201 



But this, in general, is not the case. Fresnel has shown, 

 however, that the displacement may be resolved in two direc- 

 tions in the plane of the wave, at right angles to one another, 

 such that the elastic force called into action by each compo- 

 nent will be in the plane passing through the component, 

 and normal to the wave ; and thus each component will give 

 rise to a wave, in which the direction of the vibrations is pre- 

 served, and which therefore will be propagated with a con- 

 stant velocity. 



The two directions, above alluded to, are those of the great- 

 est and least diameters of the section of the surface of elasticity 

 made by the plane of the wave ; so that if the original dis- 

 placement be resolved into two, parallel to these directions, 

 each component will give rise to a plane wave, in which the 

 vibrations preserve constantly the same direction. The velo- 

 city of propagation being represented by the radius-vector of 

 the surface of elasticity in the direction of the displacement, 

 the velocities of the two parts of the wave will be proportional 

 to the greatest and least diameters of the section of the surface 

 of elasticity, to which the vibrations are parallel. Thus it 

 appears that an incident plane wave, in which the vibrations 

 are in any direction, will be resolved into two within the 

 crystal ; and these will be propagated with different veloci- 

 ties, and consequently assume different directions. 



(213) The vibrations in these waves being parallel to two 

 fixed lines, namely, the greatest and least diameters of the 

 section of the surface of elasticity, it follows that the two re r 

 fracted rays are polarized, and that their planes of polarization 

 are at right angles, being the planes passing through the di- 

 rection of the ray and these two lines. Hence it follows, that 

 the plane of polarization of one of the rays bisects the dihedral 

 angle made by the two planes, which pass through the nor- 

 mal to the ware and the normals to the two circular sections of 



