through, a cardboard slide was inserted from behind, into which was cut the exposed figure.  A covered electric light illuminated the figure with a yellowish-white light, so that all the subject saw, besides a dim outline of the apparatus and the walls of the room, was the illuminated figure.  An upright strip of steel, 11/2 mm. wide, movable in either direction horizontally by means of strings, and controlled by the subject, who sat about four feet in front of the table, divided the horizontal line at any point.  On the line, of course, this appeared as a movable dot.  The line itself was arbitrarily made 160 mm. long, and 11/2 mm. wide.  The subject was asked to divide the line unequally at the most pleasing place, moving the divider from one end slowly to the other, far enough to pass outside any pleasing range, or, perhaps, quite off the line; then, having seen the divider at all points of the line, he moved it back to that position which appealed to him as most pleasing.  Record having been made of this, by means of a millimeter scale, the subject, without again going off the line, moved to the pleasing position on the other side of the center.  He then moved the divider wholly off the line, and made two more judgments, beginning his movement from the other end of the line.  These four judgments usually sufficed for the simple line for one experiment.  In the course of the experimentation each of nine subjects gave thirty-six such judgments on either side the center, or seventy-two in all.

In Fig. 1, I have represented graphically the results of these judgments.  The letters at the left, with the exception of X, mark the subjects.  Beginning with the most extreme judgments on either side the center, I have erected modes to represent the number of judgments made within each ensuing five millimeters, the number in each case being denoted by the figure at the top of the mode.  The two vertical dot-and-dash lines represent the means of the several averages of all the subjects, or the total averages.  The short lines, dropped from each of the horizontals, mark the individual averages of the divisions either side the center, and at X these have been concentrated into one line.  Subject E obviously shows two pretty distinct fields of choice, so that it would have been inaccurate to condense them all into one average.  I have therefore given two on each side the center, in each case subsuming the judgments represented by the four end modes under one average.  In all, sixty judgments were made by E on each half the line.  Letter E¹ represents the first thirty-six; E squared the full number.  A comparison of the two shows how easily averages shift; how suddenly judgments may concentrate in one region after having been for months fairly uniformly distributed.  The introduction of one more subject might have varied the total averages by several points.  Table I. shows the various averages and mean variations in tabular form.