Arch, or Arc In geometry, a part of a curve line, as of a circle or an ellipse, etc. Arch, in architecture, an aperture, the upper portion of which is bounded by curve lines, as we see in porches, bridges, etc.; they are of various forms, and are designated by various names, according to their figure, as circular, elliptical, cycloidal, etc. Arch of equilibrium, in the theory of bridges, is that arch which is in equilibrio in all its parts, and therefore equally strong throughout, having no tendency to break in one part more than another. The arch of equilibration is not of any determinate curve, but varies according to the figure of the extrados; every different extrados requiring a particular intrados, so that the thickness in every part may be proportional to the pressure. The subject has occupied the attention of several eminent mathematicians, and has been fully treated by Dr. Hutton, in his " Principles of Bridges," and in some of his tracts; where the proper intrados is investigated for every particular form of extrados; and it shews, that in semicircular and semi-elliptical arches, and, in fact, in all arches springing perpendicularly from a horizontal line, the line of their extrados becomes assymptotical as it approaches a perpendicular passing through the points from which they spring, and that such arches require to be loaded infinitely over the haunches.
But the researches of mathematicians upon this subject, although they are not without utility, have not been of any great service to the practical builder, who, guided by a set of maxims which are the fruits of observation and experience, constructs arches of immense span, differing widely from the form assigned by theory, which are, nevertheless, stable and durable. This arises, perhaps, not from the theory being false, but from its being imperfect; mathematicians calculating the effects of gravitation only, without allowing for those of cohesion, friction, and some other forces, which undoubtedly operate in an arch, although it is difficult to estimate their several quantities. Hence in practice it is found sufficient if the arch of equilibrium be comprised within the boundaries of the voussoir, or stones, forming the arch, without its being necessary for either the intrados or extrados to conform exactly to that curve. For good practical views on this subject, we refer our readers to Gwilt's Equilibrium of Arches, and to the article " Bridges," in the Edinburgh Encyclopedia.