TABLE I.
                         Left.  Right. 
                      Div.  M.V.  Div.  M.V.
        A 54 2.6 50 3.4
        B 46 4.5 49 5.7
        C 75 1.8 71 1.6
        D 62 4.4 56 4.1
        E¹ 57 10.7 60 8.7
        F 69 2.6 69 1.6
        G 65 3.7 64 2.7
        H 72 3.8 67 2.1
        J 46 1.9 48 1.3
                 —­ —–­ —­ —–­
Total 60 3.9 59 3.5

Golden Section = 61.1.

¹These are E’s general averages on 36 judgments.  Fig. 1, however, represents two averages on each side the center, for which the figures are, on the left, 43 with M.V. 3.6; and 66 with M.V. 5.3.  On the right, 49, M.V. 3.1; and 67, M.V. 2.7.  For the full sixty judgments, his total average was 63 on the left, and 65 on the right, with mean variations of 9.8 and 7.1 respectively.  The four that E squared in Fig. 1 shows graphically were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1.  On the right, 49, M.V. 3.1; and 69, M.V. 3.4.

[Illustration:  FIG. 1.]

Results such as are given in Fig. 1, appear to warrant the criticism of former experimentation.  Starting with the golden section, we find the two lines representing the total averages running surprisingly close to it.  This line, however, out of a possible eighteen chances, only twice (subjects D and G) falls wholly within the mode representing the maximum number of judgments of any single subject.  In six cases (C twice, F, H, J twice) it falls wholly without any mode whatever; and in seven (A, B twice, E, F, G, H) within modes very near the minimum.  Glancing for a moment at the individual averages, we see that none coincides with the total (although D is very near), and that out of eighteen, only four (D twice, G twice) come within five millimeters of the general average, while eight (B, C, J twice each, F, H) lie between ten and fifteen millimeters away.  The two total averages (although near the golden section), are thus chiefly conspicuous in showing those regions of the line that were avoided as not beautiful.  Within a range of ninety millimeters, divided into eighteen sections of five millimeters each, there are ten such sections (50 mm.) each of which represents the maximum of some one subject.  The range of maximum judgments is thus about one third the whole line.  From such wide limits it is, I think, a methodological error to pick out some single point, and maintain that any explanation whatever of the divisions there made interprets adequately our pleasure in unequal division.  Can, above all, the golden section, which in only two cases (D, G) falls within the maximum mode; in five (A, C, F, J twice) entirely outside all modes, and in no single instance within the maximum on both sides the center—­can this seriously play the role of aesthetic norm?