This purposive unity cannot well be secured without spatial contiguity; here, as in sculpture, a unified life demands a unified material. Yet sometimes detached structures belong together functionally, and may be felt as one aesthetically, provided they are similar in design and some one of them is dominant; otherwise, each claims to be a distinct individual, and aesthetic rivalry is the result. Functional unity, although necessary, is not sufficient for aesthetic unity; in addition, there must be formal unity--design, composition. To study this adequately would require a separate treatise, which has not yet been written, so far as I know, with anything approaching philosophical depth and completeness; but for our plan it will be sufficient to show how the general principles of aesthetic form are illustrated in architecture; and because of the perspicuity of things spatial, these principles are nowhere else so lucidly manifest. Since architecture is a spatial art, unity in variety is chiefly a matter of harmony and balance rather than of evolution, and of these harmony is perhaps the most conspicuous. Harmony is secured in many ways. First, by giving the whole building or parts of the building a simple geometrical form readily perceived,--for example, the cruciform plan of many Gothic cathedrals, the oblong plan and oblong surmounted by a triangle in the facade of the Greek temple, the octagonal shape of a Renaissance chapel. A higher degree of harmony is obtained when the same shape is repeated throughout the various parts of the building,--the cylinder in the columns, the triangle or semicircle in the arches and gables. A step further is taken in the same direction when the different similar parts are all of the same size, as in the Greek temple, where the columns are all of one size, and similar parts of columns of equal size, and the metopes and triglyphs likewise.