Physics. — “Deduction of the dissociation-equilibrium from the 
theory of quanta and a calculation of the chemical constant 
based on this.” By Prof. P. Enrunrest and V. Trkat. 
(Communicated at the meeting of February 28, 1920). 
Introduction. 
Nernst’s theorem, the theory of the specific heat of solids, of the 
vapour-pressure and of the dissociation-equilibrium must have their 
common root in the general foundations of statistical mechanies and 
in the quantum-hypothesis. O. Stern’) and H. TrrropE’) have shown 
how from Nernst’s theorem by means of EINSTEIN’s formula for the 
specific heat of solids and a vapour-pressure formula for high tem- 
peratures (derived kinetically) the chemical constants (hence also 
the dissociation-equilibrium) may be calculated. Notwithstanding the 
great advantages of this method a desire must be felt to calculate 
the chemical constants and the dissociation-equilibrium more directly 
by considering the hot gases themselves, without the use of a cycle 
consisting of a condensation, cooling of the crystals to the absolute 
zero, chemical transformation at 7’=0, heating of the new erystals 
and evaporation at the high temperature. 
This desire explains the fact, that even after the publication of 
STERN’s paper (1913) attempts have been made again and again to 
improve the earlier methods of calculating the chemical constants 
as given by O. Sackur*) in 1911-1913 and H. Terrope*) in 1912. 
These consist in considering a gas of N equal molecules in a volume 
V at the temperature 7’, calculating statistically by means of some 
formulation of the quantum-hypothesis the “thermodynamic proba- 
bility W” and by comparing r log W with the thermodynamic 
entropy of the gas fixing the indeterminate constant in the entropy. 
It is not an aecident that it is always the same point that remains 
obscure in these theories’), viz, how an expression of the form V—% 
1) O. Srern, Phys. Ztschr. 14 (1913), p. 629. 
2) N. Terrope. Verslag Kon. Ak. v. Wetensch., Amsterdam 28 (II), (1915), 
p. 1110. Proceedings Amsterdam 17 (1915), p. 1167. [henceforth to be quoted as 
‘“TInd paper’’|. 
3) O. SACKUR. Ann. d. Phys. 36 (1911), p. 958 ; 40 (1913), p. 67; Nernst-Festschrift 
(1912), p. 405. 
+) H. Terrope. Ann. d. Phys. 38 (1912), p. 434. [to be quoted as “I st paper”’). 
