710 ) 
dn, + 2dn, = 0. 
As the condition on which ¢ is maximum we find. 
an, ky, 
oes ae 
Moreover 
1 1 
— — dn,’ seers <0 
ny, n, 
which is identically satisfied. So the “true” state of equilibrium for 
a dissociated gas is stable. 
10. To caleulate Y we have only to consider that Y¢ taken for 
all possible values of m, and 7, yields the total number of the 
systems of the ensemble, that is N. We shall further understand 
by nm, and n, the numbers of free atoms and molecules in the state 
of equilibrium; we can then denote a deviating state by the ex- 
pressions 7,-— 2r and ,-+ 7. The number of the systems deviating 
in this way is then; 
¥ —n 
a ad ofl | 1-25 
kot Ah EE a en 
Er ® (220m) (4 FUN)" Varnes em 2h." 2an ny 2na 
sr = € 
nnn,” 22n, Zan, 
Here n/ has been developed according to the formula of STIRLING. 
If we put #, small with respect to 2 we find by summing with 
respect to t from —o to + o: 
bt a 
N — Nee (220m)* (Aaen) Vente es keta 
i) 
to | 
n‚tin,? 
Also when », is not small with respect to 7 the sum yields a 
factor of the order of unity, which is without influence on the value 
of W; strictly speaking the limits for tT are —n, and n—~n,; but 
we may take — oo and + o for them, because for somewhat high 
values of r very small amounts are found. 
So we have for W: 
ay 
Li € 
5) 
ap == nlog Aan + 9 n log (2%Om) + (n,+n,) log V + 
+ n,logk,, — n, logn, —n, logn, — n, log 2 — n,. 
From this follows for the pressure of the ir gas : 
ae Ba 2 +. (log V + log k l l 2 
me =. ( — —— ra 2 — 
ae —y (log V +- log k,, og n, og & an 
On, 
+. (log V — logn, — > 
