In accepting the honour of being your President, I was told that the office carried only a single duty—that of delivering an address at a then distant date: even the selection of the topic could be deferred for a time. So there lay before me a primrose path of dalliance. I had some hesitation about the selection of a topic. One decision, however, was immediate; my determination was instantly framed to avoid any discussion of the place of mathematics in education, an unending subject, of which perhaps you have heard only too much. It would have been possible to select some special topic, such as functionality, in its historical development; and you would have had a mere mathematical lecture. I have preferred to choose a general subject: my text seems highly technical in phrase, but I shall not keep very closely to it; my purpose rather is to fall back upon my own experience over a wide range of teaching and to exhibit for your consideration some reflexions based on that experience. Moreover, technical as its title is, my address will contain no mathematical symbols. Though my work as a teacher and writer is largely associated with differential equations—probably in the course of a year I receive (with a request for solution) a greater number of insoluble equations than any one here—the reason for its selection is not to be found in any specially personal relation. The reason is that the particular processes affect many subjects in mathematics, and consequently allow general comparisons to be made, as well as particular inferences to be drawn: they constitute a method as powerful in operation and effective in results as any within our domain.