STATEMENT AND EXPOSITION OF ^ 



bbth. An application of the criterion of the ring-like form as stated in Con- 

 sistency 54^A, was, as far as might be, made use of [(60), (61), and (62)] in 

 determining as to whether it would be preferable to attribute to the asteroid- 

 mass (in the progress of its development) at any period, a whole-planet or a 

 half-planet arrangement; without the assertion that either is, beyond contro- 

 versy, supposable. 



In favor of the supposition of a lialf-planet arrangement, we had : — 



(a) That we do not find the equation here in question justified when a com- 

 parison is instituted between the whole-planet arrangement and Mars ; but, 

 with an appropriate distribution of the mass for a half-planet arrangement we 

 find, (60), a close approximation to the fulfilment of the equation in question. 



(6) This might seem to have the less weight, were it not also true that the 

 limit of equal attraction between the exterior half-asteroid mass and Jupiter, 

 (60), is 3.35790, and that between the interior half-asteroid mass and Mars, 

 is 2.14438; which limits very well mark the range of the mean distances of 

 the known asteroids; and, (61), the respective distances 3.34083 and 2.47748 

 of the exterior and interior half-asteroid masses approximate to the aphelion 

 and perihelion distances of several of the existing asteroids ; so that the case 

 in that respect may possibly resemble that of Mercury, commented on in (50). 



(c) Other circumstances discussed in (65), and referred to in Consistencies 

 31si and 45^7i, seem to indicate that (with the wide range and great eccentricity 

 of the asteroid-orbits) Mars may have acquired material of slower motion; 

 which caused that planet {p>erceptihly) to fall in. Such is the look, when Fact 

 and Law in Table (B) in (14) are compared. 



[Tlais is again alluded to here because of its present connexion with the 

 other considerations; though formally noticed in Consistency 45^7i.] 



(fZ) Though we may not attribute too much weight to our results when the 

 data are imperfect — yet, in this connexion, we find that the formula derived 

 from Kirkwood's Analogy, which, (107), signally fails (for reasons assigned) 

 to give us the length of the sidereal day of Uranus, yet, (108), .approximates 

 to a true result in the case of Mars, referred on the one side to the Earth and 

 on the other to the interior half-asteroid mass. 



bQth. In view of the secular variations of the planetary orbits, we have exhibited 

 in (99) the close approximation to coincidence of the planes of those orbits in very 

 ancient times. 



In (99) we make the suggestion that the mean inclination of the sun's equator 

 (of nearly 5°) to these may have arisen from the fact that the acquisition of mate- 

 rial of a planet from the extra-equatorial regions of the sun's nebulous atmosphere, 

 may have been mainly from one side ; the changes in the two half-spheroids not 

 being simidtaneous. 



But this is a region for speculation in which our sources of information are 

 very restricted. [Not quite discordant with it, however, is the fact mentioned in 

 (99), and its Note (5), that the great planetary masses of Table (F)'[in (45)] are 

 alternately white and yellow or ruddy.] 



