94 
MR. J. G, LEATHEM ON" THE THEORY OF THE 
Plane Waves in a Metallic Medium. 
7. In the case of plane Avaves in a metallic medium, let us assume 
x+mz 
{u, V, w) = (A, B, C) e'-’-’-'' 
where l represents \/ — 1, and write 
P = oP . . . . . . . 
Substituting these values in the equations of propagation, we get 
(H(o^ -j- 4771^^) A = ('*73^ — Vs^) 
— H^l (— niB) + 7^2 — IC) + 773 (/B) 
HV ( 77,0 - 773 A) 
( 773 A - 77 ,B) 
(Hco' W imp) B 
{Hco® + 477177 ) C 
(14) 
• (15). 
— H V/i 1 77 , (— ??iB) + 772 (niA — 
1 
/C) 4- 773(/B)| 
(16). 
ex 
Addition of I times the first of these to m times the last gives, as was to be 
IA + mC = 0 .(17), 
and hence if we eliminate A, B, and (1, we get 
/ o 
H^C0“773 Hoj^ -j- 477 
+ 477tp + H®/??i772 — IBlmy^ — Hb7r773 
m 
— H®(y®77j 0, 
H^m~7)2 
which reduces to 
(HojS _j_ _p pp^2 (7^^ _p ^ ^ 
(18). 
This equation gives the possible values of corresponding to given values of I 
and p. It is a quartic and thei’efore has four roots, of which two have their 
imaginary parts negative and their real parts positive ; let us denote these roots by 
nil ^^ 2 , ^i^cl the corresponding values of w by coi and 0,3 respectiA-ely, so that 
+ 4771/7 = + t. (/t 7^ + 7?lj773) 
+ 477tp = — t. (lyi + m^ys) J 
(19). 
