit of Halley's (retrograde) comet very nearly (now) intersects that of Phocea. 



' For additional proof of a half-planetary arrangement in the Asteroid region, see Article (108). 



