910 Mr. S. A. Shorter : Application of tlie Theory of 



a pressure equal to its own vapour-pressure, equation (5) 

 gives the value of / (0, II , 0)—f Q {s, II , 6) in terms of the 

 osmotic pressure. If we equate this to the value given in 

 equation (8) we immediately obtain a relation between this 

 special osmotic pressure and the vapour-pressure. A much 

 more general equation can, however, be deduced without 

 difficulty. Suppose that we have a solution of concentration 

 s under a pressure p in osmotic equilibrium with a solution 

 of concentration s f under a pressure //. Let II and II' be the 

 respective vapour-pressures of the two solutions. A relation 

 between these four pressures may readily be deduced from 

 the three equilibrium equations 



f o (s,p,e)=/ <t ( s ',p',0), 

 /„(.<, n,0,=F o (n, 6), 

 f (s',w,e)=Y (n',e). 



These three equations may be combined so as to form a single 

 equation containing three potential differences, whose values, 

 in terms of quantities which may be measured experimentally, 

 are given by the equations 



f (s, P , 0)-/ o (s, n, o)=( P -ri)F (s, n+p, e\ 

 Ms',/, ey-Ms', it, 6y=(p'-n')P (s', n'-^', e\ 



F (IT, 0)-F o (n,0)=\ Y(x,6)dx. 

 J n 



On substituting these values in this equation we obtain the 

 equation 



j 



n 



.... (9) 



This equation (which, of course, is exact) may be regarded 

 as the fundamental equation connecting the vapour-pressures 

 of two solutions and the pressures under which they co-exist 

 in osmotic equilibrium *. 



If we suppose that s>s', ihen p>p' ; and rearranging the 

 terms of the equation so as to involve directly the difference 



* If the concentration of one of the solutions is made equal to zero, and 

 the two terms on the right-hand side of the equation are written in the 

 form of definite integrals, we obtain Porter's result (loc. cit.) connecting 

 the osmotic pressure and vapour-pressure of a solution. 



