SECT. 2 .

OF THE ARCIIES.

27

stituent parts of the arch, established by the foregoing the-ories, is of that nice and critical nature, that the whole hangsin a kind of tottering state of balance, from the perfect po-lish of the parts, so that any the least accidental extraneousforce or pressure, on any particular part, would destroy theequilibrium, and cause the whole to fall down, except lorthe length of the joints and stones. The theory also sup-poses the parts, constituting the fabric, to be exceedinglysmall, and may be even round, small, polished globules.But because of the shape and roughness and magnitude ofthe parts, of which an arch is constituted, it comes to pass,that a moderate degree of imperfection in the structure, orany accidental shocks or pressure from external objects, hasno sensible effect in displacing or deranging the materials:for the wedge-like form prevents any piece from easilydropping out by itself', and the roughness of the sides pre-vents the wedges from sliding; also the considerable mag-nitude of the stones, or other matter, while it enables themto bear the weight and pressure of the whole fabric, withoutbeing crushed to pieces, admits of a small displacing of ma-terials, or deviation from a perfect balance, as prescribed bytheory, without suffering any sensible inconvenience.

It has been supposed in this proposition, that the direc-tions of the joints, cd, ef, gh, &c, when produced, all meetin the same point o, of the vertical line oar. This howeveris not necessary in the theory; as the directions of thejoints may meet the vertical inso many different points o, o,o,

&c, as in this fig. and yet allthe parts and their affectionshave still the same properties.

This will be made evident byconstituting the small trian-gles, obd, obf, &c, apart, as inthis figure, by drawing, from one point o, the lines <>b, od,of, &c, still parallel to the joints ah, cd, ef, &c, meetingthe horizontal line in the points b, d,J\ &c; for, because