/- ..=(..-.., '^ '"-' 



!)2il 



V 



(26) 



l-b'k 8 

 in wliieli 6 i« detonnincd tliroiigh (c). (cj now becomes namely : 



yielding 



ö + 1 =- (1 - h'k) — ^- ..... (26a) 



^^- — ^-'n 



But here too there is no con\'ei-gency for i\ , l>^. For small values 

 of bic — ^0 (26) namely approaches to 



because 1 — b'k and {6 -\- 1) -. 6 then approach to 1, while between 

 [] again 1 has been omitted by the side of (?;^- : r^)^, which approaches 

 to infinite. The first member is =1, the second member approaching 

 to 0X0!°°, hence to oo. 



Also when {v — v^)—^ had been assumed, we should have found the 

 same impossibility; even still intensified, because then (v/^ : ?;„)"/'^'(^''''"~''o) 



would have become [(n:—Vo):(^'o—^'o)]^''''~'"-^'^'''''~''"M'>ecause of which 

 the root of the power would ai)proach x for all the values of 6^- — b^ ^). 



In the same way the functions may be tested, in which v : {b — b^) 

 is written instead of v : ^. The functions — ƒ {v) and f" (v) then 

 become somewhat more intricate, but the divergency at v^, b„ 

 continues to exist. 



And as for van der Waals's equation in the general form 



b—b„ 



V — b 



bn — b, 



(27) 



the so-called "equation of state of the molecule" — this leads to 

 such complicated expressions foi- ƒ and n, in order to satisfy the 

 relations (24), that no physical significance can possibly be assigned 

 to these expressions. Also when v — v^ is substituted for v^). We 

 shall, therefore, enter no further into all these calculations, and 

 leave their execution to the reader. 



Before leaving this kind of functions, which all lead to failures, 

 I will just point out that if one should want e.g. to derive from the 



1) Also the supposition f{v) = i j — I \ leads to the same impos- 



