The purpose of the investigation to be reported here differs in one essential respect from the purpose of most statistical studies on problems of communication. We wish to state this difference from the beginning, in order to avoid misunderstanding of the methods used later on. Most communication problems are, broadly speaking, engineering problems; that is, they deal with the construction and evaluation of new methods of communication, using one's knowledge of "Nature," acquired elsewhere. Our problem is, broadly speaking, physical; we seek to improve our knowledge, or at least our description, of "Nature" by using models in which some statistical concepts, developed in the study of recent communication problems, are used side by side with such concepts of physics as were already used to solve older engineering problems. This difference of purpose will also explain an unessential character of this paper: the calculations are much simpler than in other papers of the symposium, because here one could choose the problems leading to simple theories by the present methods (but not by previous ones), whereas in other papers the problems were imposed.