Does the Surface Pressure Equal the Weight per Unit Area of a Hydrostatic Atmosphere?

The common statement that the surface pressure in a hydrostatic atmosphere is equal to the weight per unit area of the air aloft is shown to be true only for a Cartesian world. Here the unit area is the surface area of the base of the atmospheric column. For either a cylindrical or a spherical planet the surface pressure is always less than the weight per unit area of the overlying atmosphere. In these curved geometries, lateral pressure forces help support an individual column, thereby reducing the load carried by the surface pressure at the column's base. It is estimated that the surface pressure is a factor of 0.25% less than the weight per unit area of a resting atmosphere similar to that on Earth.