THE ART AND SCIENCE 
 
 LIBRARY OF CONGRESS 
 
 DDOmaOHBDH 
 
LIBRARY OF CONGRESS. 
 
 • \ H i fci 
 
 Shelf... 
 
 UNITED STATES OF AMERICA. 
 
I 
 
 i 
 
w 
 
1 
 
THE 
 
 ART AND SCIENCE 
 
 OF 
 
 STAIR BUILDING 
 
 BY THE AUTHOR OF 
 
 *^ Carpenters' and Builders' Assistant," "American 
 
 Stair Builders' Guide." and "Steel 
 
 Square Problems." 
 
 \- ^ 
 
 Ilhistrated by Thirty -six Engraved PlaJe^TT^^ 
 
 ^ ..,i[- i t 
 
 V '^'^ 
 
 JAN 26 1005- 
 
 NEW YORK: S^^f WlkSHV^^ 
 
 WILLIAM T . C O M S T O C K , 
 6 Astor Place. 
 
 1885. 
 
^//^SZy6 
 
 .Q 
 
 7 
 
 Copyright, 1884, by L. D. Gould. 
 
 .\\ 
 
 L. J. HAROHAM, PRINTER. NEWARK. 
 
PREFACE. 
 
 It has been the object of the author of this work, which 
 he now presents to the public for their inspection, to reduce 
 the art and science of Stair Building to the shortest and 
 most simple system of lines which will reach the end 
 desired. He has confidence in believing that it will be 
 favorably received, and that the contents are the most valu- 
 able and the price the lowest of any work which has been 
 published. 
 
IPlate 1 
 
 O D O O O 
 
 SCALE 1 IN. — 1 FPOT 
 
STAIR BUILDING. 
 
 PLATE L 
 
 Fig. I . To describe a7i elliptical cu7've with a thread or cord 
 and pencil. 
 
 Draw the major and minor axis A B and C D, Fig. i. To 
 find the points to place pins : From the point D as a centre, 
 with S B or S A as a radius, describe arcs, cutting the major 
 axis in the points 2 and 3 ; place pins in the points, and, by 
 the use of thread or cord and pencil, describe the elipse 
 required. Care should be taken to keep the thread or cord 
 to an even tension. Suppose the curve to be the centre of a 
 mould required for a hand-rail : Set off each way from the 
 point D equal half the width of rail ; from the points draw 
 parallel to D 2 and D 3, cutting the major axis in the points 
 for pins to describe the outside and inside curves. 
 
 To find the points for pins to describe a curve parallel to 
 A C B : Set off from C to P equal B N ; from the point P 
 as a centre, with S N as a radius, describe arcs cutting the 
 major axis in the points 4 and 5 ; place pins and describe 
 the curve required. 
 
 Fig. 2 exhibits a plan and elevation of handrail at the 
 starting. To find the easing and points to bore for balus- 
 ters : Set up from 2 to 3 on the pitch-board, equal the differ- 
 ence in the heights of newel post and short baluster ; square 
 over for the newel cap ; mark from the pitch-board for the 
 point to bore for baluster. 
 
 To continue the height of rail at the starting to its termin- 
 ation, care should be taken to measure the rise from the 
 points to bore for balusters, as shown by the dotted lines, 
 Fig. 3- 
 
3?late 2 
 
 SCALE 1j IN. = 1 FOOT 
 
 I 
 
STAIR BUILDING. 
 
 PLATE II 
 
 Exhibits rules for findijig the major axis of the elliptical 
 curves^ the point of contact, and the length of curve required 
 for the mould. Also, a practical rule for finding the vertical 
 and horizontal lines to bevel the plank to form the wreath. 
 
 To find the major axis of the elliptic curve for centre of 
 mould : Set up from A to B equal the rise of rail from D to 
 A ; from the point B draw the common pitch B C ; join B 
 N and C S ; square up from L to P, equal A R. Then L B 
 equals half the major, and L P equals half the minor axis of 
 the elliptic curve required. 
 
 To find the points for pins : From the point P as a centre, 
 with L B as a radius, describe arcs cutting the major axis ifi 
 2 and 3. By the use of thread or cord and pencil, describe 
 the curve for centre of mould. 
 
 To find the length of curve and point of contact : From 
 the point L as a centre, with C B as a radius, describe an arc 
 cutting the curve in H ; from the point H as a centre, with 
 N B as a radius, describe an arc cutting the curve in J ; 
 then J is the point of contact, and H J equals the length 
 required. 
 
 To find the direction of the straight rail : From the points 
 H and J as centres, with S C and B C as radius, describe 
 arcs cutting each other in F ; join H F and F J extended 
 for the direction required. 
 
 To find the vertical angles to bevel the plank : Fit a piece 
 to the tangents R A and R D ; draw the pitch C B on the 
 side R A, and the pitch C S on the side R D. Cut to the 
 marks and apply the bevel as shown for the angles required. 
 
 The above rules contain all the science required to con- 
 struct handrails for any staircase that may be designed, by 
 anyone that has acquired the use of tools. 
 
riate 3 
 
STAIR BUILDING. 
 
 PLATE III 
 
 Exhibits the plan for a platform stairs, where the radius of 
 circle for the centre of rail equals half the width of step. 
 
 To draw the elevation of the handrail, Fig. 2 : Square up 
 from D to A and B equal two (2) risers ; place the pitch- 
 board at A and B ; draw the common pitch A C and B C j 
 drop a line from C parallel to B D ; then S L, Fig. i, equals- 
 the radius of semicircle for the centre of rail on the plan. 
 
 To draw the mould, Fig. 3 : Square up from A to D equal 
 S L, Fig. I ; set off from A to B equal A C, Fig. 2 ; from 
 the point D as a centre, with A B as a radius, describe an 
 arc cutting the major axis in the points 2 and 3 ; place pins- 
 in the points ; by the use of thread or cord and pencil, 
 describe the centre curve ; set off each way from D equal 
 half the width of rail ; from the points describe the outside 
 and inside curves. The pitch-board equals the angle for the 
 vertical cuts at the joint B. 
 
 The rule applies to larger circles, by placing the risers half 
 the width of step from the centre of rail. 
 
JPlate -4. 
 
 SCALE 3 IN. = 1 FOOT 
 
STAIR BUILDING. II 
 
 PLATE IV 
 
 Exhibits the plan of a round rail^ on a four-inch cylinder at 
 the landing. 
 
 To find the length of curve required for the easing or 
 wreath : Square up from A to B equal the riser ; from the 
 centre of baluster, draw D E equal half the riser ; draw E C 
 at right angles to E D ; join C S parallel to B A ; join S R, 
 Fig. I, equal S A. Then A R equals the length of curve 
 required. 
 
 To find the vertical and horizontal sides of the wreath : 
 Fit a piece to the tangents S A and S R, Fig. i ; draw the 
 pitch B C, Fig. 2, on the side S A ; square over on the side 
 S R ; cut to the marks ; apply the bevel to the sides for the 
 angles required. 
 
 To draw the mould, Fig. 3 : Square up from A to B, equal 
 C A, Fig. I ; Set off from A to C and from B to 2 and 3, 
 equal B S, Fig. 2 ; place pins in the points 2 and 3 ; by the 
 use of thread or cord and pencil, describe the centre curve. 
 
 To find the length of curve and the direction of straight 
 rail : From the point C as a centre, with B P, Fig. 2, as a 
 radius, describe an arc cutting the curve in D, the point 
 required ; from the points D and C as centres, with S R, 
 Fig. I, and B C, Fig. 2, as radii, describe arcs cutting 
 each other in J ; draw C J and J D the direction required ; 
 set off each way from C and D equal half the width of rail ; 
 from the points, describe the outside and inside curves ; cut 
 the joints at right angles to the tangents and face of plank. 
 
IPlate o 
 
STAIR BUILDING. I3 
 
 PLATE V 
 
 Exhibits the plan of a round rail Ofi a four-inch cylinder^ at 
 the starting of the second flight. 
 
 To find the length of curve required for the easing or 
 wreath : Square up from A to B equal one riser ; from the 
 point B, draw the common pitch ; set up from A to C equal 
 half the riser, and the rise of the rail from the riser to the 
 point to bore for the baluster for the centre of level rail ; 
 draw D R parallel to B A, and R P equal R A. Then A P 
 equals the length of curve required. 
 
 To find the vertical and horizontal sides of the wreath : 
 Fit a piece to the angle of the tangents R A and R P, Fig. i ; 
 square over on the side R P ; draw the pitch D B on the 
 side R A ; cut to the marks ; apply the bevel to" the sides 
 for the angles required. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 A D, Fig. I ; from the point B as a centre, with B J, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 place pins in the points ; by the use of thread or cord and 
 pencil, describe the centre curve. 
 
 To find the length of curve and point of contact : From 
 the point C as a centre, with B S, Fig. 2, as a radius, describe 
 an arc cutting the curve in. the point D. 
 
 To find the direction of the straight rail : From the points 
 C and D as centres, with A R, Fig. i, and D B, Fig. 2, as 
 radii, describe arcs cutting each other in N ; join C N 
 and N D the direction required ; set off each way from C 
 and B equal half the width of rail ; from the points, describe 
 the outside and inside curves. 
 
I'late G 
 
SRAIR BUILDING. 15 
 
 PLATE VI 
 
 Exhibits the plan of a round rail for a platfor7n stairs^ on a 
 four-inch cylinder. 
 
 To draw the elevation of the tangents : Square up from 
 A to C equal the riser ; from the points B and C draw the 
 common pitch to S and R. 
 
 To find the vertical and horizontal sides of the wreath : 
 Fit a piece to the angle of the tangents F H D, Fig. i ; draw 
 the pitch B S on the side D H, and the pitch S P on the side 
 H F ; cut to the marks ; apply the bevel to the sides for the 
 angles required. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 C D, Fig. I ; set off from A to L, and from B to 2 and 3 
 equal P J, Fig. 2 ; place pins in the points 2 and 3 ; by the 
 use of thread or cord and pencil, describe the centre curve. 
 
 To find the point of contact and the length of curve : 
 From the point A as a centre, with S P as a radius, describe 
 an arc cutting the curve in D ; from the point D as a centre, 
 with N P as a radius, describe an arc cutting the curve in C. 
 Then D is the point of contact, and D C the length required. 
 
 To find the direction of the straight rail : From the points 
 D and C as centres, with B S and P S, Fig. 2, as radii, 
 describe arcs cutting each other in H ; join C H and H D 
 for the direction required ; set off each w^ay from B and L 
 equal half the width of rail ; from the points, describe the 
 outside and inside curves. 
 
I>late •? 
 
STAIR BUILDING. I7 
 
 PLATE VII 
 
 Exhibits a plan for turnout at the starting of a staircase. 
 
 To draw the elevation of the tangents P J L, Fig. i : 
 Square up from the riser and intersection of the tangents L 
 and J indefinitely ; from the point D, draw the common 
 pitch D C ; Set up from A to B equal the difference in the 
 heights of the newel-post and the short baluster, less or 
 minus the rise of the common pitch from the riser to the 
 point to bore for the baluster ; join B C. Then BCD 
 equals the elevation required. 
 
 To draw the mould, Fig. 3 : Square up from C to D equal 
 H P, Fig. I ; from the point D as a centre, with D N, Fig. i, 
 as a radius, describe arcs cutting the major axis in the points 
 2 and 3 ; place pins in the points ; by the use of thread or 
 cord and pencil, describe the centre curve. 
 
 To find the point of contact : From the point D as a cen- 
 tre, with Y S, Fig. I, as a radius, describe an arc ; from the 
 point C tangent, to the arc, draw C S, cutting the curve in 
 S, the point required. 
 
 To find the length of curve : From the point S as a cen- 
 tre, with D R, Fig. i, as a radius, describe an arc cutting the 
 curve in B, the length required. 
 
 To find the direction of the straight rail : From the points 
 S and B as centres, with B C and D C, Fig. i, as radii, 
 describe arcs cutting each other in L ; draw B L, and L S 
 the direction required ; set off each way from D equal half 
 the width of rail ; also from the points 2 and 3 for pins to 
 describe the outside and inside curves. 
 
 To find the vertical sides of the wreath : Fit a piece to the 
 angle of the tangents J P and J L, Fig. i ; draw the pitch 
 B C on the side P J, and the pitch C D on the side J L ; cut 
 to the marks ; apply the bevel as shown in Fig. 2. 
 3 
 
IPlate 8 
 
STAIR BUILDING. I9 
 
 PLATE VIII 
 
 Exhibits the pla?i of a quarter cylinder at the landing. 
 
 To find the length of curve required for the easing : Draw 
 the common pitch from the point B indefinitely ; set up from 
 L to S equal half the riser ; from the point S, draw the cen- 
 tre of level rail, cutting the pitch in R ; draw R P parallel 
 to B D, and P J equal P D. Then D J equals the length of 
 curve required. ' • 
 
 To find the vertical and horizontal sides of the easing : 
 Fit a piece to the angle of the tangents D P J ; square over 
 on the side P J ; draw the pitch R B on the side P D ; cut 
 to the marks ; apply the bevel as shown in Fig. 2. 
 
 To draw the mould for the easing, Fig. 3 : Square up from 
 C to P equal C D, Fig. i ; set off from C to R, and from P 
 to 2 and 3 equal B N, Fig. i ; with pins in the points 2 and 
 3, by the use of thread or cord and pencil, describe the cen- 
 tre curve. From the point R as a centre, with B F, Fig. i, 
 as a radius, describe an arc cutting the curve in L, the point 
 of contact. From the points R and L as centres, with J P 
 and B R, Fig. i, as radii, describe arcs cutting each other 
 in S ; join R S and S L ; set off each way from P equal half 
 the width of rail. The bevel applied to the width of rail 
 determines the width of mould at R. 
 
Plate 9 
 
 SCALE 1J IN. =1 FT 
 
STAIR BUILDING. 21 
 
 PLATE IX 
 
 Exhibits a plaii of handi'ail for platform stairs ; the steps 
 placed in the cyHnder. 
 
 To draw the elevation of the tangents : Square up from 
 C and B indefinitely ; from the point D draw the common 
 pitch cutting the line from C in P ; set up from P to L equal 
 the riser ; join P L. 
 
 To draw the elliptic curve for the centre of the mould, 
 Fig. 3 : Square up from A to B equal N J, Fig. i ; from the 
 point B as a centre, with S R, Fig. 2, as a radius, describe 
 arcs cutting the major axis in 2 and 3 ; with pins in the 
 points, by the use of thread or cord and pencil, describe the 
 centre curve ; from the point A as a centre, with P S, Fig. 2, 
 as a radius, describe an arc cutting the curve in D ; from 
 the point D as a centre, with S T, Fig. 2, as a radius, 
 describe an arc cutting the curve in C ; from the points C 
 and D as centres, with D P and S P, Fig. 2, as radii, 
 describe arcs cutting each other in H ; join C H and D H ; 
 set off each way from B equal half the width of rail ; from 
 the points describe the outside and inside curves. 
 
 To find the vertical and horizontal sides of the wreath : 
 Fit a piece to the angle of the tangents F C J, Fig. i ; draw 
 the pitch D P on the side F C, the pitch P S on the side C 
 J ; cut to the marks ; apply the bevel as shown in Fig. 4. 
 
IPlate lO 
 
 SCALE 1 IN. = 1 FOOT 
 
STAIR BUILDING. 23 
 
 PLATE X 
 
 Exhibits a plan for turnouts^ at the starting of stairs and 
 stoops. 
 
 To draw the elevation of the rail : Square up from A C 
 and D, Fig. i, indefinitely ; draw R L the common pitch, 
 and R S at right angles to R D. 
 
 To find the elliptic curve for the centre of the mould, Fig. 
 3 : Set up from A to B equal A N, Fig. i ; from the point 
 B as a centre, with L T, Fig. 2, as a radius, describe arcs 
 cutting the major axis in the points 2 and 3 ; with pins in 
 the points, and by the use of thread or cord and pencil, 
 describe the centre curve ; set up from A to C equal N C, 
 Fig. I. From the point as a centre, with L R bisected as 
 a radius, describe arcs cutting the curve in D and Y ; join 
 C Y and C D the direction of straight rail ; D Y should 
 equal L P, Fig. 2 ; set off each way from B equal half the 
 width of rail ; from the points describe the outside and 
 inside curves. 
 
 To find the angle to bevel the plank for the vertical sides 
 of the wreath : Fit a piece to the angle of the tangents A 
 C J, Fig. I ; draw the pitch R L, Fig. 2, on the sides ; cut 
 to the marks ; apply the bevel to the sides for the angle 
 required. 
 
I^late 11 
 
 SCALE 1 IN. = 1 FOOT 
 
STAIR BUILDING. 2$ 
 
 PLATE XI. 
 
 Fig. I exhibits a plan of winders, at the starting of the 
 stairs, the wreath in one piece forming its own easing at the 
 newel post. 
 
 To draw the elevation of handrail : Set up from A to 5 
 equal five risers ; place the pitch-board ; draw the common 
 pitch and the easing to the point B ; set up from the step to 
 centre of rail at the newel post, equal the difference in 
 height of post and short baluster, minus the rise of the com- 
 mon pitch from the riser to the point to bore for the balus- 
 ter ; join B C, the pitch and length of tangents required for 
 the mould. 
 
 To find the angles to form the wreath : Fit a piece to the 
 tangents S N, S A and A D, Fig. i ; draw the pitch C B on 
 the sides S N and S A ; cut to the marks ; apply the bevel 
 to the sides A D and S N for the angles required. 
 
 To draw the mould, Fig. 3 : Square up from C to D and 
 S, equal P S and P N, Fig i ; from the point D as a centre, 
 with B J as a radius, describe arcs cutting the major axis in 
 the points 2 and 3 ; place pins in the points, and by the use 
 of thread or cord and pencil, describe the centre curve. 
 From the points C and S as centres, with B R as radius, 
 describe arcs cutting each other in H ; join S H, the tan- 
 gent ; set off each way from D equal half the width of rail ;: 
 from the points describe the outside and inside curves. Cut 
 the plank parallel to the centre curve 3-16 inch wider than 
 the rail ; the joints at right angles to the tangent and face of 
 plank. 
 
Flate IS 
 
STAIR BUILDING. 27 
 
 PLATE XII 
 JExhibits a plan of stairs zvith winders at the starting ; the 
 curve described from centres of unequal radii ; the wreath 
 . in one piece. 
 
 To draw the elevation of the tangents A B, B C and C D, 
 Fig. I : Set up from step to pitch board equal four risers ; from 
 the point draw the common pitch 4 S ; set up from E to F equal 
 the difference in the heights of the newel and the short 
 baluster, minus the rise of the common pitch from the riser to 
 the point to bore for the baluster ; join S F ; parallel to S F 
 •draw 4 L ; square over from* L to H ; join S H and H P. 
 Then P H equals the elevation of A B, H S equals the 
 ■elevation of B C, and S 4 equals the elevation of C D, Fig. i. 
 
 To draw the mould, Fig. 3 : Square up from C to D and 
 J equal P N R, Fig. i ; from the point J as a centre, with S 
 H, Fig. 2, as a radius, describe arcs cutting the major axis 
 in 2 and 3, the points for pins ; and by the use of thread or 
 •cord and pencil, describe the curve from the point J ; set off 
 from J to N equal R S, Fig. 2 ; from the point N as a cen- 
 tre, with S 4 as a radius, describe an arc cutting the curve in 
 •S ; join N S ; from the point S as a centre, with L 4, Fig. 2, 
 as a radius, describe an arc cutting the major axis in L ; 
 from the point J as a centre, with D L as a radius, describe 
 arcs cutting the major axis in the points 4 and 5 for pins to 
 ■describe the curve J L ; set off each way from J equal half 
 the width of rail ; from the points describe the outside and 
 inside curves. 
 
 To find the angles to bevel the plank for the vertical sides 
 of the wreath : Fit a piece to the angles of the tangents. 
 Fig. I ; draw the pitch 4 S on the side D C, and the pitch S 
 H on the side C B ; cut to the marks ; apply the bevel to 
 the sides A B and D C for the angles required. 
 
I»late 13 
 
STAIR BUILDING. 29 
 
 PLATE XIII. 
 
 Fig. I exhibits the pla7i and elevation of handrail for a 
 quarter platform stairs. 
 
 To draw the elevation : Square up from A B and L indefi- 
 nitely ; set up from S to D equal the height of riser, and 
 from E to F equal half the height of riser ; extend the pitch 
 from D to H ; join H F. 
 
 To find the angles to form the wreath : Fit a piece to the 
 tangents ABC, Fig. i ; draw the pitch D H on the side 
 A B, and the pitch H F on the side B C ; cut to the marks, 
 and apply the bevels as shown at Fig. 2. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 S A, Fig. I ; set off from A to L, and from B to 2 and 3 
 equal D J, Fig. i ; place pins in the points 2 and 3 ; by the 
 use of a thread or cord and pencil, describe the elliptical 
 curve B L for the centre of the mould ; square over from 
 A B to C equal D H ; draw the tangent C D equal H F, 
 Fig. I. 
 
 To find the width of the mould at B : Apply the bevel to 
 the width of the rail ; place pins and draw the outside and 
 inside curves. Cut the plank to a parallel width, three- 
 sixteenths wider than the rail ; the joints at right angles to 
 the tangents and face of plank. 
 
Flate 14 
 
STAIR BUILDING. 3I 
 
 PLATE XIV 
 
 Exhibits the plaii for a quarter platform stairs. 
 
 To continue the common pitch in the wreath : Set off 
 from the centre of rail A, to B and C equal half the width 
 of step to face of risers. 
 
 To draw the mould, Fig. 3 : Square up from A to J equal 
 E D, Fig. I ; from the points A and J as centres, with L P, 
 Fig. 2, as a radius, describe arcs cutting each other in C and 
 D*; then C D should equal L I, Fig. 2. Set up from A to 
 B equal E S, Fig. i ; from the point B as a centre, with L R, 
 Fig. 2, as a radius, describe arcs cutting the major axis in 
 the points 2 and 3 ; place pins, and by the use of thread or 
 cord and pencil, describe the centre curve. Set off each 
 way from B equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To find the vertical angle to bevel the plank for the 
 wreath : Fit a piece to the angle of the tangents A D and 
 A E, Fig. I ; draw the pitch L P on the sides ; cut to the 
 marks ; apply the bevel for the angle required. 
 
I>late 15 
 
STAIR BUILDING. 35 
 
 PLATE XV. 
 
 Fig. I exhibits the plaji for a?i obtuse-angled staircase, at 
 the landing. 
 
 To find the length of curve required for the easing : Draw 
 the common pitch A B ; set up from C to D equal half the 
 riser ; from the point D, draw the centre of level rail ; draw 
 B F parallel to A E, and F H equal F E, the angle required; 
 join H A equal the radius, and H E equal the length of 
 curve. 
 
 To find the vertical angles to form the wreath : Fit a 
 piece to the tangents E F H ; draw the pitch B C on the 
 side F E ; square over on the side F H ; cut to the marks ; 
 apply the bevel as shown at Fig. 2. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 A H, Fig. I ; set off from A to C, and from B to 2 and 3 
 equal A J, Fig. i ; place pins in the points 2 and 3 ; by the 
 use of thread or cord and pencil, describe the centre curve. 
 
 To find the length of curve : From the point C as 
 a centre, with A L, Fig, i, as a radius, describe an arc 
 cutting the curve in S. 
 
 To find the direction of straight rail : From the points C 
 and S as centres, with H F and A B, Fig. i, as radii, 
 describe arcs cutting each other in the point R ; join C R 
 and R S, the direction required ; set off each way from B 
 half the width of rail. The bevel applied to the width of 
 rail equals the width of mould at the joint C. 
 
Plate 16 
 
 SCALE 1 IN. = 1 FOOT, 
 
STAIR BUILDING. 35 
 
 PLATE XVI. 
 
 Fig. I exhibits the plan for an acute-angled platform stairs. 
 
 To continue the common pitch in the tangents : Set off 
 from A to B equal one and one-half step ; square up from 
 A to 4 equal four risers ; from the points i and 4 draw the 
 common pitch to the point D. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents A B R, Fig. i ; draw 
 the pitch I D on the side R B, and the pitch D 4 on the side 
 B A ; cut to the marks ; apply the bevel to the sides for the 
 angle required. 
 
 To draw the mould, Fig. 3 : Square up from C indefi- 
 nitely ; set up from C to S equal C D, Fig. i, and from S to 
 R and P equal J 4, Fig. 2, bisected ; from the points R and 
 P as centres, with D 4, Fig. 2, as radius, describe arcs cut- 
 ting each other in L ; draw L P and L R the direction of 
 straight rail ; set up from C to D equal C A, Fig. i ; from 
 the point D as a centre, with S 4, Fig. 2, as a radius, describe 
 arcs cutting the major axis in the points 2 and 3 for pins, 
 and by the use of thread or cord and pencil, describe the 
 centre curve ; set off each way from D equal half the width 
 of rail ; from the points describe the outside and inside 
 curves. 
 
riate 17 
 
STAIR BUILDING. 37 
 
 PLATE XVII. 
 
 Fig. I exhibits the plan of an obtuse-angled platform stairs. 
 
 To draw the elevation of the handrail : Set up from A to 
 B equal two (2) risers ; draw the common pitch D C and 
 B C ; from the point of intersection, draw C S parallel to 
 B A, and S R equal S A. 
 
 To find the angle to bevel the plank for the wreath : Fit 
 a piece to the tangents A S R, Fig. i ; draw the pitch C D 
 on the side S R, and the pitch C B on the side S A ; cut to 
 marks ; apply the bevel for the angle required. 
 
 To draw the mould for the wreath, Fig. 3 : Square up 
 from A to L and J, equal LPS, Fig. i ; set off from L to 
 R and D equal N B, Fig. 2, bisected ; draw J R and J D 
 the direction of straight rail ; set up from A to B equal L A, 
 Fig. I ; from the point B as a centre, with F B, Fig. 2, as a 
 radius, describe arcs cutting the major axis in 2 and 3 ; 
 place pins in the points ; by the use of thread or cord and 
 pencil, describe the centre curve ; set off each way from B 
 equal half the width of rail ; from the points describe the 
 outside and inside curves. 
 
r»late 18 
 
STAIR BUILDING. 39 
 
 PLATE XVIII 
 
 Exhibits a quarter circle of winding stairs. 
 
 To draw the elevation of the handrail : Set up from A to 
 B equal five risers ; from the points B and C, draw the com- 
 mon pitch ; from th^ pitch as tangents, describe the easings ; 
 join C B tangent to the easings. 
 
 To find the angle to bevel the plank in the joints : Fit a 
 piece to the tangents DSP; draw the pitch R N on the 
 sides ; cut to the marks ; apply the bevel as shown in Fig. 2. 
 
 To draw the mould, Fig. 3 : Square up from C to D and 
 L, equal D S and D P, Fig. i ; from the points C and L as 
 centres, with R B bisected as a radius, describe arcs cutting 
 each other in P and R ; then P R should equal R J ; join 
 L R and L P ; extend L P to N equal R T, Fig. i ; from 
 the point D as a centre, with R L, Fig. i, as a radius, 
 describe arcs cutting the major axis in 2 and 3 ; with pins 
 in the points, and by the use of thread or cord and pencil, 
 describe the curve P D R ; set off each way from D equal 
 half the width of rail ; from the points describe the outside 
 and inside curves. 
 
Flate 19 
 
STAIR BUILDING. 4! 
 
 PLATE XIX 
 
 Exhibits a quarter circle of winders at the landing. 
 
 To draw the elevation of rail : Set up from A to B equal 
 four risers ; from the point C draw the common pitch and 
 easing ; tangent to the easing draw C B ; set up from B to 
 D equal half the riser, plus the rise of common pitch from 
 the riser to the point to bore for baluster, as shown on the 
 pitch-board. 
 
 To draw the mould, Fig. 3 : Square up from C to D and 
 L equal T S and T R, Fig. i ; draw L R and L B, equal 
 L B, Fig. 2, bisected, and B R equal L P, Fig. 2 ; extend 
 L B to N equal L J, Fig. 2 ; from the point D as a centre, with 
 L N, Fig. 2, as a radius, describe arcs cutting the major axis 
 in 2 and 3 ; with pins in the points, by the use of thread or 
 cord and pencil, describe the curve B D R ; set off each 
 way from D equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
JPlate SO 
 
 LEVEL RAIL 
 
STAIR BUILDING. 4$ 
 
 PLATE XX 
 
 Exhibits a plan of stairs with winders at the landi?ig. 
 
 To draw the elevation of the rail : Set up from A to B 
 -equal five risers, and from B to D equal half the riser, plus 
 the rise of the common pitch from the riser to the point to 
 bore for baluster ; bisect A B in Y ; square over to C ; join 
 C D ; place the pitch-board ; draw the common pitch, also 
 the easing ; tangent to the easing, draw F C. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 C D, Fig. I ; from the point B as a centre, with R S, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 ■with pins in the points, by the use of thread or cord, describe 
 the centre curve ; from tlie point A as a centre, with P C, 
 Fig. 2, as a radius, describe an arc cutting the curve in C ; 
 from the point C as a centre, with R N, Fig. 2, as a radius, 
 •describe an arc cutting the curve in J ; from the points C 
 and J as centres, with P C and R C, Fig. 2, as radii, describe 
 arcs cutting each other in L ; draw C L and L J extended to D, 
 •equal P F, Fig. 2 ; set off each way from B equal* half the 
 width of rail ; from the points draw the outside and inside 
 •curves. 
 
 To find the angles to bevel the plank for the wreath ; Fit 
 a piece to the angle of the tangents H F D, Fig. i ; draw 
 the pitch P C on the side H F, the pitch C R on the side 
 F D ; cut to the marks ; apply the bevel to the sides for the 
 angles required. 
 
 To draw the mould for the upper wreath. Fig. 4 ; Draw 
 A B equal R D, Fig. 2, and B C equal C D, Fig. i ; set off 
 €ach way from A equal half the width of rail ; from the 
 points describe the curves required. 
 
r»late 31 
 
 I 
 
STAIR BUILDING. 45 
 
 PLATE XXI 
 
 JExhibits a continuation of of stairs with u inders at the land- 
 ings to the starting of second flight. 
 
 To draw the elevation of handrail : Square up from A to 
 B equal five risers ; from the point B, draw the common 
 pitch B C ; set up from S to J equal half the riser and the 
 rise of the common pitch from the riser to the point to bore 
 for the baluster ; join C J. 
 
 To draw the mould for the lower wreath, Fig. 3 : Draw 
 A B and B C equal R J and J P, Fig. 2 ; from the point A 
 as a centre, describe the arc B 2 cutting the major axis in 
 the point for pins to describe the centre curve ; set off each 
 way from A equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To draw the mould for the upper wreath, Fig. 4 : Square 
 up from A to B equal H D, Fig. i ; from the point B as a 
 centre, with P C, Fig. 2, as a radius, describe arcs cutting 
 the major axis in 2 and 3 ; with pins in the points, by the 
 use of thread or cord and pencil, describe the centre curve ; 
 from the point A as a centre, with C N, Fig. 2, as a radius, 
 describe an arc cutting the curve in R ; from the point R 
 as a centre, with P L, Fig. 2, as a radius, describe an arc 
 cutting the curve in D ; draw R E equal P C, and D E equal 
 N C, Fig. 2 ; set off each way from B equal half the width 
 of rail ; from the points describe the outside and inside 
 curves. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents HDL, Fig. i ; draw 
 the pitch P C on the side H D, and the pitch C N on the 
 side D L ; cut to the marks ; apply the bevel to the sides 
 for the angles required. 
 
Plate 2S 
 
STAIR BUILDING. 47 
 
 PLATE XXII 
 
 Exhibits a plan for platform stairs. For want of room at 
 the landing of return flight, the step at the starting is placed 
 in the cylinder. 
 
 To draw the elevation of the handrail.: Set up from A to 
 S equal one riser, and from R to B equal two risers ; from 
 the points draw the common pitch to intersect the lines 
 squared up from D and E. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 C S, Fig. I ; from the point B as a centre, with R L, Fig. 2,. 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point A as a 
 centre, with R J, Fig. 2, as a radius, describe an arc cutting 
 the curve in N ; from the point N as a centre, with R P, 
 Fig. 2, as a radius, describe an arc cutting the curve in D ; 
 from the points D and N as centres, with R J and S J as 
 radii, describe arcs cutting each other in P ; set off each 
 way from B equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents SDL, Fig. i ; draw the 
 pitch S J on the side S D, the pitch J R on the side D L ; 
 cut to the marks ; apply the bevel to the sides for the angles 
 required. 
 
Flate 23 
 
STAIR BUILDING. 49 
 
 PLATE XXIII 
 
 Exhibits a quarter platform stairs^ placed one step below 
 second floor. 
 
 To draw the elevation of handrail : Set up from A to S 
 equal one riser, from L to B equal three risers, and from B 
 to C equal half the riser, plus the rise of the common pitch 
 from the riser to the point to bore for the baluster ; draw 
 S J the common pitch ; join J C. 
 
 To draw the mould. Fig. 3 : Square up from A to B equal 
 C Y, Fig. I ; from the point B as a centre, with R P, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point A as a 
 centre, with S J, Fig. 2, as a radius, describe an arc cutting 
 the curve in S ; from the point S as a centre, with R N, Fig. 
 2, as a radius, describe an arc cutting the curve in D ; from 
 the points D and S as centres, with S J and R J as radii, 
 describe arcs cutting each other in C ; set off each way trom 
 B equal half the width of rail ; from the points describe the 
 outside and inside curves. 
 
 To draw the mould. Fig. 4 : Set off from B to A and from 
 B to C equal C D and D B, Fig. 2 ; the dotted curves from 
 B cuts the major axis in the points for pins to describe the 
 centre curve. 
 
 To find the angles to bevel the plank for the wreath, Fig. 
 3 : Fit a piece to the angle of the tangents D C Y, Fig. i ; 
 •draw the pitch S J on the side D C, the pitch J R on the 
 side C Y ; cut to the marks ; apply the bevel to the sides 
 for the angles required. 
 
I'late 24 
 
STAIR BUILDING. 5 1 
 
 PLATE XXIV 
 
 Exhibits a plan of hajidrail for quarter platform stairs at 
 the landing. 
 
 To draw the elevation : Set up from A to P equal one 
 riser, from D to R equal three risers, and from R to S equal 
 half the riser, plus the rise of the common pitch from the 
 riser to the point to bore for the baluster. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 C B, Fig. I ; from the point B as a centre, with L J, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point A as a 
 centre, with P H, Fig. 2, as a radius, describe an arc cutting 
 the curve in D ; from the point D as a centre, with L N, 
 Fig. 2, as a radius, describe an arc cutting the curve in C ; 
 from the points C and D as centres, with P H and L H as 
 radii, describe arcs cutting each other in S ; set off each 
 way from B equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To draw the mould, Fig. 4 : Set off from A to B and C 
 equal L S and E S, Fig. 2 ; from the point B as a centre, 
 describe an arc from A cutting the major axis in the points 
 for pins to describe the centre curve. 
 
 To find the angles to bevel the plank for the wreath, Fig. 
 3 : Fit a piece to the angle of the tangents H B C, Fig. i ; 
 draw the pitch P H on the side H B, and the pitch H L on 
 the side B C ;■ cut to the marks ; apply the bevel to the sides 
 for the angles required. 
 
I»late So 
 
STAIR BUILDING. 53 
 
 PLATE XXV 
 
 Exhibits the plan for a quarter circle of winders and plat- 
 form. 
 
 To draw the elevation of the handrail : From the point J 
 draw the common pitch and easing ; set up from A to B 
 equal five risers ; from the point B draw B D, the common 
 pitch, and D J tangent to the easing. 
 
 To draw the mould, Fig. 3 : Square up from A to R and 
 B equal L T and L N, Fig. i ; from the points A and B as 
 centres, with S E, Fig. 2, bisected, describe arcs cutting each 
 other in C and D ; from the point R as a centre, with E C, 
 Fig. 2, as a radius, describe arcs cutting the major axis in 2 
 and 3 ; with pins in the points, by the use of thread or cord 
 and pencil, describe the centre curve ; set off each way from 
 R equal half the width of rail ; from the points describe the 
 outside and inside curves ; extend B D equal S J, Fig. 2. 
 
 To draw the mould, Fig. 4 : Square up from C to B equal 
 L T, Fig. I ; from the point B as a centre, with E F, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; draw C J equal B D, and 
 J D equal E H, Fig. 2 ; from the paints J and D as centres, 
 with E D and B D, Fig. 2, as radii, describe arcs cutting 
 each other in P ; set off each way from B equal half the 
 width of rail ; from the points describe the outside 'and 
 inside curves. 
 
 To find the angles to bevel the plank : Fit a piece to the 
 angle of the tangents N T L, Fig. i ; draw the pitch E D 
 on the side L T, and the pitch D B on the side T N ; cut to 
 the marks ; apply the bevel to the sides for the angles 
 required. 
 
Flate 36 
 
STAIR BUILDING. 55 
 
 PLATE XXVI 
 
 JExhibiis a plan of ivindhig stairs at the landijig. 
 
 To draw the elevation of the rail : Draw the common 
 pitch and easing ; set up from A to B equal five risers ; draw 
 B P tangent to the easing ; set up from B to C equal half 
 the riser, plus the rise of the common pitch from the riser to 
 the point to bore for the baluster. 
 
 To draw the mould, Fig. 3 : Square up from A to J and 
 B equal C D and C J, Fig. i ; draw B C and B D equal S J, 
 Fig. 2, bisected, and C D equal J R, Fig. 2 ; from the point 
 J as a centre, with J H, Fig. 2, as a radius, describe arcs 
 cutting the major axis in 2 and 3 ; with pins in the points, 
 by the use of thread or cord and pencil, describe the centre 
 curve ; set off each way from J equal half the width of rail ; 
 from the points describe the outside and inside curves 
 extend B C to L equal S P, Fig. 2 ; then L D equals the 
 length of lower wreath, and C D the length of upper wreath. 
 
 To find the angle to bevel the plank : Fit a piece to the 
 angle of the tangents C D J, Fig. i ; draw the pitch S C on 
 the sides ; cut to the marks, and apply the bevel for angle. 
 
Flate Sr 
 
 SCALE H IN. = i FOOT 
 
STAIR BUILDING. 57 
 
 PLATE XXVII 
 
 Exhibits the plan for a scroll at the starting of the stairs. 
 
 To draw the scroll : Describe the eye one inch wider than 
 the rail ; divide the diameter into four equal parts ; sub- 
 divide, as shown by the figures, for the points to describe 
 the curves. 
 
 To draw the elevation of the scroll : Square up from B to 
 C ; draw the common pitch C D ; join D E. 
 
 To draw the mould, Fig. 2 : Square up from A to B equal 
 A R, Fig. I ; from the point B as a centre, with C J, Fig. i, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point A as a 
 centre, with C D as a radius, describe an arc cutting the 
 curve in C ; from the point C as a centre, with C P, Fig. i, 
 as a radius, describe an arc cutting the curve in D ; draw 
 D J equal L D, and C J equal C D, Fig. i ; set off each way 
 from B equal half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angles of the tangents R A B, Fig. i ; draw 
 the pitch L D on the side R A, the pitch D C on the side 
 A B ; cut to the marks ; apply the bevel to the sides for the 
 angles required. 
 
Flate 28 
 
 FIRST STEP \ 
 
 SCALE 1 IN, = 1 FOOT 
 
STAIR BUILDING. 59 
 
 PLATE XXVIII 
 
 Exhibits a plan for half circle of winder at the starti7igj the 
 curve drawn from centres of unequal radii. 
 
 To draw the elevation of the tangents : Set up from the 
 step to A equal the difference in the heights of newel and 
 short baluster, minus the rise of the common pitch from the 
 riser to the point to bore for baluster ; also from the step to 
 B equal five risers ; draw the common pitch B C ; at right 
 angles to C A, draw R P, Fig. i ; join P D. 
 
 To draw the mould, Fig. 3 : Square up from the point C 
 to L and J, equal C S and S P, Fig. i ; from the point J as 
 a centre, with L N as a radius, describe arcs cutting the 
 major axis in 2 and 3, the points for pins to describe the 
 curve J N ; from the point J as a centre, with S T, Fig. 2, as 
 a radius, describe arcs cutting the major axis in 4 and 5, the 
 points for pins to describe the curve J D ; draw R D equal 
 D S, Fig. 2 ; set off each way from J equal half the width 
 of rail ; from the points describe the outside and inside 
 curves. 
 
 To draw the mould, Fig. 4 : Square up from A to B equal 
 C P, Fig. I ; from the point B as a centre, with J R, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3, 
 the points for pins to describe the centre curve ; from the 
 point A as a centre, with J C, Fig. 2, as a radius, describe an 
 arc cutting the curve in D ; from the point D as a centre, 
 with J H, Fig. 2, as a radius, describe an arc cutting the 
 curve in C ; draw D S equal S C, and C S equal J C, Fig. 2 ; 
 extend S C for the direction and length of straight rail ; set 
 off each way from B equal half the width of rail ; from the 
 points draw the outside and inside curves. 
 
 To find the angles to bevel the plank for the wreaths : Fit 
 a piece to the angles of the tangents. Fig. i ; draw the 
 pitches on the sides over which they are placed ; cut to the 
 marks ; apply the bevel for the angles required. 
 
.Flate 29 
 
 Fig.3 
 
 SCALE I IN. = 1 FOOT 
 
STAIR BUILDINCx. 6l 
 
 PLATE XXIX 
 
 Exhibits a plan for circular stairs. 
 
 To find the common pitch : Square up from the tangent 
 E C to S equal four risers ; join S R, the pitch required. 
 
 To draw the mould for the arc B C, Fig. i : Square up 
 from A to C, Fig. 2, equal S E, Fig. i ; draw C D and C E 
 equal S R bisected, and D E equal S Y ; set up from A to 
 B equal S B, Fig. i ; from the point B as a centre, with S J 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, describe the centre curve ; set off 
 each way from B half the width of rail ; from the points 
 describe the outside and inside curves. 
 
 To draw the elevation of the tangents ALB, Fig. i : 
 Square up from B to J, Fig. 6, equal three risers ; set up 
 from first step to P, equal the difference in the heights of 
 the newel and short baluster ; draw J N the common pitch ; 
 join N P. 
 
 To draw the mould for the arc A B, Fig. i : Square up 
 from A to B, Fig. 3, equal A L, Fig. i ; from the point B as 
 a centre, with J C as a radius, describe arcs cutting the 
 major axis in 2 and 3 ; with pins in the points, describe the 
 centre curve ; from the point A as a centre, with P N as a 
 radius, describe an arc cutting the curve in D ; from the 
 point D as a centre, with J S, Fig. 6, as a radius, describe an 
 arc cutting the curve in C ; draw C T equal P C, and D T 
 equal J N, Fig. 6 ; set off each way from B equal half the 
 width of rail ; from the points describe the outside and in- 
 side curves. 
 
 To draw the elevation of the tangent C H, Fig. r : Set up 
 from C to D equal two and one-half risers, plus the rise of 
 
STAIR BUILDING. 63 
 
 the common pitch from the riser to the point to bore for the 
 baluster ; from the point D, square over for centre of level 
 rail ; draw C Y the common pitch, Y H parallel to D C, and 
 H R equal H C. 
 
 To draw the mould for the arc C R, Fig. i : Square up 
 from A to B, Fig. 4, equal S C, Fig. i ; from the point B as 
 a centre, with C J, Fig. 5, as a radius, describe arcs cutting 
 the major axis in > and 3 ; with pins in the points, describe 
 the centre curve ; from the point D as a centre, with C P, 
 Fig. 5, as a radius, describe an arc cutting the curve in E ; 
 draw D L equal H R, Fig. i, and E L equal C Y, Fig. 5 ; 
 set off each way from B equal half the width of rail ; from 
 the points describe the outside and inside curves. 
 
 To find the angles to bevel the plank for the wreaths : Fit 
 a piece to the tangents ALB, Fig. i ; draw the pitch N J 
 on the side L B, the pitch N P on the side L A ; cut to the 
 marks ; apply the bevel to the sides for the angles required. 
 
I?late 30 
 
STAIR BUILDING. 65 
 
 PLATE XXX 
 
 ^Exhibits the plan of circular stairs cotitinued to the starting of 
 secofid flight. 
 
 To find the common pitch : Square up from A to B equal 
 two risers ; join B C the pitch required ; set up from A to 
 D equal three and one-half risers ; draw D E parallel to 
 B C, and the tangent E F equal E A ; then A F equals the 
 length of curve required for the mould. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 A C, Fig. I ; from the point B as a centre, with D J, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, and by the use of thread or cord and 
 pencil, describe the centre curve ; from the point C as a 
 centre, with P D, Fig. 2, as a radius, describe an arc cutting 
 the curve in D ; draw D R equal D E, Fig. 2, and C R 
 equal F E, Fig. i ; set off each way from B equal half the 
 width of rail ; from the points describe the outside and 
 inside curves ; cut the plank parallel to the centre curve, 
 3-16 wider than the rail ; the joints at right angles to the 
 tangents and face of plank. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents A E F, Fig. i ; square 
 over on the side E F ; draw the pitch E D on the side E A ; 
 cut to the marks ; apply the bevel to the sides for the angles 
 required. 
 
ria-te 31 
 
STAIR BUILDING. 67 
 
 PLATE XXXI 
 
 Exhibits the plan of an irregular elliptical staircase. 
 
 To find the common pitch : Set up from A to B equal 
 three and one-half risers ; join B C the pitch required. 
 
 To draw the elevation of the tangents D L A : Set up 
 from A to E equal two risers ; draw E F the common pitch ; 
 join F H. 
 
 To draw the mould, Fig. 3 : Square up from C to D equal 
 D L, Fig. I ; from the point D as a centre, with E R, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point C as a 
 centre, with H F, Fig. 2, as a radius, describe an arc cutting 
 the curve in S ; from the point S as a centre, with E S, Fig, 
 2, as a radius, describe an arc cutting the curve in P ; from 
 the points P and S as centres, with H F and E F, Fig. 2, 
 as radii, describe arcs cutting each other in J ; set off each 
 way from D equal half the width of rail ; from the points 
 describe the outside and inside curves ; extend the wreath 
 at P equal half the depth of rail. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents D L A, Fig. i ; draw 
 the pitch H F on the side D L, and F E on the side L A ; 
 cut to the marks ; apply the bevel to the sides for the angles 
 required. 
 
T»late 32 
 
 SCALE I IN. = 1 FOOT 
 
STAIR BUILDING. 69 
 
 PLATE XXXII. 
 
 PLATE XXXI CONTINUED. 
 
 To find the elevation of the tangents A C N, Fig. i, and 
 the common pitch : Set off from P to H equal the tangents 
 A C and N C ; square up from P to S equal seven risers ; 
 join H S, the elevation and common pitch required. 
 
 To find the major axis of the elliptical curve for the centre- 
 of the mould : Set off from P to J equal A N ; join J S, cut- 
 ting the tangent A C in R ; then S R equals half the length 
 of major axis, and S J equals the length of curve required. 
 
 To draw the mould, Fig. 2 : Square up from L to D equal 
 P C, Fig. I ; draw D R and D P equal H S bisected, and 
 R P equal J S, Fig. i ; set up from L to N equal P A, Fig. 
 I ; from the point N as a centre, with S R, Fig. i, as a 
 radius, describe arcs cutting the major axis in 2 and 3 ; with 
 pins in the points, describe the centre curve ; set off each 
 way from N equal half the v/idth of rail ; from the points 
 describe the outside and inside curves. 
 
 To find the angle to bevel the plank to form the wreath : 
 Fit a piece to the angle of the tangents A C N, Fig. i ; draw 
 the common pitch on the sides ; cut to the marks ; apply 
 the bevel for the angle required. 
 
T>late 33 
 
STAIR BUILDING. 7 1 
 
 PLATE XXXIII. 
 
 PLATE XXXII CONTINUED. 
 
 To draw the elevation of the tangent L F : Square up 
 from L to B equal three and one-half risers ; join D B the 
 ■common pitch ; set up from L to R equal two and one-half 
 risers, plus the rise of the rail from the riser to the point to 
 bore for the baluster ; square over for the centre of level 
 rail ; draw L S parallel to D B, S F parallel to R L, and F H 
 equal F L. 
 
 To draw the mould, Fig. 3 : Square up from D to C equal 
 C L, Fig. I ; from the point C as a centre, with L J, Fig. 2, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point L as a 
 centre, with L P, Fig. 2, as a radius, describe an arc cutting 
 the curve in R ; draw R J equal L S, Fig. 2, and L J equal 
 F H, Fig. I ; set off each way from C equal half the width 
 of rail ; from the points describe the outside and inside 
 curves. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents L F H ; square over on 
 the side F H ; draw the pitch S L on the side F L ; cut to 
 the marks ; apply the bevel to the sides for the angles 
 required. 
 
Plate 34 
 
STAIR BUILDING. 73 
 
 PLATE XXXIV 
 
 Exhibits the elliptical staircase continued to the starting of 
 second flight. 
 
 To find the common pitch : Extend C A to D ; set up 
 from A to B equal three and one-half risers ; join B D the 
 pitch required ; draw D E tangent to the curve R E, F R 
 tangent to the curve A R, F H parallel to D B, and F N at 
 right angles to F A. 
 
 To draw the mould, Fig. 2 : Square up from A to B equal 
 S A, Fig. I ; from the point B as a centre, with H J, Fig. i, 
 as a radius, describe arcs cutting the major axis in 2 and 3 ; 
 with pins in the points, by the use of thread or cord and 
 pencil, describe the centre curve ; from the point A as a 
 centre, with F R, Fig. i, as a radius, describe an arc cutting 
 the curve in D ; from the point D as a centre, with B L, Fig. 
 I, as a radius, describe an arc cutting the curve in C ; from 
 the points D and C as centres, with B N and R F, Fig. i, as 
 radii, describe arcs cutting each other in L ; extend D L to 
 R equal N D, Fig. i. 
 
 To extend the mould from the point R to E, Fig. i : From 
 the points D and R as centres, with B P and E D, Fig. i, as 
 radii, describe arcs cutting each other in S ; join R S ; draw 
 S 4 at right angles to S R, and C 4 at right angles to A D ; 
 from the point 4 as a centre, describe the curve C S ; set off 
 each way from B equal half the .width of rail ; from the 
 points describe the outside and inside curves. 
 
 To find the angles to bevel the plank for the wreath : Fit 
 a piece to the angle of the tangents A D E, Fig. t ; square 
 over on the side D E ; draw the pitch D B on the side D A; 
 cut to the marks ; apply the bevel to the sides for the angles 
 required. 
 
r»late 35 
 
 LEVEL RAIL 
 
 SCALE 1j IN. = 1 FOOT 
 
STAIR BUILDING. 75 
 
 PLATE XXXV 
 
 Exhibits a plan of stairs at the landing. 
 
 To draw the elevation of the handrail : Place the step 
 A B ; from the point A, draw the pitch A C and the floor ; 
 set up from the floor to the centre of level rail, equal half 
 the riser B C, and the rise of the rail from the riser to the 
 point to bore for the baluster on the common pitch ; draw 
 D F parallel to C B, and J S at right angles to J F ; then 
 R J equals the length of curve required for the mould. 
 
 To find the angles to form the wreath : Fit a piece to the 
 tangents R F and F J, Fig. i ; draw the pitch of the rail on 
 the side R F ; square over on the side F J ; cut to the 
 marks ; apply the bevel, as shown in Fig. 2. 
 
 To draw the mould, Fig. 3 : Square up from A to B equal 
 S R, Fig. I ; set off from A to C, and from B to 2 and 3 
 equal N H ; place pins in the points 2 and 3, and by the use 
 of a thread or cord and pencil, describe the centre curve. 
 
 To find the length of curve and point of contact : Set up 
 from C to D equal L J, Fig. i ; set off from D to R equal 
 N E, Fig. I ; square up from D to S equal J F, Fig. i ; join 
 S R, and extend for the straight rail ; set off from B each 
 way half the width of the rail ; the bevel applied to the 
 width of the rail determines the width of the mould at D 
 and R. 
 
I>late 36 
 
STAIR BUILDING. 77 
 
 PLATE XXXVI 
 
 Exhibits a plan of stairs at the starting of second flight. 
 
 To draw the elevation of the handrail : Place the step 
 A B ; set up from the floor to centre of level rail, equal half 
 the riser, and the rise of the rail from the riser to the point 
 to bore for. the baluster ; square up from Y to C ; draw the 
 tangent C D equal C R ; join D S at right angles to D C ; 
 then R D equals the length of curve required for the mould. 
 
 To find the angles required to form the wreath : Fit a 
 piece to the angle of the tangents R C and C D, Fig. i ; 
 draw the pitch on the side C R ; square over on the side 
 C D ; cut to the marks ; apply the bevel, as shown at Fig. 2. 
 
 To draw the mould, Fig. 3 : Square up from the point A 
 to B equal S R, Fig. i ; set off from A to C, and from B to 
 2 and 3, equal P J, Fig. i ; place pins in the points 2 and 3, 
 and by the use of the thread or cord and pencil, describe 
 the centre curve. 
 
 To find the length and point of contact : From the point 
 C as centre, with P L, Fig. i, as radius, describe an arc cut- 
 ting the curve in N, the point of contact and length required. 
 
 To find the direction of straight rail : draw C J equal 
 C D, and N J equal P Y, Fig. i ; set off each way from B 
 half the width of the rail ; the bevel applied to the width 
 of the rail determines the width of the mould at C. 
 
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