## Nikola Tesla Books

Books written by or about Nikola Tesla

# Nikola Tesla: Colorado Springs Notes, 1899-1900Page 52

June 30, 1899

C = $! { {T_{1}^{2} \times 10^{14}} \over 4 L }$! . . . . . . . . . . . .         (2)

Introducing jars for C we have C = n x 0.003

therefore n = $! { {T_{1}^{2} \times 10^{17} \over 12 L} }$! . . . . . . . . . . . .         (3)

Introducing again λ in miles in place of T1

T1 being = $! {λ \over 187,000}$! we have:

λ = $! {374 \over 10^{4}} \sqrt{L C}$! or, since usually $! {λ \over 4}$! is needed

$! {λ \over 4} = {93.5 \over 10^{4}}{\sqrt{LC}}$! . . . . . . . . . . . .         (4)

Observations made in experiments with oscillators, 36 1/2 turns and additional coil:

The additional coil is, as observed in the New York apparatus, an excellent means of obtaining excessive electromotive force. But it is peculiar that to properly develop the independent vibration of such a coil its momentum should be very great with respect to the impressed vibration. When such a relation exists the free vibration asserts itself easily and prominently. But when the impressed vibration is very large and the coil’s own momentum small, the free vibration can not assert itself readily. It is exactly as in mechanics. A pendulum with great momentum relative to the impressed momentum swings rigorously through its own period but when impressed momentum is very large relatively it is hampered, for then the impressed dominates more or less. This I look upon as distinct from the magnifying factor which depends on $! {pL \over R}$!.

It was evident that in such excitation of the additional coil there should be, for the best result, three vibrations falling together: that of the coil, that of the secondary and that of the combined system. In view of the above it is of advantage to place inductance between the secondary and additional coil to free the latter, when impressed vibration is too powerful to allow the intended vibration of the coil to take place readily.

From experiments it further appeared as though it would be of advantage to have some self-induction in the primary spark gap. This is to be ascertained. The use of condensers in series with the supply secondary is sometimes of advantage but little so when the vibration of the secondary is in resonance with the primary. Then there is less short circuiting of the secondary of the supply transformer and sparks are loud and sharp.

52

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;