The difficulties which arise in teaching the elementary power series appear to form part of a larger question, namely, the proper course of mathematical education after a sufficient knowledge of Elementary Geometry, Algebra and Trigonometry has been acquired. The question of Geometry is hardly germane to the present discussion, and I will only mention it so far as to say that I believe it is the hope of many teachers of mathematics that boys of 15 or 16 may in the future learn far more of Projective and Descriptive Geometry than is the case at present.