The transition matrix formulation of acoustic scattering given previously by Waterman [J. Acoust. Soc. Am. 45, 1417 (1969)] is extended to the case of an arbitrary number of scatterers. The resulting total transition matrix is expressed in terms of the individual transition matrices and in terms of functions which describe a translation of the origin for the spherical (and cylindrical) wave solutions of Helmholtz equation. Explicit formulas are given for the case of two and three scatterers and the (finite) iteration scheme for the general case is described. Some numerical calculations concerning some aspects of the scattering from two spheres are also reported.

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