the Theory of Solutions. 607 



the osmotic pressure is then defined by the equation, 



ir=p-p (1) 



at the same time 



ir = <j>(c,p,T), ...... (2a) 



where <fi is a single-valued, continuous function of c,pfa.ndT*. 

 When p is introduced from equation (1), we get 



7T=<£(C, 7T+p , T). 



This on solving for it gives 



w=<£o( c >Po> T ) (2.6) 



Consequently it is immaterial, whether we consider it as a 

 function ol p or of p . 



We shall now try to find the innuence**of the external 

 pressure upon the osmotic pressure. For this purpose we 

 find the partial derivatives of tt with regard to p or p — that 



fi 77" /i 77" 



is to say, the quantities ^— and =^— . Let us suppose, that 



we have dissolved a ponderable substance in a ponderable 



Fisr. 3. 



®(* 4 VJ 



(XoVo^q 



Solvent 



fluid. The solution is separated from the solvent by a semi- 

 permeable membrane, that forms a closed surface which we 

 can suppose given by the equation 



+C« jy ,#)=0. (Fig. 3.) 



* See Duhem, Mecanique Chimique, tome iii. livre vi. 



