( 631 ) 



position that if* there is a specific factor f, for t lie mutual attraction 



of the molecules of the first kind of which we do not know with 

 what property of these molecules it is in connection, and if there 

 is also a perfectly different factor e s for the mutual attraction of the 

 second substance, we must not represent the specific factor for the 

 attraction of the different molecules inter se by s la , but by l/^a- 

 It is true that this supposition renders the calculations simpler ; I had 

 already drawn attention to this in my Theorie Moleculaire (Cont. II, 

 p. 45). But whether the calculations are somewhat more or some- 

 what less easy does not seem a sufficient ground, after all, to intro- 

 duce a supposition which involves that naturally a great number of 

 possible cases, among others also for the course of the spinodal line, 

 are excluded. If we put all possibilities for the value of a 13 , then 



da x a a ~ a l<i 



— can also be =0, viz. for- =: . We need not go so far 



dx 1 — x a x — a 12 



however, to give sufficient width also to the left region. 



The course of the ^-lines. 



The value of I — J = q is found from the value of \p : 

 \ax J 



*=** r/ ï^ +ƒ(■£)*■ 



For x = this expression is negatively infinite, for x = 1 it is 

 positively infinite, so that we have q = — oo and q x = -j- oo. 

 But it follows also from the equation of state that for all values 



J\dx 



of x the value of 1 I -=— 1 civ is also positively intinite for the line v=b. 



V 



It is true that for such small volumes the equation of state 



MRT a 



p = is not accurate when b is not made to depend on 



1 v~b u 2 v 



v, and the quasi association in the liquid state is left out of account, 

 and that the conclusion : I ( — J civ is infinitely large for v equal to the 



V 



limiting volume, calls for further consideration before we may accept 

 this as an incontestable truth. But it seems to me that simple con- 

 siderations lead to this conclusion. For the limiting volume /; is 



fdp\ 

 infinitely great, and if b increases with x, I -j- ] is infinitely large 



43 



Proceedings Royal Acad. Amsterdam. Vol. IX. 



