Calculating secondary resonance of bipolar coils

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Original poster: "Terry Fritz" <twftesla-at-uswest-dot-net>

Hi all,
I sent a mail to the list a couple of days ago regarding secondary bipolar coil
resonance calculations. As there has not yet been a reply, I thought I should
elaborate on the question I originally asked. 
Most TCs are of the up-right quarter wave resonant type, topped with a top load
such as a torroid. I have recently wound a secondary more suited for use as a
bipolar or half wave resonant secondary. The primary is positioned in the
middle of this secondary coil; and the there will be no earth connection at the
mid point of the secondary.
Now, I know that it possible to calculate the resonant frequency of a quarter
wave coil using medhurst and the standard LC resonance formula. It is also
possible to treat the secondary as a Tx line by determining the wave velocity
from the coil inductance and capacitance per unit length. Medhurst, I believe,
was derived from empirical measurement, while the Tx-line method relies on
modelling. Either way, it seems that these methods do not work when considering
half-wave resonators, the frequencies tend to be much greater than, say, the
medhurst calculation. So, has there been found a method of calculating the
half-wave resonance of a coil? 
 
Thank you in advance for your help.
 
Gavin