VALIDITY OF THE PRINCIPLE OF LE CHATELIER. 



27 



5.ri 5//1 



a system of linear equations, which we solve for — , ^y; and obtain 



(23) 



8yi 

 and a similar expression for 777 . 



Condition of Stability. A general solution of (18), (19) can be 

 written ^ in the form of exponential series 



x= Poi- Pie"'' + Poj''^' + Pne^^'' + 



where Xi X2 are the roots of 



(24) 



(25) 



A(X) 



,6x 

 dx 



- X 



^df, 

 \dy 



dJ^ 

 dy 



-X 







(26) 



The condition for stability "^ of the equilibrium is that the real parts 

 of all the roots X are negative. This in turn demands that the abso- 

 lute term A(0) be positive. But this absolute term is, evidently, 



A(0) 



(27) 



6 A. J. Lotka, Proc. Am. Ac, 1920, p. 139. 



7 Idem, loc. cit., p. 144; Hurwitz, Math. Ann., 1875, vol. 46, p. 521 ; Blondel, 

 Jl. de Physique, 1919, pp. 117, 153. 



