340 PRINCIPLES OF GENERAL PHYSIOLOGY 



point of fact, it is kept in the blood and at a A of 0'56. We have thus made the 

 work of the kidneys too great by the amount required to raise 3 - 455 litres to the 

 osmotic pressure corresponding to a A of - 56. A A of 1'85, as we saw (page 155), 

 is equivalent to the osmotic pressure of a molar solution, that is 22*4 atmospheres ; 



therefore, 0'56 means an osmotic pressure of 22*4 x = 6'8 atmospheres at the 



1 o5 



freezing point, or 7 '7 atmospheres at 37. We have to subtract, then, 3'455 x 7'7 

 = 26*6 litre atmospheres, from our first value of 45'6, leaving 19 litre atmospheres 

 as the correct value, on our simple assumption of mere total concentration. 



But, as already remarked, this is not all. We must take account of the 

 relative concentrations of the different constituents of the urine, since they are by 

 no means equally compressed. The urine is not merely a glomerular filtrate boiled 

 down, as it were. This question is treated in the paper by von Rhorer (1905), to 

 which the reader is referred for more details than can be given here. It will be 

 clear that a completely accurate measurement of the total work done could only 

 be obtained by taking each constituent of the urine for itself. As an illustra- 

 tion of the method, we may take the two chief constituents of the urine, sodium 

 chloride and urea, as is done by von Rhorer (pp. 388-390), and, indeed, the osmotic 

 concentration of the other constituents is comparatively small, so that our result 

 will not be far wrong. 



Instead of the complex glomerular filtrate, we imagine, in the first place, a pure 

 solution of sodium chloride of the same concentration as that in which it exists in 

 the blood, that is 0'18 molar, inclusive of ions. We have to concentrate this 

 solution to that of the sodium chloride in urine, that is, to 0'36 molar. It will 

 be instructive to treat the problem in the way done by van't Hoff, described 

 in one form on page 157 above. We imagine a cylinder closed at the end, and 

 containing a piston impermeable to sodium chloride, but permeable to all the 

 other solutes of the glomerular filtrate and to water. We compress the filtrate 

 until the concentration of the sodium chloride below the piston is raised to 

 0'36 molar. In the kidney the concentration is only raised from 0'18 to 0'36, while 

 in our imaginary model no sodium chloride passes through the piston, but water 

 does, so that the original concentration of 0' 18 molar above the piston is lowered; 

 we must therefore add continuously sodium chloride to the solution above the 

 piston in order to maintain its concentration constant at 0'18 molar. We keep 

 thus the osmotic pressure above the piston unaltered at p , while below it the 

 pressure during the operation is a variable one, p, and is raised gradually from 

 p to 2p (0'18 to - 36). The work done consists, then, in raising the pressure of 

 a volume of solution by a series of infinitesimal steps from p to a higher one, 

 through the variable pressure differences of p -p . That is : 



dA = (p- Po )dv. 

 The integral of this expression consists of two members 



"v 

 A= I .pdv-v,. I dv 



where v is the initial volume and v the final one, the actual process being 

 performed by the diminution of the volume from v to v. p , being kept constant, is 

 not subject to integration. 



The first member we know already (page 33) as 



wBT x 2-3 x log,-?- 

 e < v 



The second is simply : 



-p (v-v). 



?? c 



Instead of - we can put (concentrations instead of dilutions), and since 

 v c 



vc = v, c = n (c being the number of mols. dissolved in v), 



, n j n 

 v - and v = -. 



