ARBOR. The spindle or axis which communicates motion to the other parts of a machine.
ARCH. (Lat. arena, a bow.) In build ing, is structure of stones or bricks, or distinct blocks of any hard material, dis posed in a bow-like form, and support ing one another by their mutual pres sure. In describing arches some techni cal terms are made use of, which it will be convenient to define. The 'arch itself is formed by the vouissoirs, or stones cut into the shape of a truncated wedge, the uppermost of .which at C is called the key-stone. The seams or planes, in which two adjacent voussoirs are united, are called the joints ; the solid masonry, A E and B F, against which the extrem ities of the arch abut or rest, are called the abutments ; and the line from which the arch springs et A a B b, the impost. The lower line of the arch-stones, A CB, is the intrados or soffit • the upper line, the extrados or back. The beginning of the arch is called the spring of the arch ; the middle, the crown ; the parts be tween the spring and the crown, the haunches. The distance A B between the upper extremities of the piers, or the springmg lines, is called the span, and 1) is the height of the arch.
There is considerable difficulty in de termining the form which an arch ought to have, in order that its strength may be the greatest possible, when it sustains a load an addition to its own weight ; in fact, the deterinination cannot be accu rately made, unless we know not only the weight of the materials the arch has, to support, but also the manner in which the pressure is connected ; that is to unless we know the amount and direction of the pressure on every point of the arch. Supposing, however, that the arch has to sustain only its own weight, and supposing further, that the friction of the arch-stones is reduced to nothing, a relation between the curve and the weight of the voussoirs may be found by comparing the pressures which are exerted on the different joints. Thus the pressure on any joint, a q for ex ample, arises from the weight of that portion of the arch which is between q and the summit C H. Now, the por tion of the arch C q S II is sustained by three forces : the pressure on the joint s q, the pressure on C H, and its own weight. Let 8 q beprolonged till it meets C 3) in 0 let as be its inter section with A B. It is a theorem in statics, that when a body is held in equilibrium by three forces balancin,g each other, these forces are proportional to the three sides of a triangle formed by lines respectively perpendicular to the directions of the forces. The three forces sustaining C q 8 H are, therefole, proportional to the sides of the triangle O ID n ; for the pressure on s q acts in the direction perpendicular to a q or O a; the pressure on C 11 is perpendicu lar to D 0, and n D is perpendicular to the direction of gravity. The pressure
on a q is, therefore, to the pressure on C II as n D to D O. In like manner, the voussoir pr q a being so shaped that r p, when produced, meets 0 H in the point 0; the pressure on the joint r p is to that on C H, as m D to D O. Hence, the pressure on s q is to the pres sure on r p as D n to D m. e are I thus led, to infer that the voussoirs ought to increase in length, from the key-stone to the piers, proportionally to the lines D n, D sc. ; for in this case, the sur faces of the joints being increased in proportion to the pressure they sustain, the pressure on every point ot the arch will be equal. It will also be observed that the angle n 0 D is equal to the angle made by a tangent to the curve at q, and the horizontal line parallel to A B; the angle m 0 D equal to that made by the tangent at p and the hori zontal line ; and the radius D 0 remain ing constant, D n is the tangent of the point of these angles, and BP m of the second; hence the pressures on the suc cessive joints are proportional to the dif ferences of the tangents of the arches reckoned from the crown. From this property, when the in_trados is a circle given in position, and the depth of the key-stone is given, the curve of the ex trados may be found. When the weights of the voussoirs are all equal, the arch of equilibration is a catenarian curve, or a curve having the form which a flexible chain of uniform thickness would as sume if hanging freely, the extremities being suspended from fixed points. Such is the form which theory shows to be the best adapted to give strength to an arch, on the supposition that there is no superineumbent pressure. But it seldom if ever happens that this is the case, and therefore it is entirely unneces sary, in the actual construction of an arch, to adhere closely to the form deter mined on the above supposition. In deed, on account of the friction of the materials and the adhesion of the cement, the form of the arch, within certain lim its, is quite immaterial, for the deviation from the form of equilibration must be very considerable before any danger can arise from the slipping of the arch-stones. The Roman arches are almost semi-cir cles, yet they have lasted many centuries. The arch is not found in an Egyptian building nor in the earlier Greek. The Romans understood the advantage of the arch from an early period. The cloaca maxima is of the age of the Tarquins. The Etruscans originated the arched dome, and the Romans first applied the well to bridges and aqueducts. The pointed arch was introduced in the mid dle ages by the associated architects, who have left extant the noblest piles of architecture, and in which the arch is multiplied and combined in all possible ways. (See BRIDGE.)