[5] Zelsing, A.:  ‘Aesthetische Forschungen,’ 1855, S. 172;
   ‘Neue Lehre von den Proportionen des menschlichen Koerpera,’
   1854, S. 133-174.

   [6] Wundt, W.:  ‘Physiologische Psychologie,’ 4te Aufl.,
   Leipzig, 1893, Bd.  II., S. 240 ff.

   [7] op. cit., S. 262.

   [8] Witmer, L.:  ‘Analytical Psychology,’ Boston, 1902, p. 74.

   [9] Kuelpe, O.:  ‘Outlines of Psychology,’ Eng.  Trans., London,
   1895, pp. 253-255.

These citations show, in brief form, the history of the interpretation of our pleasure in unequal division.  Zeising and Wundt were alike in error in taking the golden section as the norm.  Zeising used it to support a philosophical theory of the beautiful.  Wundt and others too hastily conclude that the mathematical ratios, intellectually discriminated, are also sensibly discriminated, and form thus the basis of our aesthetic pleasure.  An extension of this principle would make our pleasure in any arrangement of forms depend on the mathematical relations of their parts.  We should, of course, have no special reason for choosing one set of relationships rather than another, nor for halting at any intricacy of formulae.  But we cannot make experimental aesthetics a branch of applied mathematics.  A theory, if we are to have psychological explanation at all, must be pertinent to actual psychic experience.  Witmer, while avoiding and condemning mathematical explanation, does not attempt to push interpretation beyond the honored category of unity in variety, which is applicable to anything, and, in principle, is akin to Zeising’s unity and infinity.  We wish to know what actual psychophysical functionings correspond to this unity in variety.  Kuelpe’s interpretation is such an attempt, but it seems clear that Weber’s law cannot be applied to the division at the golden section.  It would require of us to estimate the difference between the long side and the short side to be equal to that of the long side and the whole.  A glance at the division shows that such complex estimation would compare incomparable facts, since the short and the long parts are separated, while the long part is inclosed in the whole.  Besides, such an interpretation could not apply to divisions widely variant from the golden section.

This paper, as I said, reports but the beginnings of an investigation into unequal division, confined as it is to results obtained from the division of a simple horizontal line, and to variations introduced as hints towards interpretation.  The tests were made in a partially darkened room.  The apparatus rested on a table of ordinary height, the part exposed to the subject consisting of an upright screen, 45 cm. high by 61 cm. broad, covered with black cardboard, approximately in the center of which was a horizontal opening of considerable size, backed by opal glass.  Between the glass and the cardboard, flush with the edges of the opening so that no stray light could get