Chapter II: Part 2

The method adopted in this work is as follows:--The plan of centre line of rail is first laid down, and the tangents and face of risers drawn. Next the centre line of rail is unfolded, or developed, on a board, with position of risers thereon. Then the centre falling line of rail is drawn, resting on the corners of the full-size steps and continued across the well. And here it is where good taste and judgment is required, so as to get a good falling. After the falling line has been drawn it will be seen at once if any improvement can be made in the position of the risers. The development of tangents is next drawn to suit the falling line of rail.

The face moulds are next got out of some thin stuff. The tangents on the moulds will equal the tangents developed in the elevation. This will be better understood by referring to the succeeding drawings. Two face moulds are used, one for each side of the plank. The tangents and sections are the same on each mould, but as the width is on the inside of one mould and on the outside of the other, this gives the wreath the necessary twist. The wreath having been cut out square through the plank and the joints made, and the tangents squared across the joints, the face moulds are then tacked on, with the ends of both moulds flush with the joints, and the tangents on both face moulds are put to the tangents squared across the joints of wreath, there being no pushing or sliding the mould in any shape or form. The inside and outside is now sawn off, the saw always being held in the same direction as the section lines on the face moulds. A bevel is obtained for each section and set off on a board. The width of rail is also drawn on the same board, and where the bevel cuts the centre of width of rail, is the centre of plank. Now as the face mould gives the height of the centre of plank at each section, these heights are transferred to the elevation, which shows at once if the falling line is any, and how much, out of the centre of plank. Then the sections of rail are drawn on the board above, or below, where the bevel cuts the centre of width of rail, according to what the falling line is out of the centre of plank at each section. This shows what superfluous stuff there is to come off the top side of the wreath at each section, which is marked on to the wreath before the face moulds are removed. This superfluous stuff is then sawn off, keeping the saw in the direction of the section lines, after which the wreath is gauged to a thickness and the superfluous stuff sawn off the bottom.

I may say that this system has been put to practical test, and some of the very best examples of handrailing have been done by it with the very best results. But it was found to be a great advantage to use a machine gig-saw: they can be bought the same as any other saw, and if it is fixed into a bow-saw frame, or a frame made for it, no difficulty will be experienced in sawing out any wreath shown in this book.

The advantages of this system are:--

1. The tangents are made to conform to the falling line of rail, instead of the falling line having to conform to the tangents, as is the case in most systems.

2. The wreath being sawn out to the section lines instead of vertical, as is the case with cylindrical wreaths, saves more than half the time in squaring.

3. The wreath being straight across on the inside and outside in the direction of the section line, instead of concave on the inside and convex on the outside, as is the case with a cylindrical wreath, is much easier to mould, and has a much better appearance by far when finished.

4. It has all the advantages of falling moulds without the trouble of getting them out, and it can always be ascertained what any part of the falling line is out of the centre of the plank.

5. It takes the minimum thickness of stuff, as it can always be seen exactly what thickness will be required.

6. The system of bevelled joints does away with the short ramps, and thereby saves both labour and material; besides there is only one joint instead of three.

It will be seen that in no case in this book is extra thickness of stuff required.

PLATE XII.

ON OBLIQUE PLANES AND THEIR TRACES.

If the surface of a solid is neither horizontal or perpendicular it is oblique.

Thus, if we place a box on the table, the top of the table represents the horizontal plane and the side of the box the vertical plane, and the intersection of the box and the table is the ground line, or X Y. Draw a line out square from the box on the table, marked N N, Fig. 1. Hold the end of a book on this line, with its edge against the side of the box in an inclined position; mark a line on the side of the box: this line is the vertical trace, because the oblique plane has cut the vertical plane on this line. Before moving the book mark a line on the table: this is the horizontal trace, for the same reason that the oblique plane has cut the horizontal plane on this line.

Fig. 2 shows the horizontal trace inclined 60° to the vertical plane. Draw the dotted line N N on the table, making an angle of 60° with the box. Place the end of a book on this line, and while in an inclined position mark the vertical and horizontal traces the same as in Fig. 1. To find the true inclination of the oblique plane take F for centre, and for radius F R, strike the arc to cut X Y in P; join E P, which is the true length and inclination of a line on the oblique plane, to stand vertically over F R. All lines on the oblique plane parallel to the horizontal trace will be level, and all lines square to it will be the true inclination of the surface of the oblique plane.

Fig. 3. It is required to cut a block of wood the size of the square A B C O, its side A B to be 5 inches high, and its top surface inclined 30° to the horizontal plane. On the oblique surface project an ellipse that will stand vertically over the quarter of circle on plan. Let A B C O be the plan and B C R N the elevation. Project 7, 8, 9 on to the oblique surface, as shown by 1, 2, 3.

Fig. 4 shows a cuneiform sketch of the block. Make B N and C R equal corresponding letters, Fig. 3; join R N; square out lines from N R; make N A´, R O´ equal A B, Fig. 3. To complete the figure, make A A´ equal B N, and O O´ equal C R. To draw the ellipse, make N 1 2 3 R equal N 1 2 3 R, Fig. 3. Make 1 7 and 2 8 and 3 9 equal 4 7 and 5 8 and 6 9, Fig. 3. Trace the curve through A´ 7 8 9 R as shown. If this block is cut out in a vertical direction to the ellipse on its surface it will stand correctly over the quarter of circle, its plan.

Fig. 5. Cut a block of wood so that its edge will stand vertically over A B C O. The top of the block to be hard down at A. From A to B rise 3 inches, and from B to C 4 inches more. Make B F equal 3 inches and C 5, 7 inches. Join 5, F extended to cut X Y in E. Join E A, which is the horizontal trace, and E F 5, the vertical trace. F 5 will be the inclination of the edge of the block over B C. To get the length and inclination of the edge over A B, take B for centre and B A for radius, strike an arc to cut X Y in H. Join F H for the required edge.

The process of getting the lines on the oblique surface of this block, as shown at Fig. 6, is the same as most of the face moulds as laid down in this book, and let it be understood that if the problems on this and the following Plate are properly mastered, the foundation upon which this system depends has been laid, and all the plates that follow are purely a matter of detail. Let the instructions given here be carried out, and cut the blocks of wood as described, when the meaning and intention of every line will be clearly illustrated, and the way cleared for further progress.

Make E F 5 equal E F 5, Fig. 5. Take the distance F H, Fig. 5, in the compasses, with F, Fig. 6, as centre, strike an arc at A. With E A, Fig. 5, as a radius, and E, Fig. 6, as centre, strike an arc to intersect the first one at A. Join E A for horizontal trace and F A for the top edge of the block over A B. Draw from 5 parallel to F A, and from A parallel to F 5. Then O will be the centre of the ellipse, as it will be vertical over the centre on plan. A line drawn on an oblique plane square to the horizontal trace and passing through its centre is the major axis, and a line drawn parallel to the H T and passing through its centre is the minor axis. Make 2 3 0 5 equal 2 3 0 5, Fig. 5. Make 3 6 and 0 7 equal 8 6 and 0 7, Fig. 5, and trace the curve through A 6 7 5.

PLATE XIII.

ON PROJECTION OF OBLIQUE PLANES, ETC.

Should any part of a plan be a circle, it will when projected on to an oblique plane be an ellipse.

Thus, take any one round piece of wood, cut one end off square to its side, this end will be a true circle. Cut the other end to any angle, which will then be an ellipse, and when the piece is stood on end will be vertical over the circle, its plan. Fig. 1 shows this. And it will be seen, no matter what angle the oblique plane may be, the minor axis never changes, it is always the same length as on plan, as are all lines parallel to it; but not so with the major axis, which always lengthens as the angle increases.

Fig. 2 shows a quarter of a circle projected on to an oblique plane, inclined 45° to the horizontal plane.

Fig. 3 shows a plank inclined 45° to the horizontal plane, with a quarter of an ellipse traced on its oblique surface. At any point on the curve draw a section line and a normal tangent. Cut the plank square through to the section line. Draw a level line on the square cut, and produce a bevel that will, when the stock is held to the section line on the oblique surface, produce with its blade a line across the cut that will be perpendicular to the level line on the square cut.

At any point on the curve, say at S, draw a line square to, and to cut the major axis in P; draw the level line on the edge to cut the vertical line from the centre O in N; draw R N square to the major axis. Join R S, which is the section line; draw the tangent square to it through S. Cut the plank through to the lines S R and R N; join N S after the cut is made. To get the bevel, draw A A parallel to, and at a distance away from O N, equal to minor axis or radius of circle on plan. Take the compasses, and for centre put one foot at O, and for radius strike an arc just touching the tangent through S, bring it around to cut A A in H, join O H for the required bevel. This bevel, when applied across the cut, will be square to the level line S N.

PLATE XIV.

LEVEL LANDING WREATH, OR HALF TWIST.

Fig. 1 shows the plan of the rail, with the top riser placed in the springing and the level rail 4 inches above the landing, so that when the rail is raised to its proper height, 2 feet 8 inches above the treads, measured vertically over the face of the risers to the top of rail, it will be 3 feet from the landing to top of level rail. To get the radius of the centre line of rail, make B H, Fig. 3, equal 4 inches; then A B will be the required radius. At Fig. 2 set up one step and landing. Draw the centre falling line resting on the corners, also draw the level rail 4 inches above the landing. Make N C equal the stretch-out of the centre line of rail, Fig. 1, and complete the falling line from A to C, as shown.

Fig. 4 shows the face mould. Draw A B C at right angles. Make A S equal A S, Fig. 2, and A B equal A H, Fig. 3, and B C equal B C, Fig. 1, and C P equal C P, Fig. 2. From A draw A O parallel to B C, and from C draw C O parallel to A B. Then O will be the centre, A O the semi-minor axis, and O C the semi-major axis. To get points in the curve and draw section lines, take O C, Fig. 1, for radius and C, Fig. 4, for centre; strike an arc on the left; draw V L through the centre, and tangent to this arc; draw from C square to V L. Say there are to be two sections marked 5 and 6, Fig. 1. Make C 2 1 equal C 2 1, Fig. 1. Draw from 1 and 2 parallel to V L to cut O C in 3 and 4. From 3 and 4 draw parallel to A O, and make 4 5 and 3 6 equal 1 6 and 2 5, Fig. 1; then 5 and 6 will be points in the curve. From 3 and 4 draw square to and cut V L in 7 and 8; from 7 and 8 draw square to and cut O C in 9 and 10; join 9 5 and 6 10 for section lines. To get bevels, width of mould, &c:--On a piece of board draw two parallel lines, at a distance apart equal to radius of centre line of rail, as shown by the lines R R, Fig. 5; also draw the width of rail, as shown by W W. For the section at C, make 1 2, Fig. 5, equal O C, Fig. 4; draw section of rail; draw E F parallel to 1 2, to cut the top corner of section of rail. Then O C will be half thickness of plank and E C F the width of mould. For section 5, with O, Fig. 4, as centre, strike an arc to just touch the tangent from 5; make 3, 4, Fig. 5, equal this distance. Make O 5 equal half thickness of plank and draw R N parallel to 3 4, then R 5 N will be width of mould on this section. The process of getting bevel and width of mould for section 6 is the same, always squaring out the line from the centre of section of rail and setting off half thickness of plank, and drawing the top or bottom side of plank parallel to the bevel line through the centre of section. To complete the face mould make C E and C F equal C E and C F, Fig. 5. For section 5 make 5 R and 5 N equal 5 R and 5 N, Fig. 5. For section 6 make 6 S and 6 P equal 6 S and 6 P, Fig. 5. The section on the minor axis requires no bevel, as was explained in Plates XII. and XIII. This line never exceeds its plan, therefore on this line the face mould never exceeds the width of rail. Complete the face mould as shown.

PLATE XV.

LEVEL LANDING WREATH, OR HALF TWIST--_continued_.

Fig. 1 shows the plank from which the wreath is to be cut out. Lay the face mould on, and transfer the tangents on the face of the stuff. Mark off each side of the tangent at P, O H to equal C H, Fig. 5, Plate XIV., and cut the wreath out square through the plank, as shown by dotted lines, taking care to have the wreath cut full on the minor axis at A, and along the shank to S, as this part does not exceed the width of the rail.

Fig. 2 shows the wreath after being cut out square through the plank. Plane one side perfectly true, then get it to its required thickness. It is very important that the stuff should be got to the same thickness as drawn at the sections, that is, twice the thickness of O C, Fig. 5, Plate XIV. Now make the joints square to the face of stuff and square to the tangents, applying the square as shown. So much depends upon the trueness of the joints that too much care cannot be taken with them.

Fig. 3 shows the face mould for the other side of the stuff. Lay the face mould, Fig. 4, Plate XIV., on a thin piece of stuff, and mark off on to it the tangents S A B C P and the section lines, stick a bradawl through 5 and 6, and mark off on the section lines, on each side of C 5 and 6, the width as shown opposite to the first face mould. Fig. 4 shows the application of moulds.

PLATE XVI.

LEVEL LANDING WREATH, OR HALF TWIST--_continued_.

Fig. 1 shows the same wreath after the inside and outside has been cut off, so that a straightedge will touch both face moulds all round when held in the direction of the section lines, as shown marked across the inside.

To cut the wreath out get a machine gig-saw and either make a frame for it or fit it into a bow-saw frame: this saw will be found to be much better than the ordinary bow-saw, as it is much stiffer and will not bend in the cut, and being thick on the teeth and thin on its back edge, works free.

Every wreath shown in this book can be squared with this saw, and if care is taken in cutting the superfluous stuff off, very little cleaning up is required. The saw must always be held in the same direction as the section lines. After the inside and outside has been cut off and cleaned up, before taking the face moulds off mark down from the top on each section, inside and out, the distances as shown by the shaded parts on each section at Fig. 5, Plate XIV., and marked F Y, R J, S K, &c. The shaded part at Fig. 1 shows this; the moulds can now be removed and the superfluous stuff cut off to the lines traced through E J K on the inside and Y A B on the outside. The bottom can be gauged from the top with an ordinary gauge, but should be sawn full and jointed to the straight rails before being cleaned up.

Fig. 2 shows the same wreath, only the rail is cut out of the top of the plank all round, instead of the centre, as at Fig. 1. And this wreath has a much better appearance on the inside when finished. The face moulds and their application are the same, but as the rail is to come out of the top of the plank, it will throw the level rail too high on the landing. To obviate this the rising landing must be brought out from the springing. Make A B, Fig. 3, equal A B, Fig. 4, draw section of rail at H as shown, draw S S parallel to A H, make P P equal half thickness of rail, make B A N, Fig. 4, equal B A N, Fig. 3, and draw riser as shown.

PLATE XVII.

HALF-SPACE LANDING, WITH STRAIGHT FLIGHT ABOVE AND BELOW.

Fig. 1 shows the plan of rail with the risers landing and starting, placed half a tread from C on each side along the centre line of rail. By this arrangement we get two balusters on the landing the same distance apart as on the steps, and the centre falling line straight.

Draw plan of rail and enclose the centre line with tangents A B C D E. Mark off from C along centre line of rail on each side half a tread, and draw face of risers landing and starting.

Fig. 2 shows the elevation. Make A N equal stretch-out of centre line of rail. Set up two steps and landing, taking care to draw the face of risers as they occur on the centre line of rail, Fig. 1. Draw the falling line resting on the corners as shown. For development of tangents make F D S equal E D C, Fig. 1. From D, square up a line to cut the falling line in R, then E R will be the pitch of the tangent over E D, Fig. 1; join R S for pitch of tangent over D C, Fig. 1. Make E D F, Fig. 1, equal F D C, Fig. 2, join F C, which is the horizontal trace.

Fig. 3 shows the face mould. Make E D S equal E R C, Fig. 2, with D for centre, and R S, Fig. 2, as radius; strike an arc at C with S as a centre, and F C, Fig. 1, as radius; strike an arc to intersect the first one at C, join D C. From C draw parallel to D E, and from E draw parallel to D C; these lines will meet at the centre O. Join S C, which is the horizontal trace. Draw the semi-major axis square to it through the centre and the semi-minor axis parallel. With F as centre, and O N, Fig. 1, as radius, strike an arc at H; draw V L through the centre and tangent to the arc. Say we have one section between the minor axis and C marked 1. Make H N equal O N, Fig. 1. Draw N J parallel to V L. Make J I equal N I, Fig. 1. Draw J P square to V L and P R square to F O; join R I for section line. For bevels, width of moulds, &c., take O for centre and for radius open the compasses to touch each tangent; transfer these distances to Fig. 4, always making the distance between the lines N R, Fig. 4, equal the radius of centre line of rail on plan. Draw the section of rail on each bevel and set off half thickness of plank, and complete the sections as shown. For width of mould make C I P and 1 3 4 and E 6 5 on section lines Fig. 3 equal C I P and 1 3 4 and E 6 5 at sections Fig. 4. It will be noticed that, while at sections C and I the face mould has less stuff on the inside, at section E, on the other side of the minor axis, it has more.

Fig. 5 shows the face mould for the other side of the plank. To cut the wreath out, lay either mould on and transfer the tangents on to the stuff, and mark off on each side of face mould on the minor axis. The stuff should be cut full on this line. Mark off on each side of the tangents at the joint C the distance C P as seen at the section, and on each side of E, E Y as seen at Fig. 4. Draw around roughly from P to the minor axis to Y. The stuff is cut square through the plank to this line inside and out. Plane the stuff true and gauge it to its proper thickness and make the joints square to face of stuff and to the tangents. The application of the face moulds is seen at Fig. 6; the tangents on both face moulds must lie on the tangents marked across both joints of the wreath. Now saw the inside and outside off as shown by the shaded parts at Fig. 6, keeping the saw in the direction of the section lines. Clean up the wreath both inside and out, always keeping the straight edge in the direction of the section lines. Before removing the moulds mark from the top side 22, 33, 44, 55, 66 and 77, as shown by the shaded parts of sections at Fig. 4. Cut the superfluous stuff off the top to these lines, after which, gauge to a thickness, set the gauge full so as to allow the wreaths being cleaned up after the pair are bolted together. Before they are bolted and dowelled together at the centre joint them to the straight rails, and clean off any superfluous stuff there may be on the shanks in a line with the straight rails, and mark the section of rail on the ends of shanks before removing the straight rail; now joint the two together.

But before cleaning the pair off it would be well to test the correctness of the centre joint. Make N Y, Fig. 2, equal S Y, Fig. 1, and join E Y; now if the distance from the centre of the thickness of one wreath to the centre of the thickness of the other on the inside at the sections, at the springing, equals E Y, Fig. 2, the joint will be correct. Having proved the joint in this way, clean them off while together, then take them apart before glueing up. Mark the pattern of rail on the joint and mould them; use a handrail screw to bolt the joints together with and keep them as near as possible the centre of section of rail. There should be two dowels in each joint to keep them from twisting, placed according to pattern of rail.

In taking the length of straight rails, take the length of strings from springing to springing and allow for length of shanks of wreaths, as measured from the joint to springing, in a line with straight rails.

PLATE XVIII.

FROM THE LEVEL TO THE RAKE.

The principal thing to consider in planning stairs of this kind is to place the riser starting, so as to get a good falling line. Fig. 1 shows the plan with the centre line enclosed with tangents A B C D E.

Fig. 2 shows the elevation with the centre falling line and development of tangents. Make R N S equal stretch-out of centre line of rail, Fig. 1. Draw the landing and the level part of falling line 4 inches above it to cut the centre line at H. Draw H E to pitch of pitch-board and complete the falling line from E to J; set up the height of a riser above the landing on the right, and draw the top of step to cut the line H E for position of riser. Make E P, Fig. 1, equal S P and draw face of riser starting on plan. This riser must be slightly curved, so as to get it the same width on the end as the others. For development of tangents, make 1 2 3 4 E equal A B C D E, Fig. 1. From 4 square down a line to cut H E in D; from where the falling line cuts the centre line, square out a level line to cut 3 in C; join D C extended to cut the line 2 in B; draw A B level. Then A B and B C will be the tangents for the bottom mould, and C D and D E for the top mould; make E F, Fig. 1, equal W F, Fig. 2, and join F C for H trace.

Fig. 3 shows the face mould for the upper wreath. Make E D F equal E D F, Fig. 2, and F C equal F C, Fig. 1, and D C equal D C, Fig. 2. Draw the major axis through the centre square to F C. With S as centre and O N, Fig. 1, as radius, strike an arc at N; draw V L through the centre and tangent to the arc. For section marked 3, make N H equal O H, Fig. 1, draw H J parallel to V L, make J 3 equal H 3, Fig. 1. Draw J P parallel to S N, and P L square to major axis, join L 3 for section line.

Fig. 4 shows the sections, width of mould, &c. The process of getting the bevels being the same in every case, it would be useless repetition to describe it every time. The shaded parts of sections show the superfluous stuff to come off the top side of wreath at each section.

Fig. 5 shows the face mould for the other side of the wreath. In applying these moulds care must be taken to get the twist the right way.

Fig. 6 shows the face mould for the lower wreath. As this one has only one pitch, draw A B C at right angles and make A B and B C equal A B and B C, Fig. 2. With A as centre and A O, Fig. 1, as radius, strike an arc, draw V L through the centre and tangent to the arc; make H S equal O S, Fig. 1; draw S 4 parallel to V L, make 4 2 equal S 2, Fig. 1. Draw 4 5 parallel to A H, and 5 6 square to major axis A O; join 6 2 for section line.

Fig. 7 shows the sections for this wreath. The section at the joint C will be in the centre of plank, but that at A and 2 will be below the centre. The difference between O H, Fig. 6, and Y J, Fig. 2, is what the section on shank will be below the centre; and that between O 5, Fig. 6, and 5 6, Fig. 2, for section 2. Draw the sections below the centre as shown at Fig. 7.

Fig. 8 shows a sketch of the bottom wreath with the inside and outside worked. The shaded parts show the superfluous stuff to come off top and bottom.

PLATE XIX.

FROM THE LEVEL TO THE RAKE--_continued_.

The plan, elevation and falling line, and position of risers in this case are the same as in Plate XVII., but show a different way of getting out the wreaths. This may not be such a correct method as the former one, as the centre joint will be vertical instead of square to the tangent across the well as was the case there, but nothing could be more simple than the method here described. Having the plan and elevation drawn, square out a bevel line from C, to cut the springing in R. Make R F equal E D, Fig. 1; say the joint is to be at S on the right, join S F, draw the joint S P square to the straight rail, and draw S N square to the tangent F E S.

Fig. 3 shows the face mould. Draw S E D C at right angles, make S E D equal S E F, Fig. 2, and C D equal C D, Fig. 1. To complete the mould, make O N and C N equal E R and F R, Fig. 2. Draw V L through O N; make C R and P H equal C R and R H, Fig. 1. As will be seen, the straight rail is not in a line with the tangent, and as the joint must be square to the straight rail it cannot be square to the face of the plank. Therefore, the face mould for the top side will require to be a trifle longer, while the mould for the bottom side must be the same distance shorter. To find out how much the joint will require to be bevelled, mark off along S N, Fig. 2, S J to equal half thickness of plank; then the distance between the two lines S P and S N at J is what the joint will be out of square to face of plank through half its thickness. The shank of top face mould must be increased, and that of the bottom reduced to this amount as shown by the shaded parts. The face mould shown at Fig. 3, being for the under side, is reduced.

Fig. 5 shows the application of the face moulds; as there is no bevel on the shank E S the joint will only be out of square to face of plank and not to the tangent. Fig. 6 shows the bottom half; this having no twist can be struck with the compasses, the same as the plan. It must be the distance C H, Fig. 2, thicker than the rail. The shaded part shows how the superfluous stuff must be taken off top and bottom.

Fig. 7 shows the pair in position after being squared.

PLATE XX.

HALF-SPACE LANDING, WITH THE RISERS IN THE SPRINGING.

Fig. 1 shows the plan of a half-space landing with the centre line of rail struck with a 9-inch radius, and the risers starting and landing placed in the springing. As the steps are only 10 inches it is very evident that if the tangents A B and D E were the same pitch as the straight rail the tangent across the well would pitch the wrong way, which of course would not do. To obviate this the tangent A B must only rise half a riser over B, and the tangent D E only fall half a riser over D, and the tangent across the well level and the joint on the end of shanks must be bevelled so as to joint square to the straight rail.

Fig. 1 shows the plan with the risers in the springing.

Fig. 2 shows the elevation. Make S N equal stretch-out of centre line of rail. Set up one step above and below and draw landing; also draw the centre falling as shown, this line must pass through the centre at the height of half a riser above the landing, and make a good easing into the straight rail above and below the springing. For development of tangents make F B equal A B, Fig. 1, and draw from B to the joint below the springing; draw R P square to the straight rail, which will be the joint, and R N square to the tangent A B.

Fig. 3 shows the face moulds. As the tangent B C is level draw A B C at right angles; make R A B equal R A B, Fig. 2, and B C equal B C, Fig. 1, and complete the mould as usual. It will be seen that the sections will be in the centre of the plank at both joints. For section P, make F H, Fig. 2, equal A P, Fig. 1, and H J, Fig. 2, equal H J, Fig. 3. The difference between J and the falling line is what the section is out of the centre of plank as shown at Fig. 4. The difference between the tangent A B and the falling line at the springing shows that the section A is out of the centre. The stuff must be thick enough to get this section out as required. Make R Y, Fig. 2, equal half thickness of plank. Add Y C to the end of shank of one face mould and reduce the other to the same amount, as shown by the shaded parts.

PLATE XXI.

WINDERS IN THE HALF-SPACE AND LEVEL LANDING AT TOP.

Fig. 1 shows the plan with the centre line enclosed with tangents. Having laid down the risers on plan, keeping the narrow ends of winders as near as possible half a step, then with one baluster on each they will be the same distance apart as on the square steps which have two. This is not intended as a fixed rule but merely as a guide. The risers must be placed so as to get a good falling line, and this can only be ascertained by developing or unfolding the centre line and tangents on a board.

Fig. 2 shows the development of centre line and tangents. Set up all the treads and risers as they occur on the centre line of rail, Fig. 1. Draw the springing through A and E. Draw the centre falling line resting on the corners of square step at bottom and 4 inches above the landing at top. It is better for the falling line to be a little higher over the winders, especially near the top. To develop the tangents make the distance between the lines 1 2 3 D E equal A B C D E, Fig. 1. Draw D E level. From the centre joint on the falling line square out a line to cut the line 3 at C, join D C extended to cut the line 2 in B. From where the falling line cut the lower springing, square out a line to cut the line 1 in A; join A B; then A B C will be the tangents for the lower wreath and C D E for the top. Decide where the joint is to be below the springing, and draw a line parallel to the tangent A B, and tangent to the curve of the falling line where the joint is to be. The joint must be square to this line. It will be necessary to have a ramp here to ease into the straight rail, this is shown by the dotted lines. In the next plate is shown a method of easing the wreath into the straight rail without the aid of a ramp.

Fig. 3 shows the bottom face mould. Make C B F and B A equal C B A and B A, Fig. 2, and F A equal F A, Fig. 1, and complete the mould as usual. To find what each section is out of the centre of the plank, make W 4 5, Fig. 2, equal C 4 5 on the centre line of rail, Fig. 1; make 4 4 and 5 5, Fig. 2, equal N O and N H, Fig. 3. The difference between the falling line and 4 is what the section 4 on the minor axis is above the centre; and that between 5 and the falling line is what the section 5 is out of the centre. The section at both joints is in the centre, but at the springing A the falling line is a little above the centre, as it cut the springing above the level line A W, which is the height of the centre of the plank there. Get out the mould for the opposite side of the plank in the usual way, by laying Fig. 3 on a thin piece of stuff, and transfer the tangents and section lines on to it. Stick a bradawl through A 5 4 C and mark off out to it A 7 5 8 and 5 9, and C 10 and C 11, only on the opposite side. Work the inside and outside off first with a gig-saw, as before described. The shaded parts of sections at Fig. 4 show the superfluous stuff there is to come off the top side.

Fig. 5 shows the face mould for the top half. Draw C D E at right angles, and to equal C D E, Fig. 2. To see what the sections are out of the centre, make E 3 2, Fig. 2, equal E 3 2 on centre line of rail, Fig. 1. Make 2 2 and 3 3, Fig. 2, equal S R and S L. The difference between 2 and the falling line is what the section 2 is below the centre of plank, and that between 3 and the falling line is what the section 3 is below the centre. And that between E and the falling line is what it is below there.

Fig. 6 shows the sections, and the shaded part shows the superfluous stuff there is to come off the top at each section, after the inside and outside have been cut off.

Fig. 7 shows the wreath after the inside and outside have been cut off; the dotted lines show the wreath cut square through the plank.

PLATE XXII.

WINDERS IN THE HALF-SPACE, WITH A STRAIGHT FLIGHT ABOVE AND BELOW, WREATH TO FORM ITS OWN EASING.

Fig. 1 shows the plan with face of risers laid down. It will be noticed that the winders commence at the springing at the top, while they are brought past the springing at the bottom; this causes the rail to be high at E and, therefore, safer for any one coming down the stairs with their hand on the rail; and by bringing the winders below the springing it makes a better easing into the straight rail. This will be understood by referring to Fig. 2, where the centre line and tangents are developed. Set up the treads and risers as they occur on the centre line of rail, Fig. 1; also draw the springing and the centre line W. Draw the centre falling line resting on the corners of square steps top and bottom, and continue it up over the winders as shown by the dotted line. To develop the tangents make the distance between 1 2 3 4 5 equal A B C D E, Fig. 1. From where the falling line cuts the centre line square out a level line to cut the line 3 at C. Continue the top tangent down in a line with the straight rail to cut the line 4 in D. Join D C extended to cut the line 2 in B. Now make the joint below the springing, as near to it as possible, so that it will be clear of the easing. There being no ramp on the straight rail, the joint should be well clear of the easing and into the straight so as to avoid any signs of a cripple when the wreath is jointed to the straight rail, which there would be if the joint was made in the easing. Square out a level line from the joint P, and make P R equal the distance between the line 1 and the springing. Join R B, this has cut the line 1 at A. From A draw A W level. From R draw the joint square to the straight rail, and R P square to the tangent A B R. Make D F, Fig. 1, equal 4 F, Fig. 2, and join F E for the horizontal trace of the top wreath. Make B S, Fig. 1, equal 6 S, Fig. 2, and join S A for the horizontal trace of the bottom wreath.

Fig. 3 shows the face mould for the top wreath. Make C D F equal C D F and D E equal D E, Fig. 2, and F E equal F E, Fig. 1. Draw from E parallel to D C and from C parallel to D E to meet at the centre O. Draw the major axis square to the horizontal trace F E. With M as centre and O M, Fig. 1, as radius strike an arc at N; draw V L through the centre and tangent to the arc, and complete the mould as usual; M S will equal M S, and T J will equal S J, Fig. 1.

Fig. 4 shows the sections. S S will equal the radius of centre line of rail, Fig. 1, and for bevels place one foot of the compasses on the centre O, Fig. 3, and open out to touch each tangent, then transfer these distances to each section, Fig. 4. To find what each section is out of the centre of the plank, make E J K, Fig. 2, equal E J K on the centre line of rail, Fig. 1. Make J J and K K, Fig. 2, equal N H and N O, Fig. 3. Now the difference between E and the falling line is what the section is below the centre at the springing, and that between J and the falling line is what the section is below the centre, and that between K and the falling line is what the section on the minor axis K is above the centre; the sections at both joints are in the centre of the plank.

Fig. 5 shows the bottom face mould. R A B will equal R A B, and S B C will equal S B C, Fig. 2, and A S will equal A S, Fig. 1. Proceed as usual to get bevels, sections and width of mould. Now, as the tangent A B is not in a line with the straight rail, and the joint being square to the latter, the end of shank must be bevelled so as to joint correctly to the straight rail. Draw P P, Fig. 7, to the same bevel as that for the shank marked O O, Fig. 6. Draw C D, Fig. 7, square to P P, make C N equal 2 2 at section A, Fig. 6, draw the level line through N to cut P P in E and C D in D. Now, at Fig. 2 mark off along R P, R S to equal 2 2 or 1 1, Fig. 6. Make C S and C S, Fig. 7, equal S S, Fig. 2, and join S E and S D for bevels T and S. Apply the bevel T as shown and S as shown at Fig. 8. The face mould for the under side will be S S, Fig. 2, longer, and that for the top side the same amount shorter.

PLATE XXIII.

QUARTER-SPACE LANDING, WREATH IN ONE PIECE.

Fig. 1 shows plan of centre line of rail enclosed with tangent A B C. Draw risers, landing, and starting half a tread from B. This will cause the tangents on face moulds to be the same pitch as the straight rail. This arrangement answers very well if the rail is small, but if the rail is a wide one, say 4 inches or more, the inside has a crippled and awkward appearance.

Fig. 2. Make R S equal stretch-out of the quadrant, Fig. 1. Set up one tread and riser above and below, as they occur on the centre line of rail, Fig. 1. For development of tangents make C 2 1 equal A B C, Fig. 1. Square out a level line from the springing at S to cut the line 1 at A. Join A C for tangents, which will be the same pitch as the straight rail.

Fig. 3 shows face mould. Make C B S equal C B A and B C equal B C, Fig. 2, and S C equal the diagonal of the square on plan. Draw C O and B O parallel to A B and B C. Draw sine major axis and sine minor through O. Notice the major axis is parallel to the diagonal from A to C, and the minor axis is the other diagonal. Both pitches being the same throws the horizontal trace parallel to the diagonal from the centre to B. One bevel will do for both shanks, as the pitches are the same. The falling line will be in the centre of plank at both ends and at the minor axis.

Fig. 4 shows the section, which is the same for both ends, only of course the reverse hand.

SIDE WREATH STARTING FROM A NEWEL.

Fig. 6 shows the plan of centre line of rail of a side wreath starting from a newel. Lay down the tangents A B and B C equal in length and to the required angle, according to circumstances, the size of the hall, &c. The farther it stands out into the hall the better it will look, but it must not obstruct the passage or be out of proportion to the size of the stairs. B should be in front of the second riser, or it will make the rail too high at the newel. A will be the face of the newel. Draw from A square to A B, and from C square to C B to meet in O. Then O A will be the radius of the centre line of rail, which draw. Then A B being level will be the horizontal trace.

Fig. 7 shows the elevation. Set up a tread and risers and draw the springing C as it occurs on the plan. Make C 3 equal C B, Fig. 6, and draw B C S resting on the corners.

Fig. 8 shows the face mould. Draw the line A P, and make A D P equal A D O, Fig. 6. Draw V L through P at right angles to A P. Draw D 8 parallel to V L, make D 8 equal B 3, Fig. 7; join A 8 extended to cut V L in O; then O will be the centre. Make A B and 8 C equal A B and D C, Fig. 6. The completion of the mould will be understood. The tangent C B will equal C B, Fig. 7, if the drawing is correct.

Fig. 9 shows the sections which will be in the centre of plank all round.

PLATE XXIV.

QUARTER-SPACE LANDING, WREATH IN TWO PIECES.

It was said in a previous case that with a wide rail and the tangents on the same pitch as the straight rail, the inside of rail has a crippled appearance. This can be remedied by having the wreath in two pieces.

Fig. 1 shows the plan laid down so as to make the inside falling line of rail a straight line; and the risers landing and starting placed in the springing. To find the radius of centre line of rail, Fig. 1. Make S N, Fig. 7, equal one step. From N draw N R at 45° with S N, and from S draw a line at 60° with S N to meet the line from N in R, from R draw square to and cut S N in P; then R P will be the radius for the inside of the rail on plan.

Fig. 2 shows the development. Make H R equal stretch-out of centre line of rail on plan. Set up one tread and risers above and below, with the risers in the springing. Draw the centre falling line, resting on the corners and passing through the centre, at the height of half a riser above the landing. To develop tangents, make C S R Fig. 2, equal C B A, Fig. 1, and complete tangents as shown. To draw the horizontal trace at Fig. 1, make A B F, Fig. 1, equal R S F, Fig. 2. Join F C for the required trace. Draw N O square to it.

Fig. 3 shows the face mould. Make A B F equal A B F and B C equal B C, Fig. 2, and F C equal F C, Fig. 1. Make C P equal C N, Fig. 1. Draw the major axis from N square to N C F. Draw from A parallel to F C P to cut major axis in 7. Now if the drawing is correct A 7 will equal A R, Fig. 1. With P as centre and N R, Fig. 1, as radius, strike an arc at S; again, with 7 as centre and A R, Fig. 2, as radius, strike an arc to intersect the first one in S. Join 7 S and P S extended, and P N equal O N, Fig. 1. Draw from N parallel to 7 S to cut the major axis in O, then O will be the centre.

Fig. 4 shows the sections and bevels. Make N N equal radius of centre line of rail, Fig. 1, with O as centre, and for radius just touching each tangent, which distances transfer to Fig. 4. All the sections in this case will be in the centre of the plank.