This account of the theory of the circular functions and their applications to plane trigonometry begins with the measurement of angular magnitude and of lines, and proceeds to circular functions, the expansion of functions of multiple angles, trigonometrical tables, the solution of triangles, and properties of triangles and quadrilaterals. 1928 edition. I have taken the opportunity afforded by the need for a new edition to subject the whole work to a careful revicion, and to introduce a considerable amount of new matter. In Chapter I. I have inserted a theory of the lengths of circular arcs, and of the areas of circular sectors, based upon arithmetic definitions of their measures. Much of that part of the work which deals with Analytical Trigometry has been re-written.