The curve of the dome is described from s' as a center with a radius s' c". This is also the curve of the outside of the rafter. The center of the plan s is the point from which the curved outline of the plate a is described, on which the feet of the rafters f rest. At c is the upper plate, which receives the upper ends of the rafters f, and at the same time forms a circular opening, called the eye of the dome, which admits light and ventilation. About half way up the curved outline, at b', is shown a line of purlins cut in between the main rafters to receive the upper ends of the small jack-rafters g. This line of purlins is shown at b in the plan, and it is at about this point that the main rafters are spaced at a uniform distance of from 16 inches to 24 inches apart, the jack-rafters being then inserted between their lower ends and spiked to the plate a and the purlins b.

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Fig. 81.

The method of forming, or building up, the plate a is the same as described for the conical roof in Art. 144, and the rafters are bent, or sawed, in the same manner as the curved rafters of the ogee roof, described in Art. 148. Where bent rafters are used they are composed of thin strips bent over a form, each layer being nailed together. When the dome is for exterior effect only, and the inside is not to form part of any particular room, the rafters need not be sawed to a curved line on the under side, but may retain the straight edge of the board from which it is sawed, as shown by the dotted line v'w', or, if composed of two pieces, by the lines x'y' and y' z'.

205. There are two methods of boarding over the curved surface of this dome. The first method is shown in Fig. 82, where n of is the outline of the curve of the plan of the dome, and a b is the outline of the curve of the elevation. From c, the center of the plan, we draw the line c d of indefinite length, but at right angles to c b, the axis of the elevation, and at e r on the plan, we lay off the width of one of the roofing boards, o e and o r being each equal to one-half the width of a board; the lines ec and rc then represent this board in place on the plan. The line a b is then divided into any number of equal parts, the points of division being marked s, s', s", etc., and these parts are then laid off on c d from o so that o d represents the length of the line a b folded out straight, and of, of, etc. are each equal to a s, as', etc. From s, s', etc. we now draw perpendiculars through co, cutting c e and c r at l, l', etc. From the points f, f', etc., on the line o d, draw lines at right angles thereto, and make t f "equal to one-half of ll; f f equal to one-half of /' /', etc. A curved line drawn through the points t, t', etc., to tvi, will be the outline of the gore, or covering board required, and if this be laid out on a sheet of heavy paper and cut to the lines, it will form a templet, by which all the boards may be marked and cut. To support the gores curved purlins as shown at e', Fig. 81, are inserted between the rafters. These purlins are spaced to suit the curvature. A conical roof, such as is shown in Fig. 55, is also boarded in this manner, and small purlins must there, too, be framed in between the rafters to receive the boarding. The boarding of the conical roof, however, requires no curvature, but simply tapers from the plate towards the apex in a straight line.

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Fig. 82.

206. A second method of covering the dome is shown in Fig. 83. The boards in this case are laid in short horizontal courses. One-half the elevation ae, Fig. 83, is divided into any number of equal parts, ab, bc, cd, etc., each part being equal to the width of one of the covering-boards; the line b e is drawn from the point b through the point c and is prolonged until it intersects the axis of the dome prolonged at h; then from the point c through d a. line is drawn until it intersects the axis line at j, and so with each of the other parts, until we get the points k l m, etc., on the axis line. With h as a center and a radius h b, we can now describe the curve which will form the lower edge of the board b c, while with the same center and a radius hc we describe the arc c p, which marks the curvature of the upper edge of the board. From the point j as a center, and with the radii jc and jd, we describe the arcs c t and d u, which mark the outline of the board c d, and in the same manner for each of the boards in the dome, until the top opening, or eye, is reached, which, when not to be framed, is closed over with a flat, circular piece of board, the center of whose curvature would be at e.

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Fig. 83.

207. When a dome is comparatively small, and great neatness is required in the perfection of its semicircular outline, it is desirable that the joints should be planed down to round the surface, whether the boards run horizontally around the dome, as in Fig. 83, or extend from bottom to top, as in Fig. 82.

When a dome is large and well above the eye, as on the roof of a high building, such nicety is not • required, as the covering material will round the form to the desired outline.

208. An interior dome is sometimes built under a flat roof, and is very commonly seen over a stair hall, which is illuminated through an ornamental glass skylight inserted in the eye of the dome. These interior' domes are generally elliptical in form, but whether the outline is a semicircle or semiellipse, the method of framing is precisely the same.

Fig. 84 is the plan of an interior dome whose outline is an ellipse, with a length a c and a width b d. In its center is shown the eye, whose length kg and whose width c f are in direct proportion to the length and breadth of the larger ellipse. The plan of the dome abcd is formed by cutting the curved sides from separate boards and nailing these boards around the opening framed in the floor or roof over which the dome is to be built. The eye of the dome is made of four or more pieces of board securely nailed together to receive the upper ends of the ribs when set in place.

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Fig. 84.