TC math /wheeler's rewritten?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Having investigated the classical Wheeler's formula for a bank wound coil
L=.2*a^2xn^2/(3*a+9*b+10*c)
where
a is average radius
b is winding length
c is winding depth
 
could this not be better rewritten
 
L=a^2*n^2/(15a+45b+50c)
 
The numbers in the denominator should give a clue as to how to wind a
bank-wound coil for highest Q
notably b and c should be 3 and 3 1/3 times a, respectively; quantities a, b
and c being equal.
 
Is this correct?
 
I understand possible to "unpick" Wheeler's formulae for solenoidal and flat
spiral coils by looking at the numbers in the denominator and use this info to
design coils for maximum Q; the same can be done more laboriously be
number-crunching a coil with fixed wire length on a spreadsheet although
hitherto the multi-layer
bank-wound coil has appeared (to me at least!) to be more difficult to deduce
than either of  the single-layer coils.