  If the reported measurements of the time variation of the fine structure
constant from observations of distant QSOs are correct, combined with the Oklo
limit they would strongly constrain the class of the quintessence potential. If
these results prove valid, future satellite experiment (STEP) should measure
the induced violation of the weak equivalence principle. Future cosmological
observations of nearby $(z \siml 0.5)$ absorption systems would make it clear
whether the variation is significant or not.
