Roy Lewallen wrote:
Of course, any rays reaching the center would
continue on through, Cecil's unique theories notwithstanding.

The way the incoming fields were defined, they all converge
at a point in the center of the sphere. Presumably, that's
where the isotropic antenna is located. Replacing the isotropic
with a Yagi whose feedpoint is logically located at the point
of convergence means that any part of the field that doesn't
encounter parts of the Yagi before the point of convergence will
converge at the feedpoint on the driven element of the Yagi in
a defaulting isotropic manner. Given the definition of the
spherical fields, there is no part of the fields that will not
encounter the Yagi.

Therefore, the isotropic and the Yagi receive the same amount of
energy, i.e. all that exists in the spherical fields. Any energy
not received by the Yagi beam elements is received in a default-
isotropic mode at the Yagi feedpoint.
--
73, Cecil http://www.qsl.net/w5dxp