754 



fdp\ 

 modified, as — will then get a more intricate form — the more 

 \dtj, 



so as also b will appear to be a function of T '). 



I do not consider the theoretical grounds, on which v. d. W. 

 bases the dependence of a on ?;, convincing enough; with his con- 

 siderations (especially those on p. 365 and 366), for so far as I am 

 able to follow them, 1 cannot entirely concur '). 



II. Investigation for hydrogen. 



We shall not discuss this at any length, but communicate the 

 result of the investigation desired by v. d. W. concerning the region 

 above the critical temperature. No other substance is so well adapted 

 for this as hydrogen, of which we possess determinations of the 

 isotherms from —257° C. = 16° abs. to 100° C. = 373° abs. inclu- 

 sive through the exceedingly accurate investigations of Kamkrmngh 

 Onnes and his collaborators. Further the very accurate experiments 

 by Schalkwijk at 20° C. and those of Amagat from 0° to 200° C. 

 The critical temperature of H, lies at 33° abs., so that the examined 

 region extends from '/» "Ik (below which H, becomes solid, viz. at 

 14° abs.) to more than 14 7Y; hence it also includes the Boyle- 

 point at 3'/^ 7\. 



Already in 1903 I was occupied with the course of the values 



') Gf. also my paper: "On the Values of Some DitTerential Quotients etc." in These 

 Proc. of April 1912 especially i'. 1099 — 1101. There also the temperature function 

 1 + ^^(1— m) — V2(l — ^)t in which m = T: Tyt, proposed ^/«ew by v. d. Waals, which 

 is in good harmony with the results, was discussed. But also in this formula the 

 critical temperature plays a very special part, and for values of T'> Tk (m > 1) 

 it yields moreover imaginary values. 



') In passing I draw attention with what was said on p. 360, where in the 

 transition case I = ïlr {l-\- 2r = distance of the centres, 2r diameter molecule) 

 the available space for the movement of a molecule is assumed to be = 8m (m = 

 the volume of a molecule). It is easy to see that this must be about 16m. For 

 in the case in question the lineary distance of two centres is just twice as great 

 as at contact, hence the volume 8 times as great. Hut the volume at contact is 



6 



not = m, but = — X m = 1,91 m, so that the available volume becomes = 15,3 m. 



And as Vj^ is assumed to be = 26 = 8m by v. d. W. [this is however only the 

 case for substances with comparatively high critical temperature, see "New Relations" I 

 (These Proc. of Febr. 1914), where Vj^ibj^ in general was found = 2y], the volume 

 in question is not = rA;, but almost ^vk- For v = vk, (/ + 2r): 2r is therefore not 

 = 2, but about l3^^4, so that the conclusions drawn by v. d. W. with respect 

 to Vk are untenable. 



