( 786 ) 
equation (10) can be reduced as follows: 
db db 
v a wv r 
) 1 da ! ] {4 b da bn 
Ae de v—b Ee Oke Rn. REE v—b 
db 
Wb — «x - 
b a db EN) b de 
Ae itn en 1 {j+—_ =--1(v)+ er mn =] 
i rde r v v 
2b, (1—a) + 26,,2 
ANNE ee en E En 
So these terms too perfectly agree with those of equation (9), 
provided the higher powers of : are neglected. So the 7 (7’) of equa- 
; 
tion (8) should be chosen so that the functions only dependent on 
temperature disappear from the thermodynamic potential, and the 
whole expression is multiplied by p/ 7. So the two methods, the 
kinetic and the thermodynamic method supplement each other. 
Thermodynamically it can be shown that the quantity which occurs 
in the exponent of equation (8), must necessarily be the thermody- 
namie potential, at least as regards its dependence on + and x; but 
concerning its pure functions of the temperature thermodynamics 
cannot give a decision. On the other hand the kinetic theory is 
adequate to show, that we must get an equation of the form of 
equation (8) for NV, and it can determine the 7 (7). It can, howewer, 
show with only a very rough approximation — until a proper ex- 
pansion into series for b is known — that the occurring function of 
the volume and the concentration is the same as that which occurs 
in the thermodynamic potential. If these two methods are combined, 
we may, in my opinion, conclude with certainty, that the number 
of particles under investigation is really represented by the formula: 
u 
N= OUT RT EN oee er EN 
in which « represents the thermodynamic potential without its 
functions only dependent on the temperature. 
6. Now it is easy to draw up the equation for the “osmotic 
temperature’ by means of formula (11). A stationary state will, 
namely, set in when the number of molecules going to pass through the 
membrane on one side of it has increased by rise of temperature 
as much as it has decreased by the addition of the dissolved sub- 
stance, or in other words, when : 
