In order to direct attention to the quantitative description of intellectual deficiency which is here proposed, let us state the percentage definition in its most general form. _Individuals whose mental development tests in the lowest X per cent. of the population are_ PRESUMABLY INTELLECTUALLY DEFICIENT, _unless their deficiency is caused by removable handicaps_. Above these is a group of Y per cent. within which the diagnosis of intellectual deficiency is uncertain on the basis of our present tests. The size of the presumably deficient X group is to be determined by the number of intellectually weak which society is at present justified in indefinitely isolating. The doubtfully deficient Y group should include all those who are so intellectually deficient as to be expected to need assistance indefinitely. _The feeble-minded, or_ MENTALLY DEFICIENT, _are those who require social care indefinitely because of deficiency in mental development_. They include the X group, that portion of the doubtful Y group which is found to require isolation, guardianship or social assistance, and any others not detected by the tests but requiring prolonged social care on account of their failure to develop mentally. Under the principle which we stated at the close of the last section the combination of Y ability and persistent serious delinquency brings the case within the group presumed to be feeble-minded. Besides the greater definiteness and significance of such a definition of intellectual deficiency, it affords the simplest practical criterion for determining the borderline of passable intellects with a scale of mental tests. A detailed comparison of the percentage plan with other forms of quantitative definition will be found in Part Two. We may note here, however, that it guards against a number of the absurdities of current descriptions of the borderline with measuring scales. It is a criterion which may be consistently applied to the borderline of both the immature and the mature. It may be adapted with comparative ease to any system of tests. It aids in comparing the frequency of intellectual deficiency among different groups, for example, among different types of delinquents, regardless of whether the investigators have used the same series of tests, provided only that each series has been standardized for similar random groups. Any form of quantitative definition, on the other hand, involves certain assumptions which must be defended before it can claim to be of advantage for practical purposes. B. THE ASSUMPTIONS OF A QUANTITATIVE DEFINITION. (a) DEFICIENCY IS A DIFFERENCE IN DEGREE NOT IN KIND.