becomes: If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain. where the subscript n indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now: where ρs is the density of the sample. The ratio of the sample and water forces is: This is called the apparent relative density, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a hydrometer (the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does RDA depend on the actual volume of the pycnometer. Further manipulation and finally substitution of RDV, the true relative density (the subscript V is used because this is often referred to as the relative density ), for ρs/ρw gives the relationship between apparent and true relative density: In the usual case we will have measured weights and want the true relative density. This is found from Since the density of dry air at 101.325 kPa at 20 °C is 0.001205 g/cm3 and that of water is 0.998203 g/cm3 we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where the relative density of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller. The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and ASTM standard: ASTM D854. Types Gay-Lussac, pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 mL as above, with ground-in thermometer, adjusted, side tube with cap Hubbard, for bitumen and heavy crude oils, cylindrical type, ASTM D 70, 24 mL as above, conical type, ASTM D 115 and D 234, 25 mL Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL Digital density meters Hydrostatic Pressure-based Instruments: This technology relies upon Pascal's Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between