152 LOTKA. 



Furthermore, in the absence of inertia, the velocities being never- 

 theless finite, these must be held in check by dissipative resistances. 

 The transformations which we have l)een considering are accordingly 

 typical irreversible ^^ jyroeesses, and the history of the system under- 

 going such transformation is a typical example of evolution. It is, 

 indeed, with a view to preparing the ground for a general investiga- 

 tion of the dynamics of evolution, that the reflections here set forth 

 were conceived along broad and comprehensive lines. Attention 

 may be drawn to the fact that, while we have spoken of the variables 

 X as the masses of the components of a system in chemical reaction, 

 there is nothing in the method followed to restrict us to such interpre- 

 tation. The X's may be masses of any species of material complexes 

 in any mutual relation of interpendence. For example, they may be 

 the masses of biological species dependent on each other for food and 

 in other ways. The equations developed by Sir Ronald Ross ^^ rela- 

 tive to the interpendence of the malaria parasite, the anopheles 

 mosquito and man, fall within the type here considered, and their 

 solution is comprehended in the general solution given above. 



Summary 



The differential ecj^uations relating to a physical system undergoing 

 change of state are of the general form 



= Fi(Xi, X2, . ■ .Xn] Pu Pi,- ■ ■ Pj) 



dt 



= F'JXi, A2, • . Xn', Pi, P-2, ■ ■ -Pj) 



dX, 



dt 



dXn 



dt 



— Fn\Xi, Xi, . . .Xn, Pi, P2, ■ ■ ■ -Pj) 



(1) 



where Xi, X2, ■ ■ .Xn are the masses of the components of the system 

 and the quantities P measure certain parameters defining the state 

 of the system (e. g. pressure, temperature). 



The functions F commonly considered in discussions of this subject 

 are those defined by the law of mass action. Some other special cases 



18 In the thermodynamical sense. 



i5 Nature, Oct. 5, 1911, p. 466; A. J. Lotka, ibid. Feb. 8, 1912, p. 497. 



