114 



THE ARCH. 



of 2 1 inches. At the same timo that tlic chain was defloctGd 

 under the load at any point, it was seen that the radius o± 

 curvature of the chain was sharporwd there, under the load, 

 but flattened along the other parts. This latter elfoct we 

 at once know mud be the case, for the chain would other- 

 wise have been lengthened. 



If now, while the engine is in nud span, we ])rick through 

 every link of the chain into the j)aper behind, we shall 

 obtain the new line of equilibrated, curvature, and shall see 

 exactly how the equilibrated curve of the line A has been 

 modified by the added load of the 5()-ton engine on the 

 middle of the arch. Lot us draw a dotted line through 

 these points, and then turn the drawing the other way up. 

 Now consider what we get then. We get the true form of 

 the constriicted arch under the new load, as pointed out 

 by the hand of nature, and we know that the line of thrust 

 must assume that new form m order to support the com- 

 bined loads WW placed u7)on it. We tliereforo see that, in 

 order to carry in truly balanced form this 50-ton load on 

 the middle of the constructed arch, the equilibrated curve 

 of thrust is there raised 2 J inches, though the curvature 

 is depressed somewhat along the other parts, whioli are not 

 similarly loaded; the dotted line will accordingly be 2f 

 inches above the line A at the crown and gradually run into 

 it lower down. We know that the line of thrust, under the 

 load, 7nust and does pass along a line represented, by that 

 dotted curve through the solid arch, though nothing of this 

 is visible in the constructed arch. 



Again, we know that under the 50 tons added load there 

 would also be an increased amount of thrust, which would 

 render necessary an increased thickness of arch. Let us 

 reckon what this increase amounts to. 



As the engine stands upon the crown of the arch, it 



