Transparent Inactive Crystal Plates. 163 



OX OY 3Z 

 On substituting the values of -^- , — , 5 y of equation (7) 



in (6) we obtain a system of partial differential equations : 



3 9hL ( a ^ +a *> r > +a *& - h ^+«^+«»£) (10) 



which are free from the components of the electric force and 

 of the electric current. 



Equations (4) and (5) are of general validity and obtain 

 therefore, even at the boundary surface of a crystal plated lit 

 is apparent from the last equation of (5) that, as (X.) 1 = (X) a , 



( Y)= (T), at the boundary, (|^ = (-£) or (w) = (w\ for 



periodic vibrations. The boundary conditions for a crystal 

 plate may therefore be written : 



(«), = (,«)„ (.), = w„ (■»), = w„ (f ) i = (f )_ 



(SHE). (11) 



of which only four are independent. The last equation of 

 the set may accordingly be discarded. The fourth equation 



( -=- ) = ( -pr- ) can be expanded by means of (T) and (4) and 

 becomes for the general case of two adjoining crystal plates : 

 /9w 9v\ /9u 9ic\ /9v 9u\ _ 



a "W - 9i) + a - W ~ 9~?) + a >* W ~W)~ 



These boundary equations, together with equation (8), are 

 of general validity for transparent, inactive plates, and form 

 the basis on which all detailed work rests. 



The partial differential equations (10) representing the move- 

 ment of the magnetic vector are satisfied by the components 

 u, v, w of the vibration of a plane polarized, advancing wave 

 of constant amplitude. This vibration is defined by the usual 

 equations of the general form : 



