We present in Fig. 8 a graph from E. L. Thorndike, showing the number of 10-year-old children in Connecticut (1903) in each school grade. If the children are all intellectually equal, all the 10-year-olds ought to be in the same grade, or near it. Numerous explanations of their wide distribution suggest themselves; as a working hypothesis one might adopt the suggestion that it is because the children actually differ in innate ability to the extent here indicated. This hypothesis can be tested by a variety of mental measurements. S. A. Courtis' investigation of the arithmetical abilities of the children in the schools of New York City will be a good beginning. He measured the achievements of pupils in responding to eight tests, which were believed to give a fair idea of the pupil's capacity for solving simple arithmetical problems. The results were, on the average, similar to the result he got in a certain eighth-grade class, whose record is shown in Fig. 9. It is evident that some of the children were good in arithmetic, some were poor in it; the bulk of them were neither good nor bad but half way between, or, in statistical language, mediocre. [Illustration: VARIATION IN ABILITY FIG. 9.--Diagram to show the standing of children in a single class in a New York City school, in respect to their ability in arithmetic. There are wide divergences in the scores they made.] The literature of experimental psychology and anthropology is crammed with such examples as the above. No matter what trait of the individual be chosen, results are analogous. If one takes the simplest traits, to eliminate the most chances for confusion, one finds the same conditions every time. Whether it be speed in marking off all the A's in a printed sheet of capitals, or in putting together the pieces of a puzzle, or in giving a reaction to some certain stimulus, or in making associations between ideas, or drawing figures, or memory for various things, or giving the opposites of words, or discrimination of lifted weights, or success in any one of hundreds of other mental tests, the conclusion is the same. There are wide differences in the abilities of individuals, no two being alike, either mentally or physically, at birth or any time thereafter. [Illustration: ORIGIN OF A NORMAL PROBABILITY CURVE FIG. 10.--When deviations in all directions are equally probable, as in the case of shots fired at a target by an expert marksman, the "frequencies" will arrange themselves in the manner shown by the bullets in compartments above. A line drawn along the tops of these columns would be a "normal probability curve." Diagram by C. H. Popenoe.] Whenever a large enough number of individuals is tested, these differences arrange themselves in the same general form. It is the form assumed by the distribution of any differences that are governed absolutely by chance.