Atomic Clocks and Variations of the Fine Structure Constant

We describe a new test for possible variations of the fine structure constant 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 via relativistic contributions of order (Z) ^2. Recent H-maser vs Hg^+ clock comparison data improve laboratory limits on a time variation by 100-fold to give \. {}/3. 710^-14/yr. Future laser cooled clocks (Be ^+, Rb, Cs, Hg ^+, etc. ), when compared, will yield the most sensitive of all tests for \. {}/.