666 PROCEEDINGS OF THE AMERICAN ACADEMY. 



difference between the refractive indices, (/x £ — /u^). In Babinet's com- 

 pensator, since the optic axis in the second wedge is at right angles to 

 that in the first, the wave retarded in the first wedge is accelerated in 

 the second, and vice versa. Hence 



8 = (e — e') (fi e — fx a ), 



With plane-polarized light the dark central fringe occurs where 8 = 0, 

 namely, where the thickness of the first wedge, e, is equal to the thick- 

 ness of the second, e'. This is the zero position. But when the inci- 

 dent light has already undergone double refraction, the central dark 

 fringe will be shifted x cm. from the zero position to that point where 

 the separation 8 of the compensator is equal and opposite to the separa- 

 tion produced by the doubly refracting substance under observation. 

 If i be the acute angle of the compensator wedges, 



(e — e') = 2 x tan i 



and at this point the separation due to the compensator is 

 8 = 2 x tan i • (jtt e — fi M ) 



Since 8, x, and (fi e — fi^) all vary with the color of the light, and since 

 (fjL e — /x u ) here refers to quartz, it is better to write the last equation 

 with the subscripts A, and Q, thus, (for quartz) 



8a = 2 x K tan i • (/*« — fi^)^ Q) 



In carbon bisulphide, in which yu« > /x w 



S\ = / • (ii e — n„) (x> CSj) 



at a given temperature, and given strength of electric field. In the 

 voltage band the central fringe appears shifted by just the amount x\ 

 necessary to cause the compensator to counteract the separation induced 

 by the electric field; or, stated algebraically, 



Sa = I ■ 0*. — |Uco) ( a, cs 2 ) = 2x k tan * ' 1 * — fV)(A, Q) 0) 



For sodium light, X = D and (1) becomes 



&d = l ' 0*« — /*»)<!>, cs 2 ) = 2x d tan • ' (/*« — P»){D, Q) ( 2 ) 



By dividing the first of these equations by the second, the double 

 refraction in CS 2 for any wave-length can be expressed in terms of the' 

 double refraction for D light, = (^ — ^)(d,cs„): as standard: 



Sa_ _ f (/J e — /Qa ~| _ #A_ |~ (|"6 —l*J)\ "I /gx 



<$z> L G"« — h-d^J CS„ x D [_ (ji t — (4 U ) d J Q 



