BEARING OF MOLECULAR ACTIVITY ON FISSION. 167 



table. Collisions in the rising parts of the curved courses take precedence 

 in time, and hence in probability, over collisions in the declining courses; 

 for if collision is realized in the first part of the course the molecule is likely 

 to lose its chance in the latter part by being either thrown back to the sphe- 

 roid by the first collision or else thrown outwards where collisions are less 

 imminent. In any case, the collisions probably result either in an earlier 

 return of the molecules to the spheroid, or in throwing them into new 

 paths, of the orbital type, which will bring them back to this point of last 

 collision and not to the spheroid. This point of collision lies above the sphe- 

 roid, and does not require the orbit to cut any part of the spheroid, though 

 it may do so in a portion of the cases. The predominant effect will appar- 

 ently be to drive the outer molecules into larger orbits and throw the inner 

 ones back to the spheroid. Apparently this will be a self-adjusting process, 

 so far as frequency and efficiency are concerned, for the number of molecular 

 flights per unit of time will be cumulative as the acceleration of rotation 

 approaches the critical stage when, as we have seen, any molecular incre- 

 ment forward will lead to quasi-orbital flight. This will increase the 

 contingencies of collision, and hence a cumulative number of molecules 

 will be driven into independent orbits. 



Now the most significant element in this process is the partition of mo- 

 ment of momentum that is involved. Each molecule that passes into a 

 free orbit necessarily takes with it more than a mean portion of moment of 

 momentum. Those molecules which make elliptical flights and return to 

 the spheroid without collision carry back whatever moment of momentum 

 they took out, but those thrown into permanent orbits retain, as a rule, 

 not only what they took out but also the additional moment of momentum 

 gained from the collisions which gave these free orbits. It follows that every 

 molecule that goes into a free orbit takes a disproportionate amount of the 

 moment of momentum of the spheroid and thus reduces its rotation, or else 

 retards its increase of rotation, to that extent. 



If the quantitative value of this loss of moment of momentum by the 

 spheroid could be compared with the increment of rotation assignable to 

 shrinkage, it would be possible to determine whether the spheroid could 

 ever, under these conditions, reach the critical stage requisite for the sep- 

 aration of any portion of its mass bodily. A mode by which a rigorous 

 demonstration can be reached has not yet been found, but, from the nature 

 of the case, I entertain, with others, the view that the separation must take 

 place molecule by molecule, and it seems to me inevitable that these mole- 

 cules must go into orbits each carrying an excess of moment of momentum 

 at the expense of the spheroid, and hence that the critical stage of exact bal- 

 ance between the centrifugal and centripetal factors of the spheroid is never 

 reached. If so, bodily separation is excluded by the conditions of the case. 



The conviction that such rotating gaseous spheroids must shed portions 

 of their matter molecule by molecule, if they do so at all, has long been 

 held by students of the subject, but I am not aware that the loss of moment 

 of momentum from the spheroid has been urged as a reason why the crit- 

 ical state prerequisite to bodily separation may not be attainable. 



