Atomic Clocks and Variations of the Fine Structure Constant

We describe a new test for possible variations of the fine structure constant $\ensuremath{\alpha}$ by comparisons of rates between clocks based on hyperfine transitions in alkali atoms with different atomic number $Z$. H-maser, Cs, and Hg ${}^{+}$ clocks have a different dependence on $\ensuremath{\alpha}$ via relativistic contributions of order $(Z\ensuremath{\alpha}{)}^{2}$. Recent H-maser vs ${\mathrm{Hg}}^{+}$ clock comparison data improve laboratory limits on a time variation by 100-fold to give $\stackrel{\ifmmode \dot{}\else .\{}.fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}\ensuremath{\le}3.7\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}14}/$yr. Future laser cooled clocks (Be ${}^{+}$, Rb, Cs, Hg ${}^{+}$, etc.), when compared, will yield the most sensitive of all tests for $\stackrel{\ifmmode \dot{}\else .\{}.fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$.