SECRETION 339 



and T at 37 C. is 310, so that 



A= 58-61 litre atmospheres, \ v 



1421-4 gram calories, > x log 



or 605 - 5 kilogram metres ) 



The same expression, as we saw before, applies to the alteration of the con- 

 centration of a solution when produced in any way. Of course, when electrolytes 

 are concerned, changes in electrolytic dissociation must be taken into account. 



Incidentally, it may be remarked that, as regards calculations involving energy factors, 

 living organisms have the advantage of their reactions being carried on in a practically 

 isothermal system, so that the formulae are comparatively simple. Any change of temperature 

 is so small as to have only a minimal effect on the results of the calculation. 



To proceed, the total osmotic concentration of the blood is about 0-3 molar, 

 and from this, under ordinary conditions, the kidneys produce a urine which 

 is about molar, that is, the osmotic pressure is increased rather more than 

 threefold. 



Instead of volumes in our formula, it is convenient to take concentrations, 

 which are the reciprocals of the volumes in which 1 gram-molecule is dissolved. 

 Further, since the osmotic pressure (IT) and the depression of the freezing 

 point (A) are a l so i n direct relation to one another, we can take, in place 



of ^, either ' 2 , * 



' ' 



Strictly speaking, the use of the last expression is only permissible at the temperature of 

 the freezing points in question, since electrolytic dissociation may not be the same. But the 

 experimental error of the freezing point measurements exceeds the very small errors possible 

 on account of differences of dissociation. 



Accordingly, the minimal work which the kidney must do in order to produce, 

 from a glomerular filtrate of Ap a urine of A2> ^ n an amount which contains 

 1 gram-molecule at 37 is 



A= 58*61 log ^ litre atmospheres = 1421-4 log -TT gram calories 



A, 

 = 605-5 log r^ metre kilograms. 



If n mols. are compressed instead of one, the work is increased rc-fold. The 

 molar concentration, in practice, can be best obtained from the depression of 

 the freezing point, to which it is related, as we have seen (page 155), and in 

 the following way : 



which gives the number of mols in v litres of solution. 



The depression of the freezing point of urine (A2) i s between l-5 and 2, 

 so that, for simplicity of calculation, we may take it as l-85, and there are, 

 in man, about 1'5 litres produced per day, hence: 



1-85x1-5 



1-85 ' 5 ' 



A! (that of blood) is 0'56. 



Inserting these values in the above equation, we have 



A = 1-5 x 58-61 x log ^ = 45-6 litre atmospheres, as the daily osmotic work of 



the kidneys. 



But, as Dreser points out, we must remember that to produce 1-5 litres of 

 urine of A = l-85 from blood of A = 0'56, 



1-5 x p.*,. = 4-955 litres of blood are required. 



In the calculation, the difference between this quantity and that of the urine 

 secreted, namely, 4-955 - 1'5 = 3'455 litres, has been reckoned as pure water. In 



