_Polymorphism._ It has been shown in Chapter VII. that Mitscherlich had in several instances proved the possibility of the occurrence of the same substance in two different forms, notably sodium dihydrogen phosphate NaH_{2}PO_{4}.H_{2}O, calcium carbonate CaCO_{3} (as calcite and aragonite), the metallic sulphates known as vitriols, and the chemical element sulphur, and that he gave to the phenomenon the name “dimorphism.” Since that time large numbers of dimorphous substances have been discovered, and several which occur in three forms and even a few in no less than four totally distinct forms. Until the establishment of the geometrical theory of crystal structure, as expounded in Chapter IX., this phenomenon of polymorphism gave rise to endless fruitless discussion. It was most generally attributed to the different nature of the so-called “physical molecule,” which was supposed to be an aggregate of chemical molecules and the unit of the space-lattice determining the crystal system; the different polymorphous varieties were supposed to be built up of structural units or physical molecules consisting of an aggregation of a different number of chemical molecules. Several attempts were made by various investigators, notably by Muthmann and by Fock, to determine the number of chemical molecules constituting the physical molecule. All these efforts, however, ended unsatisfactorily, and in the year 1896 the author showed, in a memoir[11] on “The Nature of the Structural Unit,” that in general the physical molecule is a myth, and that the chemical molecule is the only structural unit possessing the full chemical composition of the substance in question; and that its centre of gravity, or better, any representative point within it, such as a particular atom, is the unit point of the Bravais space-lattice of the crystal structure, while the atoms of which the chemical molecule are composed, arranged stereometrically identically similarly in all the molecules, are the points of the individual point-systems which make up the combined point-system. This does not imply a necessarily parallel and identically orientated arrangement of all the molecules, as at first postulated by Sohncke and which is a fact for his sixty-five point-systems; for in accordance with the conclusions of Schönflies, von Fedorow, and Barlow discussed in Chapter IX., cases are possible in which alternate molecules may be arranged as each other’s mirror images. Such are the cases of external molecular compensation or molecular combination, two oppositely enantiomorphous sets of molecules balancing each other within the structure, but by exterior compensation as regards the molecule itself. Moreover, the principle of mirror-image symmetry enters, as stated in Chapter IX, altogether into the constitution of no less than 165 of the 230 types of homogeneous structure possible to crystals.