A great number of habits, more or less specific, must be automatized. There are all the combinations used in addition and subtraction, the multiplication tables, the reading of large numbers, the manipulation of fractions, the placing of the decimal point, and many others. These habits are of very unequal difficulty. Ranschburg has shown, for instance, that 5 + 2 is a much easier operation than is 2 + 5, and that 5 + 5 is easier than either. The difficulty of a combination is augmented by increase in the second member. The difficulty increases, also, as either or both of the members increase in value. The addition of two identical numbers, of whatever value, seems always to follow a different course from that of two unlike numbers, resembling multiplication in the time taken. These are a few illustrations of the subtleties of habit formation in arithmetic, which are revealed only by laboratory methods. They suggest, also, the complexity and multiplicity of connections, which enter into ordinary achievement in arithmetic. Since the functions are thus highly complex and specialized, what are their interrelations? How are they organized, as regards the amounts of each found in given individuals? IV. THE ORGANIZATION OF ARITHMETICAL ABILITIES Thorndike and his students have shown that in general the correlation between ability in any one important feature of computation and ability in any other important feature of computation is positive and high. Thorndike holds that if enough tests were made to measure each individual fully in subtraction, multiplication with integers and decimals, division with integers and decimals, multiplication and division with common fractions, and computing with per cents, there would probably appear intercorrelations for a thousand 14-year-olds of near .90. Correlation between problem-solving and computation would doubtless be much less, probably not over .60. Thorndike expresses the following inferences, based on interpretation of existing data. “It should be noted that even when the correlation is as high as .90, there will be some individuals very high in one ability and very low in the other. Such disparities are to some extent, as Courtis and Cobb have argued, due to inborn characteristics of the individual in question, which predispose him to very special sorts of strength and weakness. They are often due, however, to defects in his learning, whereby he has acquired more ability than he needs in one line of work, or has failed to acquire some needed ability, which was well within his capacity. “In general, all correlations between an individual’s divergence from the common type or average of his age for one arithmetical function, and his divergence from the average for any other arithmetical function, are positive. The correlation due to original capacity more than counterbalances the effects that robbing Peter to pay Paul may have.”