Mercury barometer

A measured mercury column represents pressure through its actual mass density and local gravitational acceleration. An equivalent reference column therefore obeys ${\rho }_0{g}_s{h}_s=\rho (T)gh$. If the indicated scale length expands as $1+{\alpha }_s\Delta T$ and mercury volume as $1+\beta \Delta T$, the first-order thermal factor multiplying the scale reading is $1+({\alpha }_s-\beta )\Delta T$. These factors describe a pressure-unit reduction, not a physical change in local gravity.^[ref]

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]