4 
PROFESSOR A. E. H. LOVE ON THE INTEGRATION OF THE 
radiation. When there is no screen, such sources are determined for any imagined 
hounding surface simply and directly by the incident radiation. [But, when there is a 
screen, the distril)ution of the sources is not determined in the same way by the 
portion of the incident radiation that would come to the aperture if the screen were 
away. It is proved l3elow that tlie state of the medium on that side of the screen to 
which the incident radiation comes can be expressed by means of two superposed fields 
of electric and magnetic force. The forces of one of these fields are expressed in 
terms of integrals taken over the surface of the aperture ; and the corresponding 
disturbance is a system of standing waves, the amplitudes of which diminish rapidly 
as the distance from the aperture increases. This disturbance can be described as the 
“ efiect of the aperture.” The forces of the other field are determined by the actual 
sources of radiation and the l)oundary conditions that hold over all the unperforated 
])ortion of the screen. This disturbance can be described as the “ incident radiation, 
as modified by the action of the screen.” It is proved that, when the latter 
disturbance is known, the system of standing waves, described as the efiect of the 
aperture, is also known. Further, it is proved that the distribution, over the aperture, 
of sources that would give rise to the transmitted radiation, is determined by the 
incident I'adlatlon, as modified by the action of the screen, in the same way as, if 
there were no screen, it would be determined by the incident radiation, unmodified. 
The ordinary optical rule ignores the modification of the incident radiation by the 
action of the screen, and the success of tliis rule appears to show that the efiect of 
this modification on the transmitted radiation is practically unimportant when the 
wave-length is short.] 
6. The results obtained, in regard to the efiect of an aperture, can be applied also 
to the problem of the communication of electrical vibrations from a condenser to the 
external medium, the outer conducting sheet of the condenser being perforated by a 
small aperture, for, in this case, full account has been taken of the boundary- 
conditions at the conducting surfaces in calculating the normal modes of vibration. 
The communication of electrical oscillations from an electrical vibrator to the 
surrounding medium presents a problem, which has hitherto been solved in a few 
very special cases. The best known example is that of a spherical conductor, over 
which, at some instant, charge is distributed otherwise than according to the 
equilibrium law. The waves emitted have definite periods, l3ut they decay so rapidly 
as to l)e j)i'actically dead-beat.* Such a system sends out into the medium a pulse 
of radiation, i-ather than a train of radiation. The greater permanence of the 
vibrations of Hertz’s “ resonators,” and of condensing systems, has been connected 
with the existence of greater electrostatic capacity! in such systems; but no 
* The problem is solved by J. J. Thomson, ‘Recent Researches,’ pp. 361 et seq. The rate of decay 
of the oscillations is discussed on p. 370. 
t J. J. Thomson, ‘Recent Researches,’ p. 396. Cf. J. Larmor, ‘London Math. Soc. Rroc.,’ vol. 26 
(1895), p. 123, footnote. 
