THE AECH. 



115' 



would of itself, as lias been already explained, add 2-32 cwt. 

 to the 7 cwt. load on the sqnare foot at the crown. This, 

 multiplied by the radius of curvature, which is now 104 

 feet, as shown by the dotted line, instead of ] 10 'foot as 

 formerly, will give us an additional horizontal thrust of 10 

 tons on the foot in breadth of the arch. This additional 

 thrust will add 3^ inches to the necessary thickness of the 

 arch at the crown, and 4-4 inches at the springing. If 

 these additional thicknesses are added on to the original 

 necessary thickness, they will make 12|- + 3J=16j- inches at 

 the crown and 15 + 4'4=]9'4 at the springing, as shown by 

 the lower dotted line under the line B, they will give us the 

 necessary thickness under the new load all round, and will 

 still leave an ample safety margin of about 8 inches every- 

 where. 



It has been asked. What would be the effect of a train of 

 such engines standing upon the bridge ? 



To show the effect of this by means of the chain model 

 would be simply to stick upon every rod throughout the 

 model one of the small brass weights used to represent the 

 load of the 5()-ton engine. The eifo<',t of this is to ])racti- 

 cally restore the original curvature of the " line of thrust," 

 and to add a little to the horizontal thrust. Thus, putting it 

 into figures : The original radius of curvature of the " line 

 of thrust" at the crown was 110 feet, and this was sharpened 

 to 104 feet by the 50-ton engine, while the rest of the chain 

 was flattened. This fact proved simply that, as compared 

 with the original lino of thrust, the proportion of the vertical 

 load to the horizontal thrust had been increased at the 

 crown and diminished elsewhere ; but now, by the addition 

 of the increased weight to every rod all along tlio model, 

 we have practically restored that proportion, and there is 

 now left only the increased horizontal thrust to be taken 



