﻿488 Mr. S. A. Shorter : Application of the Theory 



the cases of osmotic pressure (equation (5) of Part I.) and 

 vapour-pressure (equation (8) o£ Part L). The process of 

 obtaining an exact formula is more complicated in the 

 present case than in the two other cases, because we have 

 to deal with variations of temperature, and the temperature 

 derivative of the chemical potential is not connected with 

 quantities which may be determined experimentally in such 

 a simple manner as the pressure derivative. 



We will first calculate the lowering of the solvent potential 

 at the freezing-point of the solution. From equations (5) and 

 (6) we obtain 



T 

 /o.(0, p, T ) -/„(*, j>, T)= f V'O, 0)d9, 



but 



SO 



that 



T 



C 



/e(o, & t 9 ) =/ (a, lh T}+ /o'(0, p, eye, 



A O,p,T)=f r o (p,ff)d0 .... (7) 



The value of F is known for one value of the temperature, 

 viz., the value T . We have the well-known relation* 



T {p, Ty) = r - . 



The value of the temperature derivative of r o is known 

 for any value of the temperature, We have the well-known 

 relations f 



T<£u"(0, T) = —Js{p, T), 



t/o"(0,j?, T ) = — 7ofe t), 

 so that r ,, , ^ Vd(p, t) 



The value of T at any temperature 0, between T and T , 

 is therefore given by the equation 



1 o Jo T 



* Dnhem, i« Mecanique Chimiqae, vol. ii. pp. 5 and 54; Preston, 

 $ Theory of Heat,' p. 776 (second edition). 



t Puhein, loc. cit. vol. i. p. 110 : Preston, foe. cit. p, 770. 



