Let us think for a few moments of the whole reading public as a College, which Truth, as Head-Master, is endeavouring to instruct and educate; and of men of Genius, discoverers, reformers, as assistant-masters, to each of whom is committed the task of teaching the subject of which he knows most. The comparison would be an impertinent one, if we illustrated it by reference to classes in such subjects as History or Language; because the school-teacher in such subjects is obliged to require from his pupils a kind of docility which readers are not expected to give to an author. But every mathematical teacher who deserves the name endeavours to accustom his pupils to take nothing for granted till it has been proved to their own personal satisfaction. The mathematician, therefore, is related to his class in much the same way as a writer to his readers. In my imaginary College, the various teachers are in the habit of attending each other's classes whenever they wish to do so; a practice which actually does prevail to a certain extent in some schools, and with the happiest results; for the teacher who takes his place among the pupils of a colleague, can, if he will, set the class an excellent example of courteous and intelligent questioning. But if the various teachers thought of each other's work in the same spirit as the leaders of Literature and Science do, and if the pupils thought of their teachers as the reading public do of writers and preachers, the result would be not only moral confusion, but intellectual chaos.
The chief reason why courtesy, reverence, and a certain kind of docility are needful for those who would learn, is this:—Truth is never received into the human
