I feel somewhat diffident in addressing you on this subject, because I am only too conscious of the fact that my qualifications for doing so are but slight. Most of my audience will have had some experience of teaching algebra to the higher forms in schools, some will have had considerable experience. I have had none. My only knowledge of the subject on which I address you has been gained as an examiner and, a little, as a university don teaching undergraduates who come from your schools. I am as ready as the next man to admit that the examiner does not see everything; to admit, too, that he does not even see all that he thinks he sees. But when all has been said against the examiner—and more than a little has been said of late—the examiner does see something. And so, with these admittedly slight qualifications, I venture to put before you some few points about algebra.