  Theories unifying gravity with other interactions suggest spatial and
temporal variation of fundamental "constants" in the Universe. A change in the
fine structure constant, alpha, could be detected via shifts in the frequencies
of atomic transitions in quasar absorption systems. Recent studies using 140
absorption systems from the Keck telescope and 153 from the Very Large
Telescope, suggest that alpha varies spatially. That is, in one direction on
the sky alpha seems to have been smaller at the time of absorption, while in
the opposite direction it seems to have been larger.
  To continue this study we need accurate laboratory measurements of atomic
transition frequencies. The aim of this paper is to provide a compilation of
transitions of importance to the search for alpha variation. They are E1
transitions to the ground state in several different atoms and ions, with
wavelengths ranging from around 900 - 6000 A, and require an accuracy of better
than 10^{-4} A. We discuss isotope shift measurements that are needed in order
to resolve systematic effects in the study. The coefficients of sensitivity to
alpha-variation (q) are also presented.
