## Nikola Tesla Books

Books written by or about Nikola Tesla

# Nikola Tesla: Colorado Springs Notes, 1899-1900Page 429

the oscillator starts to produce oscillations of two frequencies, and when the spark is broken it gives a third frequency which is determined by the secondary oscillatory circuit. With a third circuit (“extra coil”) the oscillation of the system becomes even more complicated, the oscillations during break being determined by the secondary circuit and the “extra coil”. Neglecting for the moment the “extra coil”, the three frequencies which a Tesla oscillator with tight inductive coupling(31) and equal natural resonant frequencies of the coupled circuits can be expected to produce are

ω0 = $! {1 \over \sqrt{LC}}$!   ω1 = $! {1 \over \sqrt{LC(1 - k)}}$!   ω2 = $! {1 \over \sqrt{LC(1 + k)}}$!

where k is the coupling coefficient. Thus ω1 can be interpreted as the natural frequency of a circuit with capacity C and inductance L(1 - k). For the primary inductance of Tesla's oscillator (see 9 November) one obtains the “reduced” L, i.e. L(1 - k) = 23,094 cm; Tesla measured L = 24,063 cm.

December 6

The photographs of the inside of the laboratory show the 100-turn “extra coil” raised above the floor in the center. With this coil Tesla again got similar results for the “reduced” inductance of the primary. However, aware of the indeterminacy of this “reduction”, and hence also of the oscillation frequency, he notes that the secondary should be broken at more points when the primary is used as a measuring inductance. This would ensure monochromatic oscillation of the oscillator by reducing the coupling of the primary and secondary (i.e. the circuit of the “extra coil”). The measurements with the secondary eliminated are more reliable, and the accuracy with which the values sought are determined depends mainly on the accuracy to which the inductance and capacitance in the exciting circuit of the oscillator are known.

January 1

Photograph XVII shows lamps connected into a resonant circuit consisting of one square turn. According to the data Tesla gives, one side of the square was about 1.3 m from the secondary coil of the oscillator. The capacity of the oscillatory circuit consisted of two condensers in parallel. The lamps are paralleled.

Tesla calculates the inductance of the square turn from the formula for the inductance of two parallel conductors, as if there were two such pairs connected in series. The formula for a square coil (Fleming, p. 155),

L = 8l(In $!{d \over r}$! - 0.774)

yields a value 12.6% less than Tesla found. The calculated resonant frequency is therefore somewhat higher than it should be, so that the inductance of the oscillator primary, as Tesla calculates it, is still less. In fact, because of the tight coupling of the secondary the oscillator must have been producing a complex spectrum, probably with its strongest component at the resonant frequency of the oscillatory circuit of the square coil.

In connection with photographs XVIII - XXI showing the secondary producing intense discharges, Tesla makes an interesting remark about signalling over great distances. Comparing this with other induction apparatuses he had constructed, he concludes that

429

31

Fleming J.A. and Dyke G.B. “Some resonance curves taken with impact and spark-ball dischargers", Proc. Phys. Soc. London, vol. 13, Feb. 1911, p. 136.

## 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;