Peter's, instead of merely treating it with a columnar order of vast size, with all its details magnified in proportion, we should not have the fault to find with it that it does not produce the effect of its real size. In another sense, the word "proportion" in architecture refers to the system of designing buildings on some definite geometrical system of regulating the sizes of the different parts. The Greeks certainly employed such a system, though there are not sufficient data for us to judge exactly on what principle it was worked out. In regard to the Parthenon, and some other Greek buildings, Mr. Watkiss Lloyd has worked out a very probable theory, which will be found stated in a paper in the "Transactions of the Institute of Architects." Vitruvius gives elaborate directions for the proportioning of the size of all the details in the various orders; and though we may doubt whether his system is really a correct representation of the Greek one, we can have no doubt that some such system was employed by them. Various theorists have endeavored to show that the system has prevailed of proportioning the principal heights and widths of buildings in accordance with geometrical figures, triangles of various angles especially; and very probably this system has from time to time been applied, in Gothic as well as in classical buildings. This idea is open to two criticisms, however. First, the facts and measurements which have been adduced in support of it, especially in regard to Gothic buildings, are commonly found on investigation to be only approximately true. The diagram of the section of the building has nearly always, according to my experience, to be "coaxed" a little in order to fit the theory; or it is found that though the geometrical figure suggested corresponds exactly with some points on the plan or section, these are really of no more importance than other points which might just as well have been taken. The theorist draws our attention to those points in the building which correspond with his geometry, and leaves on one side those which do not. Now it may certainly be assumed that any builders intending to lay out a building on the basis of a geometrical figure would have done so with precise exactitude, and that they would have selected the most obviously important points of the plan or section for the geometrical spacing. In illustration of this point, I have given (Fig. 25) a skeleton diagram of a Roman arch, supposed to be set out on a geometrical figure. The center of the circle is on the intersection of lines connecting the outer projection of the main cornice with the perpendiculars from those points on the ground line. This point at the intersection is also the center of the circle of the archway itself. But the upper part of the imaginary circle beyond cuts the middle of the attic cornice. If the arch were to be regarded as set out in reference to this circle, it should certainly have given the most important