1839] The comparative cheapness of Large and Small arched Bridges, li? 



md less costly, as it has fewer of these piers. In these summaries the 

 first position only seems to deserve investigation ; for, if I am rightly 

 inforraed, the difference in the amount of materials in the two cases, 

 varies only as the span of the arch, and is not affected at all, by the 

 number of piers ; that is, the strength of the piers may be regulated in 

 direct proportion to the span of arch ; if the span be double, the piers too 

 must be tvv'ice as thick ; so that in the whole length of the bridge, the 

 solid dimensions of the pier work are equal, whatever be the distance 

 apart ; but on the other hand, wider arches "must be thicker than narrow, 

 or they will not stand. 



Architects tell us, that a bridge arch (of any but the very smallest di- 

 mensions), is not safe, unless it have at least one and a half feet of 

 thickness at the apex, and it seems to be further agreed, that this thick- 

 ness is sufficient for a span of 36 feet ; all smaller arches therefore would 

 seem to involve a waste of strength, or have a thicker platform than is 

 required, and therefore they ought not to be built. 



In proportion as this limit is exceeded, il^ppears, then, that the plat- 

 fonn must be thickened, whilst the piers must also be,augmented, as be- 

 fore described, in such a ratio, as to make the total of their thickness, 

 just what it would be, if the spans were no more than 36 feet; we may 

 therefore conclude that a brick bridge contains the smallest possible 

 quantity of materials compatible with strength, if its arches have a span 

 of 36 feet : but is it therefore less expensive ? 



To determine this, keeping out of sight for the present the question 

 of risk from more impeded water-way, the following propositions should 

 be solved : namely, whether, two piers, say of 6 feet, can be built for 

 the same m^oney as one of 12 feet; whether the difficulty and conse- 

 quent liability to error is increased or diminished by multiplying the 

 works in the bed of a river ; whether (remembering that bricklayers are 

 paid by the day and not by the quantity of work done) we are to sup- 

 pose that more or fewer tiers of arch-work will be laid in the same time^ 

 each series requiring a fresh adjustment, by having fewer or more angles 

 of direction to consult for the joints ; whether (all arches being consi- 

 dered works of skill), the likelihood of individual or partial failure is di- 

 minished or increased by the numerical amount of such works of skill ; 

 whether a sinking of the piers is more to be anticipated when the foun- 

 dations are many and narrow, or few and broad ; whether danger of un- 

 equal subsidence of the arches is greater or less, as there are many or 

 few arches to subside ; and, lastly, whether all these sources of error 

 and hindrances to the workmen would not in the end render the many 

 arched bridge a work costing more money than one, more nearly ap- 



