1172 
peculiar to another.) This new position is a priori as probable as 
the preceding one. 
As it is now tacitly assumed by simply integrating the righthand 
side of (7) over the range from —o to + that a molecule cannot 
leave its place, the thus obtained integral must still be multiplied 
by v'/, this being the number of the interchanges possible between 
the molecules of the solid body. 
When this is taken into account, we find: 
nic 
@ wd “) —= Ie FT (2ZamkTyle ni (kT) IF, … (B) 
3\ Ve 
in which ZZ denotes the product of the 37 values Gas 
Ji 
This is therefore the probability that the molecules from | to n 
inclusive form a gas with the volume v, the nm’ remaining ones a 
solid body with the volume v' = V — v.’) 
It is. however, of no importance whatever for thermodynamies 
whether it is just the molecules numbered 1 up to ” that are in 
the gas state. What we want to know is rather the probability that 
n arbitrary molecules are in the gas state, the remaining ones in 
the solid state. This probability, which we shall call W(), is obtained 
N! 
by multiplying the expression (8) by 
. : nin’! 
being the number of 
different ways in which the MN molecules can be divided between 
gas and solid body on the condition that always remain in the gas. 
We get: 
= ne 
Win} =F = e kT (AamkTy lan orks Hs tdk 
n 
Mr 1 ft. ; / 
Bearing in mind that — — is the frequency r; for the vari- 
‘ mL 
me 
able g;', we may also write: 
ne 
log W(ny==log [+ Nlog N — N—nlogu + n — — + $nlog (2am) + | 
a | kT, (10) 
+ $n log (k T) +n loy v — u log p+ a log (RT), | 
in which loy rv is the mean value of loy v;. 
1) In this it is assumed that the energy required for a molecule to slip through 
the surrounding ones, is not infinite; at any rate it is, however, possible to imagine 
the interchange of the molecules to be brought about by evaporation and renewed 
condensation, which must really continually take place at the surface. 
2) As we have assumed the density of the solid substance to be pee © 
» = V—v’' is determined by wn’, and therefore by x. 
