This method of division is related to several methods which have been published from time to time. The advantage of the method given below is the advantage that iteration has, of substituting a repetition of a number of easy operations for a more difficult one, and the fact that at each operation the work starts at the beginning so that errors (except in the last operation) are automatically corrected.

In view of the difficulty of arranging for meetings under existing conditions, the Council has set up an Executive Committee to conduct the business usually transacted by the Council. This Committee consists of the President, the Treasurer, the Secretaries, the Librarian, the Editor of the Mathematical Gazette, the Chairman and the Secretary of the Teaching Committee, together with Mr. Siddons, Mr. Hope-Jones and Miss Punnett.

Members of the Association will deeply regret to hear of the death of F C. Boon. Readers of the Gazette and members attending the Annual Meetings will not need to be told of the immense work he did for the Association, in his contributions to the Gazette, his part in discussions, the way he literally carried the London Branch as Secretary and as Chairman, his years of strenuous and fruitful service on the Teaching Committee. His stalwart defence of the so-called “duffer”, the essential soundness of his outlook, his fatherly treatment (the boys at Dulwich called him “Daddy Boon”), his patience and kindliness in debate, by these he was known.

My remarks this morning will be devoted mainly to general considerations and to principles. Dr. Topping and Mr. Verity are to deal with the courses in detail, but behind all that they say there must be a background of principle, and I hope that a statement of my creed will not find them active dissenters.

I take as my text a quotation from Ruskin which I placed on the flyleaf of a little book I wrote in 1925, and of the truth of which I am as convinced as ever—“Know what you have to do, and do it, for I believe that failure is less frequently attributable to either insufficiency of means or impatience of labour, than to a confused understanding of the thing actually to be done.”

As his presidential lecture the President of the Edinburgh Mathematical Society read, on November 4, 1938, the opening paper of a debate on School Algebra of the First Year The algebra of the Mathematical Association 1933 Report and the 1937 British Association Colloquium was for short referred to as 1933-1937 algebra or as N-D-S algebra (Nunn-Durell-Siddons), and was taken as an authoritative map of the present position in first year algebra.

In accepting the invitation to address the members of the Association I made one condition, that if I came I should be allowed to speak informally You will, I hope, forgive me if owing to the pressure of meetings, during which I have been trying not to square the circle but to get a “square deal”, I have been unable to prepare a set discourse.

In the Report of the Council for 1938 members will have read an account of the work of several sub-committees of the Teaching Committee.

At the meeting of the Teaching Committee in January, 1939, it was agreed that information on work in progress should appear at frequent intervals in the Gazette, for the benefit of members of the Association.

It is hoped that any members who desire to contribute to the work of any of the sub-committees will do so by writing in the first instance to the Secretary of the sub-committee concerned.

Attention has been recently drawn to the rapid mathematisation of science during the past half-century and the contributions to educational technique which are being made by teachers of mathematics in technical colleges.

The kind of mathematics with which they deal may be called “Applied” Mathematics, although it is far different from what is ordinarily termed applied mathematics. It may be said to include certain portions of pure mathematics, practical mathematics, theoretical mechanics and, in rare cases, such practical mechanics as is considered necessary to illustrate the theory—whereas, in fact, it should cover all applications of mathematics to the various fields of knowledge.

This lecture grew out of an attempt to trace the consequences of putting together two examination questions. The subject-matter of both is the reflections X, Y, Z of a point P in the sides of a triangle ABC. In the first question we have to show that the perpendiculars from A on YZ, from B on ZX, from C on XY meet in P′, the centre of the circle XYZ, and that the relation between P and P′ is mutual.

Since AY = AP =AZ, the perpendicular from A to YZ bisects it. Hence this perpendicular passes through the centre of the circle XYZ, as do similarly the other two perpendiculars. Let X′, Y′, Z′ be the reflections of P′ in the sides of ABC. Since BC is the common perpendicular bisector of PX and P′X′, PX′ =P′X, and similarly PY′ = P′Y, PZ′ =P′Z. Hence P is the centre of the circle X′Y′Z′, and the two radii are equal.