Mr. A. B. Basset on an 



156 

 accordingly 



^ = Lcos^{i,(i + i)-«}sin^(i--i-) ; 



whence, if -^ be the angle through which the plane of polari- 

 zation is rotated after the wave has passed through a length 

 z of the medium, 



Substituting the values of Y l5 V 2 from (14), we obtain 

 f = - ^(A 2 -27t / 7/t)-*-(A 2 + 27 7 )/t)-^ 



27t 2 j?z _ 2tt 2 pz 

 AV = "AX 2 " 



(15) 



to a first approximation, where X is the wave-length in the 

 medium. 



This result is in accordance with the law which was experi- 

 mentally deduced by Biot, viz. that the rotation is directly 

 proportional to the thickness of the length of the medium tra- 

 versed by the ivave, and inversely proportional to the wave-length 

 of the particular light employed. 



5. We must now consider the theory of quartz. Taking 

 the axis of the quartz as the axis of z, we must put A=B, 

 p 1 =p 2 = 0, whence writings for p 3 , (10) become 



g=A W -£+, 



dt 2 



dt 2 



A 2 V 2 <7- 



= C 2 V 2 A 



dx 



da 



dz 



\dz 



dh\ 



dy) 



d (dh 



dz \dx 



dn 



dz 



d (df 

 ^dz{dy 



dz j 



is 



dx 



(16) 



)j 



We have already pointed out that if a plane wave be 

 travelling perpendicularly to the axis, no rotation is pro- 

 duced. Now if the wave is travelling parallel to the axis of 

 x, we must have/=0 ; whilst g and h are functions of x and t 

 alone ; when this is the case we see from (16) that the 

 rotatory terms vanish, as ought to be the case. Similarly 

 we see that the rotatory terms vanish when the wave is 



