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.