in each luminosity range than in the earlier publications. This factor of two uncertainty can be propagated through the subsequent estimates for volume densities and densities per solid angle.

Profile width and detectability at large redshift
-------------------------------------------------

The integral line flux observed from a cosmologically distant emitter at redshift $z$ is (Wieringa et al 1992) $$\begin{aligned}
S &=& \frac{L_{OH}}{4\pi d_L^2}
\label{cosmflux.eqn}\\
&=& \frac{L_{OH}}{\pi}\left(\frac{H_o}{4c}\right)^2
\frac{\Omega_o^4}
     {[\Omega_oz+(\Omega_o-2)(\sqrt{1+\Omega_oz}-1)]^2}\nonumber\end{aligned}$$ where $d_L$ is the luminosity distance, $H_o$ is the Hubble constant and $\Omega_o$ is the cosmological mass density normalized to the critical density. If the line of width $\Delta V$ km s$^{-1}$ is emitted at rest frequency $\nu_o$ and redshifted to $\nu= \nu_o/(1+z)$, the observed frequency width of the line will be $\Delta\nu \approx  \nu\,\Delta V/c$, providing an average flux density over the line profile of $S_{\nu}\approx S/\Delta\nu\propto S(1+z)$. Thus, the line width is squeezed in frequency as a line of velocity width $\Delta V$ is observed toward higher redshifts, leading to a partial compensation for the reduction in the integral line flux by the inverse square law (Eq.(\[cosmflux.eqn\])), The range of line widths observed for OH megamaser galaxies is illustrated in Fig. \[velwid.fig\], where the line width is plotted as a function of maser 