Boyle's Law, proposed by Robert Boyle in 1662, states that for a closed isothermal (constant temperature) system, the product of the pressure (P) and volume (V) is a constant,

Equivalently, the product at two different states must be the same,

where V is the reservoir volume and A is the cross-sectional area of the sealed tube, as shown schematically below.

Suppose that the final compressed pressure and volume are given by,

According to Boyle's law, we have,

For a typical manometer, . The unknown pressure P_i can be reduced to a function of the height difference h,

Furthermore, the volume of the reservoir is usually much larger than the tube,

This allows us to drop the area term, resulting in a simple quadratic function for the pressure,