THK ARCH. 



109 



as drawn, and the, ends of tlie suspend od rods sliow the 

 horizontal road line. 



This is a practical proof of the accuracy of tlic curve 

 calculated from the formula, and of its coincidence with the 

 true line of thrust. 



But this model will toll us more than this, and luore than 

 wo can find out from our formula. Tor instance, though we 

 may now be prepared to grant tliat the arcli may at present 

 1)0 in true equilibrium as it stands, we may still wish to 

 know how it would be affected by a very heavy load passing 

 over tho bridge from end to end. This tlie model will at 

 onco toll us in an equally simple and pi'actical manner. 



Let us take, for example, tho heaviest locomotive engine,. 

 say of ,50 tons weight, ou a wheel base of IG feet, passing 

 over tho bridge ; what effect will such a load have in dofloct-i, 

 ing the curve of equilibration ? 



First, we must recollect that this wheel base of IG x 5 

 feet on a permanent way would bo spread, by i-ho coliosion 

 and friction of the structure, at an angle of at least 1:1, 

 and that tlierefore tho load would take a bearing on tlie 

 arch below of 27 foot long by IG feet wide ; that is to say, 

 that on IG feet in breadth of the arch a now load of 50 tons 

 would bo placed, extending 27 feet in length. This would 

 add 62| cwt. to tho load on each foot in breadth of the IG 

 feet. Now, as wo suppose the chain model to represent one 

 foot in breadth of tho arch, then the imposition of this 50-ton 

 engine will add a load of 62^ cwt. to 27 feet run of this 

 model ; and as the rods arc 9; inches apart, it will come on 

 34 rods with a load of 1-84 cwt. on each rod. We have here 

 34 small brass weights which represent 1-84 cwt. on the 

 scale of the model, and if we stick these wciglits on 34 suc- 

 cessive rods in any part of the arch, wo shall see precisely 

 the effect on the equilibrated curve, of the 50-ton engine 



