EQUATIONS OF PROPAGATION OF ELECTRIC WAVES. 
5 
problem of the decay of oscillations of a system with large capacity, through tire 
gradual transmission of the energy to a distance, has so far been solved. For a 
condenser with concentric spherical conducting surfaces, the outer conducting sheet 
being very thin, and having a small circular aperture, the problem can be solved by 
means of previously known analysis and of results obtained in this paper. It 
appears that, so dong as the outer conducting sheet, and the size of the aperture, 
remain the same, tire rate of decay of the oscillations diminishes, as the capacity 
dirrriirishes ; the oscillatioirs of a corrdeirser with sirrall capacity, obtained by irraking 
the radius of the iirner sheet srrrall compared with that of the outer, are much irrore 
slowly darrrped than those of a condenser of large capacity, obtairred by rrraking the 
radii rrearly equal. Tiris result applies to the oscillations of high frequency, 
involving a large iruirrber of irodes, as well as to those of lower frequeircy ; and it 
suggests that the coirrparative perirraireirce of the oscillations of condeirsing systems 
is to be traced, rather to the screening action, than to the iircrease of capacity.* A 
further result, that the oscillatio 2 rs of high frequerrcy aird irrarry rrodal divisioirs, are 
more rapidly darrrped than those of lower frequency aird fewer irodal divisions, is in 
accordance with the coirclusions arrived at by Sir G. Stokes,! for the like probleirrs 
concerning sound. 
\_Added, March, 1901.—Since the paper was seirt iir, I have found that a similar 
irrethod of integration has been employed by V. Cereijti, ‘ Eoirre, E. Acc. Liircei, 
Eend.,’ 1879-80, for the equatioirs of sirrall irrotion of an elastic solid. The furrda- 
nrenta] particular solutions, there used, are the same as (17) of § 11 infra-, and the 
solution of the problem of the vibrations of a solid, with a given bourrdary, over which 
the displacemeirts, or the tractioirs, have assigned values, is developed on the basis 
of an existeirce-theoreirr, of the same kind as that assuirred iir § 21 ; no application is 
made of the results to problems of radiation.] 
Kirchhoff’s Integral. 
7. Suppose that is a function with the following properties : 
(1) Outside a given closed surface S, ^ and its first and second differential coeffi¬ 
cients, with respect to x, y, z, are everywhere finite and continuous ; 
(2) (j) vanishes at infinite distances from S ; 
March, 1901.—Mr. Larmor has called my attention to the fact that the work in the paper does not 
show that all methods of increasing the capacity, without altering the outer conductor or the aperture, 
are accompanied by increased dissipation.. For instance, the capacity of the condenser might be increased 
by displacing the inner conductor relatively to the outer, without altering its size and shape, or by 
replacing part of the dielectric plate by conducting material. In such cases there are some analogies with 
other physical problems, which suggest a diminished rate of dissipation. Against them must be set the 
analogy with the problem worked out in the present paper. 
t ‘Phil. Trans.,’ vol. 158 (1868). 
