The object of the present paper is to invite discussion as to the safest lines upon which to proceed in the teaching of Indices and Surds. And firstly, I am inclined to think that the beginner would get a firmer grasp of the theory of fractional indices (with which alone I am concerned) if a short course of surds, or, at least, of surd-forms, were made to precede; the simple theorem

would suffice, as shown later: and it seems more intelligible than its rival