Art wrote,
(snip)
By experimentation he came up with desirable' form
factors ' that related to number of turns wound in relationship to the form
diameter upon which the coils were wound,
(snip)

What! He didn't use the calculus of variations? What kind of an
academic was he? I've got a question for you, Art. How would
you set up an experiment that would solve the brachystochrone
problem? Or, if that's too hard, how would you set up an
experiment to tell you which, of all plane figures of equal
perimeters, would give you the most enclosed area?
After you've told me that, then you can tell me how I can
set up an experiment that will tell me what coil configuration
I can use that will give me the most inductance with the least
amount of loss.
73,
Tom Donaly, KA6RUH