From Thurstone's theoretical learning curve, a solution for the difficulty of the problem and the learning constant of the subject has been developed. The curve is an equilateral hyperbola. Therefore the semi-major axis represents the learning situation in one constant. The vertex of the curve is a point where all of the animals are equated, since they are all making errors at the rate of one error per trial.

A seven-decimal table is presented of the area under the unit normal curve, for abscissae expressed in terms of the “probable error” or PE. From the method of calculation, the partial verification by means of other tables, and the safeguards taken in the routine of computation, it is safe to consider the table reliable. Errors in previously published tables are pointed out.

A comparison is made between the scales constructed by the Method of Paired Comparison, Rank Order, and the Method of Successive Intervals. Application of the three psychophysical methods to handwriting specimens and to nationality preferences results in mutually linear scales. Choice of scaling methods becomes, then, a matter of practical convenience rather than of relative validity.

A closed solution of the integral equation obtained by N. Rashevsky, with the assumption that the inhibitory influence between centers is a constant, i.e., independent of the distance apart, is obtained. Furthermore, a more general kernel, representing a variable inhibitory influence, which in our case is a monotonic (increasing or decreasing) function of the distance between centers, is introduced. The resulting integral equation is solved and some properties of the solution discussed.

In an attempt to investigate the concept of neurotic tendency thirty-nine of the forty-two most discriminative items in the Thurstone Neurotic Inventory were administered as a questionnaire to a group of five hundred male college students. An analysis of the table of intercorrelations by Thurstone's centroid method showed that eight factors were sufficient to account for the observed intercorrelations with negligible residuals. The eight centroid factors were then transformed into a simple structure. It is concluded that a single trait of neurotic tendency cannot be postulated and tentative hypotheses are formed as to the nature of the primary traits revealed by the analysis.

Readministering the same test to the same students a week later showed a high consistency of response both on the test as a whole, and on the individual items.

By the use of the Seashore tests of Pitch Discrimination, Intensity Discrimination, Time Discrimination, and the test of Tonal Memory, it is shown that the easiness of an item, as determined by absolute scaling methods, is proportional to the logarithm of the magnitude of the stimulus. It is proposed that this is a case of Fechner's psychophysical law and that the unit of absolute scaling as applied to test items may become a satisfactory unit of all S-scales in the more traditional psychophysical problem.

It is shown that from a somewhat more precise form of the fundamental postulates, used in a previous paper as a starting point for a system of mathematical biophysics of psychological phenomena, a mechanism can be derived, which represents the important features of conditioning.

A nomograph for the computation of point biserial r, biserial r, and fourfold correlation coefficients is presented, with instructions for use.