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Nikola Tesla Books

Books written by or about Nikola Tesla

Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 421

October 6-8

From the measured inductance of the new secondary and mutual inductance of the primary and secondary, and the primary inductance measured earlier (see September 25th), it follows that the coupling coefficient was 0.58, i.e. tight coupling*. An oscillator with this much coupling will probably produce three pronounced components, even with very rapid interruption of the spark in the primary; this is indicated by the results Tesla obtained with spark oscillators with looser coupling (see the commentary on 26 September).

As before, Tesla determined the wavelength of the oscillator from the period of the primary circuit (see, e.g., June 20th). He compares one quarter wavelength with the total length of wire in the secondary, special coil and extra coil (when no other coils were used, he considered that the length of the secondary windings should be one quarter wavelength).

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

* The regulating coil in series with the primary reduced the coupling. The new coupling coefficient is found to be $! {k' = k \sqrt{L_{p} / (L_{p} + {L_{r}}_{c})} < k} $!.

** 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.

421

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 &amp; Sharpe (B &amp; 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&nbsp;angular velocity in physics.&nbsp;