C. L. Speyers — Molecular Weights of Liquids. 429 



number of grammolecules of each liquid when considered as 

 solute; N" 1? !N" 2 , the number of grammolecules of the same 

 liquids when considered as solvent, in computing which the 

 ordinary molecular weight in the vapor state is to be used;^? n 

 p^ the vapor tensions of the pure liquids; p^p^p/^p^., the 

 vapor tensions of the same liquids in the solutions. Here and 

 elsewhere the two coexisting solutions or phases are distin- 

 guished by ' and " . 



At some fixed temperature let us add liquid 1 to a fixed 

 quantity of 2. We have for the two components 



< _ P~P* . < _P i -P 1 ' 



* .' ~ p; ' n/ - P} 



which hold until the phase disappears entirely. When, on 

 continued addition of 1, a second phase appears, we have the 

 additional two equations 



Since the phases are in equilibrium, p/=p/, p^p^, and so 



n l _ n " n * _ n " 



2 2 1 1 



The proportion of 1 to 2 is different in each phase, wherefore 

 the activity factor, a, for each liquid must be different in each 

 phase. Moreover, the quantity of 1 in 2 being greater in the 

 second phase than in the first, the activity factor, a, is greater in 

 the second phase than in the first, while a^^xi". A jump 

 then in the mutual effects of two liquids, the one upon the other, 

 accompanies the formation of two liquid phases, a jump in the 

 effect of 1 upon 2 being balanced by the jump in the effect of 2 

 upon 1. 



Following custom, we call that temperature above which 

 two liquids dissolve in each other in all proportions, the criti- 

 cal temperature of solution, or for shortness just critical tem- 

 perature. The composition belonging to the critical tem- 

 perature we call critical composition and a solution of such 

 composition a critical solution. 



Let us start above the critical temperature with a solution of 

 critical composition and with liquid 1 as solute, 2 as solvent, 

 and cool the solution. As we pass down through the critical 

 temperature, the homogeneous liquid separates into two phases, 

 and as the change due to lowering the temperature is continu- 

 ous, at a temperature infinitesimally below the critical tempera- 

 ture, the compositions of the two phases are only infinitesimally 



