Nikola Tesla Books
Books written by or about Nikola Tesla
or T approx. = $! {{{6.28 \times 13} \over 10^{7}}} $! = $! {82 \over 10^{7}} $!
This would give n = 10,000,000 : 82 = 122,000 per second.
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160
From this again we get λ = 186 : 122 = 1.524 miles, or length of secondary roughly = $! {λ \over 4} $! = 0.38 miles or wire length = 2000 feet approx. When two primary turns in series are to be used we shall have $! {λ \over 4} $! or length of wire = 4000 feet.
This to follow up.
The effects of distributed capacity in some experiments with the secondaries constituted of wire No. 10 (or cord) were so striking that it seemed worth while to carry on some investigations with very thin wire and consequently very small capacity in the secondary. It was decided to use wire No. 31 in these experiments. The diameter of this wire was only $! {1 \over 11.4} $! of that of wire or cord No. 10 hence the capacity of the new secondary, assuming all other things to remain the same, would be only $! {1 \over 11.4} $! of the capacity of the old secondary. The capacity of the new coil would be, however, reduced or increased in proportion to the length of the new wire relatively to the old and would be furthermore regulated by the distance of the turns. It was resolved to adopt 122,000 per second (see note before) in the primary as compared with 21,000 per second with the old secondary which was obtained with 15 jars on each side of the primary. For this vibration (122,000) the length of the new secondary should be about 2000 feet, this being the length of a quarter wave. Calling now the distance between the turns of the new coil d, its capacity as compared with that of old secondary of a length of 5280 feet would be:
C1 = $! {{1 \over 11.4} \times {20 \over 53} \times {d \over d_{1}} C} $!, C being capacity of old secondary and d1 the distance of turns in same. We may call $! {d \over d_{1}} $! = D a number which will modify the capacity according to the distance of the turns, and we then have the capacity of the new coil C1 = $! {{1 \over 11.4} \times {20 \over 53} \times DC} $!. Now L being the inductance of old coil and L1 that of the new, we have, disregarding effect of the smaller diameter of wire for the present, L1 = $! {({14 \over 36})^{2} DL} $! for the inductance will evidently be changed in accordance with the same number D. This relation follows from the fact that 2000 feet of new secondary with 143 feet average length of turn give $! {2000 \over 143} $! = 14 turns or nearly so, and there were 36 turns in old secondary, the length being preserved the same in both coils. From this it follows that the new system
71
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.
