AT BROUGHTON. 393 



its effect in the direction ba is = a? x cos. bah. 

 But COS. BAH = cos. BCF = 8in. 33M0'=.547, 

 and tension of side chain = 396.6 tons, Art. 4, 

 .'. X X .547 = 396.6, whence x = 735 tons. 



In the piers of this bridge, I understand, there 

 are no ci*amps, and the solid content of tlie wedge 

 is 150 yds. and its weight about 280 tons. Hence 

 the weight of the wedge is little more than i 

 of what it ought to be, if the surface represented 

 by the line ab were a smooth one, and there 

 were no allowance made for the tenacity of the 

 cement. The resistances from roughness of 

 surface and tenacity cannot be estimated, but 

 considering that perhaps not | of the wedge 

 would be removed at all, the rest separating 

 from it, it seems fair to conclude, that the pier 

 would give way in this place when the chains 

 were not more than half loaded to their breaking 

 weight. 



From the preceding inquiry it appears, that 

 were the bridge overloaded it would give way, — 

 1st in the pier as above, — 2nd in the side 

 chain, — 3rd in the top link of the catenary, — 

 4th in the succeeding ones, and 5th at the bottom 

 at C, Fig. 1. 



3 D 



