1881.] ^^'"^ [Chase. 



- times as great as velocity of rotation at the same limit. This leaves r: — 

 1 units of Earth's subsident rotating velocity to he converted into orbital 

 ■vis viva. Taking Earth's mass and semi-axis major as the units of mass 

 and distance, the foregoing relative theoretical values of nodal mass yield 

 the following comparative results : — 



Orbital Vis Viva = Mass h- Rad. Vect. • Theoretical Vis Viva. 



Earth 1 



Venus (331668-^ 427630) 



1 =1. j 1. 



.72333 = 1.0723 (;r — l)-- 2 = 1.0708 



Mars (331668 -^ 3101613) -- 1.52369 = .0702 (tt — 3j -- 2 =r .0708 



2.1425' TT — 1 2,1416 J 



(26) 



The influences of vis viva which are represented by the two outer plan- 

 ets, (11) (13), are somewhat more intricate, but no less interesting than 

 those of their companions. Orbital velocity, in the path of any given 

 planet, varies inversely as radius vector, following the same law as varia- 

 tions of rotating velocity in an expanding or contracting nebula, and as 

 variations of orbital vis viva in revolving particles at diflFerent distances 

 from a controlling centre. Hence there are tendencies to maximum and 

 mean accelerations and retardations at secular and mean apsides, which 

 are shown in the amounts of nodal planetary aggregation that are required 

 to maintain the cyclical equilibrium of orbital vis viva. The ratio of ISTep- 

 tune's vis viva to the mass at the chief centre of condensation. Earth, is 

 determined by cardinal nodes of Neptune, Uranus and Earth ; the like 

 ratio of the vis viva of Uranus, by cardinal nodes of Uranus, Jupiter and 

 Eailh. Earth's nodes are those of incipient subsidence and rupture at the 

 centre of density, secular aphelion and perihelion ; the node of Uranus 

 "which is influential upon Neptune is that of incipient subsidence ; the 

 three other nodes are of mean subsidence or rupture. Earth's secular 

 aphelion has modified the aphelion i3lanet, Avhile its secular perihelion 

 has modified the perihelion planet of the outer two-planet belt. 



Atomic phyllotaxy, times and acquii'ed velocities of subsidence, orbital 

 velocities resulting from subsident vis viva, and the relations of density 

 to distance from a controlling centre in an elastic medium, are all illus- 

 trated by the exact equality, (21) (23) :— 



(t, -^ t,y'^ = P.-^Po (27) 



The order of importance of the equilibrating manifestations of cosmical 

 vis viva in the solar system, seems to be the following : — 



1. The relation of Sun's mass to mass at principal centre of density. 

 Earth, which satisfies necessary tendencies to subsidence, oscillation, and 

 orbital revolution (22). 



2. The combined orbital vis viva at the chief centre of densitj^ and at the 

 centre of primitive nebulosity (1). 



3. The incipient tendency to rupture, between the chief centres of nucle- 

 ation and of nebulosity. Sun and Jupiter (2). 



