D O C U M E N T 4 2 0 N O V E M B E R 1 9 2 6 3 9 9 Thereby nothing special occurs except that the lowest quantum state is filled at the expense of the higher ones.[6] [Stronger than according to eq. (1). According to eq. (3), this preference for the lowest quantum state would emerge as weaker than according to eq. (1).] § 2. Einstein obtains a different result because he proceeds as follows: He develops each term of the sum (4) in a series and exchanges the summation se- quence 5) Thereupon he approximates the inner sum by an integral 6) = and then he’s astonished that the expression thus formed, which should describe the n’s 7) for all ெpermissible” values of α (that is, ), cannot exceed a specific finite value. From this he concludes that if one then does press more molecules into vol- ume V, Nature wriggles out of this embarrassment by separating out part of the molecules into a condensed phase. Then it would also be amusing to see the predicament Nature would be in if mol- ecules were forbidden from assuming zero translational energy, as Schrödinger does! And one understands how happy the Fermi-Dirac gases were that their plus sign prevented them from falling into this predicament. We would, however, like to ask Privy Councilor Einstein, with all due modesty, whether he seriously believes that his integral approximation discussed here for this domain is still valid, THEREBY performing THE PURELY MATHEMATI- CAL miracle of still keeping the quantity (4) for α equal to finite, simply by transforming it into the form of 7? § 3. ெHow is your commendable northward trajectory going?” § 4. P.S.: Who’ll be plucking out the next feather from the tail of Bose-Einstein statistics?! Leyden, Instit. for Theor. Physics. n αeβεs )– p 1 – 0 p ∞ 0 s ∞ ¦¦( p 1¦e–βεs(p – 1+ ) 0 s ∞ 0 ∞ ¦α– = = p 1+ ) 0 s ∞ ¦e–βεs( α e–βε0 e–βε0