1181 
NEN 2amkT / v ar 2d kT 
ae eee f cr apes! NI +. 5 IV log — iq 
(34) 
: 27d kT x. 225 kT 5 , 
de i N log — ———— | , N a eee — + N log (S2r*) +3 A | 
IE 1 
Without entering further into the caleulation it is yet easy to see 
the analogy of the formulae (35), (54), and (16). If we write the 
last in the form: 
oper vias: anh T os aha 
Pal dN LOG OG ar eat , 
= h? Wile a 
we see that in each of the three expressions per degree of freedom 
2amkT 2aJkT 
first of all a term + N log Mags EED 4 N log occurs, ac- 
2 ¢ 
le 
cording as it is one of rectilinear or of rotatory motion. For the 
three degrees of freedom of rectilinear motion moreover a term 
log ae is everywhere found. In this » is the three-dimensional ex- 
tension of the coordinates denoting the place of the centre of gravity 
of a molecule, while the division by N/ is caused by the inter- 
changeability of the molecules, as has been fully set forth in § 3. 
We find in (33) 4 instead of v and in (34) 82? for the rotatory 
motion. In (33) 4a is the two-dimensional extension of the angular 
coordinates, which indicate the direction of that axis of the molecule 
round which it does not revolve, while in (84) another factor 22 
is added, being the extension of the third angular coordinate, which 
denotes the revolution round the said axis, which now, indeed, does 
take place. Finally there is everywhere still a term 4 N per degree 
of freedom, 
§ 8. On the general definition of the thermodynamic probability 
for gases and liquids. 
We know from ordinary statistical mechanics that the changes 
of the expressions (32) and (81) denote generally the change of the 
entropy, resp. free energy. for changed values of v and 7. As they, 
as we have seen, indicate for a system in one definite condition 
(ideal gas), the absolute values of S and # (i.e. those with the 
accurate additive constant), they will have to do this for all eondi- 
tions. In this it should of course be taken into account that ¢ for 
smaller values of v can also depend on the mutual distances (and 
possibly orientations) of the molecules. 
The formulae (31) and (32) are therefore of general validity on 
the suppositions made, also for non-ideal gases and for liquids, 
