The method previously described of solving electromagnetic scattering problems as power series in k is here applied to the ellipsoid, the first three terms in the series being obtained. The second term in the series for the wave zone field (that proportional to k3) vanishes, and the same is true of any body possessing a center of symmetry. Thus the terms in k2, k4 in the wave zone field are here obtained. The direction and polarization of the incident wave, and the electromagnetic constants of the ellipsoid, are arbitrary. The final results are expressed in terms of certain elliptic integrals which are functions of the three principal axes of the ellipsoid. These integrals can all be expressed simply in terms of just two such integrals; they become elementary integrals in the case of a spheroid. Various special cases are considered, including that of a perfectly conducting elliptical disk and the complementary problem of diffraction through an elliptical hole in a perfectly conducting screen.

1.
F.
Möglich
,
Ann. Phys.
,
83
,
609
(
1927
).
2.
F. V. Schultz, Scattering by a Prolate Spheroid, Report UMM‐42, University of Michigan (1950).
3.
C. T. Tai, Trans. Inst. Radio Engrs. (February, 1952).
3aNote added in proof:‐Dr. K. M. Siegel has since informed me that numerical calculations, based on Schultz’s work, have now been made for the prolate spheroid and that similar calculations are in progress for the oblate spheroid.
4.
Lord
Rayleigh
,
Phil. Mag.
44
,
28
(
1897
). Rayleigh only considered the case where the direction of propagation was along a principal axis of the ellipsoid, with the electric vector along another principal axis. But to this approximation the general case can be deduced by superposition.
5.
R.
Gans
,
Ann. Physik
62
,
331
(
1920
).
6.
J. A. Stratton, Electromagnetic Theory (McGraw‐Hill Book Company, Inc., New York), p. 563 and following. References to the original papers are given.
7.
C. J.
Bouwkamp
,
Philips Research Repts.
5
,
401
(
1950
);
J.
Meixner
and
W.
Andrejewski
,
Ann. Physik
7
,
157
(
1950
);
H. Levine and J. Schwinger, Theory of Electromagnetic Waves, (Intersdence Publishers, Inc., New York, 1951), p. 1;
J. W.
Miles
,
J. Appl. Phys.
20
,
760
(
1949
);
J. W.
Miles
,
21
,
468
(
1950
).,
J. Appl. Phys.
8.
A. F.
Stevenson
,
J. Appl. Phys.
24
, preceding paper (
1953
). We shall refer to this paper as “EMS.”
9.
These relations are special cases of relations which connect the integrals I(ξ),Ia(ξ), ⋯, and which are useful in deriving and checking the solutions. We shall not give these more general relations, however.
10.
The coefficients of 1/R5 in E0R and of 1/R in E2R were also calculated, as these furnish checks on the work.
11.
Expansions from which the field can be determined to this order axe given by Stratton (reference 6), p. 571, but some of Stratton’s formulas are in error.
12.
See, for instance,
J.
Meixner
,
Z. Naturforsch.
,
3A
,
506
(
1948
).
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