R. A. Fisher's method of determining a set of weights for the linear combination of the scores in a battery of tests is explained and illustrated. The relationship of this method to combination by multiple regression methods is shown.

A case of interaction between two groups of “active” and one group of “passive” individuals, in which the efforts of the influencing active groups decrease with increasing total success in the past, is studied. In that case the numbers of passive individuals, exhibiting respectively the two opposite behaviors, fluctuate periodically, with a positive damping.

In generalization of a previous study, a mathematical approach to the theory of the average size of cities as well as of the distribution of city sizes is outlined.

By application of the technique presented earlier, the factors found by the Guilfords in two studies of personality factors are reanalyzed. The rotation technique for the isolation of meaningful factors relates the factors of the two studies to each other through three common items, and to other factors and traits appearing in the literature of personality measurement. For each of four of the factors resulting from the analysis of the first battery there is close agreement with its counterpart from the analysis of the second battery with respect to loadings of the three common items. These factors are interpreted as perseverance, surgency, flexibility, and tension. Other factors appearing in only one or the other of the batteries are tentatively identified.

This article presents a Coefficient of Imbalance applicable to any type of communication that may be classified into favorable content, unfavorable content, neutral content, and non-relevant content. The combined influence of the average presentation of relevant content and the average presentation of total content is reduced to two components, the coefficients of favorable imbalance and of unfavorable imbalance. A precise definition of imbalance is developed and measured against ten criteria.

Intercorrelation coefficients among Thurstone's seven primary mental abilities scores were obtained from scores of 170 freshmen engineering students on the experimental edition of the Primary Mental Abilities Tests. These correlation coefficients were factored to four factors, interpreted as a general factor, a reasoning factor, a verbal factor, and, tentatively, a specific memory factor. The finding of a general factor for a college population corroborates the Thurstones' finding of a general factor for eighth-grade children.

The second of two parts of this article extends a mathematical theory of non-symbolic learning and conditioning to cases where reward and punishment are involved. The preceding results are generalized to the case where stimuli and responses are related psychophysically, thus constituting a theory of transfer, generalization, and discrimination.