This quotation from Einstein is merely one of the many disturbing statements that a teacher of geometry may find in recent books on physics or even in the newspapers. It will not be long before some of our pupils will ask if it is worth while to continue the study of a subject of which the principal results are apparently contradicted by the latest discoveries. The object of the present article is to examine these apparent contradictions. To do this we shall trace the evolution of ideas concerning the nature of geometry and consider their relation to school work. The conclusion will be reached that certain changes in our teaching are desirable. Fortunately these changes will actually make school geometry easier as well as more scientific.

There can be few teachers who, when taking part in a discussion on the relative merits of two methods of teaching a given topic, have not wished that it were possible to produce in evidence a clear, accurate and unbiassed account by the child himself of the way in which the particular method under discussion affects him. As it is, we are forced to rely on the experience and insight of the teacher—experience, which is at best very limited, and insight which, if it is often true and sympathetic, can never fully penetrate into the child mind, and is moreover scarcely ever free from a prejudice in favour of one method or the other.

This is a remarkable book in many respects, and well worthy of the attention of those teachers of mechanics who have not yet made its acquaintance at first hand. Though written in 1784, some of its pages are greatly superior to those in many of the text-books now in use in schools, and one is particularly impressed by the stress laid on experimental verification of the various laws of mechanics, and by the extreme care shown in the planning and execution of the experiments proposed. The following quotations from it and the notes thereon are given, because I feel sure that they will prove of use to those who want Mechanics to become a more interesting subject to their pupils and to stand for something more than what is usually covered by the name “Applied Mathematics.” I have added a few parentheses, but only, I hope, where they were necessary.