Eepoet on the Recent Progress in T H E Theory of Linear Groups

divided. Suppose the section of FresneVs wave surface by a coordinate plane to consist of a circle and an ellipse and let O be the center of a wave disturbance in the surface of a crystal. Draw any radius vector OBC, cutting the circle at B and the ellipse at C; the intersection of tangents at B and C will be 8, a point on the tangent plane at the point of incidence. Then 8B and SC will be the wave fronts of an ordinary and an extraordinary ray. Since these two lines are tangents at the points of intersection of a single radius vector OBC< the latter is the path of both an ordinary and an extraordinary ray. Therefore from the indices of refraction we may compute an incident ray which will not be divided but will move along OBC, and since there are an infinite number of points 8 there are an infinite number of directions for which the ray is not divided. The locus of the point S is a curve of the eighth degree and may be expressed in a simple and symmetrical form. By a simple transformation of the equation uniaxial crystals are included in this treatment.