From the standpoint of an oculist, astigmatism is that difference in the curvature of the meridians of the refracting media of an eye which causes rays of light from a point after being refracted to be focused in a line, oval or circle, but never in a point. In examining the refraction of such eyes, it is seldom necessary to study more than the meridians of greatest and least curvature, the so-called principal meridians, which are, as a rule, at right angles to one another. When the error of refraction for these has been corrected, it is corrected for all meridians excepting in cases of irregular astigmatism. Astigmatism may exist in the cornea alone, in the lens alone, or in both, while that of the cornea may be augmented or neutralized by that of the lens. We are, consequently, obliged to take under consideration the radii of curvature of the