The technology was invented by Thomas Edison, who sold the rights to Jay Gould, the owner of the Atlantic and Pacific Telegraph Company, in 1874 for the sum of $30,000 (equivalent to $808,000 in 2023).
To stop the rate war Western Union bought Atlantic Pacific (and the rights to the Quadruplex from Jay Gould) for $5 million dollars (equivalent to $135,000,000 in 2023).
The problem of sending two signals simultaneously in opposite directions on the same wire had been solved previously by Julius Wilhelm Gintl and improved to commercial viability by J.
The method combined a diplex (multiplex two signals in the same direction), which Edison had previously invented, with a Stearns style Duplex (simultaneous bi-directional communication).
Since telegraphs use a single wire, the current must flow through the signal (noise producing) relay at both ends (local and remote).
To increase practicality, Edison found other additional relays were necessary to provide hysteresis that prevented the switch from being indeterminate or fluttering at the moment of current reversals, and to send the separated signal to the appropriate sound emitter.
While this is conceptually elementary to modern engineers, one has to appreciate that multiplexing was a patent-worthy breakthrough and a huge economic win for telegraphy, since most of the challenge and expense was in the long wires between stations.
Without this, only short transmission distances were possible because the impedance mismatch of the reactive long wire would not balance the currents in the two halves of the local relay, activating it.