B. THE CURVES OF MENTAL DEVELOPMENT. When we endeavor to make our ideas of mental development more definite, we are assisted by thinking of the various stages in graphic form. This is especially true when trying to think of the position of the deficient individuals, relative to the average individuals and to genius. In diagrammatically presenting these concepts in Fig. 3 and Fig. 5 we do not wish to assume that all the principles on which the developmental curves have been plotted have been decided. If they make clearer the points still under discussion and direct the discussion to specific features so that more data may be brought to bear upon the empirical determination of their characteristics, they will serve a useful purpose. For our present ends, we shall consider only certain features which have a bearing upon the interpretation of developmental scales and the quantitative definition of the borderline. In the graphic presentation of the curves of development in Figures 3 and 5 the relative position at various ages has been suggested hypothetically for those of the best ability and median, or middle ability, as well as the borderline of the deficients. It is evident that these graphs should represent equivalent ability at each stage of development measured by as objective a scale of measurement as possible. In the graphs this scale is assumed to be composed of physical units with its zero at zero ability. The deficient group is distinguished by the portion with a grated shading. The distribution curves of individual ability we have already mentioned in connection with scales of measurement. Fig. 3 is constructed on the assumption of a normal distribution of ability at each age extending to the same zero ability. Fig. 5 on the assumption of distributions of varying form. Otis has given a very able logical analysis of certain concepts underlying the testing of mental development (_163_). His discussion differs from the present in its aim to determine the proper mental age for particular tests, a question which I have not considered. It also supplements the present discussion by showing the changing value of the same intelligence quotient with normal distributions of ability under certain assumptions as to range of ability and decrease in the annual increments of ability with age. (a) THE SIGNIFICANCE OF AVERAGE CURVES OF DEVELOPMENT. Some investigators are apparently inclined to question the significance of any curve of mental development on account of the very different forms of development which they have found in particular cases. A quotation from Goddard will state this problem: