i,-.., psn the corresponding quantities of motion, then the proba- 
bility that at an arbitrarily chosen moment the system will be in 
a state for which the coordinates will suecessively have values lying 
between g, and g, + dg, q, and q, + dq, ete., and the quantities 
of motion between p, and p, + dp,, etc, will be given by: 
w dG = w (p,,-+ + 93N) dp, ---dqsn = Ie kT dp,..:dq3n;, .@ 4) 
in which Z is the energy of the system, and 
1 me 
= fe «dp... dg 
the integration being extended over all the values of the q’s within 
the volume V and all the p's from —o tot + 0!) 
If we now assume that 7’ and V have. been chosen so that part 
of the system is gaseous, the other solid, we may write for the 
probability that the molecules 1 up to # (w inclusive) are in the 
gaseous state, 7 +1 up to N (N inelusive) on the other hand in 
the solid state, as follows : 
, 
(frre) = rfe « _k1 dp, ++ ~dd3n je kT dpd +»: dqaN, (B) 
in which the 6n-fold integral must be taken with respeet to the 
gaseous part of the system, the 6(N—n)-fold one with respect to 
the solid part. The volumes of both are determined by JV" and the 
volume of the solid part that is only dependent on V—v.*) Further : 
il > 2 
Ee ee (p, 4. eee Pp, ) 
is the energy of the gas, 
é=epte,tre= LaF ” + k ) + 
et d et Ln Ps nt se Psy 
3N 3N 3N 
+2 aij giqy+ hath, + ne, 
Bal 8n--1 3n-+-1 
in which N—n=n' is put, the energy of the solid body, s 
e+:'=F. ce and the a’s and /’s are constants; —c is the work 
which is to be applied to detach a molecule resting in its position 
) Wee may Et say that the system, as it is at a definite moment, forms part 
of a canonical ensemble, with modulus kT’. 
2) In principle also other arrangements of the molecules than those of solid 
substance or gas are of course conceivable, at least for a short time; they will, 
however, be so improbable, that they may be disregarded. Nor is it necessary to 
consider a solid phase of variable density. 
