I shall now proceed to the interpretative part of the paper. Bilateral symmetry has long been recognized as a primary principle in æsthetic composition. We inveterately seek to arrange the elements of a figure so as to secure, horizontally, on either side of a central point of reference, an objective equivalence of lines and masses. At one extreme this may be the rigid mathematical symmetry of geometrically similar halves; at the other, an intricate system of compensations in which size on one side is balanced by distance on the other, elaboration of design by mass, and so on. Physiologically speaking, there is here a corresponding equality of muscular innervations, a setting free of bilaterally equal organic energies. Introspection will localize the basis of these in seemingly equal eye movements, in a strain of the head from side to side, as one half the field is regarded, or the other, and in the tendency of one half the body towards a massed horizontal movement, which is nevertheless held in check by a similar impulse, on the part of the other half, in the opposite direction, so that equilibrium results. The psychic accompaniment is a feeling of balance; the mind is æsthetically satisfied, at rest. And through whatever bewildering variety of elements in the figure, it is this simple bilateral equivalence that brings us to æsthetic rest. If, however, the symmetry is not good, if we find a gap in design where we expected a filling, the accustomed equilibrium of the organism does not result; psychically there is lack of balance, and the object is æsthetically painful. We seem to have, then, in symmetry, three aspects. First, the objective quantitative equality of sides; second, a corresponding equivalence of bilaterally disposed organic energies, brought into equilibrium because acting in opposite directions; third, a feeling of balance, which is, in symmetry, our æsthetic satisfaction.

It would be possible, as I have intimated, to arrange a series of symmetrical figures in which the first would show simple geometrical reduplication of one side by the other, obvious at a glance; and the last, such a qualitative variety of compensating elements that only painstaking experimentation could make apparent what elements balanced others. The second, through its more subtle exemplification of the rule of quantitative equivalence, might be called a higher order of symmetry. Suppose now that we find given, objects which, æsthetically pleasing, nevertheless present, on one side of a point of reference, or center of division, elements that actually have none corresponding to them on the other; where there is not, in short, objective bilateral equivalence, however subtly manifested, but, rather, a complete lack of compensation, a striking asymmetry. The simplest, most convincing case of this is the horizontal straight line, unequally divided. Must we, because of the lack of objective equality of sides, also say that the bilaterally equivalent muscular innervations are likewise lacking, and that our pleasure consequently does not arise from the feeling of balance? A new aspect of psychophysical æsthetics thus presents itself. Must we invoke a new principle for horizontal unequal division, or is it but a subtly disguised variation of the more familiar symmetry? And in vertical unequal division, what principle governs? A further paper will deal with vertical division. The present paper, as I have said, offers a theory for the horizontal.

To this end, there were introduced, along with the simple line figures already described, more varied ones, designed to suggest interpretation. One whole class of figures was tried and discarded because the variations, being introduced at the ends of the simple line, suggested at once the up-and-down balance of the lever about the division point as a fulcrum, and became, therefore, instances of simple symmetry. The parallel between such figures and the simple line failed, also, in the lack of homogeneity on either side the division point in the former, so that the figure did not appear to center at, or issue from the point of division, but rather to terminate or concentrate in the end variations. A class of figures that obviated both these difficulties was finally adopted and adhered to throughout the work. As exposed, the figures were as long as the simple line, but of varying widths. On one side, by means of horizontal parallels, the horizontality of the original line was emphasized, while on the other there were introduced various patterns (fillings). Each figure was movable to the right or the left, behind a stationary opening 160 mm. in length, so that one side might be shortened to any desired degree and the other at the same time lengthened, the total length remaining constant. In this way the division point (the junction of the two sides) could be made to occupy any position on the figure. The figures were also reversible, in order to present the variety-filling on the right or the left.

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 æsthetic 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 æsthetic 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.

In all, five sets of the corrected figures were used. Only the second, however, and the fifth (chronologically speaking) appeared indubitably to isolate one element above others, and gave uniform results. But time lacked to develop the fifth sufficiently to warrant positive statement. Certain uniformities appeared, nevertheless, in all the sets, and find due mention in the ensuing discussion. The two figures of the second set are shown in Fig. 2. Variation No. III. shows a design similar to that of No. II., but with its parts set more closely together and offering, therefore, a greater complexity. In Table II. are given the average divisions of the nine subjects. The total length of the figure was, as usual, 160 mm. Varying numbers of judgments were made on the different subjects.

Fig. 2.

TABLE II.
No. I.No. II.No. I. (reversed).No. II. (reversed).
L.R.L.R.R.L.R.L.
A550480590500
B590440630520
C580560520500
D600560600550
E7459736574607567
F6167606665646265
G6464626863645367
H7668756466736771
J490410500420
————————
Total.6164576561655467