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GIFT OF

*aacrutj
LIBRARY

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GEOMETRICAL

STAIR BUILDER,

SIMPLIFIED.

By JOHN" THOMAS.

Entered according to Act of Congress, A. D. 18B3,

BY JOHN THOMAS,
In the Clerk's Office of the District Court of the United States for the Northern District of California.

Any infringement on the copyright of this book will be prosecuted to the utmost extent of the law.

GIFT OF

Bancroft
LIBRARY

TOWNE & BACON, BOOK AND JOB PRINTKBS, 536 CLAY STREET, SAN FKANCISCO.

INTRODUCTION.

THERE has been so much said and written on the art of Stair Building for the last few
years, that it has been considered as bad as heresy to pretend that a hand rail could be
got up without the use of prisms, parallelograms, ordinate lines and tangent boxes, and
a host of lines and terms accompanying them ; although nine-tenths of the mechanics at
the sight of such geometrical problems turned from them in disgust, and could only
know what they heard related of them. Even the practical Stair Builder had to bring
his book along with him to his shop, like a school boy, for fear he might forget one of
the many lines given therein and in several cases they are entirely wrong and then
spend half a day at what this work teaches to do in ten minutes or less. Is there a man
that will go to the trouble to set out and make two moulds, one to cut his stuff by and
the other to slide, which is termed a slide mould, whilst he can make one do ; or crack
his brain studying for hours over any of the preceding works on Stair Building, whilst
he has only to look at the " Geometrical Stair Builder Simplified," which teaches him to
set out a wreath for any stairs with eight or ten lines, and in as many minutes.

In presenting this work to the mechanic, all technicalities and high sounding phrases
are carefully avoided, so that any man can understand it. For simplicity and correct-
ness it cannot be equaled ; for quickness, I defy the world to beat it, unless a rail can be
set out without a line, or done by magic.

JOHN THOMAS,,

STAIR BtriLDER'v ' r-; i V

SAN FRANCISCO, JANUARY, 1863.

t
' ,

Tlate I.

Fig. 1 is a quadrant ; to find the stretch out B C the quadrant, F C the diameter,
with the distance F C in the compass, describe two arcs, cutting each other at
G, and draw the tangent B E parallel to F C, cutting the quadrant at B ; from the
point G draw a line through C, cutting the tangent at D, then B E is the required
length.

Fig. 2, another method. A B C is a semicircle ; A C the diameter, with the distance
A C as a radius ; describe two arcs, cutting each other at G, draw the tangent D E
through B, extended parallel to A C, the diameter ; draw the lines G D and G E
through the points A and C, and from the equilateral triangle D E G, any side of which
is equal to the semicircle ABC.

Fig. 3 shows the method of setting a gauge for an octagon without drawing the figure,
the square being given from P, open the compass to O the center, and draw the arcs
O C, then C is the point to set the gauge.

The attention of the workman is called to Plate II, Fig. A and Fig. B A. The
lengths of the tangents are found at Fig. B. A. From the base line 1 8 the perpendic-
ular is drawn and united by the hypotenuse, and from the relative positions of the tan-
gents to the perpendicular and hypotenuse lines the spring bevels are found. To apply
.them s^/J*late III.
.. ,'JWhen th'fe, taaigents are of equal length, one bevel squares both ends.

In no case does it require thicker stuff than the width of the rail to get out a wreath
for any stairs.

PL ATP, I.

Fig. 3.

PLAT I; L'.

OPlate II.

Fig. A, the tangents, is at obtuse angles ; 1 2 8, the tangent enclosing the center line
of the rail ; 1 8, the base line ; 8 3, the perpendicular. Fig. B A is a board with two
gauge lines drawn on it equal in width to one of the tangents at 1, draw a line at right
angles to 1 3, and on it place the pitch board, the point resting at 1, and where the
pitch line cuts the gauge line at 2, then 2 1 is the length of the bottom tangent ; from

1 raise up to 3, the heighth you want to overcome, and draw the line 3 2, which is the
length of the upper tangent, make 8 3, Fig. A, equal to 1 3 on the board, and draw the
hypotenuse 1 3, then make 1 2, Fig. A, equal to 1 2 on the board, and 2 3, Fig. A, equal
to 2 3 on the board, and you have the required tangents, and when placed in position
with two pitches, will cover exactly the tangents 1 2 8, on the ground plan, to find the
bevel for the joint joint at 3 set one leg of the compass in 3 and open it to 2, revolve

2 round to 7, then take the distance 1 2, and put one leg in 8 and cut the arcs at 7 ;
then draw the line 7 3, then take equal distances on these two tangents 3 7, 3 2, at T T ;
then square down to J J, and from J J describe two arcs cutting each other at M, and
draw two lines from this point to J J, and the angle formed is the required bevel for
the joint at 3. To find the bottom bevel for the joint at 1, reverse the bottom tangents
on the perpendicular and hypotenuse lines, as shown at Fig. B, and you find the bevel
in the same manner as you found the middle bevel.

Fig. C and Fig. D, the tangents are at right and acute angles. Fig. B C is the board
for Fig. C, Fig. B D the board for Fig. D, the tangents for both of these figures are
found in the same manner as for Fig. A. The dotted lines show the tangents reversed,
for to get the bottom bevel, the tangents and bevels for all rails are found in the same
manner as Figures A and B.

III.

Fig. A shows the ground plan of a platform stairs with the risers in the cylinder. To
draw the face mould ; 128,. the tangents, enclosing the center line of the rail, 1 8 the
hase line, 8 3 the perpendicular. Fig. B is a board with two gauge lines equal in width
to one of the tangents ; at 4 draw a line at right angles to 4 3, extended hoth ways on
this line place the pitch board, letting the point 5 project beyond the line 4 3 the same
distance as from 1 to 5 Fig. A ; from 4 to 3 raise up the height of one riser and a half,
which is the required height, then draw the pitch line cutting the gauge line at 2, and
1 2 is the length of the bottom tangent ; draw the line from 3 to 2, which is the length
of the top tangent, make 8 3 Fig. A equal to 1 3. Fig. B, and draw the hypotenuse 3 1,
then make 1 2 Fig. A equal to 1 2 Fig. B, and 2 3 Fig. A equal to 2 3 Fig. B, and you
have the required tangents. 123, when placed in position with 1 resting in 1 on the
ground plan, 2 3 will exactly cover 2 8 on the ground plan. The bevel for the joint 3
is shown at M, and the bottom bevel is found by reversing the tangents on the perpen-
dicular and hypotenuse lines ; with a bevel transfer the tangents 123 Fig. A to Fig. P,
the board you cut the pattern from, intersect the tangents by dividing each into eight
equal parts, and the intersected line is the center line of the rail ; with half the width
of the rail in the compass, put one leg in the center line and describe arcs on each side
of it, which gives you the pattern an equal width. The one pattern answers for the
top and bottom wreaths ; the joints are cut at right angles to the tangents, and square
from the face of the plank ; the bottom bevel is applied by putting the stock on the
face of the wreath at 1, the blade passing down through the center with the end of the
stock pointing in to the stairs ; the top bevel is applied reversed, with the end of the
stock pointing out and the blade passing down the center ; from these lines square the
rail.

PLATE ,'i.

Fig. P.

Fig.B

1 K

relate IV.

Fig. A is the ground plan of a platform stairs with the risers at the springing of the
cylinder. To draw a face mould : 1 2 8 the tangents enclosing the center line of the
rail, 1 8 the base line, 8 3 the perpendicular, Fig. B the board with the two gauge lines
equal in width to one of the tangents ; from 1 draw a line at right angles to 1 3, and
on this line place the pitch board, the point resting in 1 , as you require to raise but one
riser from R to S ; then divide the heighth of the riser on the pitch board and square
over to 3, and draw the lines 123, which is the required length of the tangents ; make
8 3 Fig. 1 equal to 1 3 Fig. B, and draw the hypotenuse 1 3, then make 1 2 equal to 1
2 Fig. B, and 3 2 equal to 3 2 Fig. B, 1 2 3 are the tangents. The middle bevel is
found as usual at M, and the bottom bevel is shown at Fig. A B with the tangents
reversed on the perpendicular and hypotenuse lines with the bevel ; transfer the tan-
gents to the board you cut your pattern from, and intersect the tangents and make the
pattern as usual, leaving some stairwood at 1 to connect with the straight rail.

Fig. R shows the second flight starting from a level landing or floor round a cylinder
to flyers. 12845 the tangents enclosing the center line of the rail, 1 8 the base line,
8 3 the perpendicular, Fig. B C the board with the two gauge lines from 1 to 5, is the
required heighth ; 1 2 the pitch line, from 2 to 4 divide into two equal parts and square
over to 3 and draw the lines 12345, which is the length of the tangents for the
upper and lower wreaths ; make 8 3 Fig. C equal to 1 3 Fig. B C, and draw the hypot-
enuse 1 3 ; make 1 2 equal to 1 2 Fig. B C, and 2 3 equal to 2 3 Fig. B C, 1 2 3 are
the required tangents for the upper wreath ; extend the tangent 2 3 to 4, and make 4 3
equal to 3 2 ; from 4 square down to 5, and make 5 4 equal to 5 4 Fig. B C ; transfer
the tangent to the board you cut the pattern from, as at Plate 3, Fig. P. The bevels
for the upper wreath are found as usual ; the bevel for the lower wreath at the joint 5,
is shown at 3 Fig. B C. The lower wreath can be set out by the compass, as the tan-
gents are nearly equal in length.

I^late

A shows the ground plan of a geometrical 'staircase with winders round the semicircle.
Fig. B shows the manner of setting out the face string before it is bent round the drum.
It is generally one and a half inches thick, cut out in the center as shown at V Y. The
yeneer, which is equal to the stretch out of the semicircle ABC, W W the winders,
G G the graduating steps, F F the flyers, P P the splices. If you want to raise the
rail so that the long bannister goes over the cylinder, you must not have a graduating
step on the lower part of the cylinder, but put a winder in the place of a graduating
step between the springing and the flyers ; on the upper portion of the cylinder put a
winder in place of the graduating step, and one graduating step between it and the
flyers, in order to give room to form an easing between the upper wreath and the
straight rail. To form the upper and lower easing you set out an elevation of the flyers
and winders, and the angle formed between is the place to make the casings, as shown
at Plate 9. If the face string is to be moulded, gauge the width of the opening on the
string before bending it ; and when bent, cut it off and set it back the required depth
for the moulding, and then plant in the moulding, which will hide the saw kerf.

PLAT I:

Fiq A

Fiy.B

Fig. P.

Ilate

Shows the method of drawing the face mould for the geometrical staircase shown at
Plate 5. With the short bannisters over the winders, enclose the center line of the rail,
as usual, with the tangents I 2 8 on the ground plan ; Fig. A, 8 1 the base line, 8 3 the
perpendicular ; Fig. B the board with the two gauge lines equal in width to one of the
tangents on the line 1 4 ; place the pitch board and draw the pitch line 1 2, and from
4 raise up to L, the number of risers in the cylinder ; divide it in two equal parts,
squaring over to 3, and draw the line 3 2 ; make 8 3 Fig. A equal to 1 3 Fig. B, and
draw the hypotenuse 1 3 ; make 1 2 equal to 1 2 Fig. B, and 2 3 equal to 2 3 Fig. B,
and 123 are the required tangents. Transfer them to Fig. P, the board you cut the
pattern from, and proceed as usual with the formation of the mould. The one pattern
answers for the upper and lower wreaths. The bevels for both ends are found as usual
in all cases.

Fig. A is the ground plan of a staircase, the lower part constructed of flyers, with
winders round the semicircle to land on a level floor. Fig. B the face string without a
graduating step. Fig. C the rail, the lower wreath forming a perfect easing over the
flyers, L the landing, with the rail raised four inches over it, so that the long bannisters
can go on the landing. E E Fig. B, the easings of the cylinder ; P the splice to con-
nect with the face string.

PLATE 7.

W<ATT: a.

HPlate

Shows the manner of getting the face mould for the stairs Plate 7. 12845 Fig. A,
the tangents enclosing the center line of the rail ; 1 8 the hase line ; 8 3 the perpendic-
ular. Fig. B a hoard with two gauge lines equal in width to one of the tangents ; from
the line 1 3 square over to 4, and on it place the pitch hoard from 4 to L, the heighth
of four risers, and four inches from where the pitch line cuts the gauge line at 2, divide
from 2 to L in two equal parts and square over to 3, then draw the line 2 3, and make
8 3 Fig. A equal to 1 3 Fig. B, and draw the hypotenuse 1 3 ; make 1 2 Fig. A equal
to 1 2 Fig. B, and 2 3 equal to 2 3 Fig. B, and draw the tangents 1 2 3 to form the
upper wreath ; extend the tangent 2 3 to 4, and make 3 4 equal to 3 2 ; from 4 square
down to 5, and make 4 5 equal to 4 5 on the ground plan. Transfer the tangents as
usual, and form the pattern, leaving ahout three inches of straight wood on the upper
wreath at 5. The bevels for the lower wreath are found as usual ; the bevel for the top
wreath is shown at T Fig. B.

JPlate IX.

Fig. A shows the ground plan of a staircase, the lower part of which is constructed
of flyers with winders round the semicircle to land on a level floor.

Fig. B the face string ; W the winders, with one winder in the place of a graduating
step, in order to raise the rail so that the long bannisters can go round the cylinder.

Fig C the rail, with the center line raised up four inches from the corner of the step
and riser, which gives a most graceful easing at E ; if there was a graduating with the
winder, it would make the easing too long and too far from the curve of the rail as it
passes round the cylinder. If you want to put the short bannisters over the winders,
you can do it on this plan ; but it would be better to put in two graduating steps, and
by so doing you produce the same easing as shown at E.

PLATE !).

PLATE If i.

fig. P

To draw the face mould of the hand-rail of the stairs, as shown at Plate IX. 128
4 5 Fig. A, the tangents enclosing the center line of the rail ; 1 8 the base line ; 8 3 the
perpendicular. Fig. B the board, 1 4 the gauge lines, 4 L the heighth of four risers,
123 the length of the tangents ; transfer those tangents to Fig. A as usual, 12345
Fig. A are the tangents.

The middle bevel for the joint at 3 is shown at M ; the bottom bevel for the joint at
1 is found as usual by reversing the tangents. The bevel for the upper wreath is shown
at the angle T Fig. B.

relate XI.

To draw the face mould for a staircase with winders, landing the well hole, formed by
two quadrants of unequal radii. 12845 Fig. A, the tangents enclosing the center line of

the radii ; 1 8 the base line ; 8 3 the perpendicular ; Fig. B tlio board with three gauge lines
equal in width to 4 8 8 2 Fig. A. From L square over to D, and on this line place the
graduating step with the point resting at 1 ; then draw the pitch line to 2, which is from
1 to 2, the length of the bottom tangent for the lower wreath ; from L raise up the
heighth of four risers and four inches, then draw the line 4 2 through. 3, and 3 2 is the
length of the top tangent of the lower wreath, and 3 4 the length of the bottom tan-
gent of the upper wreath ; make 8 3 Fig. A equal to 1 3 Fig. B, and draw the hypote-
nuse ; make 1 2 equal to 1 2 Fig. B, and 2 3 equal to 2 3 Fig. B. To form the upper
wreath, extend the tangent 3 2 to 4, and make 4 3 equal to 4 3 Fig, B ; from 4 square
over to 5, and make 4 5 equal to 4 5 on the ground plan Fig. A. The bevel for the
joint 3 is shown at M ; the bottom bevel is found as usual. The bevel for the upper
wreath is shown at T Fig. B.

PLATE It.

XII.

To draw the face mould for a quarter circle rectangular stairs. 128 Fig. A, the tan-
gents enclosing the center line of the rail ; 1 8 the base line ; 8 3 the perpendicular,
which is' equal in heighth to four risers ; 1 3 the hypotenuse ; Fig. B the board with the
two gauge lines equal in width to one of the tangents. From 4 to L, the heighth of four
risers, divide that line into two equal parts at 2, and draw the lines 1 2 and 2 3, which
is an equal length with the distance 1 2 Fig. B in the compass ; put one leg in 1 Fig. A,
and describe the arcs at 2, then change the compass from 1 to 3 and cut the arcs at 2,
and draw the tangents 1 2 2 3, as they are an equal length, the bevel B will square both
ends.

REMARK. At the time of building the stairs, set out the tangents on the board Fig.
B, in order to have the tangents an equal length, and for them to come parallel to the
pitch line of the graduating step. From 4 to R, the heighth of one riser, square over
to O, then draw O W parallel to R 4, and from 1 to "W is the width of the graduating
step. If the stairs should be built, extend the tangent 2 1 down until it cuts the pitch
line of the flyers; the same with the tangent 2 3, and the angles formed will be the
casings.

XXIX.

The ground plan of a staircase with winders round the quarter circle, starting from a
newel and miter cap to draw the face mould in one piece with a perfect easing at the
newel cap. 12834 the tangents enclosing the center line of the rail ; 4 8 the base
line of Fig. B ; 8 3 the perpendicular ; Fig. B A the board with the two gauge lines ;
G the graduating step, with the point resting at 4. From 4 to L raise up the heighth
of three risers and two inches, which is the required heighth from the bottom of the
newel cap to the center of the rail at 4 Fig. B, where the pitch line cuts the gauge line
at 5. From 5 to L divide in two equal parts at O, square over to 3 and draw the line
354, w r hich is the length of the tangents for Fig. B ; make the perpendicular 8 3 Fig.
B equal to 4 3 Fig. B A, and draw the hypotenuse 3 4 ; transfer the tangents as usual,
453 Fig. B A to 4 5 3 Fig. B ; 1 8 the base line for Fig. A ; 8 3 the perpendicular,
equal in heighth to O L Fig. B A ; make 3 2 equal to 3 5 Fig. B, and 1 2 equal to 1 2
on the ground plan. With the bevel transfer the tangents of the upper half of the
wreath to the board you cut the pattern from, as shown at Fig. P ; then transfer the
tangents of Fig. A to the same board and unite the two 3 3, keeping the lines 3 5 and
3 2 on a straight line ; intersect them as shown, and when in position with 1 2, covering
1 2 on the ground plan, 2335 will exactly cover 2 8 3 on the ground plan, and 5 4
will exactly cover 3 4. Also having the pitch of the graduating step G, always leave a
few inches of straight wood at 4 and at 1, for the purpose of squaring up from the bot-
tom to make the miter for the newel cap. The bevel for the joint at the newel cap is
shown at B Fig. B A. The bevel for the center of the wreath 3 3 is shown at M ; and
to find the bevel for the joint at 4, you reverse, as usual, the tangents of Fig. B, then
you have three points to square the a il from.

PLAT.K 73.

PLATE Ik.

A G \

Flate

To draw the face mould for a hand rail over winders. The ground plan is formed by
the quadrant of a given radius, with the arcs of a circle added by a smaller radius, start-
ing from a newel and miter cap.

It is useless to describe this drawing, for it would be only a repetition of Plate XIII,
and all former plates. You see that the principle is the same, and that they are num-
bered alike ; the only difference is the arcs of a circle added. Bear in mind that the
wreath, starting from the newel cap at Plates XIX and XXI, is just the same as this,
and the wreaths landing are the same as in Plate XV.

Tlate

Shows the ground plan of a staircase with winders round the quarter circle, landing
on a level floor. To draw the face mould for the wreath over the winders and the eas-
ing over the landing at L in one piece, with the long bannisters over the winders : 1 2 8

3 4 the tangents enclosing the center line of the rail ; 1 8 the base line for Fig. A ; 8 3
the perpendicular ; Fig. B A the board with the two gauge lines, equal in width to one
of the tangents. From 1 to 4 square over, and on this line place the pitch board of the
winders G, the point resting in 1, and draw the pitch line, cutting the gauge line at 2.

From 4 raise up to L the heighth of four risers ; from 2 to L divide in two equal parts,
square over to 3, then draw the line 3 2, and you have the tangents for the lower wreath.

4 3 the base line of Fig. B, 4 5 the perpendicular ; then make 3 4 equal to 2 3 Fig.
B A, and make 4 5 equal to 3 4 on the ground plan ; unite the tangents as at Plate
XIII to cut your pattern. The tangent 1 2 Fig. P, when placed in position, will exactly
cover 1 2 on the ground plan, and 2 4 will cover 2 3 ; and 4 8 will be perfectly level,
covering 3 4 on the ground plan. The bevel for the joint at 5 is shown as usual at T
Fig. B A. The bevel for the center at 3 3, is shown as usual at M. The bottom bevel
is found by reversing the tangents of Fig. A.

PLATE 15.

PLATE 16

. H.

To construct the face mould for a hand rail, starting from a newel with a miter cap,
the ground plan being either an elliptic curve or the arc of a circle. To find the position
of the tangents on the ground plan : Fig. C the pitch board from 1 to 5 is six inches, the
heighth of the center of the newel cap from the first step ; from 5 square over to 3, then
draw the tangent 8 2 Fig. A, extended ; at 8 place the point of the pitch board ; from
the pitch board at 6 to 2, make it equal to 5 3 Fig. C, and from the miter cap draw
the tangent 1 2 ; from 2 square up to 7, and where the pitch line cuts at 7, from 7 to
8 is the length of the tangent. On the base line 1 8 erect the perpendicular 8 3, and
make it equal to 7 2 ; then make 3 2 equal to 7 8, and 1 2 equal to 1 2 on the ground
plan, and you have the required tangents ; and when placed in position, with 1 2 rest-
ing on 1 2 on the ground plan, 3 will exactly cover 8, and the tangent 2 3 will have the
pitch of the flyers. The bevel for the bottom is shown at B ; the bevel for the top is
shown at S.

Always leave a few inches of straight wood at joint 1 to square up to form. 'the miter
for the cap.

Shows the face string with the easing E, the pannel P, and also the best manner of
putting the step and risers together, B B. The blocking and the risers should be
screwed from the back to the step, and the blocking glued and nailed. Fig. A shows
the manner of setting out the length of the rail at the newel cap ; and to find the miter
of the rail for the cap, from the top of the step to the center of the rail should be six
inches, and the center of the straight rail cutting through the corner of the steps and
risers at C ; the center of the newel projecting three -fourths of an inch outside the face
of the first riser, so that you may have a longer easing at D. Fig. B shows the board
you cut the miter of the newel cap in ; T T are two cuts in the board equal to the
width of the rail, with a screw in the center to fasten the cap to it. Mark the width
of the rail on the cap, and bring one of these marks opposite the cut T ; cut the miter
half way and turn the cap round until the other mark is opposite the other cut T, thei

cut the miter through and you have it correct from the saw.

PL ATM 77.

AV.

Ftq.B

Tlate

Fig. A is the plan of a staircase with the tangents on the ground plan at acute angles.
It also shows that no matter in what position the tangents on the ground plan are placed,
iccording to this system, the difficulties in stair railing can be overcome by the few sim-
ple lines laid down in this work. It is useless to describe this Plate, as it would only
3nter into a repetition of Plate XII.

JPlate XIX.

Exhibits the ground plan of an elliptical staircase. To find the face mould : 1 2 3

the tangents enclosing Fig. A ; 3 4 5 the tangents enclosing the center line of the rail

Fig. B ; 5 6 7 enclosing the center line at Fig. C ; 7 8 9 at Fig. E, and 9 10 11 Fig. F;

5 7 the base line of Fig. C ; 7 7 the perpendicular ; Fig. C C the board with the twri

gauge lines ; 7 6 and 11 12 equal in width to one of the tangents. On line 7 6 raise up

the heighth of the number of risers that the base line 5 7 covers ; divide it in two

equal parts and square over to 5, and draw the lines 7556, which is the length of the

tangents for Fig. C ; make the perpendicular 7 7 Fig. C equal to 7 6 Fig. C C, and draw

the hypotenuse 7 5 ; make 5 6 Fig. C equal to 7 5 Fig. C C, and 6 7 equal to 5 6, th<

tangents 567 will cover the corresponding figures on the ground plan. From the tan

gents Fig. C C you find the pitch for the lower wreath Fig. B and Fig. A, and also for

the wreath Figs. E and F ; from the gauge line 11 12 Fig. C C, draw the line 8 9 equal

in width to the tangent 5 4 Fig. B, then continue the tangent 6 5 to cut the line 8 9 at

4 Fig. A B. From 5 set down the heighth from the newel cap to the tangent 5 Fig. B,

then square over to 8 and divide the line 8 4 in two equal parts, and square over to 2J

and draw the lines 8 2 and 2 4 and 4 5, which is the length of the tangents for t 1

lower wreath ; 5 3 the base line Fig. B ; 3 8 the perpendicular, equal to 2 5 Fig. A B

and make 5 4 equal to 5 4 Fig. A B, and 4 8 equal to 4 2, then 5 4 8 is the tangent fo:

the wreath Fig. B ; 1 3 the base line Fig. A ; 3 8 the perpendicular, epual to 1 2 Fig

A B, and 2 8 equal to 2 8 Fig. A B, and 1 2 equal to 1 2 on the ground plan. On tb

board you cut the pattern from, unite the tangents as usual, as shown at Fig. A B, Pla

XX, which is the wreath to cover from the newel cap to the tangent 5 Fig. B. Th

length of the tangents for the upper wreath are found on the board Fig. E F ; 7 A

is equal to the pitch of the tangent 5 7 Fig. C C. From 7 to C is five risers and four

inches. To raise the rail on the landing, from A to C divide in two equal parts and

square over to B, and draw the line C B B A, and you have the required length of the

tangents for the wreaths Figs. E and F, which are numbered 7 A B and BCD. Th

bevel for the joint D is shown at T Fig. E F ; and the bevel for joint 1 at the newel cap

is shown at A Fig. A B. The other bevels are found as usual. Plate XX shows the

patterns.

PLATE -fd

PLATE >

Fig. C.

Fig.

E.F.

PLATE 2

XX.

The ground plan of a circular staircase. Enclose the center line of the rail with the

tangents 123,345,667,789.91011. It is useless to describe this rail, as it would

be only a repetition of Plate XIX. Although Plate XIX is elliptical and this circular,

still the principle is the same ; and as this Plate and Plate XIX are numbered alike, you
can read the instruction for Plate XIX, and you will find the wreaths. Figures A B, C C
and E F are the boards, to find the lengths of the tangents.

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