An explanation is given of the advantages and the limitations of the arrangement whereby analytical and similar weights of accuracy approaching one part per million (for example, 0.1 mg on 100 g) are adjusted and tested on the basis of weighings in air without applying buoyancy corrections. The paper has been occasioned by a decision taken recently by a number of national standards laboratories, including the National Physical Laboratory, to base their weight-in-air tests, as from 1 July, 1959, exclusively on the densities 8.0 g/ml. for the weights and 0.0012 g/ml. for the air.