The boy D, of IQ 184, was described first by Terman, in _The Intelligence of School Children_. His achievements are most remarkable in every kind of intellectual activity, including music and drawing. Among his favorite pastimes since infancy has been the manipulation of numbers. His calculations, dating from the time his hand could wield a pencil, have covered hundreds of pages. As a child of 7, 8, and 9 years, D found the keenest satisfaction in deriving formulæ to render himself unbeatable at family games based on number. At the age of 12 years he has completed the mathematical curriculum of the elementary and secondary schools, through arithmetic, algebra, geometry, and trigonometry. (It should be added that he has also completed the curriculum of the elementary and secondary schools in all other respects, and is ready at 12 years to enter college.) Figure 15 shows D’s calculations on Test 2, of Army Alpha, Form 5, five minutes being allowed for the performance. Figure 16 shows his calculations on Test 6, of the same form of Alpha, three minutes being allowed. D was 10 years 11 months old on the date of these calculations. He had never previously seen either of these tests. [Illustration: FIG. 15.—Showing D’s calculations on Test 2, Army Alpha, Form 5, at the age of 10 years 11 months, five minutes being allowed for the performance. The only figuring done on paper appears in the margin. ] [Illustration: FIG. 16.—Showing D’s calculations on Test 6, Army Alpha, Form 5, at the age of 10 years 11 months, three minutes being allowed for the performance. ] The second child to whom we wish to refer briefly is R, of IQ 187. He, too, has delighted in number from about the third year of life. When first seen by the present writer, at the age of 6 years 6 months, R’s memory span for digits was at least eight (beyond this he was not tested), and he could easily reverse seven digits at least (beyond this the test did not go). He has been taught short cuts and other mechanics of lightning calculation till now, at the age of 8, he can with great speed calculate the answer to such a series as “2 × 2 × 2 × 2 multiplied by twice the square of 2; square it,” or “2255^2 − 2245^2.” In Figure 17 is shown R’s calculation on Test 2, Army Alpha, Form 5, and in Figure 18, his performance in Test 6, the time limits being the same as indicated for D. R was 7 years 6 months old on the date of these performances. The ordinary child of that age can, of course, make no score whatever. R had never previously seen either of the tests.