Doctrine of Extraneous Force. 117 



2. Now when polarized light is transmitted through a 

 crystal, and when rajs in any one of the principal planes are 

 examined, it is found that — 



(1) A ray with its plane of polarization in the principal 

 plane travels with the same speed, whatever be its direction 

 (whence it is called the " ordinary ray " for that principal 

 plane) ; and (2) A ray whose plane of polarization is per- 

 pendicular to the principal plane, and which is called " the 

 extraordinary ray " of that plane, is transmitted with velocity 

 differing for different directions, and having its maximum 

 and minimum values in two mutually perpendicular direc- 

 tions of the ray. 



3. Hence and by § 1, the velocities of all rays having their 

 vibrations perpendicular to one principal plane are the same ; 

 and the velocities of rays in a principal plane which have their 

 directions of vibration in the same principal plane, differ accord- 

 ing to the direction of the ray, and have maximum and mini- 

 mum values for directions of the ray at right angles to one another. 

 But in the laminar shearing or distortional motion of which 

 the wave-motion of the light consists, the "plane of the 

 shear"* (or "plane of the distortion,'" as it is sometimes 

 called), is the plane through the direction of the ray and the 

 direction of vibration; and therefore it would be the ordinary 

 ray that would have its line of vibration in the principal plane, 

 if the ether's difference of quality in different directions were 

 merely the aeolotropy of an unstrained elastic solidf. Hence 

 ether in a crystal must have something essentially different 

 from mere intrinsic aeolotropy; something that can give 

 different velocities of propagation to two rays, of one of which 

 the line of vibration and line of propagation coincide 

 respectively with the line of propagation and line of vibra- 

 tion of the other. 



4. The difficulty of imagining what this something could 

 possibly be, and the utter failure of dynamics to account 

 for double refraction without it, have been generally felt to be 

 the greatest imperfection of optical theory. 



It is true that ever since 1839 a suggested explanation has 

 been before the world; given independently by Cauchy and 

 Green, in what Stokes has called their " Second Theories of 

 Double Eefraction," presented on the same day, the 20th of 



* Thomson and Tait's 'Natural Philosophy.' § 171 (or l Elements, 

 § 150). 



t The elementary dynamics of elastic solids, shows that on this 

 supposition there might be maximum and minimum velocities of propa- 

 gation for rays in directions at 45° to one another, hut that the velocities 

 must essentially be equal for every two directions at 90° to one another, in 

 the principal plane, when the line of vibration is in this plane. 



