through a dozen books; he must be not only teacher, but text-book. I know of no School Arithmetic which does not groan under a weight of sham practical work, and that does not, with an absurd priggishness, exclude the use of algebraic symbols. Except for one little volume, I know of no sane book which deals with arithmetic and elementary algebra under one cover or gives any helpful exercises or examples in squared paper calculations. Such books, I am told, exist in the seclusion of publishers’ stock-rooms, but if I, enjoying as I do much more leisure and opportunity of inquiry than the average mathematical master, cannot get at them, how can we expect him to do so? And the thing to do now is obviously to discover or create these books, and force them kindly but firmly into the teachers’ hands. The problem is much simpler in the case of mathematical teaching than in the case of English, because the educational theory and method have been more thoroughly discussed. There is no need for the ten years of experiment and trial I have suggested for the organization of English teaching. The mathematical reformer may begin now at a point the English language reformer will not reach for some years. Suppose now a suitably authenticated committee were to work out--on the basis of Professor Perry’s syllabus perhaps--a syllabus of school mathematics, and then make a thorough review of all the mathematical textbooks on sale throughout the English-speaking world, admitting some perhaps as of real permanent value for teaching of the new type, provisionally recognizing others as endurable, but with clear recommendations for their revision and improvement, and condemning the others specifically _by name_. Let them make it clear that this syllabus and report will be respected by all public examining bodies; let them spend a hundred pounds or so in the intelligent distribution of their report, and the scholastic profession will not be long before it is equipped with the recommended books. Meanwhile, the English and American scholastic publishers will become extremely active, the warned books will be revised, and new books will be written in competition for the enormous prize of the committee’s final approval, an activity that a second review, after an interval of five or six years, will recognize and reward.