to the Wave Theory of Light. 51 



58. We have seen (15) that there is a circle of contact on 

 the biaxal surface of refraction. If an incident ray S'OS be 

 taken, cutting the sphere in .8, so that the line US produced 

 may pass through the circumference of this circle, it is manifest 

 that the direction of the refracted ray will be the same through 

 whatever point II of the circumference the line US may pass, 

 because that direction is perpendicular to the tangent plane at 

 II, which is in fact the plane of the circle itself. If, therefore, 

 the line US move parallel to itself along the circumference of 

 the circle, cutting the sphere in a series of points 8 9 every inci- 

 dent ray S'OS which passes through a point S so determined 

 will be refracted into two rays, of which one will have a fixed 

 direction in the crystal, being perpendicular to the plane of the 

 circle of contact, and therefore coinciding (16) with nOn, one of 

 the nodal diameters of the wave surface. But though the direc- 

 tion On of the refracted ray is fixed, its polarization changes 

 with the incident ray from which it is derived ; for if n be the 

 point in which the line ES, corresponding to any position of 

 the incident ray, crosses the circle of contact, the vibrations of 

 the refracted ray On will be contained in the plane of the lines 

 On, OH, and will be perpendicular to On. Conceive a circle 

 described on the diameter nf in a plane perpendicular to the 

 figure (Fig. 12). This circle, and the circle of contact on the 

 surface of refraction, are (20) sections of the same cone. Let FT 

 therefore be the point at which On, in any position of the inci- 

 dent ray, crosses the circumference of the circle nf\ and the line 

 ttn, drawn to the node of the wave surface, will be the corre- 

 sponding direction of the vibrations in the ray On. 



59. With regard to the general law of polarization in the 

 theory of FRESNEL, it may be observed, that if the ellipsoid abc 

 which generates the biaxal surface of refraction be cut by a 

 plane perpendicular to OP, the vibrations of the ray P will be 

 parallel to the greater axis of the section, and therefore the plane 

 of polarization will pass through OP and the less axis ; whence 

 it is easy to show that the plane of polarization of a ray P bisects 

 one of the angles made by two planes intersecting in OP and 



E2 



