110 



THE ARCH. 



standing on that part of the arch. Or, if we start from one 

 end and stick the weights on the first 34 rods, and after- 

 wards move them forward one by one, we shall see the oflfoct 

 of the 50-ton engine as it passes over the whole length of 

 the bridge. We shall find that its greatest effect is when 

 it gets near the centre, when it depresses the " line of 

 thrust " 2 1 inches. 



It may be well to pause a moment here in order to form 

 a clear conception of what is meant by the " line of thrust " 

 in an arch. For this purj)oso we may with advantage look 

 first to the suspended arch ; for its equilibration is self- 

 formed and therefore both visible and measurable ; we must 

 also recollect, that every constructed arch has its suspended 

 counterpart, in which the forces in every direction are the 

 same, the nominal difference being, that what are tensions in 

 the suspended, are thrusts in the " constructed " arch. 



In the model bridge as drawn, the line of thrust may be 

 supposed to pass tliroiigli tlio centre, in thickness, of the 

 arch; while in its suspended countci'part, the chain model, 

 it passes through the centre of the chain; but this really 

 makes no difference, for if the lino of tension is supposed to 

 pass through the rods, half the thickness of the arch below 

 their tops, so that the, tops of the rods should, when the 

 model is turned np, represent the soffit of the constructed 

 arch, and the line of tension be thus brought into the middle 

 of what represents the arch thickness in the constructed 

 arch, yet it would not have made the least difference to the 

 curvature, or to the comparative thrusts and tensions any- 

 where, but it would have added a great diiliculty to the 

 manufacture of the chain model. The model, as it stands, 

 is not really perfect ; for example, in our calculations from 

 the formula, wo assume the distances apart of the rods to bo 

 the same horizontally, but they are not so, for the links of 



