ESS101C
Prof. Jin-Yi Yu
Balance  of Force in the Vertical: Hydrostatic Balance
Vertical pressure force =  Gravitational force
              - (dP) x (dA) = r x (dz) x (dA) x g
                              dP =  -rgdz
 
Since P= rRT,
                              dP =  -P/RT x gdz
                           dP/P =  -g/RT x dz
                                P =  Ps exp(-gz/RT)
(from Climate System Modeling)