Similarly, starting with the pure [beta] modification, the freezing point after fusion will gradually fall owing to the formation of the [alpha] modification; and the composition of the liquid phase will pass along the curve BC. If, now, the rate of cooling is not too great, or if the velocity of isomeric transformation is sufficiently rapid, complete solidification will not occur at the eutectic point; for at this temperature solid and liquid are not in stable equilibrium with one another. On the contrary, a further quantity of the [beta] modification will undergo isomeric change, the liquid phase will become richer in the [alpha] form, and the freezing point will _rise_; the solid phase in contact with the liquid being now the [alpha] modification. The freezing point will continue to rise until the point D is reached, at which complete solidification will take place without further change of temperature.
The diagram also allows us to predict what will be the result of rapidly cooling a fused mixture of the two isomerides. Suppose that either the [alpha] or the [beta] modification has been maintained in the fused state at the temperature _t'_ sufficiently long for equilibrium to be established. The composition of the liquid phase will be represented by _x'_. If the liquid is now _rapidly_ cooled, the composition will remain unchanged as represented by the dotted line _x'_G. At the temperature of the point G solid [alpha] modification will be deposited. If the cooling is not carried below the point G, so as to cause complete solidification, the freezing point will be found to rise with time, owing to the conversion of some of the [beta] form into the [alpha] form { 200} in the liquid phase; and this will continue until the composition of the liquid has reached the point D. From what has just been said, it can also be seen that if the freezing point curves can be obtained by actual determination of the freezing points of different synthetic mixtures of the two isomerides, it will be possible to determine the condition of equilibrium in the fused state at any given temperature without having recourse to analysis. All that is necessary is to rapidly cool the fused mass, after equilibrium has been established, and find the freezing point at which solid is deposited; that is, find the point at which the line of constant temperature cuts the freezing point curve. The composition corresponding to this temperature gives the composition of the equilibrium mixture at the given temperature.