# RE: Variable Capacitance and Inductance

```Original poster: "David Thomson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>

Hi Ed,

>one thing which is evident is that he is assuming that the capacitance of
his bottle primary capacitor is constant. Perhaps someone who had played
with bottle capacitors could comment on their stability.

You can see Tesla's own concern for the accuracy of his primary capacitors
on page 242.

>He makes no mention of the sharpness of tuning

This is on page 211.  Tuning was "very sharp" at least on October 5.

>As far as Wheeler's formulae (there are several), it IS NOT based on
empirical measurements, but on fitting simple
expressions to the more exact solutions over limited ranges of geometry.

Does this not have the same effect as being empirically based?  You may be
correct on the terminology, but the end result is that Wheeler's formula is
not based on first principles.  It has a fudge factor built into it.  And as
far as I know, the nature of what is being fudged has not been determined.
Wheeler's formula is just a bunch of seemingly relevant variables and
numbers that happens to put out a close approximation of an air coil's
inductance.  Is it OK to question why Wheeler's formula seemingly has a
fudge factor built into it?

>>     4 pi^2 N^2 R^2
>> L = --------------
>>           H
>>
>> Where L is in 1000 inches.

>	What does H stand for in this expression?

The same as Wheeler's formula.  H is the winding length, R is the radius, N
is the number of turns.  R and H are in inches.

>What do you mean by "Where L is in 1000 inches".

If you strictly solve for R, H and N the units of the answer is 1000 inches.

>Is L the inductance or the length or what?

I'm told that L is the inductance expressed in length of 1000 inches.  My
improvement to this formula (that I posted in another lifetime) corrects the
units and outputs inductance as henry.  But I don't post that here as
correct units seem to be forbidden by the experts on this list.

>Wheeler's formula is not empirical.

I've never seen Wheeler's paper.  All I can go on is the word of those who
post to this list.  Several people in a recent discussion on Wheeler's
formula referred to the formula as being empirically based.  If you can
provide some kind of solid answer to resolve this it would be much
appreciated.  But regardless of whether the formula is empirical or derived
from picking good numbers from a hat, it isn't based solely on the physical
characteristics of the coil and the permeability of the medium.

>I've read through these pages several times and I can find NO statement
implying that the thought the inductance was a function of the voltage
across the coil.  His statement "Small corrections should have been made for
the e.m.f. making it smaller..."  seems to tie in with the statement at the
bottom of page 271 where he says "To ascertain approximately their
inductances readings were taken etc.".  In other words, he might be saying
that the inductance should be corrected by using the results of the e.m.f.
measurement (he was measuring the voltage due to a measured current which
would give the reactance from which the inductance can be calculated).

Like I said in my post, I have no conclusions but this caught my attention
and I'll research the notes closer for a clearer understanding.  I'm not in
a position to agree or disagree on this at this time.

>> This would imply that the closer to earth, the lower the inductance.  The
>> further from the earth, the closer the coil gets to its unbiased
inductance
>> value.
>	I can't find the implication.

If it can be assumed that the true inductance of an air coil in free space -
and not affected by a large body such as the earth - is represented as the
product of the permeability of free space times the physical characteristics
of the coil; and it can be further assumed that Wheeler's formulas for
inductance use fudge factors that compensate for a uniform electrostatic?
effect by the earth on air core coils; then it would follow that the closer
one gets to a large charged body the lower the inductance will be and the
further away from said body, the closer the inductance will be to coil's
calculated inductance of permeability of free space times the physical
characteristics of the coil.

The implication is based on the assumptions.

Dave

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