200 Prof. P. E. Chase on the Correlations of Central Force. 



velocity of superficial equatorial rotation varying as - ; then 



v = \_v / ~] = \_r // ~] = nv / = n 2 v J/ =n\/fr — limit of tangential velo- 

 city, both of revolution and of rotation, under a reduction of sphe- 



r 

 roidal volume to an equatorial radius = -g. Under such reduc- 

 tion all the particles in the equatorial planes would have the 

 velocity of free revolution, or of perfect fluidity, provided the 

 sphere were homogeneous. 



77. If contraction were to go still further, the centrifugal 

 force of rotation would give the nucleal particles orbits of in- 

 creasing ellipticity. Those orbits would finally become linear, 

 leading to complete dissociation when the mean linear velocity 



2 



- [yjj~\ was sufficient to produce a constant motion with the pa- 

 rabolic perifocal velocity [>/2/r]. These velocities coincide at 



2r , nV 2 s/fr _ nir 

 ^- 2 when y^ X « ~V2 X ^ = n7rv /h thus 



showing that the limiting velocity between complete dissociation 

 and incipient aggregation is it x the limiting velocity between 

 complete aggregation and incipient dissociation (n*Sfr ; see J). 



6. Let t — time of describing J r in virtual approach to the 

 centre, under the action of a central force/, = time of descri- 

 bing r in circular revolution or motion under constant pres- 

 sure ; fr= s/fr ; irt = time of free semicircular oscillation ; 

 mrt = time of constrained semirotation ; nirft = nir */fr = 

 velocity acquired in the time of semirotation. Therefore 

 the velocity of any central impulses which are capable of 

 producing cosmical aggregation, free revolution, and nucleal 

 rotation = velocity produced by constant equatorial pressure 

 acting for a half-rotation. 



t. If the central force is solar gravity, the limiting velocity 

 (ft7r \//r) of uniform impulses which would account for solar 

 aggregation, solar rotation, and planetary revolution is the ve- 

 locity of light. For Earth's distance from Sun being 214*86 

 solar radii, the velocity of light is (214-86r-f-497-825) = *4316r 

 per sec. If we make this velocity = mr s/fr 7 and find the value of 

 s/fr= s/Jr = 2irr x 214-86-^(365-2564 x 86400) = -00062705 r 

 per sec, n = *431 6 -f- 7r\//r= 219*0894, and v„= s/fr-^n = 

 •0000028622 r per sec. The accordance of this value with other 

 estimates (/a) is as follows, the unit being r~ 10000000000: — 



Sporer. Nebular. Light. Scbwabe. 



29533 29192 28622 28511. 



