Nikola Tesla Books
Books written by or about Nikola Tesla
Calling now Cs the capacity of the excited system when the structure was not attached to it, and Cs' that when this was the case we have:
$! {T_{1} = {{2 \pi \over 10^{3}} \sqrt{C_{s} L'}} = {{2 \pi \over 10^{3}} \sqrt{{9238 \over 10^{9}} \times 0.1287}}} $!
and
$! {T_{2} = {{2 \pi \over 10^{3}} \sqrt{{C'_{s} L'}} = {{2 \pi \over 10^{3}} \sqrt{{63,902 \over 10^{9}} \times 0.1287}}}} $!
L' being the inductance of the excited coil. L' was previously measured and found to be L' = 18,650,000 cm. Now from above:
$! {C_{s} = {{9238 \times 0.1287} \over {10^{9} \times {18,650,000 \over 10^{9}}}} = {{9238 \times 0.1287} \over 18,650,000}} $!;
and
$! {C'_{s} = {{63,902 \times 0.1287} \over 18,650,000}} $!; $! {C'_{s} \over C_{s}} = {63,902 \over 9238} $!; $! {C'_{s} = C_{s} {63,902 \over 9238}} $!
Cs expressed in centimeters is:
$! {C_{s} = {{9238 \times 0.1287 \times 9 \times 10^{5}} \over {1865 \times 10^{4}}} = {{11.583 \times 9238} \over 1865} =} $! 57.375
from this Cs' = $! {63902 \over 9238} $! x 57.375 = 6.92 x 57.375 = 397.03 cm.
C = Cs' - Cs = 339.655 cm.
This is a result inferior to the calculated value but it was to be expected as before stated since it can not be correct to assume that all pipes are connected in multiple unless the vibration is very slow. Another coil is to be used with an inductance much higher so as to examine the truth of this opinion. There is, however, a possibility that the reading, when the structure was attached to the excited coil, was too low. In this case namely, the tuning is not sharp owing to the large capacity of the system but when the structure is not attached it is quite sharp, hence it there is any error in the adjustment of the circuits it can be only then when the structure was connected. This is to be investigated also. A slight error might have been also caused by the wire which connected the coil to the structure, for although this wire was placed at a distance of 4 feet with its nearest point there might have been enough influence exerted by the structure to make the reading with the spark wires alone larger. This will be ascertained. From previous tests on the increase of capacity with elevation I should expect to find the capacity of the structure much larger than the calculated value.
On the present occasion readings were also taken with the view of determining the inductance of the connections alone+flexible cable on regulating coil + 1/2 turn of regulating coil. This namely is the lowest value which it is possible to give with the regulating coil in circuit. In this case the readings were E1 = 10.5, E = 10.2 across the 2 primaries+all these connections and across the two primaries alone, respectively. With reference
263
November 6
Tesla carefully measured the capacitance of the aerial pole by the resonance method, from the known inductance of the 550-turn coil (see September 8th) and known frequency of the oscillator, with two measurements, one with and the other without the capacity to be measured. He did not make use of his earlier results for the inductance of the regulating coil and connections from October 30th, although he could have done. A calculation check shows that the results of October 30th were rather high (by as much as 10% for 2 1/8 turns of the regulating coil), but Tesla probably thought that the new procedure was better and so did not use the old results. An analysis shows that if the old values had been used the final result would not have been essentially affected, so that Teslaâs conclusion that the measured capacity of the pole was less than the theoretical value of November 5th remains valid.
From the relatively lengthy discussion following the measurements it may be seen that Tesla expected just the opposite. As usual when his expectations were not fulfilled, he considers ways for getting more reliable results.
November 6
He measures the capacitance of the structure with the sphere by means of the resonant method very carefully, on the basis of known coil inductance of 550 turns (please see Sept. 8) and known oscillator frequency, from two measurements he finds the desired capacitance. The first measurement is without connected structure and the second with it. The resonance he determines on the basis of the maximum spark and the frequency on the basis of inductance and capacitance in the oscillator circuit. In a series of separate measurements he determines the value of a regulating coil as well as the inductance of the connections by following a new procedure.
The primary coil, and the regulating coil with connections as in the measuring circuit is connected to the source of low frequency (most probably as previously 140 Hz) and it measures the voltage ratios shown in the figure. From the previously determined primary coil inductance and the voltage ratio, the total inductance of the connections and regulating coil is obtained. It is interesting that he did not use the results for regulating coil inductance and the inductance of connections obtained on Oct. 30, as he could use them. The calculation check of the previous result indicates that the values obtained on Oct. 30 were somewhat higher (even more than 10% higher for two 2-1/8 regulating coil turns), considered that the newest procedure is better and that is why he did not use the old results. The analysis indicated that even with the old values final results would not change much and Tesla's conclusion is still valid in that the measured value of the structure capacitance is smaller than theoretical value obtained on Nov. 5. From Tesla's relatively long explanation after he performed measurements, it could be seen that he expected exactly the opposite effect. As always so far when his expectations were not met, he continues the considerations about further steps for the purpose of achieving more reliable results.
