The Thermodynamics of Cryohydrates. 407 



Therefore, 



<m 1 <f> + m 2 ty (1) 



Again, if a saturated solution contains a weight M x of the 

 salt, and a weight M 2 of the liquid, its thermodynamic 

 potential will be 



^^MjFi + M^, 



where ^i = (f>, F 2 <i/r ; 



therefore 



^> / =M 1 </) + M 2 F 2 



<M^ + M 2 ^ (2) 



At the freezing-point of the cryohydrate these two solutions 

 are identical with the cryohydrate itself; and we therefore 

 have 



(D^M^o + M^oJ l) 



where </> and -^ are the values of (f> and i/r at this tempera- 

 ture. 



The solutions we have been studying may he conveniently 

 represented by a diagram. Take three rectangular axes, and 

 let the axis of a; denote the temperature, the axis of y the 



pressure, and the axis of z the quantity h = — , so that h is 

 the strength of the solution. m2 



The weakest and strongest stable solutions will be repre- 

 sented in the diagram by two surfaces which meet along the 

 freezing line of the cryohydrate, and all other stable solutions 

 will be represented by points lying between these two sur- 

 faces. 



Our principal object in this paper is to find the effect of 

 pressure upon the freezing-point and composition of the cryo- 

 hydrate. For the former purpose we make use of the im- 

 portant equations (3). 



Thus, let us suppose that at any point ( p, t) on the freezing 

 line of the cryohydrate (v, V, S, <£>) represent respectively 

 the volume, energy, entropy, and thermodynamic potential at 

 constant pressure of unit mass of the cryohydrate, and let 

 ( v i) Ui, Si, <I?i) be respectively the sums of the volumes, 

 energies, entropies, and thermodynamic potentials at the same 

 pressure and temperature of the salt and ice of which the 

 cryohydrate is composed. 



2E2 



