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

New measurements relating the quantized Hall resistance R
H
(= h/ie
²
), International System (SI) Ohm (Ω
SI
), and the National Physical Laboratory maintained ohm (Ω
NPL
) 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 Ω
NPL
and Ω
SI
can be described by the equation Ω
NPL
− Ω
SI
= −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 R
H
and Ω
NPL
is R
H
= 25 812.8(1 + 1.452(0.038) × 10
⁻⁶
+ 0.0694(0.0772) · [t − 1986.0] × 10
⁻⁶
) Ω
NPL
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 R
H
and Ω
SI
, using a more direct method of measurement R
H
= 25 812.8106(17) Ω
SI
in which the relative combined uncertainty is 0.067 × 10
⁻⁶
.