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The two principal systems of duplex telegraphy are described, as are the more significant proposals, beginning in 1853, for duplexing short land lines. J.B. Stearns's involvement with the British Post Office Telegraphs in 1870 and the introduction of duplex working on that system are described in detail. The introduction of gutta percha insulated cables in the late 1840s, the subsequent understanding of current flow in such cables as a result of W. Thomson's theoretical approach and the qualitative reasoning of Samuel Alfred Varley led to the first models of submarine cables. Successful duplexing of long land lines and submarine cables by Stearns, Muirhead and others from 1873 was only made possible by accurate modelling. It is suggested that the credit for the first artificial line belongs to Samuel Alfred Varley.