504 



BRIDGE. 



Theory, qual to the resistance of any pressure that is likely 

 \ to be opposed to it. And when the arch is a seg- 

 ment much smaller than a semicircle, the rules we 

 have already given for its equilibration must be con- 

 sidered. 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 does by no means 

 act by mere dead weight. It has a tendency to slide 

 down towards a horizontal position; and, of course, 

 possesses, in some slight degree, the qiiaquavcrsitm 

 pressure of a fluid. This may act on our arch in a man- 

 ner altogether new, and produce strains for which 

 hitherto we have made no provision. We shall first 

 consider the back of the arch as filled up with a fluid 

 substance, as water. The pressure in every part 

 will be in a direction perpendicular to the curve, and 

 will b~e proportional to the depth. A pressure per- 

 pendicular to the curve will be equivalent, in eftect, 

 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. Take the thickness of matter 



at the crown rr of radius, the weight of one de- 

 m 



gree k, then the horizontal thrust will be 5"7^-k, 

 and the height of fluid necessary for this will be 574 

 times the thickness at vertex, provided the specific 

 gravity of the fluid be the same with that of the 

 arch. But if not, let /= the gravity of the fluid, 



and Sr= that of the arch at vertex, then ^ will 



fm 



be the height required. Suppose the arch made of 

 brick, which is about double the specific gravity of 

 water ; and we have, for water filling up the flanks, 

 till just covering the crown of the arch, a depth at 

 the springing nearly equal to the radius : and, of 

 course, the thickness at crown should be about ~^ R, 

 or T 4-j of the span, when in equilibration at the spring- 

 ing. We take no notice of the effect of the arch in 

 assisting this. Water, therefore, is much too light 

 for equilibrating an arch at the springing, in any 

 moderate thickness of crown. It might, however, 

 be eo employed. The quantity requisite is always 

 finite, even at the vertical spring courses ; and by 

 expanding the arch, or otherwise employing its hy- 

 drostatical properties, the requisite weight of fluid 

 could without doubt be obtained in any case. But 

 it is unnecessary to pursue this speculation farther 

 than merely to observe, that its weight on the arch, 

 where a vasiation is requisite, might be adjusted, by 

 attending to the modes of altering the density which 

 we have noticed, when speaking of filling up the 

 arch by masonry alone. 



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 materials 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 fric- 



tion among themselves, it will require a much greater T 

 pressure acting horizontally, to make the matter rise, '"" 

 than in the case of a fluid. We must not, however, be 

 too confident. 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 ma- 

 te-rials 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 

 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 

 upper 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 adhe- 

 sion 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 pre- 

 sent. We look upon their use in this case as radi- 

 cally bad, and would recommend its discontinuance. 

 If the reader wishes for more information on the sub- 

 ject, he will find it when we come to speak of retaining 

 iralla. In the meantime we may remark, that the dan- 

 gerous consequences of this mode of backing are, ill 

 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 imper- 

 vious 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 thicken- 

 ing them below, or curving them horizontally or ver- 

 tically. 



The thickness of the archstones is an important on tl 

 department of the theory of arches. It is natural thick' 

 that we should endeavour to make them as small as of th 

 possible. That will diminish the expense of the struc- stM 

 ture, lessen the pressures in the arch, and increase 

 the security at the springing. But there is an evi- 

 dent 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 



