Studies thus far made would convince us that arithmetical skill consists in the automatization and integration of a hierarchy of habits, which can be acquired to a passable degree by all children of average intelligence. Lightning calculation results from building up and rendering automatic still further habits, and can be achieved by persons of great general intelligence. It remains an open question whether a generally stupid person can ever become a prodigious calculator, but it seems certain that interest in and aptitude for arithmetic may be especially marked in generally superior children. Arithmetical ability may develop, without simultaneous development of ability in other branches of mathematics. One may calculate prodigiously, without comprehending algebraic and geometric principles, or being interested in them. Also one may be more or less adept, either by nature or by training, in one kind of arithmetical function than in others. Drill is the means for improving arithmetical ability, so far as speed and accuracy of calculation are concerned. Ability in problem solving can probably not be much affected by drill, since “a problem” is, by definition, something that requires independent adjustment, and not the response of automatic habit. It therefore calls on general intelligence, and cannot be improved after the mechanics of reading and calculating have been mastered up to the limits of capacity. REFERENCES ANDERSON, C. I.—“The Use of the Woody Scale for Diagnostic Purposes”; _Elementary School Journal_, 1918. BINET, A.—_Psychologie des grands calculateurs et joueurs d’échecs_; Paris, 1894. BROWN, W.—“An Objective Study of Mathematical Intelligence”; _Biometrika_, 1910. COBB, M.—“The Inheritance of Arithmetical Abilities”; _Journal of Educational Psychology_, 1917. COLLAR, D. J.—“A Statistical Survey of Arithmetical Ability”; _British Journal of Psychology_, 1920. GILLINGHAM, A.—_One Child’s Struggle in the Preparation for Life_; Pedagogical Seminary, 1913. LANTERNE, S.—_Psychologie du nombre et des opérations élémentaires de l’arithmétique_; Paris, 1907. LAZAR, E., and PETERS, W.—“Rechenbegabung und Rechendefekte bei abnormen Kindern”; _Fortschritte der Psychologie_, 1915. LINDLEY, E. H., and BRYAN, W. L.—“An Arithmetical Prodigy”; _Psychological Review_, 1900. MÁDAY, H. V.—“Die Fähigkeit des Rechnens beim Menschen und beim Tiere”; _Zeitschrift für angewandte Psychologie_, 1913. MILLER, G. A.—“Mathematical Prodigies”; _Science_, 1907. MITCHELL, F. B.—“Mathematical Prodigies”; _American Journal of Psychology_, 1907. MÖBIUS, P. J.—_Ueber die Anlage zu Mathematik_, 2nd edition; Barth, Leipzig, 1907. RANSCHBURG, P.—_Die Rechenschwäche (Arithmasthenie) der Schulkinder im Lichte des Experiments_; J. Springer, Berlin, 1916.