CERTAIN HARMONIES OP THE SOLAR SYSTEM. 43 



The first and last of these, toward one limit and the other, also indicate the 

 range of the mean distances of the asteroids better than the result in (49). [The 

 middle limit 2.94068 here given, is a little outside of the centre of gyration of the 

 two half-planet masses, which is at whole-planet distance (A) of Table B, =2.87831 

 — the more dense material being inward: a state of things of which there is a 

 distinct semblance, (19), in the previous example of Satu7-n's rings. In the case of 

 the Earth and Vertus, (39), the centre of gyration is without the neutral point, as 

 it ought to be, because of the superior density of the earth.] 



The exterior limit, 3.35790, at which the attraction of the outer mass and that 

 of Jupiter would seem to have been in equilibrio, is scarcely 0.017 (of the Earth's 

 mean distance) outside of the position due to the exterior half-planet.^ 



(61) The distances 3.34083 and 2.47748, respectively due to the exterior and 

 interior half-planets, themselves exhibit approximations to the aphelion and the 

 'perihelion distances of several of the existing asteriods ; insomuch that their case in 

 that respect resembles that of Mercury, already commented on in (50) : with the 

 marked difference, however, that while the orbit of Mercury is, indeed, limited in 

 its aphelion by a whole-planet distance, and in its perihelion by the succeeding 

 half-planet distance, the existing planet seems to have combined in itself the mate- 

 rial which would have appertained to both the whole and the half-planet. 



(62) The very small mass due to the exterior half-planet (0.4274 of the interior 

 ~half-planet, or 0.2518 of Mars) would itself suggest the probability that but few 



asteroids were to be looked for at a mean distance, near to the outer limit 3.35790 ; 

 and the progress of discovery, thus far, has justified such a conclusion. 



Special Relations of the Moments of {simultaneous) Botation {around the same 

 centre) of the tioo supposed Asteroid-masses and that of Mars, 



(63) The moments of (simultaneous) rotation of the two Asteroid-masses (Jialf- 

 planetary in position) and that of Mars have, respectively, the ratio of the following 

 representative numbers : — 



Exterior Asteroid-mass ...... 2.8108") 



Interior " " ....... 2.0tl2| ^'^«"' ^-^^O 



Mars 2.4679. 



Of Missing Terms, or, at least. Varieties in Planetary or Satellite Series, other than 

 those heretofore noticed; and the Explanation of the same. — A Resisting Medium. 



(64) As " the comet of Lexell" had its orbit tioice changed, as a special con- 

 sequence of its periodic time being very nearly | that of Jupiter, so that the 

 comet was for the second time brought very near to that disturbing planet after 

 only two revolutions ; so, also, it has been well argued that when the periodic time 



' So that, as has often been surmised, the o'ermastering attraction of Jupiter must (it would 

 seem) have interfered with the existence of the outer half-planet as such ; and this, by an action 

 not Tery unlike that of Saturn, (43), in preventing the continuance of anything like a half-planet 

 interior to Uranus. 



