Abstract
A number of neutral-hydrogen-rich extragalactic objects avoid recognition because their optical brightness profiles lie close to or below the threshold for detection on survey plates. Recently, several such objects have been discovered by chance in observations that were designed for other purposes. The large volume of space that has been probed both by H I surveys that are targeted on normal galaxies and by "blind" surveys in the 21 cm line places constraints on the space density of these low surface brightness (LSB) objects. The space density of objects such as the "protogalaxy" reported by Giovanelli and Haynes and the giant H I ring system in Leo, which have M_HI_ of a few times 10^9^ M_sun_, appears to be about a factor of one hundred less than that of galaxies of comparable H I mass. Although giant H I-rich galaxies (M_H I_ ~10^11^ M_sun_) are rarer than L_*_ galaxies by more than a factor of 300, making it unlikely that one lies within 15 h^1^ Mpc of the Milky Way, several thousand such objects could be closer than the prototype, Malin 1. Evidence from H I surveys does not support the presence of a surge in the space density of LSB dwarfs with M_HI_ in the range 10^6^-10^8^ M_sun_. A substantial improvement in our understanding of the H I mass function of extragalactic objects in the local universe could be obtained by conducting a systematic survey with a telescope of quite modest aperture.
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