Out of nowhere, a 26 year old derived the Telegrapher's Equations for the first time. His name was Oliver Heaviside. In 1876, "On the Extra Current", Heaviside introduced the new ideas of Maxwell's dynamic theory of electromagnetism to unlock to a new mode of propagation which went beyond the conventional diffusion model - a wave.
This is the story of how the Telegrapher's Equations came to be. Starting with Fourier's magnus opus, to William Thomson's (Lord Kelvin) application of the diffusion equation to the 2000 mile transatlantic cable, and finally to Heaviside, who made the final leap, incorporating wave like properties.
Correction:
00:50 the date on the cable should be 1858, not 1958!
