The research reported in this document represents only one phase of the two-year work on water waves in thermally stratified lakes and long rivers. The purpose of the study is to develop a systematic method for calculating the resonance frequencies of water bodies with shorelines as generally encountered in oceangraphical or hydraulic problems. The approach is based upon the so-called geometrical optics method, or ray method, originally developed for the study of electromagnetic wave propagation. The application of this method to water waves is of quite recent orgin, and, as the research has shown, further developments of this method for surface wave problems are very promising. (Author)