Mr. P. E. Chase on the Cosmical Activity of Light. 251 



v 1 

 3. The velocity of gravitating fall at the same point, =— » 



1 r 



varying as ^ . v s . 



The limiting velocity (v ), towards which these three veloci- 

 ties all tend, is the velocity of light. 



If the theory of Boscovich is true, or if matter is infinitely 

 divisible, or if all the internal resistances, of heat-volume, mass- 

 inertia, and every other kind could be dissipated, so as to allow 

 an indefinite contraction of r, the limits of equality may be found 

 either tangentially or radially. 



When the tangential v^v^ we reach the limit between total 

 aggregation and commencing dissociation (/,). If further 

 shrinkage takes place, the rotating particles gradually assume 

 orbits of increasing excentricity. 



When the radial velocity acquired by fall from an infinite dis- 

 tance, \/2 x i?j, becomes equal to the mean velocity of radial 



oscillation synchronous with rotation l-v 2 ), we reach the limit 



between total dissociation and commencing aggregation (/ 2 ). 



The upper limit (/ 2 ) would be reached by all the subordinate 

 planets before they had attained the lower limit (/J for the prin- 

 cipal planets of their respective belts. 



The upper limit would be reached by the principal planets, 

 Earth and Jupiter, when they had attained the present limiting 

 velocity of circular revolution at Sun's equator. 



The limit of solar aggregation [I { ) is - the velocity of light. 



The limit of solar dissociation (/ 2 ) is the velocity of light. 



M 



The time of revolution at -^ (M being the solar modulus of light) 



is equivalent to the time of rotation for a sun expanded to Jupi- 

 ter's centre of oscillation (f of Jupiter's radius vector). 



The ratio of retarded velocity in solar rotation ( -* I = — 



-f- Jupiter's radius vector. 



The limit of planetary dissociation (t?, at Sun's equator) would 

 carry a particle round the sun while a ray of light would tra- 

 verse the linear pendulum of Sun's outermost planet (f Neptune's 

 radius vector). 



The angular velocity of revolution at twice Neptune's distance 

 = angular velocity of rotation due to a solar radius extending 

 to Mercury's mean distance — a coincidence suggesting asteroidal 

 or planetary masses, both beyond Neptune and below Mercury. 

 Inasmuch as the linear velocity communicated by infinite fall to 

 twice Neptune's distance equals the velocity of circular revolu- 

 tion at Neptune, this accordance seems to have fixed the prin- 



