slight familiarity. In the previous three years there has been work on the applications of the simplest algebraic formulae and geometrical propositions to problems of surveying, or of some other scientific work involving calculations. In this way arithmetic has been carefully strengthened by the insistence on definite numerical results, and familiarity with the ideas of literal formulae and of geometrical properties has been gained; also some minor methods of manipulation have been inculcated. There is thus no long time to be wasted in getting used to the ideas of the sciences. The pupils are ready for the small body of algebraic and geometrical truths which they ought to know thoroughly. Furthermore, in the previous period some boys will have shown an aptitude for mathematics and will have pushed on a little more, besides in the final year somewhat emphasizing their mathematics at the expense of some of the other subjects. I am simply taking mathematics as an illustration.
Meanwhile, the cycle of language is in its stage of generalization. In this stage the precise study of grammar and composition is discontinued, and the language study is confined to reading the literature with emphasized attention to its ideas
