In the $L_{60}>>L_{60}^*$ regime, which will characterize the hosts of the brightest OH line emitters, $\Phi(L_{60})$ may be approximated as $$\label{phiapprox.eq}
\Phi(L_{60}) \approx 
  C(\alpha+\beta)L_{60}^{*-1}(L_{60}/L_{60}^*)^{-(\alpha+\beta+1)}.$$

The effective OH luminosity function $\Theta(L_{OH})$
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The strong correlation between OH and 60$\mu$m luminosity, $L_{OH}\propto L_{60}^2$ (cf. Baan et al, 1992a) provides a way to recast the 60$\mu$m luminosity function for luminous FIR galaxies to obtain an OH megamaser luminosity function $\Theta(L_{OH})$ as shown in Fig. \[OHLumfnct.fig\]. In this paper, this has been accomplished in two complementary ways: one by numerical integration of $\Phi(L_{60})$ to obtain the number of OH sources falling in logarithmically spaced bins of $L_{OH}$, and the second by noting that the masers that are detectable at cosmological distances inhabit host galaxies that are far more luminous than $L_{60}^*$ and then using the approximation in Eq.(\[phiapprox.eq\]) to derive an analytic expression.

The advantages of computing $\Theta(L_{OH})$ numerically are that it (1) simplifies inclusion of the spread of OH luminosities in a band of width ${\sim}10^{{\pm}0.7}$ about the $L_{OH}\propto L_{60}^2$ relation (Baan et al 1992a), and (2) allows for varying the probability $f_m$ that luminous FIR galaxies will appear to be megamasers as a function of $L_{60}$. Here, the range of FIR luminosities 