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Variable Capacitance and Inductance

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

We have discussed on this list individual observations of variations in
inductance measurements of coils.  It has brought about sometimes heated debate
as to whether this was a malfunction of machinery or a change of atmospheric
conditions.  At least one person on this list has proposed to run a test over
time to see if there were indeed a variation in inductance in a coil.
Today I was going through Tesla's writings and came across this article written
in 1901.  Apparently Tesla also noticed the variation of capacitance and
inductance.  If you have been part of this debate, you will find this article
quite interesting.  
New York Sun

Jan. 30, 1901


Capacity of Electrical Conductors is Variable

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Not Constant, and Formulas Will Have to Be Rewritten - Capacity Varies With
Abso­lute Height Above Sea Level, Relative Height From Earth and Distance From
the Sun.


Nikola Tesla announced yesterday another new discovery in electricity. This
time it is a new law and by reason of it, Mr. Tesla asserts, a large part of
technical literature will have to be rewritten. Ever since anything has been
known about electricity, scientific men have taken for granted that the
capacity of an electrical conductor is constant. When Tesla was experimenting
in Colorado he found out that this capacity is not constant - but variable.
Then he determined to find out the law governing this phenomenon. He did so,
and all this he explained to The Sun yesterday. Here is what he said:


“Since many years scientific men engaged in the study of physics and electrical
research have taken it for granted that certain quantities, entering
continuously in their estimates and calculations, are fixed and unalterable.
The exact determination of these quantities being of particular importance in
electrical vibra­tions, which are engrossing more and more the attention of
experimenters all over the world, it seems to be important to acquaint others
with some of my observations, which have finally led me to the results now
attracting universal attention. These observations, with which I have long been
familiar, show that some of the quantities referred to are variable and that,
owing to this, a large portion of the technical literature is defective. I
shall endeavor to convey the knowledge of the facts I have discovered in plain
language, devoid as much as possible of technicalities.


“It is well known that an electric circuit compacts itself like a spring with a
weight attached to it. Such a spring vibrates at a definite rate, which is
deter­mined by two quantities, the pliability of the spring and the mass of the
weight. Similarly an electric circuit vibrates, and its vibration, too, is
dependent on two quantities, designated as electrostatic capacity and
inductance. The capacity of the electric circuit corresponds to the pliability
of the spring and the induct­ance to the mass of the weight.


“Exactly as mechanics and engineers have taken it for granted that the
pliability of the spring remains the same, no matter how it be placed or used,
so electricians and physicists have assumed that the electrostatic capacity of
a conducting body, say of a metallic sphere, which is frequently used in
experiments, remains a fixed and unalterable quantity, and many scientific
results of the greatest importance are dependent on this assumption. Now, I
have discovered that this capacity is not fixed and unalterable at all. On the
contrary, it is susceptible to great changes, so that under certain conditions
it may amount to many times its theoretical value, or may eventually be
smaller. Inasmuch as every electrical conductor, besides pos­sessing an
inductance, has also a certain amount of capacity, owing to the varia­tions of
the latter, the inductance, too, is seemingly modified by the same causes that
tend to modify the capacity. These facts I discovered some time before I gave a
technical description of my system of energy transmission and telegraphy
without wires, which, I believe, became first known through my Belgian and
British patents.


“In this system, I then explained, that, in estimating the wave-length of the
electrical vibration in the transmitting and receiving circuits, due regard
must be had to the velocity with which the vibration is propagated through each
of the circuits, this velocity being given by the product of the wave-length
and the number of vibrations per second. The rate of vibration being, however,
as before stated, dependent on the capacity and inductance in each case, I
obtained discordant values. 


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. In determining the
length of the coils or conductors such as I employ in my system of wireless
telegraphy, for instance, the rule which I have given is, in view of the above,
important to observe.


“Far more interesting, however, for men of science is the fact I observed
later, that the capacity undergoes an annual variation with a maximum in
summer, and a minimum in winter. In Colorado, where I continued with improved
methods of inves­tigations begun in New York, and where I found the rate of
increase slightly great­er, I furthermore observed that there was a diurnal
variation with a maximum during the night. Further, I found that sunlight
causes a slight increase in capa­city. The moon also produces an effect, but I
do not attribute it to its light.


“The importance of these observations will be better appreciated when it is
sta­ted that owing to these changes of a quantity supposed to be constant an
electrical circuit does not vibrate at a uniform rate, but its rate is modified
in accordance with the modifications of the capacity. Thus a circuit vibrates a
little slower at an elevation than when at a lower level. An oscillating
system, as used in teleg­raphy without wires, vibrates a little quicker when
the ship gets into the harbor than when on open sea. Such a circuit oscillates
quicker in the winter than in the summer, though it be at the same temperature,
and a trifle quicker at night than in daytime, particularly if the sun is


“Taking together the results of my investigations I find that this variation of
the capacity and consequently of the vibration period is evidently dependent,
first on the absolute height above sea level, though in a smaller degree;
second, on the relative height of the conducting surface or capacity with
respect to the bodies surrounding it; third, on the distance of the earth from
the sun, and fourth, on the relative change of the circuit with respect to the
sun, caused by the diurnal rotation of the earth. These facts may be of
particular interest to meteorologists and astronomers, inasmuch as practical
methods of inquiry may result from these ob­servations, which may be useful in
their respective fields. It is probable that we shall perfect instruments for
indicating the altitude of a place by means of a cir­cuit, properly constructed
and arranged, and I have thought of a number of other uses to which this
principle may be put.


“It was in the course of investigations of this kind in Colorado that I first
noted certain variations in electrical systems arranged in peculiar ways. These
variations I first discovered by calculating over the results I had previously
no­ted, and it was only subsequently that I actually perceived them. It will
thus be clear that some who have ventured to attribute the phenomena I have
observed to or­dinary atmospheric disturbances have made a hasty conclusion.”