THE THEORY OF OSMOTIC PRESSURES. 287 



and w the latent heat of fusion of ice = 79 cal.), then the 

 work can be reckoned from the following formula : — 



( /A = ry x dv. 



Thus for 1 per cent, solution of cane-sugar (A = '055) 



dk - '° 5579 x dv. 

 273 



To reduce this result to gravitation units we must 



multiply by 424, and we thus find that to separate the volume 



dv of pure water as ice from 1 per cent, cane-sugar solution, 



a force is necessary equal to the pressure of a column of 



c 'Oss x 79 x 424 . • , . , . 

 water of — — — ^— — metres in height. 



2 73 



A depression of A = - 1 ° corresponds therefore to an 



_ 79 x 424 

 osmotic pressure of ; that is to say, to 1227 



metres of water. We have therefore to multiply A by 

 1227 in order to obtain the osmotic pressure in water of 

 any solution. 



We must now consider how these results can be applied 

 to determine the amount of work done by the kidney cells 

 in secreting a given specimen of urine. Dreser takes for an 

 example the case in which during a night 200 c.c. urine 

 were secreted with A = - 2-3°. This was separated by 

 the kidneys from the blood with A = — 0*56°. We have to 

 determine what work has been done in this process. This 

 can be calculated from a simple formula. Let a be the 

 amount of dissolved substance (a constant). This is dis- 

 solved in the variable quantity v, forming a solution con- 



. a y 

 taining y per cent. We thus get the equation -= — ; 



the concentration;/ is, however, also a measure of the osmotic 

 pressure. The amount of work necessary for pressing 

 through a volume of water dv is therefore dA = ydv, or, 



since y= l °° a \ dA = ^ dv. Therefore A = iooa|-= 



J v v J V 



icort log 6 v 4- C. If the original quantity of the solvent 



f^i dv 



was v„ and the final amount v 2 , A = iootf -— - or A = iooa 



V 2 v 



(log, v, - log, v 2 ). 



