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While the problem of the multiple scattering of particles by a random distribution of scatterers has been treated classically through the use of the Boltzmann integro-differential equation, the corresponding problem of the multiple scattering of waves seems to have received scant attention. All previous treatments have considered the problem in the "geometrical optics" limit, where the rays are regarded as trajectories of particles and the treatment for particles is then applied, so that the interference phenomena in wave scattering are neglected. In this paper the problem of the multiple scattering of scalar waves by a random distribution of isotropic scatterers is considered in detail on the basis of a consistent wave treatment. The introduction of the concept of "randomness" requires averages to be taken over a statistical ensemble of scatterer configurations, Equations are derived for the average value of the wave function, the average value of the square of its absolute value, and the average flux carried by the wave. The second of these quantities satisfies an integral equation which has some similarities to the corresponding equation for particle scattering. The physical interpretation of the results is discussed in some detail and possible generalizations of the theory are outlined.INTRO DUCTIO N HE problem of the multiple scattering of particles by a random distribution of scatterers has been treated in some detail in literature. ' These treatments are all based essentially on the Boltzmann integro-differential equation of conservation in phase space and are thus classical rather than. quantum-mechanical in foundation. On the other hand, a consistent treatment, based on the wave equation itself, of the multiple scattering of waves by a randomly distributed collection of scatterers, has not, to the writer's knowledge, yet appeared in liter3.ture. Those treatments which have appeared, for example, in discussions of the problem of the propagation of light through stellar atmospheres and through turbid media, ' are all based on the * Publication assisted by Ernest

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