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... CAL GAZETTE. THE MATHEMATICAL GAZETTE. and should be found extremlely useful, but we fancy that there is room for considerable revision of the solutions. Der Naturwissenschaftliche Unterricht in England inbesondere in Physik und Chemie. By Dr. KARL T. FISCHER. Pp. viii and 94. 3 m. 60. (Teubner.) This elegantly got-up volume hardly comes within the scope of the Gazette, being an account, impartial and with but few exceptions correct, of the provisions made for the teaching of science-physics in particular-in English schools. Dr. Fischer, who is a Privatdozent and teacher of Physics in the Royal Technical High School at Munich, was sent by the Bavarian Government to make a study of the position of science in the curricula of English schools. A good deal of attention is paid to the Heuristic method of teaching, with which Professor Armstrong's name is indissolubly linked. The general conclusion is not, however, of the most favourable character. The most striking quotation made by the author is from some remarks of Mr. Earl, to whom the science side of Tonbridge School is so deeply indebted. He prefers boys from the classical side to boys from the modern; " they prove better, being of higher standard in character." Elementary Geometry. By W. C. FLETCIER. Pp. iv., 84. is. 6d. 1902. (Arnold.) The revolt against formality is already beginning to bring forth fruit in the shape of books such as this before us, embodying most of the recommendations of the various committees that have been dealing with the question of reform in our mathematical teaching. Within the compass of 80 pages or so, the author gives us a guide and a summary to the whole of the substance of Euclid I.-iv. and vi., with the exception of the "elegant but unimportant proposition iv. 10." It contains "the irreducible minimum of geometrical knowledge, less than the whole of which is not worth considering as knowledge at all." He confesses that the book is " frankly unorthodox-there is no reference to axioms or rather postulates . . . this is not work for a boy, but for mature and subtle minds.' With the sets of riders are incorporated suggestions for drawing, plotting, and measurement, in accordance with the principle that the early stages of abstract geometry must be as far as possible associated with concrete illustration. We cannot speak too highly of Mr. Fletcher's work. It is of course a skeleton which must be provided with flesh by teacher and pupil in judicious combination. It has been constructed with admirable skill, and every teacher will find it most suggestive.