A new apparatus is being set up for measuring the density of mercury at 20 C with a relative uncertainty of 0.5 ϫ 10 -6 by hydrostatic weighing of a sinker of known volume and mass. Two small sinkers of about 50 cm 3 were calibrated by hydrostatic comparison with silicon density standards. Thus, in the first stage, a relative uncertainty of 2 ϫ 10 -6 of the mercury density can be reached. The quantity of mercury needed for the measurements is 1 l. Also, density comparisons of different mercury samples can be carried out with a relative uncertainty of 0.5 ϫ 10 -6 . To reach a relative uncertainty of 0.5 ϫ 10 -6 in the density of mercury, a 500 cm 3 hollow cube is to be manufactured from tantalum. Its volume will be determined by means of an interferometer, with a relative uncertainty of 0.15 ϫ 10 -6 . Measurements will be performed for the gravitation experiment of Zürich University using 1 m 3 of mercury, and for mercury samples used in primary pressure standards. Design and results of first tests of the hydrostatic weighing apparatus are reported.