MENAI BRIDGE. c4M 



than r^th of the whole span. Had it been 



greater, the piers must have been larger, and 

 the bridge would perhaps have been more liable 

 to agitation; otherwise the quantity of iron 

 in the main chains might have been considerably 

 less, as will be seen from below. 



^' Suppose, between two fixed points in a 

 horizontal line, a number of uniform catenaries 

 be suspended of different lengths and thickness, 

 but all having the same quantity of matter in 

 them. That catenary will bear the greatest 

 weight, distributed uniformly along its curve, 

 which has its versed sine about jrd of its span ; 

 and the curve so proportioned would bear, 

 along its length, more than double what it 

 would with the proportion of verse<l sine to 

 span used in chain bridges generally. For it 

 might be shewn that, if with a span of 200 

 and versed sine 14.81 (nearly the ratio of the 

 Menai Bridge), the weight borne was 28, other 

 versed sines as below would nearly give for 

 the weights borne those which follow. 



ver. sines, 16.82, 25.53, 44.13, 57.67, 65.85, 77.15. 



weights, 31.63, 44.3, 60.7. 65.49, 80.2, 65.72. 



This last matter, in a different form, has been 

 pursued by Mr. Davies Gilbert, Phil. Trans. 



