36 LOTKA. 



while at the same time the system is stable towards H both when 

 a- = constant and also when x = xi, then the Le Chatelier principle 

 holds. In this case the curves <p {x, G, H) — (x constant) 



and ^ (a-i, G, II) = 



both slope from left to right upwards, and the curves of constant 

 composition are again steeper than the equilibrium curves. An 

 example of this type is that in which // is temperature and G is heat 

 absorbed by the system (when // < He, G increases). 



Finally, be it remarked that the results here deduced depend solely 

 on ki7idic stahility, i.e. on the fact that the system when displaced 

 from equilibrium has a velocity (rate of change of displacement) 

 towards that equilibrium. The conclusions reached are therefore 

 wholly independent of energetic (thermodynamic) consideration, since 

 no reference whatever has been made to forces or energies or in any 

 way whatsoever to the physical dimensions of the parameters involved. 



This completes the present enquiry into the conditions of validity 

 of the principle of Le Chatelier. It remains now only to point out the 

 place which this communication occupies in the general plan of the 

 series of investigations of which it forms part. This series of investi- 

 gations has for its object the study of material systems evolving in 

 accordance with a system of differential equations 



^ = I\{X„ X,, ...Xn; A; P;Q) (65) 



in which the symbols A' denote the masses of certain components S 

 of the system, the symbol A has been written to denote collectively 

 the initial values of the masses of certain components, the P's are 

 parameters defining the state of the system (extension-in-space, 

 topography, climatic conditions, etc.); and the Q's are parameters 

 defining the character of the components S. 



In a previous communication the kinetics of such a system were 

 studied for the case in which the ^'s, P's and Q's are constant. This 

 left open for discussion the effect of changes in these parameters. 

 One phase of this subject has been dealt with by the writer elsewhere, ^^ 

 namely the 'eft'ect of slow changes in these parameters. The present 

 communication now extends the field of enquiry to the effect of 



< 



11 "Note on Moving Equilibria"; to appear in a forthcoming issue of the 

 Proc. Nat. Ac. 



