The summer meeting of the North Wales branch was held on 22nd May at the County School, Beaumaris, where the headmaster, Mr. Madoc Jones, entertained the members present. In opening a discussion on the teaching of geometry, Mr. Botting, mathematical tutor at the Normal College, Bangor, referred to the recent circular of the Board of Education, which recommends three stages, each occupying one year : (1) children to be grounded in fundamental ideas of space, lines, angles, etc., without actual de-finitions, and accustomed to instruments of measurement ; (2) the acquisition of a number of fundamental propositions, but not in a formal way, e.g. I. 13-15 in Euclid, and some propositions about parallel lines, the equality of triangles, etc.; (3) rigid deductive proofs to be begun, all fresh propositions being treated as original work like riders. He also said that propositions should not be taken singly, but in groups together, and that the power of working riders is the only real test of advance in geometry