"If the materials employed here be only a solid mass of masonry, it is not easy to see, everything being steady, how it can act in any other way than in the vertical direction. If, however, a motion takes place in the arch, the mass of materials lying nearly over the springing, when the arch is not very difliirent from a semicircle, will have such an enor mous friction, if well built and bonded together, as would appear equal to the resistance of any pressure that is likely to be opposed to it. And when the arch is a segment much smaller than a semicircle, the rules we have already given for its equilibration must be considered. But, instead of solid courses of masonry, the haunches of arches are often filled up with coarse gravel, or shiver, and sometimes with mere earth or sand. Materials of this description do by no means act by mere dead weight. They have a tendency to slide down towards a horizontal position; and, of course, possess, in some slight degree, the quaquaver sum pressure of a fluid. This may act on our arch in a manner altogether new, and produce strains for which hitherto we have made no provision. We shall first consider the back of the arch as tilled up with a fluid substance, as water. The pressure in every part will be in a direction perpendicular to the curve, and will be proportional to the depth. A pressure perpendicular to the curve will be equivalent, in effect, to a vertical pressure, which exceeds it in the ratio of the secant of the inclination to the vertical. Of course, the pressure at the springing, when all is equilibrated, must be equal to the horizontal thrust in a semicircular arch.
"Though the action of sand, gravel, or mould, in situations such as this, be not exactly the same with that of water, in following the laws of hydrostatical pressure ; yet these mate rials resemble water, and may be conceived to hold the middle place between the fluid and the solid backing. In some respects they are more advantageous than the fluid. They are stiffer, so to speak, affording a lateral abutment to the arch, if it is likely to yield ; and as the parts have a great friction among themselves, it will require a much greater pressure, acting horizontally, to make the matter rise, than in the case of a fluid. We must not, however, be too con fident. Materials of this kind are compressible ; and we have already seen that very slight shifts are attended with dangerous consequences. At the same time, we need not be much afraid of a trivial departure from exact equilibration; for it is not likely that materials of this kind will act with the powerful effort of hydrostatical pressure.
" But there is another case, where matter of this kind is likely to be attended with more pernicious effects than even a fluid of equal density would be. We mean, when the back of the arch is gorged up with water from land-floods : if the backing be open gravel, or shiver, we have superadded to its weight that of the whole quantity of water admitted into the structure. This, even if it acts equally on both sides, must
be a dangerous experiment on any arch ; but where it is confined to one side, as is generally the case, and between lofty side-walls, the effects are likely to be serious indeed. Accordingly, the builder forms gutters in the side-wall to let off the water are it collect ;—a practice which is in general highly useful, but which, in the case of sand, clay, or mould, is of small service. The water enters into such matter by its capillary attraction ; and fills it to the upper su•f:tee, in spite of our gutters. It of course expands it, and this with a force which we cannot measure, but which we are sure is very great. Here the friction of the parts, which was so useful in the former instance, proves extremely hurtful. For as the matter cannot easily rise, and probably the adhesion of its particles is increased by the water, the expanding force becomes an enormous hydrostatical pressure acting perpen dicularly- on the side-walls and extrados of our arch, and which in all probability they may not sustain.
"The dangerous consequences of this mode of backing arc, in some degree, prevented by ramming the layers of matter, especially if it consists of mould or the like : or, by puddling them, so as to form a mass impervious to water. And here we should observe, that as this ramming will produce an extraordinary lateral pressure, we must attend to equilibra tion, as we rise along the arch, and secure the side-walls by thickening them below or curving them horizontally or vertically.
"The thickness of the arch-stones is an important depart ment of the theory of arches. It is natural that we should endeavour to make them as small as possible. That will diminish the expense of the structure, lessen the pressures in the arch, and increase the security at the springing. But there is an evident limit to this diminution ; for though we take every pains to render the joints close, the stones may conic at length to be so small as to crush by the thrust of the arch. This is, indeed, a curious branch of inquiry. It depends intimately upon the corpuscular actions of the par ticles of stone ; a subject on which, we regret to say, our information has been hitherto very scanty.
"The question evidently depends on the amount of the tangential pressure. At the crown this is the horizontal thrust. We shall suppose all the joints to be duly drawn to equilibration, the sections fairly abutting on each other, and no weakness arising from acute angles.
"Stone, it is said, will carry from 250,000 to S50,0001b. avoirdupois per foot square, and brick 300.000lb. They have been made practically to carry one-sixth of this, and even more. The pillar in the centre of the Chapter-house at Elgin carries upwards of 40,000lb. on the square foot, and there was formerly a heavy lead roof on it. It is a red sand stone, and has borne this pressure for centuries.