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.”

The purpose of the author was to urge that specific volume should precede density, because (1) the idea of specific volume is more important and fruitful than the idea of density; (2) the notion of specific volume is easier to acquire. Dealing first with the second reason, evidence was quoted from experienced science teachers and examiners to the effect that boys frequently failed to grasp the idea of density although they could formulate a correct definition, and carry out and describe a density determination with unimpeachable correctness. On the other hand the author had found that the idea of density had been readily acquired where the class had approached the subject through a preliminary lesson on specific volume. A short demonstration was then given of a method by which the relative specific volumes of substances or their comparative “roominess” (Raümigkeit), i.e. the volume occupied by 1 lb. of each, could be readily and effectively brought home to the class. (In subsequent discussion the chairman suggested the word ‘roomage’ in place of specific volume.)

My object is to indicate what seem to be the fundamental ideas connected with homography which would be readily understood and appreciated by a beginner.

If a pencil of concurrent rays is cut by any transversal, the ratios between the parts into which it is divided are the same as for any parallel transversal. This is not the case when the two transversals are not parallel, and it becomes an important problem to find out what property of the segments is common to both transversals in such a case. To the Greeks, who so exhaustively studied the properties of the conic sections as sections of a cone, this problem must have presented itself quite early, and it appears that not only Pappus, but also Euclid, and therefore probably Apollonius, knew the solution.

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.

A Meeting was held at King Edward VI. Grammar School on Friday evening, March 11th. The president, Professor E. L. Watkin took the chair. The meeting was considered as the First Annual General Meeting of the new Society. Professor Watkin was re-elected president for 1910 and C. H. Holmes hon. secretary and treasurer.

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.