Let us, first of all, consider the hydrostatic equilibrium of the atmosphere. Consider a thin vertical slice of the atmosphere, of cross-sectional area , that starts at height above ground level, and extends to height . The upward force exerted on this slice by the gas below it is , where is the pressure at height . Likewise, the downward force exerted by the gas above the slice is . The net upward force is . In equilibrium, this upward force must be balanced by the downward force due to the weight of the slice, which is , where is the mass density of the gas, and the acceleration due to gravity. It follows that the force balance condition can be written

(6.63) |

which reduces to

(6.64) |

This result is known as the

We can express the mass density of a gas in the following form,

(6.65) |

where is the

It follows that the equation of hydrostatic equilibrium can be rewritten