MECHANICS. 149 



This is nothing more than the general proposition above, 

 applied to a particular case. In Fig. 17. if B be the 

 crown of a circular arch, the weight of the voussoir 

 LKNM should be to that of the voussoir MNPO, 

 as the tangent of BN minus the tangent of BK, to 

 the tangent of BP minus the tangent of BN ; or if, 

 from a given point D, DH be drawn perpendicular 

 to AC, and if the joints KL, &c. be produced, to cut 

 it in E, F, and G, the weights of the voussoirs must 

 be as the segments DE, EF, FG, in order to pro- 

 duce an equilibrium. 



As the stones themselves cannot always be made in 

 the proportion thus required, the wedges, of which 

 they make parts, are supposed to be extended up- 

 ward, by courses of masonry. The whole mass in- 

 cluded between the planes of the joints produced, 

 as far as that masonry extends, is understood to 

 make up the weight of the voussoir. It is the busi- 

 ness of the theory to calculate this weight ; and to 

 construct the curve which bounds the voussoirs, when 

 so produced. 



231. In an arch, of which the in trades is a 

 circle given in position, the depth of the key-stone 

 being given, it is required to describe the curve of 

 the extrados. 



Let AGE (fig. 18.) be one-half of the arch, C the 

 centre, AB the height or depth of the key-stone. 

 From the centre E, with a distance equal to CB, 

 intersect CA in D ; through D, draw DH per- 

 pendicular to AC; and through G, any point in 



the 



