960 



Dr. S. A. Shorter : Contribution to the 



composition o£ the ether phase is the same as that of the 

 ether phase in equilibrium with water at atmospheric pressure. 

 According to Trouton, the increase of pressure necessary to 

 bring about this equality of concentration is the osmotic 

 pressure of the sugar solution. 



This statement necessarily involves the assumption that 

 the effect of the ether dissolved in the water phase is negli- 

 gible. If we make this assumption, the correct theory of 

 the experiment is quite simple. Let X represent the increase 

 of volume of a large mass of sugar solution when unit mass 

 of water is added to it, and fju the corresponding quantity in 

 the case of the etherial solution of water. Consider pure 

 water and the sugar solution under atmospheric pressure. 

 The chemical potential of the water in the sugar solution 

 will be less than that of the pure water. Now suppose that 

 if the presssure on the solution is increased by an amount 12, 

 the two potentials are equalized. 12 will, of course, be equal 

 to the osmotic pressure of the sugar solution. If we neglect 

 the variation of X with the pressure, this increase of pressure 

 will cause an increase HA, of the potential of the water in the 

 sugar solution. This quantity is therefore equal to the original 

 difference in the potentials of the water. Now consider the 

 sugar solution and an etherial solution of water of the same 

 composition as that which was in equilibrium with water 

 under atmospheric pressure. Suppose that these two solutions 

 are separate and under atmospheric pressure. The potential 

 of the water in the sugar solution will be less than that in 

 the etherial solution by an amount CLX. Now suppose that 

 the pressures on the two solutions are increased at the same 

 rate till the potential of the water has the same value in 

 both systems. The potential difference will evidently diminish 

 at the rate X — /a per unit of pressure, so that if P is the 

 increase of pressure necessary to bring about this equality 

 we have 



P(X-^) = n\. 



(66) 



Now X and fi will both be roughly equal to the specific 

 volume of pure water. Hence the ratio P/X2 will have a 

 very high positive or negative value*. Trouton's theoretical 

 deduction that this ratio has the value unity is therefore 

 quite erroneous. The verification of this deduction in one 



* In general the increase of volume of a liquid system, due to the 

 further addition of a liquid component, is slightly less than the volume 

 of the liquid added, but becomes more nearly equal to it the greater the 

 amount of the component in the system. In general, therefore, we have 

 X > fi, so that P/O is positive. 



