Various Tesla book cover images

Nikola Tesla Books

Books written by or about Nikola Tesla

Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 362

January 2, 1900

the table of 13,474 cm. This, with the 41,000 cm as before, would give an approximate inductance of 54,500 cm for the exciting circuit and from this

Tp = !$ {{2 \pi \over 10^{3}} \sqrt{0.0099 \times {545 \over 10^{7}}}} !$ = !$ {{2 \pi \over 10^{6}} \sqrt{0.00099 \times 545}} !$ =
= !$ {{2 \pi \over 10^{6}} \sqrt{0.53955}} !$ = !$ {{2 \pi \over 10^{6}} \times 0.735} !$ = !$ {4.6158 \over 10^{6}} !$

and n = 217,000 per sec. approx.

As in this case the capacity may be put approximately at 500 cm, we may roughly estimate the effective inductance in the excited circuit. Namely, calling this inductance Ls we have, for the condition of resonance,

Tp = Ts or !$ {{2 \pi \over 10^{3}} \sqrt{0.0099 \times {545 \over 10^{7}}}} !$ = !$ {{2 \pi \over 10^{3}} \sqrt{{500 \over {9 \times 10^{5}}} L_{s}}} !$

and from this

Ls = !$ {{0.0099 \times 545 \times 9} \over {5 \times 10^{4}}} !$ = !$ {48.56 \over {5 \times 10^{4}}} !$ henry

or

!$ {{48.56 \times 10^{5}} \over 5} !$ = !$ {4,856,000 \over 5} !$ = 971,200 cm.

This was the effective or actual inductance, or nearly so, of the combined system of extra coil and lamp as connected in the diagram on p. 361. Evidently, in the experiment the lamp might have been lighted by doing away entirely with the extra coil and in fact I have done so. Time did not permit taking a photograph of the experiment thus modified.

In such a case, the inductance of the wire w (see diagram) need be very small, hence the frequency of the currents impressing the vibration upon the ground plate will be very high and the potential, to which the capacity C will have to be charged in order to pass enough energy through the lamp or other working circuit, will be comparatively very small. By way of example, suppose wire w, forming practically all the inductance of the excited circuit, had 10,000 cm and C were the same structure as in the experiment last described of a capacity of 500 cm; then calling P2 the potential to which the capacity is to be charged in order to supply 50 watts to the lamp or working circuit, we would have:

50 = !$ {{{P^{2}}_{2} \times 2 n} \over {2 \times 9 \times 10^{11}}} !$ x 500 or P2 = !$ {9 \times 10^{10} \over n} !$.

Now, calling T the period, we have

T = !$ {{2 \pi \over 10^{3}} \sqrt{{10,000 \over 10^{9}} \times {50 \over {9 \times 10^{5}}}}} !$ = !$ {{2 \pi \over {3 \times 10^{7}}} \sqrt{5}} !$ = !$ {{6.28 \times 2.236} \over {3 \times 10^{7}}} !$ = !$ {4.68 \over 10^{7}} !$

and from this

n = !$ {10^{7} \over 4.68} !$ = 2,137,000 per sec.

Substituting this for n we get

P2 = !$ {{9 \times 10^{10}} \over 2,137,000} !$ or P2 = !$ {{9 \times 10^{10}} \over {214 \times 10^{4}}} !$ = !$ {{9 \times 10^{6}} \over 214} !$

362

Source:
by Professor Aleksandar Marinčić

January 2

In this entry of 21 pages (the longest in the Notes) Tesla describes 11 photographs.

The explanation to Photograph XXII concerning the transmission of power from the excited primary circuit to the "extra coil" via the earth is similar to that he gave in 1893(6). The experiment to which the photograph refers was made with the aim of estimating the power of the oscillator from the thermal effect of the HF current. What Tesla calls the "total energy set in movement" would correspond to the total energy transferred to condenser in the secondary (i.e. the power) if an energy of !${1 \over 2}!$ CV2 is transferred in each half-cycle. It can be shown that the active power dissipated in the circuit is much less than this and is inversely proportional to the Q-factor of the oscillating circuit.

The next few photographs show a movable coil which powers light bulbs by means of the high-frequency power which it picks up. One end of the coil is grounded, the other free or just connected to a short piece of wire. The bulbs are inductively coupled to the resonant coil via the auxiliary secondary. Tesla gives no data about the distance of the resonant coil from the oscillator coil.

Tesla's commentary on photograph XXVIII illustrates that he still retained a lively interest in the problem of electric lighting, even after a period of over ten years. His earlier discovery of the luminescence of the gas and not only the filament with HF currents was here again confirmed(5).

In photograph XXVIII the bulb is connected in series with the terminal capacitive load. In the calculation Tesla does not use the "total energy set in movement" but assumes that 1/2 CV2 of electrostatic energy is consumed in the bulb in each half-cycle. A similar comment applies to photograph XXIV.

Several times Tesla remarks that the principle energy transfer from the oscillating to the receiving coil takes place via the earth. He finds confirmation for this in the experiment described on p. 363 (photograph XXX). He found that the voltage induced in the receiving coil was greatly reduced if the ground connection was broken. It may be that such experiments led him to the conclusion that "transmission" through the earth was a more efficient method of wireless transmission of power than the "inductive method".

Photograph XXXI is an X-ray picture of a finger. Tesla's comments on this experiment illustrate his interest in this type of radiation, already referred to (see the commentary to 6 June 1899).

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.