The theory of compound singularities will be referred to farther on.
The most simple case is when three double points come into coincidence, thereby giving rise to a triple point; and a somewhat more complicated one is when we have a cusp of the second kind, or node-cusp arising from the coincidence of a node, a cusp, an inflection, and a double tangent, as shown in the annexed figure, which represents the singularities as on the point of coalescing.
Among other singularities of habitat, not the least curious is the freedom with which some small species, especially in the genus Dichelaspis, occupy the very jaws of large crustaceans.
- The above dual generation explains the nature of the singularities of a plane curve.
The ordinary singularities, arranged according to a cross division, are Proper.