l x x I N T R O D U C T I O N T O V O L U M E 1 4 proposed that it might be observable in hydrogen or helium (see Doc. 385, pp. 11– 12).[39] This extraordinary phenomenon had to wait seven decades for its experi- mental discovery.[40] Another result, to which Einstein attributed great importance, came out of his study of fluctuations. In calculating the number of fluctuations of the molecules in an energy cell, he found in addition to the usual expression for particle fluctuations a second, mysterious term, which he attributed to the wave nature of the mole- cules.[41] In connection with this discovery, Einstein cites Louis de Broglie’s dis- sertation: “How a (scalar) wave field can be attributed to a material particle or a sys- tem of material particles has been shown by Mr. E. (sic) De Broglie in a very significant writing.” (Doc. 385, p. 9).[42] He wrote to Langevin that “the work of De Broglie made a big impression on me. He raised a corner of the big veil” (Doc. 398). That same day he also wrote to Lorentz: “De Broglie made a very in- teresting attempt at interpreting the Bohr-Sommerfeld quantum rule (Parisian dis- sertation 1924). I believe that this is a first weak ray to light up this worst of our physical riddles. I have also found some things supporting his construction” (Doc. 399). It is perhaps not surprising that, like Ehrenfest, Adolf Smekal, Erwin Schröding- er, and others also questioned Einstein’s new statistical treatment of the ideal gas (Docs. 434, 433). But Einstein held on to his new idea. He told Schrödinger in crys- tal clear terms how different the new statistics is, and should be: “In the Bose sta- tistics that I have used, the quanta, i.e., the molecules, are not treated as mutually independent. I missed stating clearly that here a special statistics is being applied. For the time being, there will be no other verification for it than its success” (Doc. 446). He went on to explain this new statistics in some detail. But as these examples show, Einstein felt he needed to find further arguments in support of his approach, and to justify its results. He therefore presented a third paper, “On the Quantum Theory of the Ideal Gas” (Einstein 1925i [Doc. 427]), to the Prussian Academy on 29 January 1925, only three weeks after his second one. This installment is quite different from its predecessors. In a letter to Ehrenfest he writes that, on his next visit in Leyden, “I shall then convince you completely of the gas-degeneracy-equation. I found another safe, though not entirely complete, approach to it, free of the incriminating statistics” (Doc. 415). The arguments ad- vanced in this third paper indeed do not make use of the new statistics. Instead, Ein- stein invokes arguments involving dimensional analysis and adiabatic compression.[43] Einstein’s quantum theory of the monatomic ideal gas was a revolutionary step for several reasons. First, while the Planck distribution for radiation frequencies