In the address which he had the honour of giving at the Annual Meeting of the Association the object of the writer was twofold: (1) to urge Secondary School teachers to study non-Euclidean Geometry for the purpose of improving their own scholarship; and (2) to sketch a method of approach to the subject which seems both interesting in itself and much easier than that usually adopted. In preparing this paper for the Gazptte he has thought it better to omit the former and to develop the latter a little more fully than time allowed at the meeting; the title has been modified accordingly.