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 experi ment 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 ere 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 tip per surface 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 perpendicularly on the side walls and extrados of our arch, and which in all probability they may not sustain.
We do not mean to pursue the theory of the pres sures exerted by these semifluids any further at present. We look upon their use in this case as radically bad, and would recommend its discontinuance. If the reader wishes for more information on the subject, he will find it when we come to speak of retaining walls. In the meantime we may remark, that the dangerous conse quences of this mode of backing are, 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 equilibration, 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 archstones is an important de partment 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 come at length to be so small as to crush by the thrust of the arch. This is,
indeed, a curious branch of enquiry. It depends inti mately upon the corpuscular actions of the particles of stone ; a subject on which, we regret to say, that our information has been hitherto very scanty. The writers of this article have, at present, a series of experiments in sonic forwardness, which will throw much light on this, as well as on many other departments of architecture. i\leanwhile, that we may not disappoint the reader by leav ing the subject untouched, we shall endeavour to draw some information respecting it, from the present state of our knowledge, and the dimensions of structures already existing.
The question evidently depends on the amount of the tangential pressure. At the crown this is the horizon tal 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 850,000lb. avoirdupois per foot square, and brick 300,000tb. They have been made practically to carry 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 cen turies.
We shall therefore take 50,000lb. per foot as a load, which may be safely laid on every square foot in the arch. A cubic foot of stone weighs about 160/b. per foot; and brick weighs less. Suppose, therefore, the arch to be one foot thick at the crown, and the key stone one cubic foot, it will hear a horizontal thrust of 50,000/b. that is, 3122 times its weight.
But, 50,000 : 160 : : R : Tang. I l' 0" which will be the angle of the key-stone it) that case. So that an arch of 5124 feet radius, or a semicircular arch of 625 feet span, might bear to have a key-stone of a foot deep, without risking its being crushed more than in struc tures which have already stood for many years. And this may be called the limit of stone arch building ; for if we double the depth of the stone, we will thereby double the weight also, and its ratio to the horizontal thrust will still be the same. Indeed this limit does not much exceed what has been actually executed. A con siderable portion of the bridge of Neuilly is an arch of 250 feet radius ; and Gautier mentions a platband in the church of the Jesuits at Nismes, the camber of which, after settling, would make it a portion of an arch of 280 feet radius. The length or span is 262 French feet, the rise only 4 inches, and therefore the diameter of its circle would be 560 English feet.