Chase.] 



630 



[Sept. IT, 



According to the latest estim ates* the masses of the four exterior 

 I)laiiets, taking Sun as the unit, are 



Jupiter 0009543269 Uranus 0000454545 



Saturn 0002855837 Neptune 0000507614 



the aggregate being .0013361265. Tlie distribution of the aggregate, ac- 

 cording to the hypothesis here given, involved the following steps : — 

 1. The squai'e of the radius of spherical gyration being .4, in order that 

 mr^ may equal mjr^^ the masses must vary inversely as the square of 

 radius. This gives .0009543761 for Jupiter, and .0003817504 for Saturn, 

 Uranus, and Neptune. 2. Taking Saturn and Neptune as secondary 

 centres of rotation for the remaining mass, and taking a nodal division 

 midway between Saturn and Uranus, tlie Saturnian rotation-radius 

 = 7.1402 solar radii, the Neptune-Uranian radius = 21.1508, and the 

 masses varying inversely as radius, we obtain .0002854019 for Saturn and 

 ,0000963485 for Uranus and Neptune. 3. The equal moments of Neptune 

 and Saturn requiring that their masses should be inversely as the squares 



of their rotation-radii, Neptune = f ^'^•'^'^^L] ^x Saturn = .0000510257, 



^ L 49.0168 J 



leaving for Uranus .0000453228. The closeness of coincidence is shown 

 below : 



I published the second theoretical equality in the 13th Volume of the 

 Pi'oceedings of the American Philosophical Society (p. 141), without 

 knowing that it had ever been previously noticed, but I find, from Prof. 

 Alexander's recent Memoir, f that he announced it to the American Asso- 

 ciation, at its Montreal Meeting, in 1857. The other nine accordances 

 I think are entirely new. The last three introduce the following con- 

 siderations : 



1. If the aggregate planetary mass were at Jupiter's centre of linear 

 oscillation, the centre of gravity of the system would be at Sun's surface. 



* For authorities, see Alexander's " Statement and Exposition," p. 3. 

 tOp. cit., p. 38 



