If we disregard the natural antipathy of many people to anything which tends to limit the charming vagueness of their mental outlook, we may endeavor to chart this horizon of tested deficiency with something of the definiteness of figures, which shall at the same time indicate a range of error. As soon as our aim comes to be to plot the borderline on a measuring scale of mental ability, we find that the borderline must be so stated that we can deal with either adults or children. Two sorts of limiting regions must be described, one for mature minds and one for immature minds. The latter will be in the nature of a prediction as to what sort of ability the children will show when they grow up. We must keep in mind, therefore, that we should attempt our quantitative definition for both growing and adult minds. As soon as the growing mind passes the lower limit for the mature it is then guaranteed access to the social seas although it may never swim far from shore nor develop further with advancing years. In seeking greater definiteness, our aim should then be to describe both the limit for the mature individuals and the limit for the immature of each age. In this paper the definition will be restricted to _intellectual deficiency_, _i. e._, tested deficiency. It will take the form of describing _the positions on a scale below which fall the same lowest percentage of intellects_. This percentage definition of intellectual deficiency offers such a simple method of consistently describing the borderlines for mature and immature that it is surprising so little attempt has previously been made to work it out for a system of tests. Although the principle on which the definition is based depends upon the distribution curve of ability, it is concerned only with the lower limit of the distribution. Since the exact form of this distribution is uncertain I have preferred to call it a percentage definition of intellectual deficiency rather than to state the limits in terms of the variability of ability. Moreover the lowest X per cent. in mental development requires no further explanation to be understood by the layman. B. FORMS OF MENTAL DEFICIENCY NOT YET DISCOVERABLE BY TESTS.