DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
501 
Let us take as an example the case mentioned above, where the chemical action is 
expressed by the equation 
HoSO, + 2NaN0 3 = 2HN0 3 + Na 3 S0 4 ; 
here the equivalent molecules are H 2 S0 4 , 2NaN0 3 , 2HN0 3 , and Na 3 S0 4 ; and, if 
A, B, C, D, denote sulphuric acid, sodium nitrate, nitric acid, and sodium sulphate 
respectively, p — L d = 2, r — 2, s = 1. 
Let m 1; m 3 , m 3 , m 4 , denote the masses of the molecules of A, B, C, D, respectively. 
Then, if these are gases, by what we have proved before (p. 486), the value of 
L equals 
where w is the mean potential energy of the four gases, and the remaining notation is 
the same as that on p. 486. 
The quantities A rj, £, e, are not independent of each other; in fact, there are three 
relations between them. Thus suppose, for example, that {A} consists of the two 
components a, (3 ; {B} of y, § ; {0} of a and y ; {D} of /3 and 8, then the chemical 
reaction is expressed by the equation 
(a/3) + (yS) = (ay) + (/3S), 
so that we have evidently 
£ + £ = a constant, 
. , 
v 4 - £=.> 
so that 
d£ = dr] = — dt, = — de .(46) 
Thus, if £ be increased by dg, the change in L equals 
dg 
e \ m x p (c 1 + B 1 log - Kj) + m,q (c z + B 3 log ^ - K 3 
m 3 r (c 3 + B 3 log ~ ~ r> h s ( c ± + 1{ i lo 8 ' P " ~ 
myre 
-K 
m 4 se 
and by Hamilton’s principle the quantity in square biackets must vanish when there 
is equilibrium. 
For perfect gases (i.e., gases which obey Boyle’s Law) 
R 1 m 1 — = BoWig = Bprq, 
(47) 
