on Osmotic Theory. 269 



for compartments (2), (3), (5), and (6), for the substance B 

 and membranes permeable to it only. There are thus twelve 

 fundamental equations, from which all possible combinations 

 can be derived. My original intention had been to carry 

 out the necessary cycles in the manner of Prof. Porter's 

 paper (loc. cit. ante), but Mr. G. W. Walker pointed out to 

 me that we are able to obtain more information by taking 

 the compartments in pairs. A formal demonstration is 

 reserved until such time as there is a prospect of measuring 

 experimentally the quantities involved. 



Incidentally, the following two relations between com- 

 partments (2) and (5) can be obtained directly, although 

 they can also be derived by the previous method. 



Thus, supposing both halves of the horizontal membrane 

 to be open, pass a grammes of A and b grammes of B from 

 (5) to (2), change the pressures to p' and yfr „ pass the 

 substance back again and restore original pressures. We 

 get 



rp' r* P < ft? 



\ sdp = a\ <r a dp + b\ <rdp. . . . (2) 



Jp J+p h v 



In the method by which equation (2) was derived 

 a and b grammes of the respective components were simul- 

 taneously passed through the membrane ; we can, however, 

 get the same result by performing two cycles one after the 

 other, thus : 



Let the right-hand half-membrane be closed and perform 

 our standard cycle by passing a gramme of A through it ; 

 we get 



M ** d P = A P o-Jp; 



(3) 



then perform a similar cycle with the left-hand half, and we 

 get 



b\ s b dp = b\ crpdp, (4) 



from which (2) is at once obtained. 

 If a = a, then from (3) and (4) we get 



n p' rvi 



sdp = \ 



Jp ' J ^p 



dp (5). 



