§ XIII. We will again take the three arches with their gables in succession, and on each of the sides of the gable, between it and the arch, we will describe another arch, as at g, h, i. Then the curves so described give the pointed arches belonging to each of the round arches; g, the flat pointed arch, h, the central pointed arch, and i, the lancet pointed arch.
§ XIV. If the radius with which these intermediate curves are drawn be the base of f, the last is the equilateral pointed arch, one of great importance in Gothic work. But between the gable and circle, in all the three figures, there are an infinite number of pointed arches, describable with different radii; and the three round arches, be it remembered, are themselves representatives of an infinite number, passing from the flattest conceivable curve, through the semicircle and horseshoe, up to the full circle.
The central and the last group are the most important. The central round, or semicircle, is the Roman, the Byzantine, and Norman arch; and its relative pointed includes one wide branch of Gothic. The horseshoe round is the Arabic and Moorish arch, and its relative pointed includes the whole range of Arabic and lancet, or Early English and French Gothics. I mean of course by the relative pointed, the entire group of which the equilateral arch is the representative. Between it and the outer horseshoe, as this latter rises higher, the reader will find, on experiment, the great families of what may be called the horseshoe pointed,—curves of the highest importance, but which are all included, with English lancet, under the term, relative pointed of the horseshoe arch.
| Fig. XXXII. |
§ XV. 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. 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. XXXIII.], to be described hereafter: with such caprices we are not here concerned.
§ XVI. 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. XXXI.] (suppose the equilateral), here at b, in [Fig. XXXIII.], 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 detestable ugliness, wherever it occurs on a large scale. It is eminently characteristic of Tudor work, and it is the profile of the Chinese roof (I say on a large scale, because this as well as all other capricious arches, may be made secure by their masonry when small, but not otherwise). Some allowable modifications of it will be noticed in the chapter on Roofs.
| Fig. XXXIII. |
§ XVII. There is only one more form of arch which we have to notice. When the last described arch is used, not as the principal arrangement, but as a mere heading to a common pointed arch, we have the form c, [Fig. XXXIII.] Now this is better than the entirely reversed arch for two reasons; first, less of the line is weakened by reversing; secondly, the double curve has a very high æsthetic value, not existing in the mere segments of circles. For these reasons arches of this kind are not only admissible, but even of great desirableness, when their scale and masonry render them secure, but above a certain scale they are altogether barbarous; and, with the reversed Tudor arch, wantonly employed, are the characteristics of the worst and meanest schools of architecture, past or present.
This double curve is called the Ogee; it is the profile of many German leaden roofs, of many Turkish domes (there more excusable, because associated and in sympathy with exquisitely managed arches of the same line in the walls below), of Tudor turrets, as in Henry the Seventh’s Chapel, and it is at the bottom or top of sundry other blunders all over the world.