178 
The question, therefore, is how those authors, who confined 
themselves to the consideration of a single gas, were able to obtain 
a “thermodynamic probability”, the logarithm of which yields an 
admissible entropy-equation, in other words, how do they manage, 
that the entropy does not contain a term of the form 
~ 
V 
RlogV. but. Blogs on % nn 
Ni 
1. ©. Sackur') reaches the desired result by a special method ot 
“quanticising” the motion of the gas-molecules: we may express it 
by saying, that he quanticises, as if each molecule were separately 
esa 
contained in a cell of volume We 
i 
2. M. Puanck’) similarly only obtains the term (63) in the correct 
form by dividing the phase-space of the molecules (u-space) into an 
increasing number of “elementary” portions, as the number of mole- 
cules is larger (G == Ng). The justification of this procedure and 
the fixing of g he considers to be open problems’), 
3. H. Terropr [1st Paper]|‘) attaches a factor to the expres- 
1 
N;! 
sion for the “thermodynamic probability”, 7 order that its logarithm 
may show the law of dependence on N which is needed in the entropy. 
But he does not justify this procedure on combinatory grounds *). 
1) O. Sackur, Annalen d. Physik, 40, p. 76 (1915). 
2) M. Pranck, Wärmestrahlung, 2 Aufl. § 126, § 133. 
3) M. Prancx, Theorie der Wärmestrahlung, 2 Aufl. p, 131; also M. PrancKk 
Vorträge der Wolfskeh!-Stiftung 1918 in Göttingen (Teubner 1914) p. 7; Phys. 
Zeitschr. 14 (1913), p. 258. In a later paper (Sitzber. d. Preuss. Akad., Berlin, 
1916, p. 653 —667) PranckK once more returns to the problem; here he takes in- 
to account the permutability of the molecules, but he does not himself look upon 
this discussion as giving a combinatory justification of his assumption as to the 
“elementary regions”. 
4) H. Terrope, Ann- d. Phys. 88, p. 434 (1912). 
5) H. A. Lorentz, (Versl. Kon. Ak. v. Wetensch. Amsterdam 28 (1) (1914, p. 
515, — Proceedings Amsterdam 19. (1917), p. 737), at the end of section 5 draws 
attention to this. H. Trrrope in his 2nd paper, where he gives the new deduction 
by means of the process of evaporation, à propos of Lorenrz’s remark in an 
appendix once more returns to his previous deduction. But again he explains — only 
more fully — that the division by the factor Ni! is required, in order that the 
entropy may show the desired law of dependence on Ni. P. ScHERRER, Gött. 
Nachr. 1916, p. 154 in following the same procedure simply refers to J. W. Griess, 
Statistical Mechanics without any further comment. 
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