We show that suitably shaped objects made of a dielectric material can function as electrical resonators for high frequency oscillations. We develop the theory of such resonators very briefly and compute their resonant frequencies and losses in some very simple cases. The paper concludes with an observation on the behavior of dielectric wave guides.

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4.
This definition of energy stored in the resonator is to some extent arbitrary. In general the field immediately outside the resonator will be comparable with that inside, and it might seem that we should include the energy of this part of the field. The reason we do not is that one cannot say just how much of the field outside to include; certainly one should not include it all, since the incoming and outgoing waves, even though they be extremely feeble, contain an infinite amount of “stored” energy spread out over all space. Perhaps one should include all the energy out to the point where the field stops decreasing exponentially and starts oscillating. In the cases we have calculated this would produce only a small change in our estimate of the stored energy. The change is small, partly because the exponential decrease is rapid, and partly because the dielectric constant, which enters into the energy expression, is smaller outside the resonator than inside.
5.
See G. N. Watson, Theory of Bessel Function (Cambridge University Press, 1922),
or Courant Hilbert, Methoden der Mathematische Physik, second edition (Julius Springer, Berlin, 1931), p. 456.
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See
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9
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654
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7.
We should really speak of wave‐fronts in this case instead of nodes, since we have used running waves in the φ‐direction, represented by exp (imφ).
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