154 Prof. A. Schuster on the Number of Electrons 
convenient to have a name for that quantity, and I call it 
the coefficient of optical length, the name of refractive index 
being reserved for another complex quantity occurring in 
investigations concerning the transmission of light through 
opaque bodies. The coefficient of optical length depends in 
general on the angle between the planes of equal phase and 
of equal amplitude, but here we have assumed this angle to 
be zero. By substituting (8) into (7) we find that 

TEM BS ree ae 
a = (v+2x)?. 
Hence, comparing with (6), and separating real and 
imaginary quantities, and noting that — = V’, where V is 
the velocity of light 7n vacuo, we find 
aay fe AnCo i 
v2 —K7 = | +(NoAe— he “ c . (9) 
: 2CVXA ¥ 
Ive= {2 Pen + N,BeV?. e ° e e (10) 
These are Drude’s equations providing for a change in the 
notation. If we neglect the absorption due to the sympathetic 
vibration of the molecule, as is done in Sellmeyer’s equation, 
we may put B=0. The ordinary method of introducing 
frictional forces to account for the absorption is in my opinion 
faulty, and I shall take another opportunity of discussing 
this question. It is sufficient for the present to note that the 
principle of the conservation of energy leads to the conclusion 
that there must be absorption, and hence that B has a 
positive value. Hence by neglecting it and putting 
| CVy 
ow ae Caco 
we shall undervalue o and overestimate p in (38). 
If vx is obtained by observation of the reflecting properties 
of metals, equation (11) allows us to calculate o. It is found 
that the square of oCw is sufficiently great to allow us to 
neglect unity in comparison with it, at any rate in the case of 
those metals which have a conductivity greater than that of 
lead. Hven in the case of mercury, the error committed by 
omitting the first term of the denominator of (11) is only 
6 per cent. The equation thus simplifies to 
ee WX 
*~ Cw? 
rn? 
Cara CV 
VA 
(11) 
V 

