112 



THE ABCH. 



is still within tlio base. Seeing no movomont in the pillar, 

 the workman occasionally adds another plank or two, until, 

 in the end, the last plank he adds sends the line of thrust 

 outside the base, and then the whole falls to the ground. 



This exactly represents the relation of the " line of 

 thrust " to the constructed arch. The arch, once built, 

 cannot move ; it can only tumble down whenever the " line 

 of thrust " is driven outside of the arch in any part. 



In the chain model, therefore, we see that the chain 

 (every link of which is freely movable in any direction in 

 ixnswor to the forces applied to it) must accurately asKumo 

 the truly equilibrated curve-line of tension, and must also 

 thus show us the corresponding " line of thrust " in the 

 constructed arch, both as it stands under the dead load 

 only, or under any added load. In the same way wo have 

 seen that the weight of each rod and its link tells us the 

 precise vertical load at that point. Thus we get the load of 

 7 cwt. on the square foot at the crown of the aroh repre- 

 sented by the weight of the central rod and. its link. We 

 get the thrust against the abutments, 44'9 tons on the foot 

 in width of the arch, by the pull of the chain at its extremi- 

 ties, as measured by a delicate and well-constructed spring 

 balance ; and the horizontal thrust throughout the arch, 38'6 

 tons on the foot in width of the arch, by the pull of the 

 chain in its centre, where the chain is horizontal. 



We may also got, in like manner, exact measurements of 

 all the increased strains or thrusts caused by any added load 

 on any part of the arch ; such as those that would bo caused, 

 tor example, by the passage of the 50-ton engine over the 

 whole length of the bridge. 



Now, as in the suspended nrch, the chain must bo made 

 strong onongh to bear the dead load of the whole structure, 

 together with the greatest live load that can ever bo placed 



