ECENTLY Dr. Milner B. Schaeffer (1943) has made a contribution to our knowledge concerning the relationship between fishing effort and fish mortality. His results lead him to suggest that parts of the writer's 1940 paper, on the same general topic, stand in need of revision. Though the basis of this criticism is apparently Schaeffer's misunderstanding of the definition of "uniform recruitment," the need for revision is a real one. A number of developments have made this clear. In addition to Schaeffer's work, an inconsistency has been found by Mr. Ralph P. Silliman, in the course of recent efforts to apply the formulae to a west-coast fishery, and another was adumbrated in some correspondence from Mr. Michael Graham. What has done most to clarify the various problems in the writer's mind, however, is the perusal for the first time of the text of Baranoff's (1918) pioneer work in this field, in which the "modern theory of fishing" appears, practically in its present form, and applied to the plaice fisheries of the North Sea. The mistakes in the 1940 paper could equally well be regarded as approximations. Considered in that light, they are sufficiently close to reality that none of the general conclusions based on them are invalidated when a more rigorous treatment is applied to the same questions. Nevertheless it seems worth while to take this opportunity of developing more exact calculations, since it is conceivable that the approximate methods may not always be serviceable. In addition, it will be useful to give a resume of the various concepts used by Baranoff and some later writers, with their mutual interrelationships in various types of fisheries, and to develop these relationships somewhat farther than they have yet been carried. In the earlier paper two types of fish population were set up for analysis, and these will still serve as a useful point of departure. In populations of type I natural mortality and recruitment were presumed to be negligible during the fishing season. In type II both natural mortality and recruitment were present, the latter occurring at a uniform rate throughout the season-which meant the same absolute number of recruits added per day. Schaeffer (1943) has treated fisheries in which recruitment is absent, but natural mortality is present. We will call this situation type IB, assigning the modified label IA to the original type I. It would seem that type IB populations will rarely be found in nature, for if fishing extends over a period long enough for natural mortality to be appreciable, there will usually also be appreciable recruitment during that period. Nevertheless, a population of this sort may sometimes be under consideration when a group of tagged or marked fish is being studied, and consequently it is of some practical importance in research. It may be observed too that the fisheries postulated in a paper by Thompson and Bell (1934) are essentially of type IB; for in them recruitment (and, as we shall see, growth also) takes place exclusively at a time of year other than that during which fishing and natural mortality occur. This anomaly makes