Simultaneous determination of mass and volume of a standard by weighings in air

Volume is an input quantity in the measurement model for the mass of a body, say, a mass standard. The classical method to determine volume, hydrostatic weighing, is time-consuming, expensive and can introduce instability in the standard mass. Some years ago an alternative method was proposed, based on weighings in air at different densities. We generalize the method, showing that also the mass of the standard can be determined with it using a weighted-least-squares adjustment. To this purpose, we discuss a measurement model taking into account the covariances between the input estimates. The method, experimentally validated, yields uncertainties for the mass estimates that are smaller than those obtained with the traditional method, and gives the further advantage of directly providing the covariance between mass and volume.