The systematic treatment of these systems by this method has been strangely neglected hitherto by English writers, the only text-book, as far as I am aware, which deals at all with the subject being Salmon’s Conics, sixth edition, 1879, pp. 389, 390, where the states that the properties have been studied by de Jonquières, Chasles, Zeuthen, and Cayley, and that references to the original memoirs will be found in Cayley’s memoir (Phil. Trans., 1867, p. 75). This I have not had the opportunity of consulting. In this article I have followed the Danish mathematician, H. G. Zeuthen, who selected the subject for his Doctor’s Thesis of 1865, which was translated and published in the Nouvelles Annales de Mathématiques in 1866, p. 241, with the title “A New Method of Determining the Characteristics of Systems of Conics.”