While gathering the materials for something in the nature of a ‘Companion’ to De Morgan’s “Budget of Paradoxes,” I came across a considerable number of his notes, short papers, and other contributions to the famous English periodical known as “Notes and Queries.” The first number appeared on Nov. 3, 1849, and from that date “N. & Q.” has been a household word among those who are afflicted with the insatiable desire to penetrate into the bye-ways of Literature, Genealogy, Heraldry, Antiquarian Lore, the Science of History and the History of Science—all formed grist for those who came to that mill. By the kind permission of the Editor of this invaluable publication, I have been permitted to reproduce from its columns what is presented to the reader in the following pages. The early numbers of “N. & Q.” are exceedingly scarce, and a complete set is hardly to be obtained by those who live at a distance from the great libraries.

The object of the “Advanced Section” being to study and find out the best methods of teaching Scholarship work, it seems advisable briefly to pass in review the higher algebra syllabus which is at present being taught to pupils in the departments of advanced mathematics in our secondary schools.

There is nothing more extraordinary in the educational world at the present day than the change of attitude among teachers towards the subject they have to teach. Teachers of bygone ages were to a large extent content to regard their pupils as so many buckets into which they were required to pour a prescribed amount of intellectual material. In most cases the teacher did not know himself the sources whence came his stock-in-trade. He had so many hard facts at his disposal which he had either got out of a printed text-book or from lecture notes, and it was his business according to his genius and ability to breathe upon these dry bones that they should live.

Aim. I take it that the object of teaching mathematics in a boys’ school is to develop, in combination, the power (i) to apply mathematics successfully to matters of human interest, (ii) to appreciate in some measure that ‘realm of order’ (the expression is borrowed from Professor Nunn) in which mathematical ideas exist.