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Galaxy formation scenarios predict a burst of star formation in normal galaxies at a redshift between z D 2 and z D 6 (e.g., Katz & Gunn 1991); such a starburst may be accompanied by a signi-cant bright- ening of the j \ 158 km line of C`. Galaxies that will evolve to a total luminosity L * \ 5 ) 1010 in L _ the current era are considered at various redshifts. When the Cluminosity is evolved in accordance with a starburst scenario, the expected spectral line antenna temperature at the focus of a 10 m telescope is about 2 mK for galaxy models at redshifts up to that at which the starburst occurs. Such a spectral line is detectable with current submillimeter wavelength instrumentation at good submillimeter-wave sites like the South Pole. If the telescope were equipped with an array receiver and wide-bandwidth spectrometers (100 channels distributed over 5 GHz), a "" blank sky II survey for such objects would likely detect several hundred during a winter of observation. The number and distribution of detections would provide a sensitive test of galaxy formation models, even if protogalaxies are shrouded in dust and faint at near-infrared wavelengths. Most of the energy released in the collapse of protogalaxies and the -rst generations of star formation may appear at Earth as submillimeter-wave radiation; testing this hypothe- sis will necessarily require submillimeter-wave observations. Subject headings: early universe E galaxies: formation E infrared: galaxies E radio lines: galaxies

Potential Measurement of the Luminosity Function of 158 Micron [Cii] at High Redshifts: A Test of Galaxy Formation Models