  Using the OPAL detector at LEP, the running of the effective QED coupling
alpha(t) is measured for space-like momentum transfer from the angular
distribution of small-angle Bhabha scattering. In an almost ideal QED
framework, with very favourable experimental conditions, we obtain:
  Delta alpha(-6.07GeV^2) - Delta alpha(-1.81GeV^2) = (440 pm 58 pm 43 pm 30) X
10^-5, where the first error is statistical, the second is the experimental
systematic and the third is the theoretical uncertainty. This agrees with
current evaluations of alpha(t).The null hypothesis that alpha remains constant
within the above interval of -t is excluded with a significance above 5sigma.
Similarly, our results are inconsistent at the level of 3sigma with the
hypothesis that only leptonic loops contribute to the running. This is
currently the most significant direct measurment where the running alpha(t) is
probed differentially within the measured t range.
