317 
Ml' = l, (1) 
M being the number of molecules per unit volume. In order to ac¬ 
count for the fact that at least apparently regular light waves can 
be propagated through the medium, we have to assume that the 
ratio of l to the wave-length X is a small quantity, say = ß. Hence 
ß = X- 1 (2) 
In the case of gaseous bodies (with which we shall be chiefly con¬ 
cerned) ß can be evaluated. If we put. for a cubic centimetre of gas 
at 0° C. and 760 millims., 
i¥=4.10 19 
(see J. H. Jeans, The Dynamical Theory of Gases, Cam¬ 
bridge 1904, § 8) we find: 
for X = 3,6.10~ 5 cm — ß = 0,0081 
for X = 8,1 . IO“ 5 cm .... ß = 0,0036. 
The effect of molecular motion in dispersion and extinction 
being very small under ordinary circumstances, will be omitted. 
§ 2. Consider a point (a?, y, z) of the medium. Let H be the 
magnetic vector at this point, E the electric vector, P the electric 
polarization and i the conduction current. We have the Maxwell- 
Lorentz fundamental equations 
curl H = 4na{i + ^+^) (I) 
curl E— — a ^ (II) 
here a is a constant coefficient which by an appropriate choice of 
units can be replaced by i/c, c being the velocity of propagation 
of waves in pure ether. 
Consider an electromagnetic disturbance propagated in the direc¬ 
tion of the axis of z. Let 
E x = E(z,t) P x = P{z, t) i x = i(z, t) H x = 0 
E y = 0 P y — 0 s = o H y = H{z,i ), 
E z = 0 P s = 0 i = 0 B e = 0; 
this represents evidently a plane, transverse, linearly-polarized wave, 
formulae (I) and (II) assume then the particular form 
Bulletin III. 
5 
