126 LECTURE XIV. 



it may completely destroy the structure ; but when the stones or blocks 

 composing it have flat surfaces in contact with each other, it is necessary 

 that the line expressing the direction of the pressure be so much disturbed, 

 as to exceed at some part the limits of these surfaces, before the blocks can 

 be displaced. When this curve, indicating the general pressure which 

 results from the effect of a disturbing force, combined with the original 

 thrust, becomes more remote from the centre of the blocks than one sixth 

 of their depth, the joints will begin to open on the convex side, but the 

 arch may still stand, while the curve remains within the limits of the 

 blocks. 



It is desirable that the piers of bridges should be so firm, as to be 

 able not only to support the weight of half of each adjoining arch, but also 

 to sustain, in case of the failure of one of those arches, the horizontal 

 thrust of the other ; and the same condition is obviously necessary for the 

 stability of walls of any kind which support an arched or vaulted roof, 

 wherever there is no opportunity of assisting the strength by ties or chains 

 of any kind. There are two ways in which such a pier or wall may give 

 way : it may either be overset, or caused to slide away horizontally ; but 

 since the friction or adhesion which resists the horizontal motion is usuallv 

 greater than one third of the pressure, it seldom happens that the whole 

 thrust of the arch is so oblique as not to produce a sufficient vertical pres- 

 sure for securing the stability in this respect ; and it is only necessary to 

 make the pier heavy enough to resist the force which tends to overset it. 

 It is not, however, the weight of the pier only, but that of the half of the 

 arch which rests on it, that resists any effort to overset it, and in order that 

 the pier may stand, the sum of these weights, acting on the end of a lever 

 equal to half the thickness of the pier, must be more than equivalent to the 

 horizontal thrust, acting on the whole height of the pier. The pier may 

 also be simply considered as forming a continuation of the arch, and the 

 stability will be preserved as long as the curve, indicating the direction of 

 the pressure, remains within its substance. 



The arches of Black Friars bridge are of an oval form, composed of cir- 

 cular arcs, and differing but little from ellipses ; the arch stones are so 

 large that the pressure in any direction might be very greatly increased 

 without causing the general result to exceed the limits of their magnitude, 

 or even to approach very near to their surfaces. (Plate XII. Fig. 156.) 



The construction of a dome is less difficult than that of an arch, since 

 the tendency of each part to fall is counteracted, not only by the pressure 

 of the parts above and below, but also by the resistance of those which are 

 situated on each side. A dome may therefore be erected without any 

 temporary support like the centre which is required for the construction 

 of an arch, and it may at last be left open at the summit, without standing 

 in need of a keystone, since the pressure of the lower parts is sufficiently 

 resisted, by the collateral parts of the same horizontal tier, to prevent the 

 possibility of their falling in, or of their forcing out the upper parts. The 

 weight of the dome may however force out its lower parts, if it rises irt a 

 direction too nearly vertical; and supposing its form spherical, and its 

 thickness equable, it will require to be confined by a hoop or chain as soon 



