## Nikola Tesla Books

Books written by or about Nikola Tesla

# Nikola Tesla: Colorado Springs Notes, 1899-1900Page 51

June 29-30, 1899

June 30, 1899

Simple formulas to be used in rough estimates of the quantities frequently wanted.

In formula T = $! { {2 \pi \over 10^{3}} {\sqrt{LC}} }$!, L is in henry but usually is wanted in cm. We may therefore use

T1 = $! { {2 \pi \over {10^{3} \times 10^{4} \times \sqrt{10}}} \sqrt{LC} }$! or approx. when L is in cm.

T1 = $! { {2 \over 10^{7}} \sqrt{LC} }$!   C in mfd.         (1)

From L = $! { {T_{1}^{2} \times 10^{14}} \over 4 \, C }$! we have

4*

51

June 29

He didn't use yesterday's calculation, because he continued with a secondary with 36 turns. First detailed tests of oscillator operation did not provide expected results and Tesla attempts to determine the reasons by calculation. He gives secondary inductance, calculates the "additional coil" inductance but he doesn't use these results; then he determines free secondary vibration from the condition that total secondary wire length is equal to one quarter of wavelength. As he is already aware that the capacitances in the secondary circuit change this condition on secondary wirelength, he says in the calculation that the capacitances are neglected. With an approximate value for secondary resonant frequency he determines the required capacitance in primary circuit.

As he used small capacitances in the experiment, he concludes that he operated with high harmonics and that was the reason why he didn't achieve success.

The next day he gave several schematics of receivers with which he experimented probably for the purpose of patent submission preparation. Leonard E. Curtis is the person who appears several times pertaining to Tesla's patents as witness (please see e.g. (8,10)), or as lawyer on several patents starting in April, 1896.

June 30

Description of electric circuits in terms of mechanical analogies was at one time very popular. The resonance of an electrical circuit was likened to the swinging of a pendulum, and coupled resonant circuits to two pendulums linked together(39). Maxwell and his followers even tried for a long time to describe the electromagnetic field in terms of a mechanical model(40). Tesla's comparison of his “additional coil” to a pendulum is not precisely formulated but rather intuitive. He correctly discriminates between the excitation (initial conditions) and the Q-factor. He does not fully explain how he imagined that the vibrations of the three systems, the primary, the secondary and the “combined system”, would be the same. By “freeing” the additional coil he means a weakening of the coupling between it and the secondary exciting it. He obviously had a clear understanding that a circuit can oscillate at its own resonant frequency if the coupling with an excitation circuit is loose.

June 30

Since Tesla very frequently used Thompson equation with LC circuit without losses, he found it helpful to prepare suitable equations on the basis of which with minimal calculations he can obtain desirable values.

In continuation of the notes he sorts out the impressions and results (maybe because that is the end of the month?). Comparison of events in electrical circuits with mechanical analogous systems was in the past popular. The resonance of the electrical circuit connected with pendulum, the event in linked resonance circuits with two pendulums which are mutually linked(39).

Even Maxwell and his followers attempted for a long time to describe the electromagnetic field by means of a mechanical model(40). Tesla's comparison of "additional coil" with pendulum was not precisely shaped - it is more by intuition. Tesla correctly segregated the excitation (initial conditions) and quality factor. He didn't thoroughly explain how he imagined that free vibrations of three systems would be the same: primary, secondary and "combined system". When he talks about "releasing" of additional coil, he foresees the weakening of its link with the secondary which excites it. Tesla had a clear imagination that the circuit tends to vibrate on its own resonant frequency if poorly linked with the excitation. It is strange that he didn't apply this logic on the secondary circuit which he intentionally designed to be in strong link with the oscillator primary circuit.

## 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;