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, aesthetically 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 aesthetics 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.