transmitted through a Metal of a Current in the Metal. 383 

 If P were = 0, tlX = and 



<xfX = F 2 {20 . X - ItlX) = V*XZl\ 

 so that ap 2 = F 2 2Z 2 . 



Writing y=f> 



we have when P is not zero, 



a/ 2 - 2/ 2 = c, 

 where c is small. 



And then 



cX = -mx, - 



cY=-mXlX- f ^(lY-mX), 

 cZ = - ntlX + ^(nX- IZ), 

 and cL = 2j? (ilfm + JV») - VZLI 



- - F Li, 



yP 

 and c + -^r Z = or L = : 



if Z = equations (2) give 



jr (c + 2? i) = o, 



iv (c + °^ i\ = o. 



Hence if c + -4^ is not zero, M = and iV = 0, and there is 



no wave. 



So if c + X=- = 0, a wave can be propagated in the metal ; 



the velocity and coefficient of absorption being determined by 

 the equation 



af2_i2_ m 2_ n? + y =0 ( 3 ) ( 



