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.”

As teachers of elementary mathematics I suppose we are all familiar with the Circular 711 of the Board of Education. That circular is now out of print, and its place has been taken by Circular 851, which, I think, is not so well known. The purpose of the latter circular is to state the matter afresh, to explain it more fully, and to justify the attitude adopted. The main practical suggestion of these two circulars has been so largely adopted in present-day teaching in this country that I propose at the outset to base my remarks largely upon it.

Probably the most interesting example of this mixture is that given by Mr. R. Steele in the Introduction (p. xvii) to The Earliest Arithmetics in English, where he quotes from a British Museum MS. (Harl. 4350) a set of dates of successive births

These form an early example, for Britain, of the transition.