The summer meeting of the North Wales branch was held on 22nd May at the County School, Beaumaris, where the headmaster, Mr. Madoc Jones, entertained the members present. In opening a discussion on the teaching of geometry, Mr. Botting, mathematical tutor at the Normal College, Bangor, referred to the recent circular of the Board of Education, which recommends three stages, each occupying one year : (1) children to be grounded in fundamental ideas of space, lines, angles, etc., without actual de-finitions, and accustomed to instruments of measurement ; (2) the acquisition of a number of fundamental propositions, but not in a formal way, e.g. I. 13-15 in Euclid, and some propositions about parallel lines, the equality of triangles, etc.; (3) rigid deductive proofs to be begun, all fresh propositions being treated as original work like riders. He also said that propositions should not be taken singly, but in groups together, and that the power of working riders is the only real test of advance in geometry

In last year’s address I called attention to the need of some symbol to denote unknown digits in approximate numerical calculations. The present note is commuunicated in the hopes that the matter may be submitted either to the Council or to a special committee of the Association in order that some definite recommendation may be adopted.

Having read with more than ordinary interest the Address delivered by Professor Perry on “The Correlation of the Teaching of Mathematics and Science,” I should like to lay before the members of the Mathematical Association a few remarks which, I trust, will be found to the point.

I need not further endorse the view that as long as a student does not specialize in mathematics or in science, the teaching of both these subjects will be greatly improved if in the hands of the same teacher Such an arrangement must benefit both teacher and student. By “science” I mean physics, and those parts of applied mechanics, electricity, and magnetism, generally comprised with certain other practical subjects under the general term of “engineering.”

Hamilton, in his Elements of Quaternions (Book I. Chapter II.), developed this system of coordinates, by means of his vectorial algebra, in connection with his theory of geometrical nets.

In the following paper I have re-proved the fundamental theorems, by other methods, and have sketched out the natural lines of development of the system.

Though few, if any, of the results arrived at are new, they are at any rate newly stated; and I believe that the elegance of method will command interest.

No one can possibly welcome more cordially than I do the widening of the school curriculum in mathematics that has taken place during the last twenty years. Even I can remember the days when ‘Conics’ and ‘Mechanics’ were the privilege of a select few, and only a prodigy was initiated into the mysteries of the Differential (much less the Integral) Calculus. All this is changed now, and it is fairly safe (at least that is my experience) to assume that a boy who has won a scholarship has learnt something about the Integral Calculus at school.