323 
has been implicitly adopted in many papers on Dispersion. From 
the stand-point of pure theor}q the assumption of course is simply 
erroneous. Nevertheless, there are undoubtedly cases where we shall 
not be going far wrong if we admit it; this will be seen clearly 
from §§11. and 27. below. From (6), § 5., we see that in this case 
&t=l; ( 2 ) 
formulae (V) thus reduce to 
v 2 —% 2 — l = 4n€l\ 2 vx = 4tc&>- (3) 
here 67 and $ are given by (4) and (5), § 5., as before L ). These 
quantities can also be written 
, T _ v 
— w)* + r* a* 
DTfc 
V) 2 +T 2 "! 2 ’ 
the constants 1), F are defined as follows: 
( 4 ) 
( 5 ) 
eW V 
m 4 u 2 c 2 ’ 
F 
TIC 
( 6 ) 
Formulae (4), (5) and (6) are of some importance since much of 
the work accomplished on Dispersion (e. g. by Ketteler, by Pflüger, 
and by other physicists) depends on these or closely allied equations. 
§ 9 . We now proceed to consider the behaviour of a body which 
contains only one category of electrons. Most of the results we shall 
obtain on this hypothesis may not apply to actual complex physical 
bodies; nevertheless this case is of paramount interest and even 
if it were not it would still be difficult to avoid its discussion. 
We have in this case 
g e 2 N n 0 2 — n 2 
m ’ (: n 0 2 — n 2 ) 2 4 k 2 n 2 
_ e 2 N 2kn 
_ _ __ 
m ' ( n o 2 — w 2 )* -f- 4 k 2 n 2 
^ _ [n 0 2 — n 2 — (co e 2 N/m)] 2 -\- 4 k 2 n 2 
(: n 0 2 — n 2 ) 2 -f- 4 k 2 n 2 
(1) 
( 2 ) 
( 3 ) 
*) See for instance equation (18) pag. 868 of the Lehrbuch der Optik 
by P. Drude (second edition, Leipzig 1906); allowing for changes of notation it 
will be seen to agree with the above equations (8). 
