This is a slight imitation of the ancient mode, which was to make the steps solid all the way, so as to have everywhere throughout its length a bracket-formed section. This, though more natural in appearance, and much stronger, Would be expensive and troublesome to execute, particularly when winders are used.
The best mode of constructing geometrical stairs, is to put up the strings, to mitre the brackets to the risers as usual, and finish the soffit with lath and plaster, which will form an inclined plane under each flight, and a winding sur face under the winders. In elegant buildings, the soffit may be divided into panels. if the risers are got out of two-inch stuff it will greatly add to the solidity.
In order to get a true idea of the twist of the hand-rail, the section of the rail, by a plane passing through the axis of the well-hole or cylinder, is every where a rectangle; that is, the plum or vertical section tending to the centre of the stair, This rectangle is everywhere of an equal breadth, but not of an equal vertical dimension in every part of the rail, unless that the risers and treads are everywhere the same from the top to the bottom : the height is greatest above the winders, because the tread is of less breadth, and less above the flyers; the tread being there the greatest. It' you Nit the rail, after squaring it, perpendicular to any of its curved sides, the section will not then be a rectangle, three of the sides will at least be curved. Hence two falling-moulds laid down in the usual way, will not square the rail, though in wide openings they may do it sufficiently near. Nor in squaring the rail can the square ever be applied at right angles to any one of the four arriscs, for the edge of the stock will not coincide with the side of the rail, being curved ; this would be easily made to appear by making a wreathed part of a rail of unusual dimensions, and cuttin.g, it in both direc tions. Therefore, to apply the square right, keep the stock to the plumb of' the stair ; and to guide the blade properly, the stock ought to be very thick, and made concave to the plan, so as to prevent the possibility of its shaking or turning from side to side ; as a little matter up, or a little down, in the direction of the blade, would make a great difference in the squaring of the rail.
All this might easily he conceived from the cylinder itself, for there is no direction in which a straight line can be drawn on the surface of a cylinder lint one, and this line is hi a plane passing through the axis of the cylinder, and as the two vertical surfaces of the rail are portions of cylinders, there can be no straight line upon such surface but what must be vertical : all others, from this principle, are curves, or the sections of the rail are bounded by curves, or by a curve on that side.
Jim gluing up a rail in thicknesses, it will be sufficiently near to get out a piece of wood to the twisted form by two filling-moulds, provided the well-hole be not less than one foot diameter. The thickness of this piece, as is there stated, must be equal to the thickness, or rather the horizontal breadth of the rail, together with the thickness which the number of saw-kerfs will amount to, and also the amount of the substance taken away by planing the veneers. We are now supposing the plan of the rail to be semicircular, with two straight parts, one above and one below, a plan more frequently adopted from motives of economy, from any property of elegance.
The first thing to be done is to make a cylinder of plank to the size of the well-hole, Draw two level lines round the surface of this cylinder at the top and bottom ; upon each of these lines set off the treads of the steps at the end next the well-hole. Draw lines between every two corresponding points at the head and foot, and these lines will be all parallel to the axis of the cylinder. Upon each of the springing lines, and also upon a middle line between these two lines, set the heights of the winders, and the height of one of the flyers above and below, or as Much as is intended to be taken (,fr the straight of the rail. Take a pliable slip of wood, straight on one edge, and bend it round ; keep the straight edge of it upon the three corresponding points, at the height of the last riser of the flyer; then draw the tread of the first winding step by the straight edge, from the line where the cylindric part commences, to the first perpendicular line the curved surtitee; take the next three points higher, and draw a line between the second and third perpendicular lines, proceed in like manner with the next three higher points, and draw a line between the next two adjoining cylindric lines, and the lines so drawn between each three points will be the section of the treads of the succeeding winding steps.