MUCH of the elementary mathematical work in Secondary Schools has to be taught by non-specialists, many of whom are unfamiliar with the higher branches of the subject, and, as a consequence, the work of the specialist who takes the advanced Mathematics is often rendered more difficult, since he has to build on foundations different from those which he would have laid himself. It is essential, therefore, that the junior work should proceed on well-defined lines and that the methods adopted in teaching this junior work should be such that they will lead up naturally to the more advanced work.