High-precision horizontally directed force measurements for high dead loads based on a differential electromagnetic force compensation system

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.

We determined the Newtonian Constant of Gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672 34 +/- 0.000 14) x 10^-11 m^3 kg^-1 s^-2. This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value of (6.672 59 +/- 0.000 85) x 10^-11 m^3 kg^-1 s^-2 [Rev. Mod. Phys. 59, 1121 (1987)] but differs from some more recent determinations as well as the latest CODATA recommendation of (6.674 28 +/- 0.000 67) x 10^-11 m^3 kg^-1 s^-2 [Rev. Mod. Phys. 80, 633 (2008)].