Pressure, hydrostatic balance, mass of atmosphere

Balance of forces (Newton's first law of motion)
Vector sum of forces that act on a body at rest is zero.
Pressure
Stress: force acting on a certain surface per unit area
For fluds, stress is perpendicular to surface.
The value does not depend on direction ... it is called pressure.
Hydrostatic balance
Consider a rectangular part of fluid at rest in a field of constant gravity
- p(z+Δz)ΔxΔy + p(z)ΔxΔy - gρΔxΔyΔz = 0 
Δp / Δz = -ρg
Vertically integrated to such a height where there is no matter above:
p = M g (M: mass above that height per unit area)
The balance approximately holds for horizontal scales > hundreds of km.
Pressure is often used as the vertical coordinate instead of height.
Global mean mass of air per unit area P_s / g = 1 × 10^4 kg/m^2
Average surface pressure (including mountains): P_s = 980 hPa
Acceleration of gravity: g = 9.8 m/s^2