Prof. P. E. Chase 07i Momentum and Vis viva. 293 

 orbital revolution at r, and also to the orbital vis vira g-ained by 



V 



contraction from r to — . The internal motions and collisions 



of the particles of the belt would favour a condensation of th(». 

 densest and comparatively inelastic materials, until the whole 



had acc[uired the mean orbital vis viva, ~ — -^ — = '-^-, which 



is the normal orbital vis viva at the nodes of aggregating col- 



lision, ^. The following Table exhibits the double tendency, 



to nebular rupture and to nebular aggregation, starting 

 from the point which would account for the orbital velocity of 

 Neptune. The approximation of ^^ B " to the planetary dis- 

 tance which would satisfy Bode's law, and the indications of 

 Neptunian aggregation during direct fall towards the centre, 

 lend new confirmation to the views which I have already ex- 

 pressed in regard to the rationale of Bode's law and the rela- 

 tive masses of the two outer planets : — 



Kupturing-nodes, Secondary nodes. 



Planets. 



2 X \l> s. a. 60-939 40-626 " B " = 38*8 



T s. a. 30-470 20-313 © s. a. =20'68 



1 „ „ 15-235 10-157 h s.a. =10-34 



i „ „ 7-617 5-078 n s. p. =-- 4-89 



The following Tables exhibit some of the modifying influ 



ences of other simple nodes: — 



^S 1-016 © 1-000 



H -702 



5 s. a. -774 



§© -667 2 s. p. -072 



IXf^ -077 



P s. p. -672 



a 5 -482 $ s. a. -477 



i© s. p. -46(3 



9 s. a. -477 



4 ^ s. a. -318 ^ s. p. -207 



I©s.p. •311 



^ s. p. -207 



In the intra-asteroidal belt and ellipse, which are bounded 

 by c^ sec. aph. and $ sec. per., we find 



Middle of belt 1-017 



,, ellipse ... -719 



Earth I'OOO 



Yenus -723. 



Jupiter is similarly situated in reference to the Neptune- 



Uranian and the Uranus-Saturnian ellipses : — 



Middle of "HT s. a. ^ s. a. 4-805 

 \l> s. p. e.) '^5-207 



Middle of© h 4-822 



„ Q k s. p. o-22o 

 S s. a. h 5-570 



h s.p. 4-886 

 h 5-203 



h s. a. 5-519 



„ ^ s. a. § 5-643 



Saturn is similarly situated in reference to the Neptune 

 Saturnian and Sun- Uranian ellipses: — 



Mid. O 6 s. p. 8-844 

 „ O^ 9-092 



„ O 5 8. a, 10-340 



Mid. h 8. a. "^ 3. p. 0-028 

 „ h s. p. '^.[> s. p. 10-432 



h s. p. 8-734 

 h 0%539 



h s. a. 10-343 



