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Cable length and speed of transmission

I can do no better than start with a quotation from "The Atlantic Cable" by Bern Dibner:
 

Prof. Thomson formulated a law for the speed of telegraphic sending which stated that for a given conductor diameter, the speed decreased as the square of the cable length increased. This recognized the capacitance of a wire surrounded by an insulating cover and metallic sheath, all laid in a conducting medium - salt water. Prof. Thomson's "doctrine of squares" of speed and cable size was challenged by Mr. Whitehouse in a paper in 1855; Thomson considered this account good, but the conclusions fallacious. *

Lord Kelvin (Prof. Thompson) was right - he was about a lot of things - but the controversy was briefly quite serious.

In modern terms we would say the speed of transmission is proportional to the reciprocal of the [resistance multiplied by the capacitance] of the cable. The cable blueprint from the Weston-super-Mare Cable Station significantly gives "RC" values for the cables.

These cables were very long with no undersea "repeaters"; so, even though the conductor was large and therefore the resistance per yard low, it all added up and, for the Atlantic crossing, this restriction of achievable speed was significant. Because it was effectively governed by the inverse square of length (both the capacitance and the resistance increase for every extra mile) it can be seen that the shortening of the route by landing at St John's, Newfoundland was of definite value. The blueprint shows a length of 1800 nautical miles for Waterville-Newfoundland compared to 2200 for Waterville-Canso. This would correspond to an increase of speed for the shorter route of a factor of 1.5, all other factors being equal.

Quotation from the Internet Valley website:

Lack of repeaters & cable capacitance in insulation restricted the cable to 2 words/minute -- signaling speed was inversely proportional to square of length, per Lord Kelvin's prediction. A "siphon receiving" mechanism raised that rate to 20 WPM in 1870. Even 2 WPM beat the next fastest method; 10 days by steamship.)

*Quoted from THOMPSON, Silvanus P., The Life of William Thompson, Baron Kelvin of Largs, London 1910; (two vols); vol. 1, page 330.
 

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