Chase.] " [March 19, 



1. If the velocity is constant, tlie radius of rotation or revolution must be 

 proportioned to the time. 



2. If radii, which were originally establislied by a constant velocity, are 

 converted into radii of free revolution under equivalent central forces, the 

 times of revolution must be proportioned to the f power of the radii. 



3. If radii of synchronous revolution and axial rotation are due to the 

 action of a primitive constant wave-velocity, while nucleal radii are due 

 to -the collision of particles moving with parabolic velocity, the former 

 velocity would be communicated in the time of a half-rotation, while the 



latter would be communicated in of the same tune. 



TT 



4. Let us suppose that the ratio of the solar year to the terrestrial day 

 originated in the constant velocity (1) of light, which is still represented 



by the equation of solar half rotation ( -^ = ^/l ); that the time-radii (^*t) 



were converted into radii of free revolution uuder equivalent central forces 

 (2) ; and that coi'responding nucleal radii (f,^^ were established by parabolic 

 collision (3). We should then have 



(j)' 



.Pi/ i/3 

 or, substituting the ratios which are represented by r^ and p^, 



S_ 3 



/I year\2 /Earth s semi-axis major\^ • ■ tt • '~2> 

 Vl. day / \ Sun's semi -diameter / 

 The sidereal year is composed of the original nebular sidereal rotation and 

 the 365.25636 additional sidereal rotations -which are due to terrestrial con- 

 densation. Making these substitutions, 



(865.25636)'2" : ic^" : : tt : ^y \ ^ 

 a; = 214.5365 j 



Among the obvious nodal influences of distance and velocity which may 

 be reasonably supposed to have modified the kinetic undulations between 

 the centres of density and of nucleation, the following may be specified : 



1. The velocity of light,V., or the projectile velocity which is equal to 



/ 



gt 

 the sum of Sun's gravitating equatorial reactions during a half rotation, -^ ' 



2. Sun's limiting velocity of revolution, Vq = V(l''> '' being the equa- 

 torial radius. 



3. Earth's limiting velocity of revolution, ®o = \,'gr, at the equatorial 

 surface. 



4. Earth's superficial equatorial velocity of rotation, v^. 



5. Earth's semi axis major, />„. 



6. Earth's diameter, 2r, or the major-axis of limiting synchronous linear, 

 elliptical and circular oscillation. 



7. Moon's semi-axis major, p^. 



