VALIDITY OF THE PRINCIPLE OF LE CHATELIER. 25 



1. Given that the system, at equilibrium, is stable with regard to 

 changes in x, and that there is a relation of the type (8), an " equation 

 of constraint " connecting the masses ^ and their initial values A, 

 then the condition which must be satisfied in order that the Le Chate- 

 lier Principle may hold with regard to the effect of a change in the 

 initial mass of some one component, is that the addition of such com- 

 ponent shall accelerate or retard the transformation (at equilibrium), 

 according as such component disappears or appears in such trans- 

 formation. 



2. Given that the conditions for the validity of the Le Chatelier 

 Principle stated under (1) are satisfied for each and every component, 

 then it is easily shown that the system is necessarily stable with 

 regard to changes in x, so that the condition of such stability with 

 regard to changes in x is automatically satisfied and does not need to 



be expressly stated. For, if t-j- > for every component which dis- 



df 

 appears in the transformation, and if rjj- < for every component 



df , df 

 which appears, then, in view of (9), the same is true of — and -rrr^ . 



of,- o§ ;• 



But 



d^i = -pidx (11) 



d^'i = + p%dx (12) 



"where pi, p'j are positive numbers, and 



df^j^ dldj,_^ ^ df_djj ^^^^ 



dx d^i dx d^'i dx 



which is necessarily a negative quantity if 



df . df 



rf > , T^ <0 (15) 



o^i d^ j 



3. It should be noted that the argument by which our conclusions 

 have been drawn depends on the existence of equations of constraint, 

 relations such as (8), connecting the ^'s and the ^'s. In the absence 



