David wrote:
Four radials form a counterpoise. The counterpoise has currents induced.
These induced currents then re-radiate, ...

Let's look at two equal radials, 180 degrees apart,
horizontal in free space. The radial currents are equal
in magnitude and opposite in direction, i.e. differential.
Theoretically, this causes considerable cancellation
of the radiating fields of those two radials. EZNEC
confirms very little horizontal radiation from two
symmetrical horizontal radials in free space. The same
thing holds true for symmetrical top hats.
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73, Cecil http://www.w5dxp.com