With unknown or varying types of distribution it is desirable to utilize percentiles as equivalent units for comparing individuals at different stages of development. They differ somewhat from ranks in an order of noticeable differences. With an indefinitely large group, such ranks would mark off only those cases which were indistinguishable in merit. These units would be numbered in order from the highest to the lowest in ranks of just distinguishable merit, a different number of individuals conceivably occurring at the single steps. Psychologically the percentiles are somewhat less significant because they are not conceivable in steps of just noticeable differences. Percentiles have less value in _comparing abilities in the same distribution_, but have decided advantages when _comparing corresponding abilities in different distributions_. Except at points where merit is indistinguishable, they signify that a certain proportion of a group is ahead in the struggle for existence. They are thus units of relative rank. Moreover, they are directly translatable into units of the deviation in case the form of the distribution of ability has been determined. This is a special advantage if the forms of distribution turn out to be normal or even uniform. In using percentiles it is to be remembered that equal differences between percentiles _are not comparable in the same distribution_ except in the sense of the same extra proportions of the group to be met in competition. A change in the degree of ability from the lowest percentile to the lowest 2 percentile would be very different from the change in the degree represented by the 50 percentile to the next percentile above. Differences in the ability of individuals ranking near each other in the middle of the same percentile series would be distinguished with difficulty while it would be easy to make such discriminations at the extremes. The special value of the percentile units in measurement of ability lies in the comparison of individuals of corresponding position in corresponding groups in which the ability may not be assumed to distribute alike. The concept that 995 out of every 1000 randomly selected individuals at his age are ahead of a particular individual in the struggle for existence has very definite and significant meaning which is quite comparable from one period of life to another regardless of the form of the distribution. We shall return to this question of equivalent units in distributions of unlike symmetry when we compare the definitions of the borderlines of deficiency in terms of intelligence quotient, coefficient of intelligence, standard deviation and percentage. Corresponding percentages of corresponding groups have a more useful definite significance of equivalence than any other units of measurement of mental ability available when the forms of distribution vary at different stages of development or are uncertain, as seems to be true with tested abilities.