AT BROUGHTON. 387 



Fio. 2. 



If DC (fig. 2. J be the top link of the catenary, 

 AC the side chain (which here is nearly straight,) 

 and CE the vertical link suspended from the 

 pillar resting on N, and supporting tlie whole; 

 and if we make df horizontal, and of vertical, 

 the angle cdf = 18°. 32'*. Now the whole 

 tension in cd =351 tonsf : resolving this into 

 its horizontal and vertical effects gives 



tons. 



351 X COS. 18o. 32': zr 351 X . 9481 = 332.8 = horiz. tension, 

 351 X sin. 18«».32' = 351 x .3179 = 111.6= weight supported. 



* The angled of the top link of the catenary with the 

 horizon at the two ends of the Bridge, are 18®. 35' and 18°. 3(y, 

 their mean therefore = 18^. 32'. 



t The chain abode (fig. \.) is uniform throughout, and has, 

 taking both cables, 13 square inches in its cross section. The 

 cables would therefore require a direct strain of 13 X 27 = 351 

 tons to break them ; the mean strength of a bar of iron an 

 inch square, being 27 tons, (Barlto'i Essay on the strength of 

 Ttmber, Appendix.^ 



I The sinc9, cosines &r. in this paper arc the natural onet. 



3c2 



