1818.] across the Mersey, at Runcorn, 21 



Road. 



50 prepared frames of wrought-iron (Fig. 7), each weigh- 

 ing 50 cwt. at 75/. per frame, for 50 frames, is 3750 



750 tons of cast-iron plate (W, Fig. 7), at 9/. per ton .... 6750 

 4100 feet of cast-iron railing, and basis, weighing one 



cwt. per foot, 410 tons at 10/ 4100 



Fitting the whole together 500 



400 tons of gravel, clay, and chalk, and laying down, &c. 

 over the cast-iron , 400 



Miscellaneous. 



Excavating to the rock, and preparing it for the cast-iron 



fulcrums, fender, piles, &c 1000 



Excavating (at R) to fix the rods, C, C 100 



The two fulcrums or abutments, S S 650 



The two lodges, earth-work at the ends, and all unforeseen 

 expenses 4551 



40000 

 If the road is formed of timber, this estimate may safely be 

 reduced to 30,000/. 



Remarks. 



The novelty of this bridge seems to require that some 

 rationale should be given of its construction, and sufficiency to 

 answer the proposed ends. This may either be done expert? 

 vieutally, algebraically, or geometrically. Experiments in matters 

 of this sort are of little use, unless made on a scale nearly as 

 large as the erection itself; and therefore, excepting for some 

 particular purposes, they have not been attempted. The alge- 

 braic calculus, though much the most convenient and accurate 

 method is not generally understood. The geometrical mode, 

 therefore, of exhibiting the composition and the resolution of 

 forces by lines, and the relation of the forces ascertained by a 

 scale, has been adopted in the following remarks, as easy of 

 comprehension, and in respect to practice as equally satisfactory 

 to the mathematician with either of the other modes. 



I. On the Strength of the suspending Rods, and those forming 

 the Basis of the Road. 



The total weight of the road and rods is as follows, viz. : 



Tons. 



Suspending rods, and rods forming the basis of the road . . 109 



Wrought-iron frarnes 125 



Cast-iron convex covering plates 750 



Cast-iron parapet railing and plinth 410 



Clay, gravel, and chalk 400 



1794 

 (or say) 1800 



