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



solution of a single involatile solute. By means of the 

 Theory o£ Chemical Potential an expression of a very general 

 nature connecting the vapour-pressures of two solutions and 

 the pressures under which they co-exist in osmotic equilibrium, 

 can be deduced with extreme ease, not only in the special 

 case ot one involatile solute, but in the general case of any 

 number of involatile solutes. Other problems, such as the 

 conditions of co-existence of a liquid and vapour under dif- 

 ferent pressures (the effect of pressure on the vapour-pressure), 

 the effect of gravity on a solution, <fcc., may also be solved in 

 a simple manner by this method. The author proposes to 

 treat these questions in a later communication. 



Si tmrna ry of JYota t i o n . 

 The following are the chief symbols used in this paper : — 



M the mass of the solvent S ; 

 Mx the mass of the solute Sj ; 



S = ^-J- the concentration of the solution ; 



M 



W the volume of the solution ; 

 II the vapour-pressure of the pure solvent ; 

 II the vapour-pressure of the solution ; 

 v(s, p, 6) the specific volume of a solution of concentration 



s at a temperature 6 and under a pressure p ; 

 r(0, p, 0) the specific volume of the pure solvent ; 

 f Q (s, p, 6). the chemical potential of the solvent in a solution 

 of concentration s at a temperature #and under 

 a pressure p ; 

 fi(s, p, 6) the chemical potential of the solute in the 



solution ; 

 /o(0, p, 6) the chemical potential of the solvent in the pure 

 liquid state ; 



F (p ; 6) the chemical potential of the solvent in the pure 



vapour state ; 

 Y(p, 6) the specific volume of the solvent vapour ; 

 Q(s, p, 6) the osmotic pressure of a solution of concentration 

 s at a temperature 6, when the pressure on the 

 pure solvent is p. 



The symbols v, / , P , &c, will sometimes be used alone 

 when there is no doubt as to the particular values of the 

 variables involved. 



