Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/347

Rh 327 AECH ARCH, in building, a portion of mason-work disposed in the form of an arc or bow, and designed to carry the building over an open space. The simplest and oldest expedient for supporting a structure over a door-way is to use a single stone or lintel of sufficient length. On account of the difficulty of procuring stones of great size, this expedient can only be used for moderate apertures ; nor can it be applied when there is to be a heavy superstructure, because the weight resting on the lintel would cause a compression of the upper, and a distension of the under side. Now, no kind of stone can bear any considerable distending strain, and thus stone-lintels are liable to fracture. The ancient Greek temples afford instances of the use of horizontal lintels of considerable size, but these architraves carry only the cornice of the building. The employment of a colonnade with flat architraves to support an upper story is contrary to sound principles, and, even in the case of ordinary houses, we see that the builder has been fain to relieve the pressure on the lintel by means of a concealed arch. In stone-work we must depend on compression alone. When a lintel had been accidentally broken in two, we may suppose that the masons had set the ends of the halves upon the door-posts, and brought the broken ends Fig. 1. Fig. 2. together. In this way there would be formed a support for the upper building much stronger than was the stone when entire ; only there is a tendency to thrust the door posts asunder, and means must be taken to resist this out- thrust. The transition from this arrangement to that of three or more wedge-shaped stones fitted together was easy, and thus the gradual development of the arch resulted. So long as such structures are of small dimensions no great nicety is required in the adaptation of the parts, because the friction of the surfaces and the cohesion of the mortar are sufficient to compensate for any impropriety of arrangement.. But when we proceed to construct arches of large span we are forced to consider carefully the nature and intensity of the various strains in order that provision may be made for resisting them. Until the laws of the equilibrium of pressures were discovered, it was not possible to investigate these strains, and thus our knowledge of the principles of bridge-building is of very recent date ; nor even yet can it be said to be perfected. The investigation is one of great difficulty, and mathematicians have sought to render it easier by introducing certain pre-supposed conditions; thus, in treatises on the theory of the arch, the structure is regarded as consisting of a course of arch-stones resting on abut ments, and carrying a load which is supposed to press only downwards upon the arch-stones. Also cohesion and friction are put out of view, in other words, the investigation is conducted as if the stones could slide freely upon each other. Now, if the line of pressure of one stone against another cross their mutual surface perpendicularly, there is no tendency to slide; and if this condition be adhered to throughout the whole structure, there must result complete stability, since the whole of the friction and the whole consistency of the cement contribute thereto. But if, in any case, the line of pressure should cross the mutual surface obliquely, the tendency to slide thereby occasioned must be resisted by the cohesion, and so the firmness of the structure would be impaired. Hence an investigation, conducted on the supposition of the non-existence of cohesion, must necessarily lead us to the best possible construction. But we can hardly say as much in favour of the hypothesis that the load presses only downwards 1 upon the arch-stones. In order to place such a supposition in accordance with the facts of the case, we should have to dress the inner ends of the arch-stones with horizontal facets for the purpose of receiving and transmitting the downward pressure. But if, as is usually the case, the inner surfaces be oblique, they cannot transmit a vertical pressure unless in virtue of cohesion, and then this hypothesis of only downward pressure on the arch-stones is not in accordance with the fundamental principle of stability. In a thorough &amp;gt; investi gation this hypothesis must be set aside, and the oblique pressure on the inner ends of the arch-stones must be taken into account. Since the depth of the arch-stones is small Fig. 3. in comparison with the whole dimensions of the structure, and since the line of the pressure transmitted from one to another of them must always be within that depth, it is admissible to suppose, for the purpose of analysing the strains, that the arch-stones form an exceedingly thin course, and that their joints are everywhere normal to the curve of the arch. Eventually, however, the depth of the arch-stones must be carefully considered. We may best obtain a clear view of the whole subject by first assuming that the load presses only downwards on the arch-stones, or that the inner ends of these are cut with horizontal facets. Let Q P APQ (fig. 4) represent a portion of such an arch Fig. 4. placed equally on the two sides of the crown A, then the whole weight of the structure included between the two vertical lines P H and PH must be supported at P and P, so that the downward pressure at the point P must be tho weight of the building imposed over AP. This pressure downwards is accompanied by a tendency to separate tho