Nikola Tesla Books
Books written by or about Nikola Tesla
will vibrate with a period T = ? which will be $! \sqrt{({14 \over 36})^{2} {20 \over {53 \times 11.4} }D^{2}} $! times the period of the old system, or $! {14 \over 36} D {\sqrt{1 \over 30}} $! or 0.07D times. From this we may calculate D.
The old primary system was 21,000 per second, the new 122,000 per second, hence we have 0.07 D x 21,000 = 122,000 or D = 83. This means to say that without any additional capacity on the free terminal the turns would have to be put at a distance only $! {1 \over 83} $! that of the former secondary. This would not be realizable because the sparks would pass between the turns. Capacity must be, therefore, added on the free terminal. Calling this capacity c and the old C, the total capacity on the new coil would be C' = $! {{20 DC \over {11.4 \times 53}} + c} $! and the inductance would be L'1 = L1 = $! {({14 \over 36})^{2}}DL $!. Hence, for estimating D and c we have the equation:
$! {1 \over {122 \times 10^{3}}} = {{2 \pi} \over 10^{3}} \sqrt{{({14 \over 36})^{2}} {} D {{38 \times 10^{6}} \over 10^{9}} ({{20 \times 1200 D} \over {11.4 \times 53}} + c) {1 \over {9 \times 10^{5}}}} $! L = 38 x 106C = 1200 (old coil)
$! {{1 \over {122 \times 10^{3}}}} $! = $! {{14 \over {36 \times 3 \times 10^{4}}}{\sqrt{D(40 D + c)}}} $! or $! {{108 \times 10^{4}} \over 3416 \pi} $! = $! {\sqrt{D(40 D + c)}} $!
Taking here now D = 1 we get approx: $! {11,664 \times 10^{7}} \over {1166 \times 10^{4}} $! = 10,000 = (40 + c) or c = roughly 10,000 cm. for same distance of wires in new coil as in old.
It was of interest to determine the period of the combined primary and secondary system of the experimental oscillator and the following method was adopted. A coil wound with thin wire, turns separated by a string to reduce distributed capacity, was placed at a distance of a few feet from the vibrating system and so that it was about equally affected by the primary and secondary. One end of the coil was connected to earth and the other end was left free. An idea was already obtained beforehand as to the frequency which was likely to be found but more wire was wound on the coil to enable the adjustment to be effected by taking off turns. Turns were then taken from the lower end of the coil until a maximum of spark length from free terminal was obtained. The coil then gave a spark 5" long. This took place when there were 1140 feet of wire on the coil, this length being found by measurement of resistance { res. of coil 38.4 ohmsres. of 12 feet 0.405 ohms
Neglecting the capacity of the coil this length should be = $! {λ \over 4} $! or the quarter of a wave length. Of course, it was less but it was surmised that it would not be very much less. The total length of wave was then λ = 4560 feet. From this would follow
n = $! {{186,000 \times 5280} \over 4560} $! = 215,370 per second.
72
July 9
In order to check the secondary distributed capacitance influence, Tesla prepares new experiments with secondary coils where considerable reduction of undesirable capacitance could be expected. He performs the operating frequency calculation by a previously established method using inductance and capacitance in the primary circuits. A new secondary is wound by thinner wire (0.23mm in diameter instead of 2.6mm), and parameters of this coil he determines according to normal coil parameters on the same core (for equations explanations, please see June 28) with factor D as parameter. When calculating the factor D (which represents the ratio between turns separation of old and new secondary), the period is exchanged with the number of periods per second by mistake, and instead of having D = 2.45, D = 83. Other numerical errors crept in on other equations from which the relationship between D and C is obtained (the number 38 is omitted under square root) and consequently C obtained was 10,000cm instead of 227 cm. Because these results were not used, it is obvious that Tesla did not want to draw attention to this mistake.
The method by which Tesla measured the oscillator frequency by means of additional (auxiliary) coil is interesting. This coil with its distributed capacitance represented actually an absorbing resonant circuit, and the spark at the coil terminals served as indicator (to a certain extent this circuit is similar to a Hertz resonator). Tesla was adjusting the coil by varying the number of its turns until he obtained the biggest spark at coil terminals.
Then he calculated the oscillations wavelength on the basis of wire length on the coil at an achieved resonance (considering that the wire length in the coil is then equal to one quarter of wavelength. The wire length he finds on the basis of measured wire resistance value and known resistance per unit of length. This method, which in itself, hides the systematic error due to neglecting the speed propagation reduction through the coil(45), is applicable for oscillators of larger power. In Tesla's present experiments this is the most reliable method for determining the oscillations' frequencies.
In the calculations method of determining the oscillation period, Tesla applies two equations: one in which he neglects the secondary influence (as e.g., the beginning of note July 9) and the other, when he takes into account the secondary influence. In the latter case he considers that the primary inductance is reduced by a ratio 1 - M2/NL, which corresponds to a primary inductance reduction when the secondary is short circuited. How much of this is correct, it is difficult to estimate, because the oscillator with intensive discharge does not follow the simple theory of an oscillator with a resonant transformer. Secondary circuit is then considerably damped, and free oscillations in secondary quickly disappear, and therefore it would be necessary to apply a theory which takes into account oscillations of a high damped level.
The same day Tesla returns to a problem of approximate distributed capacitance calculations. This time he applies the Kelvin equation for determining the capacitance of a co-axial conductor. He considers that the outside conductor consists of two adjacent turns so that the capacitance calculated for the co-axial conductor reduces the ratio of wire radius and distance between two coil turns. Although not proving the applicability of such approach (e.g., how this equation could be applied in the case when two turns are around a middle turn shown in Fig. 2 at different potential) he calculates the coil total distributed capacitance and obtains a value which he says matches the measured one. The capacitance so determined is not equal to the ideal coil capacitance, which is shown in an equivalent coil schematic in parallel with a pure inductance.
