EQUATIONS or PEOPAGATION OF ELECTPJC AVAVES. 37 
of the screen, in the same way as if this radiation passed freely through the 
aperture. 
This result diflPers from the ordinary optical rule, that the transmitted radiation 
is to he calculated from the incident radiation, unmodified, as if this radiation 
passed freely through the aperture. In the application of this rule no attention is 
paid to the boundary conditions at the screen. If we could assume that the 
disturbance at points of the aperture when the incident radiation is modified by the 
action of the screen, differs very little from the unmodified incident disturbance, then 
the result and the optical rule would be in practical agreement. The success of the 
optical rule seems to show that the modification of the incident radiation by the 
screen is unimportant, at points within tlie aperture, when the wave-length is short.] 
The result obtained may he applied with greater certainty when the disturbance 
on the nearer side of the screen has been calculated in accordance with a known 
boundary condition, holding over all the imperforated portion. This is the case 
when, instead of an incident train of waves, we have, on the nearer side, standing 
vibrations, for which the boundary condition is satisfied. In such a case, the values 
to be assigned to the components 
cos K Ct + Un sin K ct , 
of the disturbance A, ... at points of the aperture, are the values that ii, . . . 
would have if the screen were imperforated. This remark applies to the problem of 
the communication of vibrations from a condensing system to the surrounding aether. 
We shall now take up this problem, having regard especially to the example of 
concentric spherical conducting surfaces, with a very thin dielectric plate between 
them, the outer surface being perforated by a small circular aperture. 
Electrical Oscillations hetween Concentric Spheres. 
31. It has been pointed out by Larmor* that the most important modes of electrical 
oscillation in a condenser, with a thin dielectric plate, are those in which the charge 
surges over the conducting surfaces, the lines of electric force being always normal 
to these surfaces, and the lines of magnetic force tangential to them. In a condenser 
with concentric spherical conducting surfaces such modes of oscillation exist, what¬ 
ever the thickness of the dielectric plate may be ; and the analysis requisite for 
dealing with them has been developed by Lamb.I The required solutions of the 
* ‘ London Math. Soc. Proc.,’ vol. 26 (1895), p. 119* 
t ‘London Math. Soc. Proc.,’ vol. 13 (1882), p. 51; or ‘Hydrodynamics,’ pp. 555, et seq. The 
notation here used will be that of the ‘ Hydrodynamics.’ It is worth while to recall some of the properties 
of the functions defined in equations (77): they satisfy the equations 
