Abstract
THE compound singularities of algebraic curves offer a wide field for discussion, but the naming of the simple singularities has not yet been placed on an entirely satisfactory footing. The latter consist of (1) point singularities, which are nodes and cusps; (2) line singularities, which I prefer to call bitangents and inflections. Mr. Basset calls them double and stationary tangents; but if this is done, symmetry requires that the point singularities should be called double points and stationary points, and this is not admissible, because the phrase double points (as now used) includes cusps as well as nodes. If a curve has a double point Mr. Basset calls it autotomic (self-cutting); but this term is incorrect when all the double points in the curve are cusps (as in the cardioid), for the curve does not then cut itself. If it is really desirable to have a means of distinguishing curves that have nodes or cusps from those that have none, they may perhaps best be described respectively as curves with or without point singularities.
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