188 



LOTKA. 



The quantities P1P2. . ■ Pj which occur in (1) are certain parameters, 

 such as for example the volume and the temperature ^ of the system in 

 course of transformation. The case commonly considered is that in 

 which these parameters P are kept constant (or, as in radio-active 

 transformations, the case in which pressure, temperature, etc. are 

 without influence upon the transformation). We shall for the present 

 at any rate, adopt this customary convention, which in point of fact 

 represents the case of prime interest both in theory and in practice. 

 The parameters P being constant, we may, for our present purposes, 

 omit them from the functional parentheses in (1), so that we have, 

 in effect, 



di 



d_X, 

 dt 



— Fi(Xi, X^,. . .Xn) 



= F-iiXi, X2,. . .Z„) 



dXr^ 

 dt 



— Fni^l, Ao, . . .Xn) 



(2) 



It is expedient to introduce new variables as follows: 

 Putting 



Fl = F2= ... = Fn = 

 we obtain * 



^12 ^= C2 



An — t>n 



We will write 



Xi = X i C t 

 and introduce x in place of X in (2). 

 We then have: 



37 = fi{Xi, Xo,. . . Xn) 



at 



(3) 



(4) 

 (5) 



(6) . 



3 The choice of the parameters P is more or less arbitrary, but in any case 

 the general form of the equations (1), (2) is independent of the particular 

 choice made. 



4 This system of equations will in general have a number of solutions, cor- 

 responding to so many different states of equilibrium. In the cases ordinarily 

 considered in physical chemistry, however, one of these solutions is of special 

 or sole interest. 



