741 
the neighbourhood of one of the molecules J/,,M,.... My 4, in 
such a way that Av, has the same position with respect to M/, as 
Av, with respect to J/, ete. Then it might be that the element @ 
with which we are concerned in the case of the Nt molecule 
consists of the volumes Av,, Av,.... Avy_, taken together and 
combined with certain intervals for the momenta; if it were so, G 
would really be proportional to .V—1 or to N, as we may say as well. 
It must be remarked however that, when we introduced the finite 
elements G, it was expressly stated that the distribution of the 
particles over one of them will „ot be determined by probability. 
Thus, if Av,, Av,....Qvy—, must be considered as constituting a 
single element of volume, the position of the Nt molecule either in 
Av, orin Av,, Av, ete. will not be determined by our lottery. This 
can hardly be admitted; whether the Nt molecule will lie near the 
first or near any other of the molecules that are already present must 
certainly be considered as something accidental. Moreover the above 
reasoning applies only to places in the neighbourhood of one of the 
N—1 molecules, and in gases of small density these places form 
only a small minority of all those that may be occupied by the: 
Nth particle. 
§ 5. Before PranckK, Terrope *) had already calculated the entropy of 
a gas in a similar way *). He defines G in terms of-the constant 
h by the relation 
G = (wh), 
where w*, is a numerical coefficient that has to be determined 
later on. So his elementary domain does not depend on V. But 
TrerropE divides the expression (4) by N/; by this he reaches the 
same result that PLANnck obtains by putting G proportional to \. 
Substituting the value found in this way for W in BOLTZMANN's 
formula Terrope finds 
€ 
3 3 ; Se 
S=kN a log(2a Em) + log» — log Lo N | — log N + RU 5 log (wh); (6) 
This expression really fulfills the condition that ‚N shall become 7 
times greater when V, v and £ do so. Ll cannot see however a 
physical reason for the division of (4) by AN! 
1) Ann. d. Phys., 38 (1912), p. 434. 
2) Similar reasonings have been first published by SAcKUR, Ann. d. Phys. 36 
(1911), p. 958; 40 (1913), p. 67; Nernst-Festschrift (1912), p. 405, 
3) In the notation of Terrope: z, 
