302 SCHREINEMAKERS art. h 



water that the former is completely dissolved, we get a solution 

 of ether in water represented by a point of Wa. If we add so 

 little water to ether that the water completely dissolves, we 

 get a solution of water in ether represented by a point of bX. 

 If, however, we bring ether and water together in such a propor- 

 tion that their mixture is represented by a point between a and b, 

 then no homogeneous liquid is formed, but on the contrary 

 the system, or phase-complex, L(a) + L(b), i.e., a liquid a 

 containing much water and little ether, and a liquid b containing 

 much ether and httle water. 



7. In relation to the further discussion we shall deduce the 

 foregoing results also in the following way. Every chord we 

 may draw in Figs. 4 and 5 is also the ^-line of a conceivable 

 two-phase system. Thus each point of a'b' represents the 

 f -point of a system L{a) -\- L{b), each point of z'u' the ^-point 

 of a system L{z) -{- L{u), etc. So we may imagine an infinite 

 number of ^-points on every arbitrary vertical line; the lowest 

 f-point of every vertical line represents a stable state. Of all 

 the f-points we can imagine in Fig. 4 on a vertical line, the point 

 of intersection with the f-curve is lowest, and hence it follows 

 that of all conceivable ^-points of Fig. 4 only those of the f-curve 

 represent stable states. Of all chords which we may imagine 

 to be drawn in Fig. 5, one, a'b', touches the ^-curve in two 

 points. The part a'e'b' of the f-curve Ues above this chord a'b'. 

 If we now imagine vertical lines drawn through the points 

 between W and a, between a and 6, and between b and X, we 

 see that of all conceivable ^-points of Fig. 5 only those of the 

 parts Wa' and b'X' of the f-curve and those of the double 

 tangent a'b' represent stable states. This means that only the 

 liquids of Wa and bX and the system L{a) -\- L{b) are stable. 



8. We now assume that the points of WX represent mixed 

 crystals. Then their f-curve may also have the form shown 

 in Fig. 4 or Fig. 5. When Fig. 4 obtains, it follows that the 

 two solid components W and X are miscible with each other in 

 all proportions and form an unbroken series of mixed crystals. 

 When Fig. 5 obtains, then only the mixed crystals of Wa and 

 bX are stable; all others (namely between a and 6) are meta- 

 stable or unstable, and separate or tend to separate into the 



