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CENTRING FOR THE BALLOCHMYLE V.XAOIICT

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B LA OKIE § SON:

GLASGOW, EDINBURGH. LONDON & NEW-YORK

THE

CARPENTER AND JOINER’S

ASSISTANT.

BEING A COMPREHENSIVE TREATISE

ON THE

SELECTION, PREPARATION, AND STRENGTH OF MATERIALS, AND
THE MECHANICAL PRINCIPLES OF FRAMING,

WITH THEIR APPLICATION IN CARPENTRY. JOINERY, AND HAND - RAILING;

ALSO, A COURSE OF INSTRUCTION IN

PRACTICAL GEOMETRY, GEOMETRICAL LINES, DRAWING, PROJECTION, AND PERSPECTIVE; AND AN
ILLUSTRATED GLOSSARY OE TERMS USED IN ARCHITECTURE AND BUILDING.

JAMES NEWLANDS,

BOROUGH ENGINEER OP LIVERPOOL.

ILLUSTRATED BY

AN EXTENSIVE SERIES OF PLATES AND MANY HUNDRED ENGRAVINGS ON WOOD.

BLACKIE AND SON:

FREDERICK STREET, GLASGOW; SOUTH COLLEGE STREET, EDINBURGH;

AND WARWICK SQUARE, LONDON.

MDCCCLX.

GLASGOW :

w. O. BLACKIE AND CO , PRINTERS,
VILLAFIELD.

PREFACE.

The Framing of Timber for structural purposes may be regarded both as a mechanical and as a
liberal art. As a mechanical art, it embraces the knowledge of the various ways of executing different
works, of the processes of fashioning timber, of the tools which have to be used, and the manner of
handling them. As a liberal art, it includes a knowledge of geometry, of the principles of mechanics, of
the nature and strength of the material, and its behaviour under the strains to which it is subjected.

On all these branches of knowledge, there exist justly esteemed Treatises in our own and other
languages. The labours of Barlow, Emy, Jousse, llobison, Rondelet, Nicholson, Tredgold, and
many others, are devoted to elucidating the principles of the arts of Carpentry and Joinery; and there
are also many useful compilations, foremost among them that of Krafft, the object of which is to
present practical examples of the application of these principles. The works of these authors,
however, are either too costly to be within the reach of the workman, or the subject is treated in a
manner which presupposes greater knowledge of mathematical science than he is likely to possess,
or they are written in a foreign language. Further, the information which he seeks is scattered
through many separate treatises, none of which singly contains all that he requires to know.

The object of the present Publication is to provide, in a compendious form and in plain language,
a Complete and Practical Course of Instruction in the Principles of Carpentry and Joinery, with descrip¬
tions and representations of a selection of works actually executed, to illustrate the state of these arts
at the present time, and to serve as guides in preparing new designs.

The Carpenter and Joiner’s Assistant was projected by Mr. John White, author of Rural
Architecture, who prepared the greater number of the Drawings for the Plates, but died before he could
supply any portion of the Text. The task, therefore, of completing the series of Drawings and preparing
the Text devolved on the present Editor, who, while availing himself of Mr. White’s labours, has
endeavoured to expand the work into a systematic and comprehensive Treatise.

With this view the work is divided into eight parts. The First Part is devoted to Practical Geometry,
teaching various methods of constructing the angles and the rectilineal and curvilinear figures required in
the daily practice of the draughtsman. The Second Part teaches the nature and use of the various kinds
of Drawing Instruments. The Third Part is devoted to Stereography, comprehending the projection of
lines, surfaces, and solids, and the application of this projection to the problems of Descriptive Carpentry
in groins, pendentives, domes, niches, angle-brackets, roofs, hip-roofs, tfcc. These three parts thus form
a complete Treatise on Lines, a knowledge of which is an essential preliminary to the study of Carpentry
and Joinery. The Fourth Part treats of the physiology, growth, development, and diseases of Timber
Trees; of the mode of felling, squaring, and preparing timber for use, and of increasing its durability. It
includes a description of the nature, properties, and uses of the various timber trees which in this country

PREFACE.

are employed by the Carpenter and Joiner; and it elucidates so much of the principles of the composition
and resolution of forces, and of the strength and strain of materials, as belongs to Theoretical Carpentry.
In the j Fifth Part are presented examples of the construction of timber roofs, domes, and spires; of
the framing of timber, the formation of joints, straps, truss girders, floors, partitions, timber houses,
bridges, centres, and field, park, and dock gates. The Sixth Part is devoted to the illustration of Joinery;
comprehending the mouldings used, the formation of joints, gluing up of columns, &c., framing and
finishing of doors, windows, and skylights, and the various methods of hinging. The Seventh Part treats of
Stairs, Staircases and Handrailing, and in the latter, which is contributed by Mr. David Mayer, of Chelten¬
ham, the author developes simple methods of getting out the wreath by one bevel and squared ordinates,
the advantages of which he has tested in along course of practice. The Eighth Part advances the student
in his knowledge of Drawing, by instruction in the Projections of Shadows, in the method of making
Finished Drawings, and in Perspective and Isometrical Projection. To these is added an Index and
Illustrated Glossary of the Terms used in Architecture and Building.

The number and character of the Illustrations form a prominent feature of the present work. They
consist of above Eight Hundred Geometric, Constructive, and Descriptive Figures interspersed through¬
out the text, and One Hundred and Fifteen Plates, containing upwards of One Thousand Figures. The
Cuts and Plates combined, comprise, it is believed, a larger number of Illustrations than has hitherto
been embodied in any similar treatise published in this country; and by incorporating so large a propor-
tion of them in the text, in place of greatly increasing the number of separate Plates, the double advantage
to the purchaser has been gained of ready and convenient reference from the text to the figures, and of a
considerable modification in his favour in the total cost of the work.

It is impossible in a work like this to quote all the sources of information. Frequent references to
authoiities aie given in the text; but in addition to these, it ought to be stated that the sections on
Projection and Perspective are based on J. B. Cloquet’s Nouveau Traite Elementaire de Perspective.

The Editor has endeavoured to render the Work throughout essentially practical in its chai*acter,
elucidating the principles and rules not by lengthy demonstrations, but by showing their application in
frequent examples.

Liverpool, May, I860.

TABLE OF CONTENTS.

PART FIRST.

PRACTICAL GEOMETRY.

Page

Different Branches of Geometry .... 1

General Terms Used in Geometry. 1

Definitions— Point—Lines—Angles—Plane Figures—

Solids, &c. ......... 2

Construction of Angles, Rectilineal Figures, &c.—

Problems I. to LIV. .5

Construction of Circles, Circular Figures, &c.—

Problems LY. to LXXXIY.1G

Of the Ellipse, Parabola, and Hyperbola—

The Ellipse —Problems LXXXY. to XCYI. . . 22

The Parabola— Problems XCVII. to XCIX. . . 26

The Hyperbola —Problem C.27

Construction of Gothic Arches—

The Equilateral Arch—The Lancet Arch—The Drop
Arch—The Four-centred Arch—The Ogee Arch . 28

PART SECOND.

CONSTRUCTION AND USE OF DRAWING
INSTRUMENTS.

Compasses —Dividers—Hair Dividers—Spring Compasses . 31

Compasses with Moveable Legs.32

Bow Compasses—Directors, or Triangular Compasses—

Proportional Compasses. 33

Beam Compasses—Tubular Compasses—Portable or Turn-

in Compasses.34

Plain Scales — Simply divided Scales — Diagonal Scale—

Line of Chords—The Plain Protractor .... 35

Double Scales —The Sector—Plain Scales on the Sector—
Sectoral Double Scales—The Line of Lines—The Line of

PAGB

Chords—The Line of Polygons—The Line of Secants—The
Line of Sines—The Line of Tangents • ... 36

j Logarithmic Lines—

The Line of Numbers—The Line of Sines—The Line of
Tangents ..40

I Protractors and other Instruments—

Parallel Ruler—Drawing Pens—Pricker . . . .41

Drawing Paper—Tracing Paper—Drawing Boards . 42

T-Square—Straight Edges and Triangles ... 43

Sweeps and Variable Curves—Pencils—Pins ... 44

General Remarks on Drawing—Management of the Instru¬
ments . ... 45

PART THIRD.

STEREOGRAPHY—DESCRIPTIVE CARPENTRY.

Projection —Definition of.46

Projection of Points, Lines, and Planes ... 47

Projection of Solids .52

The Tetrahedron—The Cube.52

The Octahedron—The Dodecahedron .... 54

The Icosahedron—Manner of inscribing these five Solids .

in the same sphere.56

The Three Curved Bodies—The Cylinder, the Cone, the

Sphere—

Projections of the Cylinder.57

Sections of the Cylinder by a Plane .... 58

Projections of the Cone . ..58

Sections of the Cone by a Plane.59

Section of the Sphere by a Plane.60

Tangent Planes to Curved Surfaces—

Tangent Plane to a Cylinder .60

Tangent Plane to a Cone .61

Tangent Plane to a Sphere ..61

TABLE OF

Page

Intersection of Curved Surfaces—

Intersections of Cylinders .....

Intersection of a Sphere and a Cylinder ...

Intersections of Cones, ..

Intersection of a Cylinder by a Scalene Cone . . . 66

Of Helices.

Manner of Taking Dimensions.

Sections of Solids.

Sections of a Cone—of a Cuneoid—of a Cylinder—of a

Sphere.

Sections of an Ellipsoid—of a Cylindric King—of a Pyra¬
mid, &c. ^

Coverings of Solids—

Regular Polyhedrons. 119

Development of the Coverings of Prisms .... 70

Development of Cylinders ...... 71

Development of Eight and Oblique Cones . . .71

Development of the Oblique Cone ..... 72

Development of Solids whose Surface is of Double Cur¬
vature . .... 72

DESCRIPTIVE CARPENTRY.

Groins—D efinition of, and Terms Used . . . . 76

Rectangular Groined Vault—Gothic Groin ... 77

Welsh, or Under-pitched Groin—Groins on a Circular Plan

—Pan Tracery, &c.78

Pendentives—D efinition of.80

Ceiling of a Square Room Coved with Spherical Penden¬
tives, &c. ......... 80

An Elliptical Domical Pendentive Roof, &c. ... 81

Domes—D efinition of ....... 82

Rectangular Oblong Surbased Dome—Octagonal Surbased

Dome, &c. . . ....... 82

Gothic Vault—Spherical Vault—Cylindrical Vault, &c. 83

Niches.83

Spherical Niches on Different Plans.83

Elliptical Niches—Octagonal and Semicircular Niches . 84

Angle Brackets.85

Forms of Roofs.85

Hip Roofs.91

CONTENTS.

Page

102

Bending of Timber ....

Seasoning of Timber, and Means Employed to Increase

^ ... 104

its Durability.

Insects Injurious to, and Destructive of Timber . . 10o

Preservation of Wood by Impregnating it with Chemical

Solutions.

Kyanizing—Margary’s Process—Sir William Burnetts

Process—Payne’s Process, &c. 106

Protection of Timber against Fire. 108

DESCRIPTIONS OF WOODS.

Hard and Soft Woods— The Oak, various kinds of .

The Chestnut, the Elm, different species of

The Walnut—The Beech—The Ash ....

The Teak—The Green-heart—The Poplar .

The Alder—The Birch—The Hornbeam—The Maple .
The Sycamore—The Lime Tree-The Oriental Plane
The American or Western Plane . . . •

The Willow—The Acacia—The Horse Chestnut
The Pear Tree—The Apple Tree—The Hawthorn .
The Bos—Mahogany—Sabicu.

Resinous Woods.

The Great Pine Shoot of Alnpach.

The Pine, varieties of, &c. ......

The Cedar—The Yew

109

110
111
112
113

113

114
114

114

115

116
116
119

120

THEORETICAL CARPENTRY.

Resolution and Composition of Forces
Strength and Strain of Materials .... 123

Resistance of Timber to Tension.12-1

Experiments by Musehenbroek, Buffon, Barlow, Bevau,

and others.124-130

Resistance of Timber to Compression, in the Direction of

the Length of its Fibres . . . . • • 124

Resistance of Timber to Transverse Strain . . . 126

Summary of Rules 130

Table of the Properties of Timber.133

PART FOURTH.

KNOWLEDGE OF WOODS —THEORETICAL
CARPENTRY.

Physiological Notions of Woods.93

Cultivation of Trees..

Diseases of Trees..

Timbers Fit for the Carpenter ..... 97

Felling of Timber..

Squaring of Timber . qq

Management of Timber after it is Cut .... 100

PART FIFTH

PRACTICAL CARPENTRY.

Roofs, Classification of.134

Examples of the Construction of Roofs—

Couple Roofs—Roofs with Framed Principals—Hammer
Beam Roofs—Roofs with Curved Principals . . 136

Mr. Tredgold’s Rules for Strengths and Proportions of

Parts—

In a King-post Roof of Pine Timber .... 137
In a Queen-post Roof.137

Descriptions of Various Roofs .138

Mansard Roofs ........ 140

Colonel Emy’s System of Construction . . . .141

TABLE OF CONTENTS.

Page

De Lorme’s Mode of Constructing Eoofs . . . 144

Gothic Eoofs.145

Conical Eoofs ......... 145

Domical Eoofs ......... 145

Timber Steeples and Spires.145

Framing — Joints—Straps 146

Mortises—Joggles, &c.—Scarfing—Fishing . . . 147

Lengthening Beams, &c. ....... 148

Dovetailing, Halving, &c. ...... 149

Trussed Girders or Beams .149

Experiments of Messieurs Lasnier and Albony, and others 149
Girder of M. Laves, ........ 149

Floors —Bridging-joist or Single-joisted Floors . . 150

Double Floors, or Floors with Bridging-joists . . . 151

Framed Floors . . . . . . . . 151

Variations in the Modes of Constructing Floors . . 151

French Floors ........ 152

Combination of Timbers of Small Scantling, to Form Floors

of Large Span without Intermediate Support . . 153

Wall Plates—Trimmers and Trimming-joists—Binding-

joists—Girders—Ceiling-joists.154

Eules for Calculating the Strength of the Component Parts

of Floors and Ceilings, . . .... 154

Timber Partitions.155

Timber Houses.156

Bridges—T he Principles of their Construction . . .158

Essential Component Parts of a Timber Bridge . . 159

Method of determining the Strain on and the Dimensions

of the Chords.160

Diagonal Braces and Knee-braces — Floor Beams and

Timber Arches ..161

Classification of Bridges.161

American Bridges . . . . . . . . 165

Haupt’s Analysis of Strains upon Sherman’s Creek Bridge 166

Centres—T heir different Species and Modes of Construction . 171
On removing or striking Centres.175

Gates—E lementary Form, and varieties of . . . 176

Park and Entrance Gates.177

Dock Gates.177

PART SIXTH.

JOINERY.

Mouldings—

Grecian and Eoman versions of Classic Mouldings . . 178

Methods of describing Grecian and Eoman Mouldings . 179

o o

Gothic Mouldings. 180

Baking Mouldings ..181

Methods of Enlarging and Diminishing Mouldings . .181

Joinery— Definition of, &c..182

Joints —Various Forms of.182

Gluing up Columns—Diminution of Columns . . 184

Moulding . . ...... 184

Page

Framing ......... 185

Floors—-

Skirting.185

The Operation of Scribing Described . . . . 186

Doors—

Framed or Bound Doors.186

Double Margined Doors ..186

Jib and Pew Doors.187

Architraves ......... 187

Windows and Finishings of Windows—

Hinged or French Sashes—Suspended Sashes, &c. . .187

Shutters.188

Circular Window .189

Skylights—

Skylight with Curved Bars—Irregular Octagonal Skylight 189

Elliptical Domical Skylight—Octagonal Skylight, &c. . 190

Pulpit, with Acoustical Canopy.190

Hinging . . 190

Varieties of Hinges, and modes of applying them . .' 191

Labour-Saving Machines—

Sketch of the History of Labour-Saving Machines . . 191

American Saw-bench .. .192

Furness’ Planing Machine ...... 193

Furness’ Tenoning Machine.193

Furness’ Mortising Machine ..194

PART SEVENTH.

STAIRS AND HANDRAILING.

Stairs—I ntroductory—Elementary Forms of ... 195

Definitions of Terms used in Stair-building . . . 196

Method of Setting out Stairs.197

Relative Proportion of Treads and Risers . . . 197

Plans of Stairs.198

Newel Stairs—Geometrical Stairs—Wellhole Stairs . 198

Formation of Carriages for Elliptical Stairs, &c. . . 199

Method of Scribing the Skirting.200

Method of Gluing up Strings.200

Diminishing and Enlarging Brackets .... 201

Handrailing—

Definitions of Terms Used in Handrailing . . . 201

Construction of the Falling Mould .... 201

The Section of a Cylinder.202

Mr. Nicholson’s Method contrasted with the Method of

the Author . ..203

Face Moulds and Falling Moulds for Rails . . . 204

Falling Moulds and Face Moulds for Scrolls . . . 205

Sections of Handrails ....... 207

To Form the Section of the Mitre Cap .... 207

To Draw the Swan Neck at the Top of a Rail . . 207

To Form the Knee at the Bottom Newel .... 207

Methods of Describing Scrolls.207

TABLE OF CONTENTS.

PART EIGHTH.

PROJECTION OF SHADOWS—PERSPECTIVE
ISOMETRICAL PROJECTION.

Projection of Shadows—

Properties of Light—The Cone of Rays, &c.

Light and Shade—Forms of Cast Shadows, &c.

Projections of the Shadow of a Straight Line on Horizontal

and Inclined Planes.

Shadows Projected by Rays of Light which are Parallel

among themselves.

Projection of the Solar Ray considered ....
Shadows cast by a Straight Line upon a Vertical Plane and

Curved Surfaces.

Shadow cast by a Circle upon Horizontal and Vertical

Planes.

Shadow of a Circle cast upon Two Planes, &c. .

Shadow cast by a Cylinder under various conditions
Shadow cast in the Interior of a Concave Cylindrical

Surface .

Shadow of a Cone cast upon a Horizontal Plane

Shadow cast in the Concave Interior of a Cone

The Boundaries of Shade on a Sphere, and its Shadow cast

on a Horizontal Plane.

The Shadow cast in the Concave Interior of a Hemisphere .

The Shadow cast in a Niche.

Shadow cast by a Ring, the Exterior Form of which is a

Torus.

The Shadow of a Regular Hexagonal Pyramid cast upon

both Planes of Projection .

The Shadow of a Hexagonal Prism cast upon both Planes

of Projection.

The Limit of Shade on a Cylinder, and its Shadow cast
upon the Two Planes of Projection ....

Page

The Line of Shade in a Cone, and its Shadow cast upon

both Planes of Projection.222

The Shadow cast by a Cone upon a Sphere . . . 223

To determine the Shadow of a Concave surface of Re¬
volution .223

Methods of Shading—

Surfaces in the Light and Surfaces in the Shade . 224

Shading hy Flat Tints ....... 224

Shading by Softened Tints.225

Elaboration of Shading and Shadows .... 225

Perspective—I ntroduction—Elementary Illustrations . 227

Perspective Planes. 228

Point of View, Station Point, &c.. 223

To Find the Perspective of Points and Lines . . 229

To Draw a Square in Perspective.231

To Draw a Cube in Perspective.232

The Principles of Perspective applied .... 233
To Draw a Pavement of Squares in Perspective . . 235

To Draw a Circle in Perspective.236

Perspective of Solids—Tetrahedrons—Cubes—Cylinders 237
Parallel and Oblique Perspective considered . . . 239

To Draw a Sphere in Perspective .... 239

Practical Examples of Perspective Drawing applied to

Architecture, &c..240

Cross, Tower, and Spire.241

A Series of Arches in Perspective, &c.242

A Tuscan Gateway in Perspective ..... 242

A Turkish Bath in Perspective ..... 243
Gothic Spire in Perspective.243

Isometric Projection—

Projection of a Cube.243

Projection of the Combination of the Cube and Parallelo-

pipedon.' . . 244

Projections of a Pyramid, Octagon, Hexagon, Pentagon, &c. 245
Mr. Nicholson’s Table of the Isometric Radius, Semi-axis
Minor, and Semi-axis Major of Ellipses . . . 246

Page

209

210

211

212

213

214

215

216

218

219

220

221

222

THE

CARPENTER AND JOINER’S

ASSISTANT.

PART FIRST.

PRACTICAL GEOMETRY.

GEOMETRY is that branch of mathematical science which
demonstrates the properties and relative magnitudes of
extended things ; that is, of lines, surfaces, and solids.
It also teaches the drawing of lines and angles, and the
construction of all right-lined and curvilineal surfaces
and solids; that is, of figures which have length, or
which have length and breadth, or length, breadth, and
thickness.

Geometry is divided into different branches or depart¬
ments, as Elementary and Higher Geometry. Also into
Theoretical and Practical Geometry.

Elementary Geometry treats of the properties and mag¬
nitudes of straight lines, of the circle, and of circular
lines, and figures formed of such lines; and may thus be
considered either as theoretical or practical.

The Higher Geometry treats of the construction and
relative magnitudes of solids, of the properties of the
sphere, and of the higher orders of curves.

Theoretical Geometry comprehends the theory or spe¬
culative part of the science, and demonstrates the relative
positions and properties of lines, as well as of the various
figures which are formed by them; evincing the truth or
discovering the fallacy on which they are constructed,
by means of exact reasoning from established principles
laid down as axioms. In this manner, any geometrical
proposition can be solved without the aid of compasses
or any other instrument. To the architect or mechanic
this serves as the groundwork or basis for the practical
part of the science.

Practical Geometry, as the term implies, is particularly
adapted to practical purposes. Although it is from the
application of rules derived from theoretical evidence
that a geometrical problem can be solved by means of
diagrams only, yet the practical system has been brought
to such a degree of simplicity, that a person possessed of
ordinary capacity may be able, by perseverance—even
without comprehending the theory—to acquire a con¬
siderable knowledge of the science, independently of any
assistance from a teacher. Nevertheless, a proper under¬
standing of the primary reasoning on which the rules are
founded will render the study much more interesting, as
well as more satisfactory. Hence those who wish to

obtain a proficient knowledge of Practical Geometry will
be greatly benefited by an attentive study of Euclid's
Elements, as the subjects selected for the following course
are only such as are peculiarly applicable to mechanical
purposes. Being chiefly intended for the instruction of
architects, engineers, and, more particularly, uninformed
mechanics, all speculative and abstruse propositions are
studiously avoided.

GENERAL TERMS USED IN GEOMETRY.

1. A Definition is a concise description or explanation
of the properties of any term or object. To define any¬
thing is to explain its nature or mark its limits.

2. An Axiom is a statement of some fact, so self-
evident that no process of reasoning or demonstration
can make it plainer. It is an established principle, ad¬
mitting of no refutation.

3. A Postulate is a position supposed or assumed to be
practicable; or it is a demand that certain simple opera¬
tions may be performed. As, for example, 1st, that a
straight line may be drawn from any one point to any
other point; 2d, that a line may be produced, that is,
continued or lengthened out at pleasure to any extent;
and, 3d, that a circle may be described from any
centre, and with any radius, or at any distance from
that centre.

4. A Theorem is a statement of some truth, or class of
truths, to be demonstrated by a process of reasoning
deduced from facts already proved by previous theorems
or axioms, the truth of which is self-evident.

5. A Problem is something proposed to be done, as the
construction of a figure, or the solution of a question.

G. A Lemma is a proposition assumed in order to
simplify the demonstratfon of a succeeding proposition.
As lemmas rather interrupt the connection of a subject,
they should never be introduced except when they are
absolutely necessary.

7. A Proposition is a common term for a theorem,
problem, or lemma.

PRACTICAL CARPENTRY AND JOINERY.

8. A Corollary is a consequence which results irre¬
sistibly from the doctrine of a preceding proposition.

9. A Scholium is an explanatory observation or note
added to extend or elucidate some preceding doctrine.

10. A Demonstration is the highest degree of evidence,
being founded upon previously established facts, so as to
convince the inquirer beyond all doubt of the certainty
of the truth propounded.

11. A Direct Demonstration is a regular chain of
reasoning from the premises laid down, or a deduction of
one truth from another, till the proposition advanced is
clearly established.

12 An Indirect Demonstration proves the truth of
any doctrine, by showing that some inconsistency would
necessarily be involved in the supposition of its being
false.

DEFINITIONS.

1. A Point has position but not magnitude. Practi¬
cally, it is represented by the smallest visible mark or dot,
but geometrically understood, it occupies no space. The
extremities or ends of lines are points; and when two
or more lines cross one another, the places that mark
their intersections are also points.

2. A Line has length, without breadth or thickness,
and, consequently, a true geometrical line cannot be
exhibited; for however finely a line may be drawn, it
will always occupy a certain extent of space.

3. A Superficies or Surface has length and breadth,
but no thickness. For instance, a shadow gives a very
good representation of a superficies: its length and
breadth can be measured; but it has no depth or sub¬
stance. The quantity of space contained in any plane
surface is called its area.

4. A Plane Superficies is a flat surface, which will
coincide with a straight line in every direction.

5. A Curved Superficies is an uneven surface, or such
as will not coincide with a straight line in any direction.
By the term surface is generally understood the outside
of any body or object; as, for instance, the exterior of a
brick or stone, the boundaries of which are represented
by lines, either straight or curved, according to the form
of the object. We must always bear in mind, however,
that the lines thus bounding the figure occupy no part of
the surface; hence the lines or points traced or marked
on any body or surface, are merely symbols of the true
geometrical lines or points.

6. A Solid is anything which has length, breadth, and
thickness ; consequently, the term may be applied to any
visible object containing substance : but, practically, it is
understood to signify the solid contents or measurement
contained within the different surfaces of which any
body is formed.

7. Lines may be drawn in any direction, and are
termed straight, curved, mixed, concave, or convex lines,
according as they correspond ’to the following defini¬
tions.

8. A Straight Line is one that lies in the Fi s- 1 -

same direction between its extremities, and A B

is, of course, the shortest distance between two points,
as from A to B, Fig. 1.

9. A Curved Line is such that it does not lie in a
straight direction between its extremities, but is con¬
tinually changing by inflection. It may be either regu¬
lar, as A, or irregular, as B, Fig. 2.

Fig. 2. Fig- 3-

10. A Mixed or Compound Line is composed of
straight and curved lines, connected in any form, as A,
Fig. 3.

11. A Concave or Convex Line (Fig. 4), is such that it

Fig. 4. Fig. 6. Fig. A

cannot be cut by a straight line in more than two points;
the concave or hollow side is turned towards the straight
line, while the convex or swelling side looks away from
it. For instance, the inside of a basin is concave—the
outside of a ball is convex.

12. Parallel Straight Lines have no inclination, but
are everywhere at an equal distance from each other;
consequently they can never meet, though produced or
continued to infinity in either or both directions. Paral¬
lel lines may be either straight or curved (Fig. 5), pro¬
vided they are equally distant from each other through¬
out their extension.

13. Oblique or Converging Lines (Fig. 6), are straight
lines, which, if continued, being in the same plane, change
their distance so as to meet or intersect each other.

14. A Plane Figure, Scheme, or Diagram, is the
lineal representation of any object on a plane surface.
If it is bounded by straight lines, it is called a recti¬
lineal figure; and if by curved lines, a curvilineal figure.

15. An Angle is formed by the in- 7 _ a

clination of two lines meeting in a
point: the lines thus forming the angle ^
are called the sides; and the point where R
the lines meet is called the vertex or
angular point.

When an angle is expressed by three letters, as ABC,
Fig. 7, the middle letter B should always denote the an¬
gular point : where there is only one
angle, it may be expressed more con¬
cisely by a letter placed at the an¬
gular point only, as the angle at A,

Fig. 8.

16. The quantity of an angle is estimated by the arc
of any circle contained between the two sides or lines
forming the angle ; the junction of the two lines, or
vertex of the angle, being the centre from which the arc
is described. As the circumferences of all circles are
proportional to their diameters, the arcs of similar sectors
also bear the same proportion to their respective circum¬
ferences ; and, consequently, are proportional to their
diameters, and, of course, also to their radii or semi¬
diameters. Hence, the proportion which the arc of any
circle bears to the circumference of that circle, determines

i the magnitude of the angle. From this it is evident,

GEOMETRY—DEFINITIONS.

that the quantity or magnitude of angles does not depend
upon the length of the sides or radii forming them, but
wholly upon the number of degrees contained in the arc
cut from the circumference of the circle by the opening
of these lines. The circumference of every circle is
divided by mathematicians into 360 equal parts, called
degrees ; each degree being again subdivided into 60
equal parts, called minutes, and each minute into 60 equal
parts, called seconds. Hence it follows, that the arc of a
quarter circle or quadrant includes 90 degrees, that is, one-
fourth part of 360 degrees. By dividing a quarter circle,
that is, the portion of the circumference of any circle con¬
tained between two radii forming a right angle, into 90
equal parts, or, as shown in
Fig. 9, into nine equal parts of
10 degrees each, then draw¬
ing straight lines from the
centre through each point of
division in the arc, the right
angle will be divided into
nine equal angles, each con¬
taining 10 degrees. Thus,
suppose B c the horizontal
line, and A B the perpendicular ascending from it, any
line drawn from B —the centre from which the arc is
described—to any point in its circumference, determines
the degree of inclination or angle formed between it and
the horizontal line BC. Thus a line from the centre B
(Fig. 9), to the tenth degree, separates an angle of 10
degrees, and so on. In this manner the various slopes or
inclinations of angles are defined.

17. A Right Angle is produced either by one straight
line standing upon another, so as to make the adjacent
angles equal (Fig. 10), or by the intersection of two
straight lines, so as to make all the four angles equal
to one another (Fig. 11).

18. An Acute Angle is less than a right angle, or less
than 90 degrees, as the
angle ABC, Fig. 12.

19. An Obtuse Angle
is greater than a right
angle, or more than 90
degrees, as F c G, Fig. 13.

The number of degrees
by which an acute angle is less than 90 degrees, is called
the complement of the angle. Also, the difference be¬
tween an obtuse angle and a semicircle, or 180 degrees,
is called the supplement of that angle.

Thus, CBD is the complement of the acute angle ABC,
in Fig. 12; and G c E is the supplement of the obtuse
angle gcf, in Fig. 13.

20. Plane Figures are bounded by straight lines, and
are named according to the number of sides or angles
which they contain. Thus, the space included within

three straight lines, and forming three angles, is called a
trilateral figure or triangle.

21. A Right-Angled Triangle has one right angle:
the sides forming the right angle are called the base and
perpendicular; and the side opposite the Kg. n. a
right angle is named the hypotenuse.

Thus, in the right-angled triangle ABC
(Fig. 14), BC is the base, ab the per¬
pendicular, and A c the hypotenuse.

The hypotenuse, or longest side of a
right-angled triangle, may also form the
base or underline. In that case, the other two sides are
called the legs of the triangle.

22. An Equilateral Triangle is that whose three sides
are equal, as in Fig. 15.

23. An Isosceles Triangle has only two sides equal, as
Fig. 16.

24. A Scalene Triangle is that whose three sides are
all unequal, as shown in Fig. 17.

25. An Acute-Angled Triangle has all its angles acute,
as those in Figs. 15 and 16.

26. An Obtuse-Angled Triangle has one of its angles
obtuse, as in Fig. 17- It is obvious from Fig. 1.7 that a
triangle cannot contain more than one obtuse angle.

The triangle is one of the most useful geometrical
figures in taking dimensions; for since all figures that are
bounded by straight lines are capable of being divided
into triangles, and as the form of a triangle cannot be
altered without changing the length of some one of its
sides, it follows that the true form of any figure can be
preserved by having the length of the sides ot the dif¬
ferent triangles into which it is divided.

27. Quadrilateral figures are literally four-sided
figures. They are also called quadrangles, because they
have foui 1 angles.

28. A Parallelogram is a figure whose opposite sides
are parallel, as A B c D, Fig. 18.

29. A Rectangle is a parallelogram having four right
angles, as ab CD, Fig. 18.

30. A Square is an equilateral rectangle, 1 laving all its
sides equal, as B, Fig. 19.

31. An Oblong is a rectangle
whose adjacent sides are unequal,
as the parallelogram A B c D, Fi g. 1 8.

32. A Rhombus is an oblique-
angled figure, or parallelogram,
having four equal sides, whose opposite angles only are
equal, as c, Fig. 20.

Fi? 20.

Fig. 18

PRACTICAL CARPENTRY AND JOINERY.

33. A Rhomboid is an oblique-angled parallelogram,
of which the adjoining sides are unequal, as D, Fig. 21.

Fig. 31. Fig. 22. Fig. 23.

/ D /

\ E /

L --- 1

\ /

34. A Trapezium is an irregular quadrilateral figure,
having no two sides parallel, as E, Fig. 22.

35. A Trapezoid is a quadrilateral figure, which has
two of its opposite sides parallel, and the remaining two
neither parallel nor equal to one another, as F, Fig. 23.

36. A Diagonal is a straight line drawn between two
opposite angular points of a quadrilateral figure, or be¬
tween any two angular points of a polygon. Should the
figure be a parallelogram, the diagonal will divide it into

two equal triangles, the opposite n_ * lg ~ _ c

sides and angles of which will be ,.■

equal to one another. Let A B C D,

Fig. 24, be a parallelogram; join

A c, then A c is a diagonal, and the a b

triangles ADC, ABC, into which it divides the parallelo¬
gram, are equal.

37. A plane figure, bounded by more than four straight
lines, is called a Polygon. A regular polygon has all its
sides equal, and consequently its angles are also equal, as
K, L, M, and N, Figs. 26-29. An irregular polygon has its
sides and angles unequal, as H, Fig. 25. Polygons are
named according to the number of their sides, or angles,
as follows :—

38. A Pentagon is a polygon of five sides, as H or K,
Figs. 25, 26.

Fig. 25. Fig. 36. Fig. 27.

39. A Hexagon is a polygon of six sides, as L, Fig. 27.

40. A Heptagon has seven sides, as M, Fig. 28.

41. An Octagon has eight sides, as N, Fig. 29.

Fig. 28. Fig. 29. Fig. 80.

An Enneagon has nine, a Decagon ten, an Undecagon
eleven, and a Dodecagon twelve sides. Figures having
more than twelve sides are generally designated Polygons,
or many-angled figures.

42. A Circle is a plane figure, bounded by one uni¬
formly curved line, b c d (Fig. 30), called the circumfer¬
ence, every part of which is equally distant from a point
within it, called the centre, as a.

43. The Radius of a circle is a straight line drawn
from the centre to the circumference: hence all the radii
(plural ol radius) of the same circle are equal, as b a, c a,
e a,f a, in Fig. 30.

44. The Diameter of a circle is a straight line drawn
through the centre, and terminated on each side by the
circumference; consequently the diameter is exactly
twice the length of the radius; and hence the radius is
sometimes called the semi-diameter. (See b a e, Fig. 30.)

45. The Chord or Subtens ot an arc is any straight
line drawn from one point in the circumference of a circle
to another, joining the extremities of the arc, and divid¬
ing the circle either into two equal, or two unequal parts.
If into equal parts, the chord is also the diameter, and
the space included between the arc and the diameter,
on either side of it, is called a semicircle, as 6 a e in
Fig. 30. If the parts cut off by the chord are unequal,
each of them is called a segment of the circle. The same
chord is therefore common to two arcs and two segments ;
but, unless when stated otherwise, it is always under¬
stood that the lesser arc or segment is spoken of, as in
Fig. 30, the chord c d is the chord of the arc c e d.

If a straight line be drawn from the centre of a circle
to meet the chord of an arc perpendicularly, as a f in
Fig. 30. it will divide the chord into two equal parts,
and if the straight line be produced to meet the arc, it
will also divide the arc into two equal parts, as cf,f d.

Each half of the chord is called the sine of the half-arc
to which it is opposite ; and the line drawn from the
centre to meet the chord perpendicularly, is called the
co-sine of the half-arc. Consequently, the radius, the
sine, and co-sine of an arc form a right angle.

46. Any line which cuts the circumference in two

points, or a chord lengthened out so as to extend beyond
the boundaries of the circle, such as g h in Fig. 31, is some¬
times called a Secant But, in tri- rig . 31 .

gonometry, the secant is a line drawn f h

from the centre through one extre- z' j \ ^1 b

mity of the arc, so as to meet the ( /

tangent which is drawn from the a r- W

other extremity at right angles to \ )

the radius. Thus, F c b is the secant ' —L—
of the arc c e, or the angle c F e, g

in Fig. 31.

47. A Tangent is any straight line which touches the
circumference of a circle in one point, which is called the
point of contact, as in the tangent line e b, Fig. 31.

48. A Sector is the space included between any two
radii, and that portion of the circumference comprised be¬
tween them : ce F is a sector of the circle a fee, Fig. 31.

49. A Quadrant , or quarter of a circle, is a sector
bounded by two radii, forming a right angle at the
centre, and having one-fourth part of the circumference
for its arc, as F f d, Fig. 31.

50. An Arc, or Arch, is any portion of the circum¬
ference of a circle, as c de, Fig. 31.

It may not be improper to remark here that the terms
circle and circumference are frequently misapplied. Thus
we say, describe a circle from a given point, &c., instead
of saying, describe the circumference of a circle—the cir¬
cumference being the curved line thus described, every¬
where equally distant from a point within it, called the
centre; whereas the circle is properly the superficial space
included within that circumference.

51. Concentric Circles are circles within circles, de¬
scribed from the same centre; consequently, their circum¬
ferences are parallel to one another, as Fig. 32.

GEOMETRY-CONSTRUCTION OF ANGLES, RECTILINEAL FIGURES, ETC.

52. Eccentric Circles are those which are not described
from the same centre : any point which is not the centre
of a circle is also eccentric in reference to the circumfer¬
ence of that circle. Eccentric circles may also be tangent
circles, that is, such as come in contact in one point only,
as Fig. 33.

Fig. 33.

53. Altitude. The height of a triangle, or any other
figure, is called its altitude. To measure the altitude, let
fall a straight line from the vertex, or highest point in
the figure, perpendicular to the base or opposite side; or
to the base produced or continued, as at B D, Fig. 34,
should the form of the figure require its extension. Thus
C D is the altitude of the triangle ABC.

CONSTRUCTION OF ANGLES, RECTILINEAL
FIGURES, &g

Problem I.— To drain a straight line parallel to a
given straight line at any given distance.

Let A B (Fig. 35) be the given straight line, and let the
line m n represent the distance rig. 35.

required between the parallels. m - «

In AB take any two points A and o _ JL—

b, and from these points as cen¬
tres, with a radius equal to the
line m n, describe the arcs g and -

h ; draw the line c D so as to touch these arcs; that is, so
as to form their common tangent; and C I) will be parallel
to A B, as required.

Fig. 36.

Note .—This method of drawing parallels, however current in books
on practical geometry, is, to say the least, objectionable, inasmuch as
the learner has not been previously informed how to draw tangents
to circles or arcs of circles. This objection might be obviated in the
following manner: Let ab (Fig. 36) be the given straight line, and the
line m n the given distance
at which the parallel to A b is
to be drawn. From b set off
B a=mn, and from a as a
centre, with the radius m n,
describe the semicircle b e b.

Again, from b with mn or
l a in the compasses, set off
the arc b c, and having joined
these points, produce b c till
the line cd be equal to b c; join da, cutting the circumference in e,
and produce d a till af be equal to a e ; then draw f g at any angle
to d f, cutting a B in h, and make hg=fh. Lastly, through the
points e and g draw the straight line c D: it will be parallel to a b,
as required.

eg /

e D

N v cffC

\ m

a D

/ n

Problem II. — Through a given point c, to draw a
straight line parallel to a given straight line A B.

• In A B (Fig. 37) take any Fig. 37 .

point d, and from d as a centre ---r-

with the radius d c, describe / ;

an arc C e, cutting A B in e, and r ?

fr om c as a centre, with the same I /

radius, describe the arc d D, ~ ---7)

make it equal to C e, join c D, and it will be parallel to A B.

Another Method .—Let A B (Fig. 38) be the given line,
and c the given point, as before, through which a parallel
is required. From c, with a radius sufficient to reach the
nearest part of A B, describe an
arc, so that A B may form its _
tangent, as at e; then from
any point d in A B, with the
radius c e, describe the arc/: A -

Fig. 38.

through c draw C D, touching this arc: the line C D

K B

Fig. 40.

the parallel required.

This (II.) problem may be solved without having re¬
course to arcs, thus:—Let ab (Fig. 39) be the given line,
and E the point through which the parallel to AB is required
to be drawn. In A B take
any point F ; join E F,
join also A E, and pro¬
duce it till E G be equal
to A E. Likewise make
F k = a F, join G K, and make G H or k h = e f; then,
through the points E and H, draw the line CD: it will
be parallel to the given line A B.

Problem III.— To make an angle equal to a given
rectilineal angle.

From a given point E (Fig. 40), upon the straight line ef,
to make an angle equal to the given
angle ABC. From the angular point
B, with any radius, describe the arc
ef, cutting B c and B A in the points
6 and /. From the point Eon EF
with the same radius, describe the
arc h g, and make it equal to the arc
e /; then from E, through g, draw
the line ED : the angle def will be
equal to the angle ABC.

Problem IV.— To bisect a given angle.

Let ABC (Fig. 41) be the given angle. From the angular
point B, with any radius, describe an arc cutting B A and
B c in the points d and e ; also, from the points d and c as
centres, with any radius
greater than half the dis¬
tance between them, de¬
scribe arcs cutting each
other in /; through the
point of intersection /,
draw b/d : the angle ABC
is bisected by the straight line BD; that is, it is divided into
two equal angles, ABD and cbd.

Or thus. —Let abc (Fig. 42)
be the given angle, as befoi'e. In
A B take any two points D and E.

On B C set off B F equal to B D,
and B G equal to BE; join EF
and D G, intersecting each other
in H; join also bh, and pro¬
duce it to any point K: the
angle ABC is bisected by the
line bk.

Problem V. — To trisect or divide a rigid angle into
three equal angles.

Let A B c (Fig. 43) be the given right angle. From the an¬
gular point B, with any radius, describe an arc cutting L A
and B C in the points d and g ; from the points d and < 7 ,
with the radius B d or B g, describe arcs cutting the arc

Fig. 41.

Fig 42.
B

PRACTICAL CARPENTRY AND JOINERY.

Fig. 43.

Fig. 41.

Fig. 45.

d g in e and /; join B e and B /: these lines will trisect
the angle ABC, or divide it into three
equal angles.

Note .—The trisection of an angle can be
effected by means of elementary geometry
only in a very few cases; such, for instance,
as those where the arc which measures the
proposed angle is a whole circle, or a half, a
fourth, or a fifth part of the circumference.

Any angle of a pentagon is trisected by dia¬
gonals, drawn to its opposite angles.

TO ERECT OR LET FALL PERPENDICULAR LINES.

Problem VI .—From a given point c, in a given
straight line A B, to erect a perpendicular.

From the point c (Fig. 41), with
any radius less than C A or c B, de¬
scribe arcs cutting the given line A B
in d and e ; from these points as cen¬
tres, with a radius greater than c d
or C e, describe arcs intersecting each

other in /: join C/, and this line will A -

be the perpendicular required.

Problem VII.— From the point B, at the extremity of
the line A b, to erect a perpendicular.

Above the given line AB (Fig.

45 ), take any point c , and with
the radius or distance c B, de¬
scribe the portion of the circle
d Be; join d c, and extend it to
meet the opposite circumference
in e: draw the line Be, which will
be the perpendicular required.

Another Method. —From the point b (Fig. 46), with any
radius, describe the arc ede; and from the point c, where
the arc meets the line A B, with
the radius B c, cut the arc in d;
and from d, with the same ra¬
dius, cut it also in e. Again, from
the points d and e, with equal
radii — greater than half the
distance from d to e —describe
arcs intersecting each other in
/: a line joining b/ will be the perpendicular required.

Or thus. —In A B (Fig. 47) take any point c; from B as a
centre, with the radius B c, describe the portion of a circle
ce ; again, from c, with the same radius,
draw an arc cutting the former in d ;
also from d as a centre, with the same
radius, describe the arc g h ; join c d,
and extend it to meet g h in /: a line
drawn from /, the point of intersec¬
tion, to B, will be the perpendicular to
A B as before.

Another Method. —To draw a right angle or erect
perpendicular by means of any
scale of equal parts, or standard
measure of inches, feet, yards, &c.,
by setting off distances in pro¬
portion to the numbers 3, 4, and
5, or 6, 8, and 10, or any num¬
bers whose squares correspond to
the sides and hypotenuse of a
right-angled triangle.

From any scale of equal parts, as that represented by

Fig. 46. J'

Fig. 47.

Fig. 48.

O
1 _

Fig. 49.
C

the line D (Fig. 48), which contains 5; set off from B, on the
line A B, the distance B e, equal to 3 of these parts; then
from B, with a radius equal to 4 of the same parts, describe
the arc a b; also from e as a centre, with a radius equal to
5 parts, describe another arc intersecting the former in c ;
lastly join bc; the line B c will be perpendicular to A B.

Note .—This mode of drawing right angles is more troublesome
upon paper than the methods previously given; but in laying out
grounds or foundations of buildings it is often useful, since only
with a measuring rod, line, or chain, perpendiculars may be set out
very accurately. The method is demonstrated thus:—The square of
the hypotenuse, or longest side of a right-angled triangle, being equal
to the sum of the squares of the other two sides, the same property
must always be inherent in any three numbers, of which the squares
of the two lesser numbers, added together, are equal to the square
of the greater. For example, take the numbers 3, 4, and 5; the
square of 3 is 9, and the square of 4 is 16; 16 and 9 added together
make 25, which is 5 times 5, or the square of the greater number.
Although these numbers, or any multiple of them, such as 6, 8, 10,
or 12, 16, 20, &c., are the most simple, and most easily retained in
the memory, yet there are other numbers, very different in propor¬
tion, which can be made to serve the same purpose. Let n denote
any number; then w J -f-1, n 2 — 1, and 2 n, will represent the hypo¬
tenuse, base, and perpendicular of a right-angled triangle. Suppose
n=6, then n 2 -f-l=37, w 2 —1=35, and 2n=12: hence, 37, 35, and
12, are the sides of a right-angled triangle.

Problem VIII. —From a given point c, to let fall a
perpendicular to a given straight line A b.

From the point C (Fig. 49), with any radius greater than
its distance from the line
A B, describe an arc cutting
A B in the points d and e ;
also, from d and e, with
equal radii—greater than
half the distance between
these points—describe arcs
on the opposite side of A B,
intersecting each other at
/; join f c, cutting A B in
D: CD will be a perpendicular let fall upon ab, as required.

Another Method. —When the given point whence the
perpendicular is to be drawn is nearly opposite the end
of the line.

Let C be the given point (Fig. 50), and A B the given line,
as formerly. In A B, take any con¬
venient point e, and from it, with a
radius equal to e c, describe an arc
c D ; between B and e, take any
other point /; and from f with
fc as a radius, describe arcs cutting
the former arc in C and D: a straight
line drawn through these points of
intersection will be perpendicular to the given line A B.

Note .—Perpendiculars may also be erected or let fall upon straight
lines, without having recourse
to the arcs of circles, by means
of straight lines only. This
may be shown as follows:—

Let a b (Fig. 51) be a given
straight line, and c a given
point in it; it is required to
draw a line from the point c
at right angles to a b. Be¬
tween c and a take any point D ;
draw d e at any angle to d b,
and equal to n c; join e c, and
produce it to o, making c g=c d. E

On cb set off cr equal to c e ; join f g, and produce it till gh be equal

Fig. 51.

GEOMETRY—CONSTRUCTION OF RECTILINEAL FIGURES, ETC.

Fig. 54.

to OF or oc; draw cu: it will be perpendicular to ab. — Again, let ab
(Fig. 52) be the given straight line, and c the given point from which
it is proposed to let fall a perpen¬
dicular upon A b. In A b, take
any point d, and join c D ; then
towards a set off de=cd; also
towards b set off di'=de or d c;
join e c and c f. Again, pro¬
duce e c till e g be equal to e f,
and from ef cut off eh=ec;
join g n, and extend it on the
other side of a b till h k be equal to G n. Then join k e, and cut off
kl = cg; join cl, cutting ab in m: cm is the perpendicular let
fall upon a b.

Problem IX —To bisect a given straight line.

Let A B (Fig. 53) be the given
straight line. From the extreme
points A and B as centres, with any
equal radii greater than half the length
of A B, describe arcs cutting each other a
in C and D : a straight line drawn
through the points of intersection c
and D, will bisect the line A B in e.

Problem X .—To divide a given straight line into
any number of equal parts.

Let A B (Fig. 54) be the given line to be divided into five
equal parts. From the point A draw the straight line A C,
forming any angle with A B. On
the line A C, with any convenient
opening of the compasses, set off
five equal parts towards C; join
the extreme points C B ; through
the remaining points, 1, 2, 3, and 4, draw lines parallel to
BC, cutting AB in the corresponding points, 1, 2, 3, and 4:
A B will be divided into five equal parts, as required.

Another Method. —Let ab (Fig. 55) be the given straight
line, which we shall suppose, in this instance, is to be divided
into four equal parts. Draw the
straight line CD of any conveni¬
ent length, and from c set ofi’ four
equal parts. Then from c, with
a radius equal to the distance
from c to the last division, or
number 4, on the line c D, de¬
scribe an arc; and from the point

marked 4, with the same radius, c i 2 3 -> d

describe another arc cutting the former in G. From the
point of intersection G, draw G c, G 1, G 2, G 3, and G 4.
Again, from G, with a radius equal to the given line A B,
describe an arc cutting G C and G 4 in the points E and
f; join these points : the line E F will be equal to the
given line AB, and it will also Fig. 56.

be divided into four equal
parts by the lines G 1, G 2,
and G 3.

A line may be divided into
any number of equal parts
very simply, by means of a
ruler, or scale of equal parts,
without the help either of
arcs or compasses. Thus :—

Let A B (Fig. 56) be the
given straight line, and let it
be required to divide it into
any number—say five equal parts. Draw A c, making any

Fig. 58.

angle with A B ; and from A towards C, set off any five
equal parts; join 5 B, and produce it indefinitely towards D.
Again, from 5, on the line 5 D, with the same or any other
scale, set off five equal parts, as before, marked 1 , 11 , 111 , iv,
V; then join AV, 1IV, 2m, 3li, and 4l. From A set off A a —

4 1 , A b — 3 11 , A c = 2 hi, and A d= 1 iv. Join also al, b 2,
c 3, and d 4, cutting ab in 1', 2\ 3\ 4': ab is divided into
five equal parts by these lines.

The bisection of a line by
this method is exceedingly
simple, as is shown by Fig 57.

By either of the two pre¬
ceding methods, scales or
drawings may be reduced or
enlarged proportionably, so that each part of a given
scale or drawing shall bear the same proportion to simi¬
lar parts of another scale or drawing of a different size.

A fourth proportional to three given lines, may be
found, in like manner, by this problem. Assume A E,
E B, and A D (Fig. 58), to be three given lines, the two
first, A E, E B, being placed in the same straight line,
and A D, the third line, making
any angle with A B : having
joined D E, through B draw B c,
parallel to D E, meeting a d
produced in c; D c is a fourth
proportional to these three lines. For, by the first
method of this problem, D c and E B are similar portions
of the lines A c and A B : wherefore the part D c has
the same ratio to the remaining part A D that the part
EB of the line ab has to the remainder A E.

As regards scales and drawings. Let A B (Fig. 59),
represent the length of one scale or drawing, divided
into the given parts Ad, de, ef, fg, gh, and Ab; and
D E the length of another scale
or drawing required to be divided
into similar parts. From the
point B draw a line BC = de,
and forming any angle with A B ;
join A c, and through the points

d, e, f g, and A, draw d k, e l, —»-'e

fm, gn, A 0 , parallel to AC ; and the parts C k, hi, Im,
&c., will be to each other, or to the whole line B C, as
the lines A d, de, ef, &c., are to each other, or to the
given line or scale ab. By the second method, as will
be evident from the figure, similar divisions can be
obtained in lines of any given length.

Problem XI.— To describe an equilateral triangle
upon a given straight line. Fi - 60 -

Let A B (Fig. 60) be the given
straight line. From the points A and
B, with a radius equal to A B, describe
arcs intersecting each other in the
point C. Join CA and CB, and ABC will
be the equilateral triangle required.

Note. —An eminent mathematician has made the following obser¬
vation regarding this problem:—“It is remarkable that it is not
perhaps possible to resolve, without employing the arc of a circle,
the very simple problem, and one of the first in the elements of geo¬
metry, viz., to describe an equilateral triangle.” “We have often
attempted it,” continues the same author, “ but without success,
while trying how far we could proceed in geometry by means of
straight lines only.” He did right to put in 'perhaps, as the thing
happens to be possible after all, but it shows by what trifles the
greatest men will sometimes be baffled. We submit the following

PRACTICAL CARPENTRY AND JOINERY.

method as remarkably simple and easy:—Let a b (Fig. 61) be the
given straight line. It is required to describe an equilateral triangle
upon it without making use of the Fig. ci.

compasses or arcs of a circle. Bisect
a b in D (as shown in a former note),
draw a e perpendicular and equal to
a d ; join d e, and extend da to f,
making a f = d e ; join also e f ;
then from p erect the perpendicular
Dc=bf, and join a c and c b : ab c
will be an equilateral triangle.

It is easy to see that a c 2 must be
4 ad 2 ; but ac j =a D'-f-CD 1 (47 Prop.

Euclid), and c d 2 =e f 2 =f a 2 -f- a e 2 = a e 2 + d e 2 ; but de 2 =ad 2 -P
a e 2 =2 a d 2 . • . c d 2 =3 a d 2 , and a c 2 = a b 2 = 4 a d 2 . Q. E. D.

Problem XII.— To construct a triangle whose sides
shall be equal to three given
lines.

Draw AB (Fig. 62) equal to the
given line F. From A as a centre,
with a radius equal to the line E,
describe an arc; then from B as
a centre, with a radius equal to
the line D, describe another arc
intersecting the former in C ; join
C A and c B, and ABC will be the triangle required.

Problem XIII.— To find the length of the hypotenuse,
or longest side of a right-angled
triangle, whose other two sides are
equal to two given lines D and E.

Draw A B (Fig. 63) equal to the
line E, and from the point B draw
B c perpendicular and equal to
the line D. Join A c, which will n —

be the hypotenuse required. e-——

Problem XIY.— The hypotenuse a b, and one side
c D, of a right-angled triangle being given, to find the
other side.

Bisect the hypotenuse A B in e (Fig. 64), and from e as a
centre, with a radius equal to e B or e

e A, describe an arc ; also from A as 64 ‘
a centre, with a radius equal to the
given line C D, describe another arc, /
intersecting the former in E; join ~

EA and EB; and eb will be the c- d

side required of the right-angled triangle ABE.

Problem XY.— On a given line ef, to construct a
triangle similar to a given triangle abc.

From the angular point A
of the given triangle (Fig. 65),
with any radius, describe the
arc de, cutting A B and A c in
the points d and e. Also, from
E, the one extremity of the
given line E F, with the same ra¬
dius, describe the arc to n: take
the arc d e in the compasses,
and apply it from to to n,
so as to make it equal to d e.

Again, from the angular point B, with the same or any
other radius, describe the arc f g : likewise, from F, the
other extremity of E F, with the same radius, draw the arc
o p, making it equal to fg. Through the points n and p
draw lines from E and F, meeting in D ; the triangle efd
will be similar to the triangle ABC, as required.

Fig. 65.
C

Fig. 63.

Another Method. — Let abc be the given triangle (Fig. 66).
Produce one of its sides B c till
the extension CD be equal to
the corresponding side of the
proposed triangle. Through
the point C draw a line CE
parallel to B A ; also, through
the extreme point D, draw D E parallel to c A, meeting
C E in E, and the triangle ecd will be similar to the
triangle ABC.

Note .—This example illustrates some of the most important pro¬
perties of triangles; as, for instance, that the alternate angles formed
by a straight line, cutting two or more parallel lines, are equal; like¬
wise, that the angles formed by one line falling upon another, will
either be two right angles, or will be together equal to two right
angles; wherefore, the angles a c b and a c d are together equal to
two right angles.

Fitf. 66.

Fig. 67.

Problem XYI.— To change a given triangle into
another of equal area, having either its base or altitude
greater or less than Hie base or altitude of the given
triangle.

Let ABC be the given tri¬
angle (Fig. 67), and e f the
altitude of the proposed
triangle. From the given
height or altitude at/, draw
the dotted line / B ; and
through the point C, draw
another dotted line, parallel to /B, and meeting the base
line produced in D. Join /d; then the triangle AD/
will be equal in area to the given triangle ABC. Or con¬
versely : let A d/ be the given triangle, and let C, or any
point in A / produced, be the vertex or altitude of the
proposed triangle : draw a dotted line from c to D, as be¬
fore ; also, through /, draw /B, parallel to CD; join C B,
which will complete the required triangle ABC.

It must be evident from Fig. 67, that the same rule is
applicable to any given difference, either in the base or
altitude of triangles of equal area

Problem XVII.— Two dissimilar triangles being
given, to construct a third, which vAll be similar to the
one, and equal in area to the other.

Let abc (Fig. 68) be one of the given triangles, to which
the proposed triangle is to be similar, and D E F the other
given triangle to which it is required to be equal in area.
By Problem XVI., change the triangle def into another,
D H G, having its altitude equal to that of the triangle
ABC. Take any indefinite straight line kl, limited at
the one extremity
K; and from K set
off K to equal to A B,
and to L equal to
D H : bisect the

whole line K L in o;
then from o as a cen¬
tre, with a radius
equal to o K or o L
describe the semi¬
circle K n L : also,
from the point to,
draw the line to n
perpendicular to K L, meeting the circumference in n ;
to n is a mean proportional between kto and to l, or
their equals A b and D H. Lastly, draw the straight line

Fig. 68.

GEOMETRY—CONSTRUCTION OF RECTILINEAL FIGURES, ETC.

Fig. GO.

parallel to A D, and meet-
ingthe base ab producedin
E ; join E D, and B DE will E
be a triangle equal in area to the given trapezium abdc.

Problem XXI.— To construct a triangle equal in area
to a given 'pentagon.

Let abode (Fig. 72) be the pentagon to which the
triangle is to be equal. Draw (with
dotted lines) the diagonals A D and
D b ; draw also E F parallel to D A,
and C G parallel to D B, meeting the
base extended both ways in F and
G. Join DF and DG, and dfg will f a no

be a triangle equal in area to the given pentagon, abode.

In like manner, any other figure formed by straight

Fig. 72,

R S equal to m n, and upon this line (by Problem XV.) I
construct a triangle rst similar to ABC, and it will
likewise be equal in area to the triangle dbg, or its
equal def, as required.

Note .—The truth of this method may be proved shortly thus: —
Put ab = «, d n = b, and the perpendicular height of the triangles
of which a b and D H are the bases, equal to cl. Also let the base of
the triangle sought be represented by x, and its height by y. Then

by similar triangles a : x :: d : y, and y = Again, because the

triangle sought must be equal to dgh, xy=db, and y — ■— . • .
dx db

— = — or d .r — ado and x =ab, or x=R s, is a mean propor¬
tional between a and b, that is, between a b and d h.

Problem XVIII.— To inscribe a circle in a given
triangle.

Let ABC (Fig. 69) be the given triangle. Bisect any
two of its angles, as those at A
and c, by the straight lines A D
and c D. From the point D,
where the bisecting lines meet,
let fill the perpendicular D e
upon the line A c ; then from D A
as a centre, with the radius D E, describe a circle. This
circle will be inscribed in the triangle A B c, as required.

Problem XIX. —To inscribe a circle within three
given oblique lines, which, if produced, would form a
triangle, but whose angular points are supposed to be
inaccessible.

From any point g in the line C D (Fig. 70), let fall g h
perpendicular to A B ; and from the same point g erect a
perpendicular to C D, meeting A B in Jc ; bisect the angle
kgh by the line g l ; Fig. 70 .

bisect also the line
g l by the perpendi¬
cular line m n. In c -
like manner, find the
line op ; bisect it also, A ,llk

and through the point of bisection draw the perpendicu¬
lar line r n, meeting mn in the point n. Lastly, from n,
the point of intersection, let fall upon A B the perpen¬
dicular ns : ns will be the radius of the required circle.

Problem XX.— To construct a triangle equal in mag¬
nitude or area to a given trapezium.

Let abdc (Fig. 71) Fie - 71 -

be the given trapezium.

Draw the diagonal AD;
then through C draw C E

Fig. 74,

lines may be reduced to a triangle. Should the given
figure be a polygon of more than five sides, it will be
necessary to change it into another of one side less suc¬
cessively, until it be reduced to five sides, by the method
employed in the preceding examples.

Problem XXII.—To reduce a hexagon, or six-sided
figure, to a pentagon, or five-sided figure.

Let ABCDEF (Fig. 73) be the given hexagon. Draw
a diagonal between any two of _ Fig. 73 .
its alternate angles, as c F ; then
through the intermediate angular
point D draw the line D G parallel
to C F, meeting the base E F ex¬
tended in G. Join C G, and ABCGE
will be the pentagon required.

Problem XXIII.— To construct
a rectangle, or parallelogram, equal to a given triangle.

Let ABC (Fig. 74) be the given triangle, and the dotted
line AD its altitude or perpendicu¬
lar height. Bisect AD in e, and
through the point E draw FEG
parallel toBDC. Again, through
B and C, the extremities of the

base, draw B F and c G, each pa- Q u c

rallel to A D, and meeting the line F E G in the points F and
G: then B C G F is the rectangle or parallelogram required.

Problem XXIV.—To describe a square, or equilateral
rectangle, the sides of which shall be equal to a given
straight line.

Let AB (Fig. 75) be the straight line to which the sides
of the square are to be equal. Draw Fig. 75 .

c D equal to A B, and from c and D as
centres, with a radius equal to CD,
describe the arcs D F and c E, inter¬
secting each other in g: bisect the arc
eg in h: from g as a centre, with
radius g li, draw arcs cutting c E and
D F in E and F. Join D E, E F,
and F c: c D E F is the square re¬
quired. A 11

Problem XXV.—To construct a rectangle whose sides
shall be equal to two given lines.

Let ab and CD (Fig. 76) be the given lines. Draw
the straight line E F equal to Fi ?- 76 -

A B, and from E draw E H perpen- 11
dicular to E F, and equal to CD;
then from H and F as centres,
with radii equal to A B and c D,
describe arcs intersecting in G.

Join F G and G H, and EFGH will A
be the parallelogram or rectangle c D

required. Parallelograms of any form may be drawn in
a similar manner.

Problem XXVI.—To describe a square equal to a

Fig. 77.

given rectangle.

Let A B c D (Fig. 77) be
the given rectangle. Pro¬
duce A B, one side of the
rectangle, to E, and make
B E equal to B C. Bisect
A E in K, and from K as a
centre, with the radius K A
or KE, describe the semicircle AHE. Produce CB to meet

PRACTICAL CARPENTRY AND JOINERY.

Fig. 78.

the circumference in H; extend be to F, and make BF
equal to BE; then complete tlie square BFGH, and it
will be equal to the given rectangle.

Thus, by means of this, and Problem XXIII., a triangle
can be successively changed, first into a rectangle, then
from a rectangle into a square, in such a manner that
all the three figures shall still be equal in area.

Problem XXVII.— To describe a rectangle or paral¬
lelogram having one of its sides equal to a given line,
and its area equal to that of a
given rectangle.

Let AB (Fig. 78) be the given
line, and cdef the given rect¬
angle. Produce C E to G, making
E G equal to AB; from G draw
G K parallel to E F, and meeting
D F produced in H. Draw the
diagonal G F, extending it to meet
C D produced in L ; also draw L K
parallel to D H, and produce E F

till it meet LK in M; then FMKH a -b

is the rectangle required.

Note. —Equal and similar rhomboids or parallelograms of any
dimensions may be drawn after the same manner, seeing the comple¬
ments of the parallelograms which are described on or about the
diagonal of any parallelogram, are always equal to each other; while
the parallelograms themselves are always similar to each other, and
to the original parallelogram about the diagonal of which they are
constructed. Thus, in the parallelogram cmt the complements
cefd and fhke are always equal, while the parallelograms efhg
and d f m l about the diagonal g l, are always similar to each other,
and to the whole parallelogram c g k l.

Another Method. — Let cdef (Fig. 79, No. i) be tlie
given rectangle, and A B (no. 2 ) a side of the proposed
rectangle. Find a fourth proportional to the three fol¬
lowing straight lines, viz.,

AB the given line, CD
and D F sides of the
given rectangle. Thus,
from any point G (n 0 . 3 ),
draw two diverging lines
G H and G K, equal to
A B and c D, making any
angle at the point G.

Join K H, and produce
G H till h L be equal to u
D F ; then, through L, draw L M parallel to hk: it m
will be a fourth proportional to A B, c D, and D F. Upon
the given line AB describe the parallelogram abon,
having each of its sides A N and B o equal to k M, and
it will be the rectangle required.

When two sides of one rectangle are reciprocally pro¬
portional to two sides of another, the rectangles must
necessaiily be equal; because, when four straight lines
are geometrically proportional, the product of the first
and fourth, or of the extremes, is always equal to the
pioduct of the second and third, or of the mean propor¬
tionals.

Problem XXYIII. — Upon a given straight line to
construct a rectangle equal to a given square.

Let A B (Fig. 80, no. 1 ) be the given straight line, and
cdef (no. 2 ) the given square. Draw any two straight
lines G H and G K (no. 3 ), forming any angle at G. Make
gh equal to the given line a b, and gk equal to cd, a

Produce

that

Fig. 81.

side of the given square.

HL may be equal to KG;
join K H ; then draw M L
parallel to K H; join also
K M, and it will be a
third proportional to A B
and C D. Lastly, upon
A B as a base, describe a
rectangle having its al¬
titude equal to KM, and
it will be equal in area
to the given square, as
required.

Problem XXIX.— To describe a square equal to two
given squares.

Let A and B (Fig. SI) be the given squares. Place them
so that a side of each may form the right angle dce;
join D E, and upon this hypotenuse describe the square
D E G F, and it will be equal to the
sum of the squares A and B, which
are constructed upon the legs of
the right-angled triangle DCE. In
the same manner, any other recti¬
lineal figure, or even circle, may
be found equal to the sum of other
two similar figures or circles. Sup¬
pose the lines c D and c E to be
the diameters of two circles, then
D E will be the diameter of a third,
equal in area to the other two circles. Or suppose c D
and C E to be the like sides of any two similar figures,
then D E will be the corresponding side of another similar
figure, equal to both the former.

Problem XXX.— To describe a square equal to any
number of given squares.

Let it be required to construct a square equal to the
three given squares A, B, and
c (Fig. 82). Take the line
D E, equal to the side of the
square c. From the extremity
D erect D F perpendicular to
D E, and equal to the side of
the square B ; join E F ; then a
square described upon this line
will be equal to the sum of the
two given squares C and B.

Again, upon the straight line
EF erect the perpendicular FG,
equal to the side of the third
given square A ; and join G E,
which will be the side of the square G E n K, equal in
area to A, B, and c. Proceed in the same way for any
number of given squares.

Problem XXXI. —To describe a square equal to tlte
difference of two unequal squares.

Let A and b (Fig. 83) be the
given squares. Describe a right-
angled triangle,having its base CD
equal to the side of the square A,
and its hypotenuse CE equal to the
side of the square B; then E D, the
third side of the right-angled
triangle dec, is the side of a square, the area of which

GEOMETRY-CONSTRUCTION OF RECTILINEAL FIGURES, ETC.

will be equal to the difference of the areas of the two
given squares A and B.

Problem XXXII .—To describe a square which shall
be equal to any portion of a given square.

Let A (Fig. 84, No. 1 ) be the given square, and let it be
required to construct another square, whose area shall be
one-third of A. Draw the
straight line BC (no. 2 ) equal
to the side of the given
square A: produce thi3
line to D, making c D
equal to one-third of BC.

Upon the whole line B D describe a semicircle, and from c
erect c E perpendicular to bd. c e being a mean propor¬
tional between the two segments BC and CD of the line BD,
will, consequently, be a side of the square required.

In like manner, a square may be described, having any
given ratio to a given square, or which may be any given
multiple of another square. The first case of the problem
is effected (as has been shown) by making the extension
or part added to the given line equal to the required
ratio ; the second, by making the part produced equal
to the required multiple of the given square.

Remark. —Although, for the sake of brevity and simplicity, the
four preceding problems have been restricted to the construction of
squares, the same methods are equally applicable to all similar rec¬
tilineal, curvilineal, or mixilineal plane figures. For circles, as
already stated in Problem XXIX., we have only to substitute their
diameters for the sides of squares; whereas, in other cases, the lines
forming a right-angled triangle can be supposed the homologous, or
like sides of the similar figures to which they belong.

Fig. 85.

Fig. 8fi

Problem XXXIII.— To inscribe a parallelogram in
a given quadrilateral figure. ■

Let ABC D (Fig. 85) be the given quadrilateral in which
the parallelogram is to be inscrib¬
ed. Bisect each of the sides in the
points E, r, G, and H. Join ef, fg,
g H, and H E, and the rectilineal
figure E F G H, thus formed, will
be the parallelogram required.

Problem XXXIY.— To describe a rectangle equal to
a given rhomboid.

Let A B c D (Fig. 86) be the given rhomboid or parallelo¬
gram to which the rectangle is re-
quired to be equal. From each of
the angular points B and C, upon the ,/
same side, let fall perpendiculars /

Be and c F upon AD, or upon ad j _/

produced to F, and the rectangle A
B c F E will be equal in area to the
A B C D.

Problem XXXY.— To describe a rectangle equal to a
given irregular quadrilateral figure.

Let A B c D (Fig. 87, No. 1 ) be the given quadrilateral.
Between any two of its
opposite angles, as B and D,
draw the diagonal B D;
then from the other two
opposite angles, at A and
C, let fall the perpendicu¬
lars A/ and eg upon the
diagonal bd, or upon bd d "
produced if necessary. Again, bisect B D in e, and draw

D i’

given

rhomboid

, Fig. S

/ /

/ V'

-- C H

—

the straight line H K (no. 2 ) equal to B e or d«, half the
diagonal. Upon the line H K as a base, construct a rect¬
angle, having its height equal to the sum of the perpen¬
diculars A / and c g : the rectangle thus described will be
equal to the given quadrilateral aecd.

Problem XXXVI. — To describe a quadrilateral
figure equal to a given pentagon.

Let ABODE (Fig. 88) be the given pentagon. Join any
two of its alternate angles, as for rig. 88.

instance those at c and E, by the
diagonal line CE ; then through the
intermediate angular point D draw
the line DF parallel to C E, meeting
A E produced in F : join c F, and
the quadrilateral figure A B c F
[ will be equal to the given pentagon
A B c D E, as required. Upon the same principle, any recti¬
lineal figure may be reduced into another having one side
less, but still equal in area to the original given figure, as has
been already illustrated in Problems XX., XXI., and XXII.

Problem XXXVII.— Upon a given straight line to
describe any regular polygon.

Example I. Upon a given line A b (Fig. 89) to describe
a regular pentagon. — Produce A B to c, so that B c may be
equal to A B : from B as a centre, with the radius B A or
Bc, describe the semicircle adc: Fig. 89.

divide the semi-circumference
ADC into as many equal parts
as there are sides in the re- in¬
quired polygon, which in the
case before us will be five:
through the second division
from C draw the straight line
B D, which will form another side of the figure. Bisect
A B at e and BD at/, and draw e G and/G perpendiculars
to A B and B D; then G, the point of intersection, is the
centre of a circle, of which A B and D are points in the
I circumference. From G, with a radius equal to its dis¬
tance from any of these points, describe the circumference
! A B D H K; then by producing the dotted lines from the
I centre B, through the remaining divisions in the semi¬
circle A D C, so as to meet the circumference of which G
I is the centre, in H and K, these points will divide the
circle A B D H K into the number of parts required, each
part being equal to the given side of the pentagon.

Example II. Upon a given straight line to describe a
regular heptagon. —Let ab (Fig. 90) be the given straight
line. As in the former example, from B, with a radius
equal to AB, describe the semicircle adc, and produce AB
to meet it in c. Divide the semi-circumference ADC into
seven equal pai’ts—the number of sides in a heptagon.
Draw B D, as before, through the second division of the
semicircle from c: bisect also
A B in e, and B d in / and
draw e G and / G respec¬
tively perpendicular to A B and
B D. G, as formerly, is the
centre of a circle, whose circum¬
ference passes through the
points A B and D. Complete
the circle ABDH, and it will
contain the given side A B se¬
ven times, which is the number of sides required.

PRACTICAL CARPENTRY AND JOINERY.

Fig. 92.

Remark,- From the preceding examples it is evident that polygons
of any number of sides may be constructed upon the same principles,
because the circumferences of all circles, when divided into the same
number of equal parts, produce equal angles; and, consequently, by
dividing the semi-circumference of any given circle into the number
of parts required, two of these parts will form an angle, which will
be subtended by its corresponding part of the whole circumference.
And as all regular polygons can be inscribed in a circle, it must
necessarily follow, that if a circle be described through three given
angles of that polygon, it will contain the number of sides or angles
required.

The above is a general rule, by which all regular polygons may
be described upon a given straight line; but there are other methods
by which many of them may be more expeditiously constructed, as
shown in the following examples:—

Problem XXXVIII.— Upon a given straight line to
describe a regular 'pentagon.

Let A B (Fig. 91) be the given straight line; from its

extremity B erect Be perpendicular c. Fig. oi.

to A B, and equal to its half. Join
A c, and produce it till c d be equal
to bc, or half the given line AB.

From A and B as centres, with a
radius equal to B d, describe arcs
intersecting each other in e, which
will be the centre of the circum¬
scribing circle ABFG ii. The side AB applied successively
to this circumference, will give the angular points of the
pentagon; and these being connected by straight lines,
will complete the figure.

Another Method ,—Let AB (Fig. 92) be the given line,
upon which the pentagon is to
be described. Erect B d per¬
pendicular and equal to AB.

Bisect A B in c, and join cd: p/k
produce A B, making c e equal
to c d. Then from A and B as
centres, with the radius A e,
describe the arcs G H and G F,
intersecting each other in G.

Again, from the same points A and B, with the radius A B,
describe arcs intersecting the former in H and F. Join
B F, F G, G H, and H A, and the rectilineal figure abfgii
will be a regular pentagon, having A B as one of its sides,
as required.

Problem XXXIX. — Upon a given straight line to
describe a regular hexagon.

Let ab (Fig. 93) be the given
straight line. From the extremi¬
ties A and B as centres, with the
radius A B, describe arcs cutting
each other in g. Again from g,
the point of intersection, with the

same radius, describe the circle

A B c, which will contain the given

side AB six times when applied to its circumference, and
will be the hexagon required.

Another Method .—Upon the given
line A B (Fig. 94) describe (Problem
XI.) the equilateral triangle ABC.

Extend the sides A c and bc to Eg
and F, making ce and cf each equal
to a side of the triangle. Bisect the
angles A C F and B c E by the straight a b

line gcd, drawn through the common vertex c, and make

Fiu. 93.

Fig. 91.

Fig. 96.

c D and c G each equal to C E or c F. J oin B D, D E, E F,

F G, and G A ; then abdefg is a regular hexagon, de¬
scribed upon A B, as required.

Problem XL.— To describe a regular octagon upon a
given straight line.

Let ab (Fig. 95) be the given line. From the extremities
A and B erect the perpendicu¬
lars A E and B F: extend the
given line both ways to k and
l, forming external right angles
with the lines A E and B F. Bi¬
sect these external right angles,
making each of the bisecting
lines A H and B C equal to the

given line A B. Draw H G and k A 5" l

C D parallel to A E or B F, and each equal in length, to
A B. From G draw G E parallel to B C, and intersecting
A E in E, and from D draw D F parallel to A II, intersecting
B F in F. Join E F, and ABCDFEGH is the octagon re¬
quired. Or from D and G as centres, with the given line
A B as radius, describe arcs cutting the perpendiculars A E
and BF in E and F, and join GE, EF, FD, to complete the
octagon.

Othenvise, thus. —Let AB (Fig. 96) be the given straight
line on which the octagon is to
be described. Bisect it in a,
and draw the perpendicular a b
equal to Act or B a. Join kb,
and produce a b to c, making
bc equal to kb: join also A c
and B c, extending them so
as to make c E and c F each
equal to A c or B c. Through
c draw ccG at right angles
to AE. Again, through the same point
right angles to B F, making each of the lines c C, CD,
c G, and c H equal to A c or c B, and consequently equal to
one another. Lastly, join BC, CD, DE, EF, FG, G H, H A :
abcdefgh will be a regular octagon, described upon
A B, as required.

Problem XLI. — In a given square to inscribe a given
octagon.

Let A B c D (Fig. 97) be the given square. Draw the dia¬
gonals A c and B D, intersecting each
other in e ; then from the angular
points ABC and D as centres, with a
radius equal to half the diagonal, viz.,

Ac or ce, describe arcs cutting the
sides of the square in the points /, g,
h, k, l, m, n, o, and the straight
lines o /, g h, k l, and m n, joining
these points will complete the octagon, and be inscribed
in the square A B c D, as required.

Problem XLIL— To inscribe any regular polygon in
a given circle.

Let abd (Fig. 98) be the given circle, in which it is re¬
quired to inscribe a regular pentagon. Draw the diameter
AB of the given circle, and divide it into the same number
of equal parts as there are sides in the required polygon,
viz., five Bisect A b in e, and erect e C perpendicular
to A B, cutting the circumference in F ; and make F C, the
part without the circle, equal to three-fourths of the radius
Ae or cb. From c, the extremity of the extended radixis,

c, draw D H at

GEOMETRY—CONSTRUCTION OF RECTILINEAL FIGURES, ETC.

draw the straight line CD through the second division from
A of the diameter A B, producing it
to meet the opposite circumference
at D. Join D A; then the line or dis¬
tance between the point D thus
found, and the adjacent extremity
A of the diameter A B, will be a side
of the required polygon; and if
successively applied to the circum¬
ference A D B, will form the penta¬
gon, as proposed.

Again, by the second method,
when the polygon to be inscribed is a hexagon, the
diameter is divided into six equal parts; and if lines be
drawn from the extremity of a perpendicular, whose position
and height is determined as before, so as to pass through
the first division on each side of the centre, and continued
to cut the opposite circumference, the chord which is
formed by joining the points of intersection will subtend
twice 30, or 60 degrees, which is a sixth part of the cir¬
cumference, and therefore a side of the hexagon.

These are general rules for the inscription of polygons;
but there are other methods of inscribing plane figures in
circles, as will be shown in the succeeding examples.

Problem XLIII. —In a given circle to describe an
equilateral triangle, a hexagon, or a dodecagon.

Let A D G E, &c. (Fig. 99), be the given circle. From any
point A in the circumference of the , _ Kg. 99.

circle, with the radius AB, equal
to that of the given circle, describe
the arc CBD, and join CD. From
c as a centre, with the radius c D,
cut the circumference at E, also
join D E and EC, then c D E will be
the equilateral triangle required.

For the hexagon, apply the radius
ab six times round the circumference of the given circle, and
the figure ACFEGD will be the hexagon sought. Bisect
the arc A c in h, and join A h, h c, then either of these lines
applied twelve times successively to the circumference, will
form the dodecagon, and be contained in the circle.

Another Method of inscribing
an equilateral triangle. — Let
ABE (Fig. 100) be the given circle,
and C its centre. Draw the diame¬
ter AB, upon which describe the
equilateral triangle ADB : join CD,
cutting the circumference in E;
then through E draw EF parallel
to D A, and E G parallel to D B, and
meeting the opposite circumfer¬
ence in F and G ; join F G. The tri¬
angle E F G is equilateral, and inscribed in the circle abe.

Problem XLIV.— In a given
circle to inscribe a square or
an octagon.

Let abc (Fig. 101) be the
given circle. Draw the diameters
A c and B D at right angles to each
other. Join AB, BC, CD, andDA:
these lines will form the square
ABcD. Bisect the arcs ab, bc,

C D. and D A, in the points e, f, g , and h.

Fig. 100. /

/ E

\/ c V

Fig. 101.

&c., and the octagon will be completed and inscribed, as
required.

Problem XLY— To inscribe a regular pentagon or
a regular decagon in a given circle.

Let A B c D (Fig. 102) be the given circle, of which o is
the centre. Draw the diameters
A c B D at right angles to each
other: bisect the radius Ao in e,
and from E, with the distance
E b, describe the arc B F, cutting I!

A c in F ; also from B as a centre, a
with the distance BF, describe
the arc F G, cutting the circum¬
ference in G. Join G B, and four
such chords applied from G round
the circumference will terminate in B, and form the pen¬
tagon. Bisect the arc BH in Jc: join B Jc and ilk. If the
same process be repeated with each of the arcs, or if
either of the chords B Jc or k H be carried round the cir¬
cumference, a decagon will be inscribed in the circle, as
required.

Problem XLYI. — To inscribe a regular polygon in a
given circle, by finding the angle at the centre.

Divide SCO degrees, or the whole circumference of the
circle, by the number of sides in Fig. kb.

the given polygon, and the quotient
will be the number of degrees con¬
tained in the angle at the centre.

Suppose, for example, that the
polygon to be inscribed in the
given circle A is a regular hexagon.

By a scale of chords, or any other
instrument for measuring angles,
make an angle at B the centre of the circle, equal to
60 degrees, the legs of which when produced meet the
I circumference at C and D. Draw the chord C D ; this line
applied six times successively to the circumference of
the given circle, will constitute the required hexagon. To
find the angle of any polygon, we have only to subtract
the angle at its centre from 180 degrees. For instance,
the angle at the centre of a hexagon being 60 degrees,
subtract 60 from 180, and the remainder is 120, the in¬
terior angle of the hexagon, or the angle formed by any
two of its adjacent sides. Suppose the required polygon
to be an octagon, the angle at the centre of this figure
is found, as directed above, to be 45 degrees, which being
subtracted from 180, gives for the remainder 135 degrees,
the angle formed by the adjoining sides of the octagon.

Or, more simply, for the hexagon draw any radius
CD (Fig. 103), and upon CD describe the equilateral triangle
BCD, which, being repeated round the circle, will complete
the hexagon.

Again, to find the angle at the base of the elementary
triangle of any regular polygon. Find the interior angle
of the polygon, by the rules already given, and one-half
of that angle will be the angle at the base of its elemen¬
tary triangle. As an example, the interior angle of a
hexagon is 120 degrees, one half of which is 60 degrees;
this is the angle at the base of the elementary triangle,
upon which the hexagon is constructed. Also, the angle
of the octagon is 135 degrees, one-half of which is 67^,
or 67 degrees 30 minutes—the angle at the base of its
elementary triangle.

Fig. 102.
B

o \ x / '

\ K

i j

. X

PRACTICAL CARPENTRY AND JOINERY.

Tig. 104.
1 C

Problem XLYII.— To describe a square, as also an

octagon, about a given circle.

Let ABCD (Fig. 104) be the given circle. Draw the
diameters A B and 0 D, intersecting
each other at right angles: through
the extremities of these diameters
draw the lines EOF, F B G, G D H,
and h A E, at right angles to A B and
C D, and intersecting at the angular
points E, F, G, and H: the figure
E F G H is the circumscribing square.

Join E G and F H, cutting the circle
in the points a, b, c, and d: also through these points
draw the lines e f, —, g h, —, k l, —, m n, and —, at right
angles to their respective radii, and they will complete
the octagon, which is also described about the circle A D

\tf yr

^>N

B c.

Problem XLVIII.— About a given circle to describe a
regular polygon.

Let it be required to describe a regular pentagon about a
given circle (Fig. 105), whose
centre is o. Divide the circum¬
ference into five equal parts—
the number of sides contained
in the given polygon—and
from the points ABCD and E,
thus found, draw to the centre
o the radii A o, bo, Co, Do,
and E o; also through these
same points draw the lines
/ A g, gBh, h C Jc, k D l, and
l E / perpendicular to their respective radii, and intersect¬
ing one another in the angular points /, g, h, k, and l : a
regular pentagon will be formed, and be described about
the circle.

LTpon the same principle, regular polygons of any num¬
ber of sides may be described about given circles.

Problem XLIX.— Any regular polygon being given,
to describe another having the same perimeter, but twice
the number of sides.

Let the regular pentagon (Fig. 106, No. i) represent the

Fig. 106.

given polygon: bisect any two of its adjacent angles, as at
A and B, by the straight lines A c and B c, intersecting
each other in C; then ABC is the elementary triangle of
the pentagon, and c its centre. Draw the straight line
D e (no. 2) equal to half A B (no. i), and upon D E describe
the triangle def (Problem XV.), similar to AB c. Bisect
the base line DE by a perpendicular drawn through the
vertex f, and produce this perpendicular upwards to G,
making F G equal to F E or F D. Join also G D and G E;
then G D E will be the elementary triangle of the decagon,
and G the centre. From G, with a radius equal to G D or
G E, describe a circle and ten chords, each equal to D E:
the base of the elementary triangle, applied successively
to the circumference, will produce a decagon having the

Fig. 105.

same perimeter, and, of course, twice the number of sides
as the given pentagon. That the decagon thus constructed
will have the same perimeter or contour as the pentagon,
is evident, seeing that each side of the ten-sided figure
is made equal to half a side of the five-sided figure or
pentagon.

Problem L.— Any regular polygon being given, to
construct another having the same perimeter, but con¬
taining any different number of sides.

For example, let it be required to construct a regular
octagon, having its perimeter equal to that of a given
hexagon. Divide A B, a side of the given polygon (Fig. 107,
No. 1 ), into eight equal parts, the number of sides in the
required figure. Let A c be six of these equal parts: draw
D E (no. 2) equal to A c, or to six-eighths of the given line

AB; and upon DE, by Problem XXXVII., describe a
regular octagon; its perimeter will be equal to that of the
given hexagon.

In the preceding example the figure required has a
greater number of sides than that which is given; but to
reverse the process, let D E (no. 2) be the side of a given
octagon, and let a hexagon be the polygon required.
Divide the line D E into six equal parts, and extend it to
F, so as to make E F equal to two of these parts, or the
whole line D F equal to eight of these same parts, and con¬
sequently equal to A B, which also contains eight parts,
each equal to the corresponding divisions on D E. Thus,
whatever may be the difference between the number of
sides in the given and proposed polygons, it is only neces¬
sary to divide a side of the given figure into the same
number of equal parts as there are sides in the one re¬
quired—extending or contracting the given side by the
number of equal parts, indicating the excess of the one
figure above the other in the number of sides.

Problem LI.— Any regular polygon being given, to
describe another leaving the same area, but a different
number of sides.

Suppose the given polygon to be a regular pentagon:
let it be required to describe a regular nonagon, the area
of which shall be equal to that of the pentagon (Fig. 108,
No. 1 ). Find, by Problem XLIX., the elementary triangle
A B C of the given pentagon. Divide the base A B into

Fig;. 108.

nine equal parts, and make D E (no. 2) equal to five of these
parts; then upon D E, as a base, construct the triangle
D e n, having its altitude or perpendicular height equal

GEOMETRY—CONSTRUCTION OF RECTILINEAL FIGURES, ETC.

Fig. 109.

to that of the triangle ABC. The triangle thus found
will be five-ninths of ABC. Describe another triangle
FGK (no. 3), by Problem XLVI., having its altitude equal
to that of D E H, and its vertical angle 40 degrees, which
is the angle at the centre of a regular nonagon. Again,
by Problem X., find a mean proportional between the
bases D E and FG of the triangles deh and FGK, and it
will be a side of the nonagon required. Draw a line N O
(no. 4), equal to the mean proportional thus found, and
upon it describe, by Problem XXXVII., a regular nonagon
(no. 4), and its area will be equal to that of the given pen¬
tagon (no. 1 ).

Problem LII.— To find the area of any regular
polygon.

Let the given figure be a hexagon : it is required to find
its area. Bisect any two
adjacent angles, as those
at A and B (Fig. 109), by
the straight lines AC and
B c, intersecting in c,
which will be the centre
of the polygon. Mark
the altitude of this ele¬
mentary triangle, by a dotted line drawn from C perpen¬
dicular to the base A B ; then multiply together the base
and altitude thus found, and this product by the number
of sides: half gives the area of the whole figure.

Or otherwise, thus. —Draw the straight line D E, equal
to six times, i. e., as many times A B, the base of the ele¬
mentary triangle, as there are sides in the given polygon.
Upon D E describe an isosceles triangle, having the same
altitude as ABC, the elementary triangle of the given
polygon: the triangle thus constructed is equal in area
to the given hexagon ; consequently, by multiplying the
base and altitude of this triangle together, half the product
will be the area required. The rule may be expressed in
other words, as followsThe area of a regular polygon
is equal to its perimeter, multiplied by half the radius of
its inscribed circle, to which the sides of the polygon are
tangents.

Problem LIII.— To describe any figure similar and
equal to a given rectilineal figure.

Let A B C D E F (Fig. 110, No. 1 ) be the given rectilineal
figure: it is required to construct another that shall be
equal and similar to it. Divide the figure into triangles,
by the diagonals AC, CF, and D F: draw a straight line

Fig. 110.

G N (no. 2) equal to af, and upon G N construct the triangle
G K N, the three sides of which shall be respectively equal
to those of the triangle A C F. Also upon G K, which is
by construction equal to A C, describe the triangle G H K,
having its sides G H and H k respectively equal to ab and
B C. Again, upon K N, which is equal to c F, describe the
triangle K L N, having its sides K L and L N respectively
equal to CD and D F. And lastly, upon L N, which is
equal to D F, construct the triangle L M N, having its sides

LM, MN respectively equal to DE and EF; then ghklmn
will be the figure required.

Any rectilineal figure may thus be described equal and
similar to a given rectilineal figure, i. e., by dividing the
figure or polygon into. triangles, and upon a line equal
to one of the given sides, constructing a succession of
triangles equal and similar to the corresponding triangles
into which the original figure is divided.

The simplest method of constructing a triangle equal
and similar to another, is the following:—Let A c F
(Fig. 110, No. 1 ) be the given triangle. Take G N equal to
AF; from G as a centre, with a radius equal to AC, de¬
scribe an arc, and from N, with a radius equal to c F,
describe another arc cutting the former in K; then, by
joining K G and KN, the triangle KGN is formed equal and
similar to A c F. The same process may be repeated, till
all the triangles in No. 1 are exhausted.

Problem LIY.— On a given line to describe a figure
similar to a given rectilineal figure.

Let abode (Fig. 111, No. i), be the given rectilineal figure,
and F L (no. 2 ) the given straight line. Divide abode into
triangles by the diagonals
B D and B E. From the
angular point A, with any
convenient radius, describe
the arc f g ; and from F (no. 2 ),
one extremity of the given
line FL, with the same ra¬
dius, describe the arc mn,
making it equal to / g ;
likewise from the angular
point E (no. 1 ), with any ra¬
dius, describe the arc h k,
and from the point L, with
the same radius, draw the
arc 0 p equal to h /c; then
through the points F and m,
as also through L and 0 , draw the straight lines F G and
L G, intersecting in G, and the triangle F G L thus found will
be similar to ABE. In like manner, upon GL construct
the triangle G K L, and upon G K construct the triangle
GHK, similar to the corresponding triangles BD E and
BCD (no. 1 ); then F G H K L will be the figure required.

Another mode of solution .— Let abcde (Fig. 112,
No. 1 ) be the given figure, as before, and F L (no. 2 ) the given
fine, upon which a figure similar to A B c D E is to be con-

Fig. 111.

Fig. 112.

structed. Divide the given figure into the triangles ABE,
DEB, and BCD. From 0 as a centre (no. 3), with any
moderate radius, describe the circle abed, &c. 1 rom

the point a, round the circumference draw the chords

PRACTICAL CARPENTRY AND JOINERY.

ab, be, cd, de, ef fg, and gh, respectively equal to the
lines A E, A B, B E, D E, D B, c D, and B C (to. i). _ Draw also
the radii a o, bo, co, d o, &c. ( no . 3 ). On the line a 0 find
0 Jc, a fourth proportional to the lines ab,ao, and the given
line F L; then through the point k draw k l parallel to
the chord a b, and it will be equal by construction to F L
(no. 2). From the point l, where the line k l meets the
radius b 0 , draw l m parallel to bc\ draw also the parallels
m n, n 0 , 0 p, p r, and r t, meeting the different 1 adii in
the points m, n, 0 , p, r, and t. Then upon F L as a base
construct the triangle fgl, having its sides F G and G L
equal to the lines l m and m n. Also upon G L describe
the triangle G K L, having its sides K L and G K equal to
no and op. Again, upon GK as a base construct the
triangle GKH, having its sides G H and H K respectively
equal to the lines p r and r t, and the rectilineal figure
fghkl thus formed will be similar

the given recti¬

lineal figure A B c D E.

Fig. 113.
c

CONSTRUCTION OF CIRCLES, CIRCULAR
FIGURES, &c.

Problem LY .—To find the centre of a given circle.

Let A c b D (Fig. 113) be the given
circle. Draw the chord line AB between
any two points A and B in the circum¬
ference : bisect the line AB by a perpen¬
dicular line CD, produced both ways
to meet the circumference in C and D.

Again, bisect the perpendicular CD in e,
and 6 is the centre of the circle.

Problem LYI .—To draw a tangent to a given circle,
that shall pass through a given Fig. m.

point in the circumference.

Let A (Fig. 114) be a given point in
the circumference of the circle, whose
centre is B. Draw the radius AB,and
through the point A draw the line c D
perpendicular to A B, and it will be
the tangent required.

Problem LVII .—To draw a tangent
any segment of a circle, through a
given point, without having re¬
course to the centre.

Let A (Fig. 115) be a given point
in the circumference of a circle.

Take any other point in the circum¬
ference, as B: join AB, and bisect the
arc AB in e: join also A e : then from
A as a centre, with a radius equal to A e, the chord of half
the arc, describe the arc feg, making e g equal to e f;
then through the points A and g draw the straight line
cad, and it will be the tan-
gent sought.

Another Method .—Let A
(Fig. 116) be a given point
in the circumference of a cir¬
cle. Take any two other
points, as B and D in the cir¬
cumference, equidistant from
A: join B D, and through
a draw A c parallel to B D: A c is a tangent to the circle.

to a circle, or

Fig. 115.

Fig. 117.

Fig. 118.

Other methods of drawing a tangent to a circle, from
a given point in the circumference, without finding the
centre. —Let ABC (Fig. 117) be
the given circle, and B the given
point in the circumference, from
which thetangent is to be drawn,
without finding the centre. Take
any other two points A and C, in
the circumference, one on each
side of B, and join them so as to
form the triangle ABC. Produce B c to D, making B D
equal to AC, and from B, with a radius equal to A B, de¬
scribe an arc; and from D, with the radius B c, describe
another arc intersecting the former in E. Through E
draw B E F, which is the tangent sought. For, join D E,
and as the triangle deb is by construction equal and
similar to the triangle ABC, of which the angle D B E is
equal to the angle B A c, the angle in the alternate seg¬
ment of the circle, B F must consequently be a tangent
to the circle at the point B.

Othervjise, Ulus. —Let ABC (Fig. 118) be the given
circle, and B the given point, as before. Take any two
points A and c in the circumference, equidistant from B;
join A C, and bisect it in D.

From B and D as centres, with
the same radius of any conve¬
nient length, describe arcs in¬
tersecting in E. From E, with
the distance EBorED, describe
the semicircle DBF, and join
DE, and produce it to meet the
semi-circumference in F. Join
B F, and it will be a tangent to the circle. For, join B D,
and as D B F is an angle in a semicircle, it must be a
right angle, and as one of its sides, B D produced, would
pass through the centre of the circle, B F must necessarily
be a tangent to that circle.

Problem LVIII.— To draw a tangent to cl circle from
a given point without the circum¬
ference.

Let A (Fig. 119) be a given point
without a given circle, of which B
is the centre; join A B, and upon
this line, as a diameter, describe
a semicircle cutting the given cir¬
cumference in C; join AC, and it
will be the tangent required.

Another method, without finding the centre of the
given circle. —Take any point c (Fig. 120) in that part of
the given circumference which is
concave towards A; join A C, inter¬
secting the opposite part of the cir¬
cumference in B ; produce c A to D, so
as to make A D equal to A B. Upon
C D, as a diameter, describe a semi¬
circle ; draw A E at right angles to
CD, meeting the semi-circumference
in E. From A as a centre, with the
radius A E, cut the given circle in F ; join A F, and it will
be the tangent sought.

Problem LIX.— A circle and a tangent being given,
to find the point of contact.

Let A bc (Fig. 121) be a given circle, ol which the centie

Fig. 119.

GEOMETRY—CONSTRUCTION OF CIRCLES, CIRCULAR FIGURES, ETC.

is E, and c D a tangent to that circle it is required to find
the point c. In c D take any
point /: join E / and bisect it in
g\ then from g, with the radius
g E or g f, describe a semicircle in¬
tersecting the tangent and circum¬
ference in c, which is the point of
contact sought.

Problem LX.— To describe the
circumference of a circle through three given points.

Let A, b, and c (Fig. 1 22), be the given points not in a
straight line. Join A B and B c: bisect
each of the straight lines ab and bc by
perpendiculars meeting in D; then A, B,
and C are all equidistant from D; there- A
fore a circle described from d, with
the radius da, d B, or d c, will pass
through all the three points as re¬
quired.

Problem LXI.— Given the span or chord line, and
height or versed sine of the segment of a circle, to find
the radius.

Let A b (Fig. 1 23) be the given span or chord line : bisect
it in D by the perpendicular line c E,
and make DC equal to the given height
or versed sine. Join A c, and also a
bisect it by a line drawn perpendicular
to it, and meeting D E in F: join F A,
then from F as a centre, with the ra¬
dius f A or F c, describe the arc acb,
which will be the segment required.

Another Method. — Let ab (Fig. 124) be the given chord.
Bisect it (as before) in D by the line c E, drawn at right
angles to it. Make Dc equal to the
given height or versed sine : join
AC, and from the point C, with
any radius less than A C, describe
the arc / ( 7 ; and from A, with the
same radius, draw the arc li h,
making it equal to f g. Through the point k draw the
line A e, which will meet c E in E;then the angle cae
will be equal to the angle ace. Also from E, with the
radius E A or E c, describe the arc ACB, which will form
the segment of a circle subtended by the given chord ab,
and having the given height or versed sine D c.

Another Method. — Let ab (Fig. 1 25) be the given chord;
and let the line L represent the given height or versed sine
of the arc. Bisect ab in c, and r) Ti* 125.

draw c D perpendicular to A B, and
equal to the line L or given height
of the arc. Draw the line A E, equal A
to c D, and making any angle with
AB: join c E, and produce AE to
F, so as to make E F equal to A c.

Through F draw F G parallel to c E,
and meeting A B produced in G. Produce D c to n, making
c H equal to CG; then bisect D H in 0 , and it will be the
centre of the arc; that is, an arc described from 0 , with the
radius D 0 , will pass through the points A and B, and form
the segment A D B.

Note .—The radius of an arc or arch, of which the span, or chord,
and height are given, may be obtained by calculation. Thus, divide
the square of half the chord by the height of the arc: to the quotient

add the height of the arc, and the sum will be the diameter of the
circle, or double the radius sought. For example, suppose the chord
a b (Fig. 123) 22 feet, and the versed sine CD 7 feet; then half of 22
is 11, the length of the half chord D a or D b ; and 11 squared is 121,
which, divided by 7, gives 174 for the quotient then 7 added to 17?;
is 24?-, the diameter of the circle c E, one half of which, 124 feet, is the
length of the radius F a or v c.

Problem LXIL— The chord of an arc, and also the
radius of the circle, being given; to find the height or
versed sine of that arc.

let AC (Fig. 126) be the given chord: from the ex¬
tremities A and 0, with the given
radius, describe arcs intersecting
each other in D: join DA and DC.

Bisect A c in e: join also DE, and
extend it till D B be equal to D A or
D c; then B E will be the height of
the arc required.

Or otherwise, thus. —Having found D as above; from
this centre D, with the given radius, describe the arc
abc; and having bisected A c in E, join D E, and produce
it to meet the circumference in B ; B E is the versed sine,
or height of the arc as before.

Or by calculation, subtract the square root of the differ¬
ence between the square of the radius and that of half the
chord from the radius, and the remainder is the height of
the arc.

As an example, suppose the half chord E A or E c to be
16 feet, and the radius 20 feet; then the square of 20 is
400, and the square of 16 is 256, which subtracted from
400, gives 144 of a remainder, the square root of which is
12 : this subtracted from 20 leaves a remainder of 8, the
height or versed sine E B.

Another Method, —Let ab (Fig. 127) be the given
chord; and let the straight line L represent the given
radius. Produce ab to c, so as to make A c double the
length of the line L; and on
ac, as a diameter, describe
a semicircle. Bisect A B in
D, and draw c E at right
angles to A c, and equal to
AD or D B ; then through E
draw E F parallel to B c,
cutting the semicircle in the
point F. From F let fall upon
A c the perpendicular F G.

Again, from D draw D H at right angles to A B, and equal
to c G ; then D 11 is the height or versed sine of the arc.
Let h D be extended to o, so as to make H o equal to the
given radius L; an arc described from O as a centre, with
the radius o H, will also pass through A and B, the ex¬
tremities of the given chord.

Note .— Though this method may appear somewhat round about,
it is at least novel, and can be demonstrated on strictly geometrical
principles.

Problem LXIII.— To describe a circle that shall touch
two straight lines given in position, and one of them
at a given point.

Let A B and A c (Fig. 1 28) be the given straight lines,
and D a given point in A B. If the lines are not parallel,
they will meet if produced. Let them meet in the point
A. From A C cut off AE, equal to AD; and in D B take
any point F, and make E G equal to D F. Join E F and D G,

PRACTICAL CARPENTRY AND JOINERY.

intersecting in the point o. From o, with the distance o T>
or o E, which are equal, describe
a circle cutting the given line
A B in the points D and H, and
A c in E and L. Draw the radius
ho, and extend it to meet the cir¬
cumference in K; join also lo,
and produce it to meet the op¬
posite circumference in M. Again,
join E M and D K, intersecting
in s. From the point of inter¬
section s, as a centre, with the
radius s E or S I), which are
equal, describe the circle end,
and it will touch both the given
lines A B and A c, and the former in the given point D.

Another Method.— Let ab and AC (Fig. 129) be the
given lines, and D the given point in A C, as before. Make

A E equal to AD: draw do at right
angles to A B, and meeting c A in G.

Cut off A F equal to A G, and join E F,
intersecting D G in H. From H, with
the radius he or H D, describe the
circle E k D, and it will touch the
given lines, and AB in D the given
point.

The plans here given of drawing
a tangent from a given point in the
circumference, without having re¬
course to the centre, are not to be
found in any book of practical geometry that we are ac¬
quainted with. They avoid the somewhat clumsy resource
of gauging arcs with the compasses in order to obtain
equal angles, which detracts from the elegance of the
solution of a problem. The exhibition of arcs ought, if
possible, to be avoided, except when they intersect, for the
purpose of obtaining certain points. In other cases they
mar the effect of the handsomest figures. This considera¬
tion induced having recourse to the circle in the con¬
struction of similar figures.

Problem LXIV.— Two circles touching each other
being given, to find the point of contact.

First, let the circles touch each other internally, as in
Fig. 130 (no. i). Find c and B, the
centres of these circles, by Pro- Fi **
blem LV.: join c B, and produce
it to meet both the circumferences
in A. This will be the point of
contact between the two circles.

Second, let the circles touch each
other externally, as in No. v, then
the point B, where the line A c
intersects the common boundary
of the two circles, is the point of
contact; A and c being their centres.

Problem LXV.— To describe with given radii two
contiguous circles, which shall also touch a given line.

Let A B (Fig. 131) be the given line, and c D and E F the
given ladii. I rom any point g in AB, erect a perpendicular
g h equal to c d, the greater radius, and set off g k equal
to E F, the lesser. Through k draw h m parallel to A B;
and from h, the extremity of the perpendicular g h, with
a distance equal to the sum of c D and E F, describe an arc

Fig. 131.

intersecting the parallel l'em in the point m. Let fall the
line m l perpendicular to A B,
and it will be equal to E F,
one of the given radii. From
m, with the radius m l, de¬
scribe a circle. Again, from
h, with the radius g h, de- K

scribe also a circle, and it will c D E F

touch the former in n, while g and l are the respective
points of contact with the given line A B.

Problem LXV1. — From a given circle to cut off a
segment, that shall contain an angle equal to a given
angle.

Let abd (Fig. 132) represent the given circle. From
any point B in the circumference, draw a tangent BC; also

from the point of contact B draw „ ^-^ Fig. i?3.

a chord line B A, so as to form an
angle equal to the given angle ;
then the chord A B will divide
the circle into two segments. In
that segment having its portion
of the circumference concave to¬
wards the tangent B c, take any point D, and join A D and
D B: the angle A DB in this alternate segment is equal to
ABC, which was made equal to the given angle; therefore
A D B is the segment required.

Note .—If a tangent and chord be drawn from any point in the cir¬
cumference of a circle, the angle formed by these lines will be equal
to the vertical angle of any triangle having the chord for its base,
and its vertex in any part of the circumference which bounds the
alternate segment of the circle.

Problem LXYII.— To divide a given circle into any
number of equal or proportional parts by concentric
divisions.

Let ABC (Fig. 133) be the given circle, to be divided
into five equal parts. Draw the
radius A D, and divide it into the
same number of parts as those re¬
quired in the circle; and upon the
radius thus divided, describe a
semicircle: then from each point
of division on A D, erect perpendi¬
culars to meet the semi-circumfer¬
ence in e,f g, and h. From D, the
centre of the given circle, with radii extending to each of
the different points of intersection on the semicircle, describe
successive circles, and they will divide the given circle into
five parts of equal area as required; the centre part being
also a circle, while the other four will be in the form of rings.

Problem LXVIII.— To divide a circle into three con¬
centric parts, bearing to each other the proportion of one,
two, three, from the centre.

Draw the radius A D (Fig. 134), and divide it into six
equal parts. Upon the radius thus divided, describe a
semicircle: from the first and third Fig. 134.

points of division, draw perpen¬
diculars to meet the semi-circum¬
ference in e and /. From D, the
centre of the given circle, with
radii extending to e and f describe
circles which will divide the given
circle into three parts, bearing to
each other the same proportion as the divisions on A d,

Fig 133,

GEOMETRY-CONSTRUCTION OF CIRCLES,

CIRCULAR FIGURES, ETC.

which areas 1, 2, and 3. In like manner, circles may be
divided in any given ratio by concentric divisions.

Problem LXIX. —To divide a given circle into any
number of parts, equal to each other both in area and
perimeter.

Let abcd (Fig. 135) be the given circle, which we
shall suppose is to be divided into five equal and isoperi-
metrical areas. Draw the diameter A C, and divide it into
five equal parts, at the points e, /,
g, and h. Upon Ac, a/, a g, and
A h, as diameters, describe a suc¬
cession of semicircles, all upon the
same side of the diameter A c. Then a.
reversing the operation, by com¬
mencing at c, describe upon c h,
c g, c/, and c e the same number
of semicircles, on the contrary side
of A C: these opposite semicircular lines will meet in the
points e,f, g, and h, forming the five equal and isoperime-
trical figures into which the circle was to be divided.

Note .—It ought to he understood that the diameter ac in the last
example, and the directing lines in the two preceding, form no part
of the boundary lines by which the respective circles are divided
into equal or proportional parts.

Fig. 135.
B

Problem LXX. —An arc of a circle being given, to
raise perpendiculars from any given points in that arc
without finding the centre.

Let AB (Fig. 136) be the given arc, and A, c, d, and e
the given points from which the joerpendiculars are to be
erected. In the arc e B take any point /, so as to make
e f equal to ed\ from d
and / as centres, with any
equal radii greater than
half the distance between
them, describe arcs inter¬
secting each other in g:
join e g, and it will be one of the perpendiculars required:
d h and c k are found in the same manner. In order to
raise a perpendicular from A, the extremity of the arc,
suppose the perpendicular c k to be erected: from c, with
the distance c A, describe the arc A m ; and from A, with
the same radius, describe c l, intersecting Amino: make
o l equal to o m, and join A l, which will be the perpen¬
dicular sought.

Note .—The perpendicular to auy curve, means a line perpendicular
to the tangent or chord of that curve.

Problem LXXI. —To draw a straight line equal to
the circumference of a given circle.

Let ABC (Fig. 137) be the given circle. Draw the
diameter A B, and divide it into seven
equal parts: then draw the straight
line T) e, equal to three times the length
of A B, and one-seventh part more;
and it will be a very near approxima¬
tion to the length
of the circumfer- i

|_J_

ence. ^

The diameter of the circle is to the circumference in the
ratio of 1 to 3d415926, &c. As the decimals might be
continued to infinity, it will be seen that the exact pro¬
portion cannot be obtained. The simplest approximation
to this ratio is that of 7 to 22, or of 1 to 3-f, and the pre¬
ceding line is drawn according to this last proportion,

F'g. 137.

which is sufficiently near the truth for most practical
purposes.

Problem LXXII.— To draw a straight line equal to
any given arc of a circle.

Let A B (Fig. 138) be the given fig. im.
arc. Find c the centre of the arc,
and complete the circle A ub. Draw
the diameter b d, and produce it
to e, until D E be equal to c D.

J oin A e, and extend it so as to
meet a tangent drawn from B in
the point F; then B F will be
nearly equal to the arc A b.

The following method of finding the length of an arc
is equally simple and practical,
and not less accurate than the »;
one given above.

Let AB (Fig. 139) be the
given arc. Find the centre C,
and join ab, B c, and c A. Bi¬
sect the arc ab in D, and join
also C D ; then through the point
D draw the straight line edf,
at right angles to C D, and meeting c A and c B produced
in E and F. Again, bisect the lines A E and B f in
the points G and H. A straight line G H, joining these
points, will be a very near approach to the length of
the arc A B.

Note .—Seeing that in very small arcs the ratio of the chord to the
double taugeut, or, which is the same thing, that of a side of the in¬
scribed to a side of the circumscribing polygon, approaches to a ratio
of equality, an arc may be taken so small, that its length shall differ
from either of these sides by less than any assignable quantity; there¬
fore, the arithmetical mean between the two must differ from the
length of the arc itself, by a quantity less than any that can be
assigned. Consequently the smaller the given arc, the more nearly
will the line found by the last method approximate to the exact
length of the arc. If the given arc is above 60 degrees, or two-thirds
of a quadrant, it ought to be bisected, and the length of the semi-arc
thus found being doubled, will give the length of the whole arc.

Since the two preceding problems cannot be exactly
solved by any rule founded upon geometrical principles, the
two following methods may also be used, which will give
the length of a circular arc, or indeed of any curved line
whatever, as accurately perhaps as it can possibly be ob¬
tained. The first is to bend a thin slip of wood or any other
elastic substance round the curve, then this slip extended
out at length will be a very near approach to the length
required. The second is to take a small distance between
the compasses, and suppose the curve to contain this dis¬
tance any number of times with a remainder. Upon a
straight line repeat this distance, or chord, the same
number of times, and transfer also the remainder from
the curve to the straight line: the straight line thus ex¬
tended will be very nearly equal to the given curve. It
is obvious that if a given curve be divided into any
number of equal parts or arcs, and if the chords of these
arcs be transferred to a straight line, the line thus formed
must be somewhat less than the curved line, as the chord
of an arc, however small, can never be exactly equal to
the arc itself. It is also evident, however, that the smaller
the distance between the points, and the more numerous
the parts taken on the curve, the more nearly will the
straight line to which these parts, or rather their chords,

PRACTICAL CARPENTRY AND JOINERY.

are transferred, approximate to the length of the curved
line itself.

Problem LXXIII. — To construct a triangle equal to
a given circle.

Let Fig. 140 (no. i) be the given circle, of which the
radius is a b. Draw by Problem LXXI. the straight line
C D (no. 2), equal to
the circumference
of the circle: bisect
it in E, and erect
E F perpendicular
to c D, and equal
to the radius A B:
join C F and D F,
and cfd is the
triangle required.

Or, as shown by the dotted lines, make C E, which is
equal to the semi-circumference, the base of the triangle,
and make its altitude g h equal to twice A B, or to the
diameter of the circle: join c li and E h, then the triangle
c E h is also equal to the given circle. Hence the area ot a
circle is equal to the product of its circumference by half
the radius; or to the product of its semi-circumference by
half the diameter or radius.

Problem LXXIV.— To describe a rectangle equal to a
given circle.

Let Fig. 141 (xo. i) be the given
circle, of which A B is the radius.

By Problem LXXI. draw the straight
line c D (no. 2), equal to the semi¬
circumference of the circle, and upon
this line as a base construct the
rectangle c D E F, having its altitude

Fig HI.

d E equal to A B, the radius of the
given circle, and it will be such as
is required.

Problem LXXY.— To describe a square equal to a
given circle.

Let Fig. 142 (no. 1 ) be the given circle, which has AB for
its radius. Draw the line
CD (no. 2), equal to the semi¬
circumference of the given
circle. Produce CD to E,
making D E equal to the
radius A B. Upon the whole
line de describe a semicircle,
and draw D F perpendicular
to DE, and meeting the semi¬
circumference in F. Amain,
draw the straight line G H
(no. 3), equal to D f, and upon this line as a base describe
the square G H 1 k, and its area will be equal to that of
the given circle.

Problem LXXYI.— To describe a square or a rectangle
that shall be equal to a given circle.

Let ABC (lig. 143, No. 1 ) be the given circle, of which
D is the centre. Draw the diameter adc, and draw the
double tangent G F 11 parallel and equal to AC: join D G
and D H, cutting the circumference in k and L. Bisect
G K and H L m M and N, and join M N. Draw the line
? i k (no. 2), equal to M N, and upon it describe the square
PRST, which will be very nearly equal to the area of the
circle A B c. Again, draw any indefinite line v w (x 0 . 3).

In it take any point x : draw x Y at right angles tovw,
and equal to M N or P R. In x w take any point z, and

1. Fig. 143.

from z, with the radius Y z, describe the semicircle Q Y w
Cut off x a, equal to x Q, and describe the rectangle ah wx:
it will be equal to the area of the circle.

Problem LXXYI I.' — To describe an arc of a circle
through three given points, without finding the centre.

Let A, B, and c (Fig. 144), be three given points, not in
a straight line. Connect these points, so as to form
the triangle ABC, the base of which, A c, will represent
the chord of the proposed arc. From A and c, with
equal radii, describe the arcs d e and f g, cutting A B
and B c in the points li
and h. Make the arc k f
equal to the arc h e, and
d h equal g k. Divide
each of these four arcs
into the same number of
equal parts. Then from
A and C, the extremities of the chord, through the first
and second divisions on the apes d h and k g, draw straight
lines, intersecting each other respectively in the points l
and on. In like manner, from A and c, through the first
and second divisions on the arcs li e and kf draw lines
intersecting respectively in the points 01 and o. A curve
line traced through the vertical angular points of the
triangles thus formed, will be the arc required.

The vertical angles formed as above, are all equal by
construction, and as they are upon the same base, they
must (according to Euclid) be in the segment of a circle.

Fig. in.

Note .— The most expeditious, as also the most accurate method for
tracing lines of this description, is the following. Having obtained
a sufficient number of true points in the proposed curve, and having
placed small nails in the several points, bend a thin slip of wood, or
some other elastic substance, round these nails; then by drawing
the pen along this slip on the side of the nails, the required curve
line will be described.

Another Construction.

—Let A, B, and c (Fig.

145) be the given points.

Join them so as to form
the triangle ABC. Upon
AC, as a diameter, de¬
scribe a semicircle, and
produce A B and c B to meet the semi-circumference in the
points D and E. From A set off on the semicircle the arc A F,

Fiji. 145.

GEOMETRY—CONSTRUCTION OF CIRCLES, CIRCULAR FIGURES, ETC.

equal to the arc CD: join c F, and from A, with a radius
equal to cb, cut the line cf in G: join AG, and produce
it to meet the semicircle in H. Bisect the arcs DII- and
ef in the points K and L. Join A K and c L, intersecting
each other in M. From M, the point of intersection, let
fall upon A c the perpendicular M N, and it will be the
altitude of the arc proposed.

Another Method. —Let A, B, and C (Fig. 146) be the
given points, through which the arc is to be drawn. Join
these points, so as to form the triangle ABC. Upon AC
describe a semicircle, and extend the lines A B and c B
to meet the semi-circumference in D and E. In the
semicircle A D E c insert the chords C F and A G, equal
to the chords A E and c d ; then the point x, where
c F and A G intersect, is a point in the proposed arc.
Bisect each of the arcs D F and E G in the points H and k,
and join A K and CH by lines intersecting in w, which is
also a point in the curve.

Join A F and c E, and draw
the chord E F. From A F
cut off F m, equal to B E,
and through m draw m n
parallel to F E, and cut¬
ting A E in n. Again, from
A F cutoff F v, equal to E n\
also from c E cut off c Y, equal to A v ; then a curve traced
through A, v, B, w, x, Y, and c, will describe the arc required.

Problem LXXYIII.— Three points, neither equidis¬
tant nor in the same straight line, being given, through
which the arc of a circle is to be described, to find the
altitude of the proposed arc.

Let A, B, and c (Fig. 147) be the given points. Con¬
nect them by the straight lines A B, B c, and A c, forming
a triangle, the base of which, viz., A c, will be the chord
of the arc whose height is to
be determined. Bisect the
vertical angle ABC by the line
B D, meeting the base in D :
bisect also the base A C in E,
and from E draw the line Eg
perpendicular to A C. From the vertex B, with any radius,
describe the arc h 1c, cutting the sides of the triangle A B D,
in the points h and k; and from any point g in the per¬
pendicular, with the same radius, describe the arc mn,
making it equal to the arc hk: join g m, producing it to
meet the base A C in o, or A C produced if necessary ; then

draw A F parallel to o g, and meeting it produced in F :

E F is the extreme height or altitude of the arc proposed.

Problem LXXIX.— A segment of a circle being given,
to produce the corresponding segment, or to complete the
circle with out finding the centre.

Let ABC (Fig. 148) be the given segment; and let
B be situated anywhere be- Fig. us

tween A and c: join A B
and BC: bisect the vertical

angle at B by the straight

line B D, meeting A c in the

point D. From the extrem¬
ities A and c, according to the
method previously shown, de¬
scribe angles on the contrary
side of the chord A C, equal
to the angle A B D or c B D, and produce the lines forming

these angles from A and c to meet in the point e ; then the
vertex e of the triangle A c E is a point in the arc, which
is to form the opposite segment. Fig. ub.

Find by Problem LXXVII any
other number of points in the
proposed arc, as f g, li, and k, and
join the extremities of the chord
A c by a curved line passing
through these points, and it will
complete the circle as proposed.

Another Method. — Let abc
(Fig. 149) be the given segment.

From B draw the line BD, cutting AC at any angle, and pro¬
duce it until DE be a fourth proportional to B D, D A, and DC.
Take any other point F, and join F D, producing it to G,
so as to make DG a fourth proportional to FD, DA, and D c.
Find the points K, N, R, &c., in the same manner, and a
curve line traced through these points will complete the
circle.

Problem LXXX. — To describe a semicircle by means
of a carpenter’s square, or a right angle, without having
recourse to its centre.

At the extremities of
• the diameter AC (Fig. 150),
fix two pins, then by slid¬
ing the sides of the square,
or other right-angled in¬
strument, d b, b e, in con¬
tact with the pins, a pencil
held in contact with the
point B will describe the semicircle ABC

Problem LXXXI.— To describe the segment of a circle
by means of two rods or straight laths, the chord and
versed sine being given.

Take two rods, eb,bf (Fig. 151), each of which must be
at least equal in length to the chord of the proposed
segment AC: join them together at B, and expand them,

Fig. 151.

so that their edges shall pass through the extremities of
the chord, and the angle where they join shall be on the
extremity B of the versed sine D B, or height of the
segment. Fix the rods in that position by the cross
piece g h, then by guiding the edges against pirn in the
extremities of the chord line A C, the curve ABC will be
described by the point B.

Problem LXXXII. — To describe a segment at tivice by
rods or laths, forming a triangle like the last, or by a
triangular mould; the chord and versed sine being given.

Let A c (Fig. 152) be the chord of the segment, and
D B its height or versed sine: join c B, and draw B e
parallel to A C, and make fl 152

it equal to BC. Fix a
pin in C and another in
B, and with the triangle
ebc describe the arc C B. Then remove the pin c to A,
and by guiding the sides of the triangle against A and B,
describe the other half of the curve A B.

Problem LXXXIII.— Having the chord and versed

Fig 150.

PRACTICAL CARPENTRY AND JOINERY.

\ \s~~ \ _ _

Lzz 1 - -1 1

i hr - _ — ;

—- \ -

sine of the segment of a circle of large radius given, to
find any number of points in the curve by means of in¬
tersecting lines.

Let A c be the chord and D B the versed sine.

Through B (Fig. 153) draw EF indefinitely and parallel
to AC: join A B, and draw A E at right angles to A B.
Draw also A G at right angles to A c, or divide AD and
E B into the same number of equal parts, and number the
divisions from A and E respectively, and join the corres¬
ponding numbers by the lines 1 1. 2 2, 3 3. Divide also A G
into tlie same number of equal parts as ad or E B, num¬
bering the divi¬
sions from A up- ''
wards, 1,2, 3,&c.;
and from the
points 1,2, and 3,
draw lines to b;
and the points
of intersection of
these, with the
other lines at h,
k, l, will be points in the curve required. Same with B c.

Another Method. — Let AC (Fig. 154) be the chord and
D B the versed sine. Join AB, BC, and through B draw
E F parallel to A C. From the centre B, with the radius
BA or BC, describe the arcs A E, c F, and divide them
into any number of equal parts, as 1, 2, 3: from the
divisions 1, 2, 3, draw radii to the centre B, and divide
each radius into the same number of equal parts as the
arcs A E and c F; and the points g, h, l, m, n, o, thus
obtained, are points in the required curve.

Ihese methods, though not absolutely correct, are suffi¬
ciently accurate when the segment is less than the
quadrant of a circle.

Problem LXXXIV.— The chord and versed sine of
an arc being given, to find the curve, without having
recourse to the centre.

Let A B (Fig. 155) be the chord, and D c the versed sine.
From c draw the tangent eg parallel to AB; and join c B,
and bisect it in/. Make
c g equal to C /, and
from / and g raise per¬
pendiculars to the lines
C f, c g, intersecting
in e, and e will be a
point in the curve. Or,

OF THE ELLIPSE, TLIE PARABOLA, AND THE
HYPERBOLA.

The Ellipse.— This curve is produced by the section of a
cone through both of its sides, but not parallel to its base.
If we expose to the sun a circle of wire, inscribed in a square
traversed by two diameters which cross its centre at right
angles, and so dispose of it that the rays of the sun may
be perpendicular to the plane of the circle (Fig. 156), the
shadow projected on a plane parallel to the plane of the
circle, will produce a figure in all respects similar to the

Fig. 155.

f"\

\\l;

(

\\\

which istlie same thins:,

bisect the angle f eg by the straight line C e, and to this
draw the perpendicular from f or g, meeting it in e, which
is the point required.

In the same way the point h is found by bisecting the
angle ecg, then bisecting the line e c by a perpendicular
cutting the bisecting line of the angle in h. As the seg¬
ments c e, e B, are equal, another point may be found
by joining e b, bisecting it by a perpendicular in 1c, and
making the perpendicular or versed sine equal to that of
the segment already found. Proceed thus until a suffi¬
cient number of points is obtained.

Fig- Io6>

original figure of wire. But if the circle is turned on one
of its diameters A B, with¬
out changing the situation
of the plane on which the
shadow is projected, then
the shadow of the square
E f G h shall be changed
to a parallelogram efgh,‘
and the shadow of the
circle A D B c to an ellipse

AC^BC.

2 . The shadow of the
axis A B is the major axis,
and the shadow cd of CD is the minor axis of the ellipse.

3. As the circle may be so turned in regard to the sun
and the plane on which the shadow is projected, that its
shadow will be only a right line, it follows that, in
turning, it can produce all the ellipses possible between
a circle and a straight line.

4. If in the interior of the circle of wire a regular
polygon of any number of sides be inscribed, such as a
decagon or dodecagon, it is evident that when the shadow
of the circle becomes an ellipse, the shadows of the sides
of the polygon will form a corresponding polygon, of
which the angles, by reason of the parallelism of the rays
of light, will always be at an equal distance from that
diameter which is perpendicular to the axis of rotation.
Consequently, if we trace on the plane which receives the
shadows the pai'allels e f, k a, m n, r s, g li, which pass
through the angles of the polygon of twelve sides, it will
be found that when the frame is turned, the angles follow
exactly the path of those lines.

This illustration is fertile in suggesting methods for the
graphic production of the ellipse, and of figures resembling
the ellipse, composed of arcs of circles. In regard to the
first, let us suppose lines parallel to A B, drawn through
the angles of the smaller inscribed polygon, intersecting
the lines drawn through the angles of the larger polygon
perpendicular to a b, and their intersections will give
points in the elliptic curve. Hence—

Problem LXXXV.— To draw an ellipse when the
i major and minor axes are given.

GEOMETRY—CONSTRUCTION OF THE ELLIPSE, PARABOLA, AND HYPERBOLA.

Let A c (Fig. 157) be the axis major, and D B the semi¬
axis minor. On A c describe the semicircle A E c, and from
the same centre D, and with the length of the semi-axis
minor as radius, describe the semicircle fBg. Divide

both semicircles into the same number of equal parts, 1,
2, 3, 4, &c.: through the points of division of the greater
semicircle draw lines perpendicular to AC, and through
the corresponding points of division of the lesser semi¬
circle draw lines parallel to A C, and the intersections of
the two sets of lines hkl mn o, &c., will be points in the
curve required.

In regard to figures resembling the ellipse, composed of
arcs of circles, the illustration suggests the following
method of producing them graphically.

Intersect each side of the polygon by a line perpen¬
dicular to it. Continue the perpendicular from the side
of the polygon nearest to the minor axis, until it inter¬
sects the continuation of the axis. Continue the next
perpendicular to intersect the last, and so on, and the
points of intersection so obtained become the centres from
which the flat arcs are described. The intersections of
the perpendiculars of the sides nearest the major axis,
with the major axis, give the centres of the quicker curves.

Problem LXXXVT— Let a b (Fig. 158) be the axis
major, and c D the axis minoi\ On the semi-axis major,

l'i?. 15P.

from the centre E, describe the quadrant A F, and on the
semi-axis minor, from the same centre, the quadrant G C:
divide each of these into the same number of equal parts,
and through the divisions draw lines parallel to the two
axes respectively: the intersections of these lines, 1', 2', 3', 4',
indicate the angles of the polygon. N ow, through the centre
of the side 4' C, draw a perpendicular cutting the minor axis
produced in t, and t is the centre of the arc 4'c. Through
the centre of 3' 4' draw a perpendicular cutting r t in v,
and v is the centre of the arc 3' 4'; and so on until the
last arc A 1', the centi-e for which is obtained at the inter¬
section of the perpendicular with the major axis at p. As

the ellipse is a symmetrical curve divided into four equal
and similar parts by its axes, the remaining three quar¬
ters can readily be drawn.

The ellipse may also be considered as the section of a
cylinder.

Let abcd (Fig. 159) be the pi’ojection of a cylinder, of
which the circle ehfk represents the base divided into
twenty equal parts: through each division draw a line
parallel to the axis of the cylinder, dividing the moiety
of the surface of the cylinder abcd into ten equal parts.
Now if we imagine abcd to be a plane corresponding

to the diameter n K, each line will be distant from it by
the length of the corresponding perpendicular, 16, 2 c,
3 d, 4 e. Now, suppose the diagonal A c to indicate a
section of the cylinder oblique to its axis, but perpendi¬
cular to the plane ABCD, the ellipse which results from
that section will be traced by raising from the points
where the parallels meet the line A c, the indefinite per¬
pendiculars, and setting off upon these the distances
1 b, 2 c, 3 d, 4 e. From this is derived the most commonly
used method of describing an ellipse by ordinates.

Problem LXXXYII .—To draw an ellipse with the
trammel.

The trammel is an instrument consisting of two prin¬
cipal parts, the fixed part in the form of a cross efgh

(Fig. 160), and the moveable piece or tracer k l m. The
fixed piece is made of two rectangular bars or pieces of
wood, of equal thickness, joined together so as to be in the
same plane. On one side of the frame so formed, a groove
is made, forming a right-angled cross. In the groove two
studs, k and l, are fitted to slide freely, and carry attached
to them the tracer k l m. The tracer is generally made
to slide through a socket fixed to each stud, and provided
with a screw or wedge, by which the distance apart of the
studs may be regulated. The tracer has another slider
to, also adjustable, which carries a pencil or point. The
instrument is used as follows:—Let AC be the major, and
HB the minor axis of an ellipse: lay the cross of the
trammel on these lines, so that the centre lines of it may
coincide with them; then adjust the sliders of the tx-acer,
so that the distance between k and to may be equal to
the semi-axis major, and the distance between l and m
equal to the semi-axis minor; then by moving the bar
round, the pencil in the slider will describe the ellipse.

PRACTICAL CARPENTRY AND JOINERY.

In Fig. 161 a modification of the instrument is shown.
Here a square e d f is used to form the elliptical quadrant
A B instead of the cross, and the studs h l k may be simply

Jfc

square while the tracer is moved. In this case the adjust¬
ment is obtained by making the distance h l equal to the
semi-axis minor, and the distance l Is equal to the semi-

. i

axis major.

Problem LXXXYIII.— Fig. 162 shows an ellipse con-

Fig. 163.

structed on the
principle of the
trammel, without
using that instru¬
ment. From any
points, as// in the
semi - conjugate
axis B E, draw
lines so intersect¬
ing the axis ac in h and n, as that fh and l n may be equal
to the difference between the semi transverse and semi¬
conjugate axes: produce
these lines to g, m,
and from the points /, /,

&c., on the minor axis,
and with the radius D c,
strike the small arcs,
cutting the lines in g
and m. These intersec¬
tions are true points in
the curve. This method
is obviously the b
same as by the
trammel; and in practice it is very useful; a thin straight¬
edge or a piece of still' paper being used to transfer the
points at once. Thus, on the edge of the slip of paper
mark off the length of the semi-axis major, a b (Fig. 163),
and then from b set off the distance b c, equal to the semi¬
axis minor; then by applying this to the drawing and
carrying it round, keeping the points a and c one on
each diameter, any number of points in the curve may be
obtained.

Problem LXXXIX .—An ellipse may also be de¬
scribed by means of a string.

Let a B (Fig. 164) be the major axis, and D c the minor
axis of the ellipse, and F G its two foci. Take a string
E G F and pass it over the pins, and tie the ends together,
so that when doubled it may be equal to the distance
from the focus F to the end of the axis, B; then putting a

Fig. 16 k

pencil in the bight or doubling of the string at H and
carrying it round, the curve may be traced. This is based
on the well-
known property
of the ellipse,
that the sum of
any two lines
drawn from the
foci to any points
in the circumfer¬
ence is the same.

Problem XC.

—The axes of an
ellipse being giv¬
en, to draw the . ,,

’ , - o

curve by inter- e

. r\ - cl

sections.

Let A c (Fig. 165) be the major, and D b the semi-axis
minor. On the major axis construct the parallelogram
A E F c, and make
its height equal
to the semi-axis
minor. Divide A E
and eb each into
the same number
of equal parts, and

number the divisions from A and E respectively; then join
A 1, 12, 2 3, &c., and their intersections will give points
through which the curve may be drawn.

Problem XCI. — To describe an ellipse by another
method of intersecting lines.

Let AC (Fig. 166) be the major and eb the minor axis:

5 B

Fig. 165

Fig. 166

draw A f and c G each perpendicular to A c, and equal to
the semi-axis minor. Divide A D, the semi-axis major, and
the lines A f aDd c G each into the same number of equal
parts, in 1,2, 3, and 4; then from E, through the divi¬
sions 1, 2, 3 and 4, on the semi-axis major ad, draw

the lines E h, E k, E Z, and Em; and from B, through the
divisions 1, 2, 3, and 4 on the line A F, draw the lines
I, 2, 3, and 4B;and the intersection of these with the

GEOMETRY—CONSTRUCTION OF THE ELLIPSE, PARABOLA, AND HYPERBOLA.

lines e 1, 2, 3, and 4, in the points h Jc l to, will be points
in the curve. In the same manner are drawn the

Fi^* 1G8.

rampant ellipse, Fig. 167, and the segment of the ellipse,
Fig. 168, and the rampant segment in Fig. 169, the

point F in the two latter figures being the intersection of
the major and minor axes.

Problem XCII.— To describe with a compass a figure
resembling tlie ellipse.

Let A B (Fig. 170) be the given axis, which divide into
three equal parts at the points f g. From these points
as centres with the radius / A, describe circles which in¬
tersect each other, and from the points of intersection

Fig. 170.

through / and g, draw the diameters c g E, c/d. From
C as a centre, with the radius c D, describe the arc D E,
which completes the semi-ellipse. The other half of the
ellipse may be completed in the same manner, as shown
by the dotted lines.

Problem XCIII.— Another method of describing a
figure approaching the ellipse with a compass.

The proportions of the ellipse may be varied by altering
the l’atio of the divisions of the diameter, as thus:—Divide
the major axis of the ellipse A B (Fig. 171), into four equal
parts, in the points f g h. On fh construct an equilateral
triangle / c h, and produce the sides of the triangle c f
c h indefinitely, as to D and E. Then from the centres /
and h, with the radius A f describe the circles a d g. t: e g ;
and from the centre c, with the radius c D, describe the
arc D E to complete the semi-ellipse. The other half may
be completed in the same manner. Bq r this method of

construction the minor axis is to the major axis, as 14

Problem XCIV. — To describe an ellipse with the
compass, the transverse and conjugate diameters being
given.

Let A c (Fig. 172) be the transverse diameter, and D B
the conjugate semi-diameter. Divide D B into three equal
parts in f and g, and make Ah, cJc each equal to two of
these parts : join h f, then from h and Jc, with the radius

Fig. 172.
B

A h, describe the circles A to, c n. Bisect the line hf by
the perpendicular l, meeting the axis B D produced in E.
From E, through h, draw the line E h m, meeting the
circle A m, and from E, with the radius E to, describe the
arc to B n, completing the semi-ellipse.

Another Method.—The two axes of an ellipse being
given, to describe the ellipse with a compass.

Let A c B E (Fig. 173) be the axes of the ellipse: draw
A F parallel and equal to DB: bisect it in 1, and join 1 B.
Divide A D also into two equal parts in 1, and from E,

through 1, draw the line E 1 k, meeting 1 B in Ic. Bisect
Jc B by the perpendicular h, meeting the axis B E produced
in G: join G Jc, cutting the transverse axis in to. Then
from to, with the radius to a, describe the arc A Jc, and
from G, with the radius G Jc, describe the arc Jc B.

Problem XC V.—TJie two axes ac, be, being given,
to describe witJi a compass a figure still more closely
approximating to the ellipse.

Draw A F parallel and equal to D B (Fig. 174): divide it
into three equal parts, and draw 1 B, 2 B. Then divide
A D also into three equal parts in 1 2d, and from E,

PRACTICAL CARPENTRY AND JOINERY

through the points 1 2 draw lines E m, E k , cutting the
lines 1 B, 2 B, in m and 1c. Bisect k B by a perpendicular
It, meeting E b produced in G: join k G. Bisect mk by a
perpendicular l, meeting IcGinn: join mn. Then G is
the centre for the arc B k, n is the centre for the arc k m,

and o is the centre for the arc m A. From the centre D
measure the points of intersection of the lines G k, n m,
with the axis A C, and transfer the measurements to the
other side of D ; and set off and make G r equal to G n.
Through r draw r s, and the centres G ri, for the other
half of the curve, will be obtained.

Problem XCVI. — The two axes ac, eb being given,
to describe a still nearer approximation to the ellipse
with the compass.

Draw AF (Fig. 175) parallel and equal to DB: divide
it into four equal parts: divide also A D into four equal
pa'rts; and from E and B, through the divisions in D A
and A F, draw lines intersecting each other in r, n, k.
Bisect k B by a perpendicular It, meeting B E produced in

FL. 175.

G: join g k. Bisect n k by the perpendicular l, meeting
k G in m: join mn. Bisect rn by the perpendicular o,
meeting mn in p : join pr. Then the points G, m,
p, and 8 will be the centres for the arcs B k, k n, n r, and
r A respectively. The lines G t, u y, w x, and the point
v are transferred by measurement, as before.

Note. —By dividing the lines a? and a d into a g'reater number
of parts, a still nearer approximation to the elliptic curve will be
obtained.

The ellipse being a symmetrical curve divided into four
equal and similar parts by its axis, it is only necessary to
obtain one of these. Thus, on the demi-axis major describe
the quadrant ab (Fig. 176), and on the demi-axis minor
the quadrant c D. Divide each of these into three equal
parts. Through the divisions in A B draw lines parallel to
the minoi axis, and through the divisions in c D draw
lines parallel to the major axis; and the intersections of
these in ef indicate the angles of a dodecagon of one
quadrant, of' which A e, e f, J d are the sides. On the
middle of each of these sides raise an indefinite perpendi¬

cular. The perpendicular g G raised on /d will cut the
prolongation of the minor axis in G, which will be the
centre of the arc / D. The perpendicular h H raised on
e f meets the line g G in H, which will be the centre of
the arc ef. The perpendicular k K raised on A e, meets

the major axis in m, which will be the centre of the arc
A e. The three remaining quadrants of the ellipse are
easily constructed from the data thus obtained.

The Parabola. —This curve is produced by the section
of a cone parallel to one of its sides. IL/pagoAi/, its name
in Greek, is given to it on account of one of its principal
properties, viz., that the square of the ordinate is equal to
the product of the correspondent abscissa by the parameter.

When the axis c D and double ordinates A C and c B
(Fig. 177) are known, divide the axis and ordinates into
the same number of
equal parts, as, for
example, into four.

Through the points
of division of the or¬
dinates draw inde¬
finite lines parallel to
the axis; then from
A draw through the
divisions of the axis
lines cutting the pa¬
rallels in a b c. Then
by bending a flexible
ruler over these points

the curve Dft&cB may be drawn. The other side may
be done in the same manner, or it may be transferred by
drawing lines parallel to the ordinates A c, C B.

In order to draw perpendiculars to the curve, it is
necessary to find its parameter, which is a third propor¬
tional to C D and c A. For this, draw AD and bisect it
by a perpendicular, which produce until it cut the axis
in F, from which as a centre, and with F D as a radius,
describe the semicircle D A L, which meets the axis pro¬
duced in L: cl is the parameter. Having found the
parameter, to draw a perpendicular to any point M in the
curve, proceed thus:—Draw through M a line MR, parallel
to A B, and set off* half the parameter c L froffi P to n, then
draw N m o, which is the perpendicular sought.

In like manner, from the point R draw R S parallel to
A B : make S T equal to half the parameter, and through R
draw T v, which is a perpendicular to the curve at R.

GEOMETRY—CONSTRUCTION OF THE ELLIPSE, PARABOLA, AND HYPERBOLA. 2 7

Problem XCYII. —To draw a parabola by intersec¬
tions.

Let A c (Fig. 178) be the base, and D b the height of the
curve. On a c construct the rectangular parallelogram
A E F C, its height being equal to d b. Divide the side
A E into anjr
number of equal
parts, 1 2 3 E,
and the half of
the base, A D,
into the same
number of equal
parts. From these divisions raise the perpendiculars 1 e,
2 f, 3 g, &c., and intersect them by the lines 1 F>, 2 b, 3 b,
drawn from the divisions in A E to the apex of the curve
b. The points ol intersection e f g, are points in the line
of the curve.

Problem XCVIII. — To draw a parabola by intersect¬
ing lines, its axis, height, and ordinates being given.

Let A c (Figs. 179 and 180) be the ordinate, and D b the
axis, and B its ver¬
tex : produce the rig. 179 . /

axis to E, and make / x /

B E equal to DB:
join E c,E A, and
divide them each
into the same num¬
ber of equal parts,
and number the
divisions as shown
on the figures. Join
the corresponding
divisions by the
lines 11, 2 2, &c,
and their intersec¬
tions will produce
the contour of the
curve.

Problem XCIX.

—To describe a pa¬
rabola by means of
a straight rule and
a square, its double
ordinate and ab¬
scissa being given.

Let Ac (Fig. 181)
be the double ordinate, and D B the abscissa. Bisect D c
in F; join b f, and draw F E perpendicular to bf, cuttin

Fig. 181.

the axis B D pro
duced in E. From H
Bset off bg equal
to D E, and G
will be the focus
of the parabola.

Make B L equal
toBG, and lay the
rule or straight-
edge II K on L,
and parallel to
A c. Take a
string M r G, equal in length to LE; attach one of its
ends to a pin at G, and its other end to the end M of the
square M N o. If now the square be slid along the straight¬

edge, and the string be pressed against its edge M N, a
pencil placed in the bight at r will describe the curve.

The Hyperbola.— Let there be two right equal cones
(Fig. 182) having the same axis, and cut by a plane 31 m,
N n, parallel to that axis, the sections M AN, man,
which result, are hyperbolas. In place of two cones

opposite to each other, geometricians sometimes suppose
four cones, which join on the lines E H, G B (Fig. 183), and
of which the axes form two right lines, F /, f' f, crossing
the centre c in the same plane.

To comprehend this it is necessary to imagine two entire
cones (Fig. 18-1) ECG, gcii, of which the angles at the

summits taken together may be equal to 180 degrees, or
two right angles —that is to say, the one is supplement to
the other.

If these cones are each cut into two equal parts by
sections through their axes, there will be four half cones,
which being placed upon their flat and triangular surface,
and disposed so that the halves of the same cone are
opposite each other, as ecg to dc h and D c E to Gc n,
they will compose together a rectangle e d ii g, of which
the diagonals, E H, D G, will be formed by the sides of the
demi-cones. If we now imagine these half cones cut by a
plane parallel to that on which they are laid, there will
result four hyperbolas, which are called conjugate. A a
will be the first axis of the opposite hyperbolas, 31 A to,
Nan, and B b, the second axis; but if we consider the
two other hyperbolas, B b will be their first, A a their
second axis. The diagonals, ECH,DCG, which represent
the sides of the cones, are called the asymptotes, and the
point C the centre. When the axes A a and B b are equal,
as in Fig. 183, the asymptotes form right angles, and the

PRACTICAL CARPENTRY AND JOINERY.

four hyperbolas are termed equilateral or circular; because,
if from the centre C a circle is described, it will touch the
summits of the four hyperbolas, which will be alike. But
if the angles are unequal, as in Fig. 184, the curve which
shall touch the summits must be an ellipse, wherefore such
hyperbolas are sometimes denominated elliptic hyperbolas.

Hyperbolas have a focus, which is thus found:—Take A b
(Fig. IS I) equal to C / and set it from C to F, F', / /', then
F, f', f /', are the foci, which, whether the hyperbolas are
circular or elliptic, are always equidistant from the centre c.

The property of the foci is, that if a line be drawn from
any point of a hyperbola to its focus, and another line
from the same point to the focus of the opposite hyperbola
on the same axis, then the difference of these two lines
will be always equal to the axis, on the production of
which the foci are. Thus, if a line OF (Fig. 181) be
drawn from a point in the hyperbola to its focus F, and
another line from the same point to the focus of the
opposite hyperbola/, then of —o F = the axis A a.

This property furnishes a ready mode of describing the
hyperbola graphically.

The first axis of any two hyperbolas A a (Fig. 185), and
their foci F / being known, to Vo 1 - Fig. 185.
find any number of points in the
curves. On the indefinite lino
e g (Fig. 186 ) make the point e n
equal to A a in Fig. 185: then
from the foci, with a radius greater
than A f or f a, describe the inde¬
finite arcs e e : then set off this
radius on the line eg (Fig. 186),
from E to 1, and take the differ¬
ence H 1, and with that as a
radius from the foci, describe
other arcs (Fig. 185) cutting the first arcs in 1 1, which
will be points in the hyper- f Fig. isg.

bolas. In the same

way

—I—

take a radius E 2, and describe arcs from the foci as centres,
and intersect them with other arcs having a radius
equal to H 2, and so on for the points 3, 4 The
intersections are points in the
curve through which the hyper¬
bola may be drawn.

The hyperbola can also be de¬
scribed by a continuous motion.

Let h K (Fig. 187) be a rule, one
end of which moves round the
focus F as a centre. To its other
end let there be attached a thread
a little shorter than the length of
the rule, and let the other end of
the thread be fastened to the focus
f of the hyperbola to be described.

When the rule is in the line of
the axis F a, the length of the cord
or thread shall be such that the
double b fall upon the summit of
the hyperbola a. Then making
the rule move round F as a centre, and at the same time
holding the double of the line close to the rule by a pencil
or tracer, the pencil will describe a hyperbola.

To draw tangents and perpendiculars to the hyperbola,
of which the asymptotes are known. From the points from

Fig. m

which it is required to draw the perpendiculars M N (Fig.
188), draw the lines
H M, K N parallel to the
asymptotes, and make
A H equal to H C, and
B k equal to K c. Then
the line A M E is a tan¬
gent to the curve at the
point M, and the line
B N F is a tangent to the curve at the point N; and if from
these points lines
be drawn M o, Fig. iso.

N P, perpendicu¬
lars to the tan¬
gents, these lines
will also be per¬
pendiculars to the
curve.

PuOBLEM C.—

The axis, vertex,
and ordinate of

a hyperbola being given, to find points in the curve.

Let d a (Figs. E

189, 190, 191) be
the ordinates, D B
the height or abs¬
cissa, and D E the
axis. The let¬
ters of reference
are the same in
all the figures.

Through B draw
F G parallel to
A c, and through
A and c draw A F,
c G, pai’allel to
D E : divide A D, a

a F into the same number of equal parts. From
draw lines to the
divisions in A D,
and from B draw
lines to the di¬
visions in A F,
and the intersec¬
tions of the lines
from the corre¬
sponding points
will give points
in the curve.

191.

CONSTRUCTION OF GOTHIC ARCHES.

These are the equilateral, the lancet, and the drop arch,
drawn from two centres;
and the four-centred and
ogee arch, drawn fr om four
centres.

The Equilateral Arcii.

—This arch is constructed
on the equilateral triangle
abc (Fig. 192), c and a
being respectively the cen-,. v
tres of the arcs a b, c b.

GEOMETRY—CONSTRUCTION OF GOTHIC ARCHES.

The Lancet Arch.— Bisect the width ab (Fig. 193) in
C, and produce A B indefinitely to D and E : from A and B,
with the radius A C, describe semicircles cutting A B in D
and E, the centres from which the arcs are to be described.

Fig. 193. Fig. 194.

* ii

To describe a four-centred

Fig. IOC.

Let A c (Fig. 194) be the width and db the height of
the arch. Join ab, cb, and bisect the lines ab, cb, and
draw through the points of bisection the perpendiculars
gf and he, meeting the line ac produced in e and /.
From the points e and f, with Yig. 195 . b
the radius/A or e c, describe
the arcs A g B, c h B.

The Drop Arch. —Join ab
(Fig. 195) and c B as before,
and bisect them; and through
the points of bisection draw
perpendiculars, cutting A c
in e and / which two points
are the centres of the arcs
A B, B c.

The Four-centred Arch.

Gothic arch. — Divide the
width of the arch A B (Fig.

196) into four equal parts, in
e, g, f. Draw AC, BD per¬
pendicular to A B, and from
the points A and B, with the
radius A B, describe the arcs
AD, B C. Join D 6, C /, and
produce the lines to h and Jc.

Then the points e and / are
the centres of the arcs A h,

B Jc, and the points C and D
of the arcs h l, Jc l. The
height of the arch in this ex¬
ample is f ths of its span.

Another method, ■producing a fatter arch.-
AB (Fig. 197) into four equal Kg . 199 .
parts, in e, g, /. and draw the
perpendiculars AC, BD: from
the points e and/, with the
radius e / describe the arcs A
e h,fh intersecting at h, and
through the point of inter¬
section draw e h, f h, and
produce the lines both ways
to Jc and D, and l and c respec¬
tively. Then from the points
e and / with the radius e A,
describe the arcs A Jc, B l; and
from the points c and D,
with the radius c l, describe
the arcs lm, Jc to. The height
of the arch is % ths of its span. <

The

/ \

\ 9

\\ //

\ \ / /

' \ / /

j \

In Fig. 198 the centres of the arcs A Jc, B l are found as
before, by dividing A B into Fig. 193 .
four equal parts, in e, g, /
and letting fall the perpendi¬
culars in this case, not from
the extremities of the line ab a
as before, but from the cen¬
tres e and /. From these,
then, let fall the perpendi¬
culars e c, / D, to meet the
lines e h and / Ji produced,
when c and D become

■» e

J the centres of the arcs
Jc m, l m.

The arch (Fig. 199) is still flatter than the last,
line A B is divided into four Fig. 199 .
equal parts in e, g, /; then
from the centres A and B,
with the radius A /, the arcs
e h, f Ji are described, and v
through the point of their
intersection the lines eh, f h
are drawn and produced until
they meet perpendiculars let
fall from e and f The arcs
A Jc, B l are described from e
and /, with the radius A e,
and the arcs Jc to, l m from
D c, with the radius D Jc. The
height is Id of the span.

Divide the line A B (Fig. 200) into six equal parts, in
the points e, g, h, Jc, f. From
e and / let fall the perpen¬
diculars e c, / D: from the
points A and B, with the A
radius A B, describe the arcs
B c, A D cutting the perpen¬
diculars e C, f D in c and D.

Draw Del, c/to. Then e
and / are the centres of the
arcs A /, B to, and C and D the
centres of the arcs to n, l n.

The height of the arch is, like
the last, sd of the span.

To maJce tJie crown of tJie arcJi flatter than in the last
figure, proceed as before for
the centres of the haunch
arches, by dividing A B (Fig.

201 ) into six parts, in e, /
g, Jl, Jc: draw A to, B n ; then
from the centres of these
arches e Jc, with the distance
between them as radius, de¬
scribe the arcs e l, Jc l, and
through l draw the lines e l,

Jc l produced to meet the
perpendiculars let fall from
e and Jc, in c D. Then the
points c and D are the cen¬
tres of the arcs to 0 , n 0 .

To draw a four-centred
arch when tJie height, width, or span are given.— Let a c
(F ig. 202) be the span of the arch, and D B its height.

Fig. 200.

Y S h k /

\ /

/ s

^ A.

- s \

Fig. 201.

PRACTICAL CARPENTRY AND JOINERY.

Divide D B into five equal parts, in 1,2, 3, g, B, and set
off on the line A c, from A
and c, three of those parts
to A li, c lc. Then from the
point g, with the radius g h,
describe the arc n h lc o, and
from the points h lc, with the
radius A li or c lc, describe
the arcs An, co. From the
intersections of these arcs
with the arc n h lc o, and
through the centres lilc, draw
n h F, o lc E. Then bisect n B,
o B in l and m, and produce
the lines until they meet
n h F and ole E in F and E,
which two last points are
the centres of the arcs n B,
o B.

Another Method. —Bisect the width of the arch A c (Fig.
203) in D, draw the perpendicular D B, and make it equal
to the height of the arch. Fiz. m
Divide it into three equal
parts: through the second
division draw 2 E parallel to
A C, intersecting the line C E
drawn fi om c perpendicular
to A C in E. Join E B, and
draw from B the line bgf
at right angles to it. On
C A set off c H equal to D 2;
and on B F set off B G equal
also to D 2: join G H, and
bisect it at n. From the
point f, where the bisect¬
ing line meets B G F, draw F II lc. Then n will be the cen¬
tre of the arc c lc, and F the centre of the arc lc B. For
the other side of the arch, draw fto parallel to A c; and
from the centre line B D produced, set off m equal to F:
draw m l.

Another Method. —Divide the height D B (Fig. 204)
into two equal parts, and
draw 1 E parallel to A C,
and meeting the perpen¬
dicular ce in E. Join
B E, and draw B F at right
angles to it: set off from
C and B the points H and
G, equal to Dl. JoinHG,
and bisect the line in lc.

The point F, in which the
bisecting line of G H cuts
B F, is the centre of the
larger arc l B, and H is
the centre of the smaller
arc c l.

To describe a Gothic
arch by the intersection
of straight lines, when the span and height are given .—
Bisect A c (Fig. 205) in D, and from the point D and the
extremities of the line draw A E, D B, c F at right angles
to A c, and each equal to the height of the arch: join E B,
b f. Divide the line D B into any number of equal parts,

Fig. 205.

1 /

' / 7i S' j

\ \

' \

! /

/ sj/ 2

\ X, \

1 / .

\ ,

/ f

N \ »

/- _ L

1, 2. 3, B, and through the divisions draw lines parallel to
A c. Divide the line E B,

B F into the same number
of equal parts, and from A
and c draw lines A 1, A 2,

A 3; and their intersection
with the horizontal lines in
/, g, h, will be points in the A
curve required.

To draw the arches of Gothic groins, to mitre truly
with a given arch of any form. — Let A c (Fig. 206) be the
width of body range, and B D its height. Fig 206 . B
Join CB, and divide it into any num¬
ber of equal parts: from the centre D,
through the points of division, draw
straight lines D 1, D 2, D 3, D 4, meeting

the circumference of the arch in l, m,

’a -

n, o. From B, through these points in
the circumference, draw Bo, Bn, B m, B l, and produce
them to meet a perpendicular raised from c.

Let A c (Fig. 207) be the width of the groin arch, and
D B its height. Join A B, and divide it into the same
number of parts as CB in Fig. 206; and draw through the
points 1, 2, 3, 4 the lines D 1,

D 2, D 3, D 4. Then from
A draw a line perpendicu¬
lar to A c, and transfer to it
the divisions from the cor¬
responding line in Fig. 206;
and from these divisions
draw lines to b. The intersection of these lines with the
lines i) 1, D 2, &c., Avill give points through which the
curve may be traced.

To draw an ogee arch .—Divide the width A B (Fig.
208) into four equal parts,
in d, c, e\ and on d, e
erect the square cl, f g, e.

The points d, e, f, g, are the
centres of the four quad¬
rants A lc, lc l, B h, h l, com¬
posing the arch.

Another Method. — Let A C
r> B the height of the arch.

J oin A B, B c, and bisect the
lines in e,f\ then from the
centres A, e, b, /, C, with the
radius a e or e B, describe
the arcs intersecting in the
points g, li, lc, l, which are
the centres of the four arcs
composing the ogee arch.

Another Method, when the arch is equilateral.

/ / A/ \ \

/ \ \

[ / \ \ \

I \\\

Mg.

. 209) be the width and

Fig. 209

AB (Fig. 210) in c, join A h, /
b' h. From c, with the
radius A or b, describe the
arcs A d, Be; then, to find
the centres of the other Fig
arcs, from the points d, e,
and h as centres, and with
the same radius as before,
describe arcs intersecting: .
each other in the points /
and g, which are the centres

■--- A

Bisect

"''t?

\ /

' , /

/1 \ '

/ 1 \ \

\ / /

\ \

210 .

/ . X

/ ,

,j> \

\ \

of the arcs h d, h e.

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

PART SECOND.

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

Before proceeding to introduce the student to stereo¬
graphy, it is proper to describe the instruments used by
the arcliitectural draughtsman, and to explain their con¬
struction and application.

Cases of drawing instruments generally contain com¬
passes of vai'ious kinds, scales, protractors, parallel rulers,
and drawing pens. Each of these shall be described in order.

Coirp asses.

■ These are of different kinds, viz.:—dividers, compasses
with moveable legs, bow-compasses, directors, propor¬
tional-compasses, and beam-compasses.

Dividers .—These are used for taking off and transfer¬
ring measurements. The common dividers are moderately -
sized compasses, without moveable legs, working somewhat
stiffly in the joint, and having fine, well-tempered points
of equal length, lying fairly upon each other when closed.
When dimensions are to be taken with extreme accuracy,
these dividers will not, under the most skilful manipu¬
lation, work with the delicacy and certainty that are re¬
quired. In such cases, the draughtsman resorts to his hair
dividers: these are compasses in which one leg is acted
upon by a spring; and a finely-threaded screw, pressing
upon this spring, changes the direction of the point to
the nicety of a hair’s-breadth. The distance to be measured
is first taken as accurately as possible between the points
of the compasses, and the screw is then turned until the
dimension is obtained with positive exactness. This instru¬
ment is useless unless it be of the very best quality: it
must work firmly and steadily; and the points need to be
exquisitely adjusted, exceedingly fine, and well-tempered.

Instruction for using dividers, which are applied only
to measure and transfer distances and dimensions, may
appear superfluous; but there are a few simple directions
which may save the young draughtsman much perplexity
and loss of time. It is, of course, desirable to work the
compasses in such a manner that, when the dimension is
taken, it may suffer no disturbance in its transfer from the
scale to the drawing. In order to this, the instrument is
to be held by the head or joint, the forefinger resting on
the top of the joint, and the thumb and second finger on
either side. When held in this way, there is no pressure
except on the head and centre, and the dimension between
the points cannot be altered; but, if the instrument be
clumsily seized by a thumb on one leg, and two fingers
on the other, the pressure, in the act of transference, must
inevitably contract, in some small degree, the opening of
the compasses; and if the dimension has to be set off
several times, the probability is, that no two transfers will
be exactly the same. And, whilst it is all-important to
keep the dimension exact, it is also desirable to manipulate
in such a way, when setting off the same dimension a
number of times, that the point of position be never lost.
Persons unaccustomed to the use of compasses, are very
apt to turn them over and over in the same direction,

when laying down a number of equal measures, and this
necessitates a frequent change of the finger and thumb,
which direct the movement of the instrument: the con¬
sequence is, either that the fixed leg is driven deep into
the drawing, or it loses position. Now, if the movement
be alternately above and below the line on which the dis¬
tances are being set off, the compasses can be worked with
great freedom and delicacy, and without any liability to
shifting. If a straight line is drawn, and semicircles be
described alternately above and below the line, it will
show the path of the traversing foot. If the two move¬
ments are tried, the superiority of the one recommended
will at once be discovered. The forefinger rests gently
on the head; and the thumb and second finger, without
changing from side to side, direct the movement for setting
off any number of times that may be required. Before
applying the dividers to the paper, they should be opened
wider than the required distance: the point of the near
leg is then to be put gently down on the paper, the leg
resting against the thumb, and the other leg gently
brought to the required distance. The pressure is thus
resisted by the thumb, and there is no risk of making a
hole in the paper. This remark applies to the use cf com¬
passes of all kinds.

There is a third sort of dividers, named the Spring
Compasses, in which steadiness is combined with the
delicacy of adjustment of the hair compasses. The last-
named are liable to error, in consequence of the weakness
of the spring leg; and without very careful handling, the
dimension, though taken with extreme exactness, cannot
be laid down correctly. Now, the spring compasses, of
which we annex a figure (Fig. 211), have, from their
principle of construction, a steadiness and firmness which
cannot be surpassed. The legs are fixed to a steel-spring D,
whose elasticity keeps the points extended: the screw A B is
fastened by apivot-joint, and passes through
a slot at B, and the opening of the instru¬
ment is adjusted by a nut working upon the
fine thread of the screw. The legs are
jointed below the screw ; and the required
dimension can therefore be taken between
the points nearly , and afterwards more ac¬
curately determined by a gentle turn of the
nut. The instrument is worked by the
forefinger and thumb on the head; and, in
settlin'- off, the alternate motion before-
mentioned is to be observed. The figure
cives the exact size of an instrument suit-

able for small dimensions; but the draughts¬
man ought to provide himself with a variety
of sizes, which will take in all the dimen¬
sions he may ordinarily require. Anil the
advantage of having several of these instruments is, that
dimensions which occur frequently in a drawing, can be
left in one or more of them undisturbed; and thus much

Fix. 211.

PRACTICAL CARPENTRY AND JOINERY.

of the time saved that would otherwise be occupied in
re-adjustment. When purchasing spring compasses, the
vouns draughtsman must select only those in which the

JO O v .11

screw works on a pivot, since, if it be fixed immoveably
at A, it cannot adapt itself to the various extensions of
the legs, and the fine thread is then much injured by the
unequal pressure of the nut.

Compasses with Moveable Legs .—Every case of instru¬
ments is provided with a pair of compasses, of which one
leg is moveable, and may be substituted by others carry¬
ing a pen or pencil. This instrument serves, in the first
instance, as a divider ; and the additional legs enable the
draughtsman to describe arcs and circles temporarily in
pencil, or permanently in ink. As it is an object to effect
the change of leg with little loss of time, some attention
must be paid, when selecting the drawing-case, to the
contrivance for removing and securing the legs with
despatch. The worst construction is that wherein the leg
is secured by a screw, since it involves a tedious process of
fixing and unfixing; and the best is, perhaps, the bayonet
mode of inserting the leg, which is effected in an instant,
and makes a firm junction. In working with the pencil
and pen legs, it is desirable to keep them vertical to the
drawing; and indeed, with the last, it is absolutely neces¬
sary, as otherwise the arc or circle would be described
with the side of the pen, and either it would not mark at
all, or would produce a ragged, unsightly line. These legs
are therefore jointed, so that, in proportion as the com¬
passes are extended, they may be bent inward, and brought
to a vertical position. But this adaptation unfits the
instrument to describe arcs and circles of very small radii;
for the moveable leg has usually a little additional length
to compensate for the bending of the joint, and this pre¬
vents a steady adjustment when the points of the com¬
passes are brought near together. In return for this
restriction, however, we have a contrivance for describing
arcs and circles of larger radii than fall within the usual
range of the instrument. It is found, on trial, that if we
attempt to describe an arc of more than a certain radius
with the pen-leg, we require to throw the other leg into a
very oblique position, with the almost certainty of losing
its place, and making a false permanent line. To meet
this difficulty, a brass lengthening bar is provided, which
receives the pen-leg in the one end, and joins to the
compasses, by a bayonet-fixing, at the other. When thus
lengthened, the instrument will command a radius of six
or eight inches with ease and security.

The pencil-leg consists of a tube split through half its
length, with a ring to move up and down, by which a
small short pencil is fixed much on the same principle as
the chalk in a portcrayon. The pen-leg is formed of two
blades of steel, terminating in thin, rounded, and well-
adjusted points. A spring is inserted between the blades,
to separate them; and they are brought together by a
screw which passes through them, and which is capable of
adjusting the pen for a strong line, or for one as fine as
a hair. In using this leg, the screw is slackened, and ink
inserted between the blades with a quill-pen, or a camel-
hair pencil, according to the nature of the colouring fluid
used; and the blades are then brought gradually together,
until they will produce a line of the desired quality. The
draughtsman will, of course, try the line on his waste-paper
before he ventures to describe it on his drawing. A third

moveable leg, named the Dotting Pen, is sometimes in¬
cluded in the drawing-case, and though it is an instru¬
ment rather uncertain in its performance, some draughts¬
men manage to employ it with very good effect
in the drawing of dotted lines. It is jointed in
the same manner as the pen and pencil legs, and
consists of two blades terminating in a small
revolving wheel E (Fig. 212), which is retained
in its position by the screw D. The one wheel
might, of course, be permanently fixed, but usu¬
ally there are several given with the pen, to
produce dots of greater or less strength; the con¬
trivance of the screw, therefore, admits the ready
substitution of one wheel for another. When this
pen is used, ink must be inserted between the
blades over the wheel; and the latter should be
run several times over the waste-paper, until, by
its revolution, it takes the ink freely, and leaves a regu¬
larly dotted line in its course. It must be admitted that,
with every care, it sometimes fails in its duty, and leaves
blank spaces; but where much straight or curved dotted
line is required, it will very much abridge the draughts¬
man’s labour; and, if it performs well, will dot with far
greater regularity than the steadiest hand.

The compasses with moveable legs have frequently to
describe an entire circle, and an inexperienced hand finds
some difficulty in carrying the traversing leg neatly round
the circumference without the other leg losing position.
Some persons have recommended the movement of the
dividers, that is, to form half the circle in one direction,
and half in a reverse direction; and this may answer very
well with the pencil-leg, but not with the pen-leg; since
it is almost impossible, in the latter case, to unite the two
semicircles without leaving marks of junction, which very
much injure the continuity of the line that forms the circle.
This being the case, it is preferable to adopt a method that
shall answer equally well with either leg, and which, by
one continued sweep, shall complete the figure. It is very
desirable to use compasses for circles that have a due rela¬
tion to the radii of the circles to be described; that is to
say, such as will allow both the revolving and fixed leg to
be nearly vertical to the paper; for if the fixed leg is in¬
clined obliquely, it is very apt to lose position, or to work
a large unsightly hole in the drawing. When the com¬
passes are so adjusted that both legs are vertical, or very
nearly so, it is at once a simple and elegant movement that
carries the traversing point round the circle. Let the fore¬
finger rest on the head, and the thumb and second finger
on the sides; commencing the sweep at the top, and to¬
wards the right hand: the second finger becomes dis¬
engaged when a quadrant is described, and the forefinger
then winds the head along the inner part of the thumb,
until the point has performed the entire circuit. It is not
always desirable to commence the circle at the top, but
more frequently from a point which it is to touch accu¬
rately: this, however, presents no difficulty that the
method of sweeping does not meet. The only thing ne¬
cessary is to place the fingers and instrument in position,
in the first instance, with reference to the starting-point;
and this is readily done by a slight bending of the wrist.
To one familiar with the use of instruments, these in¬
structions for manipulation may appear unnecessarily
minute; but if he will place his compasses for the first

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

time in the hands of a youth, and observe his lack of in¬
tuitive dexterity, he will admit that they are in no degree
too minute for a tyro.

Bovj Compasses. —In every case of instruments, making
any pretensions to completeness, there is one pair of Bow
Compasses; but we shall advert to several kinds, each
recommended by a peculiar excellence or adaptation to
the draughtsman’s purposes. This instrument may be
described, generally, as small compasses suited for de¬
scribing arcs and circles of short radii, and which can
be worked with great facility by the finger and thumb.
The most ordinary construction, and that usually found
in the drawing-case, has the legs, one of which is a pen,
moving freely on a joint, and terminating at the top in a
small handle. The pen-blades are a little longer than the
other leg, in order that the latter may keep its vertical
position throughout a sweep, and not lose its centre. The
performance of this small instrument is very satisfac¬
tory; a succession of small arcs and circles may be de¬
scribed rapidly and delicately, without leaving the centres
strongly marked by the fixed point; and this contributes
much to the beauty of a drawing, since nothing is more
offensive than to see the paper studded with small holes
exposing every insertion of the compasses.

The annexed engraving (Fig. 213) shows an improvement
of the instrument. The vertical position of the pen-leg is
secured by the joint C; the blades B are closed by the
screw f, which, according as it is tightened or relaxed,
renders the line finer or stronger at pleasure; and the
box-screw A unites the legs and handle firmly. The leg
A D has a socket at its extremity, to admit a steel needle,
which is fastened by a clamp e. This last contrivance
is simple but valuable. The fine point of the compasses
is soon destroyed by continued use, and to renew it by
grinding reduces the length of the leg, and in course of
time renders the instrument worthless; whereas, a fresh
needle can be introduced into the socket as often as is
necessary, and a constant delicacy of point maintained.

Bow compasses can also be had carrying a pencil-leg.
They differ from those previously described only in having
a holder for the reception of a thin short pencil, which is
held tight by the screw F (Fig. 214). These have also the
joint c, the needle-point E, and box-screw joint A. Bows

to carry a pencil are seldom included in the drawing-
case; but they, and indeed all, of the other instruments,
can be purchased separately. The pencil-leg is certainly a
very useful aid to the draughtsman, since there are many
occasions where it is desirable to get all the parts of a
drawing inserted with the lead, before making them per¬
manent ; and arcs and circles of small radii are not readily
described with the larger compasses, supposing them to be
properly adapted for sweeping curves of greater magnitude.

Another sort of Bows, named Spring Bow-Compasses
(Fig. 215), though limited in their application to small
curves and circles, are very delicate and exact instru¬
ments, so far as their range extends. They are in principle
identical with the Spring Dividers, which we have already
described, and one leg is provided with a holder for a
pencil or pen. The advantages of this construction can
be appreciated only by those who know the difficulty
of securing a small radius, with perfect exactness, by
compasses that are extended and closed in the ordinary
manner; and who have experienced the mortification of
seeing an otherwise fine drawing marred and disfigured
by small curves or circles, described with a radius de¬
viating from truth in an error of perhaps not more than
a hair-breadth, yet failing in one instance to reach the
point of junction, and in another passing beyond it.

Directors, or Triangular Compasses .—This instrument
is used for taking three angular points at once, or for
laying down correctly a third point with relation to
other two- One form of construction is that of an ordin¬
ary pair of compasses, with an additional leg attached by
a universal joint; and another contrivance, much recom¬
mended for simplicity and facility in its use, is a solid
plate of three arms, each arm carrying a moveable limb,
into which a short pointed needle is inserted at right
angles. In using the first, the compasses are opened, and
two points taken, and the additional leg is extended in
any direction to take up the third point; the manage¬
ment of the second is equally easy, the needle-points are
successively adjusted to the angles by the
flexure of the moveable limbs. With either
instrument, the draughtsman is saved the
tedious process of constructing triangles, and
determining the relative position of neigh¬
bouring points in his drawing.

Proportional Compasses. —These are used
for the enlargement or reduction of drawings.

The simplest form is that named ivholes
and halves, which may be described as two
bars pointed at each extremity, and working
transversely on a box-screw joint, and form¬
ing, as it were, two compasses, the legs of .he
one being twice the length of those of the
other. If any distance be taken between the
points of the longer legs, half that distance
will be contained at the other end. The
application of the instrument to the reducing
or enlarging any drawing one-half, is suffi¬
ciently obvious. The proportional compasses,
properly so called, is a more complicated contrivance, and
admits of more varied application. Its form and general
construction are seen in the annexed engraving (Fig. 216).
It is in principle the same as the wholes-and-halves, with
this difference, that the screw-joint c passes through slides

PRACTICAL CARPENTRY AND JOINERY.

moving in the slots of the bars, and admits of the centie
being adjusted for various relative proportions between
the openings A B and d e. Different sets of numbers aie
engraved on the outer faces of the bars, and by these the
required proportions are obtained- I lie instrument must
be closed for adjustment, and the nut C loosened; the
slide is then moved in the groove, until a mark across it,
named the index, coincides with the number required;
which done, the nut is tightened again-

The scales usually engraved on these compasses are
named Lines, Circles, Planes, and Solids.

The scale of lines is numbered from 1 to 10, and the
index of the slide being brought to any one of these divi¬
sions, the distance D E will measure A B in that propor¬
tion. Thus, if the index be set to 4, D E will be contained
four times in A B.

The line of circles extends from 1 to 20; and if the
index be set to 10, D E will be the tenth part of the
circumference of the circle, whose radius is A B.

The line of planes, or squares, determines the proportion
of similar areas. Tims, if the index is placed at 3, and
the side of any one square be taken by A B from a scale
of equal parts, D E will be the side of another square of
one-third the area. And if any number be brought to the
index, and the same number be taken by A B from a scale
of equal parts, D E will be the square root of that number.
And in this latter case, D E will also be a mean propor¬
tional between any two numbers, whose product is equal
to A B.

The line of solids expresses the proportion between
cubes and spheres. Thus, if the index be set at 2, and the
diameter of a sphere, or the side of a cube, be taken from
a scale of equal parts by a b, then will D E be a diameter
of a sphere or side of a cube of half the solidity. And if
the slide be set to 8, and the same number be taken from a
scale of equal parts, then will D E measure 2 on the same
scale, or the cube root of 8.

The scale of lines and that of circles are those of most
value to the draughtsman. The first enables him to reduce
or enlarge in any required proportion ; and the second
gives him the side of the square or polygon, that can be
inscribed in a given circle. The instrument needs to be
used carefully, since its accuracy depends on the preser¬
vation of the points. If both or either of these are broken,
or diminished in length, the proportions cease to be true.
In place of using the proportional compasses in setting off
a number of times, which would soon wear the points,
rather take the distance in the Dividers.

Beam Compasses .—I he draughtsman has frequentlv to
measure and lay down distances, and to sweep with radii,
which the ordinary instruments cannot reach. In these
cases, and when extreme accuracy is necessary, he resorts
to the Beam Compasses, which are usually made of well-
seasoned mahogany, with a slip of holly or box-wood on
the lace, to carry the scale. Two brass boxes with points
are fitted to the beam, one of which moves freely to take
in any lequiied distance, and the other is connected with
a slow-motion screw working in the end of the beam, and
can thus be adjusted with extreme delicacy to any measure
or radius. Reading-plates, on the Vernier principle, sub¬
divide the divisions of the scale on the beam, and by them
any measure to three places of figures is taken with extreme

truth. Referring to Fig. 217, we proceed to describe it
more particularly. C C is the mahogany beam, whose length
may be taken at pleasure, although it is not advisable to
extend it beyond four or five feet, lest it bend by its own

weight: a a is the strip of holly or box-wood on which
the scale is engraved: B is the brass box, which moves
freely along the beam, and is secured in position by the
clamp-screw F : A is the other brass box, made fast to the
slow-motion screw D, Avhich works in the end of the beam,
and winds it into or out of the box A, to obtain perfect
adjustment; and d b are the Vernier scales, or reading-
plates. The mahogany beam is sometimes substituted by
a brass tube.

Before describing the method of setting the instrument,
we must explain, in few words, the nature of a Vernier
scale. Take any primary division of a scale, and divide
it into ten parts, then take eleven such parts and divide
the line which they form into tenths likewise; tills last
then becomes a Vernier or reading-scale. The primary
division is 100, its subdivision 10, and the excess of the
Vernier division 1; so that if the scale and Vernier are
placed parallel and close to each other, a distance or mea¬
sure may be read accurately to the unit of three places of
figures. We illustrate by a diagram (Fig. 218), which shows
the Vernier attached to the scale a b of the ordinary ba-
Fig. sis. rometer. Here a b is divided into inches and
tenths of inches; and c d is the Vernier, con¬
sisting of eleven subdivisions of a b , divided
into tenths. Now the zero , or commencement
of notation, on the Vernier is, in this case, ad¬
justed to 30 inches on the scale; and its division
10 coincides with 28 inches 9 tenths; hence
every division of the Vernier is seen to be one
and one-tenth of the scale divisions. To read oft,
therefore, the hundredths of an inch that the zero of the
Vernier may be in advance of a tenth, observe what divi¬
sion of the Vernier coincides most nearly with any division
of the scale, and that will indicate the hundredths. Thus,
taking the adjustment of the figure, the zero corresponds
exactly with 30 on the scale, and its division 10, with
28 and 9 tenths ; and we therefore read 30 inches. But
if the zero were so posited between 29 and 9 tenths and
30, that the 8 of the Vernier should correspond exactly
with a tenth of the scale, we should read 29 inches, 9
tenths, and 8 hundredths. And this is evident, for if
zero be 8 hundredths in excess of a tenth, it is only the
eighth division of the Vernier that will be found to coin¬
cide exactly with a tenth of the scale.

To adjust the beam compasses for a distance or radius
of 13 inches, 5 tenths, 3 hundredths, the box A is to
be moved by the screw D until the zero of the Vernier
corresponds with the zero of the beam, and is then to be
secured in position by the clamp e : this done, the box B
is slid along the beam until the zero of its Vernier coin¬
cides with 13 inches 5 tenths: lastly, the box B is moved

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

by the slow-motion screw, and the third division of the
Vernier brought to correspond with the third tenth of the
scale, which consequently adds 3 hundredths to the dis¬
tance or radius previously taken. The point of the slide
or box F can be removed, and a pen or pencil substituted
with accurate adjustment. The beam compasses are sel¬
dom employed, except when extreme accuracy is neces¬
sary. On many occasions, curves of long radius are drawn
by means of slips of wood, one edge of which is cut to the
required circle.

Having described the various sorts of compasses in
ordinary use, it is unnecessary to do more than advert
briefly to some modifications and improvements in form
and detail. It has been thought an advantage to joint
both legs of the instrument, in order to bring them to a
vertical position at any extension ; but this is a doubtful
advantage, especially in compasses designed for drawing
arcs and circles, since each leg being equally removed
from the centi'e of motion, there must be a tendency on
the part of the one fixed, to tear away from its position.
Mr. Brunei has introduced what are called Tubular Com¬
passes, in which the upper part of the legs lengthens out
like the slide of a telescope, thus giving greater extent
of radius when required. The moveable legs are double,
having points at one end, and a pencil or pen at the other;
and they move on pivots, so that the pen or pencil can be
instantly substituted for the points, or vice versa, and that
with the certainty of a perfect adjustment. The design
is very ingenious, and offers many conveniences, but the
instrument is too delicate for ordinary hands. Without
extreme care, it must soon be disarranged and rendered
useless. The Portable or Turn-in Compasses, is a con¬
trivance which combines dividers, compasses with move-
able legs, and bows, in a pocket instrument, folding up to
a length of not more than three inches. The upper legs are
hollow, and admit either leg of the pen and pencil bows,
which can therefore be substituted for each other. When
closed for the pocket, one leg of each bow slides into the
upper legs, and the other is turned inward towards the
head.

As a concluding remark, we recommend the draughts¬
man to choose compasses in which the joint is formed by
a box-screw, that can be tightened or relaxed at pleasure.
The cheaper kinds have merely a common screw, and
these are usually too stiff when first purchased, and in¬
conveniently loose after being some time in wear. A slight
turn of the box-screw, by means of the key, keeps tffe com¬
passes in good working order, neither so stiff as to spring,
nor so loose as to render them uncertain and unsteady
in use.

Plain and Double Scales.

Simply-divided Scales .—Scales are measures and subdi¬
visions of measures laid down with such accuracy, that any
drawing constructed by them, shall be in exact proportion
in all its details. The plain scale is a series of measures
laid down on the face of one small flat ruler, and is thus
distinguished from the sector, or double scales, in which
two similarly-divided rulers move on a joint, and open to'
a greater or less angle. In the construction of scales, the
subdivision must be carried to as low a denomination as
is likely to be required. Thus, for a drawing of limited

xj'O

extent, the primary divisions may be feet, and the sub¬
divisions inches; but for one of large area, and without
small details, the primaries may be 10 feet, and the sub-

Fjjs. 219 end 220.

2 Feet

hili

T 1 1 1 1

~r~nl-

-1- -

-1

1—. — ,

20 Feet

Ui- ;

r i i i

i i l

1- :

r-r=l

divisions tenths, or one foot each (Figs. 219 and 220).
In the case of large surveys, the primaries become miles,
and the lesser divisions furlongs. Indeed the natural size
or extent of the object or area, and the surface to be
occupied by the delineation, must determine the gradua¬
tion of the scale. But passing from these general remarks,
we proceed to the plain scales contained in the drawing
case, and laid down on the two sides of a flat ivory ruler,
six inches in length.

On one side of the plain scale there is usually a series
of simple scales, in which the inch is variously divided,
and the primaries subdivided into tenths and twelfths.
These may be applied to measurements as inches and
tenths, or twelfths; or as feet and tenths, or inches,
according to the nature of the drawing. It may be re¬
marked, however, that these small lines of measures are
of only limited use, and that the draughtsman must
usually lay down a scale with special reference to the
work before him; and in all cases it is desirable to have
the scale of construction on the margin of the drawing
itself, since the paper contracts or expands with every
atmospheric change, and the measurements will therefore
not agree at all times with a detached scale; and, more¬
over, a drawing laid down from such detached scale, of
wood or ivory, will not be uniform throughout, for on a
damp day the measurements will be too short, and on a
dry day too long. Mr. Holtzapffel has sought to remedy
this inconvenience by the introduction of paper scales;
but all kinds of paper do not contract and expand equally,
and the error is therefore only partially corrected by his
ingenious substitution of one material for another.

Diagonal Scale .—The lines to which we have referred
give only two denominations, primaries and tenths, or
twelfths; but more minute subdivision is frequently re¬
quired, and this is attained by the diagonal scale, which
consists of a number of primary divisions, one of which is
divided into tenths, and subdivided into hundredths by
diagonal lines (Fig. 221). This scale is constructed in the
following manner:—Eleven parallel lines are ruled, inclos¬
ing ten equal spaces: the length is set otf into ten equal

primary divisions, as ab, bc,c2, &c. ; and diagonals

Fi<r 2°1

.9 £ 4 2 B C ° * * 2 3 A

-j+i fin m

K "A; j i i i /

lilt H 11 1 1

....

A I b II i

J } I 1 1 [J 1 1

—

D 1

then drawn from the subdivisions between A and B, to
those between D and E, as shown in the diagram. Hence it
is evident that at every parallel we get an additional tenth
of the subdivisions, or a hundredth of the primaries, and
can therefore obtain a measurement with great exactness
to three places of figures. To take a measurement of
168, we place one foot of the dividers on the primary 1

PRACTICAL CARPENTRY AND JOINERY.

(Fig. 222), and carry it down to the eighth parallel, and
then extend the other foot to the intersection of the dia¬
gonal, which falls from the subdivision 6, with the parallel
that measures the eight-hundredth part. More examples or
further explanation would only be tedious. The primaries
may of course be considered as yards, feet, or inches; and
the subdivisions as tenths and hundredths of these respec¬
tive denominations. The diagonal scale is very useful and
satisfactory if accurately constructed; but there can be no

Fig. 222.

question, that one with a Vernier applied to the first sub¬
divisions, would give minute measures with much greater
certainty; and no case of instruments ought now to leave
the maker without having this addition on one face of the
plain scale.

The diagonals may be safely applied to a scale where
only one subdivision is required. Thus, if seven lines be
ruled, inclosing six equal spaces, and the length be divided
into primaries, as A B, B c, Ac., the first primary A B may
be subdivided into twelfths, by two diagonals running
from 6, the middle of A B, to 12 and 0. We have here a

7/\5

8/ \4

9/ \3

10/ \2

11/ XI

/ \

12 O 1 2 5 4

very convenient scale of feet and inches. From c to G, is
1 foot 6 inches; and from c, on the several parallels, to the
various intersections of the diagonals, we obtain 1 foot
and any number of inches from 1 to 12. All of which is
evident from the figure.

On the face of the plain scale that carries the diagonal
one, there is usually a line of inches and tenths, and
underneath it a decimal scale. These can be used sepa¬
rately, and in conjunction; and in the latter case the
primaries of the decimal scale being taken as feet, the
subdivisions of the upper line are inches.

Line of Chords. —This is usually introduced on the
plain scale. It is an unequally divided scale, giving the
length of the chord of an arc, from 1 degree to 90 degrees.
The quadrant, or quarter of a circle, A c, contained be¬
tween the two radii at right an¬
gles, B A and B c, has its extremi¬
ties joined by the line A c, to which
the measures of the chords are to
be transferred. The quadrant is
divided accurately into nine equal
parts; then from c as a centre, each
division is transferred by an arc
to the line AC, and the chords of every 10 degrees obtained.
These primary divisions can be subdivided into tenths,of 1
degree each, by division of the corresponding arcs. This

Fig. 224.

is rather an illustration of the construction, than a true
method of performing it. A line of chords can be laid
down accurately only from the tabular sines, delicately
set off by the beam compasses. In using this scale, it is
to be remembered that the chord of 60 degrees is equal to
radius. Therefore, to lay down an angle of any number
of degrees, draw an indefinite straight line; take in the
compasses the chord of 60 degrees, and from one termina¬
tion of the line, as a centre, describe an arc of sufficient
extent; then take from the scale the chord of the required
angle, and set it off on the arc; lastly, draw another line
from the centre cutting the arc in the measure of the
chord. To ascertain the degrees of an angle, extend the
angular lines if necessary, that they may be at least equal
to the chord of 60 degrees; with this chord in the com¬
passes describe an arc from the angular point; then take
the extent of the arc and apply it to the scale, which will
show the number of degrees contained in the angle.

The Plain Protractor .—The plain scale is sometimes
made of greater width, in order to contain all the preced¬
ing lines, and also a protractor for setting off and measur¬
ing angles. The most eligible form for this instrument is
the circle or half circle, which construction will presently
come before us. It will suffice for the present to say, that
the plain scale protractor is a portion of a semicircle, hav¬
ing radii drawn from its centre to every degree of its cir¬
cumference. If, therefore, the centre on the lower side
is made to coincide with a given point, an angle of any
number of degrees may be measured or set off around its
edges.

A small roller is sometimes inserted in a slot to make
the plain scale serve the purpose of a parallel ruler, but
considerable care is necessary in thus applying it, lest the
roller slide or shift at either extremity.

Double Scales.

Each of the scales we have described has a fixed mea¬
sure that cannot be varied; but we come now to speak of
those double scales in which we can assume a measure at
convenience, and subdivide lines of any length, measure
chords and angles to any radius, Ac.

The Sector .—This instrument consists of two flat rulers,
united by a central joint, and opening like a pair of com¬
passes. It carries several plain scales on its faces, but its
most important lines are in pairs, running accurately to
the central joint, and making various angles according to
the opening of the sector. The principle on which the
double scales are constructed, is contained in the 4th Prop,
of the 6th Book of Euclid, which demonstrates that “the
sides about the equal angles of equiangular triangles are
Fig. 225. proportionals,” Ac. Now let

A c i (Fig. 225) be a sector,
or, in other words, an arc of
a circle contained between
two radii; and let c A, c I, be
a pair of sectoral lines, or a
double scale. Draw the chord
A i, and also the lines B H,
D G, E f, parallel to A I.
Then shall C E, c D, C B, c A, be proportional to ef, d g,
b h, and A i respectively. That is, as c A : A I : : c B : B H,
Ac. Hence at every opening of the sector, the transverse

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

distances from one ruler to another, are proportional to
the lateral distances, measured on the lines cA, Cl; and
thus we may apply any radius transversely to the line of
chords to measure or lay down any given or required
angle; and apply any line transversely to the line of
lines, to divide it in any required proportions. The sector
is therefore seen to be of universal application, whilst the
use of plain scales is limited and special.

Plain Scales on the Sector. —On the outer edge of the
sector is usually given a decimal scale from 1 to 100; and
in connection with it, on one of the sides, a scale of inches
and tenths. These are identical with the lines on the
plain scale, previously mentioned, but the latter are more
commodiously placed for use. On the other side we have
logarithmic lines of numbers, sines, and tangents; but
as these are more complicated than the ordinary plain
scales, we defer the consideration of them until we have
discussed the double scales.

Sectoral Double Scales. —These are respectively named
the lines of lines, chords, secants, sines, and tangents.
These scales have one line on each ruler, and the two lines
converge accurately in the central joint of the sector.

The Line of Lines.— This is a line of 10 primaries, each
subdivided into tenths, thus making 100 divisions. Its
use is to divide a given line into
any number of equal parts; to give
accurate scale measures for the con¬
struction of a drawing; to form any
required scale; to divide a given
line in any assigned proportion; and
to find third, fourth, and middle
proportionals to given right lines.

The scale can be applied to other
purposes; but, if we take up those
mentioned, they will be sufficient
illustrations of its uses. Before en¬
tering upon these propositions, we
would remark that ^lateral distance
is one taken from the centre down
either half of the scale; and a transverse distance is one
measured across from scale to scale. Thus (Fig. 226), a 1,
0,2, a. 3, &c., are lateral distances; and 1.1, 2.2, 3.3, &c.,
transverse distances.

1. To divide a given line into 8 equal parts. Take the
line in the compasses, and open the sector so as to apply
it transversely to 8 and 8, then the transverse from 1 to

1 will be the eighth part of the line. If the line is to
be divided into 5 equal parts, apply it transversely by
the compasses to 10 and 10, and the transverse of 2 and

2 is the fifth part. When the line is too long to fall
within the opening of the sector, take the halt or the
third of it. Thus, if a line of too great length is to be
divided into 10 parts, take the half and divide into 5
parts; or if into 9 parts, take the third and divide into

3 parts. And in other cases it may be necessary to divide
the portion of the line into the original number of parts,
and set oft' twice or thrice to obtain the required division
of the whole.

2. To use the line of lines as a scale of equal measures.
Open the sector to a right angle, or nearly so, and obtain
dimensions by transverse measures from scale to scale,
taking care that the points of the compasses are directed
to the same division on both rulei’s- Thus, the transverse

measures to the primaries 1.1, 2.2, &c., will give any de¬
nomination, as feet or inches, and similar measures to the
same subdivisions on both sides will gi.7e tenths.

3. To form any required scale—say, one in which 285
yards shall be expressed by 18 inches. Now, as 18 inches
cannot be made a transverse, take in the compasses 6
inches, the third part, and make it a transverse to the
lateral distance 95, which is the third of 285. The re¬
quired scale is then made; the transverse measures to the
primaries being 10 yards, and to the subdivisions so many
additional yards.

4 To divide a given line in any assigned proportion—
say, a line of 5 inches in the proportion of 2 to 6. Take
5 inches in the compasses, and apply it to the transverse
of 8.8, the sum of the proportions; then will the trans¬
verse distances 2.2, 6.6, divide the given line as required.

5. To find a third proportional to the numbers 9 and 3,
or to lines 9 inches and 3 inches in length. Make 3
inches a transverse distance to 9.9; then take the trans¬
verse of 3.3, and this measured laterally on the scale of
inches will give 1 inch. For 9 : 3 :: 3 :1.

6. To find a fourth proportional to the numbers 10, 7,
3, or to lines measuring 10, 7, and 3 inches respectively.
Make 7 inches a transverse from 10 to 10, then the trans¬
verse 3.3 will measure on the scale of inches 2 x \ r . For
10 : 7 : : 3 : 2 t V

7. To find a middle proportional between the numbers
4 and 9, or between 2 lines measuring 4 and 9 inches
respectively. To perform this operation the line of lines
on the one leg of the sector must first be set exactly at
right angles to the one on the other leg. This is done by
taking 5 of the primary divisions in the compasses, and
making this extent a transverse from 4 on one side to 3
on the other. For 3, 4, and 5, or any of their multiples,
form a right-angled triangle. The sector being thus ad-
justed, take in the compasses a lateral distance of 6 pri¬
maries and 5 tenths, half the sum of the two lines or num¬
bers, and apply this measure transversely from 2 primaries
and 5 tenths, half the difference, when the other point of
the compasses will reach the primary 6 on the opposite leg
of the sector. For 4 : 6 :: 6 : 9.

The line of lines is marked L on each leg of the sec¬
tor; and it is to be observed that all measures are to be
taken from the inner lines, since these only run accu¬
rately to the centre. This remark will apply to all the
double sectoral lines. With reference to some of the pre¬
ceding operations by the line of lines, we may admit that
they are suggestive rather than practically useful. They
familiarize the young draughtsman with the capabilities
of scales, and offer him useful hints for the general con¬
struction and management of lineal measures.

The Line of Chords. —The scale of chords on the sector
has the same advantage over that on the plain scale that
the line of lines has over the simply-divided single scales.
With the line of lines we operate on any given line that
will come within the opening of the sector; and with the
line of chords we can work with any radius of similar ex¬
tent. This last is constructed by making the lateral dis¬
tance of the chord of 60 degrees, which is radius, equal in
length to the line of lines. All the intermediate degrees
between 1 and 60, are then set off laterally from the centre,
on both rulers, by taking on the line of lines a measure
equal to twice the natural sine of halt the angle. 1 hus, for

PRACTICAL CARPENTRY AND JOINERY.

the chord of 30 degrees, refer to Sherwin’s Tables, or to
others of equal authority, and find the natural sine of 15
decrees, which is 2588190, when radius is 10,000,000, and
the double of this sine is 5176380. Now the line of lines
as radius is equal to 100, in place of 10,000,000, and the
measure of the double sine must therefore be taken from
it in two places of figures, instead of seven. We see at
once that the length of the chord is between 51 and 52
on the line of lines. Take in the compasses, as nearly as
possible, 51 and three-fourths, and this measured from the
centre on the line of chords, will give the chord of 30 de¬
grees. The young draughtsman ought to exercise himself
and test his sector by this and similar operations; for it is
equally important that he understand the structure ol his
scale, and be able to ascei'tain that the various lines of his
sector have a due relation to each other.

The line of chords is principally used to protract and
measure angles.

To protract or lay down any angle less than 60 degrees,
say an angle of 30 degrees (Fig. 227). Open the sector at
pleasure, and with the transverse distance 60.60 in the
compasses, as a radius, describe an arc of a circle: take the
transverse distance of 30 degrees, and set it upon the arc;
then draw right lines from Fig. 227.

the centre to the points on the
arc, and the required angle is
formed. When it is desired
to measure any angle of not
more than 60 degrees, take
in the compasses the trans¬
verse distance of 60.60 at any
opening of the sector, and with this radius describe, from
the angular point, an arc across the given angle: take the
measure of the arc included in the given angle, in the com¬
passes, and apply this transversely to the line of chords,
and the similar divisions on which the points of the com¬
passes fall will express the true measure of the angle.

To protract an angle of more than 60 degrees, take as
radius the transverse distance of 60.60 at any convenient
opening of the sector, and describe an arc as in the former
case; then take the transverse distance of one-half or one-
third of the given number of degrees, and set off twice or
three times on the arc, as the case may be: afterwards
form the angle by right lines from the centre to the two
outermost points of measure on the arc. Thus if the angle
is to contain 100 degrees, having described the arc, set off'
50 degrees twice, and thus obtain the required measure.
Any angle of more than 60 degrees is measured in por¬
tions, in like manner.

To lay down an angle of less than 10 degrees, it is more
convenient to set off radius on the arc, and form an angle
of 60 degrees, and then deduct the difference between this
angle and the one required. Thus, suppose the angle to
be 7 degrees. Protract one of 60 degrees, and set off the
complement 53 degrees; then the remainder of the arc will
contain 7 degrees, the required angle. The reason for thus
laying down small angles is, that the divisions of the sec¬
toral line of chords are not so readily distinguished when
they approach within 10 degrees ot the centre of the in¬
strument. To measure any small angle, protract an angle
of 60 degrees that shall include it, then take the comple¬
ment to 60 degrees in the compasses, and this applied
transversely to the sector will show the measure of the

60 ■

supplement, which being deducted from 60 degrees, the
remainder will express the measure of the given angle.

The line of chords is distinguished by the letter c on
each leg of the sector

The Line of Polygons— This line is placed near the in¬
ner edges of the sector, and marked POL on both scales. Its
use is to divide the circumference of a circle into a number
of equal parts, and to determine the sides of regular figures
that can be inscribed within the circle or described about
it. It is constructed by setting off', from a line of chords,
lateral distances equal to the chords of the central angles
of the square, pentagon, hexagon, heptagon, octagon, nona-
gon, decagon, undecagon, and duodecagon—figures of 4,
5, 6, 7, 8, 9, 10, 11, and 12 sides respectively. The cen¬
tral angle is found by dividing 360 degrees by the num¬
ber of sides in the figure; and the length of the chord is to
be measured on a line equal in length to the sectoral line
of chords, but graduated to the full quadrant, or 90 de¬
grees; the reason of which is, that the chords of the cen¬
tral angles of the square and pentagon, the one 90 and
the other 72 degrees, could not otherwise be contained in
the length of the sector.

To inscribe a regular polygon—say a figure of five equal
F ig 22 s. sides, in any given circle.

Make the radius of the circle
a transverse distance to 6, 6,
the chord of 60 degrees, and
the transverse of 5, 5, will
then give the side of the pen¬
tagon. This set off 5 times
on the circumference of the
circle, and the points connected by chord lines, will com¬
plete the figure (Fig. 228).

To construct an octagon on any given line, make the
line a transverse to 8.8 on the line of polygons (8 being
the number of equal sides in the figure): with the sector
thus set, take the transverse of 6.6 for a radius, and from
each termination of the given line describe arcs intersect¬
ing each other. From the point of intersection, and with
the same radius, describe a circle passing exactly through
the terminations of the given line; which thus becomes
one side of the required octagon, and is to be set off eight
times round the circumference of the circle to complete the
figure. To describe a regular polygon about any circle
(that is, without the circumference), the inscribed figure
must first be drawn; then rule lines parallel to the sides of
the inscribed figure, so as just to touch the circumference,
and their intersections will define the polygon required.

As it is proposed to explain the construction and use
of every line on the sector, which is often little more to
the young draughtsman than a puzzling hieroglyphic, it
is necessary as a preliminary to define and illustrate

the geometrical character and

relation of the several lines
to which the sectoral scales refer.
We have discussed the chord,
which is simply a straight line
connecting the extremities of any
arc of a circle. In Fig. 229 we
have those lines that remain to
be described, shown in their re¬
lation to each other, c E B is an angle containing the arc
CB; EC and E B ai'e radii; AC is the sine, BD the tan-

Fig. 220.

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

gent, and E D the secant, of the angle CEB; and they are
likewise the sine, tangent, and secant of the supplemen¬
tal angle, which contains so much of the circumference
of a circle as with ceb will complete a semicircle, or 180
degrees. F E c is another angle containing the arc F c ; and
G c is the sine, F H the tangent, and E H the secant of this
angle. The complement of an angle is what it wants of a
quadrant, or right angle, or of 90 degrees. Therefore
fec and ceb are the complements of each other; and
the sine, tangent, and secant of the one are the cosine,
cotangent, and cosecant of the other. The portion of the
radius between the sine and the extremity of the arc, as
A B or G F, is named the versed sine.

The Line of Secants. —This scale, which lies on both
legs of the sector, between the line of lines and the line
of chords, and is marked s, gives the secant of any angle
to 75 degrees, whose radius can be taken in the opening
of the sector at the commencement of the scale. It is
constructed from a table of natural secants, that is, secants
whose length is expressed in natural and not in logarith¬
mic numbers. The graduation commences at one-fourth
of the length of the closed sector from the central joint;
and at every opening of the instrument the transverse of
these commencing points is the radius of a circle; and the
secants of the various angles contained in its circumfer¬
ence measure transversely from one leg to the other, ac¬
cording to the number of degrees they severally include.
Now radius is applied at one-fourth from the centre, a
distance only one-fourth so long as the line of lines ;
therefore in measuring off the graduations on the last-
named line, we take only one-fourth of the tabular se¬
cants. From the diagram (Fig. 229) just referred to, it is
evident that the secant is always more than radius; and
if the latter were applied to the transverse of the entire
length of the sector, we could get no longer transverse for
a secant. We therefore commence the scale at one-fourth
from the centre, that we may get a range of transverse
distances so far as 75 degrees; and we do not commence
nearer to the centre, because if we did so, the length of
radius would be inconveniently small. As an example of
construction, let the secant of 60 degrees be taken. On
reference to the tables we find that the length of this
secant is 200 when radius is 100, or the length of the line
of lines. Take therefore the fourth part, 50, from the
centre of the sector along the line of lines, and transfer it
to the line of secants, on each leg, as the graduation of
60 degrees. Proceed in the same manner for all other
measures until the scale is completed.

As general examples of the use of the line of secants,
take the following:—What is the secant of 60 degrees,
when radius is 20 ? Take 20 in the compasses from the
line of lines, and apply it transversely to the commence¬
ment of the line of secants. With the sector thus opened,
take the transverse of 60 degrees, which will measure 404
on the line of lines, the length of the secant required.
What is radius, when the secant of 60 degrees is 40 H
Take 401 from the line of lines and apply it as a trans¬
verse to 60.60 on the line of secants; then take the trans¬
verse of the commencing points, and this will measure
20 on the line of lines. The one operation is the converse
of the other.

One side of the sector containing the lines of lines,
chords, polygons, and secants, has now been described;

j and we proceed to the other side, on which we find the
lines of sines and tangents, and the logarithmic scales of
numbers, sines, and tangents.

The Line of Sines. —This scale is the length of the line
of lines, and gives the sine of every angle to 90 degrees.
It is constructed by transferring the measures of the na¬
tural sines to each leg of the sector. Thus the natural
sine of an angle of 30 degrees is 50 when radius is 100;
take therefore 50 from the line of lines and set it off from
the centre along the line of sines, on both legs, as the
measure of the sine of 30 degrees. Proceed in the same
way until the graduation of the scale is completed. To
exemplify the use of this scale take two example.?. What
is the length of the sine of 40 degrees when radius is 28?
Take 28 from the line of lines and apply it to 90.90 on
the sines; then the transverse 40.40 will measure 18 on
the line of lines, the length of the required sine. The
converse of this operation gives the radius, when the
measure of the sine is known.—What is the length of the
versed sine of 40 degrees when radius is 28 ? Make
radius a transverse to 90.90 ; then take the transverse of
50.50, the complement of 40 degrees, and the length it
measures on the line of lines, namely 21i, deducted from
radius, gives 6| for the versed sine.

The Line of Tangents. — This line, marked T, is laid
down twice on the sector: the lower tangents commence
at the centre and terminate at 45 degrees, which is equal
to radius; and the upper tangents commence, like the
secants, at one-foui'th from the centre, and extend to 75
degrees. For angles not exceeding 45 degrees, we apply
radius to 45.45 at the end of the sector; but for any
larger angle, radius is made a transverse to 45.45 of the
upper tangents at one-fourtli from the centre. It is thus
seen that we can command a great variation of radius for
the lower tangents, but are restricted in the upper tan¬
gents to such a radius as can be taken between the legs
of the sector at only one-fourth from the centre. These
lines are constructed on the same principle as the secants
and sines. We take the measure of the tabular tangents
from 1 to 45 degrees and set off the loiver line; and one-
fourtli of the tabular tangents from 45 to 75 degrees, to
graduate the upper line. Thus the tabular tangent of 30
degrees is 57J when radius is 100; take therefore 57f from
the line of lines, and transfer it from the centre to the line
of lower tangents on each leg, as the measure of 30 degrees.
Again, the tabular tangent of 65 degrees is about 214
when radius is 100 : take therefore the fourth part of 214,
or 53|, and transfer it from the centre to the line of upper
tangents on each leg. To illustrate the use of the two
lines take the following questions:—What is the tangent
of 30 degrees when radius is 40? Take 40 from the
line of lines and make it a transverse to 45.45 at the end
of the sector, then the transverse of 30 degrees will mea¬
sure 23 5 on the line of lines. The converse operation
gives radius when the length of the tangent is known.
What is the tangent of 70 degrees when radius is 20?
Make 20 a transverse to 45.45 at one-fourth from the
centre, and the transverse of 70.70 will measure 55 J.

The annexed diagram (Fig. 230) shows the geometrical
construction of the secants and tangents. The line CD is
a line of tangents to 75 degrees, and it is formed by draw¬
ing lines from B, the centre, through the graduations of
the quadfant, to meet the tangential line c D, standing at

PRACTICAL CARPENTRY AND JOINERY.

right angles to b c. A b is a line of secants, formed by
transfer with the compasses of the radial lines from the
centre B. It is therefore seen that
the radius, tangent, and secant, are
the base, perpendicular, and liypo-
thenuse of a right-angled triangle.

A line of sines would be formed by
graduating the radius 10 B, with
lines drawn through the degrees of
the quadrant, and parallel to B c.

The lines of sines and tangents are
frequently of use to the draughtsman
in the determination of a number of
points through which an eccentric
curve can be drawn. We here give
two examples of the use of the sec¬
toral lines in the solution of ques¬
tions in Trigonometry.

1 . A right-angled triangle has
base 12, perpendicular 16; required
the hypothenuse.—Set the sector at
right angles, by making the lateral
distance of 5 on the line of lines a
transverse to 3 and 4. Then take the transverse of 12
on one leg to 16 on the other, and this, measured on the
line of lines, will give 20 for the hypothenuse.

2. A right-angled triangle has perpendicular 30, and
the angle opposite thereto 37 degrees; required the hypo¬
thenuse.—Take 30 from the line of lines, and make it
a transverse to 37 degrees on the line of sines, then the
transverse of 90.90, will measure 50 on the line of lines,
the length of the hypothenuse.

Logarithmic Lines.

The Line of Numbers. — This line, commonly called
Gunters Line, and marked N on the sector, is divided
into spaces forming a geometrical series, and is simply
a table of logarithms expressed by relative measures of
length. It is constructed in the following manner:—
The entire line is divided into two equal parts, and each
of these parts into nine unequal primary divisions, cor¬
responding to the logarithms they are to represent. These
primaries are to be the measures of the numbers 2 to 9,
whose logarithms may be considered 30, 47, 60, 70,
78, 84, 90, and 95, as will be seen on reference to the
ordinary tables. To make a scale of equal parts for set¬
ting off these quantities, take one-half of the line in the
compasses and make it a transverse to 10.10 on the line of
lines. Then take successively the transverse distances of
30.30, 47.47, &c., and set them off from the commence¬
ment on the first half of the line of numbers for the pri¬
mary divisions 2, 3, &c. These same spaces may next be
transferred to the second half of the line for its primary
divisions. Thus we have obtained the logarithms of 20, 30,
40, 50, 60, 70, 80, 90,100 on the first half; and those of 100,
200, &c., on the second half. Now, for the subdivision
of the space between 1 and 2, we must set off from the
commencement of the line, in succession, the logarithms
of 11, 12, &c., to 19; and for that between 2 and 3, the
logs, of 21, 22, &c., to 29 ; and thus proceed till we come
to the space between 6 and 7, which is too short to admit
the decimal divisions. Graduate therefore this last space,
and all onward to 10, into two-tenths; and consequently

take the logs, of 62, 64, 66, 68; 72, 74, 76, 78; &c. All
these subdivisions, set off from the commencement on the
first half of the line, may also be set off from 1 in the
middle, in the second half. Thus, we have found on the
one half, the logs, of tens and units, and on the second half
those of hundreds and tens. But there is a farther sub¬
division of the space between 1 and 2 on the second half,
which is graduated to twenty places; and this halving of
the first subdivisions is effected by setting off successively
from 1, the logs, of 105, 115, 125, &c. This done, the line
is constructed.

In using this line any value may be attached to the
primary divisions, merely observing their relative propor¬
tion to each other. Thus, if the primaries on the first
half are units, and their subdivisions tenths, those on the
second half will be tens and their subdivisions units.
Whatever is the value of a primary or subdivision on
the first half, the corresponding primary and subdivision
on the second half will have ten times that value. We
illustrate the use of the line by a few examples. Take off
the measures of the numbers 896, 1150, 2050. For the
first, place one foot of the compasses at the beginning of
the line on the left hand, and extend the other over eight
primaries and four subdivisions, and nearly to the end of
the fifth subdivision. For the second, extend over the
ten primaries of the first half and three subdivisions of
the second half. For the third, extend over the first ten
primaries, and one primary of the second half, and half
a subdivision beyond. To multiply, say 135 by 48: take
the extent from 1 on the left hand to 48 in the first
interval, and apply it to 135 in the second interval,
when it will reach to 648, or 6480. To divide 6480 by
135 : extend backwards from 135 to 1 on the left hand,
and this will measure back from 6480 to 48. To find a
fourth proportional to the numbers 3, 8, and 15: take the
extent from 3 to 8 in the first interval, and this will
reach from 15 to 40 in the second interval; for 3 : 8:: 15:40.

The Line of Sines .—This line gives the sines of an¬
gles to 90 degrees in a geometric series; their logarithms
being expressed by relative spaces. It is constructed by
laying down the logarithms of the sines from the same
scale of equal parts by which the line of numbers was
measured. Its two intervals are not, however, of equal
length; and hence we cannot set off the primaries in both
from the same measure. We therefore require a scale of
equal parts of twice the length, or one the whole length
of the line of numbers, to enable us to set off all the sines
from the commencement of the scale on the left hand.
The simplest way is to make the length of the line of
numbers, a transverse to 10.10 on the sectoral line of
lines, and take the transverse measures of half the loga¬
rithms. Now the logs, of the primaries, 1, 2, 3, &c., to 10,
in the first interval, and of 20, 30, &c., to 90, in the second
interval, are these: 242, 543, 719, 843, 940, 1019, 1085,
1143, 1194, 1239; 1534, 1699, 1808, 1884, 1937, 1972,
1993, 2000. Take, therefore, the halves of these logs,
tranversely from the line of lines, and lay them down suc¬
cessively on the line of sines, from the beginning of the
scale. The subdivision of the primaries into minutes and
degrees is proceeded with in the same manner. The
degrees in the first interval are divided into six spaces,
each being 10 minutes; but between 10 and 20, in the
| second interval, there are 20 subdivisions, each represent¬

ing. 230.

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

ing SO minutes, or half a degree: between 20 and SO, and
30 and 40, there are 10 subdivisions, each being 1 degree:
between 40 and 50, 50 and 60, 60 and 70, there are 5
gi-aduations, each 2 degi-ees; and the space between 70
and 90 admits only of one subdivision to divide it for 80
and 90 degrees. The commencement of the scale is inter¬
fered with by the sectoral line of sines, so that the measui-e
of 50 minutes is the least sine that can be laid down on
the logarithmic line. With this sine, whose log. is 162,
we commence the subdivisions, and then proceed to the
sines of 1 ° 10 ', 1 ° 20 ', &c.; 2 ° 10 ', 2 ° 20 ', &c., until the
graduation is completed.

There is another method of construction, by which the
sines are measui’ed off from the termination of the line on
the right hand. For this purpose the logs, of the arith¬
metical complements of the sines are taken, that is to say,
the difference between them and radius. Thus, the log.
of the sine of 30 degrees, taking all the places of figures,
is 9 - 6989700,and this deducted from radius, or 10 0000000,
leaves a remainder of ‘3010300. If, therefore, 301, or its
half by the proposed scale, be laid from the end of the line
of sines at the right hand, it will reach the graduation of
30 degi'ees. There is yet another method: in place of the
arithmetical complement of the sine, take the secant of the
complementary angle, viz., 60 degrees, and set off from the
right hand as in the former case. We mention these vari-
ous inodes of construction to call the young draughtsman's
attention to the relation between different angles, and as
suggestions for more scientific inquiry concerning them.

The manner of taking off a logarithmic sine from the
scale is obvious: one foot of the compasses is placed at the
commencement, and the other extended to the required
degree or minutes. The use of the line in conjunction
with the line of numbers may be illustrated by one ex¬
ample. The base of a right-angled ti’iangle is 30, and the
angle opposite to it 30 degrees; what is the hypothenuse?

Now, Sine of Angle : 30: : Radius : Hypotlienuse.

Set one foot of the compasses on 30 degrees, and extend
the other to 30 on the line of numbers; and with this
opening, set one foot on 90 degrees of the line of sines, and
the other foot will reach to 60 on the line of numbers —
the hypothenuse inquired.

The Line of Tangents .—This line gives the logarithmic
measures of the tangents to 45 degrees, and thence back¬
wards to 88 ° 30'. The tangent of 45 degrees being equal
to i-adius, or the line of numbers, the graduation cannot
be extended beyond this angle; but the upper tangents
are obtained by reckoning backwards, 40 for 50, 30 for
60, 20 for 70, &c.; and this method of obtaining the longer
tangents is compensated by a peculiarity of operation
when the line is wrought in conjunction with the line of
numbers. This scale is constructed by measuring off,
successively, from the commencement at the left hand, the
logarithms of the primaries and subdivisions as required.
Thus, the first interval has for its primaries the degrees
from 1 to 10 ; and, in the second, every primary is 10
degrees, except the last, which is only 5. The subdivisions
in the first interval are ten minutes; and in the second,
between 10 and 20 and 20 and 30, they are 30 minutes, ox-
half a degree: and from 30 to 45, 1 degree each. Make
a scale of equal parts, as for the sines, by applying the
length of the line of nxxmbers to 10-10 on the line of lines;

then take the transverses of half the logarithmic tangents
found in the tables. Thus the logs, of 1, 2, 3, 4, 5, 6, 7,
8 , 9, 10, 20, 30, 40, 45 degrees, are 242, 543, 719, 844,
941, 1021, 1089, 1148, 1199, 1246; 1561, 1761, 1924,
2000. Take therefore the halves of these numbers from
the scale, and transfer them to the line for the primaries.*
The subdivisions are commenced at 1° 30', whose log. is
418; and then continued 1° 40', 1° 50', 2° 10', &c., until
completed. As in the case of the sines, the line of tan¬
gents may likewise be constructed by laying down the
arithmetical complements of the tangents backwards, from
45 degrees to the commencement of the scale.

The length of a logarithmic tangent is measured oft"
from the commencement of the line at the left hand, by
extending the compasses to the degree or minute requii-ed.
We give two examples of the application of the scale to
the solution of questions in trigonometiy. 1. The base of
a right-angled ti’iangle is 25, and the perpendicular 15;
what is the angle opposite to the perpendicular? Here,
if the base is considered radius, the perpendicular will be
the tangent of the angle opposite to it; therefore,

As 25 :15 :: Radius : Tangent.

Extend the compasses from 15 to 25 on the line of num¬
bers, and this opening will reach backwards from 45
degrees on the line of tangents to 31 degrees, the angle
inquired. 2. The base of a right-angled triangle is 20,
and the angle opposite to the perpendicular 50 degi'ees;
what is the perpendicular?

As Radius : Tan. 50°:: 20 : Perpendicular sought.

Extend the compasses from 45 degrees to 50 on the line
of tangents, and apply them, thus opened, from 20 towards
the right hand, to 23|, the perpendicular. This example
shows the method of working when the angle exceeds 45
degrees. The extent taken from the tangents is only from
45 to 40, the complement of 50 degrees; and we therefore
apply it from 20 towards the right hand to obtain the
length of the perpendicular; but had the angle been 40
degrees, the extent would have been applied from 20 to¬
wards the left hand , to 16f, which would, jn that case,
have been the perpendicular.

We have now gone systematically through the sector,
which contains a great deal of what may be termed me¬
chanical mathematics, and offers much that is valuable to
the draughtsman in the way of suggestion for the con¬
struction and management of scales.

Protractors.

We have ali-eady referred to the protractor on the plain
scale. The senxicircle (Fig. 231), though different in form,
Fig. 231. is the same in prin-

a.: ciple. It is a half

circle of brass, or
other metal, having
a double graduation
on its circular edge.
The degrees run
both ways to 180;
C so that any angle,
from 1 to 90 degrees, may be set off on either side. Each
graduation marks an angle and its supplement; thus,
10, 20, 30, coincide with 170, 160, 150; and are the

PRACTICAL CARPENTRY AND JOINERY.

supplements of eacli other. An angle is protracted or
measured by this instrument with great facility. To
protract an angle, draw a line, and lay the straight edge
of the protractor upon it, with its centre on the point
where the angle is to be formed: the required number of
degrees is next marked off close to the circular edge: the
instrument is then laid aside, and a line drawn from the
angular point, to the one which measures the extent of
the angle. Thus in the figure, u is the centre, or angular
point, D the measure of the angle, and B D the line by
which it is formed. The converse operation of measuring
an angle is equally simple: the angular point and the
centre of the protractor are made to coincide, and the
straight edge of the instrument is laid exactly upon one
line of the angle, when the other will intersect the cir¬
cular edge, and indicate the number of degrees. The
plain scale protractor is used in the same manner; but it
is by no means so convenient an instrument as the semi¬
circle. Either of them may be employed occasionally to
raise short perpendiculars. For this purpose, make the
centre and the graduation of 90 degrees coincide with the
line upon which the perpendicular is to be raised.

Parallel Ruler.

This is a well-known instrument, consisting of two
rulers connected by slides, moving on pivots, and so ad¬
justed, that at every opening of the instrument, the rulers
and the slides form a parallelogram. In use, its edge is
made to coincide exactly with the line to which others are
to be drawn parallel: the lower ruler is then held firmly
down, and the upper one raised to any required distance,
when a line drawn along its edge will be parallel to that

Fig. 232.

from which it started (Fig. 232). There are several
methods of uniting the rulers; but we are not Fig. 233 .
aware that any one has very decided advan- A
tages over the others. The ordinary form, as V/
shown in the figure, is perhaps the simplest,
and, therefore, the best. The right-angled
straight-edges of the drawing-board and the
T-square, are the surest means of all for
drawing parallels and perpendiculars; and the
parallel ruler will never be used when these
can be employed.

Drawing Pens.

The drawing pen differs from the pen-leg of
the compasses only in its having a long straight
handle, the top of which is sometimes made to
unscrew and form a tracer or pin, to set off
angles by the edge of the protractor (Fig. 233). i'

The dotting pen is a similar modification of the
dotting leg of the moveable compasses. The use
of both instruments is to draw straight, contin- 1
uous, or dotted lines in ink. A place is usually
provided in the drawing case for a thin pencil,
to rule in straight lines, that may afterwards
either be obliterated or made permanent by the ink pen.

Pricker.

This is a simple instrument, consisting of a fine needle¬
point firmly fixed into the end of a wooden or ivory
holder, for pricking off distances, the positions of lines,
&c., upon the paper. It is so used in conjunction with
portable scales, the edges of which, being graduated, are
applied to the sheet, and measure off the required dis¬
tance. The pricker to this extent supersedes the dividers,
and may be so employed witli facility and accuracy. It is
also used in copying drawings, by placing the drawing
on the top of the sheet upon which the copy is to be made,
and pricking through upon the vacant sheet the positions
of the lines, angles, and centres of the drawing; thus the
copying process is expedited. The ladies’ crochet needle-
holder makes a neat handle for the pricking needle.

Drawing Paper.

Drawing paper, properly so called, is made to certain

standard sizes, as follow :—

Demy,.

20 inches by 15J inches.

Medium,

22| „

m „

Royal, ...

24 „

i9i „

Super-Royal, .

27i „

m „

Imperial,

22 „

Elephant, .

28 „

Columbier,

35 „

m „

Atlas, .

34 „

26 ,.

Double Elephant, .

40 „

27 „

Antiquarian, .

53 „

31 „

Emperor,

48 „

Of these, Double Elephant is

the most generally useful

size of sheet. Demy and Imperial are the other useful
sizes. Whatman’s white paper is the quality most usu¬
ally employed for finished drawings: it will bear wet¬
ting and stretching without injury, and, when so treated,
receives shading and colouring easily and freely. For
ordinary sketching or working drawings, where damp¬
stretching is dispensed with, cartridge paper, of a coarser,
harder, and tougher quality, is to be preferred. It bears
the use of india-rubber well, receives ink on the original
undamped surface freely, shows a good line, and, as it
does not absorb very rapidly, tinting lies evenly upon it.
For delicate small-scale line-drawing, the thick blue pa¬
per, such as is mnade by Harris for ledgers, Ac., imperial
size, answers exceedingly well; but it does not bear damp¬
stretching without injury, and should be merely pinned
or waxed down to the board. With good management,
there is no ground to fear the shifting of the paper. Good
letter-paper receives light drawing very well: of course it
does not bear much fatigue.

Large sheets, destined for rough usage and frequent
reference, should be mounted on linen, previously damped,
with a free application of paste.

Tracing paper is a preparation of tissue paper, ren¬
dered transparent and qualified to receive ink lines and
tinting without spreading. When placed over a draw¬
ing already executed, the drawing is distinctly visible
through the paper, and may be copied or traced directly
by the ink-instruments: thus an accurate copy may be
made with great expedition. Tracings may be folded and
stowed away very conveniently; but, for good service,
they should be mounted on cloth, or on paper and cloth,
with paste.

Tracing paper may be prepared from double-double-

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

crown tissue paper by lightly and evenly sponging over
one surface Avith a mixture of one part of raw linseed-oil
or nut-oil,, and five parts of turpentine. Five gills of tur¬
pentine, and one of oil, will go over from H to 2 quires of
twenty-four sheets.

Tracing cloth is a similar preparation of linen, and has
the advantage of toughness and durability.

Drawing Boards.

Drawing boards are made truly rectangular, and for
common use may be of two sizes—41 by 30 inches, to carry
double-elephant paper, Avith a margin; and 31 by 24 inches,
for imperial and all smaller sizes. Boards much smaller
than this are unsuited for ordinary work, but may be
necessary for particular purposes. Drawing boards may
be of mahogany, oak, or yellow pine, well seasoned; 4
inch or ^ inch thick for mahogany, and 1 inch for pine,
or say 1} inch to alloAv for dressing up. They should be
barred and dowelled at the ends, to stiffen them, and en¬
able them to resist any tendency to twist, as well as to af¬
ford a suitable edge for the working of the drawing square.
It would be an improvement to line the working end of
the pine board Avith a strip of mahogany or other hard
Avood, as it is liable to wear slightly round at the corners.

Boards are occasionally made as loose panels placed
in a frame, all flush on the drawing surface, and bound
together by bars on the other side.

Drawing paper may be fixed down upon the ordinary
board, either by damping, and gluing its edges, or by
simply fixing it at the corners, and at intermediate points,
if necessary, with pins or Avith sealing wax or Avafers.
The latter fixing is sufficient where do shading or colour¬
ing is to be applied, and if the sheet is not too long a time
upon the board. It has the advantage, too, of preserving
to the paper its natural quality of surface. With mounted
paper, indeed, there is no other proper way of fixing. For
large, coloured, or elaborate draAvings, however, a damp-
stretched sheet is preferable: Avith colouring or flat tinting,
indeed, damp-stretching is indispensable, as the partial
wetting of loose paper by water-colour causes the surface
to buckle. Damp-stretching is done in the following
Avay: lay the sheet flat on the board, Avith that side under¬
most which is to be drawn upon, and pare the thick edges
from the paper; draw a wet sponge freely and rapidly over
the upper side beginning at the centre, damping the entire
surface, and allow the sheet to rest for a few minutes, till
it be damped through, and the surface-water disappears.
Those parts which appear to revive sooner than others,
should be retouched with the sponge. The damping
should be done as lightly as possible, as the sponge always
deprives the paper of more or less of its sizing. The sheet
is noAv turned over and placed fair with the edges of the
board—sufficiently clear of the working edges to permit
the free action of the drawing square. The square, or an
ordinary straight-edge is next applied to the paper, and
set a little Avithin one edge, say about fa of an inch, which
is then turned up over the square, and smeared all along
with melted glue. The paper is then folded back and
pressed down by the square, after Avhich the end of a
paper-folder, or other smooth article, is rubbed along the
‘ lap,” Avith a piece of stiff paper interposed, to press out
the superfluous glue and bring the paper into intimate
contact Avith the board. The same operation being

rapidly applied in succession to the other edges, the sheet
is left to dry, and ultimately, by the contraction, turns
out perfectly flat and tense. When melted glue is not
to be had conveniently, a cake of glue may be dipped in
water and rubbed on the margins of the board at the
proper places. Lip glue, or artists’ glue, which dissolves
very readily, may be used in this case.

With loose panelled boards, as described, the panel is
taken out, and the frame inverted; the paper being first
damped on the back Avith a sponge, slightly charged Avith
Avater, is applied equally over the opening to leave equal
margins, and is pressed and secured into its seat by the
panel and bars. This is a ready enough Avay of laying
a sheet, and for damp sheets is more expeditious than
the gluing system. But the large margin required dimi¬
nishes the size of the sheet, and for general use plain
boards are sufficient.

T-Square.

The T-square (Fig. 234) is a blade or “ straight-edge ” a,
usually of mahogany, fitted at one end with a stock b,

Details of T-Square.

applied transversely at right angles. The stock being so
formed as to fit and slide against one edge of the board,
the blade reaches o\ T er the surface, and presents an edge
of its own at right angles to that of the board, by which
parallel straight lines may be draAvn upon the paper. To
suit a 41-inch board, the blade should measure 40 inches
long clear of the stock, or one inch shorter than the board,
to remove risk of injury by overhanging at the end: it
should be 2| inches broad by fa inch thick, as this section
makes it sufficiently stiff laterally and vertically. If
thinner, the blade is too slight and too easily damaged by
falls and other accidents, and is liable to warp; if thicker,
it is too heavy and cumbersome; if broader, it is heavier
Avithout being stiffen The tip of the blade may be secured
from splitting by binding it with a thin strip inserted in a
saAv-cut as shown. The stock should be 14 inches loner,
to give sufficient bearing on the edge of the board, 2 inches
broad, and § inch thick, in two equal thicknesses glued
together. With a blade and stock of these sizes, a Avell
proportioned T-square may be made, and the stock Avill
be heavy enough to act as a balance to the blade, and to
relieve the operation of handling the square. The blade
should be sunk flush into the upper half of the stock on
the inside, and very exactly fitted. It should be inserted
full breadth, as shown in the figure; notching and dove¬
tailing is a mistake, as it Aveakens the blade and adds
nothing to the security. The lower half of the stock should
be only If inches broad, to leave a 3-inch check or lap, by
which the upper half rests firmly on the board, and secures
the blade lying flatly on the paper.

For the second size of board, 31 inches long, the blade
should be not more than 30± inches, of the same scan-

PRACTICAL CARPENTRY AND JOINERY.

timer 1 as above, or rather thinner; and the stock a little
© '

shorter.

One-half of the stock c (Fig. 235), is in some cases made
loose, to turn upon a brass pin to any angle Fig. 235.
with the blade a, and to be clenched by a
screwed nut and washer. The turning stock
is useful for drawing parallel lines obliquely
to the edges of the board. In most cases, how¬
ever, the sector, and the other appendages
to be afterwards described, answer the purpose,
and do so more conveniently. A square of
this sort should be rather as an addition to .

Drawing Square,

the fixed square, and used only when the with swivelling
bevil edge is required, as it is not so handy
as the other.

The edges of the blade should be very slightly rounded,
as the pen will thereby work the more freely. It is a
mistake to chamfer the edges—that is, to plane them
down to a very thin edge, as is sometimes done, with
the object of insuring the correct position of the lines;
for the edge is easily damaged, and the pen is liable to
catch or ride upon the edge, and to leave ink upon it.

A small hole should be made in the blade near the end,
by which the square may be hung up out of the way
when not in use.

No varnish of any description should be applied to the
T-square, or indeed to any of the wood instruments em¬
ployed in drawing. The best and brightest varnish will
soil the paper long after it has been applied and fur¬
bished up. The natural surface of the w T ood cleaned and
polished occasionally with a dry cloth, is the best and
cleanest for working with.

Straight-edges and Triangles.

These appendages to the T-square greatly facilitate the
operations of the draughtsman. They should be of close-
grained hardwood, as mahogany, well-seasoned; straight¬
edges, when 5 feet long and upwards, may be of ribbon-
steel. Wood is more easily kept clean, and is less likely
to soil the paper.

Straight-edges should, like square blades, be just broad
and thick enough for the necessary stiffness, and bevelled
a little at one edge. The smallest (as in Fig. 236) may be
9 or 10 inches long, | inch broad, and 5 inch thick.

triangles, or set-squares , as they are sometimes called,
should be barely inch thick, and flat on the edges, to
wear well. They should be right angled, one of them a
(Fig. 236), being made with equal sides, and angles of 45

Fig. 236,

Straight-edge and Set-squares.

degrees each; the other 6 , with angles of 60 and 30
degrees. The former, by means of its slant side, is very
useful in laying off square figures: the vertical side, too,

saves a deal of shifting of the T-square, as, when the hori¬
zontal edge is applied to that of the square, short perpendi¬
cular lines may be drawn by the upright edge. The most
convenient size for general use measures from 8 ^ to 4 inches
on the side. A larger size, 8 or 9 inches long on the side,
is convenient for use in making large scale drawings. Ap¬
plying one or other edge of the triangle b, to the square,,
the slant side gives at once the boundaries of all hex¬
agonal and triangular figures. This triangle may be of
two sizes, 5 inches high and upwards. Of the two set-
squares, the second is the more convenient for general use
in drawing perpendiculars, as it is larger and has a shorter
base, and is more easily handled. Still sharper set- squares
are sometimes used; also compound triangles, having the
slant-edge broken into two lines of different slopes. The
latter is not to be recommended. Circular openings are
sometimes made in the body of the triangle for facility
in handling. They are of no great use in that respect,
but they allow of the triangles being hung up.

Triano-les are further useful in connection with each
©

other, or with the straight-edge, for drawing short paral¬
lels and perpendiculars without the use of the T-square,
as shall be exemplified in the proper place.

Sweeps and Variable Curves.

For drawing circular arcs of large radius, beyond the
range of the ordinary compasses, thin slips of wood, termed

Fig. 237.

Fig. 238.

sweeps, are usefully employed, of which one or both edges
are cut to the required circle. For curves which are not

circular, but variously elliptic or
otherwise, “ universal sweeps,”
made of thin wood, of variable
curvature, are very serviceable.
The two examples (Figs. 237,
238) have been found from ex¬
perience to meet almost all the
requirements of ordinary draw¬
ing practice. Whatever be the nature of the curve, some
portion of the universal sweep will be found to coincide
with its commencement, and it can be. continued through-
out its extent by applying successively such parts of the
sweep as are suitable, taking care, however, that the con¬
tinuity is not injured by unskilful junction.

Variable Curve,
One-fourth full size.

Pencils.

Pencils are of various qualities, distinguished by letter-
marks. The H B (hard and black) quality is usually
recommended; but it is too soft to retain long the firm
point required for the correct execution of mechanical
I drawings; and, besides, the softer pencils are the more
i unctuous, and therefore the less ready in taking on

CONSTRUCTION AND USE OF DRAWING INSTRUMENTS.

ink lines than the harder. F pencils work pretty well
upon smooth paper; but for drawing paper of a thick
and rougher quality, especially after having been damp-
stretched, H H, and still better, H H H pencils (of
two or three degrees of hardness), are better suited to
retain their sharpness. They are further recommended
by the lightness and delicacy of the lines that may be
thrown off by them; for when a pencil drawing is made
with the view of being done over with ink lines, the
excellence of these lines, as well as the readiness with
which they are produced, depends much upon the quality
of the pencilling.

Pencil lines, intended to be made permanent in ink,
ought to be entered very delicately, and made just so
dark as to render them distinct, for the more lightly
they are executed, the titter they are to receive the ink.
A little practice, and a steady hand, will secure the end
proposed. The pencil need not be held tightly; a slight
hold, without slackness, is what is wanted, inclined a little
to the side toward which the line is drawn. Besides a
drawing pencil for straight lines, it is well to have one a
little softer for sketching in small circles, not requiring
the regular application of the pencil bows, as the rounding
and filling up of corners, ends of bolts, and the like.
Many good draughtsmen consider the following mode of
cutting as the one best calculated to prepare the pencil
for straight line drawing:—In the first place, it should
be cut down to the flat side of the lead, in a plane nearly
parallel to the axis; then cut away on the opposite side to
a bevel considerably inclined, and cut, likewise, trans¬
versely, at equal angles. The lead being thus laid bare,
should be pared down gradually on the three inclined
sides, till brought to a fine edge viewed laterally, and a
flat round point in the other aspect (as in Fig. 239). The
less inclined side, when applied to a square, admits of the
point being brought close to the edge,
by which the line is more certainly
drawn; and the roundness of' the
point keeps the pencil longer in
working order. The sharpening of
a sketching pencil is simply conical,
and brings it to a fine point, and
many prefer the lining pencil cut also
in this manner. To produce a good
working pencil, a sharp knife is in¬
dispensable ; if the knife be blunt, the
point will invariably break away be¬
fore it is properly brought up—a very fine flat file, or a
pumice-stone, or two files set in a stock, so that the sec¬
tion of the blades shall be like the letter V, are sometimes
used to bring up the point of the pencil. Amongst the
minor things requiring special attention, the cutting and
pointing of pencils is one of some consequence both in
point of economy and pleasant working A carelessly
cut pencil is constantly requiring a knife; and, at the
same time, it works with much uncertainty along the
straight edge of the square.

Pig. 239.

i . i

Drawing Pencil.

Pins.

Pins for holding down sheets not fixed by glue or
otherwise, are indispensable. These should be made

with a broad flat head, of brass, and rounded so as to

permit the squares to slide easily over it, and
the stem, of steel, rivetted into the head.
Fig. 240 shows a good form of pin. The
stem is in some cases screwed in, but is then
liable to wear loose: the taper of the stem
should be moderate, so as not to work out
when fixed into the board.

Fig. 240.

Pins.

General Remarks on Drawing.—Management of the

Instruments.

In constructing preparatory pencil-drawings, it is advis¬
able, as a rule of general application, to make no more
lines upon the paper than are necessary to the completion
of the drawing in ink; and also to make these lines just
so dark as is consistent with the distinctness of the work.
And here we may remark the inconvenience of that
arbitrary rule, by which it is by some insisted that the
pupils should lay down in pencil every line that is to be
drawn, before finishing it in ink It is often beneficial to
ink in one part of a drawing, before touching other parts
at all: it prevents confusion, makes the first part of easy
reference, and allows of its being better done, as the sur¬
face of the paper inevitably contracts dust, and becomes
otherwise soiled in the course of time, and therefore the
sooner it is done with the better.

Circles and circular arcs should, in general, be inked in
before straight lines, as the latter may be more readily
drawn to join the former, than the former the latter.
When a number of circles are to be described from one
centre, the smaller should be inked first, while the centre
is in better condition. When a centre is required to bear
some fatigue, it should be protected with a thickness of
stout card glued or pasted over it, to receive the compass-
leg, or a piece of transparent horn should be used, as before
remarked when treating of compasses.

India-rubber is the ordinary medium for cleaning a
drawing, and for correcting errors made in pencilling.
For slight work it is quite suitable; but its repeated ap¬
plication raises the surface of the paper, and imparts a
greasiness to it, which spoil it for fine drawing, especially
if ink-shading or colouring is to be applied. It is much
better to leave trivial errors alone, if corrections by the
pencil may be made alongside without confusion; as it is,
in such a case, time enough to clear away superfluous lines
when the inking is finished.

For cleaning a drawing, a piece of bread two days old is
preferable to india rubber, as it cleans the surface well and
does not injure it. When ink lines to any considerable
extent have to be erased, a small piece of damped soft
sponge may be rubbed over them till they disappear. As,
however, this process is apt to discolour the paper, the
sponge must be passed through clean water, and applied
again to take up the straggling ink. For small erasures of
ink lines, a sharp rounded pen-blade applied lightly and
rapidly does well, and the surface may be smoothed down
by the thumb-nail or a paper-knife handle. In ordinary
working drawings a line may readily be faken out by
damping it with a hair pencil and quickly applying the
india-rubber; and, to smooth the surface so roughened, a

4 G

PRACTICAL CARPENTRY AND JOINERY.

light application of the knife is expedient. In drawings
intended to be highly finished, particular pains should be
taken to avoid the necessity for corrections, as everything
of this kind detracts from the appearance.

In using the square, the more convenient way is to
draw the lines off the left edge’ with the right hand,
holding the stock steadily but not very tightly, against
the edge of the board with the left hand. The conveni¬
ence of the left edge for drawing by, is obvious, as we are
able to use the arms more freely, and we see exactly what
we are doing.

To draw lines in ink with the least amount of trouble
to himself, the draughtsman ought to take the greater
amount of trouble with his tools. If they be well made,
and of good stuff’ originally, they ought to last through
three generations of draughtsmen; their working parts
should be carefully preserved from injury; they should be
kept well set, and above all, scrupulously clean. The set¬
ting of instruments is a matter of some nicety, for which
purpose a small oil-stone is convenient. To dress up the
tips of the blades of the pen, or of the bows, as they
are usually worn unequally by the customary usage, they
may be screwed up into contact, in the first place, and
passed along the stone, turning upon the point in a directly
perpendicular plane, till they acquire an identical profile.
Being next unscrewed, and examined to ascertain the
parts of unequal thickness round the nib, the blades are
laid separately upon their backs on the stone, and rubbed
down at the points, till they be brought up to an edge of
uniform fineness. It is well to screw them together again,
and to pass them over the stone once or twice more, to
bring up any fault; to retouch them also on the outer
and inner side of each blade, to remove barbs or frasing;
and finally to draw them across the palm of the hand.

The china-ink, which is commonly used for line-draw¬
ing, ouejit to be rubbed down in water to a certain degree:
—avoiding the sloppy aspect of light lining in drawings;
and making the ink just so thick as to run freely from the
pen. This medium degree may be judged of after a little
practice by the appearance of the ink on the pallet. The
best quality of ink has a soft feel, free from grit or sedi¬
ment when wetted and rubbed against the teeth, and it has
a musky smell. The rubbing of china-ink in water tends
to crack and break away the surface at the point: this

may be prevented by shifting at intervals the position of
the stick in the hand while being rubbed, and thus round¬
ing the surface. Nor is it advisable, for the same rea¬
son, to bear very hard, as the mixture is otherwise more
evenly made, and the enamel of the pallet is less rapidly
worn off. When the ink, on being rubbed down, is likely
to be for some time required, a considerable quantity of it
should be prepared, as the water continually vaporizes: it
will thus continue for a longer time in a condition fit for
application. The pen should be levelled in the ink, to
take up a sufficient charge; and to induce the ink to
enter the pen freely, the blades should be lightly breathed
upon or wetted before immersion. After each application
of ink, the outsides of the blades should be cleaned, to pre¬
vent any deposit of ink upon the edge of the squares.

To keep the blades of his inkers clean, is the first duty
of a draughtsman who is to make a good piece of work.
Pieces of blotting or unsized paper, and cotton velvet,
washleather, or even the sleeve of a coat, should always
be.at hand while a drawing is being inked. When a small
piece of blotting paper is folded twice so as to present a
corner, it may usefully be passed between the blades of
the pen, now and then, as the ink is liable to deposit at
the point and obstruct the passage, particularly in fine-
lining; and for this purpose the pen must be unscrewed to
admit the paper. But this process may be delayed by
drawing the point of the pen over a piece of velvet, or
even over the surface of thick blotting paper; either
method clears the point for a time. As soon as any
obstruction takes place, the pen should be immediately
cleaned, as the trouble thus taken will always improve
and expedite the work. If the pen should be laid down
for a short time with the ink in it, it should be unscrewed
to keep the points apart and so prevent deposit; and when
done with altogether for the occasion, it ought to be tho¬
roughly cleaned at the nibs. This will preserve its edges
and prevent rusting.

For useful reference, to assist the judgment in the pre¬
paration of drawings on ^vaper, the drawing office should
be fitted with a vertical scale of full size feet and inches,
6 or 8 feet long, fixed against the wall; and with a hori¬
zontal scale the full length of the office, fixed to the wall
at 7 or 8 feet above the floor. The scales should be painted
conspicuously in white, with black lining and figures.

PART THIRD.

STEREOGRAPHY.

PROJECTION.

I rojection has for its object the representing on a given
surface the forms of such solid bodies as can have their
boundaries properly defined.

Since the surfaces of all bodies may be supposed to con¬
sist of points, it is obvious that if the means of determin¬

ing the position of any one point be possessed, the means
of determining the position of all the points are equally
possessed, and these will produce the surfaces to which
they belong.

As space is unlimited, the position of a point can only
be defined by referring it to some other object or objects
whose positions are known. Therefore, if it is required

STEREOGRAPHY

PROJECTION.

to convey the knowledge of the position of a point, it is
necessary to assume some objects of correlation, the posi¬
tions of which are known or may be imagined, and planes
are the objects generally selected.

Now, suppose a line to pass through the point to be
determined, and to be somewhere intersected at a given
angle by a plane whose position is known. This inter¬
section will be a point. If the plane and the point of in¬
tersection be given, it is clear that the line which passes
through the point sought may be drawn. The point
sought must be somewhere in that line. But to fix its
locality another element is required, and is obtained by
supposing another plane intersecting another straight line
passing through the point. The positions of the two planes
and the directions of the lines being known, the position
of the point is defined by the intersection of the lines.

Let abcd (Fig. 241) and D E F c be the two planes,
and G o H o the
lines, their in¬
tersection at o
establishes the
position of the
point.

Although the
planes maybe at
any angle in re¬
spect of each other, yet in practice, for the sake of simplicity,
they are supposed to be at right angles to each other, and
the lines passing through the point to be perpendicular to
the planes. The intersection of the lines with the planes
at G and H are called the projections of the point o.

In order to determine the 'position of a straight line,
it is obviously only necessary to determine any tiuo
points in it.

Let G H (Fig. 242) be a straight line, whose position it
is required to determine. Let abcd be a vertical, and
E F D c a horizontal plane,
then the position of the
point G will be determined
by its projections g G g G,
and the position of the
point H by its projections
li H g H, and, conse¬
quently, the position of
the line H G is determined;
and if the points H G are at the extremities of the line,
its length also is determined.

The planes are here shown in perspective, but in prac¬
tice they are drawn geometrically on the paper, as if they
were supposed to be
hinged at C D and laid
flat, and in this posi¬
tion they are repre¬
sented in Fig. 243. It
is obvious that all that
is required in working a c x

the problem is the line of intersection C D.

As, however, it will facilitate the comprehension of the
subject, the projections are shown both in perspective and
geometrically.

In the last figure the position of a line was defined by
the projections on two planes of two points contained
in it. These planes are not the only ones on which the

Fig. 213.
D

A 9

l’i». 244.
B

projection may be made. In Fig. 244, op are the projec
tions of the points on a plane
B K F D, and in this figure it is
seen that h g is the projection
of the line on the plane abdc,
o p is its projection on b k f d,
and g is its projection onCDFE.

In Fig. 245 it is shown with
the planes laid flat. Omitting
the boundary lines, the projection in practice would

* \S

Fig.

245.

Fig. 246.

B D

h 9

A. 9

ACE

be as in Fig. 246. By these figures it is made apparent
that the drawing of projections is less laborious when the
planes are laid flat than if they were vertical; for the
vertical and horizontal projections of the line being in¬
tersections of the horizontal and vertical planes, by a
plane, li H g’ r, perpendicular to them both, which passes
through the points H G, and which is therefore perpendi¬
cular to their intersection c D, the straight lines g' r, r h
will also be perpendicular to C D. Hence, if the projection
of a point g' on the horizontal plane be known, its pro.
jection on tlie vertical plane laid flat will be in the straight
line produced, drawn through g', perpendicular to C D.

The line h g has been supposed parallel to one of the
planes of p>rojection, and its projection on that plane is
equal to its length. If the line be oblique to both planes,
its length will be greater than either of its projections.

Let g h g li (Fig. 247) be the vertical and horizontal
projections of a straight Fig. 247.

line, its actual length
will be greater than
either; but the follow¬
ing considerations show
that it may be easily
found from them. Let
a line G K, lying in the
plane passing through
G H, be drawn through
to meet the perpendicular H li in K, then G K H is a right-
angled triangle, of which G H is the hypothenuse: its
side K H is equal to the vertical projection h h, its base
to the projection g
li. Construct this
triangle, therefore, as
shown in Fig. 248,
and g r is the length
of the line required.

The length may be
also found from the
vertical projection, thus:—Draw kg (Fig. 248) parallel
to C D and produce it to s, make k s equal to the horizon¬
tal projection li g, and join h s, which will be the length
of the line required.

The projections of a right line being given, and a
length taken on one of them, to find the original line

Fig. 243.

D r

PRACTICAL CARPENTRY AND JOINERY.

Fig. 249.

which that length represents, and the angle which it
makes with, each of its planes of projection.

Let a b a b' (Fig. 249) be the given projections, and
c d the length,
taken on
horizontal
jection. As all
the points of
the line neces¬
sarily corre¬
spond to all the
points of its

projection, if on c cl are raised the indefinite perpendicu¬
lars to the common section, these lines will cut the vertical
projection a’ b' in the points c’ and cl', and c cl will be
the length of the vertical projection of c cl.

To find the length of the original line : on c cl (Fig. 250),
raise indefinite perpendiculars, upon which from c carry
the length 1 c to c, and from cl the length 2 cl' to D, and
draw through C and D the line A B, which is the original

line sought; then through c draw c e parallel to c cl,
and the angle D c e is the angle which the original line
makes with the horizontal plane. In the same manner
the angle with the vertical plane is found on the ver¬
tical projection by carrying the length 1 c 2 cl from c
and don the perpendiculars c d' to c' d', and through c'
and D, A B', and then from c', drawing c' e', parallel to
c'd', and the angle d' c' e
is the angle sought.

The projections a’b’a'b"

(Fig. 251) of a right line
A b, being given, to find the
points wherein the prolon-
ejation of that line wonld
meet the planes of projec¬
tion.

Fig. 252.

In the perspective representation of the problem, it is
seen that A b, if prolonged, cuts the
horizontal plane in c, and the ver¬
tical plane in d, and the projections
of the prolongation become c e f d.

Hence, in the following figure, if
a b a’ b' (Fig. 252) be the projections
of A B, the solution of the problem
is obtained by producing these lines
to meet the common intersection of
the planes in f and e, and on these

points to raise the perpendiculars fee d, when
are the points sought.

c and

Fig. 253.

To draw through a given point a line parallel to the
project ions of a given line.

Let a b a b' (Fig. 253) be the projections of the ori¬
ginal line A B. From the perspective representation it
is evident that the lines a b a' b' of projections of the
planes which pass through the original line A B, and the
lines of projection of the planes which pass through any
line C D, and
parallel to the
line A B, are
parallel each to
each; therefore,
if the given
point lie in
such line C D,
the solution of
the problem is
easy.

Let ab a' b'

(Fig. 254) be
the given pro¬
jections, and e
the given point, then through e draw c d parallel to a b,
and through e! draw c d' parallel to a' b', and c d d d 1
are the projections of the line sought.

If the two lines intersect each other in space, to find
from their given projections the angles which they make
with each other.

Let A B, c D (Fig. 255) be the given lines intersecting

at E. In the perspective representation, if these lines
be supposed to lie in a plane which intersects the hori¬
zontal plane in the line A C, this line will be the base of a
triangle, aec. If the plane is perpendicular to the hori¬
zontal plane, the angle A E c is at once known; but, sup¬
pose it inclined to the horizontal plane, then, to find
the angle, it is necessary to imagine the plane turned
down horizontally on the line A c, as at A e" c. To do
this, from E let fall a perpendicular to the horizontal
plane, cutting it in e, which is the horizontal projection
of E, and the height e E is the height of the vertex of
the ti'iangle above the horizontal plane, and e f is the
projection of the line E /. There is thus obtained Che
triangle e Ef which suppose laid horizontally, by turning
on its base e f, then from / as a centre describe the
arc E g E", cutting the line e f produced in e", and join
A E c E , and A e" c is the angle sought.

In applying this to the solution of the problem, let

STEREOGRAPHY—PROJECTION.

a b c d, a' b' c d' (Fig. 256) be the projections of the
lines: from e draw indefinitely,
e e' perpendicular to the line
e' f and make e E' equal to e" e,
and draw / e' : from / as a cen¬
tre, describe the arc e' g e",
meeting e f produced in e", and
join a f", g e”: the angle a e" c
is the angle sought.

It will be observed that the
projections of the point of in¬
tersection of the two lines are
in a right line perpendicular
to the line of intersection of
the planes of projection. Hence
this corollary. The projections
of the point of intersection of
two lines which cut each other
in space, are in the same right-
line perpendicular to the com¬
mon intersection of the planes
of projection. This is further
illustrated by the nest problem.

To determine, from the projection of two lines which
intersect each other in the projections, whether the lines
cut each other in space or not.

Let a b, c d, a b', c d' (Fig. 257) be the projections of
the lines. It might
be supposed that as
their traces or pro¬
jections intersect
each other, that the
lines themselves in¬
tersect each other
in space, but, on ap¬
plying the corollary
of the preceding problem, it is found that the intersec¬
tions are not in the same perpendicular to the line of
intersection of the planes of projection a c. This is re¬
presented in perspective in Fig. 258.

Fig. 258.

We there see that the original lines »Bci) do not cut
each other, although their projections a b, c d, a b', c d', do
so. Fi’om the point of intersection e raise a perpendicular
to the horizontal plane, and it will cut the original line
c D in e, and this point therefore belongs to the line c D,
but e belongs equally to a B. As the perpendicular raised
on e passes through e on the line c D, and through e' on
the line a B, these points E E' cannot be the intersection
of the two lines, since they do not touch; and it is also the
same in regard to//'. Hence, when two right lines do
not cut each other in space, the intersections of their pro¬
jections are not, in the same right line, perpendicular to
the common intersection of the planes of projection.

Fig. 256.

llie projections of a plane and of a 'point being given ,
to dratv through the point a plane parallel to the given
plane.

In the perspective representation, suppose the problem

solved, and let B c (Fig. 259) be the given plane, and A c,
A B its projections, and E F a plane parallel to the given
plane, and G F, G E, its projections. Through any point D,
taken at pleasure on the plane E F, draw the vertical plane
H J, the horizontal projection of which, I H, is parallel to
G E. The plane H J cuts the plane E F in the line k l', and
its vertical projection G F in V. The horizontal projec¬
tion of k l' is H I, and its vertical projection k l'; and as
the point D is in k' l', its horizontal and vertical projec¬
tions will be d and cl’. Therefore, if through d be traced
a line cl I, parallel to A B, that line will be the horizontal
projection of a vertical plane passing through the original
point D; and if on I be drawn the indefinite perpendicular
11 ', and through d', the vertical projection of the given
point, be drawn the horizontal line d' V, cutting the per¬
pendicular in l’, then the line F G drawn through V, parallel
to A c, will be the vertical projection of the plane required;
and the line G E drawn parallel to A B, its horizontal pro¬
jection. Hence, all planes parallel to each other have their

projections parallel and reciprocally. In solving the pro¬
blem, let A B, A c (Fig. 260) be the projections of the given
plane, and d d' the projections of the given point. Through
d draw d I parallel to A B, and from I draw I l' perpen¬
dicular to A H : join d d', and through d' draw cl V parallel
to A H. Then F V G drawn parallel to A c, and G E parallel
to A B, are the projections required.

The projections A B, B c, and ad,d c, of two planes
which cut each other being given, to find the projection
of their intersections.

The planes intersect each other in the straight line A -c

(Figs. 261 and 262), of which the points A and c are the

PRACTICAL CARPENTRY AND JOINERY.

projections, since in these points this line intersects the
planes of projection. Now, to find these projections, it is
only necessary to let fall on the line of intersection the
perpendiculars A a, c c (Fig. 261), from the points A and c,
and join Ac, c a : Ac will be the horizontal projection, and
c a the vertical projection of c a (Fig. 261), or c A (Fig.
262), the line of intersection or arris of the planes.

The 'projections of two intersecting planes being given,
to find the angle which they make betiveen them.

The angle formed by two planes is measured by that
of two perpendiculars drawn through the same point ol
their intersections in each of the two faces. These lines
determine a third plane perpendicular to the arris. 11,
therefore, the two planes are cut by a third plane, the
solution of the problem is obtained.

On the arris A C (Fig. 263), take at pleasure any point

E, and suppose a plane passing through that point, cut¬
ting the two given planes perpendicular to the arris.
There results from the section a triangle def, inclined
to the horizontal plane, and the angle of which, D E F, is
the measure of the inclination of the two planes. The
horizontal projection of that triangle is the triangle D e F,
the base of which, F D, is perpendicular to A c, and cuts it
in the point g, and the line Eg is perpendicular to D F.
The line g E is necessarily perpendicular to the arris A c,
as it is in the plane DEF, and its horizontal projection is
g e. Now, suppose the triangle def turned on D F as an
axis, and laid horizontally, its summit will then be at
e", and D e" f is the angle sought. The perpendicular g e

is also in the vertical triangle A c c, of which the arris is
the hypothenuse, and the sides Ac, c c, are the projec¬

tions. This description introduces the solution of the pro¬
blem, which applies also to Fig. 264.

Through any point g (Fig. 264) taken at pleasure, on
the line A c, the horizontal projection of the arris a c,
draw FD perpendicular to A c; from g draw g E' perpendi¬
cular to the arris A c'; and from g as a centre, with the
radius g E', describe the arc e' e": join fe,de'. The angle
e" f d is the angle sought.

Through the projection of a given point a a!, to draw
a perpendicular to a plane, bc, CD, also given.

Let A E (Fig. rig. 2C5.

265) be the
perpendicu¬
lar drawn
through the
point A to the
plane B D, and
its intersec¬
tion with the
plane is the
point E.

Suppose a
vertical plane
a F to pass

through A E, this plane would cut B D in the line g D, and
its projection a h would be perpendicular to the projection

I’ig. 2G6.

BC. In the same way a'e', the vertical projection of A E,
would be perpendicular to c D, the vertical projection of the
plane BD. Then, if a line, perpendicular to a h, is drawn
through a, it will be the horizontal projection of the plane
passing in the line of the perpendicular A E, and h F will
be its vertical projection. From a', draw upon C D an in¬
definite perpendicular, and that line will contain the ver¬
tical projection of A E, as a h contains its horizontal projec¬
tion. Now, to find the point of intersection of the line
A E with the plane, construct the vertical projection of the
line of intersection of the two planes g D, and the point of
intersection of that line with the right line drawn through
a , will be the point sought. If from that point a perpen¬
dicular is let fall on a h, the point e will be the horizon¬
tal projection of the point of intersection E.

In Fig. 266, let B c, c D be the projections of the given
plane, and ad of the
given point. From
the given point a,
draw a g perpendi¬
cular to B c, which
will be the hori¬
zontal projection of
a plane passing
vertically through
a, and cutting the
given plane. From
a, also draw a A
perpendicular to
a g, and make it
equal to d d (Fig.

265). From h draw
li D perpendicular to h a, and make h D equal to h D.
Draw g , which will be the section of the given plane,
and the angle hg d' will be the measure of the inclination
of the given plane with the horizontal plane. There is
now to be drawn, perpendicular to this line, a line A E

ivS.

i Y\

i \ \

1 \ \

1 \ N
i \

t /

A
/ 1
/ 1
/ 1

/ 1

I /\

i ✓ i

hi/ j

\ i

\ |

g i JHE

1 7 -—

/ 1

\ 1

<■ i / /

'ii /

if /

\ i / /

/y\

1 /*

1 • /

1 /
i ✓

\ 1 /

\ 1 ''

STEREOGRAPHY—PROJECTION.

through A, ■which will be the line required. From the point
of intersection E let fall upon ah a perpendicular, which
will give e as the horizontal projection of E. Therefore: —
Where a right line in space is perpendicular to a
plane, the projections of that line are respectively per-
pendicular to the projections of the plane.

Through a given point a a', to draw a plane perpen¬
dicular to a right line b c, b' c' also given.

The foregoing problem has shown that the projections
of the plane sought must be perpendicular to the projec¬
tions of the line.

The plane D E (Fig. 267), is, by construction, perpen¬
dicular to the line B c. Take at pleasure the point A in
the plane D E, and through it draw the horizontal line A /',

which will be necessarily parallel to the projection D G,
and will cut the vertical projection G E in /'. The hori¬
zontal projection of the intersecting point will be f, that
of A will be a, and that of A/' will consequently be a f,
which, being parallel to D G, will be perpendicular to b c.
The solution of the problem consists in making to pass
through A a vertical plane A f, the horizontal projection
of which will be perpendicular to b c.

Through a (Fig. 268), draw the projection a f perpen¬
dicular to be: from
f raise upon K L the
indefinite perpendi¬
cular ff', which will
be the vertical pro¬
jection of the plane
a if, perpendicu¬
lar to the horizon¬
tal plane, and pass¬
ing through the ori-
ginal point A (Fig.

267). Then draw
through a in the
vertical projection a
horizontal line, cut¬
ting f f' in/', which point should be in the projection of
the plane sought; and as that plane must be perpendicu¬
lar to the vertical projection of the given right line, draw
through /' a perpendicular to l> c, and produce it to cut
K L in G. This point G is in the horizontal projection of
the plane sought. All that remains, therefore, is from G
to draw G D perpendicular to b c. If the projections of
the straight line are required, proceed as in the previous
problem, and as shown by the dotted lines.

A right line, a b and a! 6', being given in projection,
and also the projection of a given plane, to find the
angle which the line malccs with the plane.

Let A B (Fig. 269), be the original right line intersect¬
ing the plane c E in the Kg. %%

point B. If a, vertical plane
pass through the right line, »
it will cut the plane c E in
the line / B, and the hori¬
zontal plane in the line a b.

As the plane a B is in this case
parallel to the vertical plane
of projection, its projection
on that plane will be a quadrilateral figure a b', of the
same dimensions; and /B contained in the rectangle will
have for its vertical projection a right line D b', which
j will be equal and similar to / B. Hence the two angles,
a b' d, A Bfi being equal, will equally be the measure of
the angle of inclination
of the right line A B to the
plane c E. Thus the angle
a' b' D (Fig. 270) is the angle
sought.

This case presents no
difficulty; but when the line
is in a plane which is not
parallel to the plane of pro¬
jection, the problem is more
difficult.

In Fig. 271, the right line A B is oblique to the plane

Kg. 271.

of vertical projection. It cuts the plane c E in B. Now,
a vertical plane may be supposed, as before, to pass through
the line A B and to cut the plane C E, and the angle A B h
may at first sight be imagined to be the angle sought—
that is, the measure of the inclination of A B with the
plane C E. But it is not so; for the vertical plane which
passes through A B, and contains that angle, is oblique to
the plane C E ; and its projection a b is consequently not
perpendicular to the given plane. It is to be recollected
that the inclination of a right line to a plane is measured
by an angle situated in a plane which shall pass through
the right line, and be perpendicular to the plane, which
is always possible. If, therefore, a plane perpendicular
to C E pass through the right line A B, the projections of
the two planes will be perpendicular to each other. Thus
a f will be perpendicular to c D, and a' D to D E. These
planes intersect in the line/B. This line, as well as the
original line A B, will, therefore, be in a plane which is
perpendicular to the plane c E, and A B / wiil be the angle
sought.

Through any point A in the given line, draw a perpen-

PRACTICAL CARPENTRY AND JOINERY.

dicular A / upon the plane c e. This line will also be
perpendicular to / B, and will be the third side of a tri¬
angle a / B, rectangular at /, perpendicular to the plane
c E, and inclined to the horizontal plane. The projections
of the triangle will be a f b on the horizontal, and d'DP
in the vertical plane. The projections of the triangle
being obtained, it is only necessary to develope it on the
horizontal plane by turning it down as on a hinge. To do
this, observe that the side / B of the triangle A / B rests
on the hypothenuse of a right-angled triangle / b B, which
is vertical or perpendicular to the horizontal plane. Lay¬
ing down this triangle flat, by making it turn on its base
b f, as on a hinge, it will then appear as f b B', and its
hypothenuse will be the side or base of the triangle sought,
b/a. It has been seen that A/was perpendicular to/B:
raise on / therefore, perpendicular to / B', the side A /,
which will be / a' ; draw the line a' b', which will be the
hypothenuse of the triangle sought; and the angle/B' a'
will be the measure of the inclination of the line A B with
the plane c e. From the above description, the operation
may be performed in Fig. 272, in which CD, DE are the
projections of the Kg- 272 .

plane, and a b,
a B the projec¬
tions of the line.

Through a in the
horizontal projec¬
tion draw a f per¬
pendicular to C D,
and join / b. To
obtain the de¬
velopment of the
triangle D B b,
which is in the
vertical proj ection
of a right-angled
triangle whose
base is / b, imagine this triangle turned down on its base
as on a hinge, that is, by construction; make b B' equal to
b B, and perpendicular to / b, and join / b'. Then to ob¬
tain the development of the triangle a' D B, on / draw / A'
perpendicular to / B', and make it equal to a' D, and join
A' b'. Then the angle / b' a, is the measure of the inclina¬
tion of the line A B, on the plane E c.

PROJECTIONS OF SOLIDS.

There is no general rule for the projections of solids. Their
constructions are more or less easy, dependent on the
nature of the question; and it is possible always to accom¬
plish them more or less directly by means of the princi¬
ples about to be stated.

Given the horizontal 'projection of a regular tetrahe¬
dron, to find its vertical projection.

Let abc d (Fig. 273) be the given projection of the
tetrahedron, which has one of its faces coincident with
the horizontal plane. It is evident that the vertical pro¬
jection of that face will be the line A c B If the height
of d above the horizontal plane be known, it is set off'
from c to d', and by joining a d', B d\ the problem is
solved. In proceeding to find the height of cl', let us
consider that a perpendicular, let fall from the summit of

the tetrahedron on the horizontal plane, is also perpen¬
dicular to the right lines d A, cl B, d c, and forms with
each of the arrises a
right-angled triangle, of
which two of the sides,
the right angle, and the
direction of the third
side, are known. It is
easy, therefore, to con¬
struct one of those tri¬
angles. On cl, draw an
indefinite line perpen¬
dicular to cl c, and make
c D equal to cb, c A, or
A B; d D will be the
height sought, which is
carried to the vertical
projection from c to d'.
in other ways.

A point being given in one of the projections of a-
tetrahedron, to find the point on the other projection.

Let e be the point given in the horizontal projection
(Fig. 273). It may first be considered as situated in the
plane c B cl, inclined to the horizontal plane, and of which
the vertical projection is the triangle c B cl'. According
to the general method, the vertical projection of the given
point is to be found somewhere in a perpendicular raised
on its horizontal projection e. If through d and the point
e be drawn a line produced to the base of the triangle in
/ the point e will be on that line, and its vertical pro¬
jection will be on the vertical projection of that line f e d',
at the intersection of it with the perpendicular raised on e.
If through e be drawn a straight line g h, parallel to c B,
this will be a horizontal line, whose extremity li will be
on B cl- The vertical projection of cl B is cl' B ; therefore,
by raising on h a perpendicular to A B, there will be ob¬
tained hj, the extremity of a horizontal line represented
by h g in the horizontal plane. If through h' is drawn
a horizontal line h' g, this line will cut the vertical line
raised on e in e, the point sought. If the point had
been given in g on the arris c cl, the projection could
not be found in the first manner; but it could be found
in the second manner, by drawing through g a line
parallel to c B, and prolonging the horizontal line drawn
through h to the arris c d', which it would cut in g, the
point sought. The point can also be found by laying
down the rectangular triangle C cl D, which is the de¬
velopment of the triangle formed by the projection of
the arris C d, the height of the solid and the length of
the arris as a hypothenuse, and by drawing through g
the line g G perpendicular to c d, to intersect the hypo¬
thenuse in G, and carrying the height g G from c to g>
in the vertical projection. Thus, one or other of these
means can be employed according to circumstances. If
the point had been given in the vertical, instead of the
horizontal projection, the same operations inverted would
require to be used.

Given a tetrahedron, and the projection of a plane
cutting it, by which it is truncated, to find the projection
of the section.

1 irst, when the intersecting plane is perpendicular to the
base (Fig. 274), the plane cuts the base in two points c f,
of which the vertical projections are e and f ; and the

This problem might be resolved

STEREOGRAPHY-PROJECTIONS OF SOLIDS.

Fig. 275. //

d/Ljf

! i \

/ fc

b//

d ! !

1 !

'mJ.

arris b <1 is cut in g, the vertical projection of which
can readily be found in any of the ways detailed in the
last problem. Having found g', join e g‘,f'g', and the
triangle e' g f is the ,

projection of the inter¬
section sought.

When the intersect¬
ing plane is given in
the vertical projection,
as e! f in Fig. 275, the
horizontal projections of
the three points e g' /'
have to be found. The
point g in this case may
be obtained in several
ways. First, by draw¬
ing g' g h through g\
then through It draw¬
ing a perpendicular to the base, produced to the arris
at h, in the horizontal projection, and then drawing
h g parallel to c B, cut- d'

ting the arris B d in g,
which is the point re¬
quired. Second, take d B
as the base of a triangle
formed by the perpendicu¬
lar, and the arris of which,
d B, is the horizontal pro¬
jection, and carry this base,
d B, upon the common line
of intersection of the planes
from d to B', and draw the
arris b' d\ From g draw
the horizontal line cutting b

b' d' in G' ; carry g g ', which is the distance of the per¬
pendicular of the arris in the horizontal projection, from
d to g ; and g is the point sought.

The 'projections of a tetrahedron being given, to find
its projections when inclined to the horizontal plane in
any degree.

Let ABC d (Fig. 276) be the projections of a tetrahed¬
ron, with one of its sides
coincident with the hori¬
zontal plane, and c cl' b'
its vertical projection; it
is required to find its pro¬
jections when turned round
the arris A B as an axis.

The base of the pyramid
being a triangle, its verti¬
cal projection is the right
line c B. If this line is
raised to c", by turning
round B, the horizontal
projection will be A c 2 B.

When the point c', by the
raising of B c', describes the arc c' c", the point d' will have
moved to d", and the perpendicular let fall from that
point on the horizontal plane will give <T\ the horizon¬
tal projection of the extremity of the arris c d ; for as
the summit d moves in the same plane as c, parallel to
the vertical plane of projection, the projection of the sum¬
mit will evidently be in the prolongation of the arris C d,

which is the horizontal projection of that plane. The
process, therefore, is very simple, and is as follows:—Con¬
struct at the point B the angle required, c B c", and make
the triangle c" B d" equal to & d b' ; from d‘ let fall a per¬
pendicular cutting the prolongation of the arris c d in d s ;
and from c", a perpendicular cutting the same line in c 2 ;
Join b c 2 , A c 2 , B d 3 , a d\

The following is a more general solution of the prob¬
lem :—Let ABC d (Fig. 277) be a pyramid resting with
one of its sides on the horizontal plane, and let it be
required to raise, by its angle C, the pyramid, by turn¬
ing round the arris A B, until its base makes with the
horizontal plane any required angle, as 50°. Conceive the
right line c e turning round e, and still continuing to be
perpendicular to A B, until
it is raised to the required F >s- 277 -
angle. If a perpendicular
be now let fall from C', it
will give the point c" as the
horizontal projection of the
angle C in its new position.

Conceive a vertical plane to
pass through the line C e.

This plane will necessarily
contain the required angle.

Suppose, now, we lay this
plane down in the hori¬
zontal projection, thus:—

Draw from e the line e c',
making with e C an angle
of 50°, and from e with the
radius e c describe an arc
cutting it in c'. From c'

let fall on c e a perpendicular on the point c", which
will then be the horizontal projection of c in its raised
position. On C' e draw the profile of the tetrahedron
c'De inclined to the horizontal plane. From D let fall
a perpendicular on C e produced, and it will give d 3 as
the horizontal projection of the summit of the pyra-
mid in its inclined position. Join A cl 3 , B cl 3 , Ac", B c"
to complete the figure.

The vertical projection of the tetrahedron in its ori¬
ginal position is shown by a cl b, and in its raised position
by a, c 2 , cl\ b-

To construct the vertical and horizontal projections of
a cube, the axis of which is perpendicular to the hori¬
zontal plane.

The axis of a cube is the straight line which joins two
of its opposite solid angles. If an arris of the cube is
given, it is easy to find its axis; as it is the hypothenuse

a right-angled

triangle, the

Fig. 278.

shortest side of which is the length

of an arris, and the longest the

/ ■

diagonal of a side. Conceive the

/ - . -

cube cut by a vertical plane passing

^ ■>

through its diagonals E G, A c (Fig.

278 ), the section will be the rectan¬

/ / | V *v

gle A E G C. Divide this into two

1 }

/ - -V - ■

• C

equal right-angled triangles, by the

diagonal EC. If, in the upper and

lower faces of the cube, we draw

the diagonals fh, b D, they will cut the former diagonals
in the points fb. Now, as the lines b B, b D, f F, / H, are

PRACTICAL CARPENTRY AND JOINERY.

perpendicular to the rectangular plane ae gc , f o may
be considered as the vertical projection of BF, D H, and
from this consideration we may solve the problem.

Let A E (Fig. 279), be the arris of any cube (the letters
here refer to the same parts as those of the preceding
diagram, Fig. 278). Through A draw an indefinite line,
A c, perpendicular to A E. Set off on this line, from A
to c, the diagonal of the square of A E, and join E c,
which is then the diagonal of the cube. Draw then the
lines E G, C G, parallel respectively to A C and ae, and the
resulting rectangle, A E G C, is the section of a cube on the
line of the diagonal of one of its faces. Divide the rect¬
angle into two equal parts by the line b f, which is the

rig. 2-9.

vertical projection of the lines B F, D H (Fig. 278), and
we obtain, in the figure thus completed, the vertical pro¬
jection of the cube, as a c b d (Fig. 280).

Through c (Fig. 279), the extremity of the diagonal,
draw y z perpendicular to it, and let this line represent
the common section of the two planes of projection. Then
let us find the horizontal projection of a cube, of which
A E G c is the vertical projection. In the vertical projection
the axis E c is perpendicular to y z, and, consequently,
to the horizontal plane of projection, and we have the
height above this plane of each of the points which ter¬
minate the angles. Let fall from each of these points per¬
pendiculars to the horizontal plane, the projections of the
points will be found on these perpendiculars.

To find, for example, the horizontal projection of the
axis E c, take at pleasure, on its prolongation, any point,
c' (or e), which is the projection of both the extremities of
the axis c and e. If we suppose the rectangle aegc
turned on the line y z until it is vertical, its projection will
be a g. Through c' (or e) draw a line parallel to y z, and
find on it the projection of the rectangle a' c g', by con¬
tinuing the perpendiculars A a, G g. We have now to
find the projections of the points b f (which represent
D B F II, Fig. 278), which will be somewhere on the per¬
pendiculars b b', ff", let fall from them. We have seen
in the preceding Fig. (No. 278), that BF, d h are dis¬
tant from b f by an extent equal to half the diagonal of
the square face of the cube. Set off, therefore, on the
perpendiculars b b' and /' /", from o and m, the distance
A b in d b' and f /", and join d a, a' b', b' f", f" g, g f\
to complete the hexagon which is the horizontal projec¬
tion of the cube. The dotted lines, d c', b' c', g c', show
the arrises of the lower side. Knowing the heights of the
points in these vertical projections, it is easy to construct

a vertical projection on any line whatever, as that on R S
below. In these figures all the points are indicated by the
same letters as in the preceding figures.

To construct the projections
of a regular octahedron. —The
octahedron is formed by the union
of eight equilateral triangles; or,
more correctly, by the union of
two pj’ramids with square bases,
opposed base to base, and of which
all the solid angles touch a sphere
in which they may be inscribed.

Describe a circle (Fig. 281), and divide it into four equal
parts by the diameters,and draw the lines ad, db, be, ca;
a figure is produced which serves for either the vertical or
the horizontal projection of the octahedron, when one of
its axes is perpendicular to either plane.

One of the faces of an octahedron being given, coinci¬
dent with the horizontal plane of projection, to construct
the projections of the solid.

Let the triangle ABC (Fig. 282) be the given face. If
A be considered to be the summit of one of the two pyra¬
mids which compose the solid, B C will be one of the sides
of the base. This base makes, with the horizontal plane,
an angle, which is easily found. Let fall from A a perpen¬
dicular on B C, cutting it in d. With the length B C as
a radius, and from d as a centre, describe the indefinite
arc e f. The perpendicular A d will be the height of each
of the faces, and, consequently, of that which, turning on
A, should meet the side of the
base which has already turned
on d. Make this height turn on
A, describing from that point as
a centre, with the radius A d, an
indefinite arc, cutting the first
arc in G, the point of meeting of
one of the faces with the square
base: draw the lines G A, G d:
the first is the profile or inclina¬
tion of one of the faces on the
given face ABC, according to
the angle d AG; the second,
d G, is the inclination of the
square base, which separates the
two pyramids in the angle A d,dG.

The face adjacent to the side B c
is found in the same manner. Through G, draw the hori¬
zontal line G II equal to the perpendicular A d. This line
will be the profile of the superior face. Draw cl H, which
is the profile of the face adjacent to B C. From II let fall a
perpendicular on A d produced, which gives the point li for
the horizontal projection of H, or the summit of the supe¬
rior triangle parallel to the first: draw i k, k C, C h, h B, h k,
li i, and the projection is obtained. From the heights we
have thus obtained, we can now draw the vertical projection
M, in which the parts have the same letters of reference.

The finding the horizontal projection may be abridged
by constructing a hexagon in which may be inscribed the
two triangles A c B, h i k (Fig. 282 N), and the projection
is completed.

Given in the horizontal plane the projection of one of
the faces of a dodecahedron, to construct its projections.

Fig. 281.

Fig. 282.

STEREOGRAPHY—PROJECTIONS OF SOLIDS.

The dodecahedron is formed by the assemblage of
twelve regular and
order to construct
the projection, to dis¬
cover the inclina¬
tion of the faces
among themselves.

Let the pentagon
ABODE (Fig. 283)
be one of the faces
on which the body
is supposed to be
seated on the plane.

Conceive two other
faces, e f a h d,

D i K L c also in the
horizontal plane,
and then raised by
being turned on
their bases, ed,dc.

By their movement
they will describe in space arcs of circles, which will ter¬
minate by the meeting of the sides D H, D I.

To find the inclinations of these two faces .—From
the points I and H let fall perpendiculars on their
bases produced. If each of these pentagons were raised
vertically on its base, the horizontal projections of H and I
would be respectively in z s; but as both are raised together,
the angles h and I would meet in space above h, where
the perpendiculars intersect, therefore, h will be the hori¬
zontal projection of the point of meeting of the angles.
To find the horizontal projection of G o K, prolong indefi¬
nitely 3 I, and set off from 0 on si the length x K in k' \
then from s as a centre, with the radius s 1c, describe an
arc cutting s fi produced in the point K', from which
let fall on s k' a perpendicular K 1 c, and produce it to
x K. If, now, the right-angled triangle, s 1c k', were
raised on its base, Ic would be the projection of K'. Con¬
ceive now the pentagon CDIKL turned round on cD,
until it makes an angle equal to 1c z K' with the horizontal
plane, the summit K will then be raised above k by the
height k" K, and will have for its projection the point k.
In completing the figure practically;—from the centre 0 ,
describe two concentric circles passing through the points
h D. Draw the lines h D, h k, and carry the last round
the circumference in mnoprstv: through each of these
points draw radially the lines m C, 0 B, r A, t E, and these
lines will be the arrises analogous to h D. This being done,
the moiety or inferior half of the solid is projected. By
reason of the regularity of the figure, it is easy to see that
the six other faces will be similar to those already drawn,
only that although the superior pentagon will have its
angles on the same circumference as the inferior pentagon,
the angles of the one will be in the middle of the faces ol
the other. Therefore, to describe the superior half;—-
through the angles np s vk, draw the radial lines n 1, p 2 ,
s 3, v 4, k 5, and join them by the straight lines 1 2, 2 3, 3 4,
4 5, &c.

To obtain the length of the axis of the solid, observe
that the point k is elevated above the horizontal plane
by the height 1c K': carry that height to lc Ii": the point r,
analogous to h , is raised by the same height as that point,
that is to say h T, which is to be carried from r to R; and

the 1 ine R k" is the length sought. As this axis should
pass through the centre of the body, if a vertical line O o'
is drawn, it will cut the vertical projection of the axis in
O', and therefore o o' is the half of the height of the solid
vertically. By doubling this height, and drawing a hori¬
zontal line to cut the vertical lines of the angles of the
superior pentagon, the vertical projection of the superior
face is obtained, as in the upper portion of Fig. 283, in
which the same letters refer to the same parts.

One of the faces of a dodecahedron, abode (Fig. 284),
being given, to construct the projections of the solid, so
that its axis may be perpendicular to the horizontal plane.

The solid angles of the dodecahedron are each formed
by the meeting of three pentagonal planes. If there be
conceived a plane passing through the extremities of the
arris of the solid angle, the result of the section would be
a triangular pyramid, the sides of whose base would be
equal to one of the diagonals of the face, such as B C (Fig.
284). An equilateral triangle b cf (Fig. 285), will repre¬
sent the base of that pyramid inverted, that is, with its
summit resting on the horizontal plane. In constructing
the projection, it is required to find the height of that
pyramid, or, which is the same thing, that of the three
points of its base b c f, for as they are all equally ele¬
vated, the height of one of them gives the others. There
is necessarily a proportion between the triangle A b c
(Fig. 285) and ABC (Fig. 284), since the first is the
horizontal projection of the second. A g is the pro-

rig. 28 G.

jection of AG; but A G is a part of A H, and the projec¬
tion of that line is required for one of the faces ot the
solid; therefore, as A G: A g :: A H: x, which may be found,
by seeking a fourth proportional, to be equal to A h; or
graphically thus:—Raise on A g at g an indefinite perpendi¬
cular, take the length A G (Fig. 284) and carry it from a
to g' (Fig. 285), g being one of the points of the base,
elevated above the horizontal plane by the height g G';
its height giving also the heights ol b c f. Since A G is a
portion of A 11 , A g' will be so also. Produce A g', therefore,
and carry on it A H (Fig. 284) from A to H , and from H let
fall a perpendicular on A g produced, which gives h the
point sought. Produce H h, and carry on it the length H D
or H E from It to d and h to e ; draw the lines c d, be,

equal pentagons. It is necessary, in

PRACTICAL CARPENTRY AND JOINERY.

and the projection of one of the faces is obtained inclined
to the horizontal plane, in the angle H' A h. As the two
other inferior faces are similar to the one found, the three
faces should be found on the circumference of a circle traced
from A as a centre, and with A d or A e as a radius. Pro¬
long a n, A o, perpendiculars to the sides of the triangle,
and make them equal to A h, and through their extremi¬
ties draw perpendiculars, cutting the circumference in the
points i k, l to. Through these points draw the lines i b,
kf, If, m c, and the projections of the three inferior faces
are obtained. The superior pyramid is similar and equal
to the inferior, and solely opposed by its angles. Describe
a circle passing through the three points of the first triangle,
and draw within it a second equilateral triangle nop, of
which the summits correspond to the middle of the faces of
the former one. Each of these points will be the summit of
a pentagon, as the points b cf. These pentagons have
all their sides common, and it is only necessary therefore
to determine one of these superior pentagons to have all
the others.

To obtain the vertical projection (Fig. 286), begin with
the three inferior faces. The point A in the horizontal pro¬
jection being the summit of the inferior solid angle, will
have its vertical projection in a: the points bcf when raised
to the height g G', will be in b' c f, or simply 6'/'. The
points bg c being in a plane perpendicular to the vertical
plane, will be necessarily confounded with each other.
The line a /' will be the projection of the arris a/, and
a b' will be that of the arrises a b, Ac, and line A g,
or rather that of the triangle A b c, which is in a plane
perpendicular to the vertical plane. But this triangle is
only a portion of the pentagonal face of the solid ori¬
ginally given, and of which AH is the perpendicular let
fall from A on the side E D (Fig. 281). This side is com¬
mon to the inferior pentagon, and to the superior penta¬
gon edqpr, which is also perpendicular to the vertical
plane; and, consequently, its vertical projection will be e p ,
equal to a s'. This projection can be now obtained by
raising a vertical line through p, the summit of the superior
pentagon, and from e as a centre, and with the radius
A H' or A H, describing an arc cutting this line in p, the
point sought. But pno belong to the base of the superior
pyramid; therefore, if the height p' is transferred to n',
by drawing through p’ a line parallel to y x, n' will be
the projection of the points n and o. Through n draw
s' 7u a' parallel to a e', cutting perpendiculars drawn
through s and A in the horizontal projection. Through
s draw s /' parallel to p e, and join a /', a p; set off on
the perpendicular from r the height of s' above y z at r,
and draw r t' parallel to y z, cutting the perpendicular
from t, and join n t'. Make Ic and % the same height as
e', and draw k' i'„and join i' b\ i' t'\ and we obtain the pro¬
jection sought.

One of the faces of an icosahedron being given, to
construct the projections of the solid ivhen the given face
coincides with the horizontal plane of projection.

Let the triangle ABC (Fig. 287) be the given face. It
may be observed that B c is one of the sides of the base
of a pentagonal pyramid. Conceive this base turned on
B c and laid in the horizontal plane, it will then be the
pentagon B C clef To the centre g, draw the lines B g,
eg, d g, eg, f g, and the horizontal projection of the
pyramid is obtained. Conceive now the pyramid raised by

an arc is described cutting the perpendicular in the point
h', the line h h' will be the height of the summit of the
pentagon, the base of the pyramid; and the line l h' will
be the vertical projection or profile of l e. When l e, in
being raised, described the arc e lo, l g has described the
arc g g', and the last point g will, therefore, be the verti¬
cal projection of the centre of the pentagonal base, or the
extremity of the perpendicular let fall from the summit
of the pyramid on that base. Now, this perpendicular is
a portion of the axis of the icosahedron ; therefore, if
through g an indefinite line perpendicular to l li be
drawn, that line will be the direction of the axis of the
solid, and its length has now to be determined to define
the summits of the two opposite pyramids. As the pen¬
tagonal pyramid is placed with its summit in the hori¬
zontal plane, its base must be necessarily raised above
that plane by the height of the perpendicular let fall
from its summit upon that base in g, as g G, and this
length, g G, is now to be set off in the direction of the axis
from g‘ to G' ; then drawing G' l, G li, a portion of the pro¬
jection is obtained. From m as a centre, and with to g as
a radius, describe a circle, in the circumference of which
will be found the projections of the summits of five other
pentagonal pyramids, equal and similar to the first. To
find theseThrough / and d draw lines parallel to l e,
cutting the circumference in n o r q, or rather through
the summits of the opposite triangles; and to the centre
to draw portions of radii B n, k o, A p, i q, C r ; and through
each of the points draw perpendiculars cutting the axis
in p, and the lines A k’,
l If in o' n ; and through
these points draw the
lines shown in the figure,
and the projection is
complete.

Fig. 288 shows this
projection freed from
the lines of construc¬
tion.

Having found the heights of the different points,

Fig. 288.

STEREOGRAPHY—CYLINDER, CONE, AND SPHERE.

projection in Fig. 289, which is on a line parallel to a b,
can be easily made.

A side or an arris
of an icosahedron be¬
ing given, to construct
the projections of the
solid, so that one of its
axes may be perpendi¬
cular to the horizon¬
tal plane.

As in the preceding
example of the penta¬
gonal pyramid ab c d e
(Fig. 290), placed on its summit F on the horizontal plane,

let the side be considered as the given side of the solid.
Observe that the superior part of the solid is also a pyra¬
mid g h ilc l, equal and similar to the first, but having
its angles in the centres of the sides thereof. Thus,
there will be for the horizontal projections of these pyra¬
mids two pentagons, the arrises of which will be repre¬
sented by lines drawn from each angle to the centre.
Observe further, that the two pyramids are separated by
ten triangles, which have a certain inclination to each
other, and alternately in an inverse order; and that the
height of these triangles added to the height of the two
pyramids is the length of the axis. As all the triangles
have their sides common, the side a b may be considered
as the side or base of the triangle a H b, laid on the hori¬
zontal plane. Conceive this triangle raised by turning it
round a b until its summit meet h, one of the angles of
the base of the superior pyramid. To find its inclination,
from H let fall on the base the perpendicular n m, and draw
through h the line h H', perpendicular to H /i; then from
m as a centre, with the radius m H, describe an arc cutting
h h' in h', and join m h': the line m H' will then be the
profile or inclination of the face of the triangle a b H, ac¬
cording to the angle H m h' ; and the projection of the
summit is li. By drawing the lines h a, h b, the projection
of the triangle a H b, inclined to the horizontal plane in
a h b, is obtained, and the line h h' will be the length of the
portion of the axis comprised between the bases of the
two pyramids. To find the height of the base of the lower
pyramid above the horizontal plane:—As all its angles or
points are equally elevated, any of them maybe taken indif¬
ferently, as a. Whatever be the height of this point, such
height will always be the side of a right-angled triangle, of
which F a is the other side; and the arris, of which F a is
the projection, is the hypothenuse. Consequently, if from
a is raised an indefinite line a A, perpendicular to F a,
and upon it is set off the length of any of the arrises, such

Fig. 291.

as a b, from F to A, the height a A will be the height

sought. Thus, having obtained the data for construc¬
ting the vertical projec¬
tion, it may be proceed¬
ed with as follows:—

Through / (Fig. 291)
draw the line / c' g' n
corresponding to the
axis, and on it set up
the heights fc equal to
a A, c' g equal to li h',
and g n equal to a A.

Through d and g' draw
lines parallel to the
horizontal plane, and
on these find the points
d', e, a, b' , and l, Id, V, Id, by drawing perpendiculars from
the points in the horizontal projection, and join these by
lines, as in the figure.

To inscribe these five solids in the same sphere, pro¬
ceed as follows:—Let A B (Fig. 292) be the diameter of
the given sphere: divide H
it in three equal parts, and
make D B equal to one of
them: draw D E perpen¬
dicular to A B, and draw
the chords A E, E B. A E is
the arris of a tetrahedron,
and E B the arris of a hexa¬
hedron or cube. From the
centre c draw the perpen¬
dicular radius C F, and the
chord F B is the arris of the
octahedron. Divide B E in extreme and mean proportion
in G, and B G is the arris of the dodecahedron. Lastly,
make the tangent A n equal to A B, draw c H, and the
chord A I is the arris of the icosahedron.

Fig. 292.

THE THREE CURVED BODIES—THE CYLIN¬
DER, THE CONE, THE SPHERE.

1. —The horizontal projection of a cylinder, the axis of
ivhich is perpendicular to the horizontal plane, being
given, to find the vertical pro¬
jection.

Let the circle A B C D (Fig.

293), be the base of the cylin¬
der, and also its horizontal pro¬
jection : from the points A and C
raise perpendiculars to the hori¬
zontal plane a c, and produce
them to the height of the cylinder
—say, for example, a e, cf: draw
ef and the rectangle a efc is the
projection required.

2. — The horizontal projection
of a cylinder, whose axis is par¬
allel to the horizontal plane, being given, to construct
its vertical projection.

Let the rectangle a c (Fig. 294) be the given projection.
From each of the points a, b, c, d, draw perpendiculars to

PRACTICAL CARPENTRY AND JOINERY.

Fig. 294.

x y : on x y set off the height, which of course equals
the diameter; and through the points obtained draw a
line parallel to x y.

Conceive a b, the pro¬
jection of one of the
bases of the cylinder,
to be turned down on
the horizontal plane
on the point E, and to
be a circle E A F B;
then the original of
the point, of which a
is the projection, will
be A, which will be
elevated above the
horizontal plane
the height a A.

To obtain the
vertical projec¬
tion of a or A,
therefore, it is H
only necessary
to cany from
x to a', on the
perpendicular passing through a, the height a A. In the
same way is found the vertical projection of any point
in the base, as g: from g draw perpendicular to a b a
line cutting the circle in G and H. Draw also from g to
the vertical projection the line g g ti, and set on it the
height g G, g H, in g' and h', which are the vertical pro¬
jections of g. Thus any number of points may be found,
and a curve traced through them. It is evident that
as the base d c is similar and equal to a b, its projec¬
tions will also be similar and equal.

These circular bases being in planes which are not pa¬
rallel to the vertical plane, their projections are ellipses,
the two axes of which can always be readily found, and
the operation of projecting them may thus be shortened.

In surfaces of revolution, any point on the surface be¬
longs equally to the generating line, and to the gene¬
rating circle; consequently, if it be required to find the
projection of a point on the surface of a cylinder, it is
only necessary to draw a line through the point parallel
to the sides of the cylinder, cutting the line of projection
of one or both of its bases; to draw, from these intersec¬
tions, lines cutting the ellipses in the vertical projection;
and from these the projection of the line passing through
the point, and consequently the projection of the point
itself, is easily found. Let i be the point; through it
draw k i l, cutting the base or horizontal projection of the
generating circle in k and l- through k draw k If and
through l draw ll , and join k' V, and the intersection of
the lines lc l,ii , in the vertical projection, defines the
point. Lut it can also be found without referring to
the intersections, thus:—Through the point i, draw ilc,
i J, parallel to b c, and through it draw also i i' perpen¬
dicular to xy\ then on the last line set up the height k i,
which will give the plane of the point in i" i.

The horizontal projection of the base of a cylinder
being given , and also the angle which the base makes
with the horizontal plane, to construct the projections of
the cylinder.

Let the circle agbii (Fig. 295) be the given base, and

let the given angle be 45°. Draw the line ab', making
with A B the given angle; and from A as a centre, with
A B and A c as radii, describe arcs cutting A B' in b' and
c'. Then draw A D, b' e, perpendicular to ab’, and
equal to the length of the cylinder; and the rectangle A E
is the profile of the cy¬
linder inclined to the
horizontal plane in an
angle of 45°. Now pro¬
long indefinitely the
diameter B A, and this
line will represent the
projection on the verti- -
cal plane of the line in
which the generating
circle moves, to produce
the cylinder. If from B'
and C perpendiculars
be let fall on A B, k will
be the horizontal pro¬
jection of b' a k of the 1
diameter A B, and c of
the centre c. Through
c draw h g perpendicu¬
lar to A B, and make c h, c g, equal to C H, c G; and the
two diameters of the ellipse, which is the projection of
the base of the cylinder, will be obtained.

In like manner, draw from DFE the lines D d, F f E e,
perpendicular to the diameter A B produced, and their
intersections with the diameter and the sides of the
cylinder will give the means of drawing the ellipse which
forms the projection of the further end of the cylinder.
The ellipses may also be found by taking any number of
points in the generating circle as I J O m, and obtaining
their projections i, j, r, q. The method of doing this will
be seen by the figure without further explanation.

*0f the Sections of the Cylinder by a Plane.

A cylinder may be cut by a plane in three different
ways—1st, the plane may be parallel to the axis—2d, it
may be parallel to the base—3d, it may be oblique to the
axis or the base.

In the first case, the section is a parallelogram, whose
length will be equal to the length of the cylinder, and
whose width will be equal to the chord of the circle of
the base in the line of section. Whence it follows, that
the largest section of this kind will be that made by a
plane passing through the axis; and the smallest will be
when the section plane is a tangent—the section in that
case will be a straight line.

When the section plane is parallel to the base, the sec¬
tion will be a circle equal to the base. When the section
plane is oblique to the axis or the base, the section will
be an ellipse. As the manner of constructing the ellipse
produced by the section of the cylinder has been already
treated of, and it will again come under consideration
when treating of the sections of solids, it is not necessary
here to dilate further on the subject.

PROJECTIONS OF THE CONE.

A point in one of the projections of a cone being
given, to find it in the other projection.

STEREOGRAPHY-CYLINDER, CONE, AND SPHERE.

Fig. 296.

Let a (Fig. 296) be the given point. This point belongs
equally to the circle which is the section of the cone by
a plane parallel to the base, and to a straight line form¬
ing one of the sides
of a triangle which is
the section of the cone
by a plane perpendicu¬
lar to its base and pass¬
ing through its vertex,
and of which fag is
the horizontal, and
/' a'g' the vertical pro¬
jection. To find the
vertical projection of a,
therefore,when the ho¬
rizontal projection is
given, through a draw
a a perpendicular to
be, and its intersec¬
tion with f g' is the
point required; and
reciprocally, a in the
horizontal projection
may be found from a'
in the vertical projection, in the same manner.

Otherwise, through a, in the horizontal projection, de¬
scribe the circle a d c, and draw e e' or c c', cutting the
sides of the cone in e and c ; draw c e' parallel to the base,
and draw a a', cutting it in a, the point required.

Of the Sections of a Gone by a Plane.

A cone may be cut by a plane in five different ways,
producing what are called
the conic sections:—1st,

If it is cut by a plane
passing through its axis,
the section is a triangle,
having the axis of the
cone as its height, the
diameter of the base for
its base, and the sides for
its sides. If the plane
passes through the vertex,
without passing through
the axis, as c e" (Fig. 297),

Fig. 297

the section will still be a triangle, having for its base the
chord c' o, for its height the line E e", and for its sides
the sides of the cone, of which the lines d e, o e, are the
horizontal, and the line c e" the vertical projections. 2d.

If the cone is cut parallel to the base, as in g' h', the sec¬
tion will be a circle, of which g' h' will be the diameter.
3d. When the section plane is oblique to the axis, and
passes through the opposite sides of the cone, as to' p hi,
the section will be an ellipse, to n h. 4th. When the
plane is parallel to one of the sides of the cone, as r hi,
the resulting section is a parabola r shtu, which may be
considered as an ellipse, infinitely elongated. 5th. When
the section plane is such as to pass through the sides of
another cone formed by producing the sides of the first,
the resulting curve in each cone is a hyperbola.

Several methods of drawing the curves of the conic
sections have already been given in the section on prac¬
tical geometry. Here their projections, as resulting from
the sections of the solid by planes, are to be considered.
If the mode of finding the projections of a point on the
surface of a given cone be understood, the projections of
the curves of the conic sections will offer no difficulty.
Let the problem be:—First, to find the projections of the
section made by the plane to' hi. Take at pleasure upon
the plane several points, as p', Ac. Let fall from these
points perpendiculars to the horizontal plane, and on these
will be found the horizontal projection of the points: thus,
in regard to the point p —Draw through p' a line parallel
to A B: this line will be the vertical projection of a hori¬
zontal plane cutting the cone, and its horizontal projec¬
tion will be a circle, with s' n' for its radius. With this
radius, therefore, and from the centre c, describe a circle
cutting, twice, the perpendicular let fall from p, which will
be the projections sought of certain points in the circum¬
ference of the ellipse. In the same manner, any other
points may be obtained in its circumference. The opera¬
tion may often be abridged by taking the point p in the
middle of the line mi hi \ for then mil will be the major,
and n c the minor axis of the ellipse.

To obtain the projections of the parabola, more points
are required, such as r', 2, s', 3, h!

The projections of the section plane which produces
the hyperbola, are straight lines, q hi, z h.

The development of these curves, that is, their projec¬
tions on planes parallel to
the section planes which
produce them, may be
here illustrated.

First, The ellipse. The
development of this curve
is found by making its
major axis equal to A G,
and its minor axis g d,
equal to k l, as has been
explained.

Second, The parabola (Fig. 297 a). Draw the line
u u' parallel to E F, and the line n hi" perpendicular to it
and bisecting it. From the horizontal projection take
the length g u, and carry it from n to u and u'. Take
also g x, and carry it from n to 2; and in the same way
transfer the lengths g c, g v, Ac., to n t, n 3, Ac., and
through each of these points draw perpendiculars to E F,
and set up on them from the line u u the heights of
the corresponding points 2 s' 3, from the line to' b of the
vertical projection: the points through which to trace
the curve will thus be obtained.

Third, the hyperbola. Draw the line c c (Fig. 299) per-

PRACTICAL CARPENTRY AND JOINERY.

pendicular to d d', and make d d' equal to the base, and c c
equal to the height of the cone. From c as a centre, with
the radius c d, describe a semicircle equal to half the base
of the cone, and draw r q, the section plane, at the distance
from the centre of E q , or c h, in Fig. 297. Divide the
line r q into any number of equal parts in 1, 2, 3, h, Ac.,
and through them draw lines perpendicular to d d. From
c as a centre, with the radii cl, c 2, Ac., describe arcs
cutting d d '; and from the points of intersection draw per¬
pendiculars cutting rig , 299 .

the sides of the
cone in 1, 2, 3; and
these heights trans¬
ferred to the cor¬
responding perpen¬
diculars drawn di¬
rectly from the
points 1, 2, 3, Ac.,
in r q, will give
points in the curve.

Understanding
clearly the principles
of construction here
developed, no diffi¬
culty will be ex¬
perienced in appre¬
hending the methods of construction employed in de¬
veloping these curves under the head of Sections of Solids.

Of the Section of the Sphere by a Plane.

A point in one of the projections of the sphere being
given, to find it in the other projection.

Let a be the given point in the horizontal projection
of the sphere h xiv.

Any point whatsoever on the surface of a sphere be¬
longs to a circle of that sphere: therefore, if a (Fig.
300) be the point, and a
through that point parallel
to A B, the section of the
sphere by this plane will be
a circle, whose diameter will
be b c, and the radius, con¬
sequently, d b or d c; and
the point a will necessarily
be in the circumference of
this circle. Since the cen¬
tre d of this circle is situ¬
ated on the horizontal axis
of the sphere, d will also be
the centre of the sphere:
and as this axis is perpen¬
dicular to the vertical plane,
its vertical projection will
be the point d'. It is evi¬
dent that the vertical pro-
jection of the given point a, will be found in the cir¬
cumference of the circle described from d' with the radius,
and at that point of it where it is intersected by the line
drawn through a, perpendicular to A B. Its vertical projec¬
tion will therefore be either at or a", according as the point
a is on the superior or inferior semi-surface of the sphere.

The projection of the point may also be found by an
inverse operation, thus:—Conceive the sphere cut by a

plane parallel to the horizontal plane of projection pass¬
ing through the given point a. The resulting section
will be the horizontal circle described from Jc, with the
radius k a; and the vertical projection of this section will
be the straight line g e, or g" e"; and the intersections of
these lines with the perpendicular drawn through a, will
be the projection of a, as before.

Tlte traces of a plane cutting a sphere being given, to
find the projections of the action.

Let a b (Fig. 301) be the horizontal trace of the section
plane. On the line of
section take any num¬
ber of points, as a, c, b,
and through each of
them draw a line per¬
pendicular to y x. As <L
the point a is situated
on the circumference of
the great circle of the
sphere, its vertical pro¬
jection will be on the
vertical projection of the
circle at a'. The point
b being the extremity of
the axis of the sphere,
will have its vertical
projection b' in the pro¬
jection of the great cir¬
cle ef. The projection
of c, or of any other point in the line a b, is found in
either of the ways detailed in the preceding problem.
Practically, in this case, it is found thus:—Through c
draw g c h parallel to y x, and also c c' perpendicular to
y x ; then with the radius i g, or i h, and from the cen¬
tre b' on the vertical projection, describe arcs of a circle,
cutting the perpendicular c c" c in c and c. Then c
beam in this case the middle of the line of section a b, the
vertical projection will be an ellipse, whose major axis will
be c c", and minor axis a b'.

TANGENT PLANES TO CURVED SURFACES.

Tangent Plane to a Cylinder.

Let the lines a b, c d (Fig. 302), be tangents to the
generating circles e f g h,
ikltn, of the cylinder g l.

As the circles are parallel, the
tangents will also be paral¬
lel and perpendicular to the
radii n i, o e. If through
these two tangents a plane,
a d, pass, it will be perpen¬
dicular to the rectangle i o ;
and on the generating line
e i will, consequently, be
found the tangent points of
all circles which can be con¬
ceived to be drawn between
the base and summit of the
cylinder. And as, in the formation of the cylinder by
I the generating circle, the radius n i has been supposed

plane b c is made to pass

FiS. 300.

STEREOGRAPHY—TANGENT PLANES TO CURVED SURFACES.

to pass through all the points of the line e i, the plane
a d will contain all the tangents of all the circles sup-
posable in the cylinder, such, for example, as the circle
p q r s, the tangent of which is t u : the plane a d
is therefore a tangent to the cylinder in the right line
e i. The axis of the cylinder, o n, is named the directrix;
because, in conceiving the cylinder formed by the motion
of the generating circle, the centre of the circle will move
in the direction o n. In considering the circle as formed
by the rotation of the rectangle o i round its side o n,
it is seen that the generatrix e i is necessarily parallel to
the directrix o n, and that i is the point of contact of
the generatrix i e and the generating circle i lc l m, and
through this the tangent passes.

Consequently, if through any
tangent point on the circum¬
ference of the generating circle
of a cylinder, a line is drawn
parallel to the directrix, it will
be the line in which a tangent
plane will touch the cylinder.

Tangent Plane to a Gone.

The cone differs from the
cylinder in that the genera¬
trix a b (Fig. 303) is not paral¬
lel to the directrix c b, and that it passes always through
the summit b.

Tangent Plane to a Sphere.

Let a b (Fig. 304) be a plane perpendicular to the ex¬
tremity of the radius c e. If through any point / in
the plane there be drawn
the right lines f c, f e,
there will be formed the
right-angled triangle cef.

As the side c e of the tri¬
angle cef is equal to the d
x-adius of the sphere, the
point / will be a point in
space without the sphere;
and it will obvioxisly be
the same in regard to any
point taken in a b, except alone the point e. Therefoi-e,
every plane perpendicular to a radius of a sphere, and
at its extremity, will be a tangent to the sphere.

It may also be thus demonstrated:—If the line ef
(Fig. 304) is perpendicular to the radius of the circle
die lc, it will be a tangent to that circle; and if the line
e n is perpendicular also to the radius of the circle
dm el, it will be a tangent to that circle (the radius c e
being common to both circles). Now, two straight lines
which intellect each other are in the same plane, since the
three points nef are not in the same straight line; con¬
sequently, if a plane pass through these lines it will be per¬
pendicular to e c, and tangential to the two circles, which
are both generating circles of the same sphei’e. Hence, if
through the point of contact of two genei’ating circles of a
sphere two tangents be drawn, these tangents Avill deter¬
mine the tangent plane of the sphere at that point.

Having thus illustrated, genei'ally, the subject of tan¬
gent planes to curved surfaces, it will now be proper to
show the practical application of the principles.

Through a given point in the circumference of the
base oj a right cylinder, to draw a tangent plane.

Let c (Fig. 305) be the given point on the horizontal pro¬
jection: draw the ra- n 305

dius o e, and through
its extremity e
draw perpendicular
to it the line a b,
which is a tangent
to the circle, and is
the trace of the tan¬
gent plane sought.

Through c draw the
line e i, perpendicu¬
lar to y z, and it
gives on the vertical projection the tangent line e' i of the
plane, which is parallel to the directrix o n, as has been
seen.

Through a given point on the surface of a right cylin¬
der to draw a tangent plane.

Let a (Fig. 306) be the lioi'izontal projection of the
point: through a
draw b c parallel
to the axis d e,
and b c will be the
horizontal projec¬
tion of the tan- A,
gent line of the
plane. Find,then,
the vertical pro¬
jection of a by
the rules already H
given. Let this
be a': through a
draw V c parallel
to the axis d' e,
and this will be
the vertical projec¬
tion of the tan¬
gent line. Now,
to find the tan¬
gent plane, draw, in the horizontal projection, the cir¬
cle of the base of the cylinder / g, produce c b to B,
the tangent point of the plane with the base, draw
the radius D B, and the tangent to it I H, cutting g f
produced in H. Then I H will be the profile of the plane,
and i H its horizontal projection; and I H i will be the
angle which the plane makes with the horizontal plane.
From i draw I lc parallel to li j, and the horizontal pro¬
jection of the tangent plane is obtained in H j lc i, and
from this the vertical projection will be easily con¬
structed.

To find the tangent plane when the cylinder is oblique.

Let a (Fig. 307) be the given point on the surface of
an oblique cylinder with a circular base : on its hori¬
zontal projection draw an indefinite line parallel to the
axis b c, cutting the two bases of the cylinder, each in
two points d e, f g, which will be the extremities of
two tangent lines d /, e g, one on the upper, and the
other on the lower part of the surface of the cylinder. I o
proceed first with the line of the upper sui’face, df:
The vertical projection of d will be d , and that of / will
be/'. Since these two points are the extremities of the

02 '

PRACTICAL CARPENTRY AND JOINERY.

tangent line, draw the line d'f,' which will be the tan¬
gent. Through a draw an indefinite line perpendicular

to h j, cutting d' f in a', the vertical projection of a. To
obtain the traces of the tangent plane, through d draw
indefinitely the tangent H db, which will be the hori¬
zontal projection sought; and b' j' in the plane of the axis
b c, will be the vertical projection of the same plane. If
it is desired to limit this plane, take, on the horizontal
projection b d produced, any point desired, such as H,
whose vertical projection will be h. Through this point
draw h % parallel to the vertical K g . 308.

projection of the cylinder, and
this line will be one of the limits
sought. In the same way will be
obtained the boundaries b j, b' j’,
ij, i' j', &c. To obtain now the
tangent plane to the under part
of the surface:—Through e draw
d g, and the tangent b e k, and
operate as directed for the first
plane. In Fig. 308 the same pro¬
blem, but with the cone in place
of the cylinder, is shown; and as nearly the same letters
are used, no other description is required.

Through a given point on the surface of a sphere, to
draw a tangent plane to that surface.

Let a (Fig. 309) be the given point in the horizontal

projection. As in the case of the cylinder, it is to be
considered whether the point is on the upper or lower

pai t of the surface. Let it be on the lower surface:_

Conceive the point turned round horizontally until it
has ailived at a , on the diameter b c , which may be

considered as the horizontal projection of a great circle
of the sphere, parallel to the vertical plane; consequently,
the vertical projection of a will be a. If through this
point the tangent d s' be drawn, this line will be the
vertical projection of a tangent plane to the sphere, per¬
pendicular to the vertical plane; consequently, the line
d f', perpendicular to y z , will be the horizontal projec¬
tion of the same plane, which will be inclined to the
horizontal plane in the angle e d z: through a" draw
a horizontal line a’ g , cutting the vertical line drawn
upon a in the point a!, which will be the vertical projec¬
tion of a, or the tangent point. Conceive now the point
a turned back to its first position, and that the plane e 'd F,
which contains a! , had turned with it, it is clear that
when a' is in a, the point K will be in h, and will not
have left the horizontal plane; consequently, the trace d f,
which was perpendicular to the radius i h! , will be in
D f, and will continue perpendicular to i h. There re¬
mains only to find the vertical trace of the plane. Draw
the line a a'" parallel to d f: it will be perpendicular to the
radius i a, as a' a" was to i a! before beino- turned. This
line a a" being horizontal at the height of the point of
the tangent, and situated in the tangent plane, its ex¬
tremity will necessarily be in the vertical projection
sought. Raise on a", therefore, the vertical line, cutting
ag in Jc, the point sought. Now, D being also one of
the points of the projection, the line D k produced will
be the vertical projection sought. If the plane be limited,
its vertical and horizontal projections will be the rhom¬
buses D l, D V.

The same end can be arrived at in a way more direct,
simple, and expeditious, but which could not be so easily
understood without a knowledge of the previous mode.

Let a (Fig. 310)
be the point given.

Through it, and
the centre i, draw the
diameter a i, which
consider to be the pro¬
jection of a section
plane. It this is now
laid down in the hori¬
zontal plane, there will
be obtained a great
circle of the sphere, as
the vertical projection
of the section through
the diameter. Through a draw a line perpendicular to
a i, cutting the circle in A: through this point draw the
tangent x A li, which
will be the profile of
the tangent plane,
meeting the horizontal
plane in h. Through h
draw d/if perpendicu¬
lar to a i, and D h F will
be the horizontal pro¬
jection of the tangent
plane. Through a draw
a vertical line, and upon
it set off the height a A
from d to a'. The remain¬
der of the operation is the same as in the former example.

STEREOGRAPHY-INTERSECTIONS OF CURVED SURFACES.

The next figure (Fig. 311) shows the process when the
plane is a tangent to the upper surface.

INTERSECTIONS OF CURVED SURFACES.

When two solids having curved surfaces penetrate or
intersect each other, the intersections of their surfaces
form curved lines of various kinds. Some of these, as the
circle, the ellipse, &c., can be contained in a plane; but
the others cannot, and are named curves of double curva¬
ture. The solution of the following problems depends
chiefly on the knowledge of how to obtain, in the most
advantageous manner, the projections of a point on a
curved surface; and is in fact the application of the
principles elucidated in the pi-eceding problems. The
manner of constructing the intersections of these curved
surfaces which is the most simple and most general in
its application, consists in conceiving the solids to which
they belong as cut by planes, according to certain con¬
ditions, more or less dependent on the nature of the sur¬
faces. These section planes may be drawn parallel to one
of the planes of projection; and as all the points of inter¬
section of the surfaces are found in the section planes, or
on one of their projections, it is always easy to construct
the curves by transferring these points to the other pro¬
jection of the planes.

The projection of two cylinders which intersect at right
angles being given, to find the projections of their in¬
tersections.

Conceive, in the horizontal projection (Fig. 312), a series

of vertical planes cutting
the cylinders parallel to
their axes. The vertical
projections of all the sec¬
tions will be so many right-
angled parallelograms, si¬
milar to e or e" /",
which is the result of the
section of the cylinder by the vertical plane e f, for this
plane cuts the cylinder from surface to surface. The cir-
cumference of the second cylinder, whose axis is vertical,
is also cut by the same plane, which meets its upper sur¬
face at the two points g, h, and its under surface at two
corresponding points. The vertical projections of these
points are on the lines perpendicular to a b, raised on
each of them, so that upon the lines d /', e will be

situated the intersections of these lines at the points g’ h',
g h , and the same with the other points i, k, l , m. It is
not necessary to draw a plan to find these projections.
All that is actually required, is to draw the circle repre¬
senting one of the bases, as n o, of the cylinder laid flat
on the horizontal plane. Then to produce g h till it cuts
the circle at the superior and inferior points G G, and to
take the heights e g' , e G, and carry them, upon a b, from
g to g ,g", and from h to U, 1C.

Fig. 313 is the projection made on the line x z.

To construct the projections of two cylinders whose
axes intersect each other obliquely.

Let A (Fig. 314) be the vertical projection of the two

Fig. 8H.

cylinders, and h s d e the horizontal projection of their
axes.

Conceive, in the vertical projections, the cylinders cut
by any number of horizontal planes: the horizontal pro¬
jections of these planes will be rectangles, as in the pre¬
ceding example, and their sides will be parallel to the
axes of the cylinders. The points of intersection of these
lines will be the points sought. Without any previous
operation, six of those points of intersection can be ob¬
tained. For example, the point c is situated on d" e ,
the highest point of the cylinder; consequently, the hori¬
zontal projection of d is on d e, the hoidzontal projection
of d ! ‘ e", and it is also on the perpendicular let fall from
c', that is to say, on the line c /parallel to the axis of
the cylinder s h. The point sought will, therefore, be the
intersection of those lines at c. In the same way i is
obtained. The point j is on the line k l, which is in the
horizontal plane passing through the axis d! e’: the hori¬
zontal projections of k' V are k l, and its opposite to n\
therefore, in letting fall perpendiculars from j' p, the in¬
tersections of these with k l, to n, give the points j j, p p.
Thus six points are obtained. Take at pleasure an inter¬
mediate point q , through this point draw a line rs paral¬
lel to a b, which will be the vertical projection of a hori¬
zontal plane cutting the cylinder in q. The horizontal
projection of this section will be, as in the preceding ex¬
amples, a rectangle which is obtained by taking, in the
vertical projection, the height of the section plane above
the axis d'd, and carrying it on the base in the horizontal
projection from G to T. Through T is then to be drawn

PRACTICAL CARPENTRY AND JOINERY.

Fig. 315.

the line Q U perpendicular to gt; and through Q and
U lines parallel to the axis; and the points in which
these lines are intersected by the perpendiculars let fall
from q u! are the intermediate points required. Any
number of intermediate points may be thus obtained;
and the curve being drawn through them, the operation
is completed.

To find the intersections of a sphere and a cylinder.

Draw, in the horizontal projection, and parallel to A B
(Fig. 315), as many vertical section
planes as are considered necessary,
as ef c cl. These planes cut at the
same time both the sphere and the
cylinder, and the result of each sec¬
tion will be a circle in the case of the
sphere, and a rectangle in the case
of the cylinder. Through each of the
points of intersection g, h, i, Jc, draw
indefinite lines perpendicular to A B.

Take the radius of the circles of the
sphere proper to each of these sec¬
tions, and with them cut the cor¬
respondent perpendiculars in g g\
h h\ i i', &c., and draw through
these points the curves of intersec¬
tion. This operation should be so

obvious from the preceding problems, that it is not neces¬
sary to enter more particularly into the description.

To construct the intersection of two right cones with,
circular bases.

The solution of this problem is founded on the know¬
ledge of the means of obtaining on one of the projections
of a cone a point given on the other.

Let ab (Fig. 316) be the common section of the two
planes of projection, the circles gclefghik, the hori¬
zontal projections of the given cones, and the triangles
d'if, k l Jc, their
vertical projec¬
tions. Suppose
these cones cut by
a series of hori¬
zontal planes:
each section will
consist of two
circles, which cut¬
ting each other,
and the points of
their intersection,
will be points of
intersection of the
conical surfaces.

For example, the
section made by
a plane m'ri will
have for its hori¬
zontal projections r.'

two circles of different diameters, the radius of the one
being i m, and of the other l o. The intersecting points
of these are p and q, and these points are common to the
two circumferences; and their vertical projection on the
plane m’ n\ will be in p’ q. Thus, as many points may
be found as is necessary to complete the curve. But there
aie certain points of intersection which cannot be ricfor-

ously established by this method without a great deal of
manipulation, and it is therefore advisable to point out
another method of procedure for such cases.

The point r in the figure is one of those; for it will be
seen that at that point the two circles must be tangents
to each other, and it Avould be difficult to fix the place of
the section plane s' t' so exactly by trial, that it would
just pass through that point.

It will be seen that the point r must be situated in the
horizontal projection of the line g i, which passes through
the summits of both cones. This line g i is the projec¬
tion of a vertical plane, which contains— 1 st, the side
of the large cone, passing through the summit G, and
terminating at the base in i; and, 2 d, the side of the
smaller cone passing through the summit L, and also ter¬
minating at the base in i. These two lines must inter¬
sect each other at the surface of the cones, and the point
r will be the point of intersection. Hence, to find r:—
Through i in the horizontal projection raise on g i a
perpendicular equal to the height of the cone g g", and
draw G g, which will be the side of that cone. Through
l raise a perpendicular, and make it equal to the height of
the second cone, and draw its side L i\ and from the point
of intersection let fall a perpendicular on g i, meeting it
in r; and through r draw an indefinite line perpendicular
to a b, and set up on it from the horizontal projection
the height of the point of intersection r.

There is still another method by which the operation
is abridged. Find the two points i and r, and consider
i r as a diameter: from u as a centre, with the radius
u r, describe a circle, the circumference of which will be
the horizontal projection of the intersection of the two
cones. It now remains to find the vertical projection
of this circle, which can be done by the methods pointed
out in preceding problems.

To construct the intersections of a sphere penetrated
by an oblique scalene cone (Fig. 317).

This problem i- ig . 317 .

is not very
different from
the preceding
one; but yet
the method of
solution given
for that could
not be advan¬
tageously ap¬
plied to this,
and would be
quite inapplica¬
ble if the base
of the cone
were irregular, a circumstance which proves the necessity
of knowing several methods of solution for each case.

Conceive the cone in this case cut by a number of ver¬
tical planes, all passing through its summit and its base:
the sections made by them will all be triangles, easy to
determine; and the sections of the sphere by the same
planes will be so many circles, quite as easily constructed.
Whence it results, that the operation is resolved into find¬
ing the intersections of a straight line and a circle. Not
to overcrowd the figure, the operation is shown only in
part.

STEREOGRAPHY—INTERSECTIONS OF CURVED SURFACES.

Let cd, c'd' (Fig. SIS), be the projections of the line
given: this line will be analogous to the side cd of the
cone in Fig. 317. Conceive cd to be the horizontal projec¬
tion of a vertical plane cutting the sphere. The section
resulting from this plane will be a circle contained in the
plane, and of which the radius will be fh, or fg. If this
section be turned down on the horizontal plane, there
will result the right-angled triangle d c c, whose hypo-
thenuse d c will cut the circle of the spherical section in
i and in J. From these two points let perpendiculars fall
on dc, meeting it in ij, which will be the horizontal pro¬
jections of the points of the entry and exit of the cone
into the sphere, and the vertical projections of the same
will be i’ f. In repeating this operation for every one of
the lines in Fig. 318, points will be obtained through
which to draw the curves of intersection; but this may
be abridged, as now to be shown.

Suppose the plane containing the triangle and the circle
which was turned down on the horizontal plane, to be
raised up by turning on the point c, in describing the
arc d cl'-, then
this plane will
apply to the
vertical plane
without any
alteration; con¬
sequently, the
points i' and J'
will be eleva¬
ted above A B
to the same ex¬
tent as are the
projections ij,
and so will
likewise be the
centres f' e of the two circles. From c, as a centre,
with the radius c d, describe the arc d cV) and from the
same centre, with the radius c f, describe the arc f f.
From the last point raise a perpendicular, on which set
off the height of the radius of the sphere from f to f'; and
from F / , as a centre, with the radius FGorF H, describe a
circle, or rather an arc, cutting cl' c in I' j': from each of
these points draw lines parallel to A B, which will cut d c'
in i and j, the points of intersection sought.

To construct the intersections of two right cones with
circular bases.

To commence by a very simple example (Fig. 319).
Conceive, in the horizontal projection, a vertical plane
cutting both cones through their axes: the sections will

O O

be two triangles, having the diameters of the bases of
the cones as their bases, and the height of the cones
as their height. And as in the example the cones are
equal, the triangles will also be equal, as the triangles
c e'/, g f cl, in the vertical projection. Conceive now
this same vertical plane passing through the different
points of the base, but still passing through the summits
of the cones: the sections which result will still be tri¬
angles (as has already been demonstrated), whose bases
diminish in proportion as the plane recedes from the
centres of the bases, until at length the plane becomes a
tangent to both cones, and the result is a tangent line
whose projections are h, g, li, f, g e, f f'. It will be
observed that the circumferences of the bases cut each

other at to and i, which are the first points of their inter¬
sections, and whose vertical projections are the point to
merely. If the projections of the other points of inter¬
section on the lines of the section planes are found (an

operation presenting no difficulty, and easily understood
by the inspection of the figure), it will be seen that the
horizontal triangles ncm, to c o, 1c c p, qcr, Ac., have for
their vertical projections the triangles n e to, mf o, k e p,
Ac., and that the intersections of the cone are in a plane
perpendicular to both planes of projection, and its projec¬
tions are the right lines i m, to 3. From the known
properties of the conic sections, the curve produced by
this plane will be a hyperbola. Fig. 320 is the projection
of the cones on the line o x.

The next example (Fig. 321) differs from the first in
the inequality
of the size
of the cones.

Suppose an in¬
definite line
c D, to be the
horizontal pro¬
jection of the
vertical section
plane, cutting
the two cones
through their
axes ef. Con¬
ceive in this

plane an indefinite line ef D, passing through the sum¬
mits of the cones, the vertical projection of this line
will be e f cl': from cl, let fall on C D a perpendiculai
meeting it in D: this will be the point in which the
line passing through the summits of the cones will meet
the horizontal plane; and it is through this point, and
through the summits e and f that the section planes
should be made to pass, as in the preceding example.
The horizontal projections of these planes are O D, gd,
CD, Ac.: o D is then the projection of a tangent plane to
the two conical surfaces oe, P/; and the plane passing
through the projection G D, and the line e D, cuts the
greater cone, and forms by the section the triangles G e H
in the horizontal, and g e h in the vertical projection;
and it cuts the lesser cone, and forms the triangles i/j,
i f j. »In the horizontal projection it is seen that the
sides He, if of the triangle intersect in k, which is
therefore the horizontal projection of one of the points

PRACTICAL CARPENTRY AND JOINERY.

of intersection; and its vertical projection is Jc. In the
same manner, the other points required may be found.
It is seen at once that M N, 1l', are points in the inter¬
section, and the curve formed by it is traced through the
points M Jc l N in the horizontal, and m Jc l in the vertical

projection.

The next example (Fig. 322) is in some respects ana¬
logous to the first, the two cones being of the same
height; but the section plane through their axes is not
parallel to the plane
of projection, and the
right cone is pene¬
trated by a scalene
cone. There is, how¬
ever, no difference
in the operation,
which will be un¬
derstood by inspec¬
tion.

Constru ction of the
intersections formed
by the penetration of
a cylinder by a sca¬
lene cone.

Conceive a line ccc
(Fig. 323) parallel to
the generatrix of the cylinder, passing through the sum¬
mit of the cone; then all the vertical planes which, passing
through this line and the base of the cone, cut the latter and

the cylinder, follow lines which must be in these planes; for
the cone will be cut in triangles, and the cylinder in rect¬
angles ; and the intersections of these lines from the cone
and cylinder will give points in the line sought. Thus,
as in this case, the generatrix of the cylinder is vertical,
the line c c c drawn parallel to it through the summit of
the cone will also be vertical, and its vertical projection
will be c c , and its horizontal projection c. Through this
point c, therefore, and through the base of the cone, must
be made to pass the vertical planes required. For in¬
stance, the \ ei tical plane D (j cuts the cone through its
axis, and the section is the triangle d c' e; and it cuts the
cy lmdei, and the section is the rectangle cf . These two
figures intersect each other in e e, g g\ and these inter¬
sections give e g, two of the points sought. The plane
H C gives also a triangle and rectangle, intersecting in hh.

The plane M c, which is a tangent to the cone, gives the
line m c on the surface of the cone in the vertical projec¬
tion, and the rectangle np in the cylinder, and the points
of intersection are n and o. The problem thus presents
no difficulty.

Example 2, Fig. 324.—Conceive both the cone and
cylinder cut by a vertical plane, of which C d is the hori¬
zontal trace. Let this section be turned down on the
horizontal plane on c d as a hinge, and the triangle cde
is obtained as the section of the cone, and the circle /g h
as the section of the c}dinder. In this section the line

C D is tangent to the circle in G; and a plane parallel to
the axis or generatrix of the cylinder, passing through
the summit D or d of the cone, and through the point c,
would be a tangent to the surfaces of both the cone and
the cylinder. The point G, therefore, which is common t«
both those surfaces, and whose projections are g h, is one of
the points of intersection. The line E D, which is the lower
side of the cone, enters the circle of the cylinder at I, and
leaves it at H. These two points are also, therefore, points
in the intersection, and their projections are i h, % h'.
It is now necessary to find some other point, and to ob¬
tain it, proceed as follows: — Through J, taken at pleasure
on the line c d, draw parallel to the generatrix of the
cylinder the line K L, which will be the projection of a
plane passing through the summit and base of the cone:
the triangle K d L will be the horizontal projection of the
section formed by that plane. Since the plane of this
triangle is parallel to the axis of the cylinder, the sides
K cl, L d will enter the cylinder at the same moment—
each by its own point of intersection; and these points of
intersection—the points at which they enter and leave
the cylinder—will be on generatrices of the cylinder o p,
q r : it is necessary, therefore, to find those generatrices.
Through J, a point taken in the middle of the base of the
triangle, draw J D, which will enter the circle at M, and
leave it at N: through these points draw the generatrices
o p, q r, cutting the sides of the triangle in m m, n n,
which are the points sought.

STEREOGRAPHY—MANNER OF TAKING DIMENSIONS.

OF HELICES.

Let abed, &c. (Fig. 325), be any curve whatever,
traced on a horizontal plane. (In this example it is a
circle.) Take on this curve a series of points abed,
&c., and through each of them draw a vertical line. Then
conceive a curve cutting all these verticals in the points
a' b' c d', in such a manner that the height of the point
above the horizontal plane may be in constant relation to
the arcs ab, be, cd\ for ex- rig. 325 .

ample, that a may be the
zero of height, that b b' may
be 1, cc 2, dd' 3, &c.; then
this curve is named a he¬
lix. To construct this curve,
carry on the vertical projec¬
tion on each vertical line such
a height as has been deter¬
mined, as 1 on b, 2 on c, 3 on
d; and through these points a
will pass the curve sought. It
is easy to see that the curve
so traced is independent of
the cylinder on which it has
been supposed to be traced; a
and that if it be isolated, its
horizontal projection will be ’’
a circle. The helix is named
after the curve which is its
horizontal projection : thus
the helix in the example, is a helix with a circular
base. The vertical line fn is the axis of the helix, and
the height b b', comprised between two consecutive in¬
tersections of the curve with a vertical, is the pitch of the
helix.

The points ab c d, &c., being in the circumference of a
circle, are, of course, situate at the same distance from its
centre. Conceive now that each of these points ap¬
proaches nearer to the centre in a constant ratio, such, for
example, as 1, 2, 3, 4, 5 (Fig. 326). The curve then drawn
through these points, when supposed to be in the same
plane, is called a spiral. If these points, in addition to

approaching the centre in a constant ratio, are supposed
also to rise above each other by a constant increase of

height, a curve will be obtained, which is also called a
spiral. This spiral may be conceived to be traced on the
surface of a cone (Fig. 326). It may also be traced on the
surface of a sphere (Fig. 327). These figures do not require
detailed description.

MANNER OF TAKING DIMENSIONS.

In taking the dimensions of any triangular figure, make
a sketch of it as in Fig. 328, No. 1, and on each line of
the sketch mark the dimensions of the side of the figure

it represents. Then, in describing the figure, either to its
full dimensions, or to an}’ - proportionate scale, draw any
straight line as ab, No. 2, and make it equal to the

dimension marked on the corresponding line A B of the
sketch No. 1. From the centre A, and with the radius
AC, describe an arc at c; then from the centre B, with
the radius B c, describe an arc intersecting the former:
join A C, B C, and the triangle A c B is the figure required.

The dimensions of any figure are taken on the principle

above illustrated. If the figure is not triangular, it is
divided into triangles, in the manner shown by Fig. 329,
Nos. 1 and 2.

In Fig. 330, Nos. 1 and 2, the manner of taking dimen¬
sions, when one or more sides of the figure are bounded

No. 1 . Fig. 330,

by curved lines, is illustrated. When, as at A B (No. 1),
the side is a circular arc, its centre is obtained as fol¬
lows:—The extreme points AB, and the point of junction
C of the intermediate line E C with A c and B C, give three
points in the curve. From A and B, therefore, with any
radius, describe arcs above and below the curve; from C,
with the same radius, intersect these arcs; through the
intersections draw straight lines meeting in D; and D is
the centre of the curve, and DA, db, or D c its radius.

PRACTICAL CARPENTRY AND JOINERY.

SECTIONS OF SOLIDS.

Plate I.

Plate I. Fig. 1.— To draiv the sections of a cone made
by a line cutting both its sides.

Let adb be the vertical projection of the cone, A C B
the horizontal projection of half its base, and E F the line
of section. From the points E and F, let fall on A B the
perpendiculars eg, fh; and on GH describe the semicircle
G 4 H, which is the horizontal projection of half ol the
section. To find the vertical section—Divide the semi¬
circle G 4 h into any number of equal parts, 1 2 3 4, Ac.;
and through these divisions draw lines 1 5 K, 2 61, 3 7 m,

4 8 n, perpendicular to the line AB, and meeting the section ^
line E F in the points k l m, Ac. Through k l to, Ac., draw
k t, l u, to v, n w, perpendicular to E F, and make them
respectively equal to the corresponding ordinates, 5 1, (i 2,

7 3, Ac., of the semicircle g4h, and points will be obtained
through which the ellipse ewf may be traced. It is
obvious that, practically, it is necessary only to find the
minor axis of the ellipse, the major axis E F being given.

If through the points E k l to n, Ac., lines be drawn
parallel to A B, Ac., meeting the side of the cone, as in
o r p q r s, and from these perpendiculars be let fall on A B,
in xyz a b, then arcs described from the centre of the base
of the cone I, with the radii I G, I 1, I 2, will meet these
perpendiculars. This is applied in the two following '
figures, to finding the projections of other sections of the
cone.

Figs. 2 and 3.— To draw the sections of a cone made
by a line parallel to one of its sides.

Let A D B be the vertical projection of a right cone, and
A c B half the plan of its base; and let ef be the line of
section. In E F take any number of points, E a b c d e F,
and through them draw lines EH, a 6 1, b 7 2, Ac., per¬
pendicular to A B. Through abed e, draw also lines
parallel to A B, meeting the side of the cone in f g hkl:
from these let fall perpendiculars on A B, meeting it in
to n o p q. From the centre of the base I, with the
radii I m, in, I o, Ac., describe arcs cutting the perpendi¬
culars let fall from the section line in the points 12 3 4 5;
and through the points of intersection trace the line H 1
2 3 4 5 G, which is the horizontal projection of the section.

To find the vertical section — On E abode, raise perpen¬
diculars to E F, and make them respectively equal to the
ordinates in the horizontal projection, as E r equal to E H,
a s equal to 6 1, Ac., and the points rstwvw in the
curve will be obtained.

Fig. 4, Nos. 1-4.— To draw the section of a cuneoid
made by a line cutting both its sides.

A cuneoid is a solid ending in a straight line, in which,
it any point be taken, a perpendicular from that point
may be made to coincide with the surface. The end of
the cuneoid may be of any form; but in architecture it is
usually semicircular or semi-elliptical, and parallel to the
straight line forming the other end.

Let AC B (No. 1) be the vertical projection of the cune¬
oid, and A 5 B the plan of its base, and AB (No. 4) the
length of the arris at C, and let DE be the line of section.

Divide the semicircle of the base into any number of
parts 1 2 3 4 5, and through them draw perpendiculars to
A B, cutting it in Imno p, and join e l, c to, c n, Ac., bj T

points draw lines perpendicular to DE, and make them
equal to the corresponding ordinates of the semicircle,
either by transferring the lengths by the compasses, or by
proceeding as shown in the figure.

The section on the line D K is shown in No. 2, in which
AB equals DK; and the divisions efghlc in DK, Ac.,
are transferred to the corresponding points on AB; and
the ordinates e l, f on, g n, Ac., are made equal to the cor¬
responding ordinates 1 1, to 2, n 3, of the semicircle of the
base. In like manner, the section on the line GH, shown
at No. 3, is drawn.

Fig. 5.— To describe a cylindo'ic sectiooi through a
line given in position.

Let A B G F be a section of a right cylinder passing
through its axis; and let CD be the line of the required
section. On A B describe a semicircle, and in the arc take
any number of points, 1 2 3 4 5, from which draw lines
perpendicular to AB, cutting it in opqrs, and pro¬
duced to meet the line of section CD, in the points 6 7 8
9 10, Ac. From these points draw the lines 6 t, 7 u, 8 v,
9 w, 10 x, Ac., perpendicular to C D, and make these ordi¬
nates respectively equal to the ordinates o 1, p 2, q 3, r 4,
s 5; then through the points c tuvw, Ac., draw the curve,
which will be the section required. The heights of the
ordinates may be simply transferred by the compass, or
thus: — Produce the line of section CD to E, to meet the
diameter A B produced: draw E n perpendicular to E D, and
E n perpendicular to E B. From the points in the arc 1 2
3 4 5, draw lines 1 h, 2 k, 3 l, 4 to, 5 n, meeting the line
E n ; then with the centre E and radii E h, E k, E l, E to, e n,
describe the arcs h h, k k, Ac., and from the points h k l
on oi, where these arcs meet the line E n, draw the lines
oi x, to a, l b, k c, h d, cutting the ordinates 6 7 S 9 10, Ac.,
in the points tuvovxabcd, through which draw the
curve of the required section.

Fig. 6 .—To describe the cylindric section onade by a
curved line cutting the cylinder.

Let A B D E be the section of the cylinder, and c D the
line of the section required. On A B describe a semi¬
circle, and divide it into any number of parts as be¬
fore. From the points of division draw ordinates 1 h,
2 k, 3 l, 4 on, Ac., and produce them to meet the line of
the section in opqrstuvw. Bend a rule or slip of
paper to the line C D, and prick off on it the points c opq,
Ac.; then draw any straight line F G, and unbending
the rule, transfer the points c opq, Ac., to F abc-d, Ac.
Draw the ordinates a 1, b 2, c 3, and make them respec¬
tively equal to the ordinates h 1,1c 2, l 3, Ac., and through
the points fouud trace the curve.

Fig. 7 .—To describe the section of a sphere.

Let A B D c be the great circle of a sphere, and F G the
line of the section required. Then, since, as we have seen,
all the sections of a globe or sphere are circles, on F G
describe a semicircle F 4 G, which will be the section re¬
quired.

Or, in F G take any number of points in to l k H, and
from the centre of the great circle E, describe the arcs H ??,
k o, l p, to q, and draw the ordinates H 4, k 3, 12, to 1,
and oi 4, Oo,p2, q 1 ; then make the ordinates on F G
equal to those on B c, and the points so obtained will give
the section required.

Fig. 8. —To describe the section of an ellipsoid, when

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STEREOGRAPHY—COVERINGS OF SOLIDS.

a section through the fixed axis, and the position of the
line of the required section, are given.

Let abcd be the section through the fixed axis of the
ellipsoid, and F G the position of the line of the required
section. Through the centre of the ellipsoid, draw B D
parallel to F G; bisect FG in H, and draw A c perpendicu¬
lar to FG; join B C, and from F draw F K, parallel to B c,
and cutting A c produced in K ; then will H k be the height
of the semi-ellipse forming the section on F G.

Or, the section may be found by the method of ordi¬
nates, thus: —As the section of the ellipsoid on the line A C
is a circle, from the point of intersection of BD and A c
describe a semicircle aec. Then on H G, the line of sec¬
tion, take any number of points l in n o p, and from them
raise perpendiculars cutting the ellipse in q r s. From
qr s draw lines perpendicular to A c, cutting it in the
points 4 5 6; and again, from the intersection of B D and
A o as a centre, draw the arcs 4 l, 5 to, 6 n, C o, cutting
H G in l inn o; then H o, set oil’ on the perpendicular from
H to K, is the height of the section; and the heights
H n, H to, H l, set off on the perpendiculars from l to 3,
n to 2, and p to 1, give the heights of the ordinates.

Fig. 9 .—To find the section of a cylindrical ring
perpendicular to the plane passing through the axis of
the ring, the line of section being given.

Let A B E D be the section through the axis of the ring,
A B be a straight line passing through the concentric
circles to the centre C, and. D E be the line of section.
On AB describe a semicircle; take in its circumference
any points as 1 2 3 4 5, Ac., and draw the ordinates 1 f,
2 g, 3 li, 4 Jc, Ac. Through the points / g h k l, Ac., where
the ordinates meet the line A B, and from the centre c,
draw concentric circles, cutting the section line in in n o
p q. Ac. Through these points draw the lines to I, n 2,
o 3, Ac., perpendicular to the section line, and transfer to
them the heights of the ordinates of the semicircle /1,
g 2, Ac.; then through the points 1 2 3 4, draw the curve
D 5 E, which is the section required.

Again, let RS be the line of the required section; then
from the points t u v w c x d, Ac., where the concentric cir¬
cles cut this line, draw the lines t 1, u 2, v 3, Ac., perpen¬
dicular to R s, and transfer to them the corresponding-
ordinates of the semicircle; and through the points 12 3
4e5/, draw the curve R e/s, which is the section re¬
quired.

Fig. 10 .—To describe the section of a solid of revolu¬
tion, the generat ing curve of which is an ogee.

Let A D B be half the plan or base of the figure, A a
b B the vertical section through its axis, and E F the line
of section required. In E F take any number of points,
g hkl in n o p qr, and through them draw the lines g 1,
h 2, k 3, Ac., perpendicular to E F. Then from c as a centre,
through the points g li k, Ac., draw concentric arcs cutting
A B in r stuv, and through these points draw the ordi¬
nates r 5, s 4, t 3, Ac., perpendicular to A B. Transfer the
heights of the ordinates on A B to the corresponding ordi¬
nates on each side of the centre of E F; and through the
points 1 2 3 4 5, draw the curve E 5 F, which is the section
required.

Fig. 11 .—To find the section of a solid of revolution,
the generating curve of which is of a lancet form.

A D B is the plan of half the base, aeb the vertical
section, and F G the line of the required section. The

, G 9

manner of finding the ordinates and transferring the
heights, is precisely the same as in the last problem.

Fig. 12.— To find the section of an octangular pyra¬
mid.

Let A D E F G B be the plan of half the base of the
pyramid, A H B a section through its centre, at right
angles to any two of its opposite sides, and K L the line
of the required section. From the centre c, draw lines to
the angles of the pyramid defg; then from the points
in n o, where these intersect the line of section, draw the
lines to p, nq , or, perpendicular thereto; and through the
same points to n o, draw lines parallel to the respective
sides of the base, cutting the line A B in stu. Draw the
perpendiculars sx, tw, uv, and transfer the height s x to
the line nq, tw to in p, and u v to or; then join K p, pq,
q r, r L, and the figure K p q r L is the required section.

Fig. 13 .—To find the section of an ogee pyramid
with a hexangular base.

Let A D E F B be the plan of the base of the pyramid,
A a 6 B a vertical section through its axis, and GH the
line of the required section. Draw the arrises C D, C E,
C F. On the line of section G H, at the points of intersec¬
tion of the arrises with it, and at some intermediate points
k, to, o, q, raise indefinite perpendiculars. Through these
points klmnopq draw lines parallel to the sides of the
base, as shown by dotted lines; and from the points where
these parallels meet the line A B, draw r 4, s 3, t 2, u 1,
perpendicular to A B. These perpendiculars transferred to
the ordinates k 1, l 2, to 3. n 4, o 5, p 6, q 7, will give the
points 1 2 3 4 5 6 7, through which to draw the section.

COVERINGS OF SOLIDS.

A solid angle cannot be formed with fewer than three
plane angles. The simplest solid is therefore the pyramid
on a base which is an equilateral
triangle, and its other three sides
formed of similar triangles.

The development of this figure
(Fig. 331) is made by drawing the
triangular base A B C, and then
drawing round it the triangles form¬
ing the inclined sides.

If the diagram is made on flexi¬
ble material, such as paper, then cut
out, and the triangles folded on the lines AB, B c, C A,
the solid figure will be constructed.

Regular Polyhedrons.

These are the tetrahedron, or four-sided figure, just de¬
scribed, composed of four equilateral triangles (Fig. 331).

The hexahedron, or cube, composed of six equal squares
(Fig. 332).

The octahedron (Fig. 333), composed of eight equila¬
teral triangles.

The dodecahedron (Fig. 334), composed of twelve pen¬
tagons.

The icosahedron (Fig. 335), composed of twenty equi¬
lateral triangles.

In the three preceding Figs., A is the elevation, and B
the development.

The elements of these solids are the equilateral triangle,

Fig. 331.

PRACTICAL CARPENTRY AND JOINERY.

the square, and the pentagon. The irregular polyhedrons
may be formed from those named, by cutting off, regularly,

Fig. 330. Fig. 383.

the solid angles. Thus, in cutting off the angles of the
tetrahedron, there results a polyhedron of eight faces,
composed of four hexagons and
four equilateral triangles. The
cutting off the angles of the cube,
in the same manner, gives a poly¬
hedron of fourteen faces, composed
of six octagons, united by eight
equilateral triangles.

The same operation performed
on the octahedron produces four¬
teen faces, of which eight are hexa¬
gonal and six square.

The dodecahedron gives thirty-
two sides, namely, twelve deca¬
gons, and twenty triangles.

The isocahedron gives thirty-
two sides—twelve pentagons and
twenty hexagons. This last ap¬
proaches almost to the globular
form, and may be rolled like a ball.

The other solids which have
plane surfaces are the 'pyramids and prisms. These
may be regular or irregular: they may have their axes

Fig. 335.

perpendicular or inclined: they may be truncated or cut
with a section, parallel or oblique, to their base.

The development of a right prism or right pyramid,
of which the base and the height are given, offers no dif¬
ficulty. The operation consists, in the case of the pyra¬
mid (Fig. 336), of elevating, on each side of the base, a
triangle having its height equal to the inclined height of
each side; and in that of the prism (Fig. 337), in raising-
on each side of the base a rectangle equal to the perpen¬

dicular height of the prism; or, otherwise, connecting the
sides together, as shown
by the dotted lines in
both figures.

In an oblique pyra¬
mid the development is
found as follows:—

Let abed (Fig. 338),
be the plan of the base
of the pyramid, ab cv d
its horizontal projection,
and E F G its side. Then
on the side d c construct
the triangle cud, making
its height equal to the
sloping side of the pyramid F G: this triangle is the de¬
velopment of the side d p c of the pyramid. Then from d,
with the radius E F, describe an arc o; and from R, with

Fig. 337.

—- -1

the radius E G, describe another arc intersecting the last
at O: join R O, d O; and the triangle d R o will be the
development of the side
avd. In the same way,
describe the triangle CRT,
for the development of the
side 6pc. From R, again,
with the same radius E G,
describe an arc s, which in¬
tersect lj 3 r an arc described
from o with the radius a b;
and the triangle ORS will
be the development of the
side a P b.

If the pyramid is trun¬
cated by a line w a parallel
to the base, the develop¬
ment of that line is ob¬
tained by setting off from R on R c, and R d, the length
G a in x and 2, and on R s, R o, and R T, the length G w
in 4, 3, 1; and drawing the lines 1 x, x 2, 2 3, 3 4, parallel
to the bases of the respective triangles trc, cud, d R o,
ors. If it is truncated by a line w y, perpendicular to
the axis, then from the point R, with the radius G w, or
G y, describe an arc 1 4, and inscribe in it the sides of
the polygon forming the pyramid.

Development of the Coverings of Prisms.

In a right prism, the faces being all perpendicular to
the bases which truncate the solid, it results that their

STEREOGRAPHY—COVERINGS OF SOLIDS.

Fig. 339.

development is a rectangle composed of all the faces
joined together, and bounded by two parallel lines equal
in length to the contour of the bases.

When a prism is inclined, the faces form different
angles with the lines of the contours of the bases: whence
there results a development, the extremities of which are
bounded by lines forming parts of polygons.

After having drawn the line C C (Fig. 339), which indi¬
cates the axis of the

# o T

prism, and the lines
ab, de, the surfaces
which terminate it,
describe on the
middle of the
axis the poly¬
gon forming
the plan of the
prism, taken
perpendicularly to the
axis, and indicated by
the figures 1 to 8:
produce the sides 1 2,

6 5, parallel to the
axis, until they meet
the lines A B, D E.

These lines then indi¬
cate the four arrises of the prism, corresponding to the
angles 1 2 5 6. Through the points 8 3 74, draw lines
parallel to the axis meeting AB, DE in FH, GL : these
lines represent the four arrises 8 3 7 4.

In this profile the sides of the plan of the polygon
12345678 give the width of the faces of the prism,
and the lines ad, fh, gl, be their length. From this
profile may be drawn the horizontal projection, in the
manner shown by the dotted lines. To trace the develop¬
ment of this prism on a sheet of paper, so that it can be
folded together to form the solid, proceed thus:—On the
middle of c c raise an indefinite perpendicular M N. On
that line set off the width of the faces of the prism, indi¬
cated by the polygon, in the points 012 3 45 678:
through these points dx - aw lines parallel to the axis, and
upon them set off the lengths of the lines in profile, thus:
— From the points 0 1 and 8, set off the length M D in the
points D D D ; from 2 and 7, set oft' a H in H and H; from
3 and 6, set off b L in L and L; and so on: then draw the
lines D D, D H L E, E E, E L H D, for the contour of the upper
part of the prism. To obtain the contour of the lower
portion, set off the length M A from 0 to A, 1 to A, and 8 to
A, the length a F from 2 and 7 to F, the length b G from
3 and 6 to G, and so on; and draw A A, A F G B, B B, B G F A,
to complete the contour. The development is completed
by making on B B and E E the polygons 1 234 5 6b B, 12
3 4 5 6 EE, similar to the polygon of the plan r stpqx.

Development of Cylinders.

Cylinders may be considered as prisms, of which the base
is composed of an infinite number of sides. Thus we shall
obtain graphically the development of a right cylinder by
a rectangle of the same height, and of a length equal to
the circumference of the circle, which serves as its base,
measured by a greater or lesser number of equal parts.

But if the cylinder (Fig. 340) be oblique, and it is re¬
quired to draw its profile as inclined, describe on the

Fig. 349 .

b dJ’fi A

centre of the axis of the inclined profile, and perpendicu¬
lar to it, the circle or ellipse which forms the base; and
divide its circumference into a number of equal parts, and
through these divisions
draw lines parallel to
the axis a b, c d, e /,
gh, &c.

Then to find the pro
jection of the
base on a hori¬
zontal plane,
from the points
a c e g, where
the lines from
the divisions of the cir¬
cumference meet the
line of the base a k, let
fall perpendiculars on a line a k', parallel to the base, and
produce them indefinitely beyond it. From the points
to' n' o'p', where these perpendiculars intersect the line
a' Jc, set off on each side to' 1, to' 15, and n 2, n 14, equal
to the ordinates of the circle distinguished by the same
letters and figures, and so on with the other divisions; and
through the points thus obtained, draw the ellipse a, 4, k,
12, which is the projection of the base of the cylinder on
a horizontal plane.

To obtain the development of the cylindrical surface,
produce F. F indefinitely to G, and set out on it from E' the
divisions of the circumference of the circle 1 2 3 4, &c., in
the points mnop, &c.: tln-ough these, draw lines parallel
to the axis, and transfer to them the lengths of the cor¬
responding divisions of the profile, as E a, E b, to c, to d, ne,
nf, &c.; then draw the curves acegu, bdfh A, through
the jioints thus obtained. The addition of the elliptic
surfaces, which form the base and head of the solid, and
which are similar and equal to a', 4, Jc 12, completes the
development.

The extent e'g will not be truly the same as that of the
periphery of the circle E F, inasmuch as the distances in
the latter are but the chords of segments; if, however, the
number of divisions employed be auqfie, the amount of the
error will, for practical purposes, be inappreciable.

Development of Right and Oblique Cones.

We have considered cylinders as prisms with polygonal
bases: for the same reason we may regard cones as pyramids.

In right pyramids, with regular and symmetrical bases,
as the lines of the arrises extending from the summit to
the base are equal, and as the sides of the polygons form¬
ing the base are also equal, their developed surfaces will be
composed of similar and equal isosceles triangles, which, as
we have seen (Fig. 336, abed), will, when united, form
a part of a regular polygon inscribed in a circle, of which
the inclined sides of the polygon form the radii. Thus, in
considering the base of the cone K II (Fig. 341) as a regu¬
lar polygon of an infinite number of sides, its development
will be found in the sector of a circle^ M' A F B m" (No. 3).
the radius of which equals the side of the cone K g' (No. 1),
and its arc equals the circumference of the circle forming
its base (No. 2).

To trace on the development of the covering, the curves
of the ellipse, parabola, and hyperbola, which are the
result of the sections of the cone by the lines D I, I G, E F,

PRACTICAL CARPENTRY AND JOINERY.

it is necessary to divide the circumference of the base
A F BM (No. 2) into equal parts, as 123456, and from
these to draw radii to the centre of the circle 0", which is
the horizontal projection of the summit; then to carry
these divisions to the common intersection line K H, and
from their terminations there to draw lines to the summit
o', in the vertical projection No. 1. These lines cut the
intersecting planes, forming the ellipse, parabola, and hy¬

perbola, and by the aid of the intersections, we obtain the
horizontal projection of these figures in No. 2—the para¬
bola passing through M E' F, the hyperbola through o" L,
and the ellipse being represented by the circle T>' l'.

To obtain points in the circumference of the ellipse upon
the development, through the points of intersection o p
q r s, draw lines parallel to K n, carrying the heights to
the side of the cone g' h, in the points 1 2 3 4 5 6 7,
and transfer the lengths g' 1, G' 2, g' 3, &c., to G 1, G 2,
G 3, G 4, &c., on the radii of the development in No. 3; and
through the points thus obtained draw the curve zdix.

To obtain the parabola and hyperbola, proceed in the
same manner, by drawing parallels to the base K H,
through the points of intersection; and transferring the
lengths thus obtained on the sides of the cone G' K, G' H,
to the radii in the development
r l he projections in Nos. 4 and 5 do not require explanation.

Development of the Oblique Gone.

In the oblique cone, the position of the summit in
the horizontal projection not being coincident witli
the centre of the circle forming the base, the lines drawn
from it to the divisions in the circumference are not
radii, and are of unequal lengths. To obtain, therefore, the
proper points of intersection, it is necessary to construct
a right-angled triangle on each of these lines as a base;
then the vertical height of the cone is the other side of
the right angle, and its hypothenuse is the side of the
cone corresponding to the division. Thus, in Fig. 342 the
bases of the right-angled triangles C A, c 1, c 2, &c., are
equal to the lines C A, C 1, C 2, &c., in the horizontal projec¬
tion (Fig. 343); the height of all the triangles is equal to
the vertical height of the cone cc 1 ; and the hypothenuse
of each triangle is thus easily obtained.

To obtain the development (Fig. 344), take any point c
to represent the summit, draw c A, and make it equal to
C 2 A (Fig. 342); then from A, with the length A 1, the first
division of the circumference in the horizontal projection
(Fig 343), as radius, describe an indefinite arc; and from
c, with the hypothenuse c-1 (Fig. 342) as radius, describe
another arc, intersecting the first, and the intersection

Fit 342.

gives the point 1 in the
development. F rom

this last point, with
the constant radius
A 1, describe another
arc, and intersect it
from c by an arc
with the second hypothenuse
C 2 2 (Fig. 342), as radius; and
proceed thus till the whole
is completed.

The lines of the ellipse, pa-
rabola, and hyperbola are found in the development by
first obtaining them on the lines of the triangles, in Fig.
342, and then transferring the lengths to the development.

Development of Solids whose Surface is of Double
Curvature.

The development of the sphere, and of other surfaces of

Fig. 3)5.

double curvature, is impossible, except on the supposition

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STEREOGRAPHY—COVERINGS OF SOLIDS.

Fig. 346.

of their being composed of a great number of small faces,
either plane, or of a simple curvature, as the cylinder and
the cone. Thus a sphere or spheroid may be considered
as a polyhedron, termi¬
nated, 1st, by a great
number of plane faces,
formed by truncated
pyramids, of which the
base is a polygon, as in
Fig. 345 ; 2d, by parts
of truncated cones form¬
ing zones, as in Fig.

346; 3d, by parts of
cylinders cut in gores,
forming flat sides, which diminish in width, as in Fig.
347.

In reducing the sphere, or spheroid, to a polyhedron
with flat sides, two me¬
thods may be adopted,
which differ only in the
manner of arranging the
developed faces.

The most simple me¬
thod is by parallel circles,
and others perpendicular
to them, which cut them
in two opposite points, as
in the lines on a terres¬
trial globe. If we suppose that these divisions, in place
of being circles, are polygons of the same number of sides,
there will result a polyhedron, like that represented in
Fig. 345, of which the half, ADB, shows the geometrical
elevation, and the other half, A E B, the plan.

To find the development, first obtain the summits P, q,
r, s, of the truncated pyramids, which form the demi-
polyhedron ADB, by producing the sides A 1, 12, 23,
until they meet the axis E D produced; then from the
points P, q, r, and with the radii P A, P 1, q 1, q 2, r 2, r 3,
and a 3, s 4, describe the indefinite arcs A B, 1 b, 1 b’, 2 /,
2 f, 3 g, 3 g, 4 h, and from D 4 h', upon which set off the
divisions of the demi-polygons A E B, and draw the lines
to the summits P, q, r, s, and D, from all the points so set
out, as A 1 2 3 4 5 B, for each truncated pyramid. These
lines will represent for every band or zone the faces of the
truncated pyramids of which they constitute a part.

The same development can be made by drawing through
the centre of each side of the polygon aeb, indefinite
perpendiculars, and setting out upon them the heights
of the faces in the elevation, 1 2 3 4 D, and through
the points thus obtained drawing parallels to the base.
On each of these parallels then set out the widths h, i, k,
l, d, of the corresponding faces in the plan, and there
will be thus formed trapeziums and triangles, as in the
first development, but arranged differently. This method
is used in constructing geographical globes, the other is
more convenient in finding the stones of a spherical
vault.

The development of the sphei'e by reducing it to conical
zones (Fig. 346) is accomplished in the same manner as the
reduction to truncated pyramids, with this difference, that
the development of the arrises, indicated by A 1 2 3 4, are
arcs of circles described from the summits of cones, in place
of being polygons.

The development of the sphere reduced into parts of
cylinders, cut in gores, is produced by the second method
described, but in place of joining by lines, the points e, h,
i, lc, l , d (Fig. 345), we unite them by a curve, as in Fig.
347- This last method is used in tracing the develop¬
ment of caissons in spherical or spheroidal vaults.

The application of these principles to the cases of cover¬
ings which occur most frequently in carpentry, is illus¬
trated in Plates II., III., and IV.

Plates II., III., IY.

To find the covering of a right cylinder.

Plate II.—Let abcd {Fig. 1) be the seat or generat¬
ing section. On A D describe the semicircle A 5 D, repre¬
senting the vertical section of half the cylinder, and divide
its circumference into any number of equal parts, 1 2 3 4 5,
&c., and transfer those divisions to the lines A D and B c
produced; then the parallelogram D c, G F will be the
covering required..

To find the edge of the covering when it is oblique in
regard to- the sides of the cylinder.

Let abcd {Fig. 2) be the seat of the generating section,
the edge bc being oblique to the sides A B, DC:, draw the
semicircle A 5 D, and divide it into any number of parts,
as before; and through the divisions, draw lines at right
angles to A D, producing them to meet B c in r s tuv, &c.
Produce A D, and transfer to it the divisions of the cir¬
cumference, 1 2 3 4 5 6, &c.; and through them draw in¬
definitely the lines 1 a, 2 b, 3 c, perpendicular to D F: to
these lines transfer the lengths of the corresponding lines
intercepted between A D and B c, that is, to 1 a transfer
the length p z, to 2 b transfer o y, and so on, by draw¬
ing the lines z a, y b, x c, &c., parallel to A F, the inter¬
sections; then shall dfcg be the development of the
covering of A B C D.

To find the covering of a semi-cylindric surface con¬
tained between two paixtllel planes perpendicular to the
generating section.

Let abcd {Fig. 3) be the seat of the generating sec¬
tion : from A draw A G perpendicular to A B, and produce
C D to meet it in E : on A e describe the semicircle, and
transfer its perimeter to EG, by dividing it into equal parts,
and setting off corresponding divisions on E G. Through
the divisions of the semicircle draw lines at right angles
to A E, producing them to meet the lines A D and B c,
in ikl m, &c. Through the divisions on E G draw lines
perpendicular to it ; then through the intersections of the
ordinates of the semicircle, with the line A D, draw the
lines i a, k z, l y, &c., parallel to A G, and where these in¬
tersect the perpendiculars from E G, in the points a, z, y,
x, w, v, u, &c., trace a curved line G D, and draw parallel
to it the curved line H c; then will R c, H G, be the de¬
velopment of the covering required.

To find the covering of a semi-cylindric surface
bounded by two curved lines.

Figs. 4, 5, 6.—The construction to obtain the develop¬
ments of these coverings is precisely similar to that de¬
scribed in Fig. 3, as will be evident on inspection.

To form the edge of a cylinclric surface terminated
by a curved line, so that when the envelope is applied, to
the surface its edge may coincide until a plane passing
through three given points.

Let A E D {Figs. 7 and 8), be the base of the solid. Draw

PRACTICAL CARPENTRY AND JOINERY.

A B and D c perpendicular to A D, and make A B equal to
the height of the point whose seat is A, and D C equal to the
height of the point whose seat is D. On D c make II equal
to the height of the point whose seat is E: join B C. Draw
H L (Fig. 7) parallel to A D and H K (Fig. 8), cutting B c in L.
Draw L a parallel to D C, cutting A D in a : join a E. Divide
the arc of the base into any number of equal parts in 1 , 2 ,
3, 4, &c., and extend them on A D produced to F. Then
to find any point in the envelope—suppose that which cor¬
responds to b on the seat. Draw b q parallel to a E, cut¬
ting ad at q; draw also q n parallel to D C, cutting B C
in n. Make q o equal to q n, and o is a point in the line
required. Proceed in the same manner with other points
until the line COG (Fig. 7) and CLOG (Fig. 8 ) is ob¬
tained.

To find the covering of the f rustum of a cone, the sec¬
tion being made by a plane perpendicular to the axis.

Let A c E F (Fig. 9) be the generating section of the
frustum. On A c describe the semicircle ABC, and pro¬
duce the sides A E and c F to D. From the centre D, with
the radius D c, describe the arc C H; and from the same
centre, with the radius D F, describe the arc F G: divide
the semicircle into any number of equal parts, and run the
same divisions along the arc C H ; draw the ordinates to
the semicircle through the points of division, at right angles
to, and meeting A c; and from the points onm, <fec., where
these ordinates cut the line A B, draw lines to the point D;
and from the last division in the arc c H, draw also a
line to the point D ; then shall CHGF be half the de¬
velopment of the covering of the frustum acfe.

To find the covering of the frustum of a cone, the
section being made by a plane not perpendicular to the
axis.

Let acfe (Fig. 10) be the frustum. Proceed as in
the last problem to find the development of the covering
of the semicone: then, to determine the edge of the cover¬
ing on the line E F. From the points p q r s t, <fec., draw
lines perpendicular to E F, cutting AC in y x w v u ; and
the length u t transferred from 1 to a, v s transferred
from 2 to b, and so on, will give abode G, points in
the edge of the covering.

To find the covering of the frustum of a cone, when
cut by two cylindric surfaces perpendicular to the
generating section.

Plate III. — Let aefc (Fig. 1) be the given section,
and A k c, E p F, the lines on which the cylindrical surfaces
stand. Produce A E, C F, till they meet in the point D.
Describe the semicircle ABC, and divide it into any num¬
ber of equal parts, and transfer the divisions to the arc c H,
described from D, with the radius D c. Through the divi¬
sions in the semicircle 1 2 3 4, draw lines perpendicular
to A c, and through the points where they intersect A c
draw lines to the summit D. Draw lines also through the
points 1 2 3 4 5, &c , of the arc C H, to the summit D;
then through the intersections of the lines, from A c to D,
with the seats of cylindrical surfaces k l m n o, and p
qr st, draw lines parallel to A c, cutting c D; and from
the points of intersection in c D, and from the centre D,
describe arcs cutting the radial lines in the sector D c II
m u v w x y, and abode, and curves traced through
the intersections will give the form of the coverino-.

To find the development or covering of the surface of
the frustum of a scalene semicone.

Let ABC (Fig. 2) be the base of the semicone; A c D
the plane of its section, cut on the line A c, perpendi¬
cular to the base; and let A c E F be the seat of the en¬
velope required. Divide ABC into any number of equal
parts, as in 1 2 3, &c.; and from the points of division
draw lines perpendicular to A C, cutting it in k l m, (fee.;
and from these points draw right lines to D. To find
the true lengths of the lines radiating from D, the vertex
of the cone, to the points 1 2 3 4 B, in the circumference
of the base: — from the point s, where D s cuts A c, draw s a
perpendicular to D s, and from r draw r a perpendicular to
D r, draw also q z perpendicular to D q, py perpendicular
to d p, ox perpendicular to D o, n w to D n, m v to D m,
l u to d l, and k t to D k. Then make s a equal to s 1, r a
equal to r 2, qz equal to q 3, &c.; draw the dotted lines
D t, D u, D v, D iv, T> x, D y, D z, Da, D a', which will
give the respective lengths of the corresponding lines on
the envelope of the semicone, as shown by the concentric
dotted arcs t 9, u 8, v 7, w 6. (fee., described from the point
D. With distances exactly equal to the divisions c 1 2
3 4 B of the arc ABC, set off from c the points 12 3 4
5, &c., to H, on the corresponding concentric dotted lines,
so as that D H will be equal to D A, D 9 equal to D t, D 8
equal to D u, (fee.; then draw the curved line c H through
the points thus found. The curved line F G, forming the
inner line of the envelope, is found, in like manner, by
drawing the perpendicular lines b, c, d from the lines D k,
D l, D m, (fee., to their corresponding dotted lines. Then
H G will be made equal to A E, 9 h to t b, 8 g equal to u c,
7/ equal to v d, (fee. Then the curve being drawn through
the points thus found, the figure F G H C is the develop¬
ment of the portion of the cone shown by the lines ACEF.

To find the envelope for the f rustum of a cuneoid.

Let A B c D (Fig. 3) be the seat of the portion of
the surface to be covered ; the semicircle aed the sec¬
tion of the lesser end ; and the semi-ellipse, B M c, of the
greater end ; each being of the same altitude, that is, m E
being equal to r M. Produce ba,cd, to meet in f, and di¬
vide the semicircle aed into any number of equal parts,
as in 1, 2, 3, 4, E. From these points draw the lines 1 q, 2
p, 3 o, &c., perpendicular to AD; and from F through m n
o p q draw right lines cutting BCinrsfuu: from these
points draw til, u 2, t 3, «fec., perpendicular to B C, and
cutting the semi-ellipse in 1 2 3 4, <fec. Draw F G per¬
pendicular to F c ; on F G make F w equal to q 1, F x equal
to p 2, F y equal to o 3, fz equal to n 4, fg equal to to E.
From D, with a radius equal to D 1, describe the arc at a,
and draw w f tangent to that arc: make w a equal to F q,
and a f equal to q v. From a, with the radius D a, describe
the arc at b, and draw x g tangent to that arc: make
x b g equal to F p v. From b, with the radius D a, describe
the arc at c, and draw the tangent; and proceed with this
and the other divisions as before. Then through the points
D abode and cfghi k, draw the curved lines complet¬
ing one half of the envelope: the other half joined on the
same base, is equal and similar; and may be described thus:
—From G as a centre describe concentric circles from w x
y z, and from the same centre describe with any con¬
venient radius an arc, as 6 5 7: make the divisions on 5 7
equal to the divisions on 5 6: make 7 H equal to 6 F, and
join G n. The remainder of the operation does not require
to be described.

To find the envelope of a portion of a cuneoid contained

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STEREOGRAPHY—COVERINGS OF SOLIDS.

between two cylindric surfaces, the axes of which are per¬
pendicular to the plane passing through the axis of the

cuneoid. ,

pjg 4 _Find, in tlie manner shown and described.

in the last example, the dotted curved line F hik, cor¬
responding to one half of the semicircle enf; find also
the dotted curved line C M, corresponding to the circum¬
ference of the semi-ellipse bo c; and having completed the
development of the covering, as if for the frustum bounded
by the lines B E F C, proceed as follows: — The line e f being
a tangent to the line A D, and parallel to the chord B c,
mak eh l, i to, &c., respectively equal to s g,rf q e, &c
and draw the curve vlmyk ; then form the inner edge of
the envelope. Then make l n equal to g c, to o equal to
fb,yx equal to e a, &c., and through c n o x, &c., draw
the outer edge of the envelope.

To find the covering of a segmental dome.

Tig. 5—No. 1 is the plan, and No. 2 the elevation of
a segmental dome. Through the centre of the plan e
draw the diameter A C, and the diameter B D per¬
pendicular to A c, and produce B D to I. Let D E repre¬
sent the base of a semi-section of the dome; upon D e de¬
scribe the arc D h with the same radius as the arc fgh
(No. 2); divide the arc D k into any number of equal
parts 1 2 3 4 5, and extend the divisions upon the right
line D i, making the right line D 1 2 3 4 5 I equal in
length, and similar in its divisions, to the arc D k: from
the points of division 1 2 3 4 5 in the arc D k, draw lines
perpendicular to D E, cutting it in the points q r s, &c.
Upon the circumference of the plan No. 1, set oft the
breadth of the gores or boards l to, to n. n o, o p, &c.; and
from the points Imnop draw right lines through the
centre E: from E describe concentric arcs qv, ru, st, &c.,
and from I describe concentric arcs through the points
D 1 2 3 4 5 : l to being the given breadth at the base, make
1 w equal to qv, 2x equal to r u, 3 y equal to s t, &c.;
draw the curve line through the points l w x y, &c, to I,
which will give one edge of the board or gore to coincide
with the line l E. The other edge being similar, it will be
found by making the distances from the centre line D I
respectively equal. The seat of the different boards or
gores on the elevation are found by the perpendiculai
dotted lines p p, o o, n n, m to, &c.

To find the covering of a semicircular dome.

Fig. 6 , Nos. 1 and 2 —The procedure here is more sim¬
ple than in the case of the segmental dome; as the hori¬
zontal and vertical sections being alike, the ordinates are
obtained at once.

To find the covering of an ellipsoidal dome.

Let A B c D (Fig. 7) be the plan, and fgh the elevation
of the dome. Divide the elliptical quadrant F g (No. 2),
into any number of equal parts in 1 2 3 4 5, and draw
through the points of division lines perpendicular to F H, and
produced to a c (No. 1), meeting it in iklmn: these divi¬
sions are transferred by the dotted arcs to the gore b E c, and
the remainder of the process is as in the two last examples.

To find the covering of an ogee dome, hexagonal in

plan.

Let ABCDEF (No. 1, Fig. 8) be the plan of the
dome, and H K l (No. 2), the elevation, on the diameter
F C. Divide H K into any number of equal parts in
1 2 3 4 5 k, and through these draw perpendiculars to
H L, and produce them to meet F c (No. 1), in Imnop g.

Through the points of meeting Imnop, draw lines l d,
m e, nf, &c., parallel to the side F E of the hexagon : bisect
the side f e in N, and draw G N, which will be the seat of
a section of the dome, at right angles to the side E F. To
find this section nothing more is required than to set
up on N G, from the points t u v, &c., the heights of the
corresponding ordinates q 1, r 2, s 3, &c., of the elevation
(No. 2), to draw the ogee curve N 1 2 3 4 5 P, and then to
use the divisions in this curve to form the gore or cover
ing of one side E g h k M D.

To find the covering of a circular dome when it is re¬
quired to cover the dome horizontally.

Plate IV.— Let abc (Fig. 1) be a vertical section
through the axis of a circular dome, and let it be required
to cover this dome horizontally. Bisect the base in the
point D, and draw dbe perpendicular to A C, cutting the
circumference in B. Now divide the arc B c into equal
parts, so that each part will be rather less than the width
of a board ; and join the points of division by straight lines,
which will form an inscribed polygon of so many sides;
and through these points draw lines parallel to the base
A C, meeting the opposite sides of the circumference. The
trapezoids formed by the sides of the polygon and the hori¬
zontal lines, may then be regarded as the sections of. so
many frustums of cones; whence results the following
mode of procedure, in accordance with the introductory
illustration at page 73, and Fig. 346produce, until they
meet the line D E, the lines nf,fg, &c., forming the sides ot
the polygon. Then to describe a board which corresponds
to the surface of one of the zones, as/ g, of which the trape¬
zoid is a section,—from the point h, where the line / g pro¬
duced meets D E, with the radii hf, h g, describe two arcs,
and cut off the end of the board k on the line of a radius
h k. The other boards are described in the same manner.

To find the covering boards of an ellipsoidal dome.

Let A B c D (No. 1, Fig. 2), be the plan of the dome, and
fgh (No. 2) the vertical section through its major axis.
Produce F H indefinitely to n\ divide the circumference, as
before, into any number of equal parts, and join the divi¬
sions by straight lines. Then to describe any board, pro¬
duce the line forming one of the sides of the polygon, such
as l to, to meet F n in n ; and from n, with the radii n to, n l,
describe two arcs forming the sides of the board, and cut
off the board on the line of the radius n o. Lines drawn
through the points of the divisions at right angles to the
axis, until they meet the circumference A D C of the plan,
will give the plan of the boarding.

To find the covering of an ellipsoidal dome in gores.
The principle in this being the same as in the globe,
pao-e 72, Fig. 345, we shall merely describe the method ol
procedure. Let the ellipse abcd (Fig. 3, No.. 1) be the
plan of the dome, a c its major and B D its minor axis;
and let A B c (No. 2) be its elevation. Then, first, to de¬
scribe on the plan and elevation the lines of the gores,
proceed thus:— Through the line A C (Fig. 1) produced at
H, draw the line E G perpendicular to it, and draw bedg
parallel to the axis A C, cutting EG;, then will E G be the
length of the axis minor, on which is to be described the
semicircle efg, representing a section of the dome on a
vertical plane passing through the axis minoi.

Divide the circumference of the semicircle into any num¬
ber of equal parts, representing the widths oi the covering
boards on the line B D; and through the points ol division

7 G

PRACTICAL CARPENTRY AND JOINERY.

12 3 4 5, draw lines parallel to the axis A C, cutting the
line B D in 1 2 3 4 5. Divide the quadrant of the ellipse
C D (No. 1) into any number of equal parts in efg h ; and
through these points draw the lines ea,fb,gc, h d, in both
figures perpendicular to A C, and these lines will then be the
seats of vertical sections through the solid, parallel to E F G.
Through the points efgh (No. 1), also, draw lines parallel
to the axis A c, cutting EGinowm k ; and from H, with
the radii no, H n, IIto, II k, describe the concentric circles
o 9 9 p, n 8 S q, on z y r, <Szc. To find the diminished width
of each gore at the sections a e, bf, c g,d h :—Through the
divisions of the semicircle 1 2 3 4 5 draw the radii 1 s, 2 t,

3 u, 4 v, 5 w, 6 x ; then by drawing through the intersec¬
tions of these radii with the concentric circles, lines parallel
to H c, to meet the section lines corresponding to the circles,
the width of the gores at each section will be obtained;
and curves drawn through these points will give the re¬
presentation of the lines of the gores on the plan.

In No. 2 the intersections of the lines are more clearly
shown. The quadrant E G F is half the vertical section on
D B, and is divided as in No. 1. The parallel lines 5 5,

4 4, 3 3, show how the divisions of the arc of the quadrant
are transferred to the line D B, and the other parallels a h,
b k, cl, dm, are drawn from the divisions in the circum¬
ference of the ellipse to the line E G, and give the radii of
the arcs m n, l o, k p, h q.

To describe one of the gores, draw any line A B (No. 3),
and make it equal in length to the circumference of the
semi-ellipse A d C, by setting out on it the divisions 12 3
4 5, &c., corresponding to the divisions of the ellipse: draw
through those divisions lines perpendicular to A B. Then
from the semicircle (No. 1), transfer to these perpendiculars
the widths 6 5 to g n, 9 9 to fm, 8 8 to e l, y z to d k, and
x w to c li, and join A c, c d, d e, e f f g, and A It, h k, k l, l on
and m n; which will give the boundary lines of one half of
the gore, and the other half is obtained in the same manner.

To describe the coveo'ing of an ellipsoidal doone with
boaoxls of equal width.

Let A B c D (No. 1, Fig. 4) be the plan of the dome,
a b c (No. 2) the section on its major axis, and L M n (No.

3), the section on its minor axis. Draw the circumscribing
parallelogram of the ellipse F G H K (No. 1), and its dia¬
gonals f H G K. In No. 2 divide the circumference into
equal parts 1 2 3 4, representing the number of covering
boards, and through the points of division 1 8, 2 7, &c.,
draw lines parallel to A C. Through the points of division
draw 1 p, 2 1, 3 x, &c., perpendicular to A c, cutting the
diagonals of the circumscribing parallelogram of the ellipse
(No. 1), and meeting its major axis in p t x, &c. Com¬
plete the parallelograms, and their inscribed ellipses cor¬
responding to the lines of the covering, as in the figure.
Produce the sides of the parallelograms to intersect the
circumference of the section on the transverse axis of the
ellipse in 1 2 3 4, and lines drawn through these, parallel
to L N, will give the representation of the covering boards
in that section. To find the development of the covering,
produce the axis D B, in No. 2, indefinitely. Join by a
straight line the divisions 1 2 in the circumference, and
produce the line to meet the axis produced ; and 12 e k g
will be the axis major of the concentric ellipses of the co¬
vering i fg, 2 h k. Join also the corresponding divisions in
the circumference of the section on the minor axis, and
produce the line to meet the axis produced; and the length
of this line will be the axis minor of the ellipses of the
covering boards.

To find the covering of aoi annular vault.

Let ackgefa {Fig. 5) be the generating section of
the vault. On A c describe a semicircle ABC, and divide
its circumference into equal parts, representing the boards
of the covering: from the divisions of the semicircle b on t,
&c., let fall perpendiculars on A c, and cutting it in r s, &e.;
from the centre D of the annulus, with the radii D r, D s,
&c., describe the concentric circles s q,& c., representing the
covering boards in plan. Through the centre D draw H K
perpendicular to G C, indefinitely extending it through
K Join the points of division of the semicircle A b, 6 m,
mt, by straight lines, and produce them until they cut
the line KH,asm6»,<mn, when the points n, u, &c., are
the centres from which the curves of the covering boards
mo, t v, &c, are described.

STEREOGRAPHY—DESCRIPTIVE CARPENTRY.

Descriptive Carpentry is the application of the prin¬
ciples of stereography to carpentry, and has this special
difference that, while in stereography the bodies which are
the subjects of its operations are entire solids, in descrip¬
tive carpentry the bodies are made in ribs disposed in
parallel lines or planes, or disposed in lines tending to a
point, or in planes tending to an axis. Descriptive car¬
pentry shows thus the method of forming the separate
pieces in order to construct the whole body or solid.

GROINS.

A groin is the line made by the intersection of arched
vaults crossing each other at any angle.

When two cylindric vaults of equal span and height

cross, they produce cylindric groins : the intersection of
equal cones produces conic groins; of equal spheres, spheric
groins.

When the intersecting vaults are of different span and
width, the larger is called the body range, and a compound
word is used to denote the resultant groin. The term for
the vault of the body range is made to end in o ; as, for
instance, in the case of the body range being a cylindrical
vault, it would become cylindro, a spherical vault would
be sphero, and the intersecting vault would be cylmdric
or spheric, as the case might be. Thus a cylindro-cylin-
dric groin is one formed by a cylindrical body rauge, and
a cylindrical intersecting vault of smaller size. A cylin-
dro-spheric groin is the intersection of a sphere with a
cylinder of greater span and height; while a sphero-cylin¬
dric groin, is formed by the intersection of a cylindric

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PLATE X.

DESCRIPTIVE CARPENTRY—GROINS.

vault with a spherical vault of greater dimensions. The
curved surface between two adjacent groins is called a
sectroid.

Plates V., VI., VII., VIII., IX., X.

Problem I.— In a rectangular groined vault, in which
the openings are of different widths, but of the same
height, and when one of the arches and the seats of the
groins are given, to find the arch of the other opening, the
groin arch, and the covering of the vaults.

Plate V.—Let a a a a [Fig. 1, No. 1) be the plan of the
piers, BCD the given arch, and olm, plq the seats of
the groins. The given arch is in this case a semicircle.
Divide the quadrant of the given arch, D c, into any num¬
ber of equal parts, as 1 2 3 4 5, and from the points of
division draw the lines 5 a, 4 b, 3 c, &c., parallel to the axis
c E L, to meet the seat of the groin line L o. From the
points Labe, &c, draw the line L K G (the axis of the
other vault), and a p 5,b o 4, &c., parallel to these, and
make the lines 1 1, m 2, n 3, o 4, p 5 and K G, equal to the
ordinates 7c 1, i2, h 3, g 4, / 5, and E c, respectively; then
a curve traced through the points F 1 2 3 4 5 G, will give
a quadrant of the other arch.

To find the curve of the groin -.—From the intersections
of the lines c L 5 a, &c., with the seat of the groin M L o,
draw the perpendiculars e 1, d 2, c 3, &c., and make them
equal to the corresponding ordinates k 1 or 1 1, i 2 or m 2,
&c., and trace the curve through the points 1 2 3. By draw¬
ing lines through the points 1 2 3 in these quadrants par¬
allel to their major axes, and making qs,rt, and v x, uw,
equal to q 1, r 2, and v 1, u 2, respectively, and continuing
the curve through the points so obtained, the arches may
be completed.

To find the covering of the smaller sectroid bplod : —
On any straight line A B (No. 2), set off the divisions 12 3,
&c., equal to, and corresponding to the divisions of the
quadrant D c. Through these divisions draw the perpen¬
diculars A £, 1 g, 2 li, 3 i, and make D c equal to E L, 51
to J a, 4 1c to g b, and so on; and through the points
c l k i h g E draw a curve, and the figure aecd will be
the covering of the half sectroid bple: by proceeding
with the other ordinates m n, &c., in the same manner,
the other half of the covering, dcfb, will be obtained.

To find the covering of the larger sectroid folq h:— On
any line B c (No. 3), set off the divisions 12 3 correspond¬
ing to the divisions 1 2 3 of the greater arch fgh (No. 1);
draw the perpendiculars 1 g, 2 h, &c., as before, making them
equal to the lines l e, m d, n c, &c., in No. 1and draw a
curve through the points A g h i k l E: proceed in the same
way with the ordinates m o, n p, &c., of the other half;
and the result will be the figure baedc, which is the de¬
velopment of the covering of the sectroid as required.

It will be observed that the angle rib is shown as com¬
posed of two thicknesses of stuff It is bevelled eacli way
so as to range with both branches of the groin. One of
the thicknesses is shown on somewhat a larger scale, at
No. 4, in which D is the plan, the bevel being obtained on
the plan No. 1, at Q. When the two thicknesses are put
together, the bevelled face k A g will range with the sur¬
face of the sectroid M L K, and the bevelled face of the ;
other half of the rib with the surface of the sectroid
QLF.

The method of finding the places and lengths of the

ribs is shown in the lower part of No. 1. From the seat
of any rib, as a b, draw the lines a c,b d; then from c to d
will be the rib a b.

The curve of the larger arch, and of any groin arch in a
rectangular vault, such as the case illustrated, can be very
readily obtained by means of an elliptograph or trammel, as
shown in Fig. 2. In drawing the curve of the larger arch,
the line F II is bisected, and the perpendicular g f G drawn:
the trammel d g l f is then placed with its centre on the
intersection of the lines, and its limbs centrally upon
these: the distance between the tracer a and the stud c of
the moveable bar is made equal to half the axis major of
the ellipse, that is, half of FH; and that between the
tracer and the stud b equal to the height of the arch
or semi-axis minor. The distance between the studs
is thus equal to the difference between the major and
minor axes of the ellipse. In the same way the groin
arch is trammelled, the instrument being adjusted so that
from the tracer n to the first stud o the length is equal
to the height of the arch, and to the other stud p equal to
half the span.

A substitute for the trammel can be formed readily by
using a square in place of the cross, and a slip of wood for
the sweep. The square is placed on the axes, as shown
in Fig. 161. p. 24; two bradawls being thrust through in
place of the studs, and another used to supply the place
of the tracer: by keeping the bradawls pressed against
the limbs of the square whilst the sweep is moving, a
quadrant of an ellipse will be formed.

In the Gothic groin (Fig. 3) the curve of the diagonal
is found by ordinates in the same manner as the one de¬
scribed.

Let A A A A be the piers, as before, BCD the given
arch, and K N L the seat of the groin : divide the quad¬
rant D c into any number of equal parts, and draw from
the divisions the lines 1 k e, 2 i d, &c., meeting the seat
of the groin in e d c b a; then find the larger arch, as be¬
fore, by drawing the ordinates e l 1, dm2, cn 3, making
them equal to the ordinates of the given arch. To find
the curve of the groin from the points on the seat of the
groin e cl c b a, draw the perpendiculars e 1, d 2, c 3, b 4,
a 5, and N M, and make these ordinates equal to the cor¬
responding ordinates of the given arch. This operation
gives only one-half of each arch; therefore, in order to
complete the arches, draw from the points 12 3, the lines
1 q r and 1 s t, and the other lines parallel to the lines
F H K L in the larger arch and groin arch respectively, and
set off on them from the centre line the points of the curve.
The lengths and places of the ribs are found, as before, by
drawing from the seat of any rib, as u v, lines to the
section of the arch a y b at w and x.

In Fig. 4 is illustrated the manner of finding the arches
of a Gothic groin by intersecting lines, as explained in
Figs. 206, 207, p. 30.

Let A A A A be the piers, BCD the given arch, and K N L
the seat ol the groin. Set up the height of the large arch
I G, and ol the groin arch N M, each equal to the height of
the given arch, and from B, F, and K draw the perpendicu¬
lars B v, F z, and K z. J oin B c, and divide the line into any
number of equal parts 1 2 3 4 C; from E draw lines through
the divisions 1 2 3 4 to the circumference of the arc in the
points o p q r, and through these points draw lines from c,
cutting the perpendicular B v in s t u v. Then to find the

PRACTICAL CARPENTRY AND JOINERY.

large arch, join G F, and divide it into the same number of
equal parts as the line B c in the given arch. From I draw
lines through the points ol division; then transfer the di¬
visions of the perpendiculars B v in the given arch to the
perpendicular F z in. the large arch, at stuz; and from G
draw lines to these divisions, intersecting the lines drawn
from I. The intersections give points through which the
curve is to be traced. Proceed in the same way in draw¬
ing the groin arch: divide the line K M into the same num-
ber of parts as B C; draw through the divisions the lines
N e, N /, N g, N h ; and intersect these by lines drawn from M
, to the divisions s t u z, on the perpendiculars K z, trans¬
ferred from B v. The intersections give points in the
curve.

The lengths and places of the ribs are found as before,
by drawing from the seat of any rib, k l, lines to the sec¬
tion o p q, when m p gives the place of the rib, and mp n
its length.

To draw the side arches and groin arches in a Gothic
vault, ivhere the side arches are of the same height as the
arch of the body range.

Plate YI. Fig. 1., Nos. 1 and 2.—Let A b (No. 1) be the
centre of the body range, and EDO the given arch; FGH,
klm side arches, of different spans but the same height; O Q
the seat of the smaller, and S U the seat of the larger
groin: divide the arch C D, as before, into any number of
equal parts, through which draw lines parallel to the
axis of the body range A B: from the points of intersec¬
tion efgh with the seat of the groins o Q and su, raise
perpendiculars to these lines e 1, / 2, &c.; and from the
same points draw lines ea 1, fb 2, &c., perpendicular to
the chords of the arches F 1 H and K N M. Then from the
points efgh and abed set off the lengths of the ordi¬
nates of the given arch, to give the curve of the arches re¬
quired. No. 2 is a vertical section through the axis of
the body range, showing the timbers of the vaults; and on
the under side of the plan No. 1 is shown the method of
finding the diagonal ribs EQ,VU.

Given the arch of the body range of a groined vault,
with the imposts on an inclined line: to find the side
and groin arches.

Let abc {Fig. 2) be the given arch, ilk the seat of the
groin, and E H G the inclination of the imposts, making the
angle geo with the horizon. Proceed by dividing the arch
ABC into equal parts in 1 2 3 4, and drawing ordinates
from them, as before, meeting the seat of the groin in
e f g h L; then draw from these points the lines e a 1, / b 2,
g co, &c., perpendicular to the line a o, and set up thereon
from the points abed H, where they intersect the raking
line E G, ordinates a 1, b 2, &c., corresponding to those in
the given arch; then through the points found, trace the
curve of the arch E F G. To find the curve of the groin,
draw K N perpendicular to I K, and equal to o G, expressing
the rake or inclination of the groin; join I N; draw the
lines ei l,fk 2, g l 3, &c., perpendicular to I K, and upon
them set off from i k l m, on the line I N, the heights
1 w 3 4, &c., of the ordinates of the body range ABC.

To draw the groin rib when the highest point of the
side arch is not in the middle of its width, as in u v d,
right-hand side of Fig. 2.

Divide the body rib qes into equal parts in 1 2 3 4,
and through the points of division draw lines parallel to
Q S, to meet the line p s, which forms a right angle with

p Q. With the concentric dotted quadrants, carry the points
in P s round to meet P f or PQ produced; and from the
points therein draw lines parallel to the rake. Bisect
c D in x, and square up the line x v. On x, as a centre,
and with the radius X c or X D, describe the semicircle
u v w, and draw c tr, the line of the pier produced. From
the points of intersection of the raking parallels Avith the
semicircle, draw lines parallel to Q s, through the plan
of the groin, and intersect these by lines drawn through
the points of the body rib, parallel to the axis of the
body range. Through the points of intersection trace
the curved line e f g h z n h g f e Y, the seat of the groin.

To find the groin ribs.

Through the centre X, draw the line IT w, parallel to
the axis of the body range; and through E, where the
line v z drawn from the summit v cuts the raking line
C D, draw E r parallel to U w. Through c, draw also c o.
parallel to U w. Then on the plan join Y z, Y z, which
are chords to the intersecting line; and draw other two
lines parallel to them, touching the outside of the curve;
and the distance between them will give the thickness
of stuff required for the intersecting rib; and through the
points of intersection of the parallels, that is, through the
points on the seat of the groin efgh, &c., correspond¬
ing to the points 1 2 3 4 5 on the body and side ribs, draw
indefinite lines perpendicular to Y z, Y z. At z, set up
the height n n, corresponding to the height o p of the
side rib, and join Y n: at Y set up the height rD of the
side rib, and draw the raking line z m l, &c. Then the
heights on each side of the side rib a 1, b 2, c 3, d 4, and
E v, set up on the lines below at i 1, k 2, l 3, m 4, z a, will
give the curve of the groin iib.

To describe a Welsh or under-pitch groin; a groin
in which the side arches are lower than the arch of the
body range.

Plate VII. Fig. 1.—Let ABC (No. 1) be the body rib,
and E F G the side rib ; then to find the intersecting ribs,
divide halt the rib E F into any number of equal parts 12 3
F ; and from these points let fall perpendiculars l c, 2d,
3 e, F f, and produce them indefinitely. From the same
points 12 3 draw lines parallel to G E, intersecting l n ;
transfer the divisions from In to l m, by quadrants drawn
from l ; then from the divisions of l m draw lines parallel
to A C, intersecting the body rib A B in the points 12 3a.
From these draAv perpendiculars to A c, through c d e f,
and produce them until they intersect the perpendiculars
from the corresponding divisions of the side rib in g li i I.
Then a curve traced through the intersections will be the
place ot the intersecting ribs upon the plan.

On the inside of the curve so found draw two chords
Hi, Kl: draw two other lines parallel to these to touch
the outside of the curve; and the distance between these
lines will show the thickness of stuff required for the in¬
tersecting rib.

To find the ribs :—Through the intersecting points
g hi i draw lines perpendicular to the chords, hi k i ;
and make the heights c 1, d 2, e 3, I L, measured from the
chord line, equal to the corresponding heights c 1, d 2, e 3,
/ F, measured from the line E G to the curve of the side
rib; and a curve drawn through II 1 2 3 L will be the
mould for the intersecting rib.

To find the mould under the intersecting ribs, or the
cover of the vault ehikg :—On the line A B (No. 2)

STEREOGRAPHY—GROINS.

set off the divisions 12 3 4, corresponding to the divisions

1 2 3 F on the under side of the side rib EFG; and draw
the perpendiculars Ac, 1 d, 2 e, 3 f, 4 g, &c., and make
them equal to eh, c g, d h, e i, f I; then a line drawn
through cdefg will be half the mould required.

The under side of the plan in the same figure shows a
Gothic side arch. The method of proceeding is precisely
the same as for the semicircular arch. The side arch P R
is divided into equal parts in 1 2 3 R; these divisions are
transferred to the body rib c B; and the intersections of the
perpendiculars from the two arches in g h i N, gives the
points through which the curve of the intersecting rib is
drawn. The seat of the intersection may be made a
straight line by reversing the operation: thus, draw the
centre line of the side range R N, and intersect it by the
line b N, from the body rib B c; then join M N, and draw
upon it from the points of intersection of the divisions of
the body rib, the perpendiculars g 1, li 2, i 3, N O: set up
on these the heights corresponding to the same points in
the body rib, to find the curve of the intersecting rib; and
set up the same heights on the perpendiculars drawn on
P 1c, for the curve of the side rib.

In the side vaults s and T, the curves of the side ribs are
drawn at op r, and divided into equal parts, from which
ordinates are drawn to intersect the line o r; and through
the points of intersection, lines drawn parallel to the sides
of the vault, straight in the one case, and curved in the
other, to meet the lines from the divisions of the body
rib, give the place of the intersecting rib.

Groins on a circular plan.

The ribs are described in the same manner as above,
the lines from the ordinates abed (Fig. 2) of the body
range being portions of circles drawn from the same centre
as the lines of the plan. The lower half of the plan shows
the method of backing or bevelling the intersecting ribs :
dotted perpendiculars, i 6, k 5, &c., are drawn from the
intersection of the curved lines ae, b f, eg, &;c. with the
tangent of the curve of the intersecting line on the plan;
and the heights of the corresponding ordinates being
transferred to them, the curve 6 5 3 4 T drawn through
the points thus obtained is the bevel of the rib. Fig. 2,
No. 2, is the development of the covering of the vault
L R N; and requires no description.

To draw a Gothic groin in which the transverse axis
is a curve joining the summit of the side arch to the
summit of the body range.

Let ABC (Fig. 3) be the body range, ikl the side
arch, and S S the section on the axis H M : draw the dia¬
gonal E H G, and divide it into equal parts in a b c d e H ;
through these points draw perpendicular's to both axes, and
produce them indefinitely. Then to find the spandrels,
transfer the heights a 1, b 2 of the ordinates of the body
range, to the corresponding ordinates on the line 1 L for
the arch lR L; and to find the intersections of the ribs 1 g,

2 h, 3 1, &c., with the body rib A s, transfer the heights
ag, b li, ci, d 1c, el to the line M R in K m n o p; then
1 k, 2 m, 3 n, 4 o, 5 p, &c., will be the curve of the
spandrel rib i g, 2 h, &c.

The diagonal or intersecting rib is found by transferring
the heights of the ordinates of the body range to the ordi¬
nates a 1, b 2, c 3, &c., of the diagonal.

Groining on an octagonal plan.

Plate VIII. Fig. 1.—In the left-hand compartment,

the groin is regular; and the method of procedure will
be understood from the descriptions already given. The
chords of the arches are divided into the same number of
equal parts, and the opposite corresponding divisions are
joined by lines whose intersections give the seats of the in¬
tersecting ribs, which in this case are represented by cur¬
ved lines. The thickness of stuff required for the intersec¬
ting rib is found as in the underpitch groin, by drawing
the chords and tangents to the curved lines of the plans.

The centre compartment shows the manner of finding
the jack-ribs.

The right-hand compartment shows the method of find¬
ing the curve of the rib of the body range and diagonal,
when the plan of the intersecting ribs is a straight line in
place of a curve. It will be fully understood by inspection.

Groining on a circular plan.

Fig. 2, No. 1. — The cox-responding ordinates in this
figure have the same letters and numbers attached, so
that a mere inspection will suffice to show the method of
finding the lines.

Fig. 2, No. 2—Shows the method of describing the
mould for the under side of the intersecting rib K L; and
No. 3, that for the rib L I: the manner of backing the
intersecting rib is as before described.

N M o, No. 1, shows the manner of arranging the jack-
ribs.

To find the angle ribs of a cono-cylindric groin.

Let A D B (Fig. 3) be the conic arch, DCE the axis of
the cone, and E its apex: also let L K be the diameter of
the cylindric arch, and r M a its axis. Draw the seat of
the intersecting rib FMG; also the dotted line mG: divide
the semicircle l4k into any number of equal parts 1 2
3 4, and draw the ordinates 1 u, 2 t, 3 s, 4 r. Then from
the points of intei'section of the ordinates with the line
L K, draw the lines unm, t o l, s pic, r M a, &c., parallel
to the axis r M a. At the points where these intersect
the seat of the diagonal rib, draw ordinates n 1, o 2, p 3,
M 4, &c., equal to the ordinates of the side arch, which
will give the curve required. Or from m l Jc a, and
the l-emaining points of intersection in m G, let fall per¬
pendiculars to A B, meeting it in ill g b, &c. From the
point 4 in A B, as a centre, whei’e the perpendicular let
fall from the intersection of the axis of the side arch with
the seat of the diagonal meets A B, and with a radius
equal to r L or r K, describe a semicii'cle; and from c,
where the axis of the conical vault meets A B, with the
l'adii ci, c h, &c., describe ai'cs cutting the semicircle in
fedc, &c., which will give the places of the ordinates.

Plate IX.—Let abc (Fig. 1) be the profile of the
side arch. Bisect A c in D, and draw D B and A d per¬
pendicular to AC: join A B: divide the line A B into any
number of equal-parts, and from D draw lines through the
points of division 1 2 3 4, cutting the profile of the arch in
efgh; and from B draw lines through these last points,
meeting the line A d in a b c d.

Then to find the diagonal ribs L L L:—On KH, the seat
of the centre rib, raise the perpendiculars K I H d: make
K I equal to DB; and transfer the divisions A abed of
the line A d on the side arch to the line H d. Join I H,
and divide the line into the same number of equal parts
as the line A B. From K draw the lines K 1, K 2, K 3,
K 4, produced indefinitely. Join la, lb, i c, id: and
through the intersections of the two series of radial lines

PRACTICAL CARPENTRY AND JOINERY.

draw the curve of the rib H e f g h I. The side rib
G F E is found in the same manner.

Fan-tracery vaulting with centre pendant.

In this species of vaulting {Fig. 2), all the main ribs
have the same curvature, and form equal angles with
each other at the springing.

The plan shows the arrangement of the ribs. Those
radiating from the imposts are all of equal curvature
and equal length, as at A B in the profile; and are bounded
by the curbs C F, which are quadrants drawn from the
imposts as centres. D D is the plan of the pendants, the
ribs of which have all the same curvature, as shown at
b c in the profile. The jack-ribs between the curb of the
pendant and the curbs of the fan arches lie horizontally.

In Fig. 3 the fan ribs are of the same curvature, but
are increased in length from the sides to the centre; and
the ridge ribs are necessarily not horizontal, but rise from
I and L to G on the plan, seen also in the profile l g.

Let A B c be the profile of the side rib; then on D G,
the diagonal of the vault, set off D H equal to A c, and
draw H E perpendicular to D G; make the curve of the
• rib D E the same as A B, and continue it to F, the length
of the longest rib ; then the height G F will be the apex
of the ridge ribs. The length of the other ribs is found
thus:—From the point D as a centre, draw arcs from a c,
the intersection of the ribs with the axis I G, to meet
D g as at b d ; and draw b e, d f perpendicular to D G.
Then D e will be the profile of the rib d a, and D f that
of D c, and so on for the other ribs.

Groined vault on an octagonal plan, with an octa¬
gonal skylight.

Fig. 4.—The ribs of the octagonal groin are found by
the method of intersection as in Fig 1 . The chord line
A B of the side arch is divided into equal parts, and lines
are drawn from c through these to meet the curve; through
the points of intersection d ef, lines are drawn from B, and
produced to meet the line A c in a b c. The chord lines
D E, G I on the plan, are similarly divided into equal
parts, and the divisions of the line A c are transferred
to the perpendiculars D c, G c. The intersections of the
lines drawn from F and H, with those drawn from E and I
to the divisions in D c, G c, through these divisions, give
the points d e f d ef in the curves of the diagonals.

To find the ribs of a groined vault on an irregular
octagonal plan, with a, pendant in the centre.

Plate X.—abcdef {Fig. 1, No. 1) is the semi-plan
of the vault. Let CHD be the profile of the arch of one
of the larger sides. To find n r o, the profile of one of the
shorter sides: Bisect C D and n o in I and q respectively,
and draw I it perpendicular to C D, and q r to n o ; make
qr equal to IH, join hd ,n r, and draw the perpendiculars
DC, ni, o p: divide the chord lines HD, nr, or, into
the same number of equal parts, and draw the intersect¬
ing lines, to find the curve of the smaller arch as before.

Proceed in the manner already described to find the
profiles of the ribs M o, c s, c O, 0 0, D o, as shown by
the diagrams s u t, Ac.

The length and profile of the jack-ribs PP, PvR, are found
by drawing lines from their intersection with the ribs M 0,
K O, as shown on the left-hand side of the figure at M N K.

Fig. 1 , No. 2, shows the mode of construction: a a is the
girder supporting the floor above the groined ceiling; B B
is the ridge of the ceiling, the seat of which is A G F in the

plan No. 1; c C are the main ribs; h h, the diagonal rib
corresponding to it R in the plan ; g g are the ribs P p, and
jack-ribs of the side arches; // are the ribs of the pen¬
dant marked T T on the plan, all of equal length and
curvature; C c, an iron bolt by which the pendant is sup¬
ported; and k k, the curb marked z y 0 t w on the plan.

PENDENTIVES.

Plates XI., XII.

If a hemisphere or any other portion of a sphere a cb
(Fig. 348), be intersected by vertical planes e d, equi-dis-
tant from its centre, the angular portions h lx, between
the boundaries of the planes, are pendentives.

In like manner, in a conoid acb (Fig. 349), the angu¬
lar portions fffi between the intersecting planes, e d, are

Fig. 318.

pendentives, and the same in an ellipsoid. In these
figures, the convex surfaces of the hemisphere and con¬
oid are shown, but in
concave surfaces which
form the pendentives, as
in the following figure,
where A and B (Fig. 350)
are two of the contiguous
intersecting planes; C,
part of the concave sur¬
face of the vault; and D,
one of the pendentives.

It is scarcely necessary
to remark, that the re¬
sulting curve of the in¬
tersection of a spherical vault by a plane, will be a por¬
tion of a circle, that of an ellipsoid will be an ellipse
when the plane is parallel to the major axis, and that of
a conoid a hyperbola.

To cove the ceiling of a square room with spherical
pendentives , having a circulr skylight in centre.

Plate XI. —Let abcd {fig. 1, No. 1) be the plan of
the room: draw the diagonals of the square, and from
their intersection E describe the inscribing circle abcd,
which will be the plan of the hemispherical vault. On
any of the sides of the square ab,BC, describe a semicircle
which will be the curve resulting from the intersection
of the hemisphere by the plane of the side of the square.
To find the seat of the ribs: From the centre E describe a
circle of the size required for the skylight, and draw the
double line showing the breadth of the curb b. Divide
the circle into as many equal parts as there are ribs
required, and from the points of division draw radii for the.
centres of the ribs. Set off half the thickness of the rib

vaulting, it is of course the

Fig. 350.

PLATE XI.

\P'EM [DENT!]VIES.

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STEREOGRAPHY—PENDENTIVES.

on each side of the radial lines, and draw parallel lines
representing the sides of the rib. If the ceiling is to be
finished with plaster, the ribs should be nowhere more
than 12 inches apart.

No. 2 is a section on the line H I of the plan. Bisect
the line F G in s, and draw the semicircle for the resulting
line of the intersection of the hemisphere. From s, with
the radius E A, describe the segment aaa representing the
section of the spherical surface on the line H I; draw the
curb c from the plan, as shown by the dotted lines; and
find the intersection of the other ribs with the side arch
and the curb, by drawing lines from the plan, as from
d to / and from e to g. The projections of all the ribs
except the central rib and side ribs a a will be elliptical
curves.

To find the length of each rib.

From the centre E, with the radius E A, describe the
arc A k, and draw k n parallel to the side of the plan.
Then with the same radius, from I as a centre, describe the
arc n t for the under side of the rib A h. From E describe
the arcs d l, r m, &c., and draw l o, mp, to intersect n t
in o,p; then o t and p t will be the lengths of the ribs d e,
r f respectively. By drawing the lines o 4, p 5, and t u,
and describing arcs with the same radius as t n or ea,
all the ribs may be drawn separately, as Nos. 4, 5, 6, 7, 8.
The double dotted curves A k, d l, r m, show how the
bevel of the end of the ribs is obtained.

Fig. 2 is a spherical vault less than a semicircle, with a
plain fascia introduced in the vault above the pendentive:
the curve resulting from the intersecting planes is the seg¬
ment of a circle.

abcd is the plan of the room, E is the centre of the
segment, G m H L is the plan of the double curb over the
pendentives, and k the curb of the skylight. From
the centre E on the line E A, make E F equal to r F, and
from F describe the curves T> c, d b of the ribs DG, G a.
The dotted lines drawn from the plan show the manner
of obtaining the section of the curbs c d, b.

In the section No. 2, make r F equal to r F in the plan,
and F is the centre of the segment IK, el o. The posi¬
tion of the ribs is found by drawing lines from the plan,
as g h, m p.

Fig. 3, No. 1 and No. 2, are the plan and section of a
conical pendentive: ABCD is the plan of the room, and
the base of the cone is the inscribing circle abcd, de¬
scribed from E, and shown by a dotted line.

To find the ribs:—Make E O, No. 1, equal to the height
of the cone, and join AO, co. From the plan of the curb
draw the dotted lines intersecting A O and C O in F and
G. From the centre E describe the arcs b l, c Jc, di, e h, ’
f g, meeting E c in Iki h g; and draw the perpendiculars
l m, k n, i o, hp, g r, cutting the line c G. Then m G will
be the length of the rib b, n G the length of c, and so on.

To find the hyperbola resulting from the intersection
of the sides:—Make the perpendicular b s equal to l m, ct
equal to kn, du to io, ev to hp, and fw to g r; then
trace the curve through s t u v w.

In the section No. 2, produce A B to x and z, and make
E D equal to E o, the height of the cone; join z D and
x D. Find the hyperbola acb, as in the plan, or transfer
it by ordinates. Find also the intersections of the ribs
with the curve ACB, by drawing lines from the plan, as
* y ; and find their intersections with the curb b in the

same manner. Then from the intersection of the ribs
with the line acb, as at y, draw lines converging to D,
for the vertical projection of the ribs.

Pendentive formed by the intersection of an octagonal
domical vault by a square.

Let abcd (Fig. 4, No. 1) be the plan of the square
apartment, c e f g h I k d the plan of the octagonal
vault, and A K I c the curve of one of the longest or
diagonal ribs A c. Then to find any of the angle ribs, as
i>P:—Produce c D to M, and divide the portion M K of the
rib A c into any number of equal parts, as 1 2; and through
the points of division draw 1 l, 2 to, cutting the line D P
in l and m. On D p erect the perpendiculars 1 1, m2,
P n, and make them equal to the corresponding ordinates
l 2, m2, K n ; and through D 1, 2 n, draw the curve of
the rib.

The intermediate parallel ribs are all portions of the
same curves, and their lengths and bevels are found by
drawing lines e 1, / 2, g 3, &c., from the intersections of
the lines of the ribs with the side of the square to the
points 12 3, &c., of the rib A c.

To find the projections of the ribs in the section No. 2:—
From the points efgc in the plan, draw the perpendicu¬
lars e I,/ 2, g 3, C c, and transfer to them the heights of the
perpendiculars a 1, b 2, c 3, d M, as shown by the dotted
lines d i, &c., which will give the points 1 2 3 O, through
which the curve of the wall rib A o is to be drawn, and
the same points also give the intersections of the jack-
ribs Avith the wall rib.

Plate XII.— To draw an elliptical domical pen¬
dentive roof.

Let hkl m (Fig. 1, No. 1) be the plan of the apartment:
draw the diagonals li l, lc m, and through c the lines E F,
G H, parallel to the sides of the apartment. To find the cir¬
cumscribing elliptical base of the dome :-—From the centre
c describe the quadrant u 2 3, and bisect it at 2 ; and
through 2 draw 12 t parallel to the side of the rectangle
h k ; join t u, t v. Then from h draAV h E, h G parallel to
t v, t u, respectively, cutting the lines E F, G H in e and G;
and complete the parallelogram abdc, which will be the
circumscribing rectangle of the ellipse forming the base of
the dome. The ellipse of the curb is proportioned by
draAving a b c d to meet the diagonals of the rectangle
h k l m.

On the line B D (No. 3) describe the semicircle B r D, as
the section of the dome on its minor axis. Then, as the
dome may be considered a solid, formed by the revolu¬
tion of the semi-ellipse egf round its axis E F, it fol¬
lows that all sections of it by planes parallel to G H will
be circles. Therefore, to find the Avail rib k l on B D,
from the centre F, and with the radius c u, describe
the semicircle n p o. For the same reason, all sections
made by planes parallel to E F will be similar figures.
Hence n p o (No. 2), the wall curbs for the sides h k. m l,
will be the circumscribing ellipse of v t u on the plan.

The other ribs may be found by the method of ordi¬
nates ; but they are much more accurately and easily
drawn by the trammel, in the manner shown at E. The
points g h i Jc of the trammel being set on the major and
minor axes of the ellipse, and d e being made equal to the
minor, and df to the major semi-axis, the distance between
d and e will necessarily remain constant in describing
all the figures abode, but / will be moved nearer to

PRACTICAL CARPENTRY AND JOINERY.

e for the curve of each rib in every quadrant. Fig. A
shows the manner of finding the length of the rib marked
adg on the plan. The line a c {Fig. a) is made equal to
a c on the plan ; and the lengths a d and g c correspond
to the lengths similarly marked on the plan, showing the
intersections of the rib with the wall, and with the curb.
Perpendiculars d eh and g f drawn from d and g, give
the proper lengths of tbe rib on the curve. The lengths of
the ribs B c D E are found in the same way, as shown by
the figures B, c, D, and E.

A domical pendentive of an irregular octagonal plan
over an apartment, the plan of which is a parallelogram.

A B c D {Fig. 2, No. 1) is the plan of the apartment:
the mode of proportioning the ellipse of the base of the
dome, and the octagons of the curbs, is the same as in the
last figure. In No. 2 the elliptic curves of the centre rib
on the line of the major axis, and also the wall rib on the
side A B, are shown. No. 3 is the section across the centre
of the plan. The method of finding the other ribs will be
found by inspection, as all the corresponding parts are
similarly lettered and numbered.

DOMES.

Plates XIII., XIV., XV.

The word dome, derived from the Latin domus, a
house, is employed among the moderns to signify the ex¬
terior form of a vaulted roof springing from a polygonal,
circular, or elliptic plan. Domes are frequently used to
cover vaults, the concave ceilings of which are termed
cupolas, from their resemblance to an inverted cup. Some¬
times the dome, or exterior surface, coincides in form with
the cupola which it covers, but in constructions in carpen¬
try the dome frequently does not indicate the internal
form of the vault.

Domes in carpentry are composed of a certain number
of ribs, placed vertically in planes, which, in spherical
domes would, if prolonged, pass through the vertical axis
of the dome. When the surface of the dome is a surface
of revolution, all the ribs have the same exterior contour
or profile. In domes on polygonal plans, the angle ribs
at the intersections of the sides of the solid, alone, are in
planes which pass through the axis. The ribs generally
spring from a wall-plate or curb, forming a ring laid on
the walls which support the dome, and this ring should
be made sufficiently strong to resist the lateral thrust of
the ribs, so that the walls may have to support the down¬
ward pressure or weight of the dome only.

The central point in the curved surface of a dome is
called its pole or centre ; the imaginary straight line
drawn from the pole to the base, is its axis. When the
height of a dome is greater than the radius of its base, it is
said to be surmounted; when less, surbased. When there
is an aperture at the pole of a dome, it is called its eye.

An oblong surbased dome on a rectangular plan.

Plate XIII.—The plan, Fig. 1, No. 1, shows the mode
of placing the ribs. No. 2 is the section across the shortest
diameter of the plan; and No. 3, the section on the line of
its longest diameter. The curve of the rib e n e n F, and
of all the nbs paiallel to it, is found by dividing the seg¬
ment c n e n D, No. 2, into a number of equal parts, and

drawing lines from the divisions to meet the diagonal A B,
No. 1, in the points f g h i, and from those points drawing
lines parallel to CD, cutting E F, and produced indefinitely;
then transferring the heights of the ordinates on CD, a 1,
b 2, c 3, &c., to the corresponding ordinates on E F.

The curve of the diagonal ribs A 1: B is also found in the
manner above described, as the lines show. The positions
of the purlins n m n, and their projections on the plan,
are found by drawing lines from their sections at n e n
to meet the diagonal.

A surbased dome on an octagonal plan.

In Fig. 2, No. 1, the position of the ribs is shown, and
also the manner of finding the curve of the angle ribs.
No. 2 is a section on the line A B. On the plan No. ],
the rib standing over C G is drawn at G 1 2 3 I, c, and
divided into equal parts, from which ordinates are drawn
to the chord line, and produced to the line of the angle rib
H I; from the points h i lc l, in which these intersect H I,
the seat of the angle rib, ordinates are drawn; and the
heights F c, d 4, e 3, &c., being transferred to them, give
points through which the curve of the angle rib is to be
traced.

Fig. 3, Nos. 1 and 2, are the plan and section of a
hemispherical dome; and Fig. 4, Nos. 1 and 2, are the
plan and section of a dome which is the half of a prolate
spheroid on a circular plan. The corresponding parts in
these plans and sections are connected by dotted lines;
and the construction is so obvious that no description is
required.

Manner of dividing conical, spherical, and other
vaults, into compartments and caissons.

Plate XIV.— Let No. I, Fig. 1, represent part of the pla¬
fond of a conical vault, and N o. 2 part of a vertical sec¬
tion through its axis. Having divided the plafond into
the number of panels and ribs or fields between them that
is suitable to the design, the heights of the caissons and of
the horizontal fields between them are found as follows: —
On A e, No. 1, draw the circle b b, making it a tangent to
the generating circle of the vault, and to the lines A b,
A b ; and through its centre draw b F perpendicular to A e
Draw also the circle a a tangential to the lines A a, A a,
the width between which is equal to the width of the ribs
or fields between the panels. Produce the side of the
cone CD, No. 2, to cut the perpendicular b F in e, and
from e as a centre describe two circles, cd,fg, equal to
the circles b b, a a, No. 1; and through the centre e draw
the line e B perpendicular to the side of the cone c D, and
cutting the axis C e produced in b: draw also B c, B/, Bf/,
B d. Then, to find the height of the first field: In the
section No. 2, through the point D draw a line o D l paral¬
lel to B g, cutting the produced axis in o ; and with the
centre F, on the line b F', describe the circle k l equal to
fg; and draw lc o, cutting the side of the cone in h, which
is the height of the first field. Through the point h last
found, draw the line n lb o parallel to B d, and from the
centre G, on the line b F', describe the circle m n equal to
bb, and having n o for its tangent; and join mo: the
point where this line cuts the side of the cone is the
height of the first caisson. Proceed in the same manner
with the circles f', G', &c.

Manner of dividing a Gothic vault into compartments.

Fig. 2, No. 1, is a portion of the plan of the vault;

11 the point c is on the line of the axis produced; a a is

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PLATE XV.

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STEREOGRAPHY—NICHES.

tlie width of the panel, and b b the width of the field
between the panels. From the centre d, the circles e e,
ff are drawn, touching the lines ca, cb, cb, ca, pro¬
duced; and on the line drawn through d, perpendicular
to d c, the centres of the other circles are found.

Having determined the commencement of the divisions,
as at c, describe from that point, as a centre, the circle a d
equal to the circle ff, in No. 1; and through C draw a
line, c b, to the centre of the arc forming the side of the
vault, and cutting the axis in c. Then, through c draw
from the circumference of the circle a d the tangents c a,
c d, and also produce them beyond the centre b; and be¬
tween them, from b, as a centre, describe the little circle gg.
Through the point /, where deb cuts the arc of the vault,
and which gives the height of the first field, draw gfc-,
and from D, as a centre, describe the circle e e, equal to
e e in No. 1, and touching the line g f e; and through its
centre draw D b to the centre of the arc of the vault, cut¬
ting the axis in c. Through c draw the tangents e c, e c,
and produce them to beyond 6; and from b, as a centre,
describe the circle li h between them. It will be seen, by
inspection of the figure, how the tangents determine the
position of the circles D if D", C C c" on the perpendicu¬
lars d c"; and how, by their intersections with the profile
of the vault, the heights of the divisions are obtained.

To determine the heights of the divisions of a spherical
vault.

Fig. 3, No. 1, is part of the plafond of a spherical vault,
one-lnilf showing the divisions, and the other the mode of
framing. To find the height of the divisions:—Produce
the meridian lines d b, d b, representing the width of the
panels, and draw the circle b cb, touching the generating
circle in G, and the lines in b b ; draw also the meridians
d c, d c, representing the width of the field between the
panels, and describe the circle H. Through the centre of
the circles, a, draw a b indefinitely, and perpendicular to
d a. Then having fixed the first horizontal division on
the profile of the vault, No. 2, draw through it the line
E to n, and draw the circle H, touching it in to, and the
larger circle G, touching the lesser one in w; H and G
being respectively equal to the lesser and greater circle in
No. 1. Then draw the second line E to n tangential to the
circle G, and describe the circle n', touching this line in
n\ and so proceed, drawing the tangents and the circles
H and G alternately; and the intersections of the tangents
with the profile of the vault determines the heights of the
divisions.

To determine the horizontal divisions of the radial
panels of a cylindrical vault.

Trace the angle A c D (Fig. 4) representing one of the
vertical divisions of panels, and by means ot the arc c d
and the arcs intersecting ate, draw d/ bisecting the angle
ADO: / is the centre of the circle, which gives the size
of the first division. Through the points of intersection
of the circumference of the circle, with the centre line E C,
draw a g parallel to AD; bisect a g c, as before, to find /,
the centre of the second circle, and so on. Or, from C de¬
scribe the arc F B, and draw B /; then describe the arc
a b, and draw bf parallel to B/; the centres / being found
equally well by either method.

To determine the caissons of an ellipsoidal vault.

Plate XV. Fig. 1, No. 1, is a portion of the plan, and
No. 2 is the profile of an ellipsoidal vault, dhe circles

M m have their centres on the vertical line as before, and
their diameters are determined by the angles made be¬
tween the meridians c D, c D, b D, b D, indicating the divi¬
sions of the plafond. The points //,//, on the profile,
are determined by the intersections of the tangents to
these circles, which are also tangents to the curves G L,
n L, K L. The first of these, G L, is determined in the
manner we shall presently describe; the third, K L, is such
as to coincide with all the tangents that can be drawn
from the lower circumference of the larger circle, in all its
positions on the vertical line; and the second, H L, coin¬
cides with all the lower tangents of the smaller curve.

To describe the curve GL:—On the major axis of the
ellipse adc (Fig. 2), let a and b be the foci; divide the
profile A B into any number of equal parts in the lines 12 3
4 5, and join a 5, b 5, a 4, b 4, &c.; then bisect the angle
a 5b in c, by the line 5 c li, cutting the minor axis pro¬
duced in h\ and in the same manner bisect all the angles
formed by the lines from the foci, meeting in the divisions
1 23 4, &c.; and draw lines through defg, cutting the
minor axis in k l to n, then draw the curve o h, coinciding
with their intersections.

In Fig. 3, No. 1 is the plan of a dome, No. 2 its trans¬
verse, and No. 3 its longitudinal vertical section. The posi¬
tion of the circles opo'p' o" P" o'", on the vertical line, are
found as in the former case, and the divisions on the trans¬
verse profile of the dome are obtained by the intersection
of the tangents. Then, to find the divisions on the longi¬
tudinal section, draw the circumscribing parallelogram
B S IJ T, No. 1, and the diagonals R U, S T. Draw the di¬
visions from the profile No. 2 to the transverse axis A c,
No. 1, cutting the diagonals in Imnoprst, and through
these points draw lines parallel to A c, and the points
wherein these intersect the major axis B D, give the divi¬
sions on the longitudinal profile, Fig. 3.

NICHES.

Plates XVI., XVII., XVIII.

Plate XVI. Fig. 1, Nos. 1 and 2.— Spherical niche
on a semicircular plan.

The construction of this is precisely like that of a sphe¬
rical dome. The ribs stand in planes, which would pass
through the axis if produced. They are all of similar
curvature. No. 2 shows an elevation of the niche, with
the manner of finding the projections of the ribs from the
plan. No. 3 shows the bevelling of the back ribs, ah,
against the front rib, at fgh on the plan; a b is the
bevel of a, and b c of b.

Fig. 2 .—A spherical niche on a segmental plan.

No. 1 is the plan. The dotted lines at fg, hi show
the manner of finding the representation of the ribs in
the elevation \ a b and c d are the bevels of the back ribs,
where they abut on the front rib. In No 3, the quadrant
fg is drawn with the same radius as the plan of the
niche D A, and the lengths and bevels of the back ribs are
found by taking the distances f a, gb, from the plan, and
setting them on the line F H.

Fig. 3 .—A niche, the plan of which is a semicircle,
and its elevation a circular segment.

The plan No. 1, and elevation No. 2, will be understood
on inspection. No. 3 shows the manner of drawing the

PRACTICAL CARPENTRY AND JOINERY.

back ribs. With the radius hf equal to DA, No. 1, or
E a, No. 2, describe the segment F G. Draw H G, and make
G Jc equal to the height of the segmental head of the niche;
and draw k F at right angles to G H. Then F c will be
the centre back rib i d ; and the lengths and bevels of the
others will be found in the same manner as before.

Fig. 4.— A niche, of which both the plan and eleva¬
tion are segments of a circle.

No. 2 is the elevation of the niche, being the segment
of a circle whose centre is at E. No. 1, ABC, is the plan,
which is a segment of a circle whose centre is D. It may
be made of any depth: the manner of finding the ribs is
the same. Having drawn on the plan as many ribs as
are required, radiating to the centre D, and cutting the
plan of the front rib in a, b c, d e\ then through the
centre D draw the line G H parallel to AC; and from D
describe the curves m l, A G, c H, cutting the line G H ;
and make D F equal to E o, No. 2. Then from F as a
centre, describe the curves l l and Gin, for the depth of
the ribs; and this is the true curve for all the back ribs.

To find the leno'ths and bevel of the ribs:—From the

centre D describe the quadrant and arcs afbg, d, h, &c.,
and draw ff,gg, h h perpendicular to D H, cutting the
curve 11, and the lines of intersection will give the lengths
and bevels of the several ribs.

Fig. 5.—A niche ivhose plan is the segment of a circle
and its elevation a semi-ellipse.

Let D in the plan (No. 1) be the centre of the segment. ,
Through D draw E F parallel to A c, and continue the
curve of the segment to E F. Then to find the curve of
the back ribs:—From him n, any points in the curve of
the front rib (No. 2), let fall perpendiculars to the line
AB, cutting it in abed. Then from D as a centre, de¬
scribe the curves a e, bf, eg, e h, d h, and from the points
where they meet the line E F, draw the. perpendiculars
e k, f l, g m, h n, h o, and set up on e k the height e k of
the elevation, and the corresponding heights on the other
ordinates, when E klmno will be points, through which
the curve of the back rib may be traced. The manner of
finding the lengths and bevels of the ribs is shown on the
other side of the figure, and does not require description.

To draw the ribs of a niche elliptic in plan and
elevation.

Plate XYII.— Fig. 1: Let No. 1 be the plan, and No.

2 the elevation of the niche. The ribs being all portions
of ellipses, may be drawn by the trammel d f e g, as
shown at No. 4. The rib c, in the elevation, is seen at a D
in the plan No. 1. The bevel of the end li i is seen at A a
in No. 3, and that of the end ef at b c. It is not neces¬
sary to describe it more minutely.

To draw the ribs of a niche elliptic in plan and ele¬
vation, when the ribs are at right angles to the curve at
their points of junction.

Fig. 2: Let ABC (No. 1) be the plan of the niche, and
No. 2 its elevation. Set off the places of the ribs on
ABC. From B as a centre, with any sufficient radius, de¬
scribe a circular segment H I; join H s, I s, H t, I t. Bisect
the angles H s i, H t I, by the lines s u E, t v F, meeting
the centre line B D of the niche produced in E and F.

Complete the parallelogram agbd, and draw its dia¬
gonal G D. In B D take any points o p r, and through
them draw the lines o l, p m, r n, parallel to D A, and
meeting G D. Draw then l g, m h, n i parallel to ga;

and in the parallelograms thus formed, draw the elliptic
quadrants shown by the dotted lines, all parallel to the
original curve A B. The intersections of these curves
with the seats of the ribs will give points on which the
heights of the front rib at a 1, b 2, c 3, d 4, e f, are to be
set up, as f shown in Nos. 3, 4, and 5.

To draw the ribs of an octagonal niche.

Fig. 3: Let No. 1 be the plan, and No. 2 the elevation
of the niche. It is obvious that the curve of the centre
rib H G will be the same as that of either half of the
front rib AG, F G. In No. 3, therefore, draw abode,
the half plan of the niche, equal to abchg, Nol, and
make DGE equal to half the front rib. Divide D G into
any number of equal parts 1 2 3 4, &c.; and through the
points of division draw lines parallel to A G, meeting the
seat of the centre of the angle rib c E in ilcl m n o. On
these points raise indefinite perpendiculars, and set up on
them the heights a. 1 in i 1, b 2 in k 2, and so on. The
shaded parts show the bevel at the meeting of the ribs
at G in No. 1.

To draw the ribs of an irregular octagonal niche.

Fig. 4: Let No. 1 be the plan, and No. 2 the elevation
of the niche. Draw the outline of the plan of the niche
at A B c D E F (No. 3), and draw the centre lines of the
seats of the ribs BG,HI,CG,KG,DG, EG; draw also G L F
equal to the half of the front rib, as given in the eleva¬
tion No. 2, and divide it into any number of equal parts
1 2 3 4. Through the points of division draw d 1, c 2,
b 3, a 4, perpendicular to G F, and produced to the seat
of the first angle rib G E. Through the points of inter¬
section draw lines parallel to the side ED of the niche,
meeting the second angle rib D G; through the points of
intersection, again, draw parallels to D c, and so on. The
curve of the centre rib is found by setting up from nop
q G the heights d 1, c 2, &c., of G F, on the parallel lines
which are perpendicular to K G. The curve of the rib
B G or E G is found by drawing through the points of
intersection of the parallels, perpendiculars to the seat of
the rib, and setting up on them, as at h m r I G, the
heights d 1, c 2, &c. No. 4 shows the rib c G, and No.
5 the intermediate rib H I.

The p>lan of a semicircular niche in a concave cir¬
cular wall being given, to find the ribs.

Plate XYII I.— Fig. 1: Let abc (No. 1) be the plan
of the niche, and Ape the line of the wall. Join AC, and
bisect it at D; and draw the plan of the ribs, l s, n u, p h,
&c., and their elevation, as in No. 2, finding their inter¬
sections on the plan at r s, t u, 1 l, l m, n o, p.

The ribs being in this case segments of a sphere, will
all have the same curvature; and their lengths will be ob¬
tained by describing the quadrant ABC (No. 3), in which
the radius C A is equal to A D, No. 1; and their lengths
and bevels at their intersection with the front rib l m,
no,p (No. 1), or e fk, No. 2, will be obtained by transfer¬
ring the lengths r l, sm,t n, u o, &c., from the plan No. 1
to the points abode, &c., on the line A C, No. 3, and draw¬
ing the perpendiculars a f b g, ch, d i, ek. The back rib
i)wa:,No. 1, a b c, No. 2, and D, No. 3, is a circular segment,
its outer edge described from the centre D, No. 1, with the
radius D v, or with the radius CD, No. 3, and the curve
of its inner edge with the radius D y, No. 1.

The front rib standing over Ape in the plan is a
semi- ellipse, found as shown in Nos. 4, 5, 6. In No. 4 make

2LATF2. ZT.

AN ©LI

IB Li A © K IE"

iii.

. 1 *

f White del

,■> Feet

JW.howiy J~c.

STEREOGRAPHY—FORMS OF ROOFS.

ADC equal to AD c, No. 1 ; describe the semicircle ABC,
draw deb perpendicular to A c, and describe tlie curve of
the wall A EC. The figure is thus a plan of the niche ;
and in like manner, in No. 5, A B c is an elevation ot half
the niche on the line A c of the plan, or it is a section on
line B D of the plan. Divide the curve EAEC, No. 4, into
a number of equal parts 1 2 3 4 5, and draw 1 a, 2 6, 3 c,

4 d, 5 e, perpendicular to A C, and transfer the lengths E1,

1 2, 2 3, &c., from D towards A and C, on the line ADC, No. 6,
and draw l a, 2 b, Sc, &c., perpendicular to A C. To find the
heights la, 2 b, &c., transfer the divisions abode of the
line D C, No. 4, to g e d c b on the line AC, No. 5, and make
c / equal to D p, No. 4. Then draw the perpendiculars g o
em, &c., and transfer the heights to the corresponding or¬
dinates in No. 6, as go to DB, fn to D i, em to 1 a, d l
to 2 b, &c.; and to complete the curve more exactly, divide
the last space into two in the point g, No. 4; and draw g f,
and transfer the points, in the same manner, to Nos. 5 and
6, for the ordinates ah, gf.

To find the mould for the front ribOn the line A B,
No. 7, make the divisions xopqrstB respectively equal
to those of the curve aTcdef c, No. 6; draw A g, o h, p i,
q k, r l, s m, t n, perpendicular to A B, and make them equal
respectively to D E, a 1, b 2, c 3, d 4, e 5, fg, No. 4; and
through gliiklmnB, draw the curve g B, which is the
edge of the mould of the front rib.

°The plan of a semicircular niche in a convex circu¬
lar wall being given, to find the ribs.

Fig. 2: Let E B F (No. 1) be the plan of the niche, and
E D F the curve of the wall. Draw the ribs i k, l m, n, &c.,
as in the last figure, and draw A c perpendicular to D B.
In No. 2 the lines of the elevation are found in the man¬
ner indicated by the dotted lines. In No. 3 the lengths
and bevel of the ribs are found as in the last problem; and
Nos. 4, 5, 6, and 7 show the manner of describing the front
rib and its mould, which must be so easily understood, if
the construction of the foregoing figures lias been com¬
prehended, as not to require detailed description.

ANGLE BRACKETS.

Plate XIX.

Plate XIX.— Let cab (Fig. 1) be the elevation of the
bracket of a drive, to find the angle bracket.

First, when it is a mitre bracket in an interior angle, the
ancde being 45°, divide the curve c B into any number ot
equal parts 1 2 3 4 5, and draw through the divisions the
lines 1 d 2 e 3/14 <7, 5 c, perpendicular to A B, and cutting
it in defgc ; and produce them to meet the line D E, re¬
presenting the centre of the seat of the angle bracket;
and from the points of intersection hi kl c, draw lines
h 1, i 2, k 3, l 4, at right angles to D E, and make them
equal —h 1 to d 1, i 2 to e 2, &c.; and through f 1 2 3 4 5
draw the curve of the edge of the bracket. The dottec
lines on each side of D E on the plan show the thickness
of the bracket, and the dotted lines u r, vs,wt, show the
manner of finding the bevel of the face. In the same
figure is shown the manner of finding the bracket for an
obtuse exterior angle. Let die be the exterior ang e:
bisect it by the line I G, which will represent the seat ot
the centre of the bracket. The lines I H, m 1, n 2, o •,

p 4, co, are drawn perpendicular to I G, and their lengths
are found as in the former case.

To find the angle bracket of a cornice for interior and
exterior, otherwise re entrant and salient, angles.

Let AAA (Fig. 2) be the elevation of the cornice bracket,

E B the seat of the mitre bracket of the interior angle, and
H G that of the mitre bracket of the exterior angle. From
the points Akabcd A, or wherever a change in the form
of the contour of the bracket occurs, draw lines perpendi ¬
cular to A i or D c, cutting A i in ef g h i, and cutting the
line E B in E l m n o B. Draw the lines EG, gl and b h,
h K, representing the plan of the bracketing, and the
parallel lines from the intersections l m n o, as shown
dotted in the engraving; then make B F and H I each
equal to i A, o u to h d, nt to g c, m s to f b, l r to e a, l p
to ek, and join the points so found to give the contour of
the brackets required. The bevels of the face are found
as shown by the dotted lines xvyw.

To find the angle bracket at the meeting of a concave
curved wall with a straight wall.

Let ad BE (Fig. 3) be the plan of the bracketing on
the straight wall, and dm,eg the plan on the circular
wall; cab the elevation on the straight wall, and gmh
on the circular wall. Divide the curves c B, G H into the
same number of equal parts; through the divisions of c B
draw the lines c D, 1 d h, 2 e i, &c., perpendicular to A B,
and through those of G H draw the parallel lines, part
straight and part curved, 1 mh, 2 ni, Sole, &c. llien
through the intersections hikl of the straight and curved
lines, draw the curve D E, which will give the line from
which to measure the ordinates hi, i 2,1c 3, &c.

To find the angle bracket when the rvall is a convex

curve.

Let B E D c be the plan of the bracketing on the straight
wall, and B E G H the plan on the curved wall. From the
points AkabcdA of the bracket AAA, where its contour
changes, draw perpendiculars as before. Draw H G a
radius to the curve of the wall H B, and set on it the divi¬
sions on ml, equal and corresponding to hgfe of the
elevation AAA; and draw hi ,ou, n t, ms, l r, Ip, per¬
pendicular to G H, and make them equal to i A, h d, g c,f b,
e a , e k, of the elevation; then join the points by the
lines i u, u t, t s, s r, r p, p G, to obtain the contour of the
bracket equal and corresponding to A A A. Through the
points on ml draw concentric curves, meeting the per¬
pendiculars from the corresponding points of A A A; from
the intersections of the straight and curved lines, onml,
draw the lines B F, o u, n t, m s, l r, perpendicular to E B,
and make them equal to the corresponding lines of the
elevation, as before; then join the points F u t s r p E, to
obtain the contour of the angle bracket.

The examples in Figs. 5 and 6 do not require further

elucidation.

forms of roofs.

The most simple form of a building is one erected on a
itangular plan, with two long and two short sides
ch a building is roofed generally, either with a roof o
single slope, called a shed roof, as in lig. So — ie wa
one of the long sides of the building being carried so
ach higher than the wall parallel with it, as to give the

PRACTICAL CARPENTRY AND JOINERY.

required slope to the roof—or with a roof of double slope,
as in Fig. 352.

In the latter, the planes forming the slopes are equally
inclined to the horizon; the meeting of their highest sides
makes an arris, which is called the ridge of the roof; and
the triangular spaces in the end walls are called gables.

When a building is erected on a rectangular plan, of
which the four sides are equal, it may be covered with
a roof of two slopes. But it may happen that no neces¬
sity may exist for making any of the opposite pairs of sides
gables; or there may be reason why all the sides should
be gables. In the latter case, two roofs of equal slope
intersect each other. This roof, then (Fig. 353), has two
ridges a b, c d, and four hollow arrises f e, g e, lie, he,
made by the intersections of the planes of the slopes, and
lying over the diagonals of the square. The arrises are

termed valleys or flanks. In the former case, a mode
much more simple, and often preferable, because simpler
in construction, is to make each of the sides of the roof
spring from the sides of the square with an equal slope.
The result (Fig. 354) is a pyramid more or less obtuse or
acute, and the intersections of the sloping planes form
salient angles, or arrises. This kind of roof is called a
pavilion roof. If its base be formed by a polygon, of
which the sides are equal, the pyramid will be composed
of as many triangles as the polygon has sides. The ar¬
rises are also called hips.

When the sides of a parallelogram on which a build¬
ing is raised are not very unequal, it
may be roofed with a pavilion roof,
as in Fig. 355; the slopes on cor¬
responding and opposite sides being
equal, but those on contiguous sides
different.

The pavilion roof is applied also to buildings erected
on oblong plans. Thus, in the roof (Fig. 356) the sides
a b, c d, are truncated at their higher extremities by sides
of the same slope rising from the ends ca, db. These

form, by their meeting with the former, the arrises or hips
af, cf, be, de, and the form which results at each end

a Fig. 356. b Fig. 357.

is called a hip. The roof is called a hipped roof, and the
rafters on the lines of the arrises are called hip-rafters.
When the end of such a roof is at right angles to its side,
as a b e (Fig. 357), it is called a right hip; when the angles
are unequal, as at d c o, it is an oblique or skewed hip.

When the plan of a building is composed of two equal
parallelograms crossing each other at right angles, each
of the parallelograms may be covered with a roof of two
slopes and two gables, as in Fig. 358, or they may each

lig. 358. I’ig. S59.

be covered with a hipped roof, as in Fig. 359; in each case
forming four valleys at their intersections. When the
intersecting parallelograms are unequal in length, the

Fig. 360. rig. 361.

shortest may be roofed pyramidally, the slopes of its con¬
tiguous sides being unequal, and the longest with a ridge,
as in Fig. 360; or there may be a short ridge common to
both, as in Fig. 361.

Figs. 362 and 363 are plans of roofs having valleys,
hips, and ridges,—the slopes in both being unequal.

l'ig. 362. Fig. 863.

Great edifices are often composed of several masses of
building, which form diverse angles with each other ; and
their extremities may also abut upon streets and roads
at various angles. Ordinarily, the different ranges of the
building have their crowning cornice on the same level,
and their roof of the same height.

In Fig. 364 is represented the horizontal projection of
the roofs of a building composed of three ranges crossing
each other. Their six extremities, square or skewed,
are hipped, according to the form of the plan. The lines
formed by the intersections of the roofs are valleys.
The valleys ca, ce, co, cu are equal, because the build¬
ings A and D are equal in width, and cross each other at

STEREOGRAPHY—FORMS OF ROOFS.

right angles. The valleys b c, b d, bf, b g are unequal,
because the angles formed by the intersecting buildings
are not 90°. In this combination of roofs the hips occur
together in pairs, and the valleys four and four. In the

next figure (Fig. 365) the ranges of building inclose a
court. Their meeting forms hips on the exterior and

valleys in the interior. All the hips divide the angles
to which they correspond into two equal parts In the
same way the valleys divide the interior angle into
equal parts; and in general the hips and valleys are equal
when they result from the meeting of two ranges of build¬
ings of the same width, with roofs of equal height; but
they become irregular when the buildings are of unequal
width, though of the same height, or when the opposite
sides of the roofs are of different slopes. At the range of
building M in the figure, which meets the range A at right
angles, the slopes, and consequently the valleys, are un¬
equal, the inequality being proportionate to the deviation
from the dotted lines; and the gable is also irregular, as
shown by the section N. When the greater width of a
building causes its roof to rise higher than the roof which
it meets, as the roof of the wide range F meeting D, the
connection is completed by extending the slope of D so
as to truncate the summit of F, and form the hips b a, c a.

When two buildings of unequal width meet each
other, and the ridges of the roofs are not kept of equal

height, as in Fig. 366, the horizontal projection of the
lower roof is found by drawing a line a b from the point

in the vertical projection a, where the line of the ridge
a c of the lower roof meets the slope of the higher roof, to
the seat of the ridge *

on the plan below, Fhr- 369
and joining bd, b d
for the valleys formed „
by the intersections.

When the slopes are
equal, as in the figure, •-
db d will be a right
angle.

O ;

In Fig. 367 is
shown a pavilion
roof, truncated by a
plane parallel to its
base. a\

Fig. 368, A is the
horizontal, and B the
vertical projection of
a square building,
presenting four equal
gables and as many equal slopes; but the intersections of
the slopes, in place of lying over the diagonals of the square,
connect together the summits of the gables. This roof, it

will be seen by the dotted lines, is the section of a pyrami¬
dal roof a b c, made by four planes parallel to its diagonal.

The combination of
hips and gables may be
used for figures of any
number of sides. If
the number of sides
is even, the sides may
be alternately gabled
and horizontal, as in
Fig. 369, the plan of
which is a hexagon,
the result of the trun¬
cation of a triangular
pyramid by planes par¬
allel to its opposite
sides. Where each side
has a gable, as in
Fig. 370, the resulting
figure is a hexagonal
pyramid truncated by six planes, forming gabled sides.

PRACTICAL CARPENTRY AND JOINERY.

In Fig. 371, A is the horizontal projection of a roof with
hips or pavilion ends, truncated; B is the vertical projec¬
tion of the side, and c that of the end.

When it is desirable to keep the roofing over a wide
building of a rectangular plan low, it may be effected by
dividing the span into two, with four principal slopes, two
external and two internal. This, which
produces a section somewhat resem¬
bling the letter M (Fig. 372), is, from
its form, called an M-roof. At the
meeting of the interior slopes is formed a gutter for the
water. Fig. 373 is the horizontal projection of such a roof
with gables, and Fig. 374 the same Avith hips.

rig.

Fig. 37». Fig. 374* Fig. 375.

In order to avoid the long gutter, another roof is some¬
times introduced, as in Fig. 375, crossing between the two
ridges at right angles, and forming valleys by the inter¬
section of its slopes with the interior slopes of the longi¬
tudinal roofs ; and for the sake of Fig 370 .

external appearance, or to collect the
Avater in the centre, two cross roofs
are sometimes used, inclosing a cen¬
tral space. When the interior slopes
meet in a point, as in Fig. 376, the
roof is called a hopper roof.

Sometimes the plan of a building
is irregular, and its sides are not parallel. If the roof be
constructed so that the ridge slopes to the narroAV end, its
sides will be planes; but if the ridge be made horizontal
throughout, the sides of the roof will become tAvisted or
winding.

Let a d d' a (Fig. 377) be the plan of an irregular

the tAvo triangles a pa!, dg d, Avhich may be isosceles; and
the ridge is projected on the line p g, which is not parallel
to either of the sides a d, a! d'. Tavo cases here present
themselves: the ridge projected on p g is either horizon¬
tal, and its extremities are determined by its meeting with
the planes of the sloping ends, which may have the same
slope—the larger sides in this case being twisted; or it
has an inclination determined by the intersection of the
planes ap g d, a> p g d!, springing with equal slopes from
the Avail head. It is easy to observe that the ridge will
not in either case appear parallel to the faces of the
building. Of these two methods, the most agreeable to
the sight is the first, in which the ridge is horizontal: it is
also the most economical in construction. The two great¬
est sides of' the roof are surfaces generated by a line
which, moving from a d or a'd', to meet the ridge p g,
is kept in contact with a vertical line passing through
c or c ', where the arrises of the hips meet when produced.

The tAvist or wind of the sides being disagreeable, vari¬
ous methods are used to
get rid of it Avhere the
ridge is horizontal.

In Fig. 378, tAvo equally
inclined planes spring
from a d, a! d', and their
intersection produces an
inclined ridge pf. The points q q are taken at the level
of p, and the arris f q is thus symmetrical Avith fp.

The same plan may be covered by a roof with hori¬
zontal ridges, as in Fig.

379. The four sides of c

the roof are planes,
springing at the same in¬
clination from the walls
abed. The ridges ef
e g, are continued at the
height determined by the intersection of the hip at e;
and a pyramidal construction, efg, is added, at so low a
pitch as not to be visible from the ground. In place of
these pyramidal roofs, the three sides of the building
c b d may have roofs of tAvo slopes intersecting at the
lines eh, hf, hg, forming what is called an irregular hop¬
per roof.

In Fig. 380, another method of preserving the ridge
horizontal on one side Avithout twisting the sides, is shoAvn.
In this case one of the sides is roofed in two slopes form¬
ing an arris, a b.

building. The roof is hipped, having sloped ends forming

In Fig. 381, another method of roofing the same space
is shoAvn.

DESCRIPTIVE CARPENTRY—FORMS OF ROOFS.

The Figs. 382 to 386 show various methods of roofing a

Fig. 382. Fig. 383.

Fig. 384.

Fig. 385.

trapezium without twisting the
sides. In Fig. 382, the sides
are planes, and form an irregu¬
lar pavilion roof. In Fig. 383,
planes of the same slope rise to
the same height, and are united
by a platform. In Fig. 384,
one side, a, is twisted. In Fig.

385, two irregular pavilion
roofs cross eaclx other, forming valleys at their intersec¬
tions. In Fig. 386 there are four gables and four valleys,
as in the roof over a square plan, Fig. 353.

In the roofs over an oval plan, Fig. 387 shows one

Fig. 387.

Fig. 388.

with a straight and horizontal ridge, and, consequently,
with twisted sides; but in this case the appearance of the
side is not disagreeable.

In Fig. 388, the sides are not twisted, but slope every¬
where alike; and the roof is truncated and terminated
by a platform.

Fig. 389 is a conical roof.

Fig. 390 is a roof over a rectangular plan, with a

semicircular end. The end of the roof is consequently
a semi-cone.

Fig. 391 is an annular roof.

Fig. 392 is the roof of a crescent building, with one

end gabled and the other hipped.

Fig. 893.

Fig. 393 is the vertical, and Fig. 394 the horizontal
projection of two united conical roofs.

Fig. 395 is the junction of a large and a small conical

roof. Fig. 395.

Fig. 396 is the junction of a conical and a pavilion roof.

Fig. 397 is the junction of a span roof with a large
conical roof.

Fig. 398 shows the junction of a conical and a cre¬
scent roof.

Fig. 399 shows the junction of a conical with an annular
roof.

In Fig. 400, A is the horizontal, and Bthe vertical projec¬
tion of a round pavilion roof, formed by a conical roof cut

Fig. 397. Fig. 398.

by two span roofs, which give two horizontal ridges, four
right-lined valleys, and eight hips, which are elliptic curves.
In Fig. 401, C is the horizontal, and D the vertical pro-

PRACTICAL CARPENTRY AND JOINERY.

jection of a round pavilion roof, formed by a hemispheri¬
cal cupola cut by two span roofs, making two horizontal
ridges, four right-lined valleys, and eight hips, which are
arcs of circles.

Fig. 401. Fig. 402.

In Fig. 402, E and F are the horizontal and vertical pro¬
jections of an imperial pavilion made in the same manner.

In Fig. 403, G and H are the horizontal and vertical
sections of a roof in the form of a hemisphere, truncated
by four inclined planes, forming a pavilion roof with four
right-lined arrises, and eight arrises of portions of circles.

In Fig. 404, I and K are the horizontal and vertical
projections of a round pavilion, formed by the truncat¬
ing of a cone by four inclined planes. This is of the same

Fig. 405.

kind as the last, only the curves of the arrises are por¬
tions of ellipses.

In Fig. 405, A is a horizontal, and B a vertical projection
of a conical roof, whose summit is at c, truncated by two
sloping planes, forming a horizontal ridge a b, and four
hips having elliptic arrises a d, a c, b d, be.

Fig. c is a second vertical projection, on a plane parallel
to c d.

In Fig. 406, A and B are the horizontal and vertical
projections of a conical roof truncated interiorly by two
inclined planes.

Fig 406.

In Fig. 407, A is a horizontal projection of a roof, formed
by the setting of a square pyramidal roof diagonally on a
pavilion roof of lower elevation. This is the broach or
spire of Gothic architecture. B is the vertical projection
on a plane parallel to one of the faces of the lower pyra¬
mid, and C the vertical projection on a plane parallel to
its diagonal.

In Fig. 408, A is the horizontal, and B the vertical pro¬
jection of a pyramidal roof with a square base, set on an
octagonal pavilion roof of lower elevation.

In Fig. 409, A is the horizontal, and B the vertical pro¬
jection of a pyramidal roof, with an octagonal base, set on
a pavilion roof of lower pitch with a square base.

In big. 410, A and B are the horizontal and vertical
projections of a conical roof set on a square pyramid.

In Fig. 411, A and B are the horizontal and vertical
projections of an acute conical roof set on an octagonal
pyramid.

In Fig. 412, A is the horizontal, and B the vertical pro-

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STEREOGRAPHY -HIP-ROOFS.

jection of a roof formed by an octagonal pyramid set on

Fig

a cone.

Fig.

In Fig. 413, a is the horizontal, and B the vertical projec¬
tion of a roof formed by an acute cone set on an obtuse one.

In Fie. 414, A and B are two projections of two conical
spires set on a conical roof.

Fig. 413.

Fig. 414.

We shall now proceed to describe the methods ot deter¬
mining the places and forms of the rafters in such hip¬
roofs as are of most common occurrence in practice.

HIP-ROOFS.

Plates XX., XXI.

In its most simple form the hip-roof is a quadrilateral
pyramid, each triangular side of which is a hip, and the
rafter in each angle is a liip-rafter. The common rafters
which lie between the hip-rafters in the planes of the
sides of the roof, and which, by abutting on the hip rafters,
are necessarily shorter than the length of the sloping side,
are called jack-rafters.

The things required to be determined in a hip-roof are
these, viz.:—

1. The angle which a common rafter makes with the
plane of the wall-head; that is, the angle of the slope of
the roof.

2. The angle which the hip-rafters make with the wall
head.

3. The angles which the hip-rafters make with the ad¬
joining planes of the roofs. This is called the backing ot
the hip.

4. The height of the roof.

5. The lengths of the common rafters.

6. The lengths of the hip-rafters.

7. The length of the wall-plate contained between the
hip-rafter and next adjacent entire common rafter.

The first, fourth, fifth, and seventh of these are gene¬
rally given, and then all the others can be found from
them by construction, as is about to be shown.

The plan of a building and the pitch of the roof being
given, to find the lengths of the rafters, the backing of
the hips, and the shoulders of the jack rafters and purlins.

Plate XX.—Let abcb (Fig. 1) be the plan of the
roof. Draw G H parallel to the sides AD, B c, and in the
middle of the distance between them. From the points
A B c D, with any radius, describe the curves ab, a b, cut¬
ting the sides of the plan in a b. From these points, with
any radius, bisect the four angles of the plan in r r r r,
and from A B c D, through the points r r r r, draw the lines
of the hip-rafters A G, B G, C H, D H, cutting the ridge
line G H in G and H, and produce them indefinitely. The
dotted lines c e, elf, are the seats of the last entire common
rafters. Through any point in the ridge line I, draw E I F
at right angles to G H. Make I K equal to the height of
the roof, and join E K, F K : then E K is the length of a
common rafter. Make G o, H o equal to I K, the height
of the roof; and join A0,B0,C0,D0, for the lengths of
the hip-rafters. If the triangles aog, and B o G, be turned
round their seats, A G, B G, until their planes are perpen¬
dicular to the plane of the plan, the points o o, and the
lines Go, Go, will coincide, and the rafters A o, B o be in
their true positions.

Let A B c D (Fig. 2) be the plan of an irregular roof ,
in which it is required to keep the ridge level.

Bisect the angles of two ends by the lines a b, B b, c G,

D G, in the same manner as before; and through G draw
the lines ge,gf parallel to the sides c B, D A respectively
cutting A b, B b in E and F; join EF: then the triangle
E G F is a flat, and the remaining triangle and trapeziums
are the inclined sides. Join G b, and draw H I perpendi¬
cular to it: at the points M and N, where H I cuts the
lines G E, G F, draw M K, N L perpendicular to n I, and
make them equal to the height of the roof: then draw
H K> I L for the lengths of the common rafters. At E, set
up E m perpendicular to B E; make it equal to M K or N L,
and join B m for the length of the hip-rafter; and proceed
in the same manner to obtain A m, c m, D m.

To find the hip and valley rafters of a compound ir¬
regular roof (Fig. 3). .

In the compound roof shown by the plan, in which

the ridge is level throughout, although the buildings
are of different widths, the method of proceeding to find
the hip and valley rafters of the right-lined parts of the
roof is the same as in the two former cases, and will be
evident on inspection. In the circular part, proceed as
follows:—Draw cd a radius to the curve, as the seat of
one pair of the common rafters c b, cl b, and bisect it in
a : through a describe the curve k a w n a, which is the
seat of the circular ridge: produce the lines of the other
ridges to meet this curved line in a W k, and connect the
angles of the meeting roofs with these points, as m the
drawing: divide the seat of one pair of the common rat¬
ters in each roof, as xy,pq,tu, and efi into the same
number of equal parts; and through the points ol division

PRACTICAL CARPENTRY AND JOINERY.

draw lines parallel to the sides of their respective roofs,
intersecting the curved lines drawn through the points
of the curved roof; and through the points of intersection
draw the curves c, l, m, a, &c., which give the lines of the
hips and valleys. On c a, the meeting of the left-hand
roof with the circular roof, erect a b at a , and make it
equal to the height of roof; and join c b, for length ol
valley rafter: proceed in the same manner for the hip-
rafter z b ; and for the other hip and valley rafters.

To find tlce valley rafters at the intersection of the
roof B with the conical roof E (Fig. 4).

Let D H, f H be the common rafters of the conical roof,
and K L, i L, the common rafters of the smaller roof, both
ot the same pitch. On G H set up G e equal to M L, the
height of the lesser roof, and draw e d parallel to D F,
and from d draw c d perpendicular to D F. The tri¬
angle D d c, will then by construction be equal to the
triangle K L M, and will give the seat and the length and
pitch of the common rafter of the smaller roof B. Divide
the lines of the seats in both figures, D c, K M, into the
same number of equal parts; and through the points
of division in E, from G as a centre, describe the curves
c a, 2 g, 1 /’ and through those in B. draw the lines 3 /
4 g, M a, parallel to the sides of the roof, and intersect¬
ing the curves in f g a. Through these points trace the
curves c/pa, A /pa, which give the lines of intersec¬
tion of the two roofs. Then to find the valley rafters,
join c a, A a; and on a erect the lines a b, a b perpen¬
dicular to C a and A a, and make them respectively equal
to ML; then c 6, A b is the length of the valley rafter,
very nearly.

Plate XXI. Fig. 1 —Shows the method of finding the
backing of the liip-rafter.

Let B b, b c be the common rafters, A d the width of
the roof, and A B equal to one-half the width. Bisect B c
in a, and join A a, D a. From a set off a c, ad equal
to the height of the roof a b, and join A cl, D c; then A d,
r> c are the hip-rafters. To find the backing: from any
point h in a d, draw the perpendicular h g, cutting a a
in p; and through p draw perpendicular to A a the line
e f cutting A B, A D in e and / Make p k equal to g h,
and join k e, kf; the angle e kf is the angle of the back¬
ing of the hip-rafter c.

Fig. 2.—Where the angles of the roof are not rio-ht
angles. Bisect ad in a, and from a describe the semi¬
circle A b D; draw a b parallel to the sides AB, DC, and
join A b, D b, for the seat of the hip-rafters. From b set
oft on 6 a, 6 d, the lengths b d,b e, equal to the height of
the roof 6 c, and join A e, D d, for the lengths of the hip-raf¬
ters. To find the backing of the rafter:—In Ae, take any
point k, and draw k h perpendicular to A e. Through li
draw / h g perpendicular to A 6, meeting AB, AD in/ and
p. Make h l equal to li k, and join f l, gl) the angle fig
is the backing of the hip.

To find the bevel of the shoulder of the purlins.

Fig. 3.—First, where the purlin has one of its faces in
the plane ot the roof, as at E. From c as a centre, with
any radius, describe the arc d p; and from the opposite
extremities of the diameter, draw d h. g m perpendicular
to bc. From e and / where the upper adjacent sides of
the purlin produced cut the curve, draw ei,fl parallel to
to d h, g to; also draw ck parallel to d h. From l and
i draw l m and i h parallel to B c, and join k h, lc m.

Then c k m is the down bevel of the purlin, and c k h is
its side bevel.

When the purlin has two of its sides parallel to the
horizon. This simple case is shown worked out at f. It
requires no explanation.

When the sides of the purlin make various angles with
the horizon. Fig. 4 shows the application of the method
described in Fig. 3, to these cases.

Fig. 5 shoivs the method of finding the bevel of the
jack-rafters.

Let A B c D be the plan. Draw the hipped end of the
roof aed in any of the manners already described.
Bisect B c in E; and from E as a centre, with the radius
E c, describe the semicircle c I d. Through E draw d e
parallel to ad. Bisect the semicircle d e in I, join Ei,
and produce the line to G; ei represents the seat of the
common rafter, extending from the wall plate to the
junction of the hip-rafters, and the length of the rafter
over the seat will of course be equal to b a or c a. Make
ig, therefore, equal to B a or c a, and join ag, dg. The
triangle AGD will then show the extent of the covering
of the hip AED, and AG, DG give the lengths of the
hip-rafters.

Produce B c to f and H, and make bf,ch each equal
to the length of the common rafter c a or B a, and join
A F, D H. The triangle A F B is the covering of the tri¬
angle A E B, and D H c of de c.

To find the bevel of any jack-rafter on the hip AED:
—From its seat on the plan, shown in dotted lines g o,
h p, draw the parallel lines g lc, h l to the line of the hip-
rafter A G in the development, and k l shows the bevel of
the jack-rafter on the hip-rafter. Any of the other jack-
rafters are found in the same way, as shown by the dotted
and shaded lines. The down bevel of all the jack-rafters
is the angle c a E.

Fig. 6 shows the method of finding the length and
bevel of any single jack-rafter.

Let A B c be the plan of one angle of a hip-roof, and
B E the seat of the hip-rafter. It is required to find the
length and bevel of the jack-rafter over the seat D k e. At
the point 6, where the longest side of the jack-rafter meets
the hip-rafter, draw 6 d at right angles to side of jack-
rafter b e, and make the angle bed equal to the slope of
roof; draw also 6 c at right angles to side of hip-rafter a b,
and make it equal to 6 d. Produce 6 e, li k indefinitely,
and make bg equal to de\ and hb, f g is the length of the
jack-rafter. To obtain the bevel at h 6, draw a l at right
angles to B C and make it equal to kf or e g, and join b T
then the angle lb g is the bevel of the jack-rafter.

To find the bevel of a hip-rafter made by a plane par¬
allel to the planes of the common rafters.

Let A (Fig. 7) be the seat of the foot of the rafter, B
the horizontal projection of its upper end, l m the projec¬
tion of the bevel there, and c the vertical projection of
the rafter on a plane parallel to its plane. The backing
of the rafter 6 a cl at A, and its cross section r u q v s
at F, will be evident without description. The method
of finding the bevel at g k E h is as follows:—From g
draw the horizontal line g i, and from g as a centre,
with the radius g li, describe the arc h i. From i let
fall a perpendicular i n to the horizontal projection meet¬
ing B m produced in n, then draw l n o, and pi o is the
proper bevel.

KNOWLEDGE OF WOODS.

PART FOURTH.

KNOWLEDGE OF WOODS.

PHYSIOLOGICAL NOTIONS.

The substance named wood is, for the most part, elas¬
tic, tenacious, durable, and easily fashioned—qualities
which cause it to be in general request for articles of use
and of luxury. It is used as fuel, either in its natural
state or as reduced to charcoal: it also affords tar, to pro¬
duce which, much of it is annually consumed.

Wood* has always been indispensable in the arts.
Iron, from its power of resisting cutting instruments and
the attacks of lire, has, in some measure, rivalled it; but
wood must still be regarded as ttie substance which con¬
tributes most to the preservation of man, to his defence,
his civilization, and the development of his power. It en¬
ters largely into the fabrication of tools and machines, of
arms of warfare, of furniture and utensils, and of all kinds
of constructions, from the modest hut, the small foot¬
bridge and frail skiff, to the grandest edifices, bridges of
daring span, and mighty ships which extend man’s com¬
merce and his power, and bring together those whom
nature would seem to have separated for ever.

In the Art of Carpentry, above all, timber is employed
in the manner most remarkable, and in the largest masses.
The natural form of the tree admits of the timber being

obtained in long parallelopipedons, termed beams, girders,
&c., the combination and. framing of which constitute
the means of raising great structures in the most rapid
manner.

It is not necessary, for the purposes of this work, to
enter minutely into the discussion of the subject of vege¬
table physiology: all that is here requisite, is to state some
of the more important facts, the knowledge of which is
of consequence to the carpenter who desires to possess the •
power of discernment in the choice of timber.

The part that is characterized as timber is obtained
from the body of trees, or that part of those which grow
with a thick stem, rising high, and little encumbered with
branches or leaves, which is called the trunk. The head
of the tree consists of the branches, which are adorned
with leaves: these attain their full development in the
summer, and then, in the great majority of species, fall in
the autumn.

In carpentry, the wood of the trunk and largest branches
alone is used; and only that of the commoner species of
trees; leaving to other arts to employ that of the rarer
and smaller kinds, for which their beauty, rather than
strength, is the recommendation.

Some of the timber trees attain an immense size when
they are allowed to come to full maturity of growth.
Oaks and beeches are found to attain the height of 120
feet; the larch, the pine, the fir grow to the height of
135 feet. Other kinds, as the elm, the aspen, the maple,
the alder, and even the walnut, the poplar, and the cypress,
reach sometimes a great elevation. In warm regions, the

palm grows as large as the oak. The diameter of the
trunk varies with the kind and the climate. Oaks and
elms may be seen of the enormous size of 36 feet in cir¬
cumference.

Farner mentions an elm at Hasfield, in Massachusetts,
considered the largest in America, which measured, at the
surface of the ground, 31 feet in diameter; and at 5 feet
high, 21 feet. Condamine speaks of canoes on the Ama¬
zon river made of single trees, and measuring 90 palms
in length, and 10 in width. Other authors mention trees
of equally great dimensions, such as the firs of North
America, which shoot up to 250 feet in height; and
cypresses, which grow to 7 and 8 feet in diameter.

The Carolina pine is said to attain a size still more
astonishing, the trunk growing to 60 feet in circumfer¬
ence, and rising 300 feet before the head is formed.

The diameter which trees attain in our climate, how¬
ever, rarely exceeds 5 feet, and ordinarily they are found
of half that size.

Ship-building consumes a great quantity of timber.
For this service, the curved pieces are more useful; but
it seizes also upon the finest trees; which renders it diffi¬
cult to satisfy the wants of the other branches of carpen¬
try, and creates occasion for divers expedients to supply
the want of size in the timber, both in length and sec¬
tional area. The difficult}' - of procuring oaks of sufficient
magnitude has directed attention to pines and firs.

Botanists classify vegetables, and consequently trees,
according to their physiological and structural peculi¬
arities ; and in this way trees are divided into two great
classes,—Monocotyledonous, or Endogenous, and Dicotyle¬
donous, or Exogenous trees.

The terms Monocotyledonous and Dicotyledonous, be¬
long to the Jussieuan system of nomenclature, and are
descriptive of the organization of the seeds. Endogenous
and Exogenous are the terms used by modern botanists,
and are descriptive of the manner of growth or develop
ment of the woody matter of the tree, which is, in the-
endocrens, from the outside inwards towards the interior,
and in the exogens, outwards to the exterior.

The monocotyledonous or endogenous trees are only
used in this country in the formation of articles of luxury.
Trees of this class have no branches: their stems, nearly
cylindrical, rise to a surprising height, and are crowned
by a vast bunch of leaves, in the midst of which grow
their flowers and fruits. In this class are the palm trees,
growing oidy, in their native luxuriance, in tropical
climes, where they are of paramount importance, yielding
to the people of those countries meat, drink, and raiment,
and timber for the construction of their habitations.

The palm tree will serve as a type of the endogenous
structure. Dr. Lindleyt says of it—“ In the beginning,
the embryo of the palm consists of a cellular mass, of a
cylindrical form, very small, and not at all divided. As

* Colonel Emy, abridged and slightly altered.

t Lindley’s Vegetable Kingdom , p. 95.

PRACTICAL CARPENTRY AND JOINERY.

soon as germination commences, a certain number of cords,
of ligneous fibre, begin to appear in the radicle,* deriving
their origin from the plumule, t Shortly afterwards, as
soon as the rudimentary leaves of the plumule begin to
lengthen, spiral and dotted vessels appear in the tissue in
connection with the ligneous cords; the latter increase in
quantity as the plant advances in growth, shooting through
the cellular tissue, and keeping parallel with the outside
of the root. At the same time, the cellular tissue in¬
creases in diameter, to make room for the ligneous cords
(or woody bundles, as they are called). At last a young
leaf is developed, with a considerable number of such
cords in connection with its base; and as its base passes
all round the plumule, those cords are, consequently, con¬
nected equally with the centre which that base surrounds.
Within this a second leaf gradually unfolds, the cellular
tissue increasing horizontally at the same time; the lig¬
neous cords, however, soon cease to maintain anything
like a parallel direction, but form arcs, whose extremities
pass upwards and downwards, losing their extremities in
the leaf on the one hand, and in the roots on the other,
or in the cellular integument on the outside of the first
circle of cords; at the same time, the second leaf pushes
the first leaf a little from the centre towards the circum¬
ference of the cone of growth. In this manner, leaf
after leaf is developed, the horizontal cellular system
enlarging all the time, and every successive leaf, as it
forms at the growing point, emitting more woody bun¬
dles curving downwards and outwards, and, consequently,
intersecting the older arcs at some place or other; the
result of which is, that the first formed leaf will have the
upper end of the arcs which belong to it longest and
much stretched outwardly, while the youngest will have
the arcs the straightest; and the appearance produced in
the stem will be that of a confused entanglement of
woody bundles in the midst of a quantity of cellular
tissue. As the stem extends its cellular tissue longitudi¬
nally while this is going on, the woody arcs are, conse¬
quently, in proportion, long, and, in fact, usually appear
to the eye as if almost parallel, excepting here and there
where two arcs intersect each other. As, in all cases, the
greater number of arcs curve outwards as they descend,
and eventually break up their ends into a multitude of
fine divisions next the circumference, where they assist
in forming a cortical integument, it will follow, that the
greater part of the woody matter of the stem will be
collected near the circumference; while the centre,
which is comparatively open, will consist chiefly of cellu¬
lar tissue; and when, as in many palms, the stem has a
limited circumference, beyond which it is not its specific
nature to distend, the density of its circumference must,
it is obvious, be proportionably augmented.

“Never is there any distinct column of pith or medul¬
lary rays, or concentric arrangement of the woody arcs;
nor does the cortical integument of the surface of endo¬
genous stems assume the character of bark separating

* Radicle, the conical body which forms one extremity of the
embryo, and which, when germination takes place, becomes the des¬
cending axis or root of the plant.

t Plumule, the growing point of the embryo, situated at the
apex of the radicle, and at the base of the cotyledons, by which it is
protected when young. It is the rudiment of the future stem of a
plant.

from the wood below it: on the contrary, as the cortical
integument consists very much of the finely divided
extremities of the woody arcs, they necessarily hold it
fast to the wood, of which they are themselves prolonga¬
tions; and the cortical integument can only be stripped
oft' by tearing it away from the whole surface of the
wood, from which it does not separate without leaving
myriads of little broken threads behind.”

Such is the general structure of the most perfect among
the endogens, a family of plants which, in this country,
are little known as trees; but which, in the cereal and
other grasses, enter largely into cultivation as articles
of food for men and animals. In other countries, how¬
ever, the endogenous trees fill an important place in
structural economy, as well as contribute largely to the
food of man. One of them, the bamboo, plays so many
parts, as absolutely to make it difficult to say what it is
not used for. A recent writer enumerates some of its
most common uses in China, in the following amusing
manner:—

“ Bamboo is used in making soldiers’ hats and shields,

umbrellas, soles of shoes, scaffolding poles, measures,

baskets, ropes, paper, pencil-holders, brooms, sedan chairs,

pipes, flower-stalks, and trellis-work in gardens: pillows

are made of the shavings : a kind of cloak for wet

weather is made of the leaves. It is used for making

sails and covers for boats, fishing rods and fishing baskets,
fishing stakes and buoys, aqueducts for water, water
wheels, ploughs, harrows, and other implements of hus¬
bandry. Its roots are cut into grotesque figures, and its
stem carved into ornaments for the curious, or as incense-
burners for the gods. The young shoots are boiled and
eaten; and sweetmeats are also made of them. A sub¬
stance found in the joints, called tabasheer, is used in
medicine. In the manufacture of tea, it forms the rolling
tables, drying baskets, and sieves. The all-important
chop-sticks are made of it. It is in universal demand in
the house, on the water, in the field: the Chinaman is
cradled in it at his birth, through life it is his constant
companion in one shape or another, and in it he is carried
to his last l'esting-place to repose even there under the
shade of its long oval leaves.” With this catalogue of
the uses of the bamboo, we may dismiss the endogens.

Dicotyledonous or exogenous trees, which form the
second class, are in much greater variety, and much more
widely spread over the globe, than the trees of the first
class. The form of their trunks is generally conical,
tapering from the root to the summit: the summit or
head of the tree is formed by the prolongation of the
trunk, which divides into sundry primary branches;
these again ramify into innumerable secondary branches;
and these throw out small twigs, to which the leaves are
attached by foot-stalks, larger or smaller. At first sight
it appears as if the leaves grew by chance, but an order,
regular and constant in each species, presides in their
distribution.

On making a transverse section of a dicotyledonous
tree, we see that it is composed of three parts, easily dis¬
tinguished—the bark which envelops, the’ pith which
forms the core or centre, and the woody substance which
lies between the bark and the pith.

In the woody substance we distinguish two thicknesses:
the one which envelops the pith is the greatest; and is

KNOWLEDGE OF WOODS.

of a harder nature than that which adjoins the bark.
The former is termed perfect wood, the latter alburnum.
The inner layer of bark next the alburnum is called
the liber, a name given from its being used to form the
books ( libri ) of the ancients. Between the liber and the
alburnum there is a substance partaking of the qualities
of both, and called cambium. This is developed in the
spring and autumn; when its internal portion changes
insensibly into alburnum, and the exterior into liber.
The liber never becomes wood: it is expanded continually
by the process of growth in the tree, and forms the bark,
which rends and exfoliates externally, because of its
drying; and the layer of liber, in growing old, cannot
extend in proportion to the augmentation in the circum¬
ference of the tree.

Duhamel and Buffon long since proved that alburnum,
in process of time, became perfect wood; and there is now
no doubt in regal'd to the manner in which the tree grows
and produces its wood.

“Exogens, or outwood growers,” says Dr. Lindley,* “are
so called because, as long as they continue to grow they
add new wood to the outside of that formed in the pre¬
vious year; in which respect they differ essentially from
endogens.

“In an exogen of ordinary structure, the embryo con¬
sists of a cellular mass, in which there is usually no trace
of woody or vascular tissue; but as soon as germination
commences, line ligneous cords are seen proceeding from
the cotyledons towards the radicle, meeting in the centre
of the embryo, and forming a thread-like axis for the root.
As the parts grow, the ligneous fibres are increased in
thickness and number, and having been introduced among
the cellular mass of the embryo, are separated from each
other by a portion of the cellular substance, which con¬
tinues to augment both in length and breadth as the
woody cords extend. By degrees, the plumule or rudi¬
mentary stem becomes organized; and having lengthened
a little, forms upon its surface one, two, or more true
leaves, which gradually expand into thin plates of cellular
substance, traversed by ligneous cords or veins, converg¬
ing at the point of origin of the leaves. If at that time
the interior of the young plant is again examined, it will
be found that more ligneous cords have been added from
the bases of the new leaves down to the cotyledons, where
they have formed a junction with the first wood, and
have served to thicken the woody matter developed upon
the first growth. Those ligneous cords which proceed
from the base of the leaves, do not unite in the centre of
the new stem, there forming a solid axis, but pass down
parallel with the outside, and leave a small space of cellu¬
lar tissue in the middle; they themselves being collected
into a hollow cylinder, and not uniting in the middle until
they reach that point where the woody cords of the coty¬
ledons meet in order to form the solid centre of the root.
Subsequently, the stem goes on lengthening and forming
new leaves: from each leaf may be again traced a forma¬
tion of woody matter disposed concentrically as before,
and uniting with that previously formed, a cylinder of
cellular substance being always left in the middle. The
solid woody centre of the root proceeds in its growth in a
corresponding ratio, lengthening as the stem lengthens,

* Vegetable Kingdom, p. 235.

and enlarging in diameter as the leaves unfold, and new
woody matter is produced. The result of this is, that
when the young exogen has arrived at the end of its first
years growth, it' has a root with a solid woody axis, and
a stem with a hollow woody axis, surrounding cellular
tissue; the whole being covered with a cellular intern-
ment. But as the woody cords are merely plunged in a
cellular basis, the latter passes between them in a radiat¬
ing manner, connecting the centre with the circumference
by straight passages, often imperceptible to the naked eye,
but always present.

“ Here we have the origin of pith in the central cellu¬
lar tissue of the stem of wood in the woody axis, of bark
in the cellular integument, and of medullary processes in
the radiating passages of cellular tissue, connecting the
centre with the circumference.”

The woody axis is not, however, quite homogeneous at
this time. That part which is near the centre contains
vessels of different kinds, particularly dotted vessels (both-
renchyma): the part next the circumference is usually des¬
titute of vessels, and consists of woody tissue exclusively:
of these two parts, that with the vessels belongs to the
wood properly so called, and serves as a mould about
which future wood is added: the other belongs to the

bark, separates under the form of liber, and in like manner
serves as a mould within which future liber is disposed.

At the commencement of the second year’s growth the
liber separates spontaneously from the true wood; the
viscid substance, cambium, is secreted between them; and
the stem again lengthens, forming new leaves over its
surface. The ligneous cords of the leaves are prolonged
into the stem, passing down among the cambium, and
adhering in part to the wood, and part to the liber of the
previous year; the former again having vessels inter¬
mingled with them, the latter having none. The cellular
tissue that connected the wood and the liber is softened
by the cambium, and grows between them horizontally,
while they grow perpendicularly, extending to make
room for them; and, consequently, interposed between
the wood}' cords of which they each consist; forming, in
fact, a new set of medullary processes, terminating on the
one hand in those of the first year’s wood, and on the
other in those of the first year’s liber. The addition of
new matter takes place equally in the stem and in the
root, the latter extending and dividing at its points, and
receiving the ends of the woody cords as they diverge
from the main body.

The only respects in which the growth of exogens cor¬
responds with that of endogens are, that in both classes
the woody matter is connected with the leaves, and in
both, a cellular substance is the foundation of the whole
structure.

As new layers of alburnum are produced, they form
concentric circles, which can be easily seen on cutting
through the tree; and by the number of these circles one
can determine the age of the tree. Some authors assert
that this is not so, since a tree may produce in one year
several concentric layers of alburnum, and in another year
only one. Nevertheless, the commonly received opinion
is, that the number of concentric circles in the cross sec¬
tion of the wood, called annual layers, indicates the time
it has taken to reach its size. Although a layer of albur¬
num is deposited each year, the process of transformation

9 G

PRACTICAL CARPENTRY AND JOINERY.

of it into perfect wood, otherwise heart-wood , is slow,
and, consequently, the alburnum, or sap-wood, compre¬
hends many annual layers.

The annual layers become more dense as the tree
grows aged; and when there is a great number in a tree
of small diameter, the wood is heavy, and generally hard
also. In wood which is either remarkably hard or re¬
markably soft, the annual layers can scarcely be distin¬
guished. They cannot, for example, be distinguished in
ebony, and other tropical woods, nor in the poplai’, and
other soft white woods of our climate\ In the case of the
softer woods in our climate, the layers are frequently
thinner and more dense on the northern side than on the
opposite. In a transverse section of a box tree, about 7
inches diameter, we reckoned 140 annual layers.

The roots of a tree, although buried in the soil, have,
as we have seen, an organization resembling that of the
trunk and branches. The roots of several trees are em¬
ployed in the arts, but as none of them are used in car¬
pentry we need not dilate on the subject: we shall only
remark, that as the branches of a tree divide into smaller
branches and twigs, expanding to form a head, so the
roots divide also into branches, which expand in every
direction in the ground, and these branches again divide, j
their ultimate division being into filaments, commonly
called fibres, which appear to be to the roots what the
leaves are to the branches.

It has been remarked that there is a sympathy between
the branches and the roots in their development. Thus,
when several considerable branches of a tree are lopped
off, the corresponding roots suffer, and often perish.

CULTIVATION OF TREES.

Trees are the produce of forests, planted spontaneously,
and consequently very ancient, or of forests and planta¬
tions created by man since he has engaged in this kind
of culture.

The reproduction of trees, their culture, and the felling
of timber, belong more to the management of forests than
to the art of carpentry; but we shall remark briefly on
some qualities which are derived from growth.

.The size and fine growth of a tree is not an infallible
sign of goodness of quality in the wood. The connection
of the age of a tree with its development, and the nature
of the soil in which it grew, ought to be inquired into
to enable a judgment to be formed of the quality of the
wood.

In genera], boggy or swampy grounds bear only trees
of which the wood is free and spongy, compared with the
wood of trees of the same species grown in good soil at
greater elevations. The water, too abundant in low lying
argillaceous land, where the roots are nearly always
drowned, does not give to the natural juices of the tree
the qualities essential to the production of good wood.
Trees grown in such places are better adapted for other
works than those of the carpenter. The oak, for example,
raised in a humid soil, is more proper for the works of the
cabinet-maker than for those of the carpenter; because it
is less strong and stiff, and is softer and more easy to work
than the same wood raised in a dry soil and elevated
situation: it is also less liable to cleave and split when

only employed for small works. Its strength, compared
with that raised in a drier soil is about as 4 to 5, and its
specific gravity as 5 to 7.

Wet lands are only proper for alders, poplars, and wil¬
lows. Several other species incline to land which is moist
or wholly wet; but the oak, the chestnut, the elm, thrive
only in dry situations, where the soil is good, and where
the water does not stagnate after rain, but is retained
only in sufficient quantity to enable the ground to furnish
aliment for the vegetation. Resinous trees, too, do not
always thrive in the soils and situations proper to the
other kinds of timber, and especially in marshy soils:
sandy soils are in general the best for their production;
and several species affect the neighbourhood of the sea,
.such as the maritime pine, not less useful for its resin than
for its timber.

In fine, trees which grow in poor and stony soils, and
generally in all such soils as oppose the spreading of their
roots, and do not furnish a supply of their proper sap, are
slow and stunted in their growth, and produce wood often
knotty and difficult to work, and which is mostly used as
veneers for ornamenting furniture.

The surest tokens of good wood are the beauty, clear¬
ness, and firmness of the bark, and the small quantity of
alburnum.

It has been remarked that timber on the margin of a
wood is larger, more healthy, and of better quality than
that which grows in the interior, the effect of the action
of the sun and air being less obstructed.

DISEASES OF TREES.

Trees, like animals, are subject to disease. When, by
the effect of old age or disease, a tree dies at the bottom,
even before it has arrived at the ordinary limit of exist¬
ence of individuals of the same species, its wood loses the
qualities not only essential for timber construction, but
also for combustion. It loses flexibility, strength, and
durability; it becomes dry and soft; when it falls it ra¬
pidly rots, or becomes the prey of worms; and it burns
without flame, and with little heat. If, in place of this,
it is felled in its vigour, it ceases to live, it is true; it no
more vegetates, it becomes dry, but it preserves all its
useful qualities, and is fit for any of the purposes to
which timber can be applied. Diseases of plants are, for
the most part, dependent on chemical changes in their
component parts.

The maladies which arise from outward causes are
sores, mutilations, and fractures, which may be the result
of the action on the bark of the teeth of large animals, of
strokes given by accident or design, the effects of wind,
or of lightning. This latter agent is the most destruc¬
tive : the trees are shivered partly by mechanical agency,
partly by sudden expansion of gas.

Dr. Colin observed that the electric fluid first takes the
course of the alburnum as the best conductor, splitting off
the bark by the sudden expansion of the fluid; a part
enters the older portions of the wood, which are compara¬
tively bad conductors, taking the course of the medullary
rays, or points of conduct of the annual layers, or both;
and thus splits the tree in various directions, occasionally
threading it to the extremity of the roots.

KNOWLEDGE OF WOODS. 97

The maladies which can arise from accidents, and from
the customary regimen of vegetation, or from the state of
the atmosphere, and from meteors, are:—Ulcers, cankers,
rottenness, chaps, clefts, and other diseases caused by frost
and cold, exfoliations, tumours, knobs, warts, excrescences,
plethora, return.

Ulcers and Cankers in trees resemble the same diseases
in animals. The origin is generally in the roots. A too
great abundance of sap in some part of a tree manifests
itself in a kind of external suppuration, which is accom¬
panied by a corruption of the fluids, and speedily of the
wood adjoining the ulcerated part. The disease sometimes
spreads, causes the bark to peel off, and then the tree
perishes. Ulcers in elms are-due to a collection of corrupt
fluid from the decomposition of water or sap percolated
through decayed tissue. The fluid blackens whatever it
touches, and is extremely foetid: when a tree so infected
is felled, the odour is very disagreeable while the infected
parts are being lopped off.

Rottenness proves the existence of some disease in the
sap. In this disease, the woody fibre is reduced to powder.

Ulcers, cankers, and rottenness also proceed*from water
obtaining access to the interior of a tree at the points
where the branches leave the trunk,—through clefts,

'O'

which are generally produced by unwonted straining of
the branches by the wind.

Chaps in the bark are occasioned by scorching winds,
drought, sudden changes of season from cold to heat, or
vice versa; or from the too violent action of the sun. These
expose the wood of the tree to the action of the weather;
and their existence is the sign of deterioration in the wood.

Circular Chaps, surrounded by other chaps in rays,
are supposed to be caused by some insect.

Frost Cracks commence in the bark, penetrate the new
wood, and sometimes extend deeply into the heart-wood.
They are caused by the freezing of the water of the sap,
which splits, first the bark, and then the wood of the tree.

Rigorous frosts sometimes act upon the external layers
of alburnum, and hinder them from passing into perfect
wood, although thev continue to exei'cise their functions
in the transmission of the materials which form the new
layers, but in such manner that these do not adhere to
the layers of the year previous. When these arrive at
the state of perfect wood, a void, extending over a consi¬
derable portion of the trunk, and sometimes throughout
its circumference, is left between them and the layers in¬
jured by the frost. Two concentric cylinders are thus
formed, detached, and separated sometimes by an inter¬
val of a finger’s breadth.

Twisted Fibres are not the result of disease, but of
deformity caused by the prevalent action of the wind in
one direction on the head of the tree. The stem, when
young and tender, is thus twisted, and its fibres retain
their screw form when they pass into perfect wood.
Twisted wood is not proper for the use of the carpenter,
as in squaring it many of its fibres would be cut through.

Exfoliation. —This is a disease of the bark, in which it
detaches itself in layers. There results from this an alter¬
ation in the alburnum, and in the wood which it fur¬
nishes. It is believed that exfoliation is caused by some
insect, which as yet, however, has escaped microscopical
research.

Tumours, Warts, Excrescences, and Abscesses, all pro¬

ceed from local disease, which produces deterioration of
the alburnum, and an excessive affluence of sap at certain
points; resulting in extravasation and accumulation of
vegetable substance, forming excrescences and confused
contexture. They are often, too, caused by wounds, by
the attacks of insects, and by parasitical plants. They
injure the wood by disturbing the uniformity of the lig¬
neous fibre.

Plethora. —This is the result of an over-abundance of
nutritive juices, drawn irregularly to different parts of
the tree, and causing deformity. The quality of the
wood is consequently injured by the impairing of its
homogeneousness; and its strength could not be trusted,
especially if exposed to transverse strains.

Return. —This is the last disease of growing trees which
have passed the term of their maturity. It commences
at the top of the head;. and whether it is owing to the
obstruction of the channels which convey nourishment,
a deficiency of the nourishment itself, or weakened vital
energy, its symptoms are a drying and decay of the top
shoots, then of the branches, and lastly of the trunk itself.
On the first appearance of the symptoms the tree should
be felled, in order to save the timber.

TIMBERS FIT FOR THE CARPENTER.

In general, regularity in the roundness, and the taper,
of a tree, and a fine or uniform texture in the bark, indi¬
cate it to be of good quality.

All appearance of knots, wens, swellings, old sores, al¬
though cicatrized, all traces of canker, or of water having
reached the heart of the tree, are infallible signs of dis¬
eased wood. Fresh mosses and lichens on a tree which
has been some time felled, are symptomatic of its having
lain in a wet place. These may also indicate the locality
of some internal disease.

It requires a practised eye to judge of the qualities of
timber while yet in -the unbarked tree; but, as the car¬
penter generally receives the wood on which he operates,
squared, this knowledge is not of so much importance to
him as it is to the timber-merchant.

The qualities which fit wood for works of carpentry are
durability, uniformity of substance, straightness of fibre,*
and elasticity. AVhen wood is squared, its good quality,
especially in the case of the oak, the chestnut, and the
elm, is known by a fresh and agreeable odour which it
exhales, and which is very different from the smell of
wood, however freshly cut, which has begun to decay.
AVhen timber has been felled for a long time, and has
become dry, this peculiar odour is not so perceptible, but
the resinous trees retain the smell of the resin for a very
long time; the odour being again made perceptible by
cutting a slice from the surface. Dry and healthy timber
is solid, tenacious, sonorous, and elastic; when it is dead
or diseased, it is soft, emits a dull sound when struck, and
acquires a disagreeable smell.

The good quality of wood is known also by the unifor¬
mity and depth of the colour peculiar to its species. AVhen
the colour varies much from the heart to the circumference,
and, above all, when it lightens suddenly or too rapidly
towards the limit of the alburnum, we may be assured
that the tree is affected by some disease.

PRACTICAL CARPENTRY AND JOINERY.

The white wood or alburnum of trees should be rejected;
and where there is a double layer of white wood, sepa¬
rated by a layer of perfect wood, as is sometimes though
rarely the case, the wood is unfit for use.

Knotty and cross-grained wood is difficult to work.
Cross-grained wood is rarely of great dimensions, and is
employed chiefly in the construction of machines, and for
purposes in which the tenacity of its fibres is its recom¬
mendation. It is rejected for ordinary work, because it
is difficult, and, consequently, expensive to work, and
weighs heavy in proportion to its strength. Such timber
is very often, however, employed in hydraulic works, es¬
pecially when it is to be wholly under water. It is apt
to become shaky diagonally in drying.

A great defect is when the fibres do not approach to
equality of size. Perfect equality is impossible in tapering
timber, but such an equality as shall not render one part
of the piece of timber much less strong than another is
obtainable by proper selection.

In knotty wood, the knots interrupt that straightness
of the fibres which gives strength. The knots are the
prolongations of the branches across the perfect wood
of the tree from the points where the branches have
commenced. Such knots augment in size in the degree
that the trunk of the tree increases. If the branches have
grown with the tree to the time of its being felled, the
knots will be perfect wood, the fibres of the trunk will
only be turned slightly from their straightness, and if the
knots are few they will not be very hurtful. But if the
branch forming the knot has been suppressed or destroyed,
or has by any cause ceased growing while the tree grew,
the knot formed by it will be inclosed in the new layers
of wood, and may become a cause of destruction by the
decaying of its substance from contained moisture, and
thus a nidus of rottenness is formed within the tree. It
is therefore prudent to probe such knots, and, if they are
decayed, to cut off all the wood which is traversed by
them. In general, the prevalence of knots in a piece of
wood indicates that it has been cut from a branch and not
from the trunk of a tree.

Wood which in growing has been blighted by frost is
not fit for the carpenter. The lateral cohesion of its fibres
is destroyed, and it contains numerous little chaps which
absorb moisture and cause it to rot.

When timber in growing has been subjected to strong
frosts and thaws, the wood is often alternately alive and
dead, and filled with small clefts. It is recognized by an
appearance of marbling which it presents on being cut.

Krafft, in the introduction to his Carpentry, has the
following remarks:—“It is important,” he says, “in the
employment of timber, in pieces used vertically, to place
them with the butt on high, and the top downwards. To
know if a piece of timber is sound in the middle, saw its
two ends, then cause blows with a hammer to be struck
at one end, while the ear is placed against the other; and
if the sound is dull the timber is bad; but if, on the con¬
trary, it is clear, the timber is good.”

Generally when the tree is sound the density decreases
from the butt upwards, and from the centre to the circum¬
ference. The greatest strength is found between the centre
of the tree and the sap-wood; and the heaviest wood is
the strongest.

Sound wood under the saw cuts clean, is bright in

colour, and, when planed, has a silky lustre: unsound
timber wants this lustre, and the saw leaves a woolly
surface.

FELLING OF TIMBER.

In the clearing of a forest, where all the trees without
distinction are felled, the work of destruction commences
at the borders nearest the roads which bound or traverse
it, and proceeds with order and regularity. Care is taken
not to embarrass the outlets, or obstruct the roads. The
manner of procedure is according to the end proposed. If
that be the destruction of the forest and the freeing of
the soil from the remains of trees, in order that it may be
appropriated to some other species of culture, the trees
are removed by the roots, care being taken, in the case of
certain species tenacious of life, not to leave any shoot,
however small. If, again, the object be to produce copse,
the trunks of the trees are cut close to the ground, that
the stumps left in the soil may throw out new shoots.

In thinning a forest, such trees only are felled as have
attained the limit of their development of growth, or at
least as have acquired the qualities which fit them for the
purposes sought.

The felling of timber is performed in either of the three
following ways:—

1. The tree is felled with its trunk and stump separated
from its roots.

2. It is torn up with all its roots attached.

3. It is cut above the soil, either by the saw or by the
axe, with the intention of removing the stump afterwards,
or leaving it for the production of new wood.

In practising the first method, the earth is removed
from around the tree to the depth which will admit of
the roots being cut through; but is retained to fill up the
excavation. The roots are then hewn or sawn through,
and by means of ropes the tree is pulled over to the side
where its fall will least injure the neighbouring trees, or
obstruct the operations on them. The roots are then dug
out, and the earth is thrown back into the hole made by
the removal of the stump.

In the case of such trees as have a stump penetrating
deeply into the ground, the earth may be removed from
around the stump to such a depth only as will admit of the
lateral roots being cut through. The tree is then retained
in its vertical position by a pivot merely; and by means of
chains and levers properly applied, the resistance of this
is overcome, and the tree thrown down as before. This
mode cannot be practised in the case of trees which throw
their roots vertically downwards, such as the chestnut, the
elm, &c. To remove a tree with all its roots attached,
the method is as follows:—The earth is removed from
the principal roots, so as to admit of cords being passed
under them. Then, by means of levers the roots are
raised one after the other; cords or chains are next passed
under the stool, which is raised in the same manner; and
the tree is guided in the direction in which it is wished
it should fall.

Sometimes the tree is overturned by the aid of gun¬
powder. To effect this, it is necessary to remove the earth
from around the roots, so as to diminish the resistance of
the soil. Then, under the trunk a small metal mortar
with a large base is posited upon a piece of wood which

KNOWLEDGE OF WOODS.

is still larger. The loaded mortar is covered with a cast-
iron plate having portions of its corners cut off, so that
the force of the explosive gases may be directed against
the tree. This method is very little used.

The third mode of felling is the most generally adopted.
It is the only available method in the case of such trees
as do not throw out branches at the foot, when it is wished
to leave a stool for the reproduction of wood. The wood¬
cutter makes at the foot of the tree an incision with his
axe, cutting deeper at the side on which he wishes the
tree to fall. The cuts should nearly meet at the centre;
for if too large a solid pivot be left, the falling of the tree
would tear it out of the stool, and make a hole there, which
would cause decay, and unfit the stool for reproduction.

When a tree is felled by the axe, it should be cut as
close to the ground as possible, to get the largest amount
of trunk timber. This is, moreover, serviceable, as in¬
creasing the quality and beauty of the new wood which
the stool throws out. The top of the stool, for obvious
reasons, should be slightly convex or pyramidal.

But it is more economical to cut the tree by the saw
than by the axe. Ordinarily, facilities are afforded to the
workmen in applying the instrument, by sinking a pit
on each side, in which they can stand. As the saw makes
way, the weight of the tree would render it impossible to
work it: this is remedied by inserting small wedges in
the saw-kerf, so that the blade may work freely.

Many modifications of saws for the cutting of growing
timber have been from time to time invented, and also
machinery for giving motion to both circular and recipro¬
cating saws.

It has been observed that the costs of the three me¬
thods described bear the following relation. Tearing up
by the roots costs twelve times as much as felling by
the axe; while the method in which the horizontal roots
are cut off and the tree pulled over, costs only twice as
much. But by both these methods, the available timber
is increased to an extent which more than compensates
for the additional cost.

When, for culture of the soil, the removal of the stump
is desired, either of the two first methods of felling is more
advantageous than the last, from the effective leverage
which the falling tree exerts.

The proper season for the felling of timber has often
been debated.

In Italy and in Spain, timber is felled in summer, and is
found, nevertheless, to be very durable. But it would be
improper to draw a rule from the practice in countries
where the heat and the dryness of the atmosphere favour
the rapid dissipation of the natural juices of the tree.
Some authors argue that the tree should be felled at the
time of the year when the development of the vegetation
is at its height. Others contend that the proper season is
when vegetation has ceased. Tradition, which, in mat¬
ters of this kind, submitted to the test of daily experience,
is seldom wrong, favours altogether the latter view; and
the rule has been to cut the tree between the fall of the
leaf in autumn and the rise of the sap in spring—vegeta¬
tion being then inert.

Buffon and Duhamel advocated the practice of strip¬
ping the bark from the tree a year before felling, on the
supposition that the alburnum by this exposure became
perfect wood. The supposition, it need scarcely be said,

ill)

is wholly erroneous; and a grave evil attending the
practice is, that this depriving the tree of its bark while
it is yet growing, causes it to die, and injures the elas¬
ticity of the timber .

To diminish the quantity of sap in the tree before fell¬
ing it, some have recommended an incision to be made
all round the tree immediately above the ground, and so
deep as to leave a solid pivot merely large enough to sus¬
tain it. This is termed girdling. The connection between
the roots and the trunk and its leaves being thus dis¬
severed, it is supposed that the sap escapes more freely.
The practice does not obtain—for these reasons; it is expen¬
sive, it is not known to be beneficial, and it is dangerous
in the event of high winds. The rapid exhaustion of the
sap could be obtained by placing the tree vertically after
it is cut; but the cost of doing so would be very great.

SQUAKING OF TIMBER.

In order to fit the cylindrical stem of a tree for the or¬
dinary purposes of the carpenter, it is reduced to the form
of a rectangular prism—a form the most convenient,
whether the purpose be the connection of the pieces of
timber by uniting them together either in length or in
thickness, or in any of the diverse ways which ordinary
carpentering requires. It may be said that all the wood
delivered to the carpenter to be operated on, with the
exception of what is intended for pillars, piles, or posts,
requires to be squared.

In squaring a tree, the object to be aimed at is to ob¬
tain either as large a parallelopipedon as possible, or one
which has its dimensions suited to the purpose for which
it is to be employed.

The operation of squaring is generally performed by
the woodmen who fell the timber; and who, by long
experience, can judge at a glance what kind of squared
timber a tree, however deformed, will yield.

The carpenters thus, in general, have little to do with
the squaring of the timber, especially that of foreign
growth; but in works in which it is necessary to employ
timber the produce of our own country, the tree is often
selected and purchased while growing, and is not reduced
to the square form until it comes to the hands of the car¬
penter. The operation may be thus shortly described:—

The tree being elevated on tressels, transverse sections
are made with the saw at both ends perpendicular to its
axis, and on the perfect wood thus exposed, the rectangle
forming the base of the parallelopipedon is inscribed.*

* Tt may be shown that the largest rectangle which can be in¬
scribed in the circle is a square. For if, in Fig. 415, we divide

in the two semi-circumferences which compose the circle, each of

TOO

PRACTICAL CARPENTRY AND JOINERY.

Let the outer circle in Fig. 417 represent the smaller
end of the tree; and let the inner circle distinguish the
separation between the heart-wood and sap-wood. The
rectangle of the greatest square will be obtained by in¬
scribing the square abed in a circle which passes this a
little. The centre o of this y lg . 417 .

latter circle is easily found
geometrically. Through this
centre, two lines are drawn at
right angles to each othei’, and
from it are set oft’ along these
lines the four equal distances
0 a, 0 b, 0 c, 0 d, extending
a little way beyond the line
of the true wood; and abed
give the arrises of the squared
timbei\ When the tree is elliptical, however, a square is
not the greatest rectangle that can be obtained, and it
is necessary to proceed as follows:—On the minor axis
a b of the ellipse (Fig. fig. 418.

418) describe a circle, and
inscribe therein a square
c d e f, and produce the
sides c d, f e to g h, k m;
then will g h k m be the
largest rectangle that can
be inscribed in the el¬
lipse. In practice, having
drawn the two axes of the ellipse, draw the chord line
b 0 , and through the centre draw g m parallel therewith;
then from g and m, where this line intersects the line of
separation between the alburnum and perfect wood, draw
gh, km parallel to the major axis, and gk, hm parallel
to the minor axis, and the rectangle will be obtained.

But it rarely happens that trees are so regular in their
form as to admit of such rules being applied. In ordinary
cases where the deformity is not great, the application
of the callipers to the end will enable the operator to
discover the greatest squaring dimensions of the tree.
In some cases the deformity is so great that the only
guide is practice and a good judgment.

MANAGEMENT OF TIMBER AFTER IT IS CUT.

The management of cut timber, so as to preserve its
qualities from deterioration, and gradually to fit it for
the purpose to which it is to be applied, is a subject of
great importance.

If timber be exposed to great changes of temperature,
to alternations of wetness and drought, to a humid and
hot atmosphere, it will inevitably suffer a deterioration
of those qualities which render it serviceable for the car¬
penter.

Timber, when too suddenly dried, is liable to split:

these triangles is greater than any other triangle aec, afe, moie¬
ties of any rectangle a e cf whatever, inscribed in the same circle;
because botli sets of triangles having the same base, a c, the alti¬
tudes h b, h d of the first triangles are greater than the altitudes g e,
kf of the second triangles; and therefore the square abed, the sum
of the two triangles ab c,cda, is greater than the rectangle a e cf,
the sum of the two triangles a e c, cf a. In the same manner it may
be demonstrated that the square is the greatest rectangle that can
be formed in the quadrant a b (Fig. 416).

when exposed to too high a temperature in a close atmo¬
sphere, its juices are liable to fermentation, followed by
a loss of tenacity and a tendency to rot and become
worm-eaten. The greater the quantity of timber thus
kept together, the more rapidly is it impaired, which is
made sensible to the smell by a peculiar odour emitted
from it.

When timber is exposed to injury from the weather,
and lying long exposed on a damp soil, it is attacked
by wet rot. The alternations, too, of drought and rain,
of frosts and of heat, disorganize the woody fibre, which
breaks, and a species of rottenness ensues resembling the
decay of growing timber. The means of defending the
timber from these various causes of waste, and preserving
it in a state fit and proper to be used in construction, we
now propose to describe.

Although the carpenter has not often to undertake the
charge of the timber in the place of its growth, yet as
there are cases in which he is called upon to do so, we
shall begin by describing the means of preserving the
tree from the time it is felled to the period when it is to
be used in construction.

When the tree is felled, it should be preserved from con¬
tact with the soil, by being elevated on short pieces; and
; to prevent its too rapid desiccation, and the consequent
j formation of clefts and shakes, it should be sheltered
from the sun, but so as to permit a free circulation of air
ai'ound it. Where the felling of wood is performed on a
large scale, sheds, which may be opened on any side at
pleasure, should be constructed, in which the trees may be
deposited. In these, the trees, defended from the sun and
rain, may be exposed to the air, but with the power of
controlling and modifying its action. It has been ob¬
served, that in sheds open on all sides the timber decays
and splits more rapidly than in the open air.

In piling the timber in these sheds, the trees should
not be allowed to be in contact, but should be separated
by pieces formed of a quarter section of a tree. They
should also be carefully classed according to diameter, in
order that the different trunks may be kept level, and
each have a solid bearing, to prevent its sagging, and be¬
coming curved. The longest trees should of course be
placed undermost.

When the timber is squared and cut up, even greater
care must be bestowed on it; not alone on the ground
that it is then so much the more valuable by the labour
which it has cost, but because, by its vessels being divided,
it is more easily affected by deteriorating causes; and by
its surface being augmented, these causes have also a
larger field to operate on.

Timber of the same scantling, felled and cut up at the
same time, should be piled together; and there should not
be miugled in one pile wood of different species.

The first layer of the pile (Fig. 419) should be eleva¬
ted above the soil on sleepers, the higher the better, as
securing a freer circulation of air, and preventing the
growth of fungi. The most perfect security, however, is
obtained by paving the site of the pile, and building
dwarf walls or piers, with strong girders, to form the
foundation for the first tier.

Where the space will admit of it, and the timbers are
square, they should be laid in tiers crossing each other
alternately at right angles, and at least their own width

KNOWLEDGE OF WOODS.

101

cannot be afforded, pieces must be inserted between the
tiers, as shown in Fig. 421.

in Fig. 422. Another way is by crossing the planks, as
seen in Fig. 423; and another, which admits the pile

Fig. 424.

apart. This method will not do for thin planks, because
it would not allow a sufficient circulation of air. These

When the timber has been accidentally wetted, or when
it is necessary to hasten its desiccation, it should be set

are better when piled so that in the alternate tiers there
are only planks sufficient to keep the other tiers from
bending. Where space can be afforded, it is well to pile
square timber in this way. The diagram (Fig. 420) will
best explain this mode. Where space for this cross piling

up against a wall or formed into a hollow pile, as shown

Sometimes it is convenient to pile the wood vertically
against a wall, selecting a northern aspect, and shelter¬
ing the timber by a pent-house roof.

It is profitable to move the wood from the piles and
replace it, turning the sides, altering the relative posi¬
tions of the different pieces in the pile, and changing the
points of support; and at the same time picking out and
excluding any damaged or deteriorated piece. The pieces
between the different tiers should at the same time be in¬
terchanged ; and before being used again, they should be
carefully inspected, and, if decayed or diseased, rejected.

Every vestige of bark should be removed from the
wood before it is piled; for the bark often contains the
germs of disease, or is infested with insects, and in either
case injury is done to the pile.

being carried to a greater height, is by erecting four posts
and building the timber about them, as seen in Fig. 424.

102

PRACTICAL CARPENTRY AND JOINERY.

OF THE BENDING OF TIMBER.

Curved forms, either essential to the stability of a
structure, or necessary for its decoration, require that
the carpenter should obtain the timber naturally cur¬
ved, or should possess the power of bending it. Trees
which yield timber naturally curved, are generally used
for the constructions of the naval architect. If, in ci¬
vil constructions, where curved timber is required, it
should be attempted to be formed by hewing it out of
straight timber, two evils would ensue: the first, a loss
of wood; the second, and greater, the destruction of
its strength by the necessary cross-cutting of its fibres.
Hence, to maintain the fibres parallel among them¬
selves, and to the curve, recourse is had to curving or
bending the timber artificially. This process may be
performed on the trees while yet growing, or on the tim¬
ber after it is squared or cut up. The first process is
rarely performed, and need not be here described in de¬
tail. We shall therefore proceed to the consideration of
the second.

The process of bending timber artificially is founded
on the property which water and heat have of penetrat¬
ing into the woody substance, rendering it supple and
soft, and fitting it to receive forms which it retains after
cooling.

This process is extremely ancient. A familiar illustra¬
tion of the power of the simultaneous action of heat and
moisture in altering the form and dimensions of wood, is
the well-known little puzzle of a key sliding in a mor¬
tise : the key is in one piece, and its two ends have pro¬
jections which make their thickness twice that of the part
which slides in the mortise; and the wonder is, how,
under these circumstances, it was possible to insert the
key; and being inserted, how to remove it. The difficulty
is overcome by steeping one of the ends in boiling water
till thoroughly penetrated, and then squeezing it in a
vice till its dimensions are reduced, so that it passes
through the mortise: when the wood dries and cools, it
resumes its original bulk and form. The softening pre¬
paration for bending timber is effected in the five follow¬
ing ways:—

1. By using the heat of a naked fire.

2. By the softening influence of boiling water.

3. By softening it by vapour.

4. By softening it in heated sand.

5. By vapour under high-pressure.

Of the first method of operation, a familiar example
is afforded by the cooper, who bends the staves of his
casks by kindling within the vessel formed of straight
staves, a fire of straw or shavings. It is also used in
bending the planks used in ship-building; but it is, on
the whole, only applicable to timbers of small scantling;
and in such cases as occur seldom, and where one or two
pieces only are required to be bent.

In the second method, the timber is immersed in water,
which is heated until it boils, and is kept boiling until
the timber is wholly saturated and softened. The timber
being then withdrawn, is immediately forced to assume
the required curvature, and is secured by nails or bolts.
This proceeding has the defect of weakening the tim¬
ber, and lessening its durability. It should, therefore, be

used only in such cases as do not require the qualities of
strength and durability.

In the third process, the timber is submitted to the ac¬
tion of the steam of boiling water. For this purpose it is
inclosed in a box made perfectly air-tight. The box has
a series of grated horizontal partitions or shelves on which
the timbers are laid. From a steam boiler conveniently
situated, a pipe is carried to the box. The steam acts on
the timber, and in time softens it and renders it pliant.
The time allowed for the action of the steam to produce
this effect, is generally one hour for every inch of thick¬
ness in the planks.

The fourth method of preparing the wood for bending,
is by applying heat and moisture to it through the
medium of the sand bath. The apparatus for this pur¬
pose is a furnace with flues, traversing the stone on
which the sand is laid, in the manner of hot-house flues.
There is also provided a boiler in which water is heated.
On the stone a couch of sand is laid: in this the tim¬
bers are immersed, being set edgeways on a bed of sand
about 6 inches thick, and having a layer of sand of
the same thickness separating them, and being also co¬
vered over with sand. The fire is then lighted in the
furnace, and after a time, the sand is thoroughly mois¬
tened with boiling water from the boiler before men¬
tioned. This watering is kept up all the time that the
timber is in the stove. Thin deals require, as in the
preceding case, an hour for each inch of thickness; but
for thick scantlings the time requires to be increased;
for instance, a 6-inch timber should remain in the stove
eight hours.

The fifth mode, by means of high-pressure steam, only
differs from the third process described in this, that the
apparatus requires to be more perfect. The box, there¬
fore, is generally made of cast-iron, and all its parts are
strengthened to resist the pressure to be employed. When
the steam has a pressure of several atmospheres, the soften¬
ing of the wood is very rapid; and it is very effectually
done by this method.

After the timber is properly softened and rendered
pliable, it is bent on a mould having a contour of the
form which the timber is required to assume.

The simplest method of doing this is shown in outline
in Fig. 425. A series of stout posts, a a a, are driven

into the ground, on a line representing the desired curve.
The piece of wood m n, when softened, is inserted
between two posts at the point where the curvature is to
begin, as at a b, and by means of a tackle, applied near
that point, it is brought up to the next post, a, where
it is fixed by driving a picket, c, on the opposite side.
The tackle is shifted successively from point to point;
and the pickets, c, d, e, are driven in as the timber is
brought up to the posts. It is left in this condition
until it is cold and dried; and then it is removed to make

KNOWLEDGE OF WOODS.

103

way for another piece. The timbers of the roof, Fig. 3,
Plate XXIX., were bent somewhat in this manner. But
if the balk is required to be more accurately bent, and
out of winding in its breadth, squared sleepers, aaa (Fig.
426, Nos. 1 and 2) are laid truly level across the line
of curva ture, and the posts b b are also accurately squared
on the side next the balk. An iron strap c, which is

No. 2.

• fine

made to slide freely, is used for attaching the tackle, and
as the balk is brought up to .the curve, it is secured to
the posts b, b by two iron straps, e e, e e (seen better
in the vertical section, No. 2), which embrace the pieces
/, on the opposite side, and ai'e wedged up tight by the
wedges h It.

In operating in either of the ways described, only one
piece of timber can be bent at a time. By the following
method several pieces may be bent together:—

Fig. 427 is a vertical projection, and Fig. 428 a trans-

Fig. 427.

Fig. 428.

verse vertical section, of the apparatus. It consists of the
horizontal pieces a a, arranged with their upper surface
in the contour of the curve. They are sustained by
strong framing b b, c c, d d. The timber is laid with its
centre on the middle of the frame, and by means of pur¬
chases applied at both sides of the centre, and carried
successively along to different points towards each end,
it is curved, and secured by iron straps and wedges as
before. The frame may be made wide enough to serve
for the bending of other pieces, as m, n ; or for a greater
number, by increasing the length of the pieces a a, and
supporting them properly. The two apparatuses last de¬
scribed are taken from Colonel Emy’s work.

These methods are not quite perfect; for in place of the
timber assuming a regular curvature, it will obviously be
rather a portion of a polygonal contour. To insure per¬
fect regularity in the curve, it is necessary to make a
continuous template, in place of the several pieces a aaa.
The substitution of the template for these, we need not,
however, illustrate or describe, as its construction will be
suggested by what has already been said.

It is necessary to remark, that in all the cases, the tim¬
ber should be preserved from being injured by the iron
strap, by a piece of wood inserted between them, as shown

in the figures.

curvature given to the

Care must be taken that the
timber is such as will not too greatly extend, and, perhaps,
rupture the fibres of the convex side, and so render it
useless.

The process of bending timber which we have described,
is, as will be seen, restricted to very narrow limits. The
effect, when the curve is small, is to cripple the fibres of
the inner circumference, and to extend those of the ex¬
terior, and the result is, of course, a weakening of the
timber. Recently, however, a process has been patented
by an American gentleman, Mr. T. Blanchard, in which
the bending, effected by end pressure, is not only not at¬
tended with injurious effects, but on the contrary, gives
to the timber qualities which it did not before possess.
In an able article in Household Words, the advantages of
this new process are set forth as follows:—“ The principle
of bending, as employed in this new application, is based
on end-pressure, which, in condensing and turning at the
same time, destroys the capillary tubes by forcing them
into each other. These tubes are only of use when the
tree is growing, and their amalgamation increases the
density of the timber, the pressure being so nicely ad¬
justed that the wood is neither flattened nor spread; nor
is the outer circumference of the wood expanded, though
the inner is contracted. Now, the error of the former
process, as expounded by competent judges, has arisen
from the disintegrating of the fibre of the wood by ex¬
panding the whole mass over a rigid mould. Wood can
be more easily compressed than expanded;
therefore, it is plain that a process which in¬
duces a greater closeness in the component parts
of the piece under operation—which, as it were,
locks up the whole mass by knitting the fibres
together—must augment the degree of hardness
and power of resistance. The wood thus be¬
comes almost impervious to damp, and to the
depredations of insects, while its increased den¬
sity renders it less liable to take fire; and the
present method of cutting and shaping timber being super¬
seded, a saving of from two to three fourths of the mate¬
rial is brought about. The action of the machine throws
the cross grains into right angles, the knots are compelled
to follow the impulse of the bending, the juices are forced
out of the cells of the wood, and the cavities are filled up
by the interlacing fibres. In the same way, you may
sometimes see in the iron of which the barrels of muskets
are made, a kind of dark grain, which indicates that the
particles of the metal, either in the natural formation or
in welding, have been strongly clenched in one another.
These specimens are always valued for their extraordinary
toughness, as well as for a certain fantastical and mottled
beauty.

“ Another of the good results of this method is, that
the wood is seasoned by the same process as affects the
bending. The seasoning of wood is simply the drying
of the juices and the reduction of the mass to the mini¬
mum size before it is employed, so that there should be
no future warping. But, as we have already shown, the
compression resorted to in the American system at once
expels the sap, and a few hours are sufficient to convert
green timber into thoroughly seasoned wood. Here is an
obvious saving of time, and also of money; for the ordi¬
nary mode of seasoning by causing the wood to lie waste
for a considerable period, locks up the capital of the trader,
and of course enhances the price to the purchaser. Time
also will be saved in another way, in searching for pieces
of wood of the proper curves for carrying out certain

104

PRACTICAL CARPENTRY AND JOINERY.

varies according to the quickness of the sweep, and will
give the artist greater freedom in his designs, by allowing
him to introduce lines which are now cautiously avoided, [
in order to prevent the cost of their execution.' ” //

Mr. Mayhew further observes, that the process has the
capability of bending into a permanently set form any
wood up to 16 inches square, however hard, not only
without injuring its fibres, but positively rendering the
wood more rigid, and, at the same time, increasing its
strength to such an extent, that in a structural point of
view, in many cases, it will supersede the necessity of
using iron.

Fig. 429 shows the form of the machine for timbers

under 6 inches square.
Figs. 430 and 431
show the machine for
heavy timbers above
that scantling.

The principle, as
has been stated, is the
application of end-
pressure; but another
characteristic feature
is, that the timber,

during the process, is subjected to pressure
on all sides, by which its fibres are pre¬
vented from bursting or from being crip¬
pled; and, in short, the timber is prevented
from altering its form in any other than
the desired manner. The set imparted to
it becomes permanent after a few hours,
during which time it is kept to its form by
an enveloping band and a holding bolt, as shown in
Fig. 432.

SEASONING OF TIMBER, AND THE MEANS
EMPLOYED TO INCREASE ITS DURABILITY.

The perfect desiccation of timber appears to be one of
the best means of insuring its preservation; and this has
been sought to be accomplished by applying heat to the
pieces of wood. This must be done gradually, as the
sudden application of heat with the view of drying the
timber has the effect of rending or cracking the exterior
before the interior has time to dry. Burying the timber
in dry sand, so that the sun may evaporate the moisture
gradually, and covering it with quicklime, to produce a
gradual heat, have both been resorted to—the former with
success in warm countries—the latter, although making
the timber dry, compact, and hard, often producing rents
by the difficulty of regulating the heat. Stoves or ovens
were also resorted to; but these were injudiciously con¬
structed, and it was found that timber, when of large di¬
mensions, could not be completely dried in them. There
was no provision in them for conveying away the vapour
generated by the application of the heat. But recently
the plan of drying by subjecting the timber to the action
of a current of air highly heated, so as to have its capa¬
city for moisture greatly increased, has been adopted with
the happiest results.

But mere desiccation does not secure the end aimed
at; for it does not exhaust the vegetable matter from out

designs. ‘ How delighted/ says Mr. Jervis, the United
States inspector of timber, ‘ will the shipwright be to get
clear of the necessity of searching for crooked pieces of
timber; there need be no longer any breaking of hats in
the frame, as we have been wont to break them. We
shall see Nos. 1, 2, and 3 futtocks, at least, all in one
piece.' An English architect, Mr. Mayhew, remarks
that ‘ one of the advantages of this method is, that in its

application to all circular, wreathed, or twisted work, it
not only preserves the continuous grain of the wood, which

unsightly joints, ill concealed at best, but it will mate- 1
rially reduce the cost of all carved work, which now I

is now usually and laboriously done by narrow slips of
veneers glued on cores cut across the grain, with many

KNOWLEDGE OF WOODS.

105

the pores of the wood: it only dries it there; and when it
is exposed to humidity it becomes fluid, and resumes its
tendency to fermentation.

Immersion in water for such a time as shall permit this
matter to be dissolved and washed out of the wood pre¬
vious to the desiccating process being applied, will secure
it from the tendency to corruption when again exposed
to humidity. For this, running water is obviously pre¬
ferable to stagnant water; and it may fairly be inferred
that to the immersion for a long time in the rivers in
which they are floated down to the ports for embarkation,
is to be attributed the greater durability of the pines of
the Baltic, when they are properly treated by thorough
drying before being used. But to render this immersion
effectual, it is requisite that it be total and complete, and
that it be not too long continued. It is considered that
the limit of duration is from three to four months.

Immersion in hot water effects the same purpose much
more rapidly; but as the wood has to be submitted to the
action of the water for ten or twelve days, the expense is
prohibitory of the process, unless in cases where the con¬
densing water of a steam engine in constant operation can
be made available. As we have before remarked, when
speaking of the bending of timber, the action of the hot
water impairs its strength, and should not be used where
strength is an object.

Immersion in salt water is a means of adding to the
durability of timber. It increases its weight, and adds
greatly to its hardness. It is attended, however, by the
grave inconvenience of increasing its capacity for mois¬
ture, which renders this kind of seasoning inapplicable for
timber to be employed in the ordinary practice of the
carpenter.

The water seasoning of which we have been speaking,
has many objectors; and their strongest arguments are
founded on the facts that there are examples of roofs which
have existed for ages, the timbers of which have not been
subjected to this water seasoning. But numerous experi¬
ments prove, beyond contradiction, that timber immersed
in water immediately after being felled and squared, is
less subject to cleave and to decay, and that it dries more
quickly and more completely; which proves that the water
evaporates more readily than the sap, of which it has
taken the place. The immersion, however, impairs, to
some extent, the strength of the timber; and this consi¬
deration indicates the applicability or non-applicability
of the process. When the timber is required for purposes
for which dryness and easiness of working are essential,
then the water seasoning may be employed with advan¬
tage; but when for purposes in which strength alone is
the great requisite, it should not be used.

Sir Samuel Bentham found, that large timber, when
left with its sap-wood on, in the course of a few years
had become dry, compact, and hard in the heart; but
where the sap-wood had been taken off, as in sided timber,
the exterior became more or less crooked and damaged
before the interior ■was properly seasoned. The greatest
objection to this mode of seasoning is its costliness, aris¬
ing from the loss of interest on the capital invested.

As the condensation produced by heat increases the
hardness of timber, it has been imagined that charring
its surface, by increasing its hardness, would also increase
its durability. In this supposition it is probable that the

custom of charring the ends of piles and posts which are
to be buried in the earth, has originated. The carbon¬
ized portion of the wood may, indeed, hinder the imme¬
diate contact of the humid earth with the n on-carbonized
wood; but it is to be questioned whether the sound tim¬
ber destroyed in the charring would not have been as
good an envelope as the charred surface; and taken quite
as long to be destroyed by its contact with the earth as
the other would act as a protection. In place of charring
the ends of posts or piles, therefore, it would seem better
to coat them with some substance impervious to air. But
timbers buried in the earth begin as often to rot from
within as from without, by the fermentation of their
natural juices, as they are too often employed without
being submitted to any kind of seasoning process what¬
ever, while, in timbers so placed, the protection of tho¬
rough seasoning is especially requisite.

The gradual combination of the combustible elements
of a bod}^ with the oxygen of the atmosphere, produces a
slow combustion or oxidation, to which Liebig applies the
term eremacausis.

The eremacausis of an organic matter is retarded or
completely arrested by all those substances which prevent
fermentation or putrefaction. Mineral acids, salts of mer¬
cury, aromatic substances, empvreumatic oil, and oil of
turpentine, possess a similar action in this respect.*

Timber, after being framed, is subject to the same dis¬
eases and causes of decay as before. Often, indeed, the
latent diseases only develope themselves when the timber
has been worked and framed, and when the replacing of
the affected by a sound piece may be very difficult, or
altogether impossible.

Besides the diseases proper to the species of tree, to the
soil, or to the climate, or those caused by any of the acci¬
dents which have been described, timber is liable to the
attacks of insects, which are often detrimental to it, and
not seldom altogether destructive of it. Among the in-
sects whose attacks are most fatally injurious to the wood,
are the white ant, the Teredo navalis, a kind of Pholas,
and the Limnoria terebrans.

The white ant devours the heart of the timber, reducing
it to powder, while the surface remains unbroken, and
affords no indication of the ravages beneath.

The teredo and pholas attack wood when submerged in
the sea. The teredo, its head armed with a casque or
shell in the shape of an auger, insinuates itself into the
wood through an almost imperceptible hole; it then in
its boring operations follow's the line of the fibre of the
wood, the hole enlarging as the worm increases in size.
It forms thus a tube, extending from the lowest part of
the timber to the level of the surface of the water, which
it lines with a calcareous secretion. A piece of timber,
such as a pile in a marine structure, may be perforated
from the ground to the water level by a multitude of
these creatures, and yet no indications of their destructive
work appear on the exterior.

The pholas does not attack timber so frequently as the
teredo; and its ravages are more slowly carried on. Its
presence in the wood, therefore, though very dangerous,
is not so pernicious as the other.

For the protection of timber from disease, decay, and

* Liebig’s Chemistry of Agriculture and Physiology.

10 G

PRACTICAL CARPENTRY AND JOINERY.

the ravages of insects, various means are employed. These
may be classed as internal and external applications.

I. Preservation of Wood by impregnating it with
Chemical Solutions.

The chemicals usually employed in solution are the
deutochloride of mercury (corrosive sublimate), the prot¬
oxide of iron, the chloride of zinc, the pyrolignite of iron,
arsenic, muriate of lime, and creosote. They are either
used as baths, in which the timber is steeped, or they are
injected into the wood by mechanical means; or the air
is exhausted from the cells of the wood, and the solutions
being then admitted, fill completely every vacuum.

The saturation with corrosive sublimate is called Kyan-
izing, from the name of the inventor, Mr. Kyan. When
this is performed by steeping, the time required is gene¬
rally estimated as follows: — Scantlings of 14 inches
square, fourteen days; of 7 inches square, ten days; and
for pieces 3 inches square, seven days are sufficient.

The saturation with the solution of the chloride of zinc
is the patent process of Sir William Burnett. The in¬
jecting sulphate of iron and muriate of lime is Payne’s
patent process. The creosote is patented by Mr. Bethell.

All of these processes are advantageous under certain
circumstances; but it cannot be said that any of them is
infallible. It is not easy, however, to discover whether,
in cases of failure, there may not have been some defect
in the process; and therefore, in important work, the
additional security against the ravages of disease and
decay which the impregnation gives, when properly per¬
formed, should not be neglected. ,

But it is to be feared that against the attacks of the
marine pests—the teredo, the pholas, and the Limnoria
terebrans —the protection these processes afford is at the
best doubtful. An exception to this may probably be taken
in favour of Mr. Betheil’s creosote process. The soluble
salts are supposed to act as preservatives of the timber, by
coagulating its albumen; thus the very quality of combin¬
ing with the albumen destroys the activity of the salts as
poisons, and hence although preservatives against decay,
they may, when thus combined, be eaten by an insect with
impunity. With creosote, however, the case is different.
It fills the vessels of the wood, and its smell is so nauseous
that no animal or insect can bear it. It is also insoluble
in water, and cannot be washed out. It is thus a protec¬
tion to the wood against the ravages of insects, and also a
preservative from decay. But there is great difficulty in
injecting it into the heart of the wood; and into hard
woods it cannot be perfectly injected. Mr. Rendell con¬
siders that for marine purposes the creosote should be used
in the proportion of 10 lbs. to the cubic foot. For ordi¬
nary purposes much less is required.

Previous to the application of any of these substances,
however, and as a preparative for it, it is essential that
the timber be thoroughly deprived of its moisture. In
regard to this, Mr. Davidson says, that—

1 . Different woods and different thicknesses of wood
require different degrees of heat.

2 . Hard woods, and thick pieces of wood, require a
moderate degree of heat, from 90° to 100°.

3. The softer woods, as pine, may be safely exposed
to 120° or even to a higher temperature. When cut exceed¬
ingly thin, and well clamped, 182° or 200° have been found
to harden the fibre and increase its strength.

4. Honduras mahogany boards, of 1 inch thick, may be
exposed with advantage as regards colour, beaut} 7 , and
strength, to even 280° or 300°. A piece of this wood H
inch thick, cut fresh from the log, was deprived wholly of
its moisture, amounting to 36 per cent., by exposure to a
temperature of 300° for fifty hours.

But in practice, from 115° to 120° of temperature are
the best calculated to secure perfect desiccation in slabs of
moderate thickness. Supposing the current of heated au¬
to be kept up during twelve hours every day with this
temperature, one week may be allowed for every inch
thick of the timber, up to 4 inches; but the time must be
increased when the thickness exceeds 4 inches, to seven
weeks for 6 inches, and ten weeks for 8 inches. If the tem¬
perature is increased, and the blast of air made continuous,
the desiccation may be effected in forty-eight hours.

An exception must be made in regard to English oak,
which should never be exposed to a higher temperature
than 105°.

The velocity of the heated current should be 100 feet
per second, and the area of outlet for the moisture and
used air should be greater than the area of inlet.

When the timber is perfectly deprived of its moisture,
it is in a condition for the application of the preservative
agent. The different agents and processes in use may be
briefly desex-ibed.

Kyanizing .—In 1832, Mr. Kyan took out a patent fox-
soaking timber in chloi’ide of mercui-y or cori’osive subli¬
mate. In cases where this was pi-operly applied, it seems
to have been effective; but as it is expensive to apply the
solution of sufficient strength, the process came to be im¬
perfectly carried out, and consequently failed.

Margary's Process. —This was patented in 1837- It
consisted in soaking the timber in a solution of acetate
or sulphate of copper. It has been extensively used, and
when the solution is of proper strength, and a sufficient
quantity is absorbed, it is also efficient to a certain extent.

Sir William Burnett’s Process. —In 1838, this pi-ocess,
which consists in impregnating the timber with a solution
of chloi’ide of zinc, was patented. The principle assumed
by the patentee is, that the chloride forms an insoluble
compound with the albumen of the wood; and this is the
theory of action of the chemical compounds already named.
It appears, however, that all such agents lose, in time, their
efficacy, apparently because the aqxxeous portion evapo¬
rates, and the timber again absorbs the humidity of the
atmosphere. The constant alternations of wet and dry
so weaken the solution as to render it inoperative.

In Sir William Burnett’s pi’oeess, the hot solution of
the chloride is forced into the timber under pi-essui-e in
cylinders hermetically sealed. In heating the solution,
a horse-shoe boiler on the circulating principle is used,
and is found to answer well for this and for Margary’s
process—a sufficiently high temperatxxre being maintained
at a modei-ate cost.

Payne s Process. —This was patented in 1841. In this,
two solutions are used in succession; the first, an earthy
or metallic solutioxx, is forced into the timber under pres¬
sure; and the second, a decomposing fluid, is then foi'ced
in, and forms with the former an insoluble compound in
the pores of the wood. Thus, sulphate of iren and car¬
bonate of soda will form oxide of iron in the cells of the
timber. When this operation is well performed, as in

KNOWLEDGE OF WOODS.

107

France, the results have been satisfactory. According to
> experiments made under the direction of Captain Moor-
j som, in 1839, it would appear that the chemical preser-
i vatives injure, to some extent, the transverse strength
of the timber. The ratio of strength in Archangel deal
and American pine, in their prepared and natural states,
appears to be as 976 to 1000.

The value of tars and essential oils as preventives of 1
the decay of timber has been long known, and so early '
as 1737, a patent was granted to Alexander Emerson for
the application of hot boiled oil mixed with poisonous
substances. In 1754, a patent was granted to John
Lewis for the application of a varnish made from the
juice of the pitch {line; and also for a process for distilling
plantation tar, to be applied for the preservation of wood.
None of the processes came into extensive use, chiefly on
account of want of skill in their application. Mr. Beth-
ell, in 1838, took a patent for impregnating timber with
creosote; and this process is so effectual, that it is in con¬
stant use in cases where the odour of the creosote is not
an obstacle to its employment.

The preservative properties of ci’eosote are said to be
owing to its coagulating the albumen, preventing the
' absorption of moisture, and to its being fatal to animal
and vegetable life, thereby arresting the vegetation of the
tree, preventing the growth of fungi, and repelling the
attacks of insects.

M. Boutigny, in conjunction with M. Hutin—proceed¬
ing on the acknowledged theory, that the moisture and
oxygen of the air penetrating into the heart of the wood
by absorption and filtration, produce eremacausis, and
that these elements of destruction appear to act chiefly at
the ends of the timber—conceived that if, after the timber
was completely deprived of moisture, the ends of its pores
were hermetically sealed, absorption, and consequently
decay, would be prevented. They accordingly introduced
the system of desiccating the timber, partially charring
its ends, and then immersing them in oil of schistus, or
some analogous substance. This penetrates with rapidity,
the ends are then blazed off, and plunged to the length
of a few inches into heated pitch, tar, or gum-lac, which
completely seals the pores.

Dr. Boucherie, arguing that all the changes in woods
are attributable to the soluble parts they contain, which
either give rise to fermentation or decay, or serve as food
for the worms; and that, as the result of analysis, sound
timbers contain from three to seven per cent, of soluble
matters, and the decayed and worm-eaten rarely two—
commonly, indeed, less than one per cent.—concludes,
that since the causes of the changes it undergoes originate
in the soluble matters of the wood, it is necessary, for its
preservation, either to extract the soluble parts, or to
make them unchangeable by introducing substances which
should render them unfermentable or inalimentary. This
he considers may be effected by many of the metallic salts
and earthy chlorides. He shows, by experiments on vege¬
table matters very susceptible of decomposition, such as
the pulps of carrot and beet-root, the melon, &c., which
differ from wood only in the greater proportion of soluble
matter they contain, that in their natural states they
rapidly alter, but are preserved by the pyrolignite of iron.
Dr. Boucherie conceived that if solutions of sulphate of
copper, pyrolignite of iron, or other salts, could be made

to take the place of the natural juices of the plant while
it yet lived, the vessels of the tree would become filled
with the fluid by the process which he calls aspiration.
He supposed that by using proper solutions he should be
able to protect the wood from dry or wet rot, to augment
its haidness, to preserve and develope its flexibility and
elasticity, to render change of form impossible, to prevent
warping and cleaving, and to render it incombustible, or
at least to reduce its inflammability, and, lastly, to give
to it various colours and odours.

1 he method of proceeding first adopted was to employ
the vital energy of the tree to draw the liquid into its
vessels by means of the circulation of the sap. This was
effected either by sawing the tree above the root, and im¬
mersing it vertically in a bath of the fluid, or by girdling
the tree, that is, cutting it all round with a saw, so deep
as to leave only a pin in the centre sufficient for its sup¬
port, and surrounding the cut with a trough, into which
the fluid was poured.

When pyrolignite of iron was the fluid used, the hard¬
ness of the timber was more than doubled. The quality
of flexibility was increased by the chloride of lime and
other deliquescent salts. VY arping and splitting were
stayed by a weak infusion of the chloride of lime. Inflam¬
mability was diminished by earthy chlorides. Mineral
succeeded better than vegetable colours in the process of
dyeing the wood. Resins dissolved in essential oils, by
their being absorbed, rendered the wood impervious to
water.

It is right to add, that Mr. Bethell, already mentioned,
patented a similar process in 1838, two years before Dr.
Boucherie’s method was made known in France. Mr.
BethelTs specification says: “Trees just cut down may be
rapidly impregnated with the solutions, by merely placing
the butt ends in tanks containing them. They will thus
circulate with the sap throughout the whole tree; or it
may be done by bags of water-proof cloth affixed to the
butt ends of the trees and filled with the liquid.” Pyro¬
lignite of iron is especially mentioned as circulating freely
with the sap.

But the process now adopted is that of forcing the
liquid through the timber, and is carried on as follows:—
After the tree is felled, a saw cut is made across its centre,
and nearly through its diameter. By slightly raising the
tree under the centre by a wedge, the cut is opened a
little, and a piece of string is inserted in it a little within
the lip or edge all round. On lowering the centre, the
cut closes on the string, which forms a water-tight joint;
a hole is then bored obliquely into the cut, and a hollow
plug driven into it. A flexible tube is then fitted to the
plug, and its other end carried to a cistern containing the
solution, and placed high enough to give the requisite pres¬
sure. When the communication is completed, the liquid
flows into the cells of the wood from the centre towards
the ends, driving out the sap before it. When the solu¬
tion appears at the ends, the impregnation is complete.
When the timber cannot be divided in the middle, one
of the ends is capped by a piece of board about an inch
thick. This is attached by screws, or by screwed dogs.
The joint is made as before, the cap is tightened up, and
the liquid injected in the same manner.

To make certain that the sap has been entirely replaced
by the solutions, a chemical test is applied. For example,

108

PRACTICAL CARPENTRY AND JOINERY.

when the solution is sulphate of copper, a piece of prus-
siate of potash is rubbed oil the end of the timber, when,
if the solution has reached the end, a deep red-brown
stain is produced.

The solution now preferred for use is formed of one part
by weight of sulphate of copper, dissolved in 100 parts of
water.

All woods do not, of course, absorb the same amount
of solution, and the sap-wood absorbs more in propor¬
tion than the heart-wood. From this it may be inferred,
which is the fact, that the process is attended with the
best results when applied to the commonest and cheapest
kinds of timber. The general estimate is, that the quan¬
tity absorbed is equal in cubic extent to one-half the cubic
dimensions of the timber. The longer the injecting pro¬
cess is delayed after the felling of the timber, the slower
is its progress. In newly felled timber, a log 9 feet long
occupies two days, when the head pressure is feet.
Three months after felling, the process would occupy
three days; and four months after felling, four days. One
great advantage of this process is, that the timber requires
no drying or previous preparation of any kind.

II. Preservation by Paints and other Surface Appli¬
cations.

Timber, when wrought, and either before it is framed,
or when in its place, is coated with various preparations,
the object of which is to prevent the access of humidity
to its pores. In the application of such surface coatings,
it is essential that the timber be thoroughly dry; for if it
is not, the coating, in place of preserving it, will hasten
its destruction, as any moisture contained in it will be |
prevented from being evaporated, and will engender in¬
ternal decay. This result will be more speedily developed
as the colour of the coating is more or less absorbent of
heat.

One of the most common applications to timber con¬
structions of large size, is a mixture of tar, pitch, and
tallow. The mixture is made in a pot over a fire, and
applied boiling hot. In the use of this too great caution
cannot be employed to prevent danger from fh-e. The
bridge of Dax, on the Adour, was entirely burned imme¬
diately after its construction, and when the tarring had
just been completed. The pontoon on which the mixture
was prepared was carefully kept to the leeward of the
bridge; but the mixture in one of the pots having taken
fire, and the wind changing suddenly, the flames were
driven against one of the piles, which instantly ignited.
The fire spread with a prodigious rapidity, enveloping in
flames the whole structure, and in a short time entirely
consumed it.

Another preservative for large works is painting with
sand. It is thus performed:—When the wood is perfectly
dry, a coating of some cheap pigment, ground in drying
oil, is given to it; and while it is wet, it is dusted over
with sand, either by means of a box with a perforated
lid, or by a sieve, when the surface is horizontal, or simply
by the hand. The sand should be purely silicious, well
washed, and perfectly dry. AY hen the first coat is quite
dry, it is brushed over with a stiff brush, to detach the
loose particles of sand, and then a second coat of paint is
applied, and sanded over, like the first. When dry, this
is brushed, and a third coat is applied and sanded in like
manner. The number of coats depends on the circum¬

stances of the case. The finishing coat should be of good
oil paint of a proper colour.

When this kind of coating is executed with care and
attention, it has great solidity. It fills the cracks of the
timber and the joints of the framing, and is a good pre¬
servative. Its surface, however, is necessarily rough and
granular; and it, therefore, is not adapted for work in
which neatness is desired.

But the most universally applicable protective coatino-
is good oil paint. To render the paint fit for works of
carpentry, it is necessary that the oil should be good, the
paint insoluble in water, and thoroughly ground with
the oil, and that in its application it should be well
brushed with the end, and not with the side of the brush.
Such a coating has not the disadvantage of weight, like
the painting with sand; nor does it, like it, alter the form
of the object to which it is applied.

The timber to be painted in oil should be planed smooth;
and it is essentially requisite that it be dry. It is usual
to submit it to the action of the air for some time before
painting, and then to take advantage of a dry season to
apply the paint.

To render effectual any of the surface coatings we have
mentioned, it is necessary to take care that the joints of
framing are also coated before the work is put together.
If this be neglected, it will happen that although any
water which may fall on the work will evaporate from
the surface, some small portions may insinuate themselves
into the joints, and these remaining, will be absorbed by
the pores of the wood, and become the cause of rot. The
joints of all exposed work should, therefore, be well coated
with the protective covering before it is put together.

Besides these fluid compositions, timber exposed to the
action of marine insects is often covered with a sheathing
of metal, usually copper. This metal is, however, very
rapidly destroyed by the action of sea-water, and does
| not afford a protection against the ravages of these crea¬
tures.

Broad-headed scupper nails are sometimes used, and
the corrosion which ensues by the action of the salt-water
indurates the wood so as often effectually to protect it.

PROTECTION AGAINST FIRE.

To render wood incombustible has frequently been
attempted, but with no great success. AVhen we consider
the number of structures which are composed of timber,
and which, by a slight accident, may become a prey to
fire, we cannot wonder at the many attempts which have
been made to prevent such a disaster.

The means proposed have been—1st. To impregnate
the wood with saline solutions; 2d. To cover it with some
incombustible coating or cement; and 3d. To sheathe it
with metal. All these means are attended with great
expense, and incompletely fulfil the purpose. Some of
the saline solutions have the effect of rendering the wood
more susceptible of atmospheric influences. They enable
it to resist only the first attack; as the heat augments,
the water of the salts evaporates, and the salts themselves
decrepitate, and leave the wood a prey to the flames. It
j is said, however, that Sir William Burnett’s process for
the prevention of decay insures also the incombustibility

KNOWLEDGE OF WOODS.

109

of the wood; and that in the most intense fire, timber so
prepared, would only be charred, and would never burst
into flame.

The external coatings of non-conducting substances
serve also to resist only the first attack of the flames.
They are soon either detached from the timber, or they
become so heated as to reduce the wood to charcoal.

Metallic envelopes, infusible at the first, become soon
highly heated, and more speedily reduce the wood to
charcoal than the non-conducting coverings. It is, there¬
fore, useless to reckon on the efficacy of any of these
means of rendering wood incombustible.

DESCRIPTION OF WOODS.

HARD WOODS.

The Oak.— The oak is the greatest, the strongest, and
the most durable of all the forest trees of this country.
It is a native of temperate climates, and is not found in
either the torrid or frigid zones. Neither is it found,
even in temperate climates, at elevations where the tem¬
perature is very low. It grows naturally in the middle
and south of Europe, in the north of Africa, in Asia, in
Natolia, the Himalayas, Cochin-China, and Japan. In
America it is abundaut, especially in the United States.

Of the oak there are many species; the most common
of which, as the subjects of forest culture in this country,
are the Quercus robur or pcdunculata (common oak),
Quercus sessiliflora (the sessile-fruited oak). The former
has its fruit on a long foot-stalk or peduncle; the latter
has its fruit sessile, or on a very short stalk. The common
oak is of slower growth than the other, which, moreover,
tends to grow with a more erect stem and less tortuous
branches. The common oak is believed to be more dur¬
able than the sessile-fruited oak; but the cause of the
difference in their durability is by some assigned to the
modifications produced by soil and climate.

The oak, although growing in a wide range of soils,
prefers the clayey, and it is in the alluvial deposits of Eng¬
land and Scotland where the noblest specimens of this
tree are to be found. The oak is the most solid and durable
of European woods. It is certain that carpentry structures
of oak timber have remained in perfect preservation for
more than 600 years. When immersed in water it becomes
excessively hard, and is nearly imperishable.

Although the oak does not reach the height of some of
the pines and palms, and its trunk never attains the enor¬
mous magnitude of those varieties of which we have
spoken, it is nevertheless found of very large dimensions.
The trunks of trees of this species have been known to
grow to a height of 140 feet, and to measure more than
30 feet in circumference. An enormous oak was disco¬
vered in Hatfield Bog, Yorkshire; it was 18 feet in circum¬
ference at the upper end, and 36 feet at the lower end, and
although but a fragment, measured 120 feet in length.

The general height of British oaks, however, is from
60 to 80 feet; and of American oaks, from 70 to 90 feet.

The oak grows very slowly. It has been known at
100 years old to be only 1 foot in diameter. Until the
age of forty years it grows pretty fast, but after that its
increase becomes less and less sensible. At 200 or 300 j

years old, these trees are at their best. Vancouver, from
observations on the growth of timber in Hampshire,
arrived at the conclusion that the relative growth of wood
in that county, taking the trees at ten years’ growth,
and the oak as a standard is—Oak 10, elm 16, ash 18,
beech 20, white poplar 30. That is to say, in any given
time, if the growth of oak be 1, the growth of white
poplar will be 3.

In 1792, an oak at Wimbush, in Essex, measured 8 feet
of inches in girth, at 5 feet from the ground; while a larch
at the same height measured only 2 feet 4 inches. Thir¬
teen years afterwards, the girth of the oak was 8 feet
10 j inches, and of the larch 5 feet 1 inch.

Of the species in commonest use, the following are the
general characteristics

Quercus pcdunculata. —The Quercus pcdunculata, or
common oak, attains the greatest height of any of the
oak species, and appears to be the most valuable, in re¬
spect of the durability of its timber. The wood is more
stiff, and yet more easily split and broken, than that of
the sessiliflora. Its colour is lighter, and its specific
gravity not so great. Tredgold gives the following sum¬
mary of results of his experiments on the two kinds:—

Quei'cus

Quercus

pedunculata. sessiliflora.

Specific gravity, ... ... ,. '..

•807

•879

Weight of a cubic foot in lbs., ...

. 50-47

54-97

Comparative stiffness, or weight that

bent the piece /jths of an inch,

1G7

149

Comparative strength, or weight that

broke the piece,

322

350

Cohesive force of a square inch in lbs. ..

11,502

12,600

Weight of the modulus of elasticity iu

lbs. for a square inch, ...

. 1,648,958

1,471,256

Comparative toughness, ...

108

In the Dictionnaire des Eaux et Forets, the following

results of experiments made by Harti

g, are cited: —

Quercus

pedunculata.

sessiliflora.

The wood, when green, weighs

7613 lbs.

80 5 lbs.

When half dry,

65’9 „

67-12 „

When perfectly dry, ...

5213 „

51T0

The discrepancy in the experiments may be caused by
the different circumstances of soil and climate under which
the trees were produced.

The wood of the pcdunculata contains more of the silver
grain than the other, and is, on that account, preferred,
as more showy, for ornamental work. It also splits clean,
which renders it suitable for split-paling, laths, barrel
staves, and dowels. Its stiffness recommends it for beams,
and its quality of resisting alternations of wetness and
dryness renders it invaluable for piling.

Quercus Ilex. — This is a deciduous tree, and is on
this account called by the French chene vert. It grows
in the meridional parts of Europe. It is ordinarily tor¬
tuous, which unfits it for general use in carpentry; but as
its wood is hard, compact, heavy, and durable, it is em¬
ployed in the construction of machines.

Quercus suber. — This species is valuable, chiefly as
affording in its bark the material of which corks are
made. Its wood rots rapidly when exposed to alterna¬
tions of wetness and dryness.

Quercus Pyrenaica (the Pyrenean oak), called also
Black Oak.—This species has more alburnum than the
others. Emy says—“Its wood is very cross-grained, and

110

PRACTICAL CARPENTRY AND JOINERY.

requires to be left to dry in the bark for five or six years.
It is liable to tlie attack of worms, and grows so tough that
it is difficult to work, and breaks the workman’s tools. It
is also knotty, and is not a good wood for carpentry.”

Quercus Cerris (the Turkey, or Mossy-capped Oak).—
This fine species attains a great size. Its wood is of ex¬
cellent quality, and beautifully mottled. Of this kind is
the oak of Holland and the Sardinian oak. The former,
like all trees of humid soils and climates, grows with a
straight fibre, and has soft wood, easily worked. It is
not so strong or durable as the common oak; but under
the name of wainscot, it is extensively used for interior
finishings and for cabinet work.

The Quercus virens is one of the more than seventy
species of oaks which are indigenous to America. Its
timber in quality and in appearance approaches to that
of the British oak, and in the United States it is pre¬
ferred for the purposes of the ship-carpenter. The Quer¬
cus virens is confined to the southern states, and is not
imported into this country as timber. Stevenson says,
that “the sea air seems essential to its existence, as it is
rarely found in forests on the mainland, and never more
than fifteen or twenty miles from the shore. It is com¬
monly 40 to 50 feet in height, and 1 to 2 feet in diame¬
ter; but it is sometimes much larger.”

The Quercus alba, or White Oak, a native of the north¬
ern states of America, is the species from which the sup¬
ply is obtained for the British market. It is not equal
to the British oak in strength or durability, and it is in¬
ferior to wainscot in the beauty of its markings or champ;
it is also of coarser grain. But its comparative cheap¬
ness causes it to be extensively used in carpentry, joinery,
and cabinet-making. The best quality, where durability
is required, is the second growth of New Hampshire,
which is extensively used in America in ship-framing.
The better the quality of this oak, the more it shrinks in
drying, and it is liable to split in the sun.

The Yellow Oak is much used in ships for hatch-coam¬
ings, windlasses, Ac. ; and by agricultural implement
makers for axles, as it does not split in the sun.

The Chestnut ( Vastanea vesca).— The leaf is 5 to 7
inches long, and 18 to 24 lines broad, bordered with large
sharp teeth. The flowers are in bunches as long as the
leaves, and the fruit is within a spherical envelope, stud¬
ded with spines. There are two varieties of the chestnut
known in Europe. The one produces as fruit the common
chestnut, which is slightly flattened by two or three grow¬
ing together in the same envelope; the other produces the
large chestnut, which is nearly entirely round, and each
nut has a separate cover.

The chestnut sometimes grows to a prodigious size. The
largest tree in Europe, the Chestnut of an Hundred Horses,
on Mount Etna, is of this species. Brydone, in his Tour
in Sicily, describes it as appearing at first sight like “a
bunch of five large trees growing together;” but a short
examination convinced him that it really was a single
tree split into five parts. Careful measurement gave the
enormous circumference of 204 feet. This tree is supposed
to be more than 8000 years old. The Totworth chestnut
measured, in 1830, 50 feet in circumference.

The mean diameter of this tree, however, is about 37
inches, and it grows to an average height of 44 feet. The
wood is very like that of the oak, and is liable to be con¬

founded with it. This resemblance led to the supposition
that several old constructions in carpentry were formed
of chestnut, but which better examinations have shown
to be a variety of the sessile-fruited oak.

The chestnut was formerly much used for house car¬
pentry and for furniture. The old wood is rather brittle
and shaky, and is liable to internal decay; but the young
wood is elastic and durable, and is much used for the
rings of ships’ masts, hoops for tubs, churns, Ac. In the
Transactions of the Society of Arts for 1789, there is an
account of the comparative durability of oak and chestnut
when used for posts. “Posts of chestnut and others of
oak had been put down at Wellington, in Somersetshire,
previous to 1745. About 1763, when they had to undergo
repair, the oak posts were found to be unserviceable, but
the chestnut were little worn. Accordingly, the oak ones
were replaced by new, and the chestnut allowed to re¬
main. In twenty-five years (1788) the chestnut posts,
which had stood twice as long as the oak, were found in
much better condition than those. In 1772, a form was
made partly of oak and partly of chestnut, the trees used
being of the same age, and were what may be termed
young trees. In nineteen years the oak posts had so
decayed at the surface as to need to be strengthened by
spars, while the chestnut ones required no support. A
gate-post of chestnut, on which the gate had swung fifty-
two years, was found sound when taken up; and a barn
constructed of chestnut in 1743, was sound in every part
in 1792. It should seem, therefore, that young chestnut
is superior to young oak for all manner of wood-work that
has to be partly under ground.”

Tredgold states the weight of a cubic foot of chestnut
at from 43 to 54 8 lbs., and the specific gravity of the tim¬
ber at -535. Rondelet gives '657 as the specific gravity,
and 41 lbs. as the weight of a cubic foot. The specimens
shown in the Exhibition of 1851, weighed from 27‘5 to
36 - 6 lbs. per cubic foot, and their specific gravity was re¬
spectively, ’438 and ‘583. According to Tredgold, the
cohesive force is from 9570 to 12,000; Rondelet says
13,300.

Its stiffness to that of oak is as 54 to 100

Its strength “ “ 48 “ 100

Its toughness “ “ 85 “ 100

The Elm ( Uhnus ).—The elm is a large tree, common in
Europe. Its mean height is 44 feet, and its mean diameter
32 inches. There are fifteen species. Its bark is rough
and dark coloured. Its leaves are oval and toothed, and
their colour is a deep rich green. Its flowers appear be¬
fore its leaves, they are disposed in close bundles, and are
very numerous along the branches. Its wood is ruddy
brown, very fibrous, hard, flexible, and of a dense appear¬
ance, subject to warp, and tough and difficult to work.

It is subject to the attacks of worms, and in carpentry
it is only used in default of better for works above ground.
It is not liable to split, and bears the driving of nails or
bolts better than any other wood. When constantly wet
it is exceedingly durable, and is therefore much used for
the keels of vessels and in wet foundations, in water¬
works, for piles, pumps, and water-pipes. Its toughness
fits it for the naves of wheels, shells for tackle - blocks,
and for many uses in turnery, as it bears rough usage
without splitting.

KNOWLEDGE OF WOODS.

Ill

Wycli Elm grows sometimes to the lieight of 70 feet,
and attains a diameter of 3^ feet. The stem is less en¬
cumbered with branches; the wood is lighter, yellower,
j straighter and finer in the grain than the other. It is
tough, and is fitted for works in which it requires to
be bent; hence it is much used by coach makers for the
naves, poles, and shafts of gigs and carriages, and by
shipwrights for jolly boats; it is used, too, for dyers’ and
printers’ rollers. The Scotch elm, which is much superior
to the English elm, appears to be of this species. It is
much finer, harder, closer in the grain, and handsomer
in its appearance than the other, and is used in making
articles of furniture. In days of old the wood of this
species was held in esteem for the making of long bows.

Rock Elm is very like the last, and is used by boat
builders.

Dutch Elm is the worst of all the species.

The Twisted Elm vields an ornamental wood, used for

«/ *

furniture.

The most profitable age for elms, both for quantity and
quality of timber, is probably about fifty years.

The wood of elm is sometimes boiled to extract its sap,
then washed in aqua-fortis, and stained with a tincture of
dragon’s blood and alkanet root, to imitate mahogany.

The weight of a cubic foot when green is about 70 lbs.,
when dry about 48 lbs ; and —

Its strength to that of oak is as 82 to 100

Its stiffness “ " 78 “ 100

Its toughness “ “ 86 “ 100

Its absolute cohesive strength, according to Muschenbroek,
is 13,200 lbs. It is said to shrink -j^th part of its width
in seasoning.

The elm has been from early times much esteemed as
an avenue tree; and Mr. Loudon attributes this to the
following qualities—rapidity of growth, straightness of
trunk, facility for topping, denseness of foliage, hardness,
longevity, and the little care that it requires.

Strutt, in his Sylva Britannica , enumerates many elm
trees of prodigious size. Among these, the Chipstead elm,
60 feet high, and 20 feet circumference at the base: the
Crawley elm, on the high road from London to Brighton,
the stem of which is 90 feet high, and perforated to the
top; it measures 61 feet in circumference at the ground,
and 35 feet round the inside at 2 feet from its base: the.
elms at Mongewell, in Oxfordshire, a group of giants, the
principal tree being 70 feet high, 14 feet in circumference,
at 3 feet from the ground: the Tutbury Wych elm, and
another of the same species at Bagot’s Mile, ol immense
size, are also figured and described in the same work.

Independently of the timber it produces, the elm tree
has many economical uses. As fuel it is little inferior to
the beech; the charcoal produced is, however, inferior. Its
ashes are rich in alkali, the elm in this respect occupying
the tenth place in a list of seventy-three trees. Its leaves
and young shoots are sometimes used to feed cattle; and
the leaves have been used in some places as a substitute
for those of the mulberry in feeding silk-worms. They
are in parts of Russia used as tea. The inner bark is used
for making nets and ropes, and the bark of the Ameri¬
can elm is soaked in water, made supple by pounding,
and in the form of ribbands, used for weaving seats as
rushes are.

The Walnut (,Juglans regici ).—The walnut tree is a
native of Persia, and is of great size. Its branches form
a noble head, and its foliage is ample, and of a fine green
colour. Its trunk, in the young tree, is smooth, and of a
gray colour, but as it grows old the bark becomes chapped
and cleft. The walnut is grown in this country chiefly
as an ornamental tree. The flexibility of its timber ren¬
ders it unsuitable for beams, although it appears to have
been thus used by the ancients.

There are many varieties of the walnut. Those chiefly
used are two, the Juglans alba and the Juglans nigra,
which are procured from America. Of these the nigra,
or brown walnut, is the most esteemed.

The British walnut tree timber is white in the young
tree, and in that state is liable to the attacks of worms.
As the tree grows old, the timber darkens in colour,
increases in strength and solidity, and becomes easily
worked.

The timber of the walnut tree is seldom used in this
country for works of carpentry, but is highly esteemed
for many purposes by the cabinet-maker; and before the
introduction of mahogany it took the place which that
timber now occupies. On the Continent it is still prized.
The makers of gun stocks consume a large quantity of
it; and it is used also in making knife-handles, and in
the construction of boxes and drawers to hold articles of
polished steel, as it has the advantage of not acting
chemically on iron or steel.

The Juglans alba, the white walnut, or hickory, is,
as we have said, produced in North America. It is a
large tree, and its timber, when young, is very tough and
flexible.

The heart-wood of the black walnut, when properly
seasoned, is strong, tough, and not liable to warp. It re¬
mains sound for a long time wdien exposed to heat and
moisture. It is never attacked by worms; and it has a
grain sufficiently fine and compact to admit of a high
polish. The sap-wood, however, speedily decays.

In America the black walnut is very extensively used.
It is split for shingles. It makes excellent naves for
wheels. It is well adapted for naval purposes, as it is
not liable to be attacked by sea worms in warm latitudes.
On the river Wabash, canoes are made of a single trunk
of this tree, sometimes 40 feet long, and 3 feet wide, and
are greatly esteemed for their strength and durability.
The timber is heavier, stronger, and more durable than
the wood of the European walnut. It is fine grained
and beautifully veined, and is susceptible of a higher
polish.

The wood of the walnut, according to Loudon, weighs
when green 58 lbs. 6 oz., and when dry 46 lbs. 8 oz. But
according to other authorities this is much too high.
Muschenbroek gives the specific gravity as -671, the weight
of a cubic foot as 41 93 lbs., and its cohesive strength at
8130 lbs.

Its strength to that of oak is as 74 to 100
Its stiffness “ “ 49 “ 100

Its toughness “ “ 111 •“ 100

Tiie Beech.— Only one variety of this tree (the Fagus
sylvatica) grows in Europe. This tree grows to a great
size; and its beautiful, clear, and lustrous foliage, and its
shining gray bark, variegated with dark green and yellow

112

PRACTICAL CARPENTRY AND JOINERY.

mosses, makes the beech much prized as a forest tree, and
an especial favourite with the painter.

Its wood varies in colour from white to pale brown;
its fibres are compact, but not very hard. It is easily
distinguished by means of the fine and elongated papilla}
which cover the surface on which the bark lies, and of
which the impressions are seen in the bark.

When the wood is split transversely it presents brilliant
satiny facets, like those of the oak, but very much smaller,
and not so numerous.

The use of the beech has been long abandoned in car-
pentry works above ground, on account of its tendency
to cleave, and its liability to be attacked by worms. The
former of these defects is probably owing to injudicious
felling, and, it is said, may be avoided by felling the tree
at the commencement of summer, when it is full of sap,
and leaving it to dry for a year after it is felled; and
then, after it is squared, steeping it in soft water for six
months. It will not even by this treatment be equal to
oak, but will be quite suitable for second-class structures,
such as piles, weirs, sluices, floodgates, and the timbering
of embankments.

In this country at the present day it is used chiefly for
making chairs, bedsteads, and panels for carriages, wooden
screws, shovels, bakers’ peels, sieve rims, and herring
barrels. When used for cabinet-making, it is sometimes
stained to imitate mahogany; and when for small articles,
such as the handles of jugs and tea-pot knobs, it is
stained black fin imitation of ebony. In France and
Germany its uses are manifold. It is employed largely
in the fabrication of furniture, and is used for the frames
of saddles and horses’ collars, cases for drums, felloes of
wheels, bowls, porringers, salt boxes, screws, spinning
wheels, pestles, presses and bellows, packing boxes, and
scabbards for swords.

As fuel, beech wood is highly esteemed; it burns rapidly,
with a clear bright flame, and gives much heat. The
leaves of the beech are used in place of straw for stuffing
mattresses; its bark is used by the tanner, and its fruit
affords abundance of an excellent oil. used for buminer
and also for cooking.

For works which are constantly under water it is pecu¬
liarly adapted. It is also much used in the formation of
tools, and in cabinet-making, and in the fabrication of a
crowd of small objects. It is greatly used for sabots, into
which it is converted while yet green, and then to give
them durability it is exposed to a flame fed by chips of i
the same wood. It was formerly reduced to very thin !
leaves, and used for writing upon.

The weight of a cubic foot of the timber is 65 lbs. 13
oz. when green, 56 lbs. 6 oz. when half dry, and 50 lbs.

3 oz. when quite dry; or, according to Barlow, from 43T 2
to 53 - 37; and its absolute cohesive strength 11,500 lbs.

Its strength to that of oak is as 103 to 100
Its stiffness “ “ 77 “ 100

Its toughness “ “ 138 “ 100

The Ash (Fraxinus excelsior), Mr. Loudon says, “is
excellent for oars, blocks, and pulleys. Few other trees
become useful so soon, the wood beinof fit for walking-
sticks at four or five years’ growth, and for handles of
spades, and other instruments, at nine or ten years’
growth. An ash pole, 3 inches diameter, is indeed one

of the most valuable pieces of timber, for its bulk, that
any tree can furnish. For hop poles, hoops, crates, basket
handles, rods for training plants, or for forming bovvers,
light hurdles, fence wallings, the branches of ash, in vari¬
ous stages of growth, are particularly valuable. In the
neighbourhood of the Staffordshire potteries, the ash is
cultivated to a great extent, and cut every five or six
3 ’ears for crate-wood.”

The ash, being hard and heavy, is little used in carpen¬
try ; but these qualities, combined with its toughness and
elasticity, render it very serviceable in other arts.

Its wood is white, veined longitudinally with yellow¬
ish streaks. Its annual layers are each composed of a
zone of compact wood, and another zone in which are
many small pores, which show themselves as little holes
when a section is made perpendicular to the fibres, and
as little interrupted canals in a section parallel to the
fibres.

This tree is veiy liable to the attacks of worms; and
rots rapidly when exposed either to dampness or to alter¬
nations of dryness and moisture.

Its toughness and elasticity fit it for resisting sudden
and heavy shocks. It is used in making wheel-carriages,
implements of husbandly, tools, and the like, but it is
too flexible and not sufficiently durable for the carpenter.

The weight of a cubic foot of the green wood is 61 lbs.
9 oz., and of the dry wood 49 lbs. 8 oz.; or, according to
Barlow, from 43'12 to 53*81; and its cohesive strength
17,000 lbs.

Its strength to that of oak is as 119 to 100
Its stiffness “ *• 89 “ 100

Its toughness “ “ 160 “ 100

The Teak ( Tectona grandis). —This wood is in colour
light brown; it is porous, and grows quickly. In its fresh
state it is more or less impregnated with an aromatic oily
substance, and to this it owes much of its value. It is
largely used in carpentry and in ship-building. The best
kind is from Malabar.

Its specific gravity varies from %583 to 1 056. Couch
states it at ’657, and the weight of a cubic foot at 41'06
lbs.; and Barlow gives 15,000 lbs. as its tenacity per
square inch. In thirty-six specimens in the Exhibition
of 1851, the specific gravity was—Maximum, L056; aver¬
age, 711; minimum, - 583.

The Greenheart ( Nectandra rodicei). —This wood is
a native of Guiana, where it is in great abundance. The
trees square from 18 to 24 inches, and can be procured
from 60 to 70 feet Ions;. It is a fine but not even-errained
wood. Its heart-wood is deep brown in colour, and the
alburnum pale yellow. It is adapted for all purposes
where great strength and durability is required, such as
house frames, wharfs, bridges, &c. The weight of a cubic
foot is from 5115 to 61‘13, and its specific gravity from
•831 to 989.

The Poplar (JPopulus). — The wood of the poplar is
soft, light, and generally white, or of a pale yellow. It
has the property of being only indented and not splin¬
tered by a blow; and hence, and from its lightness, it was
used for making bucklers, and this quality fits it also for
the sides of carts and barrows used for conveying stones,
&c. The principal use of it in construction is for flooring-
boards; but it requires to be seasoned for at least two

KNOWLEDGE OF WOODS.

113

• years before it is fit for use in this way. Its whiteness
and closeness of grain render it easily kept clean by
scouring.

It is adapted for all purposes which require light¬
ness and moderate strength, such as for making the large
folding doors of barns; and when kept dry it is toler¬
ably durable. The old distich says—

“ Though heart of oak be ne’er so stout,

Keep me dry, and I’ll see him out.”

In Scotland it is sometimes used for mill-work. It is
made into dishes and casks by the cooper, and is also used
by the cabinet-maker and turner. It is sometimes em¬
ployed as a substitute for lime tree, by musical instru¬
ment makers. It weighs when green 58 lbs. 3 oz. per cubic
foot, and from 21 to 38 lbs. 7 oz when dry. It shrinks
and cracks in drying, and loses about a quarter of its bulk.
When seasoned it does not warp, and takes fire with
difficulty. According to Bevan its tenacity is 7200, and
to Muschenbroek 5500 lbs.

Alder ( Alnus ).—The wood of the alder is white when
the tree is newly cut down; but the surface of the wound
soon becomes of a deep red, this again fades into a pale
flesh colour, which is retained by the wood in its dry
state. The wood is tender and homogeneous. It has
not much tenacity. It is very durable in water. Alder
wood is used for all the purposes to which the soft homo¬
geneous woods are generally applied. It is made into
wooden vessels, chairs, and tables. When used for the
latter purpose, the timber of the old trees, full of knots,
is sought after, as it has nearly the beauty of curled maple,
with the advantage of a fine deep red colour. When used
in constructions above ground, it must be kept perfectly
dry. Its most important applications on a large scale are
for the purposes of the hydraulic engineer, such as piles
for the foundations of bridges, water-pipes, and pump-
barrels. Like its congeners, the willow and the poplar,
the alder is serviceable to the cartwright for the sides
and bottoms of stone-carts and barrows. It weighs when
green 62 lbs. 6 oz., and when dry 39 lbs. 4 oz. It shrinks
nearly one-twelfth part of its bulk. Muschenbroek states
its tenacity at 13,900 lbs.

Birch ( Betula alba and Betula nigra). —The wood
of the white birch ( Betula alba) is white, shaded with
red; its grain intermediate between coarse and fine. It
is easily worked when green, but chips under the tool
when dry. The timber of trees grown in temperate cli¬
mates is moderately durable; but that of trees grown in
the extreme north is of very great durability.

The wood of the birch is used in Russia in making
small rustic carriages; in France, for the felloes of wheels.
Chairs and other articles of furniture are also made of it;
and it is used by the cooper and the turner. The bark
of the tree is used in many ways as a defence against
humidity. It is laid as a coping on walls, and it is
wrapped round posts and sills inserted in the ground; it
is placed over the masonry of vaults, and interposed above
the foundation courses of walls—a very objectionable prac¬
tice. But the most familiar application of it as a pro¬
tector against dampness, is the thin layer of it used as an
inner sole for shoes, or a lining for hats. Its weight when
green is 65 lbs. 6 oz., when dry 45 lbs. 1 oz. Its tenacity
is 15,000 lbs. per square inch.

Hornbeam ( Carpinus betulus). —The wood of this tree
is white, and of a fine grain. In drying it shrinks much,
which closes its pores and makes it very hard. It is of
great use in framing heavy carriages and machines, and
in making screws, pulleys, and the wooden teeth of wheels.
Its weight, according to Rondelet, is 47'5 lbs. per cubic
foot; its specific gravity. 760; and Bevan gives 20,240 lbs.
as its tenacity.

The Maple {Acer campestris). —The wood of the maple
is moderately hard, compact, and more or less veined.
It is used in various departments of architecture. It is
durable when kept dry, but is liable to be attacked by
worms. The wood of some of the species takes a fine
polish, and is valued by the cabinet-maker. When green
it weighs 61 lbs. 9 oz. per cubic foot, and when dry 51 lbs.
15 oz. Its tenacity is 10,584 lbs.

The Sycamore {Acer pseudo-platanus). —The wood
of the sycamore when young is white, but becomes yellow
as the tree grows older, and sometimes even brown to¬
wards the heart. It is compact and firm, without being
hard; of a fine grain, and susceptible of a high polish.
It does not warp, but is liable to be attacked by worms.
It is used in joinery, turning, cabinet-making, and also
by musical instrument makers. Cider-presses are made of
it, and sometimes also gun-stocks. It used to be greatly
in demand for making wooden dishes and spoons, when
such articles were used.

Its strength to that of oak is as 81 to 100
Its stiffness ‘‘ ‘‘ 59 100

Its toughness “ “ 111 “ 100

It weighs when green 64 lbs. per cubic foot, and when
dry 48 lbs. It loses one-twelfth part of its bulk in drying.
Its tenacity, according to Bevan, is 13,000 lbs. per square
inch.

Lime Tree {Tilia). —The wood of the lime tree is pale
yellow or white, close-grained, soft, light, and smooth.
It cuts equally well with or across the grain, and hence
is used greatly by carvers. It is used by piano-forte
makers for sounding-boards. It is too soft to be employed
for works of carpentry, and its use is confined to the car¬
ver, the cabinet-maker, the musical instrument maker,
the turner, and the maker of toys. The weight of the
cubic foot when dry, according to M. Morin, is 46 lbs.;
and its tenacity, according to Bevan, is 23,500 lbs.

The Oriental Plane {Platanus orientalis). —Mar¬
shall classes the timber of this tree with that of the
sycamore; the French writers class it with the beech and
hornbeam. The natives of the East use it for carpenter
work, cabinet work, and for boat-building.

M. Hassinfratz says that the wood of the plane tree
weighs when dry 49 lbs. 3 oz. per cubic foot. It is of a
yellowish white colour till the tree attains considerable
age, when it becomes brown, mixed with jasper-like veins.
In this state it takes a high polish. Bevan states its weight
as 40 lbs. per cubic foot, and its tenacity 11,700 lbs.

The American, or Western Plane (Platanus occi-
dentalis). —A noble tree, of very rapid growth. It bears
a general resemblance to the Oriental plane, but it is
larger, and more rapid in growth. It is a native ot
America, where it is called button-wood, and sometimes,
from its habitat, the water-beech. It is also called cotton¬
wood, from the thick down which covers the under sur¬
face of the leaves when they first expand.

114

PRACTICAL CARPENTRY AND JOINERY.

The timber, when seasoned, is of a dull red, with a fine
and close grain. It shrinks much in drying, and is apt
to split. Its concentric circles are divided into numerous
sections by medullary rays, extending from the centre to
the circumference. When the trunk is sawn in a slanting
direction, these rays have a remarkable appearance. The
cabinet-makers of America do not like the wood on ac¬
count of its tendency to warp; but as it is easily cut in
any direction, and takes a fine polish, it is well adapted
for cabinet work.

The Willow ( Salix ).—The timber of the willow has
a wide range of uses. It is sawn into boards for flooring,
and into scantling for rafters, and in the latter capacity,
when kept dry and ventilated, has been known to last
for 100 years. But the purposes more peculiarly its
own, are such as require lightness, pliancy, elasticity, and
toughness, all of which qualities it possesses in an eminent
degree. It also endures long in water, and therefore is
in request for paddle-wheel floats, and for the shrouding
of water-wheels. It is used in lining carts for conveying
stones, or other heavy materials, as it does not splinter;
and the same quality renders it fit for guard posts, or
fenders.

It is also made into cutting boards; it is in demand by
the turners and toymakers, and the makers of shoe-lasts.
Being susceptible of a fine polish, it is dyed black, and
forms an imitation ebony. Young trees, when split in
two, are made into styles for ladders. The young and
branch timber is made into handles for hay rakes, and
other light implements, and into hop poles and props for
vines. It is split and made into crates, hurdles, and
hampers. The smaller rods and twigs are worked into
baskets. Of the strips or shavings the bodies of hats
are made. Of all the varieties of the willow, the timber
of the Salix Russeliana is the best. This is distin¬
guished from all other willow timber by being of a sal¬
mon colour when dry. When recently cut, the sap-wood
is white, and the matured wood slightly reddish; but
they both become salmon-coloured when dry.

The other varieties of willows cultivated for their tim¬
ber are— Salix alba , which will attain the height of 60
to 80 feet in twenty years: the Salix fragilis, which
is often confounded with the Russeliana —this tree
grows as rapidly as the alba, but does not attain so great
a height; the Salix caprea grows as fast as the fragi¬
lis, and will attain a height of 30 to 40 feet in twenty
years. This latter tree, according to Bose, is the most
valuable of all the tree willows grown in France. The
remarks on the properties of the timber apply, with
slight modifications, to all these four species. The specific
gravity of willow is ‘390; the weight of a cubic foot
24'37 lbs. Its tenacity, according to Bevan, is 14,000 lbs.;
Muschenbroek says 12,500 lbs.

Acacia ( Robinia pseudacacia). — The timber called,
commonly, Acacia, is the locust-wood of America. Its
colour is yellow, with brown veins. M. Hartig places
it, in regard to durability, next to the oak, and before
the larch. In England, experiments have shown that it
is heavier, harder, stronger, more rigid, and more elastic
than the best oak; and it is, consequently, fitter than oak
for tree-nails. When used for posts, its endurance is next
to the yew. Michaux states that it lasts forty years; and
on that account its great consumption in America is for

sills of doors, and for the posts of the framing of half-tim¬
bered houses that are nearest the ground. It is difficult
to procure the timber of large size; as even in districts
where the tree thrives best, nine-tenths of the trunks
do not exceed 1 foot in diameter, and 40 feet in height.
Its strength to that of oak is as 135 to 100. English-
grown acacia weighs 44 - 37 lbs. per cubic foot; its specific
gravity is - 710; and, according to Bevan, its tenacity is
16,000 lbs.

The Horse Chestnut (AEsculus Ilippocastanum).—
The wood of the horse chestnut is white, soft, and unfit
for purposes requiring strength and durability. It is,
nevertheless, applicable to such purposes as the lining of
stone carts, and it is said by Boutcher and Duhamel
to be well adapted for water-pipes which are to be
kept constantly under ground. It is sometimes used for
flooring. When green it weighs 60 lbs. 4 oz. per cubic
foot, and when dry 37 lbs. 3 oz., or, according to Loudon,
35 lbs. 7 oz.; and loses one-sixteenth part of its bulk.

The Service Tree ( Sorbus ).—The service tree, in foli¬
age and general appearance, closely resembles the moun¬
tain ash. It attains a larger size, and bears larger fruit.
In France, trees of this kind are found of the height of
50 or 60 feet. It takes two centuries to attain its full
growth, and it is believed that trees exist which are up¬
wards of 1000 years old.

The wood of the service tree has a fine and compact
grain, and is of a reddish tinge. It is very hard, and
takes a high polish. It is in high estimation for the
framing of machinery, cogs of wheels, pulleys, screws, and
for all such constructions as require great strength and the
power of enduring friction. It might, in many cases, be
substituted for box. It weighs when dry 72 lbs. 2 oz.
per cubic foot.

The Pear Tree ( [Pyrus ).—The pear tree yields a wood
which is heavy, strong, compact, and of a fine grain. It
is slightly tinged with red. Like the service tree, it is of
great value for the parts of machines which require to
endure much friction, such as screws and the teeth of
cogs, and it is used largely in making handles for tools.
It is easily stained black, and then so closely resembles
ebony as to be with difficulty distinguished from it. It
requires to be perfectly dry before it is used. The wood
of the wild pear is harder than that of the cultivated
pear. The weight of a cubic foot of the wood when
green is 79 lbs. 5 oz., and when dry 41 to 53 lbs. Its
tenacity, according to Barlow, is 9800 lbs. It shrinks
about one-twelfth part of its bulk in drying.

The Apple Tree ( Malus ).—The wood of the apple
tree, in its wild state, is fine-grained, hard, and of a
brownish colour. It requires to be thoroughly dry before
being used, and then it is easily wrought. The wood of
the cultivated tree, contrary to what is usually found,
has a finer grain than that of the wild tree.

The uses to which it is put are nearly the same as in
the case of the pear tree; but it possesses the distinguish¬
ing qualities of the latter in a greatly inferior degree.

The wild apple tree weighs from 48 to 66 lbs. per cubic
foot in a green state, and loses from one-eighth to one-
twelfth part of its bulk, and about one-tenth part of its
weight, in drying. The cultivated timber is heavier than
the other in the proportion of about 66 to 45. Its tena¬
city, as given by Bevan, is 19,500 lbs

KNOWLEDGE OF WOODS.

116

The Hawthorn (Cratcegus oxyacantlia ).—The wood
of the hawthorn is white, hard, and difficult to work.
Its grain is fine, and it takes a high polish. It is used for
the smaller parts of machines, such as cogs and staves
for mill-work. It is also made into hammer shafts, flails,
and mallets. It weighs 68 lbs. 12 oz. green, and 87 lbs. 5 oz.
dry per cubic foot; it contracts one-eighth of its volume in
drying. Its tenacity is given by Bevan as 10,500 lbs.

The Box ( Buxus ).—This tree, which seldom exceeds
the height of 12 feet in Britain, grows in Turkey as high
as 25 or 30 feet, with a diameter large in proportion to its
height.

The wood is remarkably heavy, and is the only Euro¬
pean wood that sinks in water. It is yellow in colour,
with a fine uniform grain. It works sweetly, and is very
useful for small works exposed to great strain and fric¬
tion, such as screws, and the parts for transmitting mo¬
tion in machinery. It is too valuable to be used in great
quantity. It is the only wood employed by the wood
engravers, except for large and coarse works. It weighs
80 lbs 7 oz. per cubic foot when newly cut, and from 60 to
68 lbs. 12 oz. when dry. Its tenacity, according to Bevan,
is 19,891 lbs.; Barlow states it at 20,000 lbs. It is sold
by weight.

Mahogany —The mahogany tree ( MahoganiSwietenid )
is one of the most beautiful and majestic of trees. Its
trunk is often 50 feet high, and 12 feet diameter; and it
throws the shelter of its huge arms and beautiful green
leaves over a vast extent of surface. It takes probably
not less than 200 years to arrive at maturity.

The mahogany tree abounds the most and is in greatest
perfection between latitudes 11° and 23° 10' N., including
within these limits the islands of the Caribbean Sea, Cuba,
St. Domingo, and Porto Rico, and in these the timber is
superior in quality to that of the adjacent continent of
America, owing, it is to be supposed, in some measure, to
its growing at greater elevations and on poorer soils.

Mahogany timber was used at an early period by the
Spaniards in ship-building. In 1597 it was used in the
repairs of Sir Walter Raleigh’s ships in the West Indies.
It was first imported into England in an unmanufactured
state in 1721.

The finest mahogany is obtained from St. Domingo, the
next in quality from Cuba, and the next from Honduras.

In the island of Cuba the tree is felled at the wane of
the moon from October to June. The trunks are dragged
by oxen to the river, and then, tied together in threes,
they are floated down to the rapids. At the rapids they
are separated and passed singly, then, collected in rafts,
they are floated down to the wharves for shipment. It
is considered essential to the preservation of the colour
and texture of the wood, that it should be felled when
the moon is in the wane.

The Honduras mahogany is commonly called Bay wood,
and is that most used for the purposes of carpentry. It
recommends itself for these purposes by its possessing, in
an eminent degree, most of the good and few of the bad
qualities of other timber. It works freely; it does not
shrink; it is free from acids which act on metals; it is
nearly if not altogether exempt from dry rot; and it re¬
sists changes of temperature without alteration. It holds
glue well; and it does not require paint to disguise its
appearance. It is less combustible than most woods. The

weight of a cubic foot is 50 lbs., and its tenacity is given
by Barlow at 8000 lbs.

Representing the strength of oak by 100 , that of Bay wood is 90
stiffness of oak by 100 , “ “ 93

toughness of oak by 100 , “ “ 99

Sabicu.— 1 lie wood of a beautiful tree which grows in
Cuba. It is used in the government yards for beams and
planking. The weight of a cubic foot is from 57 5 lbs.
to 65 lbs. It has been recently used by Sir William
Cubitt for the deck floor of the great landing stage at
Liverpool.

RESINOUS WOODS.

Of the timber of the resin-producing trees, belonging
to the natural order Coniferse, many varieties are used
by the carpenter. The yellow deal of Europe, the pro¬
duce of the Finns sylvestris; the white deal of Norway,
the timber of the Abies excelsa; the white pine of Amer¬
ica, which is the Pinus Strobus; the yellow pine of
America, Pinus varidbilis; the pitch pine, Pinus resin-
osa; the silver fir, Pinus Picea; and the various white
firs, or deals, the produce of the Pinus Abies, or spruce
fir; and also the larch; are all used in almost every kind
of construction for shelter or for ornament.

No other kind of tree produces timber at once so long
and straight, so light, and yet so strong and stiff'; and
no other timber is so much in demand for all the purposes
of civil architecture and engineering.

Log-houses are more conveniently made of the timber
of the pine than of any other, because it can be obtained
of great length with little taper. In Russia and America
roads are made of the trunks of pines. They are rough,
it is true, and are very significantly called corduroy
roads; but still by their use access is obtained to places
which, but for the facilities these trees afford, would be
inaccessible.

From the growing trees are obtained turpentine, liquid
balsam, and the common yellow and black rosin of the
shops. Tar is obtained by cutting the wood and roots
into small pieces, and charring them, or distilling them in
a close oven, or in a heap covered with turf. The lamp¬
black of commerce is the soot collected during this pro¬
cess. Fortunately, the trees of the pine and fir tribe, so
useful to man, are found in great abundance in America
and Europe.

The European pine and fir timber is obtained from
the extensive forests of Sweden, Norway, Prussia, Russia,
Poland, Germany, Austria, and Switzerland. In many
of these places in the Alpine districts, the forests are in¬
accessible; and in others, the timber cannot be made
available from the difficulty of conveying it to the streams
or rivers which would bear it down to the ports for ship¬
ment In'Sweden the principal river by which the tim¬
ber of that country is floated to the sea is the Gota. It
is conveyed by it to Gottenburg. It is also shipped from
Stockholm and Gefle. The timber of Norway is floated
down the Glommen to Christiana, whence it is called
Christiana deal; and down the Drammen to Dram or
Drontheim, whence it is called Dram timber.

From the immense forests of Prussia, Russia, and Po¬
land, the timber is brought down the rivers into the
ports on the southern shores of the Baltic, whence it is

116

PRACTICAL CARPENTRY AND JOINERY.

called Baltic timber. The chief ports are Memel, Dan¬
zig, Riga, Petersburg, Archangel, and Onega. The river
Memel being the principal channel through which the
pines grown in the north of Prussia reach the sea at
the town of that name, the timber they produce is
known as Memel timber. The forests of West Prussia
and Poland yield timber of a better quality, which, floated
down the Vistula and the Bug to Danzig, is known as
Danzig timber. The best of the Baltic timber is that
which, grown on the banks of the Dnieper, is trans¬
ported to the Dwina, and then, being rafted down to
Riga, comes into the market as Riga timber.

In the transport of the pines from the Alpine forests,
advantage is taken of the slope, and shoots are made, in
which the large trees hurry with astonishing velocity to
the plains below. When the nature of the ground will
not admit of the shoot being formed on the surface with
a uniform slope, constructions of great magnitude, made
of timber, are carried over gorges and ravines, and even
across valleys. ■ These shoots are troughs, the bottoms
and sides of which are formed of the trunks of trees.
They have such a slope as causes the trees to descend
by the force of gravitation alone. The slope required,
it is found, need not exceed 20°; and to diminish the
friction, a stream of water is made to flow along the
shoot. Sometimes, to preserve the timber from injury, it
is attached to a species of rude sledge. Of these shoots,
the most remarkable for extent, and for boldness of design
and construction, was the inclined plane of Alnpach. The
pines of the forests on Mount Pilat—pines of the largest
and finest quality—rotted where they grew, from the dif¬
ficulty of transporting them to the rivers. The proprie¬
tors of these forests were fully aware of the value of their
timber if it could be transported to the rivers; but the
boldest and most skilful shrunk from encountering the
difficulties that lay in the way of such an enterprise as
constructing a shoot in such wild regions. In 1816, how-
ever. M. Rapp found three proprietors bold enough, along
with himself, to make the attempt. They commenced to
make an inclined plane of three leagues in length, and
with an uninterrupted slope, to the Lake of Lucerne.
The channel of the shoot was 6 feet wide, and 3 feet deep;
its bottom was formed of three trunks of trees, placed in
juxta-position. In the centre one of the three was formed
a channel, into which was turned a stream of water, ali¬
mented at frequent intervals along the line.

The inclined plane in its course had 2000 points of
support. In several places it was attached to the wall¬
like sides of the rocks along which it had to be carried.
It bridged over ravines sometimes at an elevation of
120 feet; and at one point, in order to maintain the
slope, it had to be carried through the earth in a tunnel.

Wherever practicable, its direction was in right lines,
but these could not always be maintained; and where a
bend had to be introduced, it was formed on a wide
curve.

Great as this work was, it was completed in eighteen
months by 160 workmen. It was constructed without a
single piece of iron being used in fastening it. It con¬
sumed 25,000 trees, and cost £4167 sterling. Other
authorities state the cost at £9000, and the date of con¬
struction 1812.

From point to point along the line a chain of workmen

was established to watch the progress of the trees, and
ascertain the time that tree might succeed tree in their
passage without danger. By this living telegraph com¬
munication was established between the extremities in
three minutes.

Pines of 100 feet long, and 10 inches diameter at their
smallest end, flashed with such velocity past the watchers,
that they appeared only a foot or two in length. They
passed from the summit to the lowest extremity in two
minutes and a half.

To learn the effects produced by such a velocity, ob¬
stacles were placed in the groove so as to throw the trees
out in their passage. They were thrown from the chan¬
nel with such force as to enter the ground to the depth
of 18 to 24 feet, and one of them striking a tree growing
near, split it as if it had been burst by gunpowder.

The credit of this magnificent work is entirely due to
M. Rapp, who fought his way against a host of preju¬
dices, and overcame difficulties innumerable.

The following is a summary of the purposes for which
the woods of the various European firs and pines are
best adapted. “Memel is the most convenient for size;
Riga, the best in quality; Danzig, when free from large
knots, the strongest; Swedish, the toughest. For fram¬
ing, the best deals to be depended on are the Norway,
particularly the Christiana battens; and for panelling,
the white Christiana; yellow Christiana deals have much
sap, and, consequently, cause waste. The best for upper
floors are Dram and Christiana white battens; and for
ground floors, Stockholm and Gefle yellows. For stair¬
cases, Archangel and Onega planks. Swedish deals are
not to be depended on for framing, on account of their
warping.”*

Pinus sylvestris .—Red or yellow pine is the produce
of the Pinus sylvestris, the wild pine, or Scotch fir.
The timber grown in Britain, especially in the southern
parts of it, is not so valuable as that produced in the
Alpine countries. There are, indeed, exceptions, but this
appears to be the rule. It is not so sound; it is coarser
in the fibre, it contains more sap-wood, and is not so strong
nor so durable. Dr. Smith, however, in hjs essay on the
production of timber, says, that he has seen some Scotch
fir grown in the North Highlands, which formed the roof
of an old castle, and after 300 years it was as fresh and
full of resin as newly-imported Memel.

But although the home-grown timber is, in point of
fact, less strong and not so durable as that which is im¬
ported, it is worth while to inquire whether much of this
difference of quality is not occasioned by the treatment
the tree receives. Making every allowance for the in-
ferior timber produced by planting the Scotch fir on a
soil and in a climate not suited to the habits of the tree,
it is still hard to believe that, when the soil and climate
are judiciously chosen, the timber pi-oduced must be so
very greatly inferior in quality to the foreign timber.
In the Alpine forests the tree is felled at its maturity;
it is squared, weather-seasoned, and then water-seasoned
in the course of its progress to the port where it is ship¬
ped. It is received in this country after a long interval,
and in the hands of the user it is again submitted
to a more perfect seasoning and drying before it is

* Laxton’s Builders' Price-Book.

PLATE lx.

©ATE§

PARK AND'ENTRANCE CATES.

Fig. 2.

12963 0 12346 6 ' 789 20

. ii i l Htntiil -I- - 1 ~ -l. i" - I- 1 —i -1 :- I I

20 Foot.

TV C. Joass. DO ’.

BLACKIE & SON. GLASGOW. EDINBURGH & LONDON.

H r A. Beever. Sr

KNOWLEDGE OF WOODS.

117

finally wrought up. Here, on the contrary, the tree is
felled before it attains maturity, the whole process of
felling, barking, seasoning, and working, are very quickly
gone through, and the timber is generally in its place
in the building, whose construction is the immediate
cause of the tree’s destruction, in the widest sense, within
six months after the time the tree was marked for the
axe. Is it a thing to be wondered at, then, that the
foreign timber should possess such a superiority over that
grown in this country?

Home-grown timber may never rival that from abroad
in strength and durability; but a proper attention paid
to the selection of the trees, and to the subsequent pro¬
cesses of felling, storing, and seasoning, would render it
available for many purposes to which it cannot now be
applied; would give durability to such of it as is used in
the timbering of farm buildings, its present most frequent
application, in place of the decay which renders recon¬
struction a necessity at every renewal of a lease. As a
proof that these remarks are not uncalled for, it is only
necessary to refer to the excellence of the timber grown
in Mar Forest, where due attention has been paid to its
selection, cutting, and seasoning.

The best wild pine timber is that from the northern
parts of Europe, whence it comes in the shape of logs,

1 deals, and spars.

The wild pine timber is the most durable of the pine
species. Brindley, the celebrated canal engineer, was of
opinion that it is as durable as oak. Mr. Semple, the
engineer, in his treatise on building in water, expresses
a similar opinion. Duhamel states, that on the piles of
an old church, which had existed many centuries, being
taken up, they were found to be perfectly sound at the
centre, with a resinous smell, although the outside w 7 as
a little decayed.

The lightness and stiffness of the Scotch pine timber
renders it superior to every other kind of timber for
beams, girders, joists, rafters, and, indeed, for framing in
general. For joiners’ work, too, it is well adapted, as it
is easily worked, and stands better than the harder woods,
and if not so durable, which is questionable, it is certainly
very much cheaper than they.

In the best timber, the saw should leave a clean sur- j
face, not covered with woolly fibres; the annual layers
should be thin, never exceeding one-tenth of an inch in
thickness. The Riga and Norway timber, as we have
said, is the best, and Memel is very little inferior, and
being stiffer, it is better adapted for some purposes.

In the inferior sorts, the annual layers are thick and
soft, the dark part of the ring of a honey yellow. The
wood feels clammy; it is heavy, and chokes the saw in
cutting. Such timber should not be used where dura¬
bility is required, or where it will be exposed to great
strains. In other kinds, the wood, although not heavy,
is spongy, and in cutting it* the saw leaves a woolly
surface. The Swedish timber has often these peculi¬
arities, and is, in such cases, deficient in strength and
stiffness.

Of the timber of the Pinus sylvestris, Memel supplies
three qualities, viz.:—

Grown, in baulk, 13 X 13 inches, and from 28 to 50 feet
long. Longer timber is apt to be knotty at the small end.

Best Middling.

Second Middling , or Brack.

These are of about the same dimensions as crown, but

as they contain large knots, they are not so fit to be cut

into small scantlings.

Danzig common baulks are from 14 to 1(1 inches square.
Crown baulks are sometimes so large as 2(i and 30 inches,
and so long as 70 feet; but 40 feet is nearer their average
length. As this timber is very sound, it should be used
where whole timbers are required; the crown is especially
useful for bearing timbers.

Riga baulks are 13 to 14 inches .square, and average
about 40 feet long. The heart of the baulk is often shaky;
it should, therefore, be divided longitudinally, and the
flitches reversed. It is very hard to tell the difference
between Memel and Riga timber when in the log.

Norway timber is of smaller dimension than that from
Prussia and Russia. It is very durable, and suitable for
exposed work, and should be used where the beams do
not require to exceed 11 inches square. The timber is
also supplied in planks, deals, and battens; and their cha¬
racteristics may be briefly stated as follows, viz.: —

Prussian, Memel, and Danzig . — Very durable, adap¬
ted for bridge flooring and external work.

Russian, Archangel, and Onega .—Not fit for work
exposed to damp. The knots are often surrounded by
dead bark, and drop out when the timber is worked. Clean
specimens are suitable for joiners’ work.

Petersburg and Narva .-—Easily takes dry rot in damp
unventilated situations.

Biornburg . — The planks are 12 feet long, and are like
those of Archangel, but more knotty.

Finland and Nyland . — These are 14 feet long. They
are fit for the carpenter only, and are very durable.

Norwegian, Christiana, and Dram . — Deals and bat¬
tens. The Christiana deals have generally much sap wood,
and, consequently, cause loss and waste in working. The
wood is mellow, and works well under the plane. Of the
Dram timber, the upland is the best, the lowland the
worst.

Frederickstadt . — Durable and mellow, works easily
under the plane.

Swedish, Stockholm, Gejle.— Full-sized, and free from
sap; but liable to warp, and to be full of large coarse
knots. It is useful for ordinary carcass work where cost
is an object, as it is cheaper than Norway timber.

Gottenburg. —Durable, and fit for the carpenter, but
not for the joiner.

Ilernosand and Sundsvall. — Same characteristics as
the last, with all the faults to a greater extent.

Tredgold gives the following as the relative strength
of foreign pine and of that grown in England, and also
in Mar forest, and of oak: —

Foreign

Pine.

English

Pine.

Mar Forest
Pine.

Oak.

Strength,.

.... 80 ...

60 ...

... 100

Stiffness,.

. . 114 ...

100

Toughness,.. .

.... 56 ...

100

The best foreign timber

shrinks

about

-g^j-th part of

its width in seasoning from the log.

White Fir, or Deal (European).—This is the produce
of the Pinus Abies, or Norway spruce. It is light, elas¬
tic, but varies in durability with the conditions of soil
and climate. It is much less resinous than the Scotch fir,

118

PRACTICAL CARPENTRY AND JOINERY.

and its colour is a reddish or yellowish white. This tree
affords the Burgundy pitch of commerce, and its bark is
used for tanning.

The timber being fine-grained, takes a fine polish, and
is easily worked, either with or across the grain. It
holds glue remarkably well.

The spars are from 30 to 60 feet long, and from 6 to 8
inches thick, and are used for scaffold poles, ladders, oars,
and masts to small vessels.

The American spruce is of two kinds—the White Spruce
(.Pinus alba), and the Black Spruce ( Finns nigra). The
white American spruce timber is not so resinous as the
Norway spruce, nor so heavy; but it is tougher, and is
more liable to twist and warp in drying. It decays soon.
It is imported in deals and planks.

The black spruce is said to produce the best wood; but
as it is the bark and not the timber which gives it the
distinctive appellation, it is not possible to tell the dif¬
ference, when the wood comes mixed in its cut state.
Its distinguishing characteristics, according to Michaux,
are strength, lightness, and elasticity. In Maine and
Boston it is much used for the rafters of houses.

The peculiar characteristics of the European spruce
timber may be briefly stated as follows:—

Norway Timber. —White deals from Christiana, Fre-
derickstadt, and Dram. The two first are of the best
description; but in those from Frederickstadt the knots
are often surrounded by adhering bark, and are apt to
drop out when they are sawn into boards.

The lowland Dram timber is apt to shake and warp in
drying; the upland deals have not this tendency, and are,
therefore, to be preferred.

Swedish Timber. — Gottenburg white deals are hard
and stringy, and fit only for temporary work. The same
remark, in a greater degree, applies to those from Herno-
sand and Sundsvall.

Russian Timber. —Narva white deals are nearly equal
to the Norwegian, and so also are those from Riga, when
properly seasoned.

Petersburg white deals, however carefully seasoned,
expand and contract with every change of weather.

American white spruce deals warp and twist very much,
and soon decay. They are fit for temporary purposes only.

White deal shrinks T Vth in becoming perfectly dry, and
what are termed dry deals will shrink ■gJg-th.

Regarding oak as 100, the strength, Ac., of spruce, are—

American Norway British

Siiruce. Spruce. Spruce.

Strength,. 86 ... 104 ... 70

Stiffness,. 72 ... 104 ... 81

Toughness,. 102 ... 104 ... 60

Pinus Strobus, the Weymouth pine, or yellow pine,
the timber of which, called American white pine, is im¬
ported in large logs. Its wood is light and soft, straight¬
grained, and free from knots, which fits it for joiners’
work, especially for mouldings. Its colour is a brownish
yellow, and the colour and texture are very uniform. It
has a peculiar odour.

Michaux, in his North American Sylva (1819), says,
“ Seven-tenths of the houses, except in the larger capitals,
are built of wood, and about three-quarters of these are
built almost entirely of white pine; and even in the cities,
the beams and principal wood work of the houses are of

that wood. The ornamental work of the outer doors,
the cornices and friezes of apartments, and the mouldings
of fire-places, all of which, in America, are elegantly
wrought, are of this wood. It receives gilding well, and
is, therefore, selected for looking-glass and picture frames.
Sculptors employ it exclusively for the images that adorn
the bows of vessels, for which they prefer the kind called
the pumpkin pine. At Boston, and in other towns of the
northern states, the inside of mahogany furniture and of
trunks, the bottoms of Windsor chairs of inferior quality,
water-pails, a great part of the boxes used for packing
goods, the shelves of shops, and an endless variety of other
objects, are made of white pine. In the district of Maine
it is employed for barrels to contain salted fish, especially
the variety of the timber called the sapling pine, which is
of stronger consistence.” But the most important infor¬
mation given by Michaux to the carpenter, is, that in the
construction of the magnificent wooden bridges over the
Schuylkill at Philadelphia, and the Delaware at Tren¬
ton, and also in the bridges which unite Cambridge and
Charlestown with Boston, of which the first is 1500 feet,
and the second 3000 feet in length, the white pine has
been chosen for its durability.

The white pine is also used for shingles and clapboards.
The shingles are commonly 18 inches long, from 3 to 6
inches wide, ^-inch thick at one end, and 1 line at the
other. They are made only of the perfect wood, and
should be free from knots. In America they last from
twelve to fifteen years. They are exported in great quan¬
tities to the West Indies.

But however high this pine may rank in America as a
timber for the carpenter, it is not esteemed in this country.
It is inferior to the Baltic timber in strength and hard¬
ness, and is not to be compared to it in durability. It
is liable to dry rot, and is, therefore, and for the other
reasons given, never employed in the carpentry of the best
buildings, but is exclusively used by the joiner.

Its strengtli to that of oak is as 99 to 100

Its stiffness “ “ 95 “ 100

Its toughness “ “ 103 “ 100

Pitch Pine ( Pinus resinosa). —This pine is highly
esteemed in Canada for its strength and durability. Its
timber is close-grained, and the concentric circles small.
It is exceedingly resinous, and consequently heavy. Its
elasticity is remarkable, it may be bent round the bow of
a vessel, and after some years it will recover its straight¬
ness. The long-leaved Florida pine yields the best quality;
and the fine-grained timber is alone used by the Ameri¬
can government. The pitch pine grown in the northern
states in Virginia is not so good, as there the trees are
tapped for the pitch, which injures the durability of the
wood. It is employed in furnishing planks and deck
planks for ships, both in this country and in America.
Sometimes planks are obtained 60 feet long without a
knot. Stripped of its sap-wood, it makes excellent pumps
and troughs for mills, and maybe used in situations where
it is exposed to damp and dryness, but will not last under
ground so long as white pine. It is of a redder colour
than Scotch pine, and is sticky and difficult to plane. Its
strength compared with oak at 100 is S2; toughness, 92.

The Silver Fir (Pinus Picea). — This fir, from which
the Strasburg turpentine is obtained, produces a timber
which is elastic, lisfht, and stiff. Its grain is irregular.

KNOWLEDGE OF WOODS.

119

as the fibres which compose it are partly white and ten¬
der, and partly yellow, or fawn-coloured, and hard. The
narrower the white lines are, the more beautiful and solid
is the wood.- It is used in carpentry works of all kinds.
In England it has been used chiefly for floors; and its
stiffness gives it an advantage in the case of any slight
sinking. Like all of the pine tribe it shrinks considerably
in drying; yet Arthur Young and Mitchell affirm that
floors of the timber of a full-grown tree may be laid imme¬
diately on its being sawn up without risk of shrinkage.

Larch (Larix europcea .)—The larch is a deciduous tree,
frequently attaining great size. It is a native of the
mountainous regions of Europe, the west of Asia, and
North America. It is found in abundance in the Alpine
districts of the south of Germany, Switzerland, Sardinia,
and Italy, but not on the Pyrenees, nor in Spain. Of late
years it has been extensively cultivated in Great Britain.

Among the Romans the larch was highly esteemed for its
strength and durability. Its timber was used in the con¬
struction of the forum of Augustus, and several bridges in
Rome. Vitruvius mentions it, and attributes the decay of
buildings in his time to the fact of larch not being used in
their construction. The first account of larch trees grow¬
ing in Britain is in 1629. They are at that time spoken
of by Parkinson in his Paridisus, as being “rare, and
mirsed with but a few who are lovers of variety/’ Evelyn
mentions a large one of “ goodly stature,” as growing
in 1661, at Chelmsford, in Essex. Miller, in 1731, says,
“ This tree is now pretty common in English gardens.”
In the account of the Duke of Athole’s larch plantations,
published in the Highland Society’s Transactions, it is
stated that Goodwood, the seat of the Duke of Richmond,
near Chichester, was probably the first place where the
larch was cultivated as a forest tree, and that only on a
limited scale. In 1782, an extensive plantation was formed
at Halford; and shortly afterwards the Society of Arts of¬
fered premiums for planting the larch, and making known
the useful properties of the timber. Public attention was
thus drawn to the value of the larch, and the result was
that it was extensively planted throughout Britain.

In Scotland it is said that the first larch planted is the
one known as the crooked larch at Dalwick, in 1725. The
popular account, however, is that the Duke of Argyle in¬
troduced the larch into Scotland in 1727. Having received
them among some exotics from Italy, he treated them all in
the same manner, and placed them in a hot-liouse; when
very soon the larches withered, and being supposed dead,
were thrown out on a heap of rubbish in a garden. Here
they revived, and sending forth shoots, became vigorous
trees. In the account in the Highland Society’s Transac¬
tions before alluded to, it is said that “in 1738 Mr. Men-
zies, of Migeny, in Glen Lyon, brought a few plants of
the larch in his portmanteau from London, five of which
he left at Dunkeld, and eleven at Blair in Athole for
Duke James.” But whether this be the correct account
of its introduction or no, it is indisputable that it was
first extensively planted in Blair and at Dunkeld by the
Duke of Athole. Between 1740 and 1750 he planted 350
larches at Dunkeld, at an elevation of 180 feet above the
sea, and 873 at Blair. In 1759 he planted 700 larches,
with the view of experimenting on its value as a timber
tree. This plantation was on the face of a hill, from 300
to 400 feet above the sea, and on very poor land. His

successor, John, Duke of Athole, between 1764 and 1774,
planted 410 acres Scotch, and his plans embraced the
planting of 225 acres more. His successor completed this,
and during his life continued planting, until, in 1799, he
had planted, at Logierait, Inver, and Dunkeld, altogether,
800 acres Scotch. In 1800 he continued his operations,
and from that date to 1815, completed the planting of 2409
Scotch acres. Some of the land thus planted was at an
elevation far exceeding the range of growth of the Scotch
fir, being from 900 to 1200 feet above the sea. The success
which attended the experiment induced him to continue
planting till 1826, and at the close of that year he had
completed the planting of 8071 Scotch acres with larch
alone, or with larch mixed with other trees 8604 Scotch,
or 10,324 statute acres.

In France attention was early directed to the value of
larch timber; and in 1798 a commission was appointed
to examine into its suitableness for the construction of
ships. The result, as reported, was:—1. That the wood
was more resinous than that of Pinus Laricio, though,
at the same time, lighter in the proportion of 25 or 26 to
29. 2. That its fibres were very strong and able to resist

twisting. 3. That branches, clear from knots, might be
used as topmasts.

The wood of the larch, according to Hartig, weighs
60 lbs. 13 oz. per foot when green, 36 lbs. 6 oz. when dry.
The wood of trees produced in a good soil is of a yellow¬
ish white; but that of trees grown in a poor soil, and at
great elevations, is reddish brown, and very hard. The
timber is said to arrive at perfection in forty years; while
the Scotch pine takes eighty years to mature its timber.

From the nature of its growth, the larch is free from
large knots; and although it produces dead knots, yet
these are generally sound, and found fast-wedged, as it
were, in the timber. It is exceedingly durable, excelling,
in this respect, even the oak itself. In timber construc¬
tions it is applicable, in large baulks, or scantlings, as
beams and lintels; but when cut into deals, or smaller
scantlings, its tendency to warp or twist is so great, as to
render it much less valuable in this condition. It is said,
i however, that if the tree is barked two years before it is
| cut, the timber loses this tendency. It is difficult to work.

As post-piles, or sleepers, or in circumstances in which
it is alternately exposed to wet and dry, its durability
is very great. Hence, also, it is suitable for mill-work,
for the steps of quays, &c.

Its strength to that of oak is as 103 to 100

Its stiffness “ " 79 “ 100

Its toughness “ 134 “ 100

The Cedar. —Under the general name of cedar are
known to us, the red cedar (Juniperus Virginiana), a
native of North America; the white cedar (Oupressus
thyoides), also an American tree; the cedar of Lebanon
(Gedrus Lebani). Of these, the first-named is probably
the most familiarly known, by its wood being used for
blacklead pencils. The name red cedar has reference to
the wood of the heart of the tree merely, for the sap-
wood is perfectly white. It is so strong and durable that
it would be preferred to every other kind of wood for rural
purposes in America, were it not so scarce and high-
priced. It is admirably adapted for subterranean water
pipes. It is used for the upper parts of the frames of
vessels. In this country it is much used for drawers,

120

PRACTICAL CARPENTRY AND JOINERY.

wardrobes, and other articles of furniture, as it is not
liable to be attacked by insects; and on account of its
power of resisting heat, Mr. Brunei has used it for
covering locomotive boilers.

The timber of the white cedar, from its lightness and
its power of resisting alternations of dryness and mois¬
ture, is in common use in Baltimore and Philadelphia for
shingles. These are cut transversely to the concentric
circles; they are from 2 to 2 feet 3 inches long, 4 to 6 inches
broad, and 3 lines thick at the larger end. At Baltimore
they are called juniper shingles. These shingles are much
more durable than those of the white pine; lasting from
thirty to thirty-five years. It is made into pails, buckets,
wash-tubs, churns, &c.; and the coopers in Philadelphia
who make these articles are called cedar coopers.

The cedar of Lebanon has timber of a reddish white
colour, light, spongy, and easily worked, but very apt to
shrink and wprp, and by no means durable. In its
appearance it bears a close resemblance to the timber of
the silver fir. The weight of a cubic foot of red cedar is
260 lbs.; its specific gravity is ’426. Couch gives '753
as the specific gravity of Canadian cedar, and 47 lbs. as
the weight of a cubic foot; and Bevan states its tenacity
at 11,400 lbs. per square inch.

The Yew ( Taxus ).— The yew is a very slow-growing
tree; but if it live a long time it becomes colossal in its

dimensions. At Foullebec in France, there is a yew tree
21 feet in circumference. In England there are many
noble trees of this kind; and at Fortingall, in Scotland,
there is one, or rather the wreck of one, which was found
by Mr. Tennant to be 56 feet in circumference. As the
tree grows very slowly (so many as 150 annual layers
have been counted in a tree of 13 inches diameter), the
Fortingall yew must have been a flourishing tree at the
commencement of the Christian era.

The wood of the yew is hard, compact, and of a very
fine grain. It is flexible, elastic, and incorruptible. It
splits easily. The sap-wood, which is white, and does
not extend to a great depth, is also very hard. The
heart-wood is of a fine orange or deep brown colour. It
requires a long time to dry, but shrinks very little iri
drying. It is the finest wood for cabinet-making pur¬
poses, and is generally employed in the form of veneers.
Where it is found in sufficient quantity to be used for
large works, the yew may be considered to be indestructi¬
ble, even where the most durable of other woods perish.
In France the timber makes the strongest of all wooden
axle-trees. The weight of the specimen in the Exhibition
of 1851 was 41 7 lbs. per cubic foot, and its specific gra¬
vity '665. Muschenbroek gives 5043 lbs. as the weight
of a cubic foot, and ‘807 as the specific gravity of Spanish
yew; and Bevan gives 8000 lbs. as its tenacity.*

THEORETICAL

RESOLUTION AND COMPOSITION OF FORCES.

Carpentry is the art of combining pieces of timber to
support a weight, to sustain pressure, or to resist force.

It is broadly distinguished from joinery by this, that
while the work of the carpenter is essential to the stability
of a structure, the work of the joiner is applied more to
its completion, its decoration, and rendering it fit for use,
and may, in general, be removed without affecting its
stability.

The principles of carpentry are founded on the doc¬
trine of the composition and resolution of forces—a know¬
ledge of the relative strength of the materials; and it is
through a knowledge of these alone that skilful designs
are made.

The effects of the different forces which act on a piece
of timber at rest are these—extension and compression
in the direction of its length, lateral compression, and tor¬
sion. To the first, is opposed cohesion; to the second,
stiffness; to the third, transverse strength; and to the
fourth, the elasticity of torsion. On these resistances of
materials, direct experiments have been made, and prac¬
tical formulae for calculating them have been deduced.

It is essential, on entering on the subject, that an
accurate idea should be formed of the manner in which
several forces act when united in their effect, and we
shall therefore proceed to lay before our readers the princi¬
ples of the composition and resolution of forces when ac¬
commodated to the chief purposes of the carpenter.

If a (Fig. 433) be a force acting on a body in the di-

CARPENTRY.

rection of the line a b, and c another force acting on the
same point in the direction of the
line c b, with pressures in the pro¬
portion of the length of the lines
a b and c b respectively, then the
body will be affected precisely in
the same manner as if acted on by
a single force d, acting in the di-
rection d b, with a pressure pro¬
portioned to the line d b, which
is the diagonal of a parallelogram
formed on a b, c b, and which is called the resultant of the
two forces a c. In like manner, if
the forces a, c, d (Fig. 434), act on
a body b, in the direction of the
lines a b, d b, c b, and with inten¬
sities proportioned to the length
of these lines, then the resultant
of the two forces, a and d, is ex¬
pressed by the diagonal e b of the
parallelogram, formed on the lines
a b, d b, and the resultant of this
new force e, and the third force c,
is / acting in the direction f b, the
diagonal formed on eb, cb\ there¬
fore, / b expresses, in direction and
intensity, the resultant of the three forces a, d, c. In like

* Loudon; Strutt; Tredgold; Barlow; Bevan; Rondelet; Emy;
Michaux; The Mahogany Tree; Report of the Juries, Exhibition,
1851; Low on Landed Property; Morton's Cyclopedia; Ponts et
Chaussees; L'Ingeneur Civile, &c.

RESOLUTION AND COMPOSITION OF FORCES.

121

manner, the resultant of the forces abode (Fig. 435)
•will be found to be h, acting in the direction A o. A sim¬
ple experiment may
be made to prove this.

Let the threads a b,
acd, aef (Fig. 436)
have the weights
b d f appended to
them, and let the two
threads a c d, a e f \\
be passed over the \
pulleys c and e; then
if the weight b be
greater than the sum
of d /, the assem¬
blage will settle it¬
self in a determinate
form, dependent on
the weights. If the three weights are equal, the lines
a c, a e of the threads will make equal angles with a b;
if the weights d f p

and b be respec¬
tively 6, 8, and 10,
then the angle c a e
will be a right
angle, and the lines
c a, e a will be
of the respective
lengths of 6 and 8;
and if we produce
c a, e a to n and
vi, and complete
the parallelogram
a n o m; a n, a m
will also be 6 and
8, and the diagonal
a o will be 10. The
action of the weight
b in the direction
a o is thus iu direct
opposition to the
combined action of the two weights d f, in the direc¬
tions ca,ea ; and if we produce o a to some point 7c,
making a r, a s equal to those weights, we shall manifestly
have a k equal to a o. Now, since it is evident that
the weight b, represented by a o, would just balance
another weight l, pulling directly upwards by means
of the pulley k, and as it just balances the two weights
d f acting in the directions a c, a e, we infer that the
point a is acted on in the same manner by these weights
as by the single weight, and that two pressures acting in
the directions and with the intensities a c, a e are equal
to the single pressure acting in the direction and with
the intensity a Jc. In like manner, the pressures a, s a
are equivalent to n a, which is equal and opposite to r a;
also, o a, r a are equivalent to m a, which is equal and
opposite to s a.

In the case of a load W (Fig. 437) pressing on the two
inclined beams b c, b d, which abut respectively on the
points c and d, it is obvious that the pressures will be in
the directions b c,b d. To find the amounts of these pres¬
sures, draw the vertical line b e thimigh the centre of
the load, and give it, by a scale of equal parts, as many

units of length as there are units of weight in the load w:
diaw ef, eg parallel to cb,db\ then b g, measured on
the same scale, will
give the amount
of the pressure sus¬
tained by b c, and
b f the amount sus¬
tained by b d.

A slight consi¬
deration will serve
to show that the
amount of thrust,
or pressure, is not influenced by the lengths of the pieces
be, bd. But it must be borne iu mind, that although
the pressure is not modified in its amount by the length,
it is very much modified in its effects, these being
greatest in the longest piece. Hence, great attention
must be given to this in designing, lest by unequal yield¬
ing of the parts, the whole form of the assemblage be
changed, and strains introduced which had not been con¬
templated.

If the direction of the beam b ci be changed to that
shown by the dotted line b i, it will be seen that the
pressures on both beams are very much increased, and
the more obtuse the angle i b It the greater the strain.

By this proposition we can compare the strength of
roofs of different pitches.—Let A B, A G (Fig. 438) be rafters
of roofs of the respective Fii . 438

heights of F B, F G. Then, n

because the load on the
rafter will increase in the
same proportion as its
length, the load on the
rafter A B of the roof will
be to the load of a similar covering on A F as A B to A F;
but the action of the load on A B, by which it tends to
break it, is to that on A F as A F to A B, consequently
increased load on ab is diminished by its oblique action;
and the diminished load on A F is increased by its direct
action; and the transverse strain is the same in both.
But the strength of beams, we have seen, is inversely as
their length; therefore the power of A B to resist its
strain is to the power of A F as A F to AB. If, therefore,
a rafter A G is of a scantling just sufficient to carry its
load, a rafter A B of a greater pitch would require to be
made of a greater scantling, to enable it to carry the
same load per foot of length. Hence, steep roofs must
have stronger rafters than flat roofs to carry the same
weight of covering per square yard of surface, or the
rafters must be increased in number so as to reduce the
load on each.

The increased size of scantling may be found geome¬
trically as follows:—Let the line af (Fig. 439) be the
depth of a beam that would carry
the weight required if placed hori¬
zontally. Draw /b perpendicular
to af, and make a 6 equal to the
slope or pitch of the rafter: pro¬
duce b a, making a g equal to a /,
and draw the semicircle g d b.

Then draw a <7 perpendicular to ab,
and a d will be the depth required.

When the rafters of a roof are uniformly loaded,

Fig. 439.

122

PRACTICAL CARPENTRY AND JOINERY.

Fig. 440.

there is an angle which renders the oblique strain the
least possible: this is when the tangent of the angle
of inclination is '7071,
or the angle 35T6.

If, in place of the
weight being super¬
imposed on the beams,
we suppose it sus¬
pended from their
point of junction (Figs.

440 and 441), we ob¬
tain the strains in
the same manner; and
it is obvious that although the weight is suspended, the
strains are still compressing the beams in the direction a b,
a c ; or, in other words, rig. 441 .

the beams act as struts.

Substitute, in Fig. 441,
for the string the piece
of timber a d, and we
have now the piece a d
stretched in the direction
of its length and acting as
a tie, and the other tim¬
bers compressed in the
direction of their length.

It is very important to be able, in all cases, to discrimi¬
nate between struts and ties; and we shall therefore illus¬
trate this more at length.

In the jib of the crane b a c

(Fig. 442), formed by the pieces b a, c a, we wish to find
the measure and description of the strains exerted on these
pieces when loaded by the weight w suspended from the
point a. Produce b a and a c to d and e ; make a w equal
to the weight in equal parts; draw w d parallel to c a, and
w e parallel to b a ; then shall a e be the strain on a c, and
a d the strain on a b. On attentively considering the
figure, it will be seen that while a c is sustaining a com¬
pressing strain, b a is pulled in the direction of its length,
and its place might be supplied by a rope. Now, change
the directions of the pieces, as shown in the following
figure (Fig. 443), and both pieces will appear to be in a
state of tension; but it is not so; the place of d a could
not here be supplied by a rope; and it is therefore a strut,
and not a tie.

The following is an invariable rule by which to dis¬
criminate between a strut and a tie in any system of
framing:—

From the point where the weight or pressure acts,
draw a line in the direction of the action of the pressure,
and let the length of that line, measured on a scale of
equal parts, denote the pressure in lbs., cwts., or tons.

From the extremity opposite to the point on which the
pressure is exerted, draw lines parallel to the pieces
which sustain
the strain. The
line parallel to
the one piece will
necessarily cut
the other piece,
or its direction
produced, within
or without the
framing. If the
line cut the piece
itself, or its direc¬
tion produced
within the fram¬
ing, that piece is
compressed — it
is a strut; if it
cut its direction
produced beyond the framing, or point of pressure, the
piece is in a state of tension—it is a tie. In the crane-
jib b a c, Fig. 442, the line w e parallel to a b, cuts the
direction of a c produced within the framing; therefore
a c is, by the rule, a strut. The line w d, parallel to
c a, cuts the direction of b a, produced in the point d
without the framing—and consequently, by the rule, b a
is a tie.

In like manner, in Fig. 443, w d cuts the piece d a
which is a strut, and w c cuts the direction of b a pro¬
duced in c without the framing; b a is therefore a tie.

The following is another mode of

doing

the same

thing

Through the point a, in the two last figures,
draw a straight line m n, parallel to the transverse dia¬
gonal of the parallelograms e d, or d c. Then the parts of
the framing on that side
of this line, to which the ri *- 4t4 -
straining force would
move if left at liberty,
are in a state of com¬
pression, and the parts
on the opposite side are
in a state of tension.

In Fig. 444 the direc¬
tion of the pressure is in the line ab: we therefore set off
from a to b, on
a scale of equal
parts, a b equal
to w, the weight,
and draw from
the point 6, op¬
posite to the
point of pres¬
sure, the lines
b d, be parallel
to e a, f a,
which, cutting
the pieces / a,
e a in dc, show
that they both
act as struts. )

In Fig. 445, let w be the weight acting on the point a:
—from a draw a g in the direction of the strain, and

Fig. 445.

STRENGTH AND STRAIN OF MATERIALS.

123

make ag equal to the weight: then, proceeding as before,
we find that the parallels cut the directions of the pieces
ea,fa produced without the framing; and these pieces
'} are therefore ties.

We have shown that the angles the pieces make with
each other, influence materially the amount and propor¬
tion of the strains upon them. Generally, the strain on
any piece is proportional to the sine of the angle which
the straining force makes with the other piece directly,
and to the sine of the angle which the pieces make with
each other inversely. For, it is plain that the three pres¬
sures, A E, A F, and A G (Fig. 416), which are exerted at
the point A, are in the proportions of the lines A E, A F,
and F E (f E being equal to
A g). But, because the
sides of a triangle are pro¬
portional to the sines of
the opposite angles, the
strains are proportional to
the sines of the angles
A F E, A E F, and F A E.

Therefore, to ascertain the
strain on A B arising from any load A E acting in the
direction A E ; multiply A E by the sine of the angle E A G,
and divide the product by the sine of B A c.

It is not necessary in practice to resort to calculation
by sines. In designing framing, the measures of the
strains can be obtained with equal accuracy by drawing
the parallelogram of forces, and measuring from a scale
of equal parts.

We have hitherto considered the pieces of timber them¬
selves as being subjected to the strains; but it is obvious
that they act also as transmitters of the pressures; and it
is necessary to consider these as propagated to the points of
support, which will be pressed or pulled by the same forces
that act on the pieces serving as struts or ties. Thus we
learn what supports must be provided for these points.

In the truss, Fig. 447, if A B represent the pressure on
A in the direction A B, A c will be the strain on A E, and

the magnitude of the pressure on E in the direction A E,
and A d the pressure on the point F. The divellent force
on the tie-beam E F will be equal to the sum of k c, m D,
and the horizontal thrusts at E and F will be as k C, m D,
respectively. Further, the pressure on the walls E and F
will be unequal when the load A is not in the centre
between them. In the figure, the pressure on E will be
= A k, and on F = A in or k B.

We thus discover, also, what forces are exerted on the
joints of the timber at E and F. For let EB (Fig. 448)
be the end of the tie-beam e f, and A c the end of the
rafter, the force in the direction of the rafter being repre¬
sented by A c, then the vertical pressure on c will be
equal to A B, and the thrust in the direction B E will be
equal to B c ; and this is the measure of the force acting to
splinter off the part cl.

In a queen-post roof, if the centre of the load A (Fig.

449) corresponds to the centre of the opening E F, the
pressure on the points B and c should be alike, and may

be found by making B d equal to the load on B, and (Raw¬
ing d k and m d parallel to B c and B E. Where the
weight is not in the centre of the opening, but is in the
vertical line O C; from a convenient point o in that verti¬
cal line, draw lines to the supporting points, and B g will
be the length of the collar-beam, and g h the place of the
queen-post. To find the strains, make B r equal to the
whole load, and draw r p parallel to F 0 ; the line r p
then represents the strain on g F, the other forces being
as before.

STRENGTH AND STRAIN OF MATERIALS.

The materials employed in construction are exposed to
certain forces, which tend to alter their molecular consti¬
tution, and to destroy that attraction which exists between
their molecules, named cohesion. It is therefore necessary,
in designing constructions, to be able to determine the
relation which subsists between these destructive forces and
the resistance which the various materials are susceptible
of opposing to them.

The destructive forces in timber may operate in the
manners following:—

I. By tension in the direction of the fibres of the wood,
producing rupture by tearing it asunder.

II. By compression in the direction of the fibres, pro¬
ducing rupture by crushing.

III. By pressure at right angles to the direction of the
fibres, or transverse strain, which breaks it across, and
which, as will be seen, is a combination of the two former
strains.

IV. By torsion or wrenching.

Y. By tearing the fibres asunder.

It is to the three first of these only that attention need
be directed, so far as concerns the work of the carpenter.

Every material resists with more or less energy, and
for a longer or shorter period, these causes of destruction.

The resistance to the first-named force is called the resist¬
ance to extension, or simply, cohesion; to the second, the
resistance to compression; and the third, the resistance to
transverse force. The measures of these resistances are

124

PRACTICAL CARPENTRY AND JOINERY.

the efforts necessary to produce rupture by extension,
compression, or transverse strain.

Those materials which, when they have been submitted
to a certain force less than the amount of their resistance,
return to their normal condition when that force is with¬
drawn, are termed elastic. The knowledge of the elas¬
ticity proper to any body gives the means of calculating
the amount of extension, compression, or flexure, which
the body will sustain under a given force.

For the purposes of calculation, it is convenient to have
a measure of the resilience or elastic power of a body ex¬
pressed either in tenns of its own substance, or in weight.
This measure is termed the modulus of elasticity of the body.

If we suppose the body to have a square unit of surface,
and to be by any force compressed to one-half or extended
to double its original dimensions, this force is the modulus
of the body’s elasticity. No solid substance, it may at
once be conceived, will admit of such an extent of com¬
pression or extension; but the expression for the modulus
may nevertheless be obtained by calculation on the data
afforded by experiment. The moduli for various kinds
of woods will be found in the tables.

I. Resistance to Tension.

Although, mechanically considered, this is the simplest
strain to which a body can be subjected, it is yet the one
in regard to which fewest experiments have been made, in
consequence of the great force required to tear asunder
lengthways pieces of timber of even small dimensions.
There is, too, a want of agreement sufficiently baffling in
the results obtained by different operators. The results
of the experiments made by Muschenbroek, Buffon, Barlow,
Bevan, and others, are given in the following table, reduced
to a section of one inch square:—

Table I .—Tenacity of a square inch of different Woods, expressed in the
weight in lbs., that will produce Rupture.

Names of Experimentalists.

Muschenbroek.

Gayffair.

Bevan.

■fi

Mean Results.

Oak, English,.

17,300

13,950

17,600

9,187

12,000

8,889

19,800

7,850

13,310

Elm, .

13.4S9

14,788

14,227

14,400

6,070

14,226

Beech,.

17,300

11.376

11,461

11,467

22,000

14,720

Ash,.

12,000

17,064

12,406

17,207

14,670

Chestnut, Spanish,.

13,300

10,500

11,900

Sycamore,.

13,000

5,000

13,000

Poplar.

5,018

5.260

7.200

6,016

Alder,.

14,180

...

4,290

14,186

Acacia, .

20,582

16,000

18,291

Walnut, . .

8,130

7,800

5,360

8,465

Mahogany,.

8,912

8,000

21,000

Old.

...

18,950

Teak, .

15,642

12.922

15,090

8,200

12,460

Aspin,.

69,90

...

6,990

Lance-wood,.

23,400

Box,.

19,908

19,880

19,890

19,892

Pear,.

9,900

9,822

9,861

Larch,.

10,220

8,900

9,560

Riga fir, .

12,253

13,300

12,776

Petersburg, ..

13,300

...

13,300

Fir,.

8,506

5,000

7,818

Pitch pine,.

7.858

7,818

Cedar,.

4,973

11,400

8,186

Norway pine.

7,287

14,300

10,293

Birch, .

15,000

Hawthorn, .

10,500

Hazel,.

18,000

Holly,.

16,000

Hornbeam,.

20,240

Laburnum.

10,500

Lignum-vitae.

11,800

Lime tree,.

23,500

Maple, .

10 584

10,584

Plane,.

11,700

11.700

\V illow, .

14,000

Yew, Spanish.

8,000

Although, on many considerations, it is not to be
expected that experiments made on such small scantlings
of timber as were used by the experimentalists above
cited (some of these being only a square line in section),
would agree with each other; yet the discrepancy is so
great as to give little confidence in the results. Mr. Bar-
low, on matui’e consideration, has given the following
table of the tenacity of wood usually employed by the
carpenter; and subjoined is the mean result from the fore¬
going table, for the sake of contrast:—

Table II. — Tenacity of a square inch of Timber in lbs.

Barlow’s Mean Results.

Mean Results of Table
No. I.

Oak,.

10,000

13,316

Ash,.

17,000

14,670

Beech,.

11,500

14,720

Teak,.

15,000

12,460

Mahogany, .

8,000

18,950

Riga fir,.

12,000

12,776

As Mr. Barlow’s experiments were very carefully con¬
ducted, his table may be assumed as a safe guide.

1. As the strength of cohesion must be proportional to
the number of fibres of the wood, or, in other words, to
the ai’ea of the section, it follows that the tenacity of any
piece of timber, or the weight which will tear it asunder
lengthways, will be found by multiplying the number of
square inches in its section by the tabular number corres¬
ponding to the kind of timber.

Example. —Suppose it is required to find the tenacity
of a tie-beam of fir, of S x 6 inches scantling.

8x6 = 48, which, multiplied by 12,000, the tabular
number for fir, gives 576,000 lbs.

This is the absolute tenacity. Practically it is not con¬
sidered safe to use more than one-fourth of this weight, or
144,000 lbs.

By the rule inverted, the section of the timber may be
found when the weight is given, as follows:—

2. Rule. — Divide the given weight by the tabular
number, and the quotient multiplied by 4 is the area of
section required for the safe load.

Example. —Required the area of section of a piece of
fir to resist safely a tensile strain of 144,000 lbs.

-= 12 x 4 = 48, the section required.

12000 ’ 1

II. Resistance of timber to compression in the direction
of the length of its fibres.

Experiments on this kind of resistance are not nume¬
rous.

Mr. Rennie found that to crush a cube of 1 inch on
the side, the weights in lbs. required were, for—

African oak, ... ... ... ... 6,720 lbs.

English oak, ... ... ... 3,860 „

White deal, ... ... ... ... 1,928 ,,

Americau pine, ... ... ... 1,606 „

Elm, ... ... ... ... ... 1,284 „

M. Rondelet obtained higher results ; that is, the tim¬
ber experimented on by him presented a greater re¬
sistance. According to this author, a piece of timber
diminishes in strength as it begins to bend; so that the
mean strength of the wood of the oak, which is 44 lbs.
French for every line superficial in the case of a cube, is
reduced to 2 lbs. for a piece of the same wood, when its

STRENGTH AND STRAIN OF MATERIALS.

125

height is 72 times its base. From a great number of
experiments, he compiled the following progression:—

In a cube, the height of which is 1, the strength is T
In a piece, the height of which is 12, „

r> ?»

» » >i 3b, „

)» )) 5i 48, ))

„ „ ,, 60, „

5 ) » ?> )?

833

166

083

041

Thus, in a cube of oak of 1 inch super-1

ficial of base, submitted to the action I While the mean of

experiments gave,

the |

6,346

5,310

2,911

2,163

of a force pressing vertically, the mean
force is expressed by 144 X 44 = 6336,

In a bar of the same wood of the
same base, and 12 inches high, the
strength by the progression would be

144 X 44 X-833 = 5278, .

In a bar 24 inches high, the strength by )
the formula, 144 X 44 X '5 = 3168, i
In a bar 36 inches, the strength by the
formula, 144 X 44 X '333 = 2110,

In a bar 48 = 144 X 44 X T34 = 849.

In a bar 60 = 144 X 44 X '083 = 526.

In a bar 72 = 144 X 44 X ‘042 = 266.

In fir bars the following results were obtained:—

By Calculation. By Experiment.

In the cube of 1 inch, 144 X 52 X 1' = 7,488 7,490

In the bar of 12 inches, „ X '833 = 6,238 6,355

„ 24 „ „ X '5 = 3,744 3,429

„ 36 „ ,, X '33 = 2,471 2,575

These results, M. Rondelet observes, accord with the
experiments of MM. Perronnet, Lamblardie, and Girard.

In an experiment described by the latter, a piece of
wood 2 metres 273 millemetres long, and 155 by 104
millemetres in section, broke under a weight of 33,120
kilogrammes.

Reducing these to English measures, the length is 7'35
feet, the sides of the base 6 05 and 4'06 inches respectively.
The area of the section is therefore 24'5 inches, and as the
weight is 72,864 lbs., the weight on the square inch is
2974 lbs.

The height of the piece is about twenty-two times the
size of its base, and the progression would give a reduc¬
tion of half the strength. If, therefore, 2974 is doubled,
5948 lbs. are obtained as the absolute resistance per
square inch—a result which agrees very closely with the
experiments of M. Rondelet.

The same author arrived at the following conclusions :—

1. That the resistance does not sensibly diminish in a
prism, the height of which does not exceed eight times its
base.

2. That when the height of the prism is ten times its
base, it begins to yield by bending.

3. That when the height is 16 times the base, the piece
of wood is incapable of resistance.

Tredgold says that when the length of the wood is less
than eight times its diameter, the force causes it to expand
in the middle of its length, and split into several pieces,
but when it exceeds this length it yields by bending. As
in practice the last case is almost the only one which
occurs, we shall confine our observations to it alone.

As the first degree of flexure would prove fatal to any
piece of framing, the strength necessary to resist this is
what is required. According to Tredgold, the strain is
directly as the weight, and inversely as the strength,
which is inversely as the cube of the diameter in the case
of a column. The strain is also directly as the square of the

length, and inversely as the diameter, which is directly
as the deflection. Therefore, for cylindrical posts he gives
the formula 17 e X L 2 X W = D 4 , in which e is a con¬
stant number for the kind of timber (see p. 126).

\\ hen the post is rectangular, and D is its least side,
e x L- x W = B D 3 .

When the post is square, 4 e X L- x W = D 4 , where D
is the diagonal of the square.

The stillest rectangular post is that in which the greater
is to the less side as 10 to 6.

The equation is then 0 6 e X L- x W = D 4 .

When D is the least side, divide by 0'6 to find the
greater.

These rules, expressed in words, are as follows:—

To find the diameter of a post that ivill sustain a
given weight when the length exceeds ten times the
diameter.

Rule. —Multiply the weight in lbs. by 1'7 times the
value of e, then multiply the product by the square of
the length in feet, and the fourth root of the last product
will be the diameter in inches.

Examples. — 1 . The height of a cylindrical oak post
being 10 feet, and the weight to be supported by it
10,000 lbs., required its diameter.

The tabular value of e for oak is '0015—

therefore, 17 X '0015 x 100 x 10000 = 2550,
the fourth root of which is 7'106, the diameter required.

By inverting the operation, we find the weight, when
the dimensions are given, thus—Idle height of a cylin¬
drical oak post being 10 feet, and its diameter 7'106 inches,
required the weight it will support. The fourth power of
7'106 inches, as we have seen, is 2550, therefore—

_ __— . - 10 000

1-7 X 0015 X 100 '255

To find the scantling of a rectangular post to support
a given weight.

Rule. —Multiply the weight in lbs. by the square of the
length in feet, and the product by the tabular value of e.
Divide this product by the breadth in inches, and the
cube root of the quotient will be the thickness in inches.

2. Let the height of the post, as before, be 10 feet, and
the weight to be supported 10,000 lbs., required the thick¬
ness of the post when its breadth is 5 inches.

• 0015 X 10- X 10000 _ go()

the cube root of which is 6'69, therefore the section of
the post is 6 69 X 5 inches.

To find the dimensions of a square post that will sus¬
tain a given weight.

Rule. —-Multiply the weight in lbs. by the square of the
length in feet, and the product by four times the value of
e, and the fourth root of the product will be the diagonal
of the post in inches.

3. Let a square oak post be 10 feet long, and let the
weight to be supported be 10,000 lbs., required the dimen¬
sions of its sides. The value of e is '0015 —

thei'efore, '0015 x 4 x 100 x 10000 = 6000,
the fourth power of the diagonal of the square, therefore
the diagonal of the square is 8'8 inches, and its side 6'22.

To find the stijfest rectangular post that ivill support
a given weight.

Rule. —Multiply the weight in lbs. by 0'6 times the
tabular value of e; multiply the product by the square ot

12 G

PRACTICAL CARPENTRY AND JOINERY.

the length in feet; the fourth root of this product will [
be the least side in inches. Divide this by 06 for the
greatest side.

4. Let the length of the stiffest rectangular oak post
be 10 feet, and the weight to be supported 10,000 lbs.,
required the side of the post.

0-6 x 0015 X 10 x 10 x 10000 = 9000,
the fourth root of which is 5 - 477, the least side, which,
divided by 0'6, gives 9 - 13 as the greatest side.

From experiments made by Lamande and Girard, by
loading posts till a small amount of deflection was visible,
and thus ascertaining the values of l AY D, Mr. Tredgold
calculated the value of the constant e, so as to give the
load to which the post might be safely exposed. These
constants for different woods are found in the following
table:—

Table III .—Constant Numbers, to be used in calculating the Dimen¬
sions of Posts, Pillars, dec., of Timber, pressed in the direction of
their Lengths.

Kind of Wood.

Value of the Constant e.

English oak,.

•0015

Beech, .

■00195

Ash,.

•00168

Elm,.

•00184

Spanish mahogany, .

•00205

Honduras do.

•00161

Teak, .

•00118

Riga fir, .

•00152

Memel ditto, .

•00133

Norway spruce,.

•00142

Larch, .

•0019

III. Resistance of timbers to transverse strain.

When a piece of timber is fixed horizontally at its two
ends, then, either by its own proper weight, or by the
addition of a load, it bends, and its fibres become curved.
If the curvature do not exceed a certain limit, the tim¬
ber may recover its straightness when the weight is re¬
moved ; but if it exceed that limit, although the curvature
diminishes on the removal of the load, the timber never
recovers its straightness, its elasticity is lessened, and its
strength is partly lost. On the load being augmented
by successive additions of weights, the curvature in¬
creases until rupture is produced. Some woods, how¬
ever, break without previously exhibiting any sensible
curvature.

It may be supposed that, in the case of the timber being
exactly prismatic in form, and homogeneous in structure,
the rupture of its fibres would take place in the middle
of its length, in the vertical line, where the curves of the
fibres attain their maxima.

In the rupture by transverse strain of elastic bodies in
general, and consequently in wood, all the fibres are not
affected in the same manner. Suppose a piece of timber,
composed of a great number of horizontal ligneous layers,
subjected to such a load as will bend it, then it will be
seen that the layers in the upper part are contracted, and
those in the lower part extended, while between these
there is a layer which suffers neither compression nor
tension; this is called the neutral plane or axis.

If the position of the neutral axis could be determined
with precision, it would render more exact the means of
calculating transverse strains; but as the knowledge of
the ratios of extensibility and compressibility is not exact,
the position of the neutral axis can only be vaguely

deduced from experiment. Were the ratios of compres¬
sion and extension equal, the neutral axis would be in
the centre of the beam; but experiments show that this
equality does not exist. Barlow found that in a rectangu¬
lar fir beam the neutral axis was at about five-eighths of
the depth;* and Duhamel cut beams one-third, and one-
half, and two-thirds through, inserting in the cuts slips of
harder wood, and found the weights borne by the uncut
and cut beams to be as follows:—

Uncut Beam One-third Cut. One-half Cut. Two-thirds Cut.

45 lbs. 51 lbs. 48 lbs.. 42.

Results which clearly show, that less than half the fibres
were engaged in resisting extension; and it has been
long known that a beam of soft wood, supported at its
extremities, may have a saw-cut made in the centre,
half-way through its thickness, and a hard wood piece
inserted in the cut, without its strength being materially
impaired.

It is not here necessary to enter into an investigation
of the theory of transverse strain. The results of it, cor¬
rected by experimental evidence on which rules of practical
utility may be founded, are all that need be sought for.

The transverse strength of beams is—

Directly as tbe breadth,

Directly as the square of the depth, and
Inversely as the length;
or substituting the letter b for the breadth,

d for the depth, and
l for the length,

and placing the ratios together, the general expression of
the relation of strength to the dimensions of a beam is
obtained as follows:—

b x <P

But this forms no rule for application, since beams of
different materials do not break by the application of the
same load; and it is therefore necessary to find by experi¬
ment a quantity to express the specific strength of each
material.

Let this quantity be represented by S, and the formula
becomes—

b X cl 2 X S , . . ...

-^-= breaking weight.

By this formula experiments can be reduced so as to give
the value of S. It is only necessary to find the breaking
weight of a beam whose dimensions are known, and then
by transposition of the equation—-

l X breaking weight „
bxd* - b -

S thus becomes a constant for all beams of the same
material as the experimental beam.

Although this ratio of strength to the dimensions of the
beam is very nearly correct, it is not absolutely so; and
the French writers modify it in the manner which will be
stated subsequently. The length of a beam appears to

* Mr. Barlow’s method of operating was as follows:—He ran a
saw cut to 5-8ths of the depth of the beam, and inserted a thin slip
of pear tree, sufficiently tight to preserve the stiffness of the beam,
but not so tight as to cripple it. The beam was then loaded till it
broke. On examining the slip of pear-tree after the fracture of the
beam, the impression of the fibres was found distinctly marked on
it, strongest at top, and weakening gradually to the bottom, where
compression ceased.

STRENGTH AND STRAIN OF MATERIALS.

127

influence the strength to a greater extent than the theory
allows; for similar beams are rather more than twice as
strong when half as long, and the strength does not
increase quite so rapidly as the square of the depth.

When the value of S for various kinds of wood is deter¬
mined, the formula may be used for computing the strength
of a given beam, or the size of a beam to carry a given
load. For any three of the quantities, l, b, d, W, being
given, we can find the fourth thus:—

I. When the beam is fixed at one end and loaded at
the other, and when

l W _

b d* ~

The length, breadth, and depth being given, to find the

weight—

W =

S b cP

The weight, breadth, and depth being given, to find the
length— 7 S b d -

l =

The weight, length, and depth being given, to find the

breadth-

b =

l W
S d-

The weight, length, and breadth being given, to find the

depth—

d =

l W
b S *

When the section of a beam is square, that is, when

b — d, then b or d =

l W

II. When the beam is supported at one end, and loaded

in the middle; then

former cases—

■\y _ 4 b cl' 1 S

d= '

l W

t, = S, and we have for the

4 b d 1

1 = Hi’S ; 6= .

I w

4 d 1 S ’

; and where b = d, b or d = \ /

4 6 S V 4 S

III. When the beam is fixed at both ends—

When loaded in the Middle.

i—
b —

6 b d* S

W =

6 6 d 2 S

l w

6 d 2 S ’

b —

. 1 W

v (J4S

d —

6 = V 3 /

l W

6 S '

d =

When loaded at an Intermediate Point.

3 l b d 2 S .

2 m n ’

2 m n W

3 l d' 1 S’

2 m n W.

3 l d~ S ’

. 2 m n W

Sib S ’
s/ 2 m n W
' 31S

Where m n is the rectangle of the segments into which
the load divides the beam.

IY. When the beam is supported at both ends, but
not fixed—

When load is uniformly diffused.

2 b d- S

W =

1 =

2 b d 1 S

b =

2 bd a ’

d ~V 26 S

b — d — \ 3//

1 W

2 S

When loaded at an intermediate point.

I b d 2 S

m n

m n W .

bW s ;

_ m«W,

b ~ Id* S 5
_ . m nW

d ~V IbS ’

d = b = $/ “” W

l S

When the beam is inclined, the horizontal distance be¬
tween its supports is the length or l.

The following table contains the results of experiments
made by Mr. Barlow on the transverse strength of various
kinds of wood, with the value of S, calculated according

to the formula S = —- :—

4 6 a-

Table IY.

5. |

7* 1

Name of Woods.

Length in feet.

| Breadth in inches.

| Depth in inches.

Specific Gravity,

water being 1000.

Greatest Weight,

while elasticity

remained perfect.

Breaking Weight

in lbs.

Value o
S,

s- iV

' 4 b d

Acacia,.

4T6

710

1195

1S67

Ash,.

4-16

727

1304

702

1304

2037

Beech,.

760

225

772

2026

696

150

593

1556

Birch, Common,.

4*16

792

1164

1820

>> > >

630

1304

2037

4*06

648

1253

1785

,, Black American

651

1174

1834

Bullet tree,.

4T6

1029

1696

2646

Deal, Christiana,.

4T6

689

996

1562

,, Memel,.

4*16

590

nos

1731

Elm.

4-16

543

714

1115

Fir, New England, ...

553

150

420

1102

„ Riga.

753

125

42*2

1108

,, ,, .

738

150

467

1051

,, Mar Forest.

696

125

436

1144

»> n .

Greenheart,.

698

150

561

1262

4*16

1000

1762

Larch, .

531

125

325

S53

Norway spar,.

445

142

445

1036

577

200

655

1474

Oak, English,.

969

150

450

1181

,, Canadian,.

934

200

637

1672

872

225

673

1766

,, Danzic.

756

200

560

1457

,, Adriatic,.

993

150

526

1383

,, English,.

4T6

903

999

1561*1

„ „ .

856

677

1058

972

999

1561

835

943

1473 |

>» >» •• .

74S

1447

2261

>> i) .

756

1304

2037 J

Pitch pine,.

660

150

622

1632

Poon.

579

150

846

2221

Red pine,.

657

150

511

1341

Teak,..

745

300

938

2462

Value of
C,

l W

10 . | 11 .

i- o

£J

a h

621

679

675

552

607

679

595

605

8S2

521

577

372

367

369

350

3S0

420

584

2S4

345

491

394

557

558
4S5
448

Mean 553
544
740
447
820

Middle

Outside.

Middle.

Outside,

Middle.

Outside

Fast
grown
Slow
grown.
Fast
grown.
Slow
grown.
In store
2 years.
In store
16 years.

In using Mr. Barlow's formulae for transverse strength,
the eighth column of the table gives the constants S for
the various kinds of timber; and all the dimensions of
the timber must be in inches. The rules for two of the
cases, expressed in words, are as follows: —

To find the strength of a rectangular beam, fixed at
one end and loaded at the other.

Rule. —Multiply the value of S by the area of the sec¬
tion, and by the depth of the beam, and divide the pro¬
duct by the length in inches. The quotient will be the
breaking weight in lbs.

Example— A beam of Riga fir projects 10 feet beyond
its point of support, and its section is 8 X 6 inches, what
is its breaking weight?

Area 8 X 6 = 48, multiplied by the depth 8 = 384.
Multiply this by the constant 1108, and divide the product

by the length, = 3545 lbs. The fourth part

of this is the safe weight to impose in practice, therefore—

= 886 lbs.

To find the strength of a rectangular beam, when it is
supported at the ends and loaded at the middle.

Rule. —Multiply S by four times the depth, and by the
area of the section in inches, and divide the product by the
length between the supports in inches, and the quotient
will be the greatest weight the beam will bear in lbs.

Example. —A beam of Riga fir is 20 feet long between

128

PRACTICAL CARPENTRY AND JOINERY.

its supports, and its section is 8 x 6 inches; required its
breaking weight.

1108 x8x4x8x6 _

~240 ' “ '

The fourth part of this is the safe load, therefore —

7091

1772 lbs.

The constant C, in the same table, column 9, and in
column 11 of Table VIII., is for the formulae as given by
Mr. Tredgold, in which it is not necessary to convert the
length of the bearing into inches.

When the beam is supported at one end, and loaded at

the other, the equation is = breaking weight.

Or, in words, as follows:—Multiply the breadth in inches
by the square of the depth in inches, and by the constant
C for the kind of timber; and divide the product by four
times the length in feet, for the breaking weight.

Example .—A beam of Riga fir projects 10 feet beyond
its point of support, and is 8 X 6 inches in section; re¬
quired its breaking weight.

The value of C for Riga fir is 369, therefore—

369 x 6 x 64

= 3542‘4 = the breaking weight.

3542

= 885= safe weight.

When the beam is supported at both ends, and loaded
in the middle.

Rule .—Multiply the breadth by the square of the depth,
and by C, and divide by twice the length ; the quotient
is the breaking weight.

Example .—Let the beam be 8 x 6 in section, and 20
feet long between its supports; required the breaking

weight.

369 x 6 x 64
20

= 7084.

In the summary of formulae in the sequel (p. 130), will
be found all the rules written in words.

It has been stated that some French writers use for¬
mulae different from those here given, and intended to
unite more closely the results of theory and experiment;
but they are difficult of application in practice, and the
results vary so little from those of the formulae given, that
the correction is not worth making.

Mr. Gwilt, in his Encyclopaedia of Architecture, not
only ignores all the laborious experiments that have been
made in this country, but also speaks disparagingly of the
labours of the able men who have endeavoured to benefit
the architect and engineer by bringing the aid of mathe¬
matical investigation to found upon those experiments safe
and general rules for practice. Mr. Gwilt cites Buffon’s
experiments, as given by Rondelet, and in his introduc¬
tory notice of them says, “ They are worth more than
all which has hitherto been done in this country. The
treatises on mechanical carpentry seem to have been
written more with the view of perplexing than of assisting
the student.” And this, too, notwithstanding the labours
of Robison, Young, Barlow, Tredgold, Hodgkinson, Bevan,
Rennie, and a host of others.

But a little investigation would have made it apparent
that the constants derived by these writers from their ex¬
periments give results most singularly in accordance with
those obtained by the able French philosopher; and, which is
of greater importance, perfectly safe when applied in practice.

The discrepancy between the results of the English for¬
mulae here given and the experiments of Buffon occurs
chiefly in short bearings; and as the strength obtained by
the formulae is sufficient for long bearings, it follows that
it must be sufficient also for the short lengths, erring
only in being slightly in excess, or “a little stronger than
strong enough.’’

The rule given by Rondelet is expressed in terms of
only two of the three dimensions of the timber, and
requires a constant which is empirical, like that of the
formulae already given. It is as follows:—

Subtract from the primitive strength one-third of the
quantity which expresses the number of times the depth
is contained in the length of the beam.

Multiply jfche remainder by the square of the length.

Divide the product by the number that expresses the
relation of the depth to the length.

In the following table, the four first columns give the
result of certain of Buffon’s experiments, reduced to Eng¬
lish measures: the two other columns contain constants
for Barlow’s and Tredgold’s formulae, calculated from the
other columns:—

Table Y .—Results of certain of M. Buffon's Experiments on
Transverse Strength.

No.

Length.

Side of
Square.

Mean
Weight
which brake
the pieces.

Breaking
Weight by
Rondelet’s
Formula.

Value of S,

s _ IW

4 bd*

Value of

a-EE

^ -bd*

1 .

7'462

4-264

5,768

1670

546

8-528

4,869

4,943

1612

538

9-594

4,387

4,301

1635

545

10-660

3,946

3.799

1644

548

12-792

3,279

3,018

1623

541

7-462

5 "33

12,496

1847

616

8-528

10,626

10,750

1800

600

9-594

8,635

9,429

1440

480

10-060

7,765

8,357

1441

480

12-792

6,644

6,748

1678-5

559

14-924

5,819

4,600

1730

577

17-096

4,810

4,738

1620

540

19-188

4,120

4,066

1500

500

21-320

3,624

3,530

1531

510

23-452

3,364

3,092

1563

521

25-584

2,502

2,726

1260

420

29-848

2,112

2,151

1247

412

7-462

0-39G

20,635

19,196

1654

554

8-52S

16,804

16,562

1637

545

9-594

14,292

14,547

2011

670

10-660

12,197

12,877

1500

500

12-792

9,938

9,420

1446

482

14-924

8,210

8,6(36

1400

466

17-050

...

7,030

7,348

1365

442

19-188

6,187

6,319

1300

434

21-320

5,495

5,506

1337

446

10-660

S-528

30,148

30,363

1828

609

12-792

25,540

24,883

1804

601

14-924

21,605

20,854

1843

614

17-056

17,968

17,833

1740

580

19-18S

14,577

15,482

1587

529

21-320

13,303

13,593

1570

523

Average...

... 1621...

... 540

The constants S and C agree very nearly with those
derived from the experiments of Mr. Barlow and Mr.
Tredsold: the latter assumes 550 as the value of S.

In any beam exposed to transverse strain, it is mani¬
fest that there must be some certain proportion between
the breadth and depth which will afford the best results.
It is found that this is obtained when the breadth is to
the depth as 6 to 10. Therefore, when it is required to
find the least breadth that a beam for a given bearing
should have, the formula is as follows:—

0-6 = b

sj d

or, expressed in words—

Ride .—Divide the length in feet by the square root of the
depth in inches, and the quotient, multiplied by the decimal
06, will give the least breadth the beam ought to have.

STRENGTH AND STRAIN OF MATERIALS.

129

The nearer a beam approaches to the section given by
this rule, the stronger it will be; and from this rule is
derived the next.

To find the strongest form of a beam so as to use only
a given quantity of timber.

Rule . — Multiply the length in feet by the decimal 0 6,
and divide the given area in inches by the product, and
the square of the quotient will be the depth in inches.

Example . — Let the given length be 20 feet, and the

given area of section 60 inches.

Then

20 X 06 —

5'00,

the square of which is 25 inches, the depth required, and
the breadth is consequently 2’4 inches.

The stiffest beam is that in which the breadth is to the
depth as ‘58 to 1. The stiffest beam which can be cut out
of a round tree may be found
graphically as follows:—Let a b
(Fig. 450) be the diameter of
the circle, then with a radius
equal to the radius of the circle,
and from the extremities of the
diameter, draw the arcs c d e,
f dg; join a c, c b, b d, d a, and
the parallelogram thus formed is
the section of the stiffest beam
which can be cut from the. tree.

The French writers make the ratio of breadth to depth as
5 : 7.

It will be seen by the formulae that there is an un¬
questionable advantage obtained by fixing the ends of
bearing timbers, as the increase of strength is then as 3
to 2. This, although not easily accomplished, nor indeed
proper when the ends of the timbers are built into walls,
as the stability of these may be injured, yet may be done
in certain circumstances; and it further leads to important
practical rules. The chief of these is, that girders and
joists, and all bearing timbers whatever, when laid over
several points of support, should be made as long as pos¬
sible; and that purlins, rafters, and joists should, when¬
ever the space will admit of it, be notched on the sup¬
ports, in place of being framed between them.

But the breaking weight of a beam has seldom, for
practical purposes, to be ascertained. For when a beam
is loaded, and even by the effort of its own weight, when
its length is great compared with its other dimensions, it
sinks down or bends in the middle. If the deflection
produced by a load does not exceed a certain limit, the
timber will recover its straightness when the load is
removed; but beyond that limit, the elasticity of the
fibres becomes diminished; the timber loses part of its
strength, and the addition of weight at length causes
rupture of the fibres.

Mr. Barlow gives one-fourth of the breaking weight as
the greatest weight that should be used; but experiment
shows that one-fifth of the breaking weight produces a
permanent set in a beam, and consequently a diminution
of its strength; and the French authors invariably give
only one-tenth of the breaking weight as the safe load
when the load is fixed; but if a moving load has to be
provided for, they say that it should not exceed one-
twelfth or one-thirteenth of the breaking weight.

But the load which a beam may sustain without per¬
manent injury, may cause such an amount of deflection as

Fig. 450.

to unfit it for the purposes of the carpenter; for a beam,
forming part of a system of framing, cannot be deflected
without a sensible alteration of its length, and thus the
framing becomes deranged. Moreover, in girders, beams,
and joists which sustain floors and ceilings, where the
work should not only be true, but appear true, a very
small amount of curvature would mar its beauty. Mr.
Tredgold assumes that this curvature is not sensible when
it does not exceed the ^th part of the length of
the beam; and in forming his rules, he has taken the
fortieth part of an inch in every foot as the allowable
deflection.

The term stiffness is opposed to flexibility: thus, when
a piece of timber bends under a weight in a very small
degiee, it is said to be stiff; and when it bends consider-
ably, it is said to be flexible. Now, the stiffness of beams
is proportional to the space they are bent through by
a given weight when the lengths are the same, but that
two pieces of different lengths may be equally stiff, the
deflection should be proportional to their lengths. For
a deflection which would not be injurious in a beam 40
feet long, would be highly detrimental in. one 10 feet long.

The extension of any part of a beam is directly as the
force that produces it, and as it is known by experiment
that the deflection is as the weight, all other things beino -
the same, the deflection is therefore as the extension.

The extension is as the weight and the cube of the
length directly, and as the breadth and cube of the depth
inversely: the deflection will consequently be in the same
proportion. If L be the length in feet; W, the weight in
lbs.; B, the breadth in inches; and D, the depth in inches;
L 3 x W .

- ft* is as the deflection.

B x D 3

In order that a beam may be equally stiff, as we have
seen above, the deflection should be inversely as the
length: consequently, the weight that a beam will sus¬

tain will be

B x D 3
d x L-

= W, where d is the deflection in

L 3 x W

inches; and y> x DDZ ~ a cons ^ an ^ number for the same
kind of timber.

But, before these rules can be applied, it is necessary to
obtain, experimentally, the value of d. This being done,
B x D 3 x d

we should have pa x ~^V~ ~ a cons ^ an ^ quantity; which

being given, the deflection in any other case may be
found.

Experiments, with the view of determining this con¬
stant, have been made by various writers. Of these,
probably, the most satisfactory were by Duhamel; for this
reason, that the scantlings operated on were of the size
generally used in building. From these and other experi¬
ments, many of which were made by himself, Mr. Tred¬
gold computed the constants for the various kinds of tim¬
ber given in the following table.

o o

In computing the value of a, Mr. Tredgold assumed the
deflection to be -jV^h of an inch per foot; and the formula
BXD 3

became — a - w hen the deflection is required to

be less than this, say \ of then multiply the constant
a by 2; if -j of T \ T , multiply a by 3; or if required greater
than fu, multiply a by any number of times that the
deflection may exceed -j^th of an inch per foot.

130

PRACTICAL CARPENTRY AND JOINERY.

Table VI.— Table of the Values of “a.”

Value of a.

Oak, old, ...

... -0099

„ young,.

•0105

... -0164

,, ,, ... ... ... ...

•0197

,, Riga. .

... -0107

„ English,.

•0119

„ Canadian, ...

... -0090

„ Adriatic,

•0193

Danzic,

... -0105

9) T119

Mean,

... '0124

Mean of 10 examples of English oak,

•0124

White spruce,

... -00957

» » ••• •••

■0138

To find the scantling of a 'piece of timber which,
when laid in a horizontal position, and supported at
both ends, will resist a given transverse strain, with a
deflection not exceeding ffih of an inch per foot.

1. When the breadth and length are given, to find the
depth.

Rule .—Multiply the square of the length in feet by
the weight to be sustained in lbs., and the product by
the tabular number a (Table VI.; and column 10, Table
VIII.) ; divide the product by the breadth in inches,
and the cube root of the quotient will be' the depth in
inches.

Example .—Required the depth of a pitch pine-beam,
having a bearing of 20 feet, and a breadth of 6 inches,
to sustain a weight of 1000 lbs.

The square of the length, 20 feet = 100
Multiplied by the weight . = 1000

And the product .... 400,000

By the decimal . . . . . -016

Divide the product by the breadth,

6 inches . . . . . = 6400 000

Gives ...... 1066'666

The cube root of which is 10'2 inches, the depth re¬
quired.

2. When the depth is given.

Rule .—Multiply the square of the length in feet by
the weight in lbs., and multiply this product by the tabu¬
lar value of a: divide the last product by the cube of the
depth in inches, and the quotient will be the breadth
required.

Example .—Length of pitch-pine beam 20 feet; depth,
10'2 inches; weight, 1000 lbs.

20 x 20 x 1000 X -016
10-2 x 10 2 x 10 2

6400

1061

= 6, the breadth

required.

3. When neither the breadth nor the depth is given, but
they are to be determined by the proportion before given,
that is, breadth to depth as 0'6 to 1..

Rule .—Multiply the weight in lbs. by the tabular num¬
ber a, and divide the product by 0'6, and extract the
square root: multiply the root by the length in feet, and
extract the square root of this product, which will be the
depth in inches, and the breadth will be equal to the
depth multiplied by 0 6.

Example. —Weight, 1000 lbs.; value of a, '016; length,
20 feet. . /1000 x-016

0-6

x 20 = 106.

V 106 = 10 2, the depth required ; then 10'2 X 0 6 = 6 0,
the breadth required.

The following are the formulae given by Mr. Barlow: —

B = the breadth, D = the depth, L = the length, W =
the weight, and d = the deflection.

When the beam is supported at one end.

1. Where the weight is at the extremity, the breadth,
length, and amount of deflection being given, to find the

depth.

T? -p,-, x L = D.
E B d

{The length in feet, the breadth, depth , and deflection in inches)

2. Where the weight is uniformly spread, the breadth,
length, and deflection being given, to find the depth.

/ 3j *75 W L _ d
V E B d

{The length in feet, the breadth, depth, and deflection in inches.)

And when the beam is a cylinder, and the weight at its
end, the deflection will be 1 '7 times that of a square beam.

When the beam is supported at both ends, and the
length, weight, and deflection given.

The weight being in the middle.

W l 3
16 Ed

BD :i .

The weight uniformly spread.

625 W L 3
16 e d

= bd 3 .

{The length in feet, the breadth, depth, and deflection in inches)

And in a square beam—
W L s

16 E d

= B 4 = D 4 .

625 W L s
16 Ed -

B 4 = D 4

When the beam is a cylinder.

Multiply the quotient by 1 '7, and the fourth root of the
product is the diameter.

Table VII. — Table of the Value of E in the above Formulce.

CALCULATED.

Ash, ...

E =

•244

Beech,

... • • •

T95

Birch, ...

... )?

•240

American ditto, ...

... .. . ,

•256

Deal, Christiana,

•230, T15

Deal, Memel, .

... ••• »

T90

Elm,

... „

YOl

Fir, New England,

... ••• )>

•317

Fir, Riga,

... „

T67

Fir, Mar Forest, .

... „

•94

Greenheart,

... • • • »

•384

Larch, ...

•91 \

Do., .

... • • *

Do., ...

... v

T19 )

Norway Spar,

... ••• v

•211

Oak, English,....

... „

•210

Oak, Canadian, ...

... • • • )J

•310

Oak, Danzig, ...

... v

T49

Oak, Adriatic,

... ••• M

T42

Pitch pine,

... 9J

•177

Red pine, ...

... ••• J>

•272

Teak, ...

. ... j,

•349

Summary of Rules

I. Resistance to Tension or Tenacity.

To find the tenacity of a piece of timber.

1. Rule .—Multiply the number of square inches in its
section by the tabular number corresponding to the kind
of timber (Table I.; or column 4, Table VIII.).

STRENGTH AND STRAIN OF MATERIALS.

131

To find the area of section when the weight is given.

2. Rule. —Divide the given weight by the tabular
number, and multiply the quotient by 4 for the area of
section required for the safe load.

II. Resistance to Compression.

It is not necessary to give rules for the absolute crush¬
ing force of timber. Those that follow are applicable to
the cases of posts whose length exceeds ten times their
diameter, and which yield by bending.

To find the diameter of a post that will sustain a given
weight.

3. Rule. —Multiply the weight in lbs. by 1*7 times the
value of e (Table III.; or column 9, Table VIII.); then
multiply the product by the length in feet, and the fourth
root of the last product is the diameter in inches required.

To find the scantling of a rectangular post to sustain
a given weight.

4. Rule. —Multiply the weight in lbs. by the square of
the length in feet, and the product by the value of e:
divide this product by the breadth in inches, and the
cube root of the quotient will be the depth in inches.

To find the dimensions of a square post that will
sustain a given weight.

5. Rule. —Multiply the weight in lbs. by the square of
the length in feet, and the product by 4 times the value
of e\ and the fourth root of this product will be the
diagonal of the post in inches.

To find the stiffest rectangular post to sustain a given
weight.

6. Rule. —Multiply the weight in lbs. by 06 times the
tabular value of e, and the product by the square of the
length in feet; and the fourth root of this product will be
the least side in inches: divide the least side by 06 to
obtain the greatest side.

III. Resistance to Transverse Strain.

1st. When the beam is fixed at one end and loaded at
the other.

To find the breaking weight, when the length, breadth,
and depth are given.

7. Rule. —Multiply the square of the depth in inches by
the breadth in inches, and the product by the tabular value
of S (Table V.; or column 12, Table VIII.), and divide by
the length in inches: the quotient is the breaking weight.

To find the length, when the breadth, depth, and break¬
ing weight are given.

8. Rule. —Multiply the square of the depth by the
breadth, and by the value of S, and divide by the weight:
the quotient is the length.

To find the breadth, when the depth, length, and break¬
ing weight are given.

9. Rule. —Multiply the weight by the length in inches,
and divide by the square of the depth in inches multi¬
plied by the value of S: the quotient is the breadth.

To find the depth, when the breadth, length, and weight
are given.

10. Rule. —Multiply the length in inches by the weight,
divide the product by the breadth in inches multiplied by
S, and the square root of the quotient is the depth.

To find the side of a square beam, when the length
and weight are given.

11. Rule. —Multiply the length in inches by the weight,
divide the product by S, and the cube root of the quo¬
tient is the side of the square section.

2d. When the beam is supported at one end and loaded
in the middle.

The length, breadth, and depth, all in inches, being
given, to find the weight.

12. Rule. —Multiply the square of the depth by 4 times
the breadth, and by S, and divide the product by the
length for the breaking weight.

The weight, breadth, and depth being given, to find
the length.

13. Rule. — Multiply 4 times the breadth by the
square of the depth, and by S, and the product divided
by the weight is the length.

The weight, length, and depth being given, to find
the breadth.

14. Rule. —Multiply the length by the weight, and
the product divided by 4 times the square of the depth
multiplied by S, is the breadth.

The weight, length, and breadth being given, to find
the depth.

15. Ride. —Multiply the length by the weight, and
divide the product by 4 times the breadth multiplied
by S.

When the section of the beam is square, and the weight
and lefigth are given, to find the side of the square.

16. Rule. —Multiply the length by the weight, and
divide the product by 4 times S: the cube root of the
quotient is the breadth or the depth.

3d. When the beam is fixed at both ends and loaded
in the middle.

The breadth, depth, and length being given, to find
the iveight.

17. Rule. —Multiply 6 times the breadth by the square
of the depth, and by S, and divide the product by the
length for the weight.

o o

It is not necessary to repeat all the transpositions of
the equation.

4th. When the beam is fixed at both ends and loaded
at an intermediate point.

18. Rule. —Multiply 3 times the length by the breadth,
and by the square of the depth, and by S; and divide the
product by twice the rectangle formed by the segments
into which the weight divides the beam.

For example, if the beam is 20 feet long and the weight
is placed at 5 feet from one end, then the segments are
respectively 5 feet and 15 feet, or, in inches, 60 and 180;
and the rectangle is 60 x 180 = 10800; and twice this
amount, or 21600, is the divisor.

Suppose the beam of Riga fir, fixed at both ends, and
its section 8x6 inches, and the weight placed at 5 feet
from one end, required its breaking weight: then, three
times the length = 720, multiplied by the product of
the breadth into the square of the depth, and by the
tabular value of S = 306339840; which divided by 21600,
as above, gives 14,182 lbs. as the breaking weight.

5th. When the beam is supported at both ends, but
not fixed, and when the- load is in the middle.

To find the weight, iwhen the length, breadth, and depth
are given.

19. Rule. — Multiply 4 times the breadth by the
square of the depth and by S, and divide the product by
the length: the product is the breaking weight.

6th. When the weight is uniformly diffused.

20. Rtde. —Multiply twice the breadth by the square

132

PRACTICAL CARPENTRY AND JOINERY.

of the depth and by S, and divide the product b\ r the
length: the quotient is the breaking weight.

Note. —The beam bears twice as much when the load
is uniformly diffused, as when it is applied in the middle
of its length.

7th. When the load is at an intermediate point.

21. Rule. —Multiply the length by the breadth, by the
square of the depth, and by S, and divide the product by
the rectangle of the segment, that is, by the product of
the shorter and longer divisions multiplied together.

IY. Rules for the Dimensions of Beams to resist a
Transverse Strain with a deflection of not more than
- 4 \th of 1 inch per foot.

The following are Mr. Tredgold's formulae:—

8th. When the beam is supported at both ends and
loaded in the middle.

When the weight, and the length and breadth are
given , to find the depth.

22. Rule. —Multiply the square of the length in feet
by the weight to be supported in lbs., and the product by
the tabular value of a (Table VIII., column 10): divide
the product by the breadth in inches, and the cube root of
the quotient is the depth in inches.

When the weight, and the length and depth are given,
to find the breadth.

23. Rale. —Multiply the square of the length in feet
by the weight in lbs., and the product by the tabular
value of a: divide by the cube of the depth in inches,
and the quotient will be the breadth in inches.

When the weight and length are given, and the ratio
of the breadth to the depth is to be as 0-6 to 1.

24. Rule. —Multiply the weight in lbs. by the tabular
number a: divide the product by 0 - 6, and extract the
square root: multiply the root by the length in feet, and
extract the square root of the product, which will be the
depth in inches.

To find the breadth, —multiply the depth by 0 6.

The following are the rules given by Mr. Barlow, for
cases in which the amount of deflection is given.

9th. When the beam is fixed at one end, and loaded at
the other, the weight in lbs., length in feet, and breadth
and deflection in inches, being given, to find the depth.

25. Rule. —Divide the weight in lbs. by the tabular
value of E (Table VII.; and column 13, Table VIII.)
multiplied by the breadth and by the deflection; and the
cube root of the quotient, multiplied by the length, will
be the depth required.

10th. When the load is uniformly distributed.

26. Rule. —Take fths of the actual weight, or, which
is the same, multiply the weight by - 375, and then pro¬
ceed as above.

11th. When the beam is supported at both ends, and
loaded in the middle.

Given the weight in lbs., the length in feet, and the
deflection in inches, to find the other dimensions.

27. Rule. —Multiply the weight by the cube of the
length: divide the product by 16 times E, multiplied by
the deflection, and the quotient is the breadth multiplied
by the cube of the depth.

When the beam is intended to be square, the fourth
root of the above quotient is the depth or breadth.

When it is a cylinder, multiply the quotient by 1*7,
and the fourth root of the product is the diameter.

12th. When the load is uniformly distributed.

29. Rule .—Multiply the weight by ‘625, and by the
cube of the length, and divide the product by 16 times E,
multiplied by the deflection: the quotient is the breadth
multiplied by the cube of the depth.

If the reader has considered attentively the formulae,
he will have been led to the conclusion that in a parallel¬
sided beam exposed to transverse strain, much of the
material does not aid in resisting the force of the weight;
that, in point of fact, there must be some other form than
that of the parallelopipedon, which shall give the greatest
results with the least quantity of timber. This, which is
called the form of equal strength, has been thoroughly
investigated, and we shall here present the results.

In a beam fixed at one end, and loaded at the other,
the form of equal strength is produced when the under

side is made a parabola, and the breadth uniform (Fig.
451).

When the depth is uniform, the figure of the beam is
of a wedge form.

When the breadth and depth both vary, the form is a
cubic parabola.

In a beam fixed at one end, and having its load uni-

fonnly distributed, the form ot equal strength is a triangle
(Fig. 452).

When a beam is supported at both ends, and loaded at

the middle or any intermediate point, and the breadth is
the same throughout, its upper side should be composed of

Yig. 454.

two parabolas whose vertices are at the points of support,
and its lower side should be a straight line (Fig. 453).

STRENGTH AND STRAIN OF MATERIALS.

133

When the depth is constant, the horizontal section or

Fig. 455.

outline of the breadth should be a trapezium (Fig. 454).

When it is loaded uniformly over its length, the upper
side should be elliptical (Fig. 455).

Fig. 456.

When it is uniformly loaded, and the depth constant, the
outline of the breadth should be two parabolas (Fig. 456).

Table VIII. — Table of the Properties of Timber.

Tredgold’s

Formulae.

Barlow's

Formula).

Specific

Gravity,

Water

Weight
of a foot,

Wei glut
of a Bar,

1 foot long,

Absolute
Tenacity of
a sq. inch.

Tenacity of
a sq. inch

Modulus

Crushing
force per

Constants

for

10.

11.

12.

13.

without

of Elasticity,

sq. inch,
in lbs.

being

in lbs.

1 inch sq.,

Average,

injury,

in lbs.

in feet.

value of

Value of

1-0.

in lbs.

Acacia,.

•710

44-37

•30

18,290

1,152,000

373,900

•621

T867

Alder,.

•800

50-

•347

14,186

6,895

• . •

Apple tree,.

(

•793

49-56

•344

19,500

...

•690

43T2

. . .

)

Ash,. s

•845

53-81

17,207

3,540

1,644,800

4,970,000

8,683 >

•00168

•0105

•677

•2036

•244

{

■760

47-5

•33

1,640,000

., .

9,363 )

Bay tree,.

•822

51-37

•35

12,396

...

7,158

...

•690

43-

7,733

...

Beech,... \

to "854

5337

•315

14,720

2,360

1,353,600

4,600,000

9,363

•00195

•0127

•552

T556

T95

Birch,.

•792

49-5

•34

15,000

5,406,000

6,402

...

•0141

•643

T881

•240

„ American,.

•648

40-5

•28

11,663

1,257,600

3,388,000

11,663

. . .

•605

T834

•256

Box,.

•960

60-

•41

19,891

• . .

...

Bullet tree, .'.

1-029

6431

•446

2,601,600

5,878,000

...

. . .

■882

■2646

Cane,.

•400

25-

T74

6,300

. . .

Cedar, new,.

•909

10,293

5,674

.. .

...

„ ,, seasoned,.

•753

47-06

•32

...

4,912

Chestnut,.

"657

41-06

•285

11,900

. . .

...

•0187

Crab tree,.

•765

47-81

■33

( 7,148
( 6,499

...

. ..

Deal, Christiana, .

•698

43-62

•30

12,400

1,672,000

5,378,000

6,586

■0095

•521

•1562

•230-T15

,, Memel, ..

•590

36-87

•25

1,536,200

6,268,000

...

•0089

*577

•1731

TOO

,, Norway spruce, .

•340

2T25

T47

17,600

.. .

...

7,293

•00142

„ English spruce, .

•470

29-37

•20

7,000

...

( 9,973
\ 8,467

...

•0124

Elder, .

■695

4343

•30

10,230

• • .

Elm, . |

•544

34-

•236

3,240

1,340,000

5,680,000

10,331 !

•00184

•017

•372

T115

T01

•588

3675

13,489

699,840

...

Fir, Rica, .

•753

47-06

•32 |

11,549

12,776

...

1,328,800

869,600

4,080,000

5,748
6,819 ]

•00152

•00115

■369

•1108

•167

...

„ Red,.

...

•94

„ Mar,.

•693

43-31

•30

12,000

. ..

2,797,000

•0233

•380

T144

Hawthorn, .

•91

38T2

■26

10,500

. ..

...

Hazel, .

•86

5375

•36

18,000

. . .

...

Holly, .

•76

47*5

•32

16,000

...

Hornbeam, .

•76

47-5

•32

20,240

. . »

7,289

...

Laburnum, .

■92

57'50

•40

10,500

. . .

Lance, .

1-022

63-87

•44

23,400

...

Lai-ch, . j

•522

32-62

...

10,220

10,740,000

4,415,000

5,568 )

•0019

•0128

•284

•853

T20

•560

35-

•243

8,900

2,065

1,052,800

...

... j

Lignum-vitse,.

1-22

76-25

•53

11,800

...

•0152

Lime tree, .

•760

47-50

•32

23,500

...

Mahogany, Spanish,.

■800

50-

•34

16,500

8,198

•00205

•0137

,, Honduras,.

•560

35'

•243

18,950

3,800

1,596,300

6,570,000

...

•00161

•0109

Maple,..

•793

49-56

...

10,584

( 4,684
( 9,509
( 10,058

•0197

...

Oak, English,. j

•830

•934

52'

58-37

■36

•13,316

3,960

1,700,000

1,451,220

4,730,000

■ -0015

•0124

•553

T658

•210

,, Canadian,.

•872

54-50

•378

10,253

2,148,800

5,674,000

4,231
( 9,509

•009

•588

T766

•310

,, Danzic.

•756

47-24

•327

12,780

1,191,200

3,607,000

7,731

•0087

•560

T457

•149

,, Adriatic,.

•993

62-06

•43

974,400

2,257,000

...

•526

•1383

,, African,.

■972

60-75

■42

2,282,300

5,583,000

•0215

Pear tree,.

•661

41-31

•283

9,861

7,518

...

Piue, Pitch,. .' .

'660

41-25

•283

7,818

1,225,600

4,364,000

j 6,790)

( 5,445 j

•0166

•544

T632

T77

,, Red,.

•607

41-06

•26

10,000

1,S40,000

6,423,000

5,375 )

( 7,518 |

...

■0109

•447

T341

•272

,, American yellow,...

•461

28-81

•20

3,900

1,600,000

8,700,000

5,445

•0112

Plane tree, .

•640

40’

•28

11,700

(

10,493

'0128

Plum tree,.

•786

49-06

•338

11,351

... |

9,367
3,657, wet

...

Poplar,.

■383

23-93

T64

6,016

( 3,107 )
\ 5,124 ]

...

■0224

Sycamore, .

•69

43-1

•296

13,000

•0168

■820

•2462

•349

Teak, .

•657

41-06

■282

12,460

2,414,400

7,417,000

12,101

•00118

•0076

Walnut.

■671

41-93

■288

8,465

7,227

•020

Willow,.

•390

24-37

T67

14,000

6,128

'031

Yew, Spanish,.

•807

50-43

•347

8,000

...

134

PRACTICAL CARPENTRY AND JOINERY.

PART FIFTH.

PRACTICAL CARPENTRY.

ROOFS.

Roofs may be variously classed, according to their
forms, and the combinations of their surfaces. The sim¬
plest are those which have either plane surfaces, or cylin-
dric surfaces having their generatrix horizontal.

The slope given to a roof is for the purpose of throwing
off rapidly the water of rain or of snow, in order that
the materials of the roof may be quickly dry. Many
authors have occupied themselves in investigating the
different slopes which should be given to roofs, according
to the climate and the materials used as covering.

The flat roofs or terraces of the East, and the high-
pitched roofs of the countries of the North, the extremes
of the scale, might lead to the supposition that climate
alone had determined the proper slope to be adopted.
Accordingly, M. Quatremere de Quincy proposed to regu¬
late the slopes of roofs rigorously in accordance with the
latitude; thus, commencing at zero at the equator, he
elevates the roof 3° for each geographical climate* when
the covering materials is pan tiles, and adds 3° more
when the covering is of Roman tiles, 6° when it is of
slates, and 8° when formed of plain tiles. This proposi¬
tion of M. de Quincy has been converted into a simple
formula by M. Belmas, thus expressed:—Make the slope
of the roof equal to the excess of the latitude of the place
where it is constructed over that of the tropics. The
latitude of the tropics being 23° 28', the rule would give,
for a roof in latitude 25°, a slope of only 1° 32'. But on
so small an inclination as this, the necessary overlap of the
tiles or slates would cause them to slope the reverse way,
and the water would consequently penetrate under them.

But climate does not appear in practice to be the regu¬
lator of the slopes of roofs; for in the same place are found
roofs of various slopes, and neither the original proposi¬
tion of M. de Quincy, nor the form of it proposed by
M. Belmas, are verified by experience. Indeed, the rule
would seem to be based on a too limited series of observa¬
tion, and gives slopes too low for moderate climates, and
too high for those in warm regions where terraces are
invariably used.

The following table shows the slopes actually in use in
certain places, and the slopes accox-ding to M. de Quincy’s
rule:—

* The space comprised between the equator and each polar circle
is divided into 24 zones or climates, the limits of which are deter¬
mined by a difference of half an hour in the length of the day in the
summer solstice. Thus, leaving the equator where the latitude is zero,
and the length of the longest day 12 hours, the circles of separation
are fixed as in the following table, where the Roman numerals are
the climates, and the opposite corresponding numbers are the lati¬
tudes at which the climates finish, up to the 24th, which terminates at
the polar circle, where the length of the longest day is 24 hours:—

II.

III.

IV.

VI.

8 °

25'

VII.

45°

29'

XIII.

59°

58'

XIX.

65°

24'

VIII.

XIV.

XX.

IX.

XV.

XXI.

XVT.

XXII.

XI.

XVII.

XXIII.

XII.

XVIII.

XXIV.

Places.

Climates.

Slopes
according to
M. de Qniney’s
Rule.

Covering

used.

Actual

Slopes.

St. Petersburg,...

14°

40“

24'

Iron.

18° to 20“

Copenhagen,.

Slates.

45 to 60

Hamburg.

Plain tiles.

45 to 60

Brussels.

60°

( 32

45 to 60

Paris,.

{ 30

Slates.

33 to 45

( 24

Pan tiles.

18 to 25

Colmar,.

Plain tiles.

The empiric rule, then, giving results so widely diffe¬
rent from what experience has taught, is not to be relied
on, and some other data on which to base our practice
must be found. M. Rondelet, indeed, regards the slope
to be given to roofs as altogether arbitraiy, and depen¬
dent on taste alone, with such restrictions only as the
more or less perfect nature of the materials impose.

It is, indeed, extremely probable that the slopes of
roofs wei’e regulated originally according to the materials
used as a covering. The inclination is generally uniform
in all places where the same kind of materials is used.
A thatch of leaves, bark, straw, or reeds, probably the
fii'st kind of covering employed, inquired a very steep
slope that the water might be speedily thrown off. And
when in coui’se of time the more perfect covering of tiles
and slates came to be applied, the habit of imitation would
for a while prevent any change in the accustomed slope.
However this may be, it is evident that the variety of
slopes in the same localities shows that no precise rule can
now be drawn from existing examples. In roofs covered
with slates, the height, or pitch, of the roof is made from
one-fourth of the width of the span to the whole width of
the span, that is, the slope varies from an angle of 26° 30'
with the horizon to 60°; and writers assuming 26° 30'
as the smallest angle for common slates, have given the
following rates of inclination for other materials:—

Kind of Covering.

Inclination
to the
Horizon.

Height of Roof
iu parts of the
Span.

Weight on
a Square of
Roofing.

Copper,.

( 2° fi(Y

( 100

Lead, .•..

\ 700

Large slates,.

22 0

1120

Common slates,...

26 30

500 to 900

Stone slates,.

29 41

2380

Plain tiles,.

29 41

1780

Pan tiles,.

24 0

650

Thatch,.

45 0

Colonel Emy says, that the inclination of roofs covered
with plain tiles varies in France within the limits of
40° and 60°. As the tiles are not nailed like slates, they
are made to resist the wind by the pi’essure of their
weight. The angle of 45°, he observes, is the best for
roofs covered with slates or plain tiles, a slope that
permits the use of the interior of the roof as garrets.
When the slope is moi'e gentle, the scantling of the roof
timbers require to be inci'eased; and when more steep,
the increase of roof surface and augmentation of the

EXAMPLES OF THE CONSTRUCTION OF ROOFS.

135

length of the timbers increases the cost, without a cor¬
responding benefit, as the height gained cannot be use¬
fully occupied internally, unless by making two stories
of apartments in the roof, a practice which, in the pre¬
sent day, is very properly abandoned. The result of an
extended consideration of the subject is given by Colonel
Emy as follows:—

In roofs covered with tiles hung on laths, the slope
should not be greater than that at which the materials
would slide naturally. It should, therefore, not exceed
an angle of 27° with the horizon. Its lowest limit
should be such that the tiles should never have so small
a slope by their overlap that the water would stagnate.

In roofs with metallic coverings, the slope requires to
be only sufficient to cause the flow of the water; and,
therefore, need not exceed ^th of the span.

The following table is extracted from his work:—

Kinds of Roofs and of
Coverings.

Proportion of
the Span.

Inclination to the
Horizon.

Antique temples,.

ib and J
| i and I

{ s »

{ J

9° 28' to 14° 2'

18 26 to 26 33

33° 46'

36 52

45 0

60 0

Hollow tiles, Roman tiles,
and metal,.

Slates, lowest inclination,..

Thatch, common slates,
plain tiles, &e.,.

On the subject of the pitch of roofs, Professor Robison
remarks as follows:—“ A high-pitched roof will undoubt¬
edly shoot off the rains and snows better than one of a
lower pitch. The wind will not so easily blow the drop¬
ping rain in between the slates, nor will it have so much
power to strip them off. A high-pitched roof will exert
a smaller thrust on the walls, both because its strain is
less horizontal, and because it will admit of higher cover¬
ing. But it is more expensive, because there is more of
it. It requires a greater size of timbers to make it equally
strong, and it exposes a greater surface to the wind.
There have been great changes in the pitch of roofs: our
forefathers made them very high, and we make them
very low. It does not, however, appear that this change
has been altogether the effect of principle. In the simple,
unadorned habitations of private persons, everything
comes to be adjusted by our experiences, which have re¬
sulted from too low-pitched roofs; and their pitch will
always be such as suits the climate and covering. Our
architects, however, go to work on different principles.
Their professed aim is to make a beautiful object. The
sources of the pleasure arising from what we call taste
are so various, so complicated, and even so whimsical,
that it is almost in vain to look for principle in the rules
adopted by our professed architects.’' — “The Greeks,
after making a roof a chief feature of a house, went
no further, and contented themselves with giving it a
slope suited to their climate. This we have followed,
because in the milder parts of Europe we have no cogent
reasons for deviating from it. And if any architect should
deviate greatly in a building where the outline is exhi¬
bited as beautiful, we should be disgusted; but the dis¬
gust, though felt by almost every spectator, has its
origin in nothing but habit. In the professed architect
or man of education, the disgust arises from pedantry;
for there is not such a close connection between the form
and uses of a roof as shall give precise determinations; and

the mere form is a matter of indifference. We should
not, therefore, reprobate the high-pitched roofs of our
ancestors, particularly on the Continent. It is there where
we see them in all the extremity of the fashion; and the
taste is by no means exploded as it is with us.”

1 he conclusion to be arrived at is then, as expressed by
Professor Robison, “ that there is not such a close con¬
nection between the form and uses of a roof as shall give
precise determinations, and the mere form is a matter of
indifference.”

EXAMPLES OF THE CONSTRUCTION OF

ROOFS.

Roofs of two slopes in narrow buildings are composed
of rafters alone, with a cross piece, forming each pair of
opposite rafter sin to what is termed a couple. The rafters
without the cross piece, or tie-beam , would tend to thrust
out the walls on which they rest; and this cross piece
is intended therefore to act as a tie to counteract this
thrust. Its position is consequently of importance; and
from a false economy, or from ignorance of its function,
it is generally, in buildings of an inferior class, placed so
high as to be of little use in counteracting the thrust.

This kind of roof, the couple-roof, is only practicable in
buildings of very moderate width. In wide buildings, the
rafters would bend by their own weight, unless made of a
preposterous size or supported in some manner. When
the width of the building, therefore, exceeds these moder¬
ate limits, the rafters are kept from bending by a piece of
timber parallel to the tie-beam, and called a collar-beam..
But it will be obvious that couple-roofs so formed, inde¬
pendently of consuming a great quantity of timber, can
only, after all, be used for small spans; and hence it is
necessary to have recourse to the framed roof. In framed
roofs, the rafters are sustained by pieces of timber, which
lie under them horizontally, and divide their length into
spaces within the limit of their flexure under the weight
of the covering. These horizontal pieces are called pur¬
lins, and are sustained by trussed frames of carpentry,
distributed transversely at equal distances in the length
of the building, the distances being calculated with rela¬
tion to the strength of the purlins.

Fig. 457 illustrates this kind of roofs, in which A A, B C
is the trussed frame of carpentry, called a principal, d d

Fig. 457.

are the purlins, and e e the rafters. It will be useful here
to consider the principles of trussing.

13G

PRACTICAL CARPENTRY AND JOINERY.

Let A B, c B (Fig. *458) be two rafters, placed on walls
at A and c, and meeting in a ridge B. Even by their own
weight, and much more when loaded, these rafters would
have a tendency to spread outwards at A and c, and to

ing is the same. The rafters are compressed, the strain¬
ing beam is compressed, and the tie-beam and posts, the
latter now called queen-posts, are in a state of tension.

In some roofs, for the sake of effect, the tie-beam does
not stretch across between the feet of the principals, but
is interrupted. In point of fact, although occupying the

Fig

Fig. 159.

sink at B. If this tendency be restrained by a tie estab¬
lished betwixt A and C, and if A B, B c be perfectly rigid,
and the tie A c incapable of extension, B will become a
fixed point. This, then, is the ordinary couple-roof, in
which the tie A c is a third piece of timber; and which
may be used for spans of limited extent; but when the
span is so great that the tie A c tends to bend down¬
wards or sag, by reason of its length, then the condi¬
tions of stability obviously become impaired. Now, if
from the point B a string or tie be let down and attached
to the middle D, of A c, it will evidently be impossible
for A c to bend downwards so long as A B, B c remain of
the same length: D, therefore, like B, will become a fixed
point, if the tie BD be incapable of extension. But the
span may be increased, or the size of the rafters A B, c B
be diminished, until the latter also have a tendency to
sag; and to prevent this, pieces D E, D F are introduced,
extending from the fixed point D to the middle of each
rafter, and establishing F and E as fixed points also, so
long as D E, D F remain unaltered in length. Adopting
the ordinary meaning of the verb “to truss,” as expressing
to tie up (and there seems to be no reason why we should
seek further for the etymology), we truss or tie up the
point D, and the frame A B c is a trussed frame. In like
manner, F being established as a fixed point, G is trussed
to it. In every trussed frame there must obviously be one
series of the component parts in a state of compression,
and the other in a state of extension. The functions of
the former can only be filled by pieces which are rigid,
while the place of the latter may be supplied by strings.
In the diagram, the pieces A B, c B are compressed, and
A c, D B are extended; yet in general the tie D B is called
a Icing-post, a term which conveys an altogether errone¬
ous idea of its duties. Thus we see how the two princi¬
pal rafters, by their being incapable of compression, and
the tie-beam by its being incapable of extension, serve,
through the means of the king-post, to establish a fixed
point in the centre of the void spanned by the roof, which
again becomes the point cl’appui of the struts, which at
the same time prevent the rafters from bending, and serve
in the establishing of other fixed points; and the combina¬
tion of these pieces is called a king-post roof.

It is sometimes, however, inconvenient to have the
centre of the space occupied by the king-post, especially
where it is necessary to have apartments in the roof. In
such a case recourse is had to a different manner of truss¬
ing. Two suspending posts are used, and a fourth ele¬
ment is introduced, namely, the straining beam a b (Fig.
459), extending between the posts. The principle of truss-

place of, it does not fill the pffice of a tie-beam, but acts
merely as a bracket attached to the wall (Fig. 460). It is
then called a hammer-beam.

It is a general rule that wood should be used as struts
and iron as ties; and in many modern trusses this rule
has been admirably exemplified by the combination of
both materials in the frames.

There is another class of principals in which tie-beams
are not used. Such are the curved principals of De Lorme
and Emy. In the system of Philibert de Lorme, arcs
formed of small scantlings of timber are substituted for
the framed principals; and in that of Colonel Emy, lami-
.nated arcs are used.

The principals of roofs may therefore, in respect of
their construction, be divided broadly into two classes—
First, Those with tie-beams; and, Second, Those wdthout
tie-beams.

The first class, those with tie-beams, may be further
classified as king-post roofs and queen-post roofs.

The second class may be arranged as follows:—

1st. Hammer-beam roofs.

2d. Curved principal roofs.

And sometimes the classes are combined.

Examples of the varieties of all these will be found in
the plates; and we shall now proceed to describe these
examples. Our explanations shall, however, be limited
to such parts of the construction for which an explana¬
tion is indispensable, and which cannot be readily under¬
stood by an inspection of the engravings.

As preliminary to the explanation of the examples, it
may however be well here to give Mr. Tredgold’s rules
for proportioning the strength of the various pieces com¬
posing the roof; but while we do so, it is necessary to
caution the student that these rules are empirical and too
general to be relied on, except in simple cases. It is far
better, however, although it is commonly attended with
more labour, to trust to the formula? given in the article
on the strength of timber, applying the rules specially to
each case.

In estimating the pressure on a roof, for the purpose
of apportioning the proper scantlings of timber to be
used, not onl} r the weight of the timber and the slates,
or other covering, must be taken, but also the weight
of snow which in severe climates may be on its surface,
and also the force of the wind, which we may calculate
at 40 lbs. per superficial foot.

The weight of the covering materials, and the slope ol
roof, which is usually given, are contained in the following
table:—

EXAMPLES OF THE CONSTRUCTION OF ROOFS.

137

Material.

Inclination.

"Weight on
a Square Foot.

Tiu.

Copper.

Lead.

Zinc.

Short pine shingles....
Long cypress shingles
Slate.

Rise 1 inch to a foot.

>' t „

» 2 „ „

)! 3 „ ,,

» 5

» t> ,, ,,

»> ^ „ „

5 to lj lbs.

1 „ n „

4 )> ! . »

U „ 2 „

i* H ,

4 „ 5 „

5 „ 9 „

With the aid of this table, and taking into account
the pressure of the wind and the weight of snow, the
strength of the different parts may be calculated, as we
have said, by the rules given under the head—“ Strength
of Materials; ” but the following empirical rules, deduced
by Mr. Tredgold from these, and from experience, will
be found of easy application, and useful for simple cases.
Mr. Tredgold assumes 66 ^ lbs. as the weight on each
square foot.

It is customary to make the rafters, tie-beams, posts,
and struts all of the same thickness.

Mr. Tredgold’s Rules.

IN A KING POST ROOF OF PINE TIMBER.

To find the dimensions of the principal rafters.

Rule. —Multiply the square of the length in feet by
the span in feet, and divide the product by the cube of
the thickness in inches; then multiply the quotient by
0 96 to obtain the depth in inches.

Mr. Tredgold gives also the following rule for the
rafters, as more general and reliable:—

Multiply the square of the span in feet by the distance
between the principals in feet, and divide the product by
60 times the rise in feet: the quotient will be the area of
the section of the rafter in inches.

If the rise is one-fourth of the span, multiply the span
by the distance between the principals, and divide by
15 for the area of section.

When the distance between the principals is 10 feet,
the area of section is two-thirds of the span.

To find the dimensions of the tie-beam, when it has to
support a ceiling only.

Rule. —Divide the length of the longest unsupported
part by the cube root of the breadth, and the quotient
multiplied by P47 will give the depth in inches.

To find the dimensions of the king-post.

Rule. —Multiply the length of the post in feet by the
span in feet: multiply the product by 0 - 12, which will
give the area of the section of the post in inches. Divide
this by the breadth for the thickness, or by the thick¬
ness for the breadth.

To find the dimensions of struts.

Ride. —Multiply the square root of the length sup¬
ported in feet by the length of the strut in feet, and
the square root of the product multiplied by 0 - 8 will
give the depth, which multiplied by 0‘6 will give the
thickness.

IN A QUEEN-POST ROOF.

To find the dimensions of the principal rafters.

Rule. —Multiply the square of the length in feet by
the span in feet, and divide the product by the cube of
the thickness in inches: the quotient multiplied by 0'155
will give the depth.

To find the dimensions of the tie-beam.

Rule .—Divide the length of the longest unsupported

part by the cube root of the breadth, and the quotient
multiplied by 1 -47 will give the depth.

To find the dimensio ns of the queen-posts.

Rule. —Multiply the length in feet of the post by the
length in feet of that part of the tie-beam it supports:
the product multiplied by 0'27 will give the area of the
post in inches; and the breadth and thickness can be
found as in the king-post.

The dimensions of the struts are found as before.

To find the dimensions of a straining-beam.

Rule. —Multiply the square root of the span in feet
by the length of the straining-beam in feet, and extract
the square root of the product: multiply the result by
0'9, which will give the depth in inches. The beam, to
have the greatest strength, should have its depth to its
breadth in the ratio of 10 to 7; therefore, to find the
breadth, multiply the depth by 0 7.

To find the dimensions of purlins.

Rule. —Multiply the cube of the length of the purlin
in feet by the distance the purlins are apart in feet, and
the fourth root of the product will give the depth in
inches, and the depth multiplied by 0'6 will give the
thickness.

To find the dimensions of the common rafters, when
, they are placed 12 inches apart.

Rule. —Divide the length of bearing in feet by the
cube root of the breadth in inches, and the quotient mul¬
tiplied by 072 will give the depth in inches.

We shall, by way of practice, test the scantlings of
some of the examples of executed roofs by these rules,
which is preferable to working out supposititious examples
in this place.

It may be well here, also, before describing the exam¬
ples, to note some practical memoranda of construction
which cannot be too closely kept in mind in designing
roofs.

Beams acting as struts should not be cut into or
mortised on one side, so as to cause lateral yielding.

Purlins should never be framed into the principal
rafters, but should be notched. When notched, they
will carry nearly twice as much as when framed.

Purlins should be in as long pieces as possible.

Rafters laid horizontally are very good in construction,
and cost less than purlins and common rafters.

The ends of tie-beams should be kept with a free space
round them, to prevent decay. It is said that girders of
oak in the Chateau Roque d’Ondres, and girders of fir in
the ancient Benedictine monastery at Bayonne, which had
their ends in the wall wrapped round with plates of cork,
were found sound, while those not so protected were
rotten and worm-eaten.

It is an injudicious practice to give an excessive cam¬
ber to the tie-beam: it should only be drawn up when
deflected, as the parts come to their bearings.

The struts should always be immediately underneath
that part of the rafter whereon the purlin lies.

The diagonal joints of struts should be left a little open
at the inner part, to allow for the shrinkage of the heads
and feet of the king and queen posts.

It should be specially observed that all cranks or bends
in iron ties are avoided.

And, as an important final maxim— Every construction
should be a little stronger than strong enough.

138

PRACTICAL CARPENTRY AND JOINERY.

Description of the Plates.

Plate XXII.-— Fig. 1 is the elevation of a king-post
roof, designed by Mr. White, for a span of 30 feet.

By the rules given for calculating the scantling, it will
be found to be as follows:—

a, Tie-beam, ...

b, Principal rafters, ...

c, Struts,

D, King-post, ...

5 inches.

8£ X 5

. 4 X „

. 7| X 5 ,,

Fig. 2 is the design for a king-post roof, for a span of
33 feet 6 inches.

The purlins here are shown framed into the principals,
a mode of construction to be avoided, unless rendered
absolutely necessary by particular circumstances.

The scantling, as determined by the rules, is as follows:—
Principal rafters, . 10 X 5 inches.

Tie-beam,

King-post,

Struts,

Purlins,

111 X 6
7| X 6
4 X21
10 X 6

The principals being 10 feet apart.

Fig. 3.—A compound roof for a span of 30 feet. It is
composed of a curved rib C C, formed of two thicknesses of
2-inch plank bolted together. Its ends are let into the
tie-beam; and it is also firmly braced to the tie-beam by
the king-post and suspending pieces B B, which are each
in two thicknesses, one on each side of the rib and tie-
beam, and by the straps a a. A is the rafter; d, the
gutter-bearer; c and b, the straps of the king-post. The
second purlins, it will be observed, are carried by the
upper end of the suspending pieces B B.

Full details of the straps and bolts of this and the
succeeding examples will be found in Plates XXXVIII.
and XXXIX., “Joints and Straps."

Fig. 4.—A queen-post roof, with an iron king-bolt,
intended for a span of 32 feet.
a, Principal rafter, ...

b, Straining-piece,

c, Queen-post,
Struts,

11 X 5 inches.
11 X 5 „

9X5 „

5X4 „

c, King-bolt.

The common rafters are 8x3 inches, and project over
the walls to form a projecting cornice: a is the short
ceiling-joist of the cornice; b, an ornamental bracket.

Fig. 5 .—A queen-post roof for a span of 60 feet. The
scantlings are as follows:

Principal rafters,

Tie-beam,

Queen-post b,

Suspending post a,
Struts (large), ...
„ (small), ...

11 X 6 inches.
12£ X 6
8X6
3* X 3 „

4i X 31 „

31 X 21 „

Fig. G.—Nos. 1, 2, 3, and 4 are the elevation and details
of the queen-post roof of the railway workshops at Wor¬
cester. The principals are placed 15 feet apart, and the
purlins are trussed. The details are as follows:—

Principal rafters,

Tie-beam,

Queen-post,

Struts, ...

Straining-beam,

Common rafters,

Purlins, in two flitches each (trussed with |
stirrup pieces and iron ties),

The tie-beams are carried on iron shoes.

No. 1 is the elevation of the roof. No. 2 is a section of

inches.

5 ’

?•

one bay of the roof. No. 3 shows the under side, and.
No. 4 the side of a purlin drawn to a larger scale.

Fig. 7.—Elevation of the principal of a platform roof
for a span of 70 feet. The tie-beam in this example is
scarfed • at a and b, and the centre part of the roof has
counter-braces c c. The longitudinal pieces e e, secured
to the heads of the queen-posts, and the piece d, carry
the platform joists A. The details of the scarfing and
strengthening the tie-beam will be found described in
the section on “ Scarfing and Lengthening Beams," and
illustrated in Plate XXXIX.

Plate XXIII.— Fig. 1 is a queen-post M-roof, for a
span of 47 feet; or rather, having a king-bolt in the

centre, it is a compound roof

—

a, Tie-beam,

13 X 6 inches.

b, Principal rafter,

. 11 X 6 „

c, Straining-beam,

. 11 X 6

d, Queen-post, ...

. 7X6

e, Strut,

. 7X6 „

f, Counter-brace,

. 6X6

o, Common rafter,

. 6X 21 „

a, Wall-plate for common rafters, ... 7X9 ,,

b b, Purlins,

. 11 X 6

e g, King-bolt,

.. ... 2 inches diameter.

d, Ridge-rafter,

12 X 21 inches.

A, Gutter-bearer,

. 3 X 21 „

In this roof, the purlins

are shown framed into the

principals, a practice which has already been censured.

Fig. 2.—A simple queen-post roof for a span of 40 feet:—

a, Tie-beam, .

... ... 12 X 6 inches.

b, Principal rafter, ...

. 10 X 6 „

c, Straining beam, ...

. 9X6 „

d, Queen-post,

. 8X6

e, Strut, ... .

6X6 „

f, Common rafter, ...

. 6 X 21 „

a, Wall-plate,

. 9X6

b, Purlin,

. 12 X 9 „

c, Ridge-rafter; d, strap at foot of

common rafter; e, ditto at foot of

queen-post; /, ditto at head of ditto; Jc, straining-cill.

Fig. 3.—King-post roof for

a span of 38 feet 9 inches : —

As Executed.

Tie-beam,

11X9 ins. Ill X 6 ins.

King-post,

10 X 8 „ 8 X 6 „

Suspending posts or queen-posts, 10 X 7 „ 5 X 3 „

Principal rafters,

10 X 7 „ 8 X 6 „

Principal struts,

6X6 „ 6 X 3 „

Secondary struts, .

5X5 „ 3 X 2 „

Purlins,

7X9,,

Cleets at back of purlins,

8X6 „

Ridge piece, ...

8 X 11 „

On comparing the scantlings of this roof as executed,
with those derived from the application of Mr. Tredgold’s
formuke, there will be found an excess of strength. The
scantlings, in point of fact, are nearly as large as those of
other examples, of much greater span, which we have
given; and this roof, therefore, sutlers much in com¬
parison with the next example, where the scantlings, as
executed, are, generally speaking, of smaller dimensions
than those resulting from the application of the formula).

The tie-beam is strapped to the king and queen posts,
and the principal rafters are secured by screwed bolts and
nuts.

Fig. 4.—No. 1 is the elevation of one of the trusses of
George Heriot’s Schools, Edinburgh, designed by Alex¬
ander Black, Esq., architect, and executed under his
superintendence.

The dimensions of the scantlings by the rules are here

PLATE Xffi-

Ji O D IF 3

'•

Si 0 0 ff< ,5 ,

‘‘‘- ITE xr/i/.

J. I'lTutr ,/, /

1 1^4— - i-

•j* •><>*/<: y?»'3 Details ^ ^

li / • ^ ?-■?-! ?

=S=4|

feet .

Scale ror Elcvati/ms

4 ®.

jjo Feet

BLACK IB & S0Jr ' OLASOO-VV. EDINBUROfl. A rminnw

.* * , '

;•

•** ’

71 © © If ^ .>

Fig. 2.

plate ten

Fig.4.

Fioof oi ttu j Parish (’/lurch Elgin.

Fig. .3 .

BJ.AOKIE «.• SON . GLASGOW,EDINBURGH fie LONDON.

34 feet

40 feet

60 feet/

( Figs . 5 to 10.)

S'h&d at Salthouse Dock;.Liverpool

with details.

W . C.Joass Bell

J.If. lorirr.Jc- .

■

16 -9

' %

V - ■

r y

—■*——. x|

V '

, s

^TE XIV

EXAMPLES OF THE CONSTRUCTION OF ROOFS.

139

placed in juxtaposition with the dimensions of the scant¬

lings as executed, as follows

a, Tie-beam,

b, Principal rafters,

c, Common rafters,

D, Purlins,
e, King-post (oak),

F, Queen-posts (oak),

G, h, Inner struts, ...
i, Outer struts, ...
k, Cleets to do., ...

By the Rule. As Executed.

11| X 4 inches. 12x4 inches.

8 X 4 „ 8X4 „

... 5 X „

9 X5| inches. 9x6 „

8x4 ,, 5X4 ,,

5X5 ,, 4x4 „

4f X 3£ „ 4X4 „

3 X2J „ 4X3£ .,

6X4 „

No. 2 shows the details of the king-post to a larger
scale. The heads of the rafters and the feet of the struts
are received by cast-iron sockets bolted to the king-post.
The tie-beam is suspended to the post by an iron strap
with wedges. A section through the tie-beam, king-post,
and strap, is given at No. 3.

Nos. 4 and 5 show the scarfing of the purlins; and Nos.

6 and 7 the end of the tie-beam, with the iron shoe which
receives the foot of the rafter, and the strap which secures it.

Plate XXIV. Fig. 1. — No. 1, elevation of one of the
principals of the roof of Wellington Street Church, Glas¬
gow, designed by John Baird, Esq., architect, and erected
in 1823. No. 2, part of the upper side of the tie-beam:—

The tie-beams have cast-iron shoes, H, at each end,
with abutments formed for the rafters, and secured with
-J-inch diameter bolts, with nuts and washers.

The suspending rods are 1 inch square, and have abut¬
ment pieces for the rafters and struts.

Fig. 3.— One of the roof-principals of the City Hall,
Glasgow. The following are the dimensions of its
timbers:—

a, Tie-beam, 14 X 12 inches.

b, Cill piece, 12 X 12 inches.

c, Principal rafter, at the end, 9X7 inches, and at s, 11 inches

deep.

d, Ditto, where doubled at lower end, 8X7 inches.

e, King-post, in two thicknesses, each 10 X 6 inches.

f, Queen-posts, at top and bottom, 13X7 inches, and in middle,

10 X 7 inches.

g, Straining-beam, 10 X 7 inches.

h, Struts, 6X6 inches.

k, Common rafters, 6 X 21- inches.

m, Ridge board, 10 X 2 inches; batten over it, rounded for lead,

3| X 3 inches.

n, Wall-plates, under common rafters, 12 X 11 inches, with pole-

plate, 2X2 inches.
o o, Purlins, 8X5 inches.
p, Outer wall-plates, 14 X 3 inches.
r, Inner wall-plates, resting on corbels, 11X5 inches.

a, Tie-beam, 12X9 inches.

b, Principal rafter, 13 ins. at bottom, 11 at top, and 9 inches

thick.

c, Straining-beam, forming support of platform, and cambered,

13 ins. deep at centre, 11 at ends, and 9 inches thick.

D, Principal queen-posts, 13X9 ins. at top and bottom, and 9X9

in smallest part.

E, Second queen-posts, 10 X 9 ins. at top and bottom, and 7 by 9

in smallest part.

F, Principal strut, 9X9 inches.

G G, Secondary struts, 7X9 inches.

h, Straining piece between principal struts, 6X9 inches.
m m, Platform joists, 10 X 21 inches, and 15 ins. apart from centre
to centre, covered with boarding If inch thick for lead,
ti n, Common rafters, laid horizontally, 6 X 24 inches, covered with
slate-boarding \ inch thick.

The principals are placed 9 feet 4 inches apart. All
the timbers are joined by mortise-and-tenon joints. The
platform joists and horizontal rafters are notched on the
straining- beams and principals. The tie-beams are in
two lengths of timber, scarfed, as shown in No. 2. The
scarf is secured by iron straps, each 3 inches wide and
§ inch thick, and bolted. The iron work is of the follow¬
ing dimensions:—

Straps at feet of principal rafters, 2f X § inches.

Three-tailed straps connecting principal rafters, queen-posts, and
straining-beam, 2j X § inches; and each tail 2 feet 6 inches long.

Straps at feet of queen-posts, 2.V X -} inch, bolted and keyed.

King-bolt If inch diameter, screwed up hard,

Fig. 2. — Elevation of a roof-principal of the parish
church, Elgin, by Simpson of Aberdeen.

There are twelve principals similar to the elevation in
Fig. 2. They are placed 6 feet 6 inches apart between cen¬
tres; and the scantlings are as follows: —

a, Tie-beam, iu two flitches, each 13 X 5| inches.

b c, Principal rafters, 11 inches deep at lower end, 8 inches at top,
and 6 inches thick.

d, Collar-beam, 7 X 51 inches.

E, Struts, 5X5| inches.

F, Struts, 5 X 4f inches.

m m, Horizontal rafters, 41 X 2.V inches, 13 inches apart, and covered
with groove-and-tongued deal 1 inch thick, and lead weigh¬
ing 7 lbs. to the superficial foot.

The iron straps are 4 inches broad by f inch thick.
Their bolts are f- inch square. The bolts securing the
ends of the rafters, and the beams, are 1 inch square; and
their washers are the full breadth of the beams.

The principals are placed 12 feet apart from centre to
centre.

Fig. 4.—One of the principals of the roof of the East
parish church, Aberdeen. The following are the dimen¬
sions of the timbers:—

There are five principal trusses, placed 14 feet apart.

a, Tie-beam, in two thicknesses, 14 X 10 inches.

Principal rafters, 13 inches deep at bottom, 111 inches at top,
and 101 inches thick. The rafters bear on oak abutment pieces
11 X 71 inches, bolted between the ties and to each other.

D, Collar-beam, in two thicknesses, one on each side of the rafter,
and notched and bolted, 12 X 5J inches each.

e, Purlins. The two lower, 13 X 61 inches; the upper, 114 X 84
inches ; notched on the rafters and bolted.

F, Common rafters, 51 X 21 inches, and 13 inches apart.

The discharging posts between the bracket pieces and
the stone corbel are of oak, 6 inches square.

Binding pieces, 94 X 31 inches, extend between the tie-
beams, and are mortised into them; and into these binding
pieces the ceiling joists, which are 13 inches apart, and
G X 1 § inches, are mortised.

The dimensions of the iron work are as follows: —

King-rod, If in. square, with a cast-iron key piece at top.

Queen-rods, 11 in. square, having solid heads at rafters, and secured
at foot by being passed through solid oak pieces k, placed between
flitches of tie-beams, and securely bolted, and there fastened with
cast-iron washers and nuts.

Four bolts at abutment end of ties, ... ... ^ inch square.

Two do. at each oak piece, for suspending rods, § „ .,

Two do. at each end of collar-beam, ... ... £ „ „

Purlin bolts,.f „ „

The abutments of the rafters at both ends, and the
bearings of the bolts, have pieces of milled lead interposed;
and all the joints of the framing were coated with white
lead and oil before being put together.

Plate XX V. — Figs. 1 and 2 show a wider use of iron
in the parts of the framing acting as ties. They are the

140

PRACTICAL CARPENTRY AND JOINERY.

roofs of sheds at the Liverpool Docks. The scantlings are
as follows: —

Fig. 1. Principal rafters, ... 12 X 8 inches.

Struts, . 8X8 „

Purlins, ... ... 10 X 4 „

Common rafters, ... 4| X 2 „

Tie-rod and suspending-rod, 1| inch diameter.

Fig. 2. Principals,. 14 X 8 inches.

Collar-pieces. ... 11 X 3, one on each side of rafter.

Purlins, ... ... 16 X 4 inches.

Tie-rods and suspending-rod, If inch diameter. .

The details are similar to those of the roof shown in
Figs. 5. 6, 7. 8, 9, and 10 of the same plate.

Fig. 3.—A roof adapted to a hall or church with nave
and aisles. The framing is simple and good:—

A, Principal tie. b, Tie of aisle roof,
c, Girder supported by the iron column e.
e, Story-post.

Fig. 4 is a queen-post roof, adapted to. the same use as
the last.

Fig. 5 .—Roof of the East Quay shed of the Salthouse
Dock, Liverpool. Jesse Hartley, Esq., engineer.

The dimensions are all marked on the detailed draw¬
ings, which are made to a larger scale, and are contained
in Figs. 6 to 10. The scantlings are as follows:—

Principal rafters, ... ... ... 16 X 9 inches.

Common rafters, ... ... ... 41X 2 „

Purlins, ... ... ... ... 15 X 5 „

Collar-beam, ... ... ... ... 15 X 9 „

Tie and suspending rods, 2 inches diameter.

Plate NXVI.— Fig. 1 shows the principal of a roof of
44 feet 8 inches span. In this, wrought-iron is used for
the suspension rods, and cast-iron shoes as abutments for
the timbers acting as struts.

At c, on the wall-head, is a cast-iron shoe, to receive
the tie-beam and the foot of the principal rafter. The
sole-plate of the shoe is prolonged, to admit of its being
secured by bolts to the tie-beam.

The head of the principal rafter, and the end of the
straining beam, are inserted into a cast-iron socket, an
elevation of which is seen, enlarged, at No. 1. The sus¬
pension rod A D, it wull be seen, passes through the solid
part of the socket. It has a head at its upper end, and at
its lower end it is screwed, and secured by a nut. On the
side of the socket is cast a rest for the end of the purlin
a b. To avoid cutting the principal rafters, the other
purlin at B is also carried in a cast-iron rest bolted to the
rafter. The centre suspending rod at E passes through
a cast-iron socket, which serves as an abutment to the
two main struts. Similar abutments are provided for the
lower end of the struts.

Fig. 2.—This principal, for a roof of 45 feet span, has
details of the same kind as those described above. The
detail No. 2 is a section of the shoe at head of king-bolt,
into which upper ends of principals are inserted.

Fig. 3.—This is a principal also with wrought-iron
suspension rods. The tie - beams, principals, and struts
are first framed together; the suspending rods are then
introduced, and screwed up by the nuts at their lower
end until the framing is firmly united. A roof of this
construction, 54 feet span and 212 feet long, is erected at
the passengers’ shed of the Croydon railway station.

Fig. 4 shows a roof, the principal rafters of which are
constructed of timber and iron. They are in three thick¬

nesses, the centre flitch being timber, and the side plates
wrought-iron, bolted together through the timber, as
shown more at large in the section No. 7. No. 3 shows
the foot of one of the rafters, with the iron girder on
which it is supported; the mode of attaching the tension-
rod, and the manner of constructing the gutter. No. 4
shows the cast-iron strut at B. No. 8 is a section of the
rib of the strut on the line A. Nos. 5 and 6 show, in plan
and elevation, the manner of connecting the tension-rods
at the apex; the letters refer to the same parts in both.

Fig. 5 is a roof-principal, formed with iron rafters,
struts, straining-beam, queen-posts, purlins, and tension-
rod. The iron parts are connected together by hinge-
joints, as at C. The purlins are supported by sockets on
the principals, as at B. The common rafters are of timber.

Plate XXYII.—To diminish the excessive height of
roofs, their sharp summit is suppressed, and replaced by a
roof of a lower slope.

Francis Mansard, who died in 1666, brought this sort of
roof into fashion in France, and was for a long time re¬
garded as its inventor* The roof is known, indeed, as
the Mansard roof; and the garrets formed in such roofs
were called Mansards. The Mansard roof may be de¬
scribed in several manners:—

1st. In Fig. 461, the triangle a d b represents the pro¬
file of a high-pitched roof,
the height being equal to
the base. At the point e,
in the middle of the height
c d, draw a line horizontally
h e i, parallel to the base a b,
to represent the upper side
of the tie-beam, and make
e f equal to the half of ed\
then ah fib will be the
profile of the Mansard roof.

2d. In Fisr. 462, make c e the height of the true roof,
equal to half the width a b, and construct the two
squares a d e c, c e g 6; also make d h, e f, and g i each
equal to one-third of the side of a square; then will ah fib
be the profile required.

Fig. 4fi 1.

3d. In Fig. 463, on the base a b, draw the semicircle
a d b, and divide it into four equal parts, a e, e d, d ff b;
join the points of division, and the resulting demi-octagon
is the profile required.

4th. Fig. 464.—Whatever be the height of the Man-

* Bullet says that Mansard truncated his roofs after the example
of one at Chilly, by Metezeau. Mesanges asserts that he took the
idea from a frame composed by Segallo, and that Michael Angelo
employed it in the construction of the dome of St. Peter’s; but
Krafft, in his work on Carpentry, seeks a more remote origin for this
kind of roof. He remarks that it existed in the Louvre, built by
Pierre Lescot for Henri II., in 1570. He adds, that the houses in
Lower Brittany were covered with these roofs in the end of the
fifteenth century.

PLATE XXVI

M ® IF S

30 feet. 15

BLACK IE & SON. GLASGOW. EDINBURGH & LONDON

/ // ZoWfH f

EXAMPLES OF THE CONSTRUCTION OF ROOFS.

141

sard, c e or b g, D’Aviler makes g i equal to tlie half of
that height; aud the height, e f y of the false roof, equal
to the half of e i.

5th. Fig. 465.—Describe the semicircle a f b, aud

Fig. 464. Fig. 465.

divide each half of the base a b into three equal parts.
From the last divisions p p, the perpendiculars p r, p r
are erected, cutting the semicircle in r r; then a r f r b
is the profile.

6th. Fig. 466. — This method, which is described
by Beledor in La Science K ,,. 4B6

des Engineurs, has been 2 y 3

generally adopted on account

of its simplicity, and the i /y__ __

good effect which it produces. jj \\

Describe a semicircle on i \\

the base a b, and divide its a*- --

circumference into five equal parts, in 1 2 3 4; then the
chords a 1, b 4 are the sides of the true roof, and 1 /, 4/
those of the false roof. It is by this method that the
lines in Fig. 1, Plate XXVII., are set out.

The forms of the Mansard roof, it will be seen, may be
infinitely varied, by choosing, in the diameter or in the
semi-circumference, other points of division, or by alter¬
ing the relation between the height and width of the roof,
according to the uses to which it is to be converted.

Plate XXVII., Fig. 1.—A Mansard roof for an arched
ceiling, selected from Krafft.

Fig. 2. — A king-post Mansard roof. In this example
there is a wide space available as an apartment. The
construction would be improved by adding straps to the
feet of the story-posts.

Fig. 3.—A roof with two stories of apartments in its
height. This is an example also taken from Krafft. It
is the roof of the Chateau de Florimont, in Alsace, de¬
signed by General Klebei\ It is difficult to conceive
what good is obtained by the introduction of the story-
post in the centre.

Fig. 4.—A queen-post Mansard roof. This is regularly
trussed, and is ei'ected over the riding-house at Copenha¬
gen Colonel Emy remarks that there should be struts a
under the purlins, and a small collar-piece b added ; that
the tie B is too heavy, and that the cross-piece above D
serves no useful purpose, and might be dispensed with.

Figs. 5 to 10, on the same plate, are examples of the
modes of forming and framing dormers, such as at A and B,
in Fig. 3.

When Colonel Emy was called upon, in 1819, to con¬
struct the roof of a building upwards of 60 feet wide, at
the barracks of Libourne, it was proposed to him to follow
the method of De Lorme, a notice of whose system is
prefixed to the description of Plate XXX. But, while
acknowledging the merit of De Lorme, and the beauty
of the results obtained in constructing roofs in accord¬
ance with his method, it had yet appeared to M. Emy,
that where timber of tolerable length could be obtained,

results equally good might be produced, without cutting it
into the short scantlings required by De Lorme’s system.

Accordingly, as the country afforded pines of from 36 to
40 feet long, and fir still longer could be easily obtained
from the Pyrenees, he sought to compose a roof in which
the timber might be used in its whole length, and which
should combine the necessary solidity with the lightness,
elegance, and economy of the system of De Lorme. He
succeeded in designing a roof which, in his judgment,
satisfied all those conditions; but did not obtain authority
to carry out his designs. He was authorized at length
to make a trial at Marac, near Bayonne, in 1825, in roof¬
ing a building of nearly the same dimensions. The success
of this trial was such as, in 1826, determined the authori¬
ties to roof, in the same manner, the manege at Libourne,
for which the system was originally designed.

The execution of M. Emy’s system is within the power
of the ordinary carpenter; and the workmanship is less
than in the roofs of De Lorme, as the wood is all in
straight pieces. There are neither mortises nor tenons,
except at the ridge; and the process of construction and
setting the principals in their places is so simple, that, as
M. Emy says, twelve workmen, two-thirds of whom were
common labourers, were able to put together, and raise
and set in their places, two principals each week at
Marac.

Principals have often been constructed of great arcs, or
centres, formed of several pieces of timber superimposed
on each other. But such pieces have been of considerable
scantling. They have been very short; their connection
has been by iron; and their curvature produced by the
adze or by heat. Now, the construction invented by M.
Emy is a timber arch composed of a series of long and
thin planks applied on the flat, the flexibility of which
permits them to be easily and quickly bent without the
aid of heat; and their rigidity, properly regulated, has
the property of maintaining the form given, and destroy¬
ing the thrust.

It would be impossible to bend, even with the aid of
fire, timbers of the same scantling as these composite arcs.
Even supposing that pieces of half the length could be so
bent, then, to form the whole arch, butt-joints, occupy¬
ing the whole section of the timber, would have to be
introduced; while, by building these arch-beams of thin
planks, the joints can be properly broken without weaken¬
ing the strength of the beam.

The combination of this system may be varied infinitely
by the number, the span, and form of the arcs; and the
strength of the arcs may be increased, according to the
necessity of the case, without changing the system, or
injuring the elegance of its appearance, by simply adding
more planks either to the whole length of the arc, or
to such part as trial, always indispensable in large con¬
structions, shows to be necessary.

Since the invention of M. Emy has been made public
by his own publications, and by the report of the Society
for the Encouragement of National Industry, in March,
1831, roofs have been constructed on his principle with
great success both for large and small spans. The ex¬
amples we have engraved embrace the roof of a shed at
Marac, and the roof of the riding-house at Libourne,
constructed by himself (Plate XXVIII.); and the appli-
I cation of his system to the roof of a Gothic church erected

142

PRACTICAL CARPENTRY AND JOINERY.

at Grassendale, near Liverpool, by Mr. Arthur Hill Holme,
architect (Plate XXIX.)

Plate XXVIII.—Roof of a shed at Marac, near Bayonne,
France.

Each principal of this roof (Fig. 1) is composed of a
semicircular arch, two principal vertical pieces, two prin¬
cipal rafters, two struts, a king-post, and a collar-beam,
the whole tied together by pieces which are at right angles
to the curve. These radial pieces, as well as the sides of
the arch, are notched upon each other.

The vertical pieces are distant from the face of the wall
about 4 inches. The three first radial pieces on each side
are prolonged beyond the uprights, and enter recesses
made in the wall to receive them, as seen in Fig. 12.
The object of this is merely to steady the frames, and keep
them vertical.

Between the radial pieces, the plates composing the arc
are bolted together with cylindrical bolts, which are driven
tightly into accurately made holes by a heavy mallet.
These keep the plates from sliding on each other. The
plates are further firmly tied together by iron straps.
The bolts are -fo inch diameter, and about 2 feet 6 inches
apart.

The plates of wood forming the arc are 11 inch thick,
5 t Y inches broad, and about 40 feet long. Two and a
half plates of this length, joined end to end, make up the
whole length of the curve. The joints are so distributed
that those of one row do not correspond to those of another
row, and that each joint is carried by one of the radial
pieces. All the plates cannot, of course, have only three
joints; and several of them have only two. Thus there
may be only from ten to twelve joints in the whole arc.

The vertical pieces are 7| inches thick; the principal
rafters 5.^ inches thick.

The principals are placed 9 feet 10 inches apart; and
maintained in this position by the braces seen in Fig. 2,
and on a larger scale in Fig. 6, by the purlins, and by a
line of double ties stretching between the fourth radial
pieces.

V hen this roof was proposed, it was alleged that it
would alter its form, and exercise a thrust upon the walls,
especially when loaded with its covering. Colonel Emy,
therefore, judged it proper to make several experimental
principals on this construction, which could be submitted
to proof, and enable him to determine what weight they
could support without alteration of form, and also the
number of plates of which the arcs should be composed.
The experimental arcs were composed of five plates. They
were sustained by thick plates of oak laid on the ground,
which had first been truly levelled and beaten solid.
V hen the arc was raised up and left to itself it drooped a
little.

I hen, by long cords, there were suspended to the points
ot the arc, which represented fairly the points of pressure,
platforms of wood at about 20 inches above the ground,
these platforms were then loaded gradually with cast-
ii°n, until the weight on each reached 2200 lbs., making
the total load 10'8 tons — a weight which was one
quarter more than the principal would have to sustain.
I he plates in these experimental arcs were fastened to¬
gether solely by the radial pieces and iron straps, as
Colonel Emy wished to reserve a means of increasing the
strength by inserting the bolts after the experiment, and

when the principals were set in the places they were
finally to occupy.

As the weights were added, the arc appeared to flatten.
At the end of twenty-four hours, its curvature was tested
by a radial rod of wood of 32 - 8 feet long mounted with
iron at each end, and centred truly on an iron axis, and
established with precision on the head of a pile driven in to
the level of the springing of the arch. It was found that
the king-post had fallen down, but that the curvature of
the arc comprehended between the seventh radial pieces
had not sensibly altered. There was an augmentation of
the curvature below these points, the maximum being at
radial No. 4; and the disposition of the principal rafters
and uprights was, of course, also slightly affected. The
diameter of the arc, however, did not vary; and there¬
fore the plates must have slid on each other to the extent
of not quite an eighth of an inch each.

The conclusion derived from the experiments was, that
the stiffness of the arc should not be the same throughout,
and that it was necessary to reinforce it in the places that
had yielded the most, by supplementary plates. The
proper result was obtained by adding, on the two sides
of each arch, one supplementary plate to a part of the
extrados, and two plates to a part of the intrados. The
following is the proportion of the number of plates, and
their width, which Colonel Emy adopted as a rule :—

Width.

Ft. In.

From the springing to radial No. 1, ... 7 plates, ... 1 3

From radial No. 1 to the tie placed ( g ^ -

between radials Nos. 6 and 7, 5

From the above tie to radial No. 9, ... 6 „ ... 1 0

From radial No. 9 to king-post, . 5 „ (nearly) Oil

The supplementary plates were of oak, and of the same
thickness as the others.

The principals thus strengthened were again submitted
to proof without change of form.

The manner of constructing the principals was as fol¬
lows:—The ground having been dressed and beaten to
a level, a semicircle of 65 feet 7 inches diameter was
described, representing the intrados of the arc of five
plates; and the chief lines of the principal were then
traced, and strong sleepers were laid down and fastened
by pickets. The sleepers, twenty-four in number, and
10 inches square in section, were all laid radially, and dis¬
tributed so as to fall between the radial pieces of the arc
and the iron straps; two only were on the outside of the

to hold the draught of the principal; and the centre of the
arc was formed by an iron axis fixed on the head of a pile.
The floor being laid, and the draught made on it, pieces of
wood 8 inches square were fastened through it by long
spikes to the sleepers, and to these the template for curving
the plates forming the arc was fixed. The process of bend¬
ing timber for this and similar purposes has already been
described in detail at pages 102, 103, substituting a con¬
tinuous template for the polygon. To this the reader is
referred.

The arc being formed by the process there described, the
other parts of the principal were properly fitted, but not
fastened; and on being completed, the parts were taken
asunder, numbered, and put aside, to be raised to their
places on the completion of the whole. This was necessary,

Pl.ATI-: ATI-7/.

m & w \f $ o

Roof of the, Chateau.■ tie RLtrrim.ond,

in Alsace -. DealtjneA l>y Gen 1 KLebet

Roof of the. Ricling Rfoicse, cut Copenhagen.

jo u a 7

5 4 3 2 10

H-f- 4 - I H—I—

io feet.

PWhite id.

J. W. Lo-wry fe.

B1ACKTE k SOW : GLASGOW. EDINBURGH & LONDON

UK (0 ; 7

ROOF OF A SHED AT MARAC NEAR- BAYONNE, FRANCE
Df.'fitjneti um/ tuutrHial b\ f’oi;£m\

/’/- ///.'.\:yiw

_ Fiq.l.

Toass

Dell

BLACKIE &• SON , GLASGOW, EDINBURGH S- LONDON.

W.A. Rfever St

PLATE XXIX.

r )
LTA

ROOF OF THE SALLE DES CAT EC HIS M ES. CATHEDRAL OF AMIENS. Tigs. LZ.and details.
ROOF OF GRASSENDALE CHURCH. Figs. 3. Ac. and. details.

V aSS ■ \

N°3.Fig.3

: | .

Scale. to f las. I and

loFeet

Pale. toFlas. 3 ami 4

4oFeeL

li. ( .. loass. del

BLAOKIE fe SON . GLASGOW. EDINBURGH & LONDON

W.A Beever. Sc

EXAMPLES OF THE CONSTRUCTION OF ROOFS.

143

as Colonel Emy found himself unable to raise the princi¬
pal entire.

The erecting the principals in their places on the walls
was thus accomplished :—A moveable scaffold was pre¬
pared, easily erected and removed, and provided with a
template similar to the one on which the arc was formed.
This is shown in Figs. 3 and 4.

When the scaffold was brought exactly to the place
where the principal was to be erected, all the pieces of the
latter were raised as numbered, and put in their places;
and then, when completely fastened together, the template
or centre was detached, and the arc allowed to rest on its
wall-plates. The bolts were then added to the arc before
it received the weight of the roof timbers. Colonel Emy
considered, after completing his work in the way described,
that he might have constructed the arcs, and fitted all the
pieces on the vertical template at once, and thus have
saved time, and made the work more perfect; but the idea
came too late.

The principal being thus placed, was maintained in its
position by wedges, the ends of the radials, in the recesses
in the walls before mentioned, and by stays nailed to the
principals temporarily; and the scaffold was removed to
the place of the next principal.

We shall now describe particularly the figures on the
plate.

Fig. 1.—Transverse section of the building, and eleva¬
tion of one of the principals.

Fig. 2.—Longitudinal section.

Fig. 3.—Transverse section of the building before the
placing of the principals, and section of the scaffold.

Fig. 4.—Section of the scaffold, at right angles to the
preceding.

Fig. 5.—Elevation of the summit of the principal in
Fig. 1 drawn to a larger scale.

Fig. 6. —Section through E F of Fig. 5, showing the
counter-bracing and ties between the principals.

Fig. 7.—Section on the line G n of Fig. 5.

Fig. 8.—Section on the line I J of Fig. 5.

Fig. 9.—Section of one of the radials on the line K L,
Fig. 5, corresponding to the longitudinal point of the arc.

Fig. 10.—End elevation on the plane M N of the radial
No. 9.

Fig. 11.—Section through the arc on the line O 1>,
showing one of the iron straps.

Fig. 12.—Side elevation of the springing of one of the
arcs, showing two of the radials Q R, s T, and the recesses,
Q and s, in the wall, to receive their prolongations.

Fig. 13.—Front elevation of the same.

Fig. 14.-—Portion of the plan of the wall-plates, show¬
ing the manner in which the parts of the principal are
framed into them.

Fig. 15.—Section of the principal on the line of the
upper face of the radial No. 2, Q r, Fig. 12.

Fig. 16.—Section of the principal on the line of the
upper face of the radial No. 1, ST, Fig. 12.

Fig. 17.—Junction of the upright and principal rafter:
Q is the elevation; i> is the profile on the line u v. For
the sake of distinctness, the radial is not shown.

Fig. 18.—Iron strap and screw used in bending the
arc plates.

Fig. 19.—One of the straps used in securing the plates
to the template.

Fig. 20. — One of the ties of timber serving the same
purpose.

Figs. 21 to 24 are parts of the roof of the riding-house
at Libourne.

This roof, on the same principle, was erected in 1826.
The principals differ from those of Marac, just described,
in this: that as the walls at Libourne were of great

thickness, and strengthened by great counterforts, it
was not necessary so carefully to guard against lateral
thrust, and therefore the arcs were composed of fewer
plates each throughout.

The diameter of the intrados of the arcs is 68 feet
8 inches; the principals are placed 10 feet 6 inches apart,
from centre to centre.

In constructing these principals, a working floor was
erected at about 2 inches below the wall-plate, and the
draught was laid down on it, and a polygonal mould was
formed in the manner described at pages 102, 103. This,
as remarked at that place, is not so perfect as the con¬
tinuous template, such as was used at Alarac, and is more
apt to rupture the wood at the points of contact, unless
it is freshly cut and very flexible.

The floor on which the principals were constructed
extended only half the length of the building; therefore,
although the principals were easily raised to the vertical
position, by the application of shears and windlasses, each
had to be moved to its proper place. This was effected
by placing under each springing a little carriage running
on the wall-plates. The frames were kept upright by
proper stays, and the carriages dragged along by tackling,
and forced by levers till they reached their places.

Figs. 21 and 22.—Front and side elevations of the
springing of one of the principals. The centre of the arc
is on the line A B. The principal is mounted on one of
the carriages mentioned above.

Fig. 23.—Section through the principal on the line C D.

Fig. 24.—Horizontal section on the line A B.

Plate XXIX. — Fig. 1. Roof of the Salle des Cate-
chismes, Amiens Cathedral. Fig. 1 is a transverse, and
Fig. 2 a longitudinal section of this roof. It is composed
of principals formed with principal rafters, curved ribs,
king-post, tie-beam, and collar-beam. The ends of the
tie-beam, in addition to their wall-hold, are supported by
framed brackets, resting on stone corbels in the wall.
The brackets, tie-beam, king-post, and curved ribs are
all exposed to view, and are moulded in a very simple
and effective manner. The ceiling is vaulted, and formed
of boarding, ornamented with vertical moulded ribs,
placed about IS inches apart.

Fig. 1.— No. 1 is an elevation of the lower portion
of the king- post, showing the mode of finishing the
chamfering. No. 2 is a section through the octagonal
portion of the post. No. 3 is a vertical section of the
tie-beam. No. 4 is a section of the cornice from which
the arched ceiling springs.

Fig. 3 is the elevation, and Fig. 4 the longitudinal sec¬
tion of a Gothic roof on Col. Emy’s principle, designed
by Mr. Arthur Hill Holme, of- Liverpool, and erected
under his direction at Grassendale Church, Aigburth; and
Nos. 1, 2, and 3, Fig. 3, are the details of the same roof
drawn to a larger scale. The mode of construction was
in every respect similar to what has already been de¬
scribed, and need not therefore be repeated.

144

PRACTICAL CARPENTRY AND JOINERY.

In 1561, Philibert de Lorme published his book, entitled
New Inventions for Building Well at Little Expense.

In his address to the reader, he says, among other
things, that as it is difficult to find trees large enough to
serve for beams, and the other timbers of mansions, he
has Iona 1 sought for some invention which would enable
him to use all kinds of wood, and even the small pieces,
and so to dispense with the great trees hitherto used.
The result of his researches was the system of framing to
which the name of the inventor is given, and which is
here illustrated and described in detail.

The system of Philibert de Lorme is composed of arcs
or hemicycles formed of planks, used as substitutes for the
framed principal.

The planks forming one layer or thickness are placed
end to end, and their joints are cut radially to the centre.
The joints of one layer or thickness of plank correspond
to the middle of the planks of the second layer, and for
small spans each plank is only about 4 feet long, by about

8 inches wide and 1 inch thick. The feet of the hemi¬
cycles are tenoned into the wall-plates. The shoulders of
the tenons are about 1 inch.

The hemicycles are all traversed in the joints by ties
1 inch thick and 4 inches wide. Keys of 1 inch thick
and 1§ inch wide, and of a length nearly equal to the
width of the planks, traverse the ties. They serve to
maintain the hemicycles in their vertical planes at their
proper distance apart, which is about 2 feet, and, at the
same time, to tie, in each hemicycle, the planks together.
The mortices in the ties are a little less apart than twice
the thickness of the rib-planks. Some make only one
mortice, with the view of saving labour.

The mode of construction illustrated by all the figures
in Plate XXX., was first employed by De Lorme in
roofing the pavilions of the Chateau de la Muette, at St.
Germains-en-Laye. The walls of these pavilions were in
a defective state, and would not bear the weight either
of stone vaulting, or of heavy carpentry, even if trees
large enough to make the roof of the ordinary construc¬
tion in use at that time could have been obtained, which,
we learn from the work of De Lorme, published in 1561,
was not the case.

The advantage of the system, according to its author,
is the saving of expense, because very light and short
timbers are proper for the work, and the walls need not
be so thick as for heavier carpentry; great vehicles for
the transportation of the wood, and ropes and engines
for the raising it, are not required; and in countries
where only small scantlings of timber are obtainable,
it permits of roofs of greater span to be made than would
otherwise be possible.

In Plate XXX., fig. 5 shows a portion of one of
the hemicycles, as he called his frames, for spans of
from 24 to 30 feet. Each hemicycle, A B, in this case, is
built ot two thicknesses of wood, each of which, ef, is
in pieces ot 3 or 4 feet long, 8 inches wide, and 1 inch
thick. The joints of the one series are made to fall on
the middle ot the length of the other; each piece has a
moitice cut in the middle of its length, and a half-mor¬
tice at each end. I he mortices are 4 inches long, and a
little more than 1 inch wide. 4 hey serve to receive ties

9 9> which may be of any length, and otherwise of the
same dimensions as the mortice. The ties are secured

in their places by keys h h, driven through mortices
made in the ties, one on each side of every hemicycle.
The mortices in the ties are made with a little draw.
The keys are best when made of split wood. The two
thicknesses of timber in each hemicycle are first framed
together by small pins, to prevent their sliding, and then
the hemicycles are united by their ties, and the two fas¬
tened by the keys. They are then placed on wall-plates,
10 or 12 inches wide, and 8 or 9 inches thick, liavino-
mortices sunk at 2 feet apart to receive the ends of the
hemicycles. The mortices are 2 inches wide, 3 inches
deep, and 6 inches long.

In the roof of the pavilion of the Chateau de la Muette,
where the span was 64 feet, the scantling was increased
to 13 inches wide, and 1| inch thick. The ties were al¬
ternately double and single, and were 3 inches by 1| inch.
Each hemicycle was double tenoned into the wall-plate.
The general elevation of the roof is shown in Fig. 1, and
parts of the hemicycles to a larger scale in Fig. 6. The
same letters refer to the same parts in both figures— A A,
one of the hemicycles; B, a terrace or gallery, used as a
belvidere; c c, double ties; d d, single ties; e e, wall-plates;
ff, eaves - rafters (coyaux). The notches for double ties
are just so deep, that the outside surface of the tie is
flush with the edge of the hemicycle.

When the span is small, and the curve of the roof is
so quick that it becomes impossible to cover it with slates
or tiles, De Lorme adopts the expedient shown in Figs. 2
and 3.

Fig. 4 shows the application of the principle in the
construction of a groined vault, with a pendant in the
centre. The dimensions of the pieces of which these arcs
or hemicycles are composed, increase of course with the
increase of the span of the arch; and, as has been men¬
tioned above, the single ties give place to double and
single ties placed alternately. In the roofs of ordinary
buildings, where the span does not exceed 24 feet, the
author directs the pieces which compose the hemicycles
to be made 1 inch thick and 4 feet long; for roofs of
36 feet span, the thickness to be 1| inch; for roofs of
60 feet, the thickness to be 2 inches; for roofs of 90 feet,
the thickness to be 2b inches; and for roofs of greater
dimensions, the thickness to be 3 inches.

Plate XXXI.—Roof of the great hall, Hampton
Court.

Fig. 1 is a longitudinal, and Fig. 2 a transverse section
of the roof. The great hall at Hampton Court is 106 feet
long, 40 feet wide, and 45 feet high in the walls. It was
completed in 1536 or 1537. The roof consists of seven
bays in length, one of which is the subject of Fig. 1, and
by referring to the transverse section, Fig. 2, the con¬
struction, which is similar to that of Westminster Hall,
will be clearly comprehended. Each principal consists of
a centre arch and two half-arches, and the principals are
connected by three tiers of arches, as seen in Fig. 1.
These, with their enriched panels and pendants, produce
an exquisite richness of effect.

Fig. 4 is one of the large pendants.

Fig. 3.—One of the pendants of the second tier of arches.

Fig. 6.—One of the pendants of the third tier of arches.

Figs. 7 and 8 are two of the wall-corbels from which
the roof springs. The exterior of the roof has a double
pitch like the Mansard roof.

PI.ATE XXX.

H-

3o Feel.
—I

Scales for Figs . 1.2.3 A.

iz o -t *r

jmTTtnnn ■

-+—t ±

10 Feel .

lore*

Scale ., for Figs. S. 6 -

BLACK 1 E b SON. GLASGOW. EDINBURGH * LONDON.

Beaver. Sc.

A.F. Orridoe. del.

CFi®.© IF © o

DOMED ROOFS.ON THE SYSTEM OF PHILIBERT DE LORME.

n b

Fix. 5.

GS® © FS „

ROOF OF THE GREAT HALL. HAMPTON COURT

PLATE XXXI.

Fig. 4.

Fixj . 6.

Fig. /. |

20 Fe e t.

BLACKiE i. SON .GLASGOW EDI.VBl'RGJ-I Sfc LONDON.

11 L I BeererSc.

In •* n

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l)/n/, M'

J.W L’»ry Ji

i. sun I.l.v.um-, Kill N ni'IHill, \ I.(IN 1)1) N

!fc-£3)©F So

CIRCULAR AND POLYGONAL DOlJlES.

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40 jo"Feet.

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EXAMPLES OF THE CONSTRUCTION OF ROOFS.

145

Plate XXXII.—The figures in this plate represent the
roof of Westminster Hall. This noble hall was first
built in the reign of William Rufus, in the be<nnnino- of
the eleventh century; but, 300 years afterwards, was
rebuilt by Richard II.; and in 1399, the festivals of
Christmas were celebrated in it, by banquets of extra¬
ordinary magnificence.

In Fig. 1 is shown the half of one of the principals.
It is composed of two rafters a a, joining at the apex on
a punchion, and united in the middle of their length by
a collar-beam d. There is no tie-beam, but, in its place,
two hammer-beams e, one at each side, which receive the
ends of the rafters. These hammer-beams are horizontal,
and are sustained by the arc f The end of each hammer-
beam sustains a post g, decorated with a base and capital,
and into this post is framed the rafter or strut c, which
discharges part of the weight, and is supported at the
foot on a block h, lying on the inner end of the hammer-
beam. It is prolonged below the hammer-beam at i, and
abuts against a stile placed on the wall. Between the
collar-beam and the ridge there is another beam k] framed
into the posts n, which sustain the rafters at the point
where the purlins o rest. A great arc m springs from
the same corbel as the bracket of the hammer-beam at
the middle of the height of the walls. This arc is in two
pieces, and embraces in its thickness the posts g and the
collar-beam d. Another lesser arc r springs from the end
of the hammer-beam, and joins the great arc. This
discharges part of the framing to the point of the beam,
whence it is carried by the lower arc to the corbel.
These parts are all connected and firmly braced together,
and to the rafter, by the iron rod l, which passes through
them, and is secured by a screw and nut at the under
side of the last-mentioned arc under the hammer-beam.

Fig. 2 is a longitudinal section of one bay of the roof
comprised betwixt two principals. The roof, it will be
seen, is in three divisions: the first, rising from the cor¬
nice, terminates at the hammer-beam; the second extends
from the hammer-beam to the collar-beam ; and the third
from that to the ridge. Curved pieces w t x are intro¬
duced to support the timbers longitudinally; and a collar-
beam is introduced between the common rafters, to pre¬
vent them sagging under the weight of the covering, and
they are further strutted by the pieces u u. The lower
purlins p of the roof are also sustained by two curved
struts y abutting against the great arc.

Figs. 3 and 4 are representations, to a larger scale, of
the angels sculptured at the extremity of the hammer-
beams. Each an cel holds a shield with the arms of
England and France quartered.

Fig. 5 is the detail of the spandrel at 0 z, Fig. 2.

Fig. 6 is the spandrel at r, Fig. 1. The tracery above
the collar-beam is shown in Fig. 7, and a section of the
moulding on the line 3-4, at Fig. 9. The section of the
great arc on the line 1-2 is given in Fig. 8, and a sec¬
tion through the pillar g on the line 5-6 in Fig. 10.

Plate XXXIII.—The construction of the conical roof,
Fig. 1, Nos. 2, 3, 4, 5, and 6, will be evident from the
drawings without detailed description. The main princi¬
pals, it will be seen (No. 3), are united at the top by being
inserted into iron sockets cast in one piece; and the
frame is completed by struts and an iron tie-rod. The
other four principals are framed like a queen-post roof, as

shown in Fig. 4; and the ties of all the principals are
connected at the centre by the radiating straps seen in
No. 5, through the central circular part of which the tie-
rod No. 6 passes, and is secured by a nut. The same
letters refer to the same parts in most of the figures, ex¬
cepting a, which, in Nos. 1 and 2, is the larger circular
purlin, but in No. 4 the straining-sill between queen-posts.

Fig. 2. —Nos. 1, 2. 3, and 4 show the construction of a
domical roof. The curved ribs ai - e supported by struts
from the principals, as seen in Nos. 3 and 4. The plan
and elevation exhibit the curved arrises which the sides
of the horizontal ribs assume when cut to the curvature
of the dome, as at a, Fig. 2, No. 3.

Plate XXXIV. Fig. 1. —Nos. 1, 2, 3, and 4 show the
construction of a domical roof with a circular opening in
the centre for a skylight. Two of the main principals, CD
and the corresponding one, are framed with a king-post c,
as shown in No. 3: the others at riff lit angles to these,
with queen-posts, as seen in No. 4. The main ribs cor¬
respond to the principals, and the shorter ribs are framed
against curbs between them, as at a, Nos. 1 and 3.

Fig. 2 .—Nos. 1, 2, and 3 show the framing of an ogee
domical roof on an octagonal plan. The construction will
be readily Understood by inspection; and the method of
finding the arris ribs, shown in No. 3, will be understood
from what has already been said when treating of hip-
rafters.

Plate XXXV. —The figures on this plate illustrate the
construction of a timber steeple.

Fig. 1 is a horizontal section of the square part of the
steeple on the line A A in Figs. 2 and 6, and also a plan
of part of the roof, showing the four principals which
carry the steeple. Each principal carries three main posts
a d a, forming the carcass of the square part, and the two
interior principals carry also the additional posts b b, to
form the octagonal part above. But the explanation of
the horizontal sections will be more easily comprehended
in connection with Fig. 2, which is a vertical section of
the steeple and roof on a line coinciding with the face of
the interior principal acdca in Fig. 1.

Fig. 2. — A A are the principal rafters; B B, the tie-beam;
C C, queen-posts carried up to form the framing of the
square portion of the steeple, and marked a a in Fig. 1 ;
D, Icing-post, marked d in Fig. 1 ; F, secondary rafters;
EE, straining-piece; gkh, struts; P, the common rafter;
r, the purlin; x, the gutter-bearer; y, the straining-sill;
wu, a bolt uniting the rafters, tie-beam, and pillow-piece;
g, a strap uniting the queen-posts, rafter, and straining-
piece, and the post L, which is carried up to form the
octagonal part, and is marked b in Fig. 1. The struts
II and M serve to discharge the weight of L to the king¬
post: M is shown on the section Fig. 1 at mm; and the
strut n, shown in dotted lines, serves the same office in
respect of the outer post of the octagon, and is marked
n n in Fig. 1: N is a counter-brace, the intersection of
which with M is marked c in Fig. 1. The strut o supports
the cross-piece o at the point where the bearers h h h, in
Fig. 1, rest on it. Horizontal pieces unite the summits of
the four king-posts, and are marked 11 in Fig. 1, and g
in Fig. 2. Similar pieces, k k in Fig. 1, and g in Fig. 2,
unite the summits of the queen-posts, and also the posts
forming the octagon at successive stages. The exterior
posts of the octagon are supported by the horizontal

PRACTICAL CARPENTRY AND JOINERY.

14G

bearers shown in dotted lines on Fig. 1, and marked
eeee, ff. The posts stand on the small parallelograms
cj g g g. At the height ol the head-piece z, the squai e
portion of the steeple terminates, and the octagonal fram¬
ing is alone continued. Fig. 3 is a lioiizontal section on
the line B B, in which a a a a, bbbb are the posts stand¬
ing on the parts b g in Fig. 1. Fig. 4 is a section through
c C, in which the same posts are indicated by the same
letters; and Fig. 5 is a plan of the domical termination of
the steeple. The lines D D, E E, and E F in these figures indi- j
cate the position of the vertical section Fig. 2. The parts
of the section Fig. 2 above B B will be sufficiently under¬
stood by inspection, and need not be described in detail.
Fig. 6 is an elevation of the steeple. The horizontal lines
A A, B B, and C c are the lines of section, Figs. 1, 3, and 4.

Plate XXXV? Fig. 1.—No. 1 is a sectional elevation,
and Nos. 2 and 3 are horizontal sections of the tower
of the Town-hall, Milford, Massachusetts, erected from
the designs of Mr. Thomas W. Silloway, of Boston, U.S.,
who has kindly supplied the drawings of this and the
following example.

The mode of framing is very simple, and will be under¬
stood by inspecting the drawings. Fig. 1, No. 2, is a
horizontal section or plan at the line A-B in No. 1, imme¬
diately above the floor of the first story of the tower.

A A, A A, A A, A A are horizontal timbers framed between
the principal posts, and strongly strapped and bolted to
them, as seen in No. 1: B B, B B are dragon-pieces crossing
the angles, to support the posts C C, c C of the upper por¬
tion of the tower. Crossing the angles are also angle-
braces, and these and the dragon-pieces are securely bolted
to the horizontal timbers. No. 3 shows a horizontal sec^
tion at C-D, wherein the arrangements are of much the
same nature as in N o. 2. The principal posts carry strong
capping-pieces F F, F F, which again carry the dragon-
pieces L L, L L, and are also firmly united by the angle-
braces oo,oo. Idle use of the various struts and braces
is so obvious as not to require further description.

Fig. 2, No. 1.—In this figure, the principal posts are
capped over at the level where the tower diminishes in
diameter; and the posts for the octagonal upper portion
of the tower are, as in the preceding example, carried by
dragon-pieces resting on and bolted to horizontal timbers
framed into the principal posts, as seen at No. 2. The
arrangement of the horizontal timbers or capping-pieces for
the support of the octagonal spire, is shown in No. 3.

Plate XXXV I. — Spire of La Sainte Chapelle, Paris.

The ancient edifice which this elegant spire surmounts
was built in 1248 to contain the relics which St. Louis
brought from Palestine. It was erected from the designs
of Pierre de Montreuil, the celebrated architect, who built j
also the castle of Vincennes. The original spire was demo- j
fished a short time before the Revolution. It was said to
be a marvel of boldness and lightness. The new spire,
with the scaffold used in its erection, are figured in the
plate; and whatever may have been the merits of its
predecessor, this beautiful work may vie with it in the
qualities which have been mentioned as its characteristics.

Fig. 1 is a section of a part of the roof and an elevation
of the spire.

Fig. 2 is a horizontal section immediately above the
roof, and shows also the disposition of the principals which
support the spire.

Fig. 3 is the elevation, and Figs. 4 and 5 plans of the
scaffolding used in the erection of the spire.

Fig. 6.—The upper half of this figure is the half-plan at
A B, Fig. 1. The lower half is the half-plan on the fine c D.

Fig. 7.—The upper half of this figure is the half-plan of
the base of the spire immediately above the roof; and
the lower half is the half-plan on the fine E F, Fig. 1.

FRAMING— JOINTS —STRAPS.

Plates XXXVII.—XXXIX.

Carpentry differs from masonry as much in the nature
of the materials employed as in the mode of using them.
In masonry, stones are usually placed horizontally on
their beds, the one above the other,—their weight when
they are hewn, and the interposition of some cement
when unhewn and amorphous in form, giving them
stability. In the constructions of carpentry, on the con¬
trary, a greater or smaller number of long pieces of
wood, squared and property cut, and which may be
arranged at any inclination, are combined so that the
extremities of one set press on, or are pressed by certain
points in the length of the others. Three pieces thus
abutting form a compartment in framed work unalterable
in form, possessing the qualities of strength and stability,
and of rapidity and freedom in construction, which ren¬
ders this art susceptible of a number of applications to
which masonry is not so well adapted.

Thus the carpenter raises with remarkable celerity
houses and buildings of all kinds, and divides them into
stories in a manner wonderfully simple. He constructs
bridges of all spans, and raises and covers vast edifices;
and these results he obtains in a manner often preferable to
any other kind of construction, and at a much smaller cost.

That elementary form of the timber used in framing
which is the most simple, and which the imagination
seizes most readily, is the rectangular parallelopipedon.
It is also the form which is best adapted to ordinary
constructions, and which renders the exact execution of
work most easy. In masonry, the same form also favours
a simple and commodious arrangement of materials in a
stable manner.

That two pieces of wood may meet and abut on each
other without the one being caused to turn on its axis by
the other, it is necessary that the axes of the two pieces
pass through a point common to both. The axes, therefore,
of the two pieces should be in the same plane. The axis
of a piece of wood, it should be explained, is a right line
parallel to its arrises passing through its centre of gravity.

The meeting of two pieces of wood is called the joint.
The joint is circumscribed by the fines which mark the
intersection of the faces of the one piece with the other.

The end of a piece of wood property cut to be adjusted
in contact with another piece is called its abutment.

That a joint may be at the same time simple and easy
of execution, it is necessary 7 that the bearing faces should
be planes of the same size and shape in relation to the
planes of the axes. This can only have place when two
faces of each piece are perpendicular to the same plane,
and the other two faces parallel. This consideration will
show, if we have not already said it, that the two pieces
of wood must necessarily 7 be square.

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Elevation of one side of Scaffolding.

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F RAMIN G—JOIN TS—STRAPS.

147

When two pieces of wood are joined by the simple
contact of the end of the one piece with its bed on the
other, we say that they abut, or are joined by a plain joint.
This mode of joining does not prevent the one piece slid¬
ing on the other, unless it is fastened with nails or bolts.

The contrivances by means of which one piece is pre¬
vented from sliding on the other are called mortises,
joggles, &c.

The putting together of two pieces of wood may be
done in three ways:—

I. They may meet and form an angle; and this mode
has three cases—

1. The end of one piece may bear upon a point in the
length of the other. This case is the most frequent, and
gives rise to the mortise-'and-tenon joint, the joggle-joint,
and to all those which are modifications of these two.

2. The two pieces can be joined mutually by their
extremities under any angle whatever. This forms the
angle-joint.

3. They may cross each other; and this result is the
notch-joint.

II. Two pieces of wood may be joined in a right line
by lapping and indenting the meeting ends on each other.
This is called scarfing.

III. Two pieces of wood may be joined longitudinally
end to end, the joint being secured by covering it on
opposite sides by pieces of wood bolted to both beams.
This process is termed fishing.

It is requisite to consider the joint as formed by two
pieces only, because joints formed by more than two
pieces can always be resolved into this.

The mortise-and-tenon joint is the principle of the
greatest number of the other joints. It is necessary,
therefore, to describe it first at length.

In the simplest case of a tenon-and-mortise joint, the
two pieces of wood meet
at right angles (Fig. 467).

The tenon a is formed at
the extremity of the piece
A, in the direction of its
fibres and parallel to its
axis, m n, by two notches,
which take from each side
a parallelopipedon. The
planes of the sides / g of
the tenon are always par¬
allel to the face b of
the timber, and the other
planes of the notch at right
angles to it.

The mortise is hollowed
in the face of the piece B,
and is of exactly the same
size and form as the tenon,
which therefore perfectly

fills it. The two sides of the mortise which correspond to
the breadth of the tenon should be parallel to the direc¬
tion of the fibres of the wood. The sides of the mortice
are called its cheeks ; and the square parts of the timber
A from which the tenon projects, and which rest on the
cheeks of the mortise, are willed the shoulders of the
tenon, and its springing from these is called its root.

As the cheeks of the mortise and the tenon are exposed

to the same amount of strain in a system of framing, it
follows that each should be equal to one-third of the
thickness of the timbers in which they are made.

The length of the tenon should be equal to the depth
of the mortise, so that its end should press home on the
bottom of the mortise when its shoulders bear upon the
cheeks; but as perfection in execution is unattainable, the
tenon in practice is always made a very little shorter
than the depth ol the mortise, that its shoulders may
come close.

When the mortise-and-tenon joint is cut, adjusted, and
put together, the pieces are united by a key or trenail.
The key is generally round, with a square head, and in
diameter is about equal to a fourth part of the thickness
of the tenon. It is generally inserted at the distance of
one-third of the length of the tenon from the shoulder.

But a key should never be depended on as a means of
securing the joint; for the immobility of a system of fram¬
ing should result from the balancing of the forces and the
precision of the execution. A frame fixed definitely in
its place should be stable and solid without the aid of
keys, which are to be regarded as mere auxiliaries, useful
during its construction.

It the endeavour is made to apply the same manner of
forming the mortise and tenon when the timbers are not
at right angles, but oblique, several disadvantages arise.
Such a joint is represented in the subjoined Fig. 468

(No. 1) by a b c d. If there were no other inconveniences,
the impossibility of inserting the tenon in the mortise
when the pieces form a portion of a system, would ob¬
viously preclude its adoption, as it would require to be
thrust into the mortise in the direction of the arrow;
but added to this, there is the difficulty of working the
mortise, and the tendency of the thrust of the tenon to
rend the piece B in the line b c.

All these inconveniences are remedied in a very simple
manner, by truncating the tenon on the line af, as shown
in No. 2, by a plane perpendicular to the axis of the
mortise-piece B. The execution is thus rendered easy
and exact, the evil from the thrust of the tenon is ob¬
viated, and the pieces can be put together by dropping
the tenon-piece vertically into the mortise.

This is the simplest form of the mortise-and-tenon joint
for oblique thrusts. But, obviously, the only resistance
offered to the sliding of the tenon-piece along the mortise-
piece is offered by the strength of the tenon, which is
quite insufficient in large carpentry works; and it is
therefore necessary to modify the form so as to bring
new bearing surfaces into action.

Plate XXXVII. Fig. 1.—No. 1 shows the joint
formed by the meeting of a principal rafter and tie-
beam, c being the tenon. The cheeks of the mortise are
cut down to the line df, so that an abutment e d is
formed of the whole width of the cheeks, in addition to
that of the tenon; and the notch so formed is called a
joggle. No. 2 shows the parts detached and in perspec-

fig. 467.

143

PRACTICAL CARPENTRY AND JOINERY.

tive. It will be seen that a much larger bearing surface
is thus obtained.

Fig, 2._No. 1 is a geometrical elevation of a joint,

differing from the last by having the anterior part of the
rafter truncated, and the shoulder ot the tenon returned
in front. It is represented in perspective in No. 2.

Fig. 3.—Nos. 1 and 2 show the geometrical elevation and
perspective representation of an oblique joint, in which
a double abutment or joggle is obtained. In all these
joints, the abutment, as d e, Fig. 1, should be perpendi¬
cular to the line df\ and in execution, the joint should
be a little free at /, in order that it may not be thrown
out at d by the settling of the framing. The double
abutment is a questionable advantage; it increases the
difficulty of execution, and, of course, the evils resulting
from bad fitting. It is properly allowable only where
the angle of meeting of the timbers is very acute, and the
bearing surfaces are consequently very long.

Fig. 4.—Nos. 1 and 2 show a means of obtaining resis¬
tance to sliding by inserting the piece c in notches formed
in the rafter and the tie-beam: d e shows the mode of
securing the joint by a bolt.

Fig. 5.—Nos. 1 and 2 show a very good form of joint,
in which the place of the mortise is supplied by a groove
c in the rafter, and the place of the tenon by a tongue d
in the tie-beam. As the parts can be all seen, they can
be more accurately fitted, which is an advantage in heavy
work. In No. 1 the mode of securing the joint by a strap
a b and bolts is shown.

Fig. 6.—Nos. 1 and 2 is another mortise-joint, secured
by a strap a b and cotter or wedge a.

Fig. 7 shows the several joints which occur in framing
the king-post into the tie-beam, and the struts into the
king-post. A is the tie-beam; B, the king-post; and c J
and D, struts. The joint at the bottom of the king-post !
has merely a short tenon e let into a mortice in the tie-
beam. The abutment of the strut D is made square to
the back of the strut, as far as the width of the king-post
admits, and a short tenon/is inserted into a mortice in
the king-post. The abutment of the joint of C is formed
as nearly square to the strut as possible.

The term king-post, as has been a!ready stated, gives
quite an erroneous notion of its functions, which are those
of a suspension tie. Hence the necessity for the long strap
b a bolted at d d, and secured by wedges at c, in the
manner more distinctly shown by the section, Fig. 8, No. 2.
The old name king-piece is better than king-post.

Fig. 8.—No. 1 shows the equally inappropriately named
queen-post. A is the tie-beam; B, the post tenoned at e ;

C, the strut; and D, the straining-piece. The strap b a,
and bolts d d.

Fig. 9.—In this figure, the superior construction is
shown, in which a king-bolt of iron c D is substituted for
the king-post. On the tie-beam A, is bolted by the bolts a e,
dj, the cast-iron plate and sockets a, b c d, the inner parts
of which, kg, kg, form solid abutments to the ends of the
struts B B. I he king-bolt passes through a hole in the
middle of the cast-iron socket-plate, and is secured below
by the nut D. A bottom-plate e f prevents the crushing
of the fibres by the bolts.

Plate XXX \ III.— Figs. 1 to 5 show various methods
of framing the head oi the rafters and king-posts by the
aid of straps and bolts. Fig. 6 shows the heads of the

rafters halved and bolted at their junction, and a plate
laid over the apex to sustain the bolts which are substi¬
tuted for the king-post. One bolt necessarily has a link
formed in it for the other to pass through.

Fig. 7 shows at D what may be considered the upper
part of the same king-bolt as is shown in Plate XXXVII.,
Fig. 9, with the mode of connecting the rafters. A cast-
iron socket-piece C receives the tenons a a of the rafters
A A, and has a hole through it for the bolt, the head of
which, b, is countersunk. B is the ridge-piece set in a
shallow groove iu the iron socket-piece. An elevation
of the side is given, in which G is the bolt, F the socket-
piece, and E the ridge-piece.

Figs. 8, 9, 10, and 11 illustrate the mode of framing
together the principal rafter, queen-post, and straining-
piece. In the first three examples the joints are secured
by straps and bolts; and in the last example the queen-bolt
D passes through a cast-iron socket-piece c, which receives
the ends of the straining-piece and rafter, as those of the
two rafters are received in Fig. 7.

Figs. 12 and 13 show modes of securing the junction
of the collar-beam and rafter by straps; and Figs. 14
and 15, modes of securing the junction of the strut and
the rafter by straps.

Lengthening Beams, &c.—In large works in carpentry
it is often necessary to join timbers in the direction of their
length, in order to procure scantlings of sufficient longi¬
tudinal dimensions. When it is necessary to maintain the
same depth and width in the lengthened beam, the mode
of joining called scarfing is employed. Scarfing is per¬
formed in a variety of ways, dependent upon whether the
lengthened beam is to be subjected to a longitudinal or
transverse strain. This method of joining is illustrated
in Plate XXXIX., Figs. 1 to 13.

In Fig. 1 a part of the thickness of the timber is cut
obliquely from the end of each piece, and being lapped
over each other, the joint is secured by bolts. In this
case the joint depends entirely on the bolts. Iron plates
are interposed between the nuts and the timber, to pre¬
vent the screwing up of the nuts injuring the beam.

In Fig. 2 a key is added in the middle of the joint,
notched equally into both beams. In Fig. 3 the joint is
improved by its surface being indented on each joint, and
the key driven between. In this example continuous
plates of iron are placed to prevent injury from the bolts.
Figs. 4, 5, 6, 7, 8, 9 are all variations on the last figure.
In Fig. 10 the beams are halved together vertically, as
shown by the plan No. 2 and section No. 3. They are
keyed at the centre and secured by iron straps. In Fig.
11 the joint is made much larger and halved, the end of
each beam is scarfed and keyed, as in Fig. 3, and the
joint is secured by two straps and seven bolts. No. 1 is
the side, and No. 2 the top of the beam.

Figs. 12 and 13 are examples of scarfs formed by the
interposition of a third piece b.

When the beam does not require to be of the same
dimensions throughout, it is sometimes lengthened by the
process termed fishing. The ends of the beams a a, Fig.
14, are abutted together, and a piece of timber b b is
placed on each side, and secured by bolts and keys.

Fig. 15 is an example of a fished beam, in which the
fishing-pieces b b and timbers a a are tabled, and indented,
and keyed together.

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TRUSSED GIRDERS OR BEAMS.

140

Dovetailing, Halving, &c. — Fig. 16 shows two
pieces of timber joined together at right angles by a dove¬
tailed notch. As to dovetails in general, it is necessary to
remark that they should never be depended upon in car¬
pentry for joints exposed to a strain, as a very small de¬
gree of shrinkage will allow the joint to draw considerably.

Figs. 17 and 18 show modes of mortising wherein the
tenon has one side dovetailed or notched, and the corres¬
ponding side of the mortise also dovetailed or notched.
The mortise is made of sufficient width to admit the tenon,
and the dovetailed or notched faces are brought in contact
by driving home a wedge c. Of these, Fig. 18 is the best.

Fig. 19.—Nos. 1 and 2 show the halving of the timbers
crossing each other. Fig. 20.—Nos. 1 and 2 show a joint
similar to those in Nos. 17 and IS, but where the one
timber b is oblique to the other a.

Fig. 21.—Nos. 1 and 2 show the mode of notching a
collar-beam tie into the side of a rafter by a dovetailed
joint. The general remark as to dovetailed joints applies
with especial force to this example.

TRUSSED GIRDERS OR BEAMS.

Plates XL., XLI.

The general principle of trussing, and the object sought
to be gained by its use, have been spoken of in the intro¬
duction to the article on roofs.

Plate XL. Fig. 1.—No. 1 is an elevation of a trussed
girder, with one of the flitches removed to show the
trussing. No. 2 is a plan of the beam, and No. 3 a
section through the line ah. The trussing-bars C, No. 1,
are of iron, and are shown in section enlarged at cl, No. 3.

An iron tension-plate D extends along the bottom of the
beam, and connects the abutment bolts A A. These bolts
pass between the flitches, and are screwed down upon an
iron plate b. The central bolt B fulfils the functions ol the
king-post of a trussed roof. The beam is generally sawn in
two, and the ends reversed, when put together in a truss.

Fig. 2.—Nos. 1 and 2 are the plan and elevation of
what may be called a queen-trussed beam. The construc¬
tion is the same as the preceding, with the substitution ot
the queen-bolts B B for the king-bolt.

Fig. 3.—Nos. 1 and 2 show another example of a queen-
bolt truss, where greater depth, and consequently greater
stability, is obtained for the truss by the use ot binding
and bridging joists, A being the trussed beam, c the
binding joists, and B the bridging joists. 4 he tension-
strap is joined together at the points c c by cotter-wedges,
which have what is technically called a draw, so that the
driving home of the wedge may bring together the parts

Fig. 4 is an example of a girder trussed with a stirrup-
piece B, end-plates A A, and a tension-rod A & A. No. 1 is an
elevation of the beam; No. 2 is a plan; and No. 3 is an
enlarged vertical section through the line a b. It is diffi¬
cult to balance the tensile and compressive resistances in a
beam of this kind, so that they may be in action to the
same extent and at the same time; and this application
of iron in trussing is now considered by many practical
men to be nearly useless. The beam is considered to be
crippled before the iron begins to be strained, and there¬
fore this mode of trussing is not now in much favour.

Fig. 5. _Nos. 1 and 2 illustrate the application of the ||

tension-rod on what may be considered the queen-post
principle, there being two stirrups at a a.

Fig. 6.—Nos. 1 and 2 show a combination of timber
and wrought-iron. The beam is composed of three flitches,
the two outer being of timber, and the central of boiler¬
plate. The flitches are bolted together. In the elevation
it is the iron flitch that is shown.

Fig. 7 is an enlarged drawing of the connection of the
trussing-piece d with the abutment bolt. The portion
shown is the end of the girder, Fig. 2; b, the cog on the
tension-plate notched into the bottom of the beam; d, the
trussing-piece; a, a hole through the beam for the trans¬
verse bolt, against which the abutment bolt is pressed;
c, the cross-plate on the top of the beam, on which the
nut is screwed down.

Fig. 8 shows the connection of the trussing-pieces a b
with the abutment bolt in same girder.

Fig. 9 shows the links which connect the tension-rods
of girder, Fig. 5.

Fig. 10.—An enlarged drawing of the joints of the ten¬
sion-rods of girder, Fig. 3.

Fig. 11.—A section through a b of trussing-piece in Fig. 3.

Plate XLI.—Example from Krafft.

Fig. 1 . —Nos. 1 , 2, and 3 represent what is usually
called a truss, but what is properly a built beam in three
flitches. The three flitches are indented, as shown by the
plan, No. 2, and the parts are brought home by the keys
c c. They are then bolted together with tiers of bolts.
Krafft remarks that this and similar trusses are only suit¬
able for situations in which they are exposed to tensile
strains.

Fig. 2.—Nos. 1 and 2 are representations of a com¬
pound beam, a modification by Mr. White of the system
of M. Laves, architect to the King of Hanover.

The system of M. Laves has for its object the reducing
the weight of frames of carpentry, and economizing the
timber which enters into their composition. He effects
this by making a saw-cut horizontally along the centie
of the piece of timber, and extending nearly to its ends.
At the ends of the saw-cut he introduces bolts to prevent
its extending further, and then forces the halves asundei
in the middle of their length to a distance equal to one or
one and a half times the total thickness of the beam by
inserting pieces of wood, as shown in the figure.

Several experiments to test his system were made by
the inventor and others; also by Messieurs Lasnier and
Albony, two skilful carpenters of Paris, assisted by M.
Emmery, inspector-general of roads and bridges, and M.
Biet, architectural inspector of buildings.

In the experiments of M. Laves, four pieces of pine,
each 40 feet long, 9 in. thick, and 7| in. wide, were taken.
Three of the pieces were prepared according to his system,
the halves being forced apart to the distances respectively
of the half of the thickness of the piece, the thickness of
the piece, and one and a half times its thickness. The
other beam was used in its natural state for comparison.

Each of the four pieces was loaded with weights, be¬
ginning at 100 lbs. and increasing to 1700 lbs.

Their deflections under their loads were as follows:—-

The piece in its natural state,
The first prepared beam, ...
The second „ „

The third „ „

54 inches.

Z 2

150

PRACTICAL CARPENTRY AND JOINERY.

In the experiment of M. Albony, made in 1810, two
pieces of pine were taken from the same tree. Each piece
was 51 feet 31 inches long, 7/V inches thick, and nearly
11 inches deep. The distance between the supports was
49 feet 2A inches. The saw-kerf in the prepared piece
was as thin as could be made, and the two halves were
separated 5is inches, by a piece of timber.

Before commencing to load the beams, the deflection
due to their own weight was measured. In the unpre¬
pared beam it was found to be rather more than 1^ inch,
but in the prepared beam nothing. The beams were
loaded with weights very gradually increased until they
reached 793^ lbs., when the deflection was—in the un¬
prepared beam 19to inches, and in the prepared beam
2ia inches. Under this load the pieces broke.

M. Lasnier’s experiment was made with two beams of
very dry pine, each 19fo by 3| inches, and the distance
between the supports was 41 feet 10 inches. The halves
were forced asunder 9,1 inches.

The beams were loaded by weights of 272 lbs., applied
successively, and distributed at three points of suspension.
When the load reached 272 x 3 = 816 lbs. the prepared
beam was deflected 2fo inches, and then, after sustaining
it a few minutes, it broke. The unprepared beam broke
before the weight reached 800 lbs.

M. Emy, who records these experiments, says—“ It
does not appear that the strength of a beam prepared
according to the system of M. Laves much exceeds that
of a beam in its natural state; but its stiffness is much
augmented; which may render the preparation useful in
. several cases.”

The beam represented in Fig. 2, No. 1, has been sawn
in two horizontally, the two pieces again put together,
secured by the bolts and straps drawn to a larger scale
in No. 2, and then the two halves forced apart by the
pieces b b inserted between them.

M. Laves applied beams prepared on his system in the
construction of floors, roofs, and bridges.

Fig. 3 is a truss on the principle of the queen-post roof :
A is the tie-beam, c one of the principal braces, E one of the
queen-posts, D the straining-piece, and E and G are struts.

Fig. 4 is a truss formed by the beams A n, straining-
pieces b b, and braces and counter-braces d d. When the
braces, straining-pieces, and punchions c are inserted, the
whole frame is made rigid by screwing the nuts of the
three bolts.

Fig. 5 is a combination of iron and timber. B is a cast-
iron beam, and A a timber beam: on the top of the latter
is the tension-rod d, and on the upper side of this, and
under side of the iron beam, are sockets formed for the
punchions / and braces and counter-braces e e. Wrought
iron straps embrace the framing at each punchion, and are
tightened by cotters at c c.

Fig. 6 is the trussed framing for the gallery of a church,
where the ceiling underneath is curved. The principal
B is notched on the wall-plate G, and also on the beam E:
the tie A is secured on the wall-plate H, and bolted to the
pi incipal. F is a beam serving the office of a purlin, to
cany the gallery joists; D is a strut; b b are the floors of
the pews; and c c c the partitions, c is a hammer-piece
lesting on the beam E, and bolted to the principal B: its
outer extremity carries the piece I, which supports the
gallery front.

Fig. 7 is another example of the trussed frame for a
gallery. Here a framed principal A D c E, resting on the
wall-plate H, and front beam E, supports the beam K,
which carries the gallery joists B: a a and b b are the
floors and partitions of the pews.

Fig. 8, Nos. I, 2, and 3, shows the curb and ribs of a
circular opening c B A, No. 2, cutting in on a sloping ceil¬
ing: as, for example, a circular-headed window occurring
between two principals, such as that shown in Fig. 7.
No. 1 is a section through the centre bd, No. 2, and efi,
No. 3. The height L K is divided into equal parts in efghi,
and the same heights are transferred to the main rib in
A 1 2 3 4 5 B. Through the points A 1 2 3 4 5, in No. 2,
lines are drawn parallel to the axis bei; and through the
points efghi in No. 1, lines are drawn parallel to the
slope K H. The places of the ribs 1 2 3 4 5 in the latter,
and their site on the plan No. 3, and also the curve of the
curb, are found by intersecting lines in the manner the
student is already acquainted with.

FLOORS.

Plates XLIL—XLIV.

Floors are the horizontal partitions which divide a
building vertically into stages or stories.

The timbers which enter into the composition of floors
are bridging-joists, binding-joists, girders, ceiling joists,
and the boards which form the platform. All these,
except the last-mentioned, are comprehended under the
term “naked flooring,” and are strictly within the pro¬
vince of the carpenter.

When the bearing between the points of support is not
great, bridging-joists alone are used to support the floor¬
ing-boards, and, it may be, ceiling-joists. They are laid
across the opening or void, and rest on the wall at each
end. A piece of timber, called a wall-plate, is interposed
between the ends of the joists and the wall, to equalize
their bearing.

A floor of bridging-joists, called a single-joisted floor, is
the strongest that can be made with a given quantity of
timber; but when the bearing is long, the joists, from their
elasticity, bend under a moving weight, and thus disturb
the ceiling below. When, therefore, the bearing is of such
length as to cause the joists to bend, their elasticity is
considerably diminished by placing underneath them
stronger timbers, called binding-joists. This construction
is called a double floor. When it is calculated that the
bearing will exceed the limit of strength of the binding-
joists, a third mode of construction is adopted, in which
larger timbers, called girders, are introduced to support
the binding-joists. This construction is called a framed
floor. These three kinds of construction shall now be
described and illustrated in order.

Plate XLII. Fig. 1. Bridging-joist or Single-joisted
Floors. —No. 1 is the plan of an apartment: a a a a are
the walls, b b the wall-plates, ccc c, «fec., the bridging-joists.
d d part of the flooring-boards. The bridging-joists are
usually placed from 10 to 12 inches apart: their scantling
is dependent on their length, their distance apart, and the
weight they have to carry. Rules for calculating their
size from these data will be found in the sequel.

No. 2 shows a section through the joists at right angles

FLOORS.

151

to their direction: c c are the bridging-joists, cl the edge
of one of the flooring-boards, e e the side of a ceiling-joist.
The ceiling-joists cross the bridging-joists at right angles,
as seen at e e e, No. 1, and are notched up to them and
fastened with nails. Sometimes every third or fourth
bridging-joist is made deeper than its fellows, and the
ceiling-joists are then fixed to them only. This has the
advantages of preventing sound passing so readily, and
making the ceiling stand better.

When the bearing of single joists exceeds 8 feet, they
should be strutted between, to prevent their twisting, and
to give them stillness. When the bearing exceeds 12 feet,
two rows of struts are necessary; and so on, adding a row
of struts for every increase of 4 feet in the bearing.

There are three modes of strutting employed. The
first and most simple is to insert a piece of board, nearly
of the depth of the joists, between every two joists, so as
to form a continuous line across. The struts should fit
rather tightly, and are simply nailed to keep them in
position. The second mode is to mortise a line of stout
pieces into the joists in a continuous line across, but the
mortises materially weaken the joists. The third mode
is represented in the section, No. 2: //are double struts, of
pieces from 3 to 4 inches wide, and 14 inch thick, crossing
each other, and nailed at the crossing to each other, and at
their ends to the joists. The struts should be cut at their
ends to the bevel proper for their inclination. To save the
trouble of boring holes for the nails, two slight cuts are
made at each end with a wide-set saw, and the strut is
nailed through these with clasp-nails. Of the three modes,
the last is the best. In No. 1, /// show three lines of struts.

When some joists would, from their position, run into
a fire-place or flues in a wall, it is improper to give them
a bearing there. In the case of the floor, Fig. 1, two short
timbers, called “trimmers/’ are introduced—one on each
side of the place to be cleared, with one end resting in the
wall, and the other framed into the third joist from it:
into the outer side of these, respectively, the end portions
of the two first joists are framed, the intermediate portion
being dispensed with. The joist into which the trimmers
are framed is called the “ trimming-joist,” and is made
thicker than the others, according to the number of joists
dependent on it for support. The hearth rests on a brick
arch turned between trimmer and wall. Trimming is
is also resorted to for stair and other openings.

In order to effectually prevent the passage of sound
from one story to another, a second floor, of rough board¬
ing, is sometimes inserted between the joists, and covered
with some non-conductor of sound,—the usual composition,
which is called in England pugging, and in Scotland deafen-
ing, being a mixture of lime mortar, earth, and the light
ashes from a smithy. This sound-boarding, or deafening¬
boarding, as the secondary floor is called, is supported on
fillets nailed to the sides of the joists. It is shown in the
section, Fig. 1, No. 2, where g g is the boarding, and li h
the fillets. Along the joist next the wall a fillet is nailed,
so as to fill up the space between the joist and the wall,
and admit of the pugging being used there to effectually
stop communication.

Fig. 2. Double Floor, or Floor with Binding-joists.
No. 1, is a plan of this kind of floor: a a are the binding-
joists, having their ends resting in the walls, but with
templates b b, which are short pieces of timber or stone,

interposed to lengthen their bearing; c c are the bridg¬
ing-joists, cl d the wall-plates, e e is a trimmer opposite
the fire-place, and / part of the flooring.

The section, No. 2, shows the connection of the parts;
a one of the binding-joists, c c the bridging-joists, notched
over the binding-joist, and g g the ceiling-joists under it.
Where the saving of depth in the framing is an object, •
the ceiling-joists are framed into the binding-joists by a
chase-mortise, as at h in the same figure. No. 3 is a sec¬
tion of the same floor parallel to the direction of the
bridging and ceiling joists. The same letters of reference
apply to the same parts in both figures.

Fig. 3. Framed Floor; the third mode of construction.
—No. 1 represents the plan: A A are the girders, with
their ends bearing on templates in the walls; bbb are the
binding-joists, and c c the bridging-joists; d d the wall-
plates ; e e the trimmer at fire-place. As the wall li con¬
tains flues along nearly all its length, the binding-joists do
not rest in it, but are framed into an additional girder A.
In this case, the tenon passes through the mortise, and is
I keyed on the other side, as shown in section in No. 4, in
which A is the wall-girder, and B the binding-joist.

No. 2 is a section through the girder, showing the man¬
ner of framing the binding-joists into it; A the girder,

B B the binding-joists, c c the bridging-joists, d d the
ceiling-joists. No. 3 is a section through the floor at right
angles to the last section: in it the same letters refer to
the same parts.

In framing the binding-joists into the girders, it is
necessary to effect a compromise between two evils; for
the tenon is stronger the nearer it is to the lower side of
the joist or binder on which it is formed, and the mortise
weakens the beam or girder the least when it is near the
upper side thereof; that is, when it is above the neutx - al
axis. A contrivance, therefore, called a “ tusk tenon, is
used, which is seen in the sections Nos. 2 and 4. The
tenon a is a little above the middle of the joist; but
its efficiency is increased by the tusk b, which relieves it
of its bearing, and the shoulder above the tenon is cut
back obliquely; and thus, without unduly weakening the
girder, a great depth of bearing is obtained for the joist.
It is necessary to take great care in fitting the bearing
parts to the corresponding parts of the mortise. The tenon
a should be equal to one-sixth of the depth of the girder;
and, according to the best practice, it should be inserted
at one-third the depth of the girder from the lower side.

It is a good practice to saw girders down the middle,
and to reverse the ends and bolt the halves together with
the sawn side outwards, with slips between to admit a
circulation of air. By this means the heart of the timber
can be examined, and the beam be rejected if unsound:
the timber being reduced to a smaller scantling also dries
more readily, and is rendered less liable to decay; and as
the butt and top of a tree are rarely of the same strength,
the girder must be improved by the process, which tends
to equalize its strength throughout.

When the bearing of a girder exceeds 22 feet, it is often
difficult to get timber of a sufficient size. In this case the
process of trussing the girder is resorted to. Various
modes of trussing are figured in Plates XL. and XLI., and
described in p. 149.

Variations in the Modes of Constructing Floors .—
In framed floors, especially in Scotland, binders are

152

PRACTICAL CARPENTRY AND JOINERY.

frequently omitted, the girders are more numerous, and
the bridging-joists are either notched down on them if the
space will admit, or tenoned into them if otherwise. The
ceiling-joists, too, in place of being notched or tenoned,
are suspended to the bridging-joists by small straps of
wood. Thus, the separation between the floor and the ceil-
* ing is more complete, and sound is less readily transmitted.

Plate XLIII. Fig. 1 is the plan, Fig. 2 a transverse
section across the direction of the girders, and Fig. 3 a
longitudinal section, at right angles to the last, ot such
a floor. The same letters refer to the same parts in all
three figures.

a a, girder; b b, bridging-joists dovetailed into the
girders; c c, ceiling-joists hung to the bridging-joists by
the straps tl d ; e e, fillets for the support of the sound¬
boarding or deafening-boards, nailed to the sides of the
bridging-joists; f f, sound-boarding lying loosely on the
fillets e e; g g, flooring-boards grooved and tongued;
h h, ceiling-laths; to to, plaster ceiling; n n, pugging or
deafening, composed generally of lime, earth, and forge
ashes in equal proportions.

Fig. I is the plan, and Fig. 5 a section of part of a
warehouse floor composed of girders a a a, supported by
cast-iron columns b b b, and supporting the floor of
planks c c c.

Figs. 6 and 7 are plan and section of part of a ware¬
house floor composed of trussed girders a a, supported
on iron columns b b, bridging-joists c c, and flooring-
boards d d. Fig. 8 is a vertical section through the
floor at right angles to that shown in Fig. 7; and Figs. 9
and 10 are plan and section of the head of the cast-iron
pillar, drawn to double the scale.

Plate XLIY. French Floors. — Fig. 1 is the plan of
a portion of a floor composed of joists sustaining floor¬
ing-boards ; and various modes of disposing the latter are
shown.

Fig. 2 is a longitudinal section on the line A B of Fig. 1;
and Fig. 3 a transverse section on the line c D of the
same figure. Fig. 4 is a transverse section on the broken
line E F.

a a are the joists on which the flooring-boards are
nailed; b b boards, the full width of the deals or other
timber out of which they are cut: these are gauged to a
width, and jointed together by a groove-and-tongue joint:
they are generally 1 inch to lj- inch thick, according
as the joists are nearer or further apart. Each board is
attached to each joist by two or three nails, according to
its width; and when all the boards are laid and nailed,
the joints are dressed off with a plane.

c c shows the floor composed of narrow deals, jointed
with groove and tongue, and each deal fastened by two
nails to each joist. When the flooring-boards are of
narrow deal, they are generally planed on both sides, to
reduce them to uniform thickness; and in this case the
upper surface of each joist is also planed, and all the joists
are carefully adjusted in the same perfectly level plane.
The end joints of the boards are arranged so that the
joints of two contiguous boards shall never fall on the
same joist; and care is taken, for the sake of appearance,
to make the joints of alternate boards fall on the same
straight line across the apartment, and at the middle of
the length of the intermediate boards. But when it is
possible to obtain boards the whole length of the apart-

| ment, the preference is given to a floor without end
! joints. The end joints of the boards are, in many cases,
made also with groove-and-tongue; but as the joints
occur only on the middle of a joist, and can be well
nailed, it is by many considered superfluous.

To render a floor still more solid, and prevent the passage
of sound, a second course of boarding is laid above the
first, with a space between. This is shown on the extreme
right in Fig. 1. // are fillets nailed on the first laid

boarding, conformably with the joists; g g are the boards
of the second floor; and to deafen the floor, the intervals
between the fillets are filled with lime-mortar, or with
lime and ashes, or with dry moss.

When lime-mortar is used, the upper boarding must be
laid before it is quite dry, lest the hammering required in
fixing it should break up the deafening. When dry moss
is used, it is driven in as the upper boards are laid, and
rammed hard. The second floor-boards do not require
their joints to be grooved and tongued, as the penetration
of dust, &c., is prevented by the grooving and tongueing
of the first floor.

h h shows another method of laying the flooring-boards,
where the joints meet in a straight line on a joist; and
i i shows the manner of laying, called in this country
herring-boning. In either of these two last methods,
the width of the board should not be less than a twelfth,
nor more than a sixth of its length; and the best mode
of jointing is by grooving and tongueing.

Where it is customary to wash floors with water, M.
Emy considers a plain joint preferable to a groove and-
tongue joint for the boarding; for when the board grows
old, the surface rots or decays, and the edge of the board,
in the case of the groove-and-tongue joint, having little
solidity, the fibres splinter off.

In nailing the boards in common floors, what are called
floor-nails are used. These have the shank square in
section, the head large and round, and its top shaped like
a very flat diamond point. For better work, nails called
pointes de Paris are used. The shank of this kind of nail
is cylindrical, and the head small, so that it may be driven
under the surface of the board by a punch. But still
better are the clous a parquet, which correspond to the
English flooring-brads.

Sometimes, too, screws are used; in which case the
upper surface of the boards is countersunk by a cylin¬
drical hole, so as to receive entirely the head of the nail,
and admit of the surface of the floor being planed off.
The cylindrical holes are filled in with pieces of wood of
the same kind as the boards, with their fibres in the
same direction, and strongly glued, and driven in with a
mallet. This method is used chiefly for oaken floors.

As it is not usual in France to cover the floors with
carpets, more attention is paid to the appearance of their
surface than with us. Sometimes, boards of different
kinds of wood are used, and combined so as to produce
contrast in colour, and in the direction of the fibres; and
even with one kind of wood agreeable combinations are
produced by merely contrasting the latter.

Floors of parquetry are not here touched upon, as be¬
longing, in France, more to the cabinet-maker than the
carpenter and joiner.

The flooring-boards cover only the upper surfaces of
the joists. Sometimes their other three faces are left

PLATE XLJT.

Fig. 1 JV?1.

J J J .

Fig.2JV?J

Fig. 3 JV?1.

Fig. 3 JV?2.

Fig. .1 F° 3.

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Scale, to details

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BLACKIE & SON. GLASGOW. EDINBURGH &: LONDON.

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FRENCH FLOORS AND FLOORS CONSTRUCTED OF SHORT TIMBERS.

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FLOORS.

153

visible; but more often their under side is covered to
form a ceiling to the apartment below.

At e, Fig. 3 is a section of the platfond or ceiling,
composed of thin planks, jointed longitudinally with a
groove-and-tongue joint, and nailed on the under side of
the joists. The deal used for this purpose being preferably
lime-tree, which in French is called tilleul, the covering
itself came to be called tillis.

The joints of the platfond boards are sometimes beaded,
and the whole platfond is generally painted like the rest of
the wood-work of the apartment.

Sometimes the platfond boarding does not stretch across
die under side of the joists, but is framed in between them,
as in Fig. 5, which is a section perpendicular to the direc¬
tion of the joists a a. When the fibres of the boards are
perpendicular to the direction of the joists, the work is
more solid. When the platfond boai'ding is flush with
the under side of the joist, as in Fig. 5, the tongue has
to be worked on the upper edge of the board, in which
case any shrinkage of the timber makes a visible opening;
but when the boarding is a little recessed, as in Figs. 7
and S, the tongue can be made on the under side, and
the shrinkage is not observed.

The platfonds are frequently decorated by being divided
into compartments by the joists, and these compartments
are enriched with paintings and sculptures. This soi’t of
platfond is much in use where plaster is not easily ob¬
tained. In Figs. 6, 7, and 8 is represented a platfond
of this kind. Fig. 6 is a plan of the ceiling looking up.
Fig. 7 is a section of the floor by a vertical plane passing
through A B in Fig. 6, and Fig. 8 another vertical section
by a plane perpendicular to the former on the line c D.
In these are shown the joists, the boarding of the floor,
and the cross pieces framed between the joists with mor¬
tise and tenon, to form the compartments. In Fig. 7, the
platfond boards are cut in the direction of their fibres,
which is perpendicular to the fibres of the joists, and in
Fig. 8 they are cut across the direction of their fibres. If
such a platfond were ornamented by painting, the shrink¬
age of the wood would obviously mar the work by making
the joints visible; the practice is therefore to prepare frames
to fit the panels or compartments, and on these to stretch
cloth, on which the ornamental painting is made.

At Paris, and in other places where plaster is abundant,
flooring of stone or tile is often substituted for the timber
floor. This mode of construction is shown in Figs. 9 and
10— Fig. 9 being a section on a line crossing the direction
of the joists, and Fig. 10 a section passing through the
middle of the interval between two joists; a a the joists,
b b laths of oak crossing the joists and nailed to them, c c
composition of plaster on which the stones or tiles are laid,
d d the stone or tile floor, e e laths to support the ceiling,
/pugging or deafening between the joists, g plaster ceil¬
ing united to the deafening through the interstices between
the laths.

The pugging, /, not only prevents the passage of sound,
but also of .disagreeable odours. It is therefore especially
used over kitchens and stables.

The pugging is formed of a coarse mortar, composed of
lime and pieces of stone or of old* plaster. It is from 3 to
4 inches thick at the middle of the interval between the
joists, but at the sides it is carried up to the under side ot
the laths which support the floor, thus forming a sort of

trough; and to make it better adhere to the wood, the
sides of the joists are studded with nails or wooden pins.

When this extent of pugging is not required, the under
side of the floor laths merely is plastered, as seen in the
sections, Figs. 11 and 12.

In floors of great span, the elasticity of the joists
would break the plaster ceilings attached to them. To
prevent this, one series of joists is used to carry the floor,
and another series of slenderer joists to carry the ceiling
A vertical section of this arrangement is shown in Fig.
13, in which a a are the flooring joists, bb the flooring-
boards, and o o the ceiling joists. When strong split laths
of oak are used, the ceiling joists are placed farther apart,
as in Fig. 14, in which a a are the floor joists, bb the
flooring boards, and o o the ceiling joists.

Combination of timbers of small scantling to form
floors of large span without intermediate support.

The first variety of such floors to be described is that
invented by Sebastien Serlio, a celebrated architect, who
was born in Bologna in 1518, and died at Paris in 1552.

On the principle of construction adopted by Serlio, the
principal timbers form great rectangular divisions, each
timber having one end supported by the wall and its
other end supported by the adjacent timber.

Four great joists, a a a a {Fig. 15), have each one of
their ends a' a a a', resting in the wall of a square apart¬
ment, and they are arranged perpendicularly to each other,
so that the outer end of each beam is supported by the
middle of the next adjoining.

This principle will be familiar to most of our readers
from the amusing illustration of it shown in books of
philosophical recreations, which consists in placing three
or four knives resting on the ends of their handles and
interlacing their blades by crossing them alternately, by
which means a considerable weight may be supported at
the meeting of their points.

The spaces between the main joists and the walls are
filled in with ordinary joists resting in the wall and
framed into the main joists, which serve as trimmers,
and the central square is filled in also with joists placed
diagoually, so that the weight may be borne equally by
the four main joists.

Fig. 16 is the plan of part of a floor of the Palace in the
Wood, at the Hague. It is an extension of the system of
Serlio. The hall, of which this is the floor, is 60 feet on
the side; and the figure represents one of the four angles.
The floor is constructed of small girders of oak, forming
300 square panels. Any one of the girders, such for example
as c, is tenoned at each end into two other girders, as
b and /, and carries the ends of other two girders e and d,
which are tenoned into it at the middle of its length.
Those girders which run on the walls are tenoned into
wall-plates C D, imbedded in, and fixed to the masonry.

The floor is composed of a double thickness of boards,
crossing each other at right angles, grooved and tongued,
and nailed to the girders. Fig. 17 is a section on the
line A B on the plan, showing the two thicknesses of
boards.

The girders are cut below so as to form a slight!}' con¬
cave surface, with the object of compensating for any sag¬
ging ; which would have had a disagreeable effect. The
result, also, is to diminish the weight at the centre of the
floor. In constructing this kind of floor, the sides should

154

PRACTICAL CARPENTRY AND JOINERY.

be divided into an unequal number of spaces, that there
may be a square compartment in the centre.

Fire-proof Floors.-^Oi late, much attention lias been
given in this country, and still more in France, to the
construction of fire-proof floors. In Plate XLIII., illus¬
trations are given of both the English and the French
methods of construction. Figs. 11 and 12 are longitudi¬
nal and transverse sections of Messrs. Fox and Barrett’s
system, a a are the main girders, consisting of a pair of
rolled joists; bb,cc, the ordinary joists, which are alter¬
nately 6 inches and 44 inches deep; d d, wooden bat¬
tens, about 1 inch square, resting on the bottom flanges
of the ordinary joists and main girders, and placed like
laths with a narrow space between them. On the top of
these is spread a layer of coarse mortar, which being
pressed down between the battens, forms a good surface
of attachment for the ceiling. The space between the
main girders and the spaces between the joists are then
filled in with concrete, e e, in which are imbedded small
quarterings or joists,//, to which the flooring-boards are
nailed. The concrete sets and consolidates the whole
floor into one slab.

Fig. 13 is a French fire-proof floor on the system of
Thrasne. It consists of rolled double-flanged girders, sup¬
porting common bridging-joists of timber, b b, which sup¬
port the flooring-boards. The iron girders are connected
together by transverse tie-rods bent round the lower
flanges. These support hollow bricks, c c, which are
cemented together with plaster of Paris.

In Fig. 14 is a section of a lighter floor. The gir¬
ders are connected by light iron ties bent over them;
and with these ties are interlaced cross bars of lio-ht iron.

so as to form together a complete trellis work, on which
is run plaster of Paris; flat boards being placed provision¬
ally below the trellis as a mould, till the plaster is set.

It is now necessary to put the reader in possession
of the means of calculating the strengths of the various
timbers which enter into the composition of the three
varieties of naked flooring already described, and to give,
as guides in construction, such practical rules as experi¬
ence has developed. This will best be done by taking
each description of timber in its order.

Primarily, it may be remarked, that flooring timbers
may be of such scantling as to be sufficiently strong for
safety, and yet be deficient in stiffness. A slight de¬
flection in the flooring would injure the ceilings of the
apartment below; and for that and other obvious reasons,
the rules for calculating the scantling of timbers in naked
flooring are based on stiffness—or resistance to deflection,
and not on absolute strength—or resistance to transverse
breaking-strain.

Wall-plates. —These, like all bearing timbers, should
be increased in dimensions as the span becomes longer.
It is not possible to give a rule by which to calculate this
inciease; nor is it necessary. Tredgold has laid down the
following proportions as a guide; and they are practically
safe:—

Rule. Bearing, 20 feet. Wall-plates, 4f by 3 inches.

” ^0 » „ 6 by 4 „

» 40 » „ by 5 „

V, here wall-plates extend over openings, and have to
sustain the ends of timbers, their scantling must be calcu¬

lated by the general rules for transverse strain. Wall-
plates should be carefully notched together at every angle
and return, and scarfed at every longitudinal joint. The
notch joint is shown in Plate XXXIX., Figs. 16 and 19,
and the scarf at Plate XXXIX., Figs. 1 to 15.

Single-joisted Floor .—The timber in the joists should
be so disposed that these may be as deep as is consistent
with the thickness requisite to prevent splitting in nail¬
ing the boards. The least thickness which it is safe to
give is 2 inches.

To find the depth of the joist, when its thickness and
the length of the bearing are given, and when the distance
apart from centre to centre is 12 inches.

Rule .—Divide the square of the length in feet by the
breadth in inches, and the cube root of the quotient, mul¬
tiplied by 2-2 for fir, and 2-3 for oak, will give the depth
in inches.

Example. — Required the depth of a joist when its
length is 15 feet and its breadth 3 inches.

15 x 15

---= 75, the cube root of which is 4 - 21. Therefore,

4-21 x 2-2 = 9-26 for fir, and 4’21 x 2-3 = 9-68 for oak.

But when joists are so thick as 3 inches, they injuriously

affect the keying of the ceiling; and in the example above

a better relation between the depth and thickness would

have been obtained by making the latter 2 inches. In

this case— 15x15 , - „ K ,, , , »

—^ -r= 112'5, the cube root of which

is 4'4; which multiplied by 2-2 and 2'3, gives 1056 for
fir, and 11 for oak.

All single-joisted floors, it has been already said, should
be strutted; and, according to the rule laid down, the
rows of struts should not be more than 5 or 6 feet apart.
Sometimes, to afford a better key to the plaster of the
ceiling, the under sides of the joists are crossed with battens
1^ by 1 inch, and 12 inches apart; and to these the laths
are nailed. This process is in Scotland called brandering

Trimmers and Trimming-joists .-—The thickness of the
trimmer is found by the rule given for binding-joists.
The trimming-joists are made 4 of an inch thicker for
every joist carried by the trimmer.

In trimming, tusk tenons should be used. The tongue
of the tenon should run at least 2 inches through, and be
draw-pinned; and if it does not completely fill the length
of the mortise, it should be wedged also. A proper fillet
requires to be nailed to the trimmer to form a skew-back
for the brick arch; and each trimmer should have two or
more bolts, according to its length, to tie it to the wall.

Binding-joists. —Binding-joists should not exceed 6 feet
apart. Their depth is often, but not necessarily, regulated
by the depth of the floor; and therefore it is necessary to
know how to find the breadth when the length and depth
are given, as well as to find the depth when the length
and breadth are given.

To find the breadth, ivhen the length and depth are
given.

Rule .—Divide the square of the length in feet by the cube
of the depth in inches, and the quotient, multiplied by 40
for fir, and 44 for oak, will give the breadth in inches.

To find the depth, when the length and breadth are
aiven.

Ride .—Divide the square of the length in feet by the
breadth in inches, and the cube root of the quotient, mul-

PARTITIONS.

155

tiplied by 3*42 for fir, and by 353 for oak, will give the
depth in inches.

Girders. — To find the depth of a girder, when the length
and breadth are given.

Rule .—Divide the square of the length in feet by the
breadth in inches, and the cube root of the quotient mul¬
tiplied by 4'2 for fir, and 4-84 for oak, will give the depth
in inches.

Example .—Let the length be 20 feet clear, and the

400

breadth 10 inches. Then —— = 40, the cube root of

which, 3*41, multiplied by 4 - 2 for fir, gives 14 - 32 inches
as the depth, say 144-

To find the breadth, when the length and depth are
given.

Ride .—Divide the square of the length in feet by the
cube of the depth in inches, and the quotient, multiplied
by 74 for fir, or 82 for oak, will give the breadth in inches.
Take the same data as before—

400

2936

•136, which multiplied by 74, gives as the breadth

10 inches.

Ceiling-joists . — Divide the length in feet by the cube
root of the breadth in inches, and multiply the quotient
by 0-64 for fir, or 0'67 for oak, to obtain the depth.

Let the length be 6 feet and the breadth 2 inches.

Then ^ = 4 - 7, which multiplied by 0‘64 = 3 inches.

The foregoing rules apply to ordinary cases of floors,
such as those of dwelling-houses. The greatest load on
such floors is when they are covered with people, equal to
about 120 lbs. per superficial foot, and allowing for the
weight of the floor, altogether about 150 lbs. per foot. In
warehouse floors, however, the absolute weight must be
taken at about 24 cwts. to the yard superficial, or 300 lbs.
per foot, and to allow for the shock caused by throwing
down heavy goods, 380 lbs. to the foot should be assumed
as the dead weight.

PARTITIONS.

Plate XLV.

Timber partitions are internal vertical divisions used
in the upper stories of a building, to make the separations
required in forming the apartments. "W hen such apart¬
ments are more numerous than in the lower stories, the
partitions should be so constructed as in no way to in¬
fluence, by their weight, the integrity of the ceilings of
the rooms beneath; and their weight therefore should
be transferred, by the system of framing, to the immove¬
able points of the structure.

To accomplish this, trussed or quartered partitions are
used. These are framed on the same principle as a king
or queen post rod; and are equally capable of bearing a
strain proportionate to the scantling of the timbeis ol
which they are composed.

Timber partitions should not be used in dividing the
ground floors into apartments, because of their liability
to be affected by damp. Stones or bricks are the pi'oper
materials to use in such places.

Plate XLY.—The figures in this plate are all examples
of trussed or quartered partitions.

Fig. 1 is a partition trussed on the principle of the

queen-post roof. The object aimed at in this case is to
resolve all the pressures or weights of the partition into
vertical or downward pressure on the walls, which in the
example before us is rendered easy by the symmetrical
arrangement of the openings. For it will be readily seen
that the pieces D D, with the intertie A A, the straining-
piece h, and the struts d, acting in the same manner as
roof principals, form a queen-post truss; the intertie A A
being rendered continuous as a tie-beam by the straps at
a a. The strut c serves to discharge the downward pres¬
sure at to to the wall; and the counter-struts, the pressure
at n to the foot of the queen-post D. The actual stability
of the partition, however, depends on the upper trussing;
that is, on the framing composed of the tie A A, the posts
D D, the principals d d, and the straining-piece h.

C is the headpiece of the partition, B its cill, l the door¬
posts, and i i the door-frame; b b, b b are the joists of
the floors above and below. The counter-braces, such as
g, prevent the sagging of the main struts, and give addi¬
tional stiffness and firmness to the framing.

This partition is at right angles to the direction of the
joists b b, and therefore when the door-posts do not fall
upon a joist, it is necessary to support them by pieces,
as k. The door-casing is shown, also the headpiece, and
the joists pf the floor above at h k.

Fig. 2, No. 1.—In this example, the intertie B, the post
D, and the struts g, form a king-post truss. The door¬
posts l, are secured by the straps at o and p, the intertie
is continuous, and the king-post is rendered so by the
strap at to. The cill is sustained by the strap at n, and
thus the whole system of the framing is dependent on the
upper portion of the truss: e and f are the struts, and k k
the doorcase; A the headpiece, and h h joists of the floor
above. •

In No. 2, the upper portion of the truss is on the queen-
post principle. D is the intertie, which, as before, is the
tie-beam ; e is the strut forming the principal, and / the
straining-piece. The door-posts A B are suspended by the
straps c c, E is the cill, d a strut or brace, g a counter-brace,
and c the headpiece.

Fig. 3, No. 1.—The partition in this case runs in the
direction of the joists A and B, and the truss serves to
give strength and stiffness to the floor. The upper por¬
tion of the truss, consisting of the intertie c, struts e,
straining-pieces f, and queen-posts D D, is still in this
example the main support of the framing. The straps l l
tie up the joist to the queen-posts, which form one door¬
post of each door: the other door-post, i, is framed into
the joist and intertie, and has its strut or brace g. Be¬
tween the queen-posts are counter-braces h. The straps
li k render the intertie continuous; to to is the door¬
case.

]q 0- 2.—In this partition there is only one door at the
side, and the framing is therefore not symmetrical. The
intertie D, the post C, and the strut h, are the parts essen¬
tial to secure the stability of the framing. The braces
f g i are as before. The joist B is suspended by the strap
to, and the strap l ties together the intertie D, the post C,
and the brace h. A row of struts or dwangs (Scot.) k k, is
introduced to give stiffness to the quarterings. This par¬
tition may be regarded as half of a queen-post truss, C
being one of the posts, and the wall serving the purpose
of the other.

156

PRACTICAL CARPENTRY AND JOINERY.

The imperfections in joints, and the tendency in all
timber to shrink, frequently cause settlements in framed
partitions, and consequent cracks in the plaster. To
diminish the risk of this damage, it is essential that all
the timbers be well seasoned, and the joints made with
the Greatest exactness. It is advisable to have all parti-
tions put up some time before they are plastered, so that
auy imperfection occasioned by warping or shrinking may
be seen in time, and remedied.

The arrises of all timbers of, or exceeding, 3 inches in
thickness should be taken off, to admit of a better key
for the plastering. The distance apart of the quarterings,
or filling-in timbers, should be adapted to the length of
the laths, which is generally about 4 feet; and, therefore,
when this is the case, the timbers should be about 1 foot
apart from centre to centre.

TIMBER-HOUSES.

Plates XLYI. and XLYII.

Houses and other edifices constructed of timber, and
raised on plans of which the perimeters are right lines, are
composed—

First, Of vertical walls of carpentry forming the fa 9 ade
and returns.

Second, Of interior partitions of carpentry, dividing the
interior space horizontally into apartments.

Third, Of floors or horizontal partitions, dividing the
interior space vertically into stages, stories, or floors.

Fourth, Of roofs which cover and defend the inclosure.

Fifth, Of stairs which afford access to the different
stories.

The use of timber walls, doubtless, preceded the use of
walls of masonry. Now, however, that the means of
construction are multiplied, wooden structures are only
erected in this country where other building material is
scarce and timber plenty, when cheapness without regard
to durability is aimed at, or when expedition in construc¬
tion is the object.

Walls constructed wholly of carpentry would consume
an immense quantity of timber, and would be more ex¬
pensive than if built of brick or stone : the timber, there¬
fore, in thick walls is used only in sufficient quantity to
form a frame-work which shall insure the stability of the
structure; and the interspaces or panels of the frames are
filled in with masonry of small stones, with thin brick
work, or with lath and plaster. This mode of construction
is in the north called post and pan or post and petrail,
and the square of framing is called a pan; but such erec¬
tions are more universally called half-timbered houses.

1 he combination of principles in these timber erections
varies very little. The general type of the compositions
is presented in Fig. 470, and it may be traced in all the
figures.

Ordinarily, to preserve the apartments and the timber
from damp, the level of the first floor is raised consider¬
ably above the soil, on a wall of masonry. Frequentlv,
the walls of the first story are formed entirely of masonry,
and the carpentry work commences above this, carried up
sometimes in the same plane, and sometimes projecting on
corbels.

jiiVeiy pan is composed of a ground-cill, which receives

the tenons of the principal posts, and these posts receive
the tenons of the horizontal beams, which are termed
bressummers, and which serve to carry the floors, and
are crowned at the top by beams corresponding to the
ground-cill, and which, like it, are mortised to receive the
tenons of the posts. These crowning beams are sometimes
also named bressummers: when they support the feet of
the rafters they are called raising - plates; but a general
name for them is capping-pieces, which better describes
their place and function.

The inclined timbers in the framing, termed braces,
divide the parallelograms formed by the vertical and hori¬
zontal timbers into triangles, and thus preserve the in¬
tegrity of their form. They, as well as all the other
pieces, should be very exactly fitted at their abutments,
to diminish as much as possible the creaking by the play
of the joints, caused by the flexibility of the long timbers.
Between the beams or bressummers, the door-posts, called
jamb- posts, and the window-posts, called by old writers
priclc-posts, are framed. The horizontal pieces framed
into these to form the heads of the openings are termed
transoms and lintels, and those introduced between the
principal horizontal timbers are called interduces or
interties.

The posts which have no other function to perform than
to sustain the edifice, are called posts simply.

The panels or spaces between the doors and windows,
and between the different posts, are filled in with vertical
pieces called quarters.

Pans which are of great length should be divided into
bays, either equal or symmetrical, by principal posts, which,
like those at the angles, should rise in one piece from the
ground-cill to the capping-piece. As these interrupt the
continuity of the bressummers, the ends of the bressum¬
mers which are framed into them should be tied together
by iron straps within and without. All the beams, too,
which are framed into the corner posts, and have return
beams, should be tied in the same manner by a right-
angled strap embracing the post.

When the timber framing of the carcase is completed,
all the intervals between the posts are, in the case of post
and petrail construction, filled in with small stones or
bricks set in good mortar. When the timbering is to re¬
main visible, as is generally the case in such houses, the
masonry or brick-work filling is done with great neatness,
and the timbers are dressed on their exposed faces before
they are framed.

When this mode of construction is not adopted, and
the timbers are to be hid, the exterior and interior sur¬
faces are lathed, and the space between is either left void
or, which is better, filled with some non-conductor of heat,
and then the lathing is covered with plaster and deco¬
rated with the usual architectural decorations of strings,
cornices, architraves, &c.

In place of lathing and plastering the exterior surface,
it may be covered with boarding, and wooden mouldings
may be applied in decoration, as in Plate XLVI., Fig. 3.

To insure better connection between the masonry fill¬
ing, the plaster, and the timber, it was formerly the cus¬
tom to groove the latter, and to plant it all over with
pins of wood: now this is seldom done.

In Sweden, where timber-houses are almost universally
employed, the mode of construction is the same now as

PLATE XLYI.

so Feet

White

A.W.Lowrv /r

BLACKIE SON, GLASC-OtA , EDTN B V R(’II .V- LON 0 O X

PI ATE XL VLL.

SraLe. for Fiq . 3 .

40 J 50

—I-'-4—

= 1 =

Rafter

Section, at C. D .

3T/to.

Seale/ for Fins. 1 and.

A. F. Orridge. del.

BLACKIF, &.• SON . GLASGOW,EDINBURGH & LONDON.

W.A. .Bea r er. Sc.

TIMBER-HOUSES.

157

it has been for centuries, and is also of the type here
described.

A foundation plinth of rough granite is first laid to a
height of 2 feet above the ground. On this are laid the
ground-cills, with mortise holes for the uprights. The up¬
rights are from 6 to 8 inches square, and are mortised to
receive the bressunnners, and are otherwise tied together
by the interties, window-cills, lintels, and braces. When
this framing is completed, it is covered on the inside
with |-inch deal boarding, and on the outer side with two
thicknesses of f-inch deal, the first laid horizontally and
the second vertically.

The vertical joints are again covered by slips nailed to
them. The space between the outer and inner lining is

Fig. 469.

S3§ Wm WMmM

.: y ifv;; ' ■{.'/y ,.; ...u .. 1 -..

filled in with shavings, moss, or some non-conducting sub¬
stance (see Fig. 469).

The lowest floor is double lined, and filled in between
the linings in the same manner; and houses thus con¬
structed are impervious to the colds of winter. A house
of this kind can be erected in a few clays, and where
timber is abundant, costs veiy little. But its liability
to be destroyed by fire renders it a very hazardous kind
of building.

Fig. 470 is the elevation of part of one bay of a building
constructed of wood on stone pillars. The ground-cill a. is

pillars. These pieces are called in French poitrail, evidently
the same as the petrail of the north country, and which
gives to this style of building the name ol post and petrail.

In order to throw the weight as much as possible over
the stone pillars, discharging struts o I) are introduced at
each story. These sustain the principal posts P, and are
framed into them, and into the ground-cill, in the same way
that a principal rafter is framed into its king-post and tie-
beam, and is like it secured by iron straps d. The braces
in the panels F K are halved on each other, and form the
St. Andrew’s cross, for the sake both of effect and stiffness.
The horizontal pieces ooo are the in ter ties.

The figures given in Plate XL^ I., and about to be
described, are the kind of constructions in timber which
obtain in the present day. The more ancient edifices
were constructed much in the same manner, the framing
applicable to all such constructions not being susceptible

of great variety. Fig. 3, Plate XLVII., is the elevation
of the gable of a modern imitation of an ancient timber
gable, in which the arrangement of the timber forms the
principal decoration.

In designing pans of wood, the greatest care should be
taken to make all the principal timbers coincide verti¬
cally, so that from the ground-cill to the headpiece the
principal posts, story-posts, door-posts, and even the quar-
terings respectively of each story should be in the same
vertical line, so that they may not have the effect of twist¬
ing or bending the horizontal timbers. For the same reason
the openings of the doors and windows should be com¬
prised within the same vertical lines. This sound rule of
construction, void over void and solid over solid, is appli¬
cable to timber constructions as well as to those of stone or
brick; and produces, by the symmetry and correspondence
of parts which arise from its being adhered to, an effect
which is always agreeable.

When it is necessary to make one or more of the open¬
ings of a greater width than the others, as a gateway for
example, the panel in which it is made should, if possible,
be carried up; and the weight of the intermediate framing
above should be discharged by struts to the posts which
form the panel, so that its lintel should have nothing to
carry but the short quarterings between it and the cills of
the windows above.

As the charge to be sustained by the timbers diminishes
story by story as they ascend, it is customary and proper
to diminish their scantling. The batter which ensues is
confined to the exterior, the interior surface being kept
in the same plane throughout. The effect of this is to
increase the stability of the edifice by extending its base.

Plate XLYI., Figs. 1 and 2. —In these the principles
of construction described are exemplified, the ground-cill
A, principal posts b', bressummer E c, and diagonal struts
B B and D D, form a truss which sustains the structure. The
parts are connected by mortise-and-tenon joints, and se¬
cured by straps ab c d eg, &c. The principal posts, story-
posts, and quarterings of both stories are in the same ver¬
tical lines.

Fig. 3 shows timber construction adapted to modern
street architecture: A, the ground-cill; bfg, one of the
principal posts; B, the angle principal; cde, bressuinmers
scarfed at the points d, b, and e, and secured by straps
ab c dfg; K, an additional story-post at the angle.

Plate XLYI I.— Figs. 1 and 2 show the framing of the
Townhall of Milford, Massachusetts. Fig. 1 is an eleva¬
tion of the side of the structure: A A, the ground-cill; B B,
bressummer; D D, intertie; CC, capping-piece. The princi¬
pal vertical posts K L, K L, K L, correspond in number and
position with the principals of the roof, and all the other
principal timbers are in the same vertical lines. The same
principle of construction is developed in the end elevation,
F-ig. 2, where A A is the ground-cill; A C, F F, principal posts,
which are continued to form the tower shown in Plate
XXXV? ; b B, bressummer; E E, E E, interties, forming
trusses with B B by means of queen-bolts and struts h h ,;
g k m n are braces, and dd, dd, interties above the win¬
dows and doors.

Fig. 3 is the elevation of a gable at Chester, a recent
work, in which the ancient style is elegantly imitated,
the arrangement of the timbers forming the principal
decoration: A A is a lintel supported by the corbels, a a ;

158

PRACTICAL CARPENTRY AND JOINERY.

I) d, principal posts; B B, intertie; C c, capping-piece; E E,
story-posts; eeee, quarterings, the panels between which
are filled in with ornamental ribs.

Fig. 4 is a barge-board or gable-board from a house at
Droitwich, and Fig. 5 is an example of a gable-board from
a house at Worcester.

BRIDGES.

A bridge is a platform supported at intervals to form a
roadway over a river, valley, or other depression.

Bridges are as various in kind as the circumstances
that necessitate their construction. They are formed of
various materials, as timber, iron, stone, and brick, or of
the combination of all these. In the timber bridge, for
example, to the consideration of which this introduction
properly refers, tliei'e may be piers or abutments of stone
or brickwork, and the carpenter can only combine his
timbers by the aid of the straps, bolts, hoops, screws,
nuts, washers, and other ironwork supplied by the smith.

In bridges constructed with arches of masonry or brick¬
work, the aid of the carpenter is sometimes required in
preparing the foundation by a cofferdam, or in making
platforms of timber on which the stones or bricks are
placed, and his utmost skill is, in large constructions,
always called forth in designing and constructing the
centres or mould on which the arch is formed.

Of all the materials used in bridge construction, timber,
connected together by iron, is the most extensively avail¬
able for the platform, and although liable to serious objec¬
tions on account of its destructibility by natural decay
or by accident, and its liability to change under hygro-
metric influence, yet the readiness with which it can be
made available, its cheapness, and the ease with which it
can be renewed, added to the improvements introduced
by science to obviate its defects, render it in new coun¬
tries, and especially in those where the material is abun¬
dant, such as America, one of the most important auxili¬
aries in civilization.

It is to these countries accordingly, and preferably to
America, that it is necessary to look for the boldest ex¬
amples of timber-bridge construction.

The most simple support for a roadway is a series of
longitudinal timbers laid between two piers or abutments.
When the span becomes considerable, single beams are
insufficient and framed trusses become necessary. The
consideration of the case of a single beam involves the
principle of a framed truss. The same forces exist in both,
the manner of resisting them alone is different.

The forces which act on a single beam, when loaded
either uniformly or at certain points of its length, have
already been investigated (page 123 et seq .); but it may be
well to reproduce in this place a summary of the results,
and to extend somewhat the consideration of the subject.

In any loaded beam, as we have seen, the fibres on
the upper side are compressed, while those on the lower
side are extended; and within the elastic limits those
forces are equal. The intensity of the strain, also, varies
directly as the distance of any fibre from the neutral axis.
But there is another series of forces which has now to be
considered.

Whatever be the form of a beam, it is always necessary
that the area of cross section at the points of support be

sufficient to resist the force tending to crush the fibres in
a direction perpendicular to their length. ‘

This resistance is proportioned directly to the area, and
therefore the dimensions at the point of support must
never be less than is obtained by making the resistance
per square inch, multiplied by the breadth and depth,
equal to the weight, or, in other words, by dividing the
weight by the resistance per square inch, to find the area
of section.

This vertical strain in a loaded beam occurs at all points
between the middle and the ends. In the middle point it
is almost nothing; at each end it is equal to half the
weight of the beam and its load; and at intermediate
points, it is proportional to the distance from the middle
of the span—a consideration of great importance in bridge
construction.

In what follows, an endeavour is made to place before
the reader succinctly, and in a manner suited to the cha¬
racter of this work, the reasoning of Mr. Haupt on the
principles of bridge construction.

If the parts of a beam near the neutral axis, which, we
have seen, are little strained and oppose but little resist¬
ance, could be removed; and if the same amount of material
could be disposed at a greater distance from the axis; the
strength and stiffness would be increased in exact propor¬
tion to the distance at which it could be made to act. Hence,
in designing: a bridge truss, the material, to resist the hori-
zontal strain, must be placed as far from the neutral axis
as the nature of the structure will allow.

Suppose to the single beam A B (Fig. 471) we add another
C D, and unite them by vertical connections, then it might

Fig. 471.

be supposed that we were doing as above suggested; that
is, making a compound beam by disposing the material ad¬
vantageously at the greatest distance from the neutral axis.
But it is not so. There are only two beams resisting with
their individual strength and stiffness the load, which is
increased by the weight of the vertical connections, and
they would sink under the pressure into the curve shown
by the dotted lines. It is necessary, therefore, to use
some means whereby the two beams will act as one, and
their flexure under pressure be prevented. This is found in
the use of braces, as in the next figure (472); and we shall

Fig 472.

C CL

proceed to consider what effect a load would produce on
a truss so formed.

The load being uniformly distributed, the depression in
the case of flexure will be greatest in the middle, and the
diagonals of the rectangles ab, c d, will have a tendency
to shorten. But, as the braces are incapable of yielding

BRIDGES.

159

in the direction of their length, the shortening cannot
take place, neither can the flexure. A truss of this de¬
scription, therefore, when properly proportioned, is capa¬
ble of resisting the action of a uniform load, as in the
case of an aqueduct.

If the load is not uniformly distributed, the pressures will
be found thus:—Let the weight be applied at some point c
(Fig. 473), and represented by c P. Now resolve this into
its components in the direction CA,CB, and construct the
parallelogram Pm,Co, then c to will represent the strain

Fig. 473.

x c

on C B and C o the strain in the direction c A. By trans¬
ferring the force c to to the point B, and resolving it into
vertical and horizontal components, the vertical pressure
on B will be found equal to c n and that on A equal to
n P. That is, the pressures on A and B are directly pro¬
portional to their distance from the place of the applica¬
tion of the load.

In the same manner, if the load were at B, it would be
discharged by direct lines to A and B.

The effect of the oblique force c A acting on K is to force
it upwards, and the direction and magnitude of the strain
would be the diagonal of a parallelogram constructed on
A c, C R.

The consequence of this is, that in a truss a weight at
one side produces a tendency to rise at the other side,
and, therefore, while the diagonals of the loaded side are
compressed those of the unloaded side are extended.

Hence, while the simple truss shown in the last two
figures is perfectly sufficient for a structure uniformly
loaded, because the weight on one side is balanced by the
weight on the other, it is not sufficient for one subjected
to a variable load.

For a variable load, it is therefore necessary either that
the braces should be made to resist extension by having
iron ties added to them, or that other braces to resist com¬
pression in the opposite direction should be introduced; and
thus we obtain a truss composed of four elements, namely,

Fig. 474.

A e S' 7i B

chords A B and c D (Fig. 474), vertical ties ef,g h, k m,
braces e C, g f g to, k D, and counter-braces A fe h, k h,
B to, or, in place of the latter, tie-rods added to the braces.

It has been shown that in any of the parallelograms of
such a truss as has been described, the action of a load
is to compress the braces a d, a b, and to extend the
counter-braces a b, a c. Suppose, (Fig. 475) that the
counter-braces have been extended to the length a to,
and the braces compressed to an equal extent; then if a
wedge be closely fitted into the interval a to, it will
neither have any effect on the framing, nor will itself be
affected in any way so long as the weight which has pro¬

duced the flexure continues. But on the removal of the
weight, the wedge becomes compressed by the effort of the
truss to return to its normal condition. This effort is re-
rig. 475 . sisted by the wedge, and

there is, consequently, a
strain on the counter-brace
equal to that which was pro¬
duced by the action of the
weight. The effect of the
addition of a similar weight,
therefore, would be to relieve the strain on the counter¬
brace, without adding anything to the strain on the
brace a d.

As the vibration of a bridge is caused by its effort to
regain its normal form after the change of form produced
by a passing load, it is evident that it will be much
diminished by counterbracing in the way described.

There is thus required for the proper construction of a
bridge at least four sets of timbers.

First, The horizontal main timbers, called chords.

Second, The vertical pieces uniting those, called ties.

Third, The main braces.

Fourth, The counter-braces; and to these may be added
arch-braces, which will be noticed hereafter.

In proportioning these several parts, regard must be
had to the following considerations-

The chords being unsupported in the intervals between,
the ties must be so strong that no sagging or deflection
can take place. The braces must be incapable of yielding
by lateral bending. Now, the proper proportions of these
depend on the distance apart between the ties, and in
arranging this, care must be taken to avoid extremes of
number on the one hand, and weakness on the other.

To trace the effects of a weight through the system of
timbers which compose the truss of a bridge, would be a
very complex problem. It would, moreover, be beyond
the scope of this work, and would exceed what has been
assumed as the limit of mathematical knowledge of the
majority of its readers. Such investigations, however,
have been made, and their results assume the form of
maxims of construction. Some of the most useful of these
maxims, gleaned from the work of Mr. Haupt, are now
presented to the reader; and his investigation of the
weights and strains on the timbers and ironwork of the
Sherman's Creek Bridge is given at length in p. 165-168.

As the parts of the frame act only in distributing the
forces which are applied to it, and, whatever be the incli¬
nation of the braces, the pressure on the abutment and
the strain upon the centre of the chords must remain the
same, it might be inferred that the degree of inclination
of the braces was of little consequence, but such is not
the case. For the braces must not be so long as to yield
by lateral flexure, and the chords must be supported at
such intervals that no injurious flexure shall be produced
by the passage of a load.

Again, as the ties approach each other the angle of the
brace increases; and the number of ties and braces, and
consequently the weight of the structure, is increased.

When the maximum load and the size of the chords are
known, the limit of the intervals can be determined, by
considering the portion of the chord between every two
ties, as in the condition of a beam supported at both ends
and loaded in the middle.

1G0

PRACTICAL CARPENTRY AND JOINERY.

It has been shown that the strain upon the counter¬
braces is not increased by the passing of a load; and that
by driving a wedge at the joint of the eounter-braee, a
strain can be permanently thrown on the brace, equal to
that which would result from the passage of the maxi¬
mum load. It will therefore be safe to calculate the
strength of the counter-brace by the condition that it
shall produce the required compression on the brace.
This strain upon the counter-brace is equal to the pres¬
sure on the brace. Hence, as any accidental load that can
ever act at a single point is small when compared with
the uniform load, and it is to give the required immo¬
bility under the accidental load that the counterbracing is
used, it follows that the counter-braces may be very small
as compared with the other timbers.

It has also been shown that in a single beam supported
at the ends and uniformly loaded, there exist horizontal
and vertical forces at every point except the middle and
the extremities. At the middle, the strains are altogether
horizontal; but at other points, the distances to the extre¬
mities being unequal, the horizontal strains no longer
balance each other, and the difference must be compen¬
sated by a cross strain on the fibres.

This vertical force, at zero at the centre, increases to¬
wards the extremities, where it is equal to one-half the
whole uniform weight, and in this case the increase is
proportional to the distance from the centre. Hence it
follows that the ties and braces which resist the vertical
forces may be smaller at the centre than at the abut¬
ments. Each successive brace, therefore, as it recedes
from the centre, should theoretically be increased in size;
but as this adds greatly to the trouble and expense of
framing, it is better in practice to make them uniform in
size, and to compensate for the additional strains at the
ends by adding other braces called circh-braces.

In the construction of a bridge with arch-braces, the
simplest plan is to depend upon the latter to sustain the
weight of the structure, having only a light truss with
counter-braces or diagonal ties to give connection and stiff¬
ness to the various parts, and to resist the action of vari¬
able loads.

Instead of arch-braces, arches are sometimes used, which
are beneficial, and produce somewhat the same effects as
the arch-braces.

An arch of timber cannot alone be depended on to sus¬
tain a variable load; it requires always to be connected
with a system of trussing to give it the necessary stiffness.

The importance of Laving abeam continuous over its
supports has been pointed out; and equally great advan¬
tages also accrue from having a bridge in which there
are several spans in succession connected over the supports
so as to be made continuous. The strength of the chords
in the central span of a series would be double that of
the same span disconnected; and the extreme spans would
be stronger, in the ratio of three to two, than if discon¬
nected.

In applying these results to practice, it is necessary
first to determine the weight of the bridge and its load.
I he weight of the bridge is found by preparing a bill of
timbers of assumed dimensions, and multiplying the num¬
ber of cubic feet by the weight of a cubic foot of the
material, which may be taken on an average at 35 lbs.
I he average quantity of material in the Howe bridges on

the Philadelphia railroad is about 30 cubic feet per foot
lineal; and therefore this may be assumed as a guide in
calculations.

The greatest load a bridge can sustain would consist of
locomotive engines, which would give 1 ton per foot lineal
of the bridge.

Hence 1 ton per foot for the load, and half a ton per foot
for the weight of the structure, may be assumed as a maxi¬
mum load when the span does not exceed 200 feet.

The safe strain for timber will be considered as 1000 lbs.
per square inch, and for iron ten times as much.

To find the strain on the chords.

1 . The strain of compression on the upper chord.—
Multiply half the weight of the bridge by the distance of
the centre of gravity from the abutment (which is nearly
a quarter of the span), and divide the product by the
height of the truss, measured from the centres of the upper
and lower chords.

Example .—-Let the span be 160 feet, and the height
17 feet; required the cross section of the upper chord in
the centre.

The weight at ton per foot is 480,000 lbs.; and as¬
suming the depth of the chords at 12 inches, the distance
from centre to centre will be 16 feet.

Then, according to the rule, -g~x~T6-— 600,000,

as the maximum strain at the centre; which, divided by
1000 lbs., as the resistance per square inch, gives 600
square inches of section; which, divided by 12 inches, the
depth of the chord, gives a total breadth of 50 inches, or
25 inches to each truss, if there are two trusses.

2 . The strain of tension on the lower chord at the
centre .—This is equal to the compressive strain on the
upper chord; but from the occurrence of joints, the power
of resistance is diminished. To compensate this, the quan¬
tity of material is increased to such an extent that the
resisting area shall be obtained exclusive of the timber in
which the joint occurs. A good practical way of doing
this is to make the upper chord of'three, and the lower
chord of four timbers to each truss; and if a joint then
should occur in each panel, each piece of timber should
be equal to the length of four panels; and three of the
four timbers should therefore contain sufficient resisting
area for the whole strain.

3. Strain at the ends of the chords .—In a bridge of a
single span, the horizontal strain at the end of the brace
nearest the abutment will equal the weight on the brace,
multiplied by the co-tangent of its inclination. If the
inclination be 45°, the horizontal strain will be equal to
the vertical weight. If the angle with the horizontal line
is greater than 45°, the strain will be less than the weight.
As this is generally the case, it is safe to assume the hori¬
zontal strain at the end of the chord as equal to the ver¬
tical force acting on the first brace.

This vertical force is half of the whole weight of 12 feet
wide; and it is proper to take the strain on the whole
panel as the minimum strain. The weight on one panel
is 36,000 pounds; requiring a cross section of 36 inches,
or 9 inches to a tie, and 11 j- to a brace. This cross sec¬
tion, for a brace of 20 feet long, is so small that it would
yield with lateral flexure; and recourse must therefore be
had to the formula for long posts, unless the braces are
supported at the middle of their length.

BRIDGES.

161

The dimensions at the ends and at the centre having
been obtained, the intermediate timbers should increase
from the former towards the latter by regular additions.

4. The strain on the Counter-hraces .—It has been shown
that the strain on any counter-brace is equal to that
produced by the action of a variable load on the corre¬
sponding brace. It will consequently be equal to the
strain on the braces of the middle panel; and if each
panel contains two braces and one counter-brace, the size
of the latter should be uniform, and equal to 30 square
inches, in the truss of the dimensions assumed. Hence,
if supported in the middle, the counter-braces should be
0x5 inches.

5. Horizontal Ties and Braces at top and bottom.—The
use of these is to give lateral stiffness to the bridge, and
guard against the effects of the wind, which is the greatest
disturbing cause. Assuming the force of the wind to be
15 lbs. per square foot, and the truss to be close boarded,
and its height 18 feet, the total force over the surface
would be 43,200 lbs. or 21,600 lbs. to each series of braces
at the top and bottom of the bridge. If the calculation,
therefore, is continued with the same dimensions as before,
the half weight will be 240,000 lbs., and the cross section
to resist it 240 square inches, or little more than one-third
of the dimensions at the centre.

The dimensions at the ends and at the centre having
been obtained, a uniform increase between the points can
be made.

The size of the chords might be deduced from the for¬
mula applicable to a beam supported at both ends and
loaded in the middle, in respect of that portion of them
which lies between any two posts; but as the dimensions
determined in this way are smaller, the rule already given
is safer; and the excess of size is amply sufficient to resist
the additional cross strain from any passing load.

6. The strain on the Ties and Braces .—The end braces
which project from the abutments bear the whole of the
load, and there is a decrease of strain to the centre. The
weight of the bridge, as before, is 480,000 lbs., or 240,000
lbs. at each end; which, at 1000 lbs. per square inch, is
240 square inches of section for the ties if of wood, and
24 inches if of iron. If the panels be 12 feet wide, and
the height, as before, 16 feet, the length of the diagonal
or brace will be 20 feet, and the strain on it will be

240,000 X 20 _ 300,000 p 3S _ The section, therefore, will

require to contain 300 square inches, which, divided
among four braces, gives 75 square inches to each.

The strain at the middle is theoretically nothing, but in
practice it is the same as that on the panel, on the above
assumption. This would be estimated as the strain on a
bridge produced by a uniform load; and if the bracing is iu
squares, the diagonals will be to the sides as 1 '4:1 nearly.

The strain on the end braces will be*—^— X 1'4 = 15,120,

which, at 1000 lbs. per inch, gives only 1512 square inches
to resist the strain. Practically, the end braces in this
case might be 5x4 inches, and those at the middle of the
span very much lighter. In the middle panel, they might
even be omitted without injury.

Diagonal Braces and Knee-braces .—A lien the load-
way is on the top of the truss, braces occupying the direc¬
tion of diagonals to the cross section of the truss can be

used to prevent side motion; but where the roadway is on
the bottom, knee-braces must be used. Experience has
shown that scantlings 7x5 are large enough for diagonal
braces, and 6x5 for knee-braces.

Floor Beams .—The formula for these is the same as
in the case of other floors. The case assumed by Mr.
Haupt for the same truss is as follows:—Length of floor-
beam between supports 14 feet, depth of same 14 inches,
greatest load equal to 6 tons, applied at the centre; re¬
quired the breadth, so that the deflection shall not exceed
one-fortieth of an inch to a foot.

B =

w l' 2 x ‘0125

D 3

13,440 x I4 2 x -0125
14 3

, or, substituting the figures,

= 12 inches.

Timber Arches.— Mr. Haupt considers that the usual
course of making a truss sufficiently strong to resist the
weight, and then adding arches as greater security, should
be reversed; and that the arches should be made the main
dependence, and a light truss be used in combination with
them, to prevent change of form, and to give the proper
support to the roadway. He assumes, for the sake of illus¬
tration, the same data as before, namely, the span at 160
feet, the rise of the arches, four in number, 20 feet, and
the weight on the bridge 1^ ton per foot.

The weight is then 268,800 lbs. to each half of the
bridge, and the strain on the arches in the centre is

268 1 800o<jl0 _ 537,000 lbs.,requiring 537'6 inches of cross
20

section. Four arches 16 inches deep and 8'4 inches wide
could supply the amount of material.

The compression at the ends will be to that at the
centre as 40 2 -4- 20 2 : 40, or as 2 2 + 1 : 2; hence it
will be 537,600 x Hnearly = 601,055 lbs., and will require
601 square inches of section; therefore, if the arch is 8-4
inches wide as before, its depth must be 18 inches nearly.

As in this case the whole of the weight is sustained by
the arch, and the truss is used only to stiffen it and carry
the roadway, the braces have no more strain at the ends
than at the centre; and the principle of proportioning
them in arithmetical progression from the centre to the
end is no longer applicable.

With scarcely an exception, the examples of bridges
contained in Plates XLVIII. and LYI. maybe resolved into

the following element¬
ary figures:—

1. Trusses which are
below the roadway, and
which depend for their
stability on the abut¬
ments.

Of these, Fig. 476 is the type, and the illustrations
will be found in Figs. 3, 4, 6, and 7, Plate XLVIII.;'
Figs. 1 and 9, Plate XLIX.; Fig. 1, Plate LII.; Fig. 1,
Fig . 477 Plate LIII., and Fig. 1,

Plate LV.

2. Trusses which are
above the roadway, and
have only vertical pres¬
sure.

Of these, Fig. 477 is the type, and the illustration will
be found in Plate L.

3. Trusses below the roadway, composed of timber

Fig. 476.

162

PRACTICAL CARPENTRY AND JOINERY.

arches, and ties and braces, but dependent on the abut¬
ments for resistance to lateral thrust, the type of which
is Fig. 47S. Fig. 478.

4. Trusses above or
below the roadway, com¬
posed of timber arches,
and ties and braces, and
which have only vertical
pressure, the type of which is Fig. 479, and the illus¬
trations Figs. 1, 5, and 12, Plate LIY.

5. Lattice trusses above
the roadway, the illus¬
tration of which is Fig.

8 , Plate LIY.

The foregoing analysis
will enable the reader to
find at a glance the illustration he requires, and with this
key, the plates will now be described in their order.

Plate XLV1II.— Fig. 1 is the elevation of a timber
draw-bridge on the Gotha Canal, Sweden.

Fig. 2. Plan of the draw-bridge. In this, part of the
floor timbers is removed, in order to show the framing,
and the position of the rack for moving the bridge.

Fig. 3 is the elevation of the simplest form of trussing
for a bridge, when the roadway is above the truss, and the
abutments are sufficiently strong to resist the lateral
thrust. A chord, B strut, c straining-piece. Examples of
the same kind of truss, applied in works recently executed,
will be found in Plate XLIX., Figs. 9, 10 , and 11, and
Plate LV., Fig. 1 .

Fig. 4. Elevation of a bridge truss, in which the chord-
piece, A A, is in two lengths, joined in the middle of the
span, and the fence of the roadway is used as an auxiliary
truss, with a king-bolt, B. This would be improved in
sustaining a variable load by introducing counter-bracing.

Fig. 5. The elevation of a bridge truss, composed of
chord piece A, laminated arch B, struts and straining-
piece C C, and cross-pieces D, connecting the framing.
Further illustrations of the same principle in detail will
be found in Plate LI., Figs. 1 and 6 , in Plate LIII, Fig.
3, and in Plate LVI., Fig. 1 .

Fig. fi shows the elevation of a timber bridge of 34 feet
span, with chord-piece A, two sets of struts C C, strain¬
ing-piece B, and suspending-pieces D.

Illustrations of the extended application of this prin¬
ciple of framing will be found in the next figure in this
plate, in Plate XLIX., Fig. 1 , Plate LII., Plate LIII.,
Fig. 1 , and Plate LV., Fig. 1 .

Fig. 7. In this truss there are chord-pieces C, straining-
pieces D d, struts E F G, counter-struts, or radial posts, H,
transverse connecting pieces M M, radial straps a b, a b,
cushion and straining-pieces to the under side of the truss
K L, and cast-iron shoes, c, fixed to the abutment to receive
the ends of the struts. The joints of the struts, and between
the struts and straining-pieces, are secured by straps e, d.

Although from the contour of the under side of this truss,
and the radiating posts and straps, it assumes the form of
an arch, it has none of its characteristics: it is simply a
truss of the same nature as those belonging- to the class
illustrated in Fig. 6 ; and the material is not so well dis¬
posed as in the examples of that class above referred to,
and especially as in the following example.

Plate XLIX.— Figs. 1 to 8 show the elevation, plan, and

Fig. 47U.

details of construction, of a timber bridge erected over the
Spey at Laggan Kirk, by Telford. In this example, the
material is employed most judiciously to obtain the f
greatest l'esult by the smallest means; and the details, as
in all the works of this excellent engineer, are worthy of
careful study. The work belongs to Class No. 2 of the
generalization. As the dimensions of the timbers are
figured on the drawings, and the plan, elevation, and sec¬
tion explain themselves, it is only necessary to note that
Figs. 4, 5, and 6 represent the details of the cast-iron
sockets which serve to unite the struts to the straining-
pieces, and Figs. 7 and 8, the details of the cast-iron shoe
attached to the abutments to receive the ends of the struts.

Fig. 9 is a side elevation, Fig. 10 a transverse section,
and Fig. 11 the plan, of part of a timber bridge, belonging
to Class No. 1.

In this, there are the usual chord-pieces A, straining-
pieces B, struts u. The piers are piles d d d, and are
connected by two rows of waling timbers—one, g g, under
the chord-pieces, and the other under the abutment of the
struts. The chord-pieces are further secured to the heads
of the piles by straps c d, seen in Fig. 11.

Fig. 10 is a section on the line L K of Figs. 9 and 11.

Plate L.—Timber bridge over the river Don, at In¬
ver ury, on the Great North of Scotland Railway. This
bridge belongs to the second class. It consists of 10 bays,
or spans, four of which span the ordinary bed of the river
Don, one spans a mill-lead, and five are land or flood
openings.

It is situated about 200 yards above the confluence of
the rivers Don and Ury, crossing the former at a consider¬
able angle, adjacent to a great bend immediately above in
the course of the river, and standing at the south end of a
considerable flat, or liaugh, which is liable to be flooded.

The bays are spanned by ordinary queen-post trusses;
this form being adopted in order to obtain the greatest
height and clear water-way at the least expense.

In 1829 happened the greatest flood on record in Aber¬
deenshire : both the above rivers were swollen to an enor¬
mous extent; the level of the water, throughout the haugh
referred to and on the site of the bridge, being within 2 feet
3 inches of the level of the under side of the tie-beams of
the trusses. It was therefore necessary for the engineers to
provide sufficient water-way for a similar flood; and after
the most careful investigations of the history of that flood,
the design of construction, and extent of openings of the
viaduct, as now executed, were determined on.

It is scarcely necessary to give a detailed description of the
parts, as the accompanying drawings fully explain them¬
selves ; but a short general statement may not be out of place.

All the timber used in the structure is of the best Memel.

The piles and braces of piers are 12" x 12" scantling. The
head-pieces of the piers 12" x 9". The tie-beams of the trusses
12 " x 9". The struts, straining-beams, and queen-posts
of the trusses 12" x 12", and the diagonals 12" X 8".

All the wrought-iron work of the bolts and straps is of
B.B. crown Staffordshire iron. The toes of the pier tim¬
bers are shod with Staffordshire boiler-plate; and the caps
over the queen-posts, the shoes under the tie-beams, and
the strap bars at the springing of the trusses, are of ordi¬
nary gray cast iron.

Preparations for the erection of the viaduct were com¬
menced in the autumn of 1853, by the construction of a

TTflWDlBEK ®KD!E><DIES a

Fi^ s 1 to S. Elevation Plan ansi details, of Sri doe over die Spey at Lap pan Kirk.

PLATE TI.IX

BY THOMAS TELTORD , (’. E

J mite del 1

=SL

so feet A

> feet B

BLACKIE A. SON GLASGOW ,£D1NBL HOH..V LONDON

.nr.io.tr, /;

RBA.TE L

0. Joass, del.

Scale- to Figs. 2 2. 6.7 8.

140 160 160 170 160 190 200 210 220 230 240 26 0

Feet.

Scale* to Figs 3.4.5 .

10 20 30

5o Feet.

BLACKIE & S OJ'T , GLASGOW , EDINBURGH & LONDON.

W.A. Be ever. Sc

AM© (DEP31TKES o

Figs: Ito 5. Shew Bridge over the River Bern*. GSJSfprih of Scotland Railway,
Rios: 6 to 10. Centring ofBBdtLoohnvBle Viaduct. Glasgow and South Western Railway:

BY JOHN MILLER' C. E

FtQ. 1

Fug. 8.

12x12

PLATE LI

J Whits , del 1

A \o

J. W Lowry, fc.

90 Feet

xoFect.

BI.AC KIE Sc SOS GLASGOW, EDTNBURGH , & LONDON ,

BRIDGES.

103

temporary bridge across the Don, parallel to, and above
the site of the viaduct, with side gangways at each pier
for carrying the piling engines.

The piles were driven to varying depths, as shown in
Fig. 1 . They were shod with ordinary four-armed shoes
weighing 20 lbs. each, and driven in till a perfectly firm
rest was obtained.

The bed of the river consisted of large loose gravel and
stones, lvinw on an under stratum of strong dark-coloured
clay, into which the piles were driven several feet.

The water piers consist of seven piles, with longitudinal
braces, diagonals, and cap-cills, arranged in such manner
as to insure rigidity and strength. The distance between
the extreme piles of each pier is 45 feet, this distance be¬
ing considered necessary to resist the shocks given on the
breaking up of frost in winter, when the river, swelling to
a great height, hurls along with it enormous quantities of
ice. Lumps of ice, weighing from 5 to 8 or 10 tons, have
been seen shooting through this bridge with the velocity
of seven miles an hour; and, in severe winters, sheets of
ice half a mile in length frequently pass through.

The piers are all covered to a foot below the summer
level of the water with 3-inch planks, spiked at the
crossing of each timber. Filling-in pieces, 1 2" x 6", are
introduced at the centre pile to receive this covering.
Toe-pieces, 12" x 6", triangular in form, are faced on the
outer piles; and these, and the ends of the covering, are
further protected by sheets of boiler plate, 5 feet long,
firmly bolted and spiked. Below the planking, the inter¬
vals between the piles are filled in with rough pitching of
large rubble stones, and their exterior is surrounded with
the same material.

All joinings of the timbers of the piers are secured
by straps on each side 3" wide by f" thick, bolted toge¬
ther with f-inch diameter round bolts: where timbers
cross each other, round bolts 1 Finch diameter are used.
The ends of the timbers are tenoned into mortises formed
in adjoining beams. The diagonals of the piers are placed
so as to form supports under the ends of the struts of the
trusses.

Each truss consists of two parallel tie-beams, queen-
posts, struts, straining-beam, and diagonals. The tie-
beams are placed 9" apart, and the queen-posts and struts
pass through between them, having shoulders 1 | inches
deep on each side. The straining-beams, struts, queen-
posts, and diagonals are all mortised and tenoned together,
and fastened with straps, 3" X with f " bolts. A round
bolt 1 f" diameter is passed through each queen-post and its
cast-iron cap and shoe, and being firmly screwed up with
nut and jam-nut, the whole truss is braced together, so
as to give a slight camber to the tie-beam.

The struts of the adjoining trusses abut against each
other, the abutment being about 8 inches deep. They are
secured by straps, 3" X §", passed round the ties and
screwed at the ends, to receive the cross cast-iron bars.
The straps are increased in size in the centre to receive
bolts which pass through the ties and strut.

The tie-beams are scarfed over the piers, and secured
by bolts.

The roadway consists of transverse beams, laid 4 feet
apart from centre to centre. The beams are 18 feet long,
and 12 x 10 inches scantling: they are supported by the
trusses, which are 14 feet apart, from centre to centre.

Each beam is fastened by bolts, 1 inch diameter, to one
of the tie-beams at each end; and the whole surface be¬
tween the trusses is covered with 3" planking, on which
the railway chairs are laid, and spiked through to the
transverse beams.

The piles, the covering of the piers, and the roadway,
are payed over with two coats of Archangel tar and pitch
at a boiling heat; and the remainder of the timber work
is painted three coats in white lead and oil.

All the timber is cleaned except the planking, which is
rough from the saw.

The iron work was painted first one coat in red lead,
and then two coats in black lead and oil.

During the winter of 1853-54, the temporary bridge
was carried away by the breaking up of the ice; and two
of the permanent piles, which were not connected with
the others, and therefore unsupported, were broken over:
beyond this no casualty occurred, nor was any special
difficulty incurred in the execution of the viaduct.

The railway was opened in September, 1S54; and though
it has been severely tested by both summer and winter
floods, the whole structure still continues in excellent re¬
pair. The engineers, however, thought it advisable to pro¬
vide against extraordinary cases, and erected ice-fenders
in front of each water-pier. These ice-fenders consist of
three piles, braced, covered with planking, and faced with
boiler-plate, similar to the end part of the water-piers.
They are placed three feet clear of the piers, so as to
receive any shock without allowing the main structure to
participate in it.

These ice-fenders are not shown on the drawing.

Fig. 1 is a general elevation, and Fig. 2 a general plan.

Fig. 3, one of the bays drawn to a larger scale, with the
dimensions of the timbers figured.

Fig. 4, transverse section through the bridge.

Fig. 5, plan of the bay shown in elevation in Fig. 3.

Figs. 6 , 7, 8 , 9 and 10 on this plate will be described in
the section on “ Centres.”

Plate LI.—The figures on this plate illustrate Class 3.
They are designs by Mr. White for railway and road bridges.

Fig. 1 is an elevation of the framing of a railway
bridsre. It is a combination of a laminated arch with
light masonry.

C C is the laminated arch, abutting at the ends on iron
plates, e e.

F, the chord.

E, the straining-piece.

K N o, struts.

R s, R S, radial posts or braces, with double iron straps,
and cross-pieces at R and s.

M L, M L, braces and counter-braces.

G, a continuation in timber of the torus-moulding of
the piers.

H, the railing, or fence, which is braced and counter-
braced, and so connected to the other framing by bolts
(seen in Fig. 4 ) as to add strength and stiffness to the
structure.

Fig. 2 , a plan of part of the structure, which shows
that it is composed of six parallel trusses, o o o, like that
shown in Fig. 1 , united by transverse bracing, q q, at
each line of radial posts, and stiffened by horizontal braces,
w w. At R R are seen the plates and cross-pieces connect¬
ing the straps of the radial posts.

164

PRACTICAL CARPENTRY AND JOINERY.

z shows a portion of the planking of the floor.

Fig. 8 is a transverse section of the bridge, on the line
A b of Fig. 1, in which c c c are the arches, e e e e the
abutment-plate, and d the cross-piece and transverse-
bracing.

F, the chords.

E, the straining-pieces.

G, the torus.

ir, the fence, p the floor, / the railway sleeper, and g the
guide or guard piece.

Fig. 4 is an enlarged section, showing in greater detail
c the arch, E F o G the horizontal timbers above it, and
H the railing, q the cross timbers, p the floor, d x y the
transverse ties and braces, and t a transverse iron tie at
every radial post, bolted to the chords.

Fig. 5, an enlarged section, showing F o the chords,
and the manner in which they are embraced by the straps
and cross-pieces of the radial posts, p the floor, f the
sleeper and rail, and g the guide-piece.

Fig. 6 is the elevation of a road bridge belonging to
the same class as last example. It consists of two lami¬
nated arches in combination with straight trussing.

C o', c c' are the laminated arches, with radial posts, R s,
and braces and counter-braces, c and d.

F is the chord.

e, the straining-piece.

K, the principal struts.

ooo, vertical posts, with struts or braces, N N, and
counter-braces.

G is the timber continuation of the moulding of the
piers.

H, the fence, consisting, as in the last example, of light
framing of posts, rails, braces, and counter-braces.

Fig. 7 is a portion of the plan of the structure, show¬
ing the upper side of the trusses o o o o, the floor-timbers
q q, the planking z, the horizontal braces w w, and the
cross-bracing at each line of radial posts.

Fig. 8, a transverse section of the bridge on the line
A B, Fig. 6, in which c c are the laminated arches, E the
straining-piece, F the chord, n the fence, e e the abutment-
plate, of cast-iron, s the carriage-way, and r r the foot¬
paths of the road.

Fig. 9 is a section of one of the frames to a larger scale.

C, the lower arch.

C, the upper arch, c d the brace and counter-brace,
halved at their intersection.

E, the straining-piece.

F, the chord.

H, the fence.

x y, the cross-bracing.

t, an iion tie connecting the upper part of all the trusses.

q, the floor-timbers.

z, the planking.

G, wooden moulding.

Fig. 10 is the plan of the top of the straps which unite
the aiclies to the truss, and Fig. 11, the side elevation of
the same.

Plaie LII. Elevation, Plan, Section , and Details of
the Timber Bridge over the River Tyne, at Linton, North
British Railway. —This bridge was originally constructed
entirely of freestone. Between the abutments, from which
the struts spring, there were two stone arches, with a pier
in the centre of the river; but, owing to the insufficiency of

the foundation of this pier, it was swept aVay by a flood
of unprecedented magnitude in September, 1846, after the
opening of the North British Railway: the abutments,
however, remained uninjured. It became a matter of
importance to repair this accident as soon as possible, to
admit of the passage of trains; and with this view it was
determined to erect, between the abutments of the arches
which had fallen, the timber bridge shown on the draw¬
ings. This erection was put up very rapidly, owing to
the simplicity of its construction; and it has been found to
answer its purposes perfectly. The drawings, in them¬
selves, are so complete as to render any detailed account
of the structure unnecessary.

Fig. 1 . Elevation of the bridge, the opening of which
is 90 feet wide. The dimensions of all the parts are
figured on the drawings, and the construction is shown
in detail in Fig 4, Nos. 1 and 2 .

The bridge belongs to the third class in our enumera¬
tion.

It consists of a built or laminated chord consisting of
five planks, each 12 X 3, as seen in section, Fig. 4, No. 2.
Immediately beneath this is a straining-piece, 12 x 6
inches, and 72 feet long; and struts C, 12x9.

Under this a series of eight transverse timbers serve to
unite all the frames.

The next straining-piece is 12 x 6 , and 54 feet 5 inches
long; and the struts c are 12 X 9 inches. Under this is
another series of six transverse pieces.

The next straining-piece is 12 X 6 , and 36 feet 7 inches
long. This has a series of four transverse pieces separating
it from the next and lowest straining-piece A, which is
12 x 12 , its struts also being 12 x 12 .

The posts, E E, are 12x12 inches, and their straps are
3^ X i inch. The manner of securing the straps is shown
in detail in Figs. 5 and 6 . The lower ends of the struts
are housed in radiating cast-iron shoe pieces, attached to
a cast-iron abutment-plate, seen at F in Figs. 1 and 3,
and at D in Fig . 2.

Fig. 2 is a plan of the structure, showing A, the truss
frames; c, the transverse pieces; B, the horizontal braces;
D, the abutment-plate; E, an upper plate of iron connect¬
ing all the trusses, seen also at G in Fig. 3, and in Fig. 4,
No. 2; and F f, the rails.

Fig. 3 is a transverse section on the line A B, Fig. 1.
G is the upper connecting plate, and F the abutment-
plate.

Fig. 4. No. 1 is an enlarged elevation, and No. 2 an
enlarged section of the truss and fence rail.

A, the lowest straining-piece; B B, straining-pieces; C C,
transverse pieces; f, the upper straining-piece; g, the built
or laminated chord; E E, straps.

The fence railing is framed with rails K, and capping
piece 1 , posts G, and braces and counter - braces, H. A
bolt, e g f, No. 2 , passes through the upper rail K, the post
G, and the chord and uppermost straining-piece, and thus
unites the truss and the fence railing firmly together.

Figs. 5 and 6 show details of the head of the strap E,
already referred to.

Plate LIII.— Figs. 1 and 2 show the elevation and
plan of a skew bridge, of Class No. 2 , designed by Mr.
White. The scantlings may be nearly the same as those
in the last example.

Fig. 1 is the elevation. Each frame is composed of a

BLACK! E A SUN , GLASGOW KD.NUUac.il N LONDON

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90 Feet

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B 1 ACKIE 5 , SON, GLASGOW, EDINBURGH & 102 TD 0 TS

A m £ K 0 DA P'1 IBIR o © © E a o

Arched Tniss 'Bridge*

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Bridge over ShennoTLS Creek.
Ferai . Central Railroad .

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Improved knitter Bridge.

Tig. 12 .

J W. Lowry jc

1C Margins del'

BLACKJX & SOU , GLASGOW F.DIUBrRGH ,v 10UDOT.

BRIDGES.

165

chord N, and straining-pieces L H F, and struts A B C, D E, G,
K, and M; posts and straps ab,ab, ab; and transverse pieces
OPR connect all the frames.

Fig. 2 is the plan showing the trusses A A, six in number,
the connecting transverse pieces OPRS, and the horizontal
braces, 1 2 3 4 5 G 7. The ends of the chords rest on a cast-
iron wall-plate w w.

Figs. 3 and 4 show another design, by Mr. White, for a
bridge composed of the combination of a laminated arch
with the ordinary straight truss.

In the plan, it will be seen, there are no floor beams, but
in their place planking close-jointed, on which the floor¬
ing planks are laid, so as to cross them at right angles.

In the elevation, Fig. 3, there is shown a double chord
F E, a straining-piece D, struts BCG, and posts and straps
ab, ab, ab. Transverse pieces at c and/connect all the
frames A A A to the laminated arches.

In Fig. 4, the plan, A A are the trusses, six in number;
cf, the transverse pieces; R, the iron wall-plate; 1 2 3 4 5,
the horizontal braces.

Plate LIV.— American Bridges.

Fig. 1 is the elevation of a bridge belonging to Class 4.
Fig. 2, part of the plan of the same. Figs. 3 and 4, the
detail to a larger scale of the tension-posts, braces, and
counter-braces, upper and lower chords, and their iron
fastenings.

In this mode of combining an arch with a trussed frame,
the arches are connected with the tension-posts, and the
posts with the chords, by screw fastenings, as seen in
Fig. 4; and all is so arranged as to admit of changing the
position of the arches relatively to the chords, or of draw¬
ing together the chords without changing the position of
the arches, and thus regulating and distributing the strain
over the different parts of the bridge at pleasure.

The following are the directions of Mr. Steele, the
patentee of this mode of construction, to be attended to in
the erection of one of his bridges, extracted from Haupt’s
Treatise on Bridges

The truss must first be erected, provided with suitable
cast-iron skew-backs to receive the braces and tension-
posts; and the several parts of the chords should be con¬
nected with cast-iron gibs. Wedging under the counter¬
braces must be avoided, by extending the distance between
the top skew-backs sufficiently to bring the tension-posts
on the radii of the curve of camber of the bridge. The
tension-posts must be about eight inches shorter than the
distance between the chords; and, in screwing up the truss,
care must be taken not to bring their ends in contact with
the chords; but they must be equidistant, and about four
inches from them. When the truss is thus finished, it
must be thrown on its final bearings; and it is then ready
to receive the arches, which should be constructed on the
curve of the parabola, with the ordinates so calculated as
to be measured along the central line of the tension-posts.
They must be firmly fastened to the posts and bottom
chords by means of strong screw-bolts and connecting
plates, as shown at d d, and should foot on the masonry
some distance below the truss, which can be done with
safety, as the attachment to the posts and chords will re¬
lieve the masonry of much of their horizontal thrust. When
a bridge so constructed is put into use, it will be found,
as the timber becomes seasoned, that the weight will be
gradually thrown upon the arches, which will ultimately

bear an undue portion of the load. To avoid this, the
camber must be restored, and the posts moved up, so as
again to divide the strain between the truss and the arches.

This adjustment must take place once or twice in each
year, until the timber becomes perfectly seasoned; after
which, in a well-constructed bridge, but little attention
will be required. Plates of iron should in all cases be in¬
troduced between the abutting surfaces of the top chords
and arches; and all possible care taken to prevent two
pieces of timber from coming in contact, by which decay
is hastened : care should also be taken to obtain the curve
of the parabola for the arches; as it is the curve of equi¬
librium, and of greatest strength, as has been shown by
experiment.*

Bridges constructed on this plan, will be found to pos¬
sess an unusual amount of strength for the quantity of
material contained in them; and, if well built and protected,
great durability.

Fig. 5. Elevation of a truss of Class 4.

Fig. 6. Plan of the same.

Fig. 7. Vertical section through the centre of the bridge.

The bridge is in two spans, each 148 feet 3 inches from
skew-back to skew-back, or 154 feet 6 inches from the
middle of the pier to the end of the truss. The pier is 3
feet 2 inches wide on the top, and 6 feet at the skew-backs.

The truss consists of three rows of top and bottom
chords, and two sets of posts and braces. It is counter-
braced by rods of inch iron between the braces. The panels
increase in width from the end towards the middle of the
span. The first are 9 feet 1£ inches from centre to centre
of posts, and the middle ones 12 feet 1£ inches.

The quantity of materials in this bridge is given by
Mr. Haupt as follows:—

Timber fo',

r one Span.

3 wall-plates ...

... 8

18 feet long B.M.

576

20 chords .

4,680

10 „ .

... 8

3,120

10 „ .

2,400

20 „ .

... 6

3,600

56 posts, yellow pine 9

11,592

4 king-posts ...

... 9

1,104

15 floor-beams ...

2,520

14 „

... 7

2,058

56 lateral braces...

4£

8£

1,213

3 77 77

... 4*

103

30 roof-braces ...

850

56 check-braces

.. 9

2,520

2,898

60 main-braces

... 6

5,130

15 tie-beams

1,900

8 purlins

... 4

320

135 rafters .

10£

1,772

15 roof-posts . ..

... 4

30 knee-braces ...

„

312

16 track stringers

... 8

2,133

3300 feet B.M. f-inch sheeting

for :

roof

3,300

56 arcli-pieces ...

11,550

7000 feet B.M. inch

boards,

for

weather-boarding,

20 feet long

...

7,000

72,726

Weight per lineal foot, 1416 pounds.
No. of cubic feet per foot lineal, 40.

* The parabola is the curve of equilibrium when no load is upon
the bridge, and also when the load is uniform ; but there can be no
curve of equilibrium for the variable load of a passing train. Stiffness
can be secured in this case, only by an efficient system of counter-
Dracing.

The plan proposed fulfils every condition of a good bridge.

1G6

PRACTICAL CARPENTRY AND JOINERY.

Counter-brace Rods for one Span.

4 rods for

1st panels, each 24 ft. 3 in. long, 1 in. diam.

97*0 ft.

2d „ „ 24 „ 2

ff 1 ff

97*0 „

3d „ „ 24 „ 8

>. 1

98*7 „

4th „ „ 25 „ 0

ff 1 ff

100*0 „

5th „ „ 25 „ 2

if 1 ff

100*7 „

6th „ „ 25 „ 8

„ 1

102*7 „

7th or mid. pan. 26 „ 0

» 1 »

104*0 „

Total lineal feet 700*1

Weight in pounds at 2*65 per foot = 1855 pounds.

Arch Suspension Rods for one Span.

4 rods, each 6 feet 8 inches'

» 10 „

» 13 „

„ 15 feet 6 inches

► If inch diameter.

17 „ 2 „

* 18 „ 2 „ j

Total length 322 feet.

Weight at 4 t ° 0 1 ( j lbs. per foot, 1590 pounds.

Lateral Brace Rods for one Span.

15 rods, each 1G feet 9 inches long, 1 inch diameter, 655 pounds.

Small Bolts for one Span.

60 bolts, through arches, 47 inches long, 1 inch diam., 622 lbs.

60 bolts, through chords and posts, 34 inches long,

| inch diam. 255 n

30 roof-bolts, 36 inches long, f inch diam. 135

224 spikes for braces, f pound each. 168

Mr. Haupt lias given an analysis of the strains upon
this bridge; and as it affords an example of his process
of working out the problem of the stability of a timber
bridge of this kind, the whole is here extracted:—

Dimensions and Data for Calculation of Bridge at Sherman's

Creek.

Span at skew-backs .

Whole length of truss for one span.

Out to out of chords .

Middle to middle of chords .

Resisting cross-section of upper chords
Resisting cross-section of 6 lower chords, de¬
ductions for splice, check-brace, and bolt,

and allowing for scarf-key.

Versed sine of lower arch.

Cross-section of 8 arches .

Span 148|, and rise 20, will give radius...
And 172*25, 152*25, and 74*125, express the
proportion of the hypothenuse, perpendicu¬
lar, and base of skew-back.

Hypothenuse of skew-back covered by arches

Perpendicular „ (i

Base

. ” ”
Distance from skew-back to bottom of arch

» „ middle of skew-back to middle

148 ft. 3 in.
154 ,

400 sq. in.

280 sq. in.

20 feet.
800 sq. in.
172 25 feet.

18 inches.

7*6

4 *

of chord .. 4 ft. 5 in

Width from out to out of chords . 16 „ 2

„ between chords in the clear . 11,.

1 >istance from centre to centre of floor-beams 5J, feet.
Weight of one-half span complete (77 feet) 120,000 lbs.
Distance of centre of gravity from point of

support^. . 37 feet.

Weight of one-half span with load ... ... 275,000 lbs.

Distance between shoulder of post . 154 feet.

Calculation of Brass without the Arches.*
Let x — distance of neutral axis from top chord
19 — x = distance of ditto from bottom chord.

P = pressure per square inch on top chord.

* The reader will readily discover that Mr. Haupt, in general,
uses the approximative round numbers in his calculations, for the
sake of simplicity.

— (19 — x) — strain per square inch on bottom chord.

x = 8*3 = distance of neutral axis from top chord.

19 — x = 10*7 = distance of do. from bottom chord.

P=1532lbs.= pressure per square inch on top chord.

( I532-4-8*3)x(19 — 8*3)=1975 lbs.=strain per square
inch on bottom chord.

400 P x — 280 — (19 — x)-.

400 P x 8*3 + 280 P x~ x 107 = 275,000 x 37.

The bottom chords derive some assistance fx*om the ma¬
sonry; but as the roadway is on the bottom of the truss,
little opportunity is given for wedging the lower chords;
and for this reason the assistance to be derived from this
service is not estimated.

Ties and Braces.

The weight upon the middle panel (12j lineal feet) is
45,000 lbs. To resist this there are four posts, the cross-
section of each being 72 square inches, or the united cross-
section 288, equivalent to 156*25 lbs. per square inch.

The distance between the shoulders of the posts being
15J feet, and the width of the middle panel, exclusive
of posts, 111 feet, the diagonal will be 19*3.

19*3

The strain upon the diagonal will be 45,000 X =

1 D’O

56,000 lbs., which divided by the cross-section of the four

, , . , 56,000

braces, will make the pressure per square inch ~=

260 lbs.

The expression for the limit of the resistance to flexure,

, 9000 PD 3 . , 9000 x9 x 6 s

w = 4 x- p -, gives the present case w= — 794 ^-

= 46,000 pounds, or for

The four braces. 184,000 pounds.

The actual pressure . 56,000 „

Difference in favour of stability . 128,000 „

The strain upon the end ties, which sustain the weight
of half the bridge, will be 275,000 pounds, the cross-section
being as before 288 square inches: the strain per square
inch will thus be 955 pounds.

The width of the end panel being 8 | feet exclusive of
posts, and the distance between the shoulders of the posts
being as before i 5 1 feet, the diagonal will be 177 feet, and

the pressure in the direction of the braces

275,000X 177
J 5*5

314,000 pounds = 1451 pounds per square inch.

The limit of the resistance to flexure for the 4 braces is
. , 9000 x 9 x 6 s

expressed by w =- iff? - x 4 = 223,000 pounds.

As the pressure is 314,000 pounds, it appears that with
the assumed weight of a train of locomotives, or one ton
per lineal foot besides the weight of the structure, the end
braces would yield by lateral flexure in the direction of
the plane of the truss, if not supported in the middle.

If an intermediate support be used, the resistance will
be quadrupled, and will be amply sufficient.

It is also necessary to examine whether the braces, if
supported in the middle in the direction of the plane of
truss, could yield laterally in the direction of the perpen¬
dicular to this plane: the relative resistances in the two

BRIDGES.

1G7

cases are as 6 x 9 3 : 9 X 6 3 , or as 9 : 4. The limit in this

,, „ „ , 223,000 x 9 _ „

case would therefore be - ^ - = 502,000 pounds,

which is more than the pressure (314,000 pounds).

It appears therefore from this calculation, that if the
arches are omitted, the end braces should be supported in
the middle by diagonals in the opposite direction. As an
additional security, the depth should be increased to nine
inches. In the other panels, they should diminish gra¬
dually to the middle of the span, where the original
dimensions are sufficient.

Floor Beams.

The floor beams are 7x14 inches, width in clear between
supports 11 feet, distances from centre to centre 54 feet.

The weight on the drivers of a locomotive, 18 tons, may
be considered as distributed nearly equally over 3 floor
beams, which will give 6 tons for each beam.

6 X 3 -f- 5'5 = 3'3 tons = the equivalent weight in the
middle of the beam

R =

18 wl 18x 6600x11

= 952 pounds = maximum

b dr ~ 7x14*

strain per square inch.

Lateral Braces.

The lateral braces are 4^ X 7 ins., and 8 feet long. The
prevalent winds are in a direction nearly parallel to
the axes of the bridge, so that its exposure is not great.
Assume as the basis of a calculation that the sides are
closely boarded 20 feet high, and that the perpendicular
force of wind may be 15 pounds per square foot: the whole
pressure upon one span will be say 45,000 pounds. As
there is lateral bracing both above and below, this pres¬
sure would be resisted by 4 lateral rods 1 inch diameter =
3’14 square inches, or 14,330 pounds per square inch.

The proportional strain upon the lateral braces would
, 45,000 x 8

be-g-= 72 , 000 , to resist which, are four braces

4| x 7 = 126 square inches =571 pounds per square inch.
The bearing surface at the joints does not much exceed
one-half the area of the cross-section, consequently the
actual pressure at the joints will be about 1000 pounds.
The limit of flexure of the four braces is expressed by
9000x7x44 3 ,

w = --x4 = 360,000 pounds nearly.

The maximum pressure is 72,000 pounds.

Difference in favour of stability, 288,000 pounds.

The lateral braces cannot yield either by crushing or
bending, and are, therefore, amply sufficient.

Could the bridge, if not loaded, be blown away ?

The weight of one span has been found to be 240,000
pounds.

The resistance to sliding would be... ... 120,000 pounds.

The pressure of wind . 45,000 „

Difference in favour of stability ...

75,000

Could the bridge yield to the force of the wind by ro¬
tation around the outer edge of the chord ?

The effect of the wind, 45,000 pounds,
acting with a leverage of 10 feet, would
give for the disturbing force. 450,000 pounds.

The resistance, = weight of bridge X half¬
width from out to out = 240,000 X 8= 1,920,000 „

Difference in favour of stability ... 1,470,000

Strain upon the Knee-braces.

Let A c B D (Fig. 4S0) represent the cross-section. The
Fi g . 4 so. effect of the pressure of wind on A c

d c a is equivalent to half that pressui'e

applied at the point A. A force at
A tends to produce rotation around
B and c, which may be resisted by
a brace in the direction of the dia¬
gonal A B.

The pressure upon the bi'ace will
bear to the force at A the pi'oportion
of the diagonal to the side A d. If the bi-ace be removed,
the pressure must, nevertheless, still continue; and if it
be resisted by a brace e f the pressure upon e / will be
greater than that upon A B, in the proportion of A D to e D;
because D is a fulcrum, and A D and e D the leverages of
the acting and i-esisting forces. If e f is pai’allel to A B,
which is generally a veiy favourable direction, the lengths
e f and A B will be in proportion to the distances D e
and D A, and may be substituted for them. In the pre¬
sent case, the force of wind, 45,000 pounds, acting with
a leverage of ten feet, will give its moment 450,000, or
225,000 pounds acting at a distance of 20 feet. The length
of the diagonal is V 20 - -f- 16* = 25 - 6 feet, and the strain in

the direction of the diagonal ^,50 ( D>< -5 6 _ gg qqq p-, g>

The length of the knee-braces being 5 feet, the strain

25-6

upon them will be 36,000 X —— = 184,000 pounds. This

is resisted by 15 braces (one to each post). The cross-
section of each is 25 square inches; but, as the beax-ing
surface of the joint does not extend over the whole surface
of the section, the resisting portion will be reduced to
15 squai’e inches. The sti'ain per square inch will there-

fore be 1^4,000 — 818 pounds.

15 X 15

For the resistance to flexure of the fifteen bi-aces, w =

9000x5 X5 3 . _ ,,

- ^ -x 15 = 3,375,000, or about 20 times the pres-

sure.

The strain upon the bolts at D, will be to the vertical
component at A, in the proportion of D e to e A, or as
5 : (25'6 — 5). The vertical component at A, = 22,500 =
1 6

-=22,500 x -EiK= say 17,000. Hence the strain upon

AC 20 v >

the 15 bolts will be 17,000 x 4 = 68,000. or 4533 pounds
to each bolt, or 10,000 pounds per square inch if the bolts
are f inch diameter.

Pressure upon the Arch.

For this calculation we have, from the table of data,
Span, 148 feet.

Distance of centre of gravity from abutment, 37 feet.
Rise of ai'ch, 20 feet.

Proportion of hypothenuse, perpendicular, and base of
skew-back = J 8 , 16, and 7 6 .

Cross-section of 8 arches, 800 square inches.

800 X jg= 711 proportion to x-esist horizontal thrust at
skew-back.

800 x = 338 square inches to l'esist vertical pressure
at skew-back.

168

PRACTICAL CARPENTRY AND JOINERY.

The weight for one half span loaded is 275,000.

800 x 20 x P = 275,000 x 37-
P= 448 = pressure, per square inch, on arches, in middle.
The resisting cross-section at the skew-backs is the same
as at the crown.

Thepressureisgreaterintheproportionofthehypothenuse

to the perpendicular: it will therefore be 448 X = = 504 lbs.

The arches are therefore more than sufficient to sustain
the whole weight.

When both systems act as one,

The data required to determine the strains upon the
chords and arches are,

Distance from middle of upper to middle of

lower chord . 19 feet.

Distance from middle of skew-back to middle

of lower chord. 4'2 „

Distance from middle of top chord to middle

of arch . 3'5 „

Cross-section of upper chords..• 400 square in.

„ lower „ 280 „

,, arch at crown . 800 ,,

„ „ skew-backs. 711 „

Let x — dist. of top chord from neutral axis.

„ x — 35 = „ arch at crown „

„ 19 —— £C = ,, bottom chord ,,

,, 23 - 5 —x = ,, arch at skew-back „

„ P = pressure per sq. in. on top chord.

P ,

[x— 3*5) = „ ,, arch at crown

» -09—; x) =

„ £(28-S-«)=

back, horizontally.

The equations in this case are,

400 Px + ^r 800 (as — 3-5)* + ~ 280 (19—F) 2 -h ^ 711

bottom chord,
arch at skew-

(23 5 — x)

2 _ 97 c

75,000 X 37,

and 400 P x + 800— (a — 3 5 ) 2 = 280 — -.(] 9 — xf + 711

— (23'5 — xf.

From the second of these we find x — 11-8.
Consequently the distance of the neutral axis will be,

Below top chord

„ arch .

Above bottom chord
„ skew-back...

11-8 feet.
8-3 „
7'2 „
1C7 „

These values substituted in the first equation will give
P X 222,000 = 7.175,000 x 11-8, or
P = 381 lbs. = pressure per square inch on top chord.

8'3

381 X j = 26S lbs.^pressure per square inch on arch,
at top.

7-2

381 x | 232 lbs. = strain per square inch on lower

chord.

11-7

381 X 377 lbs. = strain per square inch on per¬

pendicular of arch, at skew-back.

Vertical Pressure.

Assuming that the weight sustained by each system
will be in proportion to its power of resistance, the greatest
weight that the truss can sustain will be the limit of
llexure of the braces in the end panels. This has al¬

ready been found to be 223,000 pounds, which will be pro-

223,000 x 15\5

duced by a vertical pressure of- '~\7 7 - = ^5,282

pounds: this is the extreme limit of the power of resist¬
ance of the end braces.

The proportion of surface at the skew-back which resists
the vertical pressure is 388 square inches. If we suppose
the vertical pressure on the base of the skew-back to be the
same per square inch as the horizontal pressure upon the
perpendicular, it will be capable of resisting 180,830 lbs.:
this, deducted from the whole pressure, . . 275,000 ,,

will leave for the portion to be sustained by

the braces. 94,170 lbs.

which is below the resisting power. The actual limit of
the resisting power of the arch is very great; but assuming
that in practice it is not safe to exceed 1000 pounds per
square inch, the proportions of the weight sustained by
the truss and arch would be,

108,663

For the truss 275,000 x 338j0 u 0 +108,663 = 66 ’ 880 -

338 000

And for the arch 275,000 x 4 , 44 /qq 3 — 208,000.

These numbers will give for the strain per square inch
206,100

on the arch,

338

; 615 lbs.

Fisr. 481.

, , 66,880 x 17-7

4 or the end braces ■ w ~ = 3o3 lbs.

lo-o X 216

It has been stated that the bridge at the western end
is sustained by an abutment- pier: it is proper to examine
whether the resistance which that is capable of opposing is
sufficient to counterbalance the thrust of the arch, on the
supposition that it should bear the whole of the load.

The dimensions of the abutment-pier are given in

Fig. 481, except the
length, which may be
taken at 16 feet

We will examine the
conditions of equili¬
brium on the supposi¬
tion that rotation takes
place around the point
B. The disturbing force
is the horizontal com¬
ponent of the thrust of
the arch = 358,750 lbs.
acting with a leverage of 16^ feet: its moment will there¬
fore be 358,750 x 1 64 = 5,919,375.

The resistances are:—

1. The weight of the masonry above C B = 110 perches,
of 3750 lbs. = 412,500 lbs. The distance of centre of gra¬
vity from B is 5 feet; the moment will be 2,062,500.

2. The adhesion of the mortar, estimating it at 50 lbs. per
square inch, or one-half the tabular strength of hydraulic
cement, will be, on a surface of 160 sq. ft., = 1,152,000 lbs.,
and its moment, with a leverage of 5 feet, = 5,760,000 lbs.

3. The vertical pressure of the arch itself, 275,000 lbs.,
acting with a leverage of 9 feet, will give a moment,
275,000 x 9 = 2,475,000.

2,062,500

The sum of the moments of the resisting forces will be <J 5,760,000

2,475,000

Total .

Moment of disturbing force

Difference in favour of stability

... 10,297,500

5,919,375

... = 4,378,125

BRIDGES.

1G9

As this difference is less than the adhesion of the mortar,
it appears that an abutment pier of dry masonry of the
same dimensions would be overturned.

It has been supposed, in this calculation, that the arch
bears the whole weight, and that the abutment resists the
whole thrust. The actual horizontal thrust, with the two sys¬
tems acting together, was found to be 377 X 711 =268,047.
The moment will be 268,047 X 164 = 4,422,775. The re¬
sistance, omitting the strength of the mortar, = 4,537,500.
From which it appears that if we disregard the adhesion
of the mortar, the system as a whole would be very nearly
in a state of equilibrium, the difference being in favour of
stability. The practice of the writer in proportioning
abutments on rock foundations is, to disregard the adhe¬
sion of the mortar, throwing this, whatever it may be, in
favour of stability: there is so little uniformity in the
strength of mortar, and so much liability to cracks occa¬
sioned by jars, when partially set, that it is not safe to
depend much upon it. If the proportions and weight of
an abutment do not prevent it from overturning, without
taking the strength of the mortar into consideration, it is
too weak.

When the base is to any extent compressible, it is not
sufficient that the disturbing and resisting forces should
be in a state of equilibrium—a condition which requires

the resultant of all the forces to pass through the point of
rotation; but it is proper that the resultant should pass

through the middle of the base.*

Summary.

Span .

148 ft.

3 in.

Width of pier on top .

3 .,

2 „

„ „ skew-back .

6 „

Timber in one span .

.. 72,726 „

No. of cubic feet per foot lineal.

40 „

Width from out to out of chords

20 „

., middle to middle of chords

Versed sine of lower arch .

20 „

Radius .

.. 17,255 „

Weight of timber per lineal foot

1,416 pounds.

Weight of iron in one span.

.. 5,280

Weight of half-span loaded.

..275,000

„

Strain upon floor beams per square inch

952

lateral brace-rods per square inch 3,444

„ lateral braces .

571

„ knee-braces per square inch

818

Pressure per square inch on top chord

381

„ „ „ arch at crown 268

„ „ „ lower chord.

232

„ „ „ arch at skew

-back 615

,, „ ,, end-braces .

353

„ „ „ middle braces 260

Fig. 8 is the elevation of the common lattice bridge:
Fig. 9, a section of the same when the roadway is above
the latticed sides; and Fig. 10, a section when the road¬
way is supported on the under side of the lattice. Fig. 11,
plan of one of the latticed sides.

Although when first introduced the lattice construction
at once obtained great favour from its simplichy, economy,
and elegant lightness of appearance, yet experience has
shown that it is only adapted for small spans and light
loads, unless fortified by arches or arch braces. When

* This calculation was made before the completion of the bridge:
the correctness of the conclusions was soon confirmed: the pier
began to crack after the opening of the road, and an increase of
thickness by the addition of buttresses was found necessary.

well constructed, however, it is useful for ordinary road
bridges where the transport is not heavy. On the subject
of lattice bridges, Mr. Haupt makes the following perti¬
nent remarks introductory to his notice and description
of the kind of construction called the improved lattice,
shown in Figs. 12, 13, and 14:—

“ One of the first defects apparent in some old lattice
bridges, is the warped condition of the side-trusses. The
cause which produces this effect cannot, perhaps, be more
simply explained than by comparing them to a thin and
deep board placed edgeways on two supports, and loaded
with a heavy weight: so long as a proper lateral support
is furnished, the strength may be found sufficient; but
when the lateral support is removed, the board twists
and falls.

A lattice-truss is composed of thin plank, and its con¬
struction is in every respect such as to render this illustra¬
tion appropriate. Torsion is the direct effect of the action
of any weight, however small, upon the single lattice.

A second defect may be found in the inclined position
of the tie. All bridge-trusses, whatever may be their par¬
ticular construction, are composed of three series of tim¬
bers; those which resist and transmit the vertical forces
are called ties and braces, and those which resist the hori¬
zontal force are known by the names of chords, caps, <fcc.

In every plan, except the common lattice, these ties
are either vertical, or perpendicular to the lower chords
or arches; and, as the force transmitted by any brace is
naturally resolved into two components, one in the direc¬
tion of, and the other at right angles to the chord or
arch, it would seem that this latter force could be best
resisted by a tie whose direction was also perpendicular.
The short ties and braces at the extremities, furnishing
but an insecure support, render these points, which require
the greatest strength, weaker than all others; this defect
is generally removed by extending the truss over the
edge of the abutment, a distance about equal to its height,
or to such a distance that the short ties will not be re¬
quired to sustain any portion of the weight, the effect of
which is to provide a remedy at the expense of economy,
by the introduction of from 15 to 30 feet of additional
truss.

A bridge whose corresponding timbers in all its parts
are of the same size, is badly proportioned; some parts
must be unnecessarily strong or others too weak, and a
useless profusion of material must be allowed, or the
structure will be insufficient.

If, for example, the forces acting on the chords in¬
crease constantly from the ends to the centre, the most
scientific mode of compensation would appear to be, to
increase gradually the thickness of the chords; and, for
similar reasons, the ties and braces should increase in an
inverse order from the centre to the ends.

In accordance with this, it is found that in bridges
that have settled to a considerable extent, the greatest
deflection is always near the abutment; that is, the chords
are bent more at this point than in the centre, and the
joints of the braces are much more compressed. It is also
found that the weakest point of a lattice bridge is near
the centre of the lower chord; this might be expected,
since, from the nature of the force and the mode of con¬
nection, the joints of the lower chords are only half as
strong as the corresponding ones of the upper chord, it

170

PRACTICAL CARPENTRY AND JOINERY.

being assumed that the resistances to compression and
extension are equal. This defect may be in a great degree
removed by inserting wedges behind the ends of the
lower chords. A variation in the size of every timber,
according to the pressure it is to sustain, would, of course,
be inconvenient and expensive; but, as the principle of
proportioning the parts to the forces acting upon them is
of great importance, such other arrangements should be
adopted as will secure its advantages, and a,t the same
time possess sufficient simplicity for practice; this is
effected by the introduction of arch-braces or arches, than
which a more simple, scientific, and efficacious mode of
strengthening a bridge could not perhaps be devised, as
they not only serve, with the addition of straining-beams,
to relieve the chords, and give them that increase of thick¬
ness at the points of maximum pressure which is essential
to strength, but they also relieve the ties and braces by
transmitting directly to the abutments or other fixed sup¬
ports, a great part of the weight that they would other¬
wise be required to sustain.

It may, perhaps, be objected that the pressure of the
arch-braces or arches would injure the abutments: in
answer to this it may be remarked, that a certain degree
of pressure is very proper; the embankment behind an
abutment exerts a very great force upon it, the tendency
of which is to push it forward. If, then, a counter-pres-
sure can be produced by the thrust of arch-braces or by
wedging behind the ends of the lower chords, two impor¬
tant advantages are gained; the abutment is not only
increased in stability, but the tension on the lower chord
of the bridge is diminished by an amount equal to the
degree of pressure thus produced.

It is, however, proper to observe, that when the situa¬
tion of the embankment exposes it to the danger of being
washed away from the back of an abutment, the pressure
on its face must not be sufficient to destroy its equili¬
brium; should this effect be apprehended, the horizon¬
tal ties must be sufficient to sustain the thrust of the
bridge.

An essential condition in eveiy good bridge is, that it
shall not only be sufficient to resist the greatest dead
weight that it can ever be required to sustain in the or¬
dinary course of service, but it must also be secure against
the effects of variable loads. This is generally effected
by the addition of counter-braces; but the lattice truss
possesses this peculiarity, that it is counterbraced without
the addition of pieces designed exclusively for this purpose:
to prove this, invert the truss, when it will be apparent
that the braces become ties, and the ties braces, possessing
the same strength in both positions.

Fig. 12 is the elevation, and Figs. 13 and 11 details of
the improved lattice. The difference between this and
the common lattice is—

1 st. The braces, instead of being single, as in the
common lattice, are in pairs, one on each side of the truss,
between which a vertical tie passes; this arrangement
increases the stiffness, upon the same principle that a
hollow cylinder is more stiff than a solid one with the
same quantity of material, and of the same length, and
obviates the defect of warping.

2d. The tie is vertical, or perpendicular to the lower
chord, a position which is more natural, and in which it
is more efficacious than when inclined.

3d. The end-braces all rest on and radiate from the
abutment, by which means a firm support is given to the
structure, and the truss is not required of greater length
than is sufficient to give the braces room.

1 th. The truss is effectually counterbraced, the braces
becoming ties, and the ties braces, when called into action
by a variable load, and are capable of opposing a resistance
on the principle of the inclined tie of the ordinary lattice
bridge.

It is readily admitted that the strength in the inverted
is less than in the erect position, but it must be remem¬
bered that the unloaded bridge is always in equilibrium;
that the action of the parts which renders counterbracing
necessary, results entirely from the variable load, and
that, therefore, a combination of timbers to resist its effects
should not be as strong as that which sustains both the
permanent and the variable loads.

Behind the ends of the lower chords at the abutments,
and between them over the piers, double wedges are
driven, the object of which is, by the compression which
they produce, to relieve the tension of the lower chord.

For ordinary spans, the dimensions of the timbers may
be—

Braces .

2 in. by 10 in. in pairs

Ties

. 3 „ 12 „

Arches or arch-braces

. (! „ 12 „

Chords .

. 3 „ 14 „ iapped.

Pius

. 2j in. in diameter.

In conclusion, it is proper to remark that the proposed
plan is not recommended as the best under all circum¬
stances, but it is as economical in first cost as any other
that can be used. The arrangement will be found even
more simple than the ordinary lattice, and it is equally
applicable for bridges on common roads or railroads, and for
roof or deck bridges. The braces, in consequence of being
placed in pairs, require a slight increase of timber over
the common plan, in the proportion of 40 to 36, but the
diminished lengths of the ties and of the truss more than
counterbalance this increase.

The cost of workmanship on the truss is very trifling,
and less than on the common lattice; if the timbers are
cut to the proper lengths, the auger will be the only tool
required in putting it together.

Plate LV., Figs. 1 to 6, illustrate the construction of
a skew bridge erected over the Leith Branch Railway,
Portobello, on the North British Railway.

This viaduct was formed of timber, principally on ac¬
count of the ground being of a nature unfavourable to the
construction of a stone bridge, and also owing to the very
great angle at which the public road and Leith Branch
Railway is crossed. To allow sufficient headway for the
Leith Branch, it is spanned by cast-iron girders of an
J elliptical form, resting on a timber sole, so as to render
! struts unnecessary. The spans beyond the crossing of
I the road and railway for the remainder of the viaduct,
i are thrown on the square by a simple method which is
shown on the plan

The details of the structure are to a great extent deline¬
ated in the plate; it is therefore unnecessary to enter into
| them here.

Fig. 1, the elevation of the bridge.

Fig. 2, the plan.

Fig. 3, a vertical transverse section.

PLATE /.V

MQM1ES AN 1© ©[ENTIRES.

BY JOHN MILLER.C E

Triq. L.

Elevation., Flan., and, Details erf She\ > Bntlqe over (lit Leith Branch Railway X-r at Portobello,

an the Ninth British Railway.

■ Fin 7

Centrina of \iadn<t ova- Diuiqhuis Burn cm the Earth Bir/isk Railn av

Seal# To Fios J. 2

10 J> O 10 20 30 40 50 JLQO J50 ^0 <> Feet

Scale >to Fias . 8. 9. 11.

10 5 0 jo 20 30 40 60 ;■( 6.0 -70 &o' . Op 100 q.0 120 130 1A0 150 1QO 170 -1B0 Peet

J. W. Lown’ fc

if. C.Joass del'

BLACK IE A SON-. GLASGOW, EDINBURGH. & LONDON ,

— -—

______

PLATT. LVL.

EKOIOXSIES AND CEWraiES;

Figs. 1.8c 2 Bridge with laminated arch, across the Tweed, at Merton n,
BY JAMES SLIGHT, C. E.

Fiq. 1.

. ♦ , A.

■ . Fig. Z.

f Figs. 3. & F. Centring of viaduct over the Lug or water near old Cumnock

BY J O H N , M I LLER. C. E.

Fig .4

Fie/. 3.

W. i Joans. del 1

Sexile, for Fiqs. JLSc 2.

20 . 30

3,0 Feet

Scale for Figs. 3. Sc 4c.

20 3,0 40

70 Feet

J W.Lowryfc

BLA.CKTE Sc SON GLASGOW, EDINBURGH,Sc LONDON .

CENTRES.

171

Fig. 4, a section to a larger scale, showing one of the
trusses and rail.

Fig. 5, details to a larger scale of piers, chords, struts,
waling pieces, and the iron work serving to unite them.

Fig. 6, the cast-iron capping of the pier piles.

Figs. 7 to 11 on this plate are described under the
section Centres.

Plate LVI.— Figs. 1 and 2 illustrate a bridge of the
third class, which is erected across the river Tweed at
Mertoun.

This bridge consists of five arches, each 70 feet span,
erected on stone abutments and piers. It was intended
originally to be built entirely of stone, and although tim¬
ber was adopted for the arches at the time of its erection,
it was considered probable that stone arches might at some
future time be substituted for the wooden framing. The
piers and abutments were therefore made of such dimen¬
sions and strength as to be sufficient for stone arches.
The work was commenced in 1S39 and finished in 1841,
by Mr. William Smith, contractor, Montrose.

The whole of the piers and abutments were built on
rock, which was reached by means of cofferdams, and
which was penetrated to the extent of from 1 to 3 feet, on
purpose to get a solid and level foundation. The depth
of the different foundations varies from G feet 3 inches to

11 feet 7 inches below the summer level of the river, and
the height from the summer level to the springing of the
arches is 18 feet. It was intended originally to make
this only 16 feet, but in consequence of an unusually
high flood occurring during the building of the piers, the
height was increased 2 feet. The extreme length of the
body of the piers in the plan is 29 feet 6 inches, and
their thickness is 10 feet. The foundation extends 1 foot
on every side beyond these dimensions, and is diminished
to them by two footings of 6 inches each. The whole of
the mason work is of freestone, obtained in the neighbour-
hood of the bridge.

Each arch consists of three laminated beams or ribs; each
rib is formed of 5 thicknesses of half logs 12x6 inches,
which were bent on a frame or centre, and fixed together,
previous to their erection. The depth of the rib at the
ends is 2 feet 6 inches, but in the centre it is di minis hed
to 2 feet, the upper layer being cut horizontally to con¬
nect it with the longitudinal beam of the roadway. Each
curved rib is bound together by eleven clasp hoops of iron,
three of them embracing also the roadway beam; and the
different layers of bent timber are kept from sliding on each
other by oak keys, to the number of 60 in each rib, inserted
horizontally, and sunk half their thickness into the con¬
tiguous layers. The longitudinal roadway beams are each

12 inches square, and connected with the curved rib by
the iron straps above mentioned; also by the insertion be¬
tween them of six upright braces 10x6 inches, and further
by clamps 6 inches square, one on each side of the rib,
halved upon the beams, so as to fit close on both beams
and braces. The outward clamps of the external trusses
extend upwards and form the posts of the parapet railing,
and all the parts are securely fixed together by |-inch bolts.
Between the upright ties, braces 12x6 inches are fitted,
reaching from the curved rib to the horizontal beam. In
each arch, the curved beams are connected by six cross ties,
notched upon them, and stiffened by four pairs of diago¬
nals, 41 inches square, all fixed by strong spikes.

The roadway is supported by cross-beams, 9x4 inches,
placed 4 feet apart between centimes, supported by the lon¬
gitudinal beams, notched 1 inch upon them, and bolted
down. On these, 3-inch planking is laid, and covered
by wood sheathing lj inch thick, crossing the planking
obliquely, and having tarred paper interposed. Over this
sheathing lies a coat of gravel, bedded in Archangel and
coal-tar pitch to the thickness of 1 inch, forming a com¬
pletely water-tight sole; covering this is a layer of stiff'
clay puddle 2 inches in depth, and over all a layer of
common road metal, blinded with fine gravel and sand.
The width of the roadway within the parapets is 18 feet.

The parapet railing is formed by posts 6 inches square,
being the continuation of the ties of the arch trusses,
secured to the roadway planking by iron stirrup straps,
and tenoned at the top into a rail, 6 inches by 4 inches; the
top rail is surmounted by a coping 7 inches broad, 1^ inch
thick in the middle, and 1 inch at the sides, and it is fur¬
ther secured by an iron strap at each post, passing over the
1 top and down each side of the post, fixed with nails.
Each compartment is fitted with braces and counter-braces,
and a panel rail at bottom, 4 inches broad by in depth,
the former halved at their crossing, and tongued into the
posts at head and foot, and the latter tenoned into the
posts. Two lines of bars, 5x2 inches, run along the inner
side of the railing, notched into and upon the posts each
^ inch, and securely nailed both to the posts and to the
diagonals. For descriptions of Figs. 3 and 4 on this plate,
see Centres.

CENTRES.

Centres are works in carpentry which serve to sustain
the masonry of vaults or arches during their construction,
and until the insertion of the keystone gives them the
power of sustaining themselves. Under this view centres
are true scaffolds.

Centres are of different species, according to the nature
of the curvature of the vault. The disposition of the tim¬
bers of which they are composed is analogous to that of
timber bridges and of roofs, and the different elementary
pieces are known by the same names. Each centre is com¬
posed of a series of frames placed parallel to each other,
and perpendicular to the axis of the vault or arch. They
are tied together horizontally, and covered with boarding,
technically termed lagging, which forms the cradle or
mould to support the masonry.

Centres are distinguished also by the mode in which
they are constructed. Thus there are flexible centres,
which may undergo a change of form during the con¬
struction of the vault, by the varying nature of the load.
Of this kind was the centre of the bridge of Neuilly,
constructed by Peronnet. There are also fixed centres,
which maintain their form under the varying load, and
these flexible and fixed centres may be either in one span
supported only at the springing of the vaults, or they may
be sustained by intermediate supports.

The flexible centre is composed of a series of triangular
trusses, arranged so as to form concentric polygons, the
angles of the one corresponding to the sides of the other.
Hardouin Mansard has the reputation of being the inven¬
tor of this principle. It was applied by him in construct-

172

PRACTICAL CARPENTRY AND JOINERY.

ing the centres for building the bridge of Moulins in 1706,
but there is proof that it had been previously proposed by
Claude Perrault for a wooden bridge designed to cross the
Seine at Sevres.

In Plate LIX., Fig. 2, is shown Peronnet’s centre for
the bridge over the Seine at Neuilly, an example on the
lamest scale of this kind of centre.

The annexed diagram (Fig. 482) is a representation of
the framing at A in the plate.

The flexibility of this system arises from the smallness
ot" the angle of inclination between the timbers, and the
number of articulations or joints on which the pieces can
turn and change their inclination relatively to each other.
The result is, that as soon as the centre is charged with
the weight of the masonry on its haunches, it sinks there
and rises at the crown. To remedy this gi’ave inconveni¬
ence, which is attended by a complete change in the form
of the vault, and Fig. 482.

may result in seri¬
ous accidents, it is
necessary to load the
crown of the centre
with such a weight
as shall equilibriate
the load on the
haunch, and to vary
this as the work pro¬
ceeds, so as to main¬
tain the integral form. In practice this equilibriating load
is really the voussoirs which are laid temporarily in their
place before being properly set, a process involving a great
expense of labour and a continual manipulation, attended
by considerable risk.

The sinking of the haunches and rising of the crown
were so great in the centres of the bridge at Neuilly, that
to restore them to their primitive form, and to enable
them to retain it during the construction of the arch, it
was found necessary to load their summits successively
with weights of 120, 420, and 448 tons. When the arches
were keyed, the general sinking of the centres amounted
to from 275 inches to 375 inches'in twenty-four hours
When the centres were struck the arch descended.

It is not necessary to enlarge further the notice of the
species of centre which has been classed as the flexible
centre, as in this country it is entirely unknown; and
although it was used in some magnificent works, and its
use was sanctioned by the high authority of Peronnet,
yet it is now abandoned in France also.

The second class, which has been termed the fixed or
inflexible centre, is that which has alone been used in this
country, which has produced examples exhibiting a happy
combination of science and constructive skill. It may
well be supposed that the art of disposing the pieces of tim¬
bers, which enter into the composition of a centre, in such
a manner that they may sustain, without change of form,
all the efforts of the voussoirs, varying with the progress
of the work until the key-stone is placed, and to determine
the dimensions of the timber, is not of easy attainment.

The theories which the learned have given to the world
on the subject of centres are so general, as to be totally
inapplicable to particular cases; and they are founded
besides on abstract reasoning, without reference to the
materials, and those means and appliances of the work¬

men which sometimes totally change the state of the
question and always modify the results. Unless, indeed,
the design of the framing of a centre be of a very simple
nature, it would be very difficult to attempt to estimate
the forces and the strengths required to sustain them. The
best that can be done is only approximative, and no more
is attempted in the rules which are subsequently given.

The result of investigations on the pressure of arch¬
stones on a centre is, that the centre should be combined
in such a manner as to withstand as advantageously as
possible the effort of the stones to slide upon their beds.

Experiment has shown that hard stones have not any
tendency to slide on the bed until it is elevated to about
30°; and it has also shown that when the stone is set in
fresh mortar it does not begin to slide until the bed is ele¬
vated to an angle of from 34° to 36°. Voussoirs of soft stone,
absorbent of moistui'e, have been raised to an angle of 45°
without sliding, when the centre of gravity did not fall
without their base.

Reasoning from these experiments, and assuming 32°
as the limiting angle of resistance, the conclusion would
be arrived at, that the centre did not requii'e to com¬
mence until the arch stones had reached that angle; and
in the Pont du Gard and the arch of Cestius at Rome,
the corbels on which the centres were supported remain
at from 25° to 28° above the springing.

Beyond 32° the weight on the centre goes on increas¬
ing as it approaches the key-stone; but in practice it is
safe to consider the whole weight of the stone as resting
on the centre, when a vertical line drawn through its
centre of gravity falls without the lower bed of the stone;
and the amount of error is not great, and is on the safe
side, if this is taken to be the case when the bed of the
stone exceeds 60°. But to make this observation more
accurate, we quote Mr. Tredgold’s words. He says, “When
the depth of the arch stone is nearly double its thickness,
the whole of its weight may be considered to rest upon
the centre, at the joint which makes an angle of about 60°
with the horizon. If the length be less than twice the
thickness, it may be considered to rest wholly upon the
centre when the angle is below 60°, and if the length
exceed twice the thickness, the angle will be considerably
above 60° before the whole weight will press on the centre."

To find the pressure of the arch stones on the centre,
in a direction perpendicular to its curve, Mr. Tredgold has
given the following formula:—W (sin a —/ cos. a) = P.
Where W is the weight of the stone, P the pressure on
the centre, a = the angle which the lower bed makes
with the horizon, and/ = the fraction; and by applying
this formula he obtains the following result:—-

When the bed makes, with the

the pressure = the weight,

horizon, an angle of

multiplied by

34° .

. -04

36 .

. -08

38 .

. -12

40 .

. -17

42 .

. -21

44 .

. -25

46 .

. -29

48 .

. -33

50 .

. -37

52 .

. -40

54 .

. -44

56 .

. -48

58 .

. -52

60 .

. -54

/ Whitedel 1

Bl.ACKJ K S- SOX; GLASGOW. EDINBURGH. Se LONDON

J.W. Lowry, fc

- '

PLATE LVm

on nrm is o.

BY THOMAS TELFORD, C E.

Fur 1

*i t’/iLri/iij r/' DcinWhBrt'liic, EilhiTnivqh .

flQ. 3 .

I I.A Kll' v SI'S r,LASr,u» EDINBCRGH s LONDON

CENTRES.

173

The application of this may be illustrated by an example.
Suppose it was required to find the pressure of the arch¬
stones on the centre, in a space comprehended between
the angles of 32° and 42°, that is in 10°, take out of the
preceding table the decimal opposite every second degree,
for the first 10°, and add them together as follows:—

Multiply this number by the weight of a portion of the
arch stones comprehended between two degrees, and the
product will be the pressure on the centre.

Suppose the centres to be 6 feet apart from outside to
outside, and the depth of the arch stones to be 8 feet, as
in Waterloo Bridge, and the space comprehended between
two degrees, measured at the middle of the depth of the
stone, is 2 feet, there is obtained—

6 feet = the distance betwixt the centres.

8 feet — depth of the arch stones.

2 feet = width of the portion sought.

6 X 8 x 2 = 96 cubic feet, which, multiplied by 160 lbs.
the weight of a cubic foot of stone, = 15,360 lbs., the
weight of two degrees; and this, multiplied by '62, gives
9523 lbs. for the pressure of 10° of the arch stones on one
centre frame.

The pressure on the centre, it has been said, may be
considered equal to the whole weight of the stone, from
60° to 90°, and from 60° to the angle of repose the pres¬
sure rapidly diminishes. It would be manifestly errone¬
ous, therefore, to make the frame of the centre equally
strong throughout; and the endeavour in designing it
should be to apply the strength only where it is really
required. How this has been managed by different de¬
signers will be seen by examining the drawings of examples
of centres in Plates L., LV., LVI., LVII., LVIII.,and LIX.

In designing centres, the observation which Mr. Smea-
ton makes on his own design for the centering of Cold-
stream Bridge may be held to be a sound practical maxim.
“What I had therefore in view,” he says, “was to distri¬
bute the supporters equally under the burden, preserving
at the same time such a geometrical connection through-
out the whole, that if any one pile or row of piles should
settle, the incumbent weight would be supported by the
rest. With respect to the scantlings, I did not so much
contrive how to do with the least quantity of timber, as
how to cut it with the least waste; for as I took it for
granted the centre would be constructed with east coun¬
try fir, I have set down the scantlings, such as they usually
are, in whole baulks, or cut in two lengthways; and as I
think the pieces will suffer less by notchings in the middle
intersection, and being cut into small pieces, it will re¬
main of value for common building after it has been done
with as a centre.” And he adds in favour of simplicity,
“As the construction is more obvious, and less exactness
required in the handling, I should expect to get a good
centre made by some in this way that would make but
bad work of the other.”

Fig. 1 , Plate LVII., shows a centre for a small span. It
consists of a trussed frame, of which A is the tie, B the
principal, or, as its outer edge is curved to the contour of
the arch, it is called by Mr. Smeaton the felloe, c the post

or puncheon, and F a strut. The centre is carried by the
piles D, on the top of which is a capping piece E, extending
across the opening; and the wedge blocks a are interposed
betwixt it and the tie-beam.

Figs. 2 and 3 are centres, also for small spans; and of
this Fig. 2 is the best in its arrangement.

In Fig. 4 the weight of the centre of the arch is carried
directly by the struts to the ends of the tie-beam, the tie-
beam struts and king-post A making a simple king-post
truss. Two other trusses support the arch above the
haunches, and have a collar-piece between them at half
the height of the arch. The ends of the cross-braces are
seen at a.

Fig. 5 shows a centre with intermediate supports and
simple framing, consisting of two trusses formed on the
puncheons over the intermediate supports as king-posts,
and subsidiary trusses for the haunches, with struts from
their centres parallel to the main struts.

In Fig. 6 the weight is fairly distributed between the
three points of support. The ends of transverse braces
connecting the trusses are seen at a.

Fig. 7 shows a system of supporting the arch rib from
the intermediate supports by radiating struts, which,
with modifications to suit the circumstances of the cases,
has been very extensively adopted in many large w T orks,
and of which other examples are here presented. The
struts abut at their upper end on straining pieces, or apron
pieces, as they are sometimes termed, which are bolted to
the rib, and serve to strengthen it. The ends of the trans¬
verse braces are seen at a a.

Fig. 8 is the centre of a bridge over the river Don, in
Aberdeenshire. The bridge consists of five arches, each
of 75 feet span. It was erected from designs of Thomas
Telford, Esq., by Messrs. John Gibb & Son, of Aberdeen,
who designed the centres.

In this centre the weight is in a very simple and inge¬
nious manner discharged to the points of support. The
piles are cross-braced; the sides of the braces are seen at
dc\ and the puncheons above are also connected by a
system of cross-bracing, b b.

Plate LVIII., Fig. 1. — Centering of Gloucester Over-
bridge.— This centre, designed and constructed by Mr.
Cargill, the contractor for building the bridge, consists of
a series of trusses supported on piles, which being in some
cases 16 feet apart, allowed the navigation to be carried on.

There are six parallel rows of piles fixed in the current
of the river, each row connected with cross-braces and
caps, and each supporting a rib, which forms the actual
centering. The piles and ribs are further steadied by
diagonal braces. Between the pile caps and the ribs are
placed the wedges or slack-blocks by which the centering
is lowered after the keying of the masonry.

Mr. Cargill, in a letter to Mr. Telford, dated March 26,
1832, thus describes the construction of the centre:-—

“ In constructing the centering for this bridge, I first
laid a platform perfectly level, and a little larger than the
centering which was to be made; I then struck it out full
size upon this platform, firmly fixing centres to the dif¬
ferent radii. The timber was Dantzic, being much harder
and of larger dimensions than Memel, and mostly 15 inches
square. The iron straps were of the best iron.

“ The piles upon which the centre was to stand were
then driven. They were of Memel timber, with wrought

174

PRACTICAL CARPENTRY AND JOINERY.

iron shoes, and caps framed upon the tops to the proper
height. Upon these caps was laid another tier of beams
lengthways of the centre one, under each rib; upon these
beams were fixed the wedges, which were of three thick¬
nesses, the bottom one being bolted down to these beams,
the tongue or driving piece in the middle being of oak,
and well hooped at the driving end; the top side of the
upper piece was laid perfectly level and straight, both
transversely and longitudinally. The wedges were rubbed
with soft soap and black lead before they were laid on
each other.

“ Each rib of the centre was then brought and put to¬
gether upon a scaffold made on the tops of these wedge-
pieces, and lifted up whole by means of two barges in the
river and two cranes on the shore. The scaffold was ex¬
tended thirty feet beyond the striking end of the wedges,
to lay the last ribs upon previous to raising, also to stand
upon for finally striking. After the ribs were properly
braced, they were covered with 4-inch sheeting piles,
which had been used in the cofferdams.

“ That this centre was well suited to its purpose is
known by its not sinking more than one inch when we
keyed the arch. My greatest dread was the coal-boats
which trade on the Ledbury Canal, forced adrift by floods
in the Severn, and striking against the centre before we
could close the arch. To prevent mischief of this kind, I
drove the piles for extending the up-stream side of the
scaffold (or rather the platform on which it was originally
constructed) very firmly into the clay, so that they might
resist the stroke of a boat before she could touch any of
the supports of the centering.

“ In the month of December, when within twenty feet
of closing the arch, a very high flood being in the Severn,
two of these boats loaded with coal came adrift, struck
the outside piles, which were of Memel logs, broke two of
them, and then sank against the main bearing piles which
supported the centre, one boat on the top of the other.
These boats being seventy feet long, raised a considerable
head of water over them, and lay there until the flood sub¬
sided, which was many weeks; had not these upper guard
piles weakened the shock, I believe the whole centre and
arch would have been destroyed.

“ When the spandrel walls were built up two courses
below the crown of the arch, and the internal brick walls
to the same height, we struck the centre, which was done
by placing beams upon the top of the work directly over
the ends of the wedges. To these beams successively was
fixed a tackle, to which, at the lower end, was slung the
heavy ram with which we drove the piles, with tail ropes
to it, and swung exactly so as to strike, in its swinging,
when pulled back, the driving end of the tongue piece of
the wedge. This ram, of 12 cwt., when pulled back by
eight men, and two men to pull it forward, gave a most
tremendous blow, yet twenty or thirty blows were re¬
quisite before we could perceive the wedges to move; but
after they once moved, they slid themselves, and we put
in pieces to stop them going further than was required.
The whole time of striking did not, I think, exceed three
hours, although we had the ram to remove and the tackle
to refix at eveiy set of wedges. I was afraid that no force
we could bring against these wedges would move them
under such a weight as the entire arch, they themselves
being a heavy body, and it was no small joy to see this

effected so easily. I am persuaded no wedges placed in the
usual way could have been disengaged, as no force could
be brought to act upon them sufficient for the purpose.

“Wethen disengaged the covering (which, it will be re¬
membered, was composed of sheeting piles from the coffer¬
dam), and let down the ribs as they were put up; took
them to pieces and carried them ashore. The whole of
the bearing piles were then drawn by two levers, each
made of two forty-feet logs and strong chains. Every
pile was drawn, and although the expense was consider¬
able, they paid well for the labour.”

Fig. 2 .—The Centering of Dean Bridge, Edinburgh,
constructed by Telford, in 1831.—The height from the
bed of the river to the roadway of this bridge is 106 feet,
and the bridge consists of four arches, each of 90 feet span.
The carriage way is carried on the inner arch, and.,the
larger wing arch, which projects 5 feet beyond the other,
supports the footpath. No. 1 sIioavs the centering for this
latter arch, and No. 2 the centering for the main arch.

Fig. 3 .—The Centering of Cartland Craigs Bridge is
here represented.-— Cartland Craigs Bridge, built by Tel¬
ford, in 1821, spans the precipitous banks of the Mouse
River. It consists of three arches, each of 52 feet span,
and the centre arch is 122 feet in height.

Plate L.— Figs. 6, 7, 8, 9, and 10, in this plate, illus¬
trate the construction of the centering used in construct¬
ing the Ballochmyle Viaduct on the Glasgow and South-
Western Railway.

The river Ayr, which the viaduct spans by an arch of
180 feet, offers natural facilities for crossing it by one
span, owing to its high and rocky banks. This viaduct
is erected on private grounds of great beauty, rendered
classic by the song of Burns, and the railway company
were bound not to interfere further than was actually
necessary Avith the natural beauties of the river and its
banks. With the view of carrying out that arrangement,
the viaduct, as represented in the plate, Avas designed and
constructed.

The main arch of this viaduct, which is semicircular,
has a span of 180 feet, and is in height, from the bed of
the river to the croAvn of the arch, about 160 feet. It
was therefore necessary to construct scaffolding and cen¬
tering of no ordinary description. The principle on which
this Avas done is new and simple. It Avas executed as much
as possible xvith Avhole timbers, of Avliich the uprights
consisted, and Avhere the distance of the points of thrust
of the frame was not great, the struts and waliugs Avere
of half timbers; the lagging consisted of battens. It Avill
be seen from the representation in Plate L., and more
distinctly in the picturesque view taken during the opera¬
tions, and which forms the engraved title to this Avork,
that the materials for constructing the viaduct Avere con-
veyed along by large Avaggons on a stage projected from
the centering, and from them removed by travelling
cranes moving longitudinally and transverse^, The
details of construction of this stage, and the general
arrangement of the centering, do not call for special re¬
mark. It may, hoAvever, be necessary to add, that the
Avhole timber Avork in connection with the construction of
this viaduct perfectly ansAvered the purpose.

Plate LY.— Fig. 7, in this plate, is the centering of
viaduct over the Union Canal, near Falkirk, on the Edin¬
burgh and Glasgow Railway.

FLA TE L LX

*■

Fiq.2:

Fig. 3.

Design for a stone B ruing arid. Centering.

<£. J

VJ -|

200

120

* 230

1 1 1 LI 1IL11J-

. —1-

—i-

-1-

— t —

— i —

-1 —

-1-

-1 —

BLACK1E &#SO!N , GLASGOW, EDIH3TJRGH & LONDON.

l\' A. Beever. So. ^

J. White, del

CENTRES.

175

The reason for constructing this large arch over the
canal, and the description of centering shown in the plate,
was to meet the requirements of a clause in the railway
company’s act, by which certain heights and widths were
to be preserved over the footway, carriage-way, towing-
path, and canal, and no piers were allowed to be placed
in the space between the abutments of the large arch,
even for temporary purposes. The figure in the plate
shows the principle on which the centering was con¬
structed and kept in its position. The centering shown on
the smaller arch of this viaduct does not call for any par¬
ticular remark. Both were constructed so as to be simply
and easily put together, using whole timber, so as to
prevent waste.

Figs. 8 to 11, also in Plate LV., illustrate *the con¬
struction of centres for the viaduct of the North British
Railway, carried over Dunglass Burn. The span of the
large arch is 132 feet, and its height 110 feet.

The principle of construction is nearly that of Balloch-
myle Viaduct, already described. The smaller land arches,
however, show a variation in the construction.

Plate LVI., Figs. 3 and 4— Fig. 3 is a longitudinal, and
Fig. 4 a transverse section Of one of the arches of a via¬
duct, illustrating the mode of constructing and supporting
the centering. The viaduct was erected over the Lugar
Water, near Old Cumnock, in 1849, by J. Miller, Esq., C.E.

The supporting framing consists of four sets of horizon¬
tal timbers, sustained at their ends either by corbels in
the piers, or by vertical timbers carried up from the
ground, and resting at their centre on the capping-pieces of
the series of seven vertical posts, seen in Fig. 4. These verti¬
cal posts rest on a sleeper below, and are firmly braced,
counter-braced, and shored to give lateral stiffness. The
two exterior posts carry the scaffolding used in the con¬
struction of the arch, and each of the five interior posts
is placed under the middle of a centre.

The upper horizontal timber supported by the posts
carries the centre striking wedges, and the two extreme
wedges are carried by the impost of the piers. On these
wedges the tie-beams of the centres rest.

Plate LIX.— Fig. 1 is the centre used in the construc¬
tion of Waterloo Bridge.

Fig. 2.—The centre used in the construction of the
elegant bridge over the river Seine at Neuilly, and already
noticed in the introductory portion of this section.

Fig. 3.—A design by Mr. White. Centre for a seg¬
mental arch of 120 feet span, somewhat after the manner
of the centre for Waterloo Bridge. A c B C A are the
felloes or arch of the centre, on which the lagging rests.
To these are bolted the abutment-pieces d d of the struts
a a a a, and the lower ends of the struts rest on iron sole-
plates on the tops of the upper striking wedges F F.
The radial posts fff are in pairs, one on each side of the
struts a a ; they are bolted together, and secured to the
felloes by iron straps: c c are transverse ties in pairs,
bolted together through the radial posts: h h additional
transverse ties, k principal tie, and b b straining pieces.
D D F F are striking wedges; e e e f struts resting on
sleepers laid on the footings of the piers, and having
capping-pieces g g, on which the striking wedges rest.

On Removing Centres.

The removal of the centres of a bridge wdien loaded

with the weight of the arch stones is always a delicate
operation, demanding prudence and patience. It is neces¬
sary to allow sufficient time for the setting of the mortar
used in the construction of the arch. It may be conceived
that unless this is done, and if the centres are struck, as it
is termed, before the mortar acquires proper consistency to
resist the pressure thrown on it, there would be a sudden
sinking of the whole arch, which might pass the limits of
safety.

In the bridge of Nemours, in France, the arches of
which were surbased, the pressure on the centres was
found to be so great that the usual mode adopted in
France for the striking of the centres could not be fol¬
lowed. The mode of supporting the arch stones on the
centres there adopted was somewhat different from the
practice of this country. In place of a continuous cover-
rig. 483. ing of boards, which is here called

lagging, the bridge in question had
the following contrivance (Fig. 483):
a is part of the centre; on this is
placed the wedge-piece b, support¬
ing the plank c, which continues
across the arch, there being one for
every course of voussoirs. The
voussoir e is supported on c by the wedge-piece d.

The striking the centres should have been performed
by withdrawing the wedge-pieces b and d of every alter¬
nate plank, and then the plank c, and then repeating the
operation, leaving a fourth-part remaining, and so on till
all were withdrawn; but, as has been said, this could not
be done, and recourse was had to the expedient of cutting
away gradually the feet of the principals, which rested on
the corbels of the abutments—a mode clumsy in the ex¬
treme, and also dangerous.

The method of striking the centres practised in this
country is preferable in every respect to the French mode.
That usually adopted is seen in Plate LIX. Figs. 1 and 3.
In Fig. 3 it will be seen that each centre frame is sup¬
ported on posts e e e, springing from the footings of the
pier. These posts have capping-pieces, g g, extending
across the whole width of the arch. Between the capping-
pieces and the frame are interposed three pieces of timber,
the two outer of which, F F, have their inner faces stepped
in wedge-shaped surfaces, and the intermediate piece, v D,
is doubly stepped in the same way to correspond. If the
position which these pieces relatively hold is remarked, it
will be seen that when the piece D is driven back towards
the arch, the two pieces F will approach each other, and
the centre will thus be gently lowered. A great advan¬
tage is the power that this mode gives of merely easing
the centre first, and then lowering it by degrees, so that
the voussoirs come gently to their bearing.

A method of striking the centre, closely resembling the
French method described above, was practised at the
Chester Bridge. Each centre frame there had a rim of
two thicknesses of 4-inch plank bent round it; and on
this the lagging, 4A inch thick, was supported by a pair
of folding wedges, 15 or 16 inches long, 10 or 12 inches
broad, and tapering about 1^ inch. As there were six
centre frames in the width of the bridge there were neces¬
sarily six pairs of striking wedges for each course of vous¬
soirs. This arrangement gave the power of easing any
portion of the arch, or of tightening one part and slacken-

176

PRACTICAL CARPENTRY AND JOINERY.

ing another, as the symptoms exhibited by the stone work
as it came to its bearing required. The able constructor
of this centre, with the power which this mode of con¬
struction gave him, preferred striking the centre while the
mortar of the arch-stones was yet green and pasty, easing
it a little at first to permit the joints to accommodate
themselves to each other, and so proceeding gradually till
they obtained their perfect bearing.

A different method was employed by the constructor of
the centre for Gloucester Bridge. In this centre the
wedges were placed under all the supports, and in this
way a very great control over its movements could be
exercised. A similar arrangement was adopted by Mr.
Telford in many of his larger works, as in the Dean Bridge
and Cartland Craigs Bridge, Plate LVIII.

GATES.

A gate, in its ordinary acceptation, may be regarded as
a moveable portion of a fence or inclosure; and under this
aspect its most obvious representative is a rectangular
plane of Avood or iron, a door, in point of fact, and this
is one of the forms it usually assumes. But in many cases
such a gate would be objectionable on account of its Aveiglit
and costliness; and there is, therefore, substituted for the
rectangular plane of wood a rectangular frame of Avood
or iron, sparred or barred in such a manner as to prevent
the passage of animals.

In- ordinary field-gates the width of the opening be¬
tween the posts, to which the gate is hinged, is usually
9 feet 8 inches, which gives a clear roadway of 9 feet
when the gate is opened. The height of the gate de¬
pends, of course, on the height of the fence, of which it
forms a part. In ordinary cases this may be five feet,
and allowing for the height of the lower bar of the frame
from the ground, there are obtained as the average dimen¬
sions of a field-gate—-length 9 feet, and height I feet.

This rectangular frame, then, is the elementary form of
the gate. Its\ T ertical sides are called styles; that to which
the hinges are attached being called the hanging-style,
and that to which the fastening is attached the fallinof-
style. The horizontal sides of the frame, and all the bars
parallel to them, are called rails.

Such a frame suspended by one of its shorter sides
would not maintain the rectangular form; it would be¬
come rhomboidal by the falling down of the other sides
by their own Aveight. To enable it to maintain the
rectangular form it is necessary to add an angle brace,
which may be applied either as a tie or a strut, as the
material used is iron or Avood.

But the gate may be resolved into a simple elementary
form thus:—Let the diagram (Fig. 484) represent —a the
hanging-style, b the
top - rail, and c the
brace or strut of a
gate, all firmly united.

This is evidently a
simple truss, like the
jib of a crane; and if a weight AV be hung to its outer
end, the rail b Avill obviously be in a state of tension,
and the brace c in a state of compression; that is, b is a
tie, and c is a strut. Again, let a (Fig. 485) be the hang¬
ing-style, b the lower rail, and c the brace, and it is now

obvious that c is a tie and b is a strut. Therefore, keep,
ing in mind the constructing maxim that iron should
be used as a tie and wood as a strut, Avhen the brace is

placed as in Fig. 484
it should be of timber,
and Avdien as in Fig.
485 it should be of
iron. But it may be
objected that, if this
rule Avere adhered to,
it Avould not be possi¬
ble to construct a timber gate, as it requires both ties and
struts. Noav, the pieces of wood of which a gate is formed
are framed together, and held in their places by bolts,
nails, orVooden pins, and the frame is hung to the posts
by iron hinges. The straps by which these hinges are
attached to the frame are generally so long as to embrace
a considerable portion of the length of the rail, and majq
therefore, be made subservient to rendering the timber
rail b (Fig. 484) competent as a tie; whereas if timber
be used for the brace c, as in Fig. 485, it is evident that
the strength of the brace has very little to do with the
stability of the framing; that, in point of fact, the stability
is due entirely to the strength of the nails, or to the slight
resistance to tearing that the fibres of the timber betAveen
Avliere the nails are driven and the end of the brace offer;
or it must be insured by adding an iron strap to each end
of the brace. But this extra iron is expensive; and as oy
simply making the brace a strut in place of a tie, the iron
strap of the upper hinge can be made to supplement the
deficiency of the upper Avooden rail as a tie.

Fig. 486 is the ordinary field gate, constructed on the
principles above described. The top rail a becomes a

tie, and is secured to the hanging-post by the strap of the
upper hinge embracing it, and being bolted through it.
The elementary frame is thus rendered perfectly rigid,
and the addition of the front or falling-post b, and the
bars e, /, g, h, completes the fence. By this mode of con¬
struction the tensile strain is thrown on the bolts and
strap of the upper hinge.

Having thus pointed out the principle of stability in
the framing of the gate, we shall proceed to give some
practical details, shoAving its application to frames of wood
and iron. In a timber gate, then, the diagonal bar should
form a strut, as in Fig. 485, and not a tie. Were we
merely to consider, in the application of the diagonal bar,
the angle which should be the best fitted to insure the
frame maintaining its form, we should adopt the angle of
45°. But the bar placed at this angle would not extend
half-way along the top rail, and the result would be the
introduction of a new element of destruction in the cross¬
strain, to which the top bar would then be exposed; for
the point of the strut would be a rigid fulcrum, o\ r er
I which the top bar would be liable to be broken, by a

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GATES.

177

weight hung to its outer end. Practically, therefore, it
is better that the strut should make a smaller angle with
the horizon; that in fact it should be attached to the top
bar, at just such a distance from the end of the latter as
shall not so much weaken it, as to prevent it forming a
perfect abutment to the thrust of the strut; and, in ordi¬
nary cases, ten inches or a foot is sufficient. The junction
of the strut and top rail should be by the same kind of joint
as that by which the toe of a rafter is let into the tie-beam.
Fig. 486 shows the general appearance; and Fig. 487 some
of the constructive details of a gate, of the construction here
advocated. The hanging-style
of the gate is 44 inches square
in section ; the falling-style is
3 inches square. The top rail
a is 44 inches square at the
hanging style; and 3 inches
by 44 at the falling-style.

It is tenoned into the styles.

The diagonal bar m is 4^
inches deep, and 2 inches
thick; tapering to the upper end for the sake of light¬
ness. It is tenoned into the hanging-style, and notched
into the top rail. The other rails e, f, g, h, are 44 inches
deep at the hanging-style, and taper to 34 inches deep
at the falling-style. They are 14 inch thick, and are
tenoned into the styles, the tenons having only one
shoulder on the outside, so as to allow of larger cheeks to
the mortises in the styles. In Fig. 487, b is a vertical
section through the rails and diagonal, looking towards
the hanging-style. The upper hinge has its straps pro¬
longed, as seen in Fig. 486, so as to embrace a considerable
portion of the top rail, that the bolts and nails which
fasten it may have a secure hold in the solid wood. The
under hinge does not require this prolongation of the
straps, as the force upon it is a thrusting, and not a draw¬
ing force.

As the bottom rail is so much thinner than the hang¬
ing-style, a small piece of wood, of the depth of the rail,
is generally added at e. Fig. 487, as a rest for the strap
of the hinge. The tenons of the rails are secured in the
mortises by pins, and the diagonal is securely nailed to
the rails at its intersection with them. Before putting
the parts together, the tenons and the intersecting parts
of the rails and diagonals should be coated with white
lead in oil. The great destroyer of the gate is rain, which
falling on the thin top bar, as usually constructed, soaks
into the joints and induces rot. The wide top rail in the
gate described, affords protection against this; and the
only parts exposed to it are the intersections of the dia¬
gonal and rails; but, by giving the upper edges of these
a slight bevel, so as to throw the water from the joint,
the risk of injury from this cause is destroyed. The top
rail should be saddle-backed, or rounded on the top. Some¬
times vertical bars are added to the gate; but these, as
we have already said, add to its weight, and not to its
strength; and, moreover, introduce new joints, exposed to
the action of the rain, and they should therefore be dis¬
pensed with.

Plate LX—Park and Entrance Gates.—Figs. 1, 2,
and 3 are examples of park gates, of open frames. Figs.
4, 5, 6 and 7 are elevations of entrance gates in various
styles.

In Fig. 5, No. 1, it will be observed that two small
rollers are inserted in the bottom rail of the gate, and run
on iron rails, laid on stone sleepers fixed in the ground.
The hinge-pin, too, is continuous between the top and
bottom hinge, and serves merely as an axis on which the
gate rotates, the whole of the weight being sustained by
the rollers. It has sufficient play to allow the gate to rise
as it opens. Fig. 5, No. 2, is the strap of the top hinge,
and the same construction of strap is applicable to all the
previous examples, where the object is to extend the hold
of the strap on the top rail. The strap of the bottom
hinge'may in all cases be very short, and not as in Fig. 1,
where for uniformity’s sake it is extended to the same
length as the upper strap.

Fig. 6, No. 2, is a section through the upper part of the
lower rail of Fig. 6, No. 1; and Fig. 7, No. 2, a section
through the rail of Fig. 7, No. 1. Both of them show
that at the lower side of the panel the moulding is sub¬
stituted by a splay or weathering to throw off the water.

Plate LXI.— Dock Gates.—Fig. 1 is an elevation of the
convex side of one of the gates of the Coburg Dock, Liver¬
pool. Fig. 2 is an elevation of its concave side. Fig. 3 a
horizontal section through the gate, immediately above
the sill. Fig. 4, a horizontal section under the top rail.

The framing of each gate or leaf consists of a heel-post,
on a pivot fixed to which the gate turns; of a head-post,
or, as it is sometimes called, a mitre-post, and thirteen
curved horizontal rails, called bars or ribs, tenoned into
the head and heel posts. The whole are fastened by iron
straps on each side securely bolted. The vertical straps,
it will be seen, have horizontal branches at each rib, and
the diagonal strap, serving as a tie, is united to it at the
top. The libs are rebated to receive the close planking
which extends to the first rib under the top, and which is
flush with their face. There are also three vertical posts
on each side of the gate, at equal distances apart, securely
bolted, extending from the bottom of the gate to the top
of the rib where the planking ends. The back of the
heel-post is formed truly circular in section to fit closely
the segmental groove in the stonework, called the hollow
quoin. Each gate is hung at the top with a wrought-iron
collar in a cast-iron anchor block let into the stone-work,
and at the bottom it turns on a pivot pin of hard brass,
moving in a cast-iron cup let into the masonry (see the
detailed drawing of this, Fig. 7, Plate LXII.) The top
of the pivot is let into a brass socket fixed in the bottom
of the heel-post by wedging, and between them there is
interposed a ball of hard steel. All these parts are truly
turned and fitted. The outer end of each gate is sup¬
ported by a brass roller with a lever adjusting apparatus.
The roller traverses the cast-iron segments let into the
masonry, as seen in Fig. 3, and detailed in section in
Fig. 6, Plate LXII.

The two central divisions, formed by the vertical bars,
contain the paddles or sluices, which are formed of cast-
iron faced with brass, and work in cast-iron framing let
into the gate.

Part of the cast-iron work of the sluices is shown in
detail in Fig. 5, Plate LXII., and the whole of their
moving parts will be understood by an inspection of
Fig. 1 of the same plate.

On the top of the gate is a gangway, supported on
brackets, and provided with iron stanchions, and chains

178

PRACTICAL CARPENTRY AND JOINERY.

or rails as a fence. The outside stanchions are fitted in
sockets, and are made to unship.

Plate LXII.— Fig. 1 is the elevation, Fig. 2 a ver¬
tical section, and Figs. 3 and 4 horizontal sections of the
top and bottom of one of the gates of the Victoria Dock,
Hull; and Figs. 5, 6, and 7 are details of the parts which
have been already referred to. The description of the
construction of the Coburg Dock gates applies equally to
this, and need not be repeated. The following is an ex¬
tract from a specification of the engineer of these works,
Mr. J. B. Hartley, for a gate of similar dimensions:—

There are to be two pairs of gates for a clear opening
of 60 feet from the outer face of the hollow quoins. The
ribs, heads, and heels of these gates are to be either of
English oak of the very best and.quickest grown timber;
or of African oak, but no mixture of these woods in the
framing of any gate will be allowed. The planking to be
of greenheart timber. Each rib, head, and heel of each
gate is to be formed of a single and self-contained piece of
timber squared through to the full dimensions figured
upon the drawings. The whole of the bolts, spikes, nuts,
washers, and all other wrouglit-iron work connected with
the gates, excepting the up and down cross and diagonal
straps, the gangway-stanchions, and anchor-bolts, are to
be galvanized in the best possible manner.

The sluices in the gates are to be faced with brass, and
fitted up in every respect in the best style of workmanship,
and in every respect in accordance with the drawings.

A cast-iron cup must be prepared and let into the
masonry to receive the pivot pin in the heel of each
gate.

These pivot pins are to be of hard brass, and to be
truly turned, so as to fit the cup, and also a steel ball
working between the top of the pin and the heel casting
as shown, &c., which must be bored to receive them, as

also must the heel castings of the gates. The heel cast¬
ings are to be of hard brass, firmly wedged into the foot
of the heel-post.

When the gates have been framed and fitted together
the heels are * to be dressed off truly round, and are to be
completely covered for 15 feet above the heel castings,
with broad, flat headed copper nails, 226 to the pound, to
fit the hollow quoins, which must be rubbed and polished
perfectly smooth, and truly vertical from top to bottom,
in the hollow between the water lines, to receive them.

The segment plates, on which the truck wheels of the
gate are to travel, are to be of cast iron, in every respect
in accordance with the drawings; they are to be carefully
bedded down, very truly, upon the masonry prepared to
receive them, and when bedded are to be fastened down
by lewis bolts, as shown upon the drawings.

Crab-boxes and gearing are to be provided on the gang¬
way of each gate to work the sluices in the gates.

Wrought-iron stanchions are to be fixed on the inside
of the gangway of each gate of a permanent character,
and are to be provided with two rails of 1^ inch round
iron, screwed up to each stanchion, on each side, as shown
in the drawings.

The stanchions on the outside of the gangways are to
be moveable, and made to ship and unship into sockets
provided for them; these moveable stanchions are to be
provided with chains of galvanized quarter-inch round
iron. Anchor-blocks are to be provided of cast iron, and
let into the top of each set of hollow quoins, from which
the anchor-bolts are to be carried into the masonry pro¬
vided for the purpose.

These bolts are to be of 2^-inch round iron, and are to be
provided at each end with sufiicient screws and washers,
and are, when let into masonry, to be run round with
lead and securely fixed.

PART SIXTH.

JOINERY.

MOULDINGS.

Plates LXIII.— LXIX.

Before entering on the consideration of the subject of
Joinery, it may be well, as introductory to it, to illustrate
and describe the various ornamental mouldings which
may have to be formed by the joiner.

Plate LXIII.—Grecian and Roman versions of the
same mouldings are shown on this plate.

Fillet or L istei right-angled mouldings require no de¬
scription.

The Astragal or Bead .—To describe this moulding,
divide its height into two equal parts, and from the point
of division as a centre, describe a semicircle, which is the
contour of the astragal.

Doric Annulets .—The left-hand figure shows the
Roman, and the right-hand figure the Grecian form of

this moulding. To describe the latter proceed thus:—
Divide the height h a into four equal parts, and make
the projection equal to three of them. The vertical divi¬
sions give the lines ot the under side of the annulets, and
the height of each annulet, c c, is equal to one-fifth of the
projection; the upper surface of c is at right angles to the
line of slope.

Listel andFascia. —(Roman.)—-Divide the whole height
into seven equal parts, make the listel equal to two of
these, and its projection equal to two. With the third
vertical division as a centre, describe a quadrant. (Gre¬
cian.)—Divide the height into four equal parts, make the
fillet equal to one of them, and its projection equal to
three-fourths of its height.

Gavetto or Hollow .—In Roman architecture this mould¬
ing is a circular quadrant; in Grecian architecture it is
an elliptical quadrant, which may be described by any of
the methods given in the first part of the work.

PL A TE L XUI.

m cl © a m © § «/■.

FLomaii .

Fillet or L islet.

Grecran..

Astragal or Bead.

Doric Annulets.

L islel a 7/d Fa cia

Cavetto or Hollow

Cvma Recta.

Gyma Reims a

J. Whites, del.

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MOULDINGS.

179

Ovolo or Quarter-round .—This is a convex moulding,
the reverse of the cavetto, but described in the same
manner.

Cyma Recta .—A curve of double curvature, formed of
two equal quadrants. In the Roman moulding these are
circular, and in the Grecian moulding elliptical.

Cyma Reversa .—A curve of double curvature, like the
former, and formed in the same manner.

Trochilus or Scotia .—A hollow moulding, which, in
Roman architecture, is formed of two unequal circular
arcs, thus:—Divide the height into ten equal parts, and
at the sixth division draw a horizontal line. From the
seventh division as a centre, and with seven divisions as
radius, describe from the lower part of the moulding an
arc, cutting the above horizontal line, and join the centre
and the point of intersection by a line which bisects; and
from the point of bisection as a centre, with half the
length of the line as radius, describe an arc to form the
upper part of the curve. There are many other methods
of drawing this moulding. The Grecian trochilus is an
elliptical or parabolic curve, the proportions of which are
shown by the divisions of the dotted lines.

The Torus .—The Roman moulding is semi-cylindrical,
and its contour is of course a semicircle. The Grecian
moulding is either elliptical or parabolic; and although
this and the other Greek mouldings may be drawn, as we
have said, by one or other of the methods of drawing
ellipses and parabolas, described in the first part of the
work, and by other methods about to be illustrated, it is
much better to become accustomed to sketch them by the
eye, first setting off their projections, as shown in this
plate, by the divisions of the dotted lines.

Plate LXIV.—The figures in this plate illustrate vari¬
ous ways of describing the ovolo, trochilus or scotia,
cyma recta, cyma reversa, and torus.

Fig. 1 .—The Quirked Ovolo .—The projection of the
moulding is in this case made equal to five-sevenths of its
height, as seen by the divisions, and the radius of the
circle b c is made equal to two of the divisions, but any
other proportions may be taken. Describe the circle b c,
forming the upper part of the contour, and from the point
g draw g h, to form a tangent to the lower part of the
curve. Draw g a perpendicular to g h, and make g f
equal to the radius d c of the circle b c, join f d by a
straight line, which bisect by a line perpendicular to it,
meeting g a in a. Join a d, and produce the line to c.
Then from a as a centre, with the radius a c or a g, de¬
scribe the curve e g.

Fig. 2 .—To draw an ovolo, the tangent d e, and the
projection b, being given.

Through the point of extreme projection b, draw the
vertical line g h, and through b draw b c parallel to the tan¬
gent d e, and draw c d parallel to g h, and produce it to a,
making c a equal to c d. Divide e b and c b each into the
same number of equal parts, and through the points of divi¬
sion in c b draw from a straight lines, and through the points
of division in e b draw from d right lines, cutting those
drawn from a. The intersections will be points in the curve.

Fig. 3 .—To draw an ovolo under the same conditions
as before, viz., when the 'projection f, and the tangent c g,
are given.

The mode of operation is similar to the last: fd is drawn
parallel to the tangent c g, and c d parallel to the perpen¬

dicular a b, cl e is made equal to c d, and d/and g f arc
each divided into the same number of equal parts.

Fig. 4.—In this the same things are given, and the
same mode of operation is followed. By these methods,
and those about to be described, a more beautiful contour
is obtained than can be described by parts of circular
curves.

Fig. 5.—Divide the height b a into seven equal parts,
and make a r equal to b o li of a division; join c r, and
produce it to d, and make c d equal to divisions. Bisect
c cl in i, and draw through i, 4 i at right angles to c d,
and produce it to e; make i e equal to b o, and from e as
a centre, with radius ec or e d, describe the arc c d. Then
divide the arc into equal parts, and draw ordinates to c cl,
in 1 /, 2 g, 3 h, 4 i, &c., and corresponding ordinates / Jc,
g l, h m, i n, to find the curve.

Fig. 6.—This is an application of Problem LXXXVIIL,
page 24. The height is divided into eight equal parts, seven
of which are given to the projection dc. Joined and the fifth
division e, and draw da at right angles to d e. Make df
equal to two divisions, and draw / g parallel to d e, then
d f is the semi-axis minor, and d g the semi-axis major
of the ellipse'; and the curve can either be trammelled or
drawn by means of the lines a li, m k, o p, being made
equal to the difference between the semi-axis, as in the
problem referred to.

Fig. 7 - —To describe the hyperbolic ovolo of the Grecian
Doric capital, the tangent a c, and projection b, being
given.

Draw d e g k a perpendicular to the horizon, and
draw g h and e f at right angles to d e g k a. Make g a
equal to cl g, and e k equal to d e ; join li k. Divide h k
and f h into the same number of parts, and draw lines
from a through the divisions of k h, and lines from d
through the divisions of / h, and their intersections are
points in the curve.

Fig. 8 is an elegant mode of drawing the Roman
trochilus. Bisect the height h b in e, and draw e /,
cutting g c in /; divide the projection h g into three
equal parts, make e o equal to one of the divisions, and
f cl equal to two of them, join d o, and produce the line
to a. Make d c equal to d g, and draw c b, and produce
it to a. Then from d as a centre, with radius cl a or d g,
describe the arc g a; and from o as a centre, with radius
o a, describe the arc a b.

Fig. 9 shows the method of drawing the Grecian tro¬
chilus by intersecting lines in the same manner as the
rampant ellipse, Fig. 167. page 24, with which the student
is already familiar.

Fig. 10 shows the cyma recta formed by two equal op¬
posite curves, imitations of the ellipse, drawn in the man¬
ner taught in Problems XY. and XVI., Figs. 174 and 175,
page 26. By taking a greater number of points as centres,
a figure resembling still closer the true elliptical curve
will be produced.

Fig. 11 shows the cyma recta formed with true ellipti¬
cal quadrants, described as taught in Problem LXXXYIII.,
or they may be trammelled by a slip of paper, as in Fig.
163, page 24.

Fig. 12 shows the cyma reversa, obtained in the same
manner. The lines c d, e h are the semi-axes major, and
the line o n is the semi-axis minor, common to both
curves. As in the former case, these lines, and the heights

180

PRACTICAL CARPENTRY AND JOINERY.

k l, ml, being obtained, the curve can be trammelled with
a slip of paper.

Figs. 13 and 14 show the cyma recta used as a base
moulding, and obtained by means of ordinates from cir¬
cular arcs. The student is familiar with this process, and
therefore no description is required.

Fig. 15.—The Grecian torus is here drawn as in Pro¬
blem LXXXVIII.; / c is the line of the major, and a h the
line of the minor axis of the ellipse.

It is obvious that the relation of the projection to the
height, in all these mouldings, may be infinitely varied;
but if the student has paid attention to the construction
of the ellipse, parabola, and hyperbola, elucidated in pages
22 to 28, and to the application of the methods there de¬
scribed, and the illustrations now offered, these variations
will not embarrass him. But it is necessary to repeat that
it is better, after the eye has become familiarized with the
graceful forms of the Grecian mouldings, to trust to the
curves produced by sketching, as then the proportions
may be varied to infinity, as in the ancient examples.

Plate LXY. contains a series of illustrations, designed
by Mr. White, of the application of the Grecian mouldings,
just described, in joiner-work. With the exception of the
beads, the curves all belong to those derived from the sec¬
tions of a cone. They are intended to show the infinite
variety that may be produced by the combination of
simple elements.

The mouldings just described are generally denomi¬
nated classic, because they are derived from examples left
us by the Greeks and Romans. But the architecture of
the middle ages affords examples of moulded work which
are no less attractive in their forms, and which possess
qualities which render them especially serviceable for the
use of the joiner. To the illustration of these we have
devoted a single plate, described below, and it is only to
the elementary forms that the limits of this work admit of
pointing the attention. But the forms and combinations
are so peculiarly suggestive, that with ordinary fancy and
intelligence the combinations may be infinitely varied.
To exhaust the subject would require a volume.

Classic architecture is usually divided into orders.
Thus, there are the Tuscan, the Doric, the Ionic, the
Corinthian, and the Composite orders. The mouldings
used in these are nearly alike in form, and their combina¬
tion chiefly marks the order to which they belong. In
Gothic architecture there are no orders, but there are dis¬
tinctive evidence of progress, of perfection, of decadence.
Hence in place of orders we have periods, which are called
styles, and these have been settled by almost general con¬
sent. First, there is the Norman period or style, then
the period of the early English, to this succeeds the Deco¬
rated style, and it is again succeeded by the Perpendicular
style.

In regard to the mouldings, those belonging to the first

O O 7 o o

period or style are distinguished by their simplicity and
strength of character. The next period shows more ela¬
boration, without much diminution of strength. The
third, or Decorated period, adds variety and intricacy;
and to this, in the fourth and last style, succeeds a poverty
and meagreness sufficiently marked, and indicative of
decay, in so far as great works are concerned, yet not
inapplicable, as we shall see, to the ordinary every-day
wants of life.

The first or Norman period is characterized generally
by square sinkings, with the angles sometimes truncated
and sometimes moulded; the second or early English
period, by deep undercut hollows, between prominent
members, and pointed or filleted boutels; the third or
Decorated period, by roll and fillet mouldings, nearly re¬
sembling the early English, and a succession of double
ogees, divided by hollows formed of three quarters of a
circle; the fourth or Perpendicular period, by larger and
coarser mouldings, wide and shallow hollows, hard edges,
in place of rounded forms, and all generally arranged on
the chamfer plane.

Plate LXV.®— Gothic Mouldings. — Fig. 1 is a jamb be¬
longing to the first period, called the Norman; a b and d c
are called chamfer planes. In Fig. 2, of the same period,
more variety is obtained by making square sinkings, and
truncating the angles by a smaller chamfer plane, as at
a b.

Fig. 3, of the second period, shows square sinkings with
the angles truncated by a shallow cavetto. Fig. 4 shows
a square sinking, the angles truncated by a cavetto, and a
pointed boutel at b, and a round boutel at a.

Figs. 5, 6, and 7 belong to the Decorated period. Here
the mouldings assume a greater variety and contrast of
form. The faces of the square sinking in Fig. 5 are joined
by a three-quarter circle in the angle at b, and the roll
and fillet moulding at a is undercut and separated from
the chamfer plane by two three-quarter circles, and the
double ogee at c is formed on the chamfer plane.

In Fig. 6 the double ogee again occurs on the chamfer
plane.

Fig. 7 shows the mouldings of a window in this style.

Figs. 8 and 9 belong to the Perpendicular period.

Fig. 10 is the section and elevation of an early English
capital and base; Fig. 11, of a Decorated capital and base;
and Fig. 12, of a Perpendicular capital and base.

Figs. 13 to 26 are sections of string-courses and cornices,
of which Figs. 13 to 16 are early English, Figs. 17 to 20
are of the Decorated period, and Figs. 21 to 26 belong to
the Perpendicular.

Fig. 27, also, is a cornice belonging to the Perpendicular
period, wherein a beautiful effect is produced by the
pieces a a.

Fig. 28, No. 1 is the section, and No. 2 the elevation of
a Perpendicular cornice.

Fig. 29, No. 1 is the side, and No. 2 the front elevation
of a bench-end. In No. 1 the sections c d a b show how
the edge proceeds from the square at k to the chamfer
plane, and from the chamfer plane to the moulding, re¬
turning to the square by the quarter circle at e f.

Fig. 30, Nos. 1 and 2 show a variety in the chamfering
at c d and a b.

Fig. 31 shows mouldings on the chamfer plane, and the
return to the square arris.

Fig. 32, Nos. 1 and 2 the front and side of a moulded
bracket.

Fig. 33 is the elevation of part of a door frame; abed
is a section showing the form and projections of the
mouldings.

Fig. 34 is the manner of ornamenting a small panel; a b
is a section through the mouldings.

Fig. 35 is a larger panel similarly ornamented.

M@y[L[D)QKl©So

EL A TE 1XV.

BL ACKIE &• SON , GLASGOW, EDINBURGH LONDON.

ft?/!. Be ever. Se

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PLATELXV «

A. F. Orridge . de.1.

BLACKIE & SOS . GLASGOW. EDINBURGH. & LONDON

\i . A. Beeve.r. Sc.

Fig. 5.

PLATE LATJ.

K A KITKI ©

d.Better.

J. White, del.

BLACK3E & SON . GLASGOW. EDINBURGH & LONDON.

PLATE LEVIl

BI.At'KIK X- SON . iVLASiiOW.KDINBUROH X- LONDON.

IT A . 8 wet \ V

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BLACKIE Sr SON . GLASGOW, EDINBURGH &: LONDON.

W.A.Beever. Sc.

MOULDINGS.

181

RAKING MOULDINGS.

Plate LXVI. — Fig. 1 shows part of the raking cornice
of a pediment, with the horizontal part of the moulding
on the left of the figure. Draw g o perpendicular to the
horizon, and o h at right augles to g o. In o k take any
point, l , and draw l d parallel to g o, and cutting the pro¬
file in d, and through d draw a line d x, parallel to the
line of rake. Then to find the section of the raking
front, draw any line, A B, perpendicular to d x, and make
A r equal to o l, and draw r x parallel to A B, cutting d x
in x\ then the point a; is a point in the raking profile.
In the same manner any other point, such as z y w v cor¬
responding to f e c b, may be found.

When the moulding is returned at the upper part, such
as at H F, the line n G must obviously be drawn parallel
to g o, that is, perpendicular to the horizon. The re¬
mainder of the procedure, and the manner of finding the
return of the bed moulding R s at H P, is too obvious to
require further description.

Fig. 2 shows a raking moulding on the spring. In this
the procedure is the same as in the last, except that in
place of drawing lines parallel to the rake, concentric
curves are described to find the points in the moulding.
But it is necessar}^ to observe that it is not where the
perpendiculars from A c intersect these arcs that the pro¬
per points are. The true points are intersections with
tangents to the curves where they cut the line A B.

Figs. 3 and 4 show the method of describing the sec¬
tion of the raking moulding on the line A B perpendicular
to the raking line, and also on the line G H parallel to g o,
in the case where the moulding is not returned, or where
the two raking sides meet. These will be readily under¬
stood on inspection.

Plate LXVII.— Fig. 1 shows the manner of drawing
a modillion in a raking cornice. The mode of operating
is precisely as in Fig. 1 of Plate LXVI., and need not
be repeated.

Fig. 2 is a raking architrave, and Fig. 3 a base mould¬
ing, both of which are sufficiently intelligible without
lengthened description.

Fig. 4 shows the method of describing the angle-bars
of a window : No. 1 being the ordinary bar; No. 2, a
mitre bar; and No. 3, a bar occupying an obtuse angle.
The line a m is in all three cases drawn perpendicular to
the axis of the bar; and the divisions, abed, &c., of
No. 1, are transferred to Nos. 2 and 3, and lines perpen¬
dicular to a m drawn to meet the lines abed, which pass
through points of the moulding.

ENLARGING AND DIMINISHING MOULDINGS.

Plate LXVIII., Fig. 1.—Let a b be the height of a
cornice which it is proposed to diminish. On A B con¬
struct an isosceles triangle aeb, and parallel to A B draw
G H, equal to the proposed height. Then from E draw
lines from the horizontal divisions of the cornice on A B,
and the points in which these cut the line G H give the
new heights. To find the projections: draw, at the right
side of the figure, any horizontal line, c D, and on it draw
perpendiculars from the projections of the various members
of the cornice; produce the extreme perpendiculars inde¬
finitely: make D F equal to the perpendicular height of

the isosceles triangle aeb, and from the divisions on C D
draw lines to the point F. On F D set off F K, equal to
the perpendicular height of the isosceles triangle GEH,
and draw l K parallel to c D. The divisions on I K, trans¬
ferred to LM, on the left of the figure, give the projections
diminished in the same ratio as the heights.

Let it now be required to enlarge the cornice at the
left side of this figure. From the point G, with the
proposed height of the cornice in the compasses, cut
the line H N in N, and join G N : the points where this line
is intersected by the horizontal lines of the mouldings are
the heights of the members, enlarged in the same ratio as
the whole height. To find the projections, from the point
L draw the line L o, making the angle mlo equal to the
angle H G N, and it will be cut by the lines of projections
produced in the same ratio as G N is by the horizontal
lines.

In place of drawing L o, as described, the same result
would be obtained by drawing a line at right angles to
G N, crossing the lines of projection.

Fig. 2 is a further exemplification of the manner of
enlarging and diminishing mouldings. First, as to en¬
larging: — From the point A, with the proposed increased
height in the compasses, cut B o in o, and join o A, and
this line will be divided by horizontal lines, drawn from
any point, as a b, in the mouldings, in the proportion that
o A bears to b a. Then, to find the projections, draw e p,
making the angle D E P equal to the angle B A o, and
vertical lines drawn from the same points in the mould¬
ings as the horizontal lines will give the corresponding
increased projections on p E.

Next, as to diminishing: — On A B construct an isosceles
triangle ACB, and draw to C radial lines from the points
of intersection of the horizontal divisions with A B. Draw
I K parallel to A B, and equal to the proposed diminished
height; then, to find the diminished projections corres¬
ponding to the divisions on I K: construct on D E an
isosceles triangle D F E, having its vertical height equal
to the vertical height of the triangle A C B on A B. To
F draw radial lines from the divisions produced by per¬
pendiculars drawn on D E from the points of projection,
and intersect these by G H drawn parallel to D E, and at
the same distance from it as I K is from A B. The divi¬
sions on G H, transferred to L M, at the right side of the
figure, are the diminished projections.

Fig. 3 shows the manner of finding the proportions of
a small moulding which is required to mitre with a larger
one, or vice versa. Let A B be the length of the larger
moulding, and A D the length of the smaller one; con¬
struct with these dimensions the parallelogram ADCB
and draw its diagonal A c ; draw parallel to B C lines a s,
b t, &c., &c., meeting the diagonal in s t, &c., and from these
points draw parallels to A B, meeting A D in n o p r; pro¬
duce them to ikl m, &c., and make n i equal to e a, o k
to / b, «fec., and thus complete the contour of the moulding
on D A, the lengths of which are diminished in the ratio
of A D to A B, but its projections remain the same as those
of the larger moulding. The operation may be reversed,
and the larger produced from the smaller moulding.

Fig. 4 shows the manner of enlarging or diminishing a
single moulding. Let A B be a moulding which it is re¬
quired to reduce to A D. Make the sides A B, D C, and
A D, B c of the parallelograms respectively equal to the

182

PRACTICAL CARPENTRY AND JOINERY.

larger and smaller moulding, and draw the diagonal A c, ||
produce D A to E, and make E A F equal to a, A, b, and
draw A F. The manner of obtaining the lengths and pro¬
jections with these data is so obvious that farther descrip¬
tion is unnecessary.

Plate LXIX.—All the figures in this plate are illustra¬
tions of architraves, with the exception of No. 12, which
is a triple corner bead. In the figures of architraves the
shaded parts are the horizontal section across the mould¬
ings, and the single line beyond the shaded part is the
outline of the block or plinth on which the architrave
stands.

JOINERY.

Joinery is the art of cutting out, dressing, uniting and
framing wood for the external and internal finishings of
buildings. It has been broadly distinguished from car¬
pentry by this, that while the work of the carpenter can¬
not be removed without affecting the stability of a struc¬
ture, the work of the joiner may. The labours of the
carpenter give strength to a building, those of the joiner
render it fit for habitation.

In joinery the parts are nicely adjusted, and the sur¬
faces exhibited to the eye are carefully smoothed.

The goodness of the work of the joiner depends first on
the perfect seasoning of the materials, and, second, on the
care of the operator. All the surfaces must be perfectly
out of winding and smooth. The stuff must be square,
the mouldings true and regular, and all must be so fixed
as to bring out the beauty of the wood. The moving
parts must work with ease and freedom.

Many of the operations described in carpentry and
joineiy appear to be common to both, and such as may
be performed indifferently by the carpenter or the joiner;
but in reality it is not so, for a man may be a competent
carpenter without being a joiner at all, and although a
joiner may be able to execute carpentry work, yet the
habits of greater neatness and precision required in the
practice of his own proper art, make his services less pro¬
fitable in carpentry work.

The timber on which the joiner operates is termed stuff,
and consists of boards, planks and battens. A board is a
piece of timber from 7 to 9 inches wide. A plank is a
piece whose width is great in proportion to its thickness,
but the term is generally applied to pieces above 9 inches
wide and not more than 4 inches thick. A batten is a
piece from 2 to 7 inches wide. These terms are used in a
more restricted sense than this in some places, as for ex¬
ample in London, where a batten means a fine flooring-
board, 7 inches broad and 1^ inch thick, but the defini¬
tion applies generally.

On stuff like this described the joiner operates by saw¬
ing, planing, mortising, grooving, dovetailing,
and moulding; and he fastens the parts of
his work together by gluing, wedging, pin¬
ning, and nailing.

Mortising in joinery is similar to the same
operation in carpentry, with the exception
of the variation arising from the smallness and neatness
of the work. The parts should fit easily together with¬
out hai-d driving, and the tenon should fill the mortise
fully and equally. The tenon is generally about one-

Fig. 489.

lJ—!

fourth of the thickness of the framing, and its width about
five times its thickness. If, therefore, the piece of wood
to be tenoned be very wide a double tenon should be
formed, as in Fig. 489.

If the piece of wood be also thick as well as wide, two
projections, resembling short tenons, and called stump-
tenons, are made, one on each side of the main tenons, and
these fit into corresponding grooves in the mortised piece;
and the tenons'at the end of framing should be set back

a little, to allow of sufficient strength of wood for the
mortising. This is called haunching.

As the stuff on which the joiner operates is of limited
width, and it is frequently necessary to cover large sur¬
faces, recourse is had to various modes of joining the pieces
laterally. In these joints, as they are termed, several
expedients, as circumstances require, are used for the pur¬
pose of preventing air or dust blowing through; and also
preventing the inevitable shrinkage of the timber detract¬
ing from the appearance of the work. These lateral joints

may be doweled, grooved
and tongued, or rebated.

Doweling consists in form¬
ing corresponding holes in
the contiguous edges of the
boards, into which cylindrical

Fist. 488.
n'

„d_

wooden or iron pins are inserted, as in Fig. 488.

Grooving and tonguing, or grooving and feathering,
consists in forming a groove or channel along the edge of
one board, and a projection or tongue to fit it on the edge
of the other board. When a series of boards has to be
joined, each board has a groove on its one edge, and a
feather or tongue on the other. When the boards are
thick, grooves are made on the contiguous edges of both
boards, and a small fillet, generally of hard wood, is in
serted into both. This is called a slip-feather or tongue.

Rebating is another method of joining boards by
cutting down the contiguous edges of two boards to half
their thickness, but on opposite sides, and thus when
they are laid together their surfaces are in the same plane.

JOINTS.

Plates LXX., LXXI.

Plate LXX.— Fig. 1 shows a joint formed by plan¬
ing the edges of the board perfectly true, and inserting
wooden or iron pins at intervals into the edges of
both boards. The pin is shown by a dotted line in the
drawing. It is called a dowel, and the joint is said to be
doweled.

Fig. 2 shows a joint formed by grooving and tonguing,
or, as it is variously called, grooving and feathering,
ploughing and tonguing, or feathering.

These two last joints are commonly used for floors. The
first is used without the dowels in common folded floors
The shrinking of the boards in this case causes the joint
to open, and the air and dust pass through. The grooved
and tongued joint is used in the better kind of floors.
The tongue or feather prevents the passage of air or dust.

Fig. 3 is a double tongued or feathered joint.

Fig. 4 is a combination of a rebate with a groove and
tongue. It affords in flooring a better means of nailing,
as the drawing shows.

PL A TE LXLT.

■

* % .*• ■ r.

■

** ■ ■ • *

• - - ‘ •

* L'.i

* ♦

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a* . •

py. Ji- * *

•

♦

t A

. 9

•J .0 J M T a IN

DOVETAIL JOINTS.

Fiq.l.JV?!.

PLATE LXX1.

FU. a. A?2.

Fie,. 4 .. V°l.

Fie,. 4. . I

Fie,. 4.. V?l.

II /life, </ef

//.'. / Beever.

BL.ACKIE S.- SON . OLAScWW, EDINBURGH & LONDON.

JOINTS.

183

la Fig. 5 the groove and tongue are angular.

Fig. 6 is a kind of grooving and tonguing resorted to
when the timber is thick, or when the tongue requires to
be stronger than it would be if formed in the substance of
the wood itself. In this mode of jointing corresponding
grooves are formed in the edges of the boards, and the
tongue or feather is formed of a slip of a harder or
stronger wood. It is called a slip feather.

Fig. 7, 8, 9 are examples of slip-feather joints; the
feather in Fig. 9 is of wrought iron.

Fig. 10 shows dovetail grooves, with a slip feather of
corresponding form, which, of course, must be inserted
endways.

Fig. 11 is a simple rebated joint. One-half of the thick¬
ness of each board is cut away to the same extent, and
when the edges are lapped the surfaces lie in the same plane.

Fig. 12 shows a complex mode of grooving and tonguing.
The joint is in this case put together by sliding the one
edge with its grooves and tongues endways into the cor¬
responding projections and recesses of the other. The
boards when thus jointed together cannot be drawn
asunder laterally or at right angles to their surface, with¬
out rending; but, in the event of shrinking, there is
great risk of the wood being rent.

Where a great surface has to be covered with boarding
not framed, the deals are cut into narrow widths, and
joined at their edges by some of the joints just described.
Fig. 490 shows the simple groove-and-tongue joint,
which it is evident the shrinkage of the wood will
cause to open and disfigure the work. To prevent this
disfigurement a small moulding, termed a bead, is some¬
times run on the Fig. 490 .

edge of each board,

{

as in Fig. 491.

The joint thus
forms one of the q
quirks of the bead,
and prevents any _
slight opening from L -
the shrinkage of the

Fiff. 491.

Fig. 492.

wood

being

observed.

This is

termed a grooved, tongued, and beaded joint. So also
in the case of the rebated joint, a bead is run on the
edges of the board, and the result is as in Fig. 492.
This is termed a rebated and beaded joint.

In joining angles formed by the meeting of two boards
various joints are used, among which are those which
follow.

Fig. 13.—The common mitre-joint, used in joining two
boards at right angles to each other. Each edge is planed
to an angle of 45°.

Fig. 14 shows a mitre-joint keyed by a slip-feather.

Fig. 15 shows a mitre-joint when the boards are of dif¬
ferent thickness. The mitre on the thicker piece is only
formed to the same extent as that on the edge of the
thinner piece; hence there is a combination of the mitre
and simple butt joint.

Fig. 16 shows a different mode of joining two boards
of either the same or of different thicknesses. One of the
boards is rebated, and only a small portion at the angle of
each board is mitred. This joint may be nailed both ways.

In Fig. 17 both boards are rebated, and a slip-feather
is inserted as a key. This also may be nailed through
from both faces.

Figs. 18 and 19 are combinations of grooving and
tonguing with the last-described modes. These can be
fitted with great accuracy and joined with certainty.

Fig. 20 is a joint formed by the combination of mitring
with double grooving and tonguing, shown in Fig. 12.
The boards must in this case be slipped together endways,
and cannot be separated by a force applied at right angles
to the planes of their surfaces.

In all these mitre-joints the faces of the boards meet at
the angle, and the slight opening which might be caused
by shrinkage would be scarcely observable. I 11 the butt-
joints which follow, the face of the one board abuts against
the face of the other, the edge of which is consequently in
the plane of the surface of the first board, the shrinkage
of which would cause an opening at the joint. To make
this opening less apparent is the object of forming the
bead-moulding seen in the next five figures.

In Fig. 21 the thicker board is rebated from the face,
and a small bead is formed on the external angle of the
abutting board.

In Fig. 22 a groove is formed in the inner face of the
one board and a tongue on the edge of the other.

In Fig. 23 the boards are grooved and tongued as in
the last figure. A cavetto is run on the external angle of
the abutting board, and the bead and a cavetto on the
internal angle of the other board.

In Fig. 24 a quirked bead run on the edge of one board,
and the edge of the abutting board forms the double quirk.

In Fig. 25 a double quirk bead is formed at the external
angle, and the boards are grooved and tongued. The
external bead is attended with this advantage, that it is
not so liable to injury as the sharp arris.

In Figs. 26 and 27 the joints used in putting together
cisterns are shown

Figs. 28 and 29 are joints for the same purpose. They
are of the dovetail form, and require to be slipped together
endways.

Figs. 30 to 35 show the same kind of joints as have
been described, applied to the framing together of boards
meeting in an obtuse angle.

Figs. 36 and 37 show methods of joining boards to¬
gether laterally by keys, in the manner of scarfing; and
Fig. 38 shows another method of securing two pieces,
such as those of a circular window frame-head by keys.

Dovetail-joint .—This joint has three varieties:— 1st, the
common dovetail, where the dovetails are seen on each
side of the angle alternately; 2d, the lapped dovetail, in
which the dovetails are seen only on one side of the angle;
and, 3d, the lapped and mitred dovetail, in which the joint
appears externally as a common mitre-joint. The lapped
and mitred joint is useful in salient angles, in finished
work, but it is not so strong as the common dovetail, and
therefore, in all re-entrant angles, the latter should be used.

The three varieties of dovetail-joint above enumerated
are illustrated in Plate LXXI.

Fig. 1, No. 1 is an elevation of the common dovetail-joint;
No. 2, a perspective representation; and No. 3, a plan of
the same.

In all the figures the pins or dovetails of the one side
are marked A, and those of the other side are marked B.

Fig. 2, Nos. 1, 2, 3.—In these the lap-joint is repre¬
sented in plan, elevation, and perspective projection.

Fig. 3, Nos. 1, 2, 3.—In these figures the mitred dove-

184

PRACTICAL CARPENTRY AND JOINERY.

tail-joint is represented in plan, elevation, and perspective
projection. T he dovetails of the adjoining sides are
marked respectively B and c in all the figures.

Fig. 4, Nos. 1 and 2, and Fig. 5, Nos. 1 and 2, show
the modes of dovetailing an angle, when the sides are in¬
clined to the horizon, as in a hopper. The pins of the
one side are marked A, and those of the other side B, on
all the figures.

Gluing up Columns, &e.— Plate LXXII. — Fig. ],
Nos. 1 to 5 show in detail the manner of framing together
and gluing up the parts of a column and its entablature.

Fig. 1, No. 4 contains four quarter plans of as many
courses of timber, forming the mouldings of the base; and
No. 5 shows the same in elevation and section, marked
with the same letters. The square plinth is first formed
by taking four pieces of equal length, mitring them to¬
gether at the angles, and securing them by screws and
b y an d strengthening them with blockings in the
angles, as at a. The upper surface of this course is then
planed true, and prepared to receive the next course. This
course is also formed of lour pieces, to form the torus, A,
No. 5. These pieces cross the angles, and are joined on
the middle ol the length of the first pieces. The surface
of this is in like manner planed true to receive the next
course B; the pieces composing which have their joints on
the middle of the pieces of the course below, and are glued
down on them. So likewise with c. When the formation
of the block is thus completed, it is turned, and the proper
rebate e formed in the upper surface to receive the lower
part of the shaft. The quadrant marked D shows a sec¬
tion of the lower part of the shaft. The half-plan at o o,
on the right hand of Fig. 1, No. 3, is the upper part of
the shaft. It will be observed that the shaft is built of
staves, which should always have their joints in the centre
of the fillet. The staves are glued together and secured by
blockings m m m, glued in the angles. The staves should
not exceed 5 inches wide, whether for columns or pilasters,
and they should be as thin as is consistent with strength.

It is well to work them to the taper necessary for the di¬
minution of the columns before gluing them together.

Fig. ], No. 3, on the left of this figure, at o o, is the
half of the horizontal section of the shaft immediately be¬
low the necking at A B, Fig. 1, No. 1; r is a quadrant of
the horizontal section at c D, and s a quadrant of the
horizontal section at E E.

Fig. 1, No. 1 is the elevation of half the capital, and the
architrave frieze and cornice, and No. 2 is a vertical sec¬
tion of the same. The framing of the architrave, frieze,
and cornice does not require description; and it is only
necessary to make this remark, that by using blockings,
the thickness of the material in the architrave and frieze
might be reduced.

Diminution of Columns.—Fig. 2.—The upper di
meter of a column is less than its iower diameter, but t
gradual diminution between them is not made by straig
but by curved lines. The usual mode of describing t!
curved contour of the diminution is as follows:—Let a
be equal to the lower diameter of the column, of whi.
let efg be the line of the axis, perpendicular to a b; t
the height of the column, and r 6 its upper diameter/ C
a b describe a semicircle, and from r and 6 draw lin
parallel to the axis, cutting the semicircle in s o; divi<
s a or o b into any number of equal parts, the more tl

better, and divide the height /<7 into the same number of
equal parts, as 1, 2, 3, 4, 5, 6 , and through these draw
lines crossing the axis perpendicularly. Then by drawing
lines parallel to the axis through the corresponding divi¬
sions in the semicircle meeting these points, the curved
contour of the column will be obtained, and by bending a
lath, so as to pass through these points, the curve may be
drawn, and the rule c d formed.

Fig. 3.—The same thing may be obtained in a manner
somewhat different, as shown in Fig. 3. In this a b is
equal to the lower, and c d to the upper diameter. The
points in which this latter cuts the semicircle being found,
the portion of the radius a: p is divided into°certain
equal parts, and the height of the column / g into the
same number of equal parts, and from the points where
lines parallel to a b, drawn through the divisions in x p,
meet the semicircle, other lines, parallel to the axis, are
diawn, as before, to intersect the lines drawn through the
divisions of the height, ], 2 , 3 , 4 , 5 , 6 .

Another method of describing the section of the column
is shown in Fig. 4. Let b e be the line of the axis of the
column, A b half of the lower diameter, and B e half of the
upper diameter. Take in the compasses the length of the
semi-diameter at the bottom, and setting one foot in the
extremity of the upper diameter at B, with the other foot
cross the axis at h, produce the lower diameter indefinitely,
as A r; and through B, and the point h on the axis, draw
a line cutting the line A r in Jc ; then from Jc as a centre,
draw any number of lines, as i 7, m 6 , &c., and make each
of them as i 7, equal to the lower semi-diameter. In the
same figure is represented a trammel for doing the same
thing as has been described, a b e is a right-angled rule,
kept to its form by the angle-piece c d. In the limb b e
is a groove, which is made to coincide with the axis of
the column, and in which slides freely a stud h. The
other arm a b of the rule carries a stud Jc. The rule / g
has a groove or slot sliding on stud Jc, and its other end
carries the stud which slides in b e. Now, it is evident
that if the points kb h g of the trammel be adjusted in
accordance with the preceding description, the point q
will, on the rule / g being slid along, guided by the
grooves, describe the elliptic curve A, 1, 2, 3, 4, 5, (>, 7 <j.

Moulding is the forming the surface of the wood into
various square and curved contours. In Plates LXIII.,
LXIV., and LXV., are examples of the classic mouldings,
and in LXV.« some of the Gothic mouldings have bee/
given. It is only therefore necessary here to observe that
the bead is of constant occurrence in joiner-work, and
under one or other of the conditions following. When
the edge of a piece of wood is reduced to a semi-cylindrical
form, as in Fig. 493, it is said to be rounded. When the
Fi<r. 493 . Fig. 491. Fig:._495. _ rounding forms more than a

semicircle, and there is a sink¬
ing on the face, as in Fig. 494 ,
the rounding is termed a
quirk-bead, the groove or sink¬
ing being termed the quirk.

When the edge is rounded
with a sinking or groove on both faces, as in Fig. 495 ,
the moulding is a double-quirk bead.

When any moulding is formed on the edge of a piece of
framing it is said to be stuck When it is formed on a
separate piece of wood, and attached to the part of the

PLATE LJXII

SLUIQ 1M OJliP

.GD:lb']'/J MS &®.

Fig l.xr° 3.

Plan af Capital.

Elevation and Section of Base of Column

PC a l. N°d.

AiF. Orrulae del 1

J W Lowi'v fo.

Indies

=±=

3 Feet -

BLACJSIE Sc SON] GLASGOW, ED IN BURGH, Se LONDON

JOINTS.

185

framing it is meant to ornament, it is said to be laid in,
or 'planted.

The modes of joining timber above described are all
more or less imperfect. The liability of wood to shrink
renders it essential that the joiner should use it in such
narrow widths as to prevent this tendency marring the
appearance of his work; and, as even when so used it will
still expand and contract, provision should be made to
admit of this. The groove-and-tongue joint admits of a
certain amount of variation, and the grooved, tongued,
and beaded joint admits of this variation with a degree of
concealment, but the most perfect mode of satisfying both
conditions is by the use of framed work.

Framing in joinery consists of pieces of wood of the
same thickness, nailed together so as to inclose a space
or spaces. These spaces are filled in with boards of a less
thickness, termed panels.

In Fig. 496, a a, b b shows the framing, and c c the
panels. The vertical pieces of the framing a a are termed
styles, and the horizontal pieces b b are termed rails. The
rails have tenons which
are let into mortises in
the styles. The inner
edges of both styles and
rails are grooved to re¬
ceive the edges of the
panels, and thus the panel
is at liberty to expand
and contract. Framing
is always used for the better description of work. The
panels should be formed of narrow pieces glued together,
with the grain reversed alternately. They should never
exceed 15 inches wide, and 4 feet long. These dimensions,
indeed, are extremes which should be avoided.

The panels may be boards of equal thickness throughout,
in which case the grooves in the styles and rails are made
of sufficient width to admit their edges, as in Fig. 497.
These are termed flat panels. Flush panels, again, have
one of their faces in the same plane as the face of the fram¬
ing, and are rebated round the edges until a tongue suffi¬
cient to fit the groove is left. Raised panels are those of
which the thickness is such that one of their surfaces is a
little below the framing, but at a certain distance from
the inner edge, all round it, begins to diminish in thick¬
ness to the edge, which is thinned off to enter the groove.
The line at which the diminution takes place is marked
either by a square sinking or a moulding. All these kinds
of panels are sometimes combined.

Flush panel framing has generally a simple bead stuck
on its edges all round the panel, and the work is called
bead flush. But in inferior work the bead is run on the
edges of the panels in the direction of the grain only, that
is, on the two sides of each panel, while its two ends are
left plain; this is termed bead butt. The nomenclature,
however, of the various descriptions of framed, and of
framed and moulded work, will be best understood by
reference to the annexed figures. Fig. 497 is the flat
panel. In this the framing is not moulded, and is termed
square. In Fig. 498 the same framing is shown with a
moulding stuck on it. In Fig. 499 the same framing is
shown with a moulding laid in or planted on each side.
Mouldings which, like these, project beyond the surface of
the framing, are termed Bolection mouldings. In Fig.

Fig. +96.

500 a bead flush panel is represented. In Fig. 501 a
bead and flush panel with moulding laid in. Fig. 502
Fig. 497. shows a bead butt panel. Fig. 503

_ra-j a raised panel with stuck mould-

^ p ( ings; and Fig. 504 a panel raised

Fig. 498.

JZ'

Fig. 499.

>-.n

r -1

Fig 500.

Fig. 601.

Fig. 502.

Fig. 503.

Fig. 504.

on one side with stuck mouldings
and bead and flush on the other.
Panels in external work, such as
doors, may be secured against being
cut through by depredators, by
boring holes across them from edge
to edge, and inserting iron wires,
or by crossing them diamond
fashion with thin hoop iron, nailed
on the inside.

In Plate LXY. a great variety
of mouldings for framed work is
given, and the use of them will
now be better understood. The
four last examples on that plate
are different from all the others, as
the groove for the panel is made
in the moulding, which is framed
and mitred.

When the labours of the mason,
bricklayer, carpenter, &c., have
prepared the carcass of the build¬
ing, it is ready for the operations of
the joiner; but, as almost all his
work is previously prepared in his workshop, he has little
more to do in the building itself than fitting and fixing.
His first operation in the building is to cut out the bond
timbers from the openings, and to fill them in with old
sashes, or with oiled paper on frames. He next prepares
the joists for the flooring boards, by trying them with
straight edges, reducing inequalities with the adze, and
filling up hollows with pieces of wood termed frrrings.
Previous to laying the flooring boards, the pugging is put
into its place, the boards are then prepared for laying,
and turned over, face downwards, until the plastering is
completed. The grounds for the various finishings are
now fixed, to serve as gauges for the plasterer, and the
staff’ beads are set; and, on this being done, the opera¬
tions of the joiner should be suspended until the plaster¬
ing; is finished.

The grounds consist of pieces of wood projecting from
the naked of the wall to the face of the plastering; they
are put round doors, windows, and other openings, to at¬
tach the architraves or other finishings to, and are also
fixed wherever skirtings or linings require to be attached.
In Fig. 507, c, c, shows the framed ground of a window,
and B, in Fig. 508, the narrow ground for skirting. The
skirting grounds are generally dovetailed at the angles,
and they require to be well blocked out to the range,
and firmly fixed.

Floors are laid in two ways, called folded and straight
joint. In folded floors, the boards are plain-jointed, and
one of them being firmly fixed in its place, at the extre¬
mity of the floor, and another parallel to it, at a distance
apart nearly equal to the aggregate width of three or four
boards, these intermediate boards are then put into this
space, and forced down and nailed. In this mode all the
heading joints of these boards, thus laid at once, neces-

2 A

180

PRACTICAL CARPENTRY AND JOINERY.

sarily occur on the same joist, and as, for obvious reasons
it is important to break joint, this of itself is enough to
condemn the practice. In straight-joint floors, the boards
maybe plain-jointed or dowelled, or grooved and tongued.
Each board is laid separately; every heading joint is made
to fall on a joist, and is broken or covered by the adjoin¬
ing board. The heading joints are also grooved and
tongued. The boards are brought close together by gentle
driving, or by the use of a flooring cramp, and they are
nailed either through the face or edge. When nailed
through the face, flooring brads, a kind of nail having
only a projection on one side, instead of a head, are used,
and are punched in below the surface, so as to admit of
the boarding bein'g dressed off with the hand-plane after
it is laid. For side or edge nailing, clasp nails are used.

If the flooring boards are not gauged to a thickness,
they require the following preparation before the} 7 are
laid. Their edges are gauged to a thickness by a rebate
plane; they are then laid with their face down in the
position they are to occupy, and are cut down with an
adze, at the place of every joist, to the gauge mark, so that
the boards form a level surface when turned into their
places. From the use of machinery now in gauging floor¬
ing boards, the operation above described has rarely to be
performed.

Skirting. —The boards with which the walls of a room
are finished next to the floor, or, in other words, the plinth,
is termed the skirting. When it consists simply of a
board, moulded on its upper edge, it is still termed the
skirting; but if the plinth is made up of more than one
piece, the plain board, next the floor, is termed the shirt¬
ing board, and the upper part the base mouldings.

In the better description of work, the skirting board is
let into a groove formed in the floor to receive it, and is
supported behind by vertical pieces or blockings, fixed at
frequent intervals, between the narrow grounds and the
floor. Sometimes, however, the skirting, in place of being
let into a groove, has a fillet nailed along the floor behind
it as a stop, and if its depth be not great, and the wood
strong enough, no blockings are used. In fixing the
skirting, the operation of scribing is performed, to accom¬
modate the outline of its lower edge to any inequalities
which may exist on the surface of the floor.

Scribing is thus performed:—The skirting board, hav¬
ing its upper edge worked, moulded, or otherwise, with
perfect precision, is applied to its place, with its lower
edge either touching the floor or supported at a con¬
venient distance above it, and so arranged by propping
it up at one end or the other that its upper edge is per¬
fectly level. Then to mark on its lower edge a line that
will perfectly coincide with any irregularity which may
exist in the floor, a pair of strong compasses is taken
and opened to the greatest distance that the lowest
edge of the skirting is from the floor throughout its
length. The outer point of the compasses is then drawn
along the floor, and the other point pressed against the
skirting board, so as to mark a line which will, of course,
be exactly parallel to the surface of the floor; and the
board is cut to this line, either by the saw or the hatchet.
It is, of course, essential that all the upper edges of
all the skirting boards of the room or apartment should
be adjusted to the same level line when this scribing is
done.

DOORS.

Plates LXXIIL—LXXV.

Doors are either lodged or framed, Ledged or barred
doors, as they are also called, are formed of plain boards
united by groove and tongue joints, and having two or
more bars or ledges nailed across them on one side to hold
them together.

Framed doors, or, as they are termed in Scotland,
bound doors, are of various kinds. In the framing of
doors, as in other framing, the vertical pieces are termed
styles and the horizontal pieces rails. When a centre
vertical piece is tenoned into mortises formed in the rails
it is called a muntin, rnontant, or mounting. The rail
next below the top rail is called the frieze rail, and that
next above the bottom rail the loch rail; any other inter¬
mediate rails have no specific name. In like manner the
panels are named frieze panels, middle panels, and bottom
panels. In ordinary framed doors the top and frieze rails
are generally of the same width as the styles, the bottom
and lock rails generally twice as wide. In Fig. 506 a a are
styles, b the rnontant, c bottom rail, d lock rail, e frieze rail,
/ top rail, g frieze panel, h middle panel, k bottom panel.

Fig. 505. Fig. 506.

When a doorway is closed by two doors of equal width
hinged to its opposite jambs, the middle or meeting styles
are frequently rebated and beaded; such a door is termed
a doubled-margined door or two-leaved door. Doors also,
which, whilst they are in one width are framed with a
wide style in the middle, beaded in the centre in imitation
of the two styles of a two-leaved door, are also called
double-margined doors. Fig. 505 shows the appearance
of the two-leaved and double-margined doors. A sash
door is one which is glazed above the lock rail. A jib
door is one which is flush with the surface of the wall of
the apartment in which it is placed; it has no archi¬
traves or other ornamental border, but is crossed by the
skirting surbase and other finishings of the apartment,
and is otherwise so finished as to be undistinguishable
from the wall itself.

Plate LXXV. Fig. 1 , No. 1 , is the elevation of a
double-margined door. No. 2 is an enlarged horizontal
section in the line A B of No. 1. A A is the double-mar¬
gined style, formed by the two styles A A, e e the centre
bead, B the panel, c c the moulding laid in. The dotted
lines show the manner in which the styles are forked on
the top and bottom rails, which is also represented in
detail in Fig. 1, No. 3, where B is an elevation of part of
the top rail, thinned to enter the fork of the styles, and

BLACKIK & SON , GLASGOW, EDINBURGH &.• LONDON*

W. A.Bearer.Sc.

PLATE LXXIV.

SLIDING AND OTHER DOORS.

Fig.

I fK ' ' A

Fig. 6.

Fig. 7.

Fig. 8.

Fit/. 9.

Fig. 10.

Fiq.J3.

I IP. I Jon ,t.i, tle.i .

Scale to Figs. 1. 2. and 3.

12 6 o 1 2 3 4 6 3 7 8 9 lO 11 12 13 14 Feet.

I h I „ [ h I iI i j I I I I I — t- - 1 . 1 - 1 - I i i

BT.ACK1F. 8c SON. GLASGOW, EDINBURGH 8c LONDON.

W.A. Beevcr. O'c

PLATE LXXV.

DOUBLE HARCINED DOORS.

Tl4.1_W°l.

Tig.Z.N?! .

Ticj.3.N?l.

Tiq. Z. Ff° Z.

Fur . 3. Ff°3.

9Teet.

J. W. Lowry fa tip*

J. White del t .

BLACKIE & SON; GLAS GOW; EDINBURGH Sc LONDON.

IFQNUSIHIQNSS ©IF WO WIDOWS

PI.ATE LXXVT.

B-LACKIE 8c SON; GLASGOW,EDINBURGH, 8c LONDON.

11..1IT, LXXVr.

IFQNOSIKIQNSS ©IF W'lWDO'WS,

'Inches ^ ^ | | ^ 1 2 3 15 6 _» _ jfeet

If. C. Jo ass dp}. Scale for Elevation/. J.W.Lotvry Jc.

BhACXlE 8c SOU. GLASGOW, EDITS! UUKGU, & LONDON.

* *

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n I TE /. .UTZZ

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BI.ACKIK &;SON, UlASCOW, GDI'NBURCT .V f.ONIlON

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RF=- -

r "*'i\

WINDOWS.

187

c part of the style in elevation, and A is the plan at
the end of the styles, showing the fork, the thinning of
the rail, and the keys a a.

Fig. 2, No. 1, is a two-leaved or double-margined door,
and Fig. 2, No. 2, a section through the meeting styles A, B,
showing the rebates d d, and beads e e, which in this case
are planted on. The panel D is let into a groove in the
moulding C, in the French manner already noticed, and
the moulding is framed and united in the manner shown
in Fig. 2, No. 3 and No. 4.

Fig. 3, No. 1, is a double-margined gothic door. Fig.
3, No. 2, is an enlarged section through the meeting styles
showing the rebates A B, the panels D, and the panel
moulding c, framed as in the last example. Fig. 3, No. 3,
is an enlarged section through one of the panels, A style,
B centre rib, c moulding, D panel.

Plate LXXIY., Fig. 1 , is the elevation of a double-
margined door of large dimensions, such as a folding-door
used to close the communication between two drawing¬
rooms. But the door here illustrated, in place of folding,
is made to slide into recesses in the wall or partition.
Fig. 2 shows the plan of the doors and recesses, and Fig. 3
is a vertical section through the recessed part of the parti¬
tion and the door. Fig. 4 is a section to an enlarged scale
showing the top rail of the door, the recess in the parti¬
tion, one of the pullies and the straps by which the door
is hung to it, and the iron bar on which the pullies run.
Figs. 5 to 13 are examples of French doors, showing many
varieties of panelling and ornamentation.

Plate LXXIII., Fig. 1 , is the elevation of a jib door in
the side of an apartment which has a base b, dado and
dado moulding a ; and Fig. 3 is a vertical section through
the door. In Fig. 2 is drawn to a larger scale a horizon¬
tal section through part of the hanging style of the jib
door and the frame in which it is hung. The dotted lines
show the line of the hinging through the base mouldings,
and the extent to which the door can be opened. Fig. 4
is a section through the dado moulding, and Fig. 5 a sec¬
tion through the skirting and base moulding, both to the
some enlarged scale as Fig. 2.

Fig. 6 is an elevation of a pew door; and Fig. 7 a
section through its hanging style and the style of the
framing to which it is hung. It will be seen that it is
treated precisely as a jib door.

The jambs of doorways are finished with wooden linings
which are either plain or framed, and moulded to cor
respond with the door; they are in either case fixed to
the grounds, and if the jamb be wide the lining may re
quire backings or cross pieces to stiffen them. The doors
are hung in their places in two ways. In the first a door
frame is set in the wall or partition; to this the door is
hinged, and the linings being kept back from the edge of
the frame to a distance equal to the thickness of the door,
thus form the rebate to receive the door and the stop
against which it shuts. In the second mode the lining
covers the whole of the jamb, and is rebated to form the
recess to receive the door, and a corresponding rebate is
formed on the other edge of the lining for appearance sake.

Doorways are in general surrounded by an ornamental
wooden margin or border, not mei'ely, however, for orna¬
ment, but especially to cover the junction between the
plaster and wooden ground in the case of a wall, or be¬
tween the plaster and door frame in the case of a partition.

These margins are sometimes plates of wood ornamented
with mouldings, and are termed architraves, examples of
which are given in Plate LXIX., or they may consist of
pillars or pilasters with proper entablature. The pilasters
are set on solid blocks of the same height as the skirting,
and so also are the architraves in good work; but in other
cases they run down and are scribed to the floor. It is
said above that the chief use of the architrave is to cover
the joint between the wooden ground or the door frame
and the plaster. The ground being fixed and the door frame
set in its place, serve as guides for floating the plaster by,
and when the plaster is dry the architrave should be
applied so as to lap over the joint and effectually cover it;
but in ignorance of good construction it is common to fix
the architraves before the plastering is complete, a practice
which cannot be too severely reprehended.

WINDOWS, AND FINISHINGS OF WINDOWS.

Plates LXXVL—LXXVIII.

Windows consist of the glazed frames called sashes, and
of the frames or cases of various kinds which contain
these. The sashes may be either fixed, or hinged to open
like a door, or suspended by lines over pullies and balanced
by weights.

The frame for the fixed sash consists of solid sides or
styles, a head piece or lintel, and a sill, which is made wider
than the other pieces and weathered. This frame is rebated
to receive the sash, and the latter is retained in its place by
a slip of wood nailed round the inside of the frame.

The hinged or French sashes, as they are termed, have
rebated solid frames, and in their construction every care
is required to make them weather tight at the sills and
where they meet in the middle. In exposed places they
should always be made to open outwards, as the effect of
wind is then to close them and make their joints tighter.

Suspended sashes are bung on frames provided with
boxes or cases to contain the balancing weights. In order
that the reader may become familiarized with the several
parts of the sash-window, its frame, its shutters, and finish¬
ings, sketches are here presented of the horizontal and
vertical sections through a window, and these being de¬
scribed and a notion of them acquired, it will not be
necessary to embarrass him with repetitions of the descrip¬
tion of the same details in the plates.

Fig. 507 shows a horizontal section, and Fig. 508 a

O 'CD

vertical section of the window frame. The frame consists
of sides or breasts of about 1 ^ inch thick, grooved down
the middle for the reception of a beaded piece o o (Fig. 508),
called a parting bead, from its serving to part the sashes.
The sides or breasts are called the pulley styles, and the
frame is completed by the sill below and the lintel above.
To the outside edge of the pulley style the beaded pieces//
forming the sides of the casing or boxing are attached,
and the beaded edge projects so far beyond the face of the
style as, with the parting bead, to form the outer path or
channel in which the sash slides. On the inner edge of the
pulley style is fixed the piece b b (Fig. 507), called the inside
lining, to which the shutters are hinged; a back piece
extending between the inside lining and outside piece /
parallel to the pulley style, is added, to complete the case
or boxing, and the box has sometimes, and should always

188

PRACTICAL CARPENTRY AND JOINERY.

have, a division in the centre to separate the weights of
the upper and lower sashes. The path for the inner sash
is formed by a slip or stop head, fixed to the styles by nails
or, preferably, by screws. In the lower end of the path
of the outer sash a hole is cut in the pulley style suffi¬
ciently large to admit the weights, so that the sashes may
be hung after the frames are fixed, and the lines repaired
at any time. This is called the pocket, and it is covered
by a piece of wood attached by screws.

The sashes themselves consist of an outer frame, which
is composed of styles and rails. The bottom rail of the

vertical bars, which divide the sashes into panes, are
termed sash bars. The vertical bars, like the styles in
framing, extend, in single pieces, between the rails of the
sash, the horizontal bars being cut to fit their places, and
dowelled together through the vertical bars.

The fittings of a window consist of the boxings for the
shutters, if there be any, the linings, the shutters, with their
back flaps, and the architraves, or other finishings of the
opening in the apartment. All these parts are exhibited in
Fig. 507 in horizontal section. The boxings are formed in
the space between the inside lining of the sash frame and
the framed ground. The back of the recess is sometimes
plastered; but, in better works, it is covered with a framed
lining, as at a in the Fig. 507, called a back lining. This
has generally bead and flush panels, and is fitted in between
the inside lining b, and the framed ground c, and is gene¬
rally tongued into both. The shutters d, are framed as

doors, and panelled and moulded in the same manner.
They are hinged to the inside lining. The back flaps are
generally lighter than the shutters, and are sometimes
framed and moulded, so that the whole exposed surface
shall present the same appearance when the shutters are
closed; but they more frequently consist of bead and flush
framing. The shutters in place of being hinged, are some¬
times suspended and balanced by weights, like the sashes.

The wood work M M, Fig. 508, which extends from the
windowsill to the skirting, is called the breast lining; and
that on the side of the recess, extending from the bottom
of the shutters to the skirting, the elbow lining. The
ceiling of the window recess P P is also formed of wood, and
is termed the soffit lining. These linings are all framed
and moulded to correspond with the doors and other
framed work of the room. The margin of the window
opening is finished with architraves or other ornamental
appliances, in the same manner as the doors.

Plate LXXYI.— Fig. 1, No 1, is the elevation of a
sashed window with its finishings. Immediately under
No. 1 is an enlarged sectiqn of one of the jambs of the
window, showing in detail the lower sash, the pulley
piece, boxing, weights, shutter boxing, back lining, archi¬
trave and shutters. Fig. 1, No. 8, is a vertical section to the
same enlarged scale, through the lower part of the window
and the window breast, showing the rail of the lower sash,
the sill of the window frame, the breast lining and skirting.

The upper part of the window is shown in Fig. 1, No.
3, at the bottom of the plate. It shows the rail of the
upper sash, the lintel of the window frame, the soffit
lining, and the architrave.

Fig. 1, No. 4, is a section through the meeting rails of
the upper and lower sashes, showing the nature of the
rebate, or check, as it is called in Scotland.

Fig. 2, No. 1, is a sashed window double-margined, in
imitation of a French window.

Fig. 2, No. 2, shows the details, on a larger scale, of
the shutters, which are so arranged as to form the pilasters
at the sides of the opening in the apartment. Fig. 2,
No. 3, is a section through the top of the window, showing
the details of the entablature over the pilasters; and Fig.
2, No. 4, is a section through the centre style of the sash.

A sash bar, full size, is shown in section on the left-
hand side of the plate.

Plate LXXYI I.— Fig. 1 shows part of the elevation,
and Fig. 2 part of the plan of a window on an irregular
octagonal plan. In this the shutter of the widest part of
the window sinks into the breast and is suspended over
pullies, and balanced by weights like the sashes. Fig.
3 shows the manner of attaching the suspending lines by
means of a bracket carried below the bottom of the shutter,
so that the pulley and weights may be entirely contained
in the window breast. Fig. 4 is a plan or horizontal sec¬
tion through the breast; and Fig. 5 is a vertical section
of the same.

The shutters of the side windows are hinged to the
frame in the usual way, as seen in Fig. 2, which repre :
sents a horizontal section of the window above the sill,
with the shutters closed.

Fig. 6 is a section of a sash bar, full size.

Plate LXXYIII.— Fig. 1 shows the finishing of a
window, looking upwards towards the soffit. The dotted
lines A B show the shutters and back flap when closed;

PLATE LXXVI11

tFO^QSKIOM©© ®\F Wa^®@W'

Fig. 1

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PLATE LXXIX.

J. White. A A

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IV A Bearer. Sc

SKYLIGHTS.

189

and the shaded parts, A B, the shutter and back flap when
folded into its boxing; CHDK is the boxing and back
lining; G the ground; and F the architrave.

Fig. 2 shows the soffit, the shutters, and finishings of a
window in a wall thicker at one side than the other ; the
drawings are so detailed as to be self-explanatory.

Fig. S, the soffit, shutters, and finishings of a window
in a circular wall.

CIRCULAR WINDOW.

Plates LXXIX, LXXX.

Plate LXXIX., Fig. 1 , No. 1 , is the plan, and No. 2,
part of the elevation of a circular window, with diamond
formed panes.

In No. 1, A are the jambs, B the sash, c the pulley
style, E F the window sill, D the inside lining. The centre
lines of the divisions for the panes are set out on the
plan of the lower rail of the sash, at c d e f ; the
thickness of the bars at a b, k l, o, &c. ; and the sites of
the crossings or intersections of the bars at h i, n, &c.
The heights are set out in a similar manner on No. 2, and
from these data the elevation can be drawn, as in the
manner already familiar to the reader. Fig. 2 is an eleva¬
tion of the lower sash on the stretch-out; and Fig. 8 the
stretch-out of the diagonal bar a d, showing the twist
occasioned by the curvature.

To find the mould for the curvature of the diagonal
sash-bar. —In Fig. 4, let A b e d be the plan of the bottom
rail, and let it be divided into any number of equal parts
—1, 2, 3, 4, <fcc. Through these draw ordinates at right
angles to the chord line A B, meeting it in a b c d, and
produced beyond it to meet the chord line A c of the dia¬
gonal bar in l m n o p. Through these points of inter¬
section draw ordinates perpendicular to A c, and make
them equal to the corresponding ordinates of A B, as l q v
to a f 1, mrw to b g 2, &c.

Fig. 5 shows the section of a sash bar, full size, with
a dowel hole A; and underneath is shown the mitring of
the bars edge, and the dowel A A, all full size.

Plate LXXX.— The figures in this plate illustrate the
framing of a circular headed sash in a circular wall.

Fig. 1, No. 1, is a plan of the window, and No. 2 an
elevation of the circular headed sash. In No. 1, A A are
the jambs, s the outside lining, B c the upper sash, G G
the pulley styles, H the inside lining, e the parting bead,
F the stop bead, or batten rod, as it is sometimes called,
M the sill.

To find the veneer for the arch-bar k l m called the
cot-bar, or chord-bar. —Set out the stretch-out of the arc
K LM, Fig. 1, on the line AB, Fig. 4, and draw lines from
the divisions in the arc to any chord line, as No, No. 1;
then make the ordinate C a D, Fig 4, equal to o z P, No. 1,
3 be equal to r t y, and so on; then gedfh, Fig. 4, will
be the veneer for the arcli-bar.

To find the mould for the radial bars. — From P in
No. 1 draw P u a tangent to the curve; and on it draw
lines from division l in the radial bars F H E G, and pro¬
duce them to cross the plan of the lower sash; then transfer
the ordinates R h i, j k l, &c. to II r s, 3 t u, and the ordi¬
nates of the bars in No. 2, and the moulds LG Fs of the
bars EGFH will be obtained.

To find the face mould for the circular outside lining.
—The dotted line aklmnop, Fig. 1, No. 2, shows the
lower edge of the lining; and lines drawn through these
points perpendicular to A c, cut the line S g (No. ]), in
abed efg. Transfer these on the stretch-out to the line
A B, Fig. 5, and draw ordinates perpendicular to A B, on
which set up the corresponding heights from No. 2, as bk
to b g, c l to c h, dm to d k, &c.

To obtain the moulds for the head of the sash frame
apply the stretch-out of the outside of the arch in No. 2
to the base line A B in Fig. 2, and set out on the ordinates
drawn through the divisions, the corresponding ordinates
from the chord I K in No. 1.

To obtain the mould for the underside of the sash, Fig.
3, set out the divisions of the underside of the arch in Fig.
1, No. 2, along the base line A B in Fig. 3, and proceed in
the same manner as above, but setting out the ordinates
from the chord line L M.

Fig. 1 , No. 3, shows the first division of the sash frame
A N in No. 2, and the plan No. 1; the thickness of stuff
required to work it out of the solid is shown at E N. T he
joint at N, No. 2, and k h, No. 3, is shown at b c in
Fig. 2, and c F in Fig. 3.

Figs. 6, 7, and 8, are sections through the sash frame
and sash at three points: 1st, above the springing; 2d,
at /; and 3d, at the centre. The part corresponding
to the pulley style is now divided into two pieces, B and
C, and the parting bead b is inserted between them, a
is the outer, and c the inner lining. The latter beaded
and grooved for the reception of the soffit lining. A is
the sash.

SKYLIGHTS.

Plates LXXXL—LXXXIII.

Plate LXXXL, Fig. 1.—In the skylight, of which No.
1 is the plan, and No. 2 the elevation, it is required to
find the length and backing of the hip.

Let A B be the seat of the hip; erect the perpendicular
A c, and make it equal to the vertical height of the sky¬
light, and draw B c, which is the line of the underside of
the hip; the dotted line g It shows its upper side.

To find the backing, from any point in B c, as n: draw
perpendicular to B C, a line n F meeting A B in F, and
through F draw a line at right angles to A B, meeting the
sides of the skylight in D and E. Then from F as a centre,
and with F n as radius, cut the line ab in in, and join
D to, E to. The angle D to E is the backing of the hip,
and the bevel k ml will give the angle of backing when
applied to the perpendicular side of the hip bar.

In Fig. 2, in which No. 1 is the plan, and No. 2 the
elevation of a skylight with curved bars, to find the hip:
let A B be the seat of the centre bar, and D E the seat of
the hip. Through any divisions 1 2 3 4 C of the rib, over
A B draw lines at right angles to A B, and produce them
to meet E D in p o n in D. From these points draw lines
perpendicular to E D, and set up on them the correspond¬
ing heights from A B, as l 1 in p 1 , k 2 in o 2, &c.

In the irregular octagonal skylight, Fig. 3, Nos. 1 and 2,
the length and backing of the hips is formed as in Fig.
1, No. 1, by drawing a c perpendicular to A B, and set¬
ting up on it the height of the skylight in A c, then

190

PRACTICAL CARPENTRY AND JOINERY.

drawing B c. The point F is found by r drawing g F per¬
pendicular to B C, from any part of B C, and through F
drawing D E at right angles to A B to meet the adjacent
sides of the skylight in D e, then making F h equal to f g,
and joining D h E h.

In the octagonal skylight, Fig. 4, No. 1 and 2, which
has curved ribs, the process of finding the hips is exactly
similar to that employed in Fig 2, and need not be
again described.

Plate LXXXII., Fig. 1.—Nos. 1, 2 and 3 are the plan,
side elevation, and end elevation of an irregular octagonal
skylight, and Fig. 2, Nos. 1, 2, and 3, the plan, side eleva¬
tion, and end elevation of an elliptical skylight, neither
of which requires detailed description.

Fig. 3, No. 1, is the plan, No. 2 the end elevation, and
No. 3 the side elevation, of an elliptical domical skylight.
The section of the skylight on the minor axis is a circular
segment, as seen in No. 2.

To find the ribs in Fig. 4, describe the quadrant A B,
and in c B make the height, D B, equal to the height of
the segment in No. 2; draw E d, and make E L equal to
the length of the rib over the minor axis, and draw c L
to find the bevil, L iv, of the end. Divide the arc E L into
any number of parts, and through them draw lines per¬
pendicular to A c, and produce them indefinitely; draw also
through, in the lower end of the rib, the line to K per¬
pendicular to A c. Then from D as a centre, with the
length of the longest semidiameter of the ellipse as radius,
cut the line to K n K, and draw D K, and produce it to
n to meet the perpendicular A n from A. Then the line
I) n will be the semi-axis major of an ellipse, as A c in
Fig. 5,. and the segment of it formed by the lines L u m K
in Fig. 4 will be the rib standing over the semi-axis major.
But all the ribs may be drawn by ordinates thus: From
D, Fig. 4, as a centre, and with the lengths of the several
ribs as radii, cut the line m K in ir G F, and through these
draw lines from D, meeting A n. Then the points where
these lines are crossed by the perpendiculars to A c, pass¬
ing through the divisions 1 2 3 4 L in the arc E L are the
places of corresponding ordinates, by which the curves may
be drawn, as D u t K in Fig. 5, D u t H in Fig. (!, D u t G
Fig. 7, and D u t F in Fig. 8.

Plate LXXXIII., Fig. 1.—No. 1 is the plan, and No.
2 the elevation, of an octagonal skylight.’ No. 3 is one of
the sides laid over on the horizontal plane of projection.
Fig. 2, No. 1, is the projection of a portion of the inside
of the skylight looking up, and No. 2 is an elevation of a
portion of the interior corresponding to the last. The
mode of finding the lengths and backings of the hips and
ribs is developed in the lower half of the plan. First, the
hip B D. Make D E equal to the vertical height, and join
B E. From any point b in B E let tall a perpendicular
meeting B D in c; make c a equal to c b, and join c a and
A a, and produce the latter to T. Then c a T is the bevil
for the backing of the hip to be applied to the vertical
side of the rib.

It will be seen that the rib K I is found in a similar
manner from the right angled triangle K I L, of which the
hypotenuse K L is the length of the rib as before.

In obtaining the ribs on the hither side of the octagon
a compendious method is adopted. Let i> q be the seat of
the hip, and N 0, G F the seats of any other ribs; on FG
construct the right angled triangle, F o H, as before, and

from any point, It, in the hypotenuse draw R S, parallel
to H G, and R e at right angles to F H. From Rasa
centre with any radius describe a circle as cl e f g, and
through e and / draw lines parallel to H G. At the points
where these cut the seats of the ribs erect perpendiculars,
as at n m Jc l, p o i h, and intersect them by tangents from
the circle parallel to H G, as d l to, g h o; then join to s,
and o S, and we obtain rso and R S to as the bevils for
the backing of the rib P Q, and in like manner the backing
of any other rib is obtained.

Fig. 3, No. 1, shows the rib at F G in Fig. 1, No. 1, to
a larger scale, and No. 2 shows a hip rib, the angle of
backing, QDS, being the same as A a c in Fig. 1, No. 1.
No. 3' shows the common bar corresponding to the line
I K in Fig. 1, No. 1, the angle P F o, being the same as
w r x in the latter Fig. No. 4 is the hip as seen in Fig.
2, Nos. 1 and 2. The manner of finding the mouldings of
the angle bars and ribs, as exemplified in this Fig.,
has been already described in detail, and on examination
it will be seen that the same letters refer to the same parts
in all the mouldings, by which their correspondence can
be readily traced.

Fig. 4 is the window bar.

Plate LXXXIII?— Pulpit with Acoustical Canopy. —
The drawings sufficiently explain the construction of the
pulpit; and of the canopy, which is novel in design; we
insert the following explanation, kindly supplied by its
author, Mr. Wydson. The concave interior surface is
generated from a point which appears in the flank eleva¬
tion, a little above the level, and in advance, of the desk.
In the first place, a parabola was drawn, plan ways and
sectionally, having its focus in what was considered as the
average position of the speaker’s mouth; and a point was
then found from which, as a centre, could be drawn, on
plan and section, a circular arc coinciding as closely as
possible with the parabolic curve, which point is the one
already mentioned. The adopting a spherical surface in
lieu of a paraboloidal one was for the purpose of simplify¬
ing the construction. The curves appear, in dotted lines,
in the plan and flank elevation. The exterior, or back,
of the canopy, bears no affinity to the interior it being
straight horizontally. The canopy stands independently
of the pulpit, and could be removed without interfering
therewith.

HINGING.

Plates LXXXIV.—LXXXVI.

The art of hanging two pieces of wood together, such
as a door to its frame, a shutter to the lining, or a back
flap to a shutter by certain ligaments that permit one or
other of them to revolve. The ligament is termed a hinge.

Hinges are of many sorts, among which may be
enumerated, butts, rising hinges, casement hinges, chest
hinges, coach hinges, folding hinges, garnets, screw hinges,
scuttle hinges, shutter hinges, desk hinges, back fold
hinges, esses, and centre-pin or centre-point hinges.

As there are many varieties of hinges, there are also
many modes of applying even the simplest of them, and
much dexterity and delicacy is frequently’ required. In
some cases the hinge is visible, in others it is necessary
that it should be concealed. In some it is required not

PLAT/-: I. XXXI.

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BLACKIE &• RON , GLASGOW. EDINBURGH &• LONDON.

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PLATE I.XXXU.

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PLATE LXXXm

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73 Feet.

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PLATE LXXX1IIH

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PLATE LXXXIV.

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Bl.A' KIK X- SON. <SV^8<;0'W. EDIIiBUBOH X- LONDON.

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. /. White. Jr/

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BLAGKIE %C SON , GLASGOW, EDINBURGH & LONDON.

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II.'A. It sever. Sc

LABOUR SAYING MACHINES.

191

only that the one hinged, part shall revolve on the other,
but it shall be thrown back to a greater or lesser distance
from the joint.

In Plates LXXXIY.—LXXXVI. are figured a great
variety of modes of hinging.

Plate LXXXIV.— Fig. 1, No. 1, shows the hinging of
a door to open to a right angle, as in No. 2.

Fig. 2, Nos. 1 and 2, and Fig. 3, Nos. 1 and 2. These
figures show other modes of hinging doors to open to 90°.

Fig. 4, Nos. 1 and 2. These figures show a manner of
hinging a door to open to 90°, and in which the hinge is
concealed. The segments are described from the centre of
the hinge g, and the dark shaded portion requires to be
cut out to permit it to pass the leaf of the hinge g f.

Fig. 5, Nos. 1 and 2, show an example of centre-pin
hinge pei'mitting the door to open either way, and to fold
back against the wall in either direction. Draw a b at
right angles to the door, and just clearing the line of the
wall, or rather representing the plane in which the inner
face of the door will lie when folded back against the
wall; bisect it in /’ and draw / d the perpendicular to a b,
which make equal to a f or / 6, and d is the place of the
centre of the hinge.

Fig. 6, Nos. 1 and 2, another variety of centre-pin
hinging opening to 90°. The distance of b from a c is
equal to half of a c. In this, as in the former case, there
is a space between the door and the wall when the former
is folded back. In the succeeding figures this is obviated.

Fig. 7, No. 1. Bisect the angle at a by the line a b ;
draw d e and make e g equal to once and a half times
a d ; draw f g at right angle to e d, and bisect the angle
f g e by the line c g, meeting a b in b, which is the centre
of the hinge.

No. 2 shows the door folded back when the point e falls
on the continuation of the line / g.

Fig. 8, Nos. 1 and 2. To find the centre draw a b,
making an angle of 45° with the inner edge of the door,
and draw c b parallel to the jamb, meeting it in b, which
is the centre of the hinge. The door revolves to the
extent of the quadrant d c.

Plate LXXXY. — Fig. 1, Nos. 1 and 2; Fig. 2, Nos. 1
and 2; and Fig. 3, Nos. 1 and 2, examples of centre-pin
joints, and Fig. 4, Nos. 1 and 2, do not require detailed
description.

Fig. 5, Nos. 1, 2, and 3, show the flap with a bead a
closing into a corresponding hollow, so that the joint can¬
not be seen through.

Fig. 6, Nos. 1, 2, and 3, show the hinge a b equally
let into the styles, and its knuckle forming a part of
the bead on the edge of the style B. The beads on each
side are equal and opposite to each other, and the joint
pin is in the centre.

Fig. 7, Nos. 1, 2, and 3. In this example, the knuckle
of the hinge forms portion of the bead on the style B, which
is equal and opposite to the bead on the style a.

In Fig. 8, Nos. 1, 2, and 3, the beads are not opposite.

Plate LXXXVI.— Fig. 1, shows the hinging of a back
flap when the centre of the hinge is in the middle of the
joint.

Fig. 2, Nos. 1 and 2, shows the manner of hinging a
back flap when it is necessary to throw the flap back from
the joint.

Fig. 3, Nos. 1 and 2, is an example of a rule-joint, such

as is required for the shutter in Fig. 2, No. 2, Plate
LXXVI. The further the hinge is imbedded in the wood,
the greater will be the cover of the joint when opened to
a right angle.

Fig. 4, Nos. 1 and 2, shows the manner of finding the
rebate when the hinge is placed on the contrary side.

Let / be the centre of the hinge, a b the line of joint on
the same side, h c the line of joint on the opposite side,
and b c the total depth of the rebate. Bisect b c in e and
join e /; on e f describe a semicircle cutting a b in g, and
through g and e draw g h cutting d c in h, and join d h,
h g, and g a to form the joint.

Fig. 5, Nos. 1 and 2, is a method of hinging employed
when the flap on being opened has to be at a distance
from the style. It is used in doors of pews to throw the
opened flap or door clear of the mouldings of the coping.

Fig. 6, Nos. 1 and 2, is the ordinary mode of hinging
the shutter to the sash frame.

LABOUR SAVING MACHINES.

In many of the operations of the joiner, in which
numerous copies of the same thing have to be produced,
accuracy is insured by introducing the principle of the
guide, either to direct the tool over the work or the work
over the tool. Examples of this are found in the mitre-
box, the shoot blocks, and in the various kinds of fences
and stops. These appliances are obviously the first step
towards seeking the aid of machinery in performing
operations requiring frequent repetition; and, accord¬
ingly, we find the principle of the guide applied first
to simple sawing, then to planing, and subsequently to
grooving, tonguing, mortising, tenoning, and shaping.

At first, as is usually the case, the applications of
machinery to these works were in direct imitations of the
actions of the workman. Thus, in the first planing
machines the work was fixed, and the plane made to pass
over it with a reciprocating motion; but, eventually the
same effect came to be better produced by means entirely
different. It was not till near the end of the last cen
jniry that circular saws were introduced into England,
although they were previously used on the Continent for
small work in all kind of materials. The first attempt
to construct a planing machine, is stated by Mr. Moles-
worth to have been made by a Mr. Hatton in 1776,*
and the next attempt was made by Sir Samuel Bentham
in 1791.

When Sir Samuel Bentham was in Russia, previous to
the date mentioned, he had made considerable progress
in contriving machinery for shaping wood, so as to insure
accuracy and save manual labour. Besides the general
operations of planing, rebating, mortising, dovetailing,
grooving, bevelling, and sawing in curved, winding, and
transverse directions, he had completed, in the way of
example, an apparatus for preparing all the parts of a
highly finished sash window; another for preparing every
part of an ornamental carriage-wheel, and nothing re¬
mained for finishing the work of the joiner or wheel¬
wright, but the putting the several component parts

* On the Conversion of Wood by Machinery, a paper read betore
the Institute of Civil Engineers, Nov. 17, 1857, by Guilford Lindsay
Molesworth.

192

PRACTICAL CARPENTRY AND JOINERY.

together. In 1793, Sir Samuel Bentham patented*
several inventions, and as Mr. Molesworth well says, “liad
his ideas been carried out and the appliances of engineer¬
ing been more perfect, he would doubtless have introduced
many of those inventions which were years afterwards
brought out and patented as new/’

In 1802, Mr. Bramah patented machinery for producing
straight, smooth, parallel, and curvilinear surfaces on
wood. In his planing machine the cutting tools were
fixed in apertures near the circumference of a horizontal
wheel, moving with great velocity on a vertical axis, and
' the timber laid on a horizontal carriage was moved for¬
ward under their action. It was in principle somewhat
the same as the machine figured in Plate LXXXVII. In
1807, Mr. Brunei’s famous block machinery was set to
work in Portsmouth dockyard. It is not necessary here to
trace the progress of conversion of timber by machinery;
suffice it to say that Thomson’s machinery for sawing,
gauging, and grooving and tonguing flooring-boards was
in operation in 1826, and in 1827, Mr. Muir, of Glasgow,
patented a machine for working flooring-boards, which
has since served as a model for those subsequently intro¬
duced in Britain. In this machine the bottom of the
board was roughly planed by a rotatory adze, while
another similar adze operated on the upper surface. The
board then passed between two fixed cutters set obliquely,
which removed a shaving of the length and width of the
deal, while two revolving cutters or saws made the sides
parallel, and two other cutters grooved or tongued the
edges. In the hands of Mr. M'Dowall, of Johnstone, the
flooring machine has in design and workmanship ap¬
proached perfection.

But it is not to these machines which we here desire
to direct the attention of the reader. Machinery so ex¬
tensive and capable of producing so much, will not supply
the requirements of the ordinary workshop. It is ex¬
pensive in its first cost, and requires a great amount of
the same kind of work to keep it in remunerative opera¬
tion. For the ordinary workshop, where the trade is
limited and much varied, the simpler though less perfect
machines, which are used in America in aid of the work¬
man, are more suitable; and it is to the description and
illustration of one or two of the more generally useful of.
these machines that we propose to devote these pages and
plates.

Plate LXXXVII. — Figs. 1, 2, 3. The small saw
bench which is here figured, is suitable for jobbing work.
It occupies little space, and can be applied in plain and
bevel sawing, mitring, tenoning, rebating, &c. The bench
is supported on four stout legs, firmly united by means
of the top rails, and the middle rails which carry the
plummer blocks of the driving pulley. It is only 3 feet
2 inches long, 2 feet 2 inches wide, and 3 feet 61 inches
high. Its dimensions are confined within these narrow
limits, by the mode adopted of banding the pulleys, about
to be described, and which is the subject of a patent.

Fig. 1 is a plan of the top; Fig. 2 is an elevation of
one end; and Fig. 3 is an elevation of the front of the

* In referring to the specification of this patent of 23d April, 1793,
the editor of the Mechanic's Magazine, a competent authority, says
it is a perfect treatise on the subject, indeed the only one worth
quoting from which has to this day been written on the subject.
Dec. 16, 1848.

bench. The same letters refer to the same parts in all the
figures, a a a a are the supports, b b rails on which the
plummer blocks of the driving pulley are fixed, and which
carry also the braced upright c c, to which the cast-iron
bracket, supporting the axis of the saw cl cl, is attached;
e e is the driving pulley, moved by a handle attached to
its axis; // are radial iron bars moving freely on the
axis of the driving pulley, and carrying at their outer
end the tension pulley g g. The diameter of the driving
pulley is 234 inches, the diameter of the tension pulley
is 7J inches, the axle of the saw is 1£ inch diameter; it is
suspended on conical steel centres, and serves as a third
pulley. The band passes over the tension pulley and
over the saw axle, and its lower web is pressed against
the periphery of the driving pulley by the weight of the
tension pulley. The saw is 8 inches in diameter, and
makes 15§ revolutions for each turn of the handle.

Fig. 1 is the plan of the top of the machine. It is com¬
posed of a front board h h, hinged to the frame at k, so
that its other end can be elevated by means of a wooden
screw m, as seen by the dotted lines in Fig. 3. Through
a slot in the top of this the saw cl cl works; n n is the
back board, which is capable of being slidden along
parallel to the blade of the saw, being guided by a fillet
on its under side, sliding in a groove in the fixed top-
board of the machine below it, seen at o o, Fig. 2. This
sliding board has various holes, some screwed and others
plain, for fixing the fences, guides, and stops to be here¬
after mentioned; and as the pins and screws which secure
these project below the bottom of the board, there are
longitudinal channels grooved out in the path of these
holes in the fixed top p p, underneath.

When the machine is used for ripping or cross-cutting,
a parallel motion fence q q is screwed by a wooden hand-
screw to the front board h h, Fig. 1. The distance between
the fence and blade of the saw regulates the scantling to
be cut off; a stop is fixed to one of the holes in the sliding
board, against which the stuff is held, and the board
beinir slidden along in the direction of the arrow, the
stuff is acted on by the saw. By raising the front board
by means of the screw to, the machine can be adjusted
for tenoning. The board is raised until just so much of
the saw is exposed as is equal to the depth of the shoulder
of the tenon, and the fence is set to the proper length of
the tenon. The stuff is passed along, and the shoulder
on one side is cut; it is then reversed and the operation
repeated for the other side. When the shoulders of all
the pieces have been cut, the front board is dropped until
the saw projects through to the length of the tenon; the
fence is then moved towards the saw, till the space
between them is just equal to the depth of the shoulder,
and the stuff is then passed through, on end, twice; and
if the adjustment has been correctly made the tenon is
formed perfectly square and clean. For bevel cutting and
mortising, the guide shown at R, Fig. 1, is used. It con¬
sists of a stock, which, by means of the handscrew r, can
be fixed to the sliding top. To the end of the stock are
hinged the arms 2 2, and to a block sliding freely in a
slot in the stock are hinged the short arms 3 3, hinged
also at their other end to 2 2. By means of the screw 4
the block is made to traverse the slot, and the arms 2 2
are moved so as to make a greater or less angle with the
stock.

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PLATE LFXXVH E

Furness's patent mortising and, tenoning machines

Fig.l. Jf.3.

Fig. 2.

I i

' i

i i

Fig.l. M 7.

Fig.l.JF8.

Fig.l. JV? 1.

A.F. OrriFlge., del.

BLACKIE & SON, GLASGOW, EDINBURGH fc LONDON.

W. A.Beever.Sc.

LABOUR SAYING MACHINES.

193

When mitring is to be performed, the arms 2 2 are
adjusted, to make an angle of 45° with the plane of
the saw, and the stuff bein£ held against one or other
of them, the top board is shot so as to bring it under the
operation of the saw.

On the inner end of the shaft of the driving pulley,
there is a crank which may be acted on by a treadle like
a turning lathe when the stuff is thin; but, in ordinary
cases, the machine requires two operators. It is not
necessary to describe further the many operations which
this little handy bench may aid in performing with accu¬
racy and despatch.

Figs. 4, 5, 6, illustrate Furness' patent planing machine.
In this machine the stuff is operated upon by cutters,
held by horizontal arms fixed to a vertical shaft, and it
is in this respect similar to the machine patented by Mr.
Bramah in 1802, but it is much simpler and less expen¬
sive. The same letters refer to the same parts in all the
figures. A A a a is the fixed framing of the machine.
B B a travelling bed piece, on which the stuff to be ope¬
rated on is fixed. Its upper surface, on which the stuff
rests, is itself planed true by the revolving cutters. It
travels on cast-iron ways b' b', and has a rack z z fixed
to its under side, into which a pinion D on the hand-
wheel 1, and also a pinion E on the bevel-wheel 2, gear.
The cutter frame C C is of cast-iron; it slides between the
vertical pieces of the main framing a a, and can be raised
and lowered by means of the toothed rack b, which is
acted upon by the winch handle c, by means of the screw
and bevel pinion d and e. This frame carries a vertical
spindle /, with a long pulley of timber g, fitted to it. The
lower end of the spindle has attached to it the arms h h,
which carry the cutters to to. On the lower part of the
frame C is fixed the cast-iron disk plate n n, which presses
on the timber while the cutters operate upon it close to
its periphery. The main driving belt gives motion to the
shaft o o, by means of the fast pulley p, and is shifted to
the loose pulley p', when the machine is to be stopped.
The pulley q on the shaft o drives the long pulley g on
the cutter shaft, and another pulley on the top of o drives
the pulley r on the shaft s. A third pulley t, fixed on the
shaft o, gives motion to a pulley v, carried by an inter¬
mediate shaft, shown by dotted lines, and through this in¬
termediate shaft and its pulleys, to the pulleys w w' w",
moving also on the shaft s. x x is a clutch, by means of
which either the pulley r or the pulleys w can be keyed
to the shaft, and while the other remains loose, and
thus it may be made to revolve in either direction. The
shaft s has two sliding bevel pinions y y, at its lower
end, either of which can be thrown into gear with the
bevel wheel 2, which, as has been said, has a pulley on
its shaft gearing into the rack Z on the under side of the
travelling bed B B. When by means of the upper handle
and clutch x x, the pulley r is made to revolve with
the shaft, the travelling bed brings the stuff forward in
the direction of the arrows, under the operation of the
cutters. When the timber has all been passed through,
r is thrown loose, and w is fixed, and the carriage moves
back with rapidity. The carriage can also be moved back¬
wards or forwards, by throwing the pinions y y out of or
into gear, and it can also be moved by hand through the
wheel s.

Plate LXXXVI1“— Fig. 1, Nos. 1 to 10 are plans,

elevations, and details of Furness’ patent tenoning ma¬
chine.

Fig. 1, No. 1 is the plan, Fig. 1, No. 2, a side elevation,
and No. 3 an end elevation. The same letters refer to
the same parts in all these. This machine, by means of
revolving cutters a a, forms both sides of the tenon simul¬
taneously. The stuff to be operated upon is laid on si
travelling bed M M, which moves transversely across the
machine, so as to pass the stuff between the cutters. The
lower cutter b is supported by the main frame B B, and the
upper cutter a by the moveable frame C C, which can be
raised or lowered, so that it can be adjusted to the thick¬
ness of stuff or depth of shoulder required; and the bed
M M can also be raised or lowered, so as to complete the
adjustment. The moveable stop p q regulates the length
of the tenon. The main driving pulley / has another
pulley z, keyed on the same shaft, a belt from which
passes over pulley h of the upper cutter, and then under
the pulley k of the lower cutter, and over a tension pulley
L, and then returns. By this arrangement the cutters
move in opposite directions; and to allow of the adjust¬
ment for the various thicknesses of wood, and keep the
belt tight on the pulleys, a simple contrivance is used.
A leather belt s s is attached to the bottom of the stirrup
spar 11 , which is attached to the hinged cross-head K, carry¬
ing the tension pulley L, and the belt then passes through
under an eccentric paul at 2 2, which holds it tight at
any point required. We shall now describe the parts of
the machine in detail. A A upright supports, which with
the rails B B form the main framing of the machine, car-
rying the driving pulley and the lower cutter b; c C
upright framing, which moves round c as a centre, and
its opposite end can be lowered or raised by adjusting
the radial slot at E, and for finer adjustment by the
vertical screw F. It is further supported by the wrouglit-
iron stay-rod g. This frame carries the upper cutter a,
and, by means of the uprights H H, and jointed cross piece
K, the tension pulley L. M M the bed frame on which
the stuff to be operated on is laid. It is-supported on
the slotted upright board to to, the under edge of which
rests on the wedge pieces n n. By means of a screw,
the handle of which is seen at o, the wedges have a back¬
ward and forward motion, and raise and lower the frame
as occasion may require; and it is fixed when adjusted
by the screw to to, working through the slots in the up¬
right supports. The moveable fence p q consists of two
parts, the distance between which can be regulated, and
indicates the length of the tenon. The stuff is placed
between the fence q and the cutter, and the fence p is set
to the proper length of the tenon; the stuff is then
advanced so as to rest against p, and the other end con¬
sequently projects through the cutters to the required
distance. The fences are kept in their position by springs,
which can be depressed by the pressure of the wood. The
wood is also pressed against the stops r r, and is kept
fast on the frame by the lever s s, the outer end of which
is grasped in the left hand of the workman, together
with a little iron handle t, fixed to the frame, which he
thus uses like pincers, and the bed frame is at the same
time pushed from him by his right hand, so as to bring
the stuff under the action of the cutters. The operation,
which takes long to describe, is performed very rapidly.

Fig. 1, No. 4 is the side view of one of the cutters.

194

PRACTICAL CARPENTRY AND JOINERY.

No. 5 is the inside view of the disk of the same, and No.

6 the front or outside of the disk, all drawn to a larger
scale.

We have described the machine as adapted for tenon¬
ing, but it can be used also for sawing and boring. Nos.

7 and 8 are a profile and front view of the saw, which
when used takes the place of the lower cutter, and is
driven by reversing the banding, so as to cause the saw
to revolve in a direction opposite to the motion of the
sliding frame.

The boring tool is seen in profile in No. 9. It is sus¬
pended between the piece u, fixed to the outside of the
frame c c, Fig. 1, No. 3, and the slotted piece v, No. 10,
which is attached to the inner side of the frame by a clamp
screw working through the slot. It is driven by a belt
from the small pulley w, Fig. 1, No. 2, passing over the
pulley x, carried by its own spindle.

Fig. 2, Nos. 1 and 2 show Furness’ patent mortising
machine.

Fig. 2 is a side elevation, and Fig. 2, Nos. 1 and 2,
details of the chisel socket.

The machine consists of a sill A, bolted to the floor or
otherwise steadied, two uprights B B, and two cross rails
c c. D is a lever moving on a centre at d, and having the
mortising tool attached to its other end at e, a treadle E,
acting on the lever D, by the two iron straps //, and the
interposed ratchet lever F. The chisel socket, besides
being attached to the lever D, is suspended to a spring
pole G fixed to the ceiling of the apartment, whose elas¬
ticity raises it after every cut. The chisel socket H slides
in the two eyes h h, formed on the ends of the bars of the
iron frame Jc It. These bars slide through the uprights
B B, and by means of the screw L can be moved forwards
or backwards, so as to move the cutting chisel further
from or nearer to the frame, according to the thickness of
stuff. I is the bench or rest on which the stuff is laid.
It is carried by the piece m, which has a bolt passing
through a slot in the upright, so that by means of the
clamping screw n it can be raised or lowered. To pre¬
vent the stuff rising with the chisel, there is a stop s s on
each side. These work through eyes in the slotted pieces
r r, and by means of screws can be adjusted along with
the chisel. The depth of the cut of the chisel is regulated
by moving the straps // to various notches in the levers
D F and E.

The Figs. 2, Nos. 1 and 2, show in detail the manner of
suspending the chisel socket. 1 is a rope attached to the
spring pole G, 2 is a triangular iron link, to the top of
which is attached the rope, and to the bottom a leather
belt 4, clamped by the screw apparatus at 3, so that it
can be lengthened or shortened at will. 5 is the end of

the lever D, showing the manner in which it is attached
to the socket; 8 is the socket turning freely round its
axis in a head 6. This head has two wings 6 6 diametri¬
cally opposite, with square notches in them, into which
the detent 7 falls. When half the length of the mortise
has been cut, the detent is withdrawn from the notch it
F.g. 509 may happen to be in, and the chisel is turned
round till the detent falls into the opposite
notch, and the remaining half of the mortise
is completed, working from its extremity again
towards the centre.

Fig. 509, c d is a side, and b a a front view
of the chisel used in mortising.

This machine is also used for making dowels or wooden
pins, by substituting a cylindrical cutter for the chisel.

In conclusion, we note a few practical points to be ob¬
served in the construction of these machines.

In machines with revolving cutters the general opinion
is, that the greater the speed of the cutting-tool the better
will be the quality of the work. The practical limit,
however, appears to be between 2500 and 3500 revolu¬
tions per minute. A higher velocity heats the bearings,
destroys the balance, and causes injurious vibrations.
To produce a good result the travel of the work should
be very slow relatively to the travel of the cutters. In
some of the planing machines the cutters revolve with a
velocity of 7000 feet per minute, while the work advances
at the rate of only 30 feet, but as a general rule the work
travels about of an inch for each stroke of the cutters.
In order to withstand this high velocity, the framing of
the machine requires to be perfectly constructed. It
should be of hard wood; and Mr. Molesworth directs—
“ that the joints be not made so as to depend simply
on mortise and tenon; they should be shouldered in.”
“ The bearings are sometimes made of an alloy, composed
of 100 parts tin, 10 parts antimony, and 2 parts copper.
In forming them the spindle is accurately fitted in its
place, and the alloy is cast round it into an iron shell,
which forms the plummer block. The parting of the base
and cap is made by inserting a thin sheet of iron in the
proper position.” “ Another peculiarity is the method of
securing steadiness in high-speeded shafts; this consists
in cutting in the journal a succession of angular threads,
with angular grooves between. The alloy is cast round
the journal as before, and great steadiness of action is
secured; whilst the oil remains in the bearings without
difficulty. An adjusting axle box is also much used; it
is centred on two set screws, so as to allow it to turn
slightly in the event of the opposite bearing being un¬
evenly worn, and thus the extra wear and chatter which
would ensue at high speeds are obviated.”

STAIRS.

195

PART SEVENTH.

STAIRS AND HAND-RAILING.*

Stairs are constructions composed of horizontal planes
elevated above each other, forming steps; affording the
means of communication between the different stories of
a building.

In the distribution of a house of several stories, the
stairs occupy an important place. In new constructions
their form may be regular, but in the reparation or re¬
modelling of old buildings, the first consideration is gen¬
erally to make the distribution suitable for the living
and lodging rooms, and then to convert to the use of the
stairs the spaces which may remain; giving to them such
forms in plan as will render them agreeable to the sight,
and commodious in the use.

A great variety of form in the plans of stairs is thus
in a measure forced on the designer, leading to many
ingenious contrivances for overcoming difficulties, disguis¬
ing defects, and enhancing accidental beauties, which
he might not have adopted if unfettered in his choice.
These inventions, originated by necessity, are again applied
in cases where the necessity may not exist, recommended
by their intrinsic beauty, or by the desire for variety in
design.

As introductory to the construction of stairs, a selec¬
tion of some of the more simple contrivances are here
presented.

That kind of
stair which, after
the common lad¬
der, is the most
simple, is formed
of a thick plank
at a con¬
venient angle to
form the ascent,
and upon it are nailed pieces of wood to give a firm foot¬
ing. This (Fig. 510) is often used in scaffolding.

The stair next in degree is composed of horizontal planks
forming steps, just sufficiently wide to give a footing; the
planks are tenoned on the ends and let into mortises in
two raking planks; the mortises are sometimes rectangular,
as at d (Fig. 511), and sometimes
they follow the inclination of the
sides, as b and c. In the better sort
the outer edge of the step has a
nosing, as at c. The tenons of the
steps are sometimes made so long
as to pass entirely through the sides,
and are secured by keys on the outside:—to preserve the
planks which form the steps from splitting, the sides of
the raking pieces are grooved to receive their ends. The
opposite side pieces, too, are often bound together by iron
rods; one end of each rod having a rivet head, and the
other end being screwed with a nut to embrace the side

Fig. 511.

pieces. Such rods should be placed near the middle of a
step, and close to its under side.

Another method of forming a stair expeditiously, is to
notch out the side pieces on their upper edge sufficiently
Fig. 5 i 2 . to receive the steps and risers, thus; a a

the side pieces, b b the risers, and c c the
step boards or treads (Fig. 512). The
risers are nailed at the ends to the sides
or strings, and the steps are nailed to the
risers and also to the strings. Such

Fig. 513.

methods as have been described are often used in ware¬
houses, factories, and agricultural buildings.

There is a contrivance for economizing space sometimes
used, which, perhaps, it may be well to mention, as the
ascent is thereby made in about one half the space other¬
wise required.

The width of this kind of stair is divided into two sets

7 of steps, both of equal
length and width, but
the risers, except the
first and last, are made
twice the usual height;
thus, if the line a B
(Fig. 513) be 72 inches,
and the width c D 33,
and it is necessary to
rise 80 in., divide the
line a B in nine equal
parts, and make the
step equal to two of
these parts; also, di¬
vide the width in two
equal parts, and the
height into ten equal
parts, which gives 8
inches for the tread, 8 inches for the bottom riser, and
16 inches for the intermediate risers a a, &c., and 8
for the top riser b. Arrange the risers in such order
that the face line of one riser shall be in the midway
betwixt the face of the one next below and the one

Fig. 514. Fig. 516.

next above, as will better be seen by reference to Fig.
514. The height of the risers is so disposed that the bot¬
tom riser shall have the face of the first step 8 inches from

* Contributed by Mr. Mayer, Montpelier Villas, Cheltenham.

196

PRACTICAL CARPENTRY AND JOINERY.

Fig. 516.

the floor, whilst the first step on b shall he 16 inches
from the floor, and the succeeding risers 16 inches each.

In using this stair, one foot is placed on a step of one
flight, as at a (Fig. 513), and the other on a step of the
other flight, as at b, and so on alternately. Such stairs
will only admit the passage of one person at a time.

When it is required to admit of two persons passing each
other, three flights are neces¬
sary, the centre flight being
made wider than the exterior
flights (Figs. 515 and 516).

This contrivance may be used
in places not sufficiently spa¬
cious to admit of stairs of
ihe usual construction.

When houses began to be built in stories, the stairs
were placed from story to story in straight flights like
ladders. They were erected on the exterior of the build¬
ing, and to shelter them when so placed, great projection
was given to the roofs. To save the extent of space re¬
quired by straight flights, the stairs were made to turn
upon themselves in a spiral form, and were inclosed in
turrets. A newel, either square or round, reaching from
the ground to the roof, served to support the inner ends
of the steps, and the outer ends were let into the walls, or
supported on notched boards attached to the walls.

At a later period the stairs came to be inclosed within
the building itself, and for a long time preserved the spiral
form, which the former situation had necessitated.

Definitions.— The apartment in which the stair is
placed, is called the staircase.

The horizontal part of a step is called the tread, the
vertical part the riser, the breadth or distance from riser
to riser the going, the distance from the first to the last
riser in a flight the going of the flight.

When the risers ai’e parallel with each other, the stairs
are of course straight.

When the steps are narrower at one end than the other,
they are termed winders.

When the bottom step has a circular end, it is called a
round-ended step; when the end is formed into a spiral,
it is called a curtail step.

The wide step introduced as a resting-place in the ascent
is a landing, and the top of a stair is also so called.

When the landing at a resting place is square, it is
designated a quarter space.

T\ hen the landing occupies the whole width of the stair¬
case it is called a half space.

So much of a stair as is included between two landings
is called a flight, especially if the risers are parallel with
each other: the steps in this case are fliers.

The outward edge of a step is named the nosing; if it
project beyond the riser, so as to receive a hollow mould¬
ing glued under it, it is a moidded nosing.

A straight-edge laid on the nosings represents the angle
of the stairs, and is denominated the line of nosings.

The raking pieces which support the ends of the steps
are called strings. The inner one, placed against the
wall, is the wall string; the other the outer string. If
the outer string be cut to mitre with the end of the riser,
it is a cut and mitred string; but when the strings are
grooved to receive the ends of the treads and risers, they
are said to be housed, and the grooves are termed housings.

Stairs in which the outer sti'ing of the upper flight
stands perpendicularly over that of the lower flight are
called dog-legged stairs, otherwise newel stairs, from the
fact of a piece of stuff called a newel, being used as the
axis of the spiral of the stair; the newel is generally or¬
namented by turning, or in some other way. The outer
strings in such stairs are tenoned into the newel, as also
are the first and last risers of the flight.

When the upper and lower strings are separated by an
interval, the space is called tli'e icell-hole. If the front
string is mitred or bracketed, it is called an open string;
if grooved, a close string. Where there is a well-hole and
no newel, and the string is continued in a curve, the
curved part of the string is said to be wreathed, and
the stair is then a geometrical stair.

Besides the support afforded by the strings the stair is
sustained by pieces placed below the fliers; these are
called carriages; they are composed of longitudinal and
transverse pieces; the former are called rough strings, the
latter pitching pieces; and the rough strings have trian¬
gular pieces called rough brackets, fitted to the underside
of the tread and riser.

The winders are supported by rough pieces called bearers,
wedged into the wall, and secured to the strings.

When the front string is ornamented with brackets, it
is called a bracketed stair.

Where communication between the stories is frequent,
the qualities necessary in the stairs are ease and conveni¬
ence in using, combined with sufficient strength and dura¬
bility. Economy of space in the construction of stairs
is an important consideration. To obtain this, the stairs
ai’e made to turn upon themselves, one flight being carried
above another at such a height as will admit of head room
to a full-grown person.

Method of setting out stairs where the building is al¬
ready erected, or the general plan of the building is
understood.

The first objects to be ascertained are the situation of the
first and last risers, and the height of the story wherein
the stair is to be placed. A sketch is made of the plan of
the hall to the extent of 10 or 12 feet from the supposed
place of the foot of the stair, and all the doorways, branch¬
ing passages, or windows which can possibly come in con¬
tact with the stair from its commencement to its expected
termination or landing are noted This sketch necessarily
includes a portion of the entrance-hall in one part, and
of the lobby or landing in the other, and on it have to be
laid down the expected lines of the first and last risers.
The height of the story is next to be exactly determined
and taken on a rod; then, assuming a height of riser
suitable to the place, a trial is made, by division, how
often this height is contained in the height of the story,
and the quotient, if there be no remainder, will be the
number of risers in the story. Should there be a remain¬
der on the first division, the operation is reversed, the
number of inches in the height being made the dividend,
and the before-found quotient the divisor, and the opera¬
tion of division by reduction is carried on, till the height
of the riser is obtained to the thirty-second part of an
inch. These heights are then set off on the story rod as
exactly as possible. The next operation is to show the
risers on the plan, but for this no arbitrary rule can be
given; the designer must exercise his ingenuity.

STAIRS.

When two flights are necessary for the stoiy, it is desir¬
able that each flight should consist of an equal number of
risers; but this will depend on the form of the staircase,
the situation and height of the doors, and other obstacles
to be passed over or under, as the case may be. Try what
the width of the tread will be by setting off, upon the line
n a in Fig. 519, the width of the landing from the wall A B;
and dividing the length of the flight into as many equal
spaces as it is intended there should be steps in each
flight. The landing covers one riser, and therefore the
number of steps in a flight will be always one fewer than
the number of risers. The width of tread which can be
obtained for each flight will thus be found, and consistent
with the situation, the plan will be so far decided. A
pitch-board should now be formed to the angle of inclina¬
tion: this is done bj r making a piece of thin board in the
shape of a right-angled triangle, the base of which is
the exact going of the step, and its perpendicular the
height of the riser.

If the stair be a newel stair, its width
will be found by setting out the plan
and section of the newel on the landing;

(if one newel, it should, of course, stand c
in the middle of the width;) then, in connection with the
newel, mark the place of the outer or front string, and
also the place of the back or wall string, according to the
intended thickness of each. This should be done not only
to a scale on the plan, but likewise to the full size on the
rod. Set off on the rod, in the thickness of each string,
the depth of the grooving of the steps into the string;
mark also on the plan the place and section of the bottom
newel; the same figure answers for the place of the top
newel of the second flight, the flights being supposed of
equal length. The front string is usually framed into
the middle of the newel, and thus the centres of the rail,
the newels, the balusters, and the front string range with
each other; the width of the flights will thus be shown
on the rod.

It is a general maxim that the greater the breadth of
a step the less should be the height of the riser; and con¬
versely, the less the breadth of step, the greater should
be the height of the riser. Experience shows that a step
of 12 inches width and 5 ^ inches rise, may be taken as
a standard; and if from this it is attempted to deduce
a rule of proportion, substituting, for the sake of whole
numbers, the dimensions in half-inches, namely 21 and 11,
then, in order to find any other width corresponding in
inverse proportion,

197

12 x 5|
8

these values for t and r in the formula, we have
= inches as the breadth of tread.

Suppose, again, the given breadth to be 13 inches, we

12 x 54

liave-

— = 5,^ inches as the height of riser.

1 O

This process of inverse proportion may be performed
graphically as follows:—

Let the tread and riser of a step of approved proportion
be represented by the sides c b, 6 a, of the triangle a b c,
Fig. 517. Through the point a, draw a line cl a f, parallel to
the step line c b. Then, to find the riser for any other step,
set off on the line c b, from the point c to d, the required

Fig. 517.

Say as 24
24
24

13-8

13-2

Thus, it will be seen that a step of 6 inches in width will
require the riser to be 11 inches, a step of 9^ inches will
need the riser to be nearly 7 inches, and that a step of 10
inches requires a riser of about 6f inches.

The same thing is thus otherwise expressed. Let T be
the tread, and R the riser of any step which is found to
have proper proportion, then to find the proportion of any

RxTTxR

other tread t, and riser r, -= t, or —-— = r.

r t

Take, for example, a step with a tread of 12 and a riser
of 54 inches as the standard, then to find the breadth of
the tread when the given riser is 8 inches, and substituting

width of a step, say 10 inches, and draw d d\ draw also
c d, and continue it to the line b a, and the point of in¬
tersection there will show the height of riser corresponding
to the tread c d. In like manner, if the width given be
18 inches, set it off in the point 6; draw 6 e and c e, and
the intersection at h will be obtained, giving 3f inches
for the height of the riser. A width of 20 inches will
show a height of 3'3 inches. On the right side of the
figure is shown each step we have mentioned, connected
with its proper riser, thus exhibiting the angle of pitch.

The same end nearly is arrived at thus:—In the
right-angled triangle a b c, Fig. 518, make a b equal to
21 inches, and b c equal to 11 inches, according to the

previous stan-

Fig. sis. dard Propor¬

tion ; then to
find the riser
corresponding
toagiventi - ead,
from b set off on
a b the length
of the tread, as
bd, and through d draw the perpendicular d e, meeting the
hypothenuse in e; then d e is the height of the riser, and
if we join b e, the angle d b e is the slope of the ascent.
In like manner, where b f is the width of the tread, / g
is the riser, and b g the slope of the stair. A width of
tread, b h, gives a riser of the height of h Jc, and a width
of tread equal to b l, gives a riser equal to l to.

It is conceived, however, that a better
proportion for steps and risers may be ob¬
tained by the annexed method:—

Set down two sets of numbers, each in
arithmetical progression; the first set show¬
ing the width of the steps, ascending by
inches, the other showing the height of the
riser, descending by half inches. It will
readily be seen that each of these steps
and risers are such as may suitably pair
together.

Treads.

Risers.

inches.

6 !

4“

198

PRACTICAL CARPENTRY AND JOINERY.

It is seldom, however, that the proportion of the step
and riser is exactly a matter of choice—the room allotted
to the stairs usually determines this proportion; but the
above will be found a useful standard, to which it is
desirable to approximate.

In better class buildings the number of steps is consid¬
ered in the plan, which it is the business of the architect
to arrange, and in such cases the height of the story rod
is simply divided into the number required.

Plans of Stairs .—Before giving examples of the vari¬
ous forms of stairs ordinarily occurring in practice, we
shall with some minuteness illustrate the mode of laying
down the plan of a stair, where the height of the story,
the number of the steps, and the space which they are to
occupy are all given.

The first example shall be of the simplest kind, or dog¬
legged stairs.

Let the height (Fig. 519) be 10 feet, the number of
risers 17, the height of each riser consequently 7 T V, and
the breadth of tread 9§; the width of the staircase 5 feet
8 inches.

Proceed first to lay down on the plan the width of the
landing, then the size of the newel a in its proper position,

A B

the centre of the newel being on the riser line of the
landing, which should be drawn at a distance from the
back wall equal to the semi-width of the staircase, and at
right angles to the side wall. Bisect the last riser a b at
o, and describe an arc from the centre of the newel, as o n,
on which set out the breadth of the winders; then to the
centre of the newel, draw the lines indicating the face of
each riser. If there be not space to get in the whole of
the steps, winders may be also introduced on the left
hand side, instead of the quarter space, as shown.

The next example is a geometrical staircase.

Let abcd (Fig. 520) be the plan of the walls where a
geometrical stair is to be erected, and the line c be the
line of the face of the first riser; let the whole height of
the story be 11 feet 6 inches, and the height of riser
fi inches, the number of risers will consequently be
twenty-three. The number of steps in each flight will
be one fewer than the number of risers, and according to
the preceding rule the tread should be 11 inches, so if
there are two flights there will be twenty-one steps; or ii
winders are necessary, there will be twenty-two steps in
all, from the first to the last riser. Having first set out the
opening ot the well-hole, or the line of balusters, divide
the width of the stairs into two equal parts, and continue

the line of division with a semicircle round the circular
part, as shown by the dotted line in the figure; then divide
this line from the first to the last riser into twenty-two
equal parts, and if a proper width for each step can thus
be obtained, draw the lines for the risers. This would,
however, give a greater width of step than is required;
take therefore 11 inches for the width of step, and this,
repeated twenty times, will reach to the line d, which is
the last riser. There is in this case eight winders in the
half space, but four winders might be placed in one
quarter space, the other quarter space might be made a
landing, and the rest of the steps being fliers, would bring
the last riser to the line A C. The usual place for the en¬
trance to the cellar stairs is at D, but allowing for the
thickness of the carriages, the height obtainable there
will be only about 6 feet, which is not sufficient. At E, in
this example, would be a better situation for the entrance
to the cellar steps.

Plates LXXXVIIL—XCIIL, XCY.

Plate LXXXVIIL, Fig. 1.—Nos. 1 and 2, show a plan
and elevation of a newel stair. The first quarter space con¬
tains three winders, the next quarter space is a landing;
the lower flight is shown partly in section, exposing the
rough string D D, and its connection with the bearers
c c. The front string A A should be tenoned into the
newels below and above.

Fig. 3,—No. 1, shows the plan of a geometrical stair
with winders. In the first quarter space, or lower half
of the figure, the lines of the steps are drawn to the
centre of the well-hole, and this is the usual way of
placing the risers; but drawn thus as radii of the circle,
they are, obviously, too narrow at the inner end next
the well hole, and too wide next the wall, and if two
persons were passing each other they would both be
forced to use parts of the tread, most inconvenient to walk
upon. Further, as the risers of the steps are all of equal
height, it follows that the slope or ramp of the string
board along the ends of the fliers, from the first to the
seventh step, will be much less steep than that which
subtends the narrow ends of the winders, and the result
will be a very ungraceful knee at their junction. Both
of these inconveniences can be overcome by adjusting the
steps in such a way as to distribute the inequality amongst
them, or as the French term it, by making the steps dance,
as is shown in the upper half of the figure. This may be
accomplished either by calculation or graphically. By the
first method, the step which is in the centre of the circular
arc is regarded as a fixed line, and the divergence from
parallelism has to be made between it and the extremes
either way. But it is not necessary to begin the diver¬
gence at the first step, nor indeed is it advisable, and in
general the first and last three or four steps are left unal¬
tered, so that they may be perfectly parallel to the landing.
Suppose then that the divergence is fixed to commence at
the fourth step, it becomes necessary to distribute eight,
spaces along the centre of the string, commencing at the
centre line of the stairs, which, from the centre line to the
fourth riser, shall follow some law of uniform progres¬
sion, say that of arithmetical progression, as being the
most simple. The progression then will consist of eight
terms, the sum of which shall be equal to the length from
the centre to the fourth step. Suppose that its develop-

'PLATE LXXXVIU.

a ir a a m s .

Fuj .2. N° 2

Fiq.l. N° 2.

./. While del '

Inches ^ c if • x f 3 p f 7 p 9 Y y y 1,4 1,5 1,6 17 ^8 i3 2| 0 ieet

J. IV. Lowrv fc.

BLACK IK So SON, GLASGOW , EDINBURGH Sc LONDON

f "V W

S T A 0 m §

GEOMETRICAL STAIRS.

1) Mi nr r. Ini'! A F (h-rult/e. del!

HLACKIK &• SOU , GLASGOW, EDINBURGH fc I,ONDOIT.

W.A. BctverJc

ST A 0 [& Id o

GEOMETRICAL STAIRS.

Fiy. 3.

Fu/A.

lxn :< i'
S,;i/r lirtntTTliH- ~

A 4

3 oT Feel.

D. Mayer, Im'!" A. A /(/<•/!

HI.M'KIP. K- SON , GI.AfROW, HIlIMBURnH K- LONDON.

W.A.Bte i

Sir AO Ga§'o

GEOMETRICAL STAIRS_ ELLIPTICAL PLAN

PLATE XCII.

Fig.l. N°l.

12. 6 O 2

Scale,’ Irrlrr inh il I

£ 6 7 8 .9 20

■ 1 1 II I —I of Feet.

1).Mayer.hiv 1 ' A.F. Orridge.DeL h

BLACKIE &: SON , GLASGOW, EDINBUHOH L-iONDON.

ITS. Beevtr. Sc.

,*■ *.

„•# *

■

PLATE XCITT.

ST#\Q ISo

CARRIAGES OF ELLIPTICAL STAIRS, AND DETAILS.

- -4

«r A

-L:

7T~

X-\

— 1 -

; E

A' /

, /y

D. J/nw /inLi. /■' Orruhn- DA'

Luciirs 12

Scale for Fias.l-2.ZA

2 a -156
- < ' '

9 9 loTeet.

./ \\ r . Lowrvjailp

BLAC’KIE &• SON; G LASOOW.EDINBTTRGTT & LONDON.

STAIRS.

199

ment is 66 inches, a length composed of the breadth of
three fliers, 4 5 6, namely 36 inches, and the sum of the
widths of the ends of the five winding steps, 7 8 9 10 11,
namely 30 inches,

Subtracting from .... 66 inches.

The width of eight steps of the same width

as the winders, .... 48 ,,

There is obtained the difference . 18 „

from which is to be furnished the progressive increase to
the steps as they proceed from the centre to riser No. 4.
Suppose these increments to follow the law of the natural
numbers 1234567 8, the sum of which is 36, divide
the difference 18 by 36, and the quotient, 0 - 5 inches, is
the first line of the progression, and the steps will increase
as follows:—

The end of step No. 11 = 6'5
„ 10 = 7

„ 9 — 7-5

The sum of which is 66

These widths, taken from a scale, are to be set off’ on the
line of balusters, and from the points so obtained, lines
are to be drawn through the divisions of the centre line.
It is easy to perceive that by this method, and by vary¬
ing the progression, any form may be given to the curve
of the string.

The graphic method, however, now to be described, is
preferable to the method by calculation, seeing that it is
important to give a graceful curve to the development of
the string.

Let the dotted line s to p, Fig. 3, No. 2, represent the
kneed line made by the first division of the stairs in the
lower part, corresponding to the nosing of the fliers, and
the upper part to n to that of the winders. Bisect the line
of the winders to n in p, and raise a perpendicular p i.
Then set off to s equal to to p, and make s r perpendicu¬
lar to s to. The intersection of these two perpendiculars,
s r and p i, gives the centre of the arc of a circle, tangen¬
tial in s and p to the sides of the angle s to p. In like
manner is found the arc to which p n,n o are tangents, and
a species of cyma is formed by the two arcs, which is a
graceful double curve line without knees. This line is
met by the horizontal lines, which indicate the surface of
the treads, the point p being always the fixed point of
the centre step, the twelfth in this example. Therefore,
the heights of the risers are drawn from the story rod to
meet the curved line of development, &• p o, and are thence
transferred to the baluster line on the plan.

Fig. 2.—Nos. 1 and 2 show the plan and elevation of a
well-hole stairs, with a landing in the half space. The
well-hole is here composed of two circular quadrants con¬
nected by a small portion of straight line; this figure is
not so graceful as the perfect semicircle in Fig. 3, No. 1,
but it allows more room on the landing.*

Plate XC. Fig. 1. —Nos. 1 and 2 are the plan and
elevation of a geometrical stair, composed of straight flights,
with quarter-space landings, and rising 15 feet 9 inches.

The first flight is shown in Fig. 1 , No. 2, partly in sec¬
tion, exhibiting the carriage c c, T the trimmer joists for
quarter space, and v the trimmer joists of the floor below,
with the lower end of the iron baluster fastened by a
screw and nut d, at the under side of the trimmer joist V.

Fig. 2.—No. 1, exhibits the plan, and No. 2, the eleva¬
tion of a geometrical stair, with straight flights connected
by winders on the quarter spaces.

Plate XCI.— Fig. 1 is a plan, and Fig. 3 an elevation
of a geometrical stair, with a half space of winders. The
positions of the rough strings or carriages are shown on
the plan by dotted lines, e g, e f, h i, fk. This is a simpler
mode of forming the carriages of stairs than that gene¬
rally practised; having fewer joints it is also stronger.
It is fully illustrated and described as applied to the more
intricate example of elliptical stairs in Plate XCII.

Fig. 2 shows the plan, and Fig. 4 the elevation of a
geometrical stair with part winders, and part landing,
well adapted for a situation where a door has to be entered
from the landing. The line A B on the plan shows the situa¬
tion where the principal carriage should be introduced.

Plate XCII. exhibits a plan {Fig. 1 , No. 1) and eleva¬
tion {Figs. 1 and 2) of an elliptical stair with winders
throughout. On the plan is shown the position of the
carriages for such a stair, and we shall now describe the
formation of such carriages.

Plate XCI 11, represents the formation of carriages for
the elliptical stairs in Plate XCII. Fig. 1 is the longest
carriage, or rough-string, and is formed of one deal,

11 inches wide by 3 or 4 in thickness; its length of bear¬
ing betwixt the walls is about 15 feet. To find the
best, position for the carriages, lay a straight edge on the
plan, and by its application find where a right line will be
divided into nearly equal parts by the intersection of the
risers. The object of this will readily be understood, if it
is considered that in a series of steps of equal width and
risers of equal height, the angles will be in a straight line,
whereas in a series of unequal steps and equal risers, the
angles will deviate from a straight line in proportion to
the inequality in the width of steps. Notwithstanding the
inequality in the width of steps, which thus often occurs,
it seldom happens that carriages may not be applied to
stairs, if their situation be carefully selected by the means
above mentioned. The double line A B is taken from the
plan {Fig. 1, No. 1, Plate XCII.), with the lines of risers
crossing at various angles of inclination. These lines re-
present the back surface of each riser, according to the num¬
ber on each. The double line A B will therefore be under¬
stood as representing the thickness of the piece. Lines
drawn from the intersections of each of the risers perpen¬
dicularly on A B {Fig. 1, Plate XCIII.), will present the
width of bevel which each notching will require in the car¬
riage at the junction of the wall. No. 8 crosses very ob¬
liquely; No. 9 with somewhat less obliquity; No. 10 with
still less, and the obliquity continually diminishes, till at
13 the crossing is at right angles, presenting only one line.
The remaining numbers are bevelled in the reverse direc¬
tion, gradually increasing to No. 19, where the carriage
enters the wall. The complete lines show the side of the
carriage next the well-hole, whilst the dotted lines repre¬
sent the side next the wall. The most expeditious method
of setting out such carriages is to draw them out at full
size on a floor. Having first set out the plan of the stairs

4 For description of Plate LXXXIX., see pages 200, 201, and 207.

200

PRACTICAL CARPENTRY AND JOINERY.

at full size, take off the width of every step, in the order
in which it occurs, marking that width, and at right
angles thereto draw the connecting riser, thus proceeding-
step by step, till the whole length of the carriage is com¬
pleted ; next set out one side of the carriage as a face side,
and square over to the back, allowing the bevel as found
on the plan; then, with a pair of compasses, prick off to
the under edge at each angle, for the strength; this will
define the curvature for the underside with its proper
wind, to suit the ceiling surface of the stairs. The bearer,
c D, Fig. 1, No. 1, Plate XCII., is a level piece wedged
in the wall, with its square end abutting against the side
of the carriage, A B. The dotted line on the upper side
of the carriage, Fig. 1, Plate XCIII., and the straight
dotted line on its under side, are intended to show the
edges of an 11-inch deal previous to its being cut; the
shaded part at each end shows its bearing in the wall;
at the riser 18 is shown a corpsing, to receive the lower
end of the carriage, Fig. 3, c L; and at the riser 16, a
similar corpsing to receive the carriage, Fig. 4, G H;
Fig. 2 is the carriage, E F Fig. 1, No. 1, Plate XCII., par¬
allel with A B, Fig. 1, against which the front string is
nailed. Each of the last mentioned is formed in the same
manner as the one already described.

This method of forming the carriages of stairs is not yet
much practised. It was introduced by the author more
than thirty years since, and has given greater satisfaction
than the more laborious process of framing for every step,
which is not only weaker from the greater number of
joints, but is also more expensive. It is now gradually
coming into use.

Plate XCV. exhibits a stair winding round a large
cylindrical newel. Fig. 1 is the plan, and Fig. 2 the
elevation. The lower part of the newel is composed of
cylindrical staving, of 2-inch plank, into which the risers
and bearers to each step are fixed, the detail of which
is better seen in Fig. 4, drawn to a larger scale. The
manner in which the steps and risers are put together
is shown in Fig. 3; the risers are grooved, and the steps
tongued into them. This figure shows the ends of the
steps before the last thin casing of string board is fixed.
They are united by a band of iron screwed to the bearers
throughout the entire length. This kind of construction
has a near resemblance to the method for carriages that
has been much in use, and called framed carriages for
well-hole stairs, the objections to which are stated above.

Method of Scribing the Skirting.—Pl. LXXXIX.
Fig. 4 shows the method of scribing down skirting on
stairs. The instrument used for this purpose is shown in
two positions, A and B. It is something like a bevel in
form, but has a slider with a steel point at the end; this
slider moves steadily in collars, so that while the steel point
rests on any point on the stairs, another point on the slide
denotes on the skirting board the corresponding point,
thus remedying a defect of the common compasses by
maintaining always a parallel motion.

Fig. o is another view of the same instrument, showing
the mortise in which the slide works.

Strings. — Fig. 6 shows a portion of a string board for
the steps {Fig. 8) ; the middle part being a flexible veneer
intended to be bent on a cylinder of a suitable curva¬
ture, and blocked on the back by pieces in a perpen¬
dicular position.

Fig. 9 is the string board in development for the
smaller end of the winders.

Fig. 7 a more enlarged view of the same, showing the
mode of easing the angle by intersecting lines.

In circular strings, the string board for the circular
part is prepared in several different ways. Each of these
will now be described, the first being that adopted in
veneered strings.

One indispensable requisite in forming a veneered string,
is called by joiners a cylinder; it is, however, in fact, a
semicylinder joined to two parallel sides. An apparatus
of this kind must first be formed of a diameter equal to
the distance betwixt the faces of the strings in the stairs.

Take some flexible material, as a slip of paper, and
measure the exact stretch-out of the circular part of the
cylinder, from the springing line on one side to the spring¬
ing line on the other. Lay this out as a straight line, on
a drawing board; then examine the plan of the stairs,
and measure therefrom the precise place of each riser
coming in contact with or near to the circular part of the
well-hole as it intersects on the line of the face of the
string, and also the distance of such riser from the spring-
ing-lines. These distances should all be carefully marked
on the slip of paper, and transferred to the drawing-board;
then, with the pitch board, set out the development of
the line of steps, by making each step equal to the width
found, and connecting with it at right angles, its proper
height of riser. When the whole development has been
set out on the drawing-board, mark from the angles of the
steps downwards, the dimension for the strength of car¬
riage; by this means it will be seen what shape and size
of veneer will be required. The whole of the setting out
must now be transferred to the face of the veneer; then
with the point of an awl prick through the angles of the
steps and risers, and trace the lines on the back, as well
as on the front. The veneer must now be bent down on
the cylinder, bringing the springing lines and centre lines
of the string to coincide as exactly as possible with those
of the cylinder; the whole string must then be carefully
backed by staving pieces glued on it, with the joints and
grain parallel to the axis of the cylinder. The lines on
the back of the string will serve to indicate the quan¬
tity of the veneer to be covered by the staving. The
whole must be allowed to remain on the cylinder, till suffi¬
ciently dry and firm. It is next fitted to the work, by
cutting away all the superfluous wood as directed by the
lines on the face of the veneer, and then being perfectly
fitted to the steps, risers, and connecting string; it must
be firmly nailed both to the steps and risers, and also to
the carriages. Each heading joint in the string should
be grooved and tongued with a glued tongue.

There is another method of gluing up the strings some¬
times practised. In this the string is set out as before
described, but instead of using a thin veneer, an inch
board is taken, on the face of which the development of
steps, risers, springing, and centre lines must be carefully
set out as before. The edge of the board must be gauged
from the face, equal to the thickness of a veneer, which
would bind round the cylinder; the string must then be
confined down on the work-bench, and grooves made by
a dado grooving plane on its back in the direction of the
riser, and at about half an inch distant from each other, till
the whole width of the cylindric surface is formed into a

HANDRAILING.

201

regular succession of grooves and projections; the string
must then be bent on the cylinder, and the grooves filled
with small bars of wood, carefully glued in. When dry,
this is to be fitted to the stairs, as in the former method.

Another method is making staves hollowed on the face
to the curvature of the well-hole, and setting out as much
of the string on each piece as will cover its width, then
gluing the staves, edge to edge, without any veneer. This
method, though expeditious, is not safe.

A fourth method is sometimes practised, when the
curved surface is of great length and large sweep, as in
the back strings of circular stairs. In this a portion of
cylindric surface is formed on a solid piece of plank, about
three or four feet in length; and the string, being set out
on a veneer of board sufficiently thin to bend easily, is laid
down round the curve, with such a number of pieces of
like thickness as will make the required thickness of the
string-board. In working this method, the glue is intro¬
duced between the veneers with a thin piece of wood, and
the veneers quickly strained down to the curved piece
with hand-screws. A string can be formed in this way to
almost any length by gluing a few feet at a time, and
when that dries, removing the cylindric curve and gluing
down more, till the whole is completed.

The manner of jointing the staves is shown in Plate
XCIII., Fig. 5, where a bevel is set with the tongue in the
line of the radius, whilst the stock coincides with the back
of the stave piece. Fig. 6 also shows how a back string is
formed for the stair in Plate XCII., and a base moulding
formed for the same in thicknesses, and applied to the string.

Fig. 7, No. 1, Plate XCIII., shows a portion of front
string with bracket, and the mitred end of a riser at a.
No. 2 shows the back of the same riser and how it is
shouldered and mitred to receive the front string and
bracket; B shows the thickness of the front string, A the
carriage, C the thickness of the tread, d the hollow, and
e the end of the bracket.

Diminishing and Enlarging Brackets. — Plate
LXXXIX. Fig. 1. To diminish the bracket of the fliers
to suit the winders, make one of the fliers marked B, the
base of a right-angled triangle, and setting off any con¬
venient distance, B C, for the perpendicular, draw a line
from the extreme point of the bracket, to form the hypo-
thenuse of the triangle; set A, the length of the shorter
bracket required to be drawn, as a perpendicular, under
the hypothenuse; draw ordinates through each member
of the original bracket, and through the points of then-
intersection with B, draw lines converging to the point c.
The intersection of these with the line A will divide it for
the corresponding set of ordinate lines, which draw, and
make equal respectively to those on the line B; trace the
contour through the various points thus obtained, and the
bracket A will be produced. To enlarge a bracket, it is
only necessary to reverse the process by making the shorter
bracket, as A, the base of the triangle, producing from it
the perpendicular and hypothenuse. This procedure is
so obvious, that no detailed description is necessary.

HANDRAILING.

Plates XCIY., XCVL— C.

Although many authors had written on the subject of
handrailing before the time of Mr. Peter Nicholson, the

methods described by them for producing the face mould
were erroneous in principle, and attended with great waste
of material. The merit of introducing a better system is
due to Mr. Nicholson, who taught the true theory of cylin¬
drical sections, and illustrated it by practical solutions ot
the problem of producing the section of a cylinder through
any three points on its surface.

In the following treatise, the author, in illustrating
the same theory, has introduced methods of solving the
problems, which will be found less intricate and easier-
understood than those of Mr. Nicholson, and, what is
not less important, more readily applied in practice. The
difference between the two methods will be described in
the sequel.

Definitions.— In the following article, there will be
frequent occasion to make use of certain terms which it is
of importance to have fully understood.

The horizontal, or ground plane, is that plane on
which the plan is drawn.

The vertical pflane is any plane considered as standing
perpendicular on the ground plane.

The oblique plane, cutting plane, or plane of the plank,
is that plane on which the mould of the rail is produced.

The trace of any plane is a line forming the termination
of one plane and its junction with another; thus the angle
of a block of marble is the trace of the plane of any one
of its sides on another side which it meets. The trace
therefore is a line, and the only line which can be drawn
common to either of two planes, meeting each other at
an angle.

A cylinder is a solid, described by geometricians as
generated by the rotation of a rectangle about one of its
sides, supposed to be at rest; this quiescent side is called
the axis of the cylinder, therefore the base and top of
the cylinder are equal or similar circles.

A prism is a solid, whose base and top are similar right
line figures, with sides formed in planes, and rising per¬
pendicularly from the base to the top.

The cylinder, so called by joiners, is a solid figure,
compounded of the two last-mentioned figures; its base
is composed of a semicircle joined to a right-angled paral¬
lelogram. This last compound figure is intended when¬
ever the word cylinder occurs in the following article,
unless the word geometrical be prefixed.

Of the Construction of the Falling Mould. —The
height of the handrail of a stair, as the following considera¬
tions will show, need not be uniform throughout, but may
be varied within the limits of a few inches, so as to secure
a graceful line at the changes of direction. In ascending
a stair the body is naturally thrown forward, and in
descending it is thrown back, and it is only when stand¬
ing or walking on the level that it maintains an upright
position. Hence the rail may be with propriety made
higher where it is level at the landings, the position of
the body being then erect, than at the sloping part, where
the body is naturally more or less bent.

The height of the rail on the nosings of the straight
part of the stairs should be 2 feet 71 inches, measuring
from the tread to its upper side; to this there should be
added at the landings the height of half a riser.

In winding stairs, regard should be had, in adjusting
the height of the rail, to the position of a person using it,
who may be thrown further from it at some points than

2 C

202

PRACTICAL CARPENTRY AND JOINERY.

at others, not only by the narrowing of the treads, but
by the oblique position of the risers. Take, for example,
the elliptical stairs {Fig. 1 , No. 1 , Plate XCII.), and sup¬
pose the rails of uniform height. A person in ascending,
with the foot on the nosing of steps 6 or 7, will find the
rail lower to the hand than when standing on the nosings
of 19 or 20. The risers of steps 3, 13, and 23 are square
with the rail, while those of the other steps are more or
less oblique. In such a case it is advisable to make the
rail of the average height over 3, 13, and 23, to raise it
several inches higher at 7, and to depress it to an equal
extent over 19 and 20; to raise it, also, at the top of the
stairs, the more especially as the easing of the rail will
tend to lower it there. It is seldom that the rail will
require to be lowered below the assumed standard more
than 3 inches, or raised above it more than 4 inches, and
unless these variations in the height are adjusted in
accordance with the foregoing considerations, the effect
will be very disagreeable.

It is necessary to guard the reader against the common
error of l’aising the rail over winders, especially such as
are of steep pitch. The height should be uniform, except
in the instances adduced above.

The falliug mould {Fig. 1, Plate XCIV.) is given in
strict agreement with Mr. Nicholson’s method, but it is
quite at variance with the rule just named.

Tiie Section of a Cylinder.

Plate XCVI. — If any cylindric body, as A B o {Fig. 1),
standing on a horizontal plane, be cut by an oblique
plane, VO p, it is obvious that a third or vertical plane,
v p B ]), may be so applied to the cylinder, that it shall
not only be at right angles to the ground plane, but
also to the plane of section. It can also be easily shown
that on such a vertical plane the oblique plane would
be projected, according to the rules of projection, as a
right line; for, if the position of the oblique or cutting
plane can in any way be defined, then the trace of the
oblique plane, on its line of intersection op on the ground
plane, can be known, and any vertical plane standing at
right angles to the trace of the oblique plane O p, will be
one on which the trace of the oblique plane will be pro¬
jected as a rigid line; that is, the representation of the
plane O p on v p will be simply a geometrical line; conse¬
quently the vertical plane, by construction, is at right
angles to the ground plane, and also to the oblique plane.
It is evident, then, that if any figure whatever be de¬
scribed on the ground plane, and it be required to describe
such a figure that its various parts in every point shall
be immediately over the figure on h p, nothing more is
necessary than to draw lines through the various parts
of the figure on h p, perpendicular from P B. Continue
those lines perpendicularly upon the vertical plane V p,
and return them on the oblique plane; and then measure
on those lines from the line V p, the same each to each on
the plane v o p, as the corresponding lines on the ground
plane ; thus, the line V 6 will be made equal to P D, the
line 5 equal to 0, and so of any other line. Those lines
are called ordinate lines, and the method here described
is called tracing by ordinates. It is thus particularly de¬
scribed, because unless the process be perfectly understood
by the learner, he cannot know anything of the way of

producing the section of a cylinder or the face-moulds
for handrails geometrically.

The manner of obtaining such face-moulds will now be
described.

To produce the section of a cylinder through any three
'points on its convex surface.

Figs. 2, 3.—First draw the plan of the cylinder, or
part of the cylinder, as A B C. Let A be the lowest point
in the section, B the seat of the intermediate height, and
c the seat of the greatest height. The height on A is
nothing, and is therefore a mere point on the plan; the
height on the point B is equal to b h, and the height on
C is equal to C p. These heights are sometimes called
the resting points. Draw a right line from A, the seat
of the lowest point of the section, to c, the point on the
plan agreeing to the highest point of the section; draw
C p and make it equal to the greatest height of the sec¬
tion ; complete the triangle A c p by drawing the line
A h p. Take the intermediate height and apply it to the
triangle wherever it can be applied, as a perpendicular
under the line A p; in other words make h b parallel with
C p, and equal in length to the third or middle height;
then draw the line from b to B, the seat of the middle
height, and it will be the leading ordinate; then at right
angles with B b, and touching the convex line of the plan
of the cylinder, draw the line a B D —this line is the trace
of the vertical plane. Draw the line C p at right angles
to a B, and passing through the point c on the plan, make
D P equal to C p; complete the triangle DPaby drawing
the line P a; continue the line b B until it intersect the
line a P at 2. This triangle completes the representation of
the vertical plane. Nothing more now remains to be done
but to draw the ordinates c d and e parallel to DP; to
square out from the line a P the corresponding ordinates

1 2 3 4 5 6, and to make them respectively equal to
the corresponding ordinates on the plan; thus 6 P is
equal to D C, 5 is equal to e, 4 equal to d, 3 equal to c,

2 is equal to B, and 1 a. is equal to a A, and the mould for
the oblique plane will be completed by tracing a line
through the points 1 2 3 4 5 6. The angle aPDis what
is usually called the pitch of the plank, the use of which
will be explained hereafter. In order further to demon¬
strate this subject, consider the figure of the ground plan
to be drawn on a level plane, and a P D to stand vertically
on its trace a D; then suppose the oblique plane to be
turned on its trace a P, so as to form a right angle with
the vertical plane, and it will follow of necessity that the
point 1 will coincide with the point A; and the point P
being thereby elevated to the full height of the section P 6
will be brought into a position parallel with D C; 6 P
being equal to D c, the point 6 will of necessity be in the
exact situation of the highest point of the section; so also
the ordinate 2, being equal to the ordinate B and parallel
to B, must bring that point equal to the intermediate
height; so also of all the other ordinates: therefore the
mould 1 2 3 4 5 6 is the section of the cylinder to the
three heights and points required.*

* The author, when a lad, in 1824, heard a fellow-workman read a
passage from Mr. Nicholson’s work, The Builder, and was struck
with the words: “ Section of a cylinder through any three given
points.” He was at that time familiar with the method of produc¬
ing groins, angle ribs, brackets, &c., by ordinates, and at once pro¬
ceeded to solve the problem indicated in Mr. Nicholson’s words.

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HANDRAILING.

203

Figs. 4 and 5 differ nothing in principle from that we
have already described. The centre line of the plan of the
rail is here substituted for the line ABcin Figs. 2 and 3.
Draw the line A C, connecting the seats of the highest
and lowest points; make C p equal to the greatest height,
and at right angles with A c; make b h equal to the in¬
termediate height, and draw the line b B, the leading
ordinate, as in the preceding figures; square from it for
the base of the section, and make all the ordinates on
the plan parallel with the leading ordinate b B. Make D P
equal to C p, the height of the section; draw P a, con¬
tinuing the ordinates to a P ; square them out from a P,
and make each ordinate on the section equal to its rela¬
tive ordinate on the plan; draw the figure through the
various points 1 2 3, &c., and the moulds will be com¬
pleted. In drawing the first triangle AC p, the line c p
may be made equal to the whole height, or to any fraction
of the height, provided the intermediate height be drawn
in the same manner; for it is evident that if the perpen¬
dicular c p be lengthened or shortened, the perpendicular
b h will be lengthened or shortened in the same propor¬
tion ; and it will sometimes be found more convenient to
use a part than the whole of the height, as will be seen
in constructing the moulds, Plate XCYII. Other means
might also be adopted of finding the trace of the oblique
plane on the ground plane, one of which we have shown
in Plate XCIV., Fig. 2.

Before proceeding further, it may be well, in a few
words, to describe the leading points of difference between
Mr. Nicholson’s method and that here taught.

In Mr. Nicholson’s method two bevels are required in
cutting the plank, and the ordinates are bevelled both on
the plan and on the oblique plane.

The seat points of the heights used are: — one at
each corner of the mould and one on the convex part of
the rail.

The heights are measured to the top side of the falling
mould for the lower wreath, and to the under side down¬
wards for the upper wreath.

The vertical plane, from which the ordinates are traced,
is generally, if not always, made to pass through the
inner angles of the joint lines of the plan.

The oblique plane, on which the face mould is pro¬
duced, is sometimes at a right angle, sometimes at an
acute angle, and sometimes at an obtuse angle to the
vertical plane. This is what he calls the spring bevel,
and it is necessary to bevel the plank in accordance with
this before the pitch bevel can be applied.

In the method here taught the pitch bevel only is used,
and the ordinates are squared on the plan and on the
oblique plane. The pitch bevel of this method is there¬
fore equivalent to the two bevels of the other.

The seat points of the heights are taken on the centre
line of the rail, and the heights are taken to the centre
line of the falling mould; the trace of the vertical plane

He succeeded in liis endeavours, and practised his own system for a
year without being aware what amount of affinity existed between it
and that of Mr. Nicholson.

The general method here explained was first taught by the author
in Cheltenham in the year 1826, and in other parts of England
previous to 1830, in which year he visited the United States of
America, and practised and taught this method in the city of Phila¬
delphia, where he resided for more than seven years.

is always square with the trace of the oblique plane, con¬
sequently the use of the spring bevel is not required, the
piece having only to be bevelled at once to the pitch
bevel.

big. 2, Plate XCIV., is intended to illustrate the dif¬
ference between the two methods, No. 1 showing the
method of the author, and No. 2 that of Mr. Nicholson;
and in order that the illustration may be complete, the
heights or resting points in both figures are taken in
accordance with the latter method.

Plate XCIV., Fig. 2, No. 1.— A base line is drawn
from 1 to 3, connecting two of the resting points, and
parallel therewith a line is drawn through 6, which
is the intermediate resting point, indefinitely towards
the point 8; the line 1 2 is drawn perpendicular to 1 3,
and equal in height to the height of the section or a
fraction of the same—in this case one-fourth—it beino-

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taken, according to Mr. Nicholson’s method, to the top
of the rail. The perpendicular 3 4 is made equal to
the intermediate height, or the same fraction of that
height (one-fourth); the line 2 4 is drawn through the
point 4 indefinitely, the line 1 3 is continued to inter¬
sect 2 4 in 5, and the line 7 8 is drawn parallel with
2 5, intersecting 6 8 at the point 8, giving the line 8 5 as
the line of the trace of the plank on the ground plane.
This gives a trace or leading ordinate precisely parallel
with that we have adopted; but we think it is far from
being so direct in its application to the subject as that we
have generally used. Mr. Nicholson’s most usual method
of finding the trace of the oblique plane is shown in Fig.
2, No. 2, where the seats and heights are the same as in
No. 1 ; P 2 being the greatest height, T 6 the inter¬
mediate height, and 9 v the least height. The line P o
is drawn connecting the corners of the plan mould ;
P 2 is drawn perpendicular to p S; 6 T is parallel to P 2,
and equal to the intermediate height; v s is parallel to
P 2, and equal to the lowest height; 2 v is drawn indefi¬
nitely till it meets a line drawn through the points P and
9 in Q, 6 L is drawn parallel to P Q, and T L parallel to
2 Q; this gives the trace of the plane L Q, which is con¬
tinued to O, where it meets the line P s; then draw the ordi¬
nate 9 on the plan, meeting p o where the ordinate g on
the vertical plane is made equal to 9 v; g 2 is then drawn,
meeting p s in O. This is Mr. Nicholson’s most usual
and roundabout method of finding the trace of the oblique
plane; but besides this it is also necessary to find the
leading ordinate on the oblique plane. To do this, draw
S M perpendicular to 2 o, and from the point O describe
the arc L M, and draw O M, the leading ordinate. This
method requires a spring bevel, which is shown at o, and
is found by setting one foot of the compass in s, and ex¬
tending the other to the line o 2, making the portion of
the arc there seen meeting the line P o; from the point
of intersection in P o, draw a line to L, and the spring
bevel will thereby be produced. The leading ordinates
being found, all other ordinates are drawn as parallels, and
the mould is traced according to the figures.

We have thus contrasted the method of Mr. Nicholson
by bevelled ordinates with our own method by squared
ordinates, to satisfy the reader that, if the same heights
and seats of heights are used, the same mould is pro¬
duced by squared as by bevelled ordinates. The plan
mould on the left is exactly the same as that on the right;

204

PRACTICAL CARPENTRY AND JOINERY.

the heights are the same, both being taken from the fall¬
ing mould Fig. 1, each height being taken from the line
A to the top of the falling mould in each case. It will
at once be seen that the mould is identical, the tracing in
one case being from the line on the concave side, and in
the other from that on the convex side of the mould.

Plate NCVII., Fig. 1, shows the face mould, and Fig. 2
the falling mould of a rail suited to the stairs, Fig. 1,
Plate XCI. For the falling mould describe the quadrant
B 3 (Fig. 2) to the radius of the concave side of the rail
on the plan, and make D B equal to its development; then
set out the lines of steps and risers in the order they
occur in the stairs, placing all the risers at their pro¬
per situation as to the springing and centre lines; make
1 equal to the last flier, 2 equal to the first winder,

3, 4, 5, and 6 equal to the succeeding winders, taken on
the concave curve of the rail; draw the bottom lines of
the falling mould, making them touch the angles of the
steps excepting where the curved part necessarily leaves
them; draw a line for the centre line of the falling mould
at a distance from the bottom equal to the half of the
depth of the rail, also a line at the distance answering to
the top of the rail, and draw lines at right angles through
the thickness of the rail for the butt-joint, as at p and A;
draw a line through the centre of the lower butt-joint
parallel to D B, meeting pb in C; make the line b h per¬
pendicular to c b, at or near the centre of the length
of the falling mould. We shall then have P c for the
greatest height, and h b for the intermediate height of the
section; the lowest point of the section being the point A
in the plan, the seats of those points on the plan must ever
be in the centre line of the rail. The method of producing
the face mould differs nothing from the general method.
In Fig. 1 draw A C; make c p perpendicular thereto,
and equal to the greatest height, or to some fraction of
the same—in this case it is one-third; then draw the
hypothenuse p h A, and take the intermediate height, or
its corresponding fraction one-third, and apply it to form
the perpendicular b h. From b to the seat of the middle
height on the plan, draw the leading ordinate b B, and
square the base of the vertical plane as a tangent to the
plan mould; draw all the oi'dinates on the plan parallel
to the leading ordinate, and through as many points as
may be needed for the tracing; make P f equal to the
greatest height, and draw the hypothenuse P a, from which
square out all the ordinates, making them respectively
equal to the corresponding ones on the plan; carry one
ordinate through the centre of the plan, and take off the
distance of that point, applying it as at n. Draw the
dotted line n 4, and make the butt-joint at 6 by squaring
from n 4 through the centre of the bevel joint. Make the
butt-joint at the straight part by simply squaring it from
the side of the mould through the centre of the bevel joint;
then trace through the points 1 2 3 4, &c., and the mould
will be complete.

The Figs. 3 and 4 of this plate are drawn on precisely the
same principle, as before described. They are here intro¬
duced as a specimen of a wreath of a small well-hole, with
a very sharp ascent, the radius of the inner curve being only
3 inches with three winders in the quarter-space. The
risers are here supposed to be drawn to the centre, the
riser between the last flier and the first winder is conse¬
quently identical with the springing line; the same line is |

! also here made the line of the middle height. The falling
mould is constructed, as before described, with the under¬
sides touching the angles of the steps, excepting only where
made conformable to a fair curve; the height of the section
is found, as in the former case, by drawing a horizontal
line through the joint line at A, and taking the height
from this line to P for the greatest height, both it and the
intermediate height being taken to the centre line of the
falling mould. A line is drawn in Fig. 3, through two of
the seat points, namely, A and C ; one third of the greatest
height is used as a perpendicular, and the same fraction is
used for the middle height, b h\ the leading ordinate is
drawn through the seat of the middle height, that is,
through the centre of the springing line; the base of the
vertical plane is squared from the leading ordinate, and
the entire height of the section set up, as P 1, the perpen¬
dicular ; and having drawn P a, and continued and squared
out the ordinates, the mould is pricked off by making each
ordinate 1 2 3 4, &c., equal to its respective ordinate on
the plan. The butt-joint is drawn by squaring it from the
line, ng, through the centre of the bevel joint. In this case
the sharp pitch of the mould produces it a great width at
each end; if this were to be cut out of the plank to its
proper bevel, c p a, it would take at least twice the amount
of material that would be absolutely needed by the means
we shall now point out. Let the centre line be pricked
out on the mould, parallel with which draw the dotted
line, shown on the same. Now if the mould be laid on
the plank in this form it will appear as at Fig. 5 ; this
may be cut quite square out of the plank, and will be
quite sufficient to produce the rail in the most peidect
shape ; C D shows the edge of the plank, the oblique line
c D being the proper bevel just mentioned, which is to be
drawn on the edge of the plank; A B is drawn on the
mould when in its position in Fig. 3, as a parallel to
P a, and is called the backing line; this line should be
drawn on the plank on both sides, and perfectly opposite
on each. When the piece has been cut out square, as
shown at Fig. 5, the point e of the mould should be slid
to the point c, where the mould is a second time to be
marked on the material, keeping the line A B on the mould
to agree with the line A B on the plank; then let the
mould be applied to the other side of the plank, by
bringing the point e on the mould to coincide with
the point D on the plank, and the line A B on the
mould to coincide with the line A B on the piece; mark
the piece again in this position of the mould; this is what
is called backing the mould, and the piece is now pro-
perly lined for wreathing. This is done by placing the
piece in the vice with the concave edge upwards, and tak¬
ing off the superfluous wood down to the lines just de¬
scribed on the surface of the plank. It will, however, be
found requisite sometimes to place the mould on the piece,
and fix both in the vice together, in order to supply that
portion of the line which will be deficient by reason of
cutting square through the plank, instead of the old
method of bevelling. When the concave cylindric surface
is thus produced, the falling mould may be applied. This
is done by making the bevel joint line of the falling mould
to correspond with the bevel joint line of the piece, while
the butt-joint lines of the falling moulds also coincide with
the butt-joints of the piece; the butt-joints of the falling
mould thus applied will now show the position of the joint

SECTIONS OF SOLIDS.

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HANDRAILING.

205

one way, whilst those of the face mould will show it the
other, thus rendering the joint complete; mark on the
piece on each side of the falling mould for the under side
and top side of the rail; square from the concave surface,
both for the top and bottom of the rail, and take off the
superfluous wood, using a pair of callipers to gauge off the
back side of the piece. What lias here been stated will
hold good as a general rule; but if the face mould be
not much wider than the rail itself, it would be absurd
to be at any undue trouble to save material. It will,
however, generally be best to cut the piece out square
from the plank, and bevel it after in the manner de¬
scribed.

Plate XGYIII.— Fig. 1 is the falling mould, and Fig. 2
the face mould of a wreath suitable to the stairs shown at
Plate XCI., Fig. 2.* Fig. 1 shows the stretch-out of A B,
the internal curve of the plan. D L is the width of the
last flier, 2 3 and 4 are widths of winders, 5 is the half
width of the landing; the line L D, Fig. 1, is equal to kg,
Fig. 2, or the length of the straight part on the plan; the
lines c d e f and P, Fig. 1, are all at equal distance from
each other, and represented at Fig. 2, by the portions of
radii, g k l, &c., drawn across the rail. The position of the
oblique plane is found here (Fig. 2) by our usual method
as shown in the former examples, C p being a third of the
greater height, and b h a third of the intermediate height;
and as B is the seat of that height, b B becomes the leading -
ordinate, and a B the base of the vertical plane; P a, is
the pitch of the plank; the lines t r and u s, show the
upper and lower surface of the plank; E F is drawn
parallel with a P at any convenient distance; p and g
are drawn through each end of the joint line, and con¬
tinued to the height from the line B a, equal to the dis¬
tance from E to the section of the falling mould at P,
Fig. 1. This section, or rather the section of the square
rail, is thus shown by the small parallelogram at P; in
like manner the section of the rail is shown at/from the
section of falling mould a f, Fig. 1 ; the parallelograms
e d c and a are produced in the same manner from e d c,
and L, in Fig. 1. It will now be needful to draw lines
through the angles of each parallelogram, and square with
the line^F; the mould is then produced by making the
ordinate 19 equal to q on the plan, and measured from
the line ef 18, the same one answering for the top, and
the other for the bottom, of the representation of the
piece; 20 and 21 are both equal to p, on the plan; 14
and 15 are equal to o on the plan, 16 and 17 to n, 10 and
11 equal to to, 12 and 13 are equal to l, and the other
points are traced in a similar way, and parallelograms
are then drawn through the points, as seen in the plate;
each of these parallelograms will represent a section ol
the solid square rail as it would appear on the plane of the
plank drawn by orthographic projection; if lines be drawn
through these angles, they will represent the square rail;
such a mould may be laid on the plank, and the piece cut
square out; the piece is then set out on the edge, as
shown in the elevation, by the vertical sections of the
square rail; the distances of the angles may be measured
and set off, and each angle found with great precision,

* This plate exhibits the method of cutting the wreath out square,
as first taught by Mr. Nicholson, but is not contained in his Car- \
penter’s Guide.

first finding the outside angle of the piece, and then gaug¬
ing the other angles therefrom.

Fig. 3 of this plate shows the manner of setting out a
wreath for such a situation as that exhibited by the
landing stairs, Fig. 1, on Plate XC. A c is the length of the
straight parts at the upper end of the piece, c D the length
of the circular, and D B the length of the straight part
at the lower end of the piece; make L the landing, equal
to the development of C D, and the half steps r and g h,
equal respectively to A C and D B, bisect C D and draw
E F; make the perpendicular at g equal to half a riser,
also the same at c; make the perpendicular at / equal
to half a riser from L the landing line, to the centre of
the rail from this point; set off the half width of the
falling mould above h, and draw the bottom line of the
falling mould by making the hypothenuse lines at r and h;
connect these by a fair curve passing through the proper
height at F; draw also the centre line and top of the
falling mould. It will be seen that if our usual method
of finding the position of the oblique plane were here
applied, it would necessarily produce the line g as the
leading ordinate, for the height F is half the height k a,
and the base k i is bisected b} r the line F; consequently
the hypothenuse should in like manner be bisected by
placing the intermediate height; this fact is mentioned
to show that there are many cases occurring where a
moment’s reflection will serve to convince the practical
man what the position of the plank should be, without
drawing one line. Therefore for the face mould (see
Fig. 4) bisect the quadrant in g, and draw the ordinate
g, from which square the ordinates from D A, and also
from the hypothenuse, and make the ordinates 1 2 3 4,
&c., equal to the corresponding ordinates kb c d, &c.; and
draw the face mould through the respective points to pro¬
duce the butt-joint square from the side of the rail through
the centre of the bevel joint.

The application of the falling mould is shown at Fig. 5,
the line F of the falling mould (Fig. 3) is placed in the posi¬
tion g, answering to g on the plan, and in the centre of the
thickness of the plank; s and S show the springing lines, A
and B the bevel joints; a butt-joint is shown at the lower
end of the piece: its application will be easily compre¬
hended, and will generally serve for the performance of
this work. No example of a perfectly straight falling
mould has been given, as it would be superfluous; it will
be easily seen, from what has been said, that the leading
ordinate in such cases must always fall in the same man¬
ner as in the last instance.

Plate XCIX.—This plate exhibits the manner of pro¬
ducing the falling moulds, and face moulds for sci'olls.
Fig. 1, No. 1 is the face mould, and No. 2 the falling
mould, for a small scroll. In tracing moulds of this de¬
scription, there is no need of any process to find the
position of the plank; no better position can be found
than that in which a plank would be if laid flat on the
nosings of the stairs, and the pitch board gives this angle
of inclination. Take the pitch board, and lay the step
side of it against the side of the straight part of the level
mould A B, and by means of the upper edge of the pitch
board, mark oft’ the line c d; draw any number of ordi¬
nates on the plan mould square with the straight rail,
continue them to c d, square them out, and prick off the
mould by making the ordinates f g h i k l, respectively,

206

PRACTICAL CARPENTRY AND JOINERY.

equal to the ordinates 1 2 3 4 5, on the plan mould, and |
draw the face mould through the points. This mould
may be drawn without using more ordinates than are
needed to find the joint, and to show the width of the
straight rail. The mould itself is merely a quarter of an
ellipsis, both for the inner and outer curve, and its trans¬
verse diameter is equal to the diameter of that circle from
which it is generated on the plan; therefore if the ordi¬
nate / be continued till equal to the length of radius, it
will represent so much of the transverse diameter, and a
line drawn through its extremity parallel to c d, will re¬
present the conjugate diameter of the ellipsis, and the
mould may be produced by the trammel, or by any of
the means explained at pages 23 and 24. The shaded
part a b shows the piece wrought and in position. The
falling mould, No. 2, is produced by making the line e,
12 3, &c., equal to the line e, 1 2 3, &c., in No. 1, on the
convex side of the rail. From the top of the ordinate
line 1, draw the line b to the pitch of the rail, and con¬
nect this line to the line 9 e, by a fair curve; this forms
the bottom line of the falling mould; the top line is
drawn parallel to it at a distance equal to the depth of
the rail. The ordinates 12 3, &c., will now show tfie
height of the rail, in as many points, from the bottom
of the scroll. The falling mould, No. 3, is produced by
making the line, 12 3, &c., equal to the internal curve
of the scroll, and the ordinates 12 3, &c., on No, 3, equal
to the ordinates 12 3, &c., on No. 2; the piece is jointed
at A on the plan (No. 1) to the level portion of the scroll, the
line 5 on the falling mould (No. 3) showing the same as a
perpendicular joint, which in this part differs but little
from a butt-joint, which might of course be used if pre¬
ferred. Fig. 2 of this plate exhibits the side view of two
pieces of handrail of similar character to the scroll pieces
just described, but are here shown as applied to a landing,
m being the landing, o the riser, and n the step below;
whilst l shows the riser, and k, the step above. Such a
landing may be seen in plan at c, Fig. 1, Plate XCI., being
the top of the first flight of stairs. The risers in this
case do not pass through the centre of the well-hole;
they are so arranged that the centre B of the rail on the
return shall be precisely half a step from the line of risers,
l o. By this arrangement the piece of rail in this part is of
the simple kind just mentioned, less indent of the well-
hole into the landing is made, and the rail itself has a
better appearance than when a greater amount of it is
thrown on the level at the landing. The pitch board is
applied with its step side against the side of the plan mould,
as at A, and the pitch line produces the line A a. Draw
all the ordinates a b c, &c., parallel to the riser line of the
pitch board, and return them on the plane of the mould
or plank at right angles to A a ; make the ordinates ab c,
&lc., equal to the ordinates 12 3, &c., on the plan, and
draw the mould. This mould, as also the preceding one
for the scroll, must be bevelled by the pitch board. Lay,
therefore, the hypothenuse of the pitch board to coincide
with the surface of the plank, and the riser line of the
board will give the bevel on the edge of the plank for
backing the mould; this will be better comprehended by
the position the piece will have when placed in the work,
as shown by c D and E f.

In Fig. 3, is shown another and somewhat more
expeditious method of working. Let B c be the plan

mould, with its centre line as shown, and h e d the pitch;
square out the line df and make it equal to e c; then square
out from the ordinate h, making it also equal to e c. The
semiconjugate and semi transverse diameters of the ellip¬
tical mould will thereby be obtained, and it may be drawn
by the trammel, or by any of the methods already men¬
tioned. It is possible, by thus working to the centre line
only, to make the rail without cutting it out one-eighth of
an inch wider in any place than its exact width.

Fig. 4 shows the same piece cut out from the square
plank; the end is then, by the xise of the pitch board,
to have the line a drawn through the centre of its thick¬
ness; which enables us to draw the centre line of the
mould / (No. 1) on the piece, as shown by the curve line at
a. By using a pair of callipers the vertical sides of the
rail may be readily produced, and the bottom and top
squared from them.

Fig. 5 shows, at No. 1, the scroll adapted for such a
stair as the elliptical stair, Plate XCII., or wherever a
scroll comes immediately in connection with winders.
First decide at what point on the plan mould the scroll
shall come to its level position; and as the plank is
usually about |-inch more in thickness than the rail is
in depth, it will be possible to obtain that extent of rising
in the first part or level portion of the scroll; this is sup¬
posed to be at the point g, on the plan mould, which is
therefore made the place of the first joint. The point c
is that point of the rail where the third riser occurs, and
may with propriety be made the place of the second joint.
Take the stretch-out of the exterior curve, d to g, and
make the line c g, in No. 2, equal thereto, and set out
the bottom line A B of the falling mould two inches below
c g. On A B, set off the height of the rail at c, equal to
two risers; draw the line l to the inclination of the rail,
and the intermediate portion of the falling mould, as a
fair curve, connecting the straight lines; make the centre
and top lines of the falling mould parallel to the bottom
line, to suit the depth of the rail. This completes the falling
mould. For the face mould, in No. 1, draw through the
centre of the joint lines the lines eg-, make cd perpendi¬
cular thereto, and draw d g. Take the distance, c e, from
No. 2, and set it out from a to b, No. 1, and make the point
b in the centre of the width of the rail; this will be the
seat of the intermediate height, and c and g the seats of
the highest and lowest heights. Take the length of ef,
No. 2, and apply it at e / No. 1, parallel to d c\ draw
the line e b for the leading ordinate and square from
it, as a tangent to the curve of the scroll; draw b t, the
base line for the wreath, and draw t s and g n perpendi¬
cular to b t, then draw the hypothenuse, and continue the
ordinates a i k l m, &c., to meet it. From the points of
intersection draw the ordinates 1 2 3 4 5 6 7, &c., making
them respectively equal to the ordinates a a t i k b l to,
&c.; and through the points thus obtained, prick off the
mould.

We have thus endeavoured to give not only one general
method of producing a face mould, and by one demonstra¬
tion sought to make it apply to any number of cases what¬
ever, but have also given a variety of instances of applying
the same in actual practice.

We shall now proceed to describe certain details, which
could not, without embarrassing the subject, be noticed
before.

II'

PLATE C.

SCROLLS.

Fiq. 3.

Inches

£4-1-4- Mi lt '? I- -I-

BLACKIR Sc SOU ; GLASOOW, KDJTNliURGH A- LONDON

J. White, del

Fig.

Fig . 1

BL ALKIE Sc HON . Gl„ A riGOW. EDINBURGH & LONDON .

Fi g. 6.

HANDRAILING.

207

Sections of Handrails.— In Plate XCIY. some of
the usual forms of the sections of handrails are given.
To describe Fig. 3, divide the width 6 6 in twelve parts,
bisect it by the line A B, at right angles to 6 6; make C B
equal to seven, A C equal to three such parts, and B i also
equal to three parts; set off one part from 6 to 7, draw the
lines 7 i on each side of the figure; set the compasses
in 4 4, extend them to 6 6, and describe the arcs at 6 6
to form the sides of the figure; also set the compasses
in B, extending them to A, and describe the arc at A to
form the top; make l B equal to two parts, and draw the
line k Ik) take four parts in the compasses, and from the
points 4 4 describe the arcs e f, then with two parts in
the compasses, one foot being placed in k, draw the inter¬
secting arcs g It ; from these intersections as centres, de¬
scribe the remaining portions of the curves, and by join¬
ing k i, k i, complete the figure.

Fig. 5 is another similar section of handrail. The width
6 6 is divided into twelve equal parts as before; the point
4 is the centre for the side of the figure, which is described
with a radius of two parts; A to is made equal to three
parts, and B to to eight parts, and to n equal to seven
parts; then will A B be the radius, and B the centre for
the top of the rail. Take seven parts in the compasses,
and from the centre 6 in the vertical line A B, describe
the arcs g h, g h) take six parts in the compasses, and
from the centre 4, describe the arcs ef,ef\ draw the line
d d through the point n ; from the intersections at e f g h,
as a centre, with the radius of four parts, and from 4, as
a centre, with the radius of two parts, describe the curve
of contrary flexure forming the side of the rail; then from
d, with the radius of one part, describe the arc at d, form¬
ing the astragal for the bottom of the rail.

In Fig. 4 divide the width C D into twelve equal parts;
make 6 to equal to 6 parts; 6 B and to h respectively,
equal to two parts, and to 1 equal to three parts; make
e h and h f respectively, equal to two parts; then in f
and e set one foot of the compasses, and with a radius
equal to one and a half parts, describe the arcs g g ; from
the point to, with the radius to A, describe the arc at A
meeting the arcs g g, to form the top reed of the figure;
from 2 with a radius equal to two parts, describe the side
reeds C and D; draw 1 d parallel to A B; and with a
radius of one part from the points d d describe the reed
d for the bottom of the rail, which completes the figure.

Fig. 6.—To describe this figure, let the width 6 6 be
divided into 12 parts; make to 4 equal to four parts, to 6
equal to 6 parts, and 6 8 equal to 2 parts; make 6 d equal
to 5 parts, and draw the dotted lines d 4; also the lines
4 g, On these lines make l 4 equal to two parts, l o equal
to half a part, and o g equal to four parts; also make to k
equal to one part, and draw the lines g k; from k, as a
centre, describe the arc at A for the top of the rail; from
g describe the arcs h o. At 4 and 4, with the radius of
two parts, describe the arcs at 6 for the sides of the rail;
then from d set off the distance of two parts on the line
d 4, and from this point as a centre, with a radius of two
parts, describe the curves of contrary flexure terminating
in d d, which will complete the curved parts of the figure.
Continue the line 6 6 the distance of four parts on each
side to the points 4': from these points, and through the
points d d, draw the lines d d for the chamfer at the
bottom of the rail, thus completing the entire figure.

To FORM THE SECTION OF THE MlTRE CAP. — Fig. 3,
Plate LXXXIX, exhibits the method of producing the
section of the mitre cap from the section of the handrail.

Let A B c D, &c., be the section of the handrail. Draw
the line G G in the centre of the section, and draw across
it, at right angles, the line A B; describe a circle 0, 1 1, j, h,
having its centre on the line G G, and its diameter equal
to the size of the cap. From the outsides of the rail A B,
draw lines A h, B j, parallel to the line G G, and meeting
the circle of the cap at hj. From the points of intersec¬
tion h j, draw lines meeting on the line G G at a point i,
as far into the mitre cap as it is proposed to carry the
mitre. Then draw lines parallel to G G, through as many
points in the rail as may be required, as B c D E F, con¬
tinuing them till they meet the mitre lines h i, j i; set
one foot of the compasses in the centre of the circle
o 11 j h, and extending the other to each of the points in
succession, describe circular arcs meeting the diameter
0, 11. From the points of meeting draw the ordinates,
1 2 3 4 5, &c., making them respectively equal to the cor¬
responding ordinates, B c D E F, &c., and draw the figure
through those points.

TO DRAW THE SWAN-NECK AT THE TOP OF A RAIL,
as in Plate LXXXVIII. Fig. 1, No. 1. — Continue the
bottom line of the rail upwards till it intersects the line
of the back of the last baluster; draw a horizontal line
through the top of the newel, measure from this line down
the back of the baluster to the intersection, and set off the
same distance downwards on the under side of the rail,
from which square out a line to intersect the horizontal
line above; this will give the centre point of the curve.
A slight variation from this will be seen in Fig. 2, Plate
LXXXIX., the rail being there brought nearer to the

newel. This variation will be
easily understood, and needs
no description.

To FORM THE IvNEE AT THE

Bottom Newel. —Draw out
the width of one step, as at
A B (Fig. 521), and the risers
connected with it above and
below B c, o A, and join A C;
continue the line of the first
riser o A upwards to the
height of half a riser at D;
and through D draw a hori¬
zontal line meeting the hypo-
thenuse A G in G. From D
set oft’ towards G, half the
width of the mitre cap D E, make G F equal to G E; draw
F M square from the under side of the rail, and make E M
perpendicular to D G, and the point M will be the centre
of the curve.

Scrolls. — Plate C.—In Fig. 1 is shown a very simple
manner of describing a scroll. Take the width of the rail
in the dividers, and repeat it three times on the line 12 3
which gives the first or greatest radius for the quadrant A.
Refer now to Fig. 1, No. 2, where the scheme of centres is
drawn out at full size. Draw 1 2 at right angles to the
first line, and make it equal to two-thirds the width of the
rail. Draw 2 3 at right angles to 1 2; make it equal
to three-fourths of 1 2, and join 3 1; through 2, and at
right angles to 3 1 draw the line 2 4; then draw the line

208

PRACTICAL CARPENTRY AND JOINERY.

3 4 at right angles to 3 2, the line 4 5 at right angles to
3 4, or parallel to 3 2, and so on with the other lines,
always squaring from the one last drawn, and thus the
centres are obtained, from which the quadrants B, C, D, E, F
in Fig. 1 are drawn.

Fig. 2, No. 1, is shown as a rail of 2§ inches in width;
the square is here made half of that width, or lj| inch, the
first radius is made times the square, and as the side
of the square is once lost by the half revolution, the
width of the scroll will be equal to 14 times the side of the
square, or 19^ inches; the construction of the square will
easily be understood by a reference to Fig. 2, No. 2, where
it is shown full size, the numbers showing the points for
the centres in succession, beginning with the least radius,
and ending with the greatest.

Fig. 3 is perhaps more simple than the preceding, and
is adapted for a large rail, where only a small scroll can be
used. The first radius is made equal to 8 inches. This
distance is divided into five equal parts, and the square is
made equal to one of the parts. The angles of the square
are the first four centres, the middle of the side is the fifth,
and the centre of the square the sixth centre.

Fig. 4 shows a ready method of producing a converging
series in geometrical progression, as such a series is often
found useful in setting off the radii of scrolls. The lengths
of any two lines being known—to form a series from the
same: take the longest line, as A B, and make it the per¬
pendicular of a right-angled triangle, the base of which
B c may be made of any convenient length; let d be the
length of the second line in the series; from A B draw the
perpendicular b d meeting AC in d and join b C; draw
the line d e at right angles to B c, continuing it to meet
B c, draw e f perpendicular to a b, then draw / g per¬
pendicular to B c, and g h perpendicular to A B ; this pro¬
cess may be continued to any extent, and the lines A B, d,
f, h, &c., and also b, e, g, &c., and b d, ef, g h, &c., will be
a series in geometrical progression.

Fig. 6 is a method of producing a scroll by sixths of a
circle. Describe a circle as A B, and divide its circumfer¬
ence into six equal parts, and draw the diameters shown
by the darker lines on the drawing. Divide one of the
divisions of the circle into six equal parts, and set off one
of the divisions, equal to 10 degrees, from each diameter;
then draw the second series of diameters shown by fainter
lines; or the ten degrees may be set off at once by a pro¬
tractor. At the distance of two inches from the centre
draw the first radius a parallel to the faint diameter and
intei’secting A B; from the point of intersection draw
the next radius parallel to the next faint diameter, inter¬
secting the next succeeding darker lined diameter, and
continue drawing the radii parallel with the faint-lined
diameter, and their points of intersection with the first
series of diameters from the centres of the curve of the
scroll. The lines so drawn form a converging series, and
their lengths are to each other in geometrical progression.
In the figure the series is continued from a inwards,
through one revolution and a half.

Figs, o, 7, and 8 are methods of drawing scrolls by
eighths of a circle. As they differ only in the quickness

of their convergency a description of one will suffice
for alL

In Fig. 7 proceed first to make the double cross by
drawing right angles and bisecting the same, as shown
on the figure. The centre of the largest arc of this scroll
is situated at a distance of two inches from the centre
of the scroll to the right, on the liue b, and the next
centre on the increasing side, 2|- inches from the centre;
the most ready method of producing the converging radii
is by cutting a small piece of paper to the angle which
the radius of the curve makes with the diameter of the
scroll, and using this as a bevel to the next diameter, and
so on in succession, either converging or diverging; thus
the angle of radius and diameter, taken at c, may be ap¬
plied at b, at a, and so on in succession, producing each
centre by its intersection with the next diameter. The
lines of the radii c b a are continued out in the open space
of the scroll in this figure, beyond where their use occurs,
that the manner of obtaining one from the other may
be the better seen.

Fig. 9.—This shows a vertical scroll, sometimes used
for terminating a hand-rail when space cannot be afforded
for a horizontal scroll. The method of drawing it is so
obvious as to need no description.

Fig. 10 is a scroll step suitable for the scroll of the
rail shown at Fig 7- The centres of the various arcs are
found as in Fig. 7, the same centres being used for the
line of balusters and the line.of nosings; then, to describe
the block and step, take the length of radius of one of the
arcs in the rail mould from its centre to the centre of the
rail, and from its corresponding centre in the block, which
will extend to the centre of the baluster, as from c to e;
draw out the section of the baluster e to the intended size;
then extend the compasses from the centre of the curve
to the inside of the baluster, and describe from each centre
in succession, to produce the interior curve of the block.
The width of the block at its neck, that is, at g, should
always be commensurate with the size of the baluster, as
there shown; from this place the outer or convex line of
the block is determined, and is struck round from the
same centres as before, which are also used for the nosing
line, thereby showing the size of the stepboard. At a is
shown what is usually called the tail of the block. It is
secured by a screw to the thick part of the riser. At i
is shown the shoulder of the riser; from this point the
riser is reduced to a veneer, which is carried round the
convex portion of the block as far as the point h, where
it is secured by a pair of counter-wedges, there shown in
section. On the back part of the step is a line indicating
the position of the second riser of the stairs, and the sec¬
tion of the baluster on the second step is shown; from this
baluster to the next at e, should be equal to half the going
of one step; and, in spacing the balusters round the scroll,
it is desirable that their distances from each other should
gradually diminish as they approach nearer to the centre
of the scroll, and that the balusters of the inner revolu¬
tion should be as near as possible in the centres betwixt
those of the outer revolution; otherwise they will look
crowded and irregular.

PROJECTION OF SHADOWS.

209

PART EIGHTH.

PROJECTION OE SHADOWS, PERSPECTIVE, ISOMETRICAL PROJECTION.

PROJECTION OF SHADOWS.

As a luminous point can be seen on all sides at the same
instant, it follows that there must proceed from it an in¬
finite number of rays diverging in every direction, and
extending indefinitely in straight lines. The point may
thus be considered as the centre of a luminous sphere, and
that sphere itself may be conceived to be composed of an
assemblage of pyramids or cones, whose summits are in its
centre, and whose sides are indefinitely extended. Thus
an eye placed at any distance from a luminous point, C,
(Fig. 522), will receive a certain number of its rays, which
may be considered as forming a cone, whose base is the
pupil of the eye, and whose summit is the luminous point.
That one of the rays which passes through the centre of
the pupil of the eye, and through the point, will be the
axis of the cone. If the eye, in place of being round, were
square or triangular, there would be a pyramid in place
of a cone of rays.

If at the distance 1, from a luminous point c, (Fig. 522),
there is placed a square plane, A B, it will intercept a cer¬
tain number of the rays from C. These rays will form a

. Fig. 522.

pyramid, whose base will be A B, and whose
apex will be c. Conceive the sides of the
pyramid prolonged -indefinitely, and on its
axis, C O, set off the equal lengths c M, M N,
N O, or, which is the same thing, divide the
axis c o into equal parts in M N O; and at each
division draw a square plane perpendicular to the axis,
and cutting the sides of the pyramid in 2 D, 3 E ; the side
of the square, 2 D, will be double the side of the square A B,
and the square itself will consequently, in area, be quad¬
ruple the extent of A B. But the surface of the second
square receives only the same number of rays as the sur¬
face of the first, consequently it will be only one-fourth
part as light. In the same way a square at 3 will have
its side three times as great as the side of the first square,
and its surface thus being nine times greater will receive
only a ninth part of the light. The light then evidently
diminishes in respect of the distance of the illuminated
object from the luminous point, in the ratio of 1 , -J-, -Jg-,

for the distances, 1, 2, 3, 4; or, as it is ordinarily ex¬
pressed : — The intensity of the light is in the inverse
ratio of the square of the distance.

It also follows, by a parity of reasoning, that if it be re¬
garded as converging towards any point, its intensity will
increase in the same manner; and hence the general rule—

that the intensity of light increases or diminishes in the
ratio of the square of the distance.

Again, suppose a (Fig. 523) to be a luminous point,
and h, c, a , a pyramid of rays, and let b c be a plane cutting
it perpendicularly. This plane receives the sum of the
rays measured by the angle, b a c. Suppose the plane
now turned round / as an axis into the position (Z e, draw
the rays d a, e a, and the plane will receive now only the

sum of the rays, measured by the angle d a e. Conceive it
further turned until it is horizontal, as d" e",then the plane,
it is evident, receives no light, and is therefore in shade.
Hence the rule: when a surface receives the light perpendi¬
cular to its plane it will be lighted to its maximum inten¬
sity, and that intensity will diminish in the ratio of the
obliquity of the surface to the direction of the light.

When a luminous body has extent, it is to be
regarded as composed of an infinite number of light¬
giving points like a , sending out rays in all directions,
which cross without confounding each other. The
following simple experiment will prove this. Insert
two tubes ab, c d, in one side of a box e f g h (Fig.
524), and let them be in the same plane, and inclined
to each other. Let there be an apertux-e in one side of the
box so that the intei’ior can be seen when the eye is ap-
Tis . 504 f plied to it. Then furnish one

tube with a blue coloured
glass, and the other with a
red coloured glass. If the
tube with the blue glass be
stopped, and the light be ad¬
mitted by the other, there
will be an oval of red light
d thrown on the side of the box
opposite to the tube at k m,
and if the red glass tube be stopped, and the blue glass
tube be opened, thei'e will be an oval of blue light at n o.
If both tubes be opened together, there will be an oval
of red and an oval of blue, although the i-ays cross each
other in their passage. Hence, the rays of light cross each
other in every dii’ection, without obstructing or confound¬
ing each other.

These preliminary notions of the properties of light are
necessary to the proper understanding of what follows on
the subject of shadows.

Let a (Fig. 525) be a luminous point from which rays
divei’ge in eveiy direction, and let b be an opaque body,
a cube for example, and c another opaque body, say a

2 D

210

PRACTICAL CARPENTRY AND JOINERY.

sphere. The parts of these bodies which receive the rays
will be more or less illuminated, and the parts which do
not receive the rays will be more or less deprived of light,
and will be, as it is termed, in shade. Thus, the face b d,

Fig. 525.

of the cube will alone be illuminated, and its other five
sides will be in shade. In the same way the rays
a e, a f, a g, &c., tangents to the sphere, determine a seg¬
ment which will be illuminated, and the other segment
will be in shade. But the rays which touch the boun¬
daries of the face of the cube, if prolonged, form an indefi¬
nite pyramid, truncated by the plane b d, the part a b d
will be a luminous pyramid formed by the unintercepted
rays, and the indefinite portion beyond will be the shadow
thrown by the opaque body. Thus, the shadow thrown
by a body may be considered as a solid, the form of which
is dependent on the luminous body emitting the light, the
opaque bodjr intercepting the light, and on the positions of
these bodies relatively to each other. The shadow there¬
fore thrown by the cube in the figure will be a quad¬
rangular pyramid, and that by the sphere, a cone.

The shadow thrown by a body will appear to increase
in intensity in pi'oportion as the light which illuminates
the body increases in intensity, but this is simply the
effect of contrast.

If the rays of the pyramid and of the cone be cut by
planes m n, o p, perpendicular to their axes, the projections
will be a square and a circle. If the planes be oblique to
the axes as to r, o s, the projections will be a lozenge and
an ellipse.

The luminous body, in respect of that which is illumi-
uated by it may have three different dimensions. 1st.
It may be smaller, and in this case it may be compared to
the light of a candle, and the portion of the opaque body
illuminated will be smaller than the portion in shade.
2nd. It may be of the same size, in which case the illu¬
minated part of the body will be equal to the shaded part.
But here another kind of shadow makes its appearance.

Let a (Fig. 526) be the luminous, and c the opaque body,
both spheres of the same size. Now, from every point of
the surface of a luminous rays emanate, but those alone
situated on the hemisphere 12 3 are projected on c. These

will be all tangents to the opaque sphere at the points
be 4, and will determine the extent of the illuminated seg¬
ment, which will manifestly be the hemisphere b 5 4.
and the other hemisphere will be in shade; the primary
shadow thrown by the body will be a cylinder, and its
intersection by the plane r s, perpendicular to the axis, will
be a circle. But as the luminous rays emanating from/p,
and the other infinity of points on the surface of the body
a, are intercepted by the opaque body b at the tangent
points 6 7, &c., the shadow of each of these points will also
be thrown on the plane rs. Therefore, and confining the
illustration for simplicity to these points in the meanwhile,
it will appear that a second shadow will be thrown on
the plane, considerably augmenting the size of the first.
On attentive consideration, however, the two shadows
will be seen to be very different, for, from the point 2
emanate rays 2 o, 2 p, which are not intercepted by the
opaque body, and which, therefore, illuminate the plane
within the space occupied by the secondary shadow, and
which consequently diminish its intensity. This will be
seen to be the case with the rays emanating from all the
points of the surface of the luminous body contained be¬
tween /and g, and by drawing the figure to a large scale,
and projecting rays from a great number of points, it will
be satisfactorily seen that the second shadow, in propor¬
tion as it extends beyond the first, will continue to decrease
in intensity. The second shadow is called a penumbra.

3d. The luminous body may be greater than the body
receiving light from it. In this case, as is made evident
by the Fig. 527, the segment of the body illuminated,

b 5 4, will be greater than the segment in shade, and the
shadow b' 4>' thrown on the plane C D will be less than the
intercepting body. The penumbra f g is analogous to
the preceding one.

It may therefore be concluded that the shadow thrown
by any body diminishes always in intensity from the first
limits of the penumbra to the last; and, further, that the
parts of the same surface which are nearest the luminous
point will be more highly illuminated than those that are
more distant.

If a luminous body at a (Fig. 528) illuminate a plane
b c, the rays a b, a c, together with the plane, will make
the triangle b a c. If it be removed to a' a ", &c., the
triangle becomes more and more acute, and its sides ap¬
proach nearer to parallel lines, and as the lines approach
parallelism, the rays emanating from a, and forming the
pyramid, approach equality in length; and hence the
plane b c will be more equally lighted the more distant
the luminous point is from it, as if, in point of fact, the
luminous body were equal to the surface illuminated.
This supposition gives great simplicity in the projection of

PROJECTION OF SHADOWS.

211

shadows, where we suppose the light of the sun or of the
moon as the illuminating medium, and from the immense
distance of these bodies consider the rays as parallel; and

Fig. 628

hence, surfaces illuminated by their light are regarded
as illuminated in equal intensity in all their extent
Before entering on the consideration of the modification

the luminous point c c, and let it be required to find tho
shadow of the line on the horizontal plane. Through c'
and d' the horizontal projections of the light and of the
line, draw the indefinite line d d' d, which will be the
trace of a vertical plane, passing through C and D;
then through D, the extremity of the straight line
in the vertical projection, draw an indefinite ray from

C, meeting the common section of the two planes in
e, which gives the place of the shadow of the point

D. Transfer this to the trace in the horizontal plane
in e', and the shadow sought will be the line d' e.

Let d, o', d', d D, he the horizontal and vertical pro¬
jections of the light, and of the straight line. Through o
and d' draw an indefinite straight line, which consider as

of shadows by reflection, and their modification also by
colour, it will be necessary to carry this investigation into
optics somewhat further; but in the meantime, enough
has been furnished as an introduction to what follows:—

ON THE PROJECTION OF SHADOWS.

The preliminary matter has unfolded the general idea
of shadows, and prepared for the consideration of the con¬
struction of shadows produced by bodies exposed to
different kinds of lights.

O •

Problem I.— The projection of a luminous point being
given, and also of a straight line, to find the length and
direction of the sliadoiv of the line on the horizontal
plane.

Let a b (Fig. 529) be the common section of the two
planes, c the luminous point, c d its projections, and
d, d' d' those of the straight line. Then draw the line
C D representing the ray from c, passing through D, and
continue it to meet the horizontal plane in e. This

Fig. 529.

point will be the shadow of the point D. Other rays
Cl, c 2, will be intercepted by D d, and there will be
behind d D, therefore, the right angled triangle due
deprived of light. This triangle may be considered as a
vertical plane cutting the horizontal plane, and its inter¬
section will therefore be the straight line d e. It may
also be considered as the projection of the hypothenuse
D e of the triangle due. Suppose the triangle pro¬
longed indefinitely to the left, and it is evident that its
plane will pass through the light C. The light, therefore,
the given straight line, and the projection of the latter,
are manifestly in the same plane; and since d e is the
projection of D e, c d will be that of c D, or rather c e
will be the projection of the ray C e, or of the hypothenuse
of the triangle c C e. Consequently, the shadow thrown
by the line d D will be found in the trace of a vertical
plane, passing through the horizontal projections of the
light, and of the given line.

Let there be given the line D d (Fig. 530), the height of ;

the trace of the vertical plane. Suppose this plane turned
over on c e' as an axis until it lies horizontally, which is
done in drawing an indefinite perpendicular to the trace
c r d, and carrying on it the height c C of the luminous
point from d to c'; and in the same manner drawing the
perpendicular to d\ and setting off" on it the height d' d' of
the straight line d D, and through c' and l)', drawing a
line meeting the trace in d, which determines the length
of the shadow d' e'.

To determine the shadow of a straight line, of which a
part is intercepted by a vertical plane.

Let / F (Fig. 530) be the given line. Through it, and
through the light C, suppose to pass a vertical plane, of
which the horizontal trace is d g, then draw the ray CF
prolonged to meet the common section, and cutting it in
g, f g would be the length of the shadow of / F if there
were no obstacle. But suppose a vertical plane to k
interposed so as to receiye a portion of the shadow, and
that it is required to find that portion. If, as before, the
triangle c c g is folded down on d g as an axis, it will
produce the triangle c c' g' on the horizontal plane, and
there will also be found the line / F in /' f', the indefinite
intersection of the plane to k in to' k', and it is only
necessary to draw o' f' meeting the vertical plane in l and
the line to' l will be the shadow.

Problem II. — Given a luminous point, and a straight
line inclined to the horizontal plane, to find the shadow
of the line on the plane.

Let A b, a b (Fig. 531, No. 1) be the projections of the
line, and d, d'd" of the point. If the former problem has
been understood this will offer no difficulty. Through b

212

PRACTICAL CARPENTRY AND JOINERY.

from d" draw a straight line, meeting the common inter¬
section in e ; draw through e an indefinite line, perpen¬
dicular to R S, the common intersection, and through B

d a straight line cutting the last perpendicular in e!\ join
A e', which will be the shadow sought. This problem
may also be solved by laying the light and the straight
line in the horizontal plane, as shown in the figure. It
is so simple that it requires no description.

When the shadow is in part intercepted by a vertical
plane.

Problem: III.— The 'projections of a straight line in¬
clined to two planes being given, to find its shadow on
the two planes.

Let F G, f g (Fig. 531, No. 2) be the projections of the
line, and d, d'd" those of the light. Now, a luminous ray
passing through G will project the shadow of that point
on the horizontal plane at li if no obstacle intervenes.
Through F draw the straight line F h, which will be the

shadow of F G inclined to the horizontal plane. But there
is interposed the vertical plane J K, which intercepts the
ray G and its shadow in i\ and as the extremity of G
touches the vertical plane, the shadow of G will be at its
point of contact, in the same way as the shadow of F at
its touching point with the horizontal plane. Draw
therefore G i, and the shadow sought will be F i, G i.

But in solving this problem there is a difficulty fre¬
quently occurring as follows:—If the extremity G, or g of
the line were more elevated than in this example, the
luminous ray would meet the horizontal plane at a dis¬
tance too great to be within the limits of the paper, and
if G were as high as the luminous point, it is evident that
the ray would be parallel to the horizontal plane. In
such cases take any" point in the straight line F G, as l, and
through it, on the horizontal projection, draw l L parallel
to d d; draw through l and through d an indefinite
straight line, and then through D and L draw a ray which
cuts d l in to, which is one of the points of the shadow
sought. Through this point and F draw a straight line,
prolonged to meet the vertical plane J K, and the point i
of intersection will be obtained as in the preceding opera¬
tion.

If it is required to operate by the projections of the
straight line and luminous point, draw the ray d" V to
meet the common intersection of the two planes in to';
and from to' let fall the perpendicular to' to, cutting the
prolongation of d, l in to, which is the point sought.

These last two pro¬
blems may be ren¬
dered very easy of
comprehension, by
the study of the
perspective diagram
531, No. 3, wherein
the same letters are
used to refer
to the same
parts.

Problem IY.— The projections of a straight line, and
of a plane inclined to the planes of projection being
given, to find the port ion of the shadow of the line inter¬
cepted by the plane.

Let A B (Fig. 532) be the common section of the two
planes; c, c o' the projections of the light; cl, d d' those of

the straight lines; EFG those of a plane inclined to the
horizontal plane. As in the former figure, it will be seen
that, if no obstacle were interposed, the shadow of the
line d d would be projected on the horizontal plane in d h;
that the triangle h c c may be considered as an indefinite
plane, cutting the plane F G in the line I J; that the incli-
| nation of that line is the same as that of the plane F G on

PROJECTION OF SHADOWS.

213

the horizontal plane; that the ray c h is intercepted by
the plane F G at the point K; that this point is at the
intersection of the ray, and the line I J; that this line,
as well as the given right line d d and the luminous point,
are all in the plane of the right angled triangle h c c, and
therefore, all that is required is to turn over this tri¬
angle, and its contained lines, so that it shall lie in the
horizontal plane, which is thus accomplished:—

Draw an indefinite line c d, which will be the trace oi
a vertical plane passing through the luminous point and
the given straight line. Then from c and d let fall per¬
pendiculars, and carry on them the heights c c', and d d.
From j draw also j J perpendicular to li c, and set off on
it j J, equal to the height of G above g. From j draw j I
which will be the intersection of the inclined plane.
Through c and d draw the ray, cutting I J in K, which is
the point sought, and from K let fall on/tca perpendicular
K k, the extremity k of which, is the horizontal projection
of K. The length of the shadow on the inclined plane
will then be I K, and its horizontal projection I lc, conse¬
quently the entire shadow will be d I K, or d F k'.

The problem may also be solved thus: through c and d
in the vertical projection draw an indefinite straight line,
and through c and d’ draw the ray, cutting F G in k ';
from this point let fall a perpendicular on c d produced,
and this gives, as in the former case, the point K.

In the same way the operation is performed in the case of
the plane P Q or p on', on the right hand, which is inclined
to the straight line in the contrary way to the former.

Problem Y. — Of shadows 'projected by rays of light
which are parallel among themselves.

In the problems already given, the distance of the
object illuminated from the light has been supposed to be
known, as it is more easy thus to conceive the construc¬
tion of shadow. For, if a luminous body, such as the sun,
had been taken as the source of the light, it would have
been impossible to have determined its place on the planes
of projection relatively to the places of the bodies illumi¬
nated by it, and the question would have appeared more
abstract. It is necessary now to see how, in the absence
of the place of the light in the planes of projection, the
shadows of bodies can be constructed.

Let c, c c' (Fig. 533) be the projections of a straight line,
and e, e e' those of the light. If the light is supposed
laid over on the horizontal plane its projection will be
E; E / will be the ray, e f the projection of the ray,
and c f the shadow of the given line. Conceive the ray
/ E produced indefinitely towards z, its projection will
also be indefinitely produced towards 0 . Conceive also the
luminous point occupying the places successively of G and
H on the prolongation of the ray, the projections of these
points will necessarily be also on the prolongation of the
projections of the ray in g h, g' h\ &c. But it is evident
that in whichever of these points, G H, the luminous point,
is placed, the direction and dimensions of the shadow c f
remain the same. Hence the actual position of the light¬
giving body, when its rays are parallel, is not required;
it is sufficient to know the projections of a single ray.

Problem VI.— The projections of a solar ray, and of
a straight line being given, to determine the shadow of
the line on the horizontal plane.

Let 0 f 0 ' / (Fig 533), be the projections of the ray, and
i, T % those of the line. If through i is drawn a line k l

parallel to / 0 , and through i' another line parallel to / 0 ,
these two lines will be the traces of a plane passing through
' the light, whatever may be its distance. These lines may
be also considered as the projections of an indefinite ray,

making certain angles with the planes of projections. As
the right line given is equal to the right line c c, the
shadow i k will be equal to the shadow c f. If it is re¬
quired to operate directly by the ray the problem is very
easy. L k is the direction of the ray, and the angle L k l
is the measure of its inclination with the horizontal plane.

The projections of a solar ray then suffices to determine
the shadows of different bodies. As the bodies can be
illumined in an infinity of ways, the artist can choose
that which is best adapted for his purpose. But architects,
and engineers, and designers generally, have long agreed
to adopt a certain angle, at which the luminous rays are
supposed to fall upon the planes of projection, as possessing
many advantages. This convention is the position that
all the rays of light are such, that every one of their pro¬
jections makes an angle of 45°, with the common inter¬
section of the planes of projection, which can only have
place in the case where the ray is in the direction of the
diagonal of a cube, one of the faces of which is parallel
to the vertical plane. The great advantage of this con¬
vention is expressed in this, that when the projections of
the light make an angle of 45°, with the common section
of the planes of projection, the length of the shadow of a
straight line perpendicular to one of the planes is equal
to the diagonal of the square of the same line. Let this
be illustrated by an example.

Since the rays of the sun are parallel, and their projec-

214

PRACTICAL CARPENTRY AND JOINERY.

f g, d h, e i, parallel to c d, and through the points fdc'
draw the rays F g, I) h, c i, parallel to E d, and their in¬
tersections will give the points of the shadow g h i on
the horizontal plane. Join these by the lines/ g, g h, h i,
parallel to c'd, f d, c d, and there is obtained the shadow
of the cube on the horizontal plane.

It is very important that the ray should not be con¬
founded with its projections, and it may be well to
demonstrate this
by taking the

points of the cube
successively. Let
c h, h e, (Fig. 535)
be the projections
of the light, making A .
an angle of 45°

° E

with the common
section of the

planes. From any
point whatever,
such as c, raise c C c
perpendicular to
c h, and make it
equal to c c'. Carry
the height c c from c to x, and continue the line C x, which
is the diagonal of the square, from clo d; draw the indefi¬
nite line C d, which will be the diagonal of the cube, or the
ray sought; and the angle C d c, which is about 35° 16',
will be the measure of the ray upon the horizontal plane,
and not 45°. For if the ray were inclined 45° to the plane,
as C x, its length would equal the height of the right
line, or the side of the square of that line, in place of its
diagonal. It is important, therefore, not to confound the
ray with its projections. Following out the construction
of the problem, the points F D E, and their projections
g h d. are found in the same manner as c and

Plate CL—The projections of the diagonals of the ima¬
ginary cube, which denote the direction of the rays of
light, being equal in both planes, it follows, that in all cases
and whatever be the form of the surface upon which the
shadow is cast, the oblique lines joining the projections of
the point which throws the shadow,and that which denotes
it, are also equal. In illustration of this, let R n' Fig. 1,
Plate Cl., be the projections of a ray of light, and A a'
those of a point, the shadow of which is required to be
projected on the vertical plane x Y. Draw the straight
lines A a, a' a’, parallel to R r', and from a', where k' a’
meets x Y, the trace of the vertical plane, draw the perpen¬
dicular a a to meet the oblique line a a, and the inter¬
section a is the position of the shadow of the point A. It
will be at once seen that the line A a in the vertical is
equal to the line a' a' in the horizontal projection, and the
point a might have been obtained by the compasses, in
setting off on A a, a length equal to k' a.

Problem YII.— To find the shadow cast on a vertical
wall by a straight line ab (PI. Cl., Fig. 1).

As we have already seen, the shadow will be a straight
line, and all that is required is to find two points in that
line. The shadow of A is already found at a, and we have
only to find that of B at b in the same manner, and to
join a and b.

Suppose, now, that in place of a mere line we have a
rectangular slip A B c l), then the. shadow cast by this will

be a similar and equal rectangle abed. Hence we have
the general proposition that when a surface is 'parallel to
a plane, its shadow thrown upon that plane is a figure
equal and similar to it.

When the object is not parallel to the plane, the shadow
is no longer an equal and similar figure, but the method
of determining it is the same. In Fig. 2 , Plate Cl., let
A B c D be the vertical projection, and A' b' the horizontal
projection of the rectangular slip, and x Y the trace of the
vertical plane, which is oblique to a' b'. Draw the lines
a' a', b' //, meeting the trace of the plane in a' and V\
draw the vertical lines a' a, b’ b, meetiug the oblique lines
A a, c c, and B b, D d, in a b c d, and join abed to
form the figure of the shadow. The mode of construction
is the same when the given plane remains parallel to the
vertical plane of projection, and the rectangular object is
oblique to it.

When there are mouldings or projections from the face
of the vertical plane, the boundaries of the shadow will
be an exact reproduction of the contour or section of such
mouldings or projections. On the vertical plane x Y (Fig.
3) there is a moulding, across which the shadow of the
rectangle is thrown. The fillet of the moulding is here
regarded as a vertical plane in advance of x Y, and the
plane of the shadow is found by drawing from its axis a
line meeting a' b' in e'. The oblique lines drawn from
E F in the vertical projection give, by their intersection
with the axis of the moulding, the situation of the shadow
across the fillet. The points abed are found as before,
and the shadow across the curved part of the moulding is
a reproduction, in the horizontal projection, of its section
or contour.

To find the shadow of the rectangular slip cast upon
two vertical planes meeting in any angle. Fig. 4. Let
X Y, Y Z, be the traces of the vertical planes, a' b' the
trace of the slip, and A' a, b' V, the projections of the rays.
From Y, the meeting of the planes, draw Y e' parallel to
A' a, and k' e' will then indicate the portion of the slip
whose shadow will fall on the plane X Y, And e' b' the
portion which will fall on Y z. The shadow in the vertical
projection will consist of two parallelograms, having a
common side, e f, in the intersections of the planes. The
method of drawing these is obvious, and need not be
described.

Figs. 5 and 6 .—To find the shadow cast by a straight
line A B upon a curved surface, either convex or concave,
whose horizontal projection is represented by the line
x e' y.

We have already explained that the shadow of a point
upon any surface whatever is found by drawing a straight
line through that point, parallel to the direction of the
light, and marking its intersection with the given surface.
Therefore, through the projections A and A ' of one of the
points in the given straight line, draw the lines a a, k'a,
at an angle of 45°; and through the point a', where the
latter meets the projection of the given surface, raise a
perpendicular to the ground-line; its intersection with
the line A a, is the position of the shadow of the first point
taken; and so for all the remaining points in the line.

If it be required to delineate the entire shadow east by
a slip ABCD, as before, upon the surfaces under consi¬
deration, we shall be enabled, by the construction above
explained, to trace two equal and parallel curves a e b,

PROJECTION OF SHADOWS.

215

c f d. representing the shadows of the sides ab and CD;
while those of the remaining sides will be found denoted
by the vertical straight lines a c and b d, also equal and
parallel to each other, and to the corresponding sides of
the figure, seeing that these are themselves vertical and
parallel to the given surfaces.

Fig. 7.—When the slip is placed perpendicularly to a
given plane x Y, on which a projecting moulding, of any
form whatever, is situated, the shadow of the upper side
A' b' which is projected vertically in A, will be simply a
line A a, at an angle of 45°, traversing the entire surface
of the moulding, and prolonged unbroken beyond it. This
may easily be demonstrated by finding the position of the
shadow of any number of points such as d', taken at plea¬
sure upon the straight line a' b'. The shadow of the
opposite side, projected in c, will follow the same rule,
and be denoted by the line c c, parallel to the former.
From this example we are led to state as a useful general
rule: that in all cases where a straight line is perpen¬
dicular to a plane of projection, it throws a shadow
upon that plane, in a straight line, forming an angle of
45° with the ground-line.

Fig. 8 represents still another example of the shadow
cast by the slip in a new position; here it is supposed to
be set horizontally in reference to its own surface, and
perpendicularly to the given plane x Y. Here we see
that the shadow commences from the side D B, which is
in contact with this plane, and terminates in the horizon¬
tal line a c, which corresponds to the opposite side A c of
the slip.

Problem YIII.— The projections of a circle and of the
light being given, to find the shadow of the circle on the
horizontal plane.

Let c d', d c' (Fig. 536) be the projections of the light,
and e f g h ijkl and g' k' those of the circle. Take in the

Fig. 5S6. / , •/ /

y h i J k

circumference of the circle as many points as may be
deemed necessary, and through each of them draw right
lines parallel to c d. These lines will be the horizontal
projections of as many luminous rays. Through each cor¬
responding point in the vertical projection, draw lines
parallel to c d, which will be the vertical projections of
the same rays. Through the intersections of these lines
with A B, draw perpendiculars cutting the horizontal pro¬
jections of the light, and each point of intersection will be
the shadow of the corresponding point. Thus the shadow

Fig. 637.

Fig. 63S.

of h will be to, that of l will be n, and so on; and the

circular shadow np to s,
will be the shadow of
the given circle. In this
simple example, the
shadow being a circle,
the lines given are
merely for the sake of
illustration. In practice
it would be sufficient to
find the shadow of the
centre, as in the vertical
projection, Fig. 1, Plate
i ' GIL

To find the shadow of the same circle on the vertical
plane (Fig. 537), points are taken arbitrarily in the cir¬
cumference as before,
and the horizontal
projections of the
rays are drawn to
meet A B, and from
each point of inter-
B section perpendicu¬
lars are raised cutting
the vertical projec¬
tions of the rays.
This shadow will be
an ellipse, because
the cylinder of rays
3 A i J A is cut by the vertical

plane obliquely to its base.—See also illustration Fig. 2,

Plate CII.

Figs. 538 and 539
present no difficulty,
but will be under¬
stood by inspection.
The subject is further
illustrated by Figs.
3 and 4, Plate CII.

In Fig. 540, the
shadow is thrown
equally on the two
planes of projection.
The construction of
this also will be ob¬
vious on inspection,
as also that of Fig.
5, Plate CII., where
the planes form a salient angle, and Fig. 6, where the
Fi g . 540. shadow is thrown on

a circular wall.

The next figure
(Fig. 541) is an ex¬
ample of the shadow
of a circle situated in
the plane of the lumi¬
nous rays.

Let c d, c'd' be the
projection of the circle,
and e f, f e' those of the
light. Through c d
draw the indefinite

Fig. 539.

line c g, which will be the trftce of a plane passing through

21G

PRACTICAL CARPENTRY AND JOINERY.

the ray. To the ellipse, which is the vertical projection
of the circle, draw
two tangents paral¬
lel to e £ and pro¬
duce them to A B;
from J k, the points
of their intersectiou
with A B, draw per¬
pendiculars, cutting
c. g in l g. These
points determine the
length l g of the
shadow sought. But
as in what follows
it is necessary to
determine exactly
the tangent points
h' i', they are found
thus on the shadow. Lay
the circle on the hori¬
zontal plane, and draw
in the direction of the
ray the tangents to it,

M g N l, which give H I
the points sought; and
by letting fall perpendi¬
culars from these on c g,
their horizontal projections h i, and consequently the
projections of h! i', are exactly determined.

It is proper to remark, that by this second operation
the shadow l g might have been easily found without
employing the vertical projection of the circle, and this
knowledge affords a ready means of solving the next pro¬
blem.

Problem IX .—To find the shadow of a circle whose
horizontal projection a h (Fig. 512) is perpendicular to
the trace c d of a plane passing through the ray.

It has been seen that when the ray is in the direction
of the diagonal of a cube,
the length of the shadow
on the horizontal plane
of a right line is equal
to the diagonal of the
square of its height.

Take therefore ea or e b,
which carry upon any
perpendicular whatever,
as e to /; and then take
/ a or f b and carry it
from e to g and g to h, c
and e h will then be the length of the shadow of tin
vertical diameter of the circle; then through g draw j ■
pei pendicular to e h, and make g j, g i, each equal to tin
radius of the circle, and the ellipse e j h i will be tin
shadow required.

Problem X. To find on the circumference of a circle
the tangent points of planes passing through the light
when the circle is not on the plane of the light.

Let c d , d c (Fig. 513) be the projections of the light,
® ® f th° se of the circle, and let the shadow of the

ciicle be found by the means already known. Produce
indefinitely the plane ef of the circle towards g , and con¬
sider/ g as the common section of the plane of projection.

In c d take any point whatever, as h, and from it raise a
perpendicular h H ; and having determined the ray H i,
the right angled triangle i h H is obtained, and its hori-
zontal projection is i h. Find on the line/# the projec¬
tion of this triangle, which is done by letting fall upon
that line perpendiculars from h' i. It is evident that the
point i will be its own projection, and the projection of h'
will be h; h! i then will be the horizontal projection of

the triangle i h H. The original point of which h’ is the
projection, will be elevated above the horizontal plane by
the height h H. Consequently this height will have to
be carried from h' to lb, and the hypothenuse h' i drawn,
which will be the ray H i brought back to the plane of
the circle f g\ for the triangle ih H being conceived to
be raised on its base, li i will be absolutely in the plane
f g, which is that of the circle.

There remains, therefore, only to draw to the circle
two tangents parallel to h', which give J K, the points
sought, the projections of which will be j k, and their
I’lg. 644. shadow on the circum¬

ference of the ellipse
will be l and m.

Problem XI.— The
projections of the light
and those of a cylin¬
der being given, to
find the shadow of the
cylinder.

This operation is re¬
duced to finding the
shadow of the centre
o of the circular top
of the cylinder, which
will be o" (Fig. 514).
From this point with
the radius o" g de¬
scribe the circle g lc h, and
draw to it the tangents
/ g e h, and the shadow is
determined.

Fig. 545 represents a cylinder, the position of which is
analagous to that of the circle in Fig. 537, and the con¬
struction is the same.

lig. 546.—lliis is analogous to Fig. 538, and is con-

PROJECTION OF SHADOWS.

217

structed in the same manner. The tangent j' z' should I
be considered as the trace of a plane perpendicular to
the vertical plane,
passing through that
luminous ray which
is a tangent to the
cylinder in the line
J j. The learner
should repeat this
projection with the
cylinder removed
further from the ver¬
tical plane, as in Fig.

2 , Plate CIII.

Fig. 517.—In this
tions of the shadows
of the two bases of
a cylinder, in the
same manner as the
shadow of the circle
is found in Fig. 539.

These formed, we
draw tangents to
the ellipses, and we
shall have the sha¬
dow of the cylinder
on the horizontal
plane. But it is ne¬
cessary, moreover,
to find the tangent ^ h J k

lines of the planes of the light, as has been done in Fig.
543, and which we shall here repeat.

Through any point a, taken at pleasure in the projec- •
tion of the direction of the light, draw a perpendicular,

upon which take again any point A; take, the height a A,
and set it from a to c; draw the line A c, the diagonal
of the square, and carry it upon a b from a to d'; then
draw A d', which will be tjie diagonal of the cube, the ray,
or the hypothenuse of the right-angled triangle A a dr, pro¬
ject this triangle on e f, the plane of the circle produced, lj
by letting fall on e f from the points a d the perpendi¬
culars a a, d d', and the line a d will be the projection of
a d', the base of the triangle. Carry the height a A from
a to a', and draw a' d, which will be the projection sought
of the ray brought into the plane of the circle. Draw
parallel to this ray the tangents m /, g h, and there will
be obtained the tangent points sought. From these points

figure we require to find the projec-

let fall on the horizontal projection of the cylinder the
lines i 1c, l n, which will be the tangent lines or limits of
the shadow of the cylinder above and below. Lastly,
carry the heights i A, l g, on the vertical projection, and
we obtain i lc' g n', as the limits of the shadow before
and behind in the vertical projection.

Fig. 548.—When we have made the two portions of
the ellipses, as in Fig. 540, let us lay down the circle x y
in the horizontal plane. Then project the ray in the
plane of the circle, and draw tangents parallel to the ray.
From a and b draw the lines a c,b d, which are the limits
of the shadows, and from e the extremity of the tan-

Fig. 548.

gent b e draw the line e f tangent to the ellipse, and this
line will be the shadow carried from the tangent line of

the cylinder to the
horizontal plane.
Lastly, lay the cir¬
cle y z in the ver¬
tical plane, and it
will be in the same
plane as the ver¬
tical projection of
the light; draw to
it two tangents gh,
i Ic parallel to the
projection of the
ray. From g and
i draw the lines
l to, n o, which are
the limits of the shadow on the vertical projection. From
k draw k p, and this line is the shadow carried on the ver¬
tical plane by
the tangent no;
and thus the
whole shadow
of the cylin¬
der is found in
the two planes.
The next figure, No.
549, is analogous to
Fig. 541, and does
not require description.
Fif. 550 is constructed
like Fig. 542. It is only
necessary to observe that the
cylinder will receive more light
in the line / e than on any
other part. K L will be the touching points of the lumin¬
ous planes tangents to the surface of the cylinder, and the

2 E

218

PRACTICAL CARPENTRY AND JOINERY.

projections of these lines will be Ic a, l b in the horizontal
plane. The shadows of these lines in the horizontal planes
will be m L n K.

Fig. 55 1 is the application to a cylinder of the prin¬
ciple of construction exemplified in Fig. 513.

Problem XII. — To find the shadoiv of the interior of a
concave cylindrical surface.

Let c l> E, c h (Fig. 552) be the projections of a concave
semicylinder. Through c draw the horizontal projection
of the light, cutting the curve in I); from this point raise
an indefinite perpendicular D d. T hrough the vertical

projection of the higher point of the cylinder (raised ver¬
tically over c), draw the vertical projection of the light,
which will cut the line raised on the point D in i'. This
point of intersection will be the shadow of /' in the in¬
terior of the cylinder

To obtain a second point of the shadow. Through any
part of the curve, as J, draw a line parallel to c D, cutting
the curve in the point k; from this point raise a perpen¬
dicular, and from j\ the vertical projection of j, draw a
line parallel to /' i', cutting the perpendicular in the point

K, which will be the shadow of /. Lastly, draw the
horizontal projection of the light in such manner as that
it may be a tangent to the curve at L. The vertical pro¬
jection of this point will be V, and it will be the commence¬
ment of the shadow in the cylindrical cavity. Through
these points (or any number similarly obtained) draw a
curve V k' i', which will be the shadow of the circular
part L, C. Then draw the straight line i'd, which will
be the shadow of/' m', a portion of the line f A, and the
shadow of the other portion m' A will be in c D in the
horizontal projection.

To find this shadow directly from the luminous rays.

If we consider CD in the
horizontal projection as the
trace of a nlane cutting the
cylinder, the resulting sec¬
tion will be the rectangle
D F. Draw through F a ray
cutting D G in i, and the
point of intersection will be
the shadow of F. Carry the
height D i from d to % in
the vertical projection, and
we have the point sought.
Repeat this for the section
J k, and we shall obtain the
point K, and the height k K
will be equal to k k'\ the tan¬
gent point L will give as its
section only the line L l',
and consequently the point
L will be itself the point in the shadow.

Fig. 553.—This is the reverse of Fig. 552, and presents
no difficulty.

Fig. 554.—The principles illustrated in Figs. 543 and

551, where the plane of the curve is not in thesame direction

as the plane of the light, are ap¬
plied in the solution of this pro¬
blem. With these in view, the
solution of this is not difficult.
Figs. 555, 55G. — Problem
E XIII. —To find the shadow of
a cone on the horizontal 'plane.

We have already seen that
the shadow on the surface of a
cylinder, and also the shadow
thrown by a cylinder on the horizontal plane, are deter¬
mined by the line wherein a plane tangent to the surface

rig. 653.

PROJECTION OF SHADOWS.

21.9

of the cylinder touches that surface. It is the same in re¬
gard to the cone.

Suppose the problem solved as in Fig. 555. Conceive
two planes c D K CFE, passing through the light through
the limits of the
projected shadow,
and by the sha¬
dow of the cone,
these planes will
be tangents to
the surface of the
cone, and conse¬
quently also to
the circle of its
base, according to
the lines D C, F c,
and the line of
their intersection,
or the axis c E,
will be in the di¬
rection of a lumin¬
ous ray passing
through the sum¬
mit C, and projec¬
ting the shadow
of that point on the horizontal plane in E. The projections
of these planes will evidently be the triangles c D E, c F E.

Hence, to solve this problem, it is sufficient that we
have the shadow of the summit (Fig. 556), or the point E,
which we can obtain by the ray c E, or by the vertical
projection c' e. From this point we draw tangents to the
circle of the base ED, E F, and the radii D c F c, which
will be the limits of the shadow on the surface of the
cone, and the tangents will be the limits of the shadow
thrown on the horizontal plane.

Suppose the cone placed on its summit. The projection
of the shadow in this case is very easy, if we are content
with a mere mechanical solution.

First find d (Fig. 557), the shadow of the centre c of
the base. From d as a centre, with a radius equal to the ra¬
dius of the base,
describe a cir¬
cle; and from the
summit c draw
the tangents c e,
c /, and the sha¬
dow projected on
the horizontal
plane will be de¬
termined.

To find the
boundaries be¬
tween light and
shade on the sur¬
face of thecone—
ls£. Draw
through the tan¬
gent point e a line parallel to C d, cutting the circum¬
ference of the base in g, and from g draw g c, and we ob¬
tain the horizontal projection of the tangent sought.

2d. From the centre C raise a perpendicular upon c e,
and the radius C g will be the line sought.

3d. On d C produced, take the point h, distant from the

centre by a space equal to c d ; from h draw to the base
of the cone the tangents h g, h i, which will give us the
points g i.

If two planes «n,/n (Fig. 55S), be conceived to pass
through the rectilineal boundaries of the projected sha¬
dows, they will be tangents to the cone in the lines c G,
c I, and will cut each other in the line c H. This line of
intersection makes with the horizontal plane an angle

II c h equal to that
made by the lumin¬
ous rays; consequent¬
ly, the point h being
the projection of H
(which is raised
above the horizontal
plane by the height
c c) will be distant
from c the extent
c d ; for a ray passing through c, and projecting a shadow
from that point on the horizontal plane, will be equal
and parallel to H c.

Problem XIV. — To draiv the shadow on the concave
interior of a cone.

Conceive a vertical plane passing through the horizontal
projection of the light, and cutting the cone (Fig. 559).
Turn down this section on the horizontal plane, and we
have the triangle A c B. To find now the shadow of the
point a: through A, its vertical projection, draw a ray which
will project the shadow of the point in D on the side B c of
the triangle ABC. This side has for its horizontal projec¬
tion the line c h, and as all the points in B c correspond
to those in c b, we have only to let fall a perpendicular
from D on b C to give us d for the point sought as the
shadow of a. Take any other point, e, and suppose a
vertical plane passing through it parallel to the first; it
is evident that the shadow of e will be found in e f, and
so on, and the result of the operation will be a hyperbola.
This method of finding the shadow, point by point, how¬
ever, is very tedious, and we shall therefore describe a
more ready solution.

Produce the plane A B indefinitely towards I ; through
the summit c draw the radius c I; from I let fill upon the

prolongation of a b a perpendicular, which will give the
point i ; from that point draw the tangents i J, i K, and
the points J K will be the commencement of the shadow
projected on the interior of the cone by the arc J a K; and
j, K, and d will be three points in the shadow sought.
Take another point, as e: then through i and the given

220

PRACTICAL CARPENTRY AND JOINERY.

point e draw i e l, which will be the trace of a plane which
we suppose to pass through the summit C. Now, every
section of a cone by a plane passing through its summit
is a triangle; draw, therefore, l c, e c, and we have the
triangle E C d', as the vertical projection of this section.
Draw now through E a ray carrying this point to H on
the side T> C of the triangle, and this gives us h on the
horizontal projection l c.

From this last operation is deduced a short method of
finding the point. The point h is situated at the inter¬
section of l C and e f which contain or form the hyper¬
bola. Through the given point e draw e f parallel to ab,
and the point sought will be found on that line. Through
i and through e draw i el, from l draw l c, and the
point sought is also to be found in that line, and must
necessarily be at h its intersection with e f.

Problem XV. — To determine the boundaries of the
shadow on the surface of a sphere, and the projection
of the shadow from the sphere on the horizontal plane.

Consider the line c d (Fig. 5G0), the horizontal projec¬
tion of the light, as the trace of a vertical plane passing

through the centre of the sphere. The resulting section
will be a great circle, which suppose turned over on to
the horizontal plane, or, to avoid confusion of lines, pro¬
jected vertically on the line a b. Consider this line a b
to be the common section of the planes of projection, and
project on it also the luminous ray at the angle of the
diagonal of a cube. This done, draw rays tangentially
to the circle, and from the points e' f let fall on c d the
perpendiculars e' e, ff and the new points e f will be
the projections of e' f. The shadow of e will be pro¬
jected on a b in g', and that of f in d', consequently the
length of the shadow projected by the great circle e! n' f
of the sphere will be g c V on a b, or g d on c d.

Now consider this vertical circle as a sphere, and it is
evident the line e f will be the boundary between the
light and daxrk portions, as well as the vertical projection
of a great circle inclined to the horizontal plane. The
point p, the extremity of a horizontal diameter, as well
as its opposite or antipodes, will have its horizontal pro¬
jection in h i, and the line ft i will be the horizontal

projection of the diameter of which p is one extremity.
The rays which pass through p and its opposite project
the shadows of these points in j, the middle of g'd' ; and
the horizontal projection of the shadows of these points
will be j ft, and we thus have—1st, the two axes, e f h i,
of an ellipse, which will be the horizontal projection of the
inclined circle (of which e' p' f is the vertical projection),
and therefore the horizontal projection of the boundaries
of the light and shade on the surface of the sphere;
2d, the two axes, g cl, j ft, of another ellipse, which will
be the section of the cylinder formed by the rays which
are tangents to the surface of the sphere by the horizontal
plane, and therefore the boundaries of the shadow thrown
by the sphere on the horizontal plane. These ellipses
may be then traced by the aid of a slip of paper, as
described ante, p. 21, Fig. 168; or they may be traced by
finding the horizontal projection of the section of the
sphere on the line n' p' o', and thus obtaining points in
its circumference, as at q, n.

Problem XVI. — To find the shadoiv in the concave
interior of a hemisphere.

Find the tangent points D B (Fig. 561), and through

the centre draw the line A o C. This line will be the hori¬
zontal projection of the light, and the tangent points
D B will be the commencement of the shadow sought.

To find another point in the shadow on the line A c,
conceive, as in the preceding case, the hemisphere to be
cut by a vertical plane, whose trace is the line A c. Turn
down this section on the horizontal plane in a' d c'.
Through a', the vertical projection of A, draw a ray, which
will give the shadow of that point in a in the concavity
of the curve. From that point let fall a perpendicular

upon A c, which will cut
the line in a, the point
sought. We have now
three points in theshadow
sought. To find others,
take any point on the arc
B A D, as e, draw through
E the horizontal projec¬
tion of a ray, which will
cut the hemisphere in E F,
and the vertical projec¬
tion of that section will
be the semicircle e' f' ; draw through e' a ray carrying
the shadow of that point on the curve, and let fall from
the intersection a perpendicular on E F : and e is the point

PROJECTION OF SHADOWS.

221

sought. Proceed in the same manner to obtain other
points, and draw through them the curve De»B, the
boundary of the shadow.

If the hemisphere is in the vertical projection, as in
Fig. 562, we take e g, the vertical projection of the light,
for the section plane, and proceed precisely as in the fore¬
going case.

Problem XVII.— To determine the shadow in a niche.

The inferior part of the niche being cylindrical and its
superior part spherical, we have to solve this problem
by the combination of methods we have just learned.

Through A and A' (Fig. 563), draw the projections of the
light, and at the extremity of a' a', raise a perpendicular,
which gives the point a. The line a a will be the boun¬
dary of the shadow in the cylindrical part. Through o,
the centre of the spherical portion, draw B b, the vertical
projection of the light, cutting the hemisphere, of which

project the section in B 2 % E. Draw the ray b 3 i! , and let
fall a perpendicular on B b, and the intersection i will be
the shadow of B in the interior of the hemisphere. (The
niche is in fact only a quarter of a sphere, but for the
purpose of the problem we regard it as a hemisphere.)
We have then the two semi-axes of an ellipse b o, i o,
consequently we can construct the quadrant d e i of that
ellipse.

Find now the horizontal projection of B in b', and
draw through it the plane b' V. Through b' draw a per¬
pendicular, cutting B i in b, the point sought, and we
can, by drawing the curve e b a, complete the boundary
of the shadow. If the drawing is large, it is necessarv to
find more points, as shown by the dotted lines.

Problem XVIII.— To determine the shadows of a
cylinder of which the axis is circular (such as a ring )
and the exterior form of which is a torus.

Let c d be the horizontal projection of the light. The
result of the section by a plane on this line will be two
equal circles, having for their diameters efgh-, and, as

these circles are in the same condition as respects the
light, the results will be equal; hence we require only to
operate for one of them. Let this be g h, and all the points

we find for this can
be transferred to e f.
Lay this circle in
the horizontal plane
in G E, and draw
the rays ld,Kl tan¬
gents to the circle
at i and K. These
points are the boun¬
daries between the
light and shade of
the circle, and the
shadows of these
points on the hori¬
zontal plane will be
at the intersections of the rays with the line c d at the
points d and l ; and if we let fall on c d perpendiculars
from the points I K, we shall have their horizontal pro¬
jections in i k, i being on the upper and 1c on the lower
side. If we now draw a ray to M, the centre of the circle,
we shall have N as the point most highly illuminated,
and n for its horizontal projection. By these operations
we have obtained the points n, 1c, l, i, d, which we transfer
upon c d in o, p, q, r, s. If we now make a section on t u,
parallel to the common section A B, we have two circles
equal to the preceding, and the projection of the light on this
plane will be the same as in the vertical plane; that is, the
line v u will make an angle of 45° with t u. Consequently,
the tangent points will have v.x as their horizontal pro¬
jections, and y u as their shadows projected on the hori¬
zontal plane. These two points are not in their place,
and, as we require only the one point u, we may, if we
think fit, reject y. Through v, the horizontal projection
of y, draw an indefinite line parallel to c d; the shadow
of v will be found in that line at z, as follows;—1st, by
raising from u a perpendicular, cutting the line in 2d,
in carrying from v to z the diagonal of the square of the
height Y v. 3d, in raising from V the line v' Y equal to
Y V and perpendicular to v z, then drawing through V' a
ray, Y z, parallel to I d, since v z is parallel to c d.

Make still another section by the line 1 2, and the pro¬
jection of the light on this plane will be an angle of 90°;
the tangent points will consequently be at 3 and 4, and
their horizontal projections in 5 and 2. The shadow
thrown on the horizontal plane by the point 4 will be 6.
We shall find this point by carrying from 2 to 6 the dia¬
gonal of the square of the height 2 4. We have now a
sufficient number of points for tracing the curve i v 2, the
quarter of the shadow of the body, and the curve d z 6 2,
the quarter of the projected shadow. The other portions
can be found from this.

Problem XIX —To find the outline of the shadow
cast upon both planes of projection by a regular hexa¬
gonal pyramid. Plate CIIL, Fig. I.

In this figure it is at once obvious that the three sides
A' B' f', a' b' cf, and A' c'd' alone receive the light; con¬
sequently the edges a' f' and A' i/ are the lines of shade.
To solve this problem, then, we have only to determine
the shadow cast by these two lines, which is accomplished
by drawing, from the projections of the vertex of the

222

PRACTICAL CARPENTRY AND JOINERY.

pyramid, the lines A b and A' a' , parallel to the ray ol
light; then raising from the point b a perpendicular to
the ground line, which gives at a' the shadow of the ver¬
tex on the horizontal plane, and finally by joining this
last point a' with the points v' and f'; the lines D a' and
F a' are the outlines of the required shadow on the hori¬
zontal plane. But as the pyramid happens to be situated
sufficiently near the vertical plane to throw a portion of
its shadow, towards the vertex, upon it, this portion may
be found by raising from the point c where the line a' a
cuts the ground line, a perpendicular c a, intersecting the
line A b in a ; the lines a d and a e, joining this point
with those where the horizontal part of the shadow meets
the ground line, will be its outline upon the vertical
plane.

Problem XX.— To find the shadoiu cast by a- hexa¬
gonal prism upon both planes of projection. Fig. 4,
Plate CIII.

The shadows cast upon the two planes of projection
are delineated in the figures, and the lines of construc¬
tion which are also given are sufficient to indicate the
mode of operation without the help of further explana¬
tions.

Problem XXI.— Required to determine the limit of
shade in a cylinder, and likeivise its shadow cast upon
the tivo planes of projection. Fig. 2, Plate CIII.

When the cylinder is placed vertically, the lines of
shade are at once found by drawing two tangents to its
base, parallel to the ray of light; and projecting, through
the points of contact, lines parallel to the axis of the
cylinder.

Draw the tangents d' d! and c' c', parallel to the ray
f'; these are the outlines of the shadow cast upon the
horizontal plane. Through the poiut of contact c draw the
vertical line c E; this line denotes the line of shade upon
the surface of the cylinder. It is obviously unnecessary
to draw the perpendicular from the opposite point d';
because it is altogether concealed in the vertical elevation
of the solid. In order to ascertain the points c' and D'
with greater accuracy, it is proper to draw, through the
centre o', a diameter perpendicular to the ray of light f'.

Had this cylinder been placed at a somewhat greater
distance from the vertical plane of projection, its shadow
would have been entirely cast upon the horizontal plane,
in which case it would have terminated in a semicircle
drawn from the centre o', with a radius equal to that of
the base. But, as in our example, a portion of the shadow
of the upper part is thrown upon the vertical plane, its
outline will be defined by an ellipse drawn in the manner
indicated in Fig. 2 of the preceding Plate.

Fig. 5.—When the cylinder is placed horizontally, and
at the same time at an angle with the vertical plane, the
construction is the same as that explained above; namely,
lines are to be drawn parallel to the ray of light, and
touching the opposite points of either base of the cylinder;
and, through the points of contact A and c, the horizontal
lines A B and c D are to be drawn, denoting the limits of
the shade on the figure. The latter of these lines only is
visible in the elevation; while, on the other hand, the
former, A b alone, is seen in the plan, where it may be
found by drawing a perpendicular from A meeting the
base f' g' in a'. The line A' e' drawn parallel to the axis
of the cylinder is the line of shade required.

The example here given presents the particular case in
which the base of the cylinder is parallel to the direction
of the rays of light in the horizontal projection. This case
admits of a simpler solution than the preceding, in which
the necessity for drawing the vertical projection of the
figure is dispensed with. All that is required in order
to determine the line A' e' is to ascertain the angle which
the ray of light makes with the projection of the figure.
Draw a tangent to the circle f' a 2 g' (which represents
the base of the cylinder laid down on the horizontal plane),
in such a manner as to make with f' g' an angle of 35° 16',
and through the point of contact A 2 draw a line parallel
to the axis of the cylinder; this line e' a' will be the line
of shade as before.

Problem XXII.— To find the line of shade in a cone,
and its shadoiu cast upon the two planes of projection.
Fig. 3, Plate CIII.

By a construction similar to that of Fig. 1, we find the
point a'; from this point draw tangents to the opposite
sides of the base; these two lines will denote the outlines
of the shadow cast upon the horizontal plane. Their
points of contact b' and o', joined to the centre A', will give
the lines A' b' and A' c' for the required lines of shade in
the plan; of these, the first only will be visible at A B in
the elevation.

If the cone be situated in the reverse position, as in
Fig. 6, the shade is determined in the following manner:
—From the centre a’ of the base, draw a line parallel
to the light; from the point al, where it intersects the
perpendicular, describe a circle equal to the base, and
from the point A' draw the lines a' b' and a' c, touching
this circle; these are the outlines of the shadow cast upon
the horizontal plane. Then, from the centre A', draw the
radii A' b' and a' c', parallel to a b' and a' c'; these radii
are the horizontal projections of the lines of shade, the
former of which, transferred to B D, is alone visible in the
elevation. But in order to trace the outline of that portion
of the shadow which is thrown upon the vertical plane,
it is necessary to project the point c' to c, from which, by
a construction which will be manifest from inspection of
the figures, we derive the point c, and the line c d as part
of the cast shadow of the line c' A'. The rest of the outline
of the vertical portion of the cast shadow, is derived
from the circumference of the base, as in Fig. 2.

Problem XXIII.— The qwojections of a cone and a
sphere being given, to determine the shadoiu thrown by
the first body on the second.

Suppose, in the first instance, that the shadows belong¬
ing to both bodies have been found.

1st. Let cd (Fig. 565), be the horizontal projection of the
light; E d the ray; e E the height of the cone; f d h the
shadow thrown by the cone on the horizontal plane;
(the horizontal projection of the sphere being supposed
removed); e f, e h the boundaries of shade on the surface of
the cone ; i E the vertical projection of the shadow of the
cone or of the lines ef eh-, c E g the vertical projection of
the cone.

The lines f d, h cl are the traces of two planes inclined
to the horizontal plane, tangents to the surface of the
cone in the lines e f e h, and intersecting each other in
the arris E cl or its horizontal projection e d. Suppose
now the sphere by which portion of the shadow is to be
intercepted, cut by the vertical plane c d in the diameter

KUOJ ECT] WW 0[F 5MAEXDWS ANE> ‘OASTT 6H A [DOT'S.

Ill, M’ltlE &• SOX GLASGOW, EDTNBTTJUlIi V LONDON .

PROJECTION OF SHADOWS.

223

l'ig. 565.

g q ; make the vertical projection of this section, and we
have the circle k to k, which will intercept the ray E d
in the point N, which has n as its horizontal projection.
This point then is' the projection of the shadow of the
summit of the
cone upon the
sphere. We could
in the same man¬
ner obtain other
points, but this
method is ope-
rose, and wants
precision, in conse¬
quence of the obli¬
quity of the inter¬
secting lines. We
proceed to consider a
method more direct
and involving less
labour.

2d. In this method
we regard the sphere
as being cut by plane

inclined to the horizontal plane, and whose trace is fd.
We find easily the inclination of the plane, because it is a
tangent to the surface of the cone in the line / e, which
is the horizontal projection of i E. We have thus a
rectangular triangle, and f e as one of its sides. Its second
side is the axis of the cone, perpendicular to e / and of
which the height e E' is known, and the hypothenuse
of the triangle is / E / . Conceive this triangle raised
on its base / e, and we shall have an idea of the
inclination of the plane d f e.

Now from 7c, the centre of the horizontal projec¬
tion of the sphere, let fall upon d f a perpendicular
a b. This line will be parallel to / e, and will serve
as the vertical plane for the projection of the sphere,
as well as the inclined section plane. Raise upon a b,
from the point e, a perpendicular, on which set off
the height e e' from e to e". Then project / in f; draw
f E", and w T e have the first right-angled triangle
e f e", similar and equal to the first, and consequently
we have also the inclination of the section plane in
the angle e f e". Now, with the radius Jc 7c' perpen¬
dicular to a b, describe a circle as the vertical projec¬
tion of the sphere. We now see that this is cut by
the inclined plane f E", or by the shadow of the cone
in the line o' p', one of the diameters of the circle
of that section. Divide the horizontal projection
op of that diameter in two equal parts at q\ let fall
from this a perpendicular on
a b, cutting the circumference 7 \ Il s- 566 -

at the points r s, and the line
r s will be the major, and o p
the minor axis of the ellipse,
which is the horizontal projec¬
tion of the circle produced by
the section of the sphere. This
ellipse, or so much of it as we require, we can trace by
means of a slip of paper. Having obtained this, we pro¬
ceed in the same way in regard to the trace 7i d, and, the
operations being completed, we transfer these shadows to
the vertical projection, Fig. 556.

vertical projection is very different from the others; and
if we were to continue to operate in the same manner we
should have the sections irregular, and the lines cutting
too obliquely to give a precise result. Conceive, there¬
fore, that the circle q r is an indefinite horizontal plane,
on which the shadow from a b is to be thrown, lo
obtain this shadow we have only to draw through y (the
vertical projection of the centre y ) a ray meeting the
plane q r in z, and from z to let fall a perpendicular cut¬
ting the horizontal projection of the line of light passing
through the centre y, and it will give z as the shadow of

Problem XXIV .—To determine i7ie sliadow of a con¬
cave surface of revolution.

Let A B be the projections of the body, and 1 2 3 4,
Ac., traces of planes cutting it in the direction of the rays
of light. Let us obtain first the vertical projection of
the section 2, which will serve as a model for the others.
Divide the concave part of the body B by horizontal sec¬
tions c d, efg 7i, i 7c, which will be expressed by so many
circles in figure A. In doing this we should avoid multi¬
plicity of lines, by making as many of the circles as pos¬
sible of the same diameter. Find now the vertical section
on 2. It is evident that the first point 2 will be on the
section q r in 2; the second point l, will be on the section
i 7c in l, and also in a b in p\ the third to, will be on
g h, c d in to and o; and the fourth n , on e f in n.
Through 2 l m n o p draw a curve, which will be the
vertical projection of 2 l to n. Through p draw the pro¬
jection of the ray, which will meet the curve in s, the first
point of the shadow sought. Find in the same manner
the points w t v u, Ac., and through them draw the curve
wtv u, which will be the portion of the shadow projected
by the arc a y.

The point u belongs to the horizontal section 4, whose

rig. 667.

224

PRACTICAL CARPENTRY AND JOINERY.

the centre of the circle a b on the horizontal plane of q r.
As the circle is parallel to this plane its shadow will also
be a circle of the same radius; therefore from the centre 0 ,
with the radius a y or b y, describe the circumference
cutting the horizontal circle q 0 r in 6, which will be a
point in the shadow sought, but as 6 is very near r, we
can take without sensible error ras its vertical projection.
Find then a point in the horizontal section i k in the same
manner. The ray y z cuts the section i k in the point 7.
By letting fall from 7 a perpendicular, we obtain the centre
7, from which we describe a circle equal to the first, or
simply an arc of it on the circumference l k of the section
i 1c, which gives a second point 8. Proceed thus with
all the sections, which will give the centres 9, 10, &c.,
and the arcs 11 , 12, of which the projections are 11 , 12 .
Through the intersections of the arcs 12, 11, 8, 6, with
the circles in A, draw a curve, which will be the horizontal
projection of the shadow thrown on the concave portion
of the figure, and the corresponding vertical projections
are obtained by drawing perpendiculars from the same
points to cut the sections q r, i k, g h, e f, in B. It is not
necessary to describe the method of obtaining the re¬
mainder of the shadow on the horizontal projection, as an
inspection of the figure, coupled with the previous pro¬
blems, should be sufficient to enable the learner to do it.

METHODS OF SHADING.

Plates CIV.—CVI.

The intensity of a shade or shadow is modified by the
various peculiarities in the forms of bodies, by the inten¬
sity of the light, and by the position which objects may
occupy in reference to it.

Flat surfaces wholly exposed to the light, and at all
points equidistant from the eye, should receive a uni¬
form tint or tone.

In geometrical drawings, where the visual rays are
imagined parallel to the plane of projection, every surface
parallel to this plane is supposed to have all its parts at
the same distance from the eye.

When two surfaces thus situated are parallel, the one
nearer the eye should receive a lighter tint than the other.

Every surface exposed to the light, but not parallel to
the plane of projection, and, therefore, having no two
points equally distant from the eye, should receive an un¬
equal tint. the tint should, therefore, gradually increase
in depth as the parts of such a surface recede from the eye.

If two surfaces are unequally exposed to the light, the
one which is more directly opposed to its rays should
receive the fainter tint.

V hen a surface entirely in the shade is parallel to the
plane of projection, it should receive a tint uniformly dark.

When two objects parallel to each other are in the
shade, the one nearer the eye should receive the darker tint.

V hen a surface in the shade is inclined to the plane of
projection, the part which is nearest the eye should
receive the deepest tint.

H two surfaces exposed to the light, but unequally
inclined to its rays, have a shadow cast upon them, the
shadow upon the lighter surface will be more intense than
that on the darker surface.

We shall now proceed to give some directions for using
the brush, or hair-pencil, and explain the usual methods em¬
ployed in producing this conventional tinting and shading.

The methods of shading most generally adopted are
either by the superposition of any number of flat tints,
or of tints softened off at their edges. The former method
is the more simple of the two, and should be the first
attempted.

Shading by Flat Tints .—Let it be proposed to shade the
prism, Fig. 4, Plate CIV., or Fig. 3, Plate CVI., by means
of flat tints. According to the position of the prism, as
shown by its plan, Fig. 1, Plate CIV., one face, a b, is
parallel to the plane of projection, and, therefore, entirely
in the light. This face should receive a uniform tint,
either of Indian ink or sepia. When the surface to be
tinted happens to be very large, it is advisable to put on
a very light tint first, and then to go over the surface a
second time with a tint sufficiently dark to give the
desired tone to the surface.

The right-hand face b g being inclined to the plane of
projection, should receive a graduated tint as it recedes.
This gradation is obtained by laying on a succession of
flat tints in the following manner:—First, divide the side
into equal parts by vertical lines. These lines should be
drawn very lightly in pencil, as they merely serve to cir¬
cumscribe the tints. A grayish tint is then spread over
the first division, c b 11, Fig. 2. When this is dry, a
similar tint is laid on, extending over the first and second
divisions, and so on, till, lastly, a tint covering the whole
surface imparts the desired graduated shade to that side
of the prism, as in Fig. 3. The number of tints designed
to express such a graduated shade depends upon the extent
of the surface to be shaded; and the depth of tint must
vary according to the number.

As the number of washes is increased, the whole shade
gradually presents a softer appearance, and the lines
which border the different tints become less harsh and
perceptible. For this reason the foregoing method of
representing a shade or graduated tint hy washes succes¬
sively passing over each other, is preferable to that some¬
times employed, of first covering the wdiole surface, and
then gradually narrowing the tint at each successive wash,
because in this way the outline of each wash remains un¬
touched, and presents, unavoidably, a harshness, which,
by the former method, is in a great measure subdued.

The left-hand face a is also inclined to the plane of pro¬
jection ; but, as it is entirely in the light, it should be
covered by a series of much fainter tints than the last
surface, which is in the shade. It should darken as it
recedes. The gradation of tint is effected in the same way
as before, as shown in Figs. 3 and 4.

Let it be proposed to shade a cylinder by means of flat
tints, Figs. 5 to 12, Plate CIV.

In shading a cylinder it will be necessary to consider
the difference in the tone proper to be maintained between
the part in the light and that in the shade. It should be
remembered that the line of separation between the light
and shade, a b , is determined by the radius, o a', Fig. 5,
drawn at an angle of 45°, and perpendicular to the rays
of light. That part, therefore, of the cylinder, which is
in the shade, is comprised between the lines a b and c d.
This portion, then, should be shaded conformably to the
rule previously laid down for treating surfaces in the shade

BLA.CKTE & SOSt; GLASGOW,EDINBURGH. & lO^DOTS.

JLASGOW, JSDrNRTTltGH , .«c LONDON

BI.ACKLE $• SON. GLASGOW. EDINBURGH. & LONDON

METHODS OF SHADING.

225

inclined to the plane of projection. All the remaining
part of the cylinder which is visible presents itself to the
light; but, in consequence of its circular figure, the rays
of light form angles varying at every part of its surface.
In order to represent with effect the rotundity, it will
be necessary to determine with precision the part of the
surface which is most directly affected by the light. This
part is situated about the line e i, Fig. 12, in the vertical
plane of the ray of light, R o, Fig. 5. As the visual rays,
however, are perpendicular to the vertical plane, and
therefore parallel to v o, it follows that the part which
appears clearest to the eye will be near this line v o, and
may be limited by the line T o, which bisects the angle
v o R and the line R O. By projecting the points e' and
TO', and drawing the lines e i and to n, Fig. 1 2 , the surface
comprised between these lines will represent the lightest
part of the cylinder.

This part should have no tint upon it whatever, if the
cylinder happen to be polished—a turned iron shaft, or a
marble column for instance; but if the surface of the
cylinder be rough, as in the case of a cast-iron pipe, then
a very light tint—considerably lighter than on any other
part—may be given it.

Again, let us suppose the half-plan of the c}dinder to be
divided into any number of equal parts. Indicate these
divisions upon the surface of the cylinder by faint pencil
lines, and begin the shading by laying a tint over all that
part of the cylinder in shade. This will at once render
evident the light and dark parts. When this is dry put
on a second tint, extending over that division which is
to be deepest in colour, then spread a third tint over this
division, and one on each side of it. Proceed in this way
until the whole of that part of the cylinder which is in
the shade is covered.

Treat in a similar manner the left-hand side, and com¬
plete the operation by covering the whole surface of the
cylinder—excepting only the division in full light—with
a very light tint.

Shading by Softened Tints. —The advantage which this
method possesses over the one just described, consists in
imparting to the shade a softer appearance; the limita¬
tions of the different tints being imperceptible. It is, how¬
ever, more difficult.

Let it be proposed to shade by this method the former
example of a prism.

Apply a narrow strip of tint to the nearest division of
the shaded side, and then, qualifying the tint in the brush
with a little water, join another lighter strip to this, and
finally, by means of another clean brush moistened with
water, soften off the edge of this second strip, which may
be taken as the limit of the first tint.

When the first tint is dry, cover it with a second, which
must be similarly treated, and should extend beyond the
first. Proceed in this manner with other tints, until the
whole face is shaded, as presented in Fig. 3, Plate CVI.

In the same way the left-hand face is to be covered,
though with a tint considerably lighter, for the rays of
light fall upon it almost perpendicularly.

Let it now be proposed to shade the cylinder, Fig. 7,
Plate CVI., by means of softened tints.

The boundary of each tint being indicated as before, the
first strip of tint must cover the line of extreme shade,
and then be softened off on each side. Other and suc¬

cessively wider strips of tint are to follow, and receive
the same treatment as the one first put on.

As this method requires considerable practice before it
can be performed with nicety, the learner need not be
discouraged at the failure of his first attempts, but per¬
severe in practising on simple figures of different sizes.

If, after shading a figure by the foregoing method, any
inequalities in the shade present themselves, such defects
may be remedied, in some measure, by washing off redun¬
dancies of tint with the brush or a damp sponge, and by
supplying a little colour to those parts which are too light.

Dexterity in shading figures by softened tints is best
acquired in practising upon large surfaces; this is the
surest way of overcoming timidity and hesitation.

Elaboration of Shading and Shadows. —Having thus
laid down the simplest primary rules for shading isolated
objects, and explained the easiest methods of carrying
them into operation; it is now proposed to illustrate
their application to more complex forms, to show where
the shading may be modified or exaggerated, to introduce
additional rules, and to offer some observations and direc¬
tions for shading architectural and mechanical drawings.

Whatman’s best rough-grained drawing-paper is better
adapted for receiving colour than any other. Of this
paper, the Double Elephant size is preferable, as it pos¬
sesses a peculiar consistency and grain. A larger paper
is seldom required, and even for a small drawing, a por¬
tion of a Double Elephant sheet should be used.

The paper for a coloured drawing ought always to be
strained upon a board with glue, or by means of a
straining frame. Before proceeding to lay on colour, the
face of the paper should be washed with a sponge well
charged with water, to remove any impurities from its
surface, and to prepare it for the better reception of the
colour. The whole of the surface is to be damped, that
the paper may be subjected to a uniform degree of ex¬
pansion. It should be only lightly touched by the sponge,
and not rubbed. Submitted to this treatment, the sheet
of paper will present, when thoroughly dry, a clean smooth
surface, not only agreeable to work upon, but also in the
best possible condition to take the colour.

The size of the brushes to be used will, of course, de¬
pend upon the scale to which the drawing is made. Long
thin brushes, however, should be avoided. Those possess¬
ing corpulent bodies and fine points are to be preferred,
as they retain a greater quantity of colour, and are more
manageable.

During the process of laying on a flat tint, if the sur¬
face be large, the drawing may be slightly inclined, and
the brush well charged with colour, so that the edge of
the tint may be kept in a moist state until the whole
surface is covered. If in tinting a small surface the brush
should be too fully charged with colour, the surface will
unavoidably present rugged edges, and an uneven appear¬
ance throughout. A moderate quantity of colour in the
brush, well and expeditiously spread on the paper, is the
only method of giving an even, close-grained aspect to the
surface.

As an invariable rule let it be remembered, that no tint,
shade, or shadow, is to be passed over or touched again
until it is quite dry, and that the brush is not to be
moved backwards and forwards through the colour.

In the examples of shading which are given in this

226

PRACTICAL CARPENTRY AND JOINERY.

work, it may be observed that all objects with curved
outlines have a certain amount of reflected light imparted
to them. It is true that all bodies, whatever may be their
form, are affected by reflected light; but, with a few ex¬
ceptions, this light is only appreciable on curved surfaces.
The judicious degree and treatment of this light is of con¬
siderable importance.

All bodies in the light reflect on the objects near them
some of the rays they receive. The shaded side of an
isolated object is lighted by rays reflected from the ground
on which it rests, or from the air which surrounds it.

In proportion to the degree of polish, or brightness in
the colour of a body, is the amount of reflected light which
it communicates to adjacent objects, and also its own sus¬
ceptibility of illumination under the reflection from other
bodies. A polished column, or a white porcelain vase,
receives and imparts more reflected light than a rough
casting or a stone pitcher.

Shade, even the most inconsiderable, ought never to
extend to the outline of any smooth circular body. On a
polished sphere, for instance, the shade should be deli¬
cately softened off just before it meets the circumference,
and when the shading is completed, the tint intended for
the local colour may be carried on to its outline. This
will give transparency to that part of the sphere influ¬
enced by reflected light. Very little shade should reach
the outlines even of rough circular bodies, lest the colour¬
ing look harsh and coarse. Shadows also become lighter
as they recede from the bodies which cast them, owing to
the increasing amount of reflection which falls on them !
from surrounding objects.

Shadows, too, are modified in intensity by the air, as
they recede from the spectator; they thus appear to
increase in depth as their distance from the spectator
diminishes. In nature this difference in intensity is only
appreciable at considerable distances. Even on exten¬
sive buildings inequalities in the depth of the shadows
are hardly perceptible; it is most important, however, for
the effective representation of architectural subjects drawn
in plan and elevation, that the variation in the distance of
each part of an object from the spectator should at once
strike the eye; and therefore a conventional exaggeration
is practised. The shadows on the nearest and most pro¬
minent parts are made very dark, to give scope for the
due modification in intensity in those parts which recede.
The same direction is applicable to shades. The shade on
a cylinder, for instance, situated near the spectator, ought
to be darker than on one more remote. As a general
rule, the colour on an object, no matter what it may be
intended to represent, should become lighter as the parts
on which it is placed recede from the eye.

Plate CYI. presents some examples of finished shad¬
ing. The remarks which we now propose to offer upon
each of these figures are applicable alike to all forms of a
similar character.

Fig. 1 represents a hexagonal prism surmounted by a
fillet. '1 he most noticeable part of this figure is the shadow
of the prism in the plan view. It presents an example
of the graduated expression which should be given to all
shadows cast upon plain surfaces. Its two extremities
are distinctly different in their tone. This difference is
an exaggeration of the natural appearance necessary for
the effect aimed at.

Figs. 2, S, and 6 exemplify the complex appearance of
shade and shadow presented on concave surfaces. It is
worthy of notice that the shadow on a concave surface is
darkest towards its outline, and becomes lighter as it nears
the edge of the object. Reflection from that part of the
surface on which the light falls, causes this gradual dimi¬
nution in the depth of the shadow; the part most strongly
illuminated by reflected light being opposite to that most
strongly illuminated by direct light.

No brilliant or extreme lights should be left on con¬
cave surfaces, as they tend to render doubtful, at first
sight, whether the objects represented are concave or con¬
vex. After the local colour has been put on, a faint wash
should be passed very lightly over the whole concavity.
This will modify and subdue the light, and tend to soften
the tinting.

The lightest part of a sphere (Fig. 4) is confined to a
mere point, around which the shade commences and
gradually increases as it recedes. This point is not in¬
dicated on the figure, because the actual shade tint on
a sphere ought not to be spread over a greater portion
of its surface than is shown there. The very delicate
and hardly perceptible progression of the shade in the
immediate vicinity of the light point, should be effected
by means of the local colour of the sphere. In like
manner, all polished or light-coloured curved surfaces
should be treated; the part bordering upon the extreme
light should be covered with a tint of local colour some-
what fainter than that used for the flat surfaces. In
curved unpolished surfaces, the local colour should be
gradually deepened as it recedes from that part of the
surface most exposed to the light. In shading a sphere,
the best way is to put on two or three softened-off tints
in the form of crescents converging towards the light point,
the first one being carried over the point of deepest shade.

A ring (Fig. 5) is a difficult object to shade. To change
with accurate and effective gradation the shade from the
inside to the outside of the ring, to leave with regularity
a line of light upon its surface, and to project its shadow
with precision, require a degree of attention and care in
their execution, greater perhaps than the shade and
shadow of a,ny other simple figure. The learner, there¬
fore, should practise the shading of this figure, as he will
seldom meet with one presenting greater difficulties.

Figs. 7 and 8 show the peculiarities of the shadows
cast by a cone on a sphere or cylinder. The rule that
the depth of a shadow on any object is in proportion to
the degree of light which it encounters on the surface of
the object, is in these figures very aptly illustrated. It
will be seen, by referring to the plan (Fig. 7), that the
shadow of the apex of the cone falls upon the lightest
point of the sphere, and this is therefore the darkest part
of the shadow. So also the deepest portion of the shadow
of the cone on the cylinder, in the plan (Fig. 8), is where
it comes in contact with the line of extreme light. Flat
surfaces are similarly affected; the shadows thrown on
them being less darkly expressed, according as their in¬
clination to the plane of projection increases. The local
colour on a flat surface should, on the contrary, increase in
depth as the surface becomes more inclined to this plane.

These figures also show that shadows as well as shades
are affected by reflected light. This is very observable
where the shadow of the cone falls upon the cylinder.

PERSPECTIVE.

227

Notwithstanding the most careful exertions of the
colourist to keep every feature of a drawing clear and
distinct, some amount of uncertainty, resulting from the
proximity and natural blending of the different parts, will
pervade the lines which separate its component members.

I 1 or practical working purposes, therefore, a completely
coloured drawing is unsuitable. On the other hand, a
mere outline, although perhaps intelligible enough to
those who are familiarly acquainted with the object de¬
lineated, has an undecided appearance. As complete
colouring renders it difficult for the eye to separate the
various parts, owing to an apparently too intimate re¬
lationship between them; a line drawing, on the contrary, |
perplexes the eye to discover any relation between them
at all, or to settle promptly their configuration. The eye
involuntarily asks the question, Is that part round or
square, is it in the plane of the contiguous parts or more
remote? As a means of avoiding the indefiniteness pre¬
sented by the outline in the coloured drawing, and the
want of adequate coherence and doubtfulness in the mere
line drawing, recourse is not unfrequently had to a kind
of semi-colouring, or rather shading and tinting the parts.

In this kind of drawing, it is advisable to follow a di¬
rection previously given, viz., to modify the colour on
every part according to its distance from the eye. It may
be as well also, for the purpose of maintaining harmony
in the colouring, and of equalizing its appearance, to
colour less darkly large shades than small ones, although
they may be situated at an equal distance from the eye.
The tinting should be very'considerably lighter than on
finished coloured drawings; and, indeed, no very dark
shading should be employed. Besides presenting too
violent a contrast between the parts coloured and those
without any colour at all, dark shading would produce,
in some measure, the indistinctness which is objectionable
in completely tinted drawings.

When, however, any architectural or other object is
represented in perspective, the aim of the artist should be
to avoid all the conventional exaggerations of which we
have spoken, and to imitate to the best of his ability the
appearance the object would have in nature.

PERSPECTIVE.

As an introduction to this study, it is necessary to ob¬
serve, that a luminous point emits rays in all directions,
and that all the points of the surface of a body are ren¬
dered visible by means of rays, which represent the axes
of different cones formed by tbe emanation of bundles of
rays from these points.

Let the line A B be placed before the eye C. It is evi¬
dent that the sum of
the visual rays which 1
emanate from each of 2
the points of that 3
line to the eye, as 4
1 C, 2 C, 3 C, &c., forms 5
a triangle 1 C 7, of
which the base is 1 7
and the summit C. It 7
is easy to see that if
in place of the line a plane or curved surface is sub¬

stituted, the result will be a pyramid of rays in place of
a triangle.

Let A B (Fig. 569) be a straight line, and let the globe
of the eye be represented by a circle, and its pupil by the

point c. The ray emanating from A, entering through c,
will proceed to the retina of the eye, and be depicted at a.
And as it follows that all the points of A B will send rays,

be depicted on the retina of the eye in a curved line a 3 b.
Conceive the line A B moved to a greater distance from
the eye, and placed at a’ b', then the optic angle will be
reduced, and the image a ^ b' will be less than before; and
as our visual sensations are in proportion to the magni¬
tude of the image painted on the retina, it may be con¬
cluded that the more distant an object is from the eye,
the smaller the angle under which it is seen becomes, and
consequently, the farther the same object is removed from
the eye the less it appears.

Observation has rendered it evident, that the greatest
angle under which one or more objects can be dis¬
tinctly seen is one of 90°. If between the object and
the eye there be interposed a transparent plane (such as
one of glass to n), the intersection of this plane with
the visual rays are termed perspectives of the points from
which the rays emanate. Thus a is the perspective of
A, b of B, and so on of all the intermediate points; but,
as two points determine the length of a straight line, it
follows that a b is the perspective of A B, and a' b' the
perspective of a' b'.

It is evident from the figure that objects appear more
or less great according to the angle under which they are
viewed; and further, that objects of unequal size may
appear equal if seen under the same angle. For draw fg,
and its perspective will be found to be the same as that
of A' b' .

It follows, also, that a line near the eye may be viewed
under an angle much greater than a line of greater di¬
mensions but more distant, and hence a little object may
appear to be much greater than a similar object of larger
dimensions. Since, therefore, unequally-sized objects may
appear equal in size, and equally-sized objects unequal,
and since objects are not seen as they are in effect, but
as they appear under certain conditions, perspective
may be defined to be a science which affords the means
of representing, on any surface whatever, objects such as
they appear when seen from a given point of view. It is
divided into two branches, the one, called linear perspec¬
tive ., occupying itself with the delineation of the contours
of bodies; the other, called aerial perspective, with the

228

PRACTICAL CARPENTRY AND JOINERY.

to say, from the plane or horizontal projection of the
point required to be found in perspective, a line is drawn
to the position or station point of the spectator, as A a c,
and another line from its vertical projection to the eye of
the spectator, as A a o. At the points of intersection of
the first set of lines with the horizontal projection of the
picture, a perpendicular a a' is drawn, and the intersection
of this with the corresponding line from the vertical pro¬
jection, gives the point a' required. All the other points
are obtained in the same manner.

A much better idea of the mode of operation will be

obtained from the following figures, in which the process is
repeated geometrically. Let o and o' be the projection of
the eye, Ere / those of the picture, and A B G , a b c d g,
of a pyramid with a square base.

Now, if from the eye a line is drawn to the points A a
of the object, we shall have for the projections of that
line, the lines A O, a o'. The points a' a", where these pro¬
jections cut the projections of the picture, are evidently
the projections of the points in which the visual rays meet

Fig. 571. 0 ---F'

gradations of shade and colour produced by distance.
The former of these only is proposed to be discussed here.

The perspective of objects, then, is obtained by the in¬
tersection of the rays which emanate from them to the
eye by a plane or other surface (which is called the
picture), situated between the eye and the objects.

From the explanation and definition we have just given,
it is easy to conceive that linear perspective is in reality
the problem of constructing the section, by a surface of
some kind, of a pyramid of rays
of which the summit and the
base are given. The eye is the
summit, the base may be re¬
garded as the whole visible ex-
tent of the object or objects to
be represented, and the inter¬
secting surface is the picture.

A good idea of this will be
obtained by supposing the pic¬
ture to be a transparent plane,
through which the object may
be viewed, and on which it may
be depicted.

Let us suppose any object, as
the pyramid ab (Fig. 570), to
be viewed by a spectator at 6
through a transparent plane D E. From the points of the
pyramid visual rays will pass to the eye of the spectator,
and if the points where they intersect the transparent plane
be joined by lines on it, a representation of the object, as
seen by the spectator, will be obtained. The transparent
plane represents the picture, and the problem in perspec¬
tive, is, as we have said, to make a section of the pyramid
or cone of rays, as the case may be, by a plane, curved, or
other surface. The figure illustrates the mode of doing this.
A horizontal projection of the visual rays is made, that is

the picture, and all that is required is to find the position
of that point on the picture itself. Conceive E f f' to be
the elevation of the face of the picture. To its base E r D
transfer the points a" b", b" g", g" c", c" d", in which the
rays in the horizontal projection cut the picture, and from
these points draw indefinite lines perpendicular to e'd.
On the line a" a set up from the base E * 1 2 D the height Ea'.
in the vertical projection of the picture, and ah will be
the perspective of the point required. Proceed in the
same manner to obtain the other points.

As on the problem of finding the perspec¬
tive of any point the whole science of per¬
spective rests, the student should make himself
thoroughly master of it, and although he may
not be able to perceive the direct utility of
what immediately follows, he is recommended
to study it with care and attention, so as
to understand the principles. The applica¬
tion of these will be developed by and by, and
methods of abridging the labour will be
pointed out; the student will also be enabled
to devise others for himself

In addition to the vertical and horizontal
planes with which we are familiar in the ope¬
rations of projection, several auxiliary planes
are employed in perspective, and particular^
the four following:—

1. The horizontal plane A B (Fig. 572), on which the
spectator and the objects viewed are supposed to stand;
this is therefore generally termed the ground plane or
geometrical plane.

2. The plane C R, which has been considered as a
transparent plane placed in front of the spectator, on
which the objects are delineated. It is called the plane
of projection or the plane of the picture. The intersec¬
tion c D of the first and second planes is called the line
of projection , the ground line , or base of the picture.

PERSPECTIVE.

*229

S. The plane E F passing horizontally through the eye
of the spectator, and cutting the plane of the picture at

right angles in the line H I, is called the horizontal plane,
and its intersection with the plane of the picture is called
the hor izon line, the horizon of the picture, or simply the
horizon.

4. The plane M N passing vertically through the eye of
the spectator, and cutting each of the other planes in a
right angle, is called the vertical plane, and sometimes the
central plane; but as the term vertical plane is applied
to any plane that is perpendicular to the ground plane,
we shall use the term central plane for the sake of avoid¬
ing confusion.

Point of vieiv, or point of sight, is the point where the
eye is supposed to be placed to view the object, as at o
(Fig. 571), and is the vertex of the optic cone. Its pro¬
jection on the ground plane in Fig. 572 is M, and is
termed the station point.

The projection of any point on the ground plane is
called the seat of that point.

Problem I.— To find the perspective of a given point.

Let k (Fig. 573) be the given point, draw the visual ray
k o, which will meet the picture in Jc, the perspective of k,
and it is only necessary now to know how to determine
the position of Jc'.

Since o is the hoi'izontal projection of the eye, if we
draw k o' it will be the horizontal pi'ojection of the visual

ray from k. We shall then have a right-angled triangle,
k o' o, which will be in the central plane M N, and will
consequently be perpendicular to the ground plane A B.
We have already seen that k o, the hypothenuse of this
triangle, cuts the picture in k 1 , and we perceive that the
side k o' of the triangle cuts the base of the picture in P;
and as the two points P Jc are in the plane of the triangle,
and in the plane of the picture, the intersection of the
picture and triangle will be the line P k’ —whence it fol¬
lows, that to determine in the picture the perspective of
k, we draw from that point a line k o', cutting the base

of the picture in p; from p we elevate a perpendicular
indefinitely; we draw then the visual ray k o, cutting
this vertical line in k', which will be the point sought.

Observe that the ti'iangle k o o' is intersected in P k'
parallel to its side o o', and consequently the points of the
triangle will be propoi'tional among themselves; thus
k o' : o o' : : k P : P k 1 , and the height of Jc' , may be ob¬
tained by seeking a fourth proportional to the three lines
k o, o o' , Jc P, which will be P Jc. These three lines may
always be known, for Jc o' is the distance of the object from
the position of the spectator o', called the station point;
o o' is the vertical height of the eye above the ground
plane, and k P is the distance of the object from the pic¬
ture. Thus the distance of the object from the station
point, is to the height of the eye as the distance of the
object from the picture is to the height of the perspective
point in the picture.

The triangles k o' o, L o' o, are similar, since they are
the same height, and are comprised between pai'allels.
These triangles will therefore be proportional; thus V, the
perspective of L, will have the same height in the picture
as Jc, the perspective of Jc.

To obtain the perspective of L, therefore, we can use the
triangle Jc o' o. To do this, pi’oject L upon the hoi'izontal
trace of the centi'al plane, M N in the point Jc, which
may then be considei'ed as the vertical projection of L.

* The x'emainder of the operation need not be described.

Problem II.— To find the perspective of a given rigid
line.

Let A B (Fig. 574) be the given line. From its extre-
mities A B, draw to the eye of the spectator the l’ays A o,
B o. It is evident that, as the pictui'e E F is not cut by
these rays, each of the points will be at the same time
the original and perspective points. Hence we have:—

Rule I. — When a straigJd line lies in the plane of
the picture, it suffers no change, hut its perspective repre¬
sentation is the same as its original.

Let the line D K be situated in the ground plane, draw
from its extremities cl O, k O, the projections of the rays

D o, K O, and we have the triangle D O K, the base of
which will be pai'allel to the line of projection; and con¬
sequently every point in its base, as D K, will be equi¬
distant from the line of projection, and the height of all
the points in the picture will be the same; therefore, the
straight line between the points d Jc, which is the perspec¬
tive of D K, will be pai'allel to the line of projection.
Further, the triangle D o K will be cut by the picture
parallel to its base D K, and the intersection dk will there¬
fore be parallel to that base and to the line of projection.
From this we obtain—

230

PRACTICAL CARPENTRY AND JOINERY.

Rule II.— When an original line is parallel to the
base of the picture, the perspective of that line will also
be parallel to it.

The line A D, it will be seen, is in the central plane;
the triangle d A o is therefore also in that plane, and
consequently vertical. The triangle, therefore, will cut
the picture in the line A d perpendicular to its base. A d
produced would be the trace of a plane perpendicular to
the original plane, which would necessarily pass through
the point of sight. The line A o' will also contain the
projection of the vertical triangle D O' o, and the inter¬
section of the triangle d AO with the picture will be the
line A d, which is the perspective of A D, and it will tend
to the projection of the point of sight.

The straight line B K, which is the base of the triangle
K B O, is not in a plane perpendicular to the original
plane, but inclined to it; for kb is beyond the central
plane, while o is in that plane. Consequently, the pro¬
jection of the inclined plane in which this triangle is
situated, will be the triangle kbo 1 on the original plane,
and its intersection with the plane of projection in the
picture will be B o' ; and, as the intersection B h is part
of B o', the perspective B K is also directed towards the
point of sight. It can be shown that this would also be
the case with all other lines perpendicular to the picture;
and therefore it can be concluded—

Rule III.— The perspectives of all l ines perpendicular
to the picture pass through the point of sight.

Let A B (Fig. 575) be a straight line, making with B C,
the base of the picture, an angle of 45°. The perspective
of the line will be d B, which, being produced, would
meet the horizon in the point d', and this will be the
point of convergence of the perspectives of all lines
parallel to A B. It is easy to perceive that the original
line A B is the base of a scalene triangle ABE, formed
by that line and the rays A E, B E, and which triangle
has its base in the original plane, and its summit in
the eye of the spectator. It will be inclined to both
planes of projection, and will cut the picture in the line

a' B. The vertical projection of this triangle in the pic¬
ture will be the triangle c e' b. Now, any triangle may
be regarded as the moiety of a quadrilateral figure;
therefore, if through E we draw a line E F parallel to
B A, and another A F parallel to the ray b e, we shall
obtain a quadrilateral figure A b e f, double the first
triangle ABE, divided into two equal parts by the diago¬

nal or ray A e. Since, then, the side E F is of the height
of the eye, it will necessarily meet the plane of the pic¬
ture at a point d' in the horizon, and the line d' B will be
the intersection of the plane A B with the picture. There¬
fore the point d’ will be the vanishing point of A B, and
consequently of all the original lines parallel to it.

Suppose perpendiculars let fall from E F upon the ori¬
ginal plane, and we obtain the points ef as the projections
of E and F, draw e B, ef, f A, and we have the quadrila¬
teral AB, ef, for the horizontal projection of the inclined
plane A E. The lines F E, fe, with the perpendiculars E e,
F f form a rectangle e F, or / E, which passes through
the perpendiculars E e, F /. Consequently, this plane is
vertical, and cuts the plane of the picture in the line d cl'.

Observe that the lines Ed', e d, being parallel to A B,
make with the picture an angle of 45°, and therefore that
E e is equal to el d". But E e is the principal ray, or the
distance of the eye from the picture, and therefore d' may
be regarded as the point of distance carried upon the
horizon from e! to cV. Hence we obtain—

Rule IY. — Tlbe perspectives of all original lines
making an angle of 45° with the picture, vanish in the
point of distance.

If the original line make a greater angle than 45° with
the picture, its vanishing point will be found between the
point of sight and the point of distance; and if a less angle,
its vanishing point will be beyond the point of distance;
and the general rule is thus expressed:—

Rule V. — The perspective of an original line,
making any angle whatever with the picture, will have
its vanishing point on the horizon at the intersection
with the picture of a plane parallel to the original line
passing through the point of sight.

We have seen that the principal ray is necessarily
parallel to the lines which are perpendicular to the pic¬
ture, and that its intersection with the picture, or the
point of sight, is the vanishing point for all such lines.
We have seen, also, that the vanishing point of lines
making an angle of 45° with the picture, is at the inter¬
section with the picture of a line drawn through the
point of sight parallel to the original line. And as in
j this, so in the case of any line making any angle whatever
with the picture. Whence follows the general rule.

Rule VI.— The vanishing point for horizontal straight
lines, forming any angle whatever with the picture, is at
the intersection with the picture of a parallel to these
lines, drawn through the point of sight.

To show this geometrically, let ABCDEFG (Fig. 576)

be the horizontal pro-
/ Fls ' 676 ‘ jection, or plan of an

A / original object, H K

\ the picture line, and

g r o the station point ;

then the vanishing

a v ___ k_ ^ o

point of A G, and all
Y | / its parallels, will be

found by drawing
o a parallel to it, to
intersect the picture
'Jy line produced, when

a is the vanishing
point. The vanishing point of A B and its parallels will
be b. The vanishing point of F E and all other lines

PERSPECTIVE.

231

\ /

\ u

e -1

-_A-/

perpendicular to the picture will be the point of sight e ;
and the lines G F, BC, D E, being parallel to the picture,
their perspectives will also be parallel to it.

The rules thus established, enable us to abridge, in
many instances, the operations of drawing perspectives,
as may be thus illustrated.

Let A B c D (Fig. 577) be the plan of a square, o the.
place of the spec¬
tator, e f the line Fig. 577.

of projection, and
O C the central
plane.

Draw ef to re¬
present the ver¬
tical projection of
the base of the
picture, G K the
horizontal line, 0
the point of sight,
and 0 o the ver¬
tical plane. Then
to draw the per¬
spective of the
square, transfer
the side C D to
o b (see Prob. I.,

Rule I.), and draw b a, which is the perspective of the
side B A of the square produced to its vanishing point
(see Prob. I., Rule III.) Then, as the diagonals of the
square form an angle of 45° with the picture, from o,
set off on the horizontal line 0 G, 0 K, each equal to the
distance O C (see Prob. I., Rule IV.), and draw 6 G, 0 K, the
perspectives of the diagonal produced to their vanishing
points, and join the points a d where these intersect the
perspectives of the sides by the line d a, parallel to the
base of the picture (see Prob. I., Rule II.), and 0 d ab will
be the perspective of the square.

If the perspective of the point A alone had to be sought,
the operation would be simply to draw b 0, and to inter¬
sect it by 0 K.

Let it be required, for example, to find the perspective
of an original point A, situated 35 feet from the central
plane of the picture, and 63 feet from the base.

Set off from any convenient scale from 0 to f (Fig. 578),
35 feet, and draw f c, c being the point of sight; set off
from / to b, 63 feet, and draw to E, the distance of the
spectator or point of distance, the line b E, and the inter¬
section of the lines at A will be the perspective of the
point required.

Let it be required to draw
the perspective of a square,

Fig. 678.

situated in the original
plane, at any angle what¬
ever to the plane of the
picture. To solve this
problem it is necessary only
to find the perspective of ~y
a single point, which may be done in various ways.

Let A B (Fig. 579) be the plan of the square, o the
place of the spectator or station point, E K the line of
projection, and O c the central plane. We see that the
point A is on the horizontal trace of the central plane,
and at the distance A c from the picture, and that, there¬

fore, the perspective of A is to be found on the central line,
in the vertical projection o c. Set off the distance A c

from c to g, and draw from g to the point of distance h
the line g h, and its intersection with the central line at
a is the perspective of A. Thus two points in the perspec¬
tive are obtained, as B, being on the base of the picture,
will have for its perspective b.

The vanishing points of the sides of the square are
found to be K and m, by drawing parallels to these sides
through O to meet the picture. Transfer the distances,
therefore, K and m, to the horizon line e f in n p, and to
these, from b and a, draw the perspective representations
of the sides of the square. The operation is shown re¬
peated above the horizon, the same parts being indicated
by the same letters accented.

In the examples hitherto, we have operated by methods
more or less indirect; it is now necessary to show the direct
method of solving the same problems.

Let it be required to draw in perspective a square the
same as the last. From the station point o (Fig. 580),
draw to the angles of the square abed visual rays o a,
O b, &o., and find the vanishing points m' k' as before.
Draw in the vertical projection the ground line m k, and
the horizon n p, and transfer to the ground line the in¬
tersection of the visual rays with the picture; draw from
a the lines a m', a k\ and their intersections with the per¬
pendiculars 1, 2, 3, will give the limits of the sides; then
draw a k', b k', intersecting at c, which completes the
square. If, as in the last figure, another square be drawn
at a height above the given plane, equal to the side of
the original square, we shall obtain the representation of
a cube.

Let Abcb (Fig. 581) be the horizontal projections of
four straight lines perpendicular to the picture B D, b d.
The perspective of these lines b a, d c, f e, It g, will con¬
verge to the point of sight i', and if the original lines
were infinite, they would appear to meet in the point

232

PRACTICAL CARPENTRY AND JOINERY.

of sight. These lines may be regarded as the boundaries
of four planes, two horizontal, one / g above, and the

Fi*. 580.

other b c below the horizontal plane, and two vertical,
be, d g ; and as the boundary lines of these planes may be
considered as of infinite extent, so may also the plaues them¬
selves. It is obvious from the figure, that the perspectives
of any line situated in a horizontal plane, can never in
any case pass the hori¬
zon ; that the horizon is
in like manner the van¬
ishing line of all hori¬
zontal planes; and that
the trace of the central
plane is the vanishing
line for all vertical planes
parallel to it.

In the example the
vertical planes are shown
to be squares, and their
diagonals are conse¬
quently inclined to the
picture in an angle of
45°. The perspectives of
these diagonals will have
their vanishing points in
the vanishing liues of
the planes which contain
them, or in the trace of
the central plane. The
distance i k, i l of these
points k l, will be equal
to the distance I i of the eye from the picture. The dia¬
gonals of the horizontal planes will have their vanishing

points in the point of distance, as we have already seen.
The plane A c being parallel to the picture, will have for

its perspective the si¬
milar square a e g c.

The line b c is evi¬
dently inclined to the
ground plane, and it
is also situated in a
vertical plane per¬
pendicular to the pic¬
ture. Its perspective
will therefore have
its vanishing point
in the vertical of the
picture, and in a
point to which wdll
be more or less high,
as the inclination of
the line is greater or
less. The perspec¬
tives of the diagonals
of the side d g will
have their vanishing
points in n to. From
this we deduce—
Rule YII.— All
lines inclined to
the horizon, parallel
among themselves,
and inclined in ver¬
tical planes perpen¬
dicular to the pic¬
ture, have their vanishing points in the vanishing line
of the planes which contain them.

Rule VIII. — The perspectives of planes parallel to
the picture cannot have vanishing points, but will always
be of the same figures as their originals.

Further to illustrate the vanishing points of inclined
lines, let A bc D (Fig. 5S2) be two original parallel lines;
their perspectives will beaBcD; the direction of which
will be to the vanishing point E, situated at the inter¬
section of the picture with a plane E /, passing through

the eye F, parallel to the planes of the triangles A a !’.,
cud, passing through the given original lines.

PERSPECTIVE.

233

The line F E is a line parallel to the given lines drawn
through the eye to meet the picture. As it is in the
plane E /, its intersection with the picture determines the
vanishing points of the lines a B, c D.

This problem may be considered in a different manner.
Let A B C D (Fig. 583) be the original lines as before:

but in place of supposing them situated in two triangles,
let us suppose them situated in a plane B c, inclined to
the original plane. Let the plane G E, passing through
the eye F, be parallel to B C, and let it cut the picture
in the line H E, which, as we know, will then be the
vanishing line for all planes parallel to B c. The line F E
is drawn through the eye parallel to the original lines
given, it lies in the plane G E, and cuts the picture in E.
It lies also, however, in the plane / E, and therefore E is
the vanishing point sought.

Let us consider the practical application of this problem,
with the view to its more perfect elucidation:—

Let A B (Fig. 584) be the plan of a cube, and c D the

elevation of one of its sides, with diagonal lines drawn on
it. Draw the visual rays o A, o B, the central plane o M,

the picture line H L, and the lines O H, O L, to determine
the vanishing points of the sides. Then to find the
vanishing points of the oblique lines; from O in the
ground plan, on the line O L, construct a right-angled tri¬
angle O L N, of which the angle N O L is equal to G c D,
and set up the height L N, from l to n, in Fig. 585, which
gives n as the vanishing point for C G and all lines parallel
to it. Set the same length oft' downwards from l to on,
and to is the vanishing point for F D, and all lines parallel
to it. In the same way find the vanishing points on the
left-hand side, by drawing the triangle O H K, and set off
the length H K in h and r above and below the vanish¬
ing point s of the horizontal lines of the cube. The
reason of this process is obvious, for we have only to
imagine the triangles OLN, o H K, revolved round o L
and O H until their plane is at right angles to the paper,
and we then perceive that N and K are the heights over
the horizontal vanishing points, that a plane passing
through o at the height of the eye of the spectator, and at
45° with the horizontal plane, would intersect the plane
of the picture.

The drawing of the figure is explained by the dotted
lines.

In what we have hitherto advanced are comprehended
all the principles of perspective, and we shall now pro¬
ceed to apply these principles in the solution of various
problems.

Problem III.— The distance of the picture and the
perspective of the side of a square being given, to com¬
plete the square, without having recourse to a plan.

1st. When the given side is parallel to the base of the
picture, let a b (Fig. 586) be the side of the square, o

the point of sight, d the
point of distance. Draw
a o, b o, for the indefinite
perspectives of the side,
and a d for the perspec¬
tive of the diagonal, and
where it intersects b o
in c, draw c e parallel
to a b, and the perspec¬
tive of the square is completed.

2d. When the diagonal of the square is perpendicular

to the base of the picture, let a (Fig. 587) be the hither
or nearest angle of the square, O the point of sight, d d'
the points of distance. The diagonal of the square being
perpendicular to the picture, will have the point of sight
for its vanishing point. Draw, therefore, a O as its inde¬
finite perspective. Set off from a to b the length of the
diagonal, and draw b d intersecting a o in c, which is the
perspective of the farther extremity of the diagonal; then
draw the sides (which make angles of 45° with the pic¬
ture) to the distance points d d’.

3d. When one side of a square is given, making any
angle with the picture; let a b (Fig. 588) be the given
side; produce it to the horizon in c. Set oft the distance

2 G

a b

234

PRACTICAL CARPENTRY AND JOINERY.

of the eye on the central line, from E to F, and draw c F,
which will be a parallel to the given side a b, and c is

consequently the vanishing point for all lines parallel
to a b.

The point a belongs equally to two sides of the square,
one the given side a b, the other the hither side of the
square. Let us see how this latter is to be found. As
this side makes a right angle with a b, from F draw
F g at right angles to F c, and continue it till it meets
the horizon. In this case the lines would extend beyond
the limits of the paper, and to avoid that inconvenience
we may adopt another method of working, viz., by the
diagonal. Therefore, from F draw F d, making an angle
of 45° with F c, and its intersection d with the horizon
will be the vanishing point of one diagonal of the square.
From F also draw F h, at an angle of 45°, with F c for the
vanishing point h of the other diagonal.

Now to complete the square, draw from the extremities
of the given side the perspectives of the diagonals a d,b h,
and produce the latter indefinitely; and to find the length
of the sides, take the following means, founded on what
has previously been learned.

Through the intersection of the diagonals at o draw a
straight line m n, parallel to the base of the picture, and
make o n equal to o m, and n will be a point in the side
of the square, through which draw r s, intersecting the
diagonals, and join b s, a r, and the square is com¬
pleted.

Problem IY. —To divide a line given in perspective
in any proportion.

Let A B or B c (Fig. 589) be the given line, and let it
be required to divide it
into two equal parts.

Now, A B being parallel
to the base of the picture,
will have its perspective
exactly the same as the
original, and if divided
into equal parts, its per¬
spective will also be di¬
vided into equal parts.

But B c being oblique to
the base of the picture will, in reality, be divided into
two equal parts in the point e, although these parts appear
unequal.

If through A and c we draw a line produced to the
horizon, the point o will be the vanishing point of all
lines parallel to A o. Hence, if we draw do,bo, these

Fig. 589.

Fig. 590.

three lines will be parallel among themselves. And as
the lines A B, B c, are comprised within the parallels A o,
B O, and are cut by the third parallel D o, it follows that
their parts are proportional among themselves. And,
therefore, if A D is the half of A B, c e will be the half
of B c.

The same will follow if the lines are in the vertical
plane, as k g divided into two equal parts in o.

From what has been stated it will be seen that the
problem reduces itself to these cases:—1. When the line
is situated in a plane parallel to the picture, the divisions
are made as in any other straight line. 2. When it makes
any angle whatever with the picture, we draw through
one of its extremities a line, either parallel to the base, or
to the side of the picture, accordingly as the given line is
situated in a horizontal or vertical plane, and we divide
this line into the number of equal parts demanded; then
through the last division, and through the other extremity
of the given line, we draw a line produced to the horizon,
and from all the points of division draw parallels to
this line, which will, by intersection, give the perspective
divisions of the line required. For example, let it be

required to divide
the line m n (Fig.
5 90) in to three equal
parts; through n
draw the horizontal
line n 3 indefinite¬
ly, and set along it
three equal divi¬
sions of the com¬
passes, opened at pleasure in 1 2 3, through the last divi¬
sion, and through m di'aw a line to the horizon, inter¬
secting it in o, which will be the vanishing point of all
parallels to 3 o, and of course of the lines 2 o, 1 o, and
by drawing these the perspective line m n is divided into

three equal parts.

When the given line is in¬
clined both to the picture and
the ground plane, as A B (Fig.
591), it is necessary to find
the divisions, first on its hori¬
zontal projection A b, and
through them to draw ver¬
tical lines which will cut the
perspective line in the points required..

Problem V. — Through a given point in a picture to
draw a line parallel to the base or side of the picture,
and perspectively equal to another given line A B.

Let a (Fig. 592) be the given point. From it draw an
indefinite line parallel to the base of the picture, or to its
side, and then to determine on either of these lines a
length perspectively equal to the given line, draw through
a any line at pleasure, cutting the base of the picture, say
at o, and the horizon at e. Set off from o a length, 0 b,
equal to the given line, and draw b e, which will cut the
indefinite horizontal line in g, and a g will be equal to
A B. In the same way proceed to obtain the length of
the line a f parallel to the side of the picture.

It is easy by this means to find the perspective height
of a figure at any distance from the base of the picture. Let
r, for example, be the point on the original plane at which
the feet of a figure are supposed to be situated, and it is

PERSPECTIVE.

235

required to know its height, and suppose A B the real
height of the figure, then through r draw a horizontal

from a or b draw a o, 6 o, which will be the perspective
direction of the diagonals of the square, and their inter-

Kig. 592.

line cutting the parallels O e, b e, in s and t, and t s will
be the height sought, which has to be carried vertically
from r to H. Or otherwise, from the point of intersection
t raise a perpendicular, which gives the point li, and t h
will equally be the height sought.

Problem VI.— To draw the perspective of a pavement
of squares, two of the sides of tice squares being parallel
to tlce base of the picture.

The squares having two of their sides parallel to the
case of the picture, their other two sides will have for
their vanishing point the point of sight, and the point of
distance will be the vanishing point of the diagonals.

No plan is required. Set off on the base of the picture
at 1 2 3, &c. (Fig. 593), divisions equal to the sides of the
square, draw through these to the point of sight O, lines
which are the perspectives of the sides of the squares,
perpendicular to the picture, and intersect these by a
diagonal drawn from any point, as 1 to D, the point of
distance, and through the points of intersection draw lines
parallel to the base of the picture. The squares can be
extended so as to fill the picture by extending the base
line and setting off more divisions. But if there is not
room to do this, any of its parallels, as A B, may be pro¬

rig. 593.

sections with the perspectives of the sides produced will

give their points.

Problem VIII. — To draw the perspective of a pavement
of squares, the sides of which form any angle with the
picture.

Let A B (Fig. 595) be the horizontal projection of the

Fig. 595

s' o' V

|jg

\ \ *

12 3 4

/ "r— n

A /1 2 / 3/^

C 7

/ 5 /f? / 7 rt

Ux/ / . > J

\ 7il

duced, and the perspective lengths of the side of the
squares set out on it, and again as at E F if necessary.

Problem VII.— To draw a pavement of squares in
perspective, when the sides are inclined at angle of 45°
to the base of the picture.

In this case let a b (Fig. 594) be the side of the square,
and its diagonal will consequently be a 1. Lay off along
the base of the picture the divisions 12 3, &c., each equal
to the length of the diagonal. Now, as the sides of the
square make angles of 45° with the picture, the distance
points will be their vanishing points, and nothing more
is required to be done than to draw from 12 3, and to
D D the lines 1 d, 2d. If it is required to fill the space

base of the picture, cutting the squares (of which only
r> two rows are here shown) at any
angle.

Transfer to the vertical projection a b of
the base of the picture the divisions 1, 2, 3,
4, 5, G, 7* Through the seat of the eye O
draw O p parallel to the sides of the squares,
and p will be the vanishing point for them.
Transfer the distance of p from the central
plane op to the horizon at o' p, and draw 1 p
2 p', &c., which gives the perspectives of the sides of the
squares parallel to to n, and we have now to find those
which are perpendicular to them. This we might do by
finding their vanishing points; but this mode would be
inconvenient, as it would extend the vanishing point far
beyond the limits of the paper, and we shall rather operate
by the diagonals. Draw therefore through o, the seat of
the eye, the lines o s, o t, parallel to the diagonals, to
meet the picture-line produced in s t, and transfer o s, o t

* This is most conveniently done by transferring them first to the
edge of 'a strip of paper, from which they can be transferred to the
picture-line.

230

PRACTICAL CARPENTRY AND JOINERY.

to the horizon-line in o' s', o' t'. Then transfer the points
4 , or v, where the diagonal meets the pictui'e-line A B, to
the vertical projection of the picture-line a b, and from
these points draw lines to the vanishing points, as shown
in the figure.

Problem IX. — To draw a hexagonal pavement in
perspective, when one of the sides of the hexagon is
parallel to the base of the picture.

Let A B (Fig. 596) be the given hexagon. Set off along
the base of the picture, divisions equal to the side of the

hexagon, then draw its diagonals, which will divide it
into six equilateral triangles, and find the vanishing
points of the diagonals. This may be done in the follow¬
ing simple manner. Let o be the intersection of the
central plane with the horizon, and 0 C be equal to the
distance of the spectator; then from C draw the lines
c D, c D, parallel to the diagonals of the hexagon, and
their intersection with the horizon in the points D D will
be the vanishing points of the diagonals. The remainder
of the operation requires no description.

Problem X.— To draw the perspective of a circle.

Let a b a b (Fig. 597) be the projections of the picture,

c c those of the eye, o the point of distance, ijkl the
given circle.

The most expeditious method of operating is to cir¬
cumscribe the circle by a square. The circle touches the
square at four points; and if the diagonals of the square
are drawn, they intersect the circle at four other points,
which gives eight points, the perspectives of which are
easily found.

Thus, then, we draw the perspectives of the square and
of its diameters and diagonals, and then project on the
base of the picture a b the points I J K L in k' and l' and
k" and l", and from these points draw the lines k" c, l" c,

which cut the diagonals in i j 1c l, and through these
and the four others E F G H the circle is to be traced
by hand.

As the circle is a figure which has very frequently to
be drawn in perspective, we shall consider it under an¬
other aspect.

Let there be any number of points taken in the cir¬
cumference of the original circle (Fig. 597), and suppose
lines drawn to them from the eye c, as the tangents M c,
N c. Now it is evident that the collection of all these
lines forms the projection of a scalene cone, having its
base circular, and its summit in the eye of the spectator.
Let us conceive this cone cut by the plane of the picture,
and its section in the picture will be the perspective
of its base or of the given circle. This operation can
be performed by the rules of descriptive geometry, and
the result will be the same as by the problem above'. The
perspective of this circle is, then, necessarily an ellipse,
since it is the result of the section of a cone by a plane
which passes through both sides, and is not parallel to its
base. It is further to be observed, that in the ellipse the
principal axis to n does not pass through the point o, the
perspective of the original centre of the circle, but is the
perspective of a chord M 1 ST, determined by the tangents
M c N c.

Problem XI.— To inscribe a circle in a square given
in perspective, and of which one side is parallel to the
base of the picture.

We know by the preceding problem that the ellipse
should touch the four sides of the square in their apparent
or perspective centres at the points e, f, g, li (Fig. 598).
We can, therefore, consider the line e f as the minor
axis of the ellipse which we seek; and as we know that
the major axis should cross it perpendicularly in its centre,

Figs. 598 and 599.

we divide e f into two equal parts, and through i, the
centre of the ellipse, draw perpendicularly to e f an inde¬
finite line, which will be the direction of the major axis,
of which we have to determine the length. Take f i, or
i e, and carry it from h to j, and draw through h and j a
straight line to the minor axis at 1c, and h lc will be equal
to half the major axis which we set off' from i to l and to.
Having now the major and minor axes of the ellipse, it is
easy to draw it with the aid of a slip of paper, or in any
other way.

In the next figure the same method may be thus ap¬
plied:—-

Let a c (Fig. 599) be the given square; through the
intersection of its diagonals draw / e, and divide it into
two equal parts in i, and through i draw an indefinite
line parallel to g h. Through q, the perspective centre of
the circle, draw a line perpendicular to g h, and produce
it both ways, when it will cut the side d c in s, and the
line l to in r. Carry the length s r fi'om g or h upon l to
to p or y, and draw g p or h y to cut s q in the point o,

PERSPECTIVE.

237

Fig. 600.

ftud either of the lines gp o or hy o will be the rule with
which to operate in describing the ellipse as before.

If it is required to divide the periphery of the circle
into any number of parts, equal or otherwise, it may be
thus performed:—

Though the points of division, on the geometrical plan
of the circle (Fig. 600), draw radii, and produce them to
intersect the sides of the cir¬
cumscribing square. Then
from the intersections visual
rays may be drawn, and the
corresponding points obtained
in the perspective square,
from which radii drawn to
the perspective centre will
cut the perspective circle in
the points required.

But we may in most cases
dispense with the visual rays, and obtain the perspective
divisions of the square by Problem IV., thus:—

From the hither angle A of the square (Fig. 601) draw
any line, as A B, A G, equal to the side of the square on
the plan, and on it set off the intersections of the radii.
Then from B draw through c a line cutting the horizon
in D, and from G through F a line cutting the horizon in
E, and from the divisions of the line A B, A G, draw lines
to these points, which will divide A c, A f perspectively in

Fig. 601.

Through the divisions in the plan of the circle (Fig. 602),
draw lines parallel to one of the sides of the square, and pro¬
duce them to intersect any of its sides, and from the per¬
spectives of these intersections draw lines to the vanish-
ing point of the side, to which the lines drawn through
the divisions of the circle are parallel.

Perspective of Solids.

Problem XII. — The horizontal projections of two
tetrahedrons being given, to draw the perspective of the
solid.

~ Fig. 603.

_ D o n

the same ratios, and from these divisions in A c, A F, draw
radii to the perspective centre, which will divide ,
the quadrants of the periphery of the circle, as re¬
quired. Repeat the operation for the other sides.

Let A b, a b (Fig. 603) be the projections of the picture,
c the point of sight, D D the points
of distance,

E F G h, I K L TO the
horizontal projections of the two given
tetrahedrons, one of which is placed on its
base, and the other on its summit.

Draw the perspectives of the horizontal
projections, then through h, the horizontal
projection of the summit, raise the perpen¬
dicular h H.

Problem XIII.— The projections of two
[| equal cubes being given (Fig. 604), one placed on one of

Fte- 664 Central

Distance

Fig. 602.

plane

There is yet another method, which is of very great
pplicability.

its angles, and the other on one of its arrises, to draw
them in perspective.

238

PRACTICAL CARPENTRY AND JOINERY.

Here the operation is so simple that no explanation is
required.

Problem XIY.— To draw three equal given cylinders
in perspective (Fig. 605).

It is not necessary to repeat the method of putting a
circle in perspective, but it may be well to observe, that

the upper surface of the cylinder may be so near the hori¬
zon that it is physically impossible to inscribe an ellipse.
In such a case an approximate solution is all that can be
arrived at. A few principal points should be obtained,
and the ellipse traced by approximation.

This example presents a singularity, which at first sight
appears a paradox, and yet is nothing less than that. The
cylinder A, although evidently further from the eye than
B, and seen consequently under a less angle, appears in
the picture to have a greater diameter. The reason is,
tli at its optical cone is cut more obliquely by the picture
than that of B, and hence the intersection of A is longer.
This, which is held to be a proof of the incorrectness of per-
spective, is, on the contrary, a proof of its correctness; for,
if the subject is attentively considered, and we proceed to
view the picture under the same conditions as to distance
and height of the eye, as we have supposed to exist in
viewing the object itself, we shall perceive that the repre¬
sentations of the objects must be seen under the same
angles as the objects themselves, and therefore, although
the diameter of the further column measures more in the
representation than that of the nearer one, yet, from the
proper point of view, the angle under which it is seen is
less, and therefore it will appear to be smaller. The
result, although geometrically correct, is yet a distorted
representation, when viewed in the way we usually look
at a picture. It is a correct section of the cone of rays,
but not made by a plane so situated relatively to the
object and spectator, as we should place a picture or a
transparent plane through which to view the object.
Before proceeding further, we shall take the opportunity
of making some remarks on the conditions under which
objects may be properly represented.

The greatest angle under which objects can be viewed
with distinctness is one of 90°. But when viewed under
this angle, it is with such an effort as to produce an un¬
comfortable sensation. Let us, however, suppose that

Fig. 606.

we view an object under an angle of 90°, and we may
consider the sum of the rays which can enter the eye
under that angle as forming a cone, having the eye at
its summit. Now, according to our proposition, the only
objects which can be distinctly seen are those contained
within the base of the cone. A picture is in this con¬
dition. Let ah, A B (Fig. 606),
be the projections of the base of
a square picture. Now, in order
that this may be inscribed within
the base of a right-angled cone,
it is necessary that the axis of
the cone be equal to the radius of
the circle of its base. Thus from
c, the centre of the picture, with
c a or c h as radius, we describe a
circle which contains the whole of
the picture. We carry the radius
in the horizontal projection from
c to c', and the line c d will of
course be the shortest distance
which we should take in order
to see distinctly the picture A B.
If we make a right angle at c,
we shall have an isosceles triangle, of which the base
o o will be equal to the diameter of the base of the
cone. Now this distance c c', which is sufficient for the
picture ABora h, is too little for the picture a G, which
has the same base as A B, but a greater height, or for
a H, which has the same height, but a greater width;
for neither of these are contained entirely within the
optic cone o d o, but require the base of the cone to be
increased to p p. The distance, therefore, ought to vary
with the height or width of the picture. So much for
the principle; but we have said that a lesser angle than
90° is better to be adopted, and it is not easy to give any
rule for this. In general, however, the distance should
never be less than the diagonal of the picture, which
would give o r o as the angle under which the square
picture A B or ah should be viewed, and p s p for the
others.

The distance, too, should depend in some measure on the
height of horizon assumed, and in general the higher the
horizon the greater should be the distance.

We now have to speak on a point to the misconception
of which we attribute much that has been said against the

art of perspective.

The central plane, it will be remembered, was defined
to be “ a plane passing vertically through the eye of the
spectator, and cutting the ground plane, the horizontal
plane, and the plane of the picture at right angles/' Now
let us take the horizontal projections of an object A A
(Fig. 607), the picture B B, the eye of the spectator c, and
the central plane c D a. The picture is parallel to the longest
side of the object, and the central plane bisects the angle
formed by the visual rays which proceed from the extre¬
mities of the object to the eye. This, then, we assume to
be the correct conditions of a picture; but suppose it were
required to introduce into the same picture other objects
B B, as seen from the same point of view, we should no
longer place the picture parallel to the long sides of the
object, with the face of the spectator directed towards
a, but we would again bisect the angle formed by the

PERSPECTIVE.

239

visual rays proceeding from the extremities of tlie object
to the eye of the spectator by the central plane c E, and
make the line of the picture perpendicular to e E, as at F F.

Perspective has been divided into parallel and oblique
perspective, and this division has introduced the miscon-

Fig. 607.

ception animadverted upon. Parallel perspective, so called,
can only exist when the central plane, bisecting the angle
formed by the visual rays, bisects also the object to be
represented. Nevertheless, in views of interiors, of streets,
and in architectural representations generally, it is un¬
scrupulously used, although the intersection of the central
plane with the picture is at one-third of the width of the
latter.

In the figures CAB (Fig. 608), three different repre¬
sentations of the same interior are given to illustrate these

Fig. 608.

B A 0

HI \/ 1

ipP

1 i\X

1 111

ipr n

™

(ivA

remarks. In fig. C the central plane bisects the visual
angle; and the lines of the further side of the apartment,
being parallel to the pictui’e, are also parallel in the repre¬
sentation. In A the central plane does not bisect the
visual angle, but is at one-third of the width of the pic¬
ture; and this is the condition animadverted on. If it be
desired to have the point of sight not in the centre of the
apartment, like C, but at one side, then the representa¬
tion is only correct when it is like B, in which the cen¬
tral plane bisects the picture, and the lines of the further
side of the apartment being no longer parallel to
the picture, have their proper vanishing points.

To revert to the example which has led to this
digression, we observe by Fig. 605, that the
distortion arises from assuming a position for the picture
in which the central plane does not bisect the visual angle.
But let us place the picture in the position E F, in which
it is perpendicular to the central plane O C, bisecting the
visual angle, and we have the cylinders in what is called
oblique perspective (a distinctive term which should not
exist), and there is no longer any distortion.

Problem XV. — To drcm a sphere in perspective.

Let a h, A B (Fig. 609) be the projections of the pic¬
ture, c e' those of the eye, the circle D that of the given
sphere. If the centre of the sphere is at the height of
the horizon, the vertical projection of its centre will be

the point of sight d. Draw from the eye c the tangents
E c F c. Draw also the chord E F, which may be re¬
garded as the base of a cone formed
by the visual rays, tangents to the
sphere, and of which the eye c is the
summit. The section of this cone
by the picture will be a circle, since
the cone is cut parallel to its base.
This circle will have for its diameter
e /; and consequently c f or c e as its
radius. Then, if with this radius from
the centre d we describe a circle, it will
be the perspective sought.

When the sphere is below the
horizon, let D (Fig. 610) be the hori¬
zontal projection of a sphere, c that
of the eye, and L M the picture-line.
Draw visual rays tangents to the
sphere, and we obtain on the picture-line e f as the per¬
spective horizontal diameter of the sphere. At K set
off the diameter e f so obtained, and from the points e f
raise indefinite perpendiculars. Now, suppose D to be the
vertical projection of the sphere, and d the vertical pro¬
jection of the eye. From c' draw visual rays tangents to
the sphere, and we obtain r s as the intersection of the
cone of rays by the picture, and the length r s as the per¬
spective vertical diameter of the sphere. But the diameter
r s is greater than the diameter e f, and therefore the
perspective representation of a sphere viewed under the
conditions premised, must be an ellipse. When we obtain
the two diameters, we obtain all the measurements neces¬
sary for the representation of the sphere when below the
horizon, and in the central plane, viz., the major and
minor axes of the ellipse, and the curve may be tram¬
melled by the aid of a slip of paper.

The point g in which the sphere touches the picture is
the projection of its centre, and of its axis D g, and its
perspective representation is h. In this there is another
of those apparent contradictions, for it is certain that a

c> Ilctiaov

sphere always appears to us to be round on whichever
side we regard it; while in perspective, in every case
except that in which its centre is in the point of sight, it
must be drawn an ellipse with its major axis directed
towards the point of sight. An attentive consideration of
the figures and description will render this evident, and
the reader may also advert to the explanation of this
apparent contradiction, which is given in the text treat¬
ing of Figs. 605—607. We shall now proceed to give
some other examples of spheres in perspective.

240

PRACTICAL CARPENTRY AND JOINERY.

Let A B, ci b (Fig. 611), be the projections of the picture,
c c' those’of the eye, d that of the given sphere in contact
with the ground plane. Draw from the eye the tangents
E c, F c, through E and F, draw parallel to the picture the

lines E G, F H, and draw also as many parallels to them,
IK, op, lm, &c., as may be considered necessary. These
parallels, then, are traces of vertical planes cutting the
sphere parallel to the picture, and all the sections made
by them will be so many circles, which will comprehend
all the visible portion of the sphere, as determined by the
tangents E c, F c. The perspectives of the circles H F, I K,
&c., which are parallel to the plane of the picture, will
also be circles. If we envelope all these perspective
circles by a curved line, this line will be the perspective
of the sphere. It is easy to find the perspectives of the
circles. First draw the diameter r s, which will be the
horizontal projection of one of the axes of the sphere, pass¬
ing through the centres of the circles H F, I K, L M, &c.
Find then the perspective direction of that axis; observe
that the point r is raised above the ground plane by the
height of the radius of the sphere, and that it touches the
picture. Its perspective consequently will be in R, and
as the axis is perpendicular to the picture, its vanishing
point will be the point of sight c'. Having drawn R (f,
the perspective of the axis, find on it the centres of the
circles. Find first the diameter of the circle E G : through
l, the centre, draw l C, cutting the picture in l, and from l
raise a vertical line cutting the axis R c' in V, the centre
sought. The radius l E has for its perspective the radius
V e, with which, from the perspective centre l, we describe
the circle e e, and so on for all the other circles, and
finally we circumscribe them by the elliptic curve.

This method is a little long, and has not all the pre¬
cision which could be desired, for the two axes of the
ellipse have not first of all been determined, which would

simplify the operation; but this figure was necessary to
show that the union of all the circles contains all the
visible parts of the sphere, and forms an ellipse in the
picture; and, moreover, it was absolutely required for the
understanding of the following method, which is a conse¬
quence of it, but which is much more simple and precise.

After having drawn the tangents E C, F C (Fig. 612), the
lines EG, F H, and found the point R, we draw the line
R c, and produce it indefinitely towards R. We then
seek on A B the intersections of the centres 1 6 of the
circles EG, FH, and from 1' 6' raise to the picture ver¬
ticals which cut the direction of the major axis in 1" 6".
We take the perspective of the radius E 1, which is e 1 or
6/, and in the picture from 1" and 6" as centres, and with
el or / 6 as radius, describe an arc to the right and left
on R d to the points 7 and 8, and the line 7 8 will be
the major axis of the ellipse. We divide this into two
equal parts, and through the middle 9" draw a line
vertical to the picture-line a b, producing it to the hori¬
zontal projection of the picture-line A B, which it will cut
in 9'. From the point of sight C we draw through this
point a line produced to meet the diameter r s, and from
the point of intersection 9' we draw parallel to the picture

a line I M ; from I we draw a line I c which cuts A B in
l. We then take l 9', the perspective of the radius L 9',
and from 9" as a centre cut the direction of the minor
axis in 10 11, and the minor axes will be determined.
Having the two axes, the ellipse is easily traced.

Practical Examples of Perspective Drawing applied
to Architecture, &c. — Plates CYII.—CXI.

Having thus described the principles of perspective, and
shown their application to the drawing of elementary
figures, we propose now, with the view to their more

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PERSPECTIVE.

241

perfect illustration, to show their application to the
drawing of architectural and other objects.

Plate CVII. — Fig. 3 is the plan of a cross, and A w,

Fig. 4, is a vertical section of the same.

Having selected the position of the spectator, or station
point S, we draw from it visual rays, including as much
of the object as we wish to represent. The angle included
b} 7 these visual rays is then bisected, and the central plane
S o drawn. The picture-line x Y is next drawn at right
angles to the central plane, and then the vanishing points
are found by drawing from the station point lines, s w, s v,
parallel to the sides of the object, to intersect the picture¬
line. The point of intersection, or vanishing point, for
the left-hand side of the figure, is at X; the vanishing
point for the right-hand side, and the lines parallel to it, are
beyond the limits of the paper. We have advisedly chosen
in this case such a point of view for the picture, and such
a distance as would throw one of the vanishing points
beyond the limits of the paper, as such conditions of both
station point and vanishing points are of constant occur¬
rence in practice, and it is right that the learner should at
the outset be made acquainted with the difficulties of the
art and the means of overcoming them. These means in
such cases may be two. The first and most ready is to fix
slips of lath to the drawing-board, on which the horizon¬
line maybe extended to the requisite distance. The other
is to draw the converging lines by the centrolinead in¬
vented by Mr. Nicholson. This instrument, however, is
not much used, probably because it requires frequent alte¬
ration to adjust it to the various vanishing points. We
prefer the simple plan of fixing laths to the board, and
inserting at each vanishing point a needle, against which
the straight-edge may work as a centre. We shall now
proceed to describe the process in detail.

We have already described the manner of drawing the
extreme visual rays, picture-line, and central plane; these
being drawn, we proceed to draw the visual rays from the
various points of the plan edcabcde, and//,//, gg, gg,
and by producing to meet the picture-line X Y, the sides
of the cross and the steps Bg 1, c 4, D 5. From the
points 1 2 3 4 5, where these intersect the picture-line,
we let fill indefinite pei’pendiculars. These lines being
in the plane of the picture will have the original heights
of the object. Intersecting, therefore, these by horizontal
lines from the different heights in the section of the cross
A w, we obtain the heights of the different parts of the
cross represented by the lines 1 2 3 4, brought into the
plane of the picture. Now let us trace the drawing of
any point in the plane, as A or B, to its perspective repre¬
sentation. From B, which is one of the angles of the shaft
of the cross, draw the visual ray B b cutting the picture¬
line in h ; and from b draw towards the ground plane of
the perspective representation in Fig. 4 the line b b, which
is an indefinite representation of the angle or arris of the
shaft. Then, from the figure B n on the left, draw from
the heights of the different horizontal divisions of the
shaft, lines to the right-hand vanishing point, and we
obtain their perspective heights on b b. In like manner
we obtain the perspective representation of the points
and the lines which join them, representing on the plan
one of the limbs of the cross, by first drawing the visual
rays, and then letting fall perpendiculars from the intersec-’
tions of these with the picture-line, and intersecting these

perpendiculars by lines drawn from the left-hand section
B H to the vanishing point. It is not necessary to parti¬
cularize farther the drawings of this figure; the letters
will enable the reader to follow the lines, and from his
previous knowledge he will be able to reproduce a per¬
spective so simple.

It will have been observed, that the labour of drawing
is abridged and simplified by producing the lines of the
object on the plan to the picture-line, a method of proce¬
dure which we shall adopt as much as possible in all the
illustrations.

It may be as well here to show how an object may be
drawn under any angle of view, that is to say, how the
extreme visual rays may be made to include such an angle
as may be determined upon. Let abcd, Fig. ], be any
object, which it is required to delineate as seen from a point
of sight G, under the angle of view AGO, &c. Let ef be
the picture-line. In Fig. 2, construct on the base B c the
triangle B A c, the included angle B A c being the angle
required. Then, from the point c, Fig. 1, draw c G parallel
to A B, and from A draw A G parallel to A c, meeting in
the point G; bisect the angle A G c by the line G o, and at
any required distance from the object draw E F perpendi¬
cular to G O, and the object will then be seen under the
angle AGO equal to bac, and EE will be the picture-line.

The next illustration is a pavilion, the plan of which
is seen in Fig. 5, and the half elevation in Fig. 6. Let s
be the station point. From s draw the extreme visual
rays, including all parts of the plan, and bisect the angle
by the central plane S O; then proceed to find the van¬
ishing points by drawing from s the lines S w, s v parallel
to the sides of the plan to meet the picture-line x y, and
from the various points of the building draw visual rays
E e, F/, D d, &c., to meet the picture-line. Then, having
drawn the ground line Q z, Fig. 7, and the horizon-lino
H H, and the central plane s o, and set off on the horizon¬
line the right and left hand vanishing points: at the in¬
tersection of the visual ray from F, the hither angle of
the building, let fall a perpendicular to the ground plane,
Fig. 7. Produce F F, Fig. 5, to meet the picture in f',
and draw the perpendicular F' F". Then from f", where
this perpendicular meets the ground line, Fig. 7, draw a
line to the left-hand vanishing point, to intersect the per¬
pendicular from the visual ray of the point F, and we
obtain the hither angle of the base of the building on the
ground plane. In like manner produce D A to the picture
in a', and draw a' a", on which the heights for the hither
angle of the body of the building are to be set up. The
perspective height of the apex of the roof is obtained by
producing the centre line of the building to the line of
the picture, and on the perpendicular drawn from its in¬
tersection setting up the height of the apex. The hither
angle of the balcony EE touches the picture-line, or comes
into the plane of the picture, consequently is of the same
height in the perspective as in the original. The divi¬
sions of the balcony railing are found by the applica¬
tion of Problem IV. as follows:—At any convenient place
draw the horizontal line 616, and set off' on it from 1 to 6
the divisions required; then from 1 draw to the vanishing
points the lines 1 p, 1 p, intersecting the perpendiculars
let fall from the visual rays of the further angles of the
balcony. From 6 6 through these points of intersection
p R draw lines as 6 Pf, intersecting the horizon in p;

242

PRACTICAL CARPENTRY AND JOINERY.

then to P as a centre draw radii from the points of divi¬
sion 2 3 4 5, and these will divide the line 1 P perspec-
tively in the same ratio, and the divisions can be trans¬
ferred to the balcony by drawing perpendiculars, as in
the example.

In the third example, which is that of a broach, or
tower and spire, seen in plan in Fig. 8, and in half
elevation in Fig. 9, the same method of procedure is
adopted. On the plan, Fig. 8, the square tower abcd,
and its porch g E F k, are represented, and also the spring¬
ing of the octagonal spire / g h h l to n r. The planes
passing through the centre of the plan are produced in
p p' and P G to meet the picture-line, and the heights of
the apices of the gables and the spire are set up on the
perpendiculars let fall from p' and G.

Plate CVIII .—To draw a series of arches in per¬
spective.

Let Fig. 1, No. 1, be the plan of the piers supporting
the arches, and let Fig. 1, No. 2, be the elevation of an
arch. From s, the station point, draw the visual rays,
and find the vanishing points and the centre of the picture
in the usual manner. Draw the ground line Q z, and the
horizon H H, and set off on the latter the centre of the pic¬
ture and vanishing points. The perspectives of the semi¬
circles, forming the arches, are shown obtained at M N in the
plan, and m' n' in Fig. 1, No. 2, in the different methods
illustrated in Problem IX., Figs. 600, 601, and 602. At
M in the plan the intersections of the radii 1 2 3 4, No. 3,
with the curve, and also with B F, are laid down at o 1 2 3
and o' 1'2' 3', and from these points visual rays are drawn
to Q z, and from the points of intersection of these with
the latter the perpendiculars 12 3 are drawn to meet the
radial line drawn to the perspective centre O. The arch
stones may be found in the same way, but in the figure
they are shown as obtained by Problem II. The length
of the line «EF, No. 2, is set off on any line afe, and
through e and f', the perspective representation of F, a
line is drawn to meet the horizon in D. The divisions of
the arch stones on the line E F, No. 2, being then carried
to the line / e, the perspective division of a f' is obtained
by drawing lines from the divisions in / e to D.

Another method of producing the perspective curve of
the arch is shown at N on the plan, and at n' in No. 2.
Through any points in the arch a 1 2 3, lines are drawn
to the plan in a 1 2 o, and a 1' 2' 3', and corresponding
lines a\ 2 o L 2', for the elevation; visual rays are drawn
from the points in the plan, and perpendiculars raised on
Q z, at the points of intersection. To obtain the heights
the line R s is produced to the plane of the picture in T,
and T b is drawn perpendicular to Q z, and on it are set up
the heights of the pier T c, and of the divisions of the arch
a' 1' 2' 3'. Lines are drawn from these to the right-hand
vanishing point, to intersect the perspective representation
of the angle ot the pier, and through these intersections
c al 2 6,are drawn lines converging to the left-hand vanish¬
ing point, intersecting the corresponding perpendiculars.

To draw a circular vault pierced by a circular headed
window.

Fig. 2, No. 1, acb is the elevation of the vault, and
Fig. 2, No. 2, an elevation of its side, with fghkl the
circular headed window. Let s be the point of sight, and
S D the distance of the spectator, that is D, the point of
distance. The positions of the divisions Goo, o o K, are

found by drawing from them lines to the point of distance,
intersecting M N, the perspective representation of L M,
and the perspective of the semicircle in the perpendiculars
outside of the vault is found by the intersection of d D,
c D, &c., with the vertical lines drawn through o o o.
Through these intersections horizontal lines are drawn,
and the points in which they are intersected by lines
drawn to the point of sight s, through the divisions in the
vault d' c H, are points through which to trace the curve
d” c” h" of the circular headed opening.

Plate CIX. — To draw a Tuscan gateway in perspec¬
tive.

Having drawn the plan M M {Fig. 1), and fixed the
station point s, draw the extreme visual rays s B 2 , s B 3 ,
and with any radius, from s as a centre, describe an arc
R R cutting the rays, and from R R describe the intersect¬
ing arcs t t ; draw the central line s o through the inter¬
sections, and the picture-line Y z at right angles to s o.
Then from s draw the necessary visual rays intersecting
the picture-line, and produce also the leading lines of the
object to intersect the picture. Draw the vanishing lines
s V, S w. In Fig. 3 draw the ground-line G G, the horizon¬
line II H, and the central line o o. Proceed now to trans¬
fer the divisions on the picture-line Y z to the line F F,
by describing arcs from N as a centre; and to draw the
perspective, by carrying the heights from Fig. 2 to meet
the lines let fall from the points where the corresponding
lines of the members of the cornice intersect the picture¬
line, as shown by the faint lines in the plate; and from
the points thus obtained draw lines to the xdght-hand
vanishing point. Thus the height B (Fig. 2) is carried
to B 4 , to meet the line let fall from N, the intersection of
B 3 B 3 , Fig. 1, with the picture-line, and from B 4 a line is
drawn to the right-hand vanishing point to meet the line
6 b l , let fall from the intersection of the visual ray s B 3
with the picture-line; thus the heights b l 6 s are obtained.
To obtain b 2 a line is drawn from 6 1 to the left-hand
vanishing point v 3 , to meet the line let fall from the inter¬
section of the visual ray s B 1 with the picture-line.

The pediment may be drawn by finding vanishing
points for the inclined lines, as described at page 232, or
in either of the following manners. Produce the centre
line a A 1 (Fig. 1), to meet the picture-line in A 1 . Transfer
the point A 1 to F F in A 2 , and let fall the perpendicular
A 2 A 3 . Draw horizontal lines from the heights of the
pediment cornice intersecting this last line, and also the
other intersecting lines of the different mouldings. From
the heights on A s draw lines to the left-hand vanishing
point V 2 , and intersect them by lines drawn from the cor¬
responding heights. For example, the height of the apex
of the pediment A is carried to od and A 3 (Fig. 3). From
A 3 a line is drawn to the left-hand vanishing point, and
from a 1 a line is drawn to the right-hand vanishing point,
and their intersection at a 2 is the perspective height of
the apex. The other method of drawing the pediment is
by visual rays from the seats of the various members
where they intersect the line A A 1 (Fig. 1), and theu draw¬
ing the heights from the line A 2 A 3 , to intersect the per¬
pendiculars let fall from the points where these visual
rays cut the picture-line. It is not necessary to give
further details of the steps of the process, which must now
* be familiar to the student.

In making a complicated drawing, there is a multipli-

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ISOMETRIC PROJECTION.

243

city of lines required, which tend to embarrass the learner.
The lines of construction are of course first drawn in pen¬
cil, and only such portions of them as are eventually to
appear in the work are drawn in ink; and it is well in
practice, after the lines which are to appear in the draw¬
ing are obtained, to ink them in, and obliterate such
lines used in obtaining them as are no longer required.

Plate CX.—This plate is an example of the method of
drawing a building in perspective. Fig. 1 is so much of
the plan of the building, which is a Turkish bath, as is
required for the operation, and Figs. 2 and 3 are eleva¬
tions of the two sides under view.

The station s is first selected, and the extreme visual
rays drawn and bisected by drawing the arc a o b, and
thus obtaining the central line S o. The picture-line x Y
is drawn at right angles to S O, and in contact with the
hither angle of the building and the vanishing lines s v, S v
are drawn parallel to the sides BC, BA respectively. The
heights in the perspective are obtained, as in the former
case, by producing the lines of the plan to intersect the
picture, and then transferring the heights of the elevation
(Fig. 3) to the corresponding perpendiculars let fall from
these intersections.

The steps and terrace D are in advance of the picture,
and their heights are obtained by setting them up on a
perpendicular let fall from the intersection of the original
line D with the picture, and' drawing lines through them
from the right-hand vanishing, point, to intersect the per¬
pendiculars let fall from the intersection of the visual rays.
The plate shows all the lines of operation, and no further
description is therefore necessary.

Plate CXI. is an example of the method of drawing a
Gothic broach or spire in perspective.

Fig. 1 shows horizontal sections of the spire at six
different heights. The first is above the moulding of the
tower, and shows the windows there; the second at the
springing of the spire, the third at the first spire light,
the fourth at the point where the lower pyramid termi¬
nates, the fifth at the second tier of lights, and the sixth
at the third tier. Fig. 2 is the elevation of one side.
Although apparently complicated, this figure is by no
means difficult, and the student is recommended to repro¬
duce this figure, or one of a similar kind, on a larger scale.
The lines of operation, if carefully studied, will render
description unnecessary.

ISOMETRIC PROJECTION.

This is a conventional manner of representing an object,
in which it has somewhat the appearance of a perspective
drawing, with the advantage of the lines situated in the
three visible planes at right angles to each other, retain¬
ing their exact dimensions. For the representation ot
such objects, therefore, as have their principal parts in
planes at right angles to each other, this kind of projection
is particularly well adapted. The name isomciriccil was
given to this projection by Professor Farisli, of Cambridge.

The principle of isometric representation consists in
selecting for the plane of the projection, one equally in¬
clined to three principal axes, at right angles to each
other, so that all straight lines coincident with or parallel
to these axes, are drawn in projection to the same scale.

The axes are called isometric axes, and all lines parallel to
them are called isometric lines. The planes containing
the isometric axes are isometric planes; the point in the
object projected, assumed as the origin of the axes, is

called the regulating point.

If any of the solid angles of a
cube (Fig. 613) be made the regulat-
D ing point, and the three lines which
meet in it the isometric axes, then
it may be demonstrated that the
plane of projection, to be such that
these axes will make equal angles
with it, must be at right angles to
that diagonal of the cube which
passes through the regulating point.
The projection of the cube will therefore beasABCDEFG
in the figure.

Let r B, s D (No. 1, Fig. 614) be the side of a cube, and
r D, the diagonal of the side, produce a D, and make c D
equal to the diagonal r D, complete the parallelogram C A,
B D, and draw its diagonal A D, which is then the diago¬
nal of a cube, of which r B D s is the side, and which is
represented in plan in No. 2, a' b' c' f'. Through D,
draw kl at right angles to the diagonal AD, and K L is
the trace of the plane of projection.

If to this line we draw through the points ECFB of
the cube, lines parallel to the diagonal AD, and therefore
perpendicular to K L, we find that the projection CD of
the edge of the cube A C, is equal to the projections of
the diagonals A B, c D, of the top and bottom surfaces of
the cube, and we know that the projection of the other
diagonal c' f' of the top (No. 2), and the projection of
one diagonal on each side of the cube, will be equal to
the original line, as they lie in planes parallel to the plane
of projection.

Produce A. D indefinitely, and at any point of it a"
(No. 3), with the radius D c or d6 describe a circle. Draw

its other diameter b" c", and produce the lines E e f/
through its circumference; join the points c" e' f 7 b fee,
to complete the hexagon, then join a" f', a"/, and we have
the isometrical projection of a cube, one ot the sides ot
which is r BSD.

The lines drawn from the plan above (No. 4), show
that the projection f' f of the diagonal C D is ot the
same size as the original, and the triangle c f j , which

244

PRACTICAL CARPENTRY AND JOINERY.

is the projection of the section of the cube by a plane C f'
(No. 1), parallel to K L, the plane of projection, shows that
the projection of one diagonal on each of the sides of the
cube must also be of the same size as the original.

The relations of the lines of the projection to the ori¬
ginal lines, are as follows:—The lines c" f', f ' f, and f c",
and all lines parallel to them, are equal to their original
lines.

The isometrical axes and isometrical lines are to the
original lines as ’8164 to 1.

The diagonals a" b", a" e', and A c' are to their originals
as -5773 to 1; or otherwise, calling the minor axis unity,
then the isometrical lines are 1-41421, and the major
axis equal to the original, is 1 73205, their ratio being as
VI, V 2, V 3.

But in practice it is not necessary to find these lengths
by computation; it is much more simple and easy to con¬
struct scales having the proper relation to each other, as
we shall proceed to show
in Fig. 615.

Let it be required, for
example, to draw the iso¬
metrical projection of a
cube of 7 feet on the side.

Now, we have seen that
the projection of one of
the diagonals of the upper
surface of the cube, is of
the same size as the ori¬
ginal. Draw, therefore,
an indefinite line A B,
and at any point of it A
draw A c, making an
angle of 45° with B A, and make A c from a scale of equal
parts equal to the length of the side of the cube, which is
here 7 feet. Also from A draw A E indefinitely, making an
angle of 30° with B A. From c draw C O perpendicular to
B A, and indefinitely produced, and cutting A E in E, then
A E is the isometrical length of the side of the cube A c.

From A, with A E as radius, cut C O produced in F,
and from F as a centre, with the same radius, describe a
circle A E, B D ; produce c F to D, draw ac'bg parallel to
C D, and join d c', d g, and B E, and we shall then have a
hexagon inscribed in the circle. Then draw the radii F A,
FB, and we obtain the projection of the cube.

Now, divide A c into seven equal parts, and through the
divisions draw perpendiculars to B A, cutting a e, and A E
will be the scale for the isometric axes and lines, and their
parallels.

The scale for E F, and the other minor diagonals, is made
by drawing lines at an angle of 30° from the divisions of
the original scale, set off on A B, intersecting the perpen¬
dicular E F. The divisions on E F form the scale for E F,

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F c', F G, and all lines parallel to them. As these ratios
are invariable, scales may be constructed for permanent
use, as in Fig. 616.

Although it is quite essential that the mode of forming
scales for the isometric and other lines should be clearly

understood, it is seldom that these scales require to be
used in practice. For as we can adopt any original scale
at pleasure, it is generally more convenient to adopt such
a scale as we can apply at once to the isometrical lines.
And in place of constructing the hexagon each time, it is
convenient to have a set square with its angles 90°, 60°,
and 30°, by means of which and a T-square or parallel
ruler, all the lines of construction may be drawn.

Having assumed a scale, therefore, and fixed on the
regulating point, suppose we wish to draw a cube, we
proceed as follows:—From the regulating point F (Fig.
615), by means of the set square of 30°, draw the rio-lit
and left hand isometricals F A, F B, and make them by
the scale equal to the side of the cube. Then with the
same set square, draw A E, be, to complete the upper
surface. Draw, by means of the set square of 90°, A c',
F D, B G, make them equal to F A, or F b, and, by the aid
of the set square of 30°, join D c', D G, and the cube is
completed.

The following figures illustrate the application of iso¬
metrical drawing to simple combinations of the cube and
parallelopipedon. In Fig. 617, one mode of construction

Fig. 618.

is shown by dotted lines, but we may proceed dii'ectly as
in drawing the cube in the manner above described, be¬
ginning at the hither angle of the largest block on the
figure, and adding the minor parts. Fig. 618 shows the
interior of what may be considered a box or a building.
Fig. 619 requires no description.

The following figures show how lines which are not
isometric may be obtained by the aid of those which are.

In Fig. 620, A is the half-plan of a pyramid with a

Fig. 616.

ISOMETRIC PROJECTION.

245

square base. By including it in an isometrical square, its
projection is readily obtained.

Fig. 621 is an octagon, Fig. 622 a hexagon, and Fig. 623

a pentagon. The projections are obtained by the inter¬
sections of their lines, or their lines produced with the
sides of the circumscribing square; and it may be observed
by these examples, that the projection of any line making
any angle whatever with the isometric lines, can be very
easily obtained. In the figures, all the lines of construc¬
tion arising from the various intersections are shown for
the sake of illustration. But in practice it is easily to be
seen, that it is only necessary to obtain a few of the inter¬
sections. As for example, in Fig. 621, the points abed ef,
and in Fig. 622 the points abedefgh.

We shall now proceed, in Fig. 624, to show how the
projection of lines at any angle may be obtained directly.

Let ab, No. 1, be the isometrical projection of a cube,
on any of the sides of which it is required to draw lines at
various angles. Draw a square, No. 2, and from any of
its angles describe a quadrant, which divide into 90°, and
draw radii through the divisions meeting the sides of the
square. These will then form a scale to be applied to the
isometric faces of the cube, No. 1; thus, from E, or any
other angle of the cube, draw a line E F at any angle; make
it equal to the side of the square, No. 2, and transfer the
divisions of that side to it. Join G F, and draw parallels
to G F through the other divisions of E F, meeting E G,
which they will divide in the same proportion, and repeat
the operation to find the divisions of the remaining sides;
or from the angle C of the square, No. 2, draw a line CD,

Fig. 624.

manner. As the figure has twelve isometrical sides, and the
scale of tangents may be applied two ways to each, it can
be applied, therefore, twenty-four ways in all. We thus
have a simple means of drawing, on the isometrical faces
of the cube, lines forming any angles with their boundaries.

We have now to consider the application of this species
of projection to curved lines.

Let A B, No. 1, Fig. 625, be the side of a cube with a
circle inscribed; and suppose all the faces of the cube to
have similarly inscribed circles. Let us draw the isome¬
trical projection of the cube, No. 2. Then, as the pro¬

jection of one of the diagonals of each face of the cube,
and consequently one of the diameters of the circle, is of
the same size as the original, we have at once the major
axis of the ellipse which the projection of the circle forms,
and as the circle touches each side of the square, we have
also four points in the circumference of the ellipse, and we
have only to find the isometric projection of its minor axis.

J From the intersections of the diagonals of the faces of the
cube, set off on the major axis the radius of the circle at
a b c de /, and through the points thus obtained draw
isometric lines cutting the minor axis in 1 2 3 4 5 6, and
we thus obtain the length of the minor axis. The ellipse
can then be sketched by hand, or trammelled by a slip of
paper.

We may divide the circumference of a circle in two
ways, as shown in Fig. 626. First, on the centre of the
line A B erect a perpendicular c D, and make it equal to
C A or c B. Then from D with any radius, describe an

Fis. 626.

I arc, and divide it in the ratio required, and draw through
the divisions, radii from D, meeting A B. Then from the
isometric centre of the circle draw radii from the divisions
on A B, cutting the circumference of the circle in the
points required.

Second, on the major axis of the ellipse describe a semi¬
circle, and divide it in the manner required. Through
the points of division thus obtained draw lines perpen¬
dicular to A E, which will divide the circumference of
the ellipse in the same ratio. On the right hand ol the
figure both methods are shown in combination, and the
intersection of the lines gives the points in the ellipse.

246

PRACTICAL CARPENTRY AND JOINERY.

Mr. Nicholson, in his Treatise on Projection, has given
the following table of the isometric radius, semi-axis

minor, and semi-axis major of ellipses, from 1 inch to
9 feet; which, in certain cases, may be found useful:—

Isometric

Radius.

Semi-axis

Minor.

Semi-axis

Major.

Isometric

Radius.

Semi-axis

Minor.

Semi-axis

Major.

Isometric

Radius.

Semi-axis

Minor.

Semi-axis

Major.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

Ft.

Ins.

101

3 |

101

3 i

o§

5§

8 i

4 1

103

lOf

Ilf

10f

103

0‘3‘

101

H£

2 1

3 f

Hi-

4§

6 I

2§

lOf

101

lOf

8} *

111

3§

9 f

10f

3 f

4 1

Example of the Use of the Table. — Let it be required to find the semi-axis of an ellipse which is the isometrical projection of a circle, the
isometrical radius being 2 feet 8 inches. In one of the columns under isometrical radius, will be found 2 feet 8 inches; and in the same
line, in the next column, on the right hand, will be found 1 foot lOf inches, under semi-axis minor; and in the same line further to the
right, under semi-axis major, will be found 3 feet 3 inches.

Examples might be introduced to show the applica¬
bility of this mode of projection to buildings and the
parts of buildings, but its principles are so obvious, and
its practice, when these are mastered, so easy, that to
multiply examples would be mere surplusage. We shall
therefore close this subject with the remark and caution,
that although isometrical projection is a valuable addition
to the ordinary plan, section, and elevation of tho

draughtsman, and may be most advantageously used as
explanatory of these, it does not give so truthful or
pleasing a representation of an object as a proper per¬
spective drawing. It should only be used, therefore, when
the object in view is the elucidation or explanation of a
subject, and never when pictorial representation alone is
intended. Within the limits which we have indicated it
is of extended utility, beyond them it is caricature.

INDEX

TO THE CARPENTER AND JOINER’S ASSISTANT;

AND GLOSSARY

OF TERMS DSED IN ARCHITECTURE AND BUILDING.

ABACISCUS

AMPHIPROSTYLE

ABACISCUS.—1. Any flat member.—2. The
square compartment of a mosaic pavement.

ABACUS.—A table constituting the upper or
crowning member of a column and its capital. It
is rectangular in the Tuscan, Doric, and Ionic
orders; but in the Corinthian and Composite orders
its sides are curved inwards. These curves are
called the arches of the abacus, and the meeting of
the curves its horns. The arches are generally de¬
corated with an ornament in the centre of the curve,
called the rose of the abacus.

The type of the abacus is found in the Grecian
Doric order, in which it is a square member. In
the Tuscan and Roman Doric it has a moulding
and fillet round its upper edge, called the cymatium.
In the Grecian Ionic the profile of its side is an
ovolo or ogee, and in the Roman Ionic an ovolo or
ogee with a fillet over; in the Corinthian and Com¬
posite orders its mouldings are a cavetto, a fillet,
and an ovolo.

IO'

Corinthian Abacus.

Grecian Done Abacus.

Roman Doric Abacus.

In mediaeval architecture the abacus is a strongly
marked feature in the earlier styles; but loses this
character in the later styles, in which there is no
real line of separation between it and the rest of
the capital.

ABELE or Abel Tree. —The white poplar,
Populus alba. See p. 112.

ABIES. See Fib.

ABSCESSES in Trees detrimental, p. 97.

ABSCISSA.—A part of the diameter, or trans¬
verse axis of a conic section, in¬
tercepted between the vertex, or
some other fixed point, and a
semi-ordinate. Thus in the para¬
bolic figure b c a, the part of the
axis D c intercepted between the
semi-ordinate B D, and the ver¬
tex c, is an abscissa.

ABUT, to. —To adjoin at the end, to be con¬
tiguous to; generally contracted to But.

ABUTMENT.—1. The solid pier or mound of
earth from which an arch springs.—2. Abutments of
a bridge, the solid extremities on, or against which,
the arches rest.

ACACIA.—Properties and uses of, p. 114.

ACANTHUS.—The plant bear’s-breech, the

leaves of which are imitated in the foliage of the
Corinthian and Composite capitals.

B a\

ACCIDENTAL POINT.—In perspective that
point in which a
right line drawn
from the eye of the
spectator parallel
to another given
right line, cuts the
plane of the picture.

Thus: let a b he

the given line, c F E the plane of the picture. D
the eye, c d the line parallel to a b, then is c the
accidental point.

ACER. See Maple.

ACOUSTICAL PULPIT, Plate LXXXIII.,
description of, p. 190.

ACROTER, Acroterium, Aceoteria. —A
small pedestal, placed on the apex or angles of a

Pediment with Acroteria, AAA.

pediment, for the support of a statue or other or¬
nament. The term is also used to denote the pin¬
nacles or other ornaments on the horizontal copings
or parapets of buildings, and which are sometimes
called Acroteral Ornaments.

ADHESION of Surfaces glued together. From
Mr. Bevan’s experiments it appears that the surfaces
of dry ash-wood, cemented by glue newly made, in
the dry weather of summer would, after twenty-
four hours’ standing, adhere with a force of 715
lbs. to the square inch. But when the glue has
been frequently melted and the cementing done in
wet w’eather, the adhesive force is reduced to from
300 to 500 lbs. to the square inch. When Sootcli
fir cut in autumn was tried, the force of adhesion
was found to be 562 lbs. to the square inch. Mr.
Bevan found the force of cohesion in solid glue to
be equal to 4000 lbs. to the square inch, and hence
concludes that the application of this substance as
a cement is capable of improvement.

ADHESIVE FORCE of Nails and Screws in
different kinds of Wood. Mr. Bevan’s experiments
were attended with the following results:—Small
sprigs, 4560 in the pound, and the length of each
T 4 0 4 5 of an inch, forced into dry Christiania deal to
the depth of 0'4 inch, in a direction at right angles
to the grain, required 22 lbs. to extract them.
Sprigs half an inch long, 3200 in the pound, driven
in the same deal to 0'4 in. depth, required 37 lbs. to
extract them. Nails 61S in the pound, each nail
1 j inch long, driven 0'5 in. deep, required 58 to
extract them. Nails 2 inches long, 130 in the
pound, driven 1 inch deep, took 320 lbs. Cast-
iron nails, 1 inch long, 380 in the pound, driven
0'5 in., took 72 lbs. Nails 2 inches long, 73 in the
pound, driven 1 inch, took 170 lbs.; when driven
If inch they took 327 lbs., and when driven 2 inches
530 lbs. The adhesion of nails driven at right
angles to the grain was to force of adhesion when
driven with the grain, in Christiania deal, 2 to 1,
and in green elm as 4 to 3. If the force of adhesion
of a nail and Christiania deal be 170, then in similar
circumstances the force for green sycamore will be
312, for dry oak 507, for dry beech 667. A common
screw j of an inch diameter was found to hold with
a force three times greater than a nail 2f inches
long, 73 of which weighed a pound, when both en¬
tered the same length into the wood.

ADZE(formerly written A ddice ).—A cutting tool
used for chopping a surface of timber. It consists

247

of a blade of iron, forming a portion of a cylindrical
surface, ground to an edge from the concave side
outwards at one end, and having a socket at the
other end for the handle, which is set radially. The
handle is from 24 to 30 inches long. The weight of
the blade is from 2 to 4 lbs. The work is gene¬
rally laid in a horizontal position, and the instru¬
ment held in both hands. The operator, standing
in a stooping posture, swings the instrument in a
circular path, nearly of the same curvature as the
blade. His arms, from the shoulder joint, which
forms the centre of motion with the tool, make
nearly an inflexible radius, and he thus makes his
strokes in a succession of short arcs. The extent
of the stroke is gauged by his right thigh, with
which his arm comes in contact at each stroke.
Standing on his work, the operator, in preparatory
work, generally directs the strokes between his feet;
but in finer work he directs them under his toe,
penetrating the wood with unerring precision, and
perfect safety to himself.— Holtzapfell.

AERIAL PERSPECTIVE.—That branch of
perspective which treats of the representation of
the effects of air and atmosphere; and the several
gradations, depths, and intensities of light, colour,
and shadow, produced by intervening air on ob¬
jects, as they recede from the eye of the spectator.

AISLE (pronounced lie ).—The wing of a build¬
ing; usually applied to the lateral divisions of a
church, which are separated from the central part,
called the nave and choir, by pillars and piers. The
nave is frequently, though incorrectly, termed the
middle aisle, and the lateral divisions side aisles.
See woodcut, Cathedral.

A LA GRECQUE, A la Grec. —One of the
varieties of the fret ornament.

A la Grecque.—Greek Border Ornament.

ALBURNUM.—The white and softer part of
the wood of exogenous plants; sap-wood. Seep. 95.

ALDER, Aldus. —For description and qualities
of, see p. 113.

ALTERNATE ANGLES.-The angles formed
by two straight lines,
united at their extremi¬
ties by a third straight
line. Thus, the lines
a B, CD, united by the
line B c, give the alter¬
nate angles ABC and
BCD. When the angles
are equal, the lines AB, CD are parallel.

AMBIT.—1. The perimeter of a figure.—2. The
periphery or circumference of a circular body.

AMBO.—A pulpit or reading-desk.

AMBRY.—1. A cupboard or closet.—2. In
ancient churches a cupboard formed in a recess in
the wall, with a door to it, placed by the side of
the altar, to contain the sacred utensils.

AMERICAN Bench Circular Saw, p. 192.

AMERICAN or Western Plane, p. 113.

AMERICAN SPRUCE ( Pinus alba, and
Pinus nigra). —Properties and uses of, p. 118.
AMPHIPROSTYLE.—Structures having the

Blau of an Amphiprostyle Building.

form of an ancient Greek or Roman rectangular
temple, with a prostyle or portico on each of its

INDEX AND GLOSSARY.

Anamorphosis.

ANAMORPHOSIS

ends or fronts, but with no columns on its sides or
flanks.

ANAMORPHOSIS.—A term in perspective,
denoting a drawing executed in such a manner as
to present a distorted image of the object repre¬
sented; but which, when viewed
from a certain point, or reflected
by a curved mirror, shows the
object in its true proportions.

ANCHOR.—An ornament
shaped like an anchor or arrow¬
head, used in all the orders of
architecture. It is applied as an
enrichment to the ovolo-echinus
or quarter-round, and as it
invariably alternates with the
egg ornament, the combination
is popularly called egg-and -
anchor, egg-and-dart , or egg-and-
tongue.

ANCON.—An elbow or an¬
gle, whence the French term
coin, a comer; also the English
quoins, or corner-stones. The
corners of walls and beams
are sometimes Ancones.

ANCONES. — Orna-
ments cut on the key-stones
of arches, or on the sides
of door-cases. Called also Consoles and Trusses.

ANGLE.—To make an angle equal to a given
angle. Prob. III. p. 5.—To bisect an angle, Prob.
IV. p. 5; Prob. V. p. 5.

ANGLE of Repose.— That angle at which one
body will just rest on another without slipping. It
is called also the limiting angle of resistance.

ANGLE-BAR.—The vertical bar at each angle
of windows constructed on a polygonal plan.

ANGLE-BEAD, Angle-Staff. —A piece of
wood fixed vertically upon the exterior or salient
angle of an apartment, to preserve it from injury,
and also to serve as a guide by which to float the
plaster. It is called also staff-bead.

ANGLE-BRACE.—1. A piece of timber fast¬
ened at each end to one of the pieces forming the
adjacent sides of a system
of framing, and subtending
the angle formed by their
junction. When it is fixed
between the opposite angles
of a quadrangularframe it is
called a diagonal brace. It
is also called angle-tie and
diagonal tie. —2. A boring
tool for working in corners
andother places where there
is not room to swing round
the cranked handle of the
ordinary brace. It is made of metal, with a pair
of bevel pinions, and a winch handle, which revolves
at right angles to the axis of the hole to be bored.

ANGLE-BRACKET.—A bracket placed in an
interior or exterior angle, and notat right angles with
the planes which form it. See Angle-Brackets,
p. 85, and PI. XIX.

ANGLE - BRACKETS for coves in straight,
concave, and convex walls, p. 85, PI. XIX.

ANGLE-CAPITAL.—An Ionic capital on the
flank column of a portico, having volutes on three
sides, the exterior volute being placed at an angle of
135° with the plane of the frieze, on front and flank.

ANGLE-IRON. p. 4.

ANGLE-RAFTER.— A rafter placed in the
line of meeting of the inclined planes of a hip-roof.
It is called also hip-rafter, and in Scotland piend-
rafter. See Hir-RooFs, p. 1)1, and Roof, p. 135,
and Plates XX. and XXI.

ANOLE-RIB.—A curved piece of timber placed
in the angle between two adjacent sides of a coved
or arched ceiling, so as to range with the common
ribs. p. 80.

ANGLES.—Construction of, Geometry, p. 5.

ANGULAR CAPITAL.—A term applied to a
comparatively modern variety of the Ionic capital,
which has its four sides alike, and all its volutes
placed at an angle of 135° with the plane of the
frieze.

ANGULAR PERSPECTIVE.—A term ap¬
plied to that kind of perspective in which neither of
the sides of the principal object is parallel to the
plane of the picture, so that in the representation the
horizontal lines of the original object converge to
vanishing points. It is called also oblique per¬
spective.

ANNULAR VAULT.—A vault springing
from two walls, both circular on the plan, the one
being concentric to the other.

ANNULATED COLUMNS.—Columns clus¬
tered together or joined by rings or bands. They
arc much used in early English architecture.

a.Anglt-brace. b. Diagonal brace.

ANNULET.—A small moulding, whose hori¬
zontal section is circular. It is used indiscriminately
as a synonym for list, cincture, fillet, tenia, &c.
Correctly, annulets are the fillets or bands which
encircle the lower part of the Doric capital, above
its neck or trachelium.

ANT.'E.—The pier-formed ends of the ptero-
mata or side walls of temples, when they are pro¬
longed beyond the face of the end walls. A term

applied to pilasters when they stand opposite a
column. A portico in antis, is one in which columns
stand between ant a'.

ANTEFIXH3.—Upright blocks ornamented
on the face, placed at regular intervals on the crown-

Antetixte.

ing member of a cornice. These ornaments were
originally used to terminate the ends of the cover¬
ing tiles of the roof.

ANTIUM.—In ancient architecture, a porch to
a southern door; that to the north was called Por-
lium.

APARTMENT.—1. Used in the singular, is
synonymous with room or chamber.—2. The term
was formerly used to denote a suite of rooms compris¬
ing, at the least, a hall, ante-chamber, chamber,
closet, cabinet, and wardrobe, with the necessaiy
conveniences for cooking and the accommodation
of domestics.

APERTURES.—The openings in the walls of
a building, such as doors and windows.

APOPHYGE, Apollusis, Apophysis.— The
parts at the top and bottom of the shaft of a column
which spring out to meet the edges of the fillets.
The apophyge is usually moulded into a concave
sweep or cavetto. and it is often called the spring
or the scape. In French it is termed conge.

APPLE TREE, The.—Description of the pro¬
perties and uses of, p. 114.

APPLICATE-ORDINATE.—A right line at
right angles applied to the axis
of any conic section, and bounded
by the curve. Thus in the figure,
the right line B A, at right angles
to C D, the axis of the parabola
boa, is termed an applicate-
ordinate.

APPLICATION of theprin-
ciples of the resolution of forces to determine the
strains on pieces of framing, and the strains trans¬
mitted by them, p. 123.

APRON.—1. A platform or flooring of plank
at the entrance of a lock, on which the gates are
shut.— 2. A term used by plumbers in the north
of England and in Scotland as synonymous with
flashing.

APRON-LINING.—The facing of the apron-
piece.

APRON-PIECE..—A piece of timber fixed into
the walls of a staircase, and projecting horizontally,
to support the carriage pieces and joisting in the
half spaces or landings. It is called also pitching-
piece, p. 196.

APSIS.—A term applied to that part of any
building which has a circular or polygonal termina¬
tion and a vaulted roof. The eastern portion of the
church, where the clergy sat and where the altar
was placed. It generally had a circular or poly-

248

/ r

ARCH

gonal termination, and was vaulted over. See
woodcut, Cathedral.

APTERAL.—A temple having no columns
along its flanks or sides.

ARABESQUE.—-Arabesques or Moresques, a
style of ornament com¬
posed of representations of
a mixture of fruit and
flowers, buildings, and
other objects. In pure an¬
cient arabesques, such as
are found in the Alhambra,
no animal representations
are used.

AR^EO STYLE.—A
term applied to a columnar
arrangement when the
columnsare far apart. The
interval assigned is four
diameters, and it is pro¬
perly applicable to the
Tuscan order only.

ARzEOSYSTYLE —

An arrangement of coupled
columns, in which four
columns are placed in a
space equal to eight diame¬
ters and a half. The cen¬
tral intercolumniation is equal to three diameters
and a half, and the others on each side to half a
diameter.

ARCADE.—A series of arches supported on
piers or pillars, used generally as the screen and
roof support of an ambulatory or walk; but in the

iMipip

Arabesque.

TTYT

Arcade, Rymsey Church, Hampshire.

architecture of the middle ages also applied as an
ornamental dressing to a wall, as in the figure.

ARCH.—A structure composed of separate
inelastic bodies, having the shape of truncated
wedges, arranged on a curved line, so as to retain
their position by mutual pressure. Arches are
usually constructed of stones or of bricks. The
separate stones which compose the arch, are called
voussoirs, or arch-stones; the extreme, or lowest
voussoirs, are termed springers, and the uppermost,
or central one, is called the key-stone. The under,
or concave side of the voussoirs, is called the intra-
dos, and the upper, or convex side, the extrados of
the arch. When the curves of the intrados and
extrados are concentric, or parallel, the arch is said

a n. Abutments $S. Sprimrera. *»», Vouwoir*. it. Imposts.

In- Intrados. k. Keystone p p, Piers. Ex. Extrados.

to be extradosed. The supports which afford rest¬
ing and resisting points to the arch, are called piers
and abutments. The upper part of the pier or
abutment where the arch rests—technically, where
it springs from—is the impost.. The span of an
arch, is in circular arches the length of its chord,
and generally, the width between the points of its
opposite imposts whence it springs. The rise of an
arch, is the height of the highest point of its intra¬
dos above the line of the impost; this point is some¬
times called the under side of the crown, the highest
point of the extrados being the crown. Arches are
designated in two ways ; first, in a general manner,
according to their properties, their uses, their posi¬
tion in a building, or their exclusive employment
in a particular style of architecture. Thus, there
are arches of equilibration, equipollent arches,
arches of discharge, askew and reversed arches, and
Roman, pointed, and Saracenic arches. Second,
they are named specifically, according to the curve
their intrados assume, when that curve is the section
of any of the geometrical solids, as circular, seg¬
mental. cycloidal, elliptical, parabolical, hyperboli¬
cal, or catenarian arches; or from the resemblance

ARCH

INDEX AND GLOSSARY.

BALUSTRADE

of the whole contour of the curve to some familiar
object, as lancet-arch, anil horse-shoe arch; or from

Equilateral Arch. Segmental Arch.

the method used in describing the curve, as three-
centred arches, four-centred arches, and the like.

Horse-shoe Arch. Four-centred or Tudor Arch.

When any arch has one of its imposts higher than
the other, it is said to be rampant,

ARCH, Equilateral, to draw, p. 28.

ARCH, the Ogee, to draw, p. 30.

ARCH, the Lancet, to draw, p. 29.

ARCH, the Drop, to draw, p. 29.

ARCH, the Eour-centred, to draw, p. 29, 30.

ARCH, Gothic. —To describe by the intersec¬
tion of straight lines, p. 30.

ARCH-BRACES in bridge construction, p. 159.

ARCHANGEL TIMBER. See Pinus syl-
VESTRIS, p. 116, 117.

ARCHITECTURE.—The art of building ; but
in a more limited and appropriate sense, the art of
constructing houses, bridges, and other buildings
for the purposes of civil life. Archilectwre is usually
divided into three classes, civil, military, and naval,
but when the term architecture is used without a
qualifying adjective, civil architecture is always
understood.— Civil architecture is the art of design¬
ing and constructing palaces, houses, churches,
bridges, and other edifices for the purposes of civil
life; but in a more limited and appropriate sense,
it is restricted to such edifices as display symmetri¬
cal disposition and fitting proportions of their parts,
and are adorned by pillars, entablatures, arches,
and other contrivances for their embellishment.—
Military architecture is the art of fortification.— ;
Naval architecture is the art of building ships.

ARCHITRAVE.— 1. The lower division of an
entablature, or that part which rests immediately on
the capital of the column. It is sometimes called
the epistylium. See woodcut. Column.— 2. The
moulded lining on the faces of the jambs and lin¬
tels of a door or window opening, or niche.

ARCHITRAVE-CORNICE.—An entablature
consisting of an architrave and cornice only, the
frieze being omitted.

ARC HITR A VES.—Illustrations of, PI. LXIX.

p. 182.

ARCHIVOLT.—The architrave or ornamental
band of mouldings on the face of an arch following
the contour of the intrados.

AREA.—The superficial content of any figure.
The method of ascertaining the area of the various
geometrical figures will be found under the name
of the figure.

ARRIERE-VOUSSURE.—A rear-vault; an
arch placed within the opening of a window or
door, and of a different form, to increase the light-

Arriere-voussure

way of the window, or to admit of the better
opening of the door; it seems also to have served
the purpose of an arch of discharge.

ARRIS.—The line in which two straight or
curved surfaces of any body, forming an exterior
angle, meet each other; an edge.

ARRIS-PILLE T.—A triangular piece of wood
used to raise the slates of a roof when they abut

against the shaft of a chimney or a wall, so as to
throw off more effectually the rain from the join¬
ing. It is called also a tilling-fillet.

ARRIS-GUTTER.— A wooden gutter of the
form of a V in section, fixed to the eaves of a
building.

ARRISAVISE.—Tiles or bricks laid diagonally
are said to be laid arris-wise.

ASH TREE.—Properties and uses of, p. 112.

ASHLERING.—Timber quarterings in garrets
for affixing lath to, in forming partitions, to cut off
the acute angle made by the meeting of the sloping
roof with the floor. They are usually two or three
feet high, perpendicular to the floor, and fixed at
top to the rafters.

ASTEL.—A board or plank used for partition¬
ing overhead in tunnelling.

ASTRAGAL.—A small moulding, semicircular
in its profile. It is frequently ornamented by being
carved into the representation of beads or berries.

ATLANTES.—-A term applied to figures or
half figures of men used in the place of columns or

Atlantes, in the Baths, Pompeii.

pilasters, to support an entablature. They are
called also Telamones.

ATTACHED COLUMNS.—Those which pro¬
ject three-fourths of their diameter from the wall.

ATTIC BASE.—A peculiar base used by the
ancients in the Ionic order or column, and by Pal¬
ladio, and others in the Doric. It consists of an

Attic Base.

upper torus, a scotia, and lower torus, with fillets
between them.

ATTIC ORDER.—An order of small square
pillars at the uppermost extremity of a building,
above the main cornice. The pillars are never less
than a quarter, nor more than one-third of the
height of the order over which they are placed.

ATTIC STORY.—The uppermost story of a
house when the ceiling is square with the sides;
distinguished from garret, in which the ceiling, or
part of the ceiling, is inclined. Rooms in the attic
story are called attics.

AUGER.—A tool used by carpenters and other
artificers in wood, for boring large holes. It con¬
sists of an iron blade ending in a steel bit, and
having a handle placed at right angles to the blade.
Modern augers have a small pointed screw at the
extremity, for better entering the wood, and a
spiral groove formed in the blade. The lower ex¬
tremities of the threads of this screw, formed by
} this groove, are sharpened, to form the bit or cutter;

I these are called screw-augers. Those made with a
I straight groove or channel are sometimes called
pod-augers. An ingenious improvement has been
recently made by an American. The cutting edges
of the lower end of the screw, in place of being
parallel to the axis, are rounded off, in imitation of
the boring apparatus of the Teredo navalis.

AWL.—An iron instrument for piercing small
holes. See Brad and Bkad-awl.

AXIS.—1. In geometry, the straight line in a
plane figure, round which it revolves to generate a
! solid.—2. Generally, a supposed right line drawn
from the centre of one end to the centre of the
other, in any figure.— Axis of a sphere, a cylinder,
cone, &c., is the straight line round which the gene¬
rating semicircle, rectangle, triangle, &c., revolves.
— Axis-minor, conjugate axis, or second axis of a
hyperbola and ellipse, a straight line drawn through
the centre perpendicularly to the axis-majorortrans-
verse axis.— Axis-major, or transverse axis in the

ellipse and hyperbola, a straight line passing through
the two foci and the two principal vertices of the
figure. In the ellipse the axis-major is the longest
diameter; in the hyperbola it is the shortest.

BACK.—The side opposite the face or breast.
When a piece of timber is laid in a horizontal or
an inclined position, the under side is called the
breast, and the upper
side the back. Thus, we
have the back of a hand¬
rail, the back of a rafter,
&c., meaning the upper
side.

BACK-FILLET.—
When the margins of a
quoin, or those of the
jambs of a door or win¬
dow, project beyond the
face of the wall, the re¬
turn of the projection is
called a back-fillet, and the margin is said to be
back-Jilletted.

Jambs with Back-filleted Margins,
a, Chamfer b, ReveaL a. Back-fillet.

c, Back-fillet.

Quoins with Back-filleted
Margins.

BACK-FLAPS, p. 188.

BACK-LINING.—The piece of a sash-frame
parallel to the pulley piece and next to the jamb.
See p. 187.

BACKER.—A term used to denote a narrow
slate laid on the back of a broad, square-headed
slate, where the slates begin to diminish in width.

BACKING of the hip, p. 91.

BADIGEON.—A mixture of plaster and free¬
stone ground together and sifted, used hy statuaries
to fill the small holes and repair the defects of the
stones of which they make their statues.

BAGUETTE.—An astragal or bead.

BALANCE-BEAM.—A long beam attached
to the gate of a lock, serving to open and shut it.

BALCONY.—A projection in front of a house;
a frame of wood, iron, or stone, supported by pil¬
lars, columns, or consoles, and encompassed with a
balustrade railing or parapet. Balconies are com¬
mon before windows.

BALECTION-MOULDINGS. See Bolec-

TION.

BALK.—Apiece of timber from 4 to 10 inches

square.

BALL-FLOWER.—

Ball-flower.

BALTIC TIMBER,

n ornament resembling a
ball inclosed in a circu¬
lar flower, the three
petals of which form a
cup round it. The ball-
flower ornament is usu¬
ally found inserted in a
hollow moulding, and
may be considered as
one of the characteristics
of the Decorated style.
Description and uses of,

p. 115-118.

BALUSTER. — A small column having a
swelling in the middle and mouldings to form a
base and capital, used in balustrades. The lateral
part of the Ionic capital is also called the baluster.

BALUSTRADE.—A row of balusters set on a

continuous plinth, and surmounted by a cap or rail,
serving as a fence for altars, balconies, terraces.

249

2 I

INDEX AND GLOSSARY.

BAMBOO

BENCH

steps, staircases, tops of buildings, &c. Balus¬
trades are sometimes used solely as ornaments.

BAMBOO.—Multifarious uses of, p, 94.

BAND.—In classic architecture, any flat mem¬
ber with small projection. In mediaeval architec¬
ture. the round mouldings or suite of mouldings
which girds the middle of the shafts in the early
English style.

BANDELET, Bandlet.— A narrow band.

BANDING PLANE.—A plane intended for
cutting out grooves and inlaying strings and bands
in straight and circular work.

BANISTER.—A corruption of baluster.

BANKER.—A bench upon which masons place
the stones about to be hewn. In Scotland termed
a siege.

BAR or Barred Door. —The Scottish synonym
for ledyecl door; a door formed of narrow deals
joined by grooving and tongueing or by rebating,
and secured by bars or ledges nailed across the back.

BAR-POSTS.—Posts driven into the ground
to form the two sides of a field gateway. They
have holes corresponding to each other, into which
bars are inserted to form the fence.

BARGE-BOARDS, called also Gable-Boards.
—The raking-boards at the gable of a building,
placed to cover the ends of the roof timbers when
they project beyond the walls. They are some¬
times called verge-boards, and are variously orna¬
mented. See illustration, Plate XLVIL, Timber-
houses ; Figs. 3 and 4, Gable-boards.

BARGE-COUPLES.—The exterior couples of
a roof which project beyond the gable.

BARGE-COURSE.—The course of tiles which
covers and overhangs the gable-wall of a building,
and is made up below with mortar; also, a coping
to a wall formed of a course of bricks set on edge.

BASE.—The bottom of anything, considered as
its support or that whereon it stands or rests. The
base of a pillar or column is that part which lies
between the top of the pedestal and the bottom of
the shaft; but where there is no pedestal it is the
moulding or series of mouldings between the bot¬
tom of the shaft and the plinth; and in the Grecian
Doric, the steps on which the column stands form
its base. The lowest part of a pedestal, and the
plain or moulded fittings which surround the bot¬
tom of a wall next the floor, are also termed the
base of the pedestal and apartment respectively.

BASE-LINE.—In perspective, the common sec¬
tion of the picture and the horizontal plane, p. 228.

BASE-MOULDINGS.—The mouldings imme¬
diately above the plinth of a wall, pillar, or pedestal.

BASEMENT.—1. The ground floor on which
the order or columns which decorate the principal
story are placed.—2. A story below the level of the
street.

BASIL.—-The slope or angle of the cutting
part of a tool or instrument, such as a chisel or
plane. All edge tools may be regarded as wedges
formed by the meeting of two straight or curved
surfaces, or of a straight and curvilinear surface, at
angles varying from 20° to 12°. Occasionally the
tool is ground with two basils, as in the case of the
hatchet, the turner’s chisel, and some others.—The
angle of the basil in cutting tools depends on the
hardness or softness of the material to be operated
upon, and on the direction of its fibres. Mr. Holt-
zapfell classifies cutting tools in the three following
groups: — 1st. Paring tools, with their edges the
angles of which do not exceed 60°; one plane form¬
ing the edge being nearly coincident with the work
produced. These tools remove the fibres princi¬
pally in the direction of their length. 2d. Scrap¬
ing tools with thick edges, varying from 60° to
120°, the planes of the edges forming nearly equal
angles with the surfaces produced. Such tools re¬
move the fibres in all directions with nearly equal
facility, producing fine dust like shavings, by act¬
ing superficially. 3d. Shearing or separating tools,
with edges from 60° to 90°, generally duplex, and
then applied on opposite sides of the substance to
be operated upon. One plane of each tool, or of
the single tool, is coincident with the plane pro¬
duced.— Holtzapfell chiefly. See Cutting Tools
and particular description under the name of each
separate tool.

BASKET - HANDLE ARCH (Fr. anse de
panier). —Any arch whose vertical height is less
than half its horizontal diameter; consequently the
term includes all surbased and semi-elliptic arches
BASS-RELIEF. See Relief.

BASSOOLAH.—The Indian adze. In place
of being circular, like the European adze, this is
formed at a direct angle of 45° to 50°. Its handle
is very short, and it is used with great precision by
the nearly exclusive motion of the elbow joint. In
different districts the instrument varies in weight,
and in the angle which the cutting face forms with
the line of the handle. The average weight, how¬

ever, may be stated at 11 lbs. 12 oz., and the
length of the handle 12 or 13 inches. In using, it
is grasped so near the blade that the fore finger
rests on the metal, the thumb nearly on the back
of the handle, the other fingers grasping the front
of it, with their nails approaching the ball of the
thumb. When the head of the instrument is made
about 2 lbs. weight, it is a very handy tool for
blocking out hard or soft woods— Holtzapfell.

BASTON, Baton, Batoon. —Another name for
the torus, or round moulding in the base of a column,
or otherwise applied. See woodcut, Column.

BATTEN.—A piece of timber from 1| inch to
7 inches broad, and ^ inch to inches thick. The
battens of commerce are 7 inches by 2i inches.

BATTEN DOOR.—A ledged door or barred
door.

BATTENING. — Narrow battens fixed to a
wall, to which the laths for plastering are nailed.
They are attached to the wall, either by nailing to
bond-timbers built in for the purpose, or fixed
directly to the wall by holdfasts of wrought iron; and
they should always be so fixed when crossing flues.

BATTER.—To incline from the perpendicular..
Thus a wall is said to batter when it recedes as it rises.

BATTLEMENT.—A parapet of a building
provided with openings or embrasures, or the em-

b b, Embiasures.

brasures themselves. The portions of wall which
separate the embrasures are called merlons.

BAULK.—A piece of whole timber, being the
squared trunk of any of the trees usually employed
in buildings.—The tie-beam of a common couple
roof is called a baulk
in Scotland.

BAY. — A term
applied in architecture
without much preci¬
sion.—1. Any opening
in a wall left for the
insertion of a door or
window.—2. Any dis¬
tinct recess in a build¬
ing.—3. The quadran¬
gular space between
the principal divisions
of a groined roof, over
which a pair of dia¬
gonal ribs extend, and
rest on the four angles.

— 4. The horizontal
space between two
principals. — 5. The
division of a build¬
ing comprised between *

two buttresses. — 6.

The part of a window
included between two
mullions, called also
day or light.—7. In a
barn, a low inclosed
space for depositing
straw or hay; or the

space between the thrashing-floor and the end of the

barn. If a barn consists of a floor and two heads,
where corn is laid, it is called a barn of two bays.

BAY-WINDOW.—A projecting window, ris¬
ing from the ground or base¬
ment on a semi-octagonal or
some other polygonal plan,
but generally understood to
be straight-sided. When a
projecting window is circu¬
lar in its plan, it is a bow-
window, when it is support¬
ed on a bracket or corbel,
and is circular or polygonal,
it is an oriel. These distinc¬
tions are too little attended
to in practice, the terms
being often used synony¬
mously.

BEAD. — A round
moulding of vei-y frequent

use, called also baguette .—

A series of beads parallel to
and in contact with each
other is called a reed. —In
joinery the bead is of con¬
stant occurrence, and is
formed, or run, as the term
is, on the edges of boards
which have to be jointed together, and thus they
serve to admit of and yet to disguise any shrinkage

250

which the wood may undergo. The bead is also
much used in framed work. When it is flush with
the face of the work it is called a quirk- bead; when
it is raised, a eoc/r-bead. See p. 183, 184, Joinery.

BEAD-BUTT. Joinery, p. 185.

BEAD-FLUSH Joinery, p. 185.

BEAK.—Synonymous with bird’s mouth (which
see).

BEAM. See Girder.

BEAM-COMPASS.—An instrument used in
describing large circles. It consists of a wooden
or brass beam, having sliding sockets, with steel and
pencil or ink points. See description and use of, p. 34.

BEAM-FILLING.—Filling in between tim¬
bers with masonry or brick-work.

BEARERS, in staircases, p. 196.

BEARING.—The space between the two fixed
extremes of a piece of timber; the unsupported part
of a piece of timber; also, the length of the part
that rests on the supports.

BED-MOULDING.—Properly those members
of a cornice which lie below the corona.

BEECH TREE.—For description of properties
and uses, see p. Ill, 112.

BEETLE.—A heavy wooden maul or hammer.

BELECTION.—SeeBALECTiON and Bolection.

BELFRY.—That part of a steeple or other
building in which a bell or bells are hung, and more
particularly the timber work for sustaining the bell.

BELL —The body of a Corinthian or Composite
capital, supposing the foliage stripped off.

BELL-GABLE. — In small Gothic churches
and chapels, a kind of turret placed on the apex of
a gable, at the west end, and carrying a bell or
sometimes two hells.

BELL-ROOF.—A roof shaped like a bell, its
vertical section being a curve of contrary flexure.
Plate XXXV? Fig. 1, No. 1.

BENCH.—A strong table on which carpenters,

Bay-window, Glastonbury.

Cabinetmaker’s Bench.

joiners, cabinetmakers, and other artisans prepare
their work. In respect of those required by the
cabinetmaker, joiner, and carpenter, a few remarks
may be made. These benches are made in various
ways, from a few rough boards nailed together, to
very complete structures, with various means and
appliances for holding and fastening the work while
being operated on. A cabinetmaker’s bench, of
the most complete kind, is shown in the figure. The
framing is connected by screw-bolts and nuts. The
top surface is a thick plank planed very true. It
has a trough at a to receive small tools, and a
drawer at z Two side-screws c d, which, with
the chop e, constitute a vice for fixing work.
An end-screw g, and sliding-piece h, form another
vice for thin works which require to be held at right
angles to the position of the other chop e ; but its
chief use is to hold work by the two ends. Work,
when laid on the top of the bench, is steadied
by the iron bench-
hookZ;, which slides in
a mortise in the top,
and has teeth at the
end which catches the
wood. When work
would be injured by
the bench-hook, the
stop to, sliding stiffly
in a square mortise in

the bench-top, serves to stay it. The stop and bench-
hook are shown separately above, drawn to a much

Iron stop. Stop.

BENCH-HOOK

INDEX AND GLOSSARY.

BRACE

larger scale. There are several square holes along
the front of the top, also, at distances apart from
each other equal to the motion of the sliding-piece h,
which has a similar hole. In these bench-holes the
iron stop n is inserted, and a similar stop is also
inserted in the hole in h. Thus, any piece of wood
whose length does not exceed the distance between
the end-hole of the bench and the stop in h when it
is drawn out to the full extent of its range, may be
secured. The face of the stop n is slightly roughened.
A holdfast o, sliding loosely in a mortise, is used in
holding square pieces of work on the bench. It is
fixed by driving on the top, and released by driving
on the back. At p is a pin, which is placed in any
of the holes shown in the piece in which it is fixed,
to support the end of long pieces, which are held by
the screws c d, at their other extremity. Various
improvements in the bench-hooks, stops, and hold¬
fasts have been from time to time suggested, such as
making them work by screws; but being in their
simple form sufficiently manageable, and the im¬
provements being more expensive, they have not
obtained general use.—The carpenter’s bench is
composed of a platform or top, supported on strong
framing. It is furnished with a bench-hook at the
left-hand end; at which end also the side-board has
the screw and screw-cheek, together forming the
vice or bench-screw. The side-board and right-hand
leg of the bench are pierced with holes, into any one
of which a pin is inserted, to hold up the end of any
long piece of work clamped in the bench-screw. The
length of the bench may be 10 to 12 feet, the breadth
2 feet 6 inches, the height about 2 feet 8 inches. The
legs should be 3J inches square, well braced; front
top-board should be 2 inches thick; the further I
boards may be 1] inch. These two benches may |
be regarded as the opposite extremes of the scale,
and between them may be many varieties both in
size and in the number of the fittings, as inclina- j
tion or the necessities of the workman may dictate.

BENCH-HOOK, Bench-Holdfast. See pre¬
vious word.

BENCH-PLANES.—The following planes,
used for surfaces by the joiner, are usually called
bench-planes:—

Length. Width.

Jack Plane, . . 12 to 17 ins. 24 to 3 ins.
Trying Plane, . 20 to 22 ,, 3| to 3| ,,

Long Plane, . . 24 to 26 ,, 3f ,,

Jointer,.... 28 to 30 ,, 3f ,,
Smoothing Plane, 64 to 8 ,, 2§ to 3| ,,

Block Plane, . . 12 „

Compass Plane, . 64 to 8 „ 2f to 3 4 ,,

Width of
Iron.

2 to 24 ins.
2| to 24 „
2f
2 -

1 ! to 2§ ;;
lj to 2| „

BENDING- TIMBER.—Various methods de¬
scribed, p. 102; Colonel Emy’s method, p. 103;
Mr. T. Blanchard’s process, p. 103.

BEVEL.—An instrument for drawing angles.
It consists of two limbs jointed together, one called
the stock, and the other the blade, which is move-
able on a pivot at the joint, so that it may be
adjusted to include any angle between it and the
stock.

BEVEL-TOOLS.—Tools used in turning hard
woods. They are in pairs, and their cutting edges
are bevelled off right and left.

BILLET.—An ornament much used in Norman
architecture. It consists of small rounded billets,

Billet-moolding.

like an imitation of small pieces of stick, placed in a
hollow moulding at intervals apart generally equal
to their length.

BILLS.—1. The ends of compasses.—2. Knee-
timbers.

BINDING-JOISTS.—Beams in framed floors
which support the bridging-joists above and the
ceiling-joists below. See Floors, Plate XLII, and
description, p. 150.— Binding-joists. Rule for find¬
ing the strength of, p. 154.

BINDING-RAFTERS.—The same as Purlins.

BIORNBURG TIMBER. See Pinus Syl-
vestris, p. 116, 117.

BIRCH.—The common birch, Betula alba; the
mahogany birch of America, Betula lenta; tall or
yellow birch, Betula excelsa; black birch, Betula
nigra. For description of qualities and uses of the
varieties generally used, see p. 113.

BIRD’S MOUTH.—An interior angle or notch
cut across the grain at the extremity of a piece of
timber, for its reception on the edge of another
piece.

BIT.—1. The cutting part of a plane.—2. A
name common to all those exchangeable boring tools
for wood applied by means of the crank-formed handle
known as the carpenter's brace. The similar tools

used for metal, and applied by the drill-bow, ratchet,
brace, lathe, or drilling-machine, are termed drills
or drill-bits. The distinction, however, is not uni¬
formly maintained: very frequently all those small
revolving borers which admit of being exchanged
in their holders or stocks, are included under the
name of bits. The variety is, therefore, very great,
and the particular names used to designate them are
derived, in most cases, from their forms and the
purposes for which they are employed. For wood,
the typical form is the shell-bit (fig. a), which is

I ;

—L

.. Mm

■O'

shaped like a gouge, with the piercing end sharpened
to a semicircular edge for shearing the fibres round
the circumference of the hole. When large, it is
termed a gouge-bit, and .when small, a qu,ill-bit.
Sometimes the piercing end is drawn to a radial
point, and it is then known as the spoon-bit —of
which the cooper's dowel-bit and the table or furni¬
ture bit are examples. Occasionally the end is bent
into a semicircular form horizontally, and it then
becomes the duck-nose bit. The centre-bit (fig. b),
is another typical form, of which there are many
modifications. The end is flat, and provided with
a centre-point or pin, filed triangularly, and which
serves as a guide for position; a shearing edge or
nicker serving to cut the fibres round the margin
of the hole, and a broad chisel-edge or cutter to pare
away and remove the wood within the circle defined
by the nicker. The plug centre-bit, used chiefly for
making countersinks for cylinder-headed screws;
the button-tool, which retains only the centre-pin
and nicker, and is used for cutting out discs of
leather and the like; the flute-drill, the cup-key tool,
the wine-cooper’s bit, are all modifications of this
borer, suited to special kinds of work. The half-
round bit (fig. c), is employed for enlarging holes in
metal, and is usually fixed in the lathe or vertically.
The cutting end is ground with an incline to the
right angle, both horizontally and vertically, three
to six degrees, according to the hardness of the
material to be bored. The rose-bit (fig. d), is cylin¬
drical, and terminates in a truncated cone, the
oblique surface of which is cut into teeth like the
rose-countersink, of which it is a modification. It
is also used for enlarging holes of considerable depth
in metals and hard woods.

BLACK WALNUT TREE.—Properties and
uses of, p. 111.

BLANK DOOR, Blank Window. —A recess
in a wall, made to appear like a door or window as
the case may be.

BLOCKING COURSE.—The course of stones

B Blocking-course.

whatever be its horizontal surface.— Body range of
a groin. The larger of the two vaults, by the inter¬
section of which the groin is formed, p. 78.— Body
of a room. The main part of an apartment, inde¬
pendent of any recesses.

BOLECTION-MOULD-
INGS.—Mouldings in framed
work which project beyond
the surface of the framing.
Called also balection and belection. See p. 185.

BOLSTERS of the Ionic Capital. —1. The
lateral part which joins two volutes.—2. Same as
balusters (which see).

BOLT.—A cylindrical piece of wrought iron
for fastening together the parts of framing or ma¬
chinery. Mr. Farey gives the following rule for
proportioning the size of the bolt to the strain to
which it is to be exposed, viz.: Divide the given
strain in lbs. by 2200, and the square root of the
quotient is the proper diameter of the pin of the
bolt.

BOND, in masonry and brickwork, signifies
that disposition of the materials by which the joints
of one course are covered by the stones or bricks
of the next course horizontally and vertically, so as
to make the whole aggregate act together, and be
mutually dependent on each other. See also Eng¬
lish Bond and Flemish Bond.

BOND-TIMBER.—Timbers placed in horizon¬
tal tiers at certain intervals in the walls of buildings
for attaching battens, laths, and other finishings of
wood.

BONING; in Scotland termed Borning. —The
act of judging of a plane surface, or of setting ob¬
jects in the same plane or line by the eye.

BORING TOOLS. See Auger, Awl, Bit,
Broach, &c.

BOSS.—An ornament placed at the intersection

or bricks erected on the upper part of a cornice to
make a termination.

BLOCKINGS.—Small pieces of wood fitted to
the interior angle of two meeting boards, and glued
there to strengthen the joint, as m m ill, Fig. 1,
Nos. 3 and 4, Plate LXXII.

BOARD.—A piece of timber sawed thin, and
of considerable length and breadth as compared
with its thickness.

BOARDING - JOISTS.—The bridging-joists
to which the floor boarding is nailed.

BOASTING or Scabbling. —In stone cutting,
an operation performed with a chisel and mallet.
The chisel is about 2 inches broad, and its cutting
edge ground quite sharp. With this tool, impelled
by the mallet, the ridges left between the grooves
formed in brotching are worked off, till the whole
surface is reduced to the plane of the draughts.
The workman commences at the angle of the stone
most remote from him on his right hand, and runs
the chisel draughts diagonally towards his left hand,
or he commences at the angle nearest to him on his
right hand.

BODY of a Niche. —The vertical surface,

251

of the ribs of groined or cross-vaulted roofs. It is
frequently richly sculptured.

BOTTOM PAN EL. — The lowest panel in
framed work. See p. 186.

BOTTOM RAIL.—A term used to denote the
lowest rail in a piece of framed work. See p. 186.

BOULTINE.—A convex moulding, the con¬
tour of whose section is a quadrant. It is gener¬
ally used below the abacus of the Tuscan and Doric
capitals. It is called more commonly ovolo or
quarter-round. Bee Plate LXIII., Mouldings.

BOW-COMPASSES.—Different kinds of, and
instructions how to use, see p. 33.

BOW - SAW ; called also Frame - Saw and
Sweep-Saw. —It is used for cutting curves. The
frame of this saw consists of a.central rod or stretch¬
er, to which are mortised two end pieces that have a
slight motion of rotation on the stretcher. These
end pieces are each adapted at one extremity to
receive the saw-blade, and the other ends are con¬
nected by a coil of string, in the middle of which
is a short lever. On turning round the lever, the
string is twisted, and thereby shortened. It thus
draws together those ends of the cross pieces to
which it is attached, and separates the opposite
ends, by which means the saw is stretched. In
using the bow-saw, the work is usually fixed verti¬
cally, and the saw worked horizontally; but the
frame is placed at all angles, so as to clear the
work.

BOWTEL.—The shaft of a clustered pillar, or
any plain round moulding.

BOX TREE. — For properties and uses, see

*’ BOXED SHUTTERS. — Those which fold
hack into a box or case.

BOXINGS of a Window.— The cases, one on
each side of the window, and opposite to each other,
into which the shutters are folded. The shutters in
this case are termed boxed-slmtters. See illustra¬
tion, p. 1S8, and Plate LXXVIIL, Window-
Finishings.

BRACE.—A piece of timber in any system of
framing extending across the angle between two
other pieces at right angles. See action of braces

BRACE AND BIT

and counterbraces, Bridges, p. 159, 166; and
illustration of braces in framing timber houses, Fig.
470, p. 157.

BRACE and BIT.—The brace is an instru¬
ment made of wood or iron. It consists of a cranked
shaft having at its one end a socket, called the
pad, to reeeive the bits or boring tools, and at the
other a swivelled head or shield, which, when the
instrument is used horizontally, is pressed forward
by the workman’s breast, and when vertically, by
his left hand, which is commonly placed against
his forehead. See Bit.

BRACKET.—A small support against a wall
for a figure, clock, &c. Brackets, in joinery, are
either cut out of deal or framed with three pieces of
timber, viz., a vertical piece attached to the wall,
a horizontal piece attached to the shelf to be sup¬
ported, and an angle brace framed between the
horizontal and vertical pieces. ,

BRACKETED STAIRS, p. 196.

BRACKETS, Diminishing and Enlarging,

P . 201 .

BRAD. — A particular kind of nail, used in
floors or other work where it is deemed proper to
drive nails entirely into the wood. To this end it
is made without a broad head or shoulder on the
shank.

BRAD-AWL.—An awl used to make holes for
brads.

BRANCHED WORK.—The carved and sculp¬
tured ornaments in panels, friezes, &c., composed
of leaves and branches.

BRANDERING.—Covering the under side of
joists with battens about 1 inch square in the sec¬
tion, and 12 to 14 inches apart, to nail the laths to,
in order to secure a better key for the plaster of a
ceiling. See p. 154.

BRANDISHING or Brattishing. —A crest,
battlement, or other parapet.

BRANDRETH.—-A fence or rail round the
opening of a well.

BREAK.—A recess; also, any projection from
the general surface of a wall or building.

BREAKING-JOINT.—That disposition of
joints by which the occurrence of two contiguous
joints in the same straight line is avoided.

BREAST-LINING, p. 188.

BRESSUMMER or Breastsummer. — A
summer or beam used in the face or breast of a
wall, as a lintel to support a superincumbent wall.
Its use is generally restricted to a beam used as a
lintel in an external wall, such as over the wide
openings of shop fronts. See Timber Houses,
p. 154.

BRICK-NOGGING.—Brick-work carried up
and filled in between timber framing.

BRICK-TRIMMER.—A brick arch abutting
against the wood trimming joist in front of a fire¬
place, and used to support the hearth. See Floors,
p. 151.

BRICK-WORK is valued by the cubic yard,
and also by the rod. A rod of brick-work is a
quantity of 272J superficial feet, of the thickness
of a brick and a half, or 13J inches. The quarter
of a foot is generally disregarded, and the round
number 272 feet is reckoned a rod. Hence a rod
of brick-work is 306 cubic feet, and contains 4500
bricks, allowing for waste.

BRIDGE.—Any structure of wood, stone, or
iron raised over a river, pond, lake, or hollow of
any kind, to support a roadway for the passage of
men, vehicles, &c. Among rude nations, bridges
are sometimes formed of other materials than those
enumerated; and sometimes they are formed of
boats, or logs of wood lying on the water, fastened
together, covered with planks, and called floating
bridges. A bridge over a marsh is made of logs or
other materials laid upon the surface of the earth.—
In suspension or chain bridges, the flooring, or main
body of the bridge, is supported on strong iron
chains or rods, hanging in the foim of an inverted
arch from one point of support to another. The
points of support are the tops of strong pillars
or towers, erected for the purpose at each ex¬
tremity of the bridge. Over these pillars the chains
pass, and are attached beyond them to rocks or
massive frames of iron firmly secured under ground.
The flooring is connected with the chains by means
of strong upright iron rods.—A draw-bridge is one
which is made with hinges, and may be raised or
opened. Such bridges are constructed in fortifica¬
tions, to hinder the passage of a ditch or moat; and
over rivers, dock-entrances, and canals, that the

passage of vessels may not be interrupted._A

flying-bridge is made of pontoons, light boats, hol¬
low beams, empty casks, or the like. It is made,
as occasion requires, for the passage of armies. A
flying-bridge is also constructed in such a manner
as to move from one side of a river to the other. It
consists of a boat secured to a long cable, made fast

INDEX AND GLOSSARY.

buttress

in the middle of the river by an anchor, and by the
action of the helm it can be made to swing from
one bank to the other.

BRIDGE.—Classification of the usual forms of
bridge trusses, p. 161.

BRIDGE-BOARD or Notch - Board. — A
board into which the ends of wooden steps are fas¬
tened. See p. 195, Fig. 512.

BRIDGE GUTTER.—Gutters formed of
boards covered with lead, supported on wooden
bearers

BRIDGE OYER.—A piece of timber which is
laid over parallel lines of support, crossing them
transversely, is said to bridge over them. Thus, in
flooring, the upper joists to which the boards
are attached bridge over the binding-joists
which extend transversely beneath them, and
they are therefore called bridging joists.

BRIDGES.—Consideration of the forces
which act on framed trusses as applied in the
construction of, p. 158.

BRIDGES.—Mr. Ilaupt’s rules for cal¬
culating the strains on the different pieces corn-

frieze of the entablature, in the Ionic and Corin¬
thian orders of architecture.

BUILDING.—A fabric or edifice constructed
for use or convenience; as a house, a church, a
shop.

BUILDING a Beam is accomplished in the
simplest manner, by laying the flitches above each
other, and bolting or hooping them together. The
sliding of the pieces is prevented by the insertion
of keys. This mode is shown in fig. 1. Another
method is to table or indent the surfaces of the
pieces together, and secure with hoops. Fig. 2 re¬
presents this mode. In the first method the prac¬
tical rule to find the size of the keys: —To the

Fig. l.

Fig. 2.

Building a Beam.

BRIDGES, TIMBER.—Theory of the

con-

struction, of, p. 158.

BRIDGES illustrated and described:—

Plate.

Page.

Timber draw-bridge, Gotha Canal,

XLVIII.

162

Simple bridge truss,

XLVIII.

162

Simple bridge truss,

XLVIII.

1C2

Laminated arch truss, .

XLVIII.

162

Elevation of a bridge 34 feet span,

XLVIII.

162

Elevation of a bridge truss, .

XLVIII.

162

Bridge over the Spey at Laggan-
kirk, .

XLIX.

162

Elevation of a timber bridge,

XLIX.

162

Bridge over the Don at Inverury,

162

Railway-bridge, designed by Mr.
White, .....

LI.

163

Road-bridge, designed by Mr.
White,.

LI.

164

Timber bridge over the Tyne at
Linton, .

LII.

164

Skew-bridge, designed by Mr.
White.

LIII.

164

Trussed bridge, with laminated
arch braces, designed by Mr.
White,.

LIIT.

165

American timber bridge,

LIV.

165

American timber bridge,

LIV.

165

Common lattice bridge,

LIV.

169

Improved lattice bridge.

LIV.

170

Skew-bridge at Portobello, on the
North British Railway,

LV.

170

Bridge over the Tweed at Mertoun,

LVI.

171

depth of the beam in inches add thrce-eigliths of the
depth, and divide the sum by the number of keys
to be used; the quotient will be the thickness of
each key, and their breadth should be twice their
thickness. In the second method the sum of the
depth of the indents should be equal to two-thiids
of the depth of the beam. The indents should be
made to form abutments to the pressure. See
p. 148.

BUILT BEAM.—One composed of several
pieces.

BULL-NOSED BRICKS.—Those with one
of their vertical angles rounded.

BULLER NAILS.—Round-headed nails with
short shanks, turned and lackered; used chiefly for
the hangings of rooms.

BULLET WOOD. — A wood of a greenish
hazel colour, close and hard, the produce of the
Virgin Isles, West Indies. It resembles green-
heart.

BULL’S-EYE.—A small circular or elliptical
window.

BLTLL’S - NOSE.—The external angle of a
polygon, or any obtuse angle.

BUTMENTS. Abutments.

BUTT END of Timber.— That which is near¬
est the root of the tree.

BUTT-HINGES.—Those which are placed on
the edges of doors, &c., with their knuckle on the
side on which the door opens. See Hinging, p.
180, and Plates LXXXIV.-LXXXVI.

BUTT-JOINT.—That formed by two pieces of
timber united endways.

BUTTRESS. — 1. A prop. — 2. A projection
from a wall to impart additional strength and sup-

BRIDGING - FLOORS.— Those in which
bridging-joists are used. See p. 150.

BRIDGING-JOISTS.—The upper joists in a
framed floor, to which the flooring boards are nailed.
See Bridge over Floors, p. 150; and illustration,
Plate XLII.

BRIDGING-JOISTS.—Rules for calculating
the strength of, p. 154.

BRIDGINGS.—Pieces of wood placed between
two beams or other timbers, to prevent their ap¬
proaching each other. More generally termed strain¬
ing or strutting pieces.

BRINGING UP, or Carrying Up, signifies
the same as building up.

BROACH. — A general
name for all tapered boring
bits or drills. Those for wood
are fluted like the shell-bit, but
tapered towards the point; but
those for metal are solid, and
usually three, four, or six sided.

Their usual forms are shown in
the annexed figures. Broaches
are also known as wideners and
rimers. Fig. a is an example of
the broach or rimer for wood,
and fig. b of those for metal.

BROACH.—An old English term for a spire;
still in use in the north of England, as Tlesslcbroach,
&c.; and in some other parts of the country, as in
Leicestershire, it is used to denote a spire springing
from the tower without auy intermediate parapet.

BROAD.—An edge tool for turning soft wood.
The edge of the broad is at right angles to the
handle, and tho blade is either square or triangular.
The triangular broad is used principally for turning
large pieces the plank way of the grain.

Bl CRANIA. — Sculptured ornaments repre¬
senting ox-skulls adorned with wreaths or other
ornaments, which were employed to decorate the

252

Buttress, Winchester Cathedral.

port..—3. A wall or abutment built archwise, serv¬
ing to support another wall on the outside, when
very high or loaded with a heavy superstructure.
Buttresses are much employed in Norman archi¬
tecture, and in all the styles of the Gothic. In the
Norman they are generally of considerable breadth
and very small projection, while in the Pointed
styles their projection is usually much greater than
their breadth. They are almost invariably divided
into stages with sloping copings : the slope of the
copings being progressively increased in each stage
of the ascent. By this means the higher copings
present to the eye of a spectator nearly as great a

BYZANTINE ARCHITECTURE

INDEX AND GLOSSARY.

CENTRES

surface as the lower ones, as they do not become so
much fore-shortened as they otherwise would do.

BYZANTINE ARCHITECTURE.—A style
of architecture developed in the Byzantine Empire
about a.d. 300, and which, under various modifi¬
cations, continued in use till the final conquest of
that empire by the Turks in a.d. 1453. It spread
so widely, and was so thoroughly identified with
all middle-age art, that its influence even in Italy
did not wholly decline before the fifteenth century.
Its ruling principle is incrustation, the incrustation
of brick with more precious materials ; large spaces
are left void of bold architectural features, to be
rendered interesting merely by surface ornament
or sculpture. It depended much on colour for its
effect, and with this intent, mosaics wrought on
grounds of gold or of positive colour, are profusely
employed. The leading forms which pervade the
Byzantine are the round arch, the dome, the circle,

Fig. X.

Fig. 2.

Byzantine Capitals.

Fig. 1. From the Apse of Murano. Fig. 2. From the Casa
Loredan, Venice.

and the ci'oss. The capitals of the pillars are of
endless variety, and full of invention; while some
are founded on the Greek-Corinthian, many ap¬
proach in character to those of the Norman; and
so varied are their decorations, that frequently no
two sides of the same capital are alike. Both the
Norman and the Lombardic styles may be consi¬
dered as varieties of the Byzantine, and all of these
are comprised under the term Romanesque, which
comprehends the round-arch style of middle-age
art, as distinguished from the Saracenic and the
Gothic, which are pointed-ax-ch styles. The mosque
of St. Sophia, Constantinople, and the church of
St. Mark’s, Venice, are prominent examples of
Byzantine architecture.

CABLE-MOULDING.—A cylindrical mould¬
ing inserted in a flute so as partly to fill it. In

Cable-moulding*

mediaeval architecture the cable is a moulding of
the torus kind, carved in imitation of a rope.

CABLING.—The filling of flutes with cable
mouldings, or the cables themselves, whether dis¬
posed in flutes or without them.

CAISSON.—A sunken panel in a ceiling or
soffit. See Coffer, which is the proper term.

CAISSONS of an Ellipsoidal Vault. —To
determine the, p. 83.

CALIBER, Calibre, Caliper Compasses.—
Compasses made with arched legs,
to take the dimensions of the ex¬
terior diameter of round bodies;
and also compasses made with
straight legs, with their points
retracted, used to measure the
interior diameter or boi'e of a
cylinder.

CAMBER.—A curve or arch.

— Cambered beam, a beam bent or
cut in a curve like an arch. Caliber Compasses.

CAMP - CEILING. —1. The
interior of a truncated pyramid.—2. The ceiling of
an attic room where all the sides ai - e equally in¬
clined from the wall to meet the horizontal part in
the centre.-

CAMPANILE.—A clock or bell tower. The
term is more especially applied to detached build¬

ings in some parts of Italy, erected for the purpose
of containing bells, and to towers of similar design
erected elsewhere.

CANADIAN TIMBER, p. 118.

CANAL.—The same as flute. — Canal of the
larmier, the hollow made in the soffit or under side
of a cornice.— Canal of a volute, a channel in the
face of the circumvolutions of the Ionic capital, in¬
closed by a list or fillet.

CANKERS in trees, p. 97.

CANOPY.—1. A decollation serving as a hood
or cover suspended over an altar, throne, chair of
state, pulpit, and the like.—2. The ornamental
projecting head of a niche or tabernacle.—3. The
label moulding or drip-stone surrounding the head
of a door or window when ornamented.

CANT, v. —To truncate or cut off the external
angle formed by the meeting of two planes. Also,
to turn over anything on its angle.

CANT, n. —An external or salient angle.

CANT-MOULDING.—Any moulding with a
bevelled face.

CANTED COLUMN.—A column polygonal
in section.

cantilever, cantaliveb.— Wooden or

iron blocks framed into the side of a house under

Cantilever.

the eaves, and projecting so as to carry a cornice,
a projecting eave, or other moulding. Cantilevers
serve the same end as modillions ; but the use of
the latter is confined to regular architecture, while
the former are in general and trivial use.

CAP.—The congeries of mouldings which
forms the head of a pier or pilaster. In joinery, the
uppermost of any assemblage of pax-ts.

CAPITAL.—The uppermost part of a column,
pillar, or pilaster, sei-ving as the head or crowning,
and placed immediately over the shaft and under
the entablature. In classic architecture the dif¬
ferent orders have their respective capitals ; but
in Egyptian, Indian, Byzantine, and Gothic archi-'
tecture they are endlessly diversified.

CAPPING PIECES.—A general name for
horizontal timbers which extend over upright
posts, and into which the posts are framed. See
p. 156.

CARACOLE.—A spiral staircase.

CARCASS.—Generally, the frame or main
parts of a thing unfinished and unornamented,
such as a building, when the work of the mason,
bricklayer, and carpenter is completed, but before
the joiner, the plasterer, and other artisans who fit
it for use have begun their operations.

CARCASS-FLOORING.—The frame of tim¬
bers which supports the floor-boards above and the
ceiling below.

CARCASS-ROOFING.—The frame of timber
work which spans the building, and carries the
slate boarding and other covering.

CARPENTER’S RULE.—A folding rule of
boxwood; in England generally 2 feet, and in
Scotland 3 feet in length.

CARPENTER’S SQUARE. See Square.

CARPENTRY.—The art of cutting, joining,
and framing together the timbers essential to the
stability of a structure. See p. 120.

CARPENTRY and JOINERY'.—Distinction
between, p. 120.

CARRIAGE of a Stair. —

The timber frame which supports
the steps of a wooden stair. See
p. 196.

CARTOUCHE.—1. A roll or
scroll.— 2. A tablet formed like a
sheet of paper, with the edges rolled
up, either to receive an inscription or
for ornament. — 3. A kind of blocks
or modillions used in the cornices of
apartments.

CARYATIDES. — Figures of
women in long robes, after the Asia¬
tic manner, used in the place of col¬
umns as supports for an entablature.

CASE-BAGS.—The joists framed
between a pair of girders in naked
flooring.

CASED SASII - FRAMES. —

Sash-frames hung in cases with ropes and pulleys,
so as to slide freely up and down.

253

CASEMENT.—1. A compartment between the
mullions of a window, but more generally a glazed
sash or frame hinged to open like a door.—2. A hol¬
low moulding equal to one-sixth or one-fourth of
a circle.

CASTING, Warping, or Buckling.— The
bending of the surfaces of a piece of timber from
their original state, caused either by the weight of
the material or by unequal temperature, unequal
moisture, or the want of uniformity of texture.

CATHEDRAL.—The see or seat of a bishop ;
the principal church in a diocese, so called from
possessing the episcopal chair, called cathedra.

Plan of Wells Cathedral.

A, Apse or apsis. B, Altar, altar-platform, and altar-steps. D E,
Eastern or lesser transept. F G, Western or greater transept. H, Cen¬
tral tower. I J. Western towers. K, North porch. L, Library or
registry. M, Principal or western doorway. N N, Western s de doors.
O, Cloister-yard or garth. P Q, North and south aisles of choir. RS,
East and west aisles of transept. T.U, North and south aisles of nave.
It R, Chapels. V, Rood-screen or organ-loft. W, Altar of Lady Chapel.

Many of the terms used to designate the different
parts of a cathedral are illustrated and explained
by the annexed woodcut and its references.

CATHERINE WHEEL.—In Gothic archi¬
tecture, a large circular window, or circular com¬
partment in the upper portion of a window, filled
with radiating divisions or with a rosette.

CATHETUS.—A perpendicular line supposed
to pass through the middle of a cylindrical body;
the axis of a cylinder; the centre of the Ionic
volute.

CAVETTO.—A hollow member or round con¬
cave moulding containing the quadrant of a circle,
and used as an ornament in cornices and between
the tori of the base of the Ionic, Corinthian, and
other orders.

CAULKING.— The mode of fixing the tie-
beams of a roof, or the binding and bridging joists
of a floor, on the wall-plates ; notching. Called
also coching (which see).

CEDAR WOOD. — Properties and uses of,
p. 119.

CEILING.—The plaster or other covering
which forms the roof of a room.

CEILING-JOISTS.—Joists to which the ceil¬
ing of a room is attached. They maybe nailed to the
under side of the binding-joists, or worked into

their sides, or suspended from the upper joists by
straps. In the figure, a is the flooring ; b. the
girder ; c c, the bridging-joists ; d d, the ceiling-
joists; and e e, the straps.

CEILING-JOISTS.—Rules for determining
the strength of, p. 155.

CENTRE or Centering. —The mould or
timber frame on which any arched or vaulted work
is constructed.

CENTRE-BIT.—A tool for boring large cir¬
cular holes. See Bit.

CENTRES.—Tredgold’s theory of the pressure
of the arch stones on the, p. 172.

CENTRES. —Smeaton’s observations on his
design for the centre of Coldstream Bridge,
p. 173.

Caryatid.

)

INDEX AND GLOSSARY.

CENTRES

CENTRES illustrated and described—

Centre for an .arch of small span, .

Centre with intermediate supports,

Centre with radiating struts, .

Centre of a bridge over the river
Don, 75 feet span,

Centre of Gloucester Overbridge, .

Centre of Dean Bridge, Edinburgh,

Centre of Cartland Craigs Bridge,

Centre of Ballochmyle Viaduct,

Centre of railway viaduct over the
Union Canal, near Falkirk,

Centre of North British Railway
viaduct at Dunglass Burn,

Centre of viaduct over the Lugar

Water,.

Centre o^ Waterloo Bridge, London,

Centre of bridge over the Seine at

Neuilly,.

Centre designed by Mr. White,

CENTRES, mode of supporting, adopted at the
Bridge of Nemours, p. 175.

CENTRES, mode of striking, adopted at
Chester Bridge, p. 175.

CENTRES, mode of striking, adopted at
Gloucester Bridge, p. 176.

CHAIN- MOULDING.—An ornament of the
Norman period sculptured in imitation of a chain.

Plate.

Plff.

PaKe-

LVII.

1-4

173

Lvn.

5, 6

173

LVII.

173

LVII.

173

LVIII.

173

LVIII.

174

LVIII.

174

6-10

174

LV.

174

LV.

8-11

175

LVI.

3, 4

175

LIX.

175

LIX.

175

LIX.

175

CHAIN-TIMBERS.—Bond timbers of alarger
size than usual, introduced to tie and strengthen a
wall. The timbers are usually of the dimensions
of a brick.

CHAIR-RAIL.—A plate of timber attached
to a wall to prevent injury to the plaster from the
backs of chairs.

CHAMFER.—To cut in a slope.

CHAMP.—A flat surface.

CHANCEL.—That part of the choir of a
church between the altar or communion table and
the balustrade or railing that incloses it, or that
part where the altar is placed, formerly inclosed
with lattices or cross-bars, as now with rails. See
Choik, as to the arbitrary use of the two words.

CHANTLATE.—Apieceof wood fastened near
the end of a rafter, and projecting beyond the wall,
to support two or three rows of slates or tiles, so
placed as to prevent the rain-water trickling down
the wall.

CHAPITER.—The upper part of the capital
of a column or pillar.

CHAPLET—A small cylindrical moulding
carved into beads and the like.

CHAPS in trees, p. 97.

CHAPTREL.—The capital of a column sup¬
porting an arch ; an impost.

" CHASE-MORTISE or Pulley-Mortise. —A

manner of mortising trans¬
verse pieces into parallel
timbers already fixed. One
end of the transverse piece
is mortised into one of the
parallel pieces, and a long
mortise being cut in the
other parallel piece, the
other end of the transverse
piece is let into it, by mak¬
ing it radiate on its already

mortised end. In this way, ceiling-joists are fixed
to the bridging-joists.

CHEEKS of a Mortise, p. 14

CHESTNUT WOOD. —Propt
of, p. 113.

CHEVAL-DE-FRTSE. — A piece of timber
pointed with iron and traversed with wooden
spikes. Used in military operations.

CHEVRON.—A carved decoration, consisting

-Properties and uses

Chevron Moulding.

of mouldings ranging in zigzag lines, peculiar to
the Norman style of architecture. It is called also
zig-zag and dancette.

CHIMNEY.—A body of brick or stone, erected
inabuilding, containingafunnelorfunnels, to convey
smoke and other volatile matter through the roof,
from the hearth or fire-place, where fuel is burned.
The lower part of the chimney in the room or apart¬
ment is called th c fire-place ; the bottom or floor of
the fire-place is called the hearth, sometimes the
inner hearth; the stone or marble in front of the
hearth is called the slab or outer hearth. The ver¬
tical sides of the fire-place opening are termed the
jambs, and the lintel which lies on them is called
the mantle. The inner wall of the fire-place is
called the breast, and the other two sides are
termed the covings. The cylindrical or parallelo-
gramical tube which conveys the smoke from the
fire-place to the top of the chimney is called the
flue. The fire-place cavity being much wider than
the flue, they are joined by a tapering part, which
is termed the funnel; the lower part of the funnel
is termed the gathering, or gathering of the wings;
and the junction of the funnel and flue is called the
throat. When several chimneys are carried up
together, the mass is called a stack of chimneys.
The part of the chimney carried above the roof, for
discharging the smoke, is the chimney-shaft, and
the upper part of the shaft is the chimney-top or
head.

CHISEL.—A cutting tool, of which there are
many different sorts, used by carpenters, joiners,
bricklayers, masons, and smiths. — Carpenters'
chisels are: 1. The socket or heading chisel, em¬
ployed in cutting mortises. Its blade is from lj
inch to 1 ^ inch wide, and it gets its name from the
top of its stem being formed into a socket to re¬
ceive a wooden handle. 2. The mortise - chisel,
which has a button on the top of its stem, with a
tang for insertion into a wooden handle. 3. The
ripping chisel, which is generally an old socket-
chisel.— Joiners’ chisels. 1. The mortise chisel,
the same as that of the carpenter’s, and of various
sizes. 2. The firmer. 3. The paring - chisel.
4. The drawing-knife, which is an oblique-ended
chisel.— Masons' chisels, called by them tools. These
are from 6 to 8 inches long, and have a button
formed on the head of the stem, to receive the
blows of the mallet or hammer. 1. The broad
boaster or batt, which is from 3 to 4^ inches wide
on the cutting edge. 2. The boaster, which is
from 2 to 3 inches wide. 3. Tools of the same
kind, called from their width the 1 ^-inch tool, the
1-inch tool, &c. 4. The point, which is from -j-’j

to 5 inch wide. There are, besides these, a great
variety of chisels or tools used for various kinds of
stone; as pitching tools, for squaring flags, granite
tools, &c.— Bricklayers’ chisels. These are of the
same nature as the chisels of the masons, and, in
addition, the bricklayers use the ripping chisel and
the iron chisel, which is a small crowbar.— Smiths’
chisels are similar to those of the masons, but
shorter.

CHOIR.—The part of a church where the ser¬
vices are chanted or recited, but the application of
the term is generally restricted to the inner or east¬
ern part of a cathedral, where service, more especi¬
ally the musical part of it, is performed. It is
separated by the transept from the nave or outer
part. See woodcut. Cathedral. —In churches the
same part is called the chancel.

CHORD, The, and versed sine of the arc of a
circle being given, to find the curve without having
recourse to the centre. Prob. LXXXIV. p. 22.

CHORDS of a Timber Bridge. —The hori¬
zontal longitudinal main timbers of the framing,
p. 159.—To find the strains on, p. 160.

CHORDS, Line of, on the Sector. —Construction
and use of, p. 37,

CHRISTIANIA TIMBER. See Pinus syl-
vestris, p. 116 , 117 .

CILERY.—Drapery or foliage carved on the
heads of columns.

CINCTURE.—A ring or list at the top and
bottom of a column, separating the shaft at the one
end from the base, and at the other from the
capital.

CINQUE-CENTO.—Literally 500, but used as
a contraction for 1500, the century in which the
revival of the architecture of Vitruvius took place
in Italy, and applied to distinguish the architecture
of the Italo-Vitruvian school generally—a school
marked by the formation of the five orders, by the
use of attached columns, unequal intercolumnia-
tions, broken entablatures, and the collocation of
arches with columnar ordinances.—In decorative
art, a term applied to that attempt at purification
of style and reverting to classical forms introduced
towards the middle of the 16th century, and prac¬
tised by Agostino Busti and others, more particu¬
larly in the north of Italy. This style aimed at a
revival of the gorgeous decorations of Rome, throw-
1 ing out all those arbitrary forms which are never

254

CIRCLE

found in ancient examples, as the scrolled shield
and tracery; and elaborating to the utmost the
most conspicuous characteristics of Greek and
Roman art, especially the acanthus scroll and the
grotesque arabesques, abounding with monstrous
combinations of human, animal, and vegetable
forms in the same figure or scroll-work, but always
characterized by extreme beauty of line. The term /

is often loosely applied to ornament of the 16th
century in general, properly included in the term
Renaissance.

CINQUE-FOIL. — An ornament in Gothic
architecture, consisting of five cuspidated divisions.
See Foliations.

CIRCLE and Circular Figures.— Construc¬
tion of, p. 18-22.

CIRCLE.—The circle contains a greater area
than any other plane figure bounded by the same
perimeter. The areas of circles are to each other
as the squares of their diameters.—The chord and
versed sine of a circle being given, to find its
diameter. Rule: Divide the sum of the squares
of the chord and versed sine by the versed sine:
the quotient is the diameter.—To find the length
of any given arc of a circle from its chord and the
chord of half the arc. From eight times the chord
of half the arc subtract the chord of the whole arc,
and one-third of the remainder is equal to the
length of the arc.—To find the area of a circle.
Multiply the square of the diameter by '7854.—To
find the area of a sector of a circle. Multiply the
length of the arc by its radius, and half the product
is the area.—To find the area of the annular space
between two concentric circles. Multiply the sum
of the larger and smaller diameters by their differ¬
ence and by '7854.—Approximate rules for prac¬
tical calculations:—

The diameter multiplied by 3T416is equal to circumference.
The circumference multiplied by -31831 is equal to the
diameter.

The square of diameter multiplied by '7854 is equal to the
area.

The square root of area multiplied by IT‘2837 is equal to
diameter.

The side of a square multiplied by 1T2S is equal to the dia¬
meter of a circle of equal area.

The diameter multiplied by ‘8862 is equal to the side of a
square of equal area.

CIRCLE.—To inscribe a circle in a given tri¬
angle, p. 9.

CIRCLE. — To inscribe a circle within three
given oblique lines, p. 9.

CIRCLE.—To cut off a segment from a circle
that shall contain an angle equal to a given angle,
p. 18.

CIRCLE.—To divide a circle into any number
of equal or proportional parts by concentric divi¬
sions, p. 18.

CIRCLE.—To divide a given circle into three
concentric parts, bearing the proportion to each
other of 1, 2, 3, from the centre, p. 18.

CIRCLE.—To divide a circle into any number
of parts equal to each other in area and perimeter,
p. 19.

CIRCLE.—To raise perpendiculars to any point
of an arc of a circle without finding the centre,
p. 19.

CIRCLE.—To find the centre of a given circle,

p. 16.

CIRCLE.—To draw a tangent to a circle pass¬
ing through a given point in its circumference,
p. 16.

CIRCLE.—To draw a tangent to a circle from
a given point without the circumference, p. 16.

CIRCLE.—To find the point of contact be¬
tween a given tangent and circle, p. 16.

CIRCLE.—Through three given points to de¬
scribe the circumference of a circle, p. 17.

CIRCLE.—To describe a circle that shall touch
two straight lines given in position and one of them
at a given point, p. 17 .

CIRCLE.—To draw a straight line equal to the
circumference of a circle, p. 19.

CIRCLE.—To draw a straight line equal to any
given arc of a circle, p. 19.

CIRCLE.—To construct a triangle equal to a
given circle, p. 20 .

CIRCLE.—To describe a rectangle equal to a
given circle, p. 20 .

CIRCLE.—Through three given points to de¬
scribe an arc of a circle without finding the centre,
p. 20 .

CIRCLE.—Three points, neither equidistant
nor in the same straight line being given, through
which the arc of a circle is to be described, to find
the altitude of the proposed arc, p. 21 .

CIRCLE.— A segment of a circle being given,
to complete the circle without finding the centre,
p. 21 .

CIRCLE

INDEX AND GLOSSARY.

CONCAMERATE

CIRCLE.—To describe a circle by means of a
carpenter’s square or right angle, p. 21 .

CIRCLE.—To describe the arc of a circle by
two straight rods, the chord and versed sine being
given, p. 21 .

CIRCLE.—To describe the segment of a circle
at twice by a triangular mould, the chord and versed
sine being given, p. 21 .

CIRCLE.—To find points in the curve of a seg¬
ment of a circle by intersecting lines, p. 21 , 22 .

CIRCLE.—The chord and versed sine of an
arc of a circle being given, to find the curve with¬
out having recourse to the centre, p. 22 .

CIRCLE. — To describe a square equal to a
given circle, p. 20 .

CIRCLE.—The shadow thrown by a circle on
the horizontal plane, p. 214.

CIRCLE.—The shadow of a circle on the ver¬
tical plane, p. 215.

CIRCLE..—To find the shadow of a circle on
two planes, p. 215.

CIRCLE.—The shadow of a circle on a curved
surface, p. 215.

CIRCLE. — To find the shadow of a circle
situated in the plane of the luminous rays,
p. 215.

CIRCLE. —To find the shadow of a circle
whose horizontal projection is perpendicular to a
trace of a plane passing through the luminous ray,
p. 216.

CIRCLES.—To find the point of contact of two
touching circles, p. 18.

CIRCLES, contiguous, to describe,which shall
also touch a given line, p. 18.

CIRCULAR CHAPS in trees, p. 97.

CIRCULAR SAW.—A saw with circular
blade mounted on a spindle like a wheel, with teeth
on its periphery. The teeth of circular saws are
generally wider apart, more inclined, and wider set
than the teeth of rectilinear saws.

CIRCULAR WINDOW. —To find the cur¬
vature of the sash - bar of a circular window,
p. 189.

CIRCULAR WINDOW or Chord Bar.—To
find the veneer for the cot-bar, p. 189. To find I
the mould for the radial bar, p. 189. To find the
face-mould for the circular outside lining, p. 189.
To obtain the moulds for the head of the sash- j
frame, p. 189. To obtain the mould for the under
side of the sash, p. 189.

CLAMP.—1. An instrument made of wood or
metal, with a screw at one end, used to hold pieces
of timber together until the glue hardens; also, a
piece of wood fixed to another in such a manner
that the fibres cross, and thus prevent casting or
warping.—2. Something that fastens or binds.—3.
A piece of timber or iron used to fasten work
together.

CLAMPING. — Fastening or binding by a
clamp.

CLASP NAILS.— Nails with heads flattened,
so as to clasp the wood.

CLASSIC ORDERS.—The Grecian Doric,
Ionic, and Corinthian, and the Roman, Tuscan,
Doric, Ionic, Corinthian, and Composite orders
are generally thus distinguished.

CLEAR.—Free from interruption.— In the
clear, the nett distance between any two bodies,
without anything intervening.

CLEARCOLE, or Claircol. —A composition
of size and white lead.

CLERE-STORY, Clair-Story. —The upper
tier of lights of the nave, choir, and transepts of a
church. The name is by some derived from the
clair or light admitted through its windows—by
others from the windows being clear of the roof of
the aisle—and by others from that story being
clear of rafters, joists, or any obstruction.

CLINKER.—A brick more thoroughly burned
than the others, by being nearer to the fire.

CLOISTER.— Literally, a close or inclosed
place. An edifice is said to be in form of a cloister
when there are buildings on each side of a court.

CLOSE-STRING.— In dog-legged stair-cases,
when the steps are housed into the strings. See
p. 196.

CLOSER.—The stone or brick laid to close the
defined length of any course.

CLOUT-NAIL. — A flat-headed nail with
which iron-work is usually fastened to wood.

CLOWRING, Clodring. — In stone-cutting,
the same as wasting (which see).

CLUSTERED COLUMN.—A pier which is
formed of a congeries of columns clustered to¬
gether, either attached or detached.

COB-WALL.—A. wall formed of unburned clay,
mixed with chopped straw and occasionally with
layers'of long straw, to act as a bond.

COCK-BEAD.—A bead which projects from
the surface of the timber on both sides.

COCKING, Cogging. — A mode of notching
timber; called also caulking. A variety of notch¬

ing, which will bo understood by inspection of the
figure.

CODDINGS.—A term used in Scotland to
denote the base or footings on which chimney-
jambs are set in the ground-floor of a building.

COFFER. — A panel deeply recessed in any
soffit or ceiling.

COIN, Coigne. — The corner of a building.
— Coin-stones, corner-stones. - See Qdoin.

COLLAR of a Shaft. —The annulet.

COLLAR-BEAM.—A beam extending be¬
tween the two opposite rafters of a framed prin¬
cipal above the tie-beam, or between two common
rafters.

COLONNADE.—A range of columns.

COLUMN.—A long solid body called a shaft,
set vertically on a congeries of mouldings, which
forms its base, and surmounted by a spreading
mass, which forms its capital. In strictness, the

1. Fillet. 2 . Cymft Recta. 3. Corona. 4. Ovolo. 5. Cavetto.
6 . Frieze. 7. Fillet. , 8. Upper FasCia. 9. Lower Fascia. 10. Abacus.
11. Ovolo. 12. Colarino or Neck. 13. Astragal. 14 Apophyges. 15 Torus.
16. Plinth.

term column should be applied only when the shaft
is in one piece. When it is built up of several
pieces it is a pillar or pile. Columns are distin-

j guished by the styles of architecture to which they
belong; thus, there are Hindoo, Egyptian, Grecian,

| Roman, and Gothic columns. In classic architec¬
ture they are further distinguished by the name of
I the order to which they belong—as Doric, Ionic,
and Corinthian columns; and again by some pecu¬
liarity of position, of construction, of form, or of
ornament—as attached, twisted, cabled, indented,
rusticated columns. Columns, although chiefly
used in the construction or adornment of buildings,
are also used singly for various purposes. Thus,
there are the astronomical column, whose use is
sufficiently indicated by its name; the gnomonic
column, used to support a dial; the chronological
column, inscribed with a record of historical events ;
the crucifcral or cross-bearing column ; the funereal
column, used to sustain an mu; the miliary co¬
lumn, set up as a centre from which to measure
distances; the itinerary column, pointing out the
direction of diverging roads; the rostral column,
adorned with the prows ( rostra ) of ships, to com¬
memorate a naval victory ; the sepulchral column,
erected over a tomb; the triumphal column, dedi¬
cated to the hero of a victory; the manubial column,
adorned with trophies, spoils, &c., and many others.

COLUMNS.—Diminution of, p. 184.

COLUMNS.—Gluing up, p. 184.

COMMON JOISTS — Those in naked flooring
to which the boards are attached, called also
bridging-joists. See Floors, p. 150.

COMMON RAFTERS—Those to which the
slate-boarding or lathing is attached.

COMMON ROOFING.—Roofing consisting of
common rafters only, without principals.

COMMON PITCH.—A term applied when
the length of the rafters is equal to about three-
fourths of the span within the walls. In this case
the angle formed at the ridge by the rafters is
83° 37', and the perpendicular height of the gable
is 5-9ths of the width of the building in the inside.

COMPASS-HEADED ARCH.—A semicir¬
cular arch.

COMPASS-PLANE.—A plane with a round
sole.

COMPASS-ROOF.—One in which the tie
from the foot of one rafter is attached to the oppo¬
site rafter at a considerable height above its foot.

COMPASS-SAW.—The same as bow-saw.

COMPASS-WINDOW.—A bay window on a
circular plan.

, COMPASSES with moveable legs, how to use,
p. 32.

COMPOSITE ARCH.—A lancet or pointed
arch.

COMPOSITE ORDER.—The last of the five
Roman orders, and so called because composed out
of parts from the other orders. Its capital has a
vase like the Corinthian, surrounded by two rows
of acanthus leaves; the top of its vase is sur¬
mounted by a fillet, an astragal is placed over that,
and on the astragal an ovolo; over this the volutes

Composite Capital.

roll angularly, till they meet the tops of the upper
row of leaves, on which they seem to rest. On the
top of each volute is an acanthus leaf, curling up¬
wards so as to sustain the horn of the abacus. The
abacus is like that of the Corinthian capital. 'Hie
height of the column is 10 diameters, its capital
occupies lj diameter, and its base nearly | dia¬
meter. The entablature is 24 diameters and 2 4
minutes in height; of this, 46 minutes are given to
the architrave, 444 1° the frieze, and 62 minutes
to the cornice. Its architrave has only two fascias,
and its cornice sometimes varies from the Corin¬
thian in having, instead of the modillion and dentil,
a species of double modillion plain on the surface.
The examples at Rome are in the arch ot Septimus
Severus, the arch of the Goldsmiths, the arch of
Titus, the temple of Bacchus, and the Baths of
Dioclesian.

COMPOSITION OF FORCES, p. 124.

COMPOUND PIER—A clustered column is
sometimes so called.

CONCAMERATE.—To arch over ; to vault.

INDEX AND GLOSSARY.

CONCAVE

CONCAVE Surface of Revolution.—To
find the shadow of a, p. 223.

CONCAVE Cylindrical Surface. —To find
the shadow of a, p. 218.

CONCAVE Interior Surface of a Cone.
—To find the shadow on the, p. 219.

CONCAVE Interior Surface of a Hemi¬
sphere. —To find the shadow on the, p. 220.

CONCENTRIC.—Having a common centre,
as concentric circles, ellipses, spheres.

CONE.—To find the surface of a cone. Mul¬
tiply half the circumference of the base by sum of
the slant side and the radius of the base; the pro¬
duct will be the whole surface.—To find the solidity
of a cone. Multiply the area of the base by the
perpendicular height, and one-third of the product
will be the solid content.—To find the surface of
the frustum of a cone. Add the circumferences of
the two bases together, and multiply half the sum
by the slant height for the upright or curved sur¬
face, to which add the areas of the two bases for
the whole surface.—To find the solid content of the
frustum of a cone. Find the areas of the two ends,
multiply them together, and take the square root
of their product; this, added to the two areas and
the sum multiplied by a third of the perpendicular
height, will give the solidity.

CONE.—To draw the sections of a cone made
by a line parallel to one of its sides, p. 68, Plate I.
Figs. 2 and 3.—To draw the sections of a cone
made by a line cutting both its sides, p. 68, Plate
I. Fig. 1.

CONE.—To construct the projections of a cone
intersected by a plane, p. 59.

CONE.—To find the shadow of a cone thrown
on a sphere, p. 222.

CONE.—To construct the projection of a cone,
p. 85.

CONE.—Tangent plane to a cone, p. 61.

CONES.—To find the limits of shade on, and
the shadow of cones, under various conditions,

p. 222.

CONES.—To find the covering of frustum of
cones made by various sections, p. 74, Plates II.
and III.

CONES.—To find the projections of intersect¬
ing cones, p. 64-66.

CONES, right and oblique development of,
p. 71, 72. _

CONGE.—The cavetto which unites the base
and capital of a column to its shaft.

CONIC GROINS.—Groins produced by the
intersection of equal conical vaults, p. 76.

CONIC SECTIONS.—The ellipse, the para¬
bola, and the hyperbola methods of drawing those
figures, and approximations to those figures, p. 22.

CONICAL ROOF.—Construction of, Plate
XXXIII. p. 145.

CONIFERJE, or resin-producing trees, p. 115.
Their various products, p. 115. Where obtained
from, p. 115, 116. Mode of transporting them
from the Alpine forests; inclined plane of Alnpach,
p. 116. Summary of the purposes for which the
various European kinds are best adapted, p. 116.

CONO-C YLINDRIC GROINS.—To find the
angle ribs of, p. 79.

CONSOLE.—A projecting ornament used as

Cornice supported by Consoles.

a bracket. It has for its outline generally a curve
of contrary flexure.

CONTINUOUS IMPOST.—In Gothic archi¬
tecture, the mouldings of an arch when carried
down to the ground without interruption, or any¬
thing to mark the impost-joint.

CORBEL.—1. A structure of stone, brick, wood,
or iron, incorporated with a wall, and projecting
from its vertical face, to support some superincum¬
bent member, and dilating from its lowest point
upwards. Corbels are of a great variety of forms,
and are ornamented in many ways. They are of fre¬
quent occurrence in Pointed architecture, forming
the supports of the beams of floors and of roofs,
the machicolations of fortresses, the labels of doors
and windows, &c.—2. The vase or tambour of the

Corinthian column; so called from its resemblance
to a basket.

Fig. l.

Fig. 2.

Corbels.

Fig. 1. From Castor Church, Northamptonshire. Fig. 2 . From Stone-
Church, Kent

CORBEL, v .—To dilate by expanding every
member of a series beyond the one under it.

CORBEL-STEPS.—Steps into which the sides
of gables from the eaves to the apex are broken ;
sometimes called corbie-steps.

CORBEL - TABLE. — A term in mediaeval

architecture, applied to a projecting course and the
row of corbels which support it.

CORINTHIAN ORDER.—The only Grecian
example of this order remaining, is in the choragic
monument of Lysicrates, vulgarly called the Lan-
thorn of Demosthenes, at Athens. It is an elegant
structure, consisting of a rusticated quadrangular
basement, surmounted by a cyclostyle of six Corin-

Corinthian Capital—Roman.

thian columns attached to a wall, which rises as
high as the top of their shafts. The order here,
although elevated on a podium, has yet the gradu¬
ated stylobate that seems to be an essential feature
in Greek architecture. The stylobate is rather
more than a diameter in height, and is divided
into three steps, the two lowest of which are equal
and have vertical faces, and the third is of less
height and moulded on the edges with exquisite
taste, preparing the eye for the ornate order above
it. The column is ten diameters in height, of
which the base occupies rather more than a third
of a diameter, and the capital a diameter and
rather less than a third. The shaft diminishes
with entasis to five-sixths of its lower diameter,
and has twenty-four flutes, with fillets between.
The flutes are semi-ellipses, and finish at the top in
leaves, to which the fillets serve as stalks. The
hypotrachelium is a groove under the capital. The
core of the capital is a perfect cylinder, rather less
than the upper diameter of the shaft. This is sur¬
rounded at the bottom by a row of water leaves,
about a sixth of the height of the capital, and bend¬
ing outwards; above this is another row of acanthus
leaves, with rosettes attaching them to the cylinder.
This row is in height equal to a third of the height
of the capital. The remaining height is occupied
by helices and tendrils and the abacus. The en¬
tablature is 2 f'j diameters in height, and if this
is divided into minutes, or 60th parts of the lower
diameter, the architrave occupies about 53 of these,
the frieze 41, and the cornice 51. The architrave
is divided into three fascias ; the faces of these
incline inwards, so that their lower angles are in
the same plane. The frieze is enriched with sculp¬
tures. The cornice consists of a bed-moulding, a
broad dentilled member supporting a cyma-recta,
with fillets serving as the bed-moulding of the
corona; the coron is crowned by a simple ovolo
and fillet.

Roman-Corinthian.— The Corinthian order
in the hands of the Romans, unlike the Doric and

256

COVE

Ionic, did not suffer deterioration, but on the
contrary acquired fulness, strength, and richness,
which rendered it one of the most beautiful and
appropriate architectural ornaments. Of no other
order are the existing examples so numerous or so
varied in proportion or ornamentation. Among
these, the order of the temple of Jupiter Stator,
of Antoninus and Faustina, of the Pantheon, and
I of the Maison Quarrde at Nismes, may be enumer¬
ated. Taking the first of these as a guide,, the
following are the proportions of this order. The
column is 10 diameters high, the base occupying
of this 4 diameter, and the capital lg diameter.
The Attic base is oftenest used. The capital is
composed of two rows of acanthus leaves, six in
each row, placed upright, side by side, but not in
contact. From these spring helices and tendrils,
trussed with foliage, and above all is the abacus,
with moulded and enriched faces. The lower row
of leaves is two-sevenths of the height of the capital,
the upper two-thirds of its height, and the abacus is
one-seventli of the height. The entablature of the
temple of Jupiter Stator is more than 2^ diameters
in height. The architrave and frieze have about
li| diameter between them, and the cornice is there¬
fore more than 1 diameter high. In the order of
the Pantheon, the architrave and frieze are about
the same height as above, and the difference is in
the cornice alone; it has therefore been proposed
to make the whole height of the entablature
diameters, and to divide three-fifths of this between
the architrave and frieze. The architrave is divided
into three unequal fascias; the middle fascia is richly
ornamented; the heads which separate the fascias
are carved, and the architrave moulding is en¬
riched. The frieze is in some cases quite plain, in
others it is sculptured' or enriched with foliage.
The cornice consists of a deep bed-mould, composed
of a bead, an ovolo, and fillet, a plain vertical
member sometimes cut into dentils, another bead,
a cyma-reversa- or ovolo, and fillet. When modil-
lions are used, this is surmounted by a plain mem¬
ber, with a cyma-reversa above it, on which the
modillions are placed, and the eyma breaks round
them. The modillions are horizontal trusses or
consoles, finishing at the inner end in a large and
at the outer end in a small volute, and having
under them generally an acanthus or other leaf.
Above the modillions is the corona, sometimes en¬
riched with vertical flutes, and its crowning mould¬
ings, which are a narrow fillet, an ovolo, a wider
fillet, and then a cyma-recta. The soffit of the cor¬
nice is generally coffered between the modillions,
and in every coffer there is a flower. The height
of the pedestal is 3 diameters.

CORNICE.—1. The highest part of an entab¬
lature resting on the frieze. See woodcut, Column.
— 2. Any congeries of mouldings which crowns or
finishes a composition externally or internally.

CORONA.—A member of a cornice situated
between the bed-moulding and the cymatium. It
consists of a broad vertical face, usually of consi¬
derable projection. Its soffit is generally recessed
upWards, to facilitate the fall of rain from its face,
and thus to shelter the wall below. This among
workmen is called the drip, and by the French
larmier, and this last term is often used by English
writers. See woodcut, Cyma-Recta.

CORPSE-GATE. See Lich-Gate.

CORPSING.—A shallow mortise sunk in the
face of a piece of stuff. See p. 200.

COULISSE.—1. A piece of timber with a
channel or groove in it, such as that in which the
side scenes of a theatre move.—2. The upright
grooved posts of a floodgate or sluice.

COUNTER-LATH.—A lath, in tiling, placed
j between every two gauged ones so as to make
equal spaces.

COUNTERBRACE. Fig. 474, p. 159.

COUNTERBRACES, Strains on.—How to de¬
termine, p. 161.

COUNTERSINK, v. —To form a cavity in
timber or other material for the reception of some¬
thing, such as the head of a bolt.

COUNTESSES, in Slating. — Slates whose
dimensions are 1 ft. 8 in. long and 10 inches wide.

COUPLED COLUMNS.—Columns disposed
in pairs. The two columns of a pair are half a
diameter apart.

COUPLES, Couple Close. — A pair of op¬
posite rafters in a roof nailed together at the top,
where they meet, and connected by a tie at the
bottom, or by a collar-beam higher up.

COURSE.—A continuous range or stratum of
material of the same height throughout its extent.
See Random Course.

COUSSINET.—The crowning-stone of a pier,
lying immediately underthe arch.—The ornament in
an Ionic capital between the abacus and the echinus.

COVE.—Any kind of concave moulding. The

COVE BRACKETTING

INDEX AND GLOSSARY.

concavity of a vault; commonly applied to tlie curve
which is sometimes used to counect the ceiling
with the walls of a room.

COVE BRACKETTING.— The wooden skele¬
ton mould or framing of a cove. Applied chiefly
to the bracketting for the cove of a ceiling.

COVED CEILING.—A ceiling springing
from the walls with a curve.

COVERINGS OF SOLIDS, p. 69.

COVING. Same as Cove.

COVING op a Fire-Place. —The vertical
sides which connect the jambs with the breast.

CRADLE.—A name given to a centering of |
j ibs latticed with spars, used in building culverts.

CRADLE-VAULT.—An improper term for
a cylindi'ical vault.

CRADLING.—Timber framing for sustaining
the lath and plastering of a vaulted ceiling. Also,
the framework to which the wooden entablature of
a shop front is attached.

CRAMP.—A piece of iron bent at the ends,
serving to hold together pieces of timber, stone, &c.

CRAMPOONS.—An apparatus used in the
raising of timber or stones, consisting of two hooked
pieces of iron hinged together, somewhat like
double calippers.

CRAPAUUINE DOORS.—Those which turn
on pivots at top and bottom. Doors hung with
centre-pin hinges.

CREASIN G.—A projecting row of plain tiles
placed under the brick on edge coping of a wall.—
Double-creasing consists of two rows of tiles used
for the same purpose and breaking joint.

CRENELLATED MOULDINGS.—Mould-

Crenellated or Embattled Moulding.

ings embattled, notched, or indented, used in the
Norman style.

CRENELLATION.—-The making of crenelles.

CRENELLES. — 1. The openings in an embat¬
tled parapet.—2. The loopholes and other openings
in the walls of a fortress, through which arrows or
other missiles might be discharged.

CRESTS.—Carved work on the top of a
building. The ridges of roofs, the copes of battle¬
ments, and the tops of gables were also called
crests.

CRIPLTNGS.—Spars set up as shores against
the sides of buildings.

CROCKET. — In Gothic architecture, an orna
ment placed at the angles of pinnacles, gables, cano¬
pies, and other members. In its usual form the

Crockets.

crocket is a foliated band, covering the angle of the
member to which it is applied, swelling out at re¬
gular intervals into knobs with considerable projec¬
tion. These knobs assume generally the form of
tufts of leaves, but often also the figures of animals.

CROSETTES.— 1 . The returns on the corners
of architraves of doors, &c., called also ears, elbows,
ancones. —2. The small projecting pieces in arch
stones which hang upon the adjacent stones.

CROSS-GARNETS.—Hinges having a long
'strap fixed to the door or closure, and a shorter
right-angled strap fixed to the frame. Termed in
Scotland cross-tailed hinges.

CROSS-GRAINED STUFF.—Timber having
the grain or fibre not corresponding to the direc¬
tion of its length, but crossing it, or irregular.
Where a branch has shot from the trunk of a tree,
the timber of the latter is curled in the grain.

CROSS-SPRINGER.—In vaulting, is the dia¬
gonal rib of a groin.

CROSS-VAULTING.—That which is formed
by the intersection of two or more simple vaults.

When the vaults spring at the same level, and rise
to the same height, the cross-vault is termed a
groin. When one of the vaults is larger in span
and greater in height than the other, a compound
woi-d is used to denote the combination. Thus,
when both vaults are cylindrical, the groin is termed
cijUndro-cylindric, the qualifying prefix ending in
o denoting always the body range or greater vault,
and the terminal word denoting the smaller vault
which intersects. See Groins, p. 76.

CROWDE or Croud.— The crypt of a church.

_ CROWN OF AN Arch.—I ts vertex or highest
point.

CROWN MEM EL TIMBER. See P IN us
SYLVESTRIS, p. 116, 117.

CROWN-POST.—The same as Icing-post.

CUBE.—A rectangular prism, with all its six
sides equal.—To find the solid contents of a cube.
Find the area of one of its sides, and multiply it by
the height. -To find the surface of a cube. Find the
area of one of its sides, and multiply it by 6 .

CUBE.—To construct the projection of a cube,
p. 53.

CULLIS. Same as coulisse.

CULTIVATION of Trees, p. 96.

CULVERT.—A passage under a road or canal,
covered with a bridge; an arched drain for the
passage of water.

CUNEOID.—To find the envelope for the frus¬
tum of a cuneoid, p. 74, Plate III. Fig. 3.

CUNEOID, to draw the section of a cuneoid,
made by a line cutting both its sides, p. 68 , Plate I.
Fig. 4, Nos. 1-4.

CUPOLA.—A spherical vault at the top of an

edifice ; a dome, or the round part of a dome. The
Italian word signifies a hemispherical roof, cover¬
ing a circular building like the Pantheon at Rome
or the Round Temple at Tivoli.

CURB.—A frame round the mouth of an open¬
ing ; a curb-plate (see next word).

CURB-PLATE.—1. The wall-plate of a circu¬
lar or elliptical domical roof, or of a skylight.— 2 .
The plate which receives the upper rafters of a curb
or Mansard roof.—3,The circular frame of a well.

CURB-RAFTERS.—The upper rafters of the
curb or Mansard roof.

CURB-ROOF.—The same as a Mansard roof .
See p. 140.

CURLING-STUFF.—Timbers in which the
fibres wind or curl at places where boughs have
shot out from the trunk of the tree.

CURTAIL-STEP.—The first step of a stair
when its outer end is finished in the form of a
scroll. See p. 196.

CURVED SURFACES, intersections of, pro¬
jection, p. 63.

CUSHION - CAPITAL.—1. A capital having
a resemblance to a cushion pressed by a weight.—

Norman Cushion-capital.

2. The variety of capital most prevalent in the
Norman style. It consists of a cube rounded off
at its lower angles.

CUSPS.—The points or small projecting arcs

257

CYLINDRICAL VAULTS

terminating the internal curves of the trefoiled,
cinquefoiled, &c., heads of windows and panels in

1 2

1 Monument of Edward III., Westminster Abbey (brass). 2. Henry
VII.'8 Chapel. 3. Monument of Kir James Douglas, Douglas Church
4. Beauchamp Chape), Warwick.

Gothic architecture. They are also called feather¬
ings.

CUT and Mitred String, p. 196.

CUT - BRACKETS.-—Those-moulded on the
edge.

CUT-ROOF.—A truncated roof.

CYCLOID.—One of the transcendental curves
described by a point in the circumference of a cir¬
cle, which rolls along an extended straight line

until it has completed a revolution. In the figui-e
let the circle B c A make one revolution on the
straight line aba, then the curved line a c A a,
traced out by a point in the cii'cumference A, is a
cycloid. The following are some of its properties :
—The base a B a is equal to the circumference of
the generating circle; and A B, the axis of the
cycloid, is of course equal to its diameter. If the
generating circle be placed in the centre of the
cycloid, the diameter a b, coinciding with its axis,
and from any point c in the curve there be drawn
the tangent F C, the ordinate C D E, perpendicular-
to the axis and the chord of the circle A D ; then
c D is equal to the circular arc A D ; the cycloidal
arc A c is double the chord a d ; the semicycloid
A C A is double the diameter of the circle a b, and
the tangent c f is parallel to the chord A D.

CYLINDER.—A round solid of uniform thick¬
ness, of which the bases are equal and parallel cir¬
cles.— To find the surface of a cylinder. Rule:
Multiply the circumference of the base by the
height, and add the area of the two bases. — To
find the solid content of a cylinder. Rule: Find
the area of the base, and multiply it by the perpen¬
dicular height or length.

CYLINDER.—To construct the projections of
a cylinder, p. 57, 58. The projections of a cylinder
cut by a plane, p. 58. To find the projections of a
cylinder intersecting a sphere, p. 64. To constiuct.
the projections of a cylinder penetrated by a sca¬
lene cone, p. 66.

CYLINDER, a, tangent planes to, p. 60, 61.

CYLINDERS.—Development of cylinders, p.
71. To find the projections of cylinders intersect¬
ing each other, p. 63. To find the coverings of right
and oblique cylinders, and cylindric and semicylin-
dric surfaces, p. 73, Plate ii. To find the shadows
of cylinders under various conditions, p. 222.

CYLINDRIC GROINS.—Those produced by
the intersection of cylindric vaults of equal span
and height. Seep. 76.

CYLINDRIC SECTION, To describe a,
through a line given in position, p. 68, Plate 1.
Fig. 5

CYLINDRIC SECTION made by a curved
line cutting the cylinder, to describe, p. 68, PI. I.
Fig. 6.

CYLINDRICAL RING.—To find the section
of a, p. 69, Plate I. Fig. 9.

CYLINDRICAL VAULT.—A vault in the
form of a half-cylinder, without either groins or
ribs. Its vertical section is a semicircle, or some
lesser arc. It is called also cradle-vault, waggon-
vault, ami barrel-vault.

CYLINDRICAL VAULTS.—To determine
the horizontal divisions of the radial panels of,
p. 83.

2 K

INDEX AND GLOSSARY.

DIAMOND FRET

CYLINDRO-CYLINDRIC VAULT

C Y L1N D RO-C YLINDRIC VAULT.—A vault
generated by the intersection of one cylindrical
vault with another of greater span and height. See
Cross-vaulting, and text, p. 76.

C Y LIN D RO-SPH ERIC GROIN. —One formed
by the intersection of a sphere with a cylinder of
greater span and height. Seep. 71>.

CYLINDROID.—A solid, which differs from
a cylinder in having ellipses instead of circles for
its ends or bases.

CYMA REC¬
TA.—A moulding
formed of a curve
of contrary flexure,
concave at the top
and convex at the
bottom. It takes
its name from its
contour resembling
a wave — hollow
above and swelling
below.

CYMA RECTA. The.—'To describe, p. 179.

CYMA REVERSA.—A moulding formed of
the above curve reversed. It is more commonly
called an ogee. See Mouldings.

CYMA REVERSA, The.—To describe, p. 179.

CYMATIUM.—The cyma recta.

CYPRESS. — The common or evergreen cy¬
press tree (Cupressus sempervircns), a native of the
islands of the Archipelago, of Greece, Turkey, and
Asia Minor, where it grows to a great size. It is
abundant in Italy, and said to have been intro¬
duced into that country from Greece. In Britain
it seldom attains a height exceeding 40 feet. It
is remarkable for its upright habit of growth and
uniformity of taper. It is cultivated as an orna¬
mental tree, and used for the embellishment of
tombs and cemeteries, as a symbol of man’s last
resting-place. The best specimen in Britain is at
Stretton Rectory, Suffolk, measuring sixty-three
feet high and two feet in diameter. The timber of
this tree possesses all the qualities of durability
ascribed to the cedar. There are many remarkable
instances of its durability recorded. The doors of
St. Peter’s, at Rome, lasted from the time of Con¬
stantine to that of Eugene III. (1100 years), and
were found perfectly sound when removed. The
statue of Jupiter,in the Capitol (according to Pliny),
had existed 600 years, and showed no symptom of
decay. The cypress doors of the temple of Diana
appeared quite new when 400 years old.

It is not, however, of sufficient size or numbers
to be generally known in this country; but it is in
common use in Candia and Malta.

I).

cyma

recta

cyma reversa
corona

Cymatium, or Cyma Recta.

DABBING, Daubing, or Picking. —A me¬
thod of working stones, in which the face of the
stone is reduced to a uniform surface and brotched,
and the beds and joints worked; it is then draught¬
ed as for nidging. The daubing is then performed
with a pick-shaped tool, or with a faced hammer,
like a nidging hammer, indented so as to form a
series of points, and by the strokes of this the whole
surface is covered with minute holes. Daubing
has the appearance of strength and neatness, and
is adapted for gateways, bridge work, and the base¬

ments of houses. When the
stone is not hard in quality,
this mode of dressing is open to
the same objections as nidging.

DADO.—That part of a
pedestal included between the
base and the cornice; the die.
—In apartments, the dado is
that part of the finishing be¬
tween the base and the sur-
base.

Pedestal.

DAIS. — 1. A platform or 0 Dadoordie. a, Surbuse.
raised floor at the upper end of c • Da, ‘'-

an ancient dining-hall, where
the high table stood.—2. A seat with a high wains-
cot back, and sometimes with a canopy, for those
who sat at the high table.—3. The high table itself.

DANCE. — In a stair of mixed flyers and j
winders, the distribution of the inequality of width i
of the inner end of the latter among them, and a j
number of the flyers, is called making th e steps dance.
See p. 198.

I 'ANCETTE.—The chevron or zigzag moulding
peculiar to Norman architecture. See Chevron.

DANZIG TIMBER. See Pinus sylvestris,
p. 116, 117-

DAY.—One of the divisions of a window con¬
tained between two mullions. In this sense, the
same as bay.

DE LORME. — System of roofing by hemi-
cycles described, p. 144.

DEAD SHORE.—An upright piece of timber
built into a wall which has been broken through.

DEAFENING.—Anything used to prevent the
passage of sound in floors or partitions. The term
used in Scotland as synonymous with pugging.
See p. 150.

DEAFENING - BOARDING.—Sound-board¬
ing, or that on which pugging or deafening is laid.
See p. 151.

DEAL.—The usual thickness of deals is 3 inches
and width 9 inches. The standard thickness is
1 £ inch and the standard length 12 feet.— Whole
deal, that which is li inch thick; slit deal, half
that thickness.

DECASTYLE.—A portico or colonnade of ton
columns.

DECORATED STYLE.—The second of the
Pointed or Gothic styles of architecture used in this
country. It was developed from the Early English
at the end of the thirteenth century, and gradually
merged into the Perpendicular during the latter
part of the fourteenth. This style is usually con¬
sidered the complete and perfect development of
Gothic architecture, which in the Early English
was not fully matured, and in the Perpendicular
began to decline. The most characteristic feature
of this style is to be found in the windows, the tra¬
cery of which is always either of geometrical figures,
circles, quatrefoils, &c., as in the earlier examples,

York Cathedral, West Front.

or flowing, wavy lines, as in later specimens. The
arches are not so lofty and the pillars not so slen¬
der as in the Early English, and the detached shafts
are only used in the early part of the period. The
equilateral form prevails both for arches and win¬
dows, and the vaulting, and consequently the roofs,
are not of so high a pitch as in the preceding style.
The buttresses are large and projecting, frequently
ornamented with canopied niches containing figures
of saints, and usually terminated in richly crochet¬
ed pinnacles. Canopies, either straight-sided or of
the ogee form, are much used over windows, doors,
and porches. They often project, and are orna¬
mented with rich and large finials and crockets.
The doors and porches are deeply recessed, and very
richly ornamented with mouldings and foliage, and
have frequently also niches containing figures of
saints or subjects from the Scriptures. The door¬
ways in the west front of York Cathedral are the
finest examples we have of this kind, and the front
itself is considered by Rickman to he “nearly, if
not quite, the finest west front in the kingdom.”
The upper part of the towers is in the Perpen¬
dicular style, showing the transition from one style
to the other during the progress of the building.
Anothercharacteristicfeature of the Decorated style
is the foliage, in which natural forms are imitated,
and drawn with the greatest freedom and elegance.

258

The capitals differ in several important features
from those of the Early English. In the latter the
foliage generally rises from the neck moulding, on

Decorated Capital, Selby, Yorkshire.

stiff stems, and curls over under the bell of the
capital; but in the Decorated it is generally carried
round in the form of a wreath, making a complete
ball of leaves. v

DECORATION.—Anything which adorns and
enriches an edifice, as vases, statues, paintings, fes¬
toons, &c.

DEMI-RELIEVO.—A species of sculpture in
relief, in which one-half of the figure projects from
the plane of the stone or other material from which
it is carved. It is also called mezzo-rilievo.

DENTILE, Dentils.— Ornaments in the form

Dentils.

of little cubes or teeth, used in the bed-moulding of
Ionic, Corinthian, and Composite cornices.

DENTIL LED, Denticulated. — Having
dentils.

DERBY.— A two-handed float. See Float.

DESCRIPTIVE CARPENTRY. Introduc¬
tion, p. 76.

DESCRIPTIVE GEOMETRY. See Stereo-

TOMY.

DIAGLYPHIC.—A term applied to sculpture,
engraving, &c., in which the objects are sunk below
the general surface.

DIAGONAL.—A right line drawn from angle
to angle of a four-sided figure.

DIAGONAL SCALE.—Construction and use
of, p. 35.

DIAMETER. — 1. A right line passing through
the centre of a circle or other curvilinear figure, ter¬
minated by the circumference, and dividing the
figure into two equal parts. Whenever any point
of a figure is called a centre, any straight line
drawn through the centre, and terminated by op¬
posite boundaries, is called a diameter. And any
point which bisects all lines drawn through it from
opposite boundaries is called a centre. Thus, the
circle, the conic sections, the parallelogram, the
sphere, the cube, and the parallelopiped, all have
centres, and by analogy diameters. In architec¬
ture, the measure across the lower part of the shaft
of a column, which being divided into 60 parts,
forms a scale by which all the parts of the order
are measured. The 60th part of the diameter is
called a minute, and 30 minutes make a module.
—2. A right line passing through the centre of a
piece of timber, a rock, or other object, from one
side to the other; as, the diameter of a tree or of a
stone.

DIAMOND FRET.—A decorated moulding

Diamond Frot.

consisting of fillets intersecting each other, so as to
form diamonds or rhombuses; used in Norman
architecture.

DIAPER

INDEX AND GLOSSARY.

DOUBLE-VAULTS

DIAPER.—Ornament of sculpture in low re- |
lief, sunk below the general surface, or of painting

Diaper, Wostminster Abbey.

or gilding, used to decorate a panel or other flat
recessed surface.

DIASTYLE.—The space between columns}
when it consists of three diameters.

DICOTYLEDONOUS or Exogenous Trees.
—General characteristics of, p. 95.

DIE.—The cubical part of a pedestal, between
its base and cornice; a dado

DIGLYPH. — A tablet with two furrows or
channels.

DIMENSIONS.—Method of taking, p. 67.

DIMENSIONS op the Timbers in a Roof.—
Rules for calculating the, p. 137.

DIMINUTION op Columns, p. 184.

DIPTERAL.—A building having double
wings.

DIPTEROS.—A double-winged temple.

DIRECTING PLANE.—In perspective, a
plane passing through the point of sight parallel to
the plane of the picture.

DIRECTING POINT. — In perspective, the
point where any original line meets the directing
plane.

DIRECTORS, or Triangular Compasses,
p. 33.

DIRECTRIX—A line per¬
pendicular to the axis of a conic
section, to which the distance of
any point in the curve is to the
distance of the same point from
the focus in a constant ratio;
also the name given to any line,
whether straight or not, that is
required for the description of a
curve. Thus a b is the directrix of the parabola
V E D, of which P is the focus.

DISCHARGE.—To transfer pressure from one
point to another.

DISCHARGING ARCH. — An arch formed
in the substance of a wall, to relieve the part below

Discharging Arch.

it of the superincumbent weight. Such arches are
commonly used over lintels and flat-headed openings.

DISEASES op Trees, p. 96.

DISHED. — Formed in a concave .—To dish
out, to form coves by wooden ribs.

DISTANCE, Point of.—In perspective, that
point in the horizontal line which is at the same
distance from the principal point that the eye is.
See p. 230.

DISTRIBUTION.—The dividing and dispos¬
ing of the several parts of a building, according to
some plan or to the rules of the art.

DIVIDERS.—Instructions in the use of, p. 31.

DIVISIONS op a Spherical Vault.— To
determine the heights of, p. 83.

DIVISIONS op the Radial Panels op a
Cylindrical Vault.— To determine, p. 83.

DOCK - GATES. — Illustrations and descrip¬
tions of, p. 177-

DODECAHEDRON.—A solid figure, consist¬
ing of twelve equal sides.—To find the superficial
area of a dodecahedron. Multiply the square of
the linear side by 20-6457788, and the product will
be the surface.—To find the solid contents of a do¬
decahedron. Multiply the cube of the linear side
by 7'6631189, and the product will be the cubical
contents.

DODECAHEDRON.—To construct the pro¬
jections of a dodecahedron, p. 54, 55.

DODECASTYLE.—A portico having twelve
columns in front.

DOG-LEGGED STAIRS, p. 196.

DOG’S-TOOTH MOULDING. —An orna¬
mental member, very characteristic of Early Eng¬
lish architecture. It has no resemblance to a dog's-
tooth, and is often called tooth-ornament (see that
term).

DOME.—The hemispherical cover of a build¬
ing; a cupola. See p. 82, and Plates XIII.-XV.

DOM E, Oblong - surbased, on a rectangular
plan, p. 82.

DOME, Surbased, on an octagonal plan.

p. 82.

DOMES.—Definition of, p. 82.

DOMES.—Manner of dividing into compart¬
ments and caissons or coffers, p. 82.

DOMES. -— To find the coverings of various
kinds of, p. 75, 76, Plate IV.

DOMES and Spherical Vaults. —To divide
into compartments and caissons, p. 82.

DOMICAL. — Related to, or shaped like a
dome or tholus. See Cupola.

DOMICAL ROOF. — Construction of, Plate
XXXIV. p. 145.

DOOR.—1. An opening or passage by which
persons enter into a house or other building, or
into any room, apartment, or closet. — 2. The
closure of the door; the frame of boards or any
piece of board usually turning on hinges, which
shuts the opening of the door, as above defined.

DOOR.—Suspended by pulleys to an iron rail,
p. 187.

DOOR-CASE. — The frame which incloses a
door.

DOOR-NAIL.—The nail or knob in ancient
doors on which the knocker struck.

DOOR-POST—The post of a door.

DOOR-STOPS.—Pieces of wood against which
the door shuts in its frame.

DOORS.—Various kinds of, p. 187.

DOORWAY.—The entrance into a building or
an apartment. The forms and designs of doorways
partake of the characteristics of the different classes
of architecture. In the edifices of the middle ages
much attention was bestowed on the design and
adornment of the doorways.

DOORWAY-PLANE.—-The plane frequently
found between the door properly so called, and
the larger opening within which it is placed. The
doorway-plane was often richly ornamented with
sculpture, &c.

DORIC ORDER.—The earliest and simplest
of the three Greek orders. It may be divided into
three parts, stylobate, column, and entablature.
The stylobate is from two-thirds of a diameter to a
whole diameter in height, and is divided into three
equal steps or courses, which recede gradually the
one above from the one below it, and the column
rests on the upper step, without the intervention
of any moulding. The column varies from four
to six diameters in height, including the capital,
which, with its necking, in this case a sunk
channel, is rather less than half a diameter. The
shaft of the column diminishes in a slightly curved
line from its base to the hypotrachelium or neck¬
ing, where its diameter is reduced from two-thirds
to four-fifths of the lower diameter. The shaft is
divided into flutes, generally twenty in number.
They are usually segments of circles meeting in an
arris. The capital consists of the necking, an
echinus or ovolo, and an abacus, corbelled out below
by three or four rings, or annulets, which encircle
the top of the column. The entablature varies
from one diameter and three-quarters to more than
two diameters in height. Four-fifths of this height
is generally equally divided between the architrave
and frieze, and the remaining fifth given to the
cornice. As a general rule, the architrave projects
so as to be nearly in a line with the lower diameter;
four or five sixths of its height is given to a broad
face, and the remainder to the taenia, which is a
continuous fillet, and the regula, a small fillet at¬
tached to it in lengths equal to the width of the
triglyphs. The frieze is divided into triglyphs and
metopes. The triglyphs are nearly a half diameter
in width, and the metopes are generally an exact
square, and in ancient examples seem invariably to
have been charged with sculptures, and, indeed,
the introduction of sculpture may be said to be
essential to this order. There is invariably a
triglyph placed on the exterior angle of the frieze,
and not over the centre of the column, as in the
Roman-Doric. The frieze has a fascia at top, pro¬
jecting slightly and breaking round the triglyphs.
The cornice is divided vertically into four parts—
one of these is given to a square fillet with mould¬
ings below it, forming the crowning member, two

259

are given to the corona, and one to a narrow sunk
face below it, with the mutules and their gutt;e
There is a mutule over every triglyph, and one over
every metope. All the curves of the mouldings in
this order are either parabolic or hyperbolic. The
Grecian-Doric order, at its best period, is one of the

Grocian-Doric Capital.

most beautiful inventions of architecture—strong
and yet elegant, graceful in outline and harmonious
in ail its forms, imposing when on a great scale,
and pleasing equally, when reduced in size, by the
exquisite simplicity of its parts.

The Roman - Doric. —The ancient example of
this order in the theatre of Marcellus at Rome may
be regarded as a deteriorated imitation of the
Grecian-Doric. The column consists of a shaft and
capital, but has no base. It is eight diameters high,
and diminishes one-fifth of its diameter. The capi¬
tal is four-sevenths of a diameter in height. The
crown mouldings and corona being destroyed, the
exact height of the entablature cannot be exactly
ascertained ; but from analogy, it may be assumed
to have been two diameters. The architrave is one-
fourth of this, or half a diameter; the frieze is two-
fifths of the whole height. The trigly phs are placed
over the centres of the columns. The width of the
metopes is equal to the height of the frieze without
its fascia.

The Roman-Doric, as executed bv the Italian
architects, is very different from this ancient ex¬
ample. They introduced a base to the column,
sometimes a large torus and sometimes the Attic
base, and improved the proportions of the parts.
The shaft of the column, as designed by Palladio,
is 8 diameters in height; of this half a diameter is
given to the base and 32 minutes to the capital.
The entablature is two diameters in height. The
architrave, including the taenia, is half a diameter,
the frieze, exclusive of the fascia, is three-fourths of
a diameter, and the cornice also three quarters. The
shaft is sometimes fluted, the flutes being twenty in
number. The necking of the capital is ornamented.
The triglyph is over the centre of each column, the
metopes are square and ornamented with shields,
paterae, or ox-skulls garlanded with acorns. Over
each triglyph is a mutule, whose guttae are sunk in
its soffit, and the soffit of the cornice between the
mutules has sunk panels, ornamented in various
ways. The curves of the mouldings are all portions
of circles. When a pedestal is used it is made 2 -jj
diameters in height.

DORMANT, Dormant-tree, Dormar. —A
summer, sommer, sommier. or sleeper; abeam.

DORMER-WINDOW.—-A window in the
sloping side of a roof, with its casement set verti¬
cally. When the window lies in the plane of the
roof, it is called a skylight.

DORSE.—A canopv.

DOUBLE-JOISTED FLOOR.—A floor with
binding and bridging joists. See p. 151, illustra¬
tion, Fig. 2, Plate XLII.

DOUBLE-VAULTS.—One vault built over

Double-Vaults

Dome of San Pietro in Montorio, Rome.

another, with a space between the convexity of the
one and the concavity of the othe?-. It is used in

INDEX AND GLOSSARY.

DOUBLE-MARGINED

domes or domical roofs when they are wished to
present the appearance of a dome both externally
and internally, and when the outer dome, by the
general proportions of the building, requires to be
of a greater altitude than would be in just propor¬
tion if the interior of its concave surface were visi¬
ble. The upper or exterior vault is therefore made
to harmonize with the exterior, and the lower vault
with the interior proportions of the building.

DOUBLE - MARGIN ED. — As double-mar¬
gined doors. See p. 186.

DOUBLE SCALES. — The sector, construc¬
tion and use of, p. 36.

DOUB LES. —In slating, slates measuring 1 foot
1 inch by 6 inches.

DOVETAIL.—The manner of fastening boards
and timbers together, by letting one piece into the

Fig. 1.

Fig. 2.

/)k

Fi}?. 1. Common Dove-tailing. Fig. 2. Lap Dove tailing.

other, in the form of a dove’s tail spread or a wedge
reversed, so that it cannot be drawn out in the
direction of its fibres. See illustration of Dove¬
tailing in Carpentry, Plate XXXIX. Fig. 16.

DOVETAIL MOULDING. —A moulding
decorated with running bands in the form of dove¬

tails, used in Norman architecture. It is some¬
times called triangular frette.

DOVE-TAILING, p. 149.

DOWEL, v. —To fasten boards together by pins
inserted in their edges. See p. 182.

DOWEL LING.—Described, p. 182.

DRAGON-BEAM, Dragon-Piece.— A beam
or piece of timber bisecting the angle formed by
the meeting of the wall-plate of two sides of a build¬
ing, used to receive and support the foot of the hip-
rafter.

DRAM-TIMBER. See Pinus sylvestris,
p. 116, 117.

DRAUGHT.—1. In masonry, a line on the
surface of a stone hewn to the breadth of the chisel.
—2. In carpentry and joinery, when a tenon is to be
secured in a mortise by a pin passed through both
pieces, and the hole in the tenon is made nearer
the shoulder than to the cheeks of the mortise, the
insertion of the pin draws the shoulder of the tenon
close to the cheeks of the mortise, and it is said to
have a draught.

DRAW - BORE. — A hole pierced through a
tenon, nearer to the shoulder than the holes through
the cheeks from the abutment in which the shoulder
is to come into contact.

DRAW-BORE PIN.—A joiner’s tool, consist¬
ing of a solid piece or pin of steel, tapered from
the handle, used to enlarge the pin-holes which are
to secure a mortise and tenon, and to bring the
shoulder of the rail close home to the abutment on
the edge of the style. When this is effected, the
draw-bore pin is removed, and the hole filled up
with a wooden peg.

DRAWBRIDGE. — A bridge which may be
drawn up or let down to admit of or to hinder com¬
munication between its points of support. The
name is applied generally to all bridges which can
be drawn from their position, either by turnino-
horizontally or vertically round an axis, or by slid¬
ing. See example of Sliding-bridge, PlateXL VlII.
Fig 1.

DRAWING.—General remarks on, p. 45.

DRAWING-BOARDS.—Useful sizes and con¬
struction of, p. 43.

DRAWING - INSTRUMENTS. — Construc¬
tion and use of, p. 31-45.

DRAWING-INSTRUMENTS.—Management

of, p. 45.

DRAWING-KNIFE.—An edge tool, used to
make an incision into the surface of wood, along
the path the saw is to follow. It prevents the
teeth of the saw tearing the surface of the timber.

DRAWING-PAPER.—Dimensions and qua- ]
lity of, p. 42.

DRAWING-PAPER.—How to stretch on the
drawing-board, p. 43.

DRAWING-PEN, p. 42.

DRAWING-PINS, p. 45.

DRESSINGS.—All mouldings which are ap¬
plied as ornaments, and project beyond the naked
of the work.

DRIFT.—A piece of iron or steel-rod used in
driving back a key of a wheel, or the like, out of
its place, when it cannot be struck directly with
the hammer. The drift is placed against the end
of the key, or other object, and the strokes of the
hammer are communicated through it to the ob¬
ject to be displaced.

DRIP.—The edge of a roof; the eaves; the
corona of a cornice.

DRIPSTONE.—The label moulding in Gothic
architecture, which serves as a canopy for an open-

Dripstoue, Westminster Abbey.

ing, and to throw off the rain. It is also called |
weather-moulding and water-table.

DROP-ARCH.—To draw, p. 29.

DROPS.—Small cylinders or truncated copes, |
used in the mutules of the Doric cornice, and in I
the member immediately under the triglyph of the |
same order. See woodcut, Gutt.e.

DROVING. — In stone-cutting, the same as
random-tooling (which see).

DROVING and Striping. — In stone-cut¬
ting, droving and striping is used when it is wished
to relieve a large surface by the character of the
work, in the absence of breaks, openings, or orna¬
ments. The stone is prepared and draughted as in j
nidging, and then with a chisel about one-fourth of
an inch wide, shallow parallel channels are run in
the direction of the length of the stone, at distances j
apart of about inch. This gives a very neat and I
finished air to a building, but it is expensive, and
is never used where economy is an object.

DRUM. — 1. The stylobate or vertical part
under a cupola or dome.—2. The solid part of the
Corinthian and Composite capitals; called also bell,
vase, basket.

DRUXY.—An epithet applied to timber with I
decayed spots or streaks of a whitish colour in it.

DRYS.—In masonry, fissures in a stone inter¬
secting it at various angles to its bed, and unfitting
it for sustaining a load.

DUCHESSES.—In slating, slates measuring
2 feet by 1 foot.

DURAMEN.—-The heart-wood of a tree.

DWANGS. -—The Scotch term for struts in¬
serted between the joists of a floor or the quarter -
ings of a partition, to stiffen them.

DWARF-WALLS.—Walls of less height than
a story of a building. The term is generally ap¬
plied to the low walls built under the ground-floor,
to support the sleeper-joists.

EARLY ENGLISH ARCHITECTURE.—
The first of the Pointed or Gothic styles of archi¬
tecture that prevailed in this country. It suc¬
ceeded the Norman towards the end of the twelfth
century, and gradually merged into the Decorated
at the end of the thirteenth. One of the leading
peculiarities in this style is the form of the win¬
dows, which are narrow in proportion to their
height, ami terminate in a pointed arch, resem¬
bling the blade of a lancet. Throughout the early
period of the style, they are very plain, particu¬
larly in small churches, but in cathedrals and other
large buildings, the windows, frequently combined
two or more together, are carried to a great height,
are richly and deeply moulded, and the jambs orna¬
mented with slender shafts. On the eastern and
western fronts of small churches the windows are

2G0

EARLY ENGLISH ARCHITECTURE

often combined in this manner, with a circular
window above and a richly moulded door below ;
but in large buildings there is often more than one
range of windows, and the combinations are very
various. Though separated on the outside, these
lancets are in the interior combined into one design
by a wide splaying of the openings, thus giving the
first idea of a compound window. The doorways
are in general pointed, and in rich buildings some¬
times double; they are usually moulded, and en¬
riched with the tooth-ornament. The buttresses
are often very bold and prominent, and are fre¬
quently carried up to the top of the building with
but little diminution, and terminate in acutely-
pointed pediments, which, when raised above the

North-west Transept, Beverley Minster.

parapet, produce in some degree the effect of pin¬
nacles. In this style, likewise, flying buttresses
were first introduced (see Flying-Bdttress), and
the buttresses themselves much increased in projec¬
tion from the comparative lightness of the walls,
which required some counter support to resist the
outward pressure of the vaulting. The roof, in the
Early English style, appears alwaysto havebeenliigli
pitched. In the interior the arches are usually lan¬
cet-shaped. and the pillars often reduced to very
I slender proportions. As if to give still greater light
ness of appearance, they are frequently made up
of a centre pillar, surrounded by slight detached
shafts, only connected with the pillar by' their capi¬
tals and bases, and bands of metal placed at inter¬
vals. These shafts are generally of Purbeck mar¬
ble, the pillar itself being of stone, and, from their
extreme slenderness, they appear as if quite inade¬
quate to support the weight above them. Some of
the best examples are to be seen in Salisbury Ca¬
thedral. The architects of this style carried their

Early English Capital, Salisbury CathodraL

ideas of lightness to the utmost limits of prudence,
and their successors have been afraid to imitate
their example. The abacus of the capitals is gen¬
erally made up of two bold round mouldings, with
a deep hollow between. The foliage is peculiar,
generally very gracefully drawn, and thrown into
elegant curves; it is usually termed stiff-leaved,
from the circumstance of its rising with a stiff stem
j from the neck-mould of the capital. The trefoil is
commonly imitated, and is very characteristic of
j the style. The mouldings of this style have great
boldness, and produce a striking effect of light and
shade. They consist chiefly of rounds separated bv
deep hollows, in which a peculiar ornament, called
the dog's-tooth, is used, whenever ornament can be
introduced. This ornament is as characteristic of
[ the Early English as the zigzag is of the Norman.

EARTH-TABLE

INDEX AND GLOSSARY.

ENTASIS

EARTH-TABLE.-—The course of stones in a
wall seen immediately above the surface of the
ground, now called the plinth. It is also termed
yrass-table and ground-table.

EAVES.—That part of a roof which projects
beyond the face of a wall.

EAVES-BOAltD; called also Eaves catch
and Eaves-i.ath.—A n arris-fillet nailed across the
rafters at the eaves of a roof, to raise the slates a
little.

EAVES-GUTTER.—A gutter attached to the
eaves.

ECHINUS.—An ornament in the form of an
egg, peculiar to the ovoio or quarter-round mould-

Ecliinus.

ing; whence this moulding is sometimes called
echinus.

EGG-and-ANCHOR, Egg-and-Dart, Egg-
and-Tongue. See Anchor and Echinus,

EGYPTIAN ARCHITECTURE.—The style
of building which prevailed in ancient Egypt, and
the remains of which, as exhibited in the pyramids,

tombs, and ancient temples scattered over that
country, alike excite our wonder, and attest the
magnificence and advanced civilization of the pe¬
riod to which they belong. Its remains are pro¬
bably the most ancient of any in the world, the only
buildings that may possibly vie with them in point
of antiquity being the rock-cut- temples and other
monuments of India. The characteristics of Egyp¬
tian architecture are solidity, boldness, and ori¬
ginality ; the object being to fill the mind of the
spectator with astonishment and awe. The col¬
umns are numerous, close, and very large, being
sometimes ten or twelve feet in diameter. They
are generally without bases, and had a great va¬
riety of capitals, from a simple square block orna¬
mented with hieroglyphics or faces, to an elaborate
composition of palm-leaves, bearing a distant re¬
semblance to the Corinthian capital. The shafts
are either plain or worked into reeds or flutes, and
frequently are constructed to represent various
plants, such as the lotus, the date-palm, or the
papyrus. The entablature is very simple, consist¬
ing of a plain architrave, surmounted by a large
torus, and a large overhanging concave moulding,
which serves as a cornice. The roofs of the tem¬
ples were formed by large blocks of stone, extend¬
ing from wall to wall or from column to column,
and not unfrequently the roof was wholly absent
In the construction of the portico of the temples
the greatest magnificence was displayed. It was
frequently approached by an avenue of sphinxes
and other sculptures, extending to a considerable

distance, and the doorway w T as flanked by two
towers of a peculiar shape, broad in front and

narrow at the sides, with the walls sloping back
at a slight angle from the perpendicular.
The walls, pillars, and interior of the temple
generally, were covered with a profusion
of hieroglyphics, pictures, and symbolical
figures. Many of the pictures still display
great brilliancy of colouring, the dryness of
the climate having preserved them nearly
intact after so great a lapse of time. No
use appears to have been made of wood, and
the stones employed in the construction of
the columns were of the most gigantic di¬
mensions. Another prominent character¬
istic of Egyptian architecture is the absence
of the arch, no specimen of which occurs
among their ancient monuments.

EIDOGRAPH.—A form of the para¬
graph, for copying, enlarging, or reducing
drawings, invented by Professor Wallace of
Edinburgh.

ELBOW-LINING.—The lining of the
elbows of a window. See p. 188.

ELBOWS.-—The upright sides which
flank any panelled work, as in windows
below the shutters.

ELEVATION.—A geometrical delinea¬
tion of any object according to its vertical
and horizontal dimensions, without regard
to its thickness or projections ; the front or
any other extended face of a building.

ELIZABETHAN ARCHITECTURE.
•—A name given to the impure architecture
which prevailed in the reigns of Elizabeth
and James I., when the worst forms of
Gothic and debased Italian were combined
together, producing singular heterogeneous¬
ness in detail, but wonderful picturesque¬
ness in general effect. Its chief character¬
istics are windows of great size, both in the
plane of the wall and deeply embayed, and
galleries of great length, combined with a
profuse use of ornamental strap-w'ork in the para¬
pets, window-heads, &c.

ELLIPSE, Description of the, p. 22.
ELLIPSE, to draw, when the major and minor
axes are given, Prob. LXXXV. p. 22, and Prob.
LXXXVI. p. 23.

Interior of the Temple of Esneh.

ELLIPSE, the, to draw, with the trammel
Prob. LXXXV11. p. 23.

ELLIPSE, the, to draw, on the method of the
trammel, without using the instrument, Prob.
LXXXVIII. p. 24.

ELLIPSE, to describe, by means of a string,
Prob. LXXXIX. p. 24.

ELLIPSE, to draw with the compass a figure
approaching the, Prob. XCIII. and XC1V. p. 25,
and Prob. XCVI. pi. 26.

ELLIPSE.—To find the circumference of an
ellipse.—Rule: Multiply half the sum of the two
diameters by 3T41G.—To find the area of an ellipse.
Rule: Multiply the largest diameter by the short¬
est, and the product by '7854.

ELLIPSES, to draw, by intersecting lines,
Prob. XC. and XCI. p. 24.

ELLIPSOID, an, to describe the section of,
p. 68, Plate I. Fig. 8.

ELLIPSOIDAL A AULTS. — To determine

the caissons of, p. 83.

ELLIPTICAL-DOMICAL PENDENTIVE,

p. 81.

ELM, The.—Properties and uses of, p 110.

ELM, Wych, p. 111.

ELM, Rock, p. 111.

ELM, Dutch, p. 111.

ELM, Twisted, p. 111.

EMBATTLEMENT, or Battlement. — An
indented parapet, belonging originally to military
works, the indents, crenelles, or embrasures being
used for the discharge of missiles. It was after¬
wards adopted extensively as a decoration in me¬
diaeval architecture.

EMBOSS, v .—To form bosses or protuberances;
to cut or form with prominent figures.

EMBRASURE.—An opening in a wall, splay¬
ing or spreading inwards. The term is usually ap¬
plied to the indent or crenelle of
an embattled parapet.

EMY’S Laminated Roofs,
p. 141.

ENCARPA, Encarfus. —A
festoon of fruit or flowers on a
frieze or capital. See Festoon.

ENDOGENOUS PLANTS.
See Endogens.

ENDOGENS.—Plants whose
stems are increased by the devel¬
opment of woody matter towards
the centre, instead of at the cir¬
cumference, as in exogens. To
this class belong palms, grasses,
rushes, &c. Stems of this sort
have no distinct concentric layers
or medullary rays.

EN DOGEN S.—G eneral char¬
acteristics of, p. 93.

ENGAGED COLUMN.—A

column attached to a wall, so that
part of it is concealed. Engaged
columns have seldom less than a
quarter, or more than a half of
their diameter in the solid of the
wall.

ENGLISH BOND.—That disposition of bricks
in brick-work which consists of courses of headers
and stretchers alternately. The figures show the
first and second courses of a 14-inch wall, a is a

Engaged Column.

course consisting of a row of stretchers a a, and
headers b b ; and B, the next succeeding course,
shows the disposition of these reversed.

ENLARGING and Diminishing Mouldings.
—Method of, p. 181.

ENNEAGON.—A polygon, with nine sides or
nine angles.

ENRICH.—To adorn with carving or sculp¬
ture.

ENSTYLE.—An intercolumniation of two and
a quarter diameters.

ENTABLATURE.—That part of an order
which lies upon the abaci of the columns. It con¬
sists of three principal divisions—the architrave,
the frieze, and the cornice. See woodcut, Column.

ENTAIL.—The more delicate and elaborate
parts of carved work.

ENTASIS.—A swelling; the curved line in

2G1

ENTERCLOSE

which the shaft of a column diminishes; the
swelling in the middle of a baluster. See Figs.
2, 3, and 4, Plate LXXII.

ENTERCLOSE.—A passage between two
rooms.

ENTRESOL.—-A low story between two other
stories.

EPISTYLIUM, Epistyle. —An ancient name
for the architrave.

EQUILATERAL Arch, to draw, p. 28.

EQUILATERAL Triangle, to describe,
Prob. XI. p. 7-

EREMACAUSIS, or slow combustion or
oxidation, the cause of decay in timber. See p.
105.

EREMACAUSIS, remedies for, p. 105.

ESCAPE.—That part of a column where it
springs out of the base; the apophyge ; the congd.

ESCUTCHEON.—1. A shield for armorial
bearings.—2. A plate for protecting the keyhole
of a door, or to which the handle is attached.

ESTRADE.—An elevated part of the floor of
a room ; a public room.

EXCRESCENCES in Trees, p. 97.

EXEDRA, Exhedra. —In ancient architec¬
ture, the name given to vestibules or apartments in
public buildings where the philosophers disputed,
and also to apartments or vestibules in private
houses used for conversation. In mediaeval archi¬
tecture, the term is sometimes applied to the porch
of a church, especially to the galilee or western
porch. The apsis, too, was sometimes termed the
exedra.

EXFOLIATION of the bark of trees, p. 97.

EXOGEN.—A plant whose stem increases by
development of woody matter towards the outside.
To this class belong all our timber trees.

EXOGENS.—General characteristics of, p. 94.

EXPANDING CENTRE-BIT.—A hand-
instrument, chiefly
used for cutting out
discs of leather and
other thin material,
and for making the
margins of circular
recesses. It consists
of a central stem a,
and point b, mount¬
ed on a transverse
bar c, which carries
a cutter d at one
end, and is adjust¬
able for radius. The
arm c being carried

round the fixed points a and b, the cutter d describes
a circle of which the radius is the distance b d.

EXTRADOS.—The exterior curve of an arch.
See Arch.

EYE.—A general term applied to the centre of
anything, as the eye of a volute, of a dome.

FAQADE.—The face or front of an edifice.

FACE-MOULD.—One of the patterns for
marking the board or plank out of which the hand¬
rails for stairs and other works are to be cut. See
Staircases and Hand-railing, in text.

FACETS, Facettes. —Small projections be¬
tween the flutings of columns.

FACIA. See Fascia.

FACING.—1. The thin covering of polished
stone, or of plaster or cement, on a rough stone or
brick wall.—2. The wood-work which is put as a
border round apertures, either for ornament or to
cover and protect the junction between the frames
of the apertures and the plaster.—3. Sometimes in
joinery used synonymously with lining.

FACTABLE.— The same as coping.

FAGUS SYLVATICA.—The beech tree. For
description, seep. 111.

FALDSTOOL.—A kind of stool placed at tl.e
south side of the altar, at which the Kings of Eng¬
land kneel at their coronation.—2. A small desk,
at which the Litany is enjoined to be sung or
said; sometimes called a Litany-stool. —3. The
chair of a bishop, inclosed by the railing of the
altar.—4. An arm-chair; a folding-chair.

FALLING MOULDS.—The two moulds
which, in forming a hand-rail, are applied, the one
to its convex, and the other to its concave vertical
side, in order to form the back and under-surface,
and finish the squaring.

INDEX AND GLOSSARY.

FALLING MOULD in Hand-railing, to
construct, p. 201.

FALLING STYLE.—That style of a gate or
door in which the lock, latch, or other fastening, is
placed. See Gates, p. 176.

FALSE ATTIC. — An architectural finish,
bearing some resemblance to the Attic order, but
without pilasters or balustrade. It is used to
crown a building and to receive a bas-relief or
inscription.

FALSE ROOF.-—The open space between the
ceiling of an upper, apartment and the rafters of
the roof.

FAN-LIGHT.—Properly a semicircular win¬
dow over the opening of a door, with radiating bars
in the form of an open fan, but now used for any
window over a door.

FAN-TRACERY VAULTING.—The very
complicated mode of roofing, much used in the Per¬
pendicular style, in which the vault is covered by

FISHING

dually to the points of suspension, from which the
ends generally hang down. The festoon, in archi¬
tecture, is sometimes composed of an imitation of
drapery similarly disposed, and frequently of an

Festoon.

assemblage of musical instruments, implements of
war or of the chase, and the like, according to the
purpose to which the building it ornaments is ap¬
propriated.

FILLET.—A small moulding, generally rect¬
angular in section, and having the appearance of
a narrow band. It has many synonymes.—In
carpentry and joinery, any small scantling less
than a batten.

FILLISTER.—A kind of plane used for
grooving timber or for forming rebates.

FINE STUFF.—Plaster used in common
ceilings and walls for the reception of paper or
colour.

FINIAL.—The ornamental termination to a

Fan-tracery, North Aisle, St. George’s Chapel, Windsor.

ribs and veins of tracery, of which all the principal
lines have the same curve, and diverge equally in
every direction from the springing of the vault, as
in Henry VII.’a Chapel, Westminster, and St.
George’s Chapel, Windsor.

FASCIA.—1. A band or fillet.—2. Any flat
member with a little projection, as the band of an
architrave.—3. In brick buildings, the jutting of
the bricks beyond the windows in the several stories
except the highest.

FASTIGIUM.—The summit, apex, or ridge of
a house or pediment.

FEATHER-BOARDING. — A covering of
boards, in which the edge of one board overlaps a
part of the one next it. It is also called weather-
boarding.

FEATHER - EDGED BOARDS. — Boards
made thin on one edge.

FEATHERINGS, or Foliations. —The cusps
or arcs of circles with which the divisions of a
Gothic window are ornamented.

FELLOE.—The outer rim of the frame of a
centre or mould under the lagging or covering-
boards. See p. 173.

FELLING of Timber. —Different modes of
procedure, p. 98.

FELLING of Timber. —Comparative cost
of various methods, p. 99.

FELLING of Timber. —Proper season for
the operation, p. 99.

FELT GRAIN.—Timber split in a direction
crossing the annular layers towards the centre.
When split conformably with the layers it is
called the quarter grain.

FEMUR.—In architecture, the interstitial
space between the channels in the triglyph of
the Doric order.

FENDER-PILES.—Piles driven to protect
work, either on land or water, from the concus¬
sion of moving bodies.

FENESTRAL.—A small window. Used
also to designate the framed blinds of cloth or t
canvas that supplied the place of glass previous '
to the introduction of that material.

FESTOON.—A sculptured ornament in imi¬
tation of a garland of fruits, leaves, or flowers,
suspended between two points. The garland is of
| the greatest size in the middle, and diminishes gra-

262

Finial.

pinnacle, consisting usually of a knot or assemblage
of foliage. By old writers finial is used to denote
not only the leafy termination, but the whole
pyramidal mass.

FINISHING COAT.—In plastering, the last
coat of stucco-work where three coats are used.

FINLAND TIMBER. See Pinus sylves-
TRIS, p. 116, 117.

FIR TREE. See description and uses, p. 116.

FIb’E-PLACE.—The lower part of a chimney
which opens into the room or apartment, and in
which the fuel is burned.

FIRMER.— A paring chisel. See Chisel.

FIRRINGS.—Pieces of wood nailed to any
range of scantlings to bring them to one plane,
applied generally to the pieces added to joists
which are under the proper level for laying the
floor. Called also furrings. See p. 185.

FIRST COAT.—The first plaster coat laid on
laths is so called when only two coats are used.
When three coats are used, it is called the pricJcing-
up coat. In brick-work, the first of two-coat work
is called rendering, and the first of tin ee-coat work
roughing up.

FISHING, Fished Beam. —A built beam,
composed of two beams placed end to end, and

Fig. 1.

r*i rN

iAi.

1 ..

Fig. 2.

_TTY H . :: J ... .

Fig. 3.

■a — tt-

-—h— a-

A ■;

:i B

■a ——

-H-Q

secured by pieces of wood covering the joint ori
opposite sides. Fishing is performed in three diffe-

FISTUCA

INDEX AND GLOSSARY.

FORMERETS

rent ways. In the first the ends of the beam are
abutted together, and a piece of wood is placed on
each side and secured by bolts, fig. 1 . Secondly,
the parts may be indented together, so as better to
resist a tensile strain, as in fig. 2. Thirdly, pieces,
termed keys, may be notched equally into the
beams and the shle-pieces, as at a b, fig. 3. See
p. 147, 148.

FISTUCA.—An instrument for driving piles,
with two handles, raised by pulley's, and guided in
its descent so as that it may fall upon the head of
the pile, and drive it into the ground. It is called
by the workmen a
monkey.

FIXED or In¬
flexible Centre,
in bridge - building,
p. 172.

FLAMBOYANT
Stile of Archi¬
tecture. — A term
applied by French
writers to that style
of Gothic architec¬
ture in France whicli
was coeval with the
Perpendicular style
in Britain. Its chief
characteristic is a
wavy, flame - like
tracery in the win¬
dows, panels, &c.;
whence the name.

FLANK. — 1
The side of a build¬
ing.— 2 . The Scotch
term for a valley in
a roof.

FLANNING.—

Flamboyant Window,
Church of St. Ouen at Rouen.

The splaying of a door or window-jamb internally.

FLAPS.—Folds or leaves attached to window-
shutters.

FLASHINGS.—In plumbing, pieces of lead,
zinc, or other metal, used to protect the joinings
where a roof comes in contact with a wall, or
where a chimney, shaft, or other object comes
through a roof. The metal is let into a joint or
groove cut in the wall, and then folded down so as to
cover and protect the joinings. When the flashing
is folded down over the upturned edge of the lead
of a gutter, it is termed in Scotland an apron.

FLAT PANELS, p. 185.

FLATTING.—A coat of paint which, from its
mixture with turpentine, leaves the work flat or
without gloss.

FLECHE —A name for a spire when the alti¬
tude is great compared with the base.

FLEMISH BOND.—That disposition of bricks
which exhibits externally alternate headers and
stretchers in each course, whereas in English

bond the headers and stretchers are in alternate
rows. The figure shows two courses of a 14-inch
wall in Flemish bond.

FLEURON.—Foliage such as that in the cen¬
tre of the abacus of the Corinthian capital. It has
been defined to be such foliage as is not in direct
imitation of nature.

FLEXIBLE CENTRES, p. 171.

FLIERS.—Steps of a stair which are parallel¬
sided ; such as do not wind. See p. 196.

FLIGHT.—A series of fliers from one level to
another. See p. 196.

FLOATING. —Reducing the surface of plaster-
work to a plane. It is thus performed: — The
whole surface of the work is divided into bays or
compartments, by ledges of lime and hair, from
6 to 8 inches wide, extending from the top to the
bottom of the walls, and across the whole width
of the ceiling. These are termed screeds, and are
formed at 4, 5, or 6 feet apart, by the plumb-rule
and straight-edge, so as to be accurately in the
same plane. They thus become gauges or guides
for the rest of the work. When the screeds are
thus prepared, the panels or interspaces are filled in
flush with plaster, and a long float being made to
traverse them, all the plaster which projects beyond
is struck off, and the whole surface reduced to one
plane.

FLOATS. — Plasterers’ tools, consisting of j
straight rules, which are moved over the surface of
plaster while soft, to reduce it to a plane. They
are of three sorts: the hand-float, used by one man;
the quick-float, used in angles; and the derby or two-
handed float, which is so long, that two men are
required to work it.

FLOOR.—1. That part of a building or room
on which we walk. See p. 150.—2. A platform of
boards, planks, or other material, laid on timbers.

FLOORING. — The whole structure of the
floor-platform of a building, including the support¬
ing timbers. The weight of flooring is estimated
at from 30 to 80 lbs. per foot superficial, and floors
of dwelling-houses are generally calculated to carry
150 lbs. per foot superficial, including their own
weight.

FLOORING-MACHINE. —A machine for
preparing complete flooring-boards with great
despatch; the several operations of sawing, plan¬
ing, grooving and tonguing being all carried on at
the same time by a series of saws, planes, and re¬
volving chisels.

FLOOR.—Constructed by Serlio at Bologna,
in 1518, p. 153.

FLOOR of the Palace in the Wood at the
Hague, p. 153.

FLOOR-TIMBERS.—The timbers on which
the floor-boards are laid.

FLOORS.—Variation in the mode of construc¬
tion common in Scotland, Plate XLIII. Figs. 1
and 2, p. 151.

FLOORS.—Mode of construction of, used in
France, Plate XLIV. p. 162.

FLOORS.—Construction of warehouse - floors,
Plate XLIII. Figs. 4-10, p. 152.

FLOORS.—Formed of a combination of small
timbers, Plate XLIV. Figs. 15-17, p. 153.

FLOORS, Fire-proof, Plate XLIII. Figs. 12-
14, p. 154.

FLOORS.—Rules for calculating the strength
of timbers which enter into the composition of,

| p. 154.

FLORIATED.—Having florid ornaments; as,
the floriated capitals of early Gothic pillars.

FLORID STYLE. — A term employed by
some writers on Gothic architecture to designate
that highly enriched and decorated architecture
which prevailed in the fifteenth and beginning of
j the sixteenth century. It is often called the Tudor
style, as it prevailed chiefly in the Tudor era.

FLUE.— A passage for smoke in a chimney,
leading from the fireplace to the top of the chim¬
ney, or into another passage; as, a chimney with
four flues. Also, a pipe or tube for conveying heat
j to water, in certain kinds of steam-boilers. The
same name is given to passages in walls for the pur-
| pose of conducting heat from one part of a building i
to the others.

FLUING. — Expanding or splaying, as the |
jambs of a window'.

FLUSH.—A term applied to surfaces which
are in the same plane.— To flush a joint, is to fill it
until the filling material is in the plane of the sur¬
faces of the bodies joined.

FLUSH PANEL, p. 185.

ELUTINGS, or Flutes, are the hollows or
channels cut perpendicularly in columns, &c. When
the flutes are partially filled by a smaller round
moulding, they are said to be cabled. See Cable.

FLYERS.—Steps in a flight of stairs which
are parallel to each other. See Fliers.

FLYING-BUTTRESS.—In Gothic architec¬

ture, a buttress in the form of an arch springing
from a solid mass of masonry and abutting against

263

another building, to resist the thrust of an arch or
of a roof. It is seen in many cathedrals; and there
its office is to act as a counterpoise against the vault¬
ing of the central pile.

FOCUS.—1. A point in which any number of
rays of light meet, after being reflected or refract¬
ed ; as, the focus of a lens.— Virtual focus or point
of divergence, the point from which rays tend after
refraction or reflection. — Geometrical focus, the
point in which rays of light ought to be concen¬
trated when reflected from a concave mirror, or re¬
fracted through a lens, the point in which they are
actually found being termed the refracted focus.
These foci are separated from one another, in pro¬
portion to the degree of spherical aberration.—2. A
certain point in the parabola, ellipsis, and hyper¬
bola, where rays reflected from all parts of these
curves concur or meet. The focus of an ellipse is
a point toward each end of the longer axis, from
which two right lines, drawn to any point in the
circumference, shall together be equal to the longer
axis. The focus of a. parabola is a point in the
axis within the figure, and distant from the vertex
by tbe fourth part of the parameter. The focus of
a hyperbola is a point in the principal axis, within
the opposite hyperbolas, from which, if any two
lines are drawn, meeting in either of the opposite
hyperbolas, the difference will be equal to the
principal axis.

FOILS. — The small arcs in the tracery of
Gothic windows, panels, &c., which are said to be

Trefoil. Quatrefoil. Cinquefoil.

trefoiled, quatrefoiled, cinquefoiled, and multifoiled,
according to the number of arcs they contain.

FOLDED FLOORING, p. 185.

FOLIATION.—The use of small arcs or foils
in forming tracery.

FOMERELL.—A lantern-dome or cover.

FONT. — A vessel employed in Protestant
churches to hold W'ater for the purpose of baptism,
and in Catholic churches used also for holy water.

Font, Colebrooke.

There are a great many fonts in England, curious
both for their antiquity and their architectural
designs. Tn the Decorated style, their form is
usually octagonal, sometimes hexagonal; and in
the Perpendicular style, the octagonal form is al¬
most invariably used.

FOOT-PACE.—A landing or resting place at
the end of a flight of steps. If it occurs at the
angle where the stairs turn, it is called a quarter-
pace,

FOOT-STALL.—The plinth or base of a pillar.

FOOTING.—A spreading course at the founda¬
tion of a wall. The footings appear like steps, as in
the figure.

FOOTING - BEAM. —

The tie-beam of a roof.

FORE-PLANE.—The
first plane used after the
saw or axe.

FORE-SHORTEN¬
ING—In perspective, the
diminution which in repre¬
sentation a body suffers in
one of its dimensions, as
compared with the others,
owing to the obliquity of the
diminished part to the plane
of the picture.

FORMERETS. — The
arches which in Gothic groins lie next the wall,
and are consequently only half the thickness of
those which divide the wall into compartments.

Footing of a Wall.

INDEX AND GLOSSARY.

FOUNDATIONS

GOTHIC

FOUNDATIONS.—The solid ground on which
the walls of a building rest; also that part of the
building or wall which is under the surface of the
ground.

FOUR-CENTERED ARCH, to draw, p. 29.

FOUR-LEAVED FLOWER.—An ornamen¬
tal member, much used in hollow mouldings, very

Four-leaved Flowers, West Front, York Cathedral.

characteristic of the Decorated period of Gothic
architecture.

FOX-TAIL WEDGING.—A method of fix¬
ing a tenon in a mortise, by splitting the end of the
tenon beyond the mortise, and inserting a wedge.
The wedge being driven forcibly in, enlarges the
tenon, and renders the joint firm. When the mor¬
tise is not cut through and through, the wedge is
inserted in the end of the tenon, and the tenon en¬
tered into the mortise, and then driven home. The
bottom of the mortise resists the wedge, and forces it
further into the tenon, which is thus made to expand,
and press firmly against the sides of the mortise.

FRAME.—A term applied to any assemblage
of pieces of timber firmly connected together.

FRAMED-FLOOR.—One with girders, bind¬
ing-joists, and bridging-joists. See p. 151, Plate
XLII. Fig. 3.

FRAMED or Bound Doors, p. 186.

FRAMING. — 1. Fitting and joining in con¬
struction. See p. 146.—2. The rough timbers of
a house, including beams, flooring, roofing, and
partitions.

FRAXINUS.—The ash-tree. See p. 112.

FREDERICKSTADT TIMBER. Seep. 116,
117, PlNUS SYLVESTRIS.

FRENCH DOORS. — Examples of, Plate
LXXIV. Figs. 5-15, p. 187.

FRESCO.—A method of painting on walls,
performed with water-coloui's on fresh plaster, or
on a wall coated with mortar not yet dry. The
colours, incorporating with the mortar, and drying
with it, become very durable. Only as much of
the wall is coated with plaster as the artist expects
to finish during a day’s work, and at the end of
the day the portion not painted on is carefully cut
off by the outline of a figure, or other well-defined
form, so as to conceal the joining in commencing
next day’s work. From difficulty of alteration
when the colour is once absorbed, the greatest pre¬
cision of design is necessary before commencing
the work. With this view, a drawing on paper,
the exact size of the work to be executed, called a
cartoon, is prepared beforehand, and from it the
outlines of the design are carefully traced on the
wet plaster. This method of painting is very
ancient. It was used by the Greeks, and in later
times was much employed by the great masters of
the Italian schools. It is called fresco, either
because it is done on fresh plaster, or because it is
used on walls and buildings in the open air.

FRET. — Work raised in protuberances. A
kind of knot or meander, consisting of two fillets
interlaced, used as an ornament in architecture.
All the embattled, crenelled, and lozenge mouldings
are frets. An (I la Grecque.

FRETTED ROOFS. — Groined roofs, much
intersected by arches.

FRIEZE.—That part of an entablature which

Sculptured Frieze, Temple on the Illyssus.

is between the architrave and cornice. It is a flat
member, usually enriched with sculptures.

FRIEZE-PANEL.—The upper panel of adoor
of six or more panels. See p. 186.

FRIEZE-RAIL.—The rail next below the top
rail of a door of six or more panels. See p. 186.

FRONTISPIECE.—The face of a building.

FRONTON.—A pediment.

FROST CRACKS in trees, p. 97.

FRUSTUM. — The part of a solid next the
base, left by cutting off the top or segment by a
plane parallel to the base; as the frustum of a
cone, of a pyramid, of a conoid, of a spheroid, or
of a sphere, which latter is any part comprised
between two parallel circular sections; and the
middle frustum of a sphere is that whose ends
are equal circles, having the centre of the sphere
in the middle of it, and equally distant from both
ends.

FURNESS’ Mortising Machine, p. 194.

FURNESS’ Planing Machine, p. 193.

FURNESS’ Tenoning Machine, p. 193.

FUST of a Column. —The shaft.

GABLE. — The triangular end of a house or
other building, from the cornice or eaves to the top.

GABLE-ROOF.—A roof open to the sloping
rafters or spars, finishing against gable-walls.

GABLE-WINDOW.—A window in a gable, or
a window shaped like a gable.

GABLET.—-A small gable or gable-shaped
decoration, frequently introduced on buttresses,
screens, &c.

GAGE, on Gauge. —1. The length of a slate or
tile below the lap; also the measure to which any
substance is confined.—2. The quantity of plaster
of Paris used with common plaster to hasten its
setting.

GAIN.—1. A bevelling shoulder —2. A lapping
of timbers.—3. The cut that is made to receive a
timber.

GALILEE.—A small gallery or balcony, open
to the nave of a conventual church, from which
visitors might view processions ; also a porch or
portico annexed to a church, and used for various
purposes.

GALLERY.—1. Anapartmentof much greater
length than breadth, serving as a passage of com¬
munication for the different rooms of a building.—
2. Any apartment whose length greatly exceeds its
breadth, used for the reception of pictures, statues,
&c., its use being denoted by a qualifying word, as
picture-gallery, sculpture-gallery, &c. — 3. A plat¬
form projecting from the walls of a building, sup¬
ported on piers, pillars, brackets, or consoles, as
the gallery of a church or of a theatre.—4. A long
portico, with columns on one side.

GALLERY of a Church. —Framing for the,

p. 150.

GARGOYLE, or Gurgoyle. —A spout in the
cornice or parapet of a building, for throwing the
roof-water beyond the walls. Gargoyles, in classic

Gargoyle, Stony-Stratford.

architecture, were ornamented with masks, and
carved into the representations of heads of animals,
especially of the head of the lion. In the architec¬
ture of the middle ages the gargoyle became longer,
and assumed a vast variety of forms.

GARNET-HINGE.—A species of hinge, re¬
sembling the letter T laid horizontally, .thus 1—;
called in Scotland a cross-tailed hinge.

GARRET.—1. That part of a house which is
on the upper floor, immediately under the roof.—
2 . Rotten wood.

GARRETTING.—Inserting small splinters of
stone in the joints of coarse masonry, after the walls
are built. Flint walls are frequently garretted.

2G4

GATES.—Dock Gates, illustrations and de¬
scriptions of, Plates LXl., LXII., audp. 177, 178.

GATES.—Park and Entrance Gates, illustra¬
tions and description of, I late LX. and p. 177.

GATEWAY.— 1. A way through the gate of
some inclosure.—2. A building to be passed at the
entrance of the area before a mansion.

GATHERING of the Wings. — The lower
part of the funnel of a chimney.

GAUGE.—Measure; dimension.

GAUGED-ARCHES are those in which the
bricks are cut and rubbed to a gauge or mould, so
as to make exactly fitting joints.

GAUGED-PILES.—Large piles placed at re¬
gular distances apart, and connected by horizontal
beams, called runners or wale-pieces, fitted to each
side of them by notching, and firmly bolted. A
gauge or guide is thus formed for the sheeting or
filling piles, which are drawn between the wale-
pieces, and fill up the spaces between the gauged-
piles. Gauged-piles are called also standard piles.

GAUGED-STUFF.—In plastering, stuff com¬
posed of three parts of putty-lime and one part of
plaster of Paris.

GAVEL. See Gable.

GEFLE TIMBER. See Pinus sylvestris,
p. 116, 117.

GEMMELS.—An old name for hinges.

GEOMETRICAL ELEVATION. — A draw¬
ing of the front or side of a building or any object.’
—The projection, on a vertical plane, of the front
or side of a building or other object.

GEOMETRICAL STAIRS.—Those stairs the
steps of which are supported at one end only by
being built into the wall. See p. 196.

GIBLET-CHECK, or Jiblet-Cheek. — A
term used by stone-masons in Scotland, to signify
a rebate made round the opening of a doorway,
forming a recess to receive a door or gate which
opens outwards.

GIBS.—Pieces of iron employed to clasp to¬
gether such pieces of a framing as are to be keyed,
previous to inserting the keys.

GIRDER.—A main beam to support the joists
of a floor. It may be in one or two pieces, plain
or trussed. See Trussed Girders, p. 149 and
Plate XL.

GIRDERS.—Rules to determine the strength
of, p. 155.

GIRDLING Trees, to exhaust their sap before
felling, p. 99.

GIRTH,—In practice, the square of the quar¬
ter girth multiplied by the length, is taken as the
solid content of a tree.

GLACIS. —An easy, insensible slope.

GLASS-PLATE. — Specific gravity, 2‘453 ;
weight of a cubic font, 153 lbs.; expansion by 180°
of heat, from 32° to 212°, ‘00086 inch.

GLAZING, as is now practised, embraces the
cutting of all kinds of ■ glass manufactured for win¬
dows, together with the fixing of it in sashes by
means of brads and putty ; also the formation of
casements, and seaming the glass by bands of lead
fastened to outside frames of iron.

GLUING-UP COLUMNS, p. 184.

GLYPHS.—In sculpture and architecture, a
notch, channel, or cavity, intended as an orna¬
ment. Used in combination chiefly, as tryglyph
(which see).

GOBBETS.—Blocks of stone; squared blocks
of stone.

GODROON, Gadroon. — An ornament, con¬
sisting of headings or cablings.

GORE.—A wedge-shaped or triangular piece.

GOING of a Step, and Going of the Flight,
p. 196.

GOTHIC.—In architecture, a term at first ap¬
plied opprobriously to the architecture of the middle
ages, but now in general use as its distinctive ap¬
pellation. By some the term Gothic is considered
to include the Romanesque, Saxon, and Norman
styles, which have circular arches, but it is strictly
applicable only to the styles which are distinguished
by the pointed arch. Gothic architecture so re¬
stricted has been divided into three distinct styles
or periods, which have been variously named by
different authors, but the terms most generally used
are those bestowed by Mr. Rickman. By him the
first period is named the Early English, it pre¬
vailed in the thirteenth century; the second, the
Decorated, prevailed in the fourteenth centuiy;
and the third, the Perpendicular style, commenced
in the end of the fourteenth, and continued in use
till the middle of the sixteenth century. The chief
characteristics of Gothic architecture are:—The
predominance of the arch and the subserviency and
subordination of all the other parts to this chief
feature ; the tendency of the whole composition to
vertical lines; the absence of the column and en¬
tablature of classic architecture, of square edges

GOTHIC ARCHES

INDEX AND GLOSSARY.

and rectangular surfaces, and the substitution of
clustered shafts, contrasted surfaces, and members
multiplied in rich variety.

GOTHIC ARCHES.-Construction of, p. 28-30.

GOTHIC GROINS, to draw the arches of, to
mitre truly with a given arch of any form, p. 30.

GOTHIC MOULDINGS.—Characteristics of
the various periods or styles of, p. 180.

GOTHIC MOULDINGS. — Illustrations of,
Plate LXVa p. 180.

GOTHIC VAULT.—Manner of dividing it
into compartments, p. 82.

GOTTENBUEG TIMBER. SeePiNUS syl-
VESTRIS, p. 116, 117.

GRADE.-—A step or degree.

GRADE, v .—To reduce to a certain degree of
ascent or descent, as a road or way.

GRADIENT.—The degree of slope or inclina¬
tion of a road.

GRAINING. — Painting in imitation of the
grain of wood.

GRASS TABLE.—In Gothic buildings, the
first horizontal or slightly inclined surface above
the ground ; the top of the plinth.

GRATING. —A framework of timber, com¬
posed of beams crossing each other at right angles,
used to sustain the foundations of heavy buildings
in loose soils. See Grillage.

GRECIAN ARCHITECTURE,—This term
is used to distinguish the architecture which flour¬
ished in Greece from about 500 years before the
Christian era, or perhaps a little earlier, until the
Roman conquest. It comprehends the Doric, Ionic,
and Corinthian orders, to which may probably be
added the Caryatic order. Of these the Doric is
the most distinctive, and may be regarded as the
national style. The architecture of the Greeks is
known to us only through the remains of their
sacred edifices and monuments, and we have no
means of ascertaining in what manner it was ap¬
plied to their houses. Simple and grand in their
general composition, perfect in proportion, en¬
riched, yet not encumbered with ornament of con¬
summate beauty, these remains cannot be sur¬
passed in harmony of proportion and beauty of
detail.

GREEN-HEART TIMBER —Description of,
and properties and uses of, p. 112 .

GREES, Grese, Gryse. —This word, which
is variously spelled, signifies a step or degree.

GREY-STOCK BRICKS. —The hardest of
the malm bricks. They are of a pale brown colour.

GRILLAGE. — A framework composed of
beams laid longitudinally, and crossed by similar
beams notched upon them, used to sustain walls,
and prevent their irregular settling in soils of un¬
equal compressibility. The grillage is firmly bedded
and the earth packed in the interstices between the
beams, a flooring* of thick planks, termed a plat¬
form, is then laid, and on this the foundation
courses of the wall rest.

GROIN.—The line made by the intersection of
simple vaults crossing each other at any angle. See
p. 76.

GROINED ARCH.—An arch formed by the
intersection of two semicylinders or arches.

Groined Arch.

GROINED ROOF, or Ceiling. —A ceiling
formed by three or more intersecting vaults, every
two of which form a groin at the intersection, and
all the groins meet in a common point, called the
apex or summit. The curved surface between two
adjacent groins is termed the sectroicl. Groined
roofs are common to classic and mediteval archi¬
tecture, but it is in the latter style that they are
seen in their greatest perfection. In this style, by
increasing the number of intersecting vaults, vary¬
ing their plans, and covering their surface with
ribs and veins, great variety and richness were ob¬
tained, and at length the utmost limit of com¬
plexity was reached in the fan groin tracery vaulting,
tiee Fan Tracery.

GROIN,S in rectangular vaults. V- 77 78.

GROINS on a circular plan, p. 79.

GROINS on an octagonal plan, p. 79, SO.

GROOVING and Tonguins, Grooving and
Feathering, Ploughing and Tonguing. — In
joinery, a mode of joining boards, which consists
in forming a groove or channel along the edge of

4 f 4 4 ~i

Grooving and Tonguing.

one board, and a continuous projection or tongue
on the edge of another board. When a series of
boards is to be joined, each board has a groove on
its one edge and a tongue on the other. See p. 182.

GROTESQUE.—1. Applied to artificial grotto-
work, decorated with rock-work, shells, &c. — 2 .
That style of ornament which, as a whole, has no
type in nature; the parts of animals, plants, and
other incongruous elements being combined to¬
gether.

GROUND-FLOOR.—Properly, that floor of a
house which is at the base, but usually that which
is on a level with or a little above the ground with¬
out.

GROUND - JOISTS.—Joists which rest on
dwarf-walls, prop-stones, or bricks laid on the
ground; sleepers.

GROUND-LINE.—In perspective, the inter¬
section of the plane of the picture with the ground-
plane. See p. 228,

GROUND-MOULD.—An invert mould, used
in tunnelling operations, or any mould by which
the surface of ground is formed.

GROUND-PLAN.—The plan of that story of
a house which is on the level of the surface of the
ground, or a little above it.

GROUND - PLANE. — In perspective, the
plane on which the objects to be represented are
supposed to be situated. See p. 228.

GROUND-PLATE, or Ground-Sill. —The
lowest horizontal timber into which the principal
and other timbers of a wooden erection are in¬
serted.

GROUND-TABLE STONES. —The top of
the plinth of a Gothic building. See Earth-Table,
Grass-Table.

GROUNDS. — In joinery, pieces of wood at¬
tached to a wall for nailing the finishings to. They
have their outer surface flush with the plastering.
See p. 185.

GROUPED COLUMNS, or Pilasters. —A
term used to denote three, four, or more columns
or pilasters assembled on the same pedestal. When
two only are placed together, they are said to be
coupled.

GROUT.—Mortar in a fluid state, used to fill
in the joints in brick-work, or the cavities in rub¬
ble building.

GUILLOCHE. — An
interlaced ornament,formed
by two or more intertwin¬
ing bands, frequently used
in classical architecture to
enrich the torus and other
mouldings.

GUTTvE.— Ornaments
resembling drops, used in the Doric entablature,
immediately under the triglyph and mutulc.

II.

HACKING.—In walling, a manner of building
j in which a course of stones, begun with single stones
! in height, is interrupted and carried on in two stones
in height, but so as to make the two courses at the
I one end equal in height to the one course at the
other.

HACKING-OUT TOOL.—A knife for remov-
I ing old putty out of the rebates of a sash, prepara-
! tory to inserting a new pane of glass.

HACKMATACK.—The popular name of the
red larch, Finns microcarpa , but more commonly
applied to the Finns pendula.

HACKS.—The rows in which bricks are laid
! to dry after they are moulded.

li AFRIT.—The fixed part of a lid or cover, to
which the moveable part is hinged.

HALF-HEADER.—In bricklaying, a brick
I either cut longitudinally into two equal parts, or
! cut into four parts by these halves being cut across

265

HANDRAILING

transversely, used to close the work at the end of a
course.

HALF-LONG (Scotch, JIaljlin ).—One of the
bench-planes.

HALF-ROUND.—A moulding whose profile is
a semicircle; a bead; a torus.

HALF-SPACE, or Foot-Pace.— The resting
place of a staircase; the broad space or interval be¬
tween two flights of steps. When it occurs at the
angle turns ol a stair, it is called a quartei'-space.
See p. 19(n

HALF-TIMBERED HOUSES. See descrip¬
tion and illustration, p. 156, Plates XLVI. and
XL VH.

HALVING. — A mode of joining two timbers
by letting them into each other. See p. 149.

HAMMER-BEAM. — A short beam attached
to the foot of a principal rafter in a roof, in the
place of the tie-beam. Hammer-beams are used in
pairs, and project from the wall, but do not extend
half way across the apartments. The hammer-
beam is generally supported by a rib rising up from
a corbel below; and in its turn forms the support

Hammer-berm Roof, Westminster Hall.

of another rib, constituting with that springing
from the opposite hammer - beam an arch. Al¬
though occupying the place of a tie in the roofing,
it does not act as a tie; it is essentially a lever, as
will be obvious on an examination of the figure,
Here the inner end of the hammer-beam A receives
the weight of the upper portion of the roof, which
is balanced by the pressure of the principal at its
outer end. See also p. 145, description of the roof
of Westminster Hall, and illustration, Plate
XXXII.

HANCE.—A term in mediaeval architecture,
and that which immediately succeeded it, which
seems to have been limited in its application to
the small arches, at the springing of three and four
centred arches, and to the small arches by which a
straight lintel is sometimes united to its jamb or
impost.

HANDRAIL.—A rail to hold by. It is used
in staircases to assJSPin ascending and descending.
When it is next to the open newel, it forms a cop¬
ing to the stair balusters.

HANDRAILING. — Definition of terms,

p. 201.

HANDRAILING, Elucidation of the princi¬
ples of. — Section of a cylinder, p. 202.

HANDRAILING.—To produce the section of
a cylinder, through any three points on its convex
surface, p. 202.

HANDRAILING.—Summary of the leading
points of difference between the method of Mr.
Nicholson and that here taught, p. 203.

HANDRAILING.—Method of producing the
face-mould and falling-mould for the stairs, Fig.
1, Plate XCI. p. 204.

HANDRAILING.—Method of producing the
falling and face moulds for the stairs, Fig. 2, Plate
XCI. p. 205.

HANDRAILING.—Method of producing the
falling and face moulds for, Fig. 1, Plate XC.
p. 205.

HANDRAILING.—Method of producing the
face and falling moulds for scrolls, p. 205, 206.

HANDRAILING. — Sections of handiails,
how to draw. p. 207.

HANDRAILING. — Mitre cap, how to form
the section of the, p. 207.

HANDRAILING:—To form the swan-neck at
the top of a rail, p. 207.

HANDRAILING.—To form the knee at the
bottom newel, p. 207.

HANDRAILING.—Scrolls, how to draw,
p. 207.

HANDRAILING. —The scroll step, how to
form, p. 208.

HANDRAILING. — Vertical scrolls, how to
j draw, p. 208.

2 L

INDEX AND GLOSSARY.

Hanging Buttress.

HANGING BUTTRESS

HANGING BUTTRESS. — A buttress not
rising from the ground, but supported on a corbel.
Applied chiefly as a decoration,
and used only in the Decorated
and Perpendicular styles.

HANGING STYLE of a
Door or Gate —That to which
the hinges are fixed.

HANGINGS.—Linings for
rooms, consisting of tapestry,
leather, paper, and the like.

They were originally invented
to hide the rudeness of the car¬
pentry or the harsh appearance
of the bare wall. Paper-hang¬
ings were introduced early in the
seventeenth centurv.

HATCHET. —A small axe
with a short handle, used with
one hand for reducing the edges
of boards, &c

HAUNCH of an Arch.—

The middle part between the ver¬
tex or crown and the springing.

HAUNCHING, p. 182.

HAWK.—A small quadran¬
gular board, with a handle un¬
derneath, used by plasterers to
hold their plaster.

HAWK-BOY.—A boy who attends on a plas¬
terer, and supplies his liarolc with stuff.

HAWTHORN, The.—Properties and uses of,
p. 115.

HEAD-PIECE.—The capping-piece of a quar¬
tered partition, or of any series of upright timbers.

HEAD-POST.—The post in the stall-partition
of a stable which is nearest to the manger.

HEAD-WALL.—The wall in the same plane
as the face of the arch which forms the exterior of
a bridge.

HEADER.—1. In masonry, stones extending
over the thickness of the wall; through stones.—
2 . In brick-work, bricks which are laid lengthways
across the thickness of the wall.

HEADING-COURSE.—A course of stones or
bricks laid lengthways across the thickness of a wall.

HEADING-JOINT.—Thejointof two or more
boards at right angles to their fibres.

HEART-BOND —In masonry, a kind of bond
in which two stones forming the breadth of a wall
have one stone of the whole breadth placed over
them.

11 EA'RT - WOOD.—The central part of the
trunk of a tree; the duramen. See description of
Exogens, p. 94-96.

HELICAL LINE of a Handrail. —The
spiral line twisting round the cylinder, representing
the squared handrail before it is moulded.

HELICES.—Projection of, p. 67.

HELIX. —A scroll or volute; in the plural,
helices. The small vol¬
ute or caulicule under
the abacus of the Cor¬
inthian capital. In
every perfect capital
there are sixteen heli¬
ces, two at each angle
and two meeting under
the middle of each face
of the abacus.

HEMICYCLE.—

A semicircle. See de¬
scription of the hemicycles of M. Philibert de
Lorrne, p. 144.

HEMISPHERE, A.—To find the shadow on
the concave surface of, p. 220 .

HENDECAGON, or Endecagon. —A figure
of eleven sides and eleven angles. To find its area.
Multiply the square of the side by 9'3656411.

HEPTAGON. — A figure having seven sides
and angles. To find its area. Multiply the square
of its side by 3-6339124.

HERNOSAND TIMBER. See Pinus syl-
VF.STRIS, p. 116, 117.

HERRING-BONE WORK.—Courses of stone

Helices.

yrc/u’J.^

r. f V Y \ ^ v **. V

Herring-bone Work.

or timber laid angularly, so that those in each course

are placed obliquely to the right and left alter¬
nately. It receives its name from the resemblance
which the courses have to the bones of herring.
See Plate XLIV., French Floors, Fig. 1, for illus¬
tration of Flooring-boards laid herring-bone fashion.

HEXJEDRON.—A cube.

IIEX/EDRON.—One of the five regular solids.
It is bounded by six squares. To find the surface.
Multiply the square of its linear side by 6'0000000.
To find the solid content. Multiply the cube of its
linear side by 1-000000.

HEXAGON. — A figure of six sides and six j
angles. To find its area. Multiply the square of I
the side by 2'5980762.

HEXAGON.—To reduce a hexagon to a pen- j
tagon, Prob. XXII. p. 9.

HEXAGON.— Upon a given straight line,
to describe a regular hexagon, Prob. XXXlX. p. I
12 .

HEXAGONAL PYRAMID, A.—To find the
shadow of, p. 221.

PIEXASTYLE, Hexastylos. — A building
with six columns in front.

HICKORY WOOD (Juglans alba), p. 111.

HILING, Heling. —The covering of the roof
of a building; slating ; tiling.

HINGED or French Sashes, p. 187.

HINGES.—The hook or joint on which a door
or gate turns. Hinges are the joints on which
doors, lids, gates, shutters, and an infinite number
of articles, are made to swing, fold, open, or shut
up. They are made in a great variety of forms, to
adapt them to particular purposes. See p. 191.

HINGING.—Various modes of, described,
p. 191.

HIP.—A piece of timber placed in the line of
meeting of the two inclined sides of a hipped roof,
to receive the jack-rafters. It is also called a hip-
rafter, and in Scotland a piend-rafter.

HIP-KNOB.—A finial or other similar oma- I
ment placed on the top of the hip of a roof, or on

the point of a gable. When used upon timber
gables, or on gables with barge-boards, the hip-
knob generally terminates with a pendant.

HIP-MOULDING, or Hip-Mould.— Any
moulding on the hip-rafter. More commonly used
to denote the backing of a hip-rafter.

HIP-RAFTER.—The rafter which forms the
hip of a roof; a piend-rafter. See p. 91.

HIP-ROOF.—A roof, the ends of which rise
from the wall-plates, with the same inclination as

Hip-roof.

the other two sides. Called in Scotland a piend-
roof. Seep. 91.

HIP-ROOFS.—Preliminary notions, p. 91.

HIP-ROOFS. — Construction of, for regular
and irregular plans, and methods of finding the
lengths of the rafters, the backing of the hips, and
the bevels of the shoulders of the jack-rafters and
the purlins, p. 91, 92.

HOARDING. — A timber inclosure round a
building, to store materials when the building is in
course of erection or undergoing repair

HOD.—A kind of tray used in bricklaying, for
carrying mortar and bricks. It is fitted with a
handle, and borne on the shoulder. A hod for
mortar is 9 inches by 9 inches, and 14 inches long.

2G6

ICOSAHEDRON

It contains 1134 cubic inches, or 8 duodecimal
inches; and two hods of mortar are equal to a
bushel nearly. Four hods of mortar will lay 100
bricks. A hod contains 20 bricks.

HOGGING.—The drooping of the extremities
and consequent convex appearance of any timber-
supported in the middle.

HOLDFAST.—A hook or long nail, with a
flat short head, for securing objects to a wall; a
bench-hook.

HOLING.—Piercing the holes for the rails of
a stair.

HOLLOW.—A concave moulding. Sometimes
called a casement.

HOLLOW NEWEL. — In architecture, an
opening in the middle of a staircase. It is used in
contradistinction to a solid newel, which has the
end of the steps built into it. In the hollow newel
the ends of the steps next the hollow are unsup¬
ported, the other ends being only supported by the
surrounding wall of the staircase.

HOLLOW QUOINS.—The part of the piers
of a lock-gate, in which the heel-post or hanging-
post of the gate turns.

HOLLOW WALL.—A wall built in two
thicknesses, with a cavity between, either for the
purpose of saving materials or of preserving a uni¬
formity of temperature in the apartments.

HOOD - MOULDING, Hood - Mould— The
upper and projecting moulding over a Gothic door
or window, &c.; called also a label, drip, or weather -
moulding. See woodcut, Dripstone.

HORIZONTAL LINE.—In perspective, the
line of intersection of the horizontal plane with the
plane of the picture. See p. 229.

HORIZONTAL PLANE.—In perspective, a
plane parallel to the horizon, passing through the
eye and cutting the plane of the picture at right
angles. See p. 228.

HORNBEAM.—For description of properties
and uses, see p. 113.

HORSE-CHESTNUT. — For description of
properties and uses, see p. 114.

HOUSE, v .—To excavate a space in one tim¬
ber for the insertion of another. See p. 196.

HOUSING.— 1. The space taken out of one
solid to admit of the insertion of the extremity of
another, for the purpose of connecting them. See
p. 196.—2. A niche for a statue.

HOVELLING.-—A mode of preventing chim¬
neys from smoking, by carrying up the two sides
which are liable to receive strong currents, to a
greater height than the others, or by leaving aper¬
tures in the sides, so that when the wind blows
over the top the smoke may escape below.

HYP /E T11R A L.—A building or temple un¬
covered by a roof, as the famous temple of Neptune
at Paestum.

HYPERBOLA.—Construction of. p. 27, 28.

HYPERBOLA.—Description of the, p. 27.

HYPERBOLA.—To find the focus of a hyper¬
bola, p. 28.

HYPERBOLA.—Mode of describing graphi¬
cally, p. 28.

HYPERBOLA.—To draw, by means of a rule
and a string, p. 28.

HYPERBOLA.—To draw tangents and per¬
pendiculars to the curve of a hyperbola, p. 28.

HYPERBOLA.—To find points in the curve
of a hyperbola, the axis, vertex, and ordinate being
given, p. 28.

HYPOTRACHELIUM. — The neck of the
capital of a column; the part which forms the
junction of the shaft with its capital. See Neck.

ICHNOGRAPHY.—In architecture and per¬
spective, the horizontal section of a building or
other object; apian.

ICOSAHEDRAL. — Having twenty equal
sides.

ICOSAHEDRON.—The projections of an, to
construct, p. 56, 57.

ICOSAHEDRON.—A solid of twenty equal
sides. The regular icosahedron is a solid, consist¬
ing of twenty triangular pyramids, whose vertices
meet in the centre of a sphere supposed to circum¬
scribe it; and therefore they have their bases and
heights equal.-—To find the surface of an icosahe¬
dron. Multiply the square of its linear side by
8'6602540.—To find the solidity of an icosahedrou.
Multiply the cube of its linear side by 2T816950.

IMPAGES

INDEX AND GLOSSARY.

ISODOMON

IMPAGES.—A term used by Vitruvius, and
supposed to signify the rails of a door.

IMPERIAL. — -A roof or dome in the form of
an imperial crown.

IMPERIALS. — In slatkig,
slates measuring 2 feet C inches
by 2 feet.

IMPOST.—The congeries of
mouldings forming a cap or cor¬
nice to a pier, abutment, or pilas¬
ter, from which an arch springs.

INCERTUM. — A mode of
building used by the Romans, in
which the stones were not squared
nor the joints placed regularly.

It corresponds to the modern
rubble-work.

INCISE. — To cut in; to
carve.

INDENTED. —Cut in the
edge or margin into points like teeth, as an in¬
dented moulding. Indented mouldings are much
used in the transition from the Norman to the
Early English style, and sometimes in the Early
English style itself.

INDIAN ARCHITECTURE. —The archi¬
tecture of Hindoostan, in its details, bears a strik¬
ing resemblance to the architecture of Persia and
Egypt, and they are considered to have a common
origin. Its monuments may be divided into two
classes, the excavated, which is either in the form
of a cavern, or in which a solid rock is sculptured
into the resemblance of a complete building; and
the constructed, in which it is actually a building,
or formed by the aggregation of different materi¬
als. The first class is exemplified in the caves of
Elephanta and Ellora, and the sculptured temples

b, Impost.

ancients, varied almost in every building. Vitru¬
vius enumerates five varieties of intercolumniation,
and assigns to them definite proportions, expressed
in measures of the inferior diameter of the c ilumn.
These are—The pycnostyle, of one diameter and a
half; the systyle, of two diameters; the diastyle,
of three diameters; the areostyle, of four diameters;
and the eustyle, of two and a quarter diameters.
It is found, however, on examining the remains of
ancient architecture, that they rarely or never agree
with Vitruvian dimensions, which must therefore be
regarded as arbitrary ; and indeed the words them¬
selves, as will be found on referring to them, con¬
vey no idea of an exactly defined space, but are in
their very vagueness more applicable to the re¬
mains of ancient art.

INTERLUDE.—An intertie. See that term.

INTERJOIST.—The space between two joists.

INTE RL ACING A RC H ES.—Circular arches
which intersect each other, as in the figure. They

Interlacing Arcado, Norwich Cathedral.

are frequent in arcades of the Norman style of the
twelfth century, and in them Dr. Milner supposed
the Pointed style to have had its origin

INTERM ODIL-

Jain Templo, Mount Aboo, Gujerat.—Fergusson's Ilindoo Architecture.

of Mavalipooram, arid the second class in the pa¬
godas of Chillimbaram, Tanjore, and others. The
architecture of India resembles, in its details, that
of Egypt, but its differences are also very striking.
In the architecture of Egypt massiveness and soli¬
dity are' carried to the extreme; in Indian archi¬
tecture these have no place. In the former the
ornaments are subordinate to the leading forms,
and enrich without hiding them. In the latter the
principal forms are overwhelmed and decomposed
by the accessories. In the one grandeur of effect
is the result, while littleness is the characteristic of
the other. Besides the various styles of Ilindoo
architecture, properly so called, there is in Ilindoo-
stan a distinct series of buildings belonging to the
Mahometan conquerors of that country, and con¬
sisting of palaces, mosques, and tombs. These par¬
take strongly of the characteristic features of Sara¬
cenic architecture.

INJURY to Timber, from being exposed to
sudden or rapid changes of temperature, p. 100.

INNER PLATE.—The innermost of the two
wall-plates in a double wall-plated roof.

INSERTED COLUMN.—The same as en¬
gaged column (which see).

INSERTUM. See Incertum.

INSULATED COLUMNS. — Those which
stand clear from the walls, as opposed to attached
or engaged columns.

INTAGLIO.— Literally, a cutting or engrav¬
ing ; hence, anything engraved, or a precious stone
with arms or an inscription engraved on it, such as
we see in rings, seals, &c.

INTERCOLUMNIATION.—The space be¬
tween two •columns. This, in the practice of the

LION.—The space be¬
twixt two modillions.

INTERPILASTER.
—The space between two
pilasters.

INTERQUARTER.
—The space between two
quarters.

INTERTTE, Inter-
puce. —A short piece of
timber introduced hori¬
zontally between uprights,
to bind them together or
to stiffen them. See p.
155, Partitions, and illus¬
tration, Plate XLV. Fig.
1, A A ; Fig. 2, No. 2,
D ; Fig. 3, No. 1, C;
andp. 156, Timber-houses,
and illustration, Fig. 470,
p. 157, OOO.

INTRADOS.—l.The
interior or under concave
curve of an arch. The
exterior or convex curve
is called the extrados.
See woodcut, Arch. —2.
a vault. It is called also

The concave surface of
douelle.

INVERTED ARCH.—An arch with its in-
trados below the axis or springing line, and of
which, therefore, the lowest stone is the keystone.

Inverted arches are used in foundations to connect
particular points, and distribute their weight or
pressure over a greater extent of surface, as in
piers and the like.

IONIC ORDER-—The second of the three
Grecian and third of the five Roman orders. The
distinguishing characteristic of this order is the
voluted capital of the column. In the Grecian Ionic
capital the volutes appear trie same on the rear as
! on the front, and are connected on the flanks by a
peculiar roll-moulding, called the baluster or bolster.
In the exterior columns of a portico, however, the
volutes are repeated on the outer flank, and are thus
necessarily angular. The Grecian Ionic may be
considered in three parts—the stylobate, column,
and entablature. The stylobate is from four-fifths
to a whole diameter in height, and is in three re¬
ceding steps. The column is rather more than nine
diameters in height. Of this two-fifths of a dia¬
meter are given to the base, and from three-fourths

267

to seven-eighths to the capital, including the hypo-
trachelium. The base is divided into three nearly
equal parts in height, with two equal fillets sepa¬
rating them. The lowest is a torus, which rests on

the stylobate; this is separated from a scotia above
by a fillet, and another fillet intervenes between the
scotia and another torus, and from a third fillet the
scape or apophyge of the shaft springs. The shaft
diminishes in a curved line to its upper diameter,
which is five-sixths of its lower diameter, or some¬
times more. It is fluted with twenty-four flutes,
with fillets one-fourth of their width between. The
hypotrachelium or necking of the capital is some¬
times separated from the shaft by a plain fillet, and
sometimes by a carved bead, and is generally orna¬
mented. Above this the mouldings of the capital
spring out. They consist generally of a bead, an
ovolo, and a torus, all richly carved, and on these
rest the square mass, on the faces of which are
the volutes, and on this rests the abacus, whose
edges are moulded into the form of an ovolo, and
sometimes ornamented with the egg-and-tongue.
The entablature is rather more than two diameters
in height. If this be divided into five parts, two
of them may be given to the architrave, two to the
frieze, and the remaining part to the cornice. If
the architrave, again, be divided into nine parts,
seven of them may be given to three equal fascias,
and the remainder to the band of architrave
mouldings. The frieze may be plain or enriched
with sculpture in low-relief. The cornice consists
of bed-mouldings, corona, and crowning mouldings.
The bed-mouldings are composed of a bead and a
cyma reversa, both carved. The cyma reversa is
contained in the depth of the corona, whose bed is
hollowed out for that purpose. The crown
mouldings are rather more than one-fourth of the
height of the cornice, and consist of a carved bead,
an ovolo, also carved, and a crowning fillet. This
is a general description of the composition of the
Ionic order of the Erechtheium on the Acropolis at
Athens, the most perfect exanqde left to us, pro¬
duced probably about 420 years B.C., the great epoch
of Athenian art.—The Roman Ionic. This order
in the hands of the Romans suffered great debase¬
ment. The angular volute of the Greeks was a
clumsy enough expedient to get rid of a difficulty
which need never have arisen if the order had been
used either in antis or attached; but the Romans,
not content with this, made in many cases volutes
at all the four angles of the column, and then curved
all the sides of the abacus. The Ionic, as used by
the Italian architects, varied much in proportions ;
but the following are those given by Sir William
Chambers, in diameters and minutes, or sixtieths
of a diameter:—The column is nine diameters high,
of which the base occupies thirty, and the capital
twenty-one minutes. The architrave, divided into
two fascias, is forty and a half minutes, the irieze
also forty and a half minutes, and the cornice
fifty-four minutes. The separation between the
fascias of the architrave is made by a fillet and
carved ovolo. The architrave mouldings consist
of a carved ogee and a fillet. The frieze is plain.
It is surmounted by an ogee serving as a bed¬
moulding to a dentil band equal in depth to rather
more than a fifth of the cornice. Over this is an
ovolo, serving as the bed-moulding of the corona ;
then the corona, in height equal to nearly a fifth
of the cornice ; and then the crowning mouldings,
consisting of an ogee, a fillet, and a cyma recta.
When a pedestal is used, the same authority
makes it two diameters and six-tenths in height.

IRON.—To find the weight of.—1. Wrought
iron close hammered: find the number of cubic
inches contained in the mass, multiply this by 28,
cut off two figures to the right hand, and the re¬
mainder is lbs. 2. Cast iron : proceed as above,
but multiply by 26 instead of 28.

IRON TIE-RODS.— Dimensions of, for various
spans. See Tie-rod.

ISLE, Ile, a spelling formerly incorrectly used,
instead of aile or aisle (which see).

ISODOMON, Isodomum. —In Grecian archi¬
tecture. a species of walling in which the courses
were of equal thickness and equal lengths.

INDEX AND GLOSSARY.

ISOMETRICAL PROJECTION

ISOMETRICAL PROJECTION, p. 242.

ITALIAN ARCHITECTURE.—Under this
term are comprehended the three great architec¬
tural schools of Italy—the Florentine, the Roman,
and the Venetian. The architecture of Florence is
best displayed in its palaces. In the facades of
these, columns are used only as ornamental acces¬
sories, and however many the horizontal divisions
or stories, the reigning cornice is proportioned to
the whole height of the building, considered as an
order, and is in general boldly pronounced and
richly decorated. This is the severest of the Italian
schools, and the exteriors of these palaces have a
solidity, monotony, and solemnity which would
make them appear as fortified places, if it were not
for their richly-ornamented cornices. In the Roman
school the architecture is less massive; columns are
introduced freely, and grandeur of effect without
severity is studied. The Venetian school is char¬
acterized by lightness and elegance, an.d the free
use of columns, pilasters, and arcades.

JACK-ARCH.—An arch of a brick in thick¬
ness.

JACK-PLANE.—One of the bench-planes. It
is about eighteen inches long, and is used in reduc¬
ing inequalities in the timber preparatory to the
use of the trying-plane.

JACK-RAFTER. See Jack-timbers, andp.
91, voce Hip-roof.

JACK-RIB. See Jack-timbers.

JACK-TIMBERS.—Those timbers in a series
which, being intercepted by some other piece, are
shorter than the rest. Thus, in a hipped-roof, each
rafter which is shorter than the side-rafters is a
j ack-rafter

JAMB-LININGS.—The linings of the vertical
sides of a doorway.

JAMB-POSTS.—The upright timbers ou each
side of a doorwav, called also prick-posts. See p.
156.

JAMB-STONES. — Those employed in con¬
structing the vertical sides of an opening.

JAMBS.—The vertical sides of any aperture,
such as a door, a window, or chimney.

JERKIN-HEAD.—The end of a roof not hip¬
ped down to the level of the side walls, the gable
being carried up higher than those walls. A trun¬
cated hipped roof.

JESTING-BEAM.—-A beam introduced for
the sake of appearance and not for use.

JETTY.—A projecting portion of a building.

JIB-DOOR.—A door with its surface in the
plane of the wall in which it is set. Jib-doors are
intended to be concealed, and therefore they have
no architraves or finishings round them, and the
plinth and dado are carried across them. See p. 187
and Plate LXXIII.

JOGGLES, or Joggle-joints.— In architec¬
ture, the joints of stones or other bodies, so con¬
structed and fitted together, as to prevent them
from sliding past each other by any force acting in
a direction perpendicular to the pressure by which

a a a, Joggle-joints. u ThL- last Joggle.

they are thus held together. In masonry, this term
is applied to almost every sort of jointing in which
one piece of stone is let or fitted into another, so as
to prevent all sliding on the joints. In carpentry,
the struts of a roof are said to be joggled into the
truss-posts and into the rafters.

JOINER.—Materials used by the, p. 182.

JOINERY.—The art or practice of dressing,
framing, joining, and fixing wood-work, for the in¬
ternal and external finishings of houses. See De¬
finition, p. 182.

JOINT.—1. In architecture, the surface of se¬
paration between two bodies that are brought into
contact, and libld firmly together by means of ce¬
ment, mortar, &c., or by a superincumbent weight.

The nearer the surfaces of separation approach each
other, the more perfect the joint, but in masonry
the contact cannot be made very close on account
of the coarseness of the cement.—2. In carpentry
and joinery, the place where one board or member
is connected with another. Joints receive various
names, according to their forms and uses. Pieces
of timber are framed and joined to one another most
generally by mortises and tenons, of which there are
several kinds, and by iron straps and bolts. When
it is required to join two pieces of timber so as to
make a beam of a given length, and equal in strength
to one whole piece of the same dimensions and
length, this is done by scarfing.—A longitudinal
joint, one in which the common seam runs parallel
with the fibres of both.— Abutting or butt joint, one
in which the plane of the joint is at right angles to
the fibres, and the fibres of both pieces in the same
straight line.— Square joint, one in which the plane
of the joint is at right angles to the fibres of one
piece, and parallel to those of the other.— Bevel-
joint, one in which the plane of the joint is parallel
to the fibres of one piece, and oblique to those of
the other.— Mitre-joint, one in which the plane of
the joint makes oblique angles with both pieces.
— Dovetail-joint. See Dovetail, also Mortise,
Tenon, and Scarfing, and p. 146, 182.

JOINTER.—The largest planeused in straight¬
ening the edges of boards to be jointed together.
In bricklaying, a crooked piece of iron bent in two
opposite directions, and used for drawing, by the aid
of the jointing-rule, the horizontal and vertical joints
of the work.

JOIN TING-RULE.—A straight-edge used by
bricklayers for guiding the jointer in drawing in
the joints of brick-work.

JOINTS AND STRAPS, p. 146, 182.

JOISTS.—The pieces of timber to which the
boards of a floor, or the laths of a ceiling are nailed,
and which rest on the walls or on girders, and some¬
times on both. They are laid horizontally, in pa¬
rallel equidistant rows. They are of a rectangular
form, and placed with their edges uppermost, as
the lateral strength of a horizontal rectangular beam
to resist a force acting upon it is proportional to
the breadth of the transverse section multiplied into
the square of the depth. Flooring with only one
tier of joists is termed single-flooring, and when two
tiers are used, it is termed double-flooring. — Trim¬
ming-joists, two joists, into which each end of a
small beam, called a trimmer, is framed. See
Trimmer. — Binding-joists, or binders, in a double
floor, are those which form the principal support of
the floor, and run from wall to wall.— Bridging-
joists, those which are bridged on to the binding-
joists, and carry the floor: they are laid across the
binding-joists.— Ceiling-joists, cross-pieces fixed to
the binding-joists underneath, to sustain the lath
and plaster. See Floors, p. 150.

JUBE.—The rood-loft, or gallery into the
choir.

JUFFERS.—Pieces of timber four or five inches
square in section.

JUGLANS ALBA.—White w'alnut or hick¬
ory, p. 111.

JUGLANS NIGRA.—Black or brown wal¬
nut. See p. Ill-

JUMP.—An abrupt rise from a level course.

JUMPER. — A name given by masons and
miners to a long iron chisel used in boring shot-
holes, for blasting large masses of stone, by which
they may be split into smaller ones.

JUTTY. — A projection in a building. The
same as jetty.

KEEP.—Tlie stronghold of an ancient castle.

KEEPING the Perpendicular. — Causing
the vertical joints in brick-work to recur in the same
straight line in each alternate course.

KERB or Kirb-plate. See Curb-plate.

KERF.—The channel or way made through
wood by a saw.

KERNEL.—The same as crenelle (which see).

KEY. —A name given to all fixing wedges.

KEY-PILE.—The centre pile plank of one of
the divisions of sheeting piles contained between
two gauge piles of a cofferdam, or similar work. It
is made of a wedge form, narrowest at the bottom,
and wheu driven, keys or wedges the whole to-
I gether.

KYANIZE

KEYED DADO.—In architecture, a dado that
is secured from warping, by having bars of wood
grooved into it across the grain at the back.

KEYHOLE SAW.—A saw used for cutting
out sharp curves, such as keyholes require, whence
its name. It consists of a narrow blade, thickest
on the cutting or serrated edge, its teeth having no
twist or set, and a long handle perforated from end
to end, into which the blade is thrust to a greater
or lesser extent, according to the nature of the work
to be performed. The handle is provided with a
pad and screw for fastening the blade when it is
adjusted. It is also called a turning-saw.

KEYING a mortise joint, p. 147.

KEYS.—In naked flooring, pieces of timber
fixed in between the joists by mortise and tenon.
When these are fastened with their ends projecting
against the sides of the joists, they are called strut¬
ting-pieces.

KEYSTONE.—The highest central stone of an
arch; that placed on the top or vertex, to bind the
two sweeps together. In some cases the keystone
projects from the face, and is moulded and enriched,
in vaulted Gothic roofs, the keystones are usually
ornamented with* a boss or pendant. See first
w oodcut under Arch.

KILLESSE, Cullis, Coulisse. — A gutter,
groove, or channel. The term is corruptly applied
in some districts to a hipped roof; as a killesscd or
cullidged roof. A dormer-window, too, is some¬
times called a killessed or cullidged window.

KING-PIECE. —Another and more appropriate
name for king-post.

KING-POST. — The post which, in a truss,

. extends between the apex of two inclined pieces
| and the tie-beam, which unites their lower ends
/ as in a king-post roof. See p. 148, and woodcut,
Roof.

KING-TABLE. — In mediaeval architecture,
conjectured to be the string-course, with ball and
flower ornaments, usual under parapets.

KIOSK.—A Turkish word signifying an open
pavilion or summer-house supported by pillars.

KIRB-PLATE. See Curb-plate.

KIRB-ROOF. See Curb-roof.

KNEE.—1. A piece of timber somewhat in the
form of the human knee when bent.—2. A part of
the back of a hand-rail, which is of a convex form,
the reverse of a ramp, which is concave.— Knee-
piece or knee-rafter, an angular piece of timber used
to strengthen the joining of two pieces of timber in
a roof.

KNOCKER.—A kind of hammer fastened to
a door, to be used in seeking for admittance. The
knockers of mediaeval buildings present many

Knocker, Village of Street, Somersetshire.

beautiful specimens of forged iron-work. They are
often highly decorated, and sometimes assume very
quaint and fantastic forms.

KNOT, or Knob.—A bunch of leaves, flowers,
or similar ornament, as the bosses at the ends of
labels, the intersections of ribs, and the bunches of
foliage in capitals.

KNOTS in Wood. — Some kinds render wood
unfit for the carpenter; some kinds are not preju¬
dicial. See p. 98.

KNOTTING.—A process to prevent the knots
of wood from appearing, by laying on a size com¬
posed of red led, white lead, and oil, or a coat of
gold size, as the preliminary process of painting.

KNOTTY and Cross-grained Wood. —Unfit
for ordinary carpentry works. See p. 98.

KNOWLEDGE OF WOODS.—Physiological
notions, p. 93.

KNUCKLE.—A joint of a cylindrical form,
with a pin as axis, such as that by wdiich the straps
of a hinge are held together. See p. 190, Hinging;
and Plates LXXXIV.—LXXXVI.

KYANIZE, v .—To steep in a solution of cor¬
rosive sublimate, as timber, to preserve it from the
dry-rot.

26 S

LABEL

INDEX AND GLOSSARY.

LONG PLANE

LABEL.—A projecting moulding over a door,
window, or other opening; called also dripstone,
weather-moulding, and, when in the interior, hood¬
moulding.

LABOUR-SAVING MACHINES.—Sketch
of the introduction of, p. 191.

LABOUR - SAVING MACHINES. — Sir
Samuel Bentham’s inventions in, p. 191.

LABOUR-SAVING MACHINES.—Ameri¬

can circular saw bench, and Furness’ planing-
machine, Plate LXXXVII. and p. 192; Fur¬
ness’ patent mortising and tenoning machines,
Plate LXXXVII a and p. 193.

LABYRINTH FRET.—A fret with many in¬
volved turnings.

LACUNARIA or Lacunars. — Panels or
coffers in a ceiling.

LADIES.—In slating, small slates measuring
about 15 inches long and 8 inches wide.

LAD\ r -CHAPEL.—A chapel dedicated to the
Virgin Mary, frequently attached to large churches.
It was various^ placed, but generally to the east¬
ward of the high altar. In churches of an earlier

• late than the thirteenth century, the lady-chapel
is generally an additional building. The term
D of modern application. See woodcut, Cathe¬
dral.

LAGGINS, Lagging.— The planking laid on
the ribs of the centering of a tunnel or bridge, to
carry the brick or stone work. See p. 171.

LAMINATED ARCHES.—Arches composed

• if thin plates of wood fastened together. See p. 141.

LANCET ARCH.—-One whose head is shaped
like the point of a lancet. See p. 29.

LANCET WINDOW. — A window with a
lancet arch. This kind of
window is characteristic
of the Early English style
of architecture. Lancet
windows have no tracery,
and were often double or
triple, and sometimes five
were placed together.

Though separated on the
outside, lancet windows
which are placed together
are in the interior com¬
bined into one design by
a wide splaying of the
openings, and thus form,
to a certain extent, a com¬
pound window.

L A N D IN G. — The Lancet Window, Comberton.

first part of a floor at the

end of a flight of steps. Also, a resting-place be¬
tween flights. See p. 196.

LANTERN.—1. A drum-shaped erection, on
the top of a dome, or the roof of an apartment, to
give light, and serve as a sort of crowning to the
fabric. It may be either circular, square, elliptical,
or polygonal (see Lodvre). Also, the lower part of
a tower placed at the junction of the cross in a cathe¬
dral or large church, having windows on all sides.—
2. A square cage of carpentry placed over the ridge
of a corridor or gallery, between two rows of shops,
to illuminate them, as in many public arcades.

LAP, v. —To lap boards is to lay one partly
over the other.

L AQUE AR.—The same as lacunaria or lacunar.

LARCH.—Description and uses of, see p. 119.

LARMIER.— The corona or drip of a cornice;
corruptly lorimer.

LATH.—1. A thin narrow board or slip of
wood nailed to the rafters of a building, to support
the tiles or covering.—2. A thin narrow slip of
wood nailed to the studs, to support the plastering;
also, a thin cleft piece of wood used in slating,
tiling, and plastering. There are two sorts of laths,
single and double ; the former being barely a quarter
of an inch, while the latter are three-eighths of an
inch thick. Pantile laths are long square pieces of
fir, on which the pantiles hang.— Lath floated and
set fair, three-coat plasterer’s work, in which the
first is called pricking up, the secoud floating, the
third or finishing is done with fine stuff.— Lath laid
and set, two-coated plasterer’s work ; except that
the first is called laying, and is executed without
scratching, unless with a broom.— Lath plastered,
set, and coloured, the same as lath laid, set, and
coloured.— Lath pricked up, floated, and set for
paper; the same as lath floated and set fair.

LATTICE.—Any work of wood or iron, made
by crossing laths, rods, or bars,
and forming open chequered or
reticulated work. — Lattice, or
lattice window, a window made
of laths or strips of iron which
cross one another like net-work,
so as to leave open interstices.

It. is only used when air rather Lattice Work, Cairo.

than light is to be admitted. Such

windows are common in hot countries, and in these

the lattice work is frequently arranged in handsome

devices.

LATTICE BRIDGE, p. 169.

LAYER BOARDS.—The boards for sustain¬
ing the lead of gutters.

LEAD, in excavator’s work, is the,distance to
which the materials have to be removed.

LEAD NAILS.—Nails used to fasten lead,
leather, canvas, &c., to wood. They are of the
same form as clout nails, but are covered with lead
or solder.

LEAF.—The side of a double door.

LEAF BRIDGE.—A bridge consisting of two
opening leaves.

LEAN TO.— A building whose rafters pitch
against or lean on to another building, or against a
wall.

LEAR BOARD. — The same as layer
hoard.

LECTERN OR Lettern. —The reading desk in
the choir of ancient churches and chapels. It was
generally of brass, and sometimes elaborately carved.
Its use has been almost entirely superseded in Eng¬
land by the modern reading desk, or rather reading
pew.

LEDGE.—A surface projecting horizontally, or
slightly inclined to the horizon; a string course;
also, the side of a rebate, against which a door or
shutter is stopped, or a projecting fillet serving the
same purpose as a door stop, or the fillet which
confines a window frame in its place.

LEDGED DOORS.—Doors formed of deals,
with cross pieces on the back to strengthen them.
See p. 186.

LEDGERS.—The horizontal timbers used in
scaffolding.

LEDGMENT.—1. A laying out; the develop¬
ment of the surface of any solid on a plane, so that
its dimensions may be readily obtained.—2. The
same as ledge; a string course or horizontal mould¬
ing.

LEDGMENT TABLE.—In medieval archi¬
tecture, a name given to any of the tables of the
base, except the ground table.

LENGTHENING BEAMS.—By scarfing and
by fishing, p. 148.

LEWIS, Lewisson (Fr. louve, louveceau). —
An instrument of iron, used in raising large stones
to the upper part of a
building, which operates
by the dovetailing of one
of its ends into an open¬
ing in the stone. It con-,
sists of two moveable
parts a a, perforated at
their heads to admit the
pin or bolted. These are
inserted, by hand, into
the cavity formed in the
stone; and between them
the part h is introduced,
which pushes their points
out to the sides of the
stone, thus filling the ca¬
vity ; e a half-ring bolt,
with a perforation at each
end; to this the tackle
above is attached by a hook. The fastening-pin
passes horizontally through all the holes, entering
at the right side d, and forelocking on the other
end c.

LICH - GATE. — A shed over the gate of a
churchyard to rest the corpse under; called also a
corpse-gate.

LIME TREE, Linden tree. — Description
and uses of, p. 113.

LINE of Lines on the Sector, p. 37.

LINE of Chords on the Sector. —Construc¬
tion and use of, p. 37.

LINE of Polygons on the Sector. — Con¬
struction and use of, p. 38.

LINE of Projection. —In perspective, the
intersection of the plane of the picture with the
ground plane.

LINE of Nosings, p. 196.

LINE of Secants on the Sector. —Construc¬
tion and use of, p. 39.

LINE of Sines on the Sector.— Construc¬
tion and use of, p. 39.

2G9

LINE of Tangents on this Sector.— Con¬
struction and use of, p. 39.

LINEAL MEASURES. See Weights and
Measures.

LINEAR PERSPECTIVE.—That branch of
perspective which regards only the positions, mag¬
nitudes, and forms of the objects delineated.

LINING.—In architecture, the covering of the
surface of any body with a thinner substance. The
term is only applied to coverings in the interior of
a building, coverings on the exterior being properly
termed casings. Lining of boxings for window
shutters, are the pieces of framework into which
the shutters are folded back. Linings of a door
are the coverings of the jambs and soffit of the
aperture.— Lining out stuff, drawing lines on a piece
of board or plank, so as to cut it into thinner pieces.

LINTEL.—A horizontal piece of timber, iron,
or stone placed over an opening. See p. 156.

LIST, Listel.—A fillet moulding.

LOBBY.—1. A small hall or waiting-room ;
also, an inclosed space surrounding or communi¬
cating with one or more apartments; such as the
boxes of a theatre. When the entrance to a prin¬
cipal apartment is through another apartment, the
dimensions of which, especially in width, do not
entitle it to be called a vestibule or antechamber,
it is called a lobby.—2. A small apartment taken
from a hall or entry.

LOCK.—1. Lock, in its primary sense, is any¬
thing that fastens; but in the art of construction
the word is appropriated to an instrument composed
of springs, wards, and bolts of iron or steel, used to
fasten doors, drawers, chests, &c. Locks on outer
doors are called stock locks ; those on chamber doors,
spring locks; and such as are hidden in the thick¬
ness of the doors to which they are applied, are
called mortise locks. —2. A basin or chamber in a
canal, or at the entrance to a dock. It has gates
at each end, which may be opgned or shut at plea¬
sure. By means of such locks vessels are trans¬
ferred from a higher to a lower level, or from a lower
to a higher. Whenever a canal changes its level
on account of an ascent or descent of the ground
through which it passes, the place where the change
takes place is commanded by a lock.

LOCK-CHAMBER.—In canals, the area of a
lock inclosed by the side walls and gates.

LOCK-GATE.—The gate of a lock provided
with paddles, &c. See Dock-gates, p. 177, and
PJates LXI. and LXII.

LOCK-PADDLE.—The sluice in a lock which
serves to fill or empty it.

LOCK-PIT.—The excavated area of a lock.

LOCK-RAIL.—The middle rail of a door, to
which the lock or fastening is fixed. See p. 186.

LOCK-SILL.—An angular piece of timber at
the bottom of a lock, against which the gates shut.

LOCK-WEAR.—A paddle-wear, in canals, an
over-fall behind the upper gates, by which the
waste water of the upper pond is let down through
the paddle-holes into the chamber of the lock.

LOCKER.—1. A small cupboard.—2. A small
closet or recess, frequently observed near an altar
in Catholic churches, and intended as a depository
for the sacred vessels, water, oil, &c.

LOCUTORY.—An apartment in a monastery,
in which the monks were allowed to converse when
silence was enjoined elsewhere.

LODGE.—1. A small house in a park, forest,
or domain, subordinate to the mansion ; a tempo¬
rary habitation; a hut.—2. A small house or cottage
appended to a mansion, and situated at the gate of
the avenue leading to the mansion; as a porter’s
lodge.

LOFT.—In modern usage this term is restricted
to the place immediately under the roof of a build¬
ing, when not used as an abode ; as liay-loft. The
gallery of a church is sometimes termed the loft in
Scotland.

LOGARITHMIC LINES on the Sector. —
Construction and use of, p. 40.

LOMBARD ARCHITECTURE.—A name
given to the round-arched Gothic of Italy, intro¬
duced by the conquering Goths and Ostrogoths,
which superseded the Romanesque, and reigned
from the eighth to the twelfth century. “ At first,
says Mr. Fergusson, “when the barbarians were
few, and the Roman influence still strong, they of
course were forced to adopt the style of their pre¬
decessors, and to employ Italian builders to execute
for them works they themselves were incapable of
producing; but as they became stronger they threw
off the trammels of an art with which they had no
sympathy, to adopt one which expressed their own
feelings; and although the old influence still lay
beneath, and occasionally even came to the surface,
the art was Gothic in all essentials, and remained
so during nearly the whole of the middle ages.

LONG PLANE, or Jointer. See Jointer.

INDEX AND GLOSSARY.'

loop-hole

LOOP-HOLE.—A narrow opening in a wall.

LOUIS-QUATORZE, Style of.—A meretri¬
cious style of ornament and ornamental decoration
developed in France during the reign of Louis XIV.
The great medium of this style was gilt stucco¬
work, and its most striking characteristics are an
infinite play of light and shade, and a certain dis¬
regard of symmetry of parts, and of symmetrical

Louis-Quatorze Ornament.

arrangement. The characteristic details are the
scroll and shell. The classical ornaments, and all
the elements of the Cinque-cento, from which the
Louis-Quatorze or Louis XIV. proceeded, are ad¬
mitted, under peculiar treatment, or as accessories;
the panels are formed by chains of scrolls, the con¬
cave and convex alternately; some clothed with an
acanthus foliation, others plain.

LOUIS-QUINZE, Style of. —A variety of
the Louis-Quatorze style of ornament, which pre¬
vailed in France during the reign of Louis XV., in
which the want of symmetry in the details, and of

Louis-Quinze Ornament.

symmetrical arrangement, which characterize the
Louis XIV. style, are carried to an extreme. An
utter disregard of symmetry, a want of attention to
masses, and an elongated treatment of the foliations
of the scroll, together with a species of crimped
conventional shell-work, are characteristics of this
style.

LOUVRE, Loover, Lover, or Lantern.—
A dome or turret rising out of the roof of the hall
in our ancient domestic edifices ; formerly open at
the sides, but now generally glazed. They were
originally intended to allow the smoke to escape,

-I

Louvre, Abbot’s Kitchen, Glastonbury.

when the fire was kindled on dogs in the middle of
the room. The open windows in church-towers are
called louvre-winclows , and the boards or bars which
are placed across them to exclude the rain, are called
louvre-boards, corruptly luffcr-boards.

LOZENGE MOULDING, or Lozenge Fret.
—An ornament used in Norman architecture, pre¬
senting the appearance of diagonal ribs inclosing
diamond-shaped panels.

BUFFER-BOARDING. See Lodvre.

LUMBER.—In America, timber sawed or split
for use.

LUNETTE.—An aperture in a concave ceiling
for the admission of light.

LYING PANELS.—Those in which the fibres
of the wood lie in a horizontal direction.

LYSIS.—A plinth or step above the cornice of
the podium which surrounds the stylobate.

M ROOF.—A kind of roof formed by the junc¬
tion of two common roofs, with a valley between
them. ,

MACHICOLATIONS.—In castellated archi¬
tecture, openings made through the roofs of portals
to the floor above, but more generally openings
made in the floor of projecting galleries for the pur¬
pose of defence, by pouring through
them boiling pitch, molten lead,

&c., upon the besiegers. ‘ In the
latter case they are formed by the
parapet or breast-work B being set
out on corbels D, beyond the face of
the wall c. The spaces E between
the corbels, which are open through¬
out, are the machicolations. From
its striking appearance, the cor¬
belled gallery with its parapet, was
frequently used when machicola¬
tions were not required for the pur-

Machicolations, Ilerstmonceux Castle.

omitted. Machicolations do not appear to have
been used earlier than the twelfth century.

MACHINES with Revolving Cutters.—
General remarks on, p. 194.

MAHOGANY, p. 115.

MAHOGANY TREE.—Description and uses
of, p. 115.

MAIN BRACES, p. 159.

MAIN COUPLE. — A name given to the
trussed principal of a roof.

MALM BRICKS.—Those composed of clay,
sand, and comminuted chalk. They burn to a pale
brown colour, more or less inclined to yellow, which
is an indication of magnesia.

MANAGEMENT of Timber after it is cut,

p. 100 .

MANNER of Dividing a Gothic vault into
compartments, p. 82.

MANNER of Dividing conical, spherical,
and other vaults, into compartments and caissons,

p. 82.

MANSARD ROOF.—A roof formed with an
upper and under set of rafters on each side, the
under set less and the upper set more inclined to
the horizon. It is called a mansard roof from the
name of the architect, Francois Mansard, who re¬
vived its use in France. It is called also a curb-
roof, from the French courber, to bend, descriptive
of the double inclination of its sides. See Man¬
sard Roof, p. 140, and Plate XXVII.

MANTELPIECE, Mantlepiece. —The orna-
I mental dressing or front to the mantle-tree.

MANTLE-SHELF.—The work over a fire¬
place in front of the chimney.

MANTLE - TREE. — The lintel of a fire¬
place.

MAPLE.—Description and uses of, p. 113.

MARBLE.—The popular name of any species
| of calcareous stone or mineral, of a compact tex¬
ture, and of a beautiful appearance, susceptible of
a good polish. Marble is limestone, or a stone
which may be calcined to lime, a carbonate of lime;
but limestone is a more general name, ctfmprehend-
ing the calcareous stones of an inferior texture, as
well as those which admit a fine polish. The term
is limited by mineralogists and geologists to the

270

METRE

several varieties of carbonate of lime, whioh have
more or less of a granular and crystalline texture.
In sculpture, the term is applied to several compact
or granular kinds of stone, susceptible of a very fine
polish. The varieties of marble are exceedingly
numerous, and greatly diversified in colour. In
modern times, the quarries of Carrara, in Italy,
almost supply the world with white marble. Of
variegated marbles, there are many sorts found in
this country of singular beauty. Marble is much
used for statues, busts, pillars, chimney-pieces,
monuments, &c.

MARGIN DRAUGHT.—In stone cutting, a
line of chiselling along the edge of a stone.

MARGIN of a Course. —In slating, that part
of a course of slating which is not covered by the
next superior course.

MARGINS, OR Margents. —The flat parts of
the styles and rails of framed or panelled work.
Doorswhich are made in two leaves are called double-
margined doors, in consequence of the styles being
repeated in the centre, as are also those in one leal,
made in imitation of a two-leaved door.

MARIGOLD WINDOW. — The same as
Catherine wheel window and rose window. See Rose
Window.

MARKET- CROSS.—A cross set up where a
market is held. Most market towns in England
and Scotland had, in early times, one of these. The
primitive form was that of simple shaft and cross
stone, but they afterwards were constructed in a
much more elaborate manner, so as frequently to
lose the cruciform structure as a distinguishing char¬
acteristic.

MARL BRICKS.—Fine bricks used for gauged
arches and the fronts of buildings.

MARQUETRY. — Inlaid work consisting of
thin pieces of wood of different colours, arranged on
a ground so as to form various figures. Used in
cabinet work. The term is also used as synonymous
with mosaic.

MASK. — A piece of sculpture representing
some grotesque form, to fill and adorn vacant
places, as in friezes, panels of doors, keys of
arches, &c.

MASON.—One who prepares and sets stones ;
a builder in stone.

MASONRY.—The art of shaping, arranging,
and uniting stones together to form walls and other
parts of buildings.

MASTIC.—A kind of cement made by mixing
litharge, or the red protoxide of lead, with pulver¬
ized calcareous stones, sand, and linseed oil. The
proportions of the ingredients vary.

MATCH PLANES.—Planes in pairs, used in
joining boards by grooving and tonguing, one plane
being used to form the groove, and the other to form
the tongue.

MAUSOLEUM.—In modern times, a sepul¬
chral chapel, or edifice erected for the reception of
a monument, or to contain tombs.

MEANDER.—An ornament composed of two

jfSJTUfiififfii

Meander.

or more fillet mouldings intertwined in various
ways; a fret.

MEDALLION.—A circular, oval, or some¬
times square tablet, bearing on it objects represented
in relief, or an inscription.

MEDIAEVAL ARCHITECTURE.—A term
properly applied to denote the architecture which
prevailed throughout the middle ages, or from the
fifth to the fifteenth century. It thus comprises
the Romanesque, the Byzantine, the Saracenic, the
Lombard, and other styles, besides the Norman and
the Gothic. In popular language, however, it is
restricted to the Norman and early Gothic styles,
which prevailed in Great Britain and on the Con¬
tinent from the eleventh to the fourteenth century.

MEMBER.—Any subordinate part of a build¬
ing, order, or composition, as a frieze or cornice;
and any subordinate part of these, as a corona, a
cymatium, a fillet.

MEMEL TIMBER, Crown Memel, Best
Middling, Second Middling, or Brack. Pinus
SYLVESTRIS, p. 116, 117-

MERLON.—The plain parts of an embattled
parapet, between the crenelles or embrasures. See
woodcut, Battlement.

METHODS of Piling newly-felled timber,

p. 100.

METOPE.—The space between the triglyphs
of the Doric frieze.

METRE.—A French measure equal to 39'37
English inches.

INDEX AND GLOSSARY.

MEZZANINE

MEZZANINE. — A story of small height intro¬
duced between two higher ones.

MEZZO-RELIEVO.—Middle relief. See
Demi-Relievo.

MIDDLE PANEL, p. 186.

MIDDLE POST. — The same as Icing-post. The
rail of a door level with the hand, and on which the
lock is generally fixed; whence it is usually termed
the loch-rail.

MILE. — -A measure of distance. The English
mile = 5280 feet; the geographical or nautical,
6075'6 feet; ratio of geographical to English,
1-15068 to 1.

MILLED LEAD. — Lead rolled out into sheets
by machinery.

MILLIARY COLUMN.—A column set up to
mark distances ; a milestone. See Column.

MINARET.—A slender, lofty turret rising by
different stages or stories, surrounded by one or
more projecting balconies, common in mosques in

Minarets, Constantinople.

Mahometan countries. The priests from the bal¬
conies summon the people to prayers at stated times
of the day ; so that they answer the purpose of bel¬
fries in Christian churches.

MINSTER.—A monastery ; an ecclesiastical
convent or fraternity; but it is said originally to
have been the church of a monastery; a cathedral
church. Both in Germany and England this title
is given to several large cathedrals; as York minster,
the minster of Strasburg, &c. It is also found in
the names of several places which owe their origin
to a monastery ; as, Westminster, Leominster, &c.

MITRE.—The line formed by the meeting of
surfaces or solids at an angle. It is commonly
applied, however, when the objects meet in a right
angle, and the mitre-line bisecting this makes an
angle of 45° with both.

MITRE-BOX.—A box or trough with three
sides, used for forming mitre-joints. It has cuts in
its vertical sides, the plane passing through which
crosses the box at an angle of 45°. The piece of
wood to be mitred is laid in the box, and the saw-
being worked through the guide-cuts, forms the
mitre-joint in the wood.

MITRE-SQUARE.—A bevel with a fixed
blade, for striking an angle of 45° on a piece of
stuff, in order to its being mitred.

MODILLION.—A block carved into the form
of an enriched bracket, used under the corona of
the Corinthian and Composite entablatures. Mo-
dillions less ornate are occasionally used in the Ionic

Modlllion.

entablature. The derivation of the word is pro¬
bably from modulus (a measure of proportion), ex¬
pressive of the arrangement of the brackets at regu¬
lated distances.

MODULAR PROPORTION.-That which is
regulated by the module.

MODULE, Modulus. —A measure which may
be taken at pleasure to regulate the proportions of
an order, or the disposition of the whole building.
The diameter or semi-diameter of the column at the
bottom of the shaft has usually been selected by
architects as their module, and this they subdivide
into parts or minutes, the diameter generally into
sixty, and the semi-diameter into thirty minutes.
Some architects make no certain or stated divisions
of the module, but divide it into as many parts as
may be deemed requisite.

MONASTERY.—A house of religious retire¬
ment or seclusion from ordinary temporal concerns,
whether an abbey, a priory, a nunnery, or a con¬
vent. The word is usually applied to the houses of
monks.

MONIAL, or Monycale. See Mullion.

MONKEY. — The ram or weight of a pile¬
driving engine. See Fistuca.

MONOCOTYLEDONOUS PLANTS, p. 93.

MONOLITHIC.—Formed of a single stone;
as a monolithic obelisk.

MONOPTEROS.—A term used, by Vitruvius
to denote a temple composed of columns arranged
in a circle, and supporting a conical roof or a tholus,
but having no cella. Such a temple, however,
would be more correctly denominated cyclostylar.

MO NOTRIGL YP il. — The in tercolunmiation
of the Grecian Doric most usually followed. It is
that in which space is left for the insertion of only
one triglyph between those immediately over two
contiguous columns.

MONTANTS, Mountings, Muntins.— The
intermediate styles in a piece of framing, which are
tenoned into the rails. See p. 186.

MOORISH, or Moresque Architecture.
See Saracenic Architecture.

MORTAR.—A mixture of lime and sand with
water, used as a cement for uniting stones and
bricks in walls. The proportions vary from 1 j part
of sand to 1 part of lime, to 4 and 5 parts of sand
to 1 of lime. When limestones contain consider¬
able portions of silica and alumina, they form what
is termed hydraulic lime, and the mortars made
with them are called hydraulic mortars, which are
used for building piers or walls under water, or ex¬
posed to it, because they soon harden in such situa¬
tions, and resist the action of the water.

MORTISE, Mortice. —A cavity cut in a piece
of wood or other material, to receive a correspond¬
ing projecting piece called a tenon, formed on another
piece of wood, &c., in order to fix the two together
at a given angle. The sides of the mortise are four
planes, generally at right angles to each other and
to the surface where the cavity is made. The junc¬
tion of two pieces in this manner is termed a mor¬
tise joint. See p. 147, Joints, and p. 182.

MORTISE LOCK.—A lock made to fit into a
mortise cut in the style and rail of a door to re¬
ceive it.

MOSAIC WORK is an assemblage of little
pieces of glass, marble, precious stones, &c., of va¬
rious colours, cut square, and cemented on a ground
of stucco, in such a manner as to imitate the colours
and gradations of painting. This kind of work was

Mosaic Pavement.

used in ancient times both for pavements and orna¬
menting walls. In recent times, two kinds of mosaic
are particularly famous—the Roman and the Flo¬
rentine. In the former, the pictures are formed by
joining very small pieces of stone. In the Floren¬
tine style larger pieces are used.

MOUCH ARABY.—A balcony with a parapet
and machicolations projected over a gate to defend
the entrance. The parapet may be either embattled
or plain.

MOULD-STONE. — The jamb stone of an
aperture.

MOULDED NOSING, p. 196.

271

NATURAL BEDS OF STONE

MOULDING, or Forming the Surface of
wood into various square and curved contours, p. 184.

MOULDING PLANES.—Joiners’ planes used
in forming the contours of mouldings.

MOULDINGS, Gothic. —Examples of, p. 180.

MOULDINGS, Greek and Roman.—M ode
of describing the various, p. 17S.

MOULDINGS, Planted or Laid in, p. 185.

MOULDINGS, Stuck, p. 184.

MULLION, Munnion, Monycale, Monial.
—A vertical division between the lights of win¬
dows, screens, &c., in Gothic architecture. Mul-
lions are rarely found earlier than the early English
style. Their mouldings are very various. Some¬
times the styles in wainscotting are called mullions.

MUTULE.—An ornament in the Doric cor¬
nice, answering to the modillion in the Corinthian,
but differing from it in form, being a square block,
from which the guttre depend.

NAIL.—A small pointed piece of metal, usu¬
ally with a head, to be driven into a board or other
piece of timber, and serving to fasten it to other
timber. The larger kinds of instruments of this
sort are called spikes; and a long, thin kind, with
a flattish head, is called a brad. Nails are exten¬
sively used in building, and generally in the con¬
structive arts. There are three leading distinctions
of iron nails, as respects the state of the metal from
which they are prepared, namely, wrought or forged
iron nails, cut or pressed iron nails, and cast iron
nails. Of the wrought or forged nails there are
about 300 sorts, which receive different names, ex¬
pressing for the most part the uses to which they
are applied, as hurdle, pail, deck, scupper, mop, &c.
Some are distinguished by names expressive of their
form: thus, rose, clasp, diamond, &c., indicate the
form of their.heads, and flat, sharp, spear, &c.,
their points. The thickness of any specified form
is expressed by the terms fine, bastard, strong.
Nails are made both by hand and by machinery.

NAIL-HEAD MOULDING.—An ornament
common in Norman architecture. It is so named
from being formed by a series of diamond-pointed
knobs, resembling the heads of nails.

NAILS, Adhesion of, in Wood. See Adhe¬
sive Force of Nails and Screws.

NAKED.—Any continuous surface, as opposed
to the ornaments and projections which arise from
it. Thus the naked of a wall is the continuous sur¬
face of the wall, as ojjposed to its projections or
ornamented parts.

NAKED FLOORING.—The supporting tim¬
bers on which the floor-boards are laid. See p. 150.

NAOS.—The body of an ancient temple, some¬
times, but erroneously, applied to the cella or inte¬
rior. The space in front of the temple was called
pronaos.

NARTHEX.—The name of an inclosed space
in the ancient basilicae when used as Christian
churches, and also of an ante-temple or vestibule
without the church. To the narthex the cate¬
chumens and penitents were admitted; and there
appears to have been several such apartments in
each church, but nothing certain is known of their
position. Narthex is frequently used as synonym¬
ous with porch and portico.

NARVA TIMBER. — Pinus sylvestris, p.
116, 117.

NATTES.— A name given to an ornament used
in the decoration of surfaces in the architecture of

the twelfth century, from its resemblance to the
interlaced withs of matting.

NATURAL BEDS of Stone are the surfaces

INDEX AND GLOSSARY.

NOTCH

NAVE

in stratified rocks, in which the laminae separate.
As all stones of this kind exfoliate rapidly when
these surfaces are exposed, it becomes necessary, in
using them in building, to lay them on their natu¬
ral beds, or, in other words, so to place them in the
wall that their exfoliating surfaces shall be horizon¬
tal, or at right angles to its face. The contrary use
of the stone is described as setting on edge.

NAVE.—The central avenue or middle part of
a church, extending from the western porch to the
transept, or to the choir or chancel, according to
the nature and extent of the church. In the larger
structures it has generally one or more aisles on
each side, and sometimes a series of small chapels
beyond these. In smaller buildings it is commonly
without aisles. See woodcut, Cathedral.

NEBULE MOULDING.—A moulding whose
edge takes the form of an undulating line. It is
used in corbel-tables and archivolts.

NECK, Necking, or Hypotrachelium. —In
architecture, the part which serves to connect a
capital or head with its body or shaft; thus the neck
of a capital is that part which lies between the
lowest moulding of the capital and the highest
moulding of the shaft. In the Grecian Doric it is
the space between the annulets and the channel,
and in the Roman Doric it is the space between the
annulets and the astragal. In the same way the
neck of a finial is the part in which the finial joins
the obelisk, and the channels, astragals, or other
members which terminate the shaft or body, are
called the neck-mouldings.

NECK-MOULDINGS. See preceding word.

NEEDLE.—A beam of timber supported on
upright posts, used to carry a wall temporarily
during alterations or repairs.

NEEDLEWORK.—A term sometimes applied
to the framework of timber, of which old houses are
constructed.

NERVITRES, Nerves, or Branches. —The
ribs which bound the sides of a groined compart¬
ment in a vaulted roof, as distinguished from the
diagonal ribs.

NEUTRAL AXIS.—That plane in a beam in
which theoretically the tensile and compressive
forces terminate, and in which the stress is there¬
fore nothing. See Strength and Strain of Ma¬
terials —Transverse Strain, p. 126,

NEWEL. — The upright cylinder or pillar,
round which, in a winding staircase, the steps turn,
and are supported from the bottom to the top. In
stairs where the steps are pinned into the wall and
there is no central pillar, the staircase is said to
have an open newel. The newel is sometimes con¬
tinued through to the roof, and serves as a vaulting-
shaft from which the ribs branch off in all directions.

NEWEL STAIRS, p. 196.

NICHE—A recess in a wall for the reception
of a statue, a vase, or of some other ornament. In
classic architecture, niches were generally semicir¬
cular in the plan, and terminated in a semi-dome
at the top. They were sometimes, however, square
in the plan, and sometimes also square-headed.
They were ornamented with pillars, architraves,
consoles, and in other ways. In the architecture

Niche, All-Souls’ College, Oxford.

of the middle ages niches were extensively used as
decorations, and for the reception of statues. In
the Norman style they were so shallow as to be
little more than panels, and the figures were fre¬

plan, and their heads were formed into groined
vaults, with ribs, and bosses, and pendants. They
were projected on corbels, and adorned with pillars,
buttresses, and mouldings of various kinds, and
had canopies added to them, sometimes fiat and
sometimes projecting in every variety of plan, and
elaborately carved and enriched. In the Perpen¬
dicular style this variety and elaboration were con¬
tinued.

NICHE, Spherical, on a circular plan, p. 83.

NICHE, Spherical, on a segmental plan, p. 83. I

NICHE, on a semicircular plan, with a seg¬
mental elevation, p. 83.

NICHE, segmental in plan and elevation, p. 84.

NICHE, segmental in plan and elliptical in ele¬
vation, p. 84.

NICHE, a, elliptical in plan and elevation, p. 84.

NICHE, a, octagonal in plan, p. 84.

NICHE, a semicircular, in a concave wall, p. 84.

NICHE, a semicircular, in a convex wall, p. 85.

NICHE, A.—To determine the shadow in the
interior of, p. 22.

NIDGING.—In masonry, nidging is a mode
of dressing used chiefly for granite, but sometimes
also applied to other stones. It is thus performed.
The face of the stone being prepared as for rubbing
or tooling, the beds and joints are squared up, and
a margin draught, about fths of an inch wide, run
round the face. Lines are then drawn around the
margin, parallel with the beds and joints, and cut
in by a sharp boaster, with light blows of the mal¬
let. The nidging then begins. The tool used for
this is a hammer about 3 lbs. weight, having its ends
formed like an axe. The axe-face of the hammer is
held crossing the stone at right angles to its length;
each blow makes a slight indentation by abrasion,
and, by a succession of blows, the stone is furrowed
all over with shallow furrows, and reduced to a
uniform surface. No portion of stone should be
left between the successive series of furrows. Nidg¬
ing, when well done, is a characteristic mode of
working hard stones; but it is not proper to be used
for soft stones, as it makes their surface more liable
to be acted on by the weather.

NOGGING.—Brick-work carried up in panels
between timber quarters.

NOGGING PIECES. — Horizontal pieces
fitted in between and nailed to the quarters for
strengthening the brick-nogging.

NOGS.—-A north of England term for wood
bricks or timber bricks.

NONAGON.—A figure having nine sides and
nine angles. To find the area of a nonagon. Mul¬
tiply the square of its side by 6T818242.

NONIUS. See Vernier.

NORMAN ARCHITECTURE.—A style of
architecture imported into England immediately
from Normandy, at the time of the Conquest, a.d.
1066. It continued in use till towards the end of
the twelfth century, when it was superseded by the

first of the Pointed or Gothic styles, the Early Eng¬
lish. The Norman is readily distinguished from
the styles which succeeded to it by its general mas¬
sive character, round-headed doors and windows,
and low square central tower. The doorways are
generally very highly enriched by a profusion of
decorated mouldings, for the most part peculiar to
the style. The windows have no mullions, and in
the early examples are quite plain. In later speci¬
mens they have frequently small shafts in the jambs,
or are enriched with the zigzag moulding peculiar to
the style. The piers which support the arches are
in the earlier examples strikingly solid and massive,
being merely plain square or circular masses of

quently carved on the back in alto-rilievo. In the
early English style they become more deeply re¬
cessed, and are highly enriched, and in the Deco¬
rated style they become infinitely varied. They
were chiefly semi-octagonal or semi-hexagonal in

masonry, sometimes having capitals and bases, and
sometimes merely an impost to relieve the outline.
The square piers were frequently recessed at the
angles, and in some cases had half pillars attached
to # their sides; and the circular ones in some in¬

stances had the plain surface relieved by lines cut in
a lozenge or spiral form. As the style advanced,
these solid piers were reduced to more moderate pro¬
portions of round or octagonal pillars, and in the
time of the transition were frequently very tall and
slender. The capitals of these piers and pillars are
among the most important features of this style. The
upper member or abacus is in general square, and

Part of the South Transept and Nave, Peterborough Cathedral.

its profile is also square, having its lower edge sloped
or chamfered off. One of the earliest forms of the
capital, and which, with various modifications, is
found in all periods of the style, is what is called
the cushion capital. (See woodcut under that term.)
It is frequently divided into two or more parts, and
is also sometimes enriched with sculpture of foliage
and figures ; but under all these modifications it
may still be taken as the primary form of the Nor¬
man capital. The arches were almost universally
round-headed until the period of the transition,
when the pointed form was used along with or fre¬
quently instead of it. The pointed arch must not
be taken as a certain criterion of transition date, as
we have examples of it combined with solid early
Norman piers, as at Malmesbury Abbey; but these
examples are rare, and the mixture of the two forms
may generally be taken as evidence of transition.
The windows were universally round-headed, until
the transition period.

NORWAY SPRUCE.—Description and uses
of, p. 117.

NORWAY TIMBER. See Pinus sylvks-
tris, p. 116, 117.

NOSING.—The projecting edge of a moulding
or drip.

NOSING of Steps. —The projecting moulding
on the edge of a step, consisting generally of a torus,
with a fillet below, joined by a sweep or cavetto to
the face of the riser. See p. 196.

NOTCH, v .—To cut a hollow on the face of a
piece of timber, for the reception of another piece.
The piece in which the hollow is cut is said to be
notched upon the other piece, and if the notched
piece is superimposed, it is said to be notched down

upon the inserted piece ; as the bridging-joists are
notched down on the binding-joists in naked floor¬
ing. (See p. 151.) The figures show the varieties
of notching in common use. a is the method termed
halving; that is, when a notch equal in depth to
half the thickness of the stuff is made in both pieces;
h is a dovetail notch; in c the notch is formed a
little way from the end of each piece, so that the
joint cannot be drawn asunder in either direction ;

NOTCH-BOAKD

INDEX AND GLOSSARY.

OVERSTORY

in d the width of the notch is not so great as the
width of the piece on which it is to be let down,
which is also partially notched to receive it. This
last, however, belongs rather to caulking or cogging
than to notching.

NOTCH-HOARD.—A board which is notched
or grooved, to receive the ends of the boards which
form the steps of a wooden stair.

NUMBERS. The line of, on the sector, p. 40.

NYLAND TIMBER. See Pinus sylvks-
tris, p. 116, 117.

0 .

OAK.—Description and uses of, p. 109.

OBELISK.—A lofty, quadrangular, monolithic
column of a pyramidal form ; not, however, termi¬
nating in a point, nor truncated, but crowned by a
flatter pyramid. The proportion of the thickness
to the height is nearly the same in all obelisks ; that
is, between one-ninth
and one-tenth; and the
thickness at the top is
never less than half,
nor greater than three-
fourths of the thickness
at the bottom. Egypt
abounded with obelisks,
which were always of a
single block 'of stone;
and many have been
removed thence to
Rome and other places.

It is generally believed
that obelisks were oii-
ginally erected as mo¬
numental structures,
serving as ornaments
to the open squares in
which they were usu¬
ally placed, or intended
to celebrate some im¬
portant event, and to
perpetuate its remem¬
brance. They were usu¬
ally adorned with hiero¬
glyphics. The two larg¬
est obelisks were erected by Sesostris, in Helio¬
polis; the height of these was 180 feet. They wero
removed to Rome by Augustus.

OBJECTIVE LINE. — In perspective, any
line drawn on the geometrical plane, the represen¬
tation of which is sought on the draught or picture.

OBJECTIVE PLANE.—Any plane situated
on the horizontal plane, whose perspective repre¬
sentation is required.

OBLIQUE ARCHES, or Oblique Bridges.
—Those arches or bridges whose direction is not at
right angles to their axes. See Skew Bridges.

OCCULT LINES.—Such lines as are required
in the construction of a drawing, but which do not
appear in the finished work. Dotted lines are also
so termed.

OCTAGON.—A figure of eight sides and eight
angles.—To find the superficies of an octagon. Mul¬
tiply the square of its side by 4 - 8284272.

OCTAGON.—Upon a given straight line, to
describe a regular octagon, Prob. XL. p. 12.

OCTAGON.—In a given square, to inscribe a
regular octagon, Prob. XLI. p. 12.

OCTAGON. — About a given circle, to describe
an octagon, Prob. XLVII. p. 14.

OCTAHEDRON, Octaedron —One of the five
regular solids. It is contained by eight equal equi¬
lateral triangles.—To find the surface of an octa¬
hedron. Multiply the square of the linear side by
3'4641016.—To find the solidity. Multiply the
cube of the linear side by 0'4714045.

OCTAHEDRON, Projections of, to con¬
struct, p. 54.

OCTANGULAR PYRAMID.—To find the
section of an, p. 69, Plate I. Fig. 12.

OCTAST YLE, Octostyle. —A temple or other
building having eight columns in front.

OCULUS.—A round window. It was some¬
times simply termed an O.

ODEUM, Odeon.— A kind of theatre, in which
poets and musicians sut niitted their works for the
judgment of the public, and contended for prizes.

(ECUS.—Iri ancient architecture, the banquet-
ing-room of a Roman house; an apartment adjoin¬
ing the drawing-toom.

OFFSET, or Set-off. —A horizontal break in

Obelisk at Luxor.

a wall at a diminution in its thickness. In Scot¬
land termed a scarccment.

OGEE. — In classic architecture, a moulding
consisting of two members, one concave and the
other convex. It is called also cyma reversa. See

Fig. 3. Fig. 2. Fig. 1.

Mouldings, and also Plate LXIII. In medieval
architecture, the ogee moulding assumed different
forms at different periods. Fig. 1 is Early English,
Fig. 2 is Decorated, Fig. 3 is late Perpendicular.

OGEE ARCH.—A pointed arch, the sides of
which are each formed
with a double curve. It
is used in the Decorated
style, and less frequently
throughout the Perpen¬
dicular style, and is gen¬
erally introduced over
doors, niches, tombs, and
windows, its inflected
curves weakening it too
much to permit of its application for the support of
a great weight.

OGEE ARCH.—Methods of drawing, p. 30.

OGEE PYRAMID, with a hexangular base,
to find the section of an, p. 69, Plate I. Fig. 13.

OGIVE.—The French term for the ogee arch,
but it is also applied to the diagonal ribs of a groined
vault. The Pointed style of architecture is termed
by the French Le style Ogival.

OILLETS, or Oylets. —In the walls of build¬
ings of the middle ages, small openings or eyelet-
holes, through which missiles were discharged.

ONEGA TIMBER. See Pinus sylvestris,
p. 116, 117.

OPEN NEWELLED STAIRS. — Winding
stairs which have no solid pillar or newel in the
centre.

OPEN STRING, p. 196.

OPISTHODOMUS.—A term applied to the
hinder part of a temple, when there is a regular
entrance, and a facade of columns, as in front.
The same as the Roman posticum.

ORATORY. — A small private chapel, or a
closet near a bed-chamber, furnished with an altar,
a crucifix, &c., and set apart for the purposes of
private devotion, such as commonly existed in the
better class of dwellings previous to the Reforma¬
tion, and is still often used by Roman Catholics.
The small chapels attached to churches were also
often called by the same name.

ORB.—A plain circular boss. The mediajval
name for the tracery of blank windows or stone
panels.

ORDERS of ARCHITECTURE.-The term
order, in architecture, signifies a system or assem¬
blage of parts subject to certain uniform established
proportions, which are regulated by the office each
part has to perform. An order may be said to be
the genus, of which the species are five, viz., Tuscan,
Doric, Ionic, Corinthian, and Composite psee these
terms), but it is usual to give to these five the name
of orders. Each order consists of two essential
parts, a column and an entablature; the column is
divided into three parts, the base, the shaft, and
the capital; and the entablature is divided into
three parts also, the architrave, the frieze, and the
cornice. In the subdivisions certain horizontal
members are used, which, from the curved forms of
their edges, are called mouldings; as the ovolo,
cyma, cavett.o, torus, &c. The character of an
order is displayed, not only in its column, but in
its general forms and detail, of which the column
is, as it were, the regulator, the expression being of
strength, grace, elegance, lightness, or richness.
The scale for the proportions-—that is, not the ac¬
tual but the relative dimensions of the different
parts compared with each other—is taken from the
lower diameter of the shaft of the column, which is
divided into two modules or sixty minutes. See
Column.

ORDONNANCE.—The right assignment, for
convenience and propriety, of the measure of the
several apartments, that they be neither too large
nor too small for the purposes of the building, and
that they be conveniently distributed and lighted.

ORIEL WINDOW.—A large bay or recessed
window in a hall, chapel, or other apartment. It
usually projects from the outer face of the wall,
either in a semi-octagonal or semi-square plan, and

273

is of various kinds and sizes. When not on the
ground floor it is supported on brackets or corbels.
Some writers restrict the term oriel window to such

Oriel Window, Baliol College, Oxford.

as project from the outer face of the wall and are
supported on corbels, and apply the term bay-
window to such as rise from the ground.

ORIENTAL PLANE. See Platanus ori¬
entals, p. 113.

ORIENTATION. — An eastern direction or
aspect; the art of placing a church so as to have its
chancel pointing to the east.

ORIGINAL LINE.—Any line belonging to
an original object.

ORIGINAL OBJECT.—In perspective, any
object whatever.

ORIGINAL PLANE.—In perspective, any
plane on which an original object is situated, or any
plane of the object itself.

ORNAMENTS. — In architecture, are the
smaller and detailed parts of the main work, not
essential to it, but serving to adorn and enrich it.

ORTHOGRAPHY.—1. In geometry, the art
of delineating the fore right plane or side of any
object, and of expressing the elevations of each part;
so called because it determines things by perpen¬
dicular lines falling on the geometrical plane.—2.
In architecture, the elevation of a building, show¬
ing all the parts in their true proportion. It is
either external or internal. The first is the repre¬
sentation of the external part or front of a building,
as seen by the eye of the spectator, placed at an
infinite distance from it. The second, commonly
called the section, exhibits the building as if the
external wall were removed and separated from it.
—3. In perspective, the fore right side of any plane,
that is, the side or, plane that lies parallel to a
straight line that may be imagined to pass through
the outward convex points of the eyes, continued
to a convenient length.

ORTHOSTYLE.—A columnar arrangement,
in which the columns are placed in a straight line.

OSTIUM.—In ancient architecture, the door
of a chamber.

OUNDY, or Undy Moulding. —A moulding
with a wave-like outline.

OUT and IN BOND.—A Scotch term for al-

Fig. 2.

Two Courses of Door rmd of Window Jamb or Rebates.

Fife. 1. Doorjamb; Fig. 2 Window jamb; e g, btretcher or outbond;
a a c, header or inbond. In Fig. 1, o /, the reveal or breast; and in
Fig. 2, a is the reveal or breast.

ternate header and stretcher in quoins, and window
and door jambs.

OUTER DOORS.—Those which are common
to the interior and exterior sides of the walls of a
building.

OUTER STRING, p. 196.

OVA.—Ornaments in the form of eggs, into
which the ovolo moulding is often carved.
OVER-STORY.—The clere-story.

2 M

INDEX AND GLOSSARY.

OVOLO

OVOLO.—A moulding, the vertical section of
which is, in Roman architecture, a quarter of a
circle; it is thence called the quarter-round. In
Grecian architecture the section of the ovolo is
elliptical, or rather egg-shaped. _

OVOLO.—To describe an ovolo, its projection
and a tangent to it being given, p. 179.

OVOLO, The Hyperbolic. —To describe, jts
projection and a tangent to it being given, p. 179.

PACE.—A portion of a floor slightly raised
above the general level; a dais.

PACKING.—In masonry, small stones im¬
bedded in mortar, used to fill up the interstices of
the larger stones in rubble walls.

PAD.—A handle.

PADDLE—A small sluice.— Paddle-lioles are
the passages which conduct the water from a dock
or the upper pond of a canal, into the lock-chamber,
and out of the lock-chamber into the lower pond.

PAGODA.—A temple in the East Indies, in
which idols are worshipped. The pagoda is gene¬
rally of three subdivisions. First, an apartment
whose ceiling is a dome, resting on columns of stone
or marble; this part is open to all persons. Second,
an apartment forbidden to all but Brahmins. Third
and last, the cell of the deity or idol inclosed with
a massy gate. The idol itself is sometimes called a
pagoda. The most remarkable pagodas are those
of Benares, Siam, Pegu, and particularly that of
Juggernaut in Orissa. Pagodas are also common
in China, where they are called taas.

PALJESTRA. —Among the Greeks, a place for
athletic exercises.

PALLET MOULDING. — In brick-making,
that kind of moulding in which sand is used to pre¬
vent the clay from adhering to the mould, one
mould only being used; and the brick when moulded
turned out on a flat board called a pallet, on which
it is carried by the assistant to the hack-barrow or
the hack.

PAMPRES. — Ornaments consisting of vine
leaves and grapes, with which the hollows of the
circumvolutions of twisted columns are sometimes
decorated.

PAN op Wood, or Pan of Framing. See
Timber Houses, p. 156.

PANACHE. The French name for a species
of pendentive, formed by a portion of a domical
vault intercepted between one horizontal and two
vertical surfaces. It occurs when a round tower or
dome is carried over a square substructure, as when

Panache.

a dome is raised on the square formed by the cross¬
ing of the nave and transept of a church. In this
case the panache P becomes a spherical triangle,
bounded by three arcs, viz., the arch of the nave A,
the arch of the transept B, and the circle c, which
serves as the springing of the dome or tower.

PANEL.—In architecture, an area sunk from
the general face of the surrounding work; also a
compartment of a wainscot or ceiling, or of the sur¬
face of a wall, &e.; sometimes inclosing sculptured
ornaments. In joinery, it is a tympanum or thin
piece of wood, framed or received in a groove by
two upright pieces or styles, and two transverse
pieces or rails ; as the panels of doors, window-
shutters, &c. In masonry, a term sometimes ap¬
plied to one of the faces of a hewn stone.

PANEL SAW.—A saw used for cutting very
thin wood in the direction of the fibres or across
them. Its blade is about 26 inches long, and it
has about six teeth to the inch.

PANELLING.—In architecture, the operation
of covering or ornamenting with panels; panelled
work.

PANELS in Joinery, p. 185.

PANTAGRAPH, Pantograph. —An instru¬
ment for copying, enlarging, or reducing drawings.
See Eidograph.

PANTHEON.—A temple dedicated to all the
gods. The term is also applied to places of public
exhibition, in which every variety of amusement is
to be found.

PANTILE, OR Pentile.— A tile in the form
of a parallelogram, straight in the direction of its
length, but with a waved surface transversely.
Each tile is about 13^ inches long and 7 inches
wide, but the development of its surface is of course
greater; it is about half an inch thick. It has a
small tongue or projection from its under side at
its upper end, which serves to hook it to the lath.
Pantiles are set either dry or in mortar. They over¬
lap laterally, the down bent edge of the one tile

covering the upturned edge of the other. Having
only 3 or 4 inches of longitudinal overlap, pan¬
tiling is little more than half the weight of plain
tiling, but it is not so warm a covering, and is more
apt to be injured by storms. The ridges and hips
of roofs covered either with pan or plain tiles, are
finished with large concave tiles, called hip or ridge
tiles, and sometimes crown tiles; these are not over¬
lapped, but are set in mortar and fastened with
nails or pins. To find the number of pantiles re¬
quired to cover a roof, the gauge being 10 inches.
Rule: Multiply the area in superficial feet by 1*80.
And to find the weight in tons. Multiply the area
in superficial feet by •00377-

PARABOLA.—Description of the, p. 26.

PARABOLA.—To draw, p. 26.

PARABOLA.—To draw by means of intersec¬
ting lines, Prob. XCVII. and XCVTII. p. 27.

PARABOLA.—To draw, by means of a straight
rule and a square, Prob. XCIX. p. 27

PARABOLA.—To find the parameter of a
parabola, p. 26.

PARABOLA.—To draw perpendiculars to the
curve of a parabola, p. 26.

PARABOLA.—To find the area of a parabola
or its segment. Multiply the base by the perpen¬
dicular height, and two-thirds of the product is the
area.

PARADISE. — In mediaeval architecture, a
small private apartment or study.

PARALLEL.—To draw a straight line par¬
allel to a given straight line, Prob. I. and II. p. 5.

PARALLEL COPING. — Coping of equal
thickness throughout.

PARALLEL PERSPECTIVE. — That in
which the picture is supposed to be situated, so as
to be parallel to the side of the principal object to
be represented. See Perspective, p. 227.

PARALLELOGRAM.—-To inscribe in a given
quadrilateral figure, Prob. XXXIII. p. 11.

PARALLELOGRAM of Forces, p. 120.

PARALLELOGRAM of Forces. —Applica¬
tion of, to discover the stress on parts of framing,
p. 121 .

PARAPET.—Literally, a wall or rampart to
the breast, or breast high.—In military structures,
the parapet is a wall intended for defence, and is
either plain or battlemented, and pierced with loop¬
holes and oillets for the discharge of missiles.—In
civil and ecclesiastical buildings, the parapet, like
the balustrade, is to be regarded chiefly in the light
of an ornament. The plain and simple embattled
parapet, indeed, is to be found in buildings of the
middle ages, from the early Norman to the latest
Perpendicular; but, in general, the parapet assumes
the character of the various styles, proceeding from
comparative plainness in the earlier styles, to being
ornamented with panelled and pierced work in
those which succeeded it.—In common language, a
parapet is abreast-wall raised on the sides of bridges,
quays, &c., for protection.

PARGE BOARD.—See Barge Board

PARGET. — 1. Gypsum; plaster stone.— 2.
Plaster laid on roofs or walls.—3. A plaster formed
of lime, hair, and cow-dung, used for plastering
flues.

PARGETTING, Pergetting, Pergeuring,
Parge-work. —Plastering; as a noun, plaster or
stucco. Also, a term used for plaster-work of va¬
rious kinds, but commonly applied to a particular
sort of plaster-work, with patterns and ornaments

274

PEAR TREE

raised or indented upon it, much used in the inte¬
rior, and often in the exterior of houses in the time

of Queen Eliza¬
beth. The term
is now seldom
used, except for
the plastering of
chimney flues.

PARING
CHISEL. — A
broad, flat chisel
used by joiners;
it is worked by
the impulsion of
the hand alone, and not by the blows of a mallet,
like the socket-chisel, firmer, &c.

PARK and Entrance Gates, p. 177.

PARPEND, or Perpend. —A stone reaching
through the thickness of a wall so as to be visible
on both sides, and therefore worked on both ends.

PARPEND WALL.—A wall built of parpends
or stones which reach through its entire thickness.

PARQUETRY.—A species of joinery or
cabinet-work, which consists in making an inlaid

floor composed of
small pieces of wood,
either square or tri¬
angular, which, by
the manner of their
disposition, are capa¬
ble of forming vari¬
ous combinations of
figures. Such floors
are much used in
France.

PARREL.—A
chimney-piece; the
dressings and orna¬
ments of a fireplace.

PARTHENON.—A celebrated Grecian temple
of Minerva in the Acropolis of Athens. It was
built of marble, and was a peripteral octostyle, with
17 columns on the sides; its length 223 feet, breadth
102 , and height from the base to the pediment
65 feet. It was almost reduced to ruins in 1687
by the explosion of a quantity of gunpowder which
the Turks had placed in it; but dilapidated as it
now is, it still retains an air of inexpressible gran¬
deur and sublimity.

PARTING BEAD.—The beaded slip inserted
into the centre of the pulley-style of a window, to
keep apart the upper and lower sashes.

PARTITION.—A wall of stone, brick, or tim¬
ber, which serves to divide one apartment from
another in a building.

PARTITIONS, Timber, p. 158.

PARTY-WALLS.—A wall formed between
houses to separate them from each other, and pre¬
vent the spreading of fire.

PATAND, Patin. —1. A piece of timber laid
on the ground to receive and sustain the ends of
vertical pieces.—2. A bottom plate; a sill.

PATERA.—1. An open vessel in the form of a
cup, used by the Greeks and Romans in their sacri¬
fices and libations.—2. The representation of a cup
or round dish in flat relief, used as an ornament in
friezes ; but many flat ornaments are called pateras
which have no resemblance to cups or dishes.

PATTEN.—The base of a column or pillar.

PAVILION.— 1. A turret or small building,
usually isolated, and having a tent-formed root,

Parquetry.

Pavilion of Flora, Tuileries, Paris.

whence its name.—2. A projecting part of a building,
when it is carried higher than the general structure,
and provided with a tent-formed roof.

PEAR TREE.—Description'of the properties
and uses of, p. 114.

INDEX AND GLOSSARY.

PECKINGS

PECKINGS. See Place-Bricks.

PECKY.—A term in America applied to tim¬
ber in which the first symptoms of decay appear.

PEDESTAL.—An insulated basement or sup¬
port for a column, a statue, or a vase. It usually
consists of a base, a die or dado, and a cornice,
called also a surbase or cap. When a range of
columns is supported on a continuous pedestal, the
latter is called a podium or stylobate.

PEDIMENT.—In classic architecture, the tri¬
angular finishing above the entablature at the end
of buildings or over porticoes. The mouldings of
the entablature bound the inclined sides of the pedi¬
ment. Also the triangular finishing over doors and
windows. In the debased Roman style the same
name is given to these same parts, though not tri¬
angular in their form, but circular, elliptical, or
interrupted. In the architecture of the middle ages,
small gables and triangular decorations over open¬
ings, niches, &c., are called pediments. These have
the angle at the apex more acute than the corre¬
sponding decoration of classic architecture.

PEEN. —The same as piend (which see).

PENCILS.—Qualities and uses of, p. 45.

PENDANT, Pendent. —A hanging ornament
used in the vaults and timber roofs of Gothic archi¬
tecture. In the former, pendants are formed of
stone and generally richly sculptured, and in tim¬
ber-work they are of wood, variously decorated with
carving. See Plate XXXI.

PENDANT? POST.—1. In a mediaeval prin¬
cipal roof-truss, a short post placed against the wall,
its lower end supported on a corbel or capital, and
its upper end carrying the tie-beam or hainmer-
beam.—2. The support of an arch across the angles
of a square.

PENDENTIVE.—The portion of a dome¬
shaped vault, which descends into a corner of an
angular building, when a ceiling of this kind is

PERSPECTIVE

panelling, parapets, buttresses, and turrets. It will
be seen that the principal mullions, instead of run¬
ning into flowing tracery, are here carried straight
through to the head of the window, and that the
subordinate tracery is likewise converted into
straight lines. In this consists the essential dif¬
ference between the' Decorated and Perpendicu'ar
styles. The Perpendicular style of Gothic archi¬
tecture was peculiar to England.

PERPENT-STONE. See Parpend.
PERRON.—A term denoting a staircase lying
open or outside the building; or more properly the
steps in the front of a building which lead into the
first story, where it is raised a little above the level
of the ground.

PERSIAN.— A figure in place of a column,
used to support an entablature. See Caryatides.

PERSPECTIVE.—1. The science which
teaches the representation of an object or objects
on a definite surface, so as to affect the eye when
viewed from a given point, in the same manner as
the object or objects themselves. Correctly defined,
a perspective delineation is a section, by the plane
or other surface, on which the delineation is made,
PERIPTERAL.—A temple, the cella of which | of the cone of rays proceeding from every part of

PERCLOSE, Parclose. —The raised carved
timber back to a bench or seat; the parapet round
a gallery; a screen or partition.

PERGETTING, or Pergeuring. See Par-
getting.

PERIBOLUS.—In ancient architecture, a
court surrounding a temple, and itself surrounded
by a wall inclosing the whole of the sacred ground.
It was commonly adorned with statues, altars, and
monuments, and sometimes contained other smaller
temples or a sacred grove. A perfect example of
the peribolus exists in the temple of Isis at Pom¬
peii, and remains of others are found at Palmyra
and elsewhere.

PERIDROMUS.—The space in a peripteral
temple, between the walls of the cella or body and
the surrounding columns.

PERIMETER.—The circuit or boundary of
any plane figure. In round figures it is equivalent
to circumference or periphery, but the term is more
frequently applied to figures composed of straight
lines.

PERIPHERY.—The circumference of a circle
or ellipse, or of any curvilinear figure.

Pendentive Roof.

placed over a straight-sided area. Thus, when a
portion of a sphere, as the hemisphere in the figure,
is intersected by cylindrical or cylindroidal arches,
as a a a, the vaults b b are formed, which are pen-
dentives. In Gothic architecture, the portion of a
groined ceiling springing from one pillar or impost,
and bounded by the apices of the longitudinal and
transverse vaults, is called a pendentive.

PENDENTIVE of an irregular octagonal plan
over an apartment, the plan of which is a parallelo¬
gram, p. 82.

PENDENTIVE formed by the intersection
of an octagonal domical vault with a square,

p. 81.

PENDENTIVE BRACKETING.—The
coved bracketing springing from the wall of a
rectangular area in an upward direction, so as
to form the horizontal plane into a complete
circle or ellipse. See Pendentive.

PENDENTIVE CRADLING.—The tim¬
ber work for sustaining the lath and plaster in
pendentives.

PENT-HOUSE.—A shed with a roof of a
single slope.

PENT-ROOF.—A roof formed like an
inclined plane, the slope being all on one side;
called also a shed-roof.

PENTADORON.—In ancient architecture,
a brick of five palms in length, used by the Greeks
in the construction of their sacred edifices.

PENTAGON.—A figure with five equal
sides and angles is a regular pentagon ; if the
sides be unequal, it is an irregular pentagon.—

To find the area of a regular pentagon. Multi¬
ply the square of its side by P7204774.

PENTAGON.—On a given straight line, to
describe a regular pentagon, Prob. XXXVIII.

p. 12.

PENTAGRAPH. See Pantagraph.

PENTASTYLE. — An edifice having five
column in front.

PERCH.—An old name sometimes applied to
a bracket or corbel.

is surrounded with columns, those on the flanks
being at a distance from the wall equal to their
intercolumniation.

PERISTYLE, Peristylium. — A range of
columns surrounding anything, as the cella of a
temple, or any place, as a court or cloister. It is
frequently but incorrectly limited in signification
i to a range of columns round the interior of a place.

PERPEND, Perpyn, Perpent. See Parpend.

PERPENDICULAR LINES.—To erect or
1 let fall, p. 6-18.

PERPENDICULAR STYLE. —The third
i and last of the pointed or Gothic styles used in this
country, called also the florid style of Gothic. It
was developed from the Decorated during the latter
part of the fourteenth century, and continued in use
till the middle of the sixteenth. The broad distinc¬
tion between this and the preceding styles lies in
the preponderance of perpendicular lines, particu¬
larly observable in the tracery of windows, the
panelling of flat surfaces within and without, and
the multiplicity of small shafts with which the
piers, &c., are overlaid. The vertical line every¬
where predominates, catdhing the eye at first sight,
so that when ohee this characteristic has been
pointed out, it is impossible to mistake a building
in this style. Another peculiarity is the increased
width of the windows and the lowness of the roofs,
which are frequently so low as not to rise above
the parapet. This is owing to the use of the four-
centred depressed arch, which gave an opportunity
of employing greater width, without increasing the
height of the windows. To such an extent is this
peculiarity carried, that the chancel of a church in
this style is almost as light as a conservatory, the
whole space between the buttresses behig occupied
with the windows. The upper tier of windows, or
clear-story, offers another peculiarity. In the pre¬
ceding styles these windows were generally small;
but in the Perpendicular, when that style became
fully developed, they are often so large, and placed
so closely together, that the whole clear-story be-

the object to the eye of the spectator. It is inti¬
mately connected with the arts of design, and is
indispensable in architecture, engineering, fortifi¬
cation, sculpture, and generally all the mechanical
arts; but it is particularly necessary in the art of
painting, as without a correct observance of the
rules of perspective, no picture can have truth and
life. Perspective alone enables us to represent fore¬
shortenings with accuracy, and it is requisite in
delineating even the simplest positions of objects.
Perspective is divided into two branches, linear and
aerial. Linear perspective has reference to the posi¬
tion, form, magnitude, &c., of the several lines or
contours of objects, &c. The outlines of such ob¬
jects as buildings, machinery, and most works of
human labour which consist of geometrical forms,
or which can be reduced to them, may be most
accurately obtained by the rules of linear perspec¬
tive, since the intersection with an interposed plane
of the rays of light proceeding from every point of
such objects, may be obtained by the principles of
geometry. Linear perspective includes the various
kinds of projections; as scenographic, orthographic,
ichnograpdtic, stereographic projections, &c. Aerial
perspective teaches how to give due diminution to
the strength of light, shade, and colours of objects
according to their distances, and the quantity of
light falling on them, and to the medium through
which they are seen.— Perspective plane, the surface
on which the object or picture is delineated, or it
is the transparent surface or plane through which
we suppose objects to be viewed ; it is also termed
the plane of projection, and the plane of the picture.
—Parallel perspective is where the picture is sup¬
posed to be so situated, as to be parallel to the side

East End of the Beauchamp Chapel, Warwick.

comes one large window, merely divided by the
mullions. The annexed view of Beauchamp Chapel
presents a very perfect instance of Perpendicular
architecture, both in the windows, and also in the

273

of the principal object in the picture; as a build¬
ing, for instance.— Oblique perspective is when the
plane of the picture is supposed to stand oblique to
the sides of the object represented ; in which case
the representations of the lines upon those sides
will not be parallel among themselves, but will
tend towards their vanishing point.—2. A kind of
painting, often seen in gardens and at the end of a
gallery, designed expressly to deceive the sight by
representing the continuation of an alley, a build¬
ing, a landscape, or the like.— Jsometrical perspec¬
tive, or more correctly isometvical projection, a kind
of orthographic projection, so named and brought
prominently into notice by Pro¬
fessor Parish, of Cambridge, by
which solids, of the form of rect¬
angular parallelopipeds, or such
as are reducible to this form,
or can be contained in it, can
be represented with three of
their contiguous planes in one
figure, which gives a more intel¬
ligible idea of their form than can be done by a
separate plan and elevation. At the same time,
this method admits of their dimensions being

INDEX AND GLOSSARY.

PERSPECTIVE

measured by a scale as directly as in the usual
mode of delineation. As applied to buildings and
machinery, it gives the elevation and ground plan

Isometrical Perspective

in one view, and is therefore considered more use¬
ful, as explanatory of the ordinary geometrical
drawings, than linear perspective. It is also easier
and simpler in its application.

PERSPECTIVE.-—Introductory observations,
p. 227.

PERSPECTIVE.—Definitions of terms, p.
228, 229.

PERSPECTIVE.—To find the perspective of
a given point, Prob. I. p. 229.

PERSPECTIVE.—To find the perspective of
a given right line. Prob. II. p 229.

PERSPECTIVE.—Rules in, p. 229-232.

PERSPECTIVE.—The distance of the picture
and the perspective of the side of a square being
given, to complete the square without having re¬
course to a plan, Prob, III. p. 233.

PERSPECTIVE.—To divide a line given in
perspective in any proportion, Prob. IV. p. 234.

PERSPECTIVE —Through a given point in
a picture, to draw a line parallel to the base or side
of the picture, and perspectively equal to another
given line, Prob. V. p. 234.

PERSPECTIVE.—To draw the perspective of
a pavement of squares, Prob. VI.-VIII. p. 235.

PERSPECTIVE.—To draw a hexagonal pave¬
ment in perspective, Prob. IX. p. 236.

PERSPECTIVE.—To draw the perspective of
a circle, Prob. X. p. 236.

PERSPECTIVE. — To inscribe a circle in a
square given in perspective, Prob. XI. p. 236.

PERSPECTIVE.—To draw a tetrahedron in
perspective, Prob. XII. p. 237.

PERSPECTIVE.—To draw a cross in perspec- )
tive, p. 241.

PERSPECTIVE.—To draw a pavilion in per¬
spective, p. 241.

PERSPECTIVE.—To draw a broach or spire
in perspective, p. 242, 243, Plate CVII. and CXI.

PERSPECTIVE.—To draw a Tuscan gateway
in perspective, p. 242, Plate CIX.

PERSPECTIVE.—To draw a Turkish bath in
perspective, p. 243, Plate CX.

PERSPECTIVE.—To draw a series of arches
in perspective, p. 242, Plate CVIII.

PERSPECTIVE.—To draw a circular vault
pierced by a circular-headed window in perspective,
p. 242, Plate CVIII.

PERSPECTIVE.—Isometric projection, defi¬
nition and illustration of, p. 242.

PERSPECTIVE. — Isometric scales, how to I
construct, p. 243.

PERSPECTIVE.—Isometrical projection, ap¬
plication of, to curved lines, p 245.

PERSPECTIVE. — To draw a cube in per¬
spective, Prob. XIII. p. 237.

PERSPECTIVE.—To draw cylinders in per¬
spective, Prob. XIV. p. 238.

PERSPECTIVE.—Proper angle at which ob¬
jects should be viewed, p. 238.

PRRSPECTi VE.—Argument against the use
of the distinctive terms parallel and oblique per¬
spective, p. 239.

PERSPECTIVE.—To draw a sphere in per¬
spective, Prob, XV. p. 239.

1 ERSPECTIVE. Practical examples of per¬
spective drawing applied to architecture, &c., p. 240.

PETERSBURG- TIMBER. See Pinus syl-
VESTRIS, p. 116, 117.

PEW DOOR, Plate LXXIII. Fig. 6, p. 187.

PHOLAS. — A marine animal, injurious to
timber, p. 105.

PIAZZA.— A square open space surrounded by
buildings or colonnades. The term is frequently,
but improperly, used to signify an arcaded or col¬
onnaded walk.

PIECE-WORK.—Work done and paid for by
the measure of quantity, in contradistinction to
work done and paid for by the measure of time.

PIEDOUCHE. — A small pedestal or base,
serving to support a bust, candelabrum, or other
ornament.

PIEDROIT.—The jamb of an opening, includ¬
ing the face and retiring side. It is more specifi¬
cally applied to the jamb of an arched opening,
when crowned with an impost moulding.

PIEND.—An arris ; a salient angle; a hip.

PIEND CHECK.—A term applied in Scot¬
land to the rebate formed on the piend or angle at

the bottom of the riser of the stone step of a stair,
as at a a a in the figure.

PIER. — 1. The support of the arches of a
bridge; the solid parts between openings in a wall,
such as the door, windows, &c. (See woodcut,
Arch.) —2. A mole or jetty carried out into the
sea, whether intended to serve as an embankment
to protect vessels from the open sea, or merely as
a landing place. For this latter purpose suspension
chain-piers are sometimes employed.—3. The pillars
in Norman and Gothic architecture are generally,
though not very correctly, termed piers.

PIER-ARCHES. — In Gothic architecture,
arches supported on piers (or pillars) between the
central parts and aisles of a church.

PILASTER.—A debased pillar: a square pillar
projecting from a pier or from a wall, to the extent
of from one-fourth to one-third of its breadth. Pil¬
asters originated in the Grecian antse. In Roman
architecture they were sometimes tapered like
columns, and finished with capitals modelled after
the order with which they were used.

PILE-DRIVER, or Pile-Engine. —An engine
for driving down piles. It consists of a large ram
or block of iron, termed the monkey, which slides
between two guide-posts. Being drawn up to the

top, and then let fall from a considerable height, it
comes down on the head of the pile with a violent
blow. It may be worked by men or horses, or a
steam-engine. The most improved pile-driver is
| that constructed by Mr. James Nasmyth, being an ;
ingenious application of the principle of his cele¬
brated steam-hammer.

PILE-PLANKS. — Planks about 9 inches
| broad, and from 2 to 4 inches thick, sharpened at
their lower end, and driven with their edges close
together into the ground in hydraulic works. Two
rows of pile-planks thus driven, with a space be¬
tween them filled with puddle, is the means used to
form water-tight coffer-dams and similar erections.

PILES.—Beams of timber, pointed at the end,

I driven into the soil for the support of some super¬
structure. They are either driven through a com¬
pressible stratum, till they meet with one that is
incompressible, and thus transmit the weight of the
structure erected on the softer to the more solid
material, or they are driven into a soft or compres¬
sible structure in such numbers as to solidify it. In
the first instance, the piles are from 9 to 18 inches
in diameter, and about twenty times their diameter
I in length. They are pointed with iron at their
I lower end, and their head is encircled with an iron

276

PISE

ring, to prevent its being split by the blows of the
pile-driver. In the second case, the piles are from
6 to 12 feet long, and from 6 to 9 inches in dia¬
meter. In constructing coffer-dams and other hy¬
draulic works, other kinds of piles besides those
described are used, such as gauge-piles, sheeting-
piles, pile-planks, key-piles. These will be found
under their proper heads.

i PILLAR.—1. A pile, or columnar mass com¬

posed of several pieces, and the form and propor¬
tions of which are arbitrary, that is, not subject to
the rules of classic architecture. A square pillar is
a massive work, called also a pier or piedroit, serv¬
ing to support arches, &c.—2. A supporter; that
which sustains or upholds; that on which some
superstructure rests.

PIN,-—A piece of wood or metal, square or
cylindrical in section, and sharpened or pointed.

| used to fasten timbers together. Large metal pins
are termed bolts, and the wooden pins used in ship¬
building treenails.

PINACOTHECA.—A picture gallery.

PINES and Firs. —Descriptions and uses of,
p. 115, et seq.

PINNACLE.— 1 . A turret, or part of a build¬
ing elevated above the main building.—2. In medi¬
aeval architecture, a term applied to any lesser

Early English Pinnacle. Perpendicular Pinnacle,
Beverley Minster. Trinity Ch., Cambridge.

structure or ornament, consisting of a body or shaft
terminated by a pyramid or spire, used either ex¬
teriorly or interiorly.

PINNING. — Fastening tiles or slates with
pins ; inserting small pieces of stone to fill vacuities.

PINNING UP. Driving in wedges in the
process of underpinning, so as to bring the upper
I work to bear fully on the work below.
PINS-DRAW1NG. p. 45.

PINUS STROBUS. — The Weymouth pine,

p. 118.

PINUS SYLVESTRIS. p. 116, 117.
PISCINA.—A niche on the south side of the
altar in Roman Catholic churches, containing a
small basin and water-drain, through which the

Piscina, Fiefield, Essex.

priest emptied the water in which he had washed
liis hands, and also that with which the chalice had
been rinsed.

PISE.—A species of wall constructed of stiff
earth or clay, rammed into moulds, which are carried
up as the work is carried up. It has been used in

INDEX AND GLOSSARY.

PITCH OF A ROOF

France of late years, but it is as old as the days of
Pliny.

PITCH of a Roof. —The inclination of the
sloping sides of a roof to the horizon, or the vertical
angle formed by the sloping side. The pitch is
usually designated by the ratio of the height to the
span.

PITCH of a Roof.— Opinions of various
authors as to the pitch which should be given to a
roof, to suit the climate and the material used for
covering, p. 134, 135.

PITCH PINE.—Properties and uses of, p. 118.

PITCH PINE. p. 118.

PITCHING PIECE, p. 196.

PITCHING PIECE.—A piece of timber pro¬
jecting horizontally from a wall, to support the
rough strings in staircasing. See Apron-Piece.

PLACE BRICKS. — Those bricks which,
having been outermost or farthest from the fire in
the clamp or kiln, have not received sufficient heat
to burn them thoroughly. They are consequently
soft, uneven in texture, and of a red colour. They
are also termed peckings, and sometimes sandel or
samel bricks.

PLAFOND, Platfond. —1. The ceiling of a
room, whether flat or arched.—2. The under side
of a cornice.—3. Generally, any soffit.

PLAIN TILES are simple parallelograms,
generally about 101 inches long, 6J inches wide, and
§-inch thick, and weighs 2 lbs. 5 oz. Each tile has
a hole at one end to receive the wooden pin by
which it is secured to the lath. Plain tiles are laid
on laths on mortar, with an overlap of 6 to 8 inches.
At 6 inches gauge, it takes to cover a square of
roofing 768 plain tiles; at 7 inches gauge, it takes
655 tiles; and at 8 inches gauge, 576 tiles. The
average square of plain tiling is 700, and weighs
14 cwts. 2 qrs.

PLAN.—A draught or form; properly, any¬
thing drawn or represented on a plane, as a map or
chart, but the word is usually applied to the hori¬
zontal geometrical section of anything, as a build¬
ing, for example. The term is applied also to the
draught or representation on paper of any projected
work, as the plan of a house, of a city, of a har¬
bour, &c.

PLANCEER, Planoher. —A ceiling, or the
soffit of a cornice.

PLANE.—The plane is a cutting instrument
on the guide principle. It is, in fact, a chisel guided
by the stock or wooden handle in which it is set.
The guide or sole of the stock is, in general, an
exact counterpart of the form it is intended to
produce. Planes are of various kinds, as the jack

/y /tax

Smoothing Plane

Plough Moulding.
-Desci'iption of pro-

Jack Plane.

plane (about 17 inches long), used for taking off the
roughest and most prominent parts of the stuff; the
trying plane, which is used after the jack plane ;
the long plane (26 inches long), used when a piece
of stuff is to be planed very straight; the jointer,
still longer than the former, which is used for ob¬
taining very straight edges; the smoothing plane
(74 inches long), and block plane (12 inches long),
chiefly used for cleaning off finished work, and giving

Compass Plane.

the utmost degree of smoothness to the surface of
the wood; the compass plane, which is similar to
the smoothing plane, but has its under surface con¬
vex, its use being to form a concave cylindrical
surface. The foregoing are technically called bench-
planes. There is also a species of planes called
rebate planes, the first of which is simply called the
rebate plane, being chiefly used for making rebates.
Of the sinking rebating planes there are two sorts,

the moving fillister and the sash fillister, the first
for sinking the edge of the stuff uext the workman,

and the second for sinking the opposite edge. The
plough, is a plane for sinking a channel or groove
in a surface, not close to the edge of it. Mould¬
ing planes are for forming
mouldings, and must vary
according to the design.

The bead plane is used for
mouldings whose section is
semicircular. Planes are also
used for smoothing metal,
and are wrought by ma¬
chinery. See Planing
Machine.

PLANE, The Oriental.
perties and uses, p. 113.

PLANE, American or Western, p. 113.

PLANE of Projection, Plane of Delinea¬
tion, Transparent Plane. —In perspective, the
same as plane of the picture. See p. 228.

PLANING MACHINE. — A tool or instru¬
ment wrought by steam power, for saving manual
labour in producing a perfectly plane surface upon
wood or metal. This is usually accomplished, in
metal-planing machines, by such an arrangement of
mechanism, as will cause the object which is to be
operated upon to traverse backwards and forwards
upon a perfectly smooth and level bed, while the
cutting tool is fixed to a cross slide above it, and
slightly penetrates the surface as it is carried along.
The tool is acted upon by screws, so as to enable
the attendant to adjust the depth of the cut, and to
move it with unerring precision over every part of
the surface which it is required to plane. Planing
machines for wood are described in the text, under
Labour-saving Machines, p. 191-193.

PLANING MACHINE. — Furness’ patent,
p. 193. ^ I

PLANK.—A broad piece of sawed timber,
differing from a board only in being thicker. Broad
pieces of sawed timber which are not more than
1 inch, or lj- inch thick, are called boards; like
pieces, from 1J to 3 or 4 inches thick, are called
planks. Sometimes pieces more than 4 inches thick
are called planks.

PLANS of Stairs. —The mode of setting out,
p. 198.

PLANTED.—In joinery, a projecting member
wrought on a separate piece

of stuff, and afterwards -/

fixed in its place, is said f j

to be planted; as a planted ^X^lLt-_!

moulding.

PLASTER.—A composition of lime, water,
and sand, well mixed into a kind of paste, and used
for coating walls and partitions of houses. This
composition when dry becomes hard, but still re¬
tains the name of plaster. Plaster is sometimes
made of different materials, as chalk, gypsum, &c.,
and is sometimes used to parget the whole surface
of a building. Plaster is also the material of which
ornaments are cast in architecture, and also that
with which the fine stuff or gauge for mouldings
and other parts is mixed, when quick setting is re¬
quired.

PLAT, OR Plot. —A word used by old authors
for plan.

PL AT-BAND. ■—1. Any flat rectangular mould¬
ing, the projection of which is much less than its
width; a fascia.—2. A lintel formed with voussoirs
in the manner of an arch, but with the intrados
horizontal.—3. The fillets between the flutes of the
Ionic and Corinthian pillars.

PLATE.—A general name for all timber laid
horizontally in a wall to receive the ends of other
timbers, such as a wall-plate.

PLATFORM.—A flat covering or roof of a
building, suited for walking on; a terrace or open
walk on the top of a building.

PLETHORA,.—A disease of trees. See p. 97.

PLINTH.—A square member serving as the
base of a column, the base of a pedestal, or of a
wall. The square member, for instance, under the
torus of the Tuscan base is the plinth. See wood-
cut, Column.

PLOT.—A plan.

PLOT, v.— To make a plan of anything.

PLOTTING.—In surveying, the describing or
laying down upon paper the several angles and lines
of a tract of land which has been surveyed and
measured. It is usually performed by means of a
protractor; sometimes by the plotting scale (which
see).

PLOTTING-SCALE.—A scale of equal parts,
with its divisions along its edge, so that measure¬
ments may be made by application. A particular
kind of plotting-scale is sometimes used in setting
off the lengths of lines in surveying. It consists of
two graduated ivory scales, one of which is perfo¬
rated nearly its whole length by a dovetail-shaped
slit, for the reception of a sliding-piece. The second

277

POLYGON

scale is attached to this sliding-piece, and moves
along with it, the edge of the second scale being
always at right angles to the edge of the first. By
this means the rectangular co-ordinates of a point
are measured at once on the scales, or the position
of the point laid down on the plan.

PLOUGH.—-A joiner’s grooving-plane. See
Plane.

PLUG CENTRE-BIT.—A modified form of
the ordinary centre-bit, in which the centre-point
or pin is enlarged into a stout cylindrical plug, which
may exactly fill a hole previously bored, and guide
the tool in the process of cutting out a cylindrical
countersink around the same, as, for example, to
receive the head of a screw-bolt.

PLUMB. — Perpendicular, that is, standing
according to a plumb-line. The post of the house
or the wall is said to be plumb.

PLUMB-LINE.—A line perpendicular + o the
plane of the horizon; or a line directed to the centre
of gravity in the earth. See Plummet, Plumb-Rule.

PLUMB-RULE.-—A simple instrument for the
same purpose as the plumb-line or plummet, used
by masons, bricklayers, and carpenters It con¬
sists of a board with parallel edges; a line is drawn
down the middle of the board, and to the upper end
of this line the end of a string is attached, carrying
a piece of lead at its lower end. When the edge of
the board is applied to a wall or other upright ob¬
ject, the exact coincidence of the plumb-line with
the line marked on the board indicates that the wall
or other object is vertical, while the deviation of
the plumb-line from that on the board, shows how
far the object is from the perpendicular. Some¬
times another board is fixed across the lower end
of the plumb-rule, having its lower edge at right
angles to the line drawn on the other. In this case
it becomes a level.

PLUMMET.—1. A long piece of lead attached
to a line, used in sounding the depth of water.—2.
An instrument used by carpenters, masons, &c., in
adjusting erections to a perpendicular line. The
terms plummet, plumb-line, and plumb-rule are
often used synonymously. See Plumb-Line.

POCKET. — A hole in the pulley style of a
sashed window. See p. 188.

POD-AUGER.—A name given in some loca¬
lities to an auger formed with a straight channel or
groove. See Auger.

PODIUM. — In architecture, a continuous
pedestal; a stylobate ; also, a projection which sur¬
rounded the arena of the ancient amphitheatre,
where sat persons of distinctiou.

POINTED, or Christian Architecture. See
Gothic.

POITRAIL, Poitrel. See Timber Houses,
p. 156.

POLE-PLATE.—A sort of smaller wall-plate
laid on the top of the wall, and on the ends of the
tie-beams of a roof, to receive the rafters.

POLINGS.— Boards used to line the inside of
a tunnel during its construction, to prevent the fall¬
ing of the earth or other loose material.

POLYCHROMY.—A modern term used to
express the ancient practice of colouring statues,
and the exteriors and interiors of buildings. This
practice dates from the highest antiquity, but pro¬
bably reached its greatest perfection in the twelfth
and thirteenth centuries.

POLY FOIL.—An ornament formed by a
moulding disposed in a number of segments of
circles.

POLYGON. — To find the area of a regular
polygon. Multiply half the perimeter by the per¬
pendicular let fall from the centre upon one of the
sides; or multiply the square of the side by the
multiplier corresponding to the figure in the follow¬
ing table :—

Table of Polygons.

Name.

No. of
Sides.

Angle at
Centre.

Perpen¬

diculars.

Multipliers.

Equilateral Triangle,

120°

0-28S6751

0-4330127

j Square,.

00°

0-500000

1 -ooooooo

Pentagon, ....

72°

0-6881910

1 -7204774

1 Hexagon, ....

00°

0-8660254

2-5980762

Heptagon, ....

51 r

1-03S2607

3-6339124

Octagon, ....

45"

1-2071008

4S284272

Nonagon, ....

40°

137373S7

61S18242

Decagon, ....

30°

1 "5388418

7-6942088

Undecagon, . . .

qo s_°

1 -7028439

9-3656411

Dodecagon,

30°

1-S660254

11 1961524

POLYGON.—

To fin

d the

area of any regular

polygon, Prob. LII. p. 15.

POLYGON of Forces, p. 120.

POLYGON, Regular. —About a given circle,
to describe any regular polygon, Prob. XLVIII.
p. 14.

POLYGON, Regular.— To describe a regular
polygon with the same perimeter as another given
polygon, but with twice the number of sides, Prob.
XLIX. p. 14.

INDEX AND GLOSSARY.

POLYGON

POLYGON, Regular. —To construct with the
same perimeter as a given polygon, but with any
different number of sides, Prob. L. p. 14.

POLYGON, Regular. —To describe with the
same area as a given polygon, but a different num¬
ber of sides, Prob. LI. p. 14.

POLYGON, Regular. —In a given circle, to
inscribe any regular polygon, Prob. XLII.p. 12,
Probs. XLIII.—XL\ I. p. 13.

POLYGONS, Regular.— On a given straight
line, to describe any of the regular polygons, Prob.
XXXVII. Examples 1 and 2, p. 11.

POLYGONS, Line of, on the Sector.—Con¬
struction and use of, p. 38.

POLYSTYLE.—An edifice in which there are
many columns.

POMEL, Pommel.— A knob or ball used as a
finial to the conioal or dome-shaped roof of a turret,
pavilion, &c.

POPLAR, The. —Description of the properties
and uses of, p. 112.

POPPY HEAD.—An ornament carved on

Poppy Head, Minster Church.

the raised ends of seats, benches, and pews in old
churches.

PORCH.—An exterior appendage to a building,
forming a covered approach or vestibule to a door¬
way. The porches in some of the older churches
are of two stories, having an upper apartment, to
which the name parviae is sometimes applied.

PORTAL.—1. The lesser gate when there are
two of different dimensions at the entrance of a
building.—2. A term formerly applied to a little
square corner of a room, separated from the rest
by a wainscot, and forming a short passage into a
room.—3. A kind of arch over a door or gate, or
the frame-work of the gate.

PORTCULLIS —A strong grating of timber
or iron, resembling a harrow, made to slide in ver¬
tical grooves in the jambs of the entrance gate of a
fortified place, to protect the gate in case of assault.
The vertical bars, when of wood, were pointed with
iron at the bottom, for the purpose of striking into
the ground when the grating was dropped, or of
injuring whatever it might fall upon. In general

Portcullis.

there were a succession of portcullises in the same
gateway. It is sometimes called a portcluse. The
portcullis, with the chains by which it was moved
attached to its upper angles, formed an armorial j
bearing of the house of Lancaster; and is of fre¬
quent occurrence as a sculptured ornament on
buildings erected by the monarchs of the Lancas¬
ter family, as on Henry VII.’s Chapel and King’s
College Chapel, Cambridge. As an architectural
device, it is usually surmounted by a crown, and
placed alternately with a rose, also surmounted by
a crown.

PORTICO.—-An open space before the en¬
trance of a building, fronted with columns. Por¬
ticoes are distinguished as prostyle or in antis, as
they project before or recede within the building.
They are further distinguished by the number of
their columns; as a tetrastyle, hexastyle, and octa-
style portico. See Amphiprosttle and Antas.

POST.—A piece of timber set upright, and in¬
tended to support something else; as the posts of a 1
house, the posts of a door, the posts of a gate, the j
posts of a fence. It also denotes any vertical piece

PUTTY

of timber, whose office is to support or sustain in a
vertical direction ; as a king-post, queen-post, truss-
post, door-post, &c. — Post and palling, a close
wooden fence, constructed with posts fixed in the
ground and pales nailed between them .—Post and
railing, a kind of open wooden fence for the pro¬
tection of young quickset hedges, consisting of posts
and rails, &c. These terms are sometimes con¬
founded.

POST AND PANE, Post and Pan, Post
and Petrail — Another name for half-timbered

PRONAOS.—The space in front of the naos
or cella of a Greek temple. The term is sometimes
used for portico. See Naos.

PROPERTIES OF TIMBER.—Table of the,
p. 133.

PROPORTION. — In architecture, the just
magnitude of each part, and of each part compared
with another in relation to the end or object in
view.

PROPORTION of Tread and Riser of a
Step, p. 196.

houses, or those in which the walls are composed
of timber framing, with panels of brick, stone, or
lath and plaster. See p. 156, Plates XLVI. and
XLVI1.

POST AND PETRAIL. See Post and Pane.

POSTERN.—Primarily, a back door or gate;
a private entrance. Hence, any small door or
gate.

POSTICUM.—The part of a temple at the
rear of the cella or body. See Pronaos.

POSTIQUE. — Superadded; done after the
main work is finished. Applied to a superadded
ornament of sculpture or architecture.

POYNTE LL.—Paving set in squares or lozenge
forms.

PRACTICAL CARPENTRY.—Introduction
to, p. 134.

PRrECINCTIONES.—The passages between
the rows of seats in the Roman theatres, called
also bailee or belts.

PRESERVATION OF TIMBER by Sur¬
face Applications, as tar, pitch, tallow, paints,
paint with sand, and sheathing with copper or
I copper nails, p. 108.

PRESERVATION OF WOOD by impreg¬
nating it with Chemical Substances. —Kyan’s
process with corrosive sublimate, called Icyanizing,
p. 106; Margary's process, acetate or sulphate of
copper, p. 106 ; Burnett’s process, chloride of zinc,
p. 106; Payne’s process, two solutions, p. 106, 107;
Bethell’s process, creosote, p. 107; Boutigny’s pro¬
cess, oil of schistus, p. 107 ; Boucherie’s process
with various chemical solutions, absorbed by as¬
piration, p. 107; inode of impregnating the wood
with solutions for its preservation, p. 107, 108.

PRICK-POST.—The same as queen-post (which
see), p. 156.

PRICKER, p. 42.

PRICKING-UP.—In plastering, the first coats
of plaster in three-coat work upon lath.

PRINCIPALS, or Principal Rafters.—
Those which are larger than the common rafters,
and which are framed at their lower ends into the
tie-beam, and at their upper ends are either united
at the king-post, or made to bear against the ends
of the straining-beams when queen-posts are used.
The principals support the purlins, which again
carry the common rafters, and thus the whole
weight of the roof is sustained by the principals.
The struts, braces, &c., used in framing with the
principal rafters, are sometimes called principial
struts, principal braces, &c.

PRINT.—A plaster cast of a flat ornament, or
an ornament of this kind formed of plaster from a
mould.

PRISM.— A solid, of which the ends are equal,
similar, and parallel rectilineals; and the other sides
are parallelograms.—To find the surface of a prism.
Rule: Find the area of one of its ends, and to its
double add the sum of the areas of the parallelo¬
grams.—To find the solidity of a prism. Rule :
Find the area of one of its ends, and multiply it by
the length or perpendicular height.

PRISM, or Pyramid. — Development of a,
p. 70.

PRISM. — Development of the covering of a
prism, p. 71.

PRISMOID.—A body that approaches to the
form of a prism; a solid having for its two ends any
dissimilar parallel plane figures of the same number
of sides, and its upright sides trapezoids.

PROFILE.—The outline or contour of any¬
thing, such as a building, a figure, a moulding.

PROJECTION, Projecture. — The jutting
out of certain parts of a building beyond the naked
wall, or the jutting out of anything in advance of a
normal line or surface.

PROJECTION. — Definition of projection, p.
46; general principles of projection, p. 47; planes
of projection illustrated, p. 47.

PROJECTION. — Intersections of lines and
planes under various conditions, p. 47-52.

PROJECTION OF SOLIDS, p. 52.

PROJECTIONS.—To find the projections of
the intersections of two cylinders under various
conditions, p. 63 ; to find the projections of the in¬
tersections of a sphere and cylinder, p. 64; to find
the projections of the intersections of two right
cones, p. 64.

278

PROPORTIONAL COMPASSES. — Differ¬
ent kinds of, and their use, p. 33.

PROPYLARUM, Propylon. — The porch,
vestibule, or entrance of an edifice.

PROSCENIUM.—That part of a theatre from
the curtain or drop-scene to the orchestra. In the
ancient theatre it comprised the whole of the
stage.

PROSTYLE.—A range of columns standing
detached from the building to which they belong.
See Portico.

PROTECTION OF WOOD against Fire,
p. 108; means adopted, p. 108; not efficacious,
p. 109.

PROTRACTOR.—An instrument for laying
down and measuring angles on paper. See p. 41.

PSEUDISIDOMON. — A manner of building
among the Greeks, in which the height, length,
and thickness of the courses differed.

PSEUDO - DIPTERAL. — Falsely or imper¬
fectly dipteral, the inner range of columns being
omitted. A term denoting a building or temple,
wherein the distance from each side of the cella to
the columns on the flanks is equal to two inter-
columniations, the inner range of columns necessary
to a dipteral edifice being omitted. As a noun, an
imperfect peripteral, in which the columns at the
wings were set within the walls. See Peripteral.

PSEUDO - PERIPTERAL.—A term applied
to a temple having the columns on its sides attached
to the walls, instead of being arranged as in a per¬
ipteral.

PSEUDO-PROSTYLE. —A term suggested
by Professor Hosking, to denote a portico, the pro¬
jection of which from the wall is less than the width
of its intercolumniation.

PTEROMA.—The space between the wall of
the cella of a temple and the columns of the peri¬
style ; called also ambulatio.

PUG-PILES.—Piles mortised into each other
by a dove-tail joint. They are also called dove-

tflilPCi Till PT

PUG - PILING.—A mode of fixing piles by
mortising them into each other by a dove-tail joint.
Also termed dove-tailed piling.

PUGGING. — Any composition, generally a
coarse kind of mortar, laid on the sound boarding
under the boards of a floor, to prevent the trans¬
mission of sound. In Scotland it is termed deaf¬
ening. See p. 151.

PULLEY -MORTISE.—The same as chase-
mortise (which see).

PULLEY-STYLE.—The style of a window-
case, in which the pulleys are fixed. See p. 187.

PULPIT, Pulpitum. — An elevated place or
inclosed stage in a church, in which the preacher
stands. It is called also a desk. Pulpits in mo¬
dern churches are of wood, but in ancient times
some were made of stone, others of marble, and
richly carved. Pulpits were also sometimes erected
on the outside of churches as well as within.

PULPIT, with Acoustical Canopy. — Illustra¬
tion and description of, Plate LXXXIIIj p. 190.

PULVINATED.— A term used to express a
swelling in any portion of an order, such for in¬
stance as that of the frieze in the modern Ionic
order.

PUMP-BTT.—A species of large auger with
removable shank, such as is commonly used for
boring wooden pump-barrels.

PUNCHEON. — A post (see Fig. 1, Plate
XXXII., Roof of Westminster Ilall, and descrip¬
tion, p. 145); a small upright piece of timber in a
partition, now called a quartci'.

PURLIN.—A piece of timber laid horizontally,
resting on the principals of a roof to support the
common rafters. Purlins are in some places called
ribs.

PURLTNS.—To find the dimensions of, p. 137.

PUTLOGS.—Short pieces of timber used in
scaffolds to carry the floor. They are placed at
right angles to the wall, one end resting on the
ledgers of the scaffold and the other in holes left in
the wall, called putlog-holes. See Ledger.

PUTTY.—1. A very fine cement made of lime
only. The lime is mixed with water until it is of
such consistence that it will just drop from the end
of a stick. It is then run through a hair sieve, to
remove the gross parts. Putty differs from fine-

PYCNOSTYLE

INDEX AND GLOSSARY.

REINS OF A VAULT

stuff in the mode of its preparation, and in having
no hair mixed with it.—2. A cement compounded
of whiting and linseed oil, kneaded together to the
consistence of dough, used for stopping small cavi¬
ties in wood-work and for fixing the glass in window
frames.

PYCNOSTYLE.—In ancient architecture, a
building where the columns stand very close to
each other. To this intercolumniation one diame¬
ter and a half is assigned.

PYRAMID.—A solid which has a rectilinear
figure for its base, and for its sides triangles with a
common vertex.—To find the surface of a pyramid.
Rule: Find separately the area of the base and the
areas of the triangles which constitute its sides, and
add them; their sum will be the whole surface.—
To find the solid content of a pyramid. Rule : Find
the area of the base, and multiply it by the perpen¬
dicular height, and one-third of the product will be
the solid content.

QUADRA.—A square frame or border inclos¬
ing a bas-relief, but sometimes used to signify any
frame or border; the plinth of a podium.

QUADRAE.—The fille<s above and below the
scotia of the Attic base.

QUADRANGLE.—A square surrounded with
buildings, as a cloister or the buildings of a college.

QUADRILATERAL figure equal to a penta¬
gon.—To describe, Prob. XXXVI. p. II.

QUARREL.—A lozenge-shaped pane of glass
used in leaded casements, or any pane of glass so
used; also, the opening in which the glass is set; a
small square or lozenge-shaped paving tile or stone. I

QUARTER-GRAIN.—When timber is split in
the direction of its annular plates or rings. When
it is split across these, towards the centre, it is called
the felt-grain.

QUARTER-ROUND.—The echinus moulding.

QUARTER-SPACE.—The name, given to the
re3ting-place or foot-pace of a stair, when it occurs
at the angle turns of the stair. See p. 196.

QUARTERED PARTITION.—A partition
formed with quarters. See Plate XLV. p. 155.

QUARTERING.—Forming partitions with
quarters.

QUARTERS.—The vertical timber-framing of
a partition to which the laths are nailed; called also
studs, and in Scotland standards. See p. 156.

QUATREFOIL.—A piercing or panel formed
by cusps or foliations into four leaves, or more cor¬
rectly the leaf-shaped figure formed by the cusps.
An ornament similar to the four leaves of a cruci-

Quatrefoils.

form flower, frequently used as a decoration in hol¬
low mouldings in the early English and Decorated
styles, but which it has been proposed to distinguish
by the term quatrelobe.

QUEEN-POST.—The suspending posts in the
framed principal of a roof, or in a trussed partition,
or other truss where there are two. See woodcut,
under Roof. When there is only one post, it is
called a king-post or crown-post. See p. 136.

QUEENS.—In slating, slates measuring 3 feet
by 2 feet.

QUERCUS ROBUR, p. 109 ; Q. pedunculata,
p. 109 ; Q. sessiliflora, p. 109 ; Q. ilex , p. 109 ;
Q. saber, p. 109; Q. pyrenaica, p. 109; Q. cerris,
p. 110 ; Q. virens, p. 110; Q. alba, p. 110.

QUIN DECAGON.—A plane figure with fifteen
sides and fifteen angles.

QUIRK.—A deep indentation; the hollow
under the abacus of a column.

QUIRK BEAD. p. 184.

QUIRK MOULDINGS.—Mouldings whose

Quirked Ogee. Plain Ogee.

apparent projection is increased by the addition of
a quicker curve.

QUIRKED OVOLO, The.—To describe,
p. 179.

QUOIN.—The external angle of a building, and
generally the stones of which that angle is formed.
When the quoin stones project beyond the general
surface of the wall, and have their arrises cham¬
fered, they are called rustic quoins. Quoins are
sometimes in Scotland called external corners.

RABBET. See Rebate.

RAD and Dab. —A substitute for brick-nogging
in partitions, consisting of cob or a mixture of clay
and chopped straw, filled in between laths of split
oak or hazel; called also wattle and dab.

RADIUS of a Circle. —The span or chord
and versed sine of a circle being given, to find the
radius, Prob. LXI. p. 17.

RAFTERS.—Pieces of timber which form the
framework of the slopes of a roof. Common rafters
are those to which the slate boarding or lathing is
attached. See Roof.

RAFTERS.—To calculate the dimensions of,
p. 137.

RAGAVORK.—A kind of rubble masonry,
formed with stones about the thickness of a brick.

RAG LET, or Raglin (corruption of regula).
— A rectangular groove cut in stone or brick
work.

RAGLINS.—A term used in the north of Eng¬
land for the slender ceiling-joists of a building.

RAILS.—The horizontal timbers in any piece
of framing. See Framing and Door, and also

p. 186.

RAISED PANELS, p. 185.

RAISING PLATE, Reson Plate.— The wall-
plate; or more generally, any horizontal timber
which, laid on walls or borne by posts or puncheons,
sustains other timbers. See p. 156.

RAKE.—A slope or inclination.

RAKER.—An iron tool used by bricklayers to
rake out decayed mortar from the joints of brick¬
work, preparatory to repointing them.

RAKING COURSES.—Diagonal courses of
brick, laid in the heart of a thick wall, between the
outside courses.

RAKING MOULDINGS.—Those which are
inclined from the horizontal line, as in the sides of
a pediment.

RAKING MOULDINGS.—To describe, p.
181.

RAMP.—Literally, a spring or bound; any
sudden rising interrupting the continuity of a slop¬
ing line ; a concave sweep connecting a higher and
lower part of some work, as the coping of a wall,
or the higher and lower parts of a stair-railing at a
half or quarter pace; a flight of steps, or the line
tangential to the steps.

RAMP and Twist. —A line which rises and
winds at the same time, as the section of a vertical
cylinder by an inclined plane.

RAMPANT ARCH.—One whose imposts are
not of the same height. See Rampant Ellipses,
Figs. 167, 169, p. 24, 25.

RANCE.—A shore or prop. [Scotch.]

RAND.—A border or margin, or a fillet cut
from a border or margin in the process of straight¬
ening it.

RANDOM TOOLING. — In Scotland called
droving, is a mode of hewing the face of a stone,
either as preparatory to some other process, or as a
finishing operation. The chisel used is from 2 40
4 inches broad, and is called variously a broad tool,
a tooler, or a drove. Having ground it to a fine
and even cutting edge, the workman holding it in
his left hand with its edge upon the stone, strikes
its head with a wooden mallet, so as to advance it
about g inch, producing a cut or indentation of
that length, and of the whole width of the tool. By
successive strokes the tool is advanced to the extre¬
mity of the stone, and the result is a series of in¬
dentations or flutings at right angles to its path, or
to the draught, as it is termed. The same opera¬
tion is repeated till the whole surface of the stone
is worked over. The excellence of the work depends
on the regularity of the minute flutings, and the
absence of ridges between the draughts.

REBATE.—A rectangular longitudinal recess
made in the edge of any substance. Thus the rect¬
angular recess made in a door-frame, into which
the door shuts, is a rebate.—Rebate joint, in joinery,

279

a joint formed by making rebates or longitudinal
recesses in the opposite edges of the boards to be
joined. See p. 182, 183.

Rebate Joints.

REBATE.—A kind of hard freestone used in
pavements; also, a piece of wood fastened to a long
stick, for beating mortar.

REBATE (more commonly spelled rybat ).—
The rebated reveal of a door or window, bee illus¬
tration, Out and In Bond.

REBATE PLANES.—Planes used in forming
and finishing rebates in joiner-work ; or, as it is
technically termed, sinking rebates. Of these there
are the moving fillister, used, in sinking rebates, on
the edge of the board next to the workman, and the
sash fillister in sinking the rebate on the edge fur¬
thest from him; and the guillaumes, skewed and
square, the former for finishing the rebate across
the direction of the fibre, and the latter for finish¬
ing it in the direction of the fibre.

RECESS.—A small cavity or niche formed in
the wa'l of a building. Exhedne, tribunes, alcoves
come under this denomination, and afford consider¬
able additional space. They add to the commodious
ness of dining-rooms, drawing-rooms, libraries, &c.

RECESSED ARCH.-—One arch within an¬
other. Such arches are sometimes called double,
triple, &e.. and sometimes compound arches.

RECTANGLE.—To construct a rectangle
j equal to a given triangle, Prob. XXIII. p. 9.-—
To construct a rectangle whose sides shall be equal
to two given lines, Prob. XXV. p. 9.—To describe
a rectangle or parallelogram having one of its sides
equal to a given line, and its area equal to a given
rectangle, Prob. XXVII. p. 10.—To construct a
rectangle upon a given line, and equal to a given
square, Prob. XXVIII. p. 10.—To describe a rect¬
angle equal to a given rhomboid, Prob. XXXIV.
p. 11.—To describe a rectangle equal to a given
irregular quadrilateral figure, Prob. XXXV. p. 11.
—To describe a rectangle equal to a given circle,
Prob. LXXIV. p. 20.

RECTILINEAR FIGURE.—To describe any
figure equal and similar to a given rectilinear figure,
Prob. LIII. p. 15.—To describe, on a given line, a
figure similar to a given rectilinear figure, Prob.
LIV. p. 15.

RED ob Yellow Pine. p. 116.

RED or Yellow Pine. —Causes to which the
rapid decay of home-grown timber may be attri-
j .buted. See p. 117.

RED or Yellow Pine. — Characteristics of
Memel, Norway, and Swedish timber. See p. 117-

REEDS.—A moulding consisting of several
beads side by side.

REGLEiT, Regula.— A small moulding, rect¬
angular in its section; a fillet or listel. Also, a
rectangular groove.

REGRATING. — Rehewing or otherwise re¬
newing the surface of a hewn stone.

REGULAR BODIES.—Those which have all
their sides, faces, and angles similar and equal.
They are only five in number—namely, the tetra¬
hedron, hexiedron, octahedron, dodecahedron, and
icosahedron. These are also called the Platonic
bodies. —To find the surface of any of the regular
i bodies. Rule: Multiply the square of its linear
side by the proper number in the annexed table
I under “surface;” and to find the solid content,
j multiply the cube of its linear side by the proper
number under “ solidity.”

No. of
Faces.

Name.

Surfuee when the
Side is 1.

Solidity when the
Side is 1.

Tetrahedron. . .

1-7320508

0-1178511

Hexiedron . . .

(j-OOOOOOO

1 0000000

Octahedron . . .

3-4641016

0 4714045

Dodecahedron . .

20-6457788

7-6631189

Icosahedron . . .

8-6602540

2 1816950

REGULAR FIGURES.—Those whose sides
and angles are equal, as the square and equilateral
triangle, pentagon, hexagon, &c. Circles can be
i inscribed within and about all the regular figures,
i and the area of any of them may be found by the
particular rule given under the proper word, or by
this general rule : Multiply half the perimeter of
the figure by the perpendicular let fall from the cir¬
cumscribed or inscribed circle, on any of its sides.

REGULAR POLYHEDRONS, The.—De¬
scription of, p. 69.

REGULAR POLYHEDRONS, The. —De¬
velopment of, p. 70.

REINS of a Vault. —The sides or walls which
sustain it.

INDEX AND GLOSSARY.

RELIEF

RELIEF, Rilievo.— The prefecture or promi¬
nence of a figure above or beyond the ground or
plane on wuich it is formed. Relief is of three
kinds: high relief ( alto rilievo), low relief (basso

High Relief.

rilievo), and half relief ( mezzo rilievo). The differ¬
ence is in the degree of projection. High relief is
formed from nature, as wile.- a figure projects as

Low Relief.

much as the life. Low relief is when the figure pro¬
jects but little, as in medals, festoons, foliages, and
other ornaments. Half relief is when one-half of
the figure rises from the plane.

REMOVING CENTRES, or Striking
Centres, p. 175.

RENAISSANCE.—A term applied to the style
of building and decoration which came into vogue
in the early part of the sixteenth century, profes¬
sedly a return to the classic architecture of Greece
and Rome. It was, nevertheless, a tasteless ad¬
herence to the dogmas and rules of Vitruvius, in
which everything was to be designed by rule and
line, and nothing left to the invention of the archi¬
tect. Chateaubriand characterizes the French ex¬
amples of the Renaissance as “bastard Roman, cold
and servile, neither in harmony with the climate,
nor suited to the wants of the people.”

RENDER.—To plaster on walls, slates, or
tiles, directly and without the intervention of laths.

RENDER and Set. —Two-coat plasteron walls.

RENDER, Float, and Set. — Three -coat
plaster on walls.

REREDOS, Rerdos, Reredosse. —The back
of a fire-place; an altar-piece; a screen or partition
wall separating the chancel from the body of a church.

RESINOUS WOODS.—General description of,
p. 115.

RESISTANCE of Timber.— To tension, p. 124.
—To compression, p. 124.— To transverse strain,
p. 126.— To torsion, p. 124.

RESOLUTION and Composition of Forces.
—The term resolution of forces or of motion, in
dynamics, signifies the dividing of any single force
or motion into two or more others, which, acting in
different directions, shall produce the same effect as
the given motion or force This is the reverse of
composition of forces or of motion. Thus let A b,
in the annexed diagram, represent the quantity and
direction of some given foroe; draw any lines a c,
a d ; and join c B, d b, and complete the parallelo¬
grams A D b e, a c b f. Then by composition of
forces the force a b is equivalent to A D and a e, or
to a c and a f. Hence it is evident that a given

force, as a b, may be resolved into as many pairs of
forces as there can be triangles described upon a
given straight line A B, or parallelograms about it.
And as the forces represented by ad, D b, or A C,
c B, may also be resolved into other pairs of forces,
it appears that by proceeding in the same manner
with the successive pairs of forces, a given force

may be resolved into an unlimited number of others,
acting in all possible directions. See p. 120.

RESPOND.—A pilaster or half pillar respond¬
ing to another similar, or to a whole pillar opposite
to it.

RESTING PLACE.—A half or quarter pace
in a stair.

RESTING POINTS. — In handrailing, the
heights set up to obtain the section of a cylinder in
forming the wreath. See p. 202.

RESULTANT.—In dynamics, the force which
results from the composition of two or more forces
acting upon a body. When the two forces act upon
a body in the same line of direction, the resultant
is equivalent to the sum of both; when they act in
opposite directions, the resultant is equal to their
difference, and acts in the direction of the greater.
If the lines of direction of the two forces are inclined
to each other, then on taking in each direction, from
the point where they intersect, a straight line to
represent each of the forces respectively, and con¬
structing a parallelogram of which these lines are
the adjacent sides, the resultant is represented in
intensity and direction by the diagonal of the paral¬
lelogram passing through the point of intersection.
By combining this resultant with a third force, a
new resultant will be obtained; and in this manner
the resultant of any number of forces may be deter¬
mined. See p. 120.

RETICULATED MOULDING.—In archi¬
tecture, a member composed of a fillet interlaced in
various ways like network. It is seen chiefly in
buildings in the Norman style.

RETICULATED WORK.—In architecture,
that wherein the stones are square and laid lozenge-

wise, resembling the meshes of a net. This species
of masonry was very common among the ancients.

RETURN.—A disease of trees. See p. 97.

RETURN, in building, denotes a side or part
that falls away from the front of any straight work.

RETURN BEAD.—One which shows the same
appearance on the face and edge of a piece of stuff,
forming a double quirk.

REVEALS, or Revels. —The sides of an
opening for a door or window, between the frame¬
work and the face of the wall. In Scotland termed
frequently rybat-head, or, probably from the way in
which it is cut, rebate-head. See woodcut, under
Back-Fillet.

RIBBING.—An assemblage of ribs.

RIBS, in carpentry and joinery, are curved
pieces of timber to which the laths are fastened, in
forming domes, vaults, niches, &c. In architecture,
projecting bands or mouldings used in ornamented
ceilings, both flat and curved, but more commonly
in the latter, especially when groined.

RIDGE.—The highest part of the roof of a
building. But in architecture the term is more par¬
ticularly applied to the meeting of the upper end of
the rafters. When the upper end of the rafters
abut against a horizontal piece of timber, it is called
a ridge-piece or ridge-plate. Ridge is also used to
signify the internal angle or nook of a vault. Ridge-
tile , a convex tile made for covering the ridge of a
roof.

RIDGE-PIECE, Ridge-Plate.— A piece of
timber at the ridge of a roof, against which the
common rafters abut. Called also ptolc-plate.

RIDGE-ROLL, or Ridge - Batten —A
rounded piece of timber, over which the lead is
turned in the ridges and hips of a roof. It is gene¬
rally about 2 inches diameter, and fixed to the ridge
I of the roof by spikes about 4 feet apart.

RIGA TIMBER. Pinus sylvestris, p. 116.

S RILIEVO. See Relief.

RING-COURSE.—The outer course of stone
j or brick in an arch.

J RIPPING SAW.—One used for cutting wood
j in the direction of the fibres.

RIS11RS OF STEPS, p. 196.

RISING HINGE.—One so constructed as to
I raise the door to which it is attached, as it opens.

ROCK-WORK, or Rocking, in masonry, as
its name implies, is that mode in which the stone
has an artificial roughness given to it to imitate
the natural face of a rock. It is thus performed:
Rough draughts are cut round the face of the stone,
from which the beds and joints are squared up.

280

ROMANESQUE

The workman then, with a pitching tool and mal¬
let, or with a hammer similar to a nidging ham¬
mer, breaks or splits away pieces from the face and
arrises of the stone, striving to avoid the appear¬
ance of formality, and taking care not to leave tool
marks. It is an especial object, in taking out the
pieces from the edges, that those in tne two con¬
tiguous stones shall correspond as nearly as may be
in size and depth, so that the whole surface of the
wall, when completed, may look as inartificial as
possible. It is only in dressing such stones as
admit of a piece being struck out of their face by a
blow, without leaving a hammer mark, that rock-
work is admissible. Rock - work, formed by the
chisel and mallet, is insipid in the extreme, and its
use evinces bad taste, as well as a lack of judg¬
ment.

ROCOCO. — A debased variety of the Louis-
Quatorze style of ornament, proceeding from it
through the degeneracy of the Louis-Quinze. It is

generally a meaningless assemblage of scrolls and
crimped conventional shell-work, wrought into all
sorts of irregular and indescribable forms, without
individuality and without expression. This term is
sometimes applied in contempt to anything bad or
tasteless in ornamental decoration.

ROD.—A measure of length equal to 16| feet.
A square rod is the usual measure of brick-work,
and is equal to 272 j square feet.

ROLL - MOULDING. — A round moulding
divided longitudinally along the middle, the upper
half of which projects over the lower. It occurs
often in the later period of the Early English and

Roll Moulding.

in the Decorated style, where it is profusely used
for drip-stones, string-courses, abacuses, &c.— Roll
and fillet moulding, a round moulding with a square

fillet on the face of it. It is most usual in the early
Decorated style, and appears to have passed by
various gradations into the ogee.

ROMAN ARCHITECTURE.—The style of
architecture used by the Romans. Founded on
the Grecian architecture, the Roman is, though less
chaste and simple, more varied, richer, and in some
respects bolder and more imposing. It embraces
two additional orders of columns, the Tuscan anil
the Composite. All its curved mouldings are more
circular and have greater projection, and its pedi¬
ments are steeper. Ornaments, too, are more fre¬
quently introduced. It is further characterized by
the use of the arch, which in its late periods was
one of its leading features, and was unknown in
the architecture of the Greeks.

ROMANESQUE.—A general term for all those
styles of architecture which, commencing with the
Christian era, sprung from the Roman, and flour¬
ished in Europe till the introduction of Gothic ar¬
chitecture. In all these there is an evident imita
tion of the features of classical Roman architecture,
altered and debased. There is still a prevalence of
horizontal lines, of rectangular faces, and square-
edged projections, and of arches supported on pillars
retaining traces of classical proportions. The open¬
ings in the walls are small, and subordinate to the
surfaces in which they occur; the members of the
architecture massive and heavy. The styles are

ROOD

INDEX AND GLOSSARY.

RULES

known in their various modifications by the names
of Byzantine, Lombard, Saxon, &c.

ROOD.—A measure equal to 36 square yards,
by which rubble masonry is valued in Scotland.
Rubble walls at and below 18 inches thick are
reduced to 1 foot, and above 18 inches thick to
2 feet.

ROOD.—A measure of land, the fourth part of
an acre, and equal to 40 square poles or 1210 square
yards.

ROOD.—A cross, crucifix, or figure of Christ
on the cross, placed in a church. The holy rood
was a cross with an effigy of our Saviour, generally
as large as life, elevated at the junction of the nave
and choir, and facing the western entrance to the
church. Sometimes images of the Virgin Mary
and St. John were placed, the one on the one side,
and the other on the other side, of the image of
Christ.

ROOD-LOFT, Rood-Tower. —The gallery in
a church where the rood and its appendages were
placed. This loft or gallery was commonly placed
over the chancel screen in parish churches, or be¬
tween the nave and chancel; but in cathedral
churches it was placed in other situations. The
rood tower or steeple was that which stood over the
intersection of the nave with the transepts.

ROOF.—The cover of a building, irrespective
of the materials of which it is composed. Roofs
are distinguished: 1st. By the materials of which
they are formed, as stone, brick, wood, slate roofs,
&c. 2d. By their form and mode of construction,

of which there is great variety, as shed, curb, hip,
gable, pavilion, and ogee roofs. 3d. They are fur-

Shed Roof. Gable Roof.

Hip Roof. Conical Roof. Ogee Roof.

Curb Roof. M Roof.

ther divided into high-pitched or low-pitched roofs,
as their inclined sides make a greater or lesser angle
with the horizon. In carpentry, roof signifies the
timber frame-work by which the roofing or cover¬
ing materials of the building are supported. This
consists in general of the principal rafters, the pur-

A, King-post. B, Tie-beam. C C, Struts or braces*

1) P, Purlins. E E, Backs or principal rafters

F F, Common rafters. G G, Wall-plates. H, Ridge-piece.

Queen-post Roof.

A A, Quern-posts.
D D, Purlins.

G G, Wall-plates.

B, Tie-beam.

E, Straining beam.
H, Ridge-piece

C C, Struts or braces.
F F, Common rafters.

fins, and the common rafters. The principal rafters,
or principals, as they are more commonly termed,
are set across the building at about 10 or 12 feet
apart; the purlins lie horizontally upon these, and
sustain the common rafters, which carry the cover¬
ing of the roof. The preceding figures show the

two varieties of principals which are in common \
use; the first, the king-post principal, and the
second, the queen-post principal, with the purlins
and common rafters in situ. The mode of framing
here exhibited is termed a truss. Sometimes, when
the width of the building is not great, common raf¬
ters are used alone to support the roof. They are
in that case joined together in pairs, nailed wheie
they meet at top, and connected with a tic at the
bottom. They are then termed couples or couple
close. See p. 85. In Asia, the roofs of houses are
flat or horizontal. The same name, roof, is given
to the sloping covers of huts and cabins, to the
arches of oven-furnaces, &c.

ROOF COVERING.—Weight of the various
kinds of, p. 137.

ROOFS.—Various forms of, as arising from
variety in the forms of buildings, p. 85-91.

ROOFS.—Practical memoranda of construction
in designing, p. 137.

ROOFS.—Classified according to their forms

ROSE-WINDOW.—A circular window divid¬
ed into compartments by mullions or tracery raui-

Rose-window, St. David's.

and the combination of their surfaces, p. 134.

ROOFS.—Slope of, according to various au¬
thors, p. 134; as settled by climate, p. 134; by
M. Rondelet considered arbitrary, p. 134 ; as settled
by material used as the covering, p. 134; Colonel
Emy’s remarks on, p. 134; Professor Robison’s
remarks on, p. 135.

ROOFS.—Examples of constructions of, p. 135.

ROOFS.—Illustration of the principles of truss¬
ing of, p. 136.

ROOFS.—Table of the weight of the usual
coverings of, p. 137.

ROOFS.—Mr. Tredgold’s rules for the dimen¬
sions of the timbers in, p. 137.

ROOFS illustrated and described:—

King-post roof, span 30 feet,
King-post roof, span 33 feet G in.,
Compound roof, span 30 feet,
Queen-post roof, span 32 feet,
Queen-post roof, span 60 feet.
Queen-post roof, Railway Work¬
shops at Worcester, .

Platform roof, span 70 feet,
Queen-post M roof, span 47 feet, .
Queen-post roof, span 40 feet,
Kiug-post roof, span 38 feet 9 in.,
Roof of George Heriot’s Schools,
Edinburgh. ....

Roof of Wellington Street Church,

Glasgow,.

Roof of the Parish Church, Elgin,
Roof of the City Hall, Glasgow, .
Roof of the East Parish Church,
Aberdeen, ....

Roof of Sheds, Liverpool Docks,
Roof of Sheds, Liverpool Docks,
Roof for a hall or church with
nave and aisles,

Queen-post roof for a hall or
church with nave and aisles,
Roof of the East Quay Shed, Salt-
house Dock, Liverpool,

Roof of 44 feet 8 inches span,

Roof of 45 feet span,

Roof of 54 feet span, .

Roof with principals constructed
of timber and iron, .

Roof with iron rafters, Ac.,
Mansard roof for an arched ceiling,
A king-post Mansard roof, .

A Mansard roof with two stories
of apartments, ....
A queen-post Mansard roof,

Roof at Marac, near Bayonne,
Part of the roof of the Riding-
house at Libourne, .

Roof of the Salle des Catechismes,
Amiens Cathedral, .

Roof of Grassendale Church, near
Liverpool, ....
Roof on the principles of DeLorme,
called heinicycle roofs,

Another example of the hemi-
cycle roof, ....
Another example of the same con¬
struction, . . . . .

Another example of the same con¬
struction, applied to a groined
vault, . . . . .

Roof of the Great Hall, Hampton
Court, .....
Roof of Westminster Hall, .
Example of a conical roof, .
Example of a domical roof. .
Example of a domical roof with a
circular opening in the centre, .
Example of an ogee domical roof
on an octagonal plan,

Example of a timber steeple.
Tower of the Townhall, Milford,
Massachusetts, . . .

Spire of La Sainte Chapelle, Paris,

Plate. Tacre

XXII.

138

XXII.

133

XXII.

138

XXII.

138 1

XXII.

138

XXII.

133

XXII.

138

XXIII.

138

XXIII.

138

XXIII.

138

XXIII.

139

XXIV.

139

XXIV.

139

XXIV.

139

XXIV.

139

XXV.

139

XXV.

140

XXV.

140

XXV.

140

XXV.

140

XXVI.

140

XXVI.

140

XXVI.

140

XXVI.

140

XXVI.

140

XXVII.

141

XXVII.

141

XXVII.

141

XXVII.

141

XXVIII.

142

XXVIII.

143

XXIX.

143

XXIX.

143

XXX.

144

XXX.

144

XXX.

144

XXX.

144

XXXI.

144

XXXII.

145

XXX111.

145

XXXIII.

145

XXXIV.

145

XXX TV.

145

XXXV.

145

XXXV? 146
XXXVI. 140

ROOT of a Tenon, p. 147.

281

ating or branching from a centre. It is called also
Catherine wheel and Mary-gold window.

ROSTRUM. —A scaffold or elevated place,
where orations or pleadings are delivered; a pulpit.

ROTTENNESS in Trees, p. 97.

ROTUNDA.—A round building; any building
that is round both on the outside and inside. The
most celebrated edifice of this kind is the Pantheon
at Rome.

ROUGH-BRACKETS, p. 19G.

ROUGH-CAST, or Rough - Casting. — A
covering for an external wall, composed of an al¬
most fluid mixture of clean gravel and lime, which
is dashed on the wall previously prepared for its
reception by a coating of soft plaster, to which the
rough-cast adheres.

ROUGH-HEW. — To hew coarsely without
smoothing, as to rough-hew timber.

ROUGH-SETTER.— A mason whobuilds rough
walling, as distinguished from one who hews also.

ROUGH-STRINGS, p. 196.

ROUTTER-GAUGE.—A gauge used for cut¬
ting out the narrow channels intended to receive
brass or coloured woods in inlaid work. It is
formed like the common marking gauge, but pro¬
vided with a narrow chisel as a cutter, in place of
the marking point.

ROUTTER - PLANE.—A kind of plane used
for working out the bottoms of rectangular cavi¬
ties. The sole of the plane is broad, and carries a
narrow cutter, which projects from it as far as the
intended depth of the cavity. This plane is vul¬
garly called the old woman's tooth.

RUBBING, or Polishing. —In stone cutting,
after a stone is dressed by boasting or scabbling,
the tool marks are, by the agency of a piece of
Yorkshire stone or grit-stone as a rubber, used first
with sand and water and then with water alone,
obliterated, and a smooth polished surface is given
to the stone. This is of all modes the best for finish¬
ing the surface of stone which is exposed to the
weather, as the pores are completely filled and the
surface does not retain moisture.

RUBBLE.—Stones of irregular shapes and di¬
mensions.

RUBBLE-WORK, or Rubble-Walling. —
Walls built of rubble stones. Rubble walls are
either coursed or uncoursed; in the former, the
stones are roughly dressed and laid in courses, but
without regard to equality in the height of the
courses ; in the latter, the stones are used as they
occur, the interstices between the larger stones
being filled in with smaller pieces. When this is
done with great nicety, and so as to preserve per¬
fectly the horizontal and vertical bond by the com¬
plete interlacing ,.of the amorphous stones, the
operation is termed snecking, and the work is called
snecked rubble.

RUDENTURE.—The figure of a rope or staff,
plain or carved, with which the flutings of columns
are sometimes filled. >See Cabling.

RULES forcalculatingthe dimensions of timbers
exposed to different strains :—

1. To find the tenacity of a piece of timber,
p. 124.

2. To find the diameter of a post that will sustain
a given weight, when the length exceeds ten times
the diameter, p. 125.

3. To find the scantling of a rectangular post to
support a given weight, p. 125.

4. To find the dimensions of a square post that
will sustain a given weight, p. 125.

5. To find the stiffest rectangular post that will
support a given weight, p. 125.

6. To find the strength of a rectangular beam
fixed at one end and loaded at the other, p. 127.

7. To find the length of a rectangular beam,
j when it is supported at both ends and loaded at
I the middle, p. 127.

2 N

INDEX AND GLOSSARY.

RULES

SAW

8. To find the strongest form of beam, so as only
to use a given quantity of timber, p. 129.

9. To find the scantling of a piece of timber
which, when laid in a horizontal position, and sup¬
ported at both ends, will resist a given transverse
strain with a deflection' not exceeding inch per
foot, p. 130.

Summary of rules expressed in words, p. 130—133.

RULES for the dimensions of the timbers in a
roof, p. 137.

RULES for calculating the strength of floor
timbers, p. 154.

RUSTIC QUOINS, or Coins.—T he stones
which form the external angles of a building, when
they project beyond the naked of the walls.

RUSTIC WORK, Rustication, Rusticated
Work. —Rustic work, in a building, is when the
stones, &c., in the face of it are hacked or picked
in holes, so as to give them a natural rough appear¬
ance. This sort of work is, however, now usually

Fi?. 2.

Rustic Work.

Fig, 1, With chamfered joint.*. Fig. 2. With rectangular joints.

called rock-worlc, and the term rustic is applied to
masonry worked with grooves between the courses,
to look like open joints, of which there are several
varieties. The same term is applied to walls built
of stones of different sizes and shapes.

RUSTIC ATED ROCK- WORK.—In masonry,
this term is sometimes applied to a kind of work in
which the faces of the stones are left rough, the
joints being chiselled either plain or chamfered. It
is more correctly termed rough-faced, rustic. It is
applied in walls where a character of rude strength
has to be expressed, as in bridges, retaining walls,
and similar works.

SAEICU WOOD. — Properties and uses of,
p. 115.

SACELLUM. — In ancient Roman architec¬
ture, a small inclosed space without a roof, conse¬
crated to some deity. In medieeval architecture,
the term signifies a monumental chapel within a
church ; also, a small chapel in a village.

SACOME.—In architecture, the exact profile
of a member or moulding.

SACRARIUM.—A sort of family chapel in the
houses of the Romans, devoted to some particular
divinity.

SACRISTY, or Sacristry. —An apartment
in a church where the sacred utensils are kept, and
the vestments in which the clergyman officiates are
deposited ; now called the vestry.

SADDLE-BACKED COPiNG.

—-A coping thicker in the middle
than at the edges; sloping both ways
from the middle.

SAFETY-ARCH. —An arch
formed in the substance of a wall, to
relieve the part below it from the superincumbent
weight. A discharging arch (which see).

SAFETY - LINTEL.—A name given to the
wooden lintel which is placed behind a stone lintel,
in the aperture of a door or window.

SAG.—To bend from a horizontal position.

SAIL-OVER, v .—To project.

SAILING OVER.—In architecture, the name
given by workmen to anything projecting beyond
the naked of a wall, of a column, &c.

SALIENT, Saliant. —In architecture, a term
used in respect of any projecting part or member.

SALIX russelana, p. 114 ; S. alba, p. 114 ;
S. fragilis, p. 114 ; S. caprea, p. 114.

SALLY.—In architecture, a projection; also,
the end of a piece of timber cut with an interior
angle formed by two planes across the fibres, as the
feet of common rafters; called in Scotland a face.

SALOON.—A lofty, spacious hall, frequently
vaulted at the top, and usually comprehending two

stories, with two ranges of windows. A magnificent
room in the middle of a building, or at the head of
a gallery, &c. A state-room much used in palaces
in Italy, for the reception of ambassadors and other
visitors.

SAP-WOOD.—The external part of the wood
of exogens, which from being the latest formed, is
not filled up with solid matter. It is that through
which the ascending fluids of plants move most
freely. For all building purposes the sap-wood is or
ought to be removed from timber, as it soon decays.

SARACENIC ARCHITECTURE. — The
name given to the architecture employed by the
Saracens, who established their dominion over the
greater part of the East in the seventh and eighth
centuries. It may with equal propriety be styled
Moslem or Mahometan architecture, from its ori¬
ginating in and diffusing itself over the world with
the religion of Mahomet, and also from its being
almost exclusively confined to nations professing j
that belief. The Saracens proper, or Arabians, do
not appear to have possessed any native architec¬
ture of their own, but adopted and modified the
existing styles as they found them among the states
which submitted to their sway. Various styles,
therefore, such as the Indian, Persian, and Egyp¬
tian varieties, arose in different countries, but may
all be classed under the general head of Saracenic
architecture. In process of time these gradually
merged into each other, and a distinct style was
formed, which, however, it is impossible minutely
to characterize, owing to the numerous local cir¬
cumstances by which it is modified. Its more pro¬
minent and familiar features are the bulb-shaped
dome, borrowed originally from the Byzantine
school, but assuming its peculiar shape under the
hands of Moslem architects, and the lofty, slender
turrets, known by the name of minarets, which are
generally attached to the edifices of Mahometan
worship. Those last are said to have been first
erected by the Caliph Walid in the commencement
of the eighth century. One branch, nevertheless,
of Saracenic architecture, the Moorish, presents so
many distinct features as to form a school of its
own, and be regarded to a great extent as a type of
the Mahometan style. It is admirably exemplified
in the architectural remains in Spain of the Moors
or African Saracens, who subdued that country in

Moorish Doorway, Cordova.

the early part of the eighth century, and after long
retaining their dominion over the greater part of it,
were only finally driven from their last hold at
Granada in 1492. The distinguishing characteristic
of Moorish architecture, is the profusion of orna¬
ment with which the interior walls of buildings are
overlaid. These ornaments are composed of mosaic
work, richly interspersed with gilding, and give a
most beautiful and fairy-like appearance to the
apartments. The ceilings are decorated in the same
manner with stucco-work, sometimes in honeycomb
or stalactite patterns, richly gilded and painted in
the most brilliant colours. In accordance with a
precept of the Koran, which prohibits all represen¬
tation of human or animal forms, no sculptured or
painted figures, or similar imitations of animated !
nature, are to be met with; but the decorations j
in the best examples consist of a multiplicity of j
lines and curves, forming geometrical figures and an
elegant variety of conventional foliage, all interlac¬
ing each other with the richest and most luxuriant |
effect. Almost every variety of arch is found in
this style, but the horse-shoe arch prevails, and the
columns supporting it are often remarkable for their
extreme slenderness and height. The exterior of
Moorish buildings is comparatively plain, but the
doorways and arches surmounting them are fre¬
quently, as shown in the annexed woodcut, adorned

282

with the most exquisite and elaborate tracery.
About the finest specimens of Moorish architecture
in existence are the mosque at Cordova, now trans¬
formed into a cathedral, and the celebrated palace
of the Alhambra at Granada.

SARCOPHAGUS.—1. According to Pliny, a
species of stone used among the Greeks for making
coffins, which was so called because it consumed the
flesh of bodies deposited in it within a few weeks.
It is otherwise called lapis Assius, and said to be
found at Assos, a city of Lycia. Hence,—2. A'
stone coffin or stone grave, in which the ancients
deposited bodies which they chose not to burn.
Sarcophagi were made either of stone, of marble,

Greek Sarcophagus, Xanthus.

or of porphyry. Among the Greeks the form was
generally oblong, the angles sometimes rounded,
the exterior being richly sculptured with figures in
relief. The lid or roof varies both in shape and or¬
namentation. The Egyptian sarcophagi are sculp¬
tured with hieroglyphics. One of the most cele¬
brated is the great sarcophagus taken by the British
in Egypt in 1801, commonly called that of Alex¬
ander. It is deposited in the British Museum.

SARKING.—The Scotch term for slateboarding.

SASH.—The framed part of a window in which
the glass is fixed.

SASH, or Sashed Door. p. 186.

SASH-FASTENER.—A latch or screw for
fastening the sash of a window.

SASH-FRAME.—The frame in which the sash
is suspended, or to which it is hinged. When the
sash is suspended, the frame is made hollow to con¬
tain the balancing weights, and is said to be cased.

SASH-LINE.—The rope by which a sash is
suspended in its frame. »

SASH-SAW.—A small saw used in cutting the
tenons of sashes. Its plate is about 11 inches long,
and has about 13 teeth to the inch.

SASHES and Sash Bars. p. 187, 188.

SAUL TREE, or Sal-Tree. —The name given
in India to a tree of the genus Shorea, the S. robusta,
which yields a balsamic resin, used in the temples
under the name of ral or dhoona. The timber called
sal, the best and most extensively used in India, is
produced by this tree.

SAW.—A cutting instrument consisting of a
blade or thin plate of iron or steel, with one edge
dentated or toothed. The saw is employed to cut
wood, stone, ivory, and other solid substances. The
best saws are of tempered steel, ground bright and
smooth. They are of various forms and sizes, ac¬
cording to the purposes to which they are to be
applied. Those used by carpenters and other arti¬
ficers in wood are the most numerous. Among
these are the following:—The cross-cut saw, for
cutting logs transversely, and wrought by two per¬
sons, one at each end. The pit saiv, a long blade
of steel with large teeth, and a transverse handle
at each end; it is used in saw-pits for sawing logs
into planks or scantlings, and is wrought by two
persons. The frame saw, consisting of a blade from
5 to 7 feet long, stretched tightly in a frame of
wood. It is used in a similar manner to the pit
saw. The ripping saw, half-ripper, hand-saw, and
panel saw are saws for the use of one person, the
blades tapering in length from the handle. Tenon
saws, sash satvs, dovetail saws, &c., are saws made
of very thin blades of steel, stiffened with stout
pieces of brass, iron, or steel fixed on their back
edges. They are used for forming the shoulders of
tenons, dovetail-joints, &c., and for many other
purposes for which a neat, clean cut is required.
Compass and kcy-liole saws are long narrow saws,
tapering from about 1 inch to g inch in width, and
used for making curved cuts. The key-hole saw is
inserted in a long hollow handle called a pad, and
by a screw it is fixed in any required place, so that
it may be made to project more or less, as required.
Small frame-saws and bow-saws, in which very thin,

SAXON ARCHITECTURE

INDEX AND GLOSSARY.

SCRIBING INSTRUMENT

narrow blades are tightly stretched, are occasion¬
ally used for cutting both wood and metal. There
are also circular saws and band-saws. Saws for
cutting stone are without teeth.

SAXON ARCHITECTURE.—The architec¬
ture which prevailed in England previous to the
Norman Conquest. Much dispute has taken place
in regard to the existing specimens of building al¬
leged to belong to the Anglo-Saxon period, it being
maintained by various parties, that all traces of this
style have now disappeared. A considerable degree
of plausibility is given to this assertion, by the cir¬
cumstance that many of the Saxon edifices were
entirely, or nearly so, constructed of timber. It is
indeed certain, that no entire Anglo-Saxon build¬
ing exists at the present day, but that portions of
some ancient churches, such as towers, windows,
and doorways, belong to the period preceding the
Conquest, seems to he satisfactorily ascertained.

"Window, Barnack Church, Northamptonshire.

It is difficult, if not impossible, to give an accurate
description of its leading characteristics, but there
can be little doubt of its being generally marked by
extreme rudeness and simplicity, a circumstance
which renders its disappearance, except to the an¬
tiquary and historian, a matter of comparatively
small regret. The heads of windows and doors in
Saxon architecture are triangular or semicircular,

Baluster Window, Monkwearmouth Church, Durham.

the former having apparently been copied from the
debased Roman form to be seen on sarcophagi in
the Roman catacombs. The semicircular arch is
the most frequent, the earliest of which were con¬
structed of large tiles, probably borrowed from the
debris of Roman edifices. These tiles were placed
on end, and the spaces between, which are nearly

Doorway of the Tower of Earls-Barton Church.

equal in width, filled in with rubble-work • the
jambs or imposts of the arches w r ere generally of
stone as well as the walls, in which were sometimes
laid courses of tile, either in horizontal layers, or
in the diagonal manner called licrring-bone, being
evidently an imitation of the Roman structures in
Britain. The Saxon mouldings were few and
simple, consisting of a square-faced projection, with
a chamfer or splay on the upper or lower edge. A

peculiar feature in the Anglo-Saxon bell-tow T ers is
to be remarked in the rude columns which divide
the openings of the windows, and form a kind of
baluster. These are seen in the towers of Monkwear¬
mouth, Jarrow, Earls-Barton, and other churches;
the tower of Earls-Barton combining in itself more
of the characteristics of the Saxon style than any
other known specimen.

SCABBLE.—In masonry, to dress a stone
with a broad chisel, called, in England, a boaster,
and in Scotland a drove, after it has been pointed
or broached, and preparatory to finer dressing.

SC AGLIOL A.—In architecture, a composition,
sometimes also called mischia, from the mixture of
colours in it being made to imitate marble. It is
composed of gypsum or sulphate of lime calcined
and reduced to a fine powder, of which, with the ad¬
dition of a solution of glue or isinglass, a fine paste
is made, in which the requisite colours are diffused.
It is used like stucco, and when fit for the opera¬
tion, it is smoothed with pumice-stone, and polished
with tripoli, charcoal, and oil. Columns are formed
of it, as those of the Pantheon in London.

SCALES for Drawing, p. 36.

SCAMILLUS, Scamilli.- —In ancient archi¬
tecture, a sort of second plinths or blocks under
statues, columns, &c.,
to raise them, but not,
like pedestals, orna¬
mented with any kind
of moulding.

SCANTLE.—

Among slaters, a gauge
by which slates are re¬
gulated to their proper
length.

SCANTLING. —1.

In carpentry, the dimen¬
sions of a piece of timber
in breadth and thickness ; also, a general name for
small timbers, such as the quartering for a parti¬
tion, rafters, purlins, or pole-plates in a roof, <Sic.
—2. In masonry, the same word is used to express
the size of stones in length, breadth, and thickness.

SCAPE, Scapement. —The apophyge or spring
of a column ; the part where the shaft of a column
springs out of the base, usually moulded into a con¬
cave sweep or cavetto ; a congd.

SCAPPLE, SCAPPLING, SCABBLE, SCABBLING.
See Scabblf. and Boasting.

SCARCEMENT.—In a wall, a set-off or table
where a wall is diminished in thickness; applied
chiefly to the set-off of a footing.

SCARFING.-—A mode of lengthening beams,
employed when it is necessary to maintain the
same depth and width of the beam throughout.
In doing this a part of the thickness of the timber
of the length of the joint is cut from each beam,
but on opposite sides, so that they may lap on each
other, and the parts, when united, are bolted or
hooped together. In bolting them, side-plates of
iron are generally used, to protect the wood from
the crushing effects of the bolts, and the ends of
these plates are generally bent inwards, and in¬
serted into the beam, as an additional security when

Fi;. l.

Fig. 3.

Fig. 6.

- -- -A

the beam is subjected to tension. In figs. 1 and 2
the strength of the scarf is dependent on the bolts,
fig. 3 shows a scarf with the surfaces tabled and
keys introduced. Fig. 4 shows fig. 1 with the

283

surfaces tabled and keyed; fig. 5, a shows fig. 2
with keys added, and B shows the same with the
parts indented; fig. 6 the simple scarf used in
joining wall-plates, in which the superincumbent
weight keeps the parts from being drawn asunder.
See p. 147j 148, and Plate XXXIX.

SCHEME ARCH, or Skene Arch. —An
arch which is any segment of a circle less than a
semicircle.

SCHOLA.—In ancient architecture, the mar¬
gin or platform which surrounded the bath. Also,
a portico corresponding to the exedra of the Greek
palaestra, intended for the accommodation of the
learned, who assembled there to converse.

SCIAGRAPH.—The section of a building to
show its interior.

SCIOGRAPHY.—The art of projecting and
delineating shadow’s.

SCONCE.—A branch to set a light upon, or to
support a candlestick ; a screen or partition to

cover or protect anything ; the head or top of
anything. The term is sometimes used as synony¬
mous with squinch.

SCONC'HEON (from the French ecoin$on ).—
A term applied to the portion of the side of the
aperture of a door or window, from the back of the
jamb or reveal to the interior of the wall.

SCOTCHING. Scutching. —A method of dress¬
ing stone either by a pick or pick-shaped chisels
inserted into a socket formed in the head of a
hammer.

SCOTIA.—The hollow moulding in the attic
base between the fillets of the tori. It takes its
name from the shadow formed by it, which seems

Scotia or Trochilus Moulding.

to envelope it in darkness. It is sometimes called
a casement, and often, from its resemblance to a
common pulley, trochilus. It is frequently formed
by the junction of circular arcs of different radii.

SCREEDS.—Ledges of lime and hair about 6
or 8 inches wide, by which any surface about to be
plastered is divided into bays or compartments.
The screeds are 4, 5, or 6 feet apart, according to
circumstances, and are accurately formed in the
same plane by the plumb rule and straight-edge.
They thus form gauges for the rest of the work,
and when they are ready the panels or compart¬
ments between them are filled in flush with pilaster,
and a long float being made to traverse them, all
the plaster which projects beyond them is struck
off, and the whole surface reduced to the same plane.

SCREEN, Builders’. —A kind of wire sieve
for sifting sand, lime, gravel, &c. It consists of a
rectangular wooden frame with metal wires tra¬
versing it longitudinally at regular intervals. It is
propped up in nearly a vertical position, and the
materials to be sifted or screened are thrown against
it, when the finer particles pass through and the
coarser remain.

SCREW-JACK.—A portable machine for rais¬
ing great weights by the agency of a screw.

SCREWS.—Adhesion of, in Wood. See Ad-
! hesive Force of Nails and Screws.

SCRIBE.—A spike or large nail ground to a
sharp point, to mark bricks on the face and back
by the tapering edges of a mould, for the purpose
of cutting them and reducing them to the proper
taper for gauged arches.

SCRIBEr—To mark by a rule or compasses ;
to mark so as to fit one piece to another. See de¬
scription of the operation of scribing, text, p. 186.

SCRIBING INSTRUMENT illustrated and
described, p. 200, Plate I.XXXIX.

INDEX AND GLOSSARY.

SCROLL

SCROLL.—In architecture, a name given to a
large class of ornaments characterized generally
by°their resembling a narrow band arranged in
convolutions or undulations.

SCUNCHEON.—The same as sconcheon
(which see). The term is used, too, as synonymous
with squinch, and applied to the stones or arches
thrown across the angles of a square tower, to sup¬
port the alternate sides of an octagonal spire. It
is also used to denote the cross-pieces of timber at
the angles of a frame, to give it strength and firm¬
ness. (See Squinch.) It is sometimes written
scutcheon, sconchon, and shownsione.

SCUTCHEON.—1. In ancient architecture, the
shield or plate on a door, from the centre of which
hung the door handle.—2. The ornamental bit of
brass plate perforated with a key-hole, and placed
over the key-hole of a piece of furniture.

SEALING.—The operation of fixing a piece of
wood or iron on a wall with plaster, mortar, cement,
lead, or other binding.

SEAM OF GLASS.—The quantity of 120 lbs.,
of 24 stones of 5 lbs. each.

SEASONING OF TIMBER, and the means
employed to increase its durability, p. 104.

SEASONING OF TIMBER.—By stoving,
p. 104 ; by burying in dry sand, 104; by immersion
in cold water, 105; by immersion in hot water,
105 ; by immersion in salt water, 105 ; by charring
the surface, 105 ; by coating the surface with sub¬
stances impervious to the air, 105; Sir Samuel
Bentham’s observations on, 105.

SECANTS, Line op, on the Sector. —Con¬
struction and use of, p. 39.

SECOND BRICKS.—Bricks of a quality next
to the finest mail stocks or cutters. They are used
in the principal fronts of buildings.

SECOND COAT.—In architecture, either the
finishing coat as in laid and set plaster, or in ren¬
dered and set plaster; or it is the floating when the
plaster is roughed in, floated, and set for paper.

SECTION.—In architecture, the projection or
geometrical representation of a building supposed
to be cut by a vertical plane for the purpose of
exhibiting the interior, and describing the height,
breadth, thickness, and manner of construction of
the walls, arches, domes, &c.

SECTOR,—Construction and use of, p. 36.

SECTROID.—The curved surface between two
adjacent groins. See p. 77.

SEDILIA.—The Latin name for a seat, which
has come to be pretty generally applied by way of
distinction to the seats for the priests in the south
wall of the choir or chancel of many churches and

Sedilia, Bolton Percy, Yorkshire.

cathedrals. In this country they are usually re¬
cessed in the wall like niches, and three in number,
for the use of the priest, the deacon, and sub-deacon,
during part of the service of high-mass.

SELF-FACED.—A term used to denote the
natural face or surface of a flag-stone, in contra¬
distinction to dressed or hewn.

SEPT ARIA.—A name given to nodules or
spheroidal masses of calcareous marl, whose inte¬
rior presents numerous fissures or seams of some
crystallized substance, which divide the mass.
When calcined and reduced to powder, these sep-
taria furnish the valuable mortar called Roman or
Parker’s cement, which has the property of harden¬
ing under water.

SERVICE TREE. — Properties and uses of

p. 114.

SET SQUARES, p. 44.

SET-OFF, or Offset.—T he part of a wall,
&c., which is exposed horizontally when the portion
above it is reduced in thickness.—-Also, the sloped
mouldings which divide Gothic buttresses into
stages. See Soarcement.

SETTING.—The quality of hardening in plaster
or cement; also, the fixing of stones in walls or
vaults.— Setting coat, the best sort of plastering
oa ceilings or walls.

SETTING-OUT ROD.—A rod used by joiners
for setting-out frames, as of windows, doors, &c.

SETTLEMENTS.—Failures in a building oc¬
casioned by sinking.

SEVEREY, Seyery, Seberfe, Sibary.—A
compartment in a vaulted roof; also, a compart¬
ment or division of scaffolding.

SHADING.—Methods of, p. 224.

SHADING by Flat Tints, p. 224.

SHADING by Softened Tints, p. 225.

SHADOWof a straight line.—To find the length
and direction of, the projections of the straight line
and of the luminous point being given, Prob. I.

p. 211.

SHADOW.—To find the shadow of a straight
line inclined to the horizontal plane, the projections
of the luminous point and of the straight line being
given, Prob. II. p. 211.

SHADOW.—To find the shadow of a straight
line inclined to two planes. Prob. III. p. 212.

SHADOW.—To find the portion of the sha¬
dow of a straight line, interrupted by a plane
inclined to the planes of projection, Prob. IV.

p. 212.

SHADOW.—To determine the shadow of a
straight line on the horizontal plane, the projec¬
tions of a solar ray and of the straight line being
given, Prob. VI. p. 213.

SHADOW.—To determine the shadow cast by
a straight line on a vertical wall, Prob. VII. p. 214.

SHADOW. — To find the shadow cast by a
straight line upon a curved surface, p. 214.

SHADOW. — To find the shadow of a circle
upon the horizontal plane, p. 215.

SHADOW.—To find the shadow of a circle on
the vertical plane, p. 215.

SHADOW.—To find the shadow of a circle on
two planes, p. 215.

SHADOW of a circle on a circular wall, p. 215.

SHADOW of a circle situated in the plane of
the luminous rays, p. 215.

SHADOW of a circle, whose horizontal projec¬
tion is perpendicular to a trace of a plane passing
through the luminous ray, Prob. IX. p. 216.

SHADOW.—To find the shadow of a cylinder
under various conditions, Prob. XI. p. 216-218.

SHADOW.—To find the shadow of the inte¬
rior of a concave cylindrical surface, Prob. XII.

p. 218.

SHADOW.—To find the shadow of a cone on
the horizontal plane, Prob. XIII. p. 218.

SHADOW.-—To find the shadow on the con¬
cave interior of a cone, Prob. XIV p. 219.

SHADOW.— To determine the shadow of a
sphere on the horizontal plane, and the boundaries
of shade on the sphere, Prob. XV. p. 220.

SHADOW.—To find the shadow on the con¬
cave interior of a hemisphere, Prob. XVI. p. 220.

SHADOW. — To determine the shadow in a
niche, Prob. XVII. p. 221.

SHADOW.—To find the shadow of a regular
hexagonal pyramid on both planes of projection,
Prob. XIX. p. 221.

SHADOW. — To find the shadow cast by a
hexagonal prism upon both planes of projection,
Prob. XX. p. 222.

SHADOW.—To determine the limit of shade in
cylinders placed vertically, and likewise its shadow
on both planes of projection, Prob. XXI. p. 222.

SHADOW.—To determine the limit of shade
in a cylinder placed horizontally, and its shadow on
both planes of projection, p. 222.

SHADOW.—To find the limit of shade in a
cone, and its shadow on the two planes of projec¬
tion, Prob. XXII. p. 222.

SHADOW.—To find the shadow thrown by a
cone upon a sphere, Prob. XXIII. p. 222.

SHADOW. — To determine the shadow of a
concave surface of revolution, Prob. XXIV. p. 223.

SHADOWS, Projection of.— Introductory
remarks, p. 209.

SHADOWS projected by rays of light which
are parallel among themselves Prob. V. p. 213.

SHADOWS.—To find, on the circumference of
a circle, the tangent points of planes passing through
the light, when the circle is not in the plane of the
light, Prob. X. p. 216.

SHADOWS.—To determine the shadows of a
cylinder whose axis is circular (such as a ring),
Prob. XVIII. p. 221.

SHAFT.—The shaft of a column is the body of
it, between the base and the capital. It is also
called the fast or trunk of the column. It always
diminishes in diameter, sometimes from the bot¬
tom, sometimes from a quarter, and sometimes
from a third of its height, and sometimes its out¬
line is a convex curve, called the entasis. In the
Ionic and Corinthian columns, the difference of the
upper and lower diameters of the shaft, varies from
a fifth to a twelfth of the lower diameter. (See

284

SHOULDERING

Column.) — Vaulting shafts, those which support
ribs, or other parts of a vault.— Shaft of a king-post,
the part between the joggles.— Shaft of a chimney,
the part which rises above the roof for discharging
the smoke into the air.

SHAFTED IMPOST. — In mediaeval archi¬
tecture, an impost with horizontal mouldings, the
section of the mouldings of the arch above the im¬
post being different from that of the shaft below it.
In a banded impost the sections are alike.

SHAKE.—A fissure or rent in timber, occa¬
sioned by its being dried too suddenly, or exposed
to too great heat. Shakes frequently occur in grow¬
ing timber from various causes.

SHANK.—Another name for the shaft of a
column.— Shanks, or legs, names given to the plain
space between the channels of the triglyph of a
Doric frieze.

SHANTY.—A hut or mean dwelling.

SHED ROOF. — The simplest kind of roof,
formed by rafters sloping between a high and a low
wall.

SHEERS. — Two masts or spars lashed or
bolted together at or near the head, provided with
a pulley, and raised to nearly a vertical position,
used in lifting stones and other building materials.

SHEET - PILES, Sheeting-Piles. —Piles
formed of thick plank, shot or jointed on the edges,
and sometimes grooved and tongued, driven closely
together between the main or gauge piles of a coffer¬
dam or other hydraulic work, to inclose the space
so as either to retain or exclude water, as the case
may be. Sheeting-piles have of late been formed of
iron.

SHELL-BIT.—A boring tool used with the
brace in boring wood ; it is shaped like a gouge,
that is, its section is the segment of a circle, and
when used it shears the fibres round the margin of
the hole, and removes the wood almost as a solid
core.

SHINGLE.—A small piece of thin wood, used
like a slate for covering a roof or building. Shingles
are from 8 to 12 inches long, and about 4 inches
broad, thicker on one edge than the other. In
America they are extensively used, and are there
manufactured by machinery of a very ingenious and
simple description.

SHINGLE-ROOFED.—Having a roof covered
with shingles.

SHINLOG.—The brick building by which the
mouth of a brick kiln is closed.

SHOE.—1. The inclined piece at the bottom of
a water-trunk or lead pipe, for turning the course
of the water, and discharging it from the wall of a
building.—2. An iron socket used in timber framing
to receive the foot of a rafter or the end of a strut.

SHOOT.—To plane straight, or fit by planing.

SHOOTING. — In joinery, the operation of
planing the edge of a board straight, and out of
winding.

SHOOTING BOARD.—An external fence or
guide used in shooting or planing the edges of
boards, in which the piece to be planed is narrower
than the face of the plane. The annexed figures

Fig. I. Fig. 2.

are sections of shooting boards, fig. 1 being used
for a rectangular joint, and fig. 2 for a mortise
joint. In both figures, a is a piece of board on
which the plane e lies on its side, and l>, another
piece on which the board to be planed, d, is laid,
c is a stop against which the edge of the wood is
pressed. There are many other forms of shooting
boards.

SHORE.—A piece of timber or other material
placed in such a manner as to prop up a wall or
other heavy body.— I)eacl-shore, an upright piece
fixed in a wall that has been cut or broken through
for the purpose of making some alterations in the
building.

SHOULDER.—Among artificers, a horizontal
or rectangular projection from the body of a thing.
—Shoulder of a tenon, the plane transverse to the
length of a piece of timber from which the tenon
projects. It does not, however, always lie in the
plane here defined, but sometimes lies in different
planes. See p. 147.

SHOULDERING.—In slating, afilletof haired
lime laid under the upper edge of the smaller and
thicker kind of slates, such as those of Argyleshire,
to raise them there and prevent their being open

INDEX AND GLOSSARY.

SHREDDINGS

at the overlap, and also to make the joint weather-
tight.

SHREDDINGS.—In old buildings, short, light
pieces of timber, fixed as bearers below the roof,
forming a straight line with the upper side of the
rafters.

SHRINE.—1. A reliquary, or box for holding
the bones or other remains of departed saints. The
primitive form of the shrine was that of a small
church with a high-ridged roof, and similar to the

Portable Shrine, Malmesbury Abbey.

hog-backed tombs of the ancient Greeks, still seen
in Anatolia. Hence,—2. A tomb, of shrine-like
configuration ; and,—3. A mausoleum of a saint,
of any form ; as the shrine of St. Thomas a Becket
at Canterbury.

SHUTTERS. — The boards which close the
aperture of a window. The shutters of principal
windows are usually in two divisions or halves, each
subdivided into others, so that they may be received
within the boxings into which the shutters are
folded or fall back. The front shutter is of the
exact breadth of the boxing, and also flush with it;
the others, which are hidden in the boxing, are
somewhat less in breadth, and are termed backfolds
or backjlaps. Shutters, as above defined, may be
considered as the doors of window openings, and
are formed upon the same principles as doors, but
sometimes in place of being hinged to fold back,
they are suspended and counterbalanced like win¬
dow-sashes, so as to slide; and they are also made
of laths jointed together and wound round a roller
placed either horizontally above the soffit, or verti¬
cally at the side of the opening. See p. 188.

SHUTTERS.—Linings for. p. 188.

SIBARY. See Severey.

SICAMORE. See Sycamore.

SIDE-HOOK.—In joinery, a rectangular pris¬
matic piece of wood, with a projecting knob at the
ends of its opposite sides. The use of the side-hook
is to hold a board fast, its fibres being in the direc¬
tion of the length of the bench, while the workman
is cutting across the fibres with a saw or grooving-
plane, or in traversing the wood, which is planing
it in a direction perpendicular to the fibres.

SIDE-POSTS.—In architecture, a kind of
truss-posts placed in pairs, each disposed at the
same distance from the middle of the truss, for the
purpose of hanging the tie-beam below. In ex¬
tended roofs, two or three pairs of side-posts are
used. Throughout the text they are called primary
and secondary queen-posts.

SIDE-TIMBERS, Side-Wavers. —The former
is the Somersetshire, and the latter the Lincoln¬
shire local name for purlins.

SIEGE.—The name given in Scotland to the
bench or other support on which a mason places his
stone to be hewn, a term derived from the French.
In England it is termed a banker.

SILL.—The horizontal piece of timber or stone
at the bottom of a framed case; such as that of a
door or window.— Ground sills' are the timbers on
the ground which support the posts and superstruc¬
ture of a timber building.—The word sill is also
used to denote the bottom pieces which support
quarter and truss partitions, and the flat stones
used to form the bottom of a drain are also called
sills.

SILVER FIR.—Properties and uses of, p 118.

SINES, Line of, on the Sector.—Construction
and use of. p. 89.

SINGLE FLOOR, Single Flooring, Single
Joists, Single-joist Floor. —Applied to naked
flooring, consisting of bridging-joists only, p. 150.

SINGLE HUNG.—Applied to a window with
two sashes, when one only is moveable.

SISSOO.—A tree well known throughout the
Bengal presidency, and highly valued on account
of its timber, which furnishes the Bengal ship¬
builders with their crooked timbers and knees. It
is universally employed both by Europeans and
natives of the north-west provinces of India, where
strength is required. It is the Dalbergia sissoo of
botanists, and belongs to the papilionaceous divi¬
sion of the natural order Leguminosce.

SITE.—The position or seat of a building; the
place whereon it stands.

SKETCH.—An outline or general delineation
of anything; a first rough or incomplete draught of
a plan or any design; as the sketch of a building.

SKEW.—A term used in Scotland for a gable¬
coping or factable.

SKEW, or Askew. —Oblique; as a steo-bridge.

SKEW - ARCH.—An arch whose direction is
not at right angles to its axis ; it is also frequently
termed an oblique arch.

SKEW - BACK. — The sloping abutment in
brick-work or masonry lor the ends of the arched
head of an aperture. In bridges, it is the course of
masonry forming the abutment for the voussoirs of
a segmental arch, and in iron bridges it is the abut¬
ment formed for the ribs.

SKEW-BRIDGE.—A bridge in which the
passages over and under the arch intersect each
other obliquely. In conducting a road or railway
through a district in which there are many natural
or artificial watercourses, or in making a canal
through a country in which roads are frequent, such
intersections very often occur. Before the introduc¬
tion of railways skew-bridges were seldom erected,
it being more usual to build the bridge at right
angles, and to divert the course of the road or the
stream to accommodate it. But in a railway, and
sometimes in a canal, such a deviation from the
straight line of direction is often inadmissible, and
it therefore becomes necessary to build the bridge
obliquely.

SKEW-BRIDGES illustrated and described:—

Plate. Page.

Skew-bridge over the river Don, . L. 102
Skew-bridge on the system of M. Somet, L1II. 104
Skew - bridge over the Leith Branch
Railway, near Portobello, . . . LV. 170

SKEW-CORBEL, Skew-Put, Skew-Table.—

A stone built into the bottom of a gable to form
an abutment for the coping.

SKEW-FILLET.—A fillet nailed on a roof
along the gable coping, to raise the slates there
and throw the water away from the joining.

SKIRTING, Skirting-Board. —The narrow
vertical board placed round the margin of a floor.
Where there is a dado this board forms a plinth for I
I its base; otherwise it is a plinth for the room itself, j
See p. 186.

SKIRTING.—Method of scribing, p. 200.

SKY-DRAIN.-—A cavity formed round the i
walls of a building, to prevent the earth from lying
against them and causing dampness, called also
air-drain and dry-drain.

SKY-LIGHT.—A window placed in the top
of a house, or a frame consisting of one or more
inclined planes of glass placed in a roof to light pas¬
sages or rooms below.

SKY-LIGHTS.—To find the length and back¬
ing of an hip, p. 189.

SKY-LIGHTS, Octagonal, Domical, &c.—To
find the ribs, window-bars, &c., p. 190.

SLABS.—The outside planks or boards, mainly
of sap-wood, sawn from the sides of round timber.

SLACK-BLOCKS.—The wedges on which the
centres used in the construction of bridges are sup¬
ported, p. 173, 175.

SLAP-DASH.—A provincial term for rough¬
casting.

SLATE-BOARDING.—Close boarding cover¬
ing the rafters of a roof, on which the slates are
laid. In Scotland, called sacking.

SLATES.—The various sizes of slates are thus
named:—

Doubles,

Ladies,

Countesses,

Duchesses,.

Imperials, .

Queens,

Welsh Longs, or Rags,

ft. in. ft. in.

11x06

13x08

1 8 x 0 10

2 0x10

2 6x20

3 0x20
3 0x20

A square of slating is 100 superficial feet. A square
of Westmoreland or Welsh Rag elating will weigh
10 cwts., and of Duchesses, Countesses, or Ladies
slating 6 cwts.

285

SPAN-ROOF

Squares.

1 ton of Westmoreland Slates will cover 2
1 ton of Welsh Rags . . ,, 11 to 2

1000 Duchess Slates . . ,, *9

1000 Countess Slates . . ,, 6

1000 Ladies Slates . . 3j

1000 Tavistock Slates . . ,, 2^

SLEEPERS.—Pieces of timber on which are
laid the ground joists of a floor, and also, and more
usually, the ground joists themselves. Formerly
the term was used to denote the valley-rafters of a
roof.—In railways, sleepers are beams of wood or
blocks of stone firmly imbedded in the ground to
sustain the rails, which are usually fixed to the
sleepers by means of cast-iron supports called chairs.

SLIDING-RULE.—A mathematical instru¬
ment or scale, consisting of two parts, one of which
slides along the other, and each having certain sets
of numbers engraved on it, so arranged that when
a given number on the one scale is brought to coin¬
cide with a given number on the other, the pro¬
duct or some other function of the two numbers is
obtained by inspection. The numbers may be
adapted to answer various purposes, and slide rules
are made to suit the necessities of the carpenter,
engineer, gauger, &c.

SLIP-FEATHER, p. 182.

SLIT-DEAL.—Fir boards a full half-inch
thick.

SLOP-MOULDING.—In brick-making, that
kind of moulding in which water is used to free the
clay from the mould, in place of the sand used in
pallet-moulding.

SMOOTHING-PLANE. See Plane.

SNECKING.—A peculiar method of building
in rubble-work. See Rubble.

SNIPE’S-BILL PLANE.-—In joinery, a plane
with a sharp arris for forming the quirks of mould¬
ings.

SOCKET-CHISEL.—A chisel made with a
socket; a stronger sort of chisel, used by carpenters
for mortising, and worked with a mallet.

SOCLE.—A flat square member of less height
than its horizontal dimension, serving to raise
pedestals, or to support vases, or other ornaments.
It differs from a pedestal in being without base or
capital. A continued socle is one continued round
a building.

SOFFIT.—The under side of the lintel or ceil¬
ing of an opening; the lower surface of a vault or
arch. It also denotes the under horizontal surface
of an architrave between columns, and the under
surface of the corona of a cornice.

SOFFIT-LINING, p. 188.

SOLAR, Sollar. —A loft; an upper chamber.
See Sollar.

SOLID of Revolution generated by an ogee
curve.—To describe the section of a, p. 69, Plate I.
Fig. 10.

SOLID of Revolution generated by a lancet-
formed curve.—To describe the section of a, p. 69,
Plate I. Fig. 11.

SOLIDS.—Sections of, p. 68.

SOLIDS.—Coverings of, p. 69.

SOLI DUM.—The die of a pedestal.

SOLIVE.—A joist, rafter, or piece of wood,
either slit or sawed. The word is French, and is
sometimes, though rarely used by English writers.

SOLLAR. — Originally an open gallery or
balcony at the top of a house, exposed to the sun ;
but latterly used to signify any upper room, loft, or
garret.

SOMMER. See Summer.

SOUND TIMBER.—Krafft’s mode of judging
of, p. 98.

SOUND-BOARDING. —The sound-boarding
of floors consists of short boards generally, and
preferably, split, not sawn, which are disposed
transversely between the joists, and supported by
fillets fixed to the sides of the joists, for holding the
substance called pugging, intended to preventsound
from being transmitted from one story to another.
See Pugging. In Scotland, sound-boarding is
termed deafening-boarding.

SOUNDING-BOARD, or Sound-Board.—
A board or structure placed over a pulpit or other
place occupied by a public speaker, to reflect the
sound of his voice, and thereby render it more au¬
dible. Sounding-boards are generally flat, and
placed horizontally, but concave parabolic sounding-
boards have been tried, and found to answer better.
See p. 190, and Plate LXXXIII^

SOURCE, Souse.— A support or under prop.

SPAN.— In architecture, an imaginary line
across the opening of an arch or roof, by which its
extent is estimated. See Arch.

SPAN-PIECE.—A name given in some places
to the collar-beam of a roof.

SPAN-ROOF.—A name sometimes given to the
common roofing, which is formed by two inclined

INDEX AND GLOSSARY.

STALLS

SPANDREL

planes or sides, in contradistinction to a shed or
Lean-to.

SPANDREL.—The irregular triangular space
comprehended between the outer curve or extrados
of an arch, a horizontal line drawn from its apex - ,
and a perpendicular line from its springing. In
Gothic architecture, spandrels are usually orna¬
mented with tracery, foliage, &c. See Plate
XXXII. Fig. 5, and Door-head with Spandrels,
under Dripstone.

SP ANDREL-BRACKETING.—A cradlingof
brackets which is placed between curves, each of
which is in a vertical plane, and in the circumfer¬
ence of a circle whose plane is horizontal.

SPANDREL-WALL.—A wall built on the
back of an arch filling in the spandrels.

SPAR.—A small beam or rafter. In architec¬
ture, spars are the common rafters of a roof, as dis¬
tinguished from the principal rafters.

SPECIFICATION.—A statement of particu¬
lars, describing the manner of executing any work
about to be undertaken, and the quality, dimen¬
sions, and peculiarities of the materials to be used.

SPERE.—An old term for the screen across
the lower end of a dining-hall, to shelter the en¬
trance.

SPERYER. — An old term for the wooden
frame at the top of a bed or canopy. Sometimes
the term includes the tester, or head piece. It signi¬
fied originally a tent.

SPHERE, ob Globe, is a solid bounded by a
curved surface, every point of which is equidistant
from a point within it called the centre.—To find
the surface of a sphere, or of any segment or zone
of it. Rule ■: Multiply the circumference of a great
circle of the sphere by the axis, or by the part of it
corresponding to the segment or the zone required:
the product will be the surface.—To find the solid
content of a sphere. Rule: Multiply the cube of the
axis by ’5236.—To find the solid content of a seg¬
ment of a sphere. 1. When the axis and height of
segment are given. Rule: From three times the
axis subtract twice the height, and multiply the re¬
mainder by the square of the height and by '5236.
2. When the height and radius of the base are given.
Rule: To three times the square of the radius add
the square of the height, multiply the sum by the
height, and by '5236. The product is the content.

To find the content of the middle zone of a sphere.
Rule: From the square of the axis or greatest dia¬
meter subtract one-third of the square of the height,
then multiply the remainder by the height and by
'7854.—To find the content of any zone of a sphere.
Rule: Add the square of the radii of the two ends to
one-third of the square of the height, then multiply
the sum by twice the height and by -7854.

SPHERE.—To find the limits of shade on,
and the shadow thrown by a sphere, p. 220.

SPHERE penetrated by a cylinder.—To find
the projections of, p. 64.

SPHERE.—To find the projections of a sphere
penetrated by an oblique scalene cone, p. 64.

SPHERE.—Development of the surface of a
sphere, p. 73.

SPHERE.—To find the projections of a scalene^
cone penetrating a sphere, p. 64.

SPHERE.—Tangent plane to a sphere, p. 61.

SPHERE.—To construct the sections of a
sphere by a plane, p. 60.

SPHERE.—To describe the section of a sphere,
p. 68, Plate I. Fig. 7.

SPHERE, The.—Development of, p. 72.

SPHERICAL BRACKETING.—Brackets so
formed, that the face of the lath-and-plaster work
which they support makes a spherical surface.

SPHERICAL PENDENTIVES.—To cover
the ceiling of a room with, p. 80.

SPHERICAL \ AULT.—To determine the
heights of the divisions of a, p. 83.

SPHERO - CYLINDRIC GROIN. — One
formed by the intersection of a cylindrical vault
with a spherical vault of greater dimensions. See
p. 77.

SPHEROID.—A body or figure approaching
to a sphere, but not perfectly spherical. In geo¬
metry, a spheroid is a solid, generated by the revo¬
lution of an ellipse about one of its axes. When the
generating ellipse revolves about its longer or major
axis, the spheroid is oblong or prolate; when about
its less or minor axis, the spheroid is oblate. The
earth is an oblate spheroid, that is, flattened at the
poles, so that its polar diameter is shorter than its
equatorial diameter.

SPHEROIDAL BRACKETING.—Bracket¬
ing which has a spheroidal surface.

SPINDLE, Circular. — A circular spindle is
the solid generated by the revolution of a segment
of a circle about its chord.—To find the solid con¬
tent of a circular spindle. Rule: Multiply the area
of £he generating segment by half the central dis¬

tance, and subtract the product from one-third of
the cube of half the length of the spindle, then four
times the remainder multiplied by 3'1416 will give
the content.

SPIRE.—The pyramidal or conical termination
of a tower or turret. The earliest spires were merely
pyramidal or conical roofs, specimens of which still
exist in Norman buildings, as that of the tower of
Than Church in Normandy. These roofs, becoming
gradually elongated, and more and more acute, re¬
sulted at length in the elegant tapering spire; among
the many existing examples of which, probably,
that of Salisbury is the finest. In mediaeval archi¬
tecture, to which alone they are appropriate,
spires are generally square, octagonal, or circular
in plan; they are sometimes solid, more frequently
hollow, and are variously ornamented with bands
encircling them, with panels more or less enriched,
and with spire lights, which are of infinite variety.
Their angles are sometimes crocketted, and they
are almost invariably terminated by a finial. In
the later styles the general pyramidal outline is ob¬
tained by diminishing the diameter of the building
in successive stages, and this has been imitated in
modern spires, in which the forms and details of
classic architecture have been applied to structures
essentially mediaeval. The term spire is sometimes
restricted to signify such tapering buildings, crown¬
ing towers or turrets, as have parapets at their base.
When the spire rises from the exterior of the wall
of the tower without the intervention of a parapet,
it is called a broach.

SPIRE-LIGHTS.—The windows of a spire.

SPIRIT-LEVEL.—An instrument employed
for determining a line or plane parallel to the hori¬
zon, and also the relative heights of ground at two
or more stations. It consists of a tube of glass
nearly filled with spirit of wine or distilled water,
and hermetically sealed at both ends; so that when
held with its axis in a horizontal position, the bubble
of air which occupies the part not filled with the
liquid rises to the upper surface, and stands exactly
in the middle of the tube. The tube is placed within
a brass or wooden case, having a long opening on
the side which is to be uppermost, so that the posi¬
tion of the air-bubble may be readily seen. When
the instrument thus prepared is laid on a horizontal
surface, the air-bubble stands in the very middle of
the tube; when the surface slopes, the bubble rises
to the higher end. It is used by carpenters and
joiners for ascertaining whether the upper surface
of any work be horizontal. When employed in sur¬
veying, it is attached to a telescope, the telescope
and tube being fitted to a frame or cradle of brass,
which is supported on three legs.

SPLAY.—A sloped surface, or a surface which
makes an oblique angle with another; as when the

Plan Section of Gothic Window.
A A, The internal Splay.

opening through a wall for a door, window, &c.,
widens inwards. A large chamfer is called a splay.

SPOKE-SHAVE.-—A sort of small plane used
for dressing the spokes of wheels and other curved
work, where the common plane cannot be applied.

SPOON-BIT.—A hollow bit with a taper point
for boring wood.

SPRING BEVEL of a Rail.— The angle
which the top of the plank makes with a vertical
plane which has its termination in the concave side,
and touches the ends of the rail-piece. See p. 203.

SPRING COMPASSES.—Instructions in the
use of, p. 31.

SPRINGER.—The point where the vertical
support of an arch terminates, and the curve begins.
The lowest of the series of voussoirs of which an
arch is formed, being the stone which rests imme¬
diately upon the impost. See woodcut, Arch. The
bottom stone of the coping of a gable is sometimes
called a springer.

SPRINGING.—The point from which an arch
springs or rises.— Springing course, the horizontal
course of stones from which an arch springs orrises.
—In carpentry, in boarding a roof, the setting the
boards together with bevel joints, for the purpose of
keeping out the rain.

SPRUCE.—Description and uses of, seep. 117.

SPUR.—Often used as a synonyme for strut.

SQUARE.—To construct a square, the sides of
which shall be equal to a given straight line, Prob.
XXV. p. 9.- To describe a square equal to a given
rectangle, Prob. XXVL p. 9.—To describe a square
equal to two given squares, Prob. XXIX. p. 10.—

28 (i

To describe a square equal to any number of given
squares, Prob. XXX. p. 10.—To describe a square
equal to the difference between two unequal squares,
Prob. XXXI. p. 10.—To describe a square equal
to any portion of a given square, Prob. XXXII.
p. 10.—To describe a square about a given circle,
Prob. XLVII. p. 14.—To describe a square equal
to a given circle, Prob. LXXV. p. 20, and Prob.
LXXVI p. 20.

SQUARE FRAMED.—In joinery, a work is
said to be square framed or framed square, when
the framing has all the angles of its styles, rails,
and mountings square without being moulded.

SQUARE FRAMING, p. 185.

SQUARE SHOOT.—A wooden trough for dis¬
charging water from a building.

SQUARE STAFF.—A square fillet used as an
angle-staff in place of a bead-moulding, in rooms
that are prepared for papering.

SQUARING a Handrail. —The method of
cutting a plank for a rail to a staircase, so that all
the vertical sections may be rectangular.

SQUARING of Timber. — Methods usually
adopted, p. 99.

S Q U I N C H.—The small pendentive arch
formed across the angle of a square tower, to sup¬
port the side of a superimposed octagon. The

Squincli, Maxstokc Priory, Warwickshire.

application of the term to these pendentives may
have been suggested by their resemblance to a corner
cupboard, which was also called a squincli or sconce.

SQUINT.—In mediaeval architecture, a name
given to an oblique opening in the wall of a church.
Squints were generally so placed as to afford a view
of the high altar from the transept or aisles.

STACK of Wood. —A pile containing 108 cubic
feet.

STAFF-ANGLE. See Square Staff.

STAFF-BEAD See Angle-Bead.

STAGE.—The part between one sloping projec¬
tion and another, in a Gothic buttress. Also, the
horizontal division of a window separated by tran¬
soms. Sometimes the term is used to signify a
floor, a story.

STAIR.—A step, but generally used in the
plural to signify a succession of steps, arranged as
a way between two points at different heights in a
building, &c. A succession of steps in a continuous
line is called a flight of stairs; the termination of
the flight is called a landing. Stairs are further
distinguished by the various epithets, dog-legged,
newelled, open newelled, &c.

STAIRCASE.—The building or apartment
which contains the stairs, see p. 196.

STAIRS and Handrailing. — Introductory
remarks, p. 195.

STAIRS.—Simple contrivances as substitutes
for stairs, p. 195.—Contrivances for economizing
space in stairs, p. 195.

STAIRS.—Definitions of terms, p. 196.

STAIRS.—Method of laying down the plan of:

As applied to dog-legged stairs, . . 198

As applied to newel stairs, . . . 198

As applied to geometrical stairs, . . 199

As applied to elliptical stairs, . . . 199

STAIRS. — Method of setting out when the
building is erected, or its general plan understood,
p. 196.

STAIRS.—Methods of lessening the inequality
of width between the ends of the winding steps by
calculation, and also graphically, p. 199.-—Forma¬
tion of carriages for various kinds of stairs, p.
199 200.

STAKE-FALD HOLES.—A local name for
putlog holes.

STALLS.—Fixed seats, inclosed either wholly
or partially at the back and sides.—The choir or
chancel of a cathedral, collegiate church, and even
of most small churches, had, previous to the Refor¬
mation, one or more ranges of wooden stalls at its
west end, the seats of which were separated from

STANCHION

INDEX AND GLOSSARY.

SUBSELLIA

each other by large projecting elbows. The stalls
were often enriched by panelling, and surmounted
by canopies of tabernacle work, enriched with

Stalls, Higham Ferrers Church, Northamptonshire.

crochets, pinnacles, &c. Many beautiful examples
of these yet remain.

STANCHION.-—-A prop or piece of timber
giving support to one of the main parts of a roof;
also, one of the upright bars, wood or iron, of a
window, screen, railing, &c.

STANDARD.—In joinery, any upright in a
framing, as the quarters of partitions, the frame of
a door, and the like.

STANZA.—An apartment or division in a
building.

STARLINGS, or Sterlings. —An assemblage
of piles driven round the piers of a bridge to give
them support. They are sometimes called stills.

STEENING, or Steaning. — The brick or
stone wall, or lining of a well or cess-pool, the use
of which is to prevent the irruption of the sur¬
rounding soil.

STEEPLES, Towers, and Spires of Timber.
—Construction of, described p. 145, 146, and illus¬
trated in Plate, XXXV., XXXVa, and XXXVI.

STEP. — One of the gradients in a stair; it is
composed of two fronts, one horizontal, called the
tread , and one vertical, called the riser.

STEREO BATE.—Thesame as stylobate (which
see).

STEREOGRAPHY.—The act or art of de¬
lineating the forms of solid bodies on a plane; a
brand i of solid geometry which shows the construc¬
tion of all solids which are regularly defined. See
p. 46.

STEREOTOMY.—A branch of stereography,
which teaches the manner of making sections of
solids under certain specified conditions.

STICKING.—The operation of forming mould¬
ings by means of a plane, in distinction from the
operation of forming them by the hand.

STILTED ARCH.—A term applied to a form
of the arch used chiefly in the twelfth century. In

Stilted Arch.

this form the arch does not spring immediately
from the imposts, but is raised as it were upon stilts
for some distance above them.

STINK-TRAP.—A contrivance to prevent the
passage of noxious vapours from sewers and drains.

Section of Drain-trap.

It is variously formed. The figure shows one of
the forms commonly used.

STIRRUP PIECE.—A name given to a piece
of wood or iron in framing, by which any part is
suspended; a vertical or inclined tie.

STOCK and Bits. See Brace and Bits.

STOCKHOLM TIMBER. See Pinus syl-
vestris, p. 116, 117.

STOOTHING.—A provincial term for batten¬
ing.

STOPS.—In joinery, pieces of wood nailed on
the frame of a door to form the recess or rebate into
which the door shuts.

STORY.—A stage or floor of a building, called
in Scotland a flat; a subdivision of the height of a
house; or a set of rooms on the same floor or level.
A story comprehends the distance from one floor to
another; as a story of nine, ten, twelve, or sixteen
feet elevation. Hence each floor terminating the
space is called a story; as a house of one story, of
two stories, of five stories. In the United States,
the floor next the ground is the first story; in
France and England this is called the ground-floor,
and the second from the ground is called the first
floor or story.

STORY-POSTS.—Upright posts to support a
floor or superincumbent wall, through the medium
of a beam placed over them.

STORY - ROD.—A rod used in setting up a
staircase, equal in length to the height of a story
of a house, and divided into as many parts as there
are intended to be steps in the stair, so that the
steps may be measured, and distributed with ac¬
curacy. See p. 196.

S TOUP. — A basin for holy water, usualiv
placed in a niche at the entrance of Roman Catholic

Stoup, Maidstone Church, Kent.

churches, into which all who enter dip their fingers
and cross themselves.

STRAIGHT ARCH.—The term is usually and
properly applied to an arch over
an aperture in which the in-
trados is straight. An arch
consisting of straight lines and
a pointed top, comprising two
sides of an equilateral triangle,
is also called a straight arch.

STRAIGHT - EDGE. - In Straight Arch '
joinery, a slip of wood made
perfectly straight on the edge, and used to ascer¬
tain whether other edges are straight, or whether
the face of a board is planed straight. It is made
of different lengths, according to the required mag¬
nitude of the work. Its use is obvious, as its ap¬
plication will show whether there is a coincidence
between the straight-edge and the surface or edge
to which it is applied. It is also used for drawing
straight lines on the surface of wood. See Winding
Sticks, p 44.

STRAIGHT-JOINT FLOOR, p. 185.

STRAIGHT LINE.—To bisect a straight line,
Prob. IX. p. 7.—To divide a straight line into any
number of equal parts, Prob. X. p. 7.—To find the
shadow of a straight line inclined to the horizontal
plane, p. 211.—To find the shadow of a straight
line inclined to two planes, p. 212.—To find the
shadow of a straight line intercepted by a plane in¬
clined to the plane of projection, p. 212.—To de¬
termine the shadow of a straight line on the hori¬
zontal plane, p. 213.—To determine the shadow of a
straight line on the vertical plane, p 214.—Shadow
thrown by a straight line on a curved surface,
p. 214.

STRAIGHT STAIRS, p. 196.

STRAIN and Strength of Materials.
p. 123.

STRAINING PIECE.—A beam placed be¬
tween two opposite beams to prevent their nearer
approach; as rafters, braces, struts, &c. If such a
piece performs also the office of a sill, it is called a
straining sill.

STRAINING PIECES in a partition. Plate
XLV. Fig. 1, h; Fig. 2, No. 2, /; Fig. 3, No. 1,
/, p- 155.

STRAP.—In carpentry, an iron plate placed
across the junction of two timbers for the purpose

287

of securing them together. See Plates XXVII.-
XXIX., and p. 146.

STRENGTH and Strain of Materials.
p. 123.

STRETCHED OUT.—In architecture, a term
applied to a surface that will just cover a body so
extended that all its parts are in a plane, or may
be made to coincide with a plane.

STRETCHER.—A brick or stone laid hori¬
zontally with its length in the direction of the face
of the wall. It is thus distinguished from a header,
which is laid lengthwise across the thickness of the
wall, so that its head or end is seen in the external
face of the wall.

STRETCHING COURSE. — A course of
stretchers ; that is, of stones or bricks laid hori¬
zontally with their lengths in the direction of the
face of the wall. See Heading Course.

STRIKE-BLOCK.—A plane shorter than a
jointer, used for shooting a short joint.

STRIKING.—In architecture, the drawing of
lines on the surface of a body; the drawing of lines
on the face of a piece of stuff for mortises, and cut¬
ting the shoulders of tenons. In joinery, the act
of running a moulding with a plane.— The striking
of a centre is the removal of the timber framing,
upon which an arch is built after its completion.

STRIKING CENTRES, p. 175.

STRING - BOARD, String-Piece, or
Stringer.— A board placed next to the well-
hole in wooden stairs, and terminating the ends of
the steps.

STRING - COURSE. — A narrow moulding
or projecting course continued horizontally aloDg
the face of a building, frequently under windows.
It is sometimes merely a flat band.

STRING S.—Formation of, by various methods,

p. 200, 201.

STRINGS in staircases, p. 196.

STRUT.—Any piece of timber in a system of
framing which is pressed or crushed in the direction
of its length.

STRUTS.—In flooring, short pieces of timber
about lg inch thick, and 3 to 4 inches wide, inserted

between flooring joists sometimes diagonally, as in
the figure, to stiffen them. See p. 151, and illus¬
trations of various modes of strutting, Plate XLII.

STRUTS and Ties. — To find whether a
piece of timber in a system of framing is acting as
a strut or a tie. p. 122.

STRUTTING BEAM, Strut-Beam.—A n old
name for a collar-beam.

STRUTTING-PIECE.—The same as strain¬
ing-piece.

STUB-MORTISE.-—A mortise which does not
pass through the whole thickness of the timber.

STUCCO.—A word applied as a general term
to plaster of any kind, used as a coating for walls,
and to give them a finished surface. The third
coat of three-coat plaster, consisting of fine lime and
sand, is termed stucco ; it is floated and trowelled.
There is a species called bastard stucco, in which a
small portion of hair is used. It is merely floated
and brushed with water.

STUCK MOULDINGS.—In joinery, mould¬
ings formed by planes, instead of being wrought by
the hand.

STUDS.—In carpentry, posts or quarters
placed in partitions, about a foot distant from each
other.

STUDWORK.—A wall of brick-work built
between studs.

STUMP-TENON, p. 182.

STYLE. See Stile, and p. 186.

STYLOBATE.—In architecture, in a general
sense, any sort of basement upon which columns
are placed to raise them above the level of the
ground or floor; but in its technical sense, it is ap¬
plied only to a continuous unbroken pedestal, upon
which an entire range of columns stand, contradis¬
tinguished from pedestals, which are merely de¬
tached fragments of a stylobate placed beneath each
column.

SUBPLINTH.—A second and lower plinth
placed under the principal one in columns and
pedestals.

SUBSELLIA.—The small shelving seats in the
stalls of churches or cathedrals, made to turn up
upon hinges so as to form either a seat, or a form

INDEX AND GLOSSARY.

SUMMARY

TILE-CREASING

to kneel upon, as occasion required. They are still
in constant use on the Continent, though compara-

Subsellia, All-Souls, Oxford, tho seat turned up.

ti vely seldom used in England. They are also called
misereres.

SUMMARY of rules for calculating the strength
of timber, p. 130.

SUMMER.—1. A large stone, the first that is
laid over columns and pilasters. The first voussoir
of an arch above the impost.—2. A large timber
supported on two stone piers or posts, serving as a
lintel to an opening.—3. A large timber or beam
laid as a bearing beam ; a girder.

SUMMERINGS, Summer Tree. The same
as summer (which see).

SUNDSYALL TIMBER. See Pinus sylves-
TRIS, p. 116, 117.

SUPERCILIUM.—In ancient architecture,
the upper member of a cornice. It is also applied
to the small fillets on each side of the scotia of the
Ionic base.

SURBASE.—The crowning moulding or cornice
of a pedestal; a border or moulding above the
base; as the mouldings immediately above the base
of a room.

SURBASED.—Having a surbase, or moulding
above the base.

SURBASED ARCH.—An arch whose rise is
less than the half-span.

SURBASEMENT.—The trait of any arch or
vault which has the form of a portion of an ellipsis.

SURFACES of double curvature. — Develop¬
ment of, p. 72.

SUSPENDED or Hung Sashes, p. 187.

SWEDISH TIMBER. See Pinus sylvestris,
p. 116, 117.

SWEEPS and Variable Curves, p. 44.

SWELLING of the Shaft of a Column. See
Entasis.

SYCAMORE, The.—Description of the pro¬
perties and uses of, p. 113.

SYSTYLE. — An intercolumniation of two
diameters.

T SQUARE.—Construction of, and mode of
using, described, p. 43.

TABBY.—A mixture of lime with shells,
gravel, or stones in equal proportions, with an equal
proportion of water, forming a mass, which, when
dry, becomes as hard as rock. This is used in
Morocco instead of bricks for the walls of buildings.

TABLE.—Found in its compounds grass-tabic,
ground-table, earth-table , factable.

TABLE of the Properties of Timber, p. 133.

TABLET. —A term used by Rickman to denote
projecting mouldings and strings, among which he
includes the cornice and drip-stones.

TABLING. — 1. A term sometimes used in
Scotland to designate the coping of the walls of
very common houses. — 2. The indenting of the
ends of the piece forming a scarf, so that the joint
will resist a longitudinal strain. See illustration to
Scarf.

TH3NIA, Tenia. — The band or fillet which
separates the Doric frieze from the architrave.

TAIL IN.—To fasten anything by one of its
ends into a wall.

TAIL TRIMMER.—A trimmer next to the
wall, into which the ends of joists are fastened to
avoid flues.

TAKING DIMENSIONS.—The manner of,
p. 67.

TALON. —The French term for the ogee
moulding.

TALUS.—A slope or inclined plane.

TAMBOUR.—1. A term applied to the naked
part of Corinthian and Composite capitals, which
bears some resemblance to a drum. It is also called
the vase, and campana, or the bell. Also, the wall
of a circular temple surrounded with columns, and
the circular vertical part of a cupola.—2. A cylin¬
drical stone, such as one of the courses of the shaft
of a column.

TANG.—The part of chisels and similar tools
inserted in the handle.

TANGENT PLANE.—To right and oblique
cylinders, p. 60, 61.—To a cone, p. 61.—To a
sphere, p. 61, 62.

TANGENT PLANES to curved surfaces,

p. 60.

TANGENTS, The line of, on the Sector.—
Construction and use of, p. 39.

TAN GENTS. — Logarithmic line of, on the
Sector, p. 41.

TAPER SHELL-BIT.—A species of boring-
bit used by joiners. It is conical both within and
without, and its horizontal section is a crescent, the
cutting edge being the meeting of the interior and
exterior conical surfaces. Its use is for widening
holes in wood.

TASSELS.—Pieces of board which tie under
the ends of the mantel-tree ; called also torscls.

TAXIS.—In ancient architecture, a term used
to signify that disposition which assigns to every
part of a building its just dimensions. It is syno¬
nymous with ordonnance in modern architecture.

TEAK.—Properties and uses of, p. 112.

TEAZE TENON.—A tenon on the top of a
tenon, with a double shoulder and tenon from each,
for supporting two level pieces of timber at right
angles to each other.

TELAMONES.—Figures of men employed as
columns or pilasters to support an entablature, in
the same manner as Caryatides. They were called
Atlantes by the Greeks. See Atlantes.

TEMPLATE.—A short piece of timber laid
under the end of a beam or girder, resting on a wall,
particularly in brick buildings, to distribute the
weight over a large space.

TEMPLET.— A pattern or mould used by
masons, machinists, smiths, shipwrights, &c., for
shaping anything by. It is made of tin or zinc
plate, sheet-iron, or thin board, according to the
use to which it is to be applied.

TENON.—The end of a piece of wood cut into
the form of a rectangular prism, which is received
into a cavity in another piece, having the same
shape and size, called a mortise. It is sometimes
written tenant. See Mortise, and p. 147.

TENON SAW (often corruptly called tenor saw).
—A small saw with a brass or steel back, used for
cutting tenons.

TENONING MACHINE.—Furness’, p. 193.

TEREDO NAYALIS, fatally injurious to
timber, p. 105.

TERMINUS.—A pillar statue; that is, either
a half statue, or bust, not placed upon, but incor¬
porated with, and, as it were, immediately springing
out of, the square pillar which serves as its pedestal.

Terminal Statue of Tan. Antique Terminal Bust.

The pillar part is generally made to taper down¬
wards, or made narrower at its base than above.
Termini are employed, not as insulated pillars, but
as pilasters, forming a small order or attic, or a
decoration to gateways, doors. &c.

TETRAEDRON. See Tetrahedron.

TETRAGON.—A figure having four angles.

TETRAHEDRON, Tetraedron. —One of the

288

five regular solids. It is bounded by four equilateral
triangles.—To find its surface. Rule : Multiply
the square of its linear side by 1'7320508.—To find
its solidity. Rule: Multiply the cube of its linear
side by 0 1178511.

TETRAHEDRON.—The horizontal projection
of a tetrahedron being given, to find the vertical
projection, p. 52.—A point in one of the projections
of a tetrahedron being given, to find the point in
the other projection, p. 52.

TETRAHEDRON.—To find the projection of
the section of a tetrahedron cut by a plane, p. 52.

TETRAHEDRON.—To find the projections of
a tetrahedron when inclined to the horizontal plane,
p. 53.

THOLE, Tholus. —In ancient architecture, a
dome or cupola; any circular building.

THOLOBATE.—In architecture, the substruc¬
ture on which a dome rests.

THREE-COAT WORK.—Plastering which
consists of pricking up or roughing in, floating, and
a finishing coat.

THROAT.—A channel or groove worked in
the projecting part of the under side of a string¬
course, coping, &c., to throw off the water and pre¬
vent it running inwards towards the wall.

THROUGH STONE.—Abond stone orheader.

TIE.—In architecture, a timber-string, chain,
or a rod of metal connecting and binding two bodies
together which have a tendency to separate or
diverge ; such as Ge-beams, diagonal ties, truss-
posts, &c.— Angle-tie, angle-brace. See under
Angle.

TIE-BEAM.—The beam which connects the
feet of a pair of principal rafters, and prevents
them from thrusting out the wall See Roof.

TIE-ROD.—The dimensions of iron tie-rods for
roofs of various spans, assuming the angle of in¬
clination of the principals at 30°, are given by Mr.
W. E. Tarn as follows:—

Span

Strain on

Diameter

in feet.

Tie-rod in lbs.

rod in inch

20 .

. 6,600 .

. i

25 .

. 8,250 .

. i

30 .

. 9,900 .

.i*

40 .

. 13,200 .

. H

50 .

. 16,500 .

. H

60 .

. 19,800 .

.i.j

70 .

. 23,100 .

. is

80 .

. 26,400 .

. i*

90 ) .

. 29,700 ).

.i 17

100 } .

. 33, 000 I .

.} 1J

TIGE.—The shaft of a column.

TILE.—A kind of thin brick or plate of baked
clay, used for covering the roofs of buildings, and
occasionally for paving floors, constructing drains,
&c. The best qualities of brick-earth are used for
making tiles, and the process is similar to that of
brickmaking. Roofing tiles are chiefly of two sorts.
plain tiles and pan-tiles. (See these terms.)—Tilts
of a semicylindrical form, laid in mortar, with their
convex or concave sides uppermost, respectively, are
used for covering ridges and gutters — Paving-tiles
are usually of a square form, and thicker than those
used for roofing. A fine kind was made in former
times, and used for paving the floors of churches
and other important buildings. They were gene¬
rally of two colours, and ornamented with a variety
of elegant devices. They were highly glazed, and
are often called encaustic tiles. They are also some-

Ornamental raving Tiles.

1 and 3 Ilaacombe, Devonshire. 2. ‘Woodperry, Oxon. 4. Wherewell,
Hants.

times, though erroneous!}', called Norman tiles,
for they belong to a much later period than the
Norman era. Encaustic tiles, of beautiful forms
and colours, have been again introduced.— Dutch,
tiles, for chimneys, are made of a whitish earth,
glazed, and printed or painted with various figures.
They are now seldom used.

TILE-CREASING.—Two rows of plain tiles
placed horizontally under the coping of a wall, and
projecting about 1J inch over each side, to throw
off the rain-water.

INDEX AND GLOSSARY.

TILIA

TILIA, Lime Tree. p. 113.

TILING.—A square of tiling is equal to 100
superficial feet.

768 plain tiles, 6-inch gauge, will cover 1 square.

665 ,, 7 ,, ,, ,, 1 ,,

676 ,, 8 ,, ,, ,, 1 ,,

180 pan-tiles, 10 ,, ,, ,, 1 ,,

A plain tile is 104 inches long, 6J inches wide,

| inch thick, and weighs 2 lbs. 5 oz.

A pan-tile is 134 inches long, 94 inches wide, 4 inch
thick, and weighs 74 lbs.

It takes 1 bundle of laths for 1 square of either
plain or pan-tiling

700 plain tiles weigh 14 cwts.

180 pan-tiles weigh 74 cwts.

TILTING-FILLET.—A Chamfered fillet of
wood laid under slating where it joins to a wall, to
raise it slightly, and prevent the water from enter¬
ing the joint.

TIMBER.—1. That sort of wood which is
squared, or capable of being squared, and fit for
being employed in house or shipbuilding, or in car¬
pentry, joinery, &c. We apply the word to stand¬
ing trees which are suitable for the uses above
mentioned, as a forest contains excellent timber;
or to the beams, rafters, boards, planks, &c., hewed
or sawed from such trees. But in the language of
the customs, when a tree is sawn into thin pieces,
not above 7 inches broad, it is called batten ; when
of greater breadth, such thin pieces are called deal.
Timber is generally sold by the load. A load of
rough or unhewn timber is 40 cubic feet, and a load
of squared timber 50 cubic feet. In regard to
planks, deals, &c., the load consists of so many
square feet: thus, a load of 1 inch plank is 600
square feet. The most useful timbers of Europe
are the oak, the ash, the Scotch pine, the larch, and
the spruce fir; those of North America are the hic-
cory, the different species of pine, and some species
of oak ; those of tropical countries are the teak tree,
the different species of bamboo, and the palm.
Wood is a general term, comprehending under it
timber, dye-woods, fancy woods, fire-wood, &c.,
but the word timber is often used in a loose sense
for all kinds of felled and seasoned wood.—2. The
body or stem of a tree.—3. A single piece or squared
stick of wood for building, or already framed ; one
of the main beams of a fabric.

TIMBER.—Felling of, p. 98; Squaring of, p.
99; Table of the properties of, p. 133; Manage¬
ment of, after it is cut, p. 100; Bending of, p. 102;
Seasoning of, p. 104. — Processes for preserving,
]>. 104-109; Kyan's, p. 106; Burnett’s, p. 106;
Margery’s, p. 106; Payne's, p. 106; Boutigny’s and
Hutin’s, p. 107; Boucherie’a, p. 107; Bethell’s, p.
107.

TIMBER BRICK.—A piece of timber of the
size and shape of a brick, inserted in brick-work to
attach the finishings to.

TIMBER BRIDGES illustrated and described.
Plates XLVIII.-LVI., p. 158.

TIMBER BRIDGES.—Analysis of the forms
of, p. 161.

TIMBER BRIDGES.—To find the strains on
the various component parts of, p. 160.—Method
of finding the strains on the various parts of, prac¬
tically exemplified in Mr. Haupt’s analysis of the
strains in Sherman’s Creek bridge, p. 166-169.

TIMBER HOUSES, p. 156.

TIMBER HOUSES.—Mode of construction
followed in Sweden, p. 156, 157-

TIMBERS fit for the Carpenter. —Char¬
acteristics of, p. 97.

TIN-SAW.—A kind of saw used by bricklayers
for sawing bricks.

TOO-FALL, or To-Fall.—A term used as
synonymous with lean-to.

TOOLING.—In stone cutting, a more perfect
description of work than Random-Tooling (which
see). In tooling, in place of working a draught from
end to end of the stone, the workman, by moving
his chisel laterally its own
width at every stroke, forms
a continuous flute across the
stone. He thus works the
flutes in successive lines,
from an eighth to a quarter
of an inch wide. Tooling is
difficult to perform well, and
unless well done it is very
unsightly.

TOOTH-ORNAMENT.

-—One of the peculiar marks
of the Early English period
of Gothic architecture. It
consists of a pyramid, hav¬
ing its sides partially cut
out, so as to have the resemblance of an inverted
flower. It is generally inserted in the hollow
mouldings of doorways, windows, &c.

TOOTHING.—Bricks or stones left projecting j
at the end of a wall, that they may be bonded into
a continuation of it when required; also, a tongue
or series of tongues.

TOOTHING PLANE.—A plane, the iron of
which, in place of being sharpened to a cutting edge,
is formed into a series of small teeth. It is used
to roughen a surface intended to be covered with
veneer or cloth, in order to give a better hold to the
glue.

TOP BEAM. —The same as Collar-Beam.

TOP RAIL.—The highest rail in a piece of
framing.

TORCH, v. —In plastering, to point the inside
joints of slating laid on lath with lime and hair.

TORSELS.—The pieces of timber lying under J
the mantel-tree. They are otherwise called tassels.

TORUS.-—A large moulding used in the bases
of columns. Its section is semicircular, and it
differs from the astragal only in size, the astragal
being much smaller. It is sometimes written tore.
See woodcut, Column.

TORUS MOULDING.—To describe the, p.

180.

TOTE.—The handle of a plane.

TOUCH-STONE.—A black, smooth stone, or
marble; so called from its employment in testing
the quality of the precious metals, by the marks
they leave when rubbed upon its surface. This
sort of marble was extensively used in the sixteenth
and seventeenth centuries for tombs. Henry
Seventh’s will directed that his tomb should be
made “ of the stone called touclie .”

TOWER.—Alofty building, of a square, round,
or polygonal form, consisting often of several
stories, and either isolated or connected with other
buildings. Towers may be classified according to
their uses for defence, as monuments, or as attached
to churches. Among the first are the donjons, and I
the towers which form part of the inclosures of
castles, walled cities, towns, &c. Belonging to the
second class are the round towers met with in
Ireland, &c. But the greatest variety is to be
found in the third class, the towers of cathedrals
and churches of the middle ages. The towers be¬
longing to the period of Saxon architecture are
square and massive; those of the Norman style
are sometimes round, but are generally square, and
of rather low proportions, seldom rising much more
than their own breadth above the roof of the
church. In the Early English style there is a
greater variety of design and proportion, and in
the Decorated style this diversity is still greater.
The magnificent church towers of the Perpendicu¬
lar style form one of its leading beauties. These
towers are seen in the greatest pe; fection in
Somersetshire and the neighbouring counties. They
are usually divided into stages by bands of quatre-
foils, each stage being filled with large windows,
frequently double. The angles have large but¬
tresses, often ornamented with shafts and niches.
The parapet is panelled and pierced, having lofty
panelled and crocheted pinnacles at the angles,
and lesser ones in the intermediate spaces. The
towers of St. Mary's, Taunton, St. John’s, Glas¬
tonbury, and St. Stephen's, Bristol, may be taken
as the best types of this kind of tower. Many
towers are finished with lofty spires, usually croch¬
eted; and some by an octagonal stage, called a
lantern, as at Boston, Fotheringay, and Newcastle-
upon-Tyne.

TRABEATION.—The same as entablature.

TRACERY.—That species of pattern work,
formed or traced in the head of a Gothic window,
by the mullions being there continued, but diverg¬
ing into arches, curves, and flowing lines, enriched
} with foliations. Also, the subdivisions of groined
| vaults, or any ornamental design of the same char-
j acter, for doors, panelling, or ceilings.

TRACING PAPER.—Preparation of, p. 42.

TRAMMELS.—Elliptic compasses, an instru¬
ment for drawing ovals, used by joiners and other
artificers. See p. 23.

TRANSEPT.—The transverse portion of a
church built in the form of a cross ; that part which
is placed between the nave and choir, and extends
beyond the sides of the area which contains these
divisions, forming the short arms of the cross, upon
which the plan is laid out. See woodcut, Ca¬
thedral.

TRANSOM.—A horizontal bar of stone or tim¬
ber across a mullioned window, dividing it into
stories ; also, the cross-bar separating a door from
the fanlight above it. See p. 156.
j TRANSOM WINDOW.—A window having
i a cross-piece nr transom.

I TRAPEZIUM.—A plane figure contained by

! four straight lines, none of them parallel.

TRAPEZOID.—A plane figure contained by
! four straight lines, two of them parallel.

280

TRUSS

TREAD.—The horizontal surface of a step.
Sec p. 196.

TREDGOLD’S Rules for Calculating the
Dimensions of Timbers in a Roof. p. 137.

TREENAIL (commonly pronounced trunnel).
—A cylindrical wooden pin.

TREES.—Cultivation of, p. 96.

TREES.—Diseases of, p. 96.

TREES. — When felled, should be preserved
from contact with the soil, and sheltered from the
sun, p. 100.

TREFOIL. — An ornamental foliation much
used in Gothic architecture in the tracery of windows,

Trefoils.

panels, &c. It is of several varieties, but always
consists of three cusps, the spaces inclosed between
them producing a form similar to a three-lobed leaf.

TRIANGLE.—To find the area of, when the
base and perpendicular height are given — Rule :
Multiply the base by the perpendicular height, and
half the product will be the area.—When two sides
and the included angle are given. Rule: Multiply
one side by half the other, and by the natural sine
of the included angle.—When three sides are given.
Rule: Add the three sides together, and from half
the sum subtract each side separately; then mul¬
tiply the half sum and the three remainders suc¬
cessively, and the square root of the last product
will be the area.

TRIANGLE.— To construct a triangle with
sides equal tothree given lines, Prob. XII. p. 8.—To
find the length of the liypothenuse of a triangle.
Prob. XIII. p. 8.-—The liypothenuse and one side of
a triangle being given, to find the other side, Prob.
XIY. p. 8.—To construct a triangle on a given line
equal to a given triangle, Prob. XV. p. 8.—To
change a given triangle into another of equal area.
Prob. XYI. p. 8.—To construct a triangle which
shall be similar to one and equal in area to another
of two dissimilar triangles, Prob. XVII. p. 8.—To
inscribe a circle in a given triangle, Prob. XVIII.
p. 9.—To construct a triangle equalin magnitude to a
trapezium, Prob. XX. p. 9.—To construct a triangle
equal in area to a pentagon, Prob. XXI. p. 9.—
To describe a triangle equal to a given circle, Prob.
LXXIII. p. 20.

TRIANGLES.— For drawing, or set-squares,
p. 44.

TRIANGULAR COMPASSES or Direc¬
tors, p. 33.

TRIGLYPH.—An ornament used in the frieze
of the Doric column, consisting of vertical angular
channels or gutters separated by narrow flat spaces,
and repeated at equal intervals. Each triglyph
consists of two entire gutters or channels, cut to a
right angle, called glyphs, and two half channels
separated by three interstices, called femora. The
| Doric frieze consists of triglyphs and metopes.
i TRIMMER.—A flat brick arch for the support

j of a hearth in an upper floor. It is turned from
| the chimney breast to a joist parallel to it, called a
I trimmer'-joist. See p. 151.

TRIMMER-JOIST.—The joist against which
j the trimmer abuts.

TRIMMING- JOISTS. — The joists thicker
than the common bridging-joists into which the
trimmer is framed.

TRIMMING OF TIMBER.—The working of
any piece of timber into the proper shape, by means
of the axe or adze.

TRINGLE.—In architecture, a little square
member or ornament, as a listel, reglet, platband,

! and the like, but particularly a little member fixed
exactly over every triglyph.

TROCHILUS.—The same as scotia.

TROCHILUS, The.— To describe, p. 179.

TROUGH GUTTER.—A gutter in form of a
trough; an eaves-gutter.

TROWEL.—A tool used by masons, plasterers,
and bricklayers, for spreading and dressing mortar
| and plaster, and for cutting bricks so as to reduce
them to the required shape and dimensions. Trowels
are of various kinds, according to the different pur¬
poses for which they are used.

TRUNK of a Column. —The shaft or fust.

TRUSS.—A combination of timbers, of iron, or
of timbers and iron-work so arranged as to consti¬
tute an unyielding frame. It is so named because
it is trussed or tied together. The simplest exem¬
plar of a truss is the principal or main couple of a
roof, fig. 1, in which a a, the tie-beam, is suspended
in the middle by the king-post b, to the apex of
the angle formed by the meeting of the rafters c c.

2 o

TRUSSED BEAM

INDEX AND GLOSSARY.

VERANDA

The feet of the rafters being tied together by the
beam a a, and being thus incapable of yielding in the
direction of their length, their apex becomes a fixed

Fig. 1.

point, to which the beam eta is trussed or tied up, to
prevent its sagging, and to prevent the rafters from
sagging there are inserted the struts d d. It is
obvious that the office of the beam a a, and of the
king-post b, could be perfectly fulfilled by a string,
as they both serve as ties. There are other forms
of truss suited to different purposes, but the condi¬
tions are the same in all—viz., the establishing of

Fig. 2.

fixed points to which the tie-beam is trussed. Thus,
in fig. 2, two points e e are substituted for the
single one, and two suspending posts 6 b are re¬
quired. These are called queen-posts, and the
truss is called a queen-post truss. See Principles
of Trussing, p. 136.

TRUSSED BEAM.—A compound beam com¬
posed of two beams secured together side by side
with a truss, generally of iron, between them. Bee
p. 149, Plates XE.. XLI.

TRUSSED GIRDER, p. 149, Plates XL.,
XLI.

TRUSSED PARTITION.—A partition the
timbers of which are framed together in the form
of a truss. Seep. 155, Plate XL V.

TRUSSED ROOF.—The principles of trussing
described, p. 136.

TRUSSING BEAMS. — System of Mons.
Laves, p. 149.

TRYING PLANE.—A plane used after the
jick-plane, for taking off or shaving the whole
length of the stuff, which operation is called trying
up. See Plane.

TUCK-POINTING. —Marking the joints of
brick-work with a narrow parallel ridge of fine white
putty.

TUDOR FLOWER.—A trefoil ornament,
much used in Tudor architecture. It is placed up¬
right on a stalk, and is employed in long rows, as
a crest or ornamental finishing on cornices, ridges,
&c.

TUDOR STYLE.—Properly, the architecture
which prevailed in England during the reign of the
Tudor family, or from the accession of Henry VII.
in 1435, to the death of Elizabeth in 1603. It thus
includes the Elizabethan style, but in the common
acceptation of the term, is generally restricted to
the period which terminated with the death of
Henry VIII., and may, perhaps, be most correctly
designated as late Perpendicular. Its principal
characteristics are the more constant use of the
depressed, four-centred arch, and the profuse use of
panelling, of fan - tracery vaulting, and of a pe¬
culiar dome-shaped turret, instead of pinnacles.
These characteristics are seen to advantage in
Henry VII.'s Chapel, Westminster; St. George’s
Chapel, Windsor; and King’s College Chapel, Cam¬
bridge, which may be taken as the time types of
this variety of the Perpendicular style. In domestic
architecture, the Tudor style presents a curious
blending of the Gothic and the Italian, when the
necessity no longer existed of consulting security
against attack as a main object, but while as yet
the old architectural ideas retained too strong a
hold over the mind to be readily abandoned. The

mansions erected in England in the latter part of
Henry VII.’s and the early part of Henry VIII.'s
reign, exhibit the character of what may be taken
as the genuine Tudor style. They retain the cas¬
tellated form outwardly, and have in general the
moat and gatehouse ; but the towers are without
strength, and are evidently intended for ornament
and show, rather than for defence. Small octagonal
turrets flank the angles, and terminate in a kind of
turret pinnacles, capped with an ogee-shaped dome,
which has frequently a large finial and bold crockets.
These turrets, with the richly ornamented stacks of
brick chimneys, large square windows, divided into
many lights bymullions and cross-bars or transoms,
the extensive use of panelling and of the Tudor
flower, and the very general use of brick as a build¬
ing material, may be considered as the leading char¬
acteristics of the style before its admixture with
foreign details. By the introduction of these, the
Tudor style became materially altered, before the
end of the reign of Henry VIII. the castellated
form was lost, and it gradually passed into what is
known as the Elizabethan style. See Elizabethan
Style.

TUMBLED IN.—The same as trimmed.

TUMOURS in Trees. —Injurious to the wood,
p. 97.

TURNING PIECE.—A centre for a thin j
brick arch.

TUSCAN ORDER.—The simplest of all the
five Roman orders, being nothing more than a ruder
Doric. It has strength as its distinguishing char¬
acteristic. The shaft of the column, including the
base and capital, is generally 7 diameters in height,
and its upper diameter is diminished to 45 minutes,
or to three quarters of the lower diameter. The
entablature is less than two diameters in height.
The frieze recedes a little from the face of the archi¬
trave, and neither of them have any ornament. The
following table exhibits the proportions assigned to
the different parts of this order by five distinguished
writers;—

Scamozzi.

Serlio.

Average.

Lower Diameter

in minutes

GO'

r.o'

CO'

60'

I >iameter at Neck

45'

48'

50'

46 j'

Height of the Col

in diameters

7-30

6’54

Height of the En-

tablature .

1441

1 -52f

1-30

1-40

1 45

1-421

Height of Archi-

trave in mins.

30V

32'

30'

25'

31V

Height of Frieze

26'

30'

35'

31V

32V

Height of Cornice

43V

41'

SO'

40'

42'

39V

For an example of the Tuscan Order, see the wood-
cut under Column.

TUSK TENON. — Described p. 151, Plate
XLIL, Figs. 2 and 4.

TYMPAN, Tympanum. —In architecture, the
space in a pediment, included between the cornice
of the inclined sides and the fillet of the corona.
The term is also used to signify the die of a pedes¬
tal, and the panel of a door. The tympan of an
arch is the spandrell.

TWISTED FIBRES.—In trees, render the
wood unfit for the carpenter, p. 97-

ULCERS in trees, p. y7.

ULMUS. — The elm tree. Description and
uses of, p. 110.

UNDER-CROFT.—A vault under the choir
or chancel of a church.

UNDERFOOT.—The same as underpin (which

UNDERPIN, v. —1. To support a wall, or a
mass of earth or rock, when an excavation is made
beneath it, by building up under it from the lower
level .—To underset and to underfoot are used in
the same sense.

UNDERPINNING. — 1. The act of bringing
up a solid building, to replace soft earth or other
material removed from beneath a wall or over¬
hanging bank of earth or rock. In Scotland this
process is called goufing. —2. Solid building substi¬

290

tuted for soft materials excavated from under a
wall, bank of earth, or mass of rock.

UNGULA.—In geometry, a part cut off from
a cylinder, cone, &c., by a plane
passing obliquely through the base
and part of the curved surface.
Hence it is bounded by a segment
of a circle which is part of the base,
and by a part of the curved surface
of the cone or cylinder, and bj r the
cutting plane.—It is so named from
its resemblance to the hoof of a horse.

Ungula.

VALLEY RAFTER.-—The rafter in the re¬
entrant angle of a roof. See Hip Roof, p. 91.

VANISHING POINT.—In perspective, the
point in which an imaginary line passing through
the eye of the observer parallel to any original line
cuts the horizon. See p. 230, 231.

\ ASE.—The body of the Corinthian and Com¬
posite capitals. See Drum and Tambour.

VAULT.—A continued arch, or an arched
roof, so constructed that the stones, bricks, or
other material of which it is composed, sustain and
keep each other in their places. Vaults are of
various kinds, cylindrical, elliptical, single, double,
cross, diagonal, Gothic, &c. When a vault is of
greater height than half its span, it is said to be
surmounted, and when of less height, surbased. A
rampant vault is one which springs from planes

1. Cylindrical, barrel, or wnpiron vault. 2. Roman vault, formed 1 y the
intersection of two equal cylinders. 3. Gothic groined vault. 4. Spherical
or domical vault.

not parallel to the horizon. One vault placed
above another constitutes a double vault. A conic
vault is formed of part of the surface of a cone, and
a spherical vault of part of the surface of a sphere,
as fig. 4. A vault is simple, as figs. 1 and 4, when
it is formed by the surface of some regular solid,
around one axis; and compound, as figs. 2 and 3,
when compounded of more than one surface of the
same solid, or of two different solids. A groined
vault, fig. 3, is a compound vault, rising to the
same height in its surfaces as that of two equal
cylinders, or a cylinder with a cylindroid.

VAULTING SHAFT, Vaulting Pillar —
A pillar sometimes rising from the floor to the
spring of the vault of a roof; more frequently, a
short pillar attached to the wall, rising from a cor¬
bel, and from the top of which the ribs of the vault
spring. The pillars between the triforium windows
of Gothic churches rising to and supporting the
vaulting may be cited as examples.

VAULTS.—Method of dividing into compart¬
ments, p. 82.

VENEER.—A facing of superior wood placed
in thin leaves over an inferior sort. Generally, a
facing of superior material laid over an inferior

rn&tcricil

1 VENETIAN WINDOW.—A window of large
size divided by columns or piers resembling pilas¬
ters into three lights, the middle one of which is
usually wider than the others, and is sometimes
arched.

VERANDA, Verandah. —An oriental word
denoting a kind of open portico, or a sort of light
external gallery in front of a building with a sloping
roof, supported on slender pillars, and frequently
partly inclosed in front with lattice-work. In
India almost every house is furnished with a ve¬
randa, which serves to keep the inner rooms cool
and dark.

VERGE-BOARDS

INDEX AND GLOSSARY.

ZOOPHORUS

VERGE-BOARDS.—See Barge-Boards.

VERMICULATED WORK. —In masonry
that in which the stones are so dressed as to have
the appearance of having been eaten into or tracked
by worms.

VERNIER—A small moveable scale, p. 34.

VERSED SINE, or Height op an Arc.— To
find, the chord and radius being given, Prob. LXII.
p. 17.

VERTICAL PLANE, p. 47, 229.

VESICA PISCIS.—A name given to a figure
formed visually by the intersection of two equal
circles cutting each other in their centres, but often
also assuming the form of an ellipse or an oval.
It is a common figure given to the aureole, or
rdory , by which representations of each of the three
persons of the Holy Trinity and of the Blessed
Virgin are surrounded in the paintings and sculp¬
tures of the middle ages. The form is also found
in panels, the tracery of windows, and other archi¬
tectural features, and is very common in ancient
ecclesiastical seals.

VESTIBULE.—1. The porch or entrance into
a house, or a large open space before the door,
but covered. 2 A little antechamber before the
entrance of an ordinary apartment.

VIGNETTE. — In architecture, ornamental
carving in imitation of vine leaves.

VITRUVIAN SCROLL.—A name given to
a peculiar ornament much used in classic architec-

Yitruvian Scroll.

ture. It is formed of a series of undulating scrolls
joined together.

VITTA. — Ornament of a capital, frieze, &c.

VOLUTE.—A kind of spiral scroll, used in the
Ionic and Composite capitals, of which it is a prin¬
cipal ornament. The number of volutes in the
Ionic order is four; in the Composite, eight. There
are also eight angular volutes in the Corinthian
capital, accompanied with eight smaller ones, called
helices.

VOMITORY.-—An opening gate or door in an
ancient theatre and amphitheatre, which gave in¬
gress or egress to the people.

VOUSSOIR.—A stone in the shape of a trun¬
cated wedge which forms part of an arch. The
under sides of the voussoirs form the intrados or
soffit of the arch, and the upper side the extrados.
The middle voussoir is termed the keystone. See
Arch.

WAGGON-HEADED CEILING or Vault¬
ing. —The same as Cylindric vaulting (which see).

WAINSCOT.—The timber-work that serves
to line the walls of a room, being usually made in
panels, to serve instead of hangings. The wood
originally used for this purpose was a foreign oak,
known by the name of wagenschot, and hence the
name of the material came by degrees to be cor¬
rupted into wainscot, and applied to the work itself.
Hence, also, the name wainscot is often applied to
oak deal.

WALES or Waling-Pieces.—T he horizontal
timbers serving to connect a row of main piles
together. 1

WALL-STRING, p. 196.

WALN UT WOOD.—Properties and uses of,

p. 111.

WARPING. See Casting.

WARTS in trees detrimental, p. 97.

WASH-BOARD.—The plinth or skirting of
a room.

WASTING.—In stone-cutting, splitting off the
surplus stone with a wedge-shaped chisel, called a
point, or with a pick. By either of these the faces
of the stone are reduced to nearly plane surfaces,
and it is said to be wasted off; in Scotland called
c/ouriny.

WEATHER, v .—To slope a surface, so that it
may throw off the water.

WEATHER-BOARDING. —Boards nailed

with a lap on each other, to prevent the penetration
of rain and snow.

WEDGE.—To find the surface of. Rule: Find
the areas of the rectangle, the two parallelograms
or trapezoids, and the two triangles of which its
surface consists, and add them together.—To find
the solidity of a wedge. Rule: To twice the length
of the base add the length of the edge, and multiply
the same by the breadth of the base and by one-
sixth of the perpendicular from the edge upon the
base ; the product will be the content.

WEIGHT OF ROOF-COVERING:—

Cwt. qrg. lbs.

1 square of pan-tiling will weigh. ..

0 cwt. qrg

do.

plain tiling.from

0 to 14 i

do.

countess or ladies’ slating

do.

Welsh rag or Westmore-

land do.

do.

7 lbs. lead.

do.

copper, 16 oz. or 1 lb. p. ft.

do.

zinc cast, T V inch thick..

do.

do. -A inch thick..

WELL-HOLE, Well. —In a flight of stairs,
the space left in the middle beyond the ends of the
steps. See p. 196.

WELSH-GROIN or Underpitch Groin.—
A groin formed by the intersection of two cylin¬
drical vaults, of which one is of less height than the
other.

WELSH LAYS.—In slating, slates measuring
3 feet by 2 feet.

WET-ROT.—Causes of, p. 100.

WEYMOUTH PINE or Yellow Pine,
called also American White Pine. —Properties
and uses of, p. 118.

WHEEL - WIND0 W. See Catherine
Wheel, and Rose Window.

WHIP-SAW.— A saw usually set in a frame
for dividing or splitting wood in the direction of the
fibres. It is wrought by two persons.

WHITE ANT destructive to timber, p. 105.

WHITE FIR or White Deal —The produce
of the Pinus abies or Norway Spruce.—Properties
and uses of, p. 117-

WHITE SPRUCE.—Properties and uses of,

p. 118.

WHITE WALNUT.—Properties of, p. 111.

WHITE WOOD or Alburnum of trees unfit
for carpentry, p. 98.

WICKET.—A small door formed in a larger
one, to admit of ingress and egress without open¬
ing the whole.

WILLOW, The —Properties and uses of,
p. 114.

WIMBLE.—An instrument used by carpenters
and joiners for boring holes; a kind of augur,

WIND.—To cast or warp; to turn or twist any
surface, so that all its, parts do not lie in the same
plane.

WIND-BEAM.-—An old name for collar-beam.

WINDERS.—Those steps of a stair which,
radiating from a centre, are narrower at one end
than at the other.

WINDING.—A surface whose parts are twisted
so as not to lie in the same plane. When a surface
is perfectly plane it is said to be out of winding.

WINDING-STICKS.-—Two slips of wood,
each straightened on one edge, and having the op¬
posite edge parallel. Their use is to ascertain
whether the surface of a board, &c., winds or is
twisted. For this purpose, one of the slips is placed
across one end of the board, and the other across
the other end, with one of the straight-edges of
each upon the surface. The workman then looks in
a longitudinal direction over the upper edges of the
two slips, and if he finds that these edges coincide
throughout their length, he concludes that the sur¬
face is out of winding; but if the upper edges do
not coincide, it is a proof that the surface winds.
bee Winding.

WINDING-STAIRS, p. 196.

WIN DO Mb—An opening in the wall of a build¬
ing for the admission of light, and of air when
necessary. This opening has a frame on the sides,
in which are set moveable sashes, containing panes
of glass. The sashes are generally made to rise and
fall, for the admission or exclusion of air, but some¬
times the sashes are made to open and shut verti¬
cally, like the leaves of a folding door.

WINDOWS and Window Finishings, p.
187.

WINDOW-FRAME.—The frame of a window
which receives and holds the sashes.

WINDOW-SASH.—The sash or light frame in
which panes of glass are set for windows. See
Sash.

WINDOW-SHUTTERS. — Hung to sink into
the breast, p. 188.

WINDOW-SILL. See Sill.

WING.—A smaller part or building attached
to the side of the main edifice.

WOOD. See Timber.

WOOD blighted by frost unfit for the carpenter,
p. 98.

WOOD-BRICKS. —Blocks of wood of the
shape and size of bricks, inserted in the interior
walls of a building as holds for the joinerv.

WREATHED STRING, p. 196.

X. Y. Z.

XYST, Xystos, Xystus. —In_ancient archi¬
tecture, a sort of covered portico or open court, of
great length in proportion to its width, in which
the athlete performed their exercises.

YELLOW PINE.—Description and uses of,

p. 116, 118.

YEW, The.—Properties and uses of, p. 120.

ZIGZAG-MOULDING.—The same as chevron
and dancette (which see).

ZOCCO, Zocle, Zocolo. —A square body under
the base of a pedestal, &c., serving for the support
of a bust, statue, or column.

ZOOPHORUS.—In ancient architecture, the
same with the frieze in modern architecture ; a part
between the architrave and cornice ; so called from
the figures of animals carved upon it.

291

ERRATA.

In the description of Fig. 434, page 120, for the reference letter d, in the ninth and sixth lines from the bottom
the right-hand column, read c; and for c in the fifth and third lines from the bottom of the same column, read d.

In page 226, twelfth line from the bottom of the left-hand column, for Plate CYI. read. Plate CV.

These Errata occur only in the first issue.

.AT AMS'

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LIST

OF PLATES,

WITH

REFERENCES TO THE PAGES WHERE THEY ARE SEVERALLY DESCRIBED.

PLATE.

I. .

Centering of Ballochmyle Viaduct, Glasgow and So.-Western Railway. Engraved Title.

Sections of Solids. Sections of a Cone, Cylinder, Sphere, &c. ......

Page.

II. .

Coverings of Solids. Covering of a Right Cylinder, &c. . ■ .

III.

Coverings of Solids. Covering of the Frustum of a Cone, &c. ......

IY.

Coverings of Solids. Covering of a Circular Dome, &c. .......

Y. .

Groins. In a Rectangular Groined Vault, ifcc. .........

VI.

Groins. The Side Arches and Groin Arches in a Gothic Vault, &c. .....

VII.

Groins. Welsh, or Under-pitch Groin, <tc. ... .......

VIII. .

Groins. Groining on Octagonal and on Circular Plans ...

IX.

Groins. Fan-tracery Vaulting, with Centre Pediment ........

Groins. Ribs of an Octagonal Vault, with Pendant in centre .......

XI.

Pendentives. Ceiling of a Square Room Coved with Pendentives, &c. . •

XII. .

Pendentives. An Elliptical Domical Pendentive Roof ........

XIII. .

Domes. An Oblong Surbased Dome on a Rectangular Plan, &c. ......

XIY. .

Domes. Manner of Dividing Vaults into Compartments and Caissons, &c. ....

XV.

Domes. To Determine the Caissons of an Ellipsoidal Vault .......

XVI. .

Niches. Spherical Riche on a Semicircular Plan, &o. ........

XVII. .

Niches. The Ribs of a Niche Elliptic in Plan and Elevation, &c. ......

XVIII. .

Niches. The Ribs of a Semicircular Niche in a Concave Circular Wall, <tc. ....

XIX. .

Angle Brackets— of a Cove, of a Cornice, of Curved and Straight Walls, &c. .

XX.

Hip Roofs. Lengths of Rafters, Backing of Hips, &c. ........

XXI. .

Hip Roofs. Backing of Hip-rafter, Bevel of Shoulder of Purlins, &c. .....

XXII. .

Roofs. Roof of Railway Workshops, Worcester, &c. ........

138

XXIII. .

Roofs. Roof of Heriot’s School, Edinburgh, &c. .........

138

XXIV. .

Roofs. Roof of Wellington Street Church, and of the City Hall, Glasgow, &c.

139

XXV. .

Roofs. Roof of Shed at Salthouse Dock, Liverpool, &c. ........

139

XXVI. .

Roofs. Principal of a Roof of 44 feet 8 inches span, &c. .......

140

XXVII.

Roofs. Curb or Mansard Roofs and Dormers—various examples.

141

XXVIII.

Roofs. Roof of a Shed at Marac, near Bayonne, by Col. Emy ......

142

XXIX. .

Roofs. Roof of the Salle des Catechismes, Cathedral of Amiens, &c. .....

143

XXX. .

Roofs. Domed Roofs on the System of Philibert de Lorme .......

144

XXXI. .

Roofs. Roof of the Great Hall, Hampton Court .........

144

XXXII.

Roofs. Roof of Westminster Hall . . * ........

145

XXXIII.

Roofs. Conical Roofs and Domes

145

XXXIV.

Roofs. Circular and Polygonal Domes.

145

LIST OF PLATES.

xii

PLATE.

Page.

XXXV. .

Roofs. Roof with Timber Steeple ...........

145

XXXV?.

Timber Steeples. American Examples ..........

146

XXXVI.

Roofs. Timber Spire and Roofing of La Sainte Chapelle, Paris.

146

XXXVII.

Joints and Straps. Joint of a Principal Rafter and Tie-beam, fire. .....

147

XXXVIII. .

Joints and Straps. Framing Head of Rafters and King-posts, <fcc..

148

XXXIX.

Joints. Scarfing, Lengthening-beams, tic. ..........

148

XL.

Truss-Girders. Queen-trussed Beam, Queen-bolt Truss, tic. .......

149

XLI. .

Trusses. Built Beam in Three Flitches; Compound Beam, tic.

149

XLII. .

Floors. Bridging-joist Floor, Double Floor, Framed Floor.

150

XLIII. .

Floors. Warehouse Floors, Firepi-oof Floors, tic.

152

XLIV. .

Floors. French Floors, and Floors Constructed of Short Timbers ......

152

XLV. .

Timber Partitions. Trussed or Quartered Partitions.

155

XLVI. .

Timber Houses. Modern Style of Construction .........

157

XLVII. .

Timber Houses. Framing of Town Hall, Milford, Massachusetts, tic. .....

157

XLVIII.

Timber Bridges. Drawbridge on the Gotha Canal, tic. ........

162

XLIX. .

Timber Bridges. Bridge over the Spey at Laggan Kirk, tic. .......

162

L. .

Bridges and Centres. Skew Bridge over the River Don, <ic. ......

162,174

LI.

Timber Bridges. Bridges with Laminated Arches ........

163

LII.

Timber Bridges. Bridge over the River Tyne at Linton .......

164

LIII. .

Timber Bridges. Skew Bridge on the System of M. Lomet, tic. ......

164

LIV.

American Bridges. Arched Truss Bridge, Bridge over Sherman’s Creek, tic. ....

165

LV.

Bridges and Centres. Skew Bridge over the Leith Branch Railway at Portobello, tic. .

170, 174

LVI. .

Bridges and Centres. Bridge across the Tweed at Mertown, tic. ......

171,175

LVII. .

Centres. Centres for Small Spans, Centre of Bridge over the River Don, tic.

173

LVIII. .

Centres. Centering of Over Bridge, Gloucester, tic. ........

173

LIX. .

Centres. Centering of Waterloo Bridge, tic. . . . .......

175

LX.

Gates. Park and Entrance Gates ............

177

LXI. .

Gates. Coburg Dock Gates, Liverpool

177

LXII. .

Gates. Outer Gate of the Victoria Dock, Hull .........

178

LXIII. .

Mouldings. Examples of Roman and Grecian Mouldings .......

178

LXIV. .

Mouldings. Manner of Describing Mouldings .........

179

LXV. .

Mouldings. Sections of Various Forms of Mouldings used in Framing .....

180

LXV? .

Gothic Mouldings. Examples of the Various Periods or Styles ......

180

LXV I. .

Raking Mouldings. Raking Cornice of a Pediment, tic. . . . • • •

181

LXVII. .

Raking Mouldings. Modillion in a Raking Cornice, tic. .......

181

LXVIII.

Enlarging and Diminishing Mouldings

181

LXIX. .

Architraves and Blocks. Sections of Various Forms.

182

LXX. .

Joints in Joinery. Joints for Panels, Angles, tic. .........

182

LXXI. .

Joints in Joinery. Dovetail Joints

183

LXXII. .

Gluing-up Columns. Diminution of Columns, tic. ...•••••

184

LXXIII.

Doors. Jib and Pew Doors.

187

LXXIV.

Doors. Sliding and other Doors ............

187

LXXV.

Doors. Double Margined Doors ............

186

LXXVI.

Finishings of A\ indows. Elevations of a Sashed Window, with its Finishings, tic.

188

LXXVII.

Finishings of Windows. Elevation and Plan of a Window on an Octagonal Plan, tic.

188

LXXVII1. .

Finishings of Windows. Soffit, Shutters, tic., in an Unequal and in a Circular Wall

18S

LXXIX.

Circular Window. Plan and Elevation of a Circular Window with Diamond-formed Panes, tic.

189

LXXX.

Circular Window. Framing of a Circular headed Sash in a Circular Wall ....

189

LIST OF PLATES.

Kill

PLATE.

LXXXI.

Skylights. Plan and Elevation of a Skylight with Curved Bars, &c. .....

Page.

189

LXXXII.

Skylights. Plan, Side and End Elevations of an Irregular Octagonal Skylight, &c.

190

LXXXIII. .

Skylights. Plan and Elevation of an Octagonal Skylight, &<*. ......

190

LXXXIII? .

Pulpit. Pulpit and Acoustical Canopy .....

190

LXXXIV. .

Hinging. Hinging of a Door to Open to a Bight Angle, etc. .......

191

LXXXV.

Hinging. Examples of Centre-pin Joints, <tc. .........

191

LXXXVI. .

Hinging. Back-flap, Buie-joint, Bebate, &c. . .

191

LXXXVII. .

Labour-saving Machines. Circular Saw-bench. Furness’ Planing Machine ....

192

LXXXVII* .

Labour-saving Machines. Furness’ Tenoning and Mortising Machines .....

193

LXXXVIII. .

Stairs. Plan and Elevation of a Newel Stair, &c. .........

198-207

LXXXIX. .

Stairs. Brackets, Mitre-cap, Scribing, Skirting, <tc. ........

200-207

XC.

Stairs. Geometrical Stairs composed of Straight Flights .......

189

XCI. .

Stairs. Geometrical Stairs with a Half-space of Winders .......

189

XCII. .

Stairs. Geometrical Stairs, Elliptical Plan ..........

189

XCIII. .

Stairs. Carriages of Elliptical Stairs, and Details .........

189

XCIV. .

Handrailing. Nicholson’s and Mayer’s Systems Contrasted .......

203

XCY. .

Stairs. Stair winding round a Cylindrical Newel .........

200

XCVI. .

Handrailing. Sections of Solids. Section of a Cylinder, &c. ......

202

XCVII. .

Handrailing. ' Face Mould and Falling Mould of a Bail, &c. .......

201

XCVIII.

Handrailing. Falling Mould and Face Mould of a Wreath, &c. ......

205

XCIX. .

Handrailing. Falling Mould and Face Mould for Scrolls .......

205

0. .

Handrailing. Scrolls.

207

Projection of Cast Shadows

214

CII.

Projection of Cast Shadows.

215

CHI. .

Projection of Shadows and Cast Shadows .........

217-222

CIV.

Methods of Shading. Shading by Flat Tints, &c. ........

224

CV.

Examples of Finished Shading.

226

CVI. .

Shaded Solids. Shading by Softened Tints, &c. .........

225

CVII. .

Perspective. A Cross, a Pavilion, and a Tower and Spire in Perspective ....

241

CVIII. .

Perspective. A Series of Arches, and a Circular Vault in Perspective .....

242

CIX. .

Perspective. A Tuscan Gateway in Perspective ....... •

242

ex.

Perspective. A Turkish Bath in Plan, Elevation, and Perspective .....

243

CXI. .

Perspective. A Gothic Spire in Plan, Elevation, and Perspective ......

243

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