In the measurement of mental ability the most commonly accepted idea of equivalent units is that they are provided by the units of standard deviation for a series of measurements which distribute in the normal form. The meaning of these units may be understood by referring to Fig. 3 which shows Gaussian or normal distributions of abilities of individuals at various periods of life in curves A, B, C, D and E. The straight lines of the measurement scales form the bases of these distribution curves. These graphs represent the normal form of distribution usually expected when any fundamental ability is measured in a random group. If the number of cases at each unit of measurement are plotted by a point placed relatively as far above the scale, used as a base line, as the number of cases found at that unit of the scale, it will be discovered that these points arrange themselves in the form of a symmetrical curve high at the middle and flaring out along the base-line scale. This bell-shaped curve, known as a normal probability curve, shows that the largest number of cases occurs at the middle or average measurement. From this middle point on the scale the number of cases falls off gradually and symmetrically in both directions. Distances along the base line of this distribution surface may then be measured in terms of the standard deviation regarded as unity. This S. D. is the best measure of the scatter of the deviations. It is the square root of the average of the squares of the deviations of the separate measurements from the average of all the measurements. There are approximately four units of the standard deviation between the average and either extreme when the distribution is normal, as in Fig. 3. Only six cases in one hundred thousand fall outside these limits.