Various Tesla book cover images

Nikola Tesla Books

Books written by or about Nikola Tesla

Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 216

October 9, 1899

of capacity of the elevated sphere with the rise from the ground would be greater than before found. The absolute rate of increase can be approximately estimated from the period of vibration. As before found the special coil with 400 turns had a self-induction of 44,772,000 cm. Now, however, with 404 turns this would be increased about 1% so that the self-induction would now be 44,772,000447,720 } 45,219,720 cm. But to this should still be added the self-induction of one turn of the secondary and wire leading to the ball and also the wire leading from the bottom of the special coil to the first turn of the secondary. The total length of these three wires is 240 feet and this is about 12% of the total length of the wire in the special coil which is 2854 feet. But inasmuch as the one secondary turn was very close to the primary and inasmuch as the other two wires were not coiled up, the self-induction of these wires was comparatively small, estimated a little over 200,000 cm so that the total self-induction was with fair approximation: 44,500,000 cm, or about 0,0445 henry (calculated). Now, with a ball of 38.1 cm capacity the period of secondary would have to be:

$! {T_{s} = {{2 \pi \over 1000} \sqrt{{38.1 \over {9 \times 10^{5}}} 0.0445}} = {{2 \pi \over {3 \times 10^{7}}} \sqrt{1695.45}} = {86.19 \over 10^{7{}}}} $! and

n = 116,000. This would be ignoring the internal capacity of the coil itself and its effect in slowing down the vibration. Now this capacity can be approximately estimated as well as the absolute increase of the capacity of the sphere from the primary vibration.

Taking the figures with the ball at a height of 33.66 feet from the ground, the primary vibration was:

$! {T_{p}' = {{2 \pi \over 1000} \sqrt{0.15264 \times {118,600 \over 10^{9}}}} = {26.7 \over 10^{6}}} $! or $! {267 \over 10^{7}} $!

This vibration is evidently slower than one of period Ts and it will be easily seen that

$! {{T_{s} \over T_{p}'} = {86.19 \over 267} = {\sqrt{{38.1 \over C + 38.1}}}} $!

where C is the internal capacity of the coil. Assuming for the present this capacity as not being distributed along the coil but in one place, we get

$! {C + 38.1 = 38.1 \times \left({267 \over 86.19}\right)^{2}} $! and $! {C = {\left[{\left({267 \over 86.19}\right)^{2} - 1}\right]} \times 38.1} $! cm.

Following this up we get for C value C = [(3.098)2 - 1] x 38.1 = (11.597 - 1) x 38.1 = 10.597 x 38.1 = 403.75 cm.

This is not the actual capacity of the coil but that ideal capacity by which the sphere should be increased to give the vibration of the primary.

We can now write

$! {T_{p}' = {{2 \pi \over 10^{3}} \sqrt{0.0445 \times {(403.75 + c) \over {9 \times 10^{5}}}}}} $!       . . . . . . . . . . 1)

216

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.