Why does the mercury in a barometer go up when the pressure is increased?

Why does the mercury in a barometer go up when the air pressure is increased?

The pressure p of the air above any point on the Earth’s surface is related ultimately to the amount of air above it. If we are standing high up, for example on the top of a tall mountain, there is less air between us and space for gravity to act upon.
Conversely, if we stand at the bottom of the Grand Canyon (one of the lowest places on Earth) then more air separates us from space, causing the air pressure p to be much greater.

A barometer is an instrument designed to measure air pressure p. It consists of a pool of liquid mercury in a trough. A long, thin glass tube (sealed at one end) is placed in the centre of the trough with its open-side beneath the surface of the liquid. The pressure of the air acts as a force on the surface of the mercury, forcing it up and into the capillary within the tube. If the air pressure is
great, then the force of the air on the mercury is also great, causing much mercury up the tube. A lower pressure is seen as a shorter length of mercury in the tube.
By performing experiments at different pressures, it is easy to prove the existence of a relationship between the air pressure p and the height h of the mercury column in the tube.
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