The fluctuation of an animal's numbers between restricted limits is determined by a balance between that animal's capacity to increase and the environmenta1 cheks to this increase. Many authors have indulged in the calculating the propressive increase of a population when no checks nrerc operating. Thus Huxley calculated that the progeny of a single Aphis in the course of 10 generations, supposing all survived,would “contain more ponderable substance than five hundred millions of stout men; that is, more than the whole population of China”, (in Thompson, 1929). Checks, however, do occur and it has been the subject of much controversy to determine how these checks operate. Certain general principles—the density-dependence concept of Smith ( 1955) , the competition theory of Nicholson (1933)—have been proposed both verbally and mathematically, but because they have been based in part upon untested and restrictive assumptions they have been severelv criticized (e.g. Andrewartha and Birch 1954). These problems could be considerably clarified if we knew the mode of operation of each process that affects numbers, if we knew its basic and subsidiary components. predation, one such process, forms the subject of the present paper.