It is well known, having been pointed out in the first instance by Plücker, that a plane quartic curve consisting of four unifolia, in Zeuthen's sense, i.e. four even circuits each containing one concave portion or bay, has all its twenty-eight bitangents, and all their fifty-six points of contact, real; since each bay has a bitangent whose points of contact bound it, and each pair of circuits have four common tangents. It has not, so far as I know, been remarked that the algorithm of Hesse and Cayley, in which each of the bitangents is indicated by a pair out of the symbols 1 2 3 4 5 6 7 8, can be applied in a very simple way to such a curve.