Cecil,

You have convinced me Corum's formula is in the right ball park. I
have not found time to study how it has been derived. It doesn't
appear to be particularly useful.

I will now tell you how to obtain ALL resonant frequencies, both
1/4-wave and 1/2-wave as you call them.

Place a single turn link winding around the CENTRE of the coil under
test. Between the link winding and the MFJ-259B connect a loosely
twisted pair (or a short length of speaker cable). The whole caboodle
can be made from a single length of thin, insulated, stranded wire.

I've a feeling that the length of the connection should not be too
long. But the 259-B should not be very near to the coil to keep the
meter outside the field of the coil. 6" or 10" seems about right
depending on the size of the coil. Ideally, length should be much
less than 1/4 wavelength at the test frequency.

Begin at a low frequency and search for the first high impedance on
the moving coil meter on the 259B. The first high impedance resonance
corresponds to the self-resonant frequency of the coil.

Increase frequency to find a low impedance resonance. Continue to find
the next high impedance resonance, etc.

The resonant frequencies may not be closely harmonically related.

You may not find very close agreement with the results obtained by
connecting the 259B directly across the coil. But both sets of
results are equally valid (or invalid).

I leave it to you to draw conclusions from the sequence of high-Z and
low-Z resonant frequencies.

Greatest accuracy is obtained by using the link coupling at the high
impedance resonances because the coil is then more isolated from its
environment. Its environment includes the input impedance of the
259-B itself.

The lower the self-resonant frequency, the greater the accuracy.

I found a coil in the junk box, 2.7" diameter, 4.0" long, 44 turns,
which has a self-resonant frequency of 13.6 MHz. I would have liked
it to be as low as 2 MHz.

I agree, a coil at sufficiently high frequencies begins to behave
something like a transmission line with a very low velocity factor.

To investigate what is really happening requires an instrument capable
of measuring impedance versus frequency from HF to VHF. It probably
doesn't exist.

When a coil is used to load a short HF vertical, it operates at a
frequency much lower than its self-resonant frequency and transmission
line effects don't matter two hoots.
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Reg, G4FGQ.