Rankin and Wr ight — Tern ary System Ca 0-A \ O.-Si O.,. 63 



separates the fields of A and AS, each of which is stable at its 

 melting point. If then a solution of the composition U on the 

 boundary 9-7 is cooled, A and ^L/S'will separate and the crys- 

 tallization curve will follow the boundary 1-9. The composition 

 of the solution will be given by points on 7-9, that of the solid 

 by a series of points on the line A-AS, the position of each of 

 which is determined by extrapolation of a line through U and 

 points on 7-9 to intercept the composition line A- AS. 

 Further, the mean composition of the solid which has separated 

 between any two points, such as 27 and Y, is determined by 

 extrapolation of a line through U and V to the composition 

 line A-AS. If now the points U and Vbe made to approach 

 each other along the curve 9-7 then the line extrapolated 

 through U and V approaches the position of a tangent, and 

 finally becomes tangent to the boundary curve ; hence at any 

 point the tangent will intercept the line joining the two phases 

 and thus give the mean composition of the solid which separates 

 at that point. It will be seen from the diagram that all tan- 

 gents to the boundary 9-1 at points between V and U will in- 

 tercept the composition line A-AS, but that all tangents to 

 9-1 between 9 and V will intercept an extension of the com- 

 position line A-AS away from A. It follows, therefore, that 

 on the boundary 9-7, A and AS will separate together from 

 £7 to* Y, but that from Y to 9, A will wholly or partially dis- 

 appear while AS crystallizes. The boundary curve 9-1 is of 

 that type along which two solid phases separate together over 

 a part of the curve and one solid phase disappears while the 

 other crystallizes over another part of the curve. The changes 

 which take place along the boundary 9-1 from Y to 9 are 

 essentially the same as those along boundary T^-4, except that 

 in the case of boundary 9-7" the mean composition of the solid 

 phase which separates will vary, while for boundary 7?'-4 the 

 mean composition of the solid phase which separates at any 

 point is constant (the composition of B') because a tangent to 

 any point on 7?'-4, which is a straight line, is that line itself. 

 There are three other boundary curves similar to the 

 boundaries 7?'-4 and 9-7, namely, 7?-17, 18-17 and 18-16. 

 Along at least a part of each of these three one solid disappears 

 while the other crystallizes. Along the boundary 72-17, CaO 

 wholly or partially disappears while 3CaO.Al 2 3 separates dur- 

 ing the course of any crystallization curve which follows this 

 boundary. Along the boundary 18-17, from 18 to Y, CaO 

 wholly or partially disappears while 3CaO.Si0 2 crystallizes and 

 from Y to 17 CaO and 3CaO.Si0 2 separate together. Along 

 the boundary 18-16 from 18 to Z 2CaO.Si0 2 and 3CaO.Si0 2 

 separate together while from Z to 16 2CaO.Si0 2 disappears 

 while 3CaO.Si0 2 separates. 



