Observe the manometer when you vary the temperature of the gas.
Remember that the pressure at two points  in the tube situated at the same height is the same: p_A = p_B
Pressure at point A is that due to the atmosphere and to the column of liquid above A, of a height h.
The pressure at point B is due to the gas.
P_{pressure of the gas} = P _atm. + d_liquid ·g · h

To calculate the manometric pressure
p = d_liquid ·g · h, you only need to measure h, as the density of the liquid in the manometer is known.

In manometers you don't have to calculate this as there is a calibrated scale in pressure units on branch A.
It should be remembered that what the manometer measures is the so-called manometric pressure, which is the value of the pressure of the gas once atmospheric pressure has been deducted.