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



Lastly, the field t b t Ci represents the molecule during its spon- 

 taneous transition from the state A to A'. 



II Distribution of Variations. 



The above considerations apply to one individual molecule. 

 The entire aggregate A will comprise : 



1. Molecules whose condition corresponds to the field t s t t . 

 These are stable; neither condition (1) nor condition (2) is 

 satisfied for their elimination from the aggregate A. 



2. Molecules whose condition corresponds to the field t 4 t b . 

 These are in meta-stable condition, but do not change because 

 condition (2) is not satisfied. 



3. Molecules whose condition corresponds to the field t h t 6 . 

 These are undergoing change, and being eliminated from the 

 aggregate. 



The number of molecules in the third class, we saw, , is* 

 always small (at any rate in ordinary cases) and is given by- 



m{t'-t). 



The distribution of the remaining molecules between the 

 first and second class is evidently closely connected with reac- 

 tion velocity and equilibrium. A change in temperature, being 

 accompanied by a change in the total energy of the system, 

 must lead to a change in the distribution of the energy in the 

 system, and so to a change in the distribution of the variations 

 in the condition of the molecules. But any agency which 

 produces such a change will affect D, and hence arises the con- 

 nection between D and the temperature. 



We still have to consider the influence of agencies which 

 affect the " limit of stability " of the molecule. 



There is one special case which is of interest here, namely, 

 that in which, while the values of E and E' are unaffected for 

 each molecule, E, is changed — lowered, say. The effect of such 

 a change will evidently be that, while the total and free energy 

 of the system as a whole is unchanged for a given composition 

 (and volume), the rate D will be changed — raised. 



We see that this corresponds exactly to the effect of introduc- 

 ing a catalyser into the system. 



We may go a step further and ask ourselves in what way the 

 value of Ej may be lowered. 



The answer ,is that this may take place in one of two ways : 



Either the character of the path A A' may be changed for 

 some or for all the molecules ; the formation of intermediate 

 compounds in certain reactions or the production of local dif- 



