Nikola Tesla Books
Books written by or about Nikola Tesla
Now the self-induction in the primary was: primary one turn + connections = 56,400 + 6600 = 63,000 and with allowance for one half turn of self-induction coil, we may say approx. $! {64 \over 10^{6}} $! henry.
The period was
$! {T_{p} = {{2 \pi \over 10^{3}} \sqrt{{64 \over 10^{6}} \times 0.06254}} = {{{8 \times 2 \pi} \over 10^{6}} \sqrt{0.06254}} = {4 \pi \over 10^{6}} = {12.5664 \over 10^{6}}} $!
and from this n = 79,600 per second. The secondary was vibrating in synchronism hence $! {T_{s} = T_{p} = {{{2 \pi \over 10^{3}} \sqrt{0.04 \times C}}}} $!, where C denotes capacity which could be associated with the coil, if it had no capacity of its own, and this capacity together with the self-induction of the coil of 0.04 H as before found would give the period $! {T_{s} = {4 \pi \over 10^{6}} = {{2 \pi \over 10^{3}} \sqrt{0.04 C}}} $!. From this follows
$! {C = {{1 \over 10^{4}} \text{ mfd. or } {{9 \times 10^{5}} \over 10^{4}} = 90 \text{ cm.}}} $!
This is the value experimentally found and more to be relied upon than that derived in other ways. Taking this value and adding to the coil a sphere of radius 38.1 cm the total capacity of the system would be 90 + 38.1 = 128.1 cm and now we should find the period of the system to be
$! {T_{s}' = {{2 \pi \over 10^{3}} \sqrt{0.04 \times {128.1 \over {9 \times 10^{5}}}}} = {{4 \pi \over {3 \times 10^{6}}} \sqrt{12.81}} = {{4 \pi \over {3 \times 10^{6}}} \times 3.58} = {14.9958 \over 10^{6}}} $!
or $! {15 \over 10^{6}} $! approx. = Ts' or n = 66,666 per sec.
We can now find the capacity in primary required for resonance with secondary. The primary period will be $! {T_{p}' = {{2 \pi \over 10^{3}} \sqrt{{64 \over 10^{6}} C_{p}}}} $! , where Cp is the capacity required in primary. Now we have then $! {T_{p}' = T_{s}' = {{2 \pi \over 10^{3}} \sqrt{{64 \over 10^{6}} C_{p}}} = {{4 \pi \over {3 \times 10^{6}}} \times 3.58}} $! (from above) and
$! {{\sqrt{{64 \over 10^{6}} C_{p}}} = {{2 \times 3.58} \over {3 \times 10^{3}}} \text{ or } {\sqrt{C_{p}}} = {3.58 \over 12} \text{ or } C_{p} = {\left(3.58 \over 12\right)^{2}} = 0.096 \text{ mfd.}} $!
Since one bottle approximates $! {0.03816 \over 36} $! mfd we would want $! {0.096:{0.03816 \over 36} = 90.6} $! bottles total or, on each side of the break 2 x 90.6 = 181.2 bottles. This would suppose that the ball could have a capacity of 38.1 cm but this is physically impossible since it would have to be removed from all objects. In reality its capacity will be always much greater and the system will vibrate much slower as a rule. In fact, the test showed that resonance was attained with the ball 10 - 18 feet from the ground with all bottles in and in addition 5 1 /2 turns in the self-induction box. The tuning was naturally not sharp as the capacity was large and the maximum appeared to be with the ball 10 - 18 feet from the ground. To get sharper tuning a smaller ball of 18" diameter was used and now resonance was obtained with the ball 10 feet from the ground and all bottles in and no self-induction in the regulating coil.
230
October 20
Tesla was measuring the capacity of the coil which he had used for determining the change of capacity of a sphere with height (up till October 9th he had called it a “special coil”). Considering the dimensions of the primary (coil diameter 15 m) and the coil being tested (diameter 64 cm, length 145 cm), the coupling between them was obviously loose, so that the frequency found from the parameters of the primary circuit (provided that the main secondary of the oscillator did not influence the oscillation of the primary) can now be accepted as accurate. It is not stated how resonance was determined, but it was probably from the sparks at the terminals of the test coil. Similar resonance methods are given in recent textbooks on electrical measurements(56). It must be noted, however, that determination of the distributed capacity of a coil from the resonance of the coil alone is not reliable, it depends on the mode of excitation and always gives lower values. It is therefore recommended to measure it with an added lumped capacity in the circuit.
October 20
He describes the measurement method for the determination of the coil distributed capacitance. The measurements are performed on a coil which is used for the determination of sphere capacitance variation with height (until October 4 this coil is named "special coil"). The coil with additional short wire he excites without having a galvanic connection with the oscillator circuit. Based on primary dimensions (coil 15 meters diameter) and the tested coil dimensions (64 cm diameter by 145 cm length) it is obvious that the coupling between them must be weak. Therefore, we can accept the accuracy of the found frequency on the basis of primary circuit parameters (on the condition that the oscillator main secondary circuit does not influence the primary operation). It was not mentioned how resonance is determined, but it could be assumed that this was done on the basis of spark length at the terminals of the tested coil*.
We are under the impression that Tesla is suspicious of the 'as found' values of the coil's distributed capacitances. He worked hard on further proofs of the measured value by searching for new methods of determination.
* Similar resonant methods are given even in today's text books on electrical measurement(56). It is mentioned however, that the determination of coil distributed capacitance on the basis of the coil self resonance is not reliable, because it depends on the excitation method and always provides lower values. Because of this it is recommended to measure this capacitance when additional capacitance in the circuit exists.
