The Patterson-synthesis

In a recent publication1 the author has given a brief account of a new method for the direct determination of the components of interatomic distances in crystals. The method is based on the application of the results of the theory of Fourier series. It is the object of the present paper to give a more detailed account of the underlying theory and to describe the application of the method to specific examples. In addition, two new results are presented which promise to increase the usefulness of the method for the investigation of complex structures.