204 Prof. P. E. Chase on ^Ethereal Nodes. 



vortices. All assumptions as to the nature of ultimate physical 

 force are now, and perhaps always will be, mere assumptions. 

 Still, like geometrical diagrams, they may help to fix the mind 

 upon ultimate physical resultants, and thus serve a useful 

 purpose. 



The velocity of rotation varies as the square root of the velo- 

 city of gravitating fall. Therefore, if the velocity of planetary 

 revolution (V gi-) at Sun's equatorial surface be taken to repre- 

 sent the velocity of aethereal rotation at the same point, the 

 present aethereal atmospheric limit, at which the equatorial 

 velocity of rotation would be equal to that of the aethereal un- 

 dulations which drive particles towards centres of inertia, is 

 near the outer limit of the asteroidal belt (at \/ light-modulus 

 = 688*3 solar radii =3*204 mean vector-radii of Earth). The 

 mean proportional between Earth's mean distance and Saturn's 

 secular aphelion is 3*216 (1) 



We have found* that the velocity at the aethereal atmo- 

 spheric limit (the velocity of light) is the limiting radial velo- 

 city at the point of equilibrium between the velocity of com- 

 plete dissociation and the velocity of incipient aggregation. 

 The limiting tangential velocity, at the point of equilibrium 

 between complete aggregation and incipient dissociation, is 



therefore f - of the velocity of light, or the velocity of aethereal 



rotation at 219*09 solar radii, Earth's mean distance being 

 214*86 (2) 



We have also found J that Jupiter, the largest extra-aste- 

 roidal, and Earth, the largest intra-asteroidal planet, are con- 

 nected by a common limiting radial velocity, the indications 

 pointing to nucleal or rotating influences in the case of Earth, 

 and to atmospheric or orbital influences in the case of Jupiter. 

 Circular-orbital velocity varies as gK The relations of g to 

 \/M (1), and of Earth's position to the unit of solar aggrega- 

 tion (2), lend importance to the approximate equality between 



log (n/M)* = -709444 and log rad. ,ec. (^^-©) = *716237. (3) 



Alexander showed § that Jupiter and Saturn are so related 

 as to suggest a possible early mutual participation in a common 

 nucleal vis viva, as if they had been formed, by interior and 

 exterior condensation, from the same nebulous belt. I have 

 shown || that the atmospheric radius varies as the f power of 



* " Correlations of Central Force," Phil. Mag. September 1876, t), i. 



t Ibid. £. X Ibid. X. 



§ Smithsonian Contributions, 280, p. 38. 



|| Correlations, k, v. The present value of modulus in solar radii is 

 given in v. 



