REPRESENTATION BY ZETA FUNCTION 301 



point e'" of the line z'u'. So the transformations 



L{a) + L{b) -^ L{e) 

 Liz) + Liu) -> Lie) 



are possible, namely a mixing of the liquids a and b or of z and u 

 to give e. But the opposite changes, i.e., a separation of the 

 liquid e into liquids a and h or into liquids 2 and u, are not 

 possible. Since these considerations apply equally to every 

 liquid e of Fig. 4, it follows that: when the ^-curve is wholly 



W 



w 



Fig. 5 



convex towards the composition axis, all the liquids are stable and 

 miscible with one another in all proportions. 



6. In Fig. 5 we can draw a double tangent line, touching the 

 f-curve in points a' and b'. Since the f-point e" of the system 

 Lia) + L{b) now lies below the f -point e' of the liquid phase e, 

 the conversion L(e) —^ Lia) + L{b) may occur, i.e., a separation 

 of liquid e into the liquids a and b. Conversely, the liquids a 

 and b cannot mix to give the liquid e. Hence we have the 

 following result for Fig. 5. All the liquids of Wa and bX are 

 stable; all the liquids between a and b are metastable or un- 

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

 Lia) + Lib). Let us take at ordinary temperature and pressure 

 W = water, X = ether. If we now add so little ether to the 



