TABLE I

ABCD
274 experiments
with each subject		248 experiments
with each subject		120 experiments
with each subject		132 experiments
with each subject
Number
of Subjects		Av. % of
difference
in favor of		Number
of Subjects		Av. % of
difference
in favor of		Number
of Subjects		Av. % of
difference
in favor of		Number
of Subjects		Av. % of
difference
in favor of
Small531.51034.6744.11046
Large335.1444.1541.5326.3
No tendency18.824.245.736.6

The per cent recorded in the no-tendency class is an average of all per cents below 10, whether in favor of the one or the other of the two remaining classes. This is true for all the following tables.

The following facts are presented by the several parts of Table I: (1) The large per cents of difference show that area is to a large extent a determinant of the judgment of relative number. (2) Different subjects show opposite tendencies. (3) A comparison of the results of individual subjects through the four series shows that this opposition in tendency occurs in the same subject at different times. The introspective notes of one of these subjects show the internal process of change from one tendency to the other. It consists in a gradual increase of analytic activity toward the compact group. At first glance the composition of the scattered group was more evident; but when attention was fairly turned toward the compact, the inability to isolate objects made them seem very numerous. The importance of a coöperating subjective factor is here evident. (4) Out of a possible 57 cases there are but 10 showing no tendency.

2. The Influence of the Internal Arrangement. As before, the Two-Group Apparatus was employed; and the factor was studied in three aspects.

A. The material consisted of two groups of gray circles (Normal Gray Darker, Prang) covering equal areas. In one group this area was filled homogeneously, in the other the circles were gathered into nuclei. In order that there might be exactly the same relation of parts when the cards were reversed, each group was so arranged on a diagonal axis of symmetry from upper left to lower right corner that each half repeated the other in reverse order. Otherwise the arrangement of circles was irregular.

Six cards only were used,—four (20 to 20), one (17 to 23), and one (23 to 17). Slight differences among them occurred in the arrangement of the equality-cards, which might help to counteract any incipient reasoning from sameness of appearance to sameness of number. The large increase in the difference-values is accounted for in part by the fact that the cards (19 to 20) and (20 to 19) were omitted, and for this reason: that when an observer tended largely to favor a particular group, the introduction of a card in which that group was objectively greater would mean an increase in the number of correct judgments; whereas the introduction of two objectively equal groups for the others would increase considerably the number of erroneous judgments.

B. The numerical character of the cards here used shows a return to the usual. The material was like that of A, except for a new internal arrangement. Here the area of one group was filled homogeneously, while that of the other contained a pattern of this sort: An ellipse just contained within the boundaries of the normal area; a circle in each of the four corners of that area; and in the centre a diamond formed of four circles. Numerical changes were always confined to the ellipse, as less open to counting than the rest of the figure.

C. Material and method repeat B but with another internal arrangement. One group, as before, showed an area homogeneously filled, and irregularly, as usual. The other group carries to an extreme the distinction of open and filled space made prominent in the other groups of this table by massing the circles in an outline completely enclosing the area and in a diagonal from upper left to lower right corner. The outline did not show even spacing; more circles were crowded in one part than in others, that counting might be more difficult.

That there might be no attempt to remember cards, in all cases where there were twenty objects in the homogeneous group the same kind of irregular arrangement was repeated. This is a different method from that employed in A. Since the length of exposure was so short and the arrangement in the group irregular, either one is probably as good as the other.

D. The material used for B and C had a kind of regularity, since definite patterns were used. The introspection of the observers showed, however, that the patterns as such were not in question in the judgment, but rather the vacancies and the crowding. With the Two-Group Apparatus an arrangement in parallel lines could rather easily be counted, but with the One-Group Apparatus and its means for instantaneous exposure this difficulty was to some extent overcome. The arrangement of the objects in parallel lines was therefore adopted and matched against the irregularity of an accompanying group. The same size of group-area was kept, but the small difference-cards were omitted. There was no other change beyond those made necessary by the apparatus and already indicated on an earlier page. The length of exposure was 125 sec. The bearing of this time-factor on the results will be considered in a later section.