A. J. Lotka — Mode of Growth of Material Aggregates. 213 



also for the spontaneous change from A' to A, is satisfied, and 

 this change actually takes place. 



Now we can continue our curves, tracing first of all the 

 value of the free energy during the change from the condition 

 A' to A. Tins part of the curve is the " path " of the spon- 

 taneous change, and must, therefore, be of type (a), as shown. 

 We then continue our set of three curves, very much as before, 

 except that now the values of E are the actual values, those of 

 E' auxiliary ("calculated"). 



The continuation of this figure then shows features precisely 

 similar to those which we noted in the earlier part, and it is, 

 therefore, unnecessary to follow up their description any 

 further. We only note that t 3 denotes the instant at which the 

 molecule of A is formed, t A a point at which the curves E E' 

 cross, t h the moment when the molecule is eliminated from the 

 aggregate A. 



The interval t 2 t b represents the length of life of the mole- 

 cule A, and this, we saw, has the value (a) for ne~ ka out of n 

 molecules counted at the moment of their formation, or, has a 



mean value -j- for all molecules. 



We can distinguish a number of separate fields in this 

 diagram. 



In the field t 3 t i the molecule is in the state A, and is stable 

 in that condition. 



In the field t i t 5 the molecule is still in the state A, though 

 in a meta-stable condition. It does not here pass into the state 

 A', for in order to do so, it would have to cover a path of type 

 (b) ; i.e., the second condition for a spontaneous change is not 

 fulfilled. 



