But the three-pieced arch is properly representative of all; and the larger and more complicated constructions are merely produced by keeping the central piece for what is called a keystone, and putting additional joints at the sides. Now so long as an arch is pure circular or pointed, it does not matter how many joints or voussoirs you have, nor where the joints are; nay, you may joint your keystone itself, and make it two-pieced. But if the arch be of any bizarre form, especially ogee, the joints must be in particular places, and the masonry simple, or it will not be thoroughly good and secure; and the fine schools of the ogee arch have only arisen in countries where it was the custom to build arches of few pieces.

§ XV. The typical pure pointed arch of Venice is a five-pieced arch, with its stones in three orders of magnitude, the longest being the lowest, as at b2, [Plate III.] If the arch be very large, a fourth order of magnitude is added, as at a2. The portals of the palaces of Venice have one or other of these masonries, almost without exception. Now, as one piece is added to make a larger door, one piece is taken away to make a smaller one, or a window, and the masonry type of the Venetian Gothic window is consequently three-pieced, c2.

§ XVI. The reader knows already where a cusp is useful. It is wanted, he will remember, to give weight to those side stones, and draw them inwards against the thrust of the top stone. Take one of the side stones of c2 out for a moment, as at d. Now the proper place of the cusp upon it varies with the weight which it bears or requires; but in practice this nicety is rarely observed; the place of the cusp is almost always determined by æsthetic considerations, and it is evident that the variations in its place may be infinite. Consider the cusp as a wave passing up the side stone from its bottom to its top; then you will have the succession of forms from e to g ([Plate III.]), with infinite degrees of transition from each to each; but of which you may take e, f, and g, as representing three great families of cusped arches. Use e for your side stones, and you have an arch as that at h below, which may be called a down-cusped arch. Use f for the side stone, and you have i, which may be called a mid-cusped arch. Use g, and you have k, an up-cusped arch.

§ XVII. The reader will observe that I call the arch mid-cusped, not when the cusped point is in the middle of the curve of the arch, but when it is in the middle of the side piece, and also that where the side pieces join the keystone there will be a change, perhaps somewhat abrupt, in the curvature.

I have preferred to call the arch mid-cusped with respect to its side piece than with respect to its own curve, because the most beautiful Gothic arches in the world, those of the Lombard Gothic, have, in all the instances I have examined, a form more or less approximating to this mid-cusped one at i ([Plate III.]), but having the curvature of the cusp carried up into the keystone, as we shall see presently: where, however, the arch is built of many voussoirs, a mid-cusped arch will mean one which has the point of the cusp midway between its own base and apex.

The Gothic arch of Venice is almost invariably up-cusped, as at k. The reader may note that, in both down-cusped and up-cusped arches, the piece of stone, added to form the cusp, is of the shape of a scymitar, held down in the one case and up in the other.

§ XVIII. Now, in the arches h, i, k, a slight modification has been made in the form of the central piece, in order that it may continue the curve of the cusp. This modification is not to be given to it in practice without considerable nicety of workmanship; and some curious results took place in Venice from this difficulty.

At l ([Plate III.]) is the shape of the Venetian side stone, with its cusp detached from the arch. Nothing can possibly be better or more graceful, or have the weight better disposed in order to cause it to nod forwards against the keystone, as above explained, Ch. X. § II., where I developed the whole system of the arch from three pieces, in order that the reader might now clearly see the use of the weight of the cusp.

Now a Venetian Gothic palace has usually at least three stories; with perhaps ten or twelve windows in each story, and this on two or three of its sides, requiring altogether some hundred to a hundred and fifty side pieces.

I have no doubt, from observation of the way the windows are set together, that the side pieces were carved in pairs, like hooks, of which the keystones were to be the eyes; that these side pieces were ordered by the architect in the gross, and were used by him sometimes for wider, sometimes for narrower windows; bevelling the two ends as required, fitting in keystones as he best could, and now and then varying the arrangement by turning the side pieces upside down.