In selecting a topic for his annual address, your President has a wealth of choice sufficient to be an embarrassment. On the one hand there are the varied activities of the Association itself ; and though it may need courage and skill to deal with the delicate questions of the present moment, there is less need of exceptional virtues in reviewing the achievements of the past, or anticipating the enterprises of the future. On the other hand there are the doings in the world of Science outside the Association, with some one of which at least your President for the time being may be presumed to have a speaking acquaintance.

The front of the scientific army is long and straggling, and the lines of communication are thin and broken. If your President happens to have any news from the front he will probably be a welcome messenger among those whose duty keeps them elsewhere. If this is not too ambitious an aim, I propose on the present occasion to attempt a brief report on a recent successful movement by the Astronomical regiment which I trust may be of interest to their Mathematical comrades. I speak of it from the outset as a regimental movement ; for though the chief credit is undoubtedly due to individuals, even the brief report I shall make will shew how much one owed to another, and he to a third: how different lines of advance converged and coalesced: and, in short, how the whole movement was organised, not in the artificial manner which man has come to associate with the word, but in the sense in which the advances of Nature, including those of Natural Science, are organised.

I believe I am the only surviving original-member of that A.I.G.T., to which the President bas referred (The Association for the Improvement of Geometrical Teaching). This Association arose out of a book which I wrote at Dr. Temple’s (the late Archbishop of Canterbury’s) suggestion, after the Commission of Inquiry into Secondary Education (the Endowed Schools Commission), that some new method, simpler than Euclid, should be brought into our geometrical teaching. It was very desirable that there should not be competition between private individual writers of text-books competing for public approval and public use, and so we formed the Association in order to unify the teaching on the new lines.

The last ten years have witnessed many changes in the methods employed in the teaching of arithmetic, which to a very considerable degree are the direct product of the activity and exertions of this Association. Two signal benefits may be mentioned ; firstly, uniformity of method in elementary processes has been secured ; and, secondly, the educational value of practical applications to mensuration, physics, etc., has received due recognition. The object of this paper is to raise for discussion a question of quite a different character.