The Siemens cycle is a technique used to cool or liquefy gases. A gas is compressed, leading to an increase in its temperature (by Gay-Lussac's law relating pressure and temperature). The compressed gas is then cooled by a heat exchanger, then the cool, compressed gas is allowed to decompress, further cooling it (again by Gay-Lussac's law). This results in a gas (or liquefied gas) that is colder than the original and at the same pressure.
Carl Wilhelm Siemens patented the Siemens cycle in 1857.