UNPUBLISHED FRAGMENTS. 421 



where n^ denotes the number of molecules of the form (D). Hence 

 we have for the solution 



If t is constant, and also JUL B , a condition realized in equilibrium, 

 when the solution is separated from the pure solvent by a diaphragm 

 permeable to the solvent but not to the solutum, the equation 

 reduces to 



v 

 Whence p - p ' = ^ Yo = A t^, [7] 



p' being the pressure where y D = 0, i.e., in the pure solvent. Here 



At 



p p f is the so-called osmotic pressure, and -^ y D is the pressure as 



JxL-Q 



calculated* by the laws of Boyle, Charles, and Avogadro for the 

 solutum in the space occupied by the solution. The equation mani- 

 festly expresses van't HofF's law. 



For a coexistent solid phase of the solvent, with constant pressure, 

 the general equation gives 



= r\ dt-\-m% dfa+v At dy D 

 for the solution, and 



for the solid coexistent phase. Here t and JUL S have necessarily the 

 same values in the two equations, and we may suppose the quantity 

 of one of the phases to be so chosen as to make the values of ra s equal 

 in the two equations. This gives 



At 



In integrating from y D = to any small value of y D , we may treat 

 the coefficients of dt and dy D as having the same constant values as 

 when y D = 0. This gives 



-At -0-t 



^/ __ *i'\ 

 If we write Q s for -^ (the latent heat of melting for the unit 



of weight of the solvent), we get 



M- 

 ~ MV D Qs w s' 



m p 

 *.__M-Q At 2 _W D At 2 rg-i 



^^ ^~ L\t - 7^ -m f - -ff y-C ) L J 



M, 



Not experimentally found. 



