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 PREFACE.

AN arch being formed (according to the usual modes of construction) by the apposition of wedges, or sections of a wedge-like form, the properties of arches seem to be naturally derived from those of the wedge, on which principle the inquiries in the ensuing Tract are founded.

By considering the subject on this ground, it appears that the theory of arches may be inferred from geometrical construction, depending only on the known properties of the wedge and other elementary laws of mechanics, without having recourse to the more abstruse branches of geometry in explaining this practical subject, to which a more direct and obvious method of inference seems better adapted.

A geometrical construction for adjusting equilibration on these principles, extended to arches of every form, with the various consequences arising from, or connected with it, are the subject of the ensuing pages, in which rules are investigated, in the first place, for establishing the equilibrium of arches on two distinct conditions, namely, either by adjusting the weights of the sections according to the angles which are contained between their sides, supposed tube given quantities; or, secondly, by supposing the weights of the wedges or sections to be given, and investigating what must be the angles contained by their sides, so that the pressures on them, may be an exact counterpoise to the weight of each section, due regard being had to its place in the arch. In the case when the arch is designed to support an horizontal plane or road, on which heavy weights are to be sustained.