In Hilton’s Plane Algebraic Curves the functions F(t) and F′(t) are used in finding inflexions and cusps of plane curves. These functions are defined, respectively, by the determinants

where f(t), ɸ(t), ψ(t) are the values, in terms of a parameter t, of the homogeneous coordinates of a point on the curve. It is shown that F(t1) vanishes if t1 is the parameter of an inflexion or a cusp and F′(t1), the derivative of F(t1), vanishes if t1 gives a cusp.