G54 Tlie Architectural Review and American Builders' Journal. [April, The rise of an arch is the clear height of its intraclos, above the line of spring- ing. A reference to the accompanying en- graving will show the variations in form of the arch : Fig. 1. An Ellipse or Elliptic Arch. This, with the segment and semicircle, might be set down as the only forms known to the ancients. It is struck from three centres, which are thus found : Divide the given line A B into four equal parts; taking together the two parts at the centre, as a base, form, on the under side, an equilateral tri- angle, whose three points will be the centres of the arcs respectively, which form the entire arch. By extending the sides D C, the limit of the springing arcs is fixed. Or, describe three circles, whose centres are the three points of division of the base line ; and it will be seen, that the arcs of the two outer cir- cles form the springings, whilst an arc turned from D, as a centre, with D C as a radius, will connect the springing arcs therewith. The point D is found by joining the intersecting points, until they meet at D. . Fig. 2. This is termed a Stilted Arch, in which the centre is above the line of the imposts, the full length of the radius of the arch, or, equal to one-half of the diameter. A B is the diameter. C D is the radius. Fig. 3. The Horse-shoe Arch. Simi- lar to the foregoing, except that the im- posts incline inwards, which curvature is determined by taking the points A and B, at the extremities of the diameter A B, and, with the diameter for a radius, describing arcs, which will be the curved imposts required. Fig. 4. An Equilateral Arch. Take A and B as centres, and with the diam- eter A B as a radius, describe the seg- ments ADC and B D C, which will enclose an equilateral triangle A C B. Fig. 5. The Lancet Arch. Divide the span from A to B into three parts. Ex- tend the line of the span one part on each side ; and, taking each of these points D D as centres, with D E, re- spectively, as radii, describe the arcs A E C and*B E C. Fig. 6. Take the height of the impost, and measure it off on the base line. Do this on each side. Now, take C and D, respectively, as centres ; and, with D E and C E, respectively, as radii, describe the arcs, as required. Otherwise, thus : Take half the span H E, as a radius ; and describe the quadrant E F. Bisect this quadrant ; and continue the line of bisection, until it cuts A B at D. Do the same at the opposite side ; and it will give the point C. From each of these points C and D, with those bisect- ing lines as radii, describe the arcs. Fig. 7. Is a Trefoil Arch. Divide the diameter A B into three parts. Take the points C and D, as centres ; and turn the quadrants A E and B E. Join the upper points ; and, from the centre of this junction line, draw a semicircle. Or, on the base line A B, divided as be- fore, at C and D, erect a square ; and proceed as before. Fig. 8. Another Trefoil, more gener- ally used than the foregoing. Divide A B into four equal parts ; divide the height into two parts at C, and join the points C D and C D. Form the points ODD. With these points, turn an arc and a three-quarter circle. Fig. 9. A Drop Arch. Divide the span A B into four parts; and, taking the points D D, at either side of the centre, with D A and D B as radii, de- scribe the segments, which will bound an equilateral triangle. Fig. 10. Ginquef oil Arch. Divide the span into five equal parts. From the extreme points A and B, with the span as radius, describe the semicircles A C and B C, respectively. Divide the seg- ments A C and B C ; and, from the points of division to the centres A and B, draw lines. Now, take A D and B D, respectively, and draw segments par- allel to the outside ones. At the inter- secting points of the division line, be-
