  We reconsider the Re187 bound on the variation of the fine-structure
constant. We combine the meteoritic measurement with several present-day lab
measurements to firmly establish the quantitative upper limit to the time
variation over the age of the solar system. We find that the relative change of
the fine-structure constant between its present value and $\alpha$ of \sim 4.6
Gyr ago is consistent with zero, Delta alpha/alpha = [-8\pm 8 (1\sigma)] x
10^{-7}.
  We also rederive this bound in models where all gauge and Yukawa couplings
vary in an interdependent manner, as would be expected in unified theories.
