460 



m= 1.95 1.43 1.13 1.04 1.01 0.98 0.94 0.91 0.88 0.81 0.74 (5.65 0.60 

 l/7n= 1.40 1.20 1.06 1.02 1.005 \ 0.99 0.97 0.95^0.94 0.90 0.86 0.806 0.775 

 0.4 im= 0.56 0.48 0.42 0.41 0.40 0.40 0.39 0.38 0.38 0.36 0.34 0.32 0.31 



;? found 0.55 0.51 0.45 0.43 0.42 j 0.39 0.37 0.37 0.36 0.35 0.34 0.33 0.323 



The values on tlie lefthand side of the dividing line might have 

 a somewhat higher factor, viz. 0,42 ; those on the righthand side of 

 the line (the liqnid valnes) a somewhat smaller factor, e. g. 0.39. 



Yet this relation can hardly satisfy for several reasons. First becanse 

 the formula /? = 0,4^/??^ would yield too large vahies oï ^3,, for 

 larger values of m ; it is at least inconceivable that the increase of 

 bg with the temperature will continue indelinitely. But secondly the 

 variability with v would disappear through this consideration, and 

 only dependence on T would be assumed. It would tlien be quite 

 indifferent, whether h was considered at large or at very small 

 volumes. That this, however, is entirely impossible, is at once seen 

 when we bear in mind that only by the assumption b=f{v) we 

 duly get r<3, 6- > V3 , and/>4! Only for "ideal" substances, 

 i.e. at the absolute zero point, can b be independent of tiie volume. 



Other relations could also be derived, among others between the 

 found values of /?, n — ^, and in'), but they may also be due to 

 chance. We shall, therefore, no longer dwell upon them. 



19. The characteristic function. 



It is known that for "ordinary" substances the value of the 

 "characteristic" function q, i. e. 



/-I * 



y 



A— 1 'hh 



in which / = — is not constantly -■= i — as would have to 



g ant 



be the case, when a or b should either not depend on T or only 



linearly — but with diminishing m increases from 1 to about 1.4 



at m = 0,6, with about 1,5 as probable limiting value wheu )n 



approaches to 0. See van der Waals, and also my Paper in These 



Proc. of 25 April 1912, p. 1099—1101, in which it appeared that 



fp = 1 -{- 6,8 (1 — m) can be put in the neighbourhood of the critical 



point, (loc. cit. p. 1101). 



1) When e. g. in the region of coexistence for the dilferent values of wi we write 

 le corresp 

 viz. ±0,23. 



the corresponding values of n and w — /3, -j-—^. appears to be about constant, 



