THE BEARING OF MOLECULAR ACTIVITY 

 ON SPONTANEOUS FISSION IN GASEOUS SPHEROIDS. 



It is a familiar view that a rotating spheroid of gas may, by cooling and 

 shrinking, so far accelerate its rate of rotation as to cause its own sepa- 

 ration into two or more parts. The resulting parts are assigned various 

 relative values, and the separated masses are given different forms, ranging 

 from fragments and rings to subequal masses. This view of possible self- 

 partition has found expression in various cosmogonic conceptions from the 

 nebular hypothesis to the formation of binary stars. 



To consider the bearings of molecular activity in a representative case, 

 let a spheroid of gas be chosen whose mass is comparable with that of the 

 solar system and whose volume is such as may be hypothetically assigned 

 it. Let its rate of rotation at the outset be such that the value of gravita- 

 tion at the equatorial surface is greater than the centrifugal component of 

 rotation. Let cooling follow, in consequence of which the rate of rotation 

 will be progressively accelerated. Let it be assumed — as has usually been 

 done — that the rate of rotation would at length reach such a velocity that 

 separation in some form would take place regardless of any question as to 

 the manner of its realization. Our question relates to the effect of mo- 

 lecular activity on the transition from an undivided spheroid to a spheroid 

 divided in some way, whether by massive fission, into larger or smaller 

 fractions, or by individual molecules. 



In a body whose molecules are bound together into a coherent mass, 

 such parts as may be affected by like general stresses are properly treated 

 as units, within the limits of cohesion, but in a body whose molecules possess 

 all degrees of freedom, and which act with complete individuality, the treat- 

 ment may with special appropriateness be based on the molecule as the 

 unit. Molecular action in a gaseous spheroid consists of encounters or 

 quasi-encounters, and of rebounds or quasi-rebounds along free paths be- 

 tween the encounters. Within the mass, the excursions and encounters of 

 the molecules give rise to an effect equivalent to viscosity which influences 

 the movement of one part of the gaseous mass upon another part, and may 

 perhaps have given rise to an impression of coherence; but on the outer 

 border of the mass — the critical portion in this case — this effect becomes a 

 vanishing quantity, and individuality of action is dominant. 



According to the laws of gaseous distribution, the density of a gaseous 

 spheroid, when controlled solely by its own gravitation, declines from a 

 maximum at the center progressively toward the surface, where the limit 

 of gaseous tenuity is reached and an ultra-gaseous state supervenes. The 

 transition from the gaseous to the ultra-gaseous state is the critical factor 

 in the case, since it is at the extreme surface of the gaseous mass that the 

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