In physics and chemistry no perfect rational systems have been established hitherto, but there are many systems approaching the ideal type in different departments of these sciences. The chemical type of the monohydric saturated alcohols, for instance, is given by the formula C_nH_{2n+1}OH, and in this formula we not only have an expression of the law of composition which all possible alcohols are to follow,--but, since we know empirically the law of quantitative relation between *n* and various physical properties, we also possess in our formula a general statement with respect to the totality of the properties of any primary alcohol that may be discovered or prepared in the future. But chemistry has still higher aims with regard to its systematics: all of you know that the so-called “periodic law of the elements” was the first step towards a principle that may some day give account of the relation of all the physical and chemical properties of any so-called element with its most important constant, the atomic weight, and it seems to be reserved for the present time to form a real fundamental system of the “elements” on the basis of the periodic law by the aid of the theory of electrons. Such a fundamental system of the elements would teach us that there can only be so many elements and no more, and only of such a kind. In crystallography a similar end has been reached already by means of certain hypothetic assumptions, and systematics has here accounted for the limited number and fixed character of the possible forms of crystalline symmetry. It is not difficult to understand the general logical type of all rational systems, and logic indeed can discover it without appealing to concrete sciences or to geometry. Rational systematics is always possible whenever there exists any fundamental concept or proposition which carries with it a principle of division; or to express it somewhat differently, which would lead to contradictions, if division were to be tried in any but one particular manner. The so-called “genus,” as will easily be perceived, then embraces all its “species” in such a manner that all peculiarities of the species are represented already in properties of the genus, only in a more general form, in a form which is still unspecified. The genus is both richer in content and richer in extent than are the species, though it must be added that its richness in content is, as it were, only latent: but it may come into actuality by itself and without any help from without.