  Using the OPAL detector at LEP, the running of the effective QED coupling
alpha(t) is measured for space-like momentum transfer, 2 \leq -t \leq 6 GeV^2,
from the angular distribution of small-angle Bhabha scattering. This is
currently the most significant direct observation of the running of the QED
coupling in a single experiment and the first clear evidence of the hadronic
contribution to the running in the space-like region. Our result is in good
agreement with standard evaluations of alpha(t), based on data in the time-like
region.
