OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OP CALCIUM FERROCYANIDE. 199 



MODIFICATION OF PORTER'S EQUATION. 



The experiments on vapour pressures and on the equilibrium pressure were done in 

 air, but Prof. PORTER'S equation is derived from the consideration of somewhat ideal 

 conditions approximating to that of a vacuum, and it is therefore necessary to obtain 

 an expression suitable to the conditions of the actual experiments. 



This may be derived in the following manner : 



Assume that the pistons in the ideal apparatus are permeable to air but not to the 

 liquids or their vapour, then no work can be done on or by the atmosphere. 



Using the notation on p. 177 with the additional symbols 



A = pressure of the atmosphere ; 



7r n0 = vapour pressure of the solvent in air when it is under a total pressure 

 of A + 7r au ; 



Tr a , = vapour pressure of the solution in air when it is under a total pressure 

 of 



and performing the thermo-dynamic cycle, as in Prof. PORTER'S paper, it is easily seen 

 that the work done in the various operations is : 



1st operation. P<A +*)%+, ~ (/V 



f"(A + ir ) 



2nd operation. pdnir M v n +(A + 7r,, (l ) ?/ (v+ff >. 



3rd operation. "" p dv. 



pA + n- f"A+7T 



4th operation. pdV-+ir a ,v a , (A.+ir t , r )8 (fL +, } + \ *pd(V+s). 

 Summing up, equating to zero, and integrating by parts, we get* 



sdp = \" vdp+\ udp (2). 



jA+ ' r ,, n . J W JA+ *O 



This equation is, in appearance, the same as Prof. PORTER'S, with the limits slightly 

 altered ; yet if we carefully consider what assumptions underlie the various operations, 

 it will appear that the quantities involved are different. 



* Since this was written, Prof. PORTER has published the second part of his paper " On the Osmotic 

 Pressure of Compressible Solutions of any Degree of Concentration" ('Proc. Roy. Soc.,' A, vol. 80) ; he points 

 out, in a private communication, that equation (2) may be directly obtained, as in Section 5 of that paper, 

 by estimating (throughout the cycle) the changes in jt> dp, which must vanish also because this integral is 

 the same as \pv\ - \pdv. 



