The density p of two silicon crystals has been determined by precision hydrostatic weighing, based on very accurate solid density standards (SDS's). Densities of additional crystals were gained from density differences measured by the temperature-of-f1oatation method. The molar mass M of the crystals was determined by comparing the isotopic abundances against the known abundances of the National Bureau of Standards (NBS) reference material SRM 990 using activation analysis and mass spectroscopy. Combining the measured values for M and p leads to M / p = (12.058 822 ± 0.000 013) cnr' / mol. With the known volume of the unit cell the following value for the Avogadro constant was calculated: N A = (6.022 137 ± 0.000 007) x 10 23 mol-I.

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A mass comparator for the comparison of 1 kg weights was built according to a hydrostatic weighing principle, where the buoyancy in a liquid serves to compensate the force due to gravity. In accordance with the method known for hydrometers or areometers, the immersion depth of a float is measured as a function of the force due to gravity, using a laser interferometer. The substitution principle can thus be quite simply realized at constant load.An essential advantage of this weighing method compared with the mechanical beam balance results from the frictionless and vibration-resistant bearing of the float in the liquid. For achieving a high accuracy with this technique, two prerequisites were important: the reduction of the influence of temperature by adapting the coefficients of expansion of buoyant body and liquid to each other, and the improvement of the wetting property of the liquid by adding a surfactant. The accuracy was further improved by the use of an electromagnetic feedback control to keep the immersion depth constant. By this method, a relative standard deviation of the weighings of better than 5 x lo-' could be achieved.