Radio atmospheric km. For ELF waves (< 3 kHz), ray theory becomes invalid, and only mode theory is appropriate. Here, the zeroth mode begins to dominate and is responsible for the second window at greater distances. Resonant waves of this zeroth mode can be excited in the Earth–ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. Their wavelengths are integral fractions of the Earth's circumference, and their resonance frequencies can thus be approximately determined by "f" ≃ "mc"/(2π"a") ≃ 7.5 "m" Hz (with "m" = 1, 2, ...; "a" the Earth's radius and "c" the
History of radio proposed electromagnetic or Hertzian waves as a navigation aid or means of communication, with Crookes writing on the possibilities of wireless telegraphy based on Hertzian waves in 1892. After learning of Hertz' demonstrations of wireless transmission, inventor Nikola Tesla began developing his own systems based on Hertz' and Maxwell's ideas, primarily working toward a means of wireless lighting, and power distribution. Tesla, concluding that Hertz had not demonstrated airborne electromagnetic waves (radio transmission), went on to develop a system based on what he thought was the primary conductor, the earth. In 1893 demonstrations of his ideas, in St. Louis, Missouri