If it be granted that the study of trigonometry in the secondary school course should not be limited to the numerical solution of triangles but should include some treatment of form as an introduction to higher mathematical analysis, then the importance of the trigonometrical identity must be admitted. A certain amount of valuable training can be obtained from the proper study of the identity if this study be systematic; but there seems little to be gained by working through the customary set of miscellaneous examples inserted at odd intervals in the trigonometrical text-book.