II. On a special form of the general equation of a cubic surface and on a diagram representing the twenty-seven lines on the surface

The existence of straight lines on a cubic surface, the number of them, and their relations to each other was first discussed in a correspondence between Salmon and Cayley. In a paper which appeared in 1849, in vol. 4 of the ‘Cambridge and Dublin Mathematical Journal,’ “On the Triple Tangent Planes of Surfaces of the Third Order,” Cayley gave a sketch of what was then known, and gave the equations of the forty-five planes in which the twenty-seven lines on the surface lie by threes, when the equation of the surface is taken in a particular form.