But it is no longer the same thing when the solid is once in the crystallized state.

There is then a solution of continuity of the various properties of the substance, and the two phases may co-exist.
We might presume also, by analogy with what happens with liquids and gases, that if we followed the curve of transformation of the crystalline into the liquid phase, we might arrive at a kind of critical point at which the discontinuity of their properties would vanish.
Professor Poynting, and after him Professor Planck and Professor Ostwald, supposed this to be the case, but more recently M.Tamman has shown that such a point does not exist, and that the region of stability of the crystallized state is limited on all sides.

All along the curve of transformation the two states may exist in equilibrium, but we may assert that it is impossible to realize a continuous series of intermediaries between these two states.

There will always be a more or less marked discontinuity in some of the properties.
In the course of his researches M.Tamman has been led to certain very important observations, and has met with fresh allotropic modifications in nearly all substances, which singularly complicate the question.

In the case of water, for instance, he finds that ordinary ice transforms itself, under a given pressure, at the temperature of -80 deg.