A. J. Lotka— Mode of Growth of Material Aggregates. 209 



I. Limit of Stability of a Molecule of the kind A. 



The circumstance which leads to the elimination of a mole- 

 cule of the kind A is its spontaneous passage from the 

 condition A to the condition A'. 



Now, in order that this passage may take place sponta- 

 neously, it is necessary : 



3 



f 



1. That the free energy E of that molecule in the state A 

 be > E ; , its free energy in the state A'. 



2. That during the passage of the molecule from the state 

 A to the state A 7 , its free energy diminish continually. 



A diagram will help to illustrate these conditions.* 

 Suppose the free energy E of the molecule plotted as ordi- 

 nate against the time as abscissa during its passage (not neces- 

 sarily spontaneous) from the state A to the state A'. 



Then, if condition (1) is satisfied, the curve E = <f> (t)', or, as 

 * It is here assumed that, whatever may be the events immediately pre- 

 ceding the change A A', during this change the molecule may be regarded as 

 an isolated system. Without this assumption the conditions for the change 

 A A' are more complicated. 



