EQUATIONS OF PROPAGATION OF ELECTRIC WAVES 
3 
results of the kind described, and in particular that the disturbances can Ije regarded 
as due to sources of two definite types. A source of one of these types is similar to 
an infinitesimal Hertzian vibrator. The character of the most impoi'tant part of the 
radiation from such a vibrator is well known ; it is periodic, with a damping coeffi¬ 
cient, and is related in a definite way to a particular axis.* The radiation from a 
source of the corresponding type is related in the same way to the axis, but its mode 
of dependence upon time is arbitrary. The assumption of infinite trains of simple 
harmonic radiation, with or without damping coefficients, is an unnecessary restriction 
of the mathematical formulse, and is inadequate to represent many phenomena. The 
other type of sources is arrived at by interchanging the roles of the electiic and 
magnetic forces in the type that is similar to Hertzian vibrators. There is a theorem 
that disturbances, which can be represented as due to sources of both types, may also 
be represented as due to sources of a single type, just as acyclic irrotational motions 
of incompressible fiuid may be regarded as due to sources and double sources, or to 
sources only.f 
4. A very general system of integrals of the system of equations that govern the 
propagation of waves having l)een obtained, it is natural to inquire after an exj)ression 
for the law of disturbance in a secondary wave that shall accord with these integrals. 
The expression arrived at is rather sinqjler than that given by Sir G. Stokes;]; as 
regards the intensity of the secondary waves, but rather more complicated as regards 
the orientation of the plane through the direction of displacement and the direction 
of propagation. This plane is either the plane of polarisation of the secondary wave, 
or else it is at right angles to that plane. At one time it might have been interesting 
to pursue the question further, and to determine the conclusion, as regards the 
relation of direction of displacement to plane of polarisation, that could Ije drawn 
from the new integrals ; but the (piestion is not now of imp(.)rtance, since it is certain, 
on many grounds, that the plane of polarisation of light contains the magnetic force, 
and is at right angles to the electric force. 
5. \_Partly re-written Metrch, 1901.]—Apart from this question of the plane of 
polarisation of scattered waves, the chief use of a law of disturljance in secondary 
waves is found in the solution l)y elementary methods of problems of diftraction ; this 
use is not affected§ by such differences as exist between the law here found and that 
obtained by Sir G. Stokes. But, in connexion with the application of any such law 
to problems of diftraction through apertures, there also arises the question of the 
distribution over the aperture of sources that would give rise to the transmitted 
* The relation to the axis is the same for the forms given by Hertz, ‘ Electric Waves,’ p. 143, as for 
those given by K. Pearson and Alice Lee, ‘Phil. Trans.’ A, 193 (1899), p. 159. The forms given in 
§ 13 include both. 
t Lamb, ‘ Hydrodynamics,’ pp. 66 and 67. 
I ‘ Papers,’ vol. 2, p. 286. 
§ Lord Rayleigh, ‘ Wave Theory of Light,’ p. 453. 
