Paradigm Lost: Nikola Tesla's True Wireless Page 9

of Sommerfeld’s theory. In 1919, the German mathematician Herman Weyl solved Sommerfeld’s configuration and ended up with a different approach that did not contain Zenneck’s wave. This result caused Sommerfeld to rework his solution, and his new findings did not agree with Zenneck.

In short, the first two decades of the 20^th century was a lively and sometimes contentious period in the theory of radio wave propagation, but there is no hint of this in Tesla’s paper. Nor is there any indication in anything he wrote that he had the sophisticated mathematical skills to comprehend what was being written by the people cited above. There were, of course, great inventors with minimal knowledge of higher mathematics (think of Edison, Morse, Bell) but these largely belonged to the 19^th century, and one does see Tesla as part of that tradition. His clinging to a sketchy circuit theory explanation seems pathetic. Incidentally, as early as 1904, a textbook of Henri Poincaré had addressed the primacy given to currents flowing through the earth in Tesla’s model of wireless telegraphy. He points out that if a coherer is placed in a hole in the ground “it will operate [as a detector of wireless telegraphy] when uncovered; if the hole be filled with earth, the oscillations produce no effect. We must look for something more than earth currents to explain the phenomena.”²¹ Recall that the most common detector in use at that time was the Branly coherer.

Putting aside theoretical considerations, Tesla’s paper is notable for the omission of major empirical findings contained in the famous and practical Austin-Cohen formula, a concise expression that describes the strength of the electric field experienced by a receiving antenna when both receiver and transmitter are over the ocean. Louis Winslow Austin and Louis Cohen had worked for the U.S. Navy in the early 1910’s, making shipboard electrical measurements of the field radiated from various transmitters manufactured by Reginald Fessenden’s company, the National Electric Signaling Company, or NESCO. By 1911, the two men had devised a successful empirical formula that gives the received field.²²

\[ I_r = 4.25 \frac{I_s h_1 h_2}{d \lambda} e^{-\alpha d / \sqrt{\lambda}}. \]

Here \( I_r \) is the current received by an antenna driving an impedance of 25 ohms, \( I_s \) is the transmitting antenna’s current, \( h_1 \) and \( h_2 \) are the lengths of the two vertical antennas, \( \lambda \) is the wavelength, \( d \) is the distance separating the antennas, and \( \alpha = .0015 \). Lengths are in kilometers and currents in amperes. The formula was effective only during the day and was so useful that it became the basis for testing new theoretical predictions of received fields. The presence of the square root of the wavelength in the exponent was later derived theoretically by the English mathematician G. N. Watson and published in 1919, only a few months after Tesla’s paper.²³ Interestingly, Tesla, speaking of the formula, states unequivocally “… the actions at a distance cannot be proportionate to the