Abstract

The derivation of the barometric equation concerns central forces in three dimensions. It has recently been shown that the sum of the incremental volume's side force components in the direction of the center of gravity (the ??(-2p z)(Dx)(Dy)(Dz)?? force) must be included in the Cartesian  rivation.That results in the side force component term (-2p z) being added to the differential equation, or dp dz=-??(NmMGz2 )+(2p z)??. Meteorological data does not, though, conform unambiguously to the corrected barometric equation.  This implies that an approximately compensating term might exist. Such a term results from consideration of the central force due to atmospheric particle random motion perpendicular to the radial from the center of gravity in a central force field (the ??+(2(f )p 3z)(Dx)(Dy)(Dz)?? force, where ?f? represents the degrees of freedom). The more-complete barometric equation is: dp dz= -(NmMG z2 )+??2(f-3)p3z??. .