THE ARCII. 



105 



and draw F G parallel tn it. Lastly, wo take Im equal to 

 R G and draw the dotted lino from G parallel to it. We 

 have thus completed the arch on that side and may com- 

 plete the other side in the same way, the two sides being 

 natiirally alike under a liorizontal road line. 



Wo have thus drawn a truly equilibrated arch between 

 the abutments A and G, in which every line in the diagram 

 shows its thrust in its own direction. 



In the diagram we have only divided the road line into six 

 equal parts for the sake of clearness, but in practice it may 

 preferably be diVidod into a much greater nuiid)or of equal 

 parts, in order to show more exactly the ti;uo curvature of 

 the arch. 



This constructive method is perfectly trxie in principle; 

 but in practice it requires so great accuracy that it can 

 hardly be relied upon for arches of wide span, because the 

 errors are accumulative. It is better, then, to make use of 

 Dr. Ilutton's formula in such cases, "whereby we may obtain 

 the true curve to any degree of accuracy. 



In the next example the crirve has been obtained by the 

 use of this formula, a copy of which is here inserted : — 



:€ 



a 





y 



7^. 



Half Spcav ■ h, 



■Rise + cv - c 



y 'h)(- 



hyp.l.g.^t^^^ 



hyp. log. 



C-tVc^'O/'' 



The largo drawing shows the elevation of a " Model 



