1 8 Note on the Subject of Conical Refraction. 



tact T\A variable, for the plane JROS in which it lies changes 



with OR. Thus we get a curve 



of contact on the tangent plane 



of the wave surface, and a cone 



of rays OT derived from the same 



incident ray. The vibrations of 



any ray OT are in the line TS 



passing through the fixed point 8, 



as follows from a general remark 



in the place referred to. 



The three right lines OQ, Or, OT, are at right angles to each 

 other, and a geometer will observe that the first two of them are 

 confined to given planes. For Or is always in the plane of the 

 circle It Or ; and the point Q must be in a given plane, because 

 the line OP, perpendicular to the plane that touches the ellip- 

 soid in Q, is in a given plane It Or. 



2. When QOq is a circle, the points T and V coincide in a 

 nodal point n, where the two sheets of the wave surface cross 

 each other. At this point there are an infinite number of tan- 

 gent planes, for OQ and Oq are now indeterminate. The same 

 refracted ray On may therefore be derived from any one of an 

 infinite number of incident rays, and its polarization will differ 

 accordingly ; for the vibrations are in the line nS drawn from 

 the node to the foot of the perpendicular OS on the tangent 

 plane. The ray On, however, is always accompanied by another, 

 but variable, refracted ray. 



The lines, OP, Oq, OS, are at right angles to each other, and 

 the first two of them are confined, as before, to given planes. 

 For Oq is in the plane of the circle QOq ; and OP, being perpen- 

 dicular to the tangent plane at Q, must lie in a given plane. 

 These given planes are parallel to two principal tangent planes 

 passing through n, and touching the circle and ellipse that com- 

 pose the wave section in the plane of the nodes : whence it is 

 easy to see that every nodal tangent plane intersects the two 

 principal tangent planes in lines that are constantly at right 

 angles ; for these lines are parallel to OP and Oq. 



