Now, as hand rails are not made of such portions of hol low cylinders or cylindroids, but of plank wood, we have only to consider how such portions may be formed from a plank sufficiently thick. As the faces of the plank are planes, we may suppose the rail contained between two pa rallel planes, that is, between the two faces of the plank. Then such figures are to be drawn on the sides of the plank, that, wren the superfluous pat ts arc cut away, the surfaces that are formed between the opposite figures are portions of the external and internal cylindrical or cylindroi dic surfaces. A mould made in the formf f o these figures, is called the face mould, which is only a section of the cy linder or cylindroid through three points in space.
The vertical, or cylindrical, or cylindroidic surfaces be ing formed, the upper and lower surfaces must next be formed. This is done, by bending- another mould round one of the cylindrical or cylindroidic surfaces, generally made to the convex side, and drawing lines on the surface round the edges of this mould. Then the superfluous wood is cut away from the top and bottom, so that if the piece were set in its place, and a straight edge applied upon the the surfaces now formed, and directed to the axis of the well hole parallel to the horizon, it would coincide with the surface. The mould thus applied upon the convex side to form the top and bottom of the piece, is called th% falling mould.
To find these moulds the plan of the steps and rail must first be laid down ; then the falling mould, which must be regulated by the heights of the steps ; and lastly the face mould is ascertained by the falling mould, which furnishes the three heights alluded to.
Plate CCCXXXVIll. Fig. 1. Is a dog-legged staircase. No. I. is the plan. No. 2. the elevation, sheaving the rough strings under the steps, and the sling rod marked into equal divisions, for regulating the work in the process of putting it up. The dotted lines above the rail, drawn by the square, show how the centres of the arcs that form the ramp are found.
Fig. 2. Geometrical staircase with winders. No. 1. is the plan. No. 2. the elevation and section. As the staircase is supposed to be cut through the middle, parallel to its length or longest dimension, it would be absurd to repre sent the whole elevation, as is frequently done ; for this rea son, only the farther half is represented, and the steps of the other half are shown by dotted lines.
Fig. 3. Geometrical staircase without winders. No. I. is the plan. No. 2. the elevation. It is in such con structions as this and the last figure, where great nicety of workmanship, and skill in geometrical lines, are found necessary.
Fig. 4. A section of the rail and mitre cap for a dog•leg ged staircase. The dotted lines are drawn from the sec tion of the rail. No. 1. to the mitre. No. 2. in straight lines. From thence in the ales of circles, to the straight line passing through the centre of the cap at right angles to the former straight lines, then perpendiculars are drawn, and made equal in length to the perpendiculars. A curve being traced through the points, gives the form of the cap. The section, No. I. is used in any kind of rail whatever.
Fig. 5. shows the section of a rail in a circular form. The sections of rails also form elliptic figures.
Fig. 6. is another form, called a toad's hack rail, to be executed in the best houses. The top is generally cross beaded, with coloured wood.
To draw the scroll for terminating the hand rail of a geometrical stair at the bottom. Let AB, Fig. 7. he the breadth given ; draw AE perpendicular to AB ; divide AB into eleven equal parts, and make AE equal to one of these parts. Join BE; bisect AB in C, and BE in F. Make CD equal to CF ; draw DG perpendicular to All ; from F, with the radius FE or FB, describe an arc cutting DG at G. Draw Gil perpendicular to BE, cutting BE at O. Draw the diagonals DOK and 1OL perpendicular to DOE. Draw IK parallel to BA ; EL parallel to ID, and so on to meet the diagonals. From D as a centre, with the distance DB, describe the arc BG. From I as a centre, with the distance IG, describe the arc GE. From K as a centre, with the distance RE, describe the arc EH. From L as a centre, with the distance LII, describe the arc HP. Pro ceed in the same manner, and complete the remaining three quarters, which will complete the outside of the scroll. Make BR equal to the breadth of the rail, viz. about two inches :ind a quarter. Then, with the centre D, and distance DR, describe the arc RS. With the centre I, and the distance IS, describe the are ST ; and with the centre T, and distance KT, describe the are TU, which will complete the scroll.