CERTAIN HARMONIES OF THE SOLAR SYSTEM. 33 



term, after the first, is -^.j+ of that which immediately precedes it; instead of 

 -| 4;, which is the whole planet ratio in the existing planetary system.^ 



Now, it is especially to be again observed, that tlie 2d term of the series in this 

 Table, in the way in which it is here obtained, supposes, and it depends upon the 

 supposition, that the material of the missing half-planet ^i passed over and was 

 combined ivith the other portion of the Saturn-forming mass, to, thus, construct the 

 existing planet Saturn; and it is, (44), by supposing that process reversed — restor- 

 ing Si to its place — and then combining in the way already indicated, (44), that the 

 2d term of the Table is obtained for the column of Fact, iind can, consistently and 

 accurately, occupy its place in the series;" so that this llth consistency, supporting 

 the hypothesis of the disappearance of the missing planet, in consequence of its 

 mass having been drawn inward and combined with the Saturn-forming mass, has 

 even more extended relations than the others. 



Having, then, as far as may be, answered the question, (41), What lias become 

 of the missi7ig mass, it may next be well to consider what more we may be taught 

 by certain other relations exhibited in Table (F). 



3Iass of the Asteroids. 



(46) With the term ['S(A)], [at the centre of gyration of Mars and the Asteroid 

 mass (A), as found in Table (F), in (45)], and also with the mass of Mars takeii 

 as imity, and the mean distances, from the sun, of Mars and (A), respectively, in 

 Table (B), in (14), we may determine m', the Asteroid-mass which will be required 

 to justify the term [% (A)] in Table (F) ; the case being similar to that of the interior 

 half-planet g* in (41); except that the value of m', the exterior mass, is here required 

 instead of m. 



Substituting in the equation, in (41), the values here indicated, Ave shall find m', 

 the Asteroid-mass, = 0.58929 of the mass of Mars. 



This, with the mass of Mars, as in Table (A), in (3), [= ^-rroo 90 oJ' '^^^^^ make 

 the mass of the asteroids = -5 is-f-jy-f of the mass of the sun. 



(47) Now M. Le Verrier, in the Comptes Bendus, tome Ixv, p. 880 (Nov. 25, 



' As R^ here approximates to r| [r being the ratio for the whole-planet terms in Table (B)], 

 ijj will also, incidentally, express very nearly the ratio of the periodic times due to the whole-planet 

 distances. Accordingly we find that the ratio of the periodic time of Saturn to that of Jupiter = 

 2.4697; while the nearly corresponding value of R^, as stated in (45), is, as near as may be, 2.4089. 



° Not only so, but if leaving out the hypothesis here in question, we attempt to form the 2d term 

 of the series with the Saturn-mass as it exists, we shall, of course, fail ; since the placing of so large 

 a portion of the same masses so much farther inward, will, at once, displace the centre of gyration 

 in the same direction, and so make the term too small. And the same effect would even be manifest, 

 if we might suppose a group of asteroids to exist in this region ; but that, (42), is inadmissible. 



On the first of these two suppositions, the centre of gyration would be displaced quite the whole 

 of the Earth's distance from the Sun [being at 11.35 instead of 12.40] ; and if the second supposition 

 were admissible, the displacement would be nearly ^ that distance [being at 11.96 instead of 12.40]. 



5 December, 1874:. 



