Euclid. The amount of geometrical ground that can be covered by means of the algebraical methods in one year by an average pupil is about equal to that which can be acquired by the same pupil in three years following the Euclidean method. And as there is no loss whatever in rigidity of proof, the natural consequence is surely that of two pupils who have devoted an equal period of time to mathematics during their school training, the one employing in his geometry the modern methods and the other the Euclidean, the former must be more prepared for the intelligent use of mathematical formulæ and reasoning in the university or the technical school than the latter. This consideration, indeed, derives still more strength from the fact that the proving of geometrical propositions by means of operations upon algebraical symbols extends the mental grasp of algebra itself.
Professor Perry appears to have hopes of speedy reform in this respect, the University of Oxford having decided to omit Euclid from the 'locals' of 1903, Oxford being capable of setting the pace for the great schools and the principles of the Society for the Improvement of Geometrical Teaching having made, during the past twenty years, sufficient theoretical headway to ensure the opportunity of the change being welcomed and grasped.
At the same time, it is to be remembered that the mathematical is not the whole or the only training even for the engineering mind. We have the constant reminder of Faraday's example in this respect. Faraday was able to reason most accurately and profoundly upon curves, centers of motion and other phenomena arising from his experiments in electricity and magnetism, although he was obliged to confess in a letter to Professor Clerk Maxwell that although he had tried hard he had never been able to understand even simple equations in algebra—a comforting confession for others to whom mathematical studies have been a great difficulty!—but perhaps more profitably to be regarded simply as a proof that a sufficiently helpful text-book was not placed within his reach at the struggling period when he laid the foundations of his marvelous self-culture.
