CERTAIN HARMONIES OP THE SOLAR SYSTEM. 35 



4. The mass of Mars itself, deduced from the mutual action of it and those of 

 the other planets.] 



But the value of the same Asteroid-mass, as derived from M. Le Verrier's equation, 



depends on i of ten times the excess above 1 of i^ ). This value, then, 



^8 ■ 58' 



albeit that it wholly depends on ascertained facts for its data, is, nevertheless, very 

 sensitive to any, the smallest, change in the value of the solar parallax. 



[In a subsequent Memoir on the Masses of the Planets and the Parallax of the 

 Sun, in the Comptes Rendus, for July 22, 1872, M. Le Verrier, as the result of a 

 discussion of the secidar variations of the elements of the orbits of Mercury, Verms, 

 the Earth, Mars, and Jupiter, states that it is probable that the attraction of the 

 minor planets amounts, up to the present time to a quantity which may be 

 neglected.^] 



(49) The value of the Asteroid-mass, which we have thus obtained, is, as far as 

 may be, confirmed by yet another consistency. 



For with this value of the mass, at distance (A) in the column of Law in Table 

 (B), and other masses and distances in Tables (A) and (B), [(3) and (14)], we shall 

 find that the neutral point, or point of equal attraction of this same mass, is, on 

 the side of Jupiter, at the distance 3.165o9 from the sun. And the similar limit, 

 on the side of Mars, is at the distance from the sun = 2.13869. 



These numbers at once suggest the limits (thus far recognized) of the mean dis- 

 tances of the asteroids. 



The supposition of a half-planet arrangement of the material in the progress of 

 its early "abandonment" will, however, better provide for all this; as well as 

 exhibit yet other consistencies, as will be shown hereafter.^ 



Peculiar Edations of the Planet Mercury. 



(60) From Table (B) in (14) and Table (F) in (45), we find that the position 

 and relations of Mercury may be represented as follows: — 



Table (B). 



Limit or term j' (©9 ) 



Whole planet ratio, r < 



I Aphelion of Mercury ] 



i planet ratio, rl ^ d -7 7 • ^1^ i 



-^ ^ [ Perihelion of Mercury ) 



Tnhle (F). 

 [©9]) 



. (at mean dist.) Mekcury 



i2i=rl 



so that Mercury, when in aphelion, is in the position due to a whole-planet ; and 

 when in perihelion his distance is that due to a half plariet. 



' As quoted in the translation of W. T Lynn, B. A , in the Monthly Notices of (he Proceedings 

 of the Royal Astronomical Society, vol xxxii., No. 9, p. 323. 

 = "See Articles (RO^ and (108). 



