New Tests for Variations of the Fine Structure ConstantWe describe a new test for possible variations of the fine structure constant, by comparisons of rates between clocks based on hyperfine transitions in alkali atomos with different atomic number Z. H- maser, Cs and Hg+ clocks have a different dependence on ia relativistic contributions of order (Z. Recent H-maser vs Hg+ clock comparison data improves laboratory limits on a time variation by 100-fold to giveFuture laser cooled clocks (Be+, Rb, Cs, Hg+, etc.), when compared, will yield the most senstive of all tests for.