Suppose that initial pressure and volume in a McLeod Gage are given by,
P_{1} = P_{i}V_{1} = V + A·h_{0}
where V is the reservoir volume and A is the crosssectional area of the sealed tube, as shown schematically below.
Suppose that the final compressed pressure and volume are given by,
P_{2} = P_{gage}V_{2} = A·h
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,
V » A·(h_{0}h)
This allows us to drop the area term, resulting in a simple quadratic function for the pressure,
