fLIBiURYOFCO^TiPtESSj 
 
 tm^' 
 
 f UNITED states' OF AMERICA '- 
 
THE 
 
 AMERICAN 
 
 Stair-Builders' Guide, 
 
 LUCIUS D. GOULD 
 
 Illustrated by 32 Original Plates. 
 
 NEW YORK: 
 A. J. BICKNELL & CO. 
 
 1875. 
 
y^ 
 
 
 
 
 ^ 
 
 Entered according to Act of Congress, in the year 1875, by 
 
 LUCIUS D. GOULD, 
 In the Ofifice of the Librarian of Congress, at Washington. 
 
 printed by 
 
 Jennings & Hardham, 
 
 newark, n. j. 
 
 ^^ 
 
 ^^ 
 
PREFACE. 
 
 To invent and draw a system of stair-railing superior 
 to any heretofore published, is claimed to be impossible. 
 But after a careful examination of the systems now in 
 use, the author of this work finds that they are not 
 faultless, but susceptible of improvements, as will be 
 demonstrated and proved to the satisfaction of every one 
 who will carefully examine the plates, and peruse the 
 descriptive matter shown in this work. 
 
 To furnish such drawings and explanations of the several 
 parts of stairs and railing, as can be comprehended by 
 workmen not versed in the science, nor much experienced in 
 the construction of stair -railing, and as will enable them to 
 execute with accuracy the most difficult designs it is neces- 
 sary to study simplicity, both in the drawings, and in the 
 terms used for their explanation. In what follows, we 
 shall aim to do this in such a manner that the inexperienced 
 workman will find no difficulty in understanding the plates 
 and the description thereof. 
 
 Newaek, N. J.,~ 
 August, 1875. 
 
Plate 1 
 
 Illustrates a few of the principles that govern the operation of constructing the face 
 mould for the wreaths, and should be throughly understood by the workman, as 
 he will FIEST draw the elliptical curves required for the mould, then find the 
 point of contact of the straight wood with the curve and the length required. 
 
 To form an Ellipse with a thread or string. 
 
 Make A B (Figure 1) the long diameter or major axis, and C D half the 
 short diameter or minor axis of the required ellipse. From the point D as 
 centre, with C B as radius, describe arcs, cutting the major axis at 2 and 3 ; 
 at the points, place pins ; around the pins, place a cord so fastened at the 
 ends that it shall reach around 2 D 3 ; | place your pencil inside the cord 
 and describe the ellipse A D B R. Care should be taken to keep the cord 
 to an even tension. Suppose the elliptic curve A D B to be the centre of a 
 mould required for a wreath, set off each way from D half the width of the 
 rail, and draw the dotted lines D 2 and D 3. From the points S and H 
 draw lines parallel to D 2 and D 3 to intersect the major axis. At the 
 points thus found, place pins and describe the outside and inside curves. 
 To draw two elliptical curves parallel to each other, set off from R to J, 
 equal to B N, from the point J as centre, with C N as radius, describe arcs, 
 cutting the major axis at A and B, the points for the pins to describe the 
 curve required. 
 
 Figure 2 shows the method of finding the point to bore for the first bal- 
 uster on the second step, when you have the length of the newel and the 
 length of the short baluster given. Let A be the pitch -board and 2 the 
 centre of the newel-post ; make 3 4 equal to the difference between the 
 lengths of the newel-post and short baluster. Square over from 4 to the 
 under-side of newel-cap, and where the line 3 4 intersects the underside 
 of rail will be the point to bore for the baluster. To continue the same 
 height of rail from the starting to its termination, care should be taken to 
 rise from the point B to C, equal to the height of the rise on the second 
 flight ; bisect the rise in D for the underside of the level rail. 
 
Plate 1 
 
Plate 2 
 
 Exhibits the ground plan and elevation of the hand-rail for a platform 
 staircase. 
 
 Figure 2, shows the method of forming the mould for the wreath. Draw 
 A B, the pitch or inclination of the stairs. Square up from A and B, equal 
 to C D, Fig. 1. Set off from C to B equal to the width of the rail. To 
 find the points for the pins, to describe the elliptical curves for the outside 
 and inside of the mould ; from the points S and C as centres, with S 2 and 
 C 3 as radii, describe arcs, cutting the line A B at 5 4 and 3 2, the points 
 required. The application of the spring-bevel, shown at Fig. 3, is seen at 
 the joint A, which gives the angle to draw the centre line and determine 
 the thickness of plank required for the wreath. The plank sawed square, 
 the straight wood one-fourth inch wider than the rail, apply the mould, as 
 shown at Fig. 4, mark the curves on both sides. To remove the corner A, 
 tack the mould on the opposite side of the plank. The same operation will 
 be required to remove the corner B. The saw or plane should be held in 
 the direction of the centre line shown at the joint. Screw the wreaths 
 together and place them over the pitches on the drawing-board, as shown 
 at Fig. 3. Find the points C and D, from which gauge the thickness 
 of the rail and form the wreath. 
 
 This system can be applied to large cylinders by extending the radius 
 from C to N and leaving the risers the same^distance from the centre of the 
 rail, as shown by the dotted lines at Fig. 1. 
 
Plate 2. 
 
Plate 3 
 
 Exhibits the ground plan and elevation for a quarter landing ; also the method 
 of determining the length of curve required for the mould. 
 
 To draw the elevation, produce the radius A C, Fig. 1, to B, Fig. 2. 
 From the point B, draw the pitch and floor lines, indefinitely. From the 
 centre of the baluster, shown at A, Fig. 1, draw the dotted line parallel to 
 A B, cutting the pitch line at J. Set up from J to P, equal to half the 
 height of riser for the centre of level rail. Draw D T parallel to B A. Then 
 A T, Fig. 1, is the length of the tangents, and A S is the length of curve 
 required. 
 
 In works heretofore published on stair-railing, the authors have given 
 geometrical methods, of finding the spring bevels for the joints, which may 
 or may not be correct ; the only evidence of their correctness, being ascer- 
 tained by their application, which in our method is practically made before 
 the mould is djawn, as the width of the mould, and thickness of the plank, 
 are determined by the bevels, which can be found by taking a piece any 
 thickness and forming the angle ATS, Fig. 1. Draw T L at right angles 
 to A T, and L D, the pitch of the stairs. Draw L C at right angles to L 
 T. Work to the lines, and apply the bevels. The bevel at C is fer the 
 joint. The bevel applied to the pitch line L D, is for the straight wood. 
 
 We will now state to the workman, that the minor or short axis of the 
 elliptic curve, required for the mould, must in all cases, be equal to the 
 radius of the circle given on the plan. The length of the major or long 
 axis, is governed by the angle, to which the cylinder may be cut, as follows : 
 Draw A B, Fig. 1, at right angles to A S, equal to S D, Fig. 3 ; produce the 
 circle from A to R; draw C D parallel to A B ; join S B and extend to R. 
 Then D R equals half the length of the major axis, and S B determines the 
 length of curve required for the mould. 
 
 The above rule will in all cases be found true, as we shall prove in the 
 following plates. 
 
 The mould for the wreath is shown at Fig. 3. Draw the major axis 
 indefinitely. To find the points for the pins, to describe the centre curve, 
 set off from C to B, equal to D R, Fig. 1. From the point A, as centre, 
 with B, as radius, describe arcs cutting the major axis at 2 and 3, the 
 points required. To find the length of curve, from the point B as centre, 
 with S B, Fig. 1, as radius, describe an arc, cutting the curve at D, the 
 length required. For the direction of the straight wood, draw D S, equal 
 to B D, Fig. 2, and B S, equal to A T, Fig. 1 ; then S D is the direction 
 required. For the width of the mould, set oflf from A each way half the 
 width of the rail ; at Fig. 2, set off from 2 to 3, the width of the rail, draw 
 3 4 at right angles to 2 b ; then 4 5 is the width of the mould at B. The 
 points for the pins to describe the outside and inside curves, are found in 
 the same manner as those for the centre curve ; the plank sawed square to 
 a parallel width from the centre curve, one-fourth inch wider than the rail ; 
 cut the joints at right angles to the tangents. The application of the bevels 
 are shown at Fig. 3, and give the direction of the centre line, from which 
 the section of rail is formed at the joints. At right angles to the joints 
 draw lines from H and B on both sides of the plank ; then place the centre 
 of the mould on the line H D, squared from the joint, and move the mould 
 until the line B S stands over the line squared from the joint B. Mark the 
 plank for the corners to be removed. The same operation is required for 
 the opposite side. Tack the mould on the opposite side of the corner to be 
 removed. In doing this, the saw or plane should be held in a vertical 
 direction. The surplus wood can be removed from the upper and lower 
 sides of the wreath, after tracing the thickness of the rail from the centre 
 of the plank. 
 
Plate 4 
 
 the ground plan for a platform staircase; also a very simple and easy 
 method of forming the face mould for the wreath; the planTc sawed square to 
 a parallel width. 
 
 The face-mould for the wreath, at Fig. 3, is found by first getting the 
 length of the major axis, and describing the elliptical curves; next, the point 
 of contact, from that the length of curve required. The length of the major 
 axis is obtained by drawing B S, Fig. 1, at right angles to B H, equal to 
 H R, Fig. 2. Produce the circle from B to E. Draw J and E D parallel 
 to B S ; then J D equals half the length of the major axis, and H S deter- 
 mines the length of curve, required for the mould. 
 
 For the mould, at Fig. 3, draw a line indefinitely ; square up from A to 
 C, equal to C H, the radius of the circle at Fig. 1 ; set off each way, from 
 the point C, half the width of the rail. To find the points for the pins, 
 from the point C as centre, with J D as radius, describe arcs, cutting the 
 major axis at 2 and 3, the points for the pins, to describe the centre curve. 
 The points, for the pins to describe the outside and inside curves, are found 
 by drawing the dotted lines parallel to C 2 and C 3, to intersect the major 
 axis at the points required. To find the point of contact, draw H J equal 
 to 2 3, Fig. 2, from the point J, as centre, with H S, Fig. 1, as radius ; de- 
 scribe an arc cutting the curve at S, the point of contact of the straight 
 wood with the circle. To find the direction of the straight wood, draw 
 J K equal to R P, Fig. 2, and S K equal to T P, Fig. 2. Draw A S, and 
 from its intersection with the curves, draw the straight wood parallel to 
 K S, indefinitely. The joints are cut at right angles to the tangents. The 
 bevel, for the straight wood, is shown at P; for the joint at H, Fig. 2. 
 
 Another example of the practical method of finding the spring bevels 
 for the joints : Fig. 4 shows a piece formed to fit the angle B G H, Fig. 1 ; 
 draw G S at right angles to G B ; draw S B the same pitch or inclination 
 as P T, Fig. 2, and S P the same pitch as P R, Fig. 2 ; apply the bevels at 
 right angles to the pitch lines. The bevel on the line S P, is for the joint 
 at J; the one on the line S B, is for the joint on the straight wood. 
 
Scale' /^z indtea = -ifoot. 
 
Plate 5 
 
 Exhibits the ground, flan of the turn-out at the starting of a staircase, the 
 wreath forming its own easing at the newel. 
 
 Before drawing the mould it is necessary to know the height of the newel, 
 which is seven inches higher than the short balusters ; or, suppose the short 
 baluster to be two feet from the top of the step to the underside of the rail, 
 and the newel two feet seven inches from the top of first step to the under- 
 side of newel-cap, then at Fig. 3 set up from the top of first step seven 
 inches to the centre of rail. To find the position of the steps, from the 
 point B, draw the common pitch indefinitely ; set up from the first step the 
 height of one riser, cutting the pitch line at C, the point for the riser, which 
 determines the position of the steps on the plan. The radius of the curve 
 will be governed by the projection of the newel, from the face of string. 
 The length of curve will be determined by the width of steps and the 
 height of newel. 
 
 Find the major axis of the elliptic curve for the centre of the face-mould 
 by drawing S D, Fig, 1, at right angles to S B, equal to L G, Fig. 3 ; pro- 
 duce the circle from S to R ; draw R P and C H parallel to S D ; join B D 
 and extend to P. Then H P equals half the length of the major axis and 
 B D determines the length of curve required for the mould. 
 
 For the face-mould. At Fig. 3 draw the major axis ; square up from the 
 point to B, equal to C S, Fig. 1. To find the points for the pins, to 
 describe the centre curve, from the point B as centre, with C D as radius, 
 describe arcs, cutting the major axis at 3 and 8, the points required. To 
 find the length of curve, and point of contact, from the point D as centre, 
 with B D, Fig. 1, as radius, describe an arc, cutting the curve at N, the 
 point and length required. The direction of the straight wood is given by 
 drawing D S equal to B L, Fig. 1, and N S equal to G B, Fig. 3. For 
 the width of the mould set off each way from B half the width of the rail. 
 At Fig. 3 make 2 3 equal to the width of the rail ; draw 3 4 at right 
 angles to 3 3. Then 3 4 is the width of the mould at D. The points for 
 the pins to describe the outside and inside curves, are found in the same 
 manner as those for the centre curve. 
 
 Figure 4 exhibits a practical method of finding the spring-bevels for the 
 joints, by fitting a piece of wood to the angle of the tangents on the plan. 
 From the point L, draw the line L C at right angles to L S ; draw D at 
 right angles to C L, and C R, the pitch of the stairs ; apply the bevels at 
 right angles to the lines, C D and C R. The bevel on the line C D, is for 
 the joint 1), and is shown at 3, Fig. 3. The bevel on the pitch-line C R 
 is for the straight wood, and is shown at 4, Fig. 3, 
 
Plate 5 . 
 
 Indies- 1 foot: 
 
 Fig.l 
 
Plate 6 
 
 Exhibits the plan and elevation for the turnout at the starting of the staircase^ 
 the rail terminating against the newel ; the flank sawed square to a parallel 
 width. 
 
 The length of the major axis is found by producing the curve D A, Fig. 
 1, to T ; draw T J and A S parallel to C B ; make A S equal to R N, Fig. 
 2 ; join D S and extend to J. Then P J equals half the length of the major 
 axis, and D S determines the length of the curve required for the mould. 
 
 At Fig. 3 draw the major axis indefinitely ; square up from to B 
 equal to C D, Fig. 1. The points, for the pins to describe the centre curve, 
 are found by taking in the compasses the distance P J, Fig. 1, with the 
 point B as centre, and describing arcs, cutting the major axis at 2 and 3, 
 the points required. The length of curve, and the direction of the straight 
 wood, is found by making C S equal to C B, Fig. 1. From the point S as 
 centre, with H N, Fig. 2, as radius, describe arcs, cutting the curve at D 
 and H ; join S H and S D. Then H D is the length of curve, and S D the 
 direction required. The width of the mould is found by setting off each 
 way from B, half the width of the rail ; the points from which to describe 
 the outside and inside curves. The points for the pins, are found by draw- 
 ing the dotted lines parallel to B 2 and B 3 to intersect the major axis. 
 The joints are cut at right angles to the tangents. One bevel answers for 
 both joints. 
 
Scale, tindv- /foot 
 
Plate 7 
 
 Exhibits the ground plan of an elliptical turnout at the starting of the staircase; 
 the 'mould formed ty ordinates; the planTc sawed square, and the joints made 
 at right angles to the face of plank. 
 
 The workman will first draw the elliptical curve required fer the turnout, 
 and attach the newel cap ; then place the steps as shown at Fig. 1. At 
 Fig. 2 is shown the elevation of the steps and risers, which gives the com- 
 mon pitch. Set up from the first step to the centre of rail, the diff'erence in 
 the heights of the newel post and short baluster, which is 6^ inches; draw 
 C L at right angles to A H; make the tangent A B, Fig. 1, equal to C L, 
 Fig. 3. From the point B, Fig. 1, draw the tangent B D indefinitely. 
 
 To form the mould for the wreath, draw D S, Fig. 1, at right angles to 
 B D, and A S parallel to B D ; set up from D to R equal to L H, Fig. 3 ; 
 join R S. At right angles to R S, draw R T, equal to D B, Fig. 1, and S J 
 equal to S A, Fig. 1 ; join J T, which should equal C H, Fig. 3; draw any 
 number of ordinates from the plan ; transfer the distances, and trace the 
 mould. The bevel for the straight wood is shown at Fig. 3, and is found 
 by drawing D F at right angles to A B, Fig. 1 ; then by extending F D 
 to intersect the pitch line at Fig. 3 ; from the point of intersection, square 
 over to K; then P K will equal D F, Fig. 1. From the point P as centre, 
 describe an arc, touching the pitch line, which determines the angle for the 
 bevel required. 
 
Plate S 
 
 Exhibits the plan for a staircase, starting with winders; the circle produced 
 leyond a quadrant; the plank sawed square to a parallel width, the wreath 
 forming its own easing at the newel. 
 
 At Fig. 3, set up from the first step to the centre of rail, the difference in 
 the heights of the newel and short baluster, find the height from the first 
 step, to the first square step above the winders, which is six risers. Place 
 the pitch-board and draw the common pitch indefinitely. Draw the easing, 
 so as to have about three inches of straight wood to the wreath. Then from 
 the point A, draw the pitch line, tangent to the curve in the rail, which com- 
 pletes the elevation. 
 
 The length of the major axis is found at Fig. 1, by producing the curve 
 D A to T, and drawing A B and T R parallel to C S; make A B equal to 
 C J, Fig. 2 ; join D B and extend to R. Then S R equals half the length 
 of the major axis or long diameter, of the elliptic curve required for the 
 centre of the mould. 
 
 For the mould, at Fig, 3 draw the major axis indefinitely ; square up 
 from C to D, equal to C D, Fig. 1. For the width of the mould, set off 
 each way from D half the width of the rail. The points, for the pins to 
 describe the centre curve, are found by taking the point D as centre, with 
 S R, Fig, 1, as radius, and describing arcs, cutting the major axis at 2 and 
 3, the points required. The points, for the pins to describe the outside and 
 inside curves, are found by drawing the dotted lines, parallel to D 3 and 
 D 2 to intersect the major axis. The length of curve, and direction of the 
 straight wood, is found by extending the line C D to S equal to C N, Fig. 
 1, from the point S as centre, with R J, Fig. 2, as radius; describe an arc, 
 cutting the curve at J, the length required ; join S J and extend to P ; then 
 S J is the direction, and J P the length of straight wood required. The 
 bevel for the joint at the newel, is shown at R. The bevel, for the straight 
 wood, is shown at K. 
 
Plate 8 [] 
 
Plate 9 
 
 Exhibits the ground flan and elevation for a staircase^ starting with winders; 
 the curve is drawn from centres of unequal radii. 
 
 Set up from the first step to the centre of rail, the difference in the heights 
 of the newel and the short baluster. To find the length of the major axis 
 of the elliptic curve for the centre of the mould, draw lines from D and A, 
 Fig. 1, parallel to C H, indefinitely; set up from D to K, equal to B C, Fig. 
 3 ; draw B R, and extend to S. Then J S equals half the length of the 
 major axis for the centre of the mould at Fig. 3. 
 
 To form the mould, draw the major axis, indefinitely. To find the points 
 for the pins, square up from C to B, equal to C D, Fig. 1. From the point 
 B as centre, with J S, Fig. 1, as radius, describe arcs, cutting the major axis 
 at 3 and 3, the points required. For the direction of the straight wood 
 and length of curve, set up from C to P, equal to C H, Fig. 1. From the 
 point P as centre, with L S, Fig. 3, as radius, describe arcs, cutting the 
 curve at R and H; join P R and P H; then P H is the direction, and R H 
 the length of curve required. For the width of the mould, and the points 
 for the pins, to describe the outside and inside curves, set off each way from 
 B half the width of the rail; from the points draw lines parallel to B 3 and 
 and B 3, to intersect the major axis. The bevel for the joints is shown at 
 Fig. 2. 
 
 The face mould for the quadrant at the newel is shown at Fig, 4; square 
 up from A to B equal to B 3, Fig. 1 ; set off from A to C equal to S B, Fig. 
 3. From the point B as centre, with A C as radius, describe arcs, cutting 
 the line A C at 3 and 3 ; the points for the pins to describe the centre curve. 
 For the width of the mould, and the points for the pins to describe the 
 outside and inside curves, set off each way from B half the width of the rail. 
 From the points draw lines parallel to B 3 and B 3 to intersect the line A C. 
 The bevel for the joint C is shown at S, Fig. 3. 
 
Plate 9 
 
 Fi|5. 3. 
 
 ^/ ScaZ& / inch - ^ foot 
 
Plate 10 
 
 Exhib U the ground plan and the e'evation for a staircase^' starting with wind- 
 
 ifx; thu curve drawn J'ri">n centres of unequil radii; the wreath in one piece 
 
 forming its own easings. 
 
 Set up licnu the first step to the point N, equal to ihe diflference in 
 the heiglits of the newel, and the short baluster; join R N; square 
 over from N to Y ; draw Y V parallel to the centre of rail ; join R V, and 
 extend to P. Then H P equals half the major, and V Y half of the minor, 
 axis of the quadrant at the starting. 
 
 To find the length of the major axis of the elliptic curve, for the centre 
 of the mould, draw lines from the points B and L, Fig, 1, parallel to C P, 
 indefinitely ; set up from B to R equal to D G, Pig. 2 ; draw A R and extend 
 to D. Then J D equals half the length of the major axis, and A R deter- 
 mines the length of curve required. 
 
 To form the mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins,- to describe the centre curve, square up from C to D, 
 equal to C B, Fig. 1. From the point D as centre, with J D, Fig. 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 For the point to cut the curve, set up from the major axis equal to 2 3, 
 Fig. 1 ; from that point draw a line parallel to the major axis, cutting the 
 curve at T. From the point T as centre, with A R, Fig. 1, as radius, describe 
 an arc, cutting the curve at N. Then T N is the length of curve required 
 for the mould standing over the curve B A, Fig. 1. For the extension of 
 the mould over the quadrant at the starting, square over from N to A equal 
 to V Y, Fig. 3; draw A B parallel to H N, equal to H P, Fig. 2. To find 
 the points for the pins to describe the centre curve from N to B, take A B 
 as radius, from the point N as centre, describe arcs, cutting the line A B, for 
 the points required. For the width of the mould, set off each way from D 
 half the width of the rail. At Fig. 2, 2 3 and 4 5 each equals the width 
 of the rail ; then 6 3 equals the width of the mould at T, and R 5 equals 
 the width of the mould at B. To find the points for the pins, to describe 
 the outside and inside curves from T to D, set off each way from 2 and 3 
 equal to T K. The points for the pins, to describe the outside and inside 
 curves from N to B, are found in the same manner as those for the centre 
 curve. The bevel for the straight wood is shown at 6 ; for the joint B, at R. 
 
Plate 11 
 
 Exhihits the ground flan for a quarter platform staircase; the risers placed at 
 the spring of the cylinder. 
 
 To find the major axis of the elliptic curve for the centre of the mould, 
 draw H B, Fig. 1, parallel to C A, equal to S C, Fig. 2; produce the curve 
 T H to J; draw T B and extend to J. Then D J equals half the length 
 of the major axis, and T B determines the length of curve required. 
 
 At Fig. 3 draw the major axis indefinitely ; square up from C to B equal 
 to C T, Fig. 1. To find the points for the pins to describe the centre curve, 
 take D J, Fig. 1, as radius, from the point B as centre, describe arcs, cutting 
 the major axis at 2 and 3, the points required. To find the point, to 
 cut the curve, set up from the major axis, equal to R S, Fig. 1 ; 
 from the point, draw a line, parallel to the major axis, cutting the 
 curve at 5. From the point 5 as centre, with T B, Fig. 1, as radius, 
 describe an arc, cutting the curve at L, the point of contact, and the 
 length of curve required. For the direction of the straight wood, draw 5 
 H, equal to D, Fig. 2, and L H equal to B D, Fig. 2. Extend H L any 
 length required. This being an arbitrary case, it is necessary to find the 
 bevels, (which in all cases govern the width of the mould,) which are shown 
 at Fig. 2. At Fig. 4 they are enlarged ; the dotted line 3 3 equals the width 
 of the rail ; then 2 4 equals the width of the straight wood at L, and 6 5 
 the width of the mould at the joint. The points for the outside and in- 
 side curves are found by setting oif each way from B, half the width of the 
 rail, from the point N, set off each way half the length of 6 5, Fig. 
 4 ; then 4 5 and 6 7 are the points from which to draw the curves. The 
 points for the pins are found by taking in the compasses C 5 as radius, from 
 the point 6 as centre, and describing arcs, cutting the major axis, at the 
 points required for the inside curve. The pins for the outside curve are 
 found in the same manner. The joints are cut square with the tangents. 
 
Plate 12 
 
 Exhibits the ground plan and elevation of the flatform^ for an acute angled 
 staircase; the, wreath in one piece; the planTc sawed square to a parallel 
 width. 
 
 To find the length of the major axis of the elliptic curve for the centre 
 of the mould, draw lines from the points A and J, Fig, 1, parallel to C F ; 
 set up from A to D, equal to S R, Fig. 2 ; draw R D and extend to E ; then 
 E G equals half the length of the major axis, and R D determines the length 
 of the curve required for the mould. 
 
 For the mould at Fig. 3, draw the major axis indefinitely. To find the 
 points for the pins, to describe the centre curve, square up from C to L 
 equal to C R, Fig. 1. From the point L as centre, with G- E, Fig. 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 To find the point to cut the curve, set up from the major axis equal to 2 3, 
 Fig. 1 ; from the point, draw a line parallel to the major axis, cutting the 
 curve at J. From the point J as centre, with R D, Fig. 1, as radius, describe 
 an arc, cutting the curve at R. For the direction of the straight wood, 
 draw R H equal to N H, Fig. 2, and J H equal to R H, Fig. 2. For the 
 width of the mould, and the points for the pins to describe the outside and 
 inside curves, set ofi" each way from L half the width of the rail. From the 
 points draw lines parallel to L 2 and L 3 to intersect the major axis. The 
 joints are cut square with the tangents, and face of plank. The bevel for 
 the joint R is shown at N ; for the straight wood at H. 
 
Plate 12. 
 
 Scale -/ inchy Ifoot. 
 
Plate 13 
 
 Exhibits the ground flan and elevation of an acute angled platform staircase; 
 the wreath in two 
 
 To find the major axis of the elliptical curve required for the centre of the 
 mould. At Fig. 1, draw B S parallel to C R, equal to C D, Pig. 2 ; produce 
 the curve A B to D ; join A S and extend to D. Then R D equals half the 
 length of the major axis, and A S determines the length of curve required 
 for the mould. 
 
 For the face mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins, to describe the centre curve, square up from C to D 
 equal to C B, Fig. 1, From the point D, as centre, with R D, Fig. 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 For the point to cut the curve, set up from the major axis equal to L J, 
 Fig. 1 ; from the point, draw a line parallel to the major axis, cutting the 
 curve at P; from the point P as centre, with A S, Fig. 1, as radius, describe 
 an arc, cutting the curve at H ; for the direction of the straight wood, draw 
 P R, equal to D B, Fig. 2, and H R equal to S B, Fig. 2 ; for the width of 
 the mould, and the points for the pins to describe the outside and inside 
 curves, set off each way from D, half the width of the rail ; from the points, 
 draw lines parallel to D 2 and D 3, to intersect the major axis. The bevel 
 for the centre joint is shown at C ; for the straight wood, at S. 
 
Plate 13 
 
 Tig 3. 
 
 MR 
 
 c^-. 
 
 Tig.l 
 
 Scale, ^yzirufieS' -ffbot. 
 
Plate 14 
 
 Exhibits the ground plan and elevation for a quarter platform staircase^ showing 
 the position of the riser's in the cylinder, to continue the same plane or inclina- 
 tion in the wreath. 
 
 At Fig. 1 set off, from A, to B and D, equal to half the width of the step. 
 To find the major axis of the elliptic curve for the centre of the mould, draw 
 lines from L and J, Fig. 1, parallel to C A; set up from L to H equal to 
 H J, Fig. 2 ; draw S H and extend to R. Then R N equals half the length 
 of the major axis. 
 
 For the mould at Fig. 3, draw the major axis indefinitely. To find the 
 points for the pins to describe the centre curve, square up from C to B equal 
 to C L, Fig. 1; from the point B as centre, with N R, Fig. 1, as radius, 
 describe arcs, cutting the major axis at 3 and 3, the points required ; for 
 the length of curve, and the direction of the straight wood, set off from C 
 to S, equal to C A, Fig. 1 ; from the points C and S as centres, with P J, Fig. 
 2, as radius, describe arcs, cutting the curve at H and J ; join S H and S J, 
 for the direction required. For the width of the mould, and the points for 
 the pins, to describe the outside and inside curves, set off each way from B 
 half the width of the rail ; from the points draw lines parallel to B 2 and 
 B 3, to intersect the major axis. One bevel answers for the joints. 
 
Plate 14^. 
 
\ 
 
Plate 15 
 
 Exhibits the ground plan and elevation for the landing of the staircase, showing 
 the method of finding the length of curve required for the mould, ly which 
 the worhnan is not obliged to mahe the joint hi the centre, as the point of in- 
 tersection of the level with the p)itch line, determines the length of curve re- 
 
 For the length of the major axis of the elliptic curve for the centre of the 
 mould, draw lines from A and S, Fig. 1, parallel to C L ; set up from A to 
 B, equal to A B, Fig. 3 ; join H B and extend to R. Then D R equals half 
 the length of the major axis, and H B determines the length of the curve. 
 
 For the face mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins to describe the centre curve, set up from C to D equal 
 to C H, Fig. 1. From the point D as centre, with D R, Fig. 1, as radius, 
 describe arcs, cutting the major axis at 2 and 3, the points required. For 
 the direction of the straight wood and length of curve ; from the point 
 R as centre, with H B, Fig. 1, as radius, describe an arc, cutting the 
 curve at S ; draw R L equal to A L, Fig. 1, and S L equal to H B, Fig. 
 3. Then S L is the direction and S R the length of curve required. For 
 the width of the mould and the points for the pins to describe the outside 
 and inside curves : at Fig. 3, A J equals the width of the rail, and B J equals 
 the width of the mould at R ; set oflf each way from D half the width of the 
 rail ; from the points describe the curves. The bevel for the straight wood 
 is shown at J ; for the joint, at B. 
 
Centre of RaiO 
 
 SccOe^ 2 'iti,nc/ri- Ifbot. 
 
 r 
 
Plate 16 
 
 Exhibits the ground plan and elevation for a staircase^ with winders in the 
 quarter circle; the wreath in one piece. 
 
 For tlie length of the major axis, of the elliptic curve for the centre of the 
 mould : At Fig. 1, from the points A and D, draw lines parallel to C 
 L ; set up from A to H equal to R T, Fig. 2 ; join B H and extend to S. 
 Then L S equals half the length of the major axis, and B H determines the 
 length of curve required for the mould. 
 
 To form the mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins to describe the centre curve, set up from C to B 
 equal to C B, Fig. 1. From the point B as centre, with L S, Mg, 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 For the point to cut the curve, set up from the major axis, equal to S T, 
 Fig. 2; from the point draw a line parallel to the major axis, cutting the 
 curve at S. From the point S as centre, with B H, Fig. 1, as radius, describe 
 an arc, cutting the curve at J. For the direction of the straight wood, 
 draw J H, equal to N H, Fig. 2, and S H, equal to T H, Fig. 2. For the 
 width of the mould, and the points for the pins to describe the outside and 
 inside curves, set off each way from B half the width of the rail ; from the 
 points draw lines parallel to B 2 and B 3, to intersect the major axis. The 
 bevel for the joint J, is shown at S; for the straight wood, at H. 
 
Plate 17 
 
 Exhibits the ground plan mid elevation of the landing, of an ohtuse a?igled stair- 
 case, showing the method of determining the radius of the circle for the 
 cylinder. 
 
 From the edge of the drawing-board, square up the line A D. At right 
 angles to^A B, draw the floor line and centre of rail. Place the pitch-board 
 at D, and draw the pitch, to intersect the centre of rail at H ; draw H B 
 parallel to D A ; then A B is the length of the tangents ; draw B S, the 
 direction required, to form the obtuse angle ; make B S equal to B A ; draw 
 S C at right angles to S B ; then C is the centre, and C A the radius of the 
 arc, required for the cylinder. 
 
 To find the length of the major axis, of the elliptic curve for the centre 
 of the mould, draw A P, Fig. 1, parallel to C B, equal to C H, Fig. 2 ; join 
 S P, and extend to R. Then R H equals half the length of the major axis, 
 and S P, determines the length of the curve, required for the mould. 
 
 To form the mould, at Fig. 3, draw the major axis indefinitely. To find 
 the points, for the pins to describe the centre curve, square up from C to S, 
 equal to C A, Fig. 1 ; set off, from C to P, equal to R H, Fig. 1. From the 
 point S, as centre, with C P, as radius, describe arcs, cutting the major axis 
 at 3 and 3, the points required. For the length of curve and direction of 
 the straight wood, from the point P, as centre, with S P, Fig. 1, as radius, 
 describe an arc, cutting the curve at J ; draw P H, equal to S B, Fig. 1, and 
 J H, equal to D H, Fig. 3. For the width of the mould, and the points for 
 the pins, to describe the outside and inside curves, set off each way from S, 
 half the width of the rail ; at Fig. 3, set off from 3 to 3, equal to the width 
 of the rail ; then 7 6 equals the width of the mould, at P. The points, for 
 the pins, are found in the same manner as those for the centre curve. The 
 bevel, for the straight wood, is shown at*B; for the joint, at C. 
 
Plate 17 
 
 '" n. 
 
 Scale- 1 's indiea^ i foot 
 
Plate IS 
 
 Exhibits the flan and elevation for a platfoi^m staircase. For want of room, at 
 the termination of the return flight, we have placed the riser at the starting, 
 leyond the cylinder. 
 
 The length of the major axis, of the elliptic curve, for the centre of the 
 mould, is found at Fig, 1, by drawing lines from B and E, parallel to C S, 
 indefinitely ; set up, from B to F, equal to R P, Fig. 2 ; join H F, and ex- 
 tend to Gr. Then J G equals half the length of the major axis, and H F 
 determines the length of the curve, required for the mould. 
 
 For the face mould, at Fig. 3, draw the major axis indefinitely; square 
 up from C to P, equal to C B, Fig. 1. To find the points for the pins, to 
 describe the centre curve, take J G, Fig. 1, as radius, from the point P, as 
 centre, describe arcs, cutting the major axis at 2 and 3, the points required. 
 To find the point of contact and length of curve, at any point, set up from 
 the major axis, equal to 2 3, Fig. 2 ; from the point, draw a line parallel to 
 the major axis, cutting the curve at J. From the point J, as centre, with H 
 F, Fig. 1, as radius, describe an arc, cutting the curve at S, For the direc- 
 tion of the straight wood, draw J R, equal to P N, Fig. 2, and S R, equal 
 to L N, Fig. 2. For the width of the mould, set off each way from P, half 
 the width of the rail. The points, for the pins, to describe the outside and 
 inside curves, are shown at the intersection of the dotted lines, with the 
 major axis. The joints are cut at right angles to the tangents. The bevel 
 for the straight wood is shown at N; for the centre joint, at R. 
 
Plate 19 
 
 ExMlits the ground plan and elevation for the landing of a staircase; the riser 
 placed on a line with the face of cylinder; the wreath in two 
 
 The length of the major axis, of the elliptic curve, for the centre of the 
 mould, is found by drawing lines from A and P, Fig. 1, parallel to D L ; set 
 up, from A to B, equal to A C, Fig. 2 ; draw R B, and extend to C. Then J 
 C equals half the length of the major axis, and R B determines the length 
 of curve, required for the mould. 
 
 To form the mould, at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins, to describe the centre curve, square up from the 
 point C to B, equal to D A, Fig. 1. To find the points, for the 
 pins, to describe the centre curve ; from the point B, as centre, with J C, 
 Fig. 1, as radius, describe arcs, cutting the major axis at 2 and 3, the points 
 required. For the points, to cut the curve, set up from the major axis, equal 
 to 2 3, Fig. 2; from the point, draw a line parallel to the major axis, cutting 
 the curve at J. From the point J, as centre, with R B, Fig. 1, as radius, 
 describe an arc, cutting the curve at L ; then L is the point of contact, and 
 L J the length of curve. For the direction of the straight wood, draw J H, 
 equal to C D, Fig. 2, and L H, equal to E D, Fig. 2. For the width of the 
 mould, and the points for the pins to describe the outside and inside curves, 
 set off each way from B, half the width of the rail. From the points, draw 
 the dotted lines parallel to B 2 and B 3, intersecting the major axis, at the 
 points required. The bevel, for the centre joint, is shown at A; for the 
 straight wood, at D, Fig. 2. 
 
 The mould, for the upper wreath, is shown at Fig. 4 ; draw A B, equal to 
 A D, Fig. 1. At right angles to A B, draw A C, equal to C F, Fig. 2 ; set 
 off, each way from B, half the width of the rail ; join B C. For the width 
 of the straight wood ; from the points set off from B, draw the dotted lines 
 parallel to B C, to intersect the line A C. The curves are drawn with the 
 compasses. The bevel required, is shown at F. 
 
Plate 20 
 
 Exhihits the continuation of the staircase, shown on Plate 19, to the starting 
 of the second flight. 
 
 To find the length of the major axis, of the elliptic curve required for the 
 centre of the mould, at Fig. 1, draw lines from the points A and P, parallel 
 to S R ; from the point A, set up to B, equal to L B, Fig. 3 ; draw C B, and 
 extend to D. Then J D equals half the length of the major axis, and C B 
 determines the length of curve required for the mould. 
 
 To form the mould, at Fig. 3, draw a line for the major axis. To find 
 the points, for the pins to describe the centre curve, square up from C to S, 
 equal to S A, Fig. 1. From the point S, as centre, with J D, Fig, 1, as 
 radius, describe arcs, cutting the major axis, at 2 and 3, the points required. 
 To find the points, to cut the curve, set up from the major axis, equal to 2 
 3, Fig. 2 ; from the point, draw a line parallel to the major axis, cutting the 
 curve at D. From the point D, as centre, with C B, Fig. 1, as radius, de- 
 scribe an arc, cutting the curve at P. .For the direction of the straight 
 wood, draw D H, equal to S C, Fig. 2, and P H, equal to B C, Fig. 3. For 
 the width of the mould, and the points for the pins to describe the outside 
 and inside curves, set off each way from S, half the width of the rail ; from 
 the points, draw lines parallel to S 2 and S 3, cutting the major axis at the 
 points required. The bevel, for the straight wood, is shown at S ; for the 
 centre joint, at B. 
 
 The mould, for the lower wreath, is shown at Fig. 4. Draw B C, equal to 
 S C, Fig. 1, and B A, equal to S H, Fig. 3 ; set off each way from C, half 
 the width of the rail. The width of the straight wood, is found by draw- 
 ing the dotted lines parallel to A C. The curves are drawn with the com- 
 passes. The bevel, for the straight wood, is shown on the line H S. 
 
I 
 
Plate 21 
 
 Exhibits the ground 'plan and elevation for a quarter circle of winders, and the 
 starting of t?ie return flight, from the spring of the cylinder; the wreath in 
 two 
 
 To find the major axis, of the elliptic curve for the centre of the moulds, 
 draw lines from A and L, Fig. 1, parallel to C P, indefinitely ; set up from 
 A to B, equal to L S, Fig. 2, and from A to D, equal to R H, Fig. 2 ; draw 
 S B, and S D, and extend to J and R; produce P C to H, Then H J equals 
 half the length of the major axis, of the elliptic curve for the centre of the 
 mould, at Fig. 3, and N R equals half the length of the major axis, for the 
 mould, at Fig. 4, and S D determines its length. 
 
 For the face mould, at Fig. 3, draw the major axis ; square up from C to 
 B, equal to C S, Fig. 1. The points for the pins, to describe the centre 
 curve, are found by taking H J, Fig. 1, as radius, from the point B as cen- 
 tre, and describing arcs, cutting the major axis at 2 and 3, the points re- 
 quired. For the direction of the straight wood, and length of curve, make 
 C H equal to C P, Fig. 1. From the points and H, as centres, with 
 B S, Fig, 2, as radius, describe arcs, cutting the curve, at S and J ; 
 draw H J, and H S, indefinitely. Then J S is the length of curve, and H S 
 the direction of the straight wood. For the width of the mould, set 
 oflf each way from B, half the width of the rail. The points for the pins, 
 to describe the outside and inside curves, are at the intersection of the dot- 
 ted lines, with the major axis. The bevel, for the joints, is shown at B.. 
 
 For the face mould, at Fig. 4, draw the major axis ; square up from A to 
 B, equal to C A, Fig. 1. The points for the pins, to describe the centre 
 curve, are found by taking N R, Fig. 2, as radius, from the point B as centre, 
 describe arcs, cutting the major axis at 2 and 3, the points required. To 
 find the point of contact, and length of curve, set up from the major axis, 
 equal to 3 2, Fig. 2 ; from the point, draw a line parallel to the major axis, 
 cutting the curve at H. From the point H, as centre, with S D, Fig. 2, as 
 radius, describe an arc, cutting the curve at J. Then H is the point of con- 
 tact of the straight wood, with the curve, and H J the length of curve 
 required. The direction of the straight wood, is found by drawing J S, 
 equal to S G, Fig. 2, and H S, equal to H G, Fig. 2. For the width of the 
 mould, set off each way from B, half the width of the rail. The points for 
 the pins, to describe the outside and inside curves, are at the intersection 
 of the dotted lines, with the major axis. The joints are cut at right angles 
 to the tangents. The bevel, for the straight wood, is shown at G ; for the 
 centre joint, at S. 
 
Plate 22 
 
 Exhibits the ground plan and elevation, for a semi-circle of winders, at the 
 termination of the staircase ; the wreath in two pieces. 
 
 To find the length of the major axis, of the elliptic curve, required for the 
 centre of the mould : At Fig. 1, draw lines from A and E parallel to L C : 
 set up from A to B, equal to B S, Fig. 2 ; draw D B, and extend to R. 
 Produce L C to H, then H R equals half of the major axis of the ellipical 
 curve, for the centre of the mould. 
 
 To draw the face mould, at Fig. 3, draw the major axis indefinitely. To 
 find the points for the pins, to describe the centre curve, square up from C 
 to D equal to C D, Fig. 1 ; from the point D as centre, with H R, Fig. 1, 
 as radius, describe arcs, cutting the major axis at 2 and 3, the points 
 required. From the point C as centre, with T R, Fig. 2, as radius ; describe 
 arcs, cutting the curve at S and J ; join C S and C J. For the direction of 
 the straight wood, draw S B and J B, parallel to C J and C S. To find 
 the points for the pins, to describe the outside and inside curves, set off' each 
 way from D, half the width of the rail ; from the points, draw the dotted 
 lines parallel to D 2 and D 3, intersecting the major axis at the points 
 required. One mould answers for both wreaths ; by removing the straight 
 wood at J, leaves the mould for the lower wreath ; the same being done 
 at S, leaves the mould for the upper wreath. One bevel answers for all the 
 joints. 
 
Plate 22, 
 
 Scaie i inch-= iihot 
 

Plate 23 
 
 Exhibits the ground plan and elevation of a quarter platform staircase. The 
 platform pilaced one step> below the flooi\ to contintie the same width of passage at 
 the landing ; the wreath in two pieces. 
 
 For the length of the major axis, of the elliptic curve, for the centre of 
 the mould, draw lines from A and J, Fig. 1, parallel to C N ; set up from A 
 to L, equal to P L, Fig. 2 ; draw S L, and extend to H. Produce N C to R, 
 then R H equals half the length of the major axis, and S L determines the 
 length of the curve, required for the face mould, shown at Fig. 3. 
 
 To form the face mould, at Fig. 3, draw the major axis indefinitely ; 
 square up from C to S, equal to C A, Fig 1. The points for the pins, to 
 describe the centre curve, are found by taking R H, Fig. 1, as radius, with 
 the point S as centre, describe arcs, cutting the major axis at 3 and 3, the 
 points required. The point of contact, is found by setting up from the 
 major axis, equal to 2 3, Fig. 2 ; from the point, draw a line parallel to the 
 major axis, cutting the curve at H, the point required. From the point H 
 as centre, with S L, Fig. 1, as radius, describe an arc, cutting the curve at 
 P. For the direction of the straight wood, draw P R equal to L B, Fig. 2, 
 and H R, equal to C B, Fig. 2. For the width of the mould, set off each 
 way from S half the width of the rail. The points for the pins, to describe 
 the outside and inside curves, are shown at the intersection of the dotted 
 lines with the major axis. The bevel shown at C, is^for the straight wood; 
 for the joint P, at B. 
 
 The mould for the wreath that connects with the level rail, is shown at Fig. 
 4 ; draw the major axis, D B, equal to L D, Fig. 2 ; square up from D to C, 
 equal to C A, Fig. 1 ; set off each way from C half the width of the rail ; 
 from the points draw the dotted lines parallel to C B, for the width of the 
 straight wood at B. The points for the pins, to describe the curves, are 
 found by drawing the dotted curves to intersect the major axis. The bevel 
 for the straight wood is shown at D, Fig. 2. 
 
:L_a_ 
 
Plate 24 
 
 Exhibits the ground plan and elevation, for a staircase, with a quarter circle of 
 winders at the landing. 
 
 To find the major axis, of the elliptic curve for the centre of the mould, 
 draw lines from the points, J and L, Fig. 1, parallel to B C, indefinitely ; set 
 up from J to P, equal to R S, Fig. 3; draw A P, and extend to D ; produce 
 B C to H ; then H D equals half the length of the major axis, and A P 
 determines the length of the curves, required for the mould. 
 
 For the mould at Fig. 3, draw the major axis indefinitely. To find the 
 points for the pins, to describe the centre curve, square up from C to S equal 
 to C A, Fig. 1 ; from the point S as centre, with H D, Fig. 1, as radius, 
 describe arcs, cutting the major axis, at 2 and 3, the points required. To 
 find the points to cut the curve, set up from the major axis, equal to 2 3, Fig. 
 2 ; from the point, draw a line parallel to the major axis, cutting the curve 
 at P ; from the point P as centre, with A P, Fig. 1, as radius, describe an 
 arc, cutting the curve at H. For the direction of the straight wood, draw 
 H R, equal to S B, Fig. 2, and P R equal C B, Fig. 2. The points for the 
 pins to describe the outside and inside curves are found, by setting oflF each 
 way from S half the width of the rail ; from the points, draw lines parallel 
 to S 2 and S 3, to intersect the major axis ; the joints are cut at right angles 
 to the tangents. The bevel for the centre joint at H, is shown at B, for the 
 straight wood, at R. 
 
 The mould for the wreath at the landing, is shown at Fig. 4 ; draw the 
 major axis indefinitely, square up from B to H, equal to J, Fig. 1 ; set off from 
 B to S, equal to S T, Fig. 2 ; for the width of the mould at S, set off each way 
 from H half the width of the rail ; from the points draw lines parallel to H S. 
 The points for the pins to describe the curves, are found by describing the 
 dotted curves to intersect the major axis. The bevel required for the 
 straight wood is shown at T. 
 
Plate 25 
 
 Exhibits the plan and elevation of a staircase^ starting with a quarter circle of 
 
 To find the major axis of the elliptic curve for the centre of the mould, 
 draw lines from H and L, Fig. 1, parallel to R C indefinitely. Set up from 
 H to S, equal to P J, Fig, 2 ; draw A S, and extend to D ; produce R C to 
 P ; then P D equals half the length of the major axis, and A S determines 
 the length of the curve required for the mould. 
 
 To draw the face mould at Fig. 3, draw lines at right angles to each other. 
 To find the points for the pins, to describe the centre curve, set up from C, 
 to B, equal to C H, Fig. 1. From the point B as centre, with P D, Fig. 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 To find the point to cut the curve, set up from the major axis, equal to 2 3 
 Fig. 2 ; from the point draw a line parallel to the major axis, cutting the 
 curve at S ; from the point S, as centre, with A S, Fig. 1, as radius, describe 
 an arc, cutting the curve at T, For the direction of the straight wood, draw 
 T L equal to H S, Fig. 2, and S L equal to J S, Fig. 2. To find the points 
 for the pins, to describe the outside and inside curves, set off each way from 
 B half the width of the rail ; from the points, draw lines parallel to B 2 and 
 B 3, to intersect the major axis. The bevel for joint T, is shown at P, for 
 the straight wood at S. 
 
 The mould for the wreath at the starting is shown at Fig. 4 ; draw the 
 major axis indefinitely, square up from C to D, equal to A, Fig. 1 ; set off 
 from C to L, equal to H V, Fig. 2. For the width of the mould set off each 
 way from D, half the width of the rail ; from the points draw lines parallel to 
 D L. The points for the pins, to describe the elliptic curves, are shown 
 at the intersection of the dotted curves, with the major axis. The bevel is 
 shown at H. 
 
Plate '23. 
 
Plate 26 
 
 Exhibits the ground plan for a staircase starting with a scroll. At Fig. 1, draw 
 the eye one inch wider than the rail ; divide the radius of the eye into four equal 
 parts ; set one part off from the centre and form the square; through the 
 centre of square draw a line parallel to 4: S ; set off from Gto D the width of 
 the rail, and draw the curves that form the scroll. 
 
 To find the major axis of the elliptic curve for the centre of the mould ; 
 at Fig. 3, draw lines from H and N, Fig. 1, parallel to J 5, i definitely ; set 
 up from H to E, equal to B C, Fig. 2, draw E E and extend to F ; then J F 
 equals half the length of the major axis, and R E determines the length of 
 curve, required for the mould. 
 
 At Fig. 3, draw the major axis indefinitely. To find the points for the pins 
 to describe the centre curve ; square up from C to S equal to R 5, Fig. 1, from 
 the point S as centre, with J F, Fig. 1, as radius, described arcs, cutting the 
 major axis, at 2 and 3, the points required. To find the point to cut the 
 curve, set up from the major axis equal to 2 3, Fig. 2 ; from the point draw 
 a line parallel to the major axis, cutting the curve at N ; from the point N 
 as centre, with R E, Fig. 1, as radius, describe an arc, cutting the curve at 
 H. For the direction of the straight wood, draw N B equal to L S, Fig 2, 
 and H B equal to C S, Fig. 2. For the width of the mould, and the points 
 for the pins to describe the outside and inside curves, set off each way from 
 S, half the width of the rail, from the points, draw lines parallel to S 2, and 
 S 3, to intersect the major axis. The bevel for the straight wood, is shown 
 on the line 2 S, for the centre joint, on the line S C. 
 
 To draw the mould for the quadrant D R : At fig. 4, draw C B, equal to 4 
 R, Fig. 1, and C D equal to P L, Fig. 2. For the width of the mould, set off 
 each way from B half the width of the rail, from the points, draw lines parallel 
 to B D, to intersect the line C D. The curves are drawn with the com- 
 passes. The bevel is shown at L. 
 
Tig. 3 
 
 Scale inch. - 1 foot. 
 
Plate 27 
 
 Exh'ibits the ground plan for the turnout, at the starting of the staircase. The 
 curve drawn from centres of unequal radie. The wreath in one piece, forming 
 its own easings at the newel. 
 
 At Fig. 1, draw the curves, and the newel cap, also the tangents. Produce 
 the radius B D, indefinitely, draw L S Fig. 2, at right angles to B D ; set up 
 from L to N the height of three raises. Place the pitch board, and draw the 
 common pitch. Set up from S to P the diflference in the heights of the 
 newel and shoit baluster. To find the positions of the steps, set up from L 
 to H, the height of one riser, draw H J parallel to L S, cutting the pitch at 
 the point required for the face of the riser, which determines the position of 
 the steps on the plan. 
 
 For the length of the major axis of the elliptic curve for the centre of the 
 mould, draw D P, Fig. 1, parallel to B C, equal to E N, Fig. 2 ; draw L P 
 and extend to J ; then H J equals half the length of the major axis, and L 
 P determines the length of curve, required for the mould. 
 
 For the mould at Fig. 3, draw the major axis indefinitely. To find the 
 points for the pins to describe the centre curve, square up from C to D 
 equal to B D, Fig. 1. From the point D as centre, with H J, Fig. 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 For the width of the mould and the points for the pins to describe the 
 outside and inside curves, set off each way from D half the width of the 
 rail. From the points, draw lines parallel to D 2 and D 3, to intersect the 
 major axis. For the length of curve, and direction of the straight wood 
 set up from C to L equal to B C, Fig 1 ; from the point L as centre, with R 
 N, Fig 3, as radius, describe arcs, cutting the curve at S and P, draw L S 
 and L P indefinitely ; set off from L to R equal to R P, Fig. 2, draw R H at 
 right angles to L R equal to R S, Fig. 1 ; extend the tangent S L to T equal 
 to L P, join T H, set off from S to A, equal to D G, Fig. 1, draw A H, indefi- 
 nitely. From the point N as centre, describe the curve from H, tangent to 
 the curve S D ; through the point N, draw the dotted line at right angles 
 to the tangent L R, on which find the centres to describe the outside and 
 inside curves. The width of the mould is shown at Fig. 2 ; by setting off 
 from 2 to 3, equal to the width of the rail, then the bevel determines the 
 width of the mould at H. The bevel for the straight wood is shown at E, 
 Fig. 2, for the joint at R, 
 
 At Fig. 4 is shown a practical method of finding the spring bevels for the 
 joints; form a piece to fit the angle D N R, Fig. 1, draw B A at right 
 angles to N B, and B C the pitch of the rail. Work to the lines and apply 
 the bevels as shown, the bevel applied to the line B C is for the straight 
 wood. The one shown as S is for the joint at the newel. 
 
Plate 28 
 
 Exhibits the ground plan and elevation for a platform staircase, the risers 
 beyond the cylinder. 
 
 To find the length of the major axis of the elliptic curve for the centre 
 of the mould, draw lines from D and H, Fig. 1, parallel to C J indefinitely. 
 Set up from D to. S, equal to B S, Fig. 2, draw P S, and extend to R ; then 
 J R equals half of the length of the major axis, and P S determines the 
 length of the curve required for the mould. 
 
 To draw the mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins, to describe the centrecurve, square up from C to B, 
 equal to C P, Fig. 1. From the point B as centre, with J R, Fig 1, as 
 radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
 To find the points, to cut the curve, set up from the major axis, equal to L 
 J, Fig. 2 ; from the point, draw a line parallel to the major axis, cutting the 
 curve at J. From the point J as centre, with P S Fig. 1, as radius, describe 
 an arc, cutting the curve at P. For the direction of the straight wood, 
 draw J H, equal to S L, Fig. 2, and P H equal to N L, Fig. 2. For the 
 width of the mould, and the points for the pins, to describe the outside and 
 inside curves, set off each way from B, half the width of the rail ; from the 
 points draw lines parallel to B 2 and B 3, to intersect the major axis. The 
 bevel for the centre joint is shown at A, for the straight wood at L. 
 
Plate 29 
 
 Exhibits the ground plan and elevation, for a staircase with a semi-circle of 
 winders ; the wreath formed in three pieces. 
 
 To find the length of the major axis of the elliptic curve, for the centre of 
 the mould, draw D S, Fig. 1, equal to L E, Fig. 3; join J S and extend to 
 R; then P R equals half the length of the major axis required. 
 
 To draw the mould at Fig. 3, draw the major axis indefinitely. To find 
 the points for the pins, to describe the centre curve, square up from C to D, 
 equal to C D, Fig. 1 ; from the point D as centre, with P R, Fig. 1, as radius, 
 describe arcs, cutting the major axis at 2 and 3, the points required. For 
 the direction of the tangents, and length of curve, make C B equal to C 
 N, Fig. 1 ; from the point B as centre, with E G, Fig. 2, as radius, describe 
 arcs, cutting the curve, at S and R; join B S and B R, the direction and 
 length required. For the width of the mould, and the points for the pins, 
 to describe the outside and inside curves, set off each way from D half the 
 width of the rail ; from the points draw lines parallel to D 3 and D 3, to 
 intersect the major axis. The joints are cut at right angles to the tangents. 
 One bevel answers for all the joints. 
 
6S avBta: 
 
Plate 30 
 
 ExTiihits the ground flan and elevations, for two staircases starting with winders ; 
 the wreath in one piece. 
 
 At Fig. 2, we have placed the centre of rail, at the newel, the height of 
 one riser above the step, to increase the length of the easing, which added 
 to the length of short baluster, gives the length of the newel, from the step 
 to the cap. The pitches over the winders, are drawn, to give an easy and 
 graceful curve to the rail when finished. 
 
 To find the major axis of the elliptic curve for the centre of the mould, 
 draw N P and D S, Fig. 1, parallel to C R, indefinitely ; set up from D to S» 
 equal G J, Fig. 2, join H S and extend to P ; then R P, equals half the 
 length of the major axis, and H S, determines the length of the curve 
 required for the mould. 
 
 At Fig. 3, draw the major axis indefinitely. To find the points for the pins, 
 to describe the centre curve, square up from C to D, equal to H, Fig. 1. 
 From the point D as centre, with R P, Fig. 1, as radius, describe arcs, 
 cutting the major axis at 3 and 4, the points required. For the point to cut 
 the curve, set up from the major axis, equal to N 4, Fig. 2, from the point, 
 draw a line parallel to the major axis, cutting the curve at S ; from the point 
 S, as centre, with H S, Fig. 1, as radius, describe an arc, cutting the curve 
 at B. For the direction of the straight wood, draw B H, equal to S 4, Fig. 
 2, and S H, equal to J 4, Fig. 2. For the width ot'the mould, and the points 
 for the pins to describe the outside and inside curves, set off each way from 
 D half the width of the rail ; from the points, draw lines parallel to D 3 and 
 D 4, to intersect the major axis. The bevel for the joint at S, is shown at B, 
 for the joint L, is shown at T, Fig. 2. 
 
 Fig. 4 is the same as Fig. 1, with two additional steps at the starting. 
 Set up from the first step to the centre of rail, the difference in the heights 
 of the newel and short baluster. Make B A, equal to A B, Fig. 4, describe 
 the curve for the easing ; from the point H, draw the pitch line tangent to 
 the curve. The mould at Fig. 6, is drawn in the same manner as that shown 
 at Fig. 3. 
 
Plate 31 
 
 ExMhits the ground planfoi' a circular staircase ; the wreath in four pieces. 
 
 To find the common pitch, at Fig. 2, extend the tangent C D to A ; at right 
 angles to A C, draw A J, equal to five risers, join C J ; then C J is the pitch 
 of the tangents, that meet at the joints F C and N. 
 
 At Fig. 1, extend the tangent, S B, to V, equal to B F ; from the points V 
 B S, and A, draw lines parallel to O S, and at right angles V A, indefinitely. 
 At any point H, Fig. 3, square over for the first step ; set up from E to C 
 the height of two risers, from H to R the height of five risers, and from E to F, 
 the difference in the height of the newel and short baluster ; join R and 
 extend to S, then R and S are the points from which the pitches are drawn. 
 Draw R P the common pitch, or the same inclination as J C Fig. 2 ; 
 join P S and extend to J; then R P, P L and L J are the tangents required 
 for the mould. 
 
 To find the length of the major axis of the elliptic curve required for the 
 of the mould : At Fig. 1, draw lines from F and N, parallel to O B, indefi- 
 nitely; set up from F to K, equal to N R, Fig. 3; join S K, and extend to 
 L ; then W L equals half the length of the major axis required. 
 
 The mould for the wreath, at the starting, is shown at Fig. 5. Draw the 
 major axis indefinitely. To find the points for the pins, to describe the 
 centre curve, square up from C to D, equal to O S, Fig. I, from the point D 
 as centre, with W L, Fig. 1, as radius, describe arcs, cutting the major axis, 
 at 2 and 3, the points required ; set up from C to S, equal to O B, Fig. 1. 
 From the point S as centre, with P R, Fig. 8, as radius, describe arcs, cutting 
 the curve at R and L ; draw S R, and S L indefinitely. For the width of 
 the mould, and the points for the pins, to describe the outside and inside 
 curves, set off each way from D half the width of the rail; from the 
 points, draw lines parallel to D 2 and D 3, to intersect the major axis. To 
 draw the extension of the mould, standing over the curve S 2, on the plan, 
 set off from S to T, equal to P L, Fig. 3, and from T to H, equal to L J Fig. 
 3 ; draw T P and H J at right angles S H, make T P, equal to R S, and H 
 J equal to 2 3, Fig. 1. At Fig. 3, 4 5 equals the width of the rail, then L 5 
 is the width of the mould at J ; find the centres on the line, T P as shown by 
 the dotted lines, and with the compasses, describe the curves, tangental to 
 the elliptical curves, all ready drawn. The bevels for the joints are shown 
 at Fig. 3. 
 
 To find the length of curve on the plan, for the wreath at the landing : At 
 Fig. 4, from the point N, draw the common pitch indefinitely ; set up from 
 the line N B, to the fioor, the height of two risers, and from the floor to the 
 centre of the level rail, half the height of one riser from the point to bore 
 for the first baluster on the floor ; from the point, draw a line parallel to N 
 
B, cutting the pitch at D ; from the point D, draw D B at right angles to N 
 B ; from the point B as centre, with B N as radius, describe an arc, cutting the 
 curve at R ; join B R, then N R is the length of curve required. 
 
 To find the length of the major axis of the elliptical curve, required for 
 the centre of the mould, shown at Fig. 6 : Draw lines fromN and G, Fig. 1, 
 parallel to O D indefinitely. Set up from N to L, equal to A J, Fig. 2, draw 
 C L and extend to X ; then H X equals half the length of the major axis. 
 
 At Fig. 6, draw the major axis indefinitely. To find the points for the 
 pins, to describe the centre curve, from the point B as centre, with H X, Fig. 1, 
 as radius, dfescribe arcs, cutting the major axis at 3 and 3, the points required. 
 For the width of the mould, and the points for the pins, to describe the outside 
 and inside curves, set off each way from B half the width of the rail ; from the 
 points draw lines parallel to B 2 and B 3, to intersect the major axis. For the 
 length of curve required for the wreath, standing over C N on the plan, set 
 up from C to T, equal to O D, Fig. 1. From the point T, as centre, with C 
 V, Fig. 2, as radius, describe arcs, cutting the curve at H and J ; join T H 
 and T J, the lines from which to square the joints. The bevel is shown at 
 Fig. 2. 
 
 For the length of the mould at the landing, square up from N to S, equal 
 to B R, Fig. 4. From the point S, as centre, with N D, Fig. 4, as radius, 
 describe an arc, cutting the curve at R. For the direction of the tangent, 
 set up from N to P, equal to S R, Fig. 4, draw P R, the direction required. 
 The bevels for the joints are shown at Fig. 4. 
 
Plate 32 
 
 Exhibits the ground plan of an elliiMcal staircase^ the planTc for the wreaths 
 sawed square to a parallel width, the joints cut at right angles to the face of 
 the plank. 
 
 To find the common pitch, at Fig. 1, extend the tangent A B to C, draw 
 A D at right angles to A C, equal to seven risers ; join C D, then C D is the 
 pitch of the tangents that meet at the joints L and A. 
 
 The mould for the centre wreath is shown at Fig. 3. Draw the dotted 
 chord A L, square up from A and L indefinitely. Through the point B, 
 draw E F, parallel to the dotted chord ; make E H equal to A D, Fig. 2 ; 
 join F H, produce OB to N ; draw F R and H J at right angles to F H, 
 equal to E A and F L ; join N R and N J, which should equal P C and P 
 D, Fig. 3 ; draw any number of ordinates and transfer the distances, through 
 the points trace the mould. The bevel for the joint is shown at Fig. 2. 
 
 At Fig. 4, is shown the development of the tangents, at the starting. 
 From the point A, draw the first step ; set up to H the centre of rail four 
 inches, which, added to the short baluster, gives the height of the newel ; 
 set up from A to B five risers, draw B C the common pitch, join C H. At 
 Fig. 1, extend the tangent L D to H, then L H equals S D, Fig. 4 ; from the 
 point J, draw J H, the directing ordinate, indefinitely ; from the points L 
 and D, draw lines parallel to J H ; through the point D, draw the seat at 
 right angles to J H ; set up from R to G, equal to S B, Fig. 4 ; square up 
 from K to F, equal to J 3, Fig. 1, and from G to P, equal to L 2, Fig. 1 ; 
 join S F and S P, then S P will equal C B, and S F will equal C L, Fig. 4 ; 
 draw any number of ordinates from the plan, transfer the distances, and 
 through the points trace the mould. The bevel for the joint F, is shown at 
 C ; for the joint P, at S, Fig. 4. 
 
 The mould for the quadrant at the scroll, is found by drawing 5 7, equal 
 to H L, Fig. 4, and 7 8 equal to 5 J. To find the points for the pins, to 
 describe the centre curve, from the point 8 as centre, with 8 9 as radius, 
 describe arcs, cutting the line 5 7, the points required. For the width of 
 the mould and the points for the pins, to describe the outside and inside 
 curves, set off each way from 8 half the width of the rail ; from the points 
 draw lines parallel to 8 4 to intersect the line 5 7. The bevel fer the joint 
 at 5 is shown at L, Fig. 4. 
 
 The length of curve on the plan, required for the mould, at the landing, 
 is found at Fig. 6. From the point A, draw the pitch line parallel to C D, 
 Fig. 2, indefinitely ; set up from the line A L, the height of four risers, to the 
 floor ; set up from the floor to centre of level rail, half a rise from the point 
 to bore for the flrst baluster ; from the point, draw a line to intersect the 
 pitch line at C ; from the point C, drop a line at right angles to A L, 
 
Plate 32. 
 
Sialf. inch. - /foot 
 
cutting the line from A at L ; draw L P tangent to tlie curve on the plan, then 
 A P is the length of curve required, and P L is the directing ordinate for 
 the mould. 
 
 To draw the mould at Fig, 7 : From the point L, draw the seat at right 
 angles to L P ; set up from S to R, equal to L C, Fig. 6 ; join L R ; square 
 up from L to H, equal to L P ; from R to B, equal to S A ; join L B, 
 which should equal A C, Fig. 6. Draw the ®rdinates, transfer the distances, 
 and through the points trace the mould. The bevel for the joint H, is 
 shown at R ; for the joint B, at Fig. 6. 
 
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