Abstract: A distillation apparatus including a pair of vertical lower vessels each open at its upper end, and a pair of elongate upper vessels each having an open lower end, slidably mounted in a respective one of the lower vessels. A heat exchanger is mounted in each of the upper vessels, with the upper end of one upper vessel being connected to the inlet of the heat exchanger in the other vessel, and vice versa. A reciprocating drive mechanism drives the two upper vessels up and down in opposite directions so as to simultaneously effect compression in the space above the liquid level in the downwardly moving vessel while expanding the space above the liquid in the other vessel, driving vapor from the downwardly moving vessel into the heat exchanger in the other vessel, where it condenses.