No. 4. The lidling-mould 6.ng the concave side of the rail is exhibited here, in order to show, that if the ramp and the curve of the scroll do not begin together, and if the rail be made absolutely square, that is, having all its plumb sections rectangles, and the convex side made agreeable to its falling mould, with an easy curve, it will be impossible to form the back with a regular curve on the concave side, and a hump will always be formed. Therefore, in reducing the hump to an agreeable curve, the rail will be thrown out of the square; but the degree by w loch it deflects font the truth is so small as not to be perceived.
The inside of the falling-mould is formed by taking the stretch out of a b, b c, c d, &c., of the corresponding parts 0 1, 1 2, 2 3, &c., in No. 1, and applying them from a to b, front b to c, from c to d, tke., No. 4 ; then drawing the per pendiculars front the points a, b, r, &e., and transferring thereto the corresponding perpendiculars insisting upon 0, 1, 2, &c., No. 2, and then tracing the curves. According to the principles of hand-railing, a vertical or plumb section of the rail at right angles to the cylindric sides, or tending to the axis of the cylinder, is level on the back ; therefore, as the concave and convex sides of the plan of the scroll are concentric circles, the are on the concave side, so far as relates to the same quadrant, will be divided equally, as well as the outside; and therefore drawing lines to the centres from the points of section on the convex side will divide each quadrant equally, and the lines thus radiating will be perpen dicular to the curve on both sides of the plan; all the parts throughout the same quadrant will be equal on the concave side as well as on the convex side ; and on the convex side the parts N1 ill be equal throughout all the quadrants; but on the concave side the parts of each succeeding quadrant, in turning towards the centre, will be quicker than those in the preceding quadrant. In the part of the rail which is straight upon the plan, the sections at right angles to the sides divide each side into equal parts, and the parts on the one side equal to those of the other: hence the reason why the hump takes place at the junction of the ramp and twist.
It' a scroll is made agreeable to the form of the plan as struck round centres with compasses, it will to the eye as if crippled at the separating section of the straight and twisted parts. To remedy this defect, the curve of the vertical sides, or that which relates to the plan, ought to be extended with an easy curve into the straight rt.
No. 5. An elevation of the shank of the scroll. The por tion of the plan is taken from No. 1, and the heights which give the curves are taken from the falling-mould, No. 2 ; its use is to show the thickness of stuff w hich is contained between two parallel lines; the lower line comes in contact with the projection at two points, the tipper one conies in contact with the projection in one point only.
To show the method V forming the curtail (ye the first stilt.
Plate VII. Figure 1, No. 1.—Draw the scroll as in the preceding Plate; set the balusters in the middle of the breadth, putting one at the beginning of every quarter ; then the front of the balusters is in the plane of the face of the riser, and the opposite side in the plane of the st•ing-boa•d : set the projection of' the nosing before the baluster on both sides, and draw two spiral lines parallel to the sides of the scroll, till the curves intersect each other, and they will then fla•n the cinlail end of the step, as required, F 0 11 1 K repre sent the convex sole of the scroll; t t N, the convex side or the curtail ; and e, 13, c, E, the centre points of the balusters.
No. 2 shows the profile of the curtail, the end of the step, and part of the end of the third.
Figure I, No. 3, shows the centres for drawing the curtail, are the same as for drawing the scroll.
To describe a section of the rail, supposing it to be two inches deep, and two and a quarter inch(s broad, the usual dimensions.
Figure 2.—Let ABCD be. a section of the rail, as squared. gnu v B desclibe an equilateral triangle, A n y; from g, as a centre, describe an are to touch , a, and to la cot 9 A and 9 : take the distance between the point of section in g A and the point A, and transfer it Inuit the point of section to k, upon the same line y A; join D k; from A-. with the distance between k and the end of the are, describe another arc, to meet n with the same distance describe a third arc, of contrary curvature, and draw a vertical line to touch it ; thus will one side of the section of the rail be formed. The counter-part is formed by a similar operation.
Figure 3 is the most simple form for tire section of a rail, being that of a circle.
To describe the mitre-eup of a rail.
Figure a circle, a e b d, to the intended size (the proportion here between the rail and the cap is as 2 to 3); draw the diameters a b and e d at right angles; produce e d, and place the middle of the section of the rail upon e d; draw B Q to touch the section of the rail, and to cut the circle a e b d in Q; draw the side p Q of the mitre; draw A B to meet the points of contact, A and of the lines parallel to e d, which are tangents to the section. Then to find any point in the curve of the section of the mitre-cap : let a be a point in the section of the rail ; draw o k, meeting P Q in k; from the centre of the circle a e b d, describe an arc, k f, meeting a b in f; from the point of section, f, draw f g, perpendicular to a b ; and make f g equal to F G.
All other points are found in the same manner ; or a series of lines may be drawn from any number of assumed points in the section, and lines parallel to e d, drawn from them to cut P Q; arcs may then be described from each point of sec tion to meet a b, and perpendiculars drawn from the points of section in a b; all these perpendiculars should be made equal to the respective ordinates of the section, and a curve drawn through their extremities will form the curve of the mitre-cap.