D O C . 4 2 7 Q U A N T U M T H E O R Y O F I D E A L G A S 6 5 7 Published in Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse. Sitzungsberichte (1925): 18–25. Presented 29 January 1925, published 5 March 1925. An abstract in Einstein’s hand is also available ([1 046]). It was published in the same issue of the Sitzungsberichte. See note 1 for its text. [1]Einstein’s abstract of this paper (see the descriptive note) reads: “Es wird durch eine Dimensio- nalbetrachtung sowie durch zwei mechanische Überlegungen gezeigt, dass die Zustandsgleichung des idealen Gases (Entartungsproblem) reduziert werden kann auf die Bestimmung einer universellen Funktion einer Variablen. Dies Resultat ist dem Wienschen Verschiebungsgesetz der Strahlungstheo- rie analog.” [2]See Bose 1924a (in Doc. 278), Einstein 1924o, and 1925f (Docs. 283 and 385). See also Pérez and Sauer 2010 for a historical discussion of the present paper. [3]A reference to the debate on the reality of light quanta, which had been especially stimulated by the discovery of the Compton effect and the proposal of a quantum theory of radiation by Bohr, Kramers, and Slater (see the Introduction, pp. lx–lxii, for further discussion). [4]Such doubts had been voiced, e.g., by Otto Halpern (see Docs. 308 and 309). Ehrenfest had also criticized Einstein’s use of statistical arguments (see Einstein 1925f [Doc. 385], §7, Doc. 334, and Doc. 415). [5]For a comment on possible quantum effects in atomic collisions, see Doc. 361. [6]The definition of probabilities of states in Boltzmann’s principle had been a matter of concern for Einstein already in his first papers on statistical physics and on the light quantum hypothesis (see, e.g., Einstein 1905i [Vol. 2, Doc. 14], p. 140, and, for further discussion, Vol. 2, the editorial notes “Einstein’s Early Work on the Quantum Hypothesis,” pp. 134–148, especially p. 137, and “Einstein on the Foundations of Statistical Physics,” pp. 41–55). [7]For more on Nernst’s theorem, see Einstein 1924o (Doc. 283), note 11. [8]Einstein presumably applied Buckingham’s theorem to arrive at this conclusion (see Pérez and Sauer 2010, sec. 5.1). [9]The hypothesis of quasi-monochromatic entropic additivity was invoked already in Einstein’s first paper on the light quantum hypothesis (see Einstein 1905i [Vol. 2, Doc. 14], p. 155). [10]Einstein 1925f (Doc. 385), p. 7.