The call for oxygen by the kidney 



Of the remaining terms in the expression for W, 



95 



the freezing points give us absolutely no evidence. Their use for this 

 purpose involves a very serious error, for these neglected numbers 

 may be relatively very large : for example, if AI represents urea, 

 d' the concentration of the urea in the urine is very large, while d 

 the concentration in the blood is extremely small. Hence the first 

 term 



e/ log ^ 



is very large and cannot be neglected. Similarly if we consider some 

 body occurring largely in the blood, and not so largely in the urine, c' 

 is small while c is large, so that 



VRTc'log- 



may be finite and negative. In order therefore to calculate W we 

 can only gain satisfactory results if we know the concentrations in 

 blood and urine of each separate important constituent. Without 

 this information, the results deduced from freezing-point measure- 

 ments are completely fallacious. 



V 



B,, (B,,) 



FIG. 56. B n B n represents the membrane used for concentrating the substance A n , 

 B n initial position. (B H ) final position. 



[An actual reversible process by which the separation might be carried out is as 

 follows : (It should be noted that I am not proposing in any way a hypothesis of 

 kidney secretion, but ani merely describing a method by which it is possible to 

 calculate the minimum work which it is necessary to do in order to separate the 

 urine). 



Let us suppose a membrane B l permeable to all the dissolved bodies except A 1 : 

 then the substance A : which, in the urine in volume V is at concentration c/, and 

 which was initially in the blood at concentration c x , must have occupied a volume 



