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two methods of jointing: stepped joints on the left and joggle joints on the right. All the joints radiate from a common centre, which is not the centre of the camber, but is placed according to taste. The " skewback " is horizontal, as there is no spreading thrust on this arch.

The Round, Roman or Semicircular Arch, as it is variously termed, Fig. 4, shows two methods of treatment in stone arches. The stepped or rebated voussoirs on the right, with curved extrados, are. used when all the structure is in stone and appearance is of less import ance f han strength. The step extrados arch shown on the left is chiefly used in conjunction with brickwork, the back joints of the arch falling on the course joints of the brickwork, the perpend being a mull iple of 3 in.

The Elliptic Arch, Fig. 5, is shown in stone on the left side and bricks on the right. In the first, which is a Irue ellipse drawn as described on page 153, the voussoirs are worked out to a level seating with bed joints normal or perpendicular to the curve, at the points they occur. The setting out is shown, and is described on page t54. The right half shows the four centred or " bricklayers' ellipse," whieh, being composed of segments of circles, is not an ellipse at all, as no part of a true elliptic curve can be struck with compasses ; but it is a convenient arrangement, as only two templets are required for the voussoirs, whilst in a true ellipse a separate templet is required for each voussoir. To draw this arch, construct a rectangle on the springing line and rise ; divide the half span and the rise each into three equal parts, as at 1, 2,4, 5. Set off on the centre line point h at a distance below the springing equal to the rise above it. Draw a line from h, through point t, until it intersects a line drawn from point 5 to the crown in point b ; then draw chord lines from b to the spring and crown ; bisect these two lines and produce the bisectors until they cut the centre line and the line k~b in points c and c'. These points are the centres of the curves and the bed joints of the voussoirs are drawn to them.

The False Ellipse, Fig. 6, is another method of describing an approximation to an ellipse which has been fully described on page 155.

Pointed arches are typical of the so-called Gothic styles of architecture, and they are always formed by combinations of segments of circles. The simplest and earliest form is the

Lancet Arch, Fig. 7. This is always described with radii greater than the span, but varying according to requirements. In the example they equal one and a half times the span. The bed joints are drawn to the centre from which the segment is struck.

The Equilateral Arch, Fig. 8, has its radii equal to the span, the centres being at the opposite springings. The bed joints are sometimes made to radiate from the centres, but a better appearance is obtained by dividing up the soffit and springing equally in the following manner. Ascertain how many voussoirs are required on either side ; then divide the springing line between the centre of the opening and the extremity of the extrados into as many equal parts as there are to be voussoirs, not counting the keystone. In the example, six are taken for the stone arch and fifteen for the brick arch. Divide the so flit between springing and keystone into the same number of parts and join the points as shown, producing the lines across the face of the arch to obtain the bed joints.

The Tudor or Four-Centred Arch, Fig. 9, typical of the latest period of Gothic architecture, is constructed from four centres, two in the springing and two in the reveals below. To draw, divide the span on the springing line into four equal parts; on that portion of the springing lying between the two outer divisions construct an equilateral triangle as shown, and produce the sides to intersect the jambs or reveals. A horizontal line joining the inf ersections will form the base of a second equilateral triangle, and the two base angles in each case, points 1, 2, 3, 4, contain the centres for describing the arcs. The sides of the triangles

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