DOUBLE EEFRACTION. 215 



planes there is (in the j^osition of tlic crystal supposed) no double i-efraction of 

 the incident polarized ray. The light is therefore transmitted without interriip- 

 tion, and being cut off by the analyzer, shows the dark cross. By rotating the 

 analyzer 90<^, the cross becomes bright, as with crystals of one axis. But when 

 the crystal itsidf is turned in azimuth, while the analyzer remains in one of the 

 principal azimuths, the arms of the cross break at the centre, two of them on 

 each side forming together a curve. At 45'^, the two curves present the appear- 

 ance of opposite hyperbolas. 



To follow these changes analytically would require a larger acquaintance 

 Avith the physical theory of double refraction than is furnished in what precedes. 

 We will therefore, next in order, turn our attention to that subject. 



5 XL DOUBLE EEFRACTION. 



We have seen that the double refraction of light is always attended with 

 polarization. It is proposed now to attempt a physical explanation of this 

 phenomenon. 



Refraction, in general, considered as a' bending of the ray, is owing to a 

 change in the velocity of the wave as it enters the refracting medium. When 

 the refraction is double — in other words, when a single wave is divided by re- 

 fraction into two waves — the velocities of the two Avaves must be unequal. It 

 is presumed that this difference of velocities is owing to a difference of elasticity 

 of the ether within the medium. But, inasmuch as the two rays often follow 

 the same track, each with its own determinate velocity, while they remain quite 

 distinct from each other, it is evident that their velocities cannot be determined 

 by the elasticity of the ether in the direction of their progress. It becomes 

 therefore a necessity to assume that their molecular movements are transverse 

 to the ray, and in the surface of the wave itself. TlxGfact of double refraction 

 is thus an incontrovertible proof of tiie truth of the doctrine of transverse vibra- 

 tions, independently of the many evidences of the same truth derived from po- 

 larizati(m and the phenomena of interference. 



But inasmuch as, in a medium in which the elasticity of the ether varies ac- 

 cording to a certain law, the elasticity Avill usually be different in each of the 

 indefinite number of planes which may pass through a given ray, it follows that 

 if the ray pursue a determinate course Avith a constant velocity, its transverse 

 vibrations must be confined to some determinate plane. Double refraction in- 

 volves, therefore, as an indispensable condition, polarization; and, as a general 

 rule, plane polarization Avould seem to be the necessity. 



Experiment proves that these theoretic inferences are correct; and also that 

 the phines of polarization of the tAvo rays which originate from a single incident 

 ray, in a doubly refracting body, are at right angles to each other. Tavo ques- 

 tions present themselves, therefore, for solution: First, hoAV is the direction of 

 molecular movement in a polarized ray related to the plane of polarization ? and 

 secondly, Avhat cause determines this movement in the doubly refracting body, 

 to these particular directions? 



In regard to the first question, Ave may arrive at a conclusion, by considering 

 the case of a crystal of one optic axis, like Iceland spar. If we suppose such 

 a crystal to be ground to a perfect sphere and polished, a ray incident perpen- 

 dicularly upon any part of its STirface Avill coincide in direction Avith the radius 

 of the sphere. Such a ray falling upon a sphere of homogeneous glass Avould 

 pass undivided through the centre. But Avith the sphere of crystal Avhich avc 

 have supposed, there is but one diameter iuAvhich this Avill happen. This is the 

 diameter coincident with the optic axis; and in this direction there is no double 

 refraction. If the incident ray is common or unpolarized light, (a supposition 

 which is to be understood in all that folloAvs,) the emergent ray Avill be unpo- 

 larized also. And, as the molecular movements of common light are iu all 



