New value for the Rydberg constant from the hydrogen Balmer-β transition

The Rydberg constant $R_{\infty }$ was determined to 3 parts in ${10}^{10}$ by direct comparison of the four H,D Balmer-β transitions with a National Bureau of Standards standard laser. This is the most precise value: $R_{\infty }$=109 737.315 73(3) ${\mathrm{cm}}^{\mathrm{-}1}$; it approaches the limits of accuracy for optical measurements. The fine-structure splittings and isotope shift are in excellent agreement with theory. The result agrees with less precise experiments by Zhao et al. and Biraben and Julien but disagrees with the result of Hildum et al.