lotka: discontinuous evolution 3 



sciences. Yet the concept is essentially physical in character, 

 and is definable in exact terms probably only in the language of 

 physics. For in its last analysis we may define evolution as 

 the history of a material systern undergoing irreversible transforma- 

 tion. To the physicist, therefore, the study of evolution is essen- 

 tially the study of irreversible changes, and the law of evolution 

 is the law of increasing entropy, or, more generally, of the increas- 

 ing probability of the successive states of any real material system. 



Now among the infinite variety of changes of which matter 

 is susceptible, there is a certain class which stands in a measure 

 apart — the so-called "changes of state" in the narrower sense. 



If an iron rod is placed in the fire, its temperature rises gradu- 

 ally, and finally the rod may become incandescent. In a per- 

 fectly general sense we might speak of this as a "change of state." 

 It is customary, however, to restrict the use of this term to denote 

 such changes as that from ice to water, from water to steam, and 

 so forth. What distinguishes these changes, and places them in 

 a class by themselves, is their discontinuity. 



In general the state of a material system may be defined by 

 indicating the values of a number of suitably chosen variables 

 x h x 2 . . . , and changes in the state of the system then natur- 

 ally find expression in terms of the changes in the values of these 

 variables. Now in the case of "change of state" in the narrower 

 sense certain of these variables are masses MiM 2 . . . , for 

 the system is composed of a number of separate portions A X A 2 

 . . . , differing from one another in their properties in a 

 discontinuous manner. The mass M i of any one A t of these 

 separate portions is in general susceptible of change by the trans- 

 formation of matter of the species A { into other forms A i} A^ 

 It is this passage of matter from one such portion 

 of the system into another or into others, which constitutes 

 "change of state" in the narrower sense. 



If, as we noted above, the separate portions A] A 2 . . . of 

 which the system is composed, differ from one another in a dis- 

 continuous manner, implicitly this conveys the idea, that each 

 portion for itself is in some sense continuous (not necessarily as 

 regards distribution in space). In the realm of physical chemis- 



