transmitted through a Metal of a Current in the Metal. 385 

 Then a 7 2 - P - vf + v? = ] 



h2M9 \Pl A (4), 



by 2 + 2v 1 v 2 y = 



m being equal to 0. 



If we put P = in equation (4) we obtain the change of 

 phase T due to the metal without the current flowing into it. 

 The additional change of phase due to the current is 



where T = - tan" ' 



p n? — i>! 2 — v£ 



and 8v lt 8v 2 are the changes in v 1 , v 2 due to the retention in 

 equations (4) of the term 



\Pl 



<tV 



We have then from (4) 



ViBi'x = v 2 8v 2 , 



v x 8v 2 + v^ = a~y= </> say. 



And therefore 8vi = <f> — 



v« 



8v 2 = <f> 



V? + v 2 



2 ' 



We obtain then 



,- 2m v ft(n a -i/ 1 8 +3i; 8 8 ) 



p (iv + v£) {(n 2 - v? - v 2 2 ) 2 + 4nV 2 2 } ' 



From this expression, using (4) with P = 0, we obtain 



2wi^ {/»(!- a) + 2y,'} 

 py^{(\-af + b 2 }( Vl 2 +v 2 2 )' 



From equations (4) 



v? = K(«7 2 - 1 2 ) + V{(«7 2 ~ * 2 ) 2 + BY}], 



v? = hi- («7 2 - 1 2 ) + VlOr - IJ + &y}]- 



Now a = n' 2 (l-k 2 ), 



b = - 1n'% 



where n' and n'k are the quantities corresponding to the refractive 

 index of the metal and the absorption coefficient, and from DruHe's 



