( 136 ) 



we cannot expect lliat the calculations requii-ed for this purpose will 

 soon be performed. Even the determination of ,? required an enormous 

 amount of work — compare the calculations of van Laar. 



For complex molecules another reason is possible for decrease of 

 h with decreasing volume. The molecules might really become 

 smaller under high kinetic pressure i.e. in the case of high density. 

 If the atoms move within the molecule — and we can hardly doubt 

 that they do so — they require free space. And it is highly pi'obable, 

 we may even say it is certain, that this space will diminish when 

 the pressure which they exercise on one another, is increased. The 

 mechanism of the molecules however being totally unknown it is 

 impossible to decide apriori whether this decrease of the volume 

 of the molecules will have a noticcai)le effect on the course of 

 the isothermal. In my application of the theory of cyclic motions 

 on the equation of state I have tried to give the formula which 

 would re])resent such a real decrease of the volume of the molecules 

 with diminishing \olume. van Laar has tested this formula to Amagat's 

 observations on hydrogen, — and though new difficulties have 

 arisen, the agreement is such that we may use the given formula 

 at any rate as an approximated formula for the dependency of h 

 on V. I will apply the formula, which may have a different form 

 in different cases, in the following form : 



1- {, r) (4) 



V — b \bfi — i,^ 



The symbols hj and A„ in tlii> formida denote the limiting values 

 for f), the first for infinitely large \()lum(\ the second for the 

 smallest volume in which the substance can be contained. For 

 more particulars I refer to my paper on "The equation of state and 

 the theory of cyclic motions." Van Laar concluded from his inves- 

 tigation that agreement is only to be obtained if />„ decreases with T, 

 a result which 1 myself had already obtained applying the formula 

 for carbonic acid (Arch. Neerl. Serie II, Tome lY, pag. 267). If this 

 is really the case and if it appears to be also true after Ave have 

 modified thg formula in some way or other compatible with the 

 manner in which it is derived, then the following difference exists 

 between the course of b with v when ascribed to a quasi-diminishing 

 and when ascribed to a real diminishing of the volume of the 

 molecules : in the first case b is independent of T, in the second 



case however it does depend on T. The fact that f — j is not per- 

 fectly constant seems to plead for the latter supposition. 



