éii 



R 1 



'/'—cv (2) 



If we put : 



p{v-h') = RT, 

 in which // is the vahie of h which would be found by leaving 

 the quasi association out of account — so the real value therefore 

 in the usual sense — , then by comparison with (1) follows : 



'■ - ''■ = ï^l-r=^{' ^ ') <' + V, 4 = '■ (l - ' + V. '^ 



so 



thus 



b' — h — V. y^x (3) 



Accoi'ding to (2), however, v . \'^ x = R : C, when v approaches 

 to ao and ,v to 0, so that we finally get ; 



in which b = 4?» according to the kinetic theory of the perfectly 

 elastic collisions of the molecules, supposed to be spherical. And as 

 C — the association constant — will always possess vi finite vakie, 

 for else there would not be quasi association, ^\e have always-. 

 h' <^b , i.e. 6'<4m (q. e. d.). 



At the head of our paper we spoke of "apparent thermodynamic 

 (liscontimiitii:-!, and mean by this what follows. 



If there were no quasi association at all, i.e. if the association 

 constant C were absolutely = 0, so that there could not exist quasi 

 association at any volume, iiowever small — then // =. h = 4???. 

 But as soon as there exists quasi association {C unite), however 

 slight it may be (according to (2) = for v = go), immediately 

 b {= 4m) is diminished by the finite quantity R : C, as z; X V^^^'^ oo X 

 is always finite, so that b' becomes <^4???. 



There is therefore discontinuity — for at an association state = 

 for V = (X), b' can have the value 4??i, and also possess all the values 

 <[ 4m. But this is only apparent, because the diminution of 4?7i 

 depends continuously on the value of the dissociation constant C, 

 which can vary from to any finite value. 



Now C is not known, and this quantity, which depends on the 

 entropy constants, could only be determined by statistical-mechanical 

 way, when we knew all the circumstances accurately and could 

 take them into account, which determine the quasi association. In 



40 



Proceedings Royal Acad. Amsterdam, Vol. XVII. 



