Chap. XXIV.
1475
An open Staircase , sustained by the steps themselves, without an arch under them, calledgeometric. There are two principal considerations for the construction of one of thesestaircases, the steps,*and the litnon or string. The steps, which are supported independentlyof the string, should be formed at their soffites by a smooth uniform ramping surface,terminated at one side by a notch or rebate, hed, and on the other by a face perpendicularto the sofhte: by means of these faces, and the steps resting on each other, the stairs arepinned into a wall, and by abutting against the quarter spaces, may be sustained inde-pendently of the string. In staircases of this kind, it is necessary to proportion the bearingto the quality of the stone; it is usual to make the section J or { the height of the step,and the part which bears upon it double; a string at the outer end of the steps preventsthe possibility of their turning, when not well pinned at the other end; this is its onlyadvantage, and it is now generally dispensed with: to form the steps, it is onlyrequired to have one mould taken from the plan, and another from the elevation.
Fig. 2680.
Fig. 2681.
Fig. 2684.
An example of a similar stairs with winders and quarter space may be constructedeither with or without a string on the outer edge; those with a string, as in the formerexample, form portions of cylinders, on the faces of which, by means of the height andbreadth of the steps, the ramps are set out. After having drawn on the elevations, takenfrom the horizontal projections, parallel lines A B, C D, to indicate the oblique sectionsof the cylinder in which the portions of the curved strings are comprised, form theelongated moulds from the projections, fig. 2687. and 2691., by raising from all the point*k, 6,o,5,p, of these projections perpendiculars till they meet the line bm , parallel to AB ;then draw through these points other perpendiculars, on which set off the distancesor corresponding widths, taken from fig. 2687. and 2691. : the moulds being found, selecta stone whose thickness is equal to the distance comprised between the parallels, and afterhaving dressed these two surfaces, and a face at right angles to them, fix the angle
5 b 2