To draw the scroll of a hand-rail, and to find the mould for executing the twist.
Plate VI. Figure 1, No. 1, represents the plan of the rail. The scroll is drawn by centres, in the following manner: Make a circle in the centre, inches in diameter; divide the diameter into three equal parts; one of which subdivide into six equal parts; set one part from the centre upwards, draw a line from the end of that part, at right angles, towards the left hand, and limit this perpendicular to two parts; from the end of the last perpendicular draw' a third downward, limiting it to three equal parts; proceed in this manner till six perpendiculars have been drawn, each differing in length by one from the preceding, and the form of a spiral fret will be obtained. The points of concourse of every two lines will give the centres, which are six in number, besides the centre of the circle, and are numbered in order from such centre: draw a straight line downward from the first centre, by continuing the line already drawn till it cuts the circle : continue the second perpendicular to the right hand, and the third upwards to the left hand ; these will Ilirm the limiting lines for the four arcs, which will complete one revolution.
Continue the lines in the same order for the next revolution, or hit• the of it required. Begin with the centre next to that of the circle for the first centre, and describe a quarter arc t'•oin the point of contact of the circle to the next limiting line ; then around the second centre, with the distance to the intersection of the preceding arc, on the preceding limiting line, describe another arc; proceed in this manner till the w hole spiral is completed. Set the breadth of the rail from o to and describe another spiral by the same centres, by turning the arcs the contrary way, till the last arc of the spiral cm: the first ; which will complete the scroll of the rail ; then the addition of a part of the straight of the rail will complete the whole.
The outer spiral consists of one revolution and a half, and the inner of only about half a revolution, which also makes the scroll itself appear only half a revolution ; but it' more is required, every additional centre will add a quarter of a rev lotion to the scroll.
To find the for the shank of the scroll.
Figure I, No. 1. Lay the base of' the pitch-boa•d upon the outside of the shank of the scroll, with the acute angle tented to the outside, or largest convexity : draw a line parallel to the base of the pitch-board, to touch the convex side of the scroll next to the straight part ; let this line cut the outside of the rail at 6: between 0 and 6 take any number of inter mediate points, 1, 2, 3, 4, 5, and draw lines I perpendienlar to the base of the pitch-board, to cet the hypothenese of the said pitch-board ; the points of' section draw lines at right angles to the h•pothenuse; let the perpendiculars parallel to the base line of the pitch-board be continued downwards, to cut the concave side of the shank; and let one of the perpen diculars he drawn from the concave, and another from the convex side of the rail, m here it is intersected by the line parallel to the base hue ; make all the lines at right angles to the hypothenuse equal to the respective ordinates of the shank taken trout both concave and convex sides of it : then curves being traced, and the straight parts joined to the angular points, will be the fitce-mould.
To find the Divide the distance between 0 and 6, Fignre 1, No, 1, into six equal parts, and run the chord on the convex side as far as the rail is required to full : upon any convenient line, A D, No. 2, run the chord of the part from 0 to 1:1; place the angular point, c, of the pitch-board at 4; with the base A c, 11p011 A I), tango the angle n c n made by the hypothetinse of the piteh-board and the line A D, with a curve to touch at, B and n, as shown at No. 3; then draw another curvilinear parallel, containing the depth of the rail between the two curves; and the lidling-mould, No. 2, will be as far as the rail has a descent, which ends at 13. The block of the scroll, which is the remaining part after the shank is taken away, is wrought out of a solid piece of wood, the height of the perpendicular upon 0. The shank is squared in the same manner as shown in Plate II.