80 THE POPULAR SCIENCE MONTHLY. 



from a recognition of the correspondence of the perceived relations 

 with some conceived relations, which supply an ideal standard of pro- 

 portion. 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 aesthetic impor- 

 tance 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 prefer- 

 ence 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 vei'tical 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 prin- 

 ciples of unity of form. In practice, these principles commonly com- 

 bine 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 bal- 

 anced against some other element opposed to it in direction (that is, 

 from the center), but resembling it in respect of magnitude and dis- 

 tance 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 poly- 

 gon with even number of sides, the circle, etc. But such arrangements 

 are apt to be too stiffly regular for art, which, needing abundance of 



