BEARING OF MOLECULAR ACTIVITY ON FISSION. 165 



a r evolutional system of molecules dynamically independent of the spheroid, 

 except that they act as minute satellites. 



In a stationary spheroid the rebounds that give rise to revolutional 

 courses are as likely to take one direction as another, and if the mass of the 

 spheroid be great, the number of molecules which will acquire revolution 

 from molecular activity alone may be neglected in this discussion. 



But in a spheroid in a state of rapid rotation, especially a spheroid 

 approaching the critical stage of centrifugal separation, the molecules shot 

 outwards in the direction of rotation will start with the sum of the common 

 velocity of rotation and the individual velocities acquired from the last 

 encounter, while the molecules shot in a direction opposite to the rotation 

 will have only the difference between the common velocity of rotation and 

 the velocity acquired from the last encounter, the meridional component 

 in each case being neglected as immaterial here. It follows from this that 

 when the velocity of rotation is high, the molecules starting from encoun- 

 ters in the direction of the spheroid's rotation will much more largely pass 

 into orbital paths than molecules starting in the opposite direction. 



In a spheroid having the mass of the solar system and a radius equal to 

 the radius of Neptune's orbit, the equatorial velocity required for separa- 

 tion by mass is above 5 kilometers per second, while the average molecular 

 velocity of all known molecules, at a temperature of 2000° C. and standard 

 terrestrial pressure, falls below this. The average molecular velocity of 

 most known substances falls much below this even at 4000° C. It seems 

 clear therefore that, for most of the known molecules, the effect of molecu- 

 lar velocity directed backward is merely to destroy a part of their rotational 

 speed, and that they still move forward relative to the center of the sphe- 

 roid. With a spheroid having the solar mass and a radius equal to the dis- 

 tance of the earth from the sun, and hence a separation-speed of nearly 30 

 kilometers per second, only a very small fraction of the molecules could 

 acquire velocities sufficient to neutralize their rotational velocities at the 

 critical stage of separation. The number of molecules that could acquire 

 the 60 kilometers per second required to neutralize their rotational veloci- 

 ties and add sufficient velocity to give them an orbital course in a retro- 

 grade direction must obviously be negligibly small in a case of this kind. 

 Practically all molecules must be regarded as having forward courses with 

 velocities which are either enhanced by being shot forward or retarded by 

 being shot backward. 



The velocity of centrifugal separation is practically identical with the 

 velocity of circular revolution about the spheroid in a minimum orbit. 

 Larger orbits involve lower velocities but require additional potential en- 

 ergy and moment of momentum. When the rate of rotation of the spheroid 

 is very near, or essentially at, the critical stage of centrifugal separation, a 

 slight addition to the velocity of an outer molecule in a forward direction, 

 arising from molecular interaction, will give to it a velocity greater than 

 that required for the minimum circular revolution; and before the critical 

 state has been actually reached, all molecules on the equatorial periphery 

 which receive forward impulses of any appreciable amount will have more 

 than the requisite velocity for minimum circular revolution. If all mole- 



