# 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 Malcolm,

>First point: he is talking about a conductive body,

This is apparent.

>in particular a sphere.

It's more complicated than that.  When the sphere is at its lowest point
there is still a long wire above it.  Also, the capacity of the adjacent
steel tower has to be factored in. Agreed, though, that he is trying to
remove these other capacities to determine the capacity of just the ball.

>> Continuing the investigation of this astonishing phenomenon I observed
that the ca­pacity varied with the elevation of the conducting surface above
the ground, and I soon ascertained the law of this variation. The capacity
increased as the conduct­ing surface was elevated, in open space, from
one-half to three-quarters of 1 per cent per foot of elevation. In
buildings, however, or near large structures, this increase often amounted
to 50 per cent per foot of elevation, and this alone will show to what
extent many of the scientific experiments recorded in technical liter­ature
are erroneous.

I need to interject a comment here.  Despite Matt's insinuation that anybody
who takes a sincere interest in Tesla's work worships him as an infallible
god, I have found several errors in Tesla's work in my studies.  Apparently
I have found another one.  In reviewing Tesla's notes specifically related
to measuring the capacitance of a "large structure" on page 282 of his CSN,
he states, "The rise in the effective capacity for 47 feet and 6" was ...
26.2%.  Per one hundred feet it would be from this: 55.16% or a little over
1/2% per foot."  It seems Tesla incorrectly remembered the details of his
notes and wrote in his article "50 per cent per foot of elevation" when he
should have written "50 per cent per one hundred feet of elevation."

His CSN correctly state the difference is 1/2% per foot, which is consistent
with the rest of his article on variable capacitance.

>He is now saying that the capacitance of the conductive body increases with
elevation.

While checking his math I discovered Tesla was using the classic formula for
inductance instead of a calibrated formula like Wheeler's (which wasn't
discovered yet).  Tesla apparently measured his inductances accurately as he
noted his measurement was considerably less than the calculated inductance
(page 253 CSN.)  Sorry Terry, but Tesla was aware that the EMF affected the
inductance of the coil.  He makes such a comment on page 273 of CSN.  He
probably was aware of this much sooner, so now I'll need to go back and look
for other references.

What's interesting is that Tesla made his correction for EMF from the
classic inductance formula values and not from Wheeler's as you and Paul are
doing now.  Why don't you try making your adjustment from the classic
inductance formula of:

4 pi^2 N^2 R^2
L = --------------
H

Where L is in 1000 inches.

and see if the new value reveals some information?  This ties in with the
variable inductance of a coil.  Not only is a coil affected by its own EMF,
but it should also be affected by proximity to the earth.  It would appear
that Wheeler's formula, being based on empirical data, is accounting for the
coil's proximity to the earth.

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.

When considering a static capacitor, one with no frequency applied to the
charge, the closer the charged body is to the earth, the higher the
capacity.  This is obvious.  The further the charged body is from the earth,
the lower the capacitance will be.  However, Tesla was measuring a dynamic
charged body.  The amount of charge a body will hold depends on the
dielectric between the charged bodies.  The further the ball was raised, the
more dielectric between the sphere and earth and hence the greater the
capacity.  What Tesla was implying with his research was that the free space
is filled with more than mere permittivity.  It is also filled with air,
solar electromagnetic influence (including sunlight,) geo electromagnetic
influence, lunar electromagnetic influence, occasional gamma rays, etc.
Within limits, as the dynamically charged sphere rises the dielectric space
is filled with more stuff that increases permittivity (to a very small
extent.)

Regarding radios, the observed effects by Tesla were specific to a "free
space" dielectric and not a material dielectric, just as the air coil
formulas are referring to a "free space" core instead of a ferromagnetic
core.  (Air has a dielectric constant just above free space.)  The effects
on a capacitor would be more pronounced with free space than with a stronger
dielectric.  The stronger the dielectric, the less effect raising a charged
conductor would have.  This explains why standard radio capacitors don't
have significant problems with elevation or extraterrestrial effects.  Their
dielectrics are often materials like tantalum and mica, which have high
dielectric constants and are not affected as much by the proximity of the
earth.

To put it simply, Tesla was measuring the effect of elevation on a dynamic
charged body, not a static charged body.  To see what effect elevation has
on a static charged body a capacitor with a vacuum dielectric, (not any
other dielectric,) and not connected to the earth, should be measured at
various elevations.  A vacuum dielectric would show the most variation due
to elevation (distance from influence of the earth,) _if any exists_.

>>Thus a circuit vibrates a little slower at an elevation than when at a
lower level.
>There is a problem here too. Included in my series of measurements are some
showing clearly that a *resonator* that is elevated shows a *rise* in its
frequency of oscillation. That is what I would expect given that it has
moved further away from the ground plane. i.e. - its capacitance to ground
has *dropped*.

As noted above, raising the terminal increases the amount of dielectric
between the sphere and ground, allowing greater potentials on the charged
bodies.  Greater potentials mean greater capacitance.  It you check CSN, you
will see that Tesla specifically tuned for greatest potential.  To know how
this affects your experiments, it would be necessary to understand the
tuning method you used.  If you did not tune for maximum potential, then
your experiment would not be comparable to Tesla's experiment.

>And so it should with the sphere, should it not? Is that not reasonable?
Please address this question and show me exactly why my reasoning is in
error.

As I pointed out, you're using static capacitance as a model for a dynamic
capacitance.  The amount of extra dielectric that can get between the
charged bodies increases.  And this is precisely why the capacitance in
variable.  The amount of free flowing dielectric "material" is always in
motion.

>If you would like the benefit of a number of days labour, I would be happy
to send you the files of measurements offlist to save you time in hunting
for them. I don't wish to bore the list with yet another re-posting.

Yes, that would be good.  I would appreciate it.

>I for one do not believe that Richard came to these conclusions without
taking a lot of measurements.

All I would need to see is the data or a report of the data, and I would
agree with you.  No such information was given in Richard's notes on CSN.

>> It reminds me of my ninth grade science teacher...
>What reminds you of that?

The fact Tesla's work is constantly being berated on this list with little
discernable effort to understand exactly where he was coming from, or
attempting to duplicate his work.  As I pointed out above, you (and others)
assumed Tesla was measuring static capacitance.  His notes made it clear he
was not.  So Tesla has been considered to be wrong in his conclusions based
on erroneous assumptions.

OTOH, I gave Tesla the benefit of the doubt on his claim of 50% increase in
capacitance per foot (especially since he is dead and cannot defend himself)
but then went back and located the place where he made his mistake.  I would
do the same for you, Malcolm, and for everyone else on this list.  I won't
shoot down respectable peoples ideas without first having examined the
evidence and providing further evidence of error.  That's the proper
scientific method.  There are several people on this list who use the "shoot
them first and ask questions later method" and then board erupts in a wild
west mud slinging contest.

>Suppose we had blindly accepted theories that the resonator was a lumped
tuned circuit. Where would that have got us?

I hope research was done before blindly knocking the guys who came up with
the lumped tuned circuit?  If it wasn't, I'll bet there was a mud slinging
contest over that.

>Suppose we had accepted theories that the resonator could be modelled as a
uniform transmission line. Where would that have got us?

I hope research was done before blindly attacking the guys who came up with
that theory, too.  What could blind mud slinging accomplish?  Ultimately all
these mud slinging contests are ended with hard core research.  So why not
do the research first and avoid the mud slinging?

>It was based on a good deal of measurement and observation. Many things I
agreed with - some I simply could not.

Well that's great, Malcolm.  Where was this "good deal of measurement and
observation" in this discussion about Tesla's article claiming variability
of capacitance and inductance?

>I don't see the point of quoting this - unless you are seeking to ascribe
those same lamentable qualities to myself or others.

Question yourself, all of you who might be offended.  Did you present
yourself as a scientist or blind critic in this discussion?  The only
laudable response to this thread in terms of informed criticism was that of
Terry Fritz, who came back with data and an interpretation of the data.  He
responded with dignity toward his "opponent" and remained focused on his
best interpretation of facts he had acquired.  In this case, Terry acquired
the data himself; he could just as well have quoted the data of someone
else.  For those who came shooting from the hip, or responded with a bunch
of meaningless one-liners, that story was for them.

>I did not and have not taken issue with variability of capacitance (or
inductance for that matter) when the experimental conditions (sun
atmosphere, height or whatever) are altered. What I am taking issue with is
the notion that elevating a conducting body *increases* its capacitance.
That is what Tesla said. I challenge you to explain why such an increase