36 STATEMENT AND EXPOSITION OF 



Tlien, at his mean distance (half-way between the two) his place is that of an 

 almost dovhle-planet, in the special arrangement in Table (Fj. 



Of these it may be said: — 



1. 



That these several peculiarities seem, at once, to he reconciled and explained 

 by the supposition that the condensing material (ring, or shell, etc.) which was in 

 position to have formed a whole planet at the aphelion distatwe, and another portion 

 of the condensing material (ring, or shell, etc.) which was in position to have 

 formed what we have termed an exterior half-planet, at the perihelion distance, 

 have been combined to form the existing planet; which, thus, is made up of a 

 whole-planet mass and a half-planet mass. 



2. 



But all this accounts for and explains in mode and in measure, the very great 

 ECCENTRICITY OF THE ORBIT OF MERCURY; his perihelion distance not extending beyond 

 the centre (or a point near the centre) of gyration of the half-planet mass (ring, or 

 shell, etc.) due there ; and his aphelion distance, reaching out to the centre of gyra- 

 tion, or near it, of the whole planet mass due there. 



Mass and Distance of a possible Planet interior to Me7-ciu'9/. 



(51) The position of the perihelion of Mercury has, (14), been shown to be that 

 due to an exterior half-planet. Hence the distance from tiie sun of the next planet 

 interior to Mercury may, most probably, be ascertained by dividing the term value 

 of Mercury's perihelion distance, in the colum of Law in Table (B), in (14), by 

 the value of rk , in accordance with Laiv 3d, in (10). 



The value of ri, for this region of the system, is 1.3733. 



Performing then the division thus indicated, we shall have the distance from the 

 sun of the planet interior to Mercury — 



5^ = 0.20836.1 



We may also ascertain the tohole-planet position next to that due to the aphelicm 

 of Mercury, by dividing the aphelion term in the column of Law in Table (B), in 

 (14), by the value of r, in accordance with Laiv 1st in (10). 



The value of r, for this region of the system, is 1.8736. Dividing the value of 

 the aphelion limit by that number, will give for the n-^iole-pkmet limit interior to 

 Mercury's aphelion distance, the value 0.24422 + . 



Thus, then, we shall have the following arrangement : — 



5 J (Whole planet limit) aph. distance .... 0.45758 



\ (Exterior ^ planet-limit) per. distance . . 0.28573 



^., I whole planet limit 0.24422 



t ///fenor half-planet 5i 0.20836 



' This is very accurately the distance required (by Kepler^s 3d Laiv) to justify the periodic time 

 of the so-called " planet Vulcan," as the same has recently been ascertained by Prof. Kirkwood, on 

 the hypothesis, that the appearances of certain solar spots were due to the transits of such a body. 



