A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



(105) The velocities along the axes are as follows : 

 Direction of propagation 



585 



Direction of the electric displacements 



Now we know that in each principal plane of a crystal the ray polarized 

 in that plane obeys the ordinary law of refraction, and therefore its velocity 

 is the same in whatever direction in that plane it is propagated. 



If polarized light consists of electromagnetic disturbances in which the 

 electric displacement is in the plane of polarization, then 



a* = b* = c' (93). 



If, on the contrary, the electric displacements are perpendicular to the plane 



of polarization, 



\ = fi = v (94). 



We know, from the magnetic experiments of Faraday, Plucker, &c., that in 

 many crystals X, ft, v are unequal. 



equations referred to and the table given in 105 may perhaps be more readily understood from 

 a different mode of elimination. If we write 



' + vn' = 



it is readily seen that 



and \lf" + ft.mG' + vnJI ' = 

 7 V*'-a'\Q 



" V - a'\P ' 



with similar expressions for G', II'. From these we readily obtain by reasoning similar to that in 

 104, the equation corresponding to (86),' viz. : 



tn.fi nv 



i -wra i~o -* ~r 



P-a*AP T V'-b'fiP ' V'-c?vP~ 

 This form of the equation agrees with that given in the Electricity and Magnetism ii. 797. 



By means of this equation the equations (91) and (92) readily follow when *' = 0. The 

 ratios of F' : G' : H' for any direction of propagation may also be determined.] 



VOL. I. 74 



