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rod, if you have not a level surface to work from, the betterway will be to lay two rods or boards, and level their topsurface to that of the floor, one of these rods being placed alittle within the string, and the other near or close to thewail, so as to be at right angles to the starting line of the firstriser, or, which is the same thing, parallel to the plan of thestring; set off the breadth of the steps upon these rods, andnumber the risers ; you may set not only the breadth of theflyers, but that of the winders also. In order to try the story-rod exactly to its vertical situation, mark the same distanceson the backs of the risers upon the top edges, as the distancesof the plan of the string-board and the rods are fromeach other.

[The methods of describing the scroll and all ramps andknees, are described geometrically in the articles Hand-IIailing and Staircasing.]

As the internal angle of the steps is open to the end, andnot closed by the string, as in common dog-legged stairs,and the neatness of workmanship is as much regarded as ingeometrical stairs ; the balusters must be neatly dovetailedinto the ends of the steps, two in every step ; the face of eachfront baluster must be in a straight surface with the face ofthe riser; and as all the balusters must be equally divided,the face of the middle baluster must of course stand in themiddle of the face of the riser of the preceding step andthe face of the riser of the succeeding one. The risersand treads are all glued and blocked previously together; andwhen put up, the under side of the step nailed or screwedinto the under edge of the riser, and then rough-bracketed tothe rough-strings, as in dog-legged stairs, the pitching-piecesand rough-strings being similar to those. In gluing up thesteps, the best method is to make a templet, so as to fit theexternal angle of the steps with the nosing.

Geometrical stairs .—The steps of geometrical stairs oughtto be constructed so as to have a very light and clean appear-ance when put up : for this purpose, and to aid the principleof strength, the risers and treads, when planed up, ought notto be less than 1^ inch, supposing the going of the stair, orlength of the step, to be 4 feet; and for every 6 inches inlength you may add ^ part more ; the risers ought to bedovetailed into the cover, and when the steps are put up, thetreads are screwed up from below to the under edges of therisers : the holes for sinking the heads of the screws oughtto be bored with a center-bit, and then fitted closely in withwood, well matched, so as to conceal the screws entirely, andto appear as one uniform surface without blemish. Bracketsare mitered to the riser, and the nosings are continued round:in this mode, however, there is an apparent defect, for thebrackets, instead of giving support, are themselves unsup-ported, depending on the steps, and are of no other use, inpoint of strength, than merely tying the risers and treads ofthe internal angles of the steps together ; and from the inter-nal angles being hollow, ora re-entrant right angle, except atthe ends, which terminate by the wall at one extremity, andby the brackets at the other, there is a want of regular finish.The cavetto or hollow is carried all round the front of theslip, returned at the end, returned again at the end of thebracket, thence along the inside of the same, and then alongthe internal angle of the back of the riser.

This is a slight imitation of the ancient mode, which wasto make the steps solid all the way, so as to have everywherethroughout its length a bracket-formed section. This, thoughmore natural in appearance, and much stronger, would beexpensive and troublesome to execute, particularly whenwinders are used.

The best mode of constructing geometrical stairs, is toput up the strings, to mitre the brackets to the risers as

usual, and finish the soffit with lath and plaster, which willform an inclined plane under each flight, and a winding sur-face under the winders. In elegant buildings, the soffit m-i/be divided into panels. If the risers are got out of two-inchstuff, it will greatly add to the solidity.

In order to get a true idea of the twist of the hand-rail, thesection of the rail, by a plane passing through the axis of thewell-hole or cylinder, is everywhere a rectangle ; that is, theplumb or vertical section, tending to the centre of the stair-This rectangle is everywhere of an equal breadth, but not ofan equal vertical dimension in every part of the rail, unlessthat the risers and treads were everywhere the same fromthe top to the bottom : the height is greatest above thewinders, because the tread is of less breadth, and less abovethe flyers ; the tread being there the greatest. If you cutthe rail, after squaring it, perpendicular to any of its curvedsides, the section will not then be a rectangle, three of thesides will at least be curved. Hence two falling-moulds laiddown in the usual way, will not square the rail, though inwide openings they may do it sufficiently near. Nor insquaring the rail can the square ever be applied at rightangles to any one of the four arrises, for the edge of the stockwill not coincide with the side of the rail, being curved ; thiswould be easily made to appear by making a wreathed partof a rail of unusual dimensions, and cutting it in both direc-tions. Therefore, to apply the square right, keep the stockto the plumb of the stair ; and to guide the blade properly)the stock ought to be very thick, and made concave to theplan, so as to prevent the possibility of its shaking or turningfrom side to side; as a little matter up, or a little down, > nthe direction of the blade, would make a great difference inthe squaring of the rail.

All this might easily be conceived from the cylinder itself)for there is no direction in which a straight line can be drawnon the surface of a cylinder but one, and this line is in a plan®passing through the axis of the cylinder, and as the tw°vertical surfaces of the rail are portions of cylinders, ther®can be no straight line upon such surface but what must h®vertical : all others, from this principle, are curves, or th®sections of the rail are bounded by curves, or by a curve o°that side.

In gluing up a rail in thicknesses, it will be sufficientlynear to get out a piece of wood to the twisted form by twofalling-moulds, provided the well-hole be not less than on®foot diameter. The thickness of this piece, as is there stated)must be equal to the thickness, or rather the horizontalbreadth of the rail, together with the thickness which th®

number of saw-kerfs will amount to, and also the amount

of

the substance taken away by planing the veneers. Wenow supposing the plan of the rail to be semicircular, wit* 1two straight parts, one above and one below, a plan mot®frequently adopted from motives of economy, than from an/property of elegance. .

The first thing to be done is to make a cylinder of pla nKto the size of the well-hole. Draw two level lines round th®surface of this cylinder at the top and bottom ; upon each 0these lines set off the treads of the steps at the end next thwell-hole. Draw lines between every two correspondingpoints at the head and foot, and these lines will be all paraH®to the axis of the cylinder. Upon each of the springing li”® 3 ’

and also upon a middle line between these two lines, set

the

heights of the winders, and the height of one of the fly e gabove and below, or as much as is intended to be taken 0the straight of the rail. Take a pliable slip of wood, strrtI ® () fon one edge, and bend it round ; keep the straight edgeit upon the three corresponding points, at the height of .last riser of the flyer ; then draw the tread, of the #