Sir William Thomson

For his scientific endeavors William Thomson was knighted by Queen Victoria and later became Lord kelvin. He had extensive maritime interests and was probably most noted for his improvements to the mariner's compass. But this does not interest this radioman. Thompson worked on the transatlantic telegraph project and first quantified what we now call bandwidth. This was half a century before Harry Nyquist was even born.

It was known that submarine cables behaved differently than land lines. It was unclear why. Michael Faraday had demonstrated that the properties cable itself limited the rate at message could be sent through it. Faraday realized that the data rate was retarded by induction between the current in the wire and the material surrounding it. It is for this reason that he suggested telegraph cables be insulated with gutta percha. For all of Faraday's cleverness he didn't manage to quantify this observation but Thompson was all over it. He developed what is sometimes called Kelvin's submarine cable theory or Thomson’s "Law of Squares". More here.

Thompson described his results in terms of a data rate. By his math, long marine telegraph cables could be run "constructed of gutta percha containing a core not exceeding 2.72 times it's own diameter that of the conductor..."  Thomson recognized that the speed of a telegraph signal was limited by two measures: capacity and resistance. He calculated that the speed decreased as the square of the cable length increased for any given diameter of the core conductor. In this sense capacity became 'capacitance' aka the amount of stored electric charge for a known electric potential of the cable.

Thompson was not done. In 1855 he published a further analysis, correlating this to profitability. Thomson contended that the speed of a signal through a given core was inversely proportional to the square of the length of the core. Thomson got all kinds of flack for this so it intimated that very long cables woudl transmit messages more slowly, and thus carry less data. Wildman Whitehouse, at the Atlantic Telegraph Company. wrote that Thomson's calculations implied that the cable must be "abandoned as being practically and commercially impossible." Whitehouse was obviously wrong, even though Thomson was proven right.