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Tracts on vaults and bridges : containing observations on the various forms of vaults; on the taking down and rebuilding London Bridge : and on the principles of arches: illustrated by extensive tables of bridges : also containing the principles of pendent bridges, with reference to the properties of the catenary, applied to the Menai Bridge : and a theoretical investigation of the catenary / Samuel Ware
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84

TO DETERMINE THE NUMBER OF SQUARE INCHES INTHE COLLECTIVE SECTIONS OF CHAINS SUPPORTINGA ROAD.

Suppose a road to be supported bychains suspended in the form of a cate-nary, and made of rope, wood, iron, steel,or any other materials ; and that the road-way be either on or below the chains;but so arranged as not to alter the catena-rian form of them : It is required to deter-mine the number of square inches in thecollective sections of the chains, whenthe weight of the road, the materials ofwhich the chains are made, and any two ofthe five quantities 9, c, x, z or y are given.

Put n for the number of square inchesin the collective sections of the chains.

g for the weight of a part of the samematerials measuring one inch square by onefoot long.

f for the weight or tension, which wouldjust overcome the force of cohesion in alike piece of the same materials.

 
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