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Nikola Tesla Books

Books written by or about Nikola Tesla

Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 217

October 9, 1899

This capacity c is now the actual capacity of the sphere at an elevation above considered, that is 33.66 feet. Namely, the total capacity was that of the sphere at that elevation - that is c - plus the ideal capacity of the coil derived from the computation of the primary vibration. This latter capacity has been called C. The inductance of the special coil being as before found, 0.0445 henry, and there being resonance under the conditions of the experiment at the elevation, named Tp’, gives the value for the secondary period.

Now at another elevation, say 34.66 feet, we shall have similarly

$! {T_{p}'' = {{2 \pi \over 10^{3}} \sqrt{0.0445 \times {407.75 + c' \over {9 \times 10^{5}}}}}} $!       . . . . . . . . . . 2)

where c' gives the value of the capacity of the sphere for the elevation of 34.66 feet. Computing I find, from experimental data above given

$! {T_{p}'' = {{2 \pi \over 10^{3}} \sqrt{0.15264 \times {129,400 \over 10^{9}}}} = {{2 \pi \over 10^{6}} \sqrt{19.75}} = {27.9 \over 10^{6}}} $! or = $! {279 \over 10^{7}} $!

Now, from equation 1 and 2, we get:

$! {{T_{p}' \over T_{p}''} = {267 \over 279} = {{\sqrt{0.0445 {403.75 + c \over {9 \times 10^{5}}}}} \over {\sqrt{0.0445 {403.75 + c' \over {9 \times 10^{5}}}}}}} $! or $! {{(1.045)^{2}} = {{403.75 + c'} \over {{403.75 + c}}}} $!

and from this: 1.092 x (403.75 + c) - 403.75 = c', but c being 38.1 we find for c' = 78.75 cm, which result shows that by lifting the ball from an elevation of 33.66 feet to 34.66 feet or one foot higher the capacity has been increased from 38.1 to 78.75 cm, or nearly 106.7%. Similarly we find the increase from 34.66 to 35.66 feet by computing the primary vibrations at these elevations. By analogy to the previous we have

$! {T_{p}''' = {{2 \pi \over 10^{3}} \sqrt{0.15264 {142.200 \over 10^{9}}}}} $! and, since $! {T_{p}'' = {{2 \pi \over 10^{3}} \sqrt{0.15264 {129,400 \over 10^{9}}}}} $!,

we get

$! {{T_{p}''' \over T_{p}''} = {\sqrt{{1422 \over 1294}}} = {\sqrt{1.099}}} $!

Now the vibration which corresponded to the primary vibration Tp'' in the special coil was $! {{2 \pi \over 10^{3}} \sqrt{0.0445 \times {{403.75 + 78.75} \over {9 \times 10^{5}}}}} $! and the one which corresponded to Tp''' was

$! {{2 \pi \over 10^{3}} \sqrt{0.0445 \times {{403.75 + c''} \over {9 \times 10^{5}}}}} $!,

where c'' will stand for the capacity of the sphere at the altitude of 35.66 feet.

217

Source:
by Professor Aleksandar Marinčić

October 9

He made the last measurements of the change of capacity of a sphere with height on October 5th, but did not give the calculation results. He subsequently improved the apparatus as a whole and in the present entry describes a different way of connecting the “special coil”, the chief effect of which was to loosen the coupling, which immediately proved its advantages. With weaker excitation it was easier to adjust the “special coil” to resonance because there were no streamers. Parasitic capacities were reduced, mainly to the distributed capacity of the “special coil”.

Tesla first determined the distributed capacity of the “special coil”. He assumed that the ball circuit resonated at ω0, determined by the primary circuit, so that one can write

Lp1Cp = Lsc (c + C)

where Lp1 and Cp are the total inductance (including the regulating coil) and capacity of the primary circuit, Lsc is the inductance of the “special coil” (including connecting wires), C is the distributed or parasitic capacity of the “special coil”, and c the capacity of the ball.

Subsequent changes in the height of the ball changed the capacity in the circuit of the “special coil”. To bring the oscillator into resonance with this circuit again, Tesla changed the inductance in the primary circuit. When resonance is achieved, according to Tesla, one can write

Lp2Cp = Lsc (c' + C)

Dividing this by the preceding equation yields

c' = $! {{L_{p}}_{2} \over {L_{p}}_{1}} $! (c + C) - C

which is in fact the equation Tesla uses to find c'. Because of an arithmetical error in calculating C, Tesla's numerical results for the ball capacity are about 10% higher than they should be, but this does not essentially affect the conclusions. To calculate the distributed capacity of the coil** he uses the relation LpCp = Lsc (C + c) for the ball at a height such that he could consider its capacity close to the theoretical capacity of an isolated sphere.

* The regulating coil in series with the primary reduced the coupling. The new coupling coefficient is found to be

** By distributed capacity Tesla used to mean the total capacity between turns of the coil. Here he uses a different definition of “internal capacity” similar to that normally used today.

Source:
by Professor Aleksandar Marinčić

October 9

He continues to improve the method for variable capacitance measurement of a sphere by varying the height. Last measurements he performed on Oct. 5, but he did not provide the calculated values.

After that he was improving the apparatus as a whole, and changed the "special coil" connection method. "Weaker Link", which was a main characteristic of the change, indicated immediately its good characteristics. Less excited "special coil" was easier to be adjusted in resonance, because there were no current streamers. The effect of parasitic capacitance was reduced to mainly distributed capacitance of the "special coil". Prior to the sphere capacitance variation measurement related to height variation, he determines the "special coil" distributed capacitance. He assumes that the circuit with a sphere resonates at frequency ω0, which is defined by oscillator primary circuit so that it could be written: Lp1Cp = Lsc(c + C), where Lp1 and Cp are total inductance (with the regulating coil included) and primary oscillator circuit capacitance, respectively. Lsc is ''special coil'' inductance (with inductances connections included). C is distributed or parasitic capacitance of the "special coil", and c is the sphere capacitance. At some other height only the sphere capacitance is changed in the circuit of the "special coil". In order to achieve the resonance between the system and the signal from the oscillator, Tesla varies the inductance in the primary circuit. When the generator frequency is equal to the resonant frequency of "free coil" circuit, according to Tesla, the following equation could be written: Lp2Cp = Lsc(c' + C).

Division of this equation by the previous one results in: c' = Lp2(c + C) - C, which corresponds to Tesla's equation from which c' is determined. Due to a calculation error when C was calculated, Tesla's various results for the sphere capacitance are higher by approximately 10%, but this does not essentially change the main conclusions. When calculating the coil distributed capacitance* he uses the relation LpCp = Lsc(c + C) for the sphere at a height, where he considers that its capacitance is close to the theoretical value for the remote sphere.

When commenting on results, he mentioned that this assumption could be the cause of the error.

* Under the term coil distributed capacitance Tesla considers the total capacitance among coil turns. Here he uses another definition "internal capacitance", which is similar to the one which is normally used even today.

Contents

Introduction
June 1 - 30
July 1 - 31
August 1 - 31
September 1 - 30
October 1 - 31
November 1 - 30
December 1 - 31
January 1 - 7
Commentaries

Appendices: I, II

Images

Glossary

Lowercase tau - an irrational constant defined as the ratio of the circumference of a circle to its radius, equal to the radian measure of a full turn; approximately 6.283185307 (equal to 2π, or twice the value of π).
A natural rubber material obtained from Palaquium trees, native to South-east Asia. Gutta-percha made possible practical submarine telegraph cables because it was both waterproof and resistant to seawater as well as being thermoplastic. Gutta-percha's use as an electrical insulator was first suggested by Michael Faraday.
The Habirshaw Electric Cable Company, founded in 1886 by William M. Habirshaw in New York City, New York.
The Brown & Sharpe (B & S) Gauge, also known as the American Wire Gauge (AWG), is the American standard for making/ordering metal sheet and wire sizes.
A traditional general-purpose dry cell battery. Invented by the French engineer Georges Leclanché in 1866.
Refers to Manitou Springs, a small town just six miles west of Colorado Springs, and during Tesla's time there, producer of world-renown bottled water from its natural springs.
A French mineral water bottler.
Lowercase delta letter - used to denote: A change in the value of a variable in calculus. A functional derivative in functional calculus. An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function.
America's oldest existing independent manufacturer of wire and cable, founded in 1878.
Lowercase lambda letter which, in physics and engineering, normally represents wavelength.
The lowercase omega letter, which represents angular velocity in physics.