pupils be in a frame of mind to receive instruction? Would the teachers themselves be likely to preserve the calmness necessary for the investigation of Truth? That the picture I have drawn is no exaggerated one, that those whose mission is to arouse the public to a perception of the relation between the essential and the accidental have to run the gauntlet of a style of criticism as senseless and frivolous as I have represented, no one can doubt. We are all aware of the absurdity of our present modes of receiving new truth; few, I fear, are sufficiently aware of its evil effects. Therefore it is well for us to reflect what effect it would have on the teaching of so simple a thing as Geometry, if teachers introduced into each other's classes the element which is so rife in our literature.
True Critique is one of the fine Arts; as sacred and beautiful as all true Art. There is no keener pleasure for a good teacher than genuine criticism from a pupil. If a question is asked which shows that the teacher has failed to make intelligible a fact perfectly clear to himself, even that is a source of great enjoyment. But when, as sometimes happens, a remark is made which proves that we have not gone deep enough into our own
subject, which opens up new avenues of thought, and forces us to reconsider a demonstration, to re-investigate a solution; when, in fact, the relation between teacher and pupil is for a time inverted, it is then that that relation becomes fullest of pleasure and profit. (And so of course it is, in a still higher degree, between a writer and the critical reader.) But what chance would a pupil have of making intelligent criticisms, or of asking suggestive questions, if it were the fashion
