“If pairs of common tangents be drawn to three circles, and if one triad of common tangents be concurrent, the other triad will also be concurrent.”

This is Casey’s enunciation * of a familiar theorem; Salmon † has the same unqualified assertion, and appends a footnote: “This principle is employed by Steiner in his solution of Malfatti’s problem…. [His] construction is: Inscribe circles in the triangles formed by each side of the triangle and the two adjacent bisectors of angles; these circles having three common tangents meeting in a point will have three other common tangents meeting in a point, and these are common tangents to the circles required.”

Dr. Robb, in his rejoinder to my criticism of his paper, asks me a direct question; and as, to me at least, the matter under discussion is of far greater importance than any mere difference of opinion between us, I hope I may be permitted to reply.

When I began to consider how I could best fulfil my promise to read you a paper, my difficulty in selecting a subject arose, not from the dearth of matter, but from the wide range before me, as I was told I might select any mathematical subject I liked. The subject of mathematics as a whole I at once put aside, as I felt it would be impossible for me in a short paper to say anything new about it. For the same reason my favourite subject geometry was unsuitable, and as I was brought up on the Elements of Euclid, anything I might have to say about geometry would probably be considered old-fashioned and antiquated.

A Meeting of the London Branch of the Mathematical Association was held at Bedford College, Regent’s Park, London, N.W., on Saturday, 22nd March, 1930, for the purpose of discussing “What Changes, if any, are advisable in the Elementary Mathematical Syllabus of the First School Certificate?” Mr. J. Katz presided.

Twenty years ago it was anticipated that “Standard Form” would prove the ideal method for decimal processes. It was designed to abolish the mechanical teaching of a mechanical rule and to base arithmetical instruction on a conscious grasp of principles. A wide and extended trial has not realised the anticipation, indeed the method appears to-day to have many followers but few champions.

The following problems recently sent to the Bureau seem of sufficient interest to justify insertion in the Gazette.