E par 
may not be juftly enumerated amongft the caufes, to which we 
owe its introduction into architecture, 
g. THE equilibration of arches, which has been fo well treated of 
by Mr. Emerfon in his E/ffay on the Conftruétion of Arches, and 
Mr. Hutton in his Effay on Bridges, may be afcertained in a 
very fimple manner, by confidering the vouffoirs, or arch-ftones, 
as fo many wedges urged by the incumbent weight, and endea- 
vouring to fplit the arch. Now the efficacy of a wedge depends 
on the magnitude of its vertical angle, the impelling force, and 
the refiftance to be overcome. On the firft account the force of 
the vouffoir, confidered as a wedge, at any point of the arch, 
is dire€ily as the radius of curvature of the arch at that point; 
on the fecond account, it is as the fquare of the fine of the angle 
formed by the tangent to the curve, at the given point, with a 
vertical line ; and on the third account, it is directly as the fine 
of the fame angle. 
to. Tue materials of which arches are compofed are fuppofed to 
be of the fame magnitude; and the joints of the ftones muft always 
be perpendicular to the curve, for every force acting againft a 
furface ats in lines perpendicular to it; and therefore the force 
of the incumbent weight to rend the curve is to be refolved into 
two, one of which muft be perpendicular to the curve, and the 
other, of confequence, in the direction of the tangent: now if 
this latter force were not perpendicular to the joints, that is, if 
the joints were not perpendicular to the curve, there would arife 
a lateral 
