§ I. On the subject of the stability of arches, volumes have been written and volumes more are required. The reader will not, therefore, expect from me any very complete explanation of its conditions within the limits of a single chapter. But that which is necessary for him to know is very simple and very easy; and yet, I believe, some part of it is very little known, or noticed. We must first have a clear idea of what is meant by an arch. It is a curved _shell_ of firm materials, on whose back a burden is to be laid of _loose_ materials. So far as the materials above it are _not loose_, but themselves hold together, the opening below is not an arch, but an _excavation_. Note this difference very carefully. If the King of Sardinia tunnels through the Mont Cenis, as he proposes, he will not require to build a brick arch under his tunnel to carry the weight of the Mont Cenis: that would need scientific masonry indeed. The Mont Cenis will carry itself, by its own cohesion, and a succession of invisible granite arches, rather larger than the tunnel. But when Mr. Brunel tunnelled the Thames bottom, he needed to build a brick arch to carry the six or seven feet of mud and the weight of water above. That is a type of all arches proper. § II. Now arches, in practice, partake of the nature of the two. So far as their masonry above is Mont-Cenisian, that is to say, colossal in comparison of them, and granitic, so that the arch is a mere hole in the rock substance of it, the form of the arch is of no consequence whatever: it may be rounded, or lozenged, or ogee'd, or anything else; and in the noblest architecture there is always _some_ character of this kind given to the masonry. It is independent enough not to care about the holes cut in it, and does not subside into them like sand. But the theory of arches does not presume on any such condition of things; it allows itself only the shell of the arch proper; the vertebræ, carrying their marrow of resistance; and, above this shell, it assumes the wall to be in a state of flux, bearing down on the arch, like water or sand, with its whole weight. And farther, the problem which is to be solved by the arch builder is not merely to carry this weight, but to carry it with the least thickness of shell. It is easy to carry it by continually thickening your voussoirs: if you have six feet depth of sand or gravel to carry, and you choose to employ granite voussoirs six feet thick, no question but your arch is safe enough. But it is perhaps somewhat too costly: the thing to be done is to carry the sand or gravel with brick voussoirs, six inches thick, or, at any rate, with the least thickness of voussoir which will be safe; and to do this requires peculiar arrangement of the lines of the arch. There are many arrangements, useful all in their way, but we have only to do, in the best architecture, with the simplest and most easily understood. We have