  We re-examine the effects of redshift space distortion in all-sky galaxy
redshift surveys in the formalism of spherical harmonics. Within this framework
we show how one can treat both the large-scale linear effects, and the
small-scale nonlinear clustering, exactly to first order. The method also
allows in principle a determination of the power spectrum of perturbations,
requiring no assumptions beyond that of linear theory. The method therefore
offers significant advantages over Fourier techniques when dealing with all-sky
surveys. We apply our likelihood analysis to both simulated data, and real
data, using the IRAS 1.2-Jy galaxy catalogue, for which we find a maximum
likelihood $\beta \simeq 1.1\pm 0.3$, and a real-space fluctuation amplitude
corresponding to $\sigma_{8,{\rm IRAS}} = 0.68\pm 0.05$.
