The efficiency of use of radiant energy by cultures of algae is defined, and the physical variables upon which the efficiency depends are introduced. Expressions for the efficiency in a rectangular growth chamber are derived from considerations of an assumed mechanism of photosynthesis, the rate of respiration, and the conditions of agitation in the culture. Both unstirred and completely stirred cultures are considered. From the equations for efficiency in the two cases, methods are developed for finding the optimum physical conditions of light intensity, population density, length of light path, and temperature under which to propagate algae. In the unstirred culture, the treatment shows that a low light intensity is required; in the completely stirred culture, the treatment shows that a very high light intensity is required. The calculated efficiency is somewhat higher in the completely stirred case.