  Evidence that the fine structure constant, alpha, was different in an early
epoch has recently been found in quasar (QSO) absorption spectra. An accurate
laboratory measurement of alpha variation could help to distinguish between
space and time variation of alpha and possibly confirm the QSO results. We have
performed calculations of the relativistic energy shifts that a variation of
alpha would cause in a wide range of atomic spectra. A laboratory measurement
of how these transition frequencies vary over time is vital in determining
whether alpha is varying today.
