ON THE STRUCTURE OP COVERED WAYS, QJj^Q 



abutment wbicb will secure tbe blocks, from sbdlng out- 

 wards, wltb tbe usbirftance of tbe force of friction. Gene- 

 rally however tbe obbquity must be mucb less tban tbis ; 

 and tbe resistance of tbe abutment becomes capable of be- 

 inu: exerted in the most tavouruble direction that its friction 

 will allow, that is, in a direction more nearly Vertical than 

 tbe perpendicular to its surface, for example L M, M L N 

 being the an^le of repose; and if we wish to have tbe thrust 

 equal throughout, we must employ blocks of such a form 

 that their divisions may make, with tbe lines converging to 

 C, angles equal to M L N; this however would lead us to 

 make the middle blocks of the form of inverted wedges 

 (Fig. 20), or at k-ast to make their divisions pdrallel : but it 

 will be sufficient in practice to cause the parts next tbe 

 abutments to converge to points somewhat nearer than the 

 point of convergence of tbe middle parts (Fig. 21); nor, 

 indeed, has this arrangement any material advantage over 

 the simpler form of lines converging to a single centre. 



From a consideration of these principles, we may derive Observatiota 

 some useful inferences with respect to arches in g-eneral, ^'^ ^' , '^^ ^" 

 especially such as are employed in buildings.- The objects 

 to be attained in the construction of an arch are to diminish 

 as much as possible the horizontal thrust, and to secure the 

 stability by such an arrangement as requires the least size 

 in the blocks and firmness in the joints. The size of the Size of the 

 blocks must be such, that the curve of equilibrium, under ^^^^^^' 

 the pressure actually produced by the walls, may be every 

 where included within their substance, and even without 

 coming very near their termination ; and the horizontal „ - . , 

 thrust will be less in proportion as the curvature at the ver- thrust. 

 tex is greater, that is, other things being equal, as the arch 

 is higher. Supposing the height of the wall supported by 

 tbe arch to be very considerable in proportion to that of the 

 arch itself, the curve of equilibrium must be very nearly a Curvature. 

 parabola : if the wall is raised but little above the arch, it 

 will approach to a segment of a circle. In order therefore 

 to find whether the size of the blocks is sufficient, describe 

 a parabola through the summit and the abutments ; and if 

 it pass wholly within I'he-blocks, they will stand ; provided 

 hovv ever that their joints are either perpendicular to the 



CUA'C, 



