Tom wrote -
I also used NEC2 to simulate the effects of a small top-hat: it was
4
radial wires at the top of a vertical, 0.001 wavelengths long. The
vertical diameter was .000001 wavelengths (as were the radials
forming
the top hat). I found that adding that top had reduced the length
for
resonance by exactly the same length in each case, for 1/4, 2/4, 3/4
and 4/4 wave tall antennas, probably within the accuracy of the
computing engine.

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The "End Effect" is thereby proved.

Marvellous things are computing engines!
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Reg.