  We determine the Zemach moments of hydrogen and deuterium for the first time
using only the world data on elastic electron-proton and electron-deuteron
scattering. Such moments are required for the calculation of the nuclear
corrections to the hyperfine structure of these hydrogenic atoms. We compare
the resulting HFS predictions to the available high-precision data and provide
an estimate of the size of the nuclear polarization corrections necessary to
produce agreement between experimental HFS and theoretical calculations.
