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the springing? as shown in Fig. 2, the bevels can then be taken and the cutting proceeded with.

A Circle on Circle Opening with splayed jambs and soffit is shown in Figs. 4, 5 and 6. Obtaining the shape of the bricks for this arch is a somewhat more complicated process llian the last case, which was, in effect, the determination of the penetrating section of two right cylinders, whilst this one is the penetration of a right cylinder by a semi-cone, and the method of obtaining the shape of the soffit is based on the process of obtaining the covering of a cone as described on page 159. Much of the previous instruction will apply to this case and it will only be necessary to recapitulate.

Having struck the arch, draw the bed joints to the centre, and project the soffit ends into the face of the plan, as shown by the dotted projectors 5 and ya. Produce the side of the reveal to the centre of the plan curve C, and draw the plans of the joints all to the same centre. These lines have not been produced in the example, to avoid confusion.

To draw the Section, Fig. 6, project the crown and springing of the arch across, as shown, to the face of the wall; continue the face line down to the springing to provide a plane to measure from. Project horizontal lines from the intersections of each joint with the back and front edges of the arch. One or two only of these are shown, and one will be traced throughout as a guide to the rest. Take the top bed joint of the seventh brick (point 7 in Fig. 4), project a horizontal across to X, also drop a projector from same point into the plan at 7«; carry this to the centre line in point yh by a perpendicular therefrom. Transfer the distance of yh from C to the line 5, Fig. 6, which gives point 7"; erect a perpendicular to meet the horizontal projector y-x in point 7°, which is a point in the curve to be drawn. Follow out each joint in like mariner on each edge of the arch, and draw the curve through the points so found.

To obtain Soffit Mould.—This has been laid out over the plan, and the mould is hatched to make it distinctive.

### 192 OCTAGONAL CHIMNEY

Draw the tangent line C-D, and produce the splayed reveal to meet it. With C as centre and C'-D as radius, describe an arc; this is the base of the semi-cone C-C'-D laid down. With the apex C as centre and side C-D as radius, describe the arc D-C". Next, produce the joint lines in the plan to meet the line C'-D, and thence erect perpendiculars to cut the curve in points i to 14. Transfer these divisions to the curve line D-C", numbering them to correspond. Draw lines from these points to C, which will be. the direction of the joint lines upon the soffit or "centre." developed. To obtain the faces of the arch, mark otf a distance on each of these lines from D-C" equal to the distance of the plan of the arch from the tangent line C'-D, at the corresponding joint, and thus obtain points through which the curves can be drawn. Trace these 011 linen and fix to the conical " centre," when the true shape of each brick will be visible. The back arch is usually " axed " to shape on the centre, as it is either covered by plaster or wood linings.

To set out an Octagonal Chimney Stack (see page 189). — •Figs. 7 and 8 are the elevation and half plans at cap and neck respectively of a group of four octagonal chimneys rising from a square base. The detail, Fig. 9, shows the, method of setting-out the stack full size to obtain shapes of the bricks and the bonding. The back pair shows the course above or below the front pair, if moved forward horizontally, and the dotted lines indicate the joints below. Only two templets are required for the shafts as shown in Fig. 11, Nos. 1 and 2, and two for the cap, Nos. 3 and 4.

Two Methods of setting-out Octagons are shown in Fig. 10 : that on the left is more suitable for draughtsmen's work with instruments, that on the right for workshop use, as this can be set out with a square ami straight edge.

First Method.— Let the width of the required octagon be given as a-b. Draw a square to the given dimension as a- b c-d, bisect one side and draw a centre line, bisect this line and find the centre c. With a-e as radius and a, b, c, d as centres, describe arcs cutting the sides of the square