The coil illustrated on page 349 is describing the extra coil at the central shack/station, which has a wire length of 2660 feet, equating to a calculated quarter wavelength frequency of 92,504 cycles. Granted this extra coil is of 1:1 geometric proportion, the assumption would be that the series mode exists at around 115,000 cycles while the parallel mode is found at roughly 123,000 cycles.
Starting from page 350 to the first half of page 355, tesla describes multiple instances whereby a separate receiving coil is used at different distances for “pickup”. Figures XXV, and XXVI are supposedly the same coil design as Tesla describes them to be, in which they possess a total length of wire 2198 feet, allowing for a calculated quarter wave frequency of 111,000 cycles per second.
By due of the photographic plates, the measured height of the coils is 68 inches, given that the coil’s diameter is 25.25 inches, allowing for a 2.7% height to diameter ratio. This means that a frequency compensation factor of 150% will entail a series mode of the coil to be 167,000 cycles per second. Likewise, the parallel mode will be 162% than of the quarter wavelength frequency, giving 179,000 cycles.
Summing up, the main station would have operated on a series mode frequency of roughly 115,000 cycles per second, with an accompanying parallel mode of 123,000 cycles.
The receiving coils which Tesla speaks of would have likely operated on a series mode of 167,000 cycles, whereas its natural parallel mode would be around 179,000 cycles per second, granted its calculated wavelength frequency is 111,000 cycles.
On a side note, I have just deduced that for a 1:1 end fed extra coil, its series mode will be roughly 120% higher than its quarter wave calculated frequency, as its parallel mode will be 130% higher, as previously stated. Yet, what is interesting is that if we take the ratio of series to parallel, 1.20/1.30, we obtain 0.92. Likewise, 1.30/1.20 yields 1.08. Now if we compare that to elongated coils and flattened coils with different aspect height to width ratios, this proportionality still seems to apply. In the example where an elongated coil possesses a 1.87% height to diameter ratio, its calculated quarter wavelength frequency is 325 kilocycles. According to VNA measurements conducted, its series mode is 476 kilocycles and parallel at 521 kilocycles. According to frequency compensation, the series mode should be 147% higher than of the “fundamental”, which it turns out to be. What is most interesting is how this coil’s parallel mode is 160% higher than of the fundamental frequency of 325 kc meaning that this coil’s series to parallel percentage ratio: 1.46/1.60 is equal to 0.91. Likewise, the opposite, 1.60/1.46 giving 1.08. Now take a look, this is awfully close to the same ratios obtained with every other 1:1 coil. I’ve tested this ratio on other coils, and surprisingly, it holds up!
I suppose in the end, this means a possibility that to determine the series mode of a coil, this depends on the coil’s geometry (frequency compensation factor), granting the parallel mode being 108% to 108.5% higher than of the series mode frequency. Therefore, the general ratio of series to parallel is derived as being,
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