1496

THEORY AND PRACTICE OF ENGINEERING.

Book II.

span, in addition to the 13 inches, and for arches exceeding these the twenty-fourth partfor the first 104 feet, and the forty-eighth for the remainder.

In the segmental arch of Wide Bargate Bridge, at Boston, in Lincolnshire , whose spanis 50 feet, the height of the key-stone is 2 feet; at Conan Bridge, in Ross-shire, whosespan is 65 feet, the key is 2 feet 6 inches; at Kelso Bridge, the span of which is 72 feet, it is3 feet 3 inches; Darlinton on the Trent, which has a span of SO feet, the key-stone is 3feet; Hobhole, near Boston , whose arch is 90 feet span, the key is 3 feet 9 inches ; Wel-lington Bridge, over the Aire, where the span is 100 feet, the depth of the key is 4 feet.The arches of Waterloo Bridge, London , are 120 feet span, and the key-stone is 4 feet 6inches. At Vieille Brioude Bridge, erected in 1454, oyer the Allier , where the span was183 feet 3 inches, the height of the key was 5 feet 3 inches ; the chord of this arch wasthe largest known, but failing in the haunches it was taken down, and replaced by the pre-sent bridge.

Nothing is more important than the right proportioning of the key-stone, and by areference to the several accounts already given of bridges, it will be seen how this has beenregulated by practice; a twenty-sixth of the span is generally given for its depth wheregranite is employed.

Whatever the form given to the arch, the walls or piers that support it may eitherbe brought up in horizontal courses, or depressed in such a manner that they graduallyincline, following out the curve: a semi-circle, or semi-ellipse, requires level abutmentsto spring from, whilst the others should be made to incline, and have their joints andfoundations radiating, or vertical to the intrados, so that the pressure they produce may becarried in a direction as nearly as possible at right angles to it: after the arch-stones are pre-pared and their two beds cut to their proper inclination and numbered, they are laid in theirsituation, so that their joints radiate vertically to the intrados ; after which the curve underit, which is a portion of the arch, must be examined and worked out to its proper form,or when the centering is removed, the whole will have a crippled appearance. The exactcurvature of the intrados, already drawn out at large, must be constantly referred to duringthe progress of setting the voussoirs, to ascertain if each is not only in its due position,but has its proportion of curvature, and its joints properly directed. Mould boards, fittedexactly to the large curve, and numbered, enable the mason to effect this portion of hiswork with great accuracy: when the voussoirs are not composed of single stones, thesame or greater care must be taken to fit in that which is to complete the one the lengthof which is not sufficient. The lewis-hole, cut in the upper part of each stone, is so placedwith relation to its centre of gravity, that it can be raised and lowered in its intendedposition without turning or twisting it round. Without this attention, it is useless for theengineer to occupy himself with the form of the curvature of an arch, for the flowing lineof an ellipsis would be destroyed and rendered unsightly, if either of its numerous voussoirswere otherwise placed than in its right position: instead of a continued and regular sweep,either a polygon or broken outline would be the result; to remedy such neglect, andbring the soffite of an entire arch, of any curvature, into the state required to please theeye and satisfy it that its strength is not impaired, would oblige, after the centre wasstruck, the erection of a scaffold and the employment of many workmen, and after all thebeautiful form first aimed at would not be produced.

The Thickness to the Abutments of Bridges. — Parent and Lab ire were the first to turntheir attention to the form of arches, but the nature of the thrust, and the manner inwhich the rupture of an arch takes place, had not been at that time sufficiently ob-served, and consequently they employed an hypothesis which does not agree withpractice: they supposed that the joints of the voussoirs were perfectly polished, fromwhence it results that for the arch to support itself in equilibrio, it is necessary that thereciprocal pressures exerted by the voussoirs perpendicularly to their beds should mutuallydestroy each other; if such were the case, it would be easy, when the thickness of thearch at the key is given with the curve of the intrados, to determine that of the extrados,and it must be observed, that in the case where the intrados is a semicircle, we have forthe extrados a curve, which is infinitely prolonged, and to which the horizontal diameterof this semicircle serves as a symptote. Hence it results that the semicircular arch couldnot support itself unless the first voussoir, setting off from the springing, had an infinitelength; these arches then would not have any thrust, and would tend on the contraryto add to tfte stability of their piers. If the arch were extradossed of equal thickness, orif the voussoirs had all the same length, the equilibrium could not subsist, unless therewere given to the curve of the intrados a particular form : when the thickness of the archis very small, this form must he a reversed catenarian curve, since the arcli being thenconsidered an assemblage of heavy spheres infinitely small in contact with each other,the conditions of equilibrium are the same as those of a heavy and inextensible cord,^hich results are deemed of little practical utility. The first writers on this subject,* Ashing to prove that they were applicable, endeavoured to determine the thick-