Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 421

October 6-8

From the measured inductance of the new secondary and mutual inductance of the primary and secondary, and the primary inductance measured earlier (see September 25th), it follows that the coupling coefficient was 0.58, i.e. tight coupling*. An oscillator with this much coupling will probably produce three pronounced components, even with very rapid interruption of the spark in the primary; this is indicated by the results Tesla obtained with spark oscillators with looser coupling (see the commentary on 26 September).

As before, Tesla determined the wavelength of the oscillator from the period of the primary circuit (see, e.g., June 20th). He compares one quarter wavelength with the total length of wire in the secondary, special coil and extra coil (when no other coils were used, he considered that the length of the secondary windings should be one quarter wavelength).

October 9

He made the last measurements of the change of capacity of a sphere with height on October 5th, but did not give the calculation results. He subsequently improved the apparatus as a whole and in the present entry describes a different way of connecting the “special coil”, the chief effect of which was to loosen the coupling, which immediately proved its advantages. With weaker excitation it was easier to adjust the “special coil” to resonance because there were no streamers. Parasitic capacities were reduced, mainly to the distributed capacity of the “special coil”.

Tesla first determined the distributed capacity of the “special coil”. He assumed that the ball circuit resonated at ω₀, determined by the primary circuit, so that one can write

L_p1C_p = L_sc (c + C)

where L_p1 and C_p are the total inductance (including the regulating coil) and capacity of the primary circuit, L_sc is the inductance of the “special coil” (including connecting wires), C is the distributed or parasitic capacity of the “special coil”, and c the capacity of the ball.

Subsequent changes in the height of the ball changed the capacity in the circuit of the “special coil”. To bring the oscillator into resonance with this circuit again, Tesla changed the inductance in the primary circuit. When resonance is achieved, according to Tesla, one can write

L_p2C_p = L_sc (c' + C)

Dividing this by the preceding equation yields

c' = $! {{L_{p}}_{2} \over {L_{p}}_{1}} $! (c + C) - C

which is in fact the equation Tesla uses to find c'. Because of an arithmetical error in calculating C, Tesla's numerical results for the ball capacity are about 10% higher than they should be, but this does not essentially affect the conclusions. To calculate the distributed capacity of the coil** he uses the relation L_pC_p = L_sc (C + c) for the ball at