HAN

490

HAN

with a saw, by an experienced hand, as to require no furtherreduction ; and when set in its place, the surface on both sideswill be vertical in all parts, and in a surface perpendicular tothe plan. In order to form the back and lower surface, thefalling-mould is applied to one side, which is generally theconvex side, in such a manner, that the upper edge of thefalling-mould at one end may coincide with the face of theplank, the same in the middle, and to leave so much wood atthe other end to be taken away, as not to reduce the plank onthe concave side. The piece of wood to be thus formed intothe wreath or twist, being agreeable to three given heights.This description is general, in order to comprehend the follow-ing construction of the moulds themselves, which whenexplained, we shall then enter into a more particular detail oftheir application.

To construct the falling and face-moidds of a rail to a levellanding, supposing the plane of the plank to rest upon themiddle point of the section, which separates the upper andlower circular parts, and to rest upon the line parallel to, andin the middle of the straight part, so as to have the grain of thewood parallel.

Plate I. Figure 1 —The falling-mould of the hand-rail :b c the extension of the semicircular part ; ba and CD thetreads of the adjoining flyers.

To find the extension of the semicircular part, from themiddle point, i, of b c, draw i K i. perpendicular to b c ; dividethe radius i k into four equal parts, and repeat one of theseparts from k to l seven times ; draw the diameter m n parallelto b c ; join l m and l n, and produce each of these lines tob and c ; then bc is the rectification of the semi-circumferencem i n. Draw b t and d h perpendicular to ad; make b eequal to the height of a step ; I o on the straight line i l, onestep and a half ; c f equal to the height of two steps ; and d hequal to the height of three steps ; join a e and h f, andthrough o draw p Q parallel to bc ; produce A e and h f tomeet p q at pand Q ; then cut off the angles at p and Q byequal touching curves, one at each ; then AEoris the middleof the falling-mould ; and as the rail is generally made twoinches deep, draw two parallel lines each an inch distant fromthis central line, and s u & will be the upper edge of thefalling-mould, and J tj the lower edge.

To find the face-mould of the hand-rail.

Figure 2.— At any convenient place lay down the half plan,abcdcf a, of the hand-rail; abcf being the straight partof the rail, and cdef the plan of the circular part ; draw gedparallel to af or b c; bisect d e at h, and draw h i perpen-dicular to g d; make h i equal to i u, Figure 1, and the angleh i k equal to the angle ghf; let h represent the middlepoint of the section between the two circular parts ; andsuppose n to represent the resting point in the middle of thesection, which separates the straight and circular parts ; makeb r, Figure 1, equal to c b or fa, Figure 2, and draw r s,Figure 1, perpendicular to a b, cutting the upper edge of thefalling-mould at s ; make h r, Figure 2, equal to b t, Figure 1,and draw rs, Figure 2, parallel to g d, cutting i k at s; makehm equal to r s, and join m n, which is the directing ordinate ;from k draw hi parallel to m n, and hi is the intersection ofthe plane of the plank ; find the countersection k t, as in theSections of Cylinders, or, as in the subsequent part of thisWork, under Solid Angles.

To find any point in the curve of the face-mould. —Drawuvw parallel to k l, cutting k d at u, and the concave side ofthe plan at v, and the convex side at w; draw u x parallel to h i,cutting hi at a:; draw x y z parallel to k t ; make xy equal tou v, and x z equal to u w ; then y is a point in the concaveside of the face-mould, and z is a point in the convex side.The pitcli-bevel shown by the dark lines, is found by drawing

a vertical line to the pitch-line, and the angle formed by thes«lines is the pitch-bevel.

In this manner as many points may be found as will ” enecessary to complete the concave and convex sides offalling-mould ; or rule each system of lines at the same bne,thus ; take as many points in the convex side of the pl»® aawill be found requisite ; through all these points draw h n f®parallel to k l, to cut gd; from all the points of division >ng d draw lines parallel to A i, cutting hi; through allpoints of division in hi draw lines parallel to kt; terrain 0 ®each line from the point of intersection equal to the corresponding outer and inner ordinates of the plan, and throngthe points found by its concave side draw a line

als°

through the points found by the convex side of the P 1

dan

draw another curve : then the corresponding points found »each extremity of the plan will complete the face-mould,is evident that the parts 3-4, 5-6 of the face-mould corre®'ponding to a b, c/on the plan, is a parallelogram, therefore^the point 6, where the concave side and the straight ? aTmeet, and the point 5, where the convex and straight p al ,meet, are found, and joined by the line 5-6; and if 5-4 a ” o6-3 be drawn parallel to hi, and the point q correspondingo, be found, by drawing 4-3 through q, the straight part of * 1face-mould will be completed. , j

The line of separation 5-6 will be more exacas follows : Through n draw n 7 parallel to h i, cutting _

7 ; then find only one of the points 5 or 6, say 5 ; draw ’then 5-6, which is a part of 5-7, is the line of separation-

This face-mould will answer for the upper, as well as 1lower half.

The angle 12 -1 is the spring of the plank, and is ’ r ,the same manner as in solid angles, and having the > nte ,section and cointersection, the face-mould is found as in 1sections of a cylinder. The face-mould might have befound as in Figure 3, by taking the heights from a line dra'over the face-mould parallel to ad, Figure 1, and laying *plan upwards, as in Figure 3, then proceeding withoperation downwards, as directed in Figure 2 upwards- ’if the drawing is inverted, the line v n, Figure 1, will "beco ^the base of the heights, and everything else will be insame position as in Figure 2. u p

In the application of the moulds, imagine the plank seto the pitch, and in the same way spring the edge fi' 001under side for the lower piece, and from the upper side i° rupper piece. To apply the moulds to the plank, nowposed to be sprung or beveled, take the pitch and drawvertical line, the stock of the bevel being applied to the aedge of the plank, upwards or downwards, as the case <- r0 ,urequire : then draw a line equal to the distance of 3-6k i, upon each plane of the plank parallel to the side ;the point 8 being kept to the end of the vertical line, an ^side 3-6 upon the parallel line, draw round all the edg .the mould ; turn the mould to the other side, apply „on

8 to the other end of the vertical line, and the part 3-u *the line drawn parallel to the face, and draw round a eedges as before ; then cut away the superfluous stun- ^ c( jysides of the piece intended to form the twist must be p®' orcylindrical, and all the parts so formed, that a straight .^ e8edge may apply to any point, at the same time that it C01 4 ,-aW 11with the surface, and is parallel to the vertical line

on the edge of the plank. t }je

The falling-mould is thus applied : Draw a line. u ?° g jjes,ends of the solid piece, at right angles to the vertica ,yfrom zero at each end, next to the upper side ; t * 1 . enthe upper edge of the face-mould next to the top of th® P,j n gand each end to the corresponding end of the piece, . t | ie nit so that all parts may be in contact with the stun >