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I remember reading somewhere that Tesla had successfully transmitted power through the earth.  Can you fill me in on the details of this astonishing achievement?

It is possible that Nikola Tesla is best known for his remarkable statements regarding the wireless transmission of electrical power. His first efforts towards this end started in 1891 and were intended to simply "disturb the electrical equilibrium in the nearby portions of the earth... to bring into operation in any way some instrument." [5] In other words the object of his experiments was simply to produce effects locally and detect them at a distance. By 1899 the electrical potential of his transmitter had increased to the point that more room was needed for the sake of safety. This and other considerations led him to temporarily shift his experiments to a location just outside of Colorado Springs.

It was at this Colorado "Experimental Station" that Tesla had some early success in wireless power transmission. In one of his demonstrations, photographs show that "a small incandescent lamp was lighted by means of a resonant circuit grounded on one end, all the energy being drawn through the earth" from the nearby transmitter. In 1907 he even went as far as to make the following statement.

"... to make the little filament glow, the entire surface of the planet, two hundred million square miles, must be strongly electrified. This calls for peculiar electrical activities, hundreds of times greater than those involved in the lighting of an arc lamp through the human body [a more spectacular demonstration]. What impresses him most, however, is the knowledge that the little lamp will spring into the same brilliancy anywhere on the globe, there being no appreciable diminution of the effect with the increase of distance from the transmitter."
     [From New York Times, Oct. 22, 1907, "Possibilities of 'Wireless'" found in Tesla Said.]

It is not clear that Tesla was referring to effects produced by his large Colorado transmitter. More likely he was writing of what he believed could be done with an even bigger transmitter such as the one that he was trying to complete at Wardenclyffe in New York.

The following books will help you to learn more about Nikola Tesla's work in wireless communications and power transmission: Nikola Tesla On His Work With Alternating Currents and Their Application to Wireless Telegraphy, Telephony and Transmission of Power, Nikola Tesla — Guided Weapons & Computer Technology, the Colorado Springs Notes, and the Tesla Coil Builder's Guide to the Colorado Springs Notes.

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