Nikola Tesla Books
Books written by or about Nikola Tesla
Colorado Springs
Oct. 4, 1899
Test to determine more exactly influence of elevation on capacity of an insulated body.
A coil was wound to suit best the special conditions of this test. On a drum of 2 feet and 1 1/4" diam. were wound 400 turns, wire cord No. 20. The insulation was very thick but of small specific inductive capacity. This wire with widely separated turns was used in order to make the capacity of the coil itself as small as possible compared with capacity of insulated body. The latter was in this case the one sphere of 30" diam. arranged to be elevated at will to a height up to nearly 40 feet from the ground.
The wire had a diam. approx. No. 20 B. & S. = 0.032" or 0.8128 mm. The circumference of wire if solid would have been about 2.4 mm. Now one turn of wire was π x 25.25" or about π x 641 mm. The total length π x 641 x 400 = 256,400 x π mm. Hence total surface of wire only π x 256,400 x 2.4 = 615,360 π sq. mm. or 6154 π sq. cm. Now the diam. of the sphere was 30" or 76.2 cm. The surface π d2 = 18,231 sq. cm. approx. The utmost we could take would be 1/2 surface of wire, that is 3000 π sq.cm. and this would be only 1/2 of surface of sphere. But other things considered, it would appear that the error due to electrostatic and distributed capacity of the coil itself would be small. This is however to be further investigated and allowance made for. It would be, of course, desiderable to entirely do away with the capacity of the coil to make the results of the observations rigorously true, but this will be hardly possible.
The number of turns on the coil was selected so as to be suitable to the apparatus used normally. The total length of the coil so far as wound was 57 1/8" or 145.1 cm, diam. of drum 25.25" = 64.14 cm. To calculate self-induction we have then the following data:
Turns: 400, length of coil 145, 1 cm, area of one loop = 3231 sq. cm. From this approximately $! {L = {{4 \pi N^{2} S} \over l} =} $! 44,772,000 cm, or 0.044772 henry approx. If we adopt 38.1 cm as the capacity of the sphere in the lowest position, the period of the system would be:
$! {T = {{2 \pi \over 1000} \sqrt{{0.044772 \times {38.1 \over {9 \times 10^{5}}}}}} =} $!
$! {= {{2 \pi \over {3 \times 10^{5}}} \sqrt{0.1706}} = {{2 \pi \over {3 \times 10^{5}}} \times 0.413} = {2.5936 \over {3 \times 10^{5}}} = {0.86455 \over 10^{5}}} $! or n = 115,668 nearly.
This is a vibration far too quick, in reality it will be much slower because of capacity in the coil.
Diagram shown illustrates arrangement used in experiments: The coil of 400 t. was excited by secondary of oscillator, and capacity and self-induction in primary were
204
October 4
Tesla was primarily interested in the change of capacity of a ball with height, so he measured the primary capacity for two elevations of the ball. In both cases he tuned for resonance of a “special coil”. In the first measurement he had Lp Cp1 = Lsc Cb1 = 1/ω21 and in the second Lp Cp2 = Lsc Cb2 = 1/ω22, where p refers to the primary circuit and b to the ball. These equations neglect the effect of interaction between the primary and secondary. They readily yield Tesla’s equation
$! {Cp_{1} \over Cp_{2}} = {Cb_{1} \over Cb_{2}} $!
The inductance of the primary Lp and of the “special coil” Lsc do not figure in the capacity ratio equation. In deriving this equation all distributed capacitance in the secondary and the secondary coil itself are neglected.
October 4
He performs the experiments in order to determine the variations of capacitance.of and isolated metal body at various distances from the ground surface. He constructs the ''special coil'' which is connected between the secondary and the globe. He particularly makes efforts to reduce the internal coil capacitance.
The oscillator frequency is reached by common method by adjustment of regulating coil and capacitor in the primary circuit. The maximum voltage (i.e., the longest spark on terminal of "special coil") is the indication of adjusted oscillator. For the secondary he enters the note on the figure that it does not "vibrate freely". Tesla is particularly interested in globe capacitance variations due to height. Because of that he performs two primary capacitance measurements for the two globe positions. In both cases he achieves the resonance on "special coil". In the first measurement the relation is LpCp1 = LscCk1 = $! {1 \over {ω_{1}}^{2}} $!, and in second LpCp2 = LscCk2 = $! {1 \over {ω_{2}}^{2}} $!
These equations do not take into account the mutual influence of the primary and secondary on the oscillator operation. On the basis of the above equations it is easy to get Tesla's equation $! {C_{p1} \over C_{p2}} $! = $! {C_{k1} \over C_{k2}} $!, where the index p is related to primary circuit and index k to the sphere. Lp (primary inductance) and Lsc ("special coil" inductance) do not enter in the equation for the capacitance relationship. When developing the last equation all distributed capacitances in the secondary are neglected as well as the secondary coil itself.
