GEOLOGY. 311 



toward one of mutual adjustment and equilibrium. The present num- 

 ber of nebulae may thus represent an inheritance from the greater prev- 

 alence of conflicting action in the past. 



(c) Those who have expressed adverse views as to the adequate 

 frequency of colHsion and close approach to rejuvenate planetary 

 systems appear to have confined themselves to one phase of the prob- 

 lem, the statistical probabihty of approach when only velocity and 

 space are considered. The considerations that weighed most in the 

 formation of the theory of close approach^ have been largely neglected. 

 A theory is entitled to the benefit of its own postulates and is not 

 responsible for assignments that replace these. It is not believed 

 that the true frequency of approach can be determined, or even fairly 

 estimated, by dealing simply with inherited velocities under observed 

 conditions of distance and direction in one part of the galaxy; it is the 

 postulate of the theory that mutual attraction, as well as the several 

 types of spacial relations and motions in a normal star assemblage, 

 must enter into any estimate that is entitled to weight. If inherited 

 motions and space relations prevalent in this part of the galaxy alone 

 are considered, the hability of stars to close approach will doubtless be 

 essentially as urged, but if the mutual attractions of stars (especially 

 under the favorable condition of sub-parallel motions held to prevail 

 in a large part of the galactic system) are considered, the inquiry takes 

 on a different aspect. The law of partition of energy applied to an 

 assemblage of bodies moving initially at random among one another 

 assigns to the inner bodies courses that traverse diversely the centroidal 

 region, while courses more largely sub-parallel prevail in the outer 

 zone of the assemblage.^ 



A numerical inspection of the relative influences of inherited motions 

 on the one hand, and of concurrent attractions on the other, made at 

 the time of preparing the original statement of the theory of disruptive 

 approach, in 1901, led to the intimation that the spacial and velocity 

 relations in this part of the galaxy had approached a stage of evolution 

 such that disruptive approaches were near a minimum and that either 

 notably higher velocities or notably lower velocities would increase the 

 number of disruptive approaches. This intimation was given weight, 

 and led to assigning to different zones of the galaxy different degrees of 

 productiveness of nebulae. Subsequent studies have led to a theoretical 

 distribution of the sizes and kinds of nebulae. Some such differential 

 assignment seems essential in the interpretation of the different classes 

 of nebulae that are being revealed by progressive observation. 



'See original paper, Aatrophysical Journal, July 1901, pp. 38-39. 



^Compare the discussion of the motions of molecules in the atmosphere, Chapter I, The Origin 

 of the Earth, The University of Chicago Press, June 1916. 



See also "The bearing of molecular activity on spontaneous fission in gaseous spheroids, Tidal 

 and Other Problems," Carnegie Inst. Wash. Pub. No. 107, 1909, pp. 163-167. 



