FRESNELS THEORY or DOUBLE REFRACTION. 



one will be retarded more than the other, in its progress 

 through the crystal. But if the second face be oblique to- 

 the direction of the rays, they will be both refracted at 

 emergence, and differently ; and they will therefore diverge 

 from one another. 



(211) To return to the general theory. Let us suppose a 

 disturbance to be produced in a medium such as we have 

 been considering, and any particle of the medium to be dis- 

 placed from its position of rest. The resultant of all the 

 elastic forces which resist the displacement will not, in ge- 

 neral, act in the direction of the displacement (as would be 

 the case in a medium uniformly elastic), and therefore will 

 not drive the displaced particle directly back to its position 

 of equilibrium. Fresnel has shown, however, that there are 

 three directions at right angles to each other, in every elastic 

 medium, in each of which the elastic forces do act in the di- 

 rection of the displacement, whatever be the nature or laws 

 of the molecular action ; and he assumes that these three di- 

 rections are parallel throughout the crystal. In fact, the 

 first principles of crystallization oblige us to admit, that the 

 arrangement of the molecules of the crystalline body is similar 

 in all parallel lines ; and the same property must belong to 

 the ether itself, if (as we have reason to presume) its 'elasti- 

 city be dependent on that of the crystal. These three direc- 

 tions Fresnel denominates axes of elasticity ; and he concludes 

 that they are also axes of symmetry, with respect to the 

 crystalline form. 



If on each of these axes, and on every line diverging 

 from the same origin, portions be taken, which are as the 

 square roots of .the elastic forces in their directions, the 

 locus of the extremities of these portions will be a surface, 

 which Fresnel denominates the surface of elasticity. Its equa- 

 tion is 



r* = a 2 cos 2 a + 6 7 cos 8 /3 + c 2 cos* 7 : 



