The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article Crystallography; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy.
Isomorphism may be defined as the existence of two or more different substances in the same crystal form and structure, polymorphism as the existence of the same substance in two or more crystal modifications, and morphotropy (after P. von Groth) as the change in crystal form due to alterations in the molecule of closely (chemically) related substances.
While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the scalar properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both scalar and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification.
It is on clinical grounds that beriberi, scarlet fever, measles, &c., are recognized as belonging to the same class, and evolving in phases which differ not in intimate nature but in the more superficial and inessential characters of time, rate and polymorphism; and the impression is gaining strength that acute rheumatism belongs to the group of the infections, certain sore throats, chorea and other apparently distinct maladies being terms of this series.
Polymorphism usually occurs, certain individuals having the form of avicularia or vibracula.
The study of polymorphism has been especially pursued by Otto Lehmann, who proved that it is an almost general property; the variety of forms which a given substance may show is often great, ammonium nitrate, for instance, showing at least four of them before melting.
Poulton, in an admirable discussion of contemporary views regarding species (presidential address to the Entomological Society of London 1904), has shown that Darwin did not believe in the objective existence of species, not only because he was led to discard the hypothesis of special creation as the explanation of the polymorphism of life, but because in practice as a working systematist he could neither find for himself nor ascertain from other systematists any settled criteria by which a group of specimens could be elevated into a genus, accepted as a species, or regarded as a variety.
Chodat does not find so general a polymorphism, but nevertheless holds that Raphidium passes through stages represented by Protococcus, Characium, Dactylococcus and Sciadium.
While, therefore, there is much evidence of a negative character against the existence of an extensive polymorphism among algae, some amount of metamorphosis is known to occur.
Chodat, " On the Polymorphism of the Green Algae," Ann.
These laws have the advantage of being applicable to the mutual transformations of isomers, whatever be the nature of the deeper origin, and so bring polymerism, metamerism and polymorphism together.
If our knowledge of the life-histories of these organisms were perfect, their polymorphism would present no difficulties to classification; but unfortunately this is far from being the case.