Atomic Clocks and Variations of the FIne Structure Constant

We describe a new test for possible variations of the fine structure constant 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 alpha via relativistic contributions of order (Z-alpha)(sup 2). Recent H-maser vs Hg(+) clock comparison data improve laboratory limits on a time variation by 100-fold to give dot-alpha less than or equal to 3.7 x 10(exp -14)/yr. Future laser cooled clocks (Be(+), Rb, Cs, Hg(+), etc.), when compared, will yield the most sensitive of all tests for dot-alpha/alpha.