If it were found that such a filling in one figure varied from one in another so that it obviously presented more than the other of some clearly distinguishable element, and yielded divisions in which it occupied constantly a shorter space than the other, then we could, theoretically, shorten the divisions at will by adding to the filling in the one respect.  If this were true it would be evident that what we demand is an equivalence of fillings—­a shorter length being made equivalent to the longer horizontal parallels by the addition of more of the element in which the two short fillings essentially differ.  It would then be a fair inference that the different lengths allotted by the various subjects to the short division of the simple line result from varying degrees of substitution of the element, reduced to its simplest terms, in which our filling varied.  Unequal division would thus be an instance of bilateral symmetry.

The thought is plausible.  For, in regarding the short part of the line with the long still in vision, one would be likely, from the aesthetic tendency to introduce symmetry into the arrangement of objects, to be irritated by the discrepant inequality of the two lengths, and, in order to obtain the equality, would attribute an added significance to the short length.  If the assumption of bilateral equivalence underlying this is correct, then the repetition, in quantitative terms, on one side, of what we have on the other, constitutes the unity in the horizontal disposition of aesthetic elements; a unity receptive to an almost infinite variety of actual visual forms—­quantitative identity in qualitative diversity.  If presented material resists objective symmetrical arrangement (which gives, with the minimum expenditure of energy, the corresponding bilateral equivalence of organic energies) we obtain our organic equivalence in supplementing the weaker part by a contribution of energies for which it presents no obvious visual, or objective, basis.  From this there results, by reaction, an objective equivalence, for the psychic correlate of the additional energies freed is an attribution to the weaker part, in order to secure this feeling of balance, of some added qualities, which at first it did not appear to have.  In the case of the simple line the lack of objective symmetry that everywhere meets us is represented by an unequal division.  The enhanced significance acquired by the shorter part, and its psychophysical basis, will engage us further in the introspection of the subjects, and in the final paragraph of the paper.  In general, however, the phenomenon that we found in the division of the line—­the variety of divisions given by any one object, and the variations among the several subjects—­is easily accounted for by the suggested theory, for the different subjects merely exemplify more fixedly the shifting psychophysical states of any one subject.