96 Chapter VI 



V . Hence if we use the membrane B^ to concentrate this body from a volume 



c \ 



c ' 

 V - - to a volume F, we have to do work against its osmotic pressure. On the 



c i 



membrane we have two osmotic pressures working, one each side, viz. : the fixed 

 osmotic pressure p 1 of A 1 in the original solution, and the gradually increasing 

 osmotic pressure p of A 1 in the gradually concentrating solution. The total work 

 done is 



v c - 



f r' \ f c /' / /-\ /' 



-Pi (F--r} + pdv = -p, V - 1 i --, ) + Vc'RT log - , 

 V c ) ]v c\cj 5 c' 



according to the gas laws: or finally, since pv-nRT, where n is the number of 



c ' 

 molecules of gas considered, putting p-^V - - Vc'RT, we find the total work to be 



C 



= - V (c,' - c,) RT+ Vc{ R T log ^ 



c i 



Using now a membrane B. 2 permeable to all the bodies except A 2 , we find we 

 have to do work 



- V (c,' -cJRT+ VcJ R T log - , 



C 1 



in concentrating A z ; &c. 



The total work W is the sum of all these terms, each of which must be positive*.] 



The considerations which have just been applied to the problem 

 preclude us therefore from drawing any comparison between the 

 gaseous exchange of the kidney and the so-called work as calculated 

 only from the freezing points of the blood and urine. The freezing 

 points give us positive assistance in another direction, however, for 

 they show that as between a kidney which is not secreting and one 

 which is secreting the latter must be doing positive work in virtue 

 of its secretion, unless the urine and the plasma are of the same 

 crystalloid concentration for each salt separately. The urine secreted 

 in response to such diuretics as sodium sulphate and urea is not of the 

 same saline concentration as the plasma, as shown either by actual 

 determinations of the salts, or by the depression of the freezing points. 

 Since the gaseous exchange of the kidney has been determined in 

 many of these experiments on sodium sulphate and urea diuresis, we 

 may proceed to see whether there is a call for oxygen in such cases. 



Let us be clear, however, how far we are relying on our freezing- 

 point determinations; we are merely using them as an indicator 

 to show that if the freezing points of the blood and the urine are 

 different, the saline concentrations of one or more salts cannot be 

 identical in the two fluids, and therefore work has been done. The 



* The above discussion of the work performed by the kidney has been con- 

 tributed by Mr A. V. Hill. 



