CONSTRUCTION X. THE ARCH LINE 161

importance, but which are all included, with English lancet, under the term, relative pointed of the horseshoe arch.

§ 15. The groups above described are all formed of circular arcs, and include all truly useful and beautiful arches for ordinary work. I believe that singular and complicated curves are made use of in modern engineering, but with these the general reader can have no concern: the Ponte della Trinita at Florence is the most graceful instance I know of such structure; the arch made use of being very subtle, and approximating to the low ellipse; for which, in common work, a barbarous pointed arch, called four-centred, and composed of bits of circles, is substituted by the English builders. The high ellipse, I believe, exists in eastern architecture.¹ I have never myself met with it on a large scale; but it occurs in the niches of the later portions of the Ducal palace at Venice, together with a singular hyperbolic arch, a in Fig. 33, to be described hereafter: with such caprices we are not here concerned.

§ 16. We are, however, concerned to notice the absurdity of another form of arch, which, with the four-centred, belongs to the English perpendicular Gothic.

Taking the gable of any of the groups in Fig. 31 (suppose the equilateral), here at b, in Fig. 33, the dotted line representing the relative pointed arch, we may evidently conceive an arch formed by reversed curves on the inside of the gable, as here shown by the inner curved lines. I imagine the reader by this time knows enough of the nature of arches to understand that, whatever strength or stability was gained by the curve on the outside of the gable, exactly so much is lost by curves on the inside. The natural tendency of such an arch to dissolution by its own mere weight renders it a feature of

¹ [The MS. here inserts:-

“But even the pure ellipse is a barbarism, it being always wrong to use a difficult curve when one easily built would have done as well (there may perhaps be some reason for it in the Trinita bridge, connected with the nature of the floods of the Arno; on this point I cannot speak with certainty”).]

IX. L

[Version 0.04: March 2008]