Illustrations of geometric tracery from the paneling belonging to Carlisle Cathedral

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ILLUSTRATIONS

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GEOMETRIC TRACERY,

FROM THE PANELING BELONGING TO

lr iTatijcDval.

BY

ROBERT WILLIAM BILLINGS,

AUTHOR OF THE ILLUSTRATIONS AND HISTORY OP CARLISLE CATHEDRAL.

ILontton:

PUBLISHED BY THOMAS AND WILLIAM BOONE, 29, NEW BOND STREKT ;
AND THE AUTHOR, MANOR HOUSE, KENTISH TOWN.

1842.

The second view of the Screen is from the Author's Illustrations of
Carlisle Cathedral. It has been thought advisable to reprint it here for the
better explanation of the subject to those who are not in possession of that
work.

R. W. B.

ILLUSTRATIONS,

Sfc. Sfc. Sfc.

THE Geometric Panels forming the present Illustrations are the remains
of an exceedingly valuable and extensive collection, for the whole Choir of
Carlisle Cathedral, eastward of the still beautiful stalls, was separated from the
aisles by Screens filled with elaborate Tracery. The same enrichment extended
also to the Chapel of St. Catherine, a small building, which may be termed
an aisle to the south" transept.

In the year 1764, the Cathedral was, according to the Churchwardens'
usual phrase, repaired and " beautified" The whole of the Choir screens were
removed, and their place occupied by a high stone wall, covered in the Choir
by a wooden arcade in the true Gothic style of that period, and in the aisles
by a carefully-executed coat of plaister. The old and useless paneling was
removed to some of the outbuildings, and by far the greater portion either lost
or destroyed.

All that remains of the original enrichments may be described as the
frame-work of an exceedingly mutilated screen, in the possession of William
Cowper, Esq. at Carlton Hall, near Penrith, from which is derived the
materials for Plates XIX. and XX., and three of the borders in Plate XVIII. j
three beautiful Panels (Plates XV. XVI. XVII.) forming part of a sideboard
at Featherstone Castle, Northumberland, the seat of Lord Wallis (formerly
proprietor of Carlton Hall) ; one Panel (Plate VIII.), and the fourth
border of Plate XVIII. inserted in the modern doorway to the aisle of the
Choir against the Bishop's Throne.

4 ILLt STU ATION8 OF GEOMETRIC TUACEin .

Fortunately, the Chapel of St. Catherine was not considered worth
beautifying, and in this building we have two M re. us, containing tin- remainder
of the subjects represented, numbering thirteen out of twenty. Three or
four Panels at present in the Chapel belonged to the Choir. The originals,
most probably, from being more beautiful, were cut away ; the ends of the
original tracery being still left, give very much the appearance of their
having been taken to fit a particular piece of furniture.

The whole of these screens are reputed to be the work of Prior Thomas
Gondibour, who presided over the Cathedral from 1484 to 1507- His
initials (C. £.) were beautifully cut in the Tracery of a Panel in the doorway
shewn in the frontispiece, but this was unfortunately pulled out and taken
away by some mischievous person in the winter of 1839. Another cypher
(T. G.) forming the cusps of a trefoil from Carlisle (see Plate XX.) may be
taken for Prior Gondibour*s. It is among the remains at Carlton Hall.
Their date may therefore fairly be taken at about 1500.

Some of these specimens are perhaps not so interesting in themselves
for elegance of design, as from the circumstance of their proving that the
majority were designed on the same ground-work, namely, the division of
a square into four parts each way, or sixteen squares. Upon the lines of
these squares the centres of all the curves are worked, and upon such a simple
calculation of parts, as to render their construction perfectly easy. It is of
essential importance to have a ready means, well known, of re-producing the
beautiful forms displayed in many of these and other specimens, and the
author trusts that the means he has adopted will effect this, for no workman,
following the descriptions given of each Plate, can possibly err in any of the
leading features.

1 'mm the direct evidence here produced of system in the minor detail of a
once beautiful church, is it not fair to assume that the mis-called Gothic
Architects had a system for objects of greater magnitude, that is the buildings
themselves ?

In the leading curves of these examples, nothing can exceed their
accuracy of projection, but all the foils contained within are (most probably
from their diminutive size) worked by hand. In fact, they are too small to
be otherwise, unless the most extraordinary fastidiousness had been exm.-i-ed

FROM THE PANELING OF CARLISLE CATHEDRAL. 5

upon them. They are all drawn half the real size, except Plates IX. and X.
which are the full dimensions.

The two screens, as shewn in the frontispiece, and in the Plate from
the author's work on Carlisle Cathedral, may be briefly described as consisting
of a basement of draped Panels, and immediately above them a series of per-
forated Geometric Panels. Above these is a plain string, surmounted in the
former Plate by a series of smaller Panels, and in the latter by the running
border shewn in Plate XI. The upper portion of the screen is a series of
detached piers, all ornamented in one screen by flying buttresses, and in the
other a buttress on each alternate pier. Above the buttresses is a square-
headed capital, and the space between this and the upper string (ornamented
alternately over each pier with a head and leaves) is filled with tracery, the
cusps of the lower arch being ornamented with leaves.

The string is surmounted by a richly decorated parapet, with a border of
leaves connected at the top by a bead. In the centre of each parapet is a
shield, the armorial bearings of which have disappeared. The whole of the
frame- work of the mutilated screen at Carlton Hall was ornamented with the
bordering, shewn in Plate XVIII. fig. B.

DESCRIPTION OF THE PLATES.

Plate 1 1. THE specimen at the side of this Plate is the simplest as regards
the division of the Panel into sixteen squares, consisting in fact of sixteen equal
quatrefoils. The construction of Plate II. is equally simple, being composed
of the arc of a circle, whose boundary touches the points b, c, d, the centre a.
being determined by the intersection of lines perpendicular to the chords b. c.
and b. <L The trefoil is composed of equal circles within the triangle e.

Plates III. IV. V. The centres of the principal figure in these exam-
ples will be found at the angles and centre of the parallelogram, containing
two equilateral triangles, as marked on the margin of Plate III. (a)

Plate III. Draw the circle A.' and arcs A. A, and within it the two circles B.
The triangular spaces left within the figure are filled with the circles c.
The upper and lower extremities have semi-quatrefoils. The circle filling
the space which should correspond with c. is larger on account of the Panel
being made square instead of the parallelogram of a hexagon, whereby the
additional space shewn in the small diagram (b) is added to the figure.

Plate IV. This is varied by changing the two inner circles, b c. from
the width to the length of the figure. The radius of the small circle d. is
one third of the largest, as figured. This example is rather less in height
than width : the inequality mentioned in the last is consequently less apparent.
Plate V. The difference of this example, from the preceding, is in the
small circle (E.) being brought to the centre of the principal figure, instead
of the extremity, and in the introduction of another circle (D.) into the
triangular space, between the circles, A. B. c.

Plate VI. This is also a variation of the preceding example, but the
divisions of the height and width, approach nearer to a square, the parallelo-
gram of the Panel being nearly in the proportion of -£-• Produce the semicircle
A. of one half the width of the Panel, and the segments B. from the centre a,
intersecting the points, b. c.

Plate VII. The arrangement of this beautiful example, differs totally
from the preceding, and the division of height and width are perfectly equal.
Divide the square into four parts, and from figure 3 of these produce the
circle a. The distance between the boundary of this circle and the intorsec-

DESCRIPTION OF THE PLATES. 7

tion of the square, at b, gives the radius of the small circle c. These circles
being produced at the intersection of the alternate squares, the outer con-
necting arc (J.) is struck from the point g, touching the small circles at e. c.
and the intersection of the square at f.

Plate VIII. This is perfectly square, and divided in the same manner as
the preceding examples. The diagonals of each square being drawn, produce
the circle A, within four of the diagonal squares. The small circle B, of two-
thirds the diameter of the preceding, completes the outline.

Plate IX. The sub-division into small squares is here dispensed with, but
the whole subject is a repetition of each figure four times. Draw the diagonals
of the square, and from the angle of the Panel draw the quadrant A, and within
it the circle B, touching a, b, c. Divide the radius of A into three parts ;
the diagonal of the first gives the radius of the smaller circle c. Within the
quadrants the space is tilled by four equal circles D.

Plates X. and XI. are small examples, above the larger Panels in the
view of the Screen. These have been terminated by an enrichment of leaves,
a portion of which is still left.

Plate X. Draw the diagonals A. A, and within them the semicircle B. from
the centre a, on the smaller side of the parallelogram. The semicircles c are
from b b, on the longer side. The semicircle D. is a repetition of this.

Plate XI. Draw the semicircles A. A ; and from a. produce that marked
B. The radius of c. is one-sixth the length of the Panel, and that of D. one-
third the width. E. is from the figure b, touching the line D. at c.

The border in this Plate belongs to the Screen in the aisle of the Choir.
The leading lines are only repetitions of the tracery described on Plate V.

Plate XII. Archway of the Screen — Draw the semicircle A. from a, and
divide its radius into 11 parts. From figure 6, produce the quadrant j, and
from b. the semicircle K. Draw a line from the centre a. through the angle B.
The point D, equal in distance from it as B, c, is the centre of the curve E.
F. is a repetition of this upon the line G. The smaller curve H, is portion of a
semicircle touching F and c, its centre being on the boundary line of the Panel.
The upper portion of the curve is a repetition of this from the point c. e is a quad-
rant from the centre a, and the lower part or continuation f, is from the centre
(d), upon a line drawn from a, through the 12th part of the scale before named.

Plate XIII. is a large Panel upside down in the view of the Screen.
This specimen did not originally belong to it, and has been placed there to

8 DESCRIPTION OF THE PLATES.

till up a gap, occasioned by tin- destruetion of the original work. It is repre-
sented at a, tin- remainder of the Plate being a portion half the full M/<-.

Plate XIV. The Pani/nt. The great semicircle forming the leading
line of the figure is the same as described in the border of Plate XI., and tin-
remainder of the tracery i- very nearly the same as in Plate V. The outline
of the border-leaf is the diagonal of a square.

Plate XV. is a repetition of the same circle, whose centre is tin- inter-
section of each division or square. — Produce the circle A. from the centre a,
and corresponding circles from b and c; their intersection cuts off 1-lJth
from each side of A, marked B and c, and represented by the dotted line.

Plate XVI. Divide the panel into four portions, and draw the diagonal-
A. A. Within each triangle strike the circle B, and in the angles of the square
the small circles c. c. The arc D is a portion of the first circle.

Plate XVII. Draw the diagonals of the square, as A. A. Within tin-
triangle draw the circle B, and within this the four smaller circles c, the
parts represented by the dotted lines being left out in the complete figure.
Draw the circle in the angles of the square (D.) The limit of the circle E. is
determined by a perpendicular, a. dropped from the centre of the circle B.

Plate XVIII — Borders. Figure A. is in the doorway of the Choir
against the Bishop's Throne. This elegant little specimen is the repetition
of semicircles whose radius is one half, and one quarter the width of the
border; the ground-work being precisely the same as the majority of tin-
Panels — namely, four squares each way.

Fig. B. is peculiar for the leafy border on each side.
Fig. c. is the same as the subject of Plate XV. And
Fig. D. very strongly resembles the Tracery of Plate V.

Plates XIX. and XX. All that remains of these Panels is the frame-
work and ends of the tracery. — No. XIX. has sufficient to identify the de-i^n,
but No. XX. is not to be depended on for originality. They are both peculiar
from the sub-division of the Panel into four distinct parts, by the diagonal
rib of Plate X IV, and the cross-rib with the angles rounded off in Plate X X.

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THE

GEOMETEIC TRACERY

OF

BRANCEPETH CHURCH,

IX THE

COUNTY OF DUBHAM.

ILLUSTRATED BY

ROBERT WILLIAM BILLINGS.

LONDON:

PUBLISHED FOR THE AUTHOR, BY
THOMAS AND WILLIAM BOONE, 29, NEW BOND-STREET;

AND BY

GEORGE ANDREWS, SADDLER. STREET, DURHAM.

1845.

DI-UUM : ruxTU) »« r. UVMBLB JU<D ION,

INTRODUCTORY ACCOUNT

OF

THE BRANCEPETH PANELS

THE title plate furnishes a complete miniature resemblance of the whole sub-
ject set forth in the following illustrations. It would perhaps be difficult to find
in any similar production of art so many designs represented in so small a com-
pass, and at the same time exhibiting memorials of Gothic skill so full of interest,
although produced at comparatively a late period, viz., about the year 1500.
Various conjectures might easily be formed as to the original use to which the
mass of ornament here delineated was applied, but according to tradition the
prototype belonged to the ancient Rood Screen of Brancepeth Church, and was
removed to the place it now occupies over the chancel arch at the time of the
erection of the present Screen by Bishop Cosin,1 who was previously Rector of
Brancepeth.

It has undoubtedly been a portion of the crowning member of a screen or a
monument, because the three divisions are slightly canted (canopy like) and
surmounted by a foliated border.

At each end of the paneling, corresponding fragments are clearly discernible,
giving undeniable evidence that the magnitude of the original work exceeded
its present dimensions. It may, however, be considered fortunate that so much
practical knowledge relating to tracery has been bequeathed to us in the con-
struction of these remarkable specimens, and although some are marred by sin-
gularity rather than distinguished by beauty, they form in the aggregate a most
interesting collection, as they bear in a remarkable manner upon the system of

1 Bishop of Durham (1660-1672.)

construction employed in the geometric paneling in Carlisle Cathedral, which
has been completely illustrated by the author of the present volume.

Possibly we are indebted to the genius of the same individual for the analo-
gous designs of which the Church of Brancepeth and the Cathedral just named
are the depositories, or, if they are not the results of one master-mind, t lu-\
must undoubtedly be ascribed to individuals guided by the same rules of art.
Upon comparison of the histories of Carlisle and Durham, arguments are ad-
ducible that the former conjecture is a true one, because two distinguished per-
sons respectively connected with each place must have been brought into inti-
mate association by their ecclesiastical position, — we mean the reputed author
of the Carlisle tracery, Thomas Gondibour, Prior of Carlisle (1484-1507), and
Richard Bell, Prior of Durham, who was Bishop of Carlisle from 1478 to 1496 ;
and our conjecture is greatly strengthened by the fact, that most of the works,
if not all, in the churches of the diocese of Durham emanated from the digni-
taries of the Cathedral establishment in that city. Hexham Abbey, in North-
umberland, equidistant between Carlisle and Brancepeth, contains in its organ
screen some tracery which forms a remarkable connecting link between the
same class of ornament in both places, and was almost to a certainty designed
by the same hand.

But the greatest proof of the relationship of these compositions is their geo-
metric foundation, — thus each series commences with a simple elementary panel
composed of a number of quatrefoils within an equal number of squares. Pro-
ceeding from that primitive form, the centres of the curves being upon the same
foundation lines, the designs become so complicated that it is by no means easy
to decipher their construction, and some indeed, without close investigation,
might, by the complexity of their apparently fanciful intersections, be said to
have refused subjection to the regularity of linear projection, and consequently
might be placed among those produced in modern times by "rule of thumb."

With their similarity in construction and size, for the paneling in both edifices
is as nearly as possible of the same dimensions, all comparison ends. Thus
that at Carlisle is pierced, and each panel U displayed separately, between the
piers of a screen, while the tracery of Brancepeth (sunk only to the depth of a
quarter of an inch) is a mass of design merely divided by small ribs. Another
remarkable difference results from the form of the mouldings, for the leading

curves of the Carlisle specimens are well defined by an upper moulding or bead a
and the minor tracery of trefoils and quatrefoils upon a lower moulding b (see
Plate 15, fig. A).

Here the Brancepeth panels suffer by comparison, for both the leading lines
and the minor tracery are upon one moulding (see B, PL 15), and there is con-
sequently an appearance of confusion and indecision in the whole composition.
To make up, however, for this defect, the ornament as well as a portion of the
ground is richly gilded, and the remainder of the ground coloured in the man-
ner of this specimen.

The partial gilding of the ground is probably
unique, and it certainly gives an air of substance
to the tracery, which is characterised by tenuity,
and is too shallow in depth to be effective. But
gilding and painting have not saved them from
decay, for the corrosions of the worm and the
despoiling agency of time are fast working the
destruction of these reliques of antiquity.

The specimens of this collection are drawn one-
third of the actual size, excepting Plates 1 and 2,

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which are one-fourth. The height of the panels slightly exceeds their width,
but this disproportion does not mar the general design of the tracery, the frame-
work of which is supposed to be a perfect square, and, generally speaking, the
additional height contains portions of a repetition of the pattern.

Throughout the diagrams, the circles used in the formation of the designs
are marked out by dotted curves, which in all cases are omitted in the complete
pattern. We have refrained from entering into very minute details of the va-
rious lines which form a key to each pattern, because the plate itself, in all the
minor points, furnishes at once to the eye a complete linear solution, and our
intended limits would have been far exceeded had we entered into lengthy
descriptions of those parts which the graphic exposition itself renders obvious.

The comparatively recent date of the specimens now before us, and perhaps
certain questionable peculiarities or anomalies discoverable in their style, may
be liable to objection. Their real value, however, consists in the beautiful
illustration of principle which they develope, and on this account they are cer-
tainly deserving of the most attentive consideration.

6

It is satisfactory to find thai the more we examine Gothic architecture, the
more we are convinced that chance was in no possible way connected with the
linear designs of construction. The most exuberant richness of contour can,
by a careful analysis, be reduced to simple geometric rules ; and in the inves-
tigation of the laws of description which we have here endeavoured to exhibit,
it has been curious to observe how extraordinary an alteration in the general
features of such panels as have fallen under our notice is affected by a very
slight deviation in that most simple of all curves — the arc of a circle.

There are several distinct geometric species in the panels under notice;
these are —

1. Those composed of circles or their arcs, having all their centres upon the
sides of a given number of squares or their diagonals. This class comprises
the Plates figured respectively 3 to 10 inclusive, numbers 1 and 2 on Plate 1,
number 1 on Plate 2, and numbers 3 and 4 on Plate 12. In some cases the
sides of these squares and their diagonals, especially the latter, form a decided
and positive portion of the pattern (sec Plate 1, No. 2, and Plates 3 and 6).

2. Where the principal frame work is a series of circles of equal radius touch-
ing each other, three of whose centres are consequently at the angular points
of an equilateral triangle (see figure A, Plate 1). The continuous curve pro-
duced by the arcs between the points of tangency of these circles in mutual
contact is known by the term "ogee." Numbers 3 and 4 on Plate 1, No. 3 on
Plate 2, and Plate 1 1 belong to this arrangement. Or this curvilinear figure may
be more easily explained by placing two equilateral triangles on each side of a
common base, and describing a circle from each of the four vertices, with radius
equal to half the side of the triangle (see B, Plate 1). But this form of the
ogee is not invariable, because it may be, and is frequently much elongated, by
substituting isosceles triangles in the place of equilateral triangles, according to
the following construction (see Figures A and B, on Plate 3). Bisect the equal
sides of an isosceles triangle, produce the base both ways, draw through the
vertex a line parallel to the base, then bisect each half side by perpendiculars
cutting the produced base or the line parallel to the base. From the points of
intersection b or d describe arcs of circles (a c) through the angular or middle
points of the sides.

The interminable variations of which this curve is capable, are doubtless that
form known to artiste as the "line of beauty," and which is represented as such

by our great painter Hogarth. Its manifold combinations form the staple of all
flowing tracery, because it is not at all necessary that the upper and lower limbs
of the curve should be segments of circles having equal radius. From this ele-
mentary principle have resulted all the beautiful compositions of the decorated
and flamboyant styles of Gothic architecture.

3. The division of the panel into rectangular parallelograms, see numbers 2
and 4 on Plate 2.

4. Panels having their origin in the subdivision of a given circle into a num-
ber of sectors. This class embraces numbers 1 and 2 on Plate 12, and Plates
13 to 20 inclusive. Some of the specimens in this subdivision are extremely
curious, and perhaps are without their parallel in any other examples, but the
architect and antiquary attach the principal value to those formed upon the square
and the triangle, because they not only form the most elegant examples, but verify
a principle, since they are based upon the same analytical elements as examples
in various other places. Some indeed are of the same pattern, or nearly so, as
examples in the Author's " Geometric Paneling of Carlisle Cathedral" ; for
instance, compare numbers 1, 3, 4 on Plate 1, and No. 3 on Plate 2, with Plates
2, 3, and 6 of the work just named.

DESCRIPTION OF THE PLATES.

*,* The numbers attached to the ribs of the title plate correspond to those upon each particular

illustration.

Plate 1, No. 1. — Consists of the mere introduction of a circle within a square,
and within this circle a quatrefoil, or four equal circles inscribed within one (see
a a). The small circular knobs, introduced within the space lying between the
four circles in mutual contact, are unusual in this class of design.

Plate 1, No. 2. — Equally simple as the former, being quatrefoils formed within
the diagonals of a given number of equal squares. The quatrefoil varies from
the preceding, by being formed of semicircles whose diameter is equal to the
side of the square (see b).

Plate 1, No. 3. — The panel is divided thus : the width into six and the height
into seven parts. Draw the semicircles c, whose radius is one part of the width,
and then removing the centres to the point of contact of the semicircles c c,
draw the inverted semicircles d d. For the ogee which runs through the frame-
work thus formed, bisect one part of the width, represented by the line e, and
let the arc of a circle, with its centre on the line^ cut the intersections ggg.

Plate 1, No. 4. — This example is in principle the same as the preceding, the
difference being only in a change of the number of parts. It is a singular de-
monstration of the fact that a very slight difference of detail frequently consti-
tutes another design. Here the introduction of the quatrefoil, instead of the
leaf of the last panel, forms the only alteration.

Plate 2. — Numbers 2 and 4 on this plate have the whole of the divisional lines
retained on the completed panel. Both have the same transverse lines (a), and
the only difference of design is the trefoil heads of Number 2, consequent upon
the enlargement of the pattern.

Number 1 retains the alternate perpendicular divisional lines in the shape of
a stem, from which the tracery branches. The height and the width are di-
vided into six parts respectively, and each part of the height is again subdi-

9

vided into three. From 2 2 on the line b draw the semicircles a a. The frame-
work is completed by the repetition of these, and the introduction of a circle
touching the semicircles a a and the perpendicular b. The examples in Plates
7, 8, are also formed by the tracery springing from stems.

Number 3 on this plate is described with plate 11.

Plate 3. — Draw the square a, then the inscribed square b, also the diagonals
c c. The intersecting of these lines with the sides of the inscribed square are
the centres of the circles d. At e is the tracery rib of the full size.

Plate 4 has the same ground-work as the last, but the result is quite dif-
ferent, owing to the doubling of the diagonal ribs and the introduction of foliage,
which really gives it the appearance of being referable to a much earlier date
than these designs generally. Divide the diagonal into eighteen parts. The
interstices between parts 8 and 10 subdivided into three are the substance of
the two ribs and the space between these latter. The middle circle (c) is of
the same radius as the angular concentric circle b, the radius of the latter de-
pending upon the width of the rib — d d, an arc connecting the diagonal ribs, is
part of the circumference of a circle which cuts the intersections d d and touches
the diagonals of the square at e e—f, is a full size section of the rib, which has a
groove or division in the centre of its face. One-half of the rib thus divided
passes under, and the other half over the portions with which it comes in contact.
The representation of bolts at the angles of the square renders this specimen
of interpenetration exceedingly singular.

Plate 5. — Divide the diagonal of one of the squares into six parts. The curves
a 2 a and a 4 a are portions of a circle passing through three intersections, two of
which are the angular points of the square, the third being at the first diagonal
subdivision from the centre. Within the space lying between four of these arcs
describe four equal circles (b), and within the figure c two equal circles in con-
tact with the segmental arcs and each other. In this class of pattern the arc
a 2 a would generally be a quadrant, described from the centre b, and the lead-
ing figure, instead of being four arcs within a square, would be a circle, which
is the case with

Plate G — which is very nearly allied to the preceding design, although dif-
ferent to the eye. Thus there are the four circles d, correspondent to those at
b in Plate 5, although, for some unknown reason, the circles of Plate 6 are not

B

10

all of equal radius. The appearance of variation in this design is caused by the
retention of the diagonal lines, and the use of four circles e e (instead of two, as
in the preceding plate), in the space bounded by the arcs be. The facility of
producing a different design upon the same ground-work is again exempliti.il
at /on the diagram.

Plate 7 has been referred to in the description of Plate 2, as having its tra-
cery springing from a stem, which in this instance would appear on the per-
pendiculars of every fourth square necessarily used in projecting the design.
On each side of the line (or stem) g, describe the circles a a. Bisect the side
of the square on the line b, and cc will be the centres of the arcs dd, touching
the divisional line h — efste two equal circles contained within the arcs d d and
the perpendicular g, and i is a circle touching ef, and the intersection k.

Plate 8. — Here the circle a branching from the central stem is the same figure
as a in Plate 7 ; but, from the circle being of larger dimensions, more detail is
introduced within it. After forming the principal circles, draw the perpendicu-
lar gt at a distance equal to half the side of one square from /.' Then b is an arc
having its centre upon the intersection of this perpendicular with the base line.
Its radius is the extent of the line o. The arc c is an inverted repetition of b,
and d is also an arc of the same radius, having its centre on the line 1, and its
circumference cutting the intersection of the circle a and the arc c at p. From
the arc c as a centre draw the circle i, touching the arcs b d. Then k k are
two equal circles between the arcs bd, and the circle / passing through their
point of contact is of the same radius as the circle i.

Plate i). — Draw the diagonals b b, and the bisecting lines of the square c c.
Then describe the arcs e e, and from the point where these intersect the line <,
at/ for instance, describe similar arcs touching the sides of the square a. Join
the extremities of the common chords k and / by the lines m m, and the inter-
section of the chords by the angular points of an equilateral triangle (g h h),
having its vertex at g, are the centres of the arcs * t. The four equal circles
within the arcs it are determined as follows : — Taking the portion of the chord
k intercepted between the lines g h, as a common base, describe an opposite
equilateral triangle. In these two triangles describe two equal circles, and two
others of equal radius touching the last-named circles and the arcs i /, betwrrn
which they lie.

11

Plate 10. — Although inferior in elegance to many of the others is a remark-
able specimen, because it is the only one in which the principal guiding line,
that constitutes the basis of the linear developement of the design, fails to be
visible in the tracery ; we allude to the circle a inscribed within the square d.
Having drawn the diagonals b b, bisect the four radii, which consist of equal
parts of the diagonals, and with these points of bisection as centres describe the
four equal circles cccc. The formation of the tracery at the angular points
of the main figure is guided by three equal circles, two of which touch the sides
of the square a a and the circles c c. The third has its centre on the line b.

Though the result of this design is perhaps unsatisfactory, the sketch of one
quarter (see page 2), which is based on the main lines just described, proves
that the foundation is not objectionable, for the introduction of a little accessory
ornament, in which the original, excepting its central portion, is deficient, pro-
duces a model much more pleasing to the eye.

Plate 11. — Although at first sight it may not be obvious, this design is based
upon the same primary curvilinear form, namely, the ogee, which is ground-
work of numbers 3 and 4 on Plate 1. From the circles a a, draw the lines 1 1,
to the centres b b at the base of the panel, and from c c the corresponding lines
2 2 to the centres d d. These lines are the stems of the elongated trefoils
marked 3 on the panel. Form the dotted circle f, and divide it into six equal
sectors, letting two of the points of division be on the line b d. Draw the lines
through the adjacent divisions, and these are the stems of the horizontal trefoils
which complete the panel. The trefoil heads are all formed by hand, which
circumstance considerably mars the effect, which this design would have had,
if they had been geometrically drawn.

Plate 1 2. — This illustration does not belong to the paneling represented in
the title plate, being a compartment of the very interesting ancient parish chest
of Brancepeth ; yet its circular panels bear much upon our subject, and from
their simplicity form a very appropriate introduction to the portion yet remain-
ing undescribed, composed, as it is, entirely of designs based upon the subdivi-
sion of a leading or primary circle. The chest (of which a view may be seen
in Surtees's Durham) has six compartments similar in general design, but vary-
ing in the circular panels, and necessarily where the grotesque forms in the
spandrils are introduced.

12

The panel numbered 1 consists of quatrefoils. The diameter of the circle is
divided into three equal parts. The diagram No. 2 exhibits the panel repre-
sented in the elevation of the compartment. About the circle describe a square
and draw its diagonals a a. Let each side of the square be divided into four
equal parts, and describe the four circles b, equal in diameter to one of these part-.
The tangents cc drawn respectively parallel to the diagonals complete the diagram .

No. 3 consists of six equilateral triangles within a given circle and touching
its circumference, being the number produced by the intersection of two equal
equilateral triangles, as in the diagram. From the centres a strike the arc- //,
and within each triangle place a trefoil. The central hexagon is filled by a
circle inclosing a quatrefoil.

No. 4.— Within the circle o, and cutting its centre, draw the lines b bb, from
the angular points of a hexagon. Divide the horizontal diameter into six part.-,
and from parts 2 and 4 draw the lines a a parallel to b. These form the width
of the hexagonal cross with trefoil heads. At B is a full-sized section of the rib.

Plate 13. — This design appears to have resulted from the stellated model de-
picted at one corner of the panel — a model, we were wont to describe in the
following manner, viz., by taking any point (c) in the circle a and drawing an
arc b b with the same radius, — then from the points where this intersects the
circumference, drawing similar and equal arcs which form the segmental rays —
of a thickness (e) thus determined. But the construction of the example under
consideration is different, for each arc only extends to the centre of the given
circle, and each ray has a distinct and separate centre lying within the circle.
The width of the radiating branch is consequently increased. The centres of
the curves are, in fact, upon the sides of two equal intersecting equilateral tri-
angles, within the circle. Divide the radius of the circle (as in the figure) into
six equal parts and from each vertex of the triangles with radius equal to one
of these parts cut the sides in two points, as at 7 7- These points are the
centres of the arcs which form the stellar rays.

Plate 14. — The outer annulus of this design is the mere sectorial division of
a circle into 48 parts. Place in each sector a semicircle (a) touching the inter-
cepted arc and the radii. Two arcs e andy^ from the centres b and d on the
circumference of the outer circle, form the internal pointed terminations, and

13

the intersection of these arcs also fixes the radius of the inner concentric circle,
in which the number of divisions is reduced to sixteen.

Plate 15 — In principle is the same as the preceding. Divide the circle a
into sixteen sectors, and in each place a semicircle b b as in the last example.
Describe the concentric circle c passing through the centres of the circles b.
Taking the intersection of this circle with the sixteen sectorial radii as centres
describe circles touching every pair of radii, observing that three other radii
always interpose between them. The intersection of two of these circles, having
their centres at d d, gives the inner point or arch of the trefoil at e, and also
fixes the size of the inner concentric circle.

Plate 16. — Divide the circle into 20 sectorial parts. From the division num-
bered 1 draw a line to 9, then from 9 to 17> and so on round the figure, always
leaving an interval of eight parts until the chords terminate at the starting point
(from 15 to 1). Their intersection, for instance of the lines 9 and 11 at a, de-
termines the size of the secondary concentric circle which contains eleven tre-
foil heads, whose size is fixed by the circles / /. From the point 7 with radius
equal to three circumferential divisions describe the arc d, and from the point 3
describe a corresponding arc from 6. Their junction at/" gives the size of the
inner circle. The small diagram at the side of the plate represents the six
leaved ornament of the centre. Within the circle describe a hexagon, draw
radii to each of the angular points, and upon each radius, and the same side of
it describe a semicircle as b. The radius of the arc d, forming the second side
of each leaf, is equal to four-thirds of the preceding.

Plate 17 has the appearance of being complex, but its construction is very
simple. Divide the circle into twelve equal sectorial parts. Within the circle
d draw three equidistant concentric circles indicated respectively a b c. Upon
each of the sectorial radii and on the same side of it draw a semicircle as e andy!
From the centre 7c, in the circumference of the second circle c, describe the arc
g of equal radius to the semicircles e f. Describe the accessory concentric
circle I, and upon it fix the centre of the arc h, touching one of the semicircles
e and passing through the intersection of the arcs f and g. This arc is also of
the same radius as the preceding. There is another panel, placed next to num-
ber 1 on the title plate, which is almost a fac-simile of this. It differs principally
in having the six leaved central ornament of the preceding example.

14

1'late 18 bears a close analogy to the last spot -mien. The circle being divid-
ed into sixteen equal sectorial parts, eight of the radii represent the central
ribs of the pattern. De-crihe eight circles touching every pair of radii that
have three other radii lying between them, as for instance the circle touching
the radii 1 and 5, the arc a being only necessary to the design. Describe the
circle b passing through the centres of the above-named eight, and from t he
centre^on the radius marked 14 describe the arc cutting the radius 11. Draw
another accessory equidistant circle </, and upon it fix the centre of the arc e,
touching two of the eight circles first named.

Plate 19. — This singular panel has its origin in the division of a circle into
thirty-four equal sectors, and its radius into five, marked respectively abode.
From the point 1 on the circle c draw a line through the intersection 7 to tin;
circumference of the outer circle, and then from point 2 draw a corresponding
line through the intersection 8. The repetition of this process upon the whole
number of thirty-four lines completes the figure in the outer ring. The inner
lines, which are sixteen in number, run exactly in an opposite direction to the
preceding. Draw a line from 14 to 27, then from 16 to 29. and so on, until
the number is completed. The central figure made by the intersection of these
chords determines the size of the circle k.

Plate 20. — Divide the breadth of the panel into five equal parts and draw
the bisecting perpendicular. Then from the point 2 at the top of the panel,
with distance equal to four-fifths of the whole width, cut the divisional line 4
in A, which is the centre of the arc 1. The inverted arcs 4 4 are of the same
radius. Draw the horizontal bisecting line C, then the bisecting line 2 5 be-
tween the arcs 1 4. Taking their point of intersection as the centre of the
figure, inscribe within each half the circles a a, touching the intersection and
the area 1 4. From the centres of the arcs 4 4, marked 2?, draw the lines B D E.
Then from D D and E describe the equal circles 5, C, 7. Then describe the
circle b touching the circles 5 6, the arc 4, and the perpendicular 5 D. The
circumference of the small circle c passes through the centre of the circle b,
and the arcs d d are repetitions of the circles 5 6.

I

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