208 A. J. Lotka — Mode of Growth of Material Aggregates. 



all sections given by t = constant are alike both for A and also 

 for A', and take the form indicated in fig. 2. 



We note that although the zero ordinate — the number of 

 molecules formed per unit time — is the same for A and A', 

 nevertheless molecules of one kind — A say — preponderate in 

 the system, as shown by the greater area of the curve A ; this 

 is because, in the " struggle for existence," the stabler (fitter) 

 molecules A have the advantage, and are, on an average, 

 " longer-lived." 



Viewed in this way, chemical action clearly presents itself as 

 a case of " Inorganic Evolution." 



The physical interpretation of these results would be some- 

 what as follows : 



From the point of view we have taken, we must suppose 

 that the condition of each molecule at a given instant in 

 general departs somewhat from the average condition of all 

 molecules. 



For a given molecule of the kind A, there will, in general, 

 sooner or later, come a moment when the variations in its con- 

 dition reach a certain limit — we may speak of it as the " limit 

 of stability " of the molecules A — at which that molecule of A 

 ceases to exist as such, and passes into the condition A'. 



The number D of molecules which are thus eliminated from 

 the aggregate A in a unit of time will depend : 



1. On the nature of the "limit of stability" of the mole- 

 cule A. 



2. On the " distribution " of the variations in the condition of 

 the molecules in the aggregate. 



Any agency which affects either of these factors will, in 

 general, affect also D, the rate at which molecules are elim- 

 inated from the aggregate. 



Let us consider each of these factors a little more closely. 



