DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
509 
The condition that L should be stationary is therefore 
— m%rc z — m 4 sc 4 + K (q — r — s) 
I / i PoQ i Po Q i Po Q 
+ * (q log — - r log — - -slog 
^ m 4 se 
die 
• (58) 
This equation may be written as 
£V 
Tj'l 
dw 1 
Qr+S-q Q e at K8. 
• (59) 
If two of the constituents, say A and C, are insoluble, then we can easily prove in a 
similar way that 
pS dv) 1 
- = Q*-?C'e^ Kl .(60) 
The Effect of Temperature on the Equilibrium. 
§ 14. If we define the coefficient of the reaction to be the value of £v/ fp'i when 
there is equilibrium, and denote it by the symbol a>, then we have 
dw 1 
O) — Qq+s-p -1 C e # ; 
(61) 
so that, if §w be the alteration in the value of to when the temperature is increased by 
S/9, we have approximately, if divjdf does not change with the temperature, and if its 
ratio to K 6 is large, so that the term in oj which varies most rapidly with the 
dw 1 
temperature is e ^ K0 , 
Sco 1 dw 89 
to Iv 9 ddj 9 ’ 
(62) 
so that the percentage change in oj for a given change in 6 varies inversely as the 
square of the absolute temperature, and directly as dwjdtj, which, when the system is 
free from strain, electrification, &c., is the amount of heat given out when one equiva¬ 
lent of A combines with one of B to form one each of C and D. 
The greater this amount of heat, the more quickly will the coefficient of the reaction 
vary with the temperature. 
We shall now proceed to reduce this expression to numbers, assuming, as an 
approximate value of K, that it is the same as for gases. In this case 
