608 Mr. L. Vegard : Contributions to 



Let its furthermore suppose that the membrane is ex- 

 ceedingly thin, and that it can, at the same time, stand a 

 great pressure ; conditions which cannot actually be realized 

 in practice, but can be approximately, by fixing the membrane 

 in a porcelain cell. 



We consider the system after an ideal state of equilibrium 

 has set in. As long as we are in one of the fluids, the 

 general condition for mechanical equilibrium must be 

 fulfilled. According to equation (1) § 1, we get : — 



(1) For the neighbourhood of a point (# 1? y u r 2 ) of the 

 solution : 



dp=s -i ^(y i) dx + a u (*«*3).iy + M dz ) . 



(2) For a point (# 2 , y 2 ? -2) °f t ne solvent : 



U means as before, the potential for the field to which the 

 system is submitted. We suppose that U, as well as its first 

 partial derivatives with regard to a, ?/, z, are continuous 

 functions in the space occupied by the system. 



Now suppose the points («a?j y± z x ) and (# 2 f/ 2 z a) approach 

 the point (^0^0^0)5 situated on the surface ^ = ; the total 

 variation of osmotic pressure along the surface will be 



+ 



y ^:) }► (3a) 



Besides, according to (2a) we have 7r as a function of T, c, 

 .and ^>. We suppose the temperature to be the same through- 

 out the system, while p and c vary with the coordinates. 

 Consequently we get 



dir = ( ^— ) dc + ^-dp, 

 \oc J p dp 



If the values for dc and dp are introduced from equations 



