A simple method of making orthogonal rotations by projecting coordinates from one plot to another is presented. An easily constructed apparatus for rapid and accurate work is described in detail. By the technique proposed 12 to 15 rotations of pairs of axes involving 20 test variables can be completed per hour by a practiced technician.

A comparison of factorial analyses made by Thurstone and by the writer shows that they differ in three important respects. The results of the two analyses are compared with respect to their social utility, which is offered as a proper criterion for judging the merit of factorial analyses performed by different mathematical procedures.

This article proposes a new descriptive statistic related to the second order parabola in the same manner in which the familiar correlation coefficient is related to the regression coefficient. The parabolic r describes in standard terms simultaneously the general trend of the regression and the extent and nature of its curvilinearity, and is relatively easy to compute and easy to communicate. Formulas for its standard error and its limits are derived and it is applied to a number of regressions.