47

Let a body be projected from B at the Fig. s.height B I from the plane I Iv in thedirection B T, so as to hit the plane in

wind, and if the section of it be a right-angled triangle,or the foreside be perpendicular to the horizon, and thebackside terminated by a sloping plane intersecting theother plane in the top of the wall; such a wall will beequally strong in all its parts to resist the wind, if theparts of the wall cohere strongly together; but if it bebuilt of loose materials, it is better to be convex on thebackside in form of a parabola. If a wall is to supporta bank of earth or any fluid body, it ought to be built con-cave, in form of a semi-cubical parabola, whose vertex is atthe top of the wall; this is when the parts of the wall stickwell together. But if the parts be loose, then a rightline or sloping plane ought to be its figure. Such wallswill be equally strong throughout.

“All spires of churches in the form of cones or pyramidsare equally strong in all parts to resist the wind. Butwhen the parts cohere not together, parabolic conoidsare equally strong throughout.

“ Likewise, if there be a pillar erected in form of thelogarithmic curve, the assymptote being the axis, it can-not be crushed to pieces in one part sooner than in ano-ther, by its own weight.

“And if such a pillar be turned upside down, and sus-pended at the thick end in the air, it will be no soonerpulled asunder in one part than another by its ownweight; and the case is the same if the small end be cutoff, and instead of it a cylinder be added whose heightis half the subtangent.”— These observations are appli-