DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
503 
equilibrium varies with the temperature, and shows that, the lower the temperature, 
the further that action which is attended by the evolution of heat goes on, and that 
the equilibrium will vary more quickly with the temperature when the heat developed 
by the reaction is great than when it is small. By determining the state of equi¬ 
librium at two different temperatures, we could determine H. 
Since, by the kinetic theory of gases, 
K 0 = = p/N, 
where p is the pressure and N the number of molecules, we see that K 0 is one-third of 
the mean energy of the molecules at the temperature 0. In many cases of chemical 
combination the heat developed by the combination of the gases is enormously greater 
than that required to raise their temperature through 300° or 400°, and in these cases 
H/K 9 will be very large, so that the combinations will nearly obey Bert helot’s Law at 
moderate temperatures. But this law will not nearly hold when only a small quantity 
of heat is developed in the reaction. 
Equation (49) only agrees with that given by Guldberg and Waage when the 
number of molecules in the equivalent is the same in each of the gases; and, if we 
look at the subject from another point of view, we shall also see reasons for supposing 
that Guldberg’s and Waage’s equation is not likely to hold when the equivalents 
contain different numbers of molecules. Let us take first the case where the molecule 
and the equivalent molecule are identical. Then, calling the four substances A, B, C, D, 
as before, combinations will take place by a molecule of A pairing with one of B. The 
number of collisions in unit time between the A and B molecules is proportional to 
and if combination takes place in a certain fraction of the number of cases of 
collision the number of A and B molecules which disappear in unit time through this 
combination, or, what is the same thing, the number of C and D molecules produced, is 
piv> 
where p is a constant. 
In a similar way we may show that the number of C and D molecules disappearing 
by their combination to form A and B molecules is 
q&, 
where q is again a constant quantity. 
When there is equilibrium the number of A and B molecules which disappear must 
equal the number which appear, so that in this case 
= q&, 
which, so long as the temperature is constant, agrees with equation (49) and with 
GuldbergIs and Waage’s equation. 
Let us now suppose that the equivalents of B and D each contain two molecules. 
