The uses of vectors are many and varied. The value of the vector notation and of vector methods of calculation is becoming recognised in mechanics and physics, but few teachers use them to any extent in teaching pure mathematics, although they appear to be equally useful in this sphere.

I have found vector methods especially useful for students who require a “practical” knowledge; they are well adapted to numerical work, and often provide a welcome change from the drudgery of memorising formulae, and calculating results by substitution of numerical values of the symbols—a dull task, lacking in educational value, which forms such a large part of the work of the technical student. Vector solutions are usually short and simple, and proceed from first principles ; they should thus be preferred on logical grounds.

Teachers of elementary Mathematics are generally very glad to find some unfamiliar field into which they can turn their pupils to exercise themselves in elementary processes. The following is a suggestion of a method of approaching certain theorems in connection with the Geometry of the Triangle which, although well known to Mathematicians, are not, as a rule, studied as part of a school course, except perhaps by specialists. The Brocard Points and Circle are generally approached, via the theory of Isogonal Conjugates (see Casey’s Sequel to Euclid, Supplementary Chapter, Section I. etc.). But many of the properties connected with these points can be obtained in a more direct manner, and this suggests some interesting investigations involving nothing but the ordinary processes of Geometry and Trigonometry.