The number, luminosity, and mass density of spiral galaxies as a function of surface brightness

I give analytic expressions for the relative number, luminosity, and mass density of disc galaxies as a function of surface brightness. These surface brightness distributions are asymmetric, with long tails to lower surface brightnesses. This asymmetry induces systematic errors in most determinations of the galaxy luminosity function. Galaxies of low surface brightness exist in large numbers, but the additional contribution to the integrated luminosity density is modest, probably 10 – 30%.