I don't have the time right now to comment fully, but I can make a
couple of comments now on the last part. I think I see what at least one
source of confusion might be, and hope I can clarify it a bit.

Richard Clark wrote:
. . .

Now, let us return to a point of analytical bias that lead me to
believe no apparent change in Rr was observable. In fact there was
no way to make it observable except through the artifice of my
sniffer antenna. For the model of the constant current generator, it
is a truism that gain (that is true gain for a system and not simply
antenna directivity) must increase for the same excitation.

The difference between gain relative to isotropic (which you're
unnecessarily calling "true gain") and directivity is only the
efficiency. If loss is zero, the gain and directivity are the same. If
there's 3 dB loss, for example, then the gain relative to isotropic is 3
dB less than the directivity.

I need to insert a reminder here for readers who aren't as familiar with
the terms as some of the rest of us. There isn't a single value of gain
for any antenna. First, it's nearly always different in different
directions. Second, the gain depends on the reference antenna, so you
can have just about any gain you want, just by choosing the reference.
EZNEC, NEC-2, and most professional publications use a theoretical
isotropic antenna as the reference, resulting in gain in dBi. The main
reasons for this are that it's unambiguous -- everyone agrees on what it
means -- and it makes it easy to calculate field strength from gain and
vice-versa.

Now, back to the comments. . .

It isn't true that the gain must increase as Rr increases, when the
source is a constant current. The gain relative to isotropic (reported
as dBi) is defined as the field strength from the antenna divided by the
field strength from an isotropic antenna *having the same power input*
-- converted to dB of course. As the Rr increases in your model antenna,
the power input increases if you're using a constant current source, as
you've pointed out. But the power input to the imaginary isotropic
comparison antenna increases by the same amount. The net result is no
change of gain due to the increased power input, or to the increased Rr.
What you're measuring with the "sniffer antenna" isn't the gain -- it's
the absolute field strength. To get the gain, you need to compare that
with the field strength you'd see if you applied *that same power* to an
isotropic antenna the same distance away. You should find that the power
dissipated in your sniffer antenna load is directly proportional to the
power applied to your transmit antenna. That would also be true for an
isotropic transmit antenna, so the ratio of power received from the two
antennas will stay the same as you change the transmit antenna power.

As I pointed out before, moving the load in the transmitted antenna
changes the current distribution, resulting in a very small change in
pattern shape, hence a very small change in gain. But that's the only
effect it has on gain.


After
all, we are changing the Rr either through the actuality of modified
length, or the artifice of a moving, variable load along the short
radiator. Such gain is only observable through a circuit
(broadcaster lingo for a transmit/receive pair).

In the back of my mind I was troubled about comparing situations in
dBi. Yesterday I expressed this as a possible source of confusion
for the effects sought in evidence against the obvious gain
differential. dBi is a dimensionless relation such that true gain is
washed out of the result.

No, dBi is the "true gain" expressed in dB, as explained above. It's the
field strength from the antenna compared to the field strength from an
isotropic antenna having the same input power. Simply
increasing your constant current source from 1 amp to 2 amps will
increase the signal detected by the "sniffer antenna". But I hope you
can see it's not changing the gain of the transmit antenna.

When I attempted to confirm my suspicions through field
expressions of mv/M for 1KW, I was struck that that too forced the
results to a constant power (not constant current) and thus hid the
gain demonstration in the same way. I then fell back on my practice
of employing a sniffer antenna to test reality and the data is found
above confirming the gain that would be expected. In other words,
the far field's power followed the diminution of Rr with a positive
correlation. It also followed the subsequent increase of Rr (with a
load applied to that shortened radiator) with a positive correlation.

The source of confusion or misinterpretation seems to be due to
mistaking field strength for gain. They're not the same thing. Even the
units are different -- Volts/meter or Amps/meter (or power density in
watts/square meter) for field strength, while gain and directivity are
dimensionless.

Gain would be a much less useful measure if it changed with power input.
Then, we'd have to specify the power input at which the gain is
measured. EZNEC correctly shows no gain change resulting from changing
the input power. As it is, it's easy to calculate the field strength at
any point in the far field from the gain in that direction, power input
to the antenna, and distance from it. In fact, EZNEC and NEC-2 actually
compute the fare field strength, and then derive the gain in dBi from it
by knowing the field strength from an isotropic antenna with the same
power input. Gain relative to isotropic becomes less useful in the near
field, so absolute field strengths are generally used in that region.

Roy Lewallen, W7EL