  Ground-state hyperfine splittings in hydrogen and muonium are very well
measured. Their difference, after correcting for magnetic moment and reduced
mass effects, is due solely to proton structure--the large QED contributions
for a pointlike nucleus essentially cancel. The rescaled hyperfine difference
depends on the Zemach radius, a fundamental measure of the proton, computed as
an integral over a product of electric and magnetic proton form factors. The
determination of the Zemach radius, (1.043 +/- 0.016) fm, from atomic physics
tightly constrains fits to accelerator measurements of proton form factors.
Conversely, we can use muonium data to extract an ``experimental'' value for
QED corrections to hydrogenic hyperfine data; we find that measurement and
theory are consistent.
