[ ms a 
a lateral preffure, whofe direQion would not be along the tangent, 
and wanting a force to fuftain it, would deftroy the equilibrium, 
Let EABF, 7, mut, reprefent two concentrical femicircles: alfo 
let AB, mm, be two vouffoirs fimilarly fituated, whofe fides, being 
perpendicular to the curves, converge in the centre C: the forces of 
thefe vouffoirs, confidered as wedges, are inverfely as the fines of 
their vertical angles, that is, becaufe of the equality of the arches, 
dire€tly as the radii of curvature: And the like holds in any 
other curves whatfoever. 
11, Acatn, let H&A be the invariable breadth of the vouffoir, 
and Gg HA the incumbent weight; this weight, becaufe the alti- 
tude G/ is fuppofed given, is dire&ly as the breadth 4 & of the in- 
cumbent column; that is, if 4H be confidered as radius, direClly as 
the fine of the angle H4, formed by the tangent at the point H 
with the vertical line gH: but the force of this entire weight muft 
be refolved into two, one g¢ K in the direCtion of the tangent, the 
other HK perpendicular to the curve, which is the force im- 
pelling the vouffoir to fplit the arch; and the line HK, which 
reprefents this latter force, becaufe gH is given, is the fine of 
the angle Hg K, which isequal to that formed by the tangent at 
H with the vertical line. Hence therefore, conjoining both thefe 
ratios, the force impelling the vouffoir is as the fquare of the 
fine of the angle formed by the tangent to the curve, at the 
given point, with the vertical line. 
12. Acain, the wedge, impelled in a direftion perpendicular 
to the curve, endeavours to fplit the arch, and therefore move 
L 2 one 
Fig. 1 
