Now suppose the atmosphere divided into layers of uniform thickness, but so thin that the density may be considered uniform throughout.
Let h = the thickness of each layer.
W = weight of a cubic foot of air at pressure H.
W₁ = weight of a cubic foot of air at H.
H₀ H₁, &c. = pressures measured in inches of mercury.
Then the pressure upon the unit of surface of any layer is greater than that upon the surface of next higher layer, by the weight of a volume of air whose base is the unit of surface and whose height is the thickness of the layer. If one foot be the unit of surface, then this quantity would be hW. And to express it by height of mercury column, it is necessary to multiply by
which gives
But W : W₀ : : H : 30.
W₀ being the weight of a cubic foot air at the level of the sea (=.0807 at 32°F).
We have from the above
