209 



directions and planes of polarization are determined by the 

 tangent planes. 



Again, it is evident that the circle and ellipse have four 

 common tangents, such as MN ; and the planes passing through 

 these tangents, and perpendicular to the plane of the section, 

 are perpendicular to the optic axes of the crystal. Fresnel 

 seems to have thought that these planes touched the wave 

 surface in the two points just mentioned, and in these only ; 

 and, consequently, that a single ray, incident upon a biaxal 

 crystal in such a manner that one of the refracted rays should 

 coincide with an optic axis, OM, will be divided into two 

 within the crystal, OM and ON, determined by the points 

 of contact. But Sir William Hamilton has shown that the 

 four planes of which we have spoken touch the wave-surface, 

 not in two points only, but in an infinite number of points, 

 constituting each a small circle of contact ; and, consequently, 

 that a single ray of common light, incident externally in the 

 above-mentioned direction, should be divided into an infinite 

 number of refracted rays within the crystal. 



Here, then, are two singular and unexpected conse- 

 quences of Fresnel's theory, not only unsupported by any 

 facts hitherto observed, but even opposed to all the analogies 

 derived from experience ; here are two remote conclusions of 

 that theory, deduced by the aid of a refined analysis, and in 

 themselves so strange, that we are inclined at first to reject 

 the principles of which they are the necessary consequences. 

 They accordingly furnish a test of the truth of that theory of 

 the most trying nature that can be imagined. 



(220) Naturally anxious to submit the wave-theory to 

 this test, and to establish or disprove its new results, Sir 

 William Hamilton requested the author of this volume to 

 examine the .subject experimentally. The result of this ex- 



