316 Prof. P. E. Chase on the Equilibrating 



gation is 1 :ir*. While I have questioned the propriety of 

 accepting the nebular hypothesis in the sense in which it is 

 commonly understood, 1 have no hesitation in yielding it the 

 qualified acceptance proposed by Herschel f, and in recognizing 

 its value for representing the results of tendencies to equili- 

 brium between centripetal and centrifugal forces. 



The position of Saturn at the mean centre of inertia of the 

 solar system, its low density, and its nebulous rings, would 

 seem likely, a priori, to furnish indications of important rela- 

 tionships between equilibrating forces. Such indications are 

 actually found, both in planetary masses and in planetary posi- 

 tions. For if we examine the masses of the supraasteroidal 

 planets, we find the following accordances : — 



1. Neptune is to Saturn, as the time of describing radius, 

 indirect fall to the centre, is to the time of circular orbital re- 

 volution, or as 1 : s/32. 



2. Neptune and Saturn are in inverse ratio to their times of 

 orbital revolution. They would therefore have equal moments 

 of inertia, near their lower nebular or nucleal radii J. 



3. Uranus is to Saturn, as the time of describing radius, in 

 a circular orbit, is to the time of orbital revolution, or as 1 : 27r. 



4. Uranus and Saturn are in inverse ratio to the square 

 roots of the times of rotation of Jovian nuclei, the radii of 

 which correspond with their respective primitive Jovicentric 

 vector radii § , or inversely as the velocities of the nucleal rota- 

 tions. They would therefore have equal momenta, with re- 

 ference to Jupiter, in the primitive nucleal arrangement. 



5. Jupiter and Saturn are in the inverse ratio to the times 

 of nucleal rotation for nucleal radii corresponding to their 

 respective vector radii. 



6. Consequently Jupiter and Saturn had equal moments of 

 inertia, if they were once parts of the same nebulous belt ||. 



7. Jupiter is to the aggregate planetary mass, as circular 

 orbital velocity is to parabolic perihelion velocity, or as 1 : >/2. 



8. If the aggregate planetary mass were collected at Jupi- 

 ter's linear centre of oscillation, the centre of gravity of the 

 system would be at Sun's surface. 



9. Jupiter and the residual supraasteroidal mass are so 



* Phil. Mag. [IV.] vol. 1. p. 251. 



t Outlines of Astronomy, Sect. 871. 



% The upper nebular or vector radii vary as the f powers of the orbital 

 times ; the lower nebular or nucleal radii, as the \ powers of the times. 



§ See Proc. Amer. Phil. Soc. Sept. 17, 1875. 



|| When I first announced this relation (Proc. Amer. Phil. Soc. vol. viii. 

 p. 141) I was not aware that it had been communicated to the American 

 Association by Professor Stephen Alexander in 1857. See his ' Statement 

 and Exposition ' (Smithsonian Contributions, 280), p. 38. 



