Abstract The key to crystalline structure is furnished by a study of molecular volumes, and one of the best criteria of its powers will be found in its application to polymorphous compounds. If it can explain consistently with our knowledge of crystalline symmetry the change in volume which accompanies the passage of a substance from one crystalline system to another, this fact alone would seem to offer presumptive evidence in its favour. There are inherent difficulties in the subject which render progress laborious and slow, so that we cannot at present offer an exhaustive account of all cases of polymorphism, and on this occasion we shall confine our attention to the single but remarkable instance of titanic oxide, which presents itself in the three well-known forms of anatase, brookite, and rutile. The chemical formula of the oxide, generally taken as Ti2O4, is based on analogy with zircon, ZrSiO4, which is isomorphous with rutile. It may be represented graphically as O Ti O Ti, O O and the simplest glyptic rendering of this gives at once the general configuration of the crystal molecule, Haüy’s “molecule intégrante,” out of which anatase, and, with slight modifications, brookite, and rutile also, are built up (see fig. 10, p. 275).