70 STATEMENT AND EXPOSITION or 



besides manifest that what would be the ascending node of the planetary orbit 

 when, in such a case, the acquisition was from the one half-spheroid, would be the 

 descending node in the instance of the other. 



And with respect to the matter here brought into question, as well as in other 

 aspects, though without deciding that they have any significant connexion; we 

 may consider some of the relations developed by Mr. Stockwell, and exhibited in 

 his Memoir ; such as — 



" The mean motion of Jupiter'' s node on the invariable plane is exactly equal to 

 that of Saturn, and tlie mean longitudes of tJiose nodes differ hy exactly 180°." 



The latter portion of that description may have some interest in this connexion. 



Mr. Stockwell states, withal, that " The mean angular distance between the peri- 

 helia of Jupiter and Uranus is exactly 180°." 



These and other relations connected with them, are shown by Mr. Stockwell to 

 be eminently harmonious and conservative; and then, after stating that he had 

 prepared separate solutions corresponding to several increments of the Earth's 

 assumed mass ; and that a comparison of the values which the different solutions 

 give for the superior eccentricity of the Earth's orbit " has suggested the inquiry 

 whether there may not be some unknown physical relation between the masses and 

 mean distances of the different planets."^ 



After having withal arrived at the conclusion that " a system of bodies moving in 

 very eccentric orbits is" . . . . " one of manifest instability ;" he says, " and if it can also 

 be shown that a system of bodies moving in circular orbits is one of unstable equi- 

 librium, it would seem that between the two supposed conditions, a system might 

 exist which should possess a greater degree of stability than either," and then 

 indicates a superlatively grand problem, viz., that " The idea is thus suggested of 

 the existence of a system of bodies in which the masses of the diff"erent bodies are 

 so adjusted to their mean distances as to insure to the system a greater degree 

 of permanence than would be possible by any other distribution of masses." He 

 adds : " The mathematical expression of a criterion for such distribution of masses 

 has not yet been fully developed ; and the preceding illustrations have been intro- 

 duced here, more for the purpose of calling the attention of mathematicians and 

 astronomers to this interesting problem tlian for any certain light we have yet been 

 able to obtain in regard to the solution."'^ 



in both respects" [Sir J. Herschel's Outlines, etc., (393)]. See, also, the enumeratio\i and classifi- 

 cation of solar spots, founded upon Mr. Carrington's observations, as reported by M. Faye (Comptes 

 Bendus, tome Ixxvi, p. 393). 



The white planets Jupiter and Venus seem to show in their atmospheres, now, traces of great 

 activity, even such as ould be consistent vrith a high temperature. As respects Jupiter, see again 

 Note 2 to (69). 



' See pp. xiv, xvi, and xvii of the Introduction to the Memoir, respectively. 



As to the existence of such a relation and also as to its connexion with the times of rotation of 

 the several planets — see, again, last Note to (44); also Article (109), and Consistency %\st of the 

 Summation in (110). 



^ See pp xiv, xvi, and xviii of the Introduction to the Memoir. 



