  We reevaluate the hadronic part of the electromagnetic vacuum expectation
value using the standard dispersion integral approach that utilizes the
hadronic cross section measured in $\ee$ experiments as input. Previous
analyses are based upon point-by-point trapezoidal integration which has the
effect of weighting all inputs equally. We use a technique that weights the
experimental inputs by their stated uncertainties, includes correlations, and
incorporates some refinements. We find the hadronic contribution to the
fractional change in the electromagnetic coupling constant at $q^2=M_Z^2$ to be
$0.02666\pm0.00075$, which leads to a value of the electromagnetic coupling
constant, $\alpha^{-1}(M_Z^2) = 129.08\pm0.10$. This value significantly shifts
the Standard Model predictions for the effective weak mixing angle measured at
the $Z$ pole and moderately shifts the predicted $Z$ width.
