One of the basic dependent variables in the sociology of science is the rate at which scientific knowledge advances. Sociologists of science have in the past assumed that the rate of scientific advance was a function of the number of talented people entering science. This assumption was challenged by Derek Price who argued that as the number of scientists increased the number of high quality scientists would increase at a slower rate. This paper reports the results of an empirical study of changes in the size of academic physics in the U. S. between 1963 and 1975. In each year we count the number of new Assistant Professors appointed in Ph. D.-granting departments. During the early 1960s there was a sharp increase in the size of entering cohorts followed by a sharp decline. A citation analysis indicates that the proportion of each cohort publishing work which was cited at least once in the first three years after appointment was relatively constant. This leads to the conclusion that the number of scientists capable of contributing to the advance of scientific knowledge through their published research is a linear function of the total number of people entering science.