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In this article, we analyze the third of three papers, in which Einsteinpresented his quantum theory of the ideal gas of 1924-1925. Although it failedto attract the attention of Einstein's contemporaries and although also todayvery few commentators refer to it, we argue for its significance in the contextof Einstein's quantum researches. It contains an attempt to extend and exhaustthe characterization of the monatomic ideal gas without appealing tocombinatorics. Its ambiguities illustrate Einstein's confusion with his initialsuccess in extending Bose's results and in realizing the consequences of whatlater became to be called Bose-Einstein statistics. We discuss Einstein'smotivation for writing a non-combinatorial paper, partly in response tocriticism by his friend Ehrenfest, and we paraphrase its content. Its argumentsare based on Einstein's belief in the complete analogy between thethermodynamics of light quanta and of material particles and invokeconsiderations of adiabatic transformations as well as of dimensional analysis.These techniques were well-known to Einstein from earlier work on Wien'sdisplacement law, Planck's radiation theory, and the specific heat of solids.We also investigate the possible role of Ehrenfest in the gestation of thetheory.

Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics