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The Hydrostatic Equation
The air pressure at any given height in the atmosphere is due to the force per unit area exerted by the weight of all the air lying above that particular height. It follows then that atmospheric pressure decreases with increasing height above the ground. The downward gravitational force on a thin horizontal slice of air is generally very closely in balance with the net upward force acting on it, due to the decrease in atmospheric pressure with height. If these two forces equal each other the atmosphere is said to be in hydrostatic balance.

The negative sign just ensures that pressure decreases with increasing height.
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