Atomic Clocks and Variations of the Fine Structure Constant

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