Mr Sang on the Construction of Oblique Arches. 303 



i-esults of that analysis I proceed to lay before the Society of 

 Arts, in the hope that, though I may be wrong in supposing 

 them new, their publication may serve to disseminate correct 

 notions on this intricate subject. It is a common idea that the 

 oblique is weaker than the right arch, and that the twist of 

 the stones causes a great waste of material. The truth is, 

 that if both bridges be skilfully constructed, there is no dif- 

 ference in point of strength between them, while the twist 

 on the arch-stone of the oblique bridge causes a most trifling 

 loss of matter, and therefore our road trustees should never 

 hesitate to adopt that which agrees best with the rest of the 

 line. There is no limit to the obliquity, nor need even the 

 several abutments run parallel with each other. 



The general question of the construction of an arch resolves 

 itself into two parts ; the first relating to the connection 

 which ought to exist between the curvature of the vault and 

 the weight piled on each portion of it, is absolutely identical in 

 the two cases of right and oblique bridges, and is therefore left 

 out in the present inquiry ; the second, however, relating to 

 the forms of the arch-stones, bears directly on the oblique 

 arch, and will therefore engross almost our whole attention. 

 The outline of the bridge and the form of the vault having 

 been determined on, the problem becomes this ; To cover the 

 surface of the centering with blocks of such sizes and forms as 

 vmy insure the stability of the structure. Now, if it be pre- 

 mised that the curved surface of the vault must never be ver- 

 tical, the solution of the problem can always be attained. 



It is clear, from the general form of a bridge, that the lines 

 of pressure ought to run from one abutment to the other, and 

 should be contained in vertical planes parallel to the walls of 

 the parapet. Imagine, then, that the vault is intersected by a 

 multitude of such planes, the lines of intersection will indicate 

 the directions in whicli the pressures ought to be transmitted 

 from block to Ijlock. Now the stability of a structure is ob- 

 tained by making the surfaces at which the pressures are com- 

 municated perpendicular to the directions of those pressures, 

 and therefore all tluit is required is to trace on the surface of the 

 centering a line which may cross all the lines of pressure at 



