252 Wisconsin Acadefny of Sciences^ Arts, and Ldters. 



towards the center. The molecule will, therefore move in this 

 line, and not in a circle ; and if the plane of the circle E H I H' 

 be the bounding surface of the crystal, or the surface of emer- 

 gence of the light, I Gr will mark the azimuth of the molecular 

 movements of the emergent ray. 



But if the planes of E H I H' do not pass through the point of 

 intersection of the spirals it must cut each spiral in a different 

 point. The figure is drawn to represent this more general case, 

 the points of intersection with the spirals being severally L and K. 



By joining L K and drawing the radius Gr I perpendicular to it, 

 Gr I will bisect the angle G L K and M', at the intersection of G 

 I and L K will be the position of the molecule in the plane E H 

 L I K, which, if the tangential force P only were acting, would be 

 at L, and if the tangential force Q only were acting, would be at 

 K. The tangential forces acting at the moment on this molecule 

 will not be represented by I P' and I Q', but will be tangents at K 

 and L. 



Now, as D H, the distance between the planes AD B and E H 

 I, is a larger part of the length of an entire turn of the spiral M S 

 N K than of the spiral M F L N', the line G I will fall on the 

 right of G H, the position it would occupy if the two undulations 

 were equal in length. We may therefore say, as before, that if 

 the plane E H I were the surface of emergence of a ray from a 

 crystal, in which it had been subject to the action of the forces 

 supposed, its plane of polarization, G I, would be turned towards 

 the right from its original azimuth. The plane of polarization 

 turns, therefore, in the direction of the loinding of the closest spi- 

 ral, or of the ray of shortest undulation ; but it turns in the direc 

 tion of the gyration of the ray of longest undulation. 



This rotation of the plane, thus demonstrates that the two rays 

 advance with unequal velocities in the axis of quartz — a remark- 

 able fact which is not true of any crystal which produces plane 

 polarization only. It also enables us to determine the relative 

 velocities, or to ascertain the index of rotatory polarization. For 

 since G I bisects the angle between the points K and L, which 

 mark the relative degrees of advancement of the two rays in their 

 respective rotations, if we take a thickness d, which produces a 



