Tom Donaly wrote:
"You and Richard need a refresher course in electromagnetics."

This Richard agrees a refresher course could help. I no longer read the
Proceedings of the IRE for fun. It`s been over 50 years since I last
darkened the halls of academia.

I remember a few things. One hangup I see here is the rule that the
current in a series circuit is always the same everywhere.

True for circuits small in terms of wavelength. False for unmatched (not
terminated in Zo) circuits of a size significant in terms of wavelength.

The standing-wave antennas of this thread are less than 1/4 wavelength,
but they`re still significant in terms of wavelength with or without
loading coils. They are open-circuited and make a big reflection from
their open-circuited ends. This reflection causes a current which varies
from zero at the open-circuit end to something substantial back a ways
from the open-circuit. Between substantial and zero is a current drop.

My favorite author. F.E. Terman depicts this current distribution in a
dipole (two 1/4-wave antennas back to back) in Fig. 23-2 on page 866 of
his 1955 edition. For a whip worked against ground, the current
distribution is either half of the dipole representation.

Look at Fig.23-2. Anyone can see the current drops to zero at the
antenna tips. Loading coils won`t change that. Coils added to bring
total antenna inductance to resonance with its capacitance occupy space.
Current through a loading coil takes time to traverse the coil. By the
time current has made the trip through the coil, current arriving from
the source is out of phase to some extent with that arriving through the
coil. The delays in transit to both ends of the coil are likely not
equal. The inequality in phase results in a difference in volts, amps,
and impedance at the two coil ends.

Recall, we are discussing r-f, traveling as a wave from both terminals
of a generator. It is not d-c emerging from one battery terminal and
entering another.

Cecil is exactly correct in his characterization of how waves supeerpose
to produce standing-wave variations in voltage, current, and impedance
in the total series circuit.

Proof has been offered by modeling, and measurement. You may accept or
reject the observations of others. You could also make your own.

Best regards, Richard Harrison, KB5WZI