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XLIIL On tke Principles of Arches. By A Correspondent. 



To Mr.TUloch. 



Sir, — At a time when so many large bridges are building, a 

 few ohjections to the principles of arches, as exhibited by the 

 writers on that siiliject, mav perhaps be of some service. 



Dr. Button lias stated, i'n his Tracts, vol. i , that there are 

 three theories ; and that they are all the same in effect, and 

 yield the same conclusions : but we will suppose there are only 

 two ; that is, the wedge theory, and the theory of Emerson, for 

 the Catenarian tlieory is tlie same in fact with Emerson's theory, 

 and is liable to the same objections. 



We think the most hkely method of ascertaining the manner 

 in which the forces act, is to examine an arch that has changed 

 its form in consequence of being overloaded either at the crown 

 or havmches. If the wedge theory is correct, the arch -stones 

 would slide on each other, and the stabdity of an equihbrated 

 arch would wholly depend on the friction of the surfaces in con- 

 tact and the cohesion of the cement. But when an arch is so 

 loaded as to press it out of its original form, the arch-stones do 

 not slide on each other, neither is there any thing like friction 

 takes place*: for instance; suppose the weight to press on the 

 crovriij then the joints would open, as shown at A, at the same 



time the joints at the back of the arch would open as shown at 

 BB : this is what every one who has paid any attention to the 

 iubject must have noticed. 



If the arch-stones were perfectly smooth, they might perhaps 

 act as wedges; but this is a mere hypothetical case, and has 

 nothing to do with the present inquiry: but suppose the arch- 

 Btones were connected with a ceme'Vc which would unite them 

 as firmly at the joints as the solid part of the stone ; it is evident 

 llie arcli would be stronger, but we are at a loss to conceive 

 how tlie wedge theory could be applied to such an arch : yet, if 

 loaded in a similar manner, the fractures would take place at the 



• A liitn writer on bridges tliinks that an arch may be balanced by the 

 friction of the ioiiits alone, by eivins them different decrees of inclination. 



Vol.46. No. 210. Ot.7. 1815. Q same 



