D O C U M E N T 1 0 3 N O V E M B E R 1 9 2 5 1 2 3 This immediately changes, however, if one relinquishes the sole assumption that you explicitly emphasize and forbid . Then a phase region of quantity in the vicinity of is inaccessible, similar to how a finite phase region of corresponding magnitude in the vicinity of is inaccessible in the Bohr atom. Starting with , then increases only very gradually to: , so that despite the enormous value of β (just as long as β does not exactly become order of magnitude N), the summed term under normal conditions may be regarded as a quasi-continuous function of index n and the sum may be approximated by an integral. I do this, but like Planck, Berl[iner] Ber[ichte] 1925, p. 52,[4] I attach to the in- tegral the first ( ) summed term that is multiplied by ϑ ( Then, for a suitable ϑ, all the subsequent formulas fit exactly, independent of the value of β. is introduced into the integral as a variable. This yields . This integral is easily evaluated however, it is more convenient to refrain from do- ing so. I now introduce and write as follows, where , for the sake of brevity: (X) . The curly bracket is the degeneracy factor. It stays very exactly = 1 with increasing β (decreasing temperature or volume) as long as β differs from l only by magni- tudes of the order of (i.e., until the difference has dropped to the order of magnitude ). I shall set . For , I set its value according to the formula indicated on the first page. = gas constant. Thus I arrive at . n 0= N!h3N E 0= E ∞ –= n 1= n3N 2 ------- nd d n3N 2 ------ - 2 3N ------ --------------- 1 n 1 2 3N ------ -– - = n 1= 0 ϑ 1).[5] ≤ ≤ y n3N 2 ------- = Ψ klg N!)® ( 3N 2 ------ - e–βyy 3N 2 ------- 1 – yd 1 ∞ ³ ϑe–β + ¯ ¿ ¾ ½ = βy x = 3N 2 ------ - l = Ψ klg N!)( ( l!)β–l® 1 e–xxl 1– xd l 1– ( )! ----------------------- - 0 β ³ ϑ------------ e–ββl l! + – ¯ ¿ ¾ ½ = l l β – l { } f(β) = β–l R Nk = Ψ§ =S E· T¹ --- – © 3R 2 ------ - lgT RlgV Rlg--------------------- 2πmk)2 ( 3 -- - h3 klgf(β) + + + =