PLATE XXXI.
THE PLAN OF RAIL FORMING PART OF AN ELLIPSE, STARTING
FROM A NEWEL OVER WINDERS.
Fig. 1 shows the plan of rail with the risers in position. The line O C is the minor axis, and O D the major axis of the ellipse on plan; and as the tangent A B is level, it is of course the H T. From the foci P P draw to A, and bisect the angle, as shown by A Y; this will be the face of the newel on plan. Draw the tangent A B square to it. Draw F S through the centre O V square to A B. Draw O E parallel to A B; this line will be the minor axis on the face mould.
Fig. 2 shows the elevation. A S will equal the stretch-out of the centre line of rail from A to C, Fig. 1; and S B will equal C B, Fig. 1. Draw the falling line as shown so as to strike the face of newel level, at a height of 12 inches above the floor. Square out A B from A and join B R for pitch of tangent. Draw the joint line square to the straight rail and R P square to the tangent.
Fig. 3 shows the face mould for the under side. Draw F S and S P at right angles, and make F S equal F S, Fig. 1; and S P equal the height S C, Fig. 2. Join F P for the major axis of face mould. Make F R equal F O, Fig. 1. Draw R O parallel to S P. Draw O E square to the major axis F P; then O E is the minor axis, and O R is the same line as is marked V L in previous plates. Make O 5 E 6 equal O 5 E 6, Fig. 1. Make F N equal F N, Fig. 1, and draw N Y parallel to R O, and Y D square to major axis. Make Y D equal N D, Fig. 1, and complete the section as usual. Also make P C equal S C, and F A B equal F A B, Fig. 1. Join C B extended, and make C R equal C R, Fig. 2. Now if the drawing is correct C B will equal C B, Fig. 2.
Fig. 4 shows the bevel and section A. Make A B equal O F, Fig. 1; and B C equal O F, Fig. 3. Draw the section of rail, and draw A 2 to cut the top corner parallel to B C. Then A O will be half thickness of plank and A 2 width of mould here.
Fig. 5 shows bevel and section D. Make A B equal O D, Fig. 1. With O as centre for radius, open out the compasses to touch the tangent from D; transfer this distance to Fig. 5, as shown by B C. Now make A D E S, Fig. 2, equal A D E S on the centre line of rail, Fig. 1. Make D N and E H, Fig. 2, equal N Y and R O, Fig. 3. The difference between N and the falling line shows that the latter is nearly in the centre of plank at the section D. Make D 3 and D 4, Fig. 3, equal D 3 and D 4 at the section.
Fig. 6 shows the section on the minor axis, which of course requires no bevel. The difference between 4 and the falling line at Fig. 2 shows what this section is out of the centre of the plank.
Fig. 7 shows bevel and section C. Make A B equal O C, Fig. 1, and with O as centre, and for radius a distance to just touch the tangent, C B, Fig. 3. Transfer this to Fig. 7 as shown by B D, and complete the section as usual.
Fig. 8 shows the bevels for the bevelled joint at R. The method of getting them and their application will be understood.
Fig. 9 shows the face mould for the top side. The difference between this mould and Fig. 3 is that A 2 and D 4 and C 7 is on the inside of A D and C, instead of the outside, as at Fig. 3. In sawing around on the inside, leave the stuff full on the section D, and gauge to a width after the moulds have been removed.