The process is now completely reduced to that of finding the section of a prism through three given points, which sup pose to be done, and the plane of section will touch the sup posed wreath at the resting points of each line of support Nxithout cutting the wreath at any such line ; then the three lines of support will be on the same side of the plane, viz., on the under side. Suppose now another section taken below, and parallel to the former, so that the wreath may be just con tained between these parallel sections or planes, and the distance between the two sections will represent the thickness of the plank. The section of the prism through its vertical surfaces is called the rake or the rake of the plan ; and a mould being cut to the rake is called the face-mould.
The manner of forming a helical line or screw is as follows : Plate V111. Figure 1. Divide the eireumference of the outer circle of the base into equal parts ; draw a line through the centre to represent the axis of the cylinder, parallel to the axis, and through the points of division in the outer circumference draw lines; divide the line of heights or the line representing the axis, into as many equal parts as the circumference of tire base is divided into, and through the points of division draw lines at right angles to the axis, inter secting, as in the figure; through the points of intersection, draw a curve which will represent the helix, or one of the arris lines of the rail.
Figure 2.—The projection of the solid helix coiling round the cylinder; which helix represents the hand-rail before it is moulded.
Figure 3.—No. 1.—A solid section of a cylinder contained between two parallel planes, a part of the side of this solid contained between two planes passing through the axis is the form of a piece from which the rail is made after it is cut out of the plank. No. 2, half the solid section, No. 3, the inclination of the cutting planes.
Such large portions as these, however, are by no means proper to be employed in hand-railing, as the size would neces sarily occasion the fibres of the wood to run in a transverse direction to the length of the rail, and consequently weaken it, but they are useful in this place to convey clear ideas of the principle upon which the art is founded.
Figure 5,—No. 1.—The proper form of a part from which a portion of the rail is to be made after it has been cut out of the blank ; exhibiting the convex side of the same, and the upper plain surthee, which is that of the plank. No. 2. The
concave side of the same, with the joints and lower surface of the plank.
Figure 4.—A portion of the rail completely squared with the concave side, the joints, the bottom part of the upper winding surface, and the upper part of the lower winding surface, brought into view. No. 3. The convex side of the same, showing the upper part of the upper surface, and the lower part of the lower surface.
The business of •and-railing is to find the mould for cutting a rail out of planks.
Though hand railing is only treated of here, as connected with cylindrical well-holes : it is equally applicable to rails erected upon any seat whatever.
The mould, which applies to the two faces of the plank, regulated by a line drawn on its edge, so as to be vertical when the plank is elevated to its natural position, is called the face-mould ; or sometimes the raking-mould.
A parallel mould, applied and bent to the side of the rail pieee, for the purpose of drawing the back and lower surface (which are to be so formed that every level straight line, directed to the axis of the well-hole, from every point of the side of the rail formed by the edges of the fidling-mould, shall coincide with the surface) is called a ftilling-mould.
When the upper surface of the plank is not at right angles to a vertical plane passing through the chord of the plan, in order to cut the corresponding portion of the rail out of the least thickness of wood, the plank is said to be sprung.
A right-angled triangular board, made to the rise and tread of a step, is called the pitch-board.
In a stair-ease, where there are both winders and flyers, two pitelt-boards will be concerned, of different treads, but of the same heights, as the height of the steps must he equal.
The bevel by which the edge of the plank is reduced front the right angle, when the plank is sprung, in order to apply the face-mould, is called the spring of the plank ; and the edge or narrow side thus reduced, is called the sprung edge.
The bevel by which the faee-mould is regulated to each side of the plank, is called the pitch.
The formation of the upper and lower surface of a rail is called the fulling of the rail.
The upper surface of the rail is called the back.