114 REPORT ON PHYSICAL OPTICS. 



while in others, finally, they receive a motion of continued rotation. 

 To the two latter cases I shall have occasion to advert hereafter. 



The phenomena of fixed polarization are ascribed by M. Biot 

 to the operation of certain forces, which he denominates polarizing 

 forces. In the case of uniaxal crystals these forces are supposed 

 to act in the planes containing the two rays and the axis of the 

 crystal, the ordinary polarizing force tending to arrange the 

 axes of the molecules in the plane containing the ray and the 

 axis, while the extraordinary polarizing force draws them towards 

 the perpendicular plane. If the molecules were similarly circum- 

 stanced in every respect, they would necessarily obey the stronger 

 of these forces, and there would be but one plane of polarization. 

 This, however, is supposed not to be the case. Owing to the 

 different phases of their fits, at their incidence upon the crystal, 

 the molecules are disposed to yield more readily to one or other of 

 these forces ; so that when a polarized ray meets a double-refracting 

 medium, some of the molecules fall under the influence of the 

 ordinary polarizing force, and have their axes of polarization 

 turned into the plane containing the ray and the axis of the 

 crystal, while others are actuated by the extraordinary force, and 

 have their axes arranged in the perpendicular plane. The number 

 of molecules which yield to one or other of these forces, or the 

 intensity of the two polarized rays, is supposed to depend on the 

 angle which the plane of primitive polarization makes with the two 

 planes just mentioned. When the plane of polarization coincides 

 with the former, the extraordinary force has no effect, and the ray 

 receives only the ordinary polarization ; the converse takes place 

 when the plane of polarization coincides with the perpendicular 

 plane. Similar suppositions were made to account for the phe- 

 nomena of polarization in biaxal crystals. 



Such was the state of the theory of double refraction when the 

 subject was taken up by Fresnel. The law of refraction, we have 

 seen, whether in the theory of emission or in that of waves, was 

 intimately connected with, and dependent on the law of velocities ; 

 so that, considered as a physical question, the problem resolved 

 itself into the determination of the latter. With the exception, 

 however, of the reasonings of Young respecting the form of the 

 wave-surface in a medium compressed or dilated in a given 

 direction,* no attempt had been made to deduce the velocity of the 



* Quarterly Seview, vol. ii. 



