318 
(III) 
This, the generalized equation of wave propagation, reduces of course 
to the well-known telegraphic equation as soon as the usual Max¬ 
wellian assumptions respecting P x and i* are admitted. 
§ 3. In what follows we shall suppose that the components 
E x: H y , P x , i x all contain the factor 
( 1 ) 
c <• n(t—bz). 
C 5 
here b is a complex constant and n represents the frequency of 
vibrations in the incident beam of light. It is well known of course 
that no natural vibration is a perfect train of waves of the simple 
type we are considering here; we must therefore bear in mind that 
the assumption we have admitted is probably no more than a first 
step towards a solution. Adopting (1) as the variable part of the 
expression of E x , H y: P x and i x we find from (III), § 2, 
( 2 ) 
Let us next assume that 
(3) be — v — ia ; 
then E % will depend upon 
/„\ ( 2jiaz . / vz\\ 
( 4 ) ex P-|- ;—H w b-77J 
and will not explicitly involve t or z in any other way; X denotes 
here the wave-length (in vacuo) to which n applies. From formula 
(4) it appears that the quantity % may be called the '"coefficient of 
extinction” of the medium x ) and that the quantity v corresponds 
to the refractive index in (perfectly) transparent bodies. 
From (2) and (3) we obtain 
(IV) = 
The equation just found is the fundamental equation in the 
Theory of Dispersion and Extinction. Further progress, however, 
q Cf. Kayser, Handbuch der Spectroscopic, Band III, Leipzig- 1905, §§ 5 and 6. 
