between Confocal Elliptic Cylinders. 

 By that of Faraday, 



~d /Y 



227 



P2 



= £ (2Z) 





(3) 



2y> 1 /' 2 B^ 



Dots denoting differential coefficients with respect to time. 



The conditions that (2) and (3) should each form a con- 

 sistent scheme are 



^ (-) + A (IUI ^-(--) =0, 

 * (±\ + 1.(L\+IA(jJ\ = o 



9x 



(4) 



It must be recalled that (X, Y, Z) and the other vectors 

 are in these equations defined by components along the 

 directions \, p., z, and not by the rectangular components. 



We now examine the possibility of a type of oscillation in 

 which two of the components (X, Y, Z) of electric force are 

 zero. 



IfY=0,Z=0. 

 Then by (4) 



X=p 2 ^,z) (5) 



2tt 

 X ' 



X 



V 2 



If A, is the wave-length of the oscillation, and k 



-FX. 



The circuital relations readily give, in this case, 



a = 0; . . . . . 

 and by combination lead to the equation for X, 



3 



(6) 



^+FX+- 4 



ds 2 



•P(X) 



But by (5), 



\—fi ' ^/i 



^».^(X,/X-,). 

 X — /J. d,u v ^ 



x= 



-P(,u 

 X— /a 



•*■ £+*♦+*& 



<£0, z); 



-fit ) 1 

 X — ju ^i 



Q2 



( 7 ) 



