It is not the quantity but the quality of the anatomical and bionomic characters which determines their taxonomic value, and a few fundamental characters are better indications of the affinities of given groups of birds than a great number of agreements if these can be shown to be cases of isomorphism or heterophyletic, convergent analogy.
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.
Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH 2 P(As)04, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements.
Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements.
The following table shows where isomorphism may be generally expected.
In 1858 he pointed out the isomorphism of the fluostannates and the fluosilicates, thus settling the then vexed question of the composition of silicic acid; and subsequently he studied the fluosalts of zirconium, boron, tungsten, &c., and prepared silicotungstic acid, one of the first examples of the complex inorganic acids.
Berzelius as to their composition; and his observation that corresponding phosphates and arsenates crystallize in the same form was the germ from which grew the theory of isomorphism which he communicated to the Berlin Academy in December 1819.
Other instances of the isomorphism of thallous with potassium salts are the nitrates, phosphates, hydrazoates, sulphates, chromates, selenates, and the analogously constituted double salts, and also the oxalates, racemates and picrates.
The chlorine is not completely precipitated by silver nitrate in nitric acid solution, the ionization apparently not proceeding to all the chlorine atoms. Thallic iodide, T11 3, is interesting on account of its isomorphism with rubidium and caesium tri-iodides, a resemblance which suggests the formula T11 (12) for the salt, in which the metal is obviously monovalent.
To these results he was aided by the law of isomorphism formulated by E.