Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 73

July 9

In calculating D (the ratio of the turn spacing of the old and new secondary) Tesla accidentally took the frequency instead of the period, so that he got D = 83 instead of D = 2.45. A second numerical error occurred in the formula relating D and C (38 omitted from under the square root) so that C came out to be 10 000 cm instead of 227 cm. Since he never made use of these results, Tesla naturally never discovered his mistakes.

Tesla's method of measuring the oscillator frequency by means of an auxiliary coil is interesting. This coil, with its own distributed capacity, in fact constituted an absorptive resonator. The size of the spark across its terminals provided an indication of the amount of power it absorbed. (In some respects it resembled Hertz’s resonator). Tesla adjusted its resonance by varying the number of turns for the biggest spark. He then calculated the wavelength on the assumption that at resonance the length of the coil winding was one quarter of a wavelength. The wire length he determined by measuring the coil resistance, the resistivity per unit length of the wire being known. This method embodies a systematic error due to neglecting the reduction in speed of propagation through the coil⁽⁴⁵⁾, and it is applicable for oscillators of high power. However, it was the most reliable method Tesla had used to determine oscillation frequency up to that time.

For theoretical calculation of the oscillation period Tesla used two formulae: one which neglects the influence of the secondary (as for example at the beginning of this entry), the other taking this influence into account. In the latter case it is taken that the primary inductance is reduced by a factor (1-M²/NL), which would be the case were the secondary short-circuited. How far this is justified it is difficult to say because an oscillator which discharges heavily does not satisfy the simple theory of the resonant transformer oscillator: the secondary is then heavily damped and free oscillations in it decay rapidly, so one would have to apply a theoretical treatment for heavily damped oscillators.

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.