conveying the C onduction Currents in Metals. 153 
be the relative displacement of the positive and negative 
charges. If the electric force is periodic and contains the 
time factor e~', the displacement ¢ is also periodic, but must 
be capable of expression in two terms, one in phase with R 
tie’ 
and the other in phase with a 
I write therefore 
BdR 
4rO=AR— a 
dor? = —w?(A +iB)R. 
The polarization current is 47K is : 
dt 
I have, in the paper quoted, written down the complete 
equations of flow in conductors, taking account of o, but the 
term involving that quantity was found to be insensible. 
except in the case of rapid changes like those of light. We 
may therefore here confine ourselves to periodic motion 
entirely, so that the differentiation with respect to the time 
may be replaced by the factor —im. Under these circum- 
stances (4) becomes 
Mh fice) =O. a os ee ) 
dw oC?w?—iwlR 
dé = 1+8Ca® * 
For the total current variation we have now 
J 
dor ay: = —(?R; 
dt 
where 
Ana -( Amal 2 ; \ 
Pe ‘f ata Qi. . 2 
. = { NwA+K ea hal a OE (8) 
and the differential equation for R is 
te Oa 8A se Goals os it x, 2 (eG) 
Assuming plane waves in which the surfaces of equal 
amplitude coincide with the surfaces of equal phase, the 
solution may be written 
EET) RCP gaa) OO CE 
In this equation X denotes the wave-length in vacuo. The 
Aw 
velocity of wave propagation is ~—, so that A/y is the wave- 
ee 2arv 
length in the medium, and y denotes a quantity which cor- 
responds to the refractive index in transparent bodies. It is 
