1880.] 



433 



[Chase. 



represents the perihelion, and Neptune (30.034) represents the aphelion, 

 Jupiter's mean aphelion (5.4274) was central. 



The centre of reciprocal rupture (Neptune's secular aphelion = 30.47), 



the paraboloidal centre (Jupiter's secular aphelion = 5.52), and the centre 



of the dense belt (Earth =1), are connected by the geometrical proportion 



1 :5.52 : : 5.52 : 30.47.... (11.) 



The masses at the centres of rotary inertia (Saturn), and of early nebu- 

 losity (Jupiter,, are proportioned to their respective gravitating tendencies 

 towards the nucleal centre (Sun), or inversely proportioned to the squares 

 of their vector-radii, so that their primitive moments of rotary inertia were 

 equal. , 



Pips' = PePe 

 5.2028Vo 

 1047.88 



l !± = 3522.3 

 Pe 



p 6 X 9.5388' 



(12.) 



Bessel's value is 3501.6, so that the theoretical mass is about .006 too 

 small. This approximation, which was first pointed out by Professor 

 Stephen Alexander, convinced me that all the cosmical masses must be 

 determined by ascertainable laws, and thus led me to the results which are 

 embodied in the present and previous communications. 



The ratio between the masses at the centre of rotary inertia (Saturn), 

 and at the centre of greatest condensation (Earth), appears to have been 

 determined by Jupiter's perihelion influence and by centrifugal force, since 

 the masses vary nearly inversely as their gravitating tendencies towards 

 the Sun, or directly as the squares of their vector radii. 



PePa 

 Pa 



Po 



Pv 



3522.3 X 1.019256 



= », X 9.538S 2 



Po 



.(13.) 



£! = 326,661 

 Pa 



The ratio between the masses at the nucleal centre (Sun), and at the 

 centre of primitive nebulosity (Jupiter), combines the projectile, the cen- 

 trifugal, and the square of the centripetal ratios, thus illustrating the ther- 

 modynamic law that equal quantities of heat correspond to equal increments 

 of vis viva in simple gases. 



Pi 

 Po 

 Ps 



(PAX x P L== (Ve Y (Pe\ 



— ■ X 



*1 



9.5388 6 X 1.019256 



• (14.) 



5.2028 4 



The centrifugal ratios between Saturn and Earth (13), and the centripetal 

 ratios between Saturn and Jupiter (12), are further illustrated by the 



PROC. AMER. PHILOS. SOC. XVIII. 105. 3D. PRINTED FEB. 28, 1880. 



