Chase] UlU [Aug. 20, 



5. In studying the phenomena of exploding hydrogen and oxygen, in 

 order to determine the comparative reaction of Eartli and Sun upon the 

 disturbed inertia, and their consequent relative masses, it is necessary to 

 consider the "centres of explosive oscillation," at | and f of the total ex- 

 cursion of particles from either extremity. 



6. In all perpetual movements of mutual alternate approach and I'e- 

 gress, there is a double tendency towards centres of gravity and centres 

 of linear oscillation, due to the action of centripetal and centrifugal 

 equilibrating forces, analogous to the tendency in simple explosion, 



7. Consequently the ratios | and f, [(|)^ and 1-(|)-], are found largely 

 prevalent in planeto-taxis. 



8. Rotation and orbital revolution are due to the operation of the same 

 forces, rotation being merely revolution retarded by internal pressure. 



9. The velocity of rotation varying inversely as radius, while the velo- 

 city of revolution varies inversely as the square-root of radius, the two 

 velocities, in a cooling and shrinking mass, tend to approximate equality. 

 If matter were infinitely divisible, or if the theory of Boscovich were true, 

 they would finally become equal, and, if shrinkage still continued, the 

 preponderating centi-ifugal force of rotation would lead to disintegration. 



10. Whatever may be the ultimate constitution of matter, the internal 

 resistances of heat-volume, mass-inertia, and other interferences of known 

 and unknown forms, must be the same in the aggregate as if the theory 

 of Boscovich were true. Therefore, by finding the limits of equality in 

 accordance with that theory, we may find the limiting velocities of the 

 primitive force. 



11. Those limits may be studied tangentially, by comparing the equa- 

 torial velocity of rotation, with the velocity of circular revolution at the 

 same point (i/m*) 5 radially, bycomparing the velocity acquired through 

 fall from an infinite distance, (i/2 gr )> with the mean velocity of radial 

 oscillation due to rotation and synchronous with it i'^ of the velocity 

 of rotation]. At the points of equality, the former limit marks the 



boundary between complete aggregation and commencing dissociation ; 

 the latter, between complete dissociation and commencing aggregation. 



12. Calculating these limits for the principal bodies of the solar sys- 

 tem, we find that complete dissociation would take place in all the sub- 

 ordiuate planets before their rotation-speed had increased to the limiting 

 velocity of aggregation in Earth and Jupiter ; complete dissociation 

 would take place in Earth and Jupitei", when their rotation-speed had at- 

 tained the present limit of possible circular revolution, at the centre of 



gravity of Sun and Jupiter ; the limit of solar aggregation is _ of the 

 velocity of light ; the potential of solar attractive force would give the 

 velocity of light ; the limit of solar dissociation is the velocity of light ; 

 the limit of planetary dissociation would carry a particle around the Sun 

 while a ray of light was passing from the orbit of Uranus, through Sun, 



