Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 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