Acoustic Radiation from a spherical source eccentrically positioned within a fluid sphere embedded in another fluid is evaluated. This configuration is an idealization of a spherical acoustic lens used as a sound projector. To effect a solution, the translational addition theorem for spherical wavefunctions is used to express series of wavemodes centered at one sphere in terms of modes centered at the other, thereby facilitating the task of satisfying the boundary conditions. Because spherical wavefunctions centered at one point are not orthogonal over the surface of a sphere centered elsewhere, each mode associated with the first sphere couples into every one of the modes associated with the other. Hence, the evaluation of the modal coefficients in the series for the radiated pressure necessitates solving an infinite set of equations. Approximate solutions are obtained by truncating the set to finite size and solving numerically. The source radiation impedance and farfield directivity have been calculated for representative values of the many parameters that characterize the problem, such as wavelength size of fluid sphere and source, relative characteristic impedances and sound velocities of the two fluids, and position and velocity distribution of the source. [Research was supported by the Ordnance Research Laboratory under contract with the U. S. Naval Ordance Systems Command.]