The purpose of the S-diagrams is to give a rapid and convenient solution of the chief problems in astronomical navigation; they are especially simple for determination of altitude and azimuth. The solution is obtained without logarithms and by referring to no more than two pages of the diagrams. The diagrams are less expensive and more accurate than the Astronomisches Rechengerät (ARG), and are, without any doubt, less difficult to use than the Astronomische Rechenatlas. The method, which was recently mentioned in a paper by H. C. Freiesleben, may, therefore, be discussed here in some detail.