from a recognition of the correspondence of the perceived relations with some conceived relations, which supply an ideal standard of proportion. This mental standard may repose either on a sense of utility or fitness of parts to a ruling end, on custom, or finally (in the case of the freer forms) on a vague feeling for the relative æsthetic importance of the several features as parts of a pleasing and well-balanced whole. If the eye has this delicate sense for quantitative relation, there is nothing intrinsically unreasonable in the doctrine put forth by Zeising, and partially countenanced by Fechner, that a special aesthetic value belongs to the division of a line into two unequal parts, of which the lesser shall be to the greater as this to the sum of the two or the whole. There is no numerical calculation involved here, and the only question to be asked is whether the eye really does prefer this peculiar division of parts, which Zeising calls "the golden section," and, if so, whether this is due to a sense of the quality of the ratios just named.
That the fact is as Zeising contends seems probable from Fechner's own investigations, in which he compares the different proportions of a large number of commonly recurring forms in ornaments, etc., where there is no apparent need of resorting to one mode of division rather than another. But does it follow that this customary preference involves a conscious comparison of the ratios here specified? In the case of a cruciform ornament, for instance, does the eye, however vaguely, sum together the vertical and horizontal magnitudes in the way supposed? May there not be a reason for choosing this particular division of a whole into parts, besides this hypothetical perception of an equality of ratios? I think there may be. It is noteworthy that, according to Zeising, the dimensions of the human figure illustrate this mode of proportion; and the question naturally arises whether this most frequent and most impressive object of contemplation may not have supplied a norm or ideal standard of proportion, to which we are apt to resort when there is no reason for selecting any other.
These three aspects or moments represent the most abstract principles of unity of form. In practice, these principles commonly combine and blend one with another. This may be seen by a reference to what is known as symmetrical arrangement.
A symmetrical division of parts aims at presenting a number of continuous features under certain aspects of contrast and similarity in relation to some central element. Each element of the design is balanced against some other element opposed to it in direction (that is, from the center), but resembling it in respect of magnitude and distance from the center. It thus supplies a large amount of the element of unity, and is indeed the most regular of all forms.
The most perfectly symmetrical figure is that which is so in respect of each pair of opposite sides or directions, as the rectangle, the polygon with even number of sides, the circle, etc. But such arrangements are apt to be too stiffly regular for art, which, needing abundance of
