  A method offering an order of magnitude sensitivity gain is described for
using quasar spectra to investigate possible time or space variation in the
fine structure constant, alpha. Applying the technique to a sample of 30
absorption systems, spanning redshifts 0.5 < z< 1.6, obtained with the Keck I
telescope, we derive limits on variations in alpha over a wide range of epochs.
For the whole sample Delta(alpha)/alpha = -1.1 +/- 0.4 x 10^{-5}. This
deviation is dominated by measurements at z > 1, where Delta(alpha)/alpha =
-1.9 +/- 0.5 x 10^{-5}. For z < 1, Delta(alpha)/alpha = -0.2 +/- 0.4 x 10^{-5},
consistent with other known constraints. Whilst these results are consistent
with a time-varying alpha, further work is required to explore possible
systematic errors in the data, although careful searches have so far not
revealed any.
