145 



From this it is evident that the tirst row of values (which 

 correspond to pjc:= 80 atm.) cannot be correct. For then ƒ would 

 steadily decrease from the value 2,77 at 169° up to the critical 

 temperature, where the value would even become <Ci 2 !, whereas 

 it is known that ƒ always passes through a minimum at 7*= about 

 0,7 or 0,8 7\., after which it increases again to 7\.. It is easily seen 

 that also with pk = S'2 atm. the decrease has not been checked up 

 to Tic, and that not until 90 atm. is reached a suitable and possible 

 course for ƒ is obtained. A further calculation, about which presently 

 more, has even taught me that the correct value of pu is still 

 somewhat higher, viz. about 95 atm. — at least when we continue 

 to assume 7^• = 968,1. 



That SiMiTs extrapolated a too low value for pk, is owing to this 

 that he used an invalid formula for this extrapolation; a formula 

 namely, which is only valid at temperatures that lie far from the 

 critical temperature — and which can therefore not serve to extra- 

 polate up to the critical temperature. 



For in the well-known relation of Clapeyron 



dp X 



dt TLv 



Lv = i\—v^ can be replaced by v, only at loiv temperature, disregard- 

 ing the liquid volume; and only at Iota temperatures v, = RT -. p may 

 be put, on the assumption that the vapour follows the law of Boyle 

 — so that only then this formula becomes: 



d log p ?. 



dt RT' 



in which X represents the (total) heat of evaporation. In imitation 

 of so many other authors, who are still of- opinion that this last 

 formula is of general validity, because van 't Hoff and others 

 always used this limiting formula for researches where the above 

 mentioned conditions are fulfilled, Smits assumed that the formula 

 with d log p would continue to be valid up to the critical temperature, 

 when it was only assumed thas A decreases linearly with the 

 temperature up to T^. This now is certainly pretty accurately 

 fulfilled at loioer temperatures, but near Tk ^ suddenly decreases 

 rapidly and becomes = at the critical temperature. On Smits' 

 assumption of linear decrease, however, X would retain a large 

 finite value still at Tk\ 



But we need not speak about this any longer, because, as we 

 observed, the whole formula, the linear decrease of A included, holds 



