( 729 ) 



according to the principle of superposition, will really be the one 

 produced bj the whole E. M. F. Each of the separate very small 

 fields will consist in a propagation of plane waves having the same 

 direction as the planes in which the corresponding element of the 

 E. M. F. is constant. The problem will therefore indeed be reduced 

 to one of plane waves. 



§ 2. In order to find the small field, corresponding to a cone of 

 definite direction, we shall take a system of coordinates OX', OY', 

 OZ', the axis OZ' coinciding with the axis of the chosen cone and 

 OX', OY' respectively with the two directions of the dielectric 

 displacement, belonging to plane waves, normal to OZ'. The wave 

 that has its dielectric displacement along OX' will be called "the 

 first wave" ; the other "the second wave". 



Again we take a system of coordinates OX, OY, OZ, the axes 

 of which coincide with the axes of electric symmetry. Denoting the 

 components of the electric force along the first axes by <£> , <?y , <$.,• 



2t 



and supposing all quantities to contain the factor e we have to 



satisfy the following equations 



ALf,. -^(jü-.(E-)=-^[a„(irv +e:o+f.,(«/ +(Ey)+euCS.' + el')] I 



A(Ev-^(<ia-.(i-)=-^ ^^(^V + e-^O+fssCS,/ +'^-y)+f3a(e-=' +S'')] ] 



It will not give rise to any misunderstanding that we have denoted 



' dm d^'B 

 here bv ^"^ the expression — — — -r-— . 



The quantities e, occurring in these formulae, have particular 

 properties, because they relate to special directions. These properties 

 will show themselves in the following development. Since, according 

 to the preceding considerations, (§.' depends only upon z', we shall 

 find for ^ a solution, likewise containing only z'. By this hypothesis 

 the equations (3) become 



(3) 





(g.' + ev)+ e,, ((iy + S^O+^.eS.' + r,')]/ 



(4) 



