Data on loudness estimates at 60, 200, 500, 1000, 5000, and 10 000 cps were continued at the University of Arkansas from 1933 to 1959. A recalculation of all data to 1950 indicated that fractional judgments required a smaller decibel change of intensity than the corresponding multiple loudness estimates. This new result, hereafter referred to as the directional dependency, accompanied by a provisional explanation, was recorded in theJournal of the Arkansas Academy of Sciencesin 1950, and reported together with certain additional experiments at the Second ICA Congress in June of 1956.Since reluctance to accept unanticipated results is considerable, a new approach to a series of experiments designed to explore this directional dependency was preceded by review of a possible dynamical explanation. The follow‐up experiments included the proposed dynamical explanation as a part of the experimental objective and included new methods in our laboratory for the recording of judgments.The results of the earlier series have been confirmed, but a satisfying explanation has not been established.