Rankin and Wright — Ternary System CaO-Al.fi \-SiO„. 55 



compositions of the solution will on extrapolation pass through 

 the point which gives the mean composition of the solid which 

 has separated. In the cases thus far considered this mean 

 composition is none other than that of a pure component. 

 However, when two phases separate together, as the compo- 

 nents S and SC along the boundary A-% the mean composition 

 of the solid which separates on cooling, provided no solid is 

 removed during the process, will be found as a point on the 

 line joining the compositions of the constituent phases. In the 

 cases mentioned this line is the side of the triangle S-CS. 

 Such a line may connect pure components, a component and a 

 compound, or two compounds. 



Since the mean composition of the total solid separated at a 

 definite temperature is on the line joining the compositions of 

 its constituent phases and also on the extrapolated portions of 

 the line through the compositions of the original and residual 

 solutions, it follows that it lies at the intersection of these two 

 lines. Thus a line joining b and 5 2 (in fig. 17) will extrapolate 

 to /3 2 on the line S-CS, which gives the mean composition of 

 the solid which has separated on cooling the solution b from 

 the temperature of the isotherm through that point to the 

 temperature of the isotherm passing through & 2 . Similarly, in 

 cooling from b to 2 the mean composition of the solid phase is 

 represented by /3 3 . When the temperature of the quintuple 

 point 2 is reached, the component CAS 2 appears as a phase in 

 the solid ; but from the definition of the eutectic point, the 

 solution and solid crystallizing are of the same composition, so 

 that no further change of concentration occurs. 



At any intermediate temperature the same reasoning is 

 applicable. Consider, for example, a solution of concentration 

 b l cooled to & 2 . Since the two solutions lie on the boundary 

 curve. S and CS crystallize together. Extrapolation through 

 b 1 and 6 2 to the side of the triangle S-CS gives A, which point 

 shows the mean composition, in terms of S and CS, of the solid 

 which has separated during the cooling from b l to & 2 . 



The amount of solid which has separated between the 

 temperatures of b and b 2 is, as above, given by the ratio 



PA 



The fraction of the original solution b which remains in solu- 

 tion b, 



PA 

 PA 



From the fundamental principle of solid separation mentioned 

 as well as from geometrical considerations it is obvious that 



