The Quadruplex telegraph is a type of electrical telegraph which allows a total of four separate signals to be transmitted and received on a single wire at the same time (two signals in each direction.) Quadruplex telegraphy thus implements a form of multiplexing.
The technology was invented by American inventor Thomas Edison, who sold the rights to Western Union in 1874 for the sum of $10,000.
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. B. Stearns; Edison added the ability to double the number in each direction.
To send two signals in a single direction at the same time, the quadruplex telegraph used one signal to vary the absolute strength or voltage of the signal (amplitude modulation) and the other signal to vary the phase (polarity) of the line (phase modulation), i.e., the direction of current flow imposed upon the wire.
Today this concept is known as polar modulation, considering amplitude and phase as radius and angle in polar coordinates.