The fact having been established that these variations were intentional, how are they to be explained? A generally accepted explanation of the curvatures in place of straight lines has been that they were intended to correct an optical effect of curvature in the opposite direction. Thus, if the contour of a column shaft were a straight line, it would appear to the eye to curve inward; similarly, the horizontal lines of the stylobate and entablature would appear to sag downward. Accordingly, the “refinements” were designed as optical corrections of optical effects of irregularity; in other words, geometrical effect is supposed to have been sought by departures from geometric fact. This, however, would not explain the other variations that have been noted. Moreover, it is contradicted even in the case of curvatures by a discovery of Professor Giovannoni of Rome, that the façade of the =Temple= at =Uri= has a curvature in _plan_.[3] The columns, that is to say, are not set to a straight line but to a curve which is concave to the exterior; consequently the entablature is correspondingly curved, the effect of which to the eye as it looks up is the very one that it was explained the architects strove to avoid--a sag downward from the ends. In this case they deliberately designed the façade to produce the effect. This explanation of optical corrections, then, as well as others, have been proved erroneous by Professor William H. Goodyear, who has made a life-long study of the subject and carried his investigations also into Gothic architecture, in which, as we shall see, he has discovered numerous instances of refinements and asymmetries. His explanation, supported by a wealth of conclusive evidence which is set forth in his “Greek Refinements,” is that the motive was æsthetic. The refinements were modulations designed to please the eye by avoiding the inartistic effects produced by formal monotony. They were planned to do away with the monotony and rigidity that result from geometrical regularity and mathematical accuracy and to introduce a suggestion of elasticity. They imparted to the structure something of the irregularity that characterises organic growth. It is because, with rare exceptions, they are not found in modern classical buildings, that the latter appear by comparison so stiff and formal. These asymmetries, in fact, were intended to offset the liability of the beauty’s becoming “faultily faultless, icily regular, splendidly null, dead perfection, no more.” * * * * *