In a previous communication (Barclay and Kermack, 1938) it has been shown that the specific legitimate fertility rates of Sweden and Denmark, viewed broadly over several decades, exhibit well-marked regularities, briefly described as conformity to a “diagonal law.” The procedure is to express the specific fertility rate, observed for any particular age-group at a certain period, as a percentage of the rate for the same age-group at a time preceding the decline of the birth-rate (“standard rate”). If now these percentages are plotted as contours on a graph, in which the abscissæ represent calendar years and the ordinates women's age, it is found that, when the age-group 15–20 is excluded, the constant percentage curves are approximately straight lines, running parallel to the diagonals in such a sense that, along any line, increase in calendar years corresponds to decrease in women's age. In Finland, the same general effect is apparent, though it is somewhat obscured by minor disturbances. It is found that, in the case of England and Wales, predictions made on the basis of the law give a reasonable agreement with estimated fertility rates calculated by the Registrar-General on the basis of census data.