When, with the other members, I received a request from the Secretary, it seemed only fair to him that I should express my willingness to do whatever might be in my power towards the provision of a subject for discussion ; and therefore, with an earnest wish that he would if possible ignore my suggestions, I proposed the rather well worn subject of this paper. To my dismay he did not ignore the suggestions, and in consequence you will have to listen to the trite observations of one who, sufficiently remote from great centres of education, and in great measure precluded from intimate contact with modern methods, is nevertheless sufficiently interested in them to form theories, or rather opinions, of his own. Those to whom the element of novelty may be absent in the points that I proceed to consider will, I trust, extend a charitable reception on the great moral principle of the Western States that the pianist who does his best is not to be shot.

In the ordinary course of lecturing to students who come stamped with the approval of some of the entrance examination Boards, and their name is legion, I find that, especially when they have had a more or less practical course, very great difficulties arise on account of their weak grasp of mathematical reasoning.