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An instrument measuring atmospheric pressure. A mercury barometer compares the hydrostatic pressure of a measured mercury column with the pressure above it. Its equation is $p_{\mathrm{atm}}=p_t+\rho gh$, with $h$ the vertical separation of the liquid levels.

A mercury barometer with its lower end in a reservoir exposed to atmospheric pressure. A fixed-cistern scale must allow for the changing reservoir level, while an adjustable cistern can restore a fixed lower reference before each reading.

An adjustable-cistern barometer associated with Jean Nicolas Fortin. Restoring the cistern surface to a fixed index makes the lower mercury level reproducible before the upper level is read.^[ref]

Observe each gas volume, temperature, pressure and moisture condition, and reduce both volumes to the same temperature, pressure and dry-gas basis. Equal scale readings alone do not establish equal amounts of gas.

Read the calibrated volume of each gas in a graduated tube or eudiometer, with the eye at the meniscus to avoid parallax. Allow the gas and the surrounding bath to reach thermal equilibrium, then read a thermometer close to the gas. Heating expands a fixed amount of gas, so a larger reading could reflect a higher temperature rather than more gas. The temperature used in a gas law must be an thermodynamic temperature.

Read the atmospheric pressure with a barometer. If a gas is confined over a liquid, also observe the difference between the inside and outside liquid levels. With $h$ the internal surface height above the external surface, the total internal pressure isHere ${\rho }_{\ell }$ is the confining density of the liquid and $g$ the gravitational acceleration; the sign reverses automatically when $h$ is negative. Equalizing the levels before taking the volume reading removes this hydrostatic pressure correction. A mercury barometer can itself require temperature and calibration corrections for accurate work.

If the gas is saturated with water vapor, subtract the vapor pressure of water at its measured temperature:The observed pressure includes both the test gas and water vapor; counting it all as test gas overestimates the amount. The saturation assumption needs time for equilibration. For a dry gas, no water vapor subtraction is made; another collecting liquid may require its own vapor pressure correction. A collecting liquid must also be chosen so that it neither appreciably dissolves nor reacts with the gas: water, for instance, is unsuitable for preserving the whole amount of freely soluble Ammonia.

For dilute gases obeying the ideal gas law, the volume $V_0$ at a common chosen $T_0,p_0$ isConsequently the corrected comparison isThis is also the ratio of amounts of substance in the ideal gas approximation. Check for leaks, trapped air, changing composition and incomplete transfer. At high pressure or near condensation, real gas behaviour may require compressibility factors; with $pV=ZnRT$, the inferred amount ratio contains the further factor $Z_2/Z_1$.

A mercury barometer balances atmospheric pressure against the hydrostatic head between the open cistern surface and the mercury surface in a closed tube. Writing $p_t$ for the pressure above the column, the ideal relation isThe relevant $h$ is the vertical difference between the two mercury levels. It is not simply the length of filled glass, and the top space need not be an absolutely perfect vacuum.

A cistern barometer needs the following corrections or controlled adjustments:

The observational precautions are also described in the Guide to Meteorological Instruments and Methods of Observation by the World Meteorological Organization.^[ref] The quantitative corrections are separated in Mercury Barometers and Manometers by W. G. Brombacher and others, particularly the cistern, temperature and gravity discussions. Reduction of a weather-station pressure to sea level is a separate atmospheric comparison, not an intrinsic correction to the instrument.^[ref]