Chap. XXV.

ON STONE BRIDGES.

1501

produced; their common point of support is necessarily carried in E to the extrados;the joints then tend to close, as is constantly observed, and some builders add to thiseffect by removing wedges, which augment the solidity of the arch, at the same timethat the energy of the pressure which these two parts exert upon each other is the meansby which they are mutually supported. The efforts of this pressure is necessarily carriedtowards the abutments and the inferior parts of the arch, which it tends to overthrow, by

Fig. 2751.

making them turn round their exterior edges K ,h; each half of the arch separates itselfinto two parts, D ,d, which serve as points of support to the upper parts, by. means of whichtheir effort is transmitted to the abutments. These points of support are necessarilyplaced at the intrados: if the abutments have not sufficient stability to resist the efforts ofthe arch, the four parts fall down, turning round the points K, D, E, and d,k : if they arecapable of supporting it, the effect of the sinking is limited to closing the joints at theextrados near the point E, to the intrados near the points d, D, and to make them open atthe intrados near the point E, and the extrados near the points D,c?. The position of thepoints D ,dy which are called points of rupture, which it is extremely important to ascertainexactly, depends on the form of the arch, and the disposition of the weights which itsupports. At the bridge of Nogent the position of the joints of rupture was indicatedbetween the sixteenth and seventeenth course of voussoirs, by the points of inflexion of thetwo lower lines traced on their heads. At the bridge of Neuilly it was not possible todiscover it by the same means, on account of their form, which is an arc of a circle ; but itwas discovered that the joints of rupture were placed between the twenty-sixth and twenty-seventh course, as it was in this place that the joint opened on the extrados.

It is seen that arches cannot fall but in proportion as the voussoirs are placed near thekey, the points of rupture and the base of the abutments separating from each other byturning round their edges: the tenacity of the mortar is opposed to this effect, and thismay be sufficiently great for the arch to support itself, as happens sometimes in ancientconstructions, although the abutments have not their proper thickness ; we cannot, however,rely on the adhesion of mortar, because its effect is only produced at the end of a certaintime, and although, on leaving the arches on their centres, time may be given for the^•masonry to become solid, it is better not to regard the increased solidity obtained by thismeans, and which it would be difficult to value exactly. These observations are foundto be confirmed by several arches which were* in danger of falling, as well as in thosewhich have been demolished : with regard to the latter, horizontal cuts were made intheir piers, and it has been remarked that the first disjunctions appeared at the intradostowards the key; that others afterwards took place towards the haunches, where theirgreatest width was at the extrados, and that, in short, the upper part lowered, dividingitself into two principal parts, each overthrowing the piers opposed to it.

This theory is equally in agreement with the direct experiments made by Gauthey on thissubject, who constructed semicircular arches and others for the purpose; their openingswere 25} inches • the voussoirs, 1 inch in width at the intrados, were made in wood, andworked with great exactness ; he endeavoured to break the equilibrium between the thrustsof the upper parts and the stability of the lower parts, by diminishing the thickness of theabutments, or by loading the summit of the arch, and he constantly remarked that therupture tended to operate with the circumstances already explained. These sameexperiments were repeated on a larger scale by M. Boistard, in arches which he constructedwith much exactness in voussoirs of brick rubbed to a face, the thickness and the heightof the section of which were 4] inches; the arches were 2 -274 metres (7 -458 feet) of opening.