The relationship between the SI Ohm, the Ohm at NPL, and the quantized Hall resistance

New measurements relating the quantized Hall resistance RH(= h/ie²), International System (SI) Ohm (ΩSI), and the National Physical Laboratory maintained ohm (ΩNPL) have now been completed at NPL in the U.K. with improvements and simplifications in the cryogenic current comparator measurements and 1000-Ω dc resistance measurements. From the measurements over the past four years the relationship between ΩNPL and ΩSI can be described by the equation ΩNPL − ΩSI = −1.049(0.020) − 0.0478(0.0074)[t − 1986.0] μΩ in which t is measured in years. For the previous two years the equivalent relationship between RH and ΩNPL is RH = 25 812.8(1 + 1.452(0.038) × 10 ⁻⁶ + 0.0694(0.0772) · [t − 1986.0] × 10⁻⁶) ΩNPL in which the uncertainties (in parentheses) are one-standard-deviation (1σ) random uncertainties of the least squares fit to the data. Combining the most recent measurements of RH and ΩSI, using a more direct method of measurement RH = 25 812.8106(17) ΩSI in which the relative combined uncertainty is 0.067 × 10⁻⁶.