  When the 2dF QSO Redshift Survey (2QZ) is complete, a powerful geometric test
for the cosmological constant will be available. By comparing the clustering
along and across the line of sight and modelling the effects of peculiar
velocities and bulk motions in redshift space, geometric distortions, which
occur if the wrong cosmology is assumed, can be detected.
  In this paper we investigate the effect of geometric and redshift-space
distortions in the power spectrum parallel and perpendicular to the observer's
line of sight. Ballinger et al. developed a model to estimate the cosmological
constant, $\Lambda$, and the important parameter $\beta \approx
\Omega_m^{0.6}/b$ from these distortions. We apply this model to a detailed
simulation of the final 25k 2QZ, produced using the Virgo Consortium's huge
{\it Hubble Volume} N-body $\Lambda$-CDM light cone simulation. We confirm the
conclusions of Ballinger et al.; the shape of the redshift-space and geometric
distortions are very similar. When all the uncertainties are taken into account
we find that only a joint $\Lambda - \beta$ constraint is possible.
  By combining this result with a second constraint based on mass clustering
evolution, however, we can make significant progress. We predict that this
method should allow us to constrain $\beta$ to approximately $\pm0.1$, and
$\Omega_{m}$ to $\pm0.25$ using the final catalogue. We apply the method to the
2QZ catalogue of 10000 QSOs and find that this incomplete catalogue marginally
favours a $\Lambda$ cosmology.
