You first, after setting out your widths as in the original, increase the whole height and that of each storey by one-third; you then increase the pillars and the jambs of the triforium and clerestory windows in the same proportion: this brings you to a stand, for the arches, being semicircles, are invariable. Either you must leave them unaltered and throw all the extra height into the wall above them, or you must stilt them each to the extent of one-third of their height unless you can make use of an elastic arch which will change its proportion at pleasure. The ellipse occurs and meets the case, but it offends your eye. At length, however, the pointed arch suggests itself, and gets rid of the whole difficulty. So similar are a Romanesque and an Early Pointed bay in all other respects, that the change of proportion which I have described seems at once to effect the whole change in style. Had the constructional motive alone existed, the pointed form would have been confined to arches of considerable span; but the demand for a variable arch adding æsthetic to the constructional claim, caused its speedy adoption in positions where strength alone would not have demanded it, though the semicircle, the plain segment, and the segmental pointed arch, were, at all subsequent periods of the style, used side by side with the true pointed form. I have been the more particular in showing the true reasons for the change in the form of the arch, because the great majority of writers treat it purely as a matter of taste and of altered fashion; indeed, some excellent writers on the history of Mediæval architecture have strangely imagined that the pointed arch had a greater outward thrust than the round, and that the increased projection of the buttresses was necessitated by its use, instead of the two being simultaneously introduced as a double means of avoiding the evils experienced from the great thrust of the round arch and the small buttresses by which it had, during the Romanesque period, been accompanied. I will now close my present lecture, but hope in the next to carry on the same inquiry into a number of other details, as well as into the general spirit and principles of the architecture of which I am treating, and to add some practical remarks on the application of the _rationale_ thus traced out to our present revival of the style, and such developments as it may give rise to. LECTURE VII. The Rationale of Gothic Architecture--_Continued_.