Since the quantum Hall resistance (QHR) measured with alternating current (ac) has reached the state of an excellent quantum standard of impedance, we have realized a quadrature bridge with two ac QHRs to accurately calibrate capacitance standards in terms of the SI value of the von-Klitzing constant, without the need for any calculable artefact. The advantages of the realized measuring chain, experimental tests of the coaxial ac bridges involved and the achieved relative uncertainty of 6 × 10 −9 (k = 1) are discussed.

A new coaxial measurement system has been developed to investigate the ac longitudinal resistance along the high-potential side of the quantum Hall resistance (QHR). A novel equivalent circuit of the QHR is used to analyse the ac measurements of the longitudinal resistances along both the low-and high-potential sides of the QHR sample. In addition, a bridge for the measurement of ac contact resistances of the sample is presented. For the first time, it is now possible to perform all the ac measurements whose dc equivalents are well established for reliable dc quantum Hall measurements. While the ac longitudinal resistances on the high-and low-potential sides of the sample are very similar, interesting differences have been observed at high resolution.

A precision measurement of the gravitational constant G has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) ×10 −11 m 3 kg −1 s −2 . The relative statistical and systematic uncertainties of this result are 16.3×10 −6 and 8.1 ×10 −6 , respectively.

The quantum Hall resistance measured at frequencies in the kilohertz range shows frequency- and current-dependent deviations from the quantized dc resistance value. This has been attributed to capacitive effects which are reflected in the ac longitudinal resistance. Nulling the ac longitudinal resistance results in a frequency- and current-independent quantum Hall resistance. This criterion is in close analogy to the dc case and shows that the quantum Hall effect measured with ac is the same as with dc. This allows application as a primary standard of impedance.

We present a new method to measure the gravitational constant G. A beam balance compares the weight of two 1-kg test masses and measures the gravitational force of two field masses with a statistical uncertainty of 10 ng. Two vessels in a refined arrangement are used as field masses. They have been filled with water as a test. G has been determined with an uncertainty of 240 ppm. The next step is to fill the vessels with mercury. Because of the larger signal and further refinement of our experiment, we hope to reach the design uncertainty of 10 ppm. [S0031-9007 (97)05223-X] PACS numbers: 04.80.CcThe gravitational constant G is known with a relative uncertainty of only 128 ppm (part per million) while the uncertainty of all other fundamental constants is rapidly decreasing to values considerably below 1 ppm [1][2][3]. The most precise device for measuring the gravitational force is the torsion balance, first applied by Cavendish 200 years ago. Until 1890 beam balances were also used to measure the gravitational force [4][5][6]. The accuracy was limited to 0.16% at best [6], and these measurements were given up in favor of the torsion balance. During past few decades, no essential progress of the technique for measuring G has been made. Recent attempts with different techniques failed to improve the uncertainty of G [7-9]. The current results, as well as several former results, show unexplained discrepancies. No significant deviations from Newton's gravitational law were found experimentally. The most obvious explanation is, therefore, systematic errors even for the traditional torsion balance technique [10,11].In order to overcome this situation, we proposed a new experiment. It is based on a beam balance which is a suitable device for measuring the gravitational force [12]. The idea of this experiment and the experience on how to operate the balance is based on our successful storage lake experiment, where the gravitational force of water has been measured in order to test Newton's inverse-square law [13,14]. This new experiment is a modern variation of the method used by von Jolly [5] and Richarz and Krigar-Menzel [6]. Our first results have already provided a significant accuracy improvement over the earlier beambalance experiments. This is possible because of a different method and the general progress grained in mechanics, automation, and weighing techniques.The principle of our new experiment is shown in Fig. 1: To large masses are moved in the vertical direction and alternately positioned in one of two states. Their gravitational field acts on two small test masses which are separately suspended on wires. The suspension devices of the test masses are alternately connected to a single-pan beam balance which measures the weight change due to the gravitational force. The arrangement of two test and field masses is symmetrical and en-ables a differential measurement such that many disturbing forces and drift effects cancel each other out.The field masses have a cylindrical shape. They have an axial bore in orde...