Transparent Inactive Crystal Plates. 161 



Boundary Conditions Applied to Transparent Inactive Crystal 



Plates. 



A crystal is distinguished electromagnetically from an iso- 

 tropic body by the variation of its specific inductive capacity 

 with the direction. If e„ e a , e 3 , be the three principal dielec- 

 tric constants of a crystal and /* the magnetic permeability, 

 = 1, as is practically the case in all known dielectrics, then the 

 general differential equations, referred to any coordinate sys- 

 tem, for the electromagnetic field in a crystal, are : 



(4) 



(5) 



u* ^ v ay c^ 



In these equations, e hk =e kh ('). 



If the magnetic force be taken as light vector, the compo- 

 nents X, Y, Z, of the electric force can be eliminated from (4) 

 and (5) by differentiating equations (5) with respect to t : 



l_SPu _ 5_/5Y\_ _3_/°>z\ l^v_ _3/^z\_ d_(dX\. 

 ~c 9t*~9z 1 \9t) fy\9t)' ~c~9f~ te'\9t) W\di)' 



1 3'to _ 9 /9X\ J>_ /5Y\ 



c 9? 9y'\9t) W\9t)' ( ' 



i X" o y iy 

 and substituting the values — , — , — from equations (4) which 



are linear functions of these quantities. If, for abbreviation, the 

 right hand side of the equations (4) be made equal respect- 



. , . k y ,, aX 9Y 9Z , , ,. 



lvely to f , n, ?, then — , — , — ■ can be expressed as linear 



functions of £, v, f, thus: 



1 A simple proof of this relation is given in Drude, Lehrbuch der Optik, 

 294, 1906. * ' 





l / 9X 9Y 3Z\ 9w 9v 



7 V" 9t + e ' 2 37 + e ' 3 9t ) ~ 9y' 9z' ~ * 





l / 9X 3Y j 3Z\ 9u 9w 

 ~c~ V 2 ' ~9t + € " ~9i + e * 3 ~9i) ~ W ~ W ~ v 





l / 9X 9Y 9Z\ 9v 9u 

 7v 31 9t +C32 ~9t + *™ ~9~i)~ Hx 1 W~ 



I 9u 



_9Y 9Z l 9v _ 9Z 9X l 9w _ 9X 9 Y 



~<i~9i 



~ 32' 3y' ' c 5< — ~9ri ~ 9Z 7 ' 7 Itt ~ 9y' ~ dx' 



