1876.J ^^^ [Chase 



These values likewise exhibit a close approximation to the perihelion 

 ratio |, between the companion planets of each pair, together with indica- 

 tions of nebular rupture between Saturn and Uranus, and of increasing con- 

 densation towards Neptune and Jupiter. The perihelion ratio of Neptune : 

 Jupiter = 1 : 3. 1 ; that of Uranus : Saturn := 1 : 3.2, or nearly that of a nodal 

 division, to the entire length, of a linear pendulum. The reversal in the 

 direction of condensation, between the central and the exterior belt, may 

 perhaps explain the retrograde satellite motions of Uranus and Neptune. 



4. If we compare the perihelion and the aphelion centres of gravity of 

 companion planets, we find that .6347 is near the centre of spherical gyration 



i\/A X 1.0019=: .6336) of 1.0019, and that .1681 is near the centre of 

 nebular rupture *(.1661) of .3323. 



3 



5. The time of revolution varying as r~, while the time of rotation with 



the velocity due to interior vis mva varies as r'^, the limiting radius of syn- 

 chronous rotation and revolution, for any given expanding or contracting 

 nucleus, is a mean proportional between the limiting radii of interior 

 and exterior nucleal rupture. I have shown that the gravitating impulses 

 are 4565 X (10)'^ per second, corresponding in frequency with the red rays 

 of light, and the modulus of light is 



365.256 X 86400 "j 2 



=F-^ ] = 473755 solar radii. If modulus were 



2 TT X 1/214.86 X 497.835 J 



3 



taken as the primitive radius of resisting Inertia, (r)^, Neptune's position 



would accord with the corresponding nucleal radius (r = 6077.2 solar radii), 



i 

 and Mercury's with the radius of internal rupture {r'^ = 77.96 solar radii) 



Saturn's place being fixed, as we have seen, by the centre of nucleal plane- 

 tary inertia, its mean aphelion radius appears to have influenced Neptune's 

 position, while Earth's secular aphelion exerted a like influence on Mer- 

 cury's position; for 1.04835 X 6077.2 = 6371, Neptunes secular perihelion 

 being 6359.5, a diflference of less than I of one per cent. ; 1.06774 X 77.96 = 

 83.24, Mercury's mean distance being 83.17, a difterence of about j^t of 

 one per cent, 



6. The mean proportional between these values of r'^ and ?■, as well as 

 between Sun's radius and modulus, is 688. 3 solar radii, or 3.203 times Earth's 

 mean radius vector, which is near the outer limit of the asteroidal belt. 

 This agrees very closely with the secular range of Uranus (2.99111), and the 

 relation is still closer to the ratio between the gravitating radii of Saturn 



♦Velocity at ]4 r = V'2gr. 



PROC. AMER. PHILOS, 80C, XVI. 97. X 



