From Glossary of Meteorology
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Literally, an instrument for measuring height; specifically, an instrument for measuring atmospheric pressure by determining the boiling point of a liquid at the station.

The relationship between the boiling point of a liquid and atmospheric pressure is given by the Clapeyron–Clausius equation. The sensitivity of the hypsometer increases with decreasing pressure, making it more useful for high-altitude work. Consequently, hypsometers are frequently used for height estimation.