rebuilding London Bridge. 29 



^ T th part of the span ; we may therefore conclude, that the thick- 

 ness of the arch of the new London Bridge there was intended to 



150 



be 1 =. 6 feet 3 inches ; ana this conclusion is confirmed by 



24 J 



the other parts of this bridge, and so far as the scale of the draw- 

 ing of it is evidence. This rule is purely empirical, and so 

 acknowledged to be : it may apply for Neuilli bridge with Saillan- 

 court stone, but it does not apply with marble for the bridge of the 

 Holy Trinity * at Florence, and ought not with granite at Waterloo 

 bridge, nor cannot apply in arches surbaissees in all their varieties. 

 The versed sine of the bridge of the Holy Trinity is between ^th 

 and ith of its span, and its thickness at the vertex is ^th part of 

 the span. The rule also, which Perronet gives in another part of 

 his work, in order to evade an obvious absurdity, viz., that the 

 thickness at the vertex of an arch should be ^jth of double the 

 radius of curvature there, leads to greater absurdities than that of 

 which the latter is an evasion. For, in the case of the bridge of 

 the Holy Trinity at Florence, the thickness of the arch at the vertex 

 is the -rg^nd part of the diameter of the circle of curvature there, 

 and that of his own bridge of Neuilli is i^jth part. It is desir- 

 able that a mode of determining this important feature of an arch 

 could be obtained directly from the strength of the material to be 

 used, and the weight to be borne, making due allowances for con- 

 tingencies ; and also, when this is derived, to determine any point 

 of thrust, and the correspondent angle, that is, the extrados of an 

 arch, and its abutment or bearing piers, from the same sources. 

 These questions M. de Prony, in the first volume of his Nouvelle 

 Hydrnulicjue f, investigated; but assuming the angle of rupture 

 with the vertical gratuitously, and not having illustrated by examples 

 the application of his formulae, the articles require more eclair- 

 cissement than M. Gamier has given them in the Introduction to the 

 second volume, before they can be available to the practical profes- 

 sor. The solution of these questions has also been given analytically 



• No. 29, Journal of Science, Roy. Inst., for April nit. 

 t Art. 353 to 379- 



