XIII._—ON THE POSSIBILITY OF ORIGINATING WAVE DISTURB- 
ANCES IN THE ETHER BY MEANS OF ELECTRIC FORCES. Parr 2. 
By GEO. FRANCIS FITZGERALD, y.a., F.1.0.D. 
[Read 19th May, 1880. ] 
In a former paper, read before the Royal Dublin Society in February last,* upon 
the present subject, I showed that if the theories of action at a distance and Clerk 
Maxwell’s of action through a medium lead to the same results m all cases, then 
there can be no production of waves propagated like light by means of such 
electrostatic or electrodynamic systems. I did not then point out where Clerk 
Maxwell practically assumes that this is the case, but he evidently does so when 
he assumes that the electrokinetic energy of a system of conductors carrying 
currents is a function of the present currents and their configuration only. 
By assuming this he has excluded the possibility of wave production, for in the 
case of wave production part of the energy of the system is in the medium, and 
what part is so, depends on the past as well as on the present configurations and 
currents, 
There seems a very great difficulty in determining what is the actual distribution 
of displacement currents in the neighbourhood of a changing current in a conductor. 
We cannot assume them to be simply due to the variations of current in the 
conductor for such displacement currents immediately re-act on one another. We 
cannot even assume that they are initially the same as if they were directly and 
simply produced by the current in the conductor, for then this initial state would 
be a discontinuous one. The distribution at the limits of space, as well as time, 
are just as difficult to determine. 
It is, however, possible to assume a distribution of electromagnetic potential 
in the neighbourhood of a conductor such that its components satisfy Maxwell’s 
equation 
MV + Ky =0 
and yet such that it shall not represent a wave propagation such as light, but 
rather the state of vibration in an organ pipe where there are fixed nodes. 
If we assume that V can be expanded in sines or cosines with regard to the 
time so that we may write 
; sin 
V=SV, ae (nt) 
where V, is a function of «, y, 2 without ¢, then if we determine V, suitably for a 
* Vide Transactions Royal Dublin Society, Vol. 1, Part 10. 
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