It I D G E. 



503 



arch other. If the overload be considerable, or if the 

 arch be thin, and of course flexible, a deviation 

 from equilibrium may produce an effect equally de- 

 structive with thnt which would arise by the sli- 

 ding of the sections. Suppose this deviation to con- 

 overloading the crown, a case very likely to 

 occur, for even the variable 



gon bears, in come cases, a very s<-i 'irtion 



to the weight at the vertex of the arch, this overload 

 will be equivalent to a greater thickness of crown, 

 and of course will sensibly increase the lir.ri/ontal 

 thrust, while the total weight of the arch, or vertical 

 pressure, is much the same as before. This is a still 

 stronger reason for backing up the spring c 

 with masonry ; for unless the stones, where their 

 joints become nearly horizontal, be sufficiently steady, 

 they may, by the increasing thrust, be pushed along 

 their beds ; for they are already near the limit of 

 steadiness from friction : a very short slide will open 

 the joints towards the crown. The same thing will 

 also be produced by the compression of the cement 

 in the arch. The vertical sections will descend. They 

 already tend strongly to do so. The separation of 

 the sections on each side of the vertex is equivalent to 

 drawing their joints to a lower point than before. 

 This will again increase the horizontal thrust. 



We have seen, that these joints are already too low 

 for equilibration in a common circular arch. The 

 motion of the lower sections, therefore,, if once be- 

 gun, will go on increasing, until the arch falls to 

 pieces. But what is perhaps of more importance, as 

 the joints towards the crown will now open below, 

 and the sections, not being in entire contact, will 

 hang by their upper corners only, these may chip and 

 crumble away, thereby forming them into more acute 

 wedges, and giving us a new cause of destruction. 

 For though the cohesion of the matter of the arch- 

 stone may effectually resist the tangential pressure, 

 when distributed over a joint of considerable superfi- 

 cies ; yet when the whole of that pressure is con- 

 densed into a small compass, or a mere point, and 

 that near the edge, and acting perhaps in a very un- 

 favourable direction, since the friction permits it to 

 act with great obliquity, its destructive tendency 

 may be irresistible. 



Suppose a motion of this kind actually going on 

 in an arch, as is generally the case when the centre 

 or scaffolding is taken from below it, How is it to 

 be prevented ? We answer not easily : For though 

 the motion be exceeding slow, or almost impercept- 

 ible, yet the quantity of matter is so enormous, that 

 its momentum is great. Nothing, therefore, but the 

 most solid work could resist it. Accordingly, in 

 striking the centres of an arch, the whole is not 

 taken away at once. It is not likely that any arch 

 could withstand that treatment ; but the centre is 

 gradually let down, stopping now and then until 

 the work settles. It does so first at the spring- 

 ing and haunches, and the crown of the arch is 

 the last part that departs from the centre. It ap- 

 pears, therefore, that every arch is a segment of a 

 greater circle, after it is finished, than before. Al- 

 lowance should be made for this in the design, 

 and in calculating the weights necessary for equi- 

 librium from the horizontal thrust. An attempt 



is sometimes made to remedy this change of i, 



by driving down the key stones. An- 1 : v -' 



is far better to render nuch expedient umirf-.iaiy 



by careful workmanship, yet this method is not 



be i! Hi 



practice of the ancient arc' An overdn 



key stone, or > is one of the 



most usual ornaments ot l!r 



"7 

 be employed with great 



of small taper have great pov. tin: horiy 



tal thrust should be in no case increased, without re 

 ry weighty reasons. 



Suppose the arch to descend somewhat at the 

 crown, the stones there will hang by their upper 

 s, even when there is no apparent opening on 

 the lower side of the joint. They will be pretty 

 close for a good way on each side, so far indeed 

 as the equilibrating superstructure extends, or to 

 about 60. And it will then be tolerably wel! 

 equilibrated, even though the superstructure should 

 not be yet applied. For the arch being then at the 

 crown, the theoretic extrados will run further dovfii 

 on the back of the curve, ere it turns up again ; and, 

 of course, will for a good way not differ much from 

 the back of the archstones. But beyond this point, 

 or about 60 from the crown, things are not likely to 

 be so steady. We do not say, the lower sections will 

 slide : their friction is likely to prevent that. But 

 the best workmanship cannot prevent them from 

 rocking a little. At least, the sum of the motions of 

 each joint will at length come to be something. The 

 haunches will slip away a little, just where the equi- 

 libration ceases. The circular arch will become 

 somewhat elliptic. The joints about that point will 

 open behind ; and if the case be dangerous, the 

 stones will chip away below. Something of this 

 kind, indeed, goes on in the building of every arch. 

 As the courses approach the crown, their thrust 

 makes the lower ones recede a little from the centre. 

 But as the process is gradual, and the finishing 

 courses are adapted to the shape of the opening 

 which receives them, perhaps the only bad effect is 

 the derangement of the crystals of lime, which hare 

 already begun to form, while the cement fixes in the 

 lower joints of the arch. With good workmanship, 

 the amount of the final derangement is so small, that 

 no joint is opened beyond the limit at which repul- 

 sion acts, especially in such great pressures ; so that 

 every stone may be still considered as butting pretty 

 fairly on its neighbours. 



Having now exhibited the effects that may be ex- 

 pected from the friction of the parts of an arch, c 

 thing only remains to be considered in this department 

 of our subject, which is, the lateral pressure likely to 

 arise on the back of the arch, from the materials cm- 

 ployed to raise the structure to the horizontal line. 



If the materials employed here be only a solid massof On tneni..- 

 masonry, it is not easy to see, everything being steady, teriaU for 

 how it can act in any other way than in the vertical *"""<? P 

 direction. If, however, a motion takes place in the ^ a 

 arch, the mass of materials lying nearly over the 

 springing, when the arch is not very different from 

 a semicircle, will have such an enormous friction, if 

 well built ar.d bonded together, as would appear e- 

 2 



