590 Prof. R. W. Wood on the 



true in the case of a concave spherical wave, which is only 

 given by a parabolic mirror. We shall find as a matter of 

 fact, if we examine the geometrical construction, that the cusp 

 of the wave, or the rim of the crater, which traces the caustic 

 as I have shown, is continuously passing through a focus. Jn 

 other words, the curvature of the crater increases as we go 

 from the bottom to the rim, at which point the radius becomes 

 zero. The inner edge is then continually passing through a 

 focus and appearing on the outside, building up, as it were, 

 the sides of the cone. These wave-fronts were drawn by 

 constructing the orthogonal surface, which was shown to be 

 in section an epicycloid formed by rolling a circle whose 

 diameter was equal to the radius of curvature of the mirror, 

 around the outside of the mirror. The evolute of this curve is 

 the caustic, itself an epicycloid, and the reflected wave-fronts 

 form a family of parallel curves, wmich are the involutes of the 

 caustic. 



Though the caustic and orthogonal surface (evolute and 

 involute) are similar epicycloids, the reflected wave-fronts, or 

 parallels to the orthogonal surface, are not epicycloids. It 

 may be well to point out here an error that sometimes appears 

 in text-books on Optics, namely, the assumption that the wave- 

 front (say in the case of a spherical wave refracted at a plane 

 surface) is an hyperboloid in the second medium, because the 

 caustic is the evolute of an hyperboloid. An hyperboloid 

 wave will not propagate itself as an hyperboloid, nor an 

 ellipsoidal wave as an ellipsoid (except in an anisotropic 

 medium), the parallels to a conic being in general curves of 

 the eighth degree. In the case above cited, we should speak 

 of the wave-fronts after refraction as the parallels to an 

 hyperboloid. 



Fi*. 1. 



Let us suppose the w r ave to be just entering the mirror. 

 The form of the portion which has already suffered reflexion 

 is a cusp extending around the upper edge of the hemisphere 



