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Based on the time - dependent, lossless scalar wave equation interior losses and radiation losses are introduced by a dissipation function. This method is well - known from classical mechanics. To illustrate the mathematical procedure all aspects are studied by a mechanical system analogous to the optical wave field. Finally, the results are transferred to optics. By this means the physical meaning of the lossy operators that correspond to the operators E and HF of the lossless wave equation, becomes clear. These lossy operators are no longer self - adjoint and as a consequence, there is no action integral for the lossy equation but only a more general variational functional. Three examples and a discussion of the necessary approximations to be made conclude the subject.