  We investigate the effect of redshift-space distortions in the power spectrum
parallel and perpendicular to the observer's line of sight, P(k_par,k_perp),
using the optically selected Durham/UKST Galaxy Redshift Survey. On small,
non-linear scales anisotropy in the power-spectrum is dominated by the galaxy
velocity dispersion; the `Finger of God' effect. On larger, linear scales
coherent peculiar velocities due to the infall of galaxies into overdense
regions are the main cause of anisotropy. According to gravitational
instability theory these distortions depend only on the density and bias
parameters via beta. Geometrical distortions also occur if the wrong cosmology
is assumed, although these would be relatively small given the low redshift of
the survey. To quantify these effects, we assume the real-space power spectrum
of the APM Galaxy Survey, and fit a simple model for the redshift-space and
geometrical distortions. Assuming a flat Omega = 1 universe, we find values for
the one-dimensional pairwise velocity dispersion of sigma_p = 410 +- 170 km/s,
and beta = 0.38 +- 0.17. An open Omega = 0.3, and a flat Omega = 0.3, Lambda =
0.7 universe yield sigma_p = 420 km/s, beta = 0.40, and sigma_p = 440 km/s,
beta = 0.45 respectively, with comparable errors. These results are consistent
with estimates using the two-point galaxy correlation function, xi(sigma,pi),
and favour either a low-density universe with Omega ~ 0.3 if galaxies trace the
underlying mass distribution, or a bias factor of b ~ 2.5 if Omega = 1.
