502 PROFESSOR 3. J. THOMSON ON SOME APPLICATIONS OF 
Let each of these quantities equal K ; then the equation of equilibrium becomes 
6 {mppp, + m 2 qc 2 - m ? rc ?j - w 4 sc 4 + K (p log + 9. log 
— s log] — (p + q — r — s) | = ~ • . 
° m 4 se ] ’ \ 
— r log 
„ Po"Q 
° 
• (48) 
We see from this equation that anything which increases dcujd^ will increase 
log p 0 Q,/mpp£ -J- . . ., and so will diminish d. so that, if there is any kind of potential 
energy which increases as ^ increases, the value of d when there is equilibrium will 
be smaller than it would have been if this energy had not been present; or, in more 
general terms, any circumstance which causes the potential energy to increase as 
chemical action goes on tends to stop the action, while, if it causes the energy to 
diminish, it will facilitate the action. 
Equation (47) may be written 
gv 
dw 
= C e Ke , 
(49) 
where C is independent of £e. 
In the case of gases combining in a vessel of constant volume, and when there 
is no action on the sides of the vessel, da>/d£, being the increase in the potential 
energy when one equivalent of C acts on one of D, to produce one each of A and B, 
may be measured by the heat developed in the reverse process, that is, when an 
equivalent of A acts on one of B to produce one each of C and D. Let us call this 
quantity of heat (measured in mechanical units) H ; then 
gv 
C e H/K h 
(50) 
If H be positive, and 6 zero, then either £ or 77 must be zero, that is, the chemical 
action which is attended by the production of heat will go on as far as possible. This 
is Bertheloi'’s Law of Maximum Work, and we see from the above expression that 
it holds at the zero of absolute temperature, but only then. Equation (49) also shows 
that the tendency of any chemical reaction to take place is greater, the larger the 
amount of heat developed by it. 
If all the equivalents contain the same number of molecules, we may put p = 1, 
q— I, r = 1, s — 1, and equation (50) takes the simple form 
~ = Ce 11 Kfl .(51) 
ST 
Guldberg and Waage put where k is a constant. This agrees with 
equation (50) if the temperature remains constant. Equation (50) shows how the 
