A rudimentary treatise on masonry and stonecutting; in which the principles of masonic projection and their application to the construction of curved wing walls, domes, oblique bridges, and Roman and gothic vaulting are concisely explained ..

Front matter

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MR. WEALE'S NEW SERIES OF RUDIMENTARY WORKS

FOR BEGINNERS.

Introduction

N. B. — The numbers refer to the articles, and not to the pages.

Object of the work, I.— Necessity for geometrical projection, II. — Application of descriptive geometry to masonic projection an interesting branch of history, III. — Knowledge of the history of stonecutting not only interesting but necessary, IV — In former times the mason required only the rules applicable to the architecture of the day, V. ; the mason of the present day is not confined to any particular style, VI. — In this volume many problems are omitted which are usually inserted in books on stonecutting, VII. — Subject-matter of the 1st Section, VIII.; of the 2nd Section, IX. ; of the 3rd Section, X.— Knowledge of geometry indispensable to the mason, X I.

Section I. On The Constkuction Of Vaults And Arches

Construction of cylindrical vaults understood and practised in ancient times, 1 ; Grecian dome-vaulting, 2 ; form of the arch did not harmonize with Grecian or Egyptian architecture, 3. — Conic sections understood by the Greek architects, 4; equilibrium of arches understood by the Romans, 5; the Romans had no knowledge of the scientific operations of stonecutting, 6 ; modern method of obtaining the profile of a groin by ordinates, 7 ; this method not known to the Romans, 8 ; a waving groin the result of the Roman expedient, ibid. ;

vaulting disused in the time of Constantine, 9 Domes of St. Sophia

at Constantinople, and St. Vi talis at Ravenna, erected in the 6th century, 10; the latter dome the first example of the re-introduction of dome-vaulting into Italy, ibid. — Nave roofs of Italian churches continued to be constructed of wood till the 13th century, ibid. ; crowns of the Roman vaults made level, 11 ; mode of constructing centering for groined vaults without finding the profile of the groins, 12; centering with diagonal ribs, ibid. ; vaulting with circular groins, 13. — This contrivance removes difficulties arising in the construction of arches of the same height and different spans, 14.~ Early Norman vaults

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CONTENTS.

in England, similar to Roman vaulting, 15; introduction of rib and pannel work, ibid. ; difficulty in obtaining the profile of the diagonal rib, 16 ; rude expedients for overcoming this, ibid. — Elliptical vaulting sometimes used, 17. — Next step in ribbed vaulting was to accommodate the curvature of the vaulting surface to that of the ribs, 18. — Characteristic differences between Roman and Gothic vaulting, 19; three classes of ribbed vaulting, viz.: —

The plain ribbed vault, the lierne vault, and the fan vault, 20. — Description of plain ribbed vaulting, 21 ; peculiarities of lierne vaulting, 22;

fan vaulting, 23 Fan vaults built partly of solid masonry, 24; same

construction followed in the later lierne vaults, ibid. ; art of stonecutting seems to have reached its highest development in the 16th century, 25; ribbed vaulting introduced into Italy, a.d. 1219, 26; peculiarities of Italian Gothic vaulting, ibid. ; lierne vaults of complex character in Germany and the Netherlands, 27; fan vaulting confined to England, ibid. ; authorities referred to, 28 ; revival of solid vaulting with elliptical groins, 29 ; cupola of the Duomo at Florence, the first great work of the revival, ibid. ; stone vaulting of the church of the Assumption, at Moscow, built about the same time, ibid. ; architects of the 15th century followed classic models, 30; dome of St. Peter's built of stone in the 16th century, 31 ; partial failure of, ibid. ; first book on stonecutting published by Philibert De Lorme, a.d. 1568, 32; geometrical projection much studied on the continent, 33; scarcity of English works on stonecutting, 34.

Oblique Arches.— Skew mdisonry first practised in England about twenty years back, 35 ; skew bridge built at Florence, a.d. 1530, ibid. ; the art not generally understood abroad, ibid. ; oblique bridges in England rendered necessary by the railway system, 36.— Skew^ bridge over the river Gaunless, built a.d. 1830, 37; principle of a skew arch, 38; usual method of building oblique arches, 39. — Enumeration of works on skew masonry, 40. — Hart's system of skew masonry, 41 ; Mr. Adie's system, as practised on the Bolton and Preston Railway, 42 ; difficulties of execution in Mr. Adie's system, 43. — Oblique Gothic arches in the Bath viaduct, Great Western Railway, 44; necessity of adopting the design of an oblique bridge to the circumstances of the case, 45.

Section II. On Peojection

Working Drawings.

Desirable to explain the routine of large works, 46. — Mason prepares stone-yard and workshops, 47 ; makes working drawings of each

CONTENTS.

V course to a large scale, 48 ; makes schedule of the blocks required/ ibid. ; sends same to quarry, ibid. ; sets out work full size on a platform, 49; prepares templets for working the blocks when they arrive, — Important that the mason should be a practical draughtsman, 50.

Materials. — Drawing paper should be mounted on linen, 51. — Indian ink, 52; common writing ink should never be used^ ibid. — Shading and colour not required, and should be avoided, 53.

Instruments. — Enumeration of principal instruments required, 54 ; needle pointer, 55 ; lead-weights, use of;, 56 ; silk thread, how used, 57 ; straight-edge, mode of testing the accuracy of, 58 ; set-square, 59; straight-edges and set-squares should be kept flat, 60; compasses, small and large size, required, 61 ; French curves, 62 ; beam-compass, simple construction of, 63 ; sweeps, mode of constructing, 64.

Scales. — Enumeration of different kinds, 65; paper scale, 66; allowance to be made for permanent contraction of paper, ibid. ; contraction and expansion of boxwood and ivory scales, too trifling to be taken into account, 67 ; standard scale, 68 ; centre lines, 69. — Paper should be divided into squares, ibid.

Figuring. — Principles on which drawings should be dimensioned, 70; datum linos, 71 ; mode of fixing height of datum line, 72.

Copying Drawings, two methods, viz.; by pricking oflf and by tracing; defects of both methods, 73 ; improved method, 74.

Platform Work, similar to drawing on paper to a large scale, 75 ; rods used should be divided from a standard scale, ibid. ; platform should be level and firm, ibid.

Linear Drawing.

Straight Lines. — To draw a straight line between two given points, 76 ; to draw straight lines parallel to a given straight line, 77 ; to divide a straight line into any given number of unequal parts which shall diminish in regular progression, and so that a given division shall pass through a given point, 78.

Angles.— To set off a right angle, 79; to set off an acute angle, 80; obtuse angles plotted by their supplements, 81 ; measurement of right-angled triangles, 82.

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CONTENTS.

Curved Lines. — Problems relating to circular curves; — given the span and rise of a circular arc, to find the radius, 83; the radius being given, to find the length of an offset at any given point on a tangent line, 84 ; often necessary to connect two straight lines by a circular curve ; data required for doing this, 85. — 1st case ; the distance of the points of contact from the point of intersection being given, to find the radius, 86.— 2nd case; the radius being given, to find the distance of the points of contact from the point of intersection, 87 ; to find the length of a circular arc, 88 ; to set off on a circular arc a distance equal to a given straight line, 89 ; mode of transferring the arch joints from the development to the elevation of an arch, 90.

Method of describing an Ellipse To find any number of points

in an ellipse, 91 ; to describe an ellipse from centres, 92 ; to set out an ellipse on a platform without making use of centres, 93 ; another method with an endless cord, 94 ; to draw a line perpendicular to the circumference of an ellipse at any given point, 95.

Spiral Curves should be drawn with templets, 96.

PRINCIPLES OF PEOJECTION.

Nature of geometrical projections, 97 ; projection of lines, 98 ; method of finding the length of inclined lines from the plan and elevation, 99; projection of surfaces, 100; projection of solids, 101; sections of solids, 102; the above sections projected with very few lines, 103; curved surfaces divided into two classes, 104 ; development of the cone, 105 ; development of the cylinder, 106 ; development of the sphere, 107.

Projections of the Cone Execution of battering wing-walls'on curved

plans requires a knowledge of the several projections of the cone, 108; to draw the projections of an inverted cone from which an oblique frustrum has been removed, 109; in building a curved wing-wall care must be taken that the plan of the coping is not more than a quarter ellipse, 110; mode of proceeding when the plan of the coping is less than a quarter ellipse. 111 ; front elevation, 112; application of the above to the delineation of curved wing-walls, 113; development, 114. — To project the lines of the coping of a curved wing-wall, 115 ; nature of the twist of the bed, ibid. ; front and back edges of the top of the wall become straight lines in side elevation, 116; top and bottom arrises of the coping not parallel to each other, 117 ; intersection of a cone and a cylinder, 118. •

CONTENTS.

vii

Projections of the Cylinder. — Necessary to return to the subject for the purpose of explaining the nature of spiral lines, 119; projection and development of a right cylinder, 120 ; projection and development of an oblique frustrum of a cylinder, 121 ; nature of spiral lines, 122 ; definition of coursing and heading spirals, 123 ; projection of a spiral,'124; in the elevation of the face of an oblique cylindrical arch to draw the spiral lines in the soffit, 125; to draw an oblique semicylindrical arch with a curved face, 126.

Intersections of Cylindrical Surfaces. — Unnecessary to give detailed descriptions to accompany the diagrams, 127 ; intersection of two semi-cylindrical vaults of equal span, 128 ; intersection of a semicylindrical with a semi-elliptical vault, 129 ; intersection of vaults of different spans with waving groins, 130 ; Welsh groins, 131.

Projections of the Sphere. — Reader referred to articles 101, 102, and 107 — 132; intersection of a hemispherical dome with four semicylindrical vaults, 133 ; unnecessary to multiply examples, 134.

Part I.— General Principles of Stonecuttikg

Formation of Surfaces. — Method of working a block of stone, 135; to form a plane surface, 136; another method, ibid.; to form a winding surface, 137; definition of a spiral plane, 138; to find the dimensions of the winding strip for working a spiral plane, 139; a spiral plane can only be produced approximately by applying the straight-edge in the length of the stone, 140 ; spiral surface whose width is less than the radius of the circumscribing cylinder, 141 ; twisting rules applied in the length of the stone, 142 ; winding strip considered as a portion of a heading spiral plane, 143; comparison of the above described methods, 144.

Solid Angles. — Nature of solid angles, 145 ; manner of applying a bevel to work a dihedral, 146 ; a trihedral consists of six parts, 147 ; description of diagram, 148; application of diagram, 149. — Case 1st ; the three plane angles of a trihedral being given, to find the dihedrals, 150.— Case 2nd ; given two plane angles and their included

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CONTENTS.

dihedral, to find the remaining angles, 151. — Case 3rd ; given one plane angle and the two adjacent dihedrals, to find the two remaining plane angles, 152.

Surfaces of Operation.— No difficulty in working a block of stone, of which the surfaces are vertical or horizontal planes, 153 ; surfaces of operation defined, 154; example of the use of vertical and horizontal surfaces of operation, 155.

PART II.— Application of Principles to particular Constructions

Each of the constructions selected as an example may be considered as the type of a class to which the same rules are applicable, 156.

Curved Wing- Walls. — Their execution requires a considerable number of templets, 157 ; arrangement of the courses, 158 ; to work the top bed, 159; to work the face, 160; to work the ends, 161; to work the bottom bed, 162; to build the wall, 163 ; to form the top of the wall to receive the coping, 164; to work the coping, 165; curve of the coping must be obtained from a separate templet in cases where the radius of the wall is small, 166; desirable to reduce the number of templets as much as possible, 167; battering walls on elliptical plans very difficult of execution, 168.

Domes. — The foregoing rules apply to all constructions built in horizontal courses with conical beds, and of which the joints lie in vertical planes, 169.

Arches. — Arches on rectangular plans. Method of working the voussoirs of a common arch, 170; another method by which the soflfit may be worked without first squaring the ends, ibid.

Oblique Arches. — The following rules apply only to cylindrical arches built in spiral courses, of which the beds radiate from the axis of the cylinder, 171; always desirable before executing an oblique arch to make a drawing to an inch scale, ibid.; plan, 172; section, 173; development, 174; arrangement of heading joints, 175; skew-backs, 176; to draw the elevation, 177; focal eccentricity, 178; spandrils, 179; calculation of principal dimensions, 180; radius, 181; oblique span, 182; length of impost, 183; development of square section, 184 ; development of heading spiral, 185; angle of intrados, 186; these dimensions may be calculated with a table of natural sines only, 187; rods for setting out the work, 188; templets for the

CONTENTS.

ix skew-backs, 189 ; mode of working the springers, 190 ; twisting-rules, 191 ; templet for the curve of the soffit, 192 ; templet for marking the heading joints on the beds, 193; templet for marking the heading joints on the soffit, 194; arch-square, 195; method of working the voussoirs, 196; centering, 197; face quoins— templets for soffits, 198; templets for angles of coursing and face joints, 199; angle of twist, 200.— Knowledge of skew masonry cannot be obtained from drawings, 201.

Groined YAVvmG.— Roman vaulting; its principles previously explained, 202 ; method of working a groin-stone with horizontal and vertical surfaces of operation, 203; another method, 204; cross vaults may be built with inclined courses, 205 ; this method sometimes employed in the middle ages, ibid,; not applicable to vaults of regular masonry, ibid.

Gothic Vaulting. — Circular curves only used, 206; elliptical groins sometimes used in the decline of the pointed style, ibid.; construction of a pointed waggon vault of solid masonry, similar to that of a cylindrical arch, ibid.; different ways of working a fan vault, ibid.; nature of rib and pannel vaulting, 207 — Six classes of ribs, viz., transverse ribs, longitudinal ribs, diagonal ribs, intermediate ribs, ridge ribs, and Hemes, 208.

Curvature of the Ribs. — Transverse ribs, 209; diagonal ribs, methods of adjustingthe curvature of, 210 ; longitudinal ribs, 211; curvature of intermediate ribs determined from middle plan of spandril solid, ibid. ; method of ascertaining the curvature of the Hemes, 212; mode of working the voussoirs, 213; springers, 214 ; boss-stones, 215; difficulties in the management of the intersections of the mouldings, ibid. ; these difficulties evaded by the employment of carved bosses, ibid. ; method employed by Gothic masons for working boss-stones by means of an upper horizontal surface of operation, 216 ; another method in which the shape of the boss-stone is obtained by sinking drafts in the soffit, 217. — The stumps on the boss-stone should be squared to receive the Hemes, 218.

LIST OF ILLUSTRATIONS.

Section I

On the Construction of Vaults and Arches. Vaulting.

Fig. Art. Description.

1 2 Dome vaulting, with horizontal beds.

2 7 Mode of obtaining the profile of a groin by ordinates. See

Atlas, plate 1.

3 8 Roman groined vault with waving groins. See Atlas, plate 1.

4 13 Centering for groined vault with semicircular diagonal ribs.

5 16 Groined vault with segmental diagonal ribs.

6 17 Groined vault with elliptical groins.

7 21 Diagram explanatory of plain ribbed vaulting.

8 22 Diagram explanatory of Heme vaulting*

9 23 Diagram explanatory of fan vaulting.

10 25 View of the top of a fan vault.

Oblique Arches,

11 39 Diagram illustrating £he common method of building an oblique

arch. See Atlas, plate 2.

12 41 Diagram illustrating Mr. Hart's system. See Atlas, plate 2.

13 42 Diagram illustrating Mr. Adie's system. See Atlas, plate 3,

SECTION II. On Projection

Working Drawings,

14 63 Beam-compass of simple construction.

15 64 Trammel for striking circular curves.

Linear Drawing.

16 77 Diagram illustrating the manner of drawing long parallel

straight lines.

17 78 Diagram illustrating the manner of dividing a straight line into

a ^iven number of uneven divisions.

18 79 Diagram showing the best way of setting off a right angle. See

Atlas, plate 1.

19 82 Solution of right-angled triangles. See Atlas, plate ].

LIST OF ILLUSTRATIONS.

xi

Fig. Art. Description.

20 83^ ^

22 86 I Diagrams illustrating problems on circular

23 86 f curves.

26 91 Mode of drawing an ellipse.

27 93 Another method.

28 94 A third method.

Principles of Projection.

29 99 Diagram illustrating the manner of obtaining the lengths of

lines inclined to the horizon from their plan and elevation. See Atlas, plate 1.

30 101 Diagram illustrating the projection of a right prism.

31 101 Diagram illustrating the projection of a right pyramid.

32 101 Diagram illustrating the projection of a right cone.

33 101 Diagram illustrating the projection of a right cylinder.

34 101 Diagram illustrating the projection of a right sphere.

35 105 Development of the cone.

36 106 Development of the cylinder.

37 102 Development of the sphere. See Atlas, plate 4.

38 109 Diagram illustrating the projections of the cone. See Atlas, plate 4.

Illustrations of curved wing-walls.

Diagram illustrating the projection of spirals on a cylinder See Atlas, plate 5.

44 126 Method of drawing an oblique arch with a curved face. See

Atlas, plate 6.

45 128 Intersection of semicylindrical vaults of equal span. See Atlas,

plate 6.

46 131 Welsh groins. See Atlas, plate 6.

47 1.33 Intersection of a hemispherical dome with four 'semicylindrical

vaults. See Atlas, plate 6.

SECTION III. Practical Stonecutting

Part I. — General Principles.

Formation of Surfaces,

48 135 Diagram explaining the use of the bevel.

49 136 Diagram explaining the mode of forming a plane surface with

diagonal drafts.

50 137 Twisting rules.

XII

LIST OF ILLUSTRATIONS.

Fig. Art. Description.

Diagrams illustrating the method of finding the winding strip for working a spiral surface.

54 1 r Diagrams illustrating the method of finding the winding strip

55 1141 < when the width of the spiral surface is less than the radius

56 J [of the circumscribing cylinder.

57 1 J Diagrams illustrating the method of finding the twisting rules to

58 J \ be applied in the length of the stone.

59 143 Mode of forming the winding strip as a portion of a spiral heading plane.

Solid Angles.

Diagrams illustrating problems on the trihedral.

Surfaces of Operation.

Example of the use of horizontal and vertical surfaces of operation in forming the voussoirs of a dome.

Part II Application of Principles to particular

Constructions.

Curved Wing-V/alls.

64 158^

65 159

66 159

68 160 (^Diagrams illustrating the construction of curved battering wing-

69 161 f walls with conical beds.

70 162

73 165 J See Atlas, plate 7.

Domes.

74 169 Mode of working a voussoir of a dome with least waste of stone.

Arches.

75 170 \ Different methods of working the soffit of an arch. See Atlas,

Oblique Arches.

77 171 Diagram explaining the construction of an oblique arch. See

Atlas, plate 7.

78 174 Adjustment of angle of intrados unnecessary in a brick arch with

stone quoins. See Atlas, plate 8.

79 176 Method of cutting the backs of the springers to bond with the

masonry of the abutments. See Atlas, plate 8.

80 180 Diagram illustrating the calculation of the principal dimensions

of a skew arch. See Atlas, plate 8.

61 1 148

63 155

LIST OF ILLUSTRATIONS.

XIU

Fig. Art. Description. 81 1 ,QQ J Method of finding the templets for working the"^ 82/^^1 skew-backs. 83 191 Twisting rules.

1 1 00 f Diagrams relating to the method of finding the tern- ,

87 193 Templet for marking the heading joints on the beds.

88 1 r Diagrams illustrating the manner of applying the

89 J [ templets in working the voussoirs. J

90 199 Instrument for measuring the angles of the coursing and face-

joints. See Atlas, plate 8.

Groined Vaulting.

Roman Vaulting.

91 203 1 Diagrams illustrating the manner of working the groin-stones.

92 204 J See Atlas, plate 8.

Gothic Vaulting.

93 209 Plan of a quarter of one compartment of a ribbed vault, with

the elevations of the ribs. See Atlas, plate 8. 94] _

95 I Qirj / Different methods of adjusting the curvature of the diagonal

96 f t ribs. See Atlas, plate 8.

98 213 Method of working the ribs.

99 215 Elevation of a boss-stone.

100 217 Templets for working a boss-stone from drafts sunk in its soffit.

INTRODUCTION.

I. This little work has been written in continuation of the articles on Masonry, contained in a previous volume^ of the Rudimentary Treatises. The reader will there find an outline of the principles of equilibrium of retaining walls and arches, and a sketch of the operations of the mason, with descriptions of the tools and implements used in stone-cutting. These subjects, therefore, have not been touched upon in the following pages, which are devoted more particularly to the scientific operations of stone-cutting, and to the explanation of the methods by which the mason obtains, from the designs of the architect, the exact shape of each stone in a building, so that when set in its place, it shall exactly fit the adjacent stones, without previous reference to them.

II. The necessity for geometrical projection, in order to construct the moulds and templates by which the mason is guided in his work, must always have existed from a very early period ; indeed, it would be impossible to erect a stone building of any architectural pretensions, without first arranging the joints of the masonry on a large drawing, and making full-sized projections of some portions, such as the profiles of the mouldings.

III. It would be interesting to trace the history of descriptive geometry in its application to masonic projection; to examine how far the geometrical rules in current use amongst masons at different periods, arose out of the necessities, so to speak, of the architecture

* Rudiments of the Art of Building— Second Series of Rudimentary Treatises, Vol. I.

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INTRODUCTION.

of the time when they were practised, and to ascertain what influence they, in their turn, exercised on the character of succeeding styles. Thus, the exquisite profiles of the Greek mouldings are true conic sections, the properties of which were well understood by the Greeks, whilst the corresponding members in Roman buildings are tame and spiritless, and composed of circular curves only. Again, whilst the later works of the Roman age betray a total want of rule and system, the architecture of the middle ages exhibits a very perfect and complex geometrical system of construction, arising naturally out of, and yet quite distinct from, that of the classical architecture of earlier times, and equally removed from that of the Italian revival of classic architecture, which sprung up at the commencement of the 15th century, and which, in the course of the 16th, spread so exsensively over Europe, as completely to obhterate, so to speak, all traces of the rules of the mediaeval architects.

IV. The history of the geometrical methods practised at different periods is not, however, merely a matter of antiquarian interest, but is also an essential branch of knowledge, in connection with the art of stone-cutting. The character of all genuine architecture, no matter of what age or country, is so dependant on its mechanical structure, that we cannot successfully imitate the style of any period, without thoroughly understanding the principles of construction which prevailed at that time. This is especially the case with Gothic masonry, which cannot be properly executed without a thorough appreciation of the peculiar characteristics of mediaeval architecture, and of the essential differences which exist between the methods of the Gothic masons and those of our own day, which are almost exclusively derived from the practice of the Italian school of architecture.

V. In former times, the mason had probably little general acquaintance with the principles of projection*

INTRODUCTION.

Having no occasion for any rules, besides those required by the architecture of his own time, he worked by them without departing from the beaten track, except when some startUng architectural novelty rendered a modification of them absolutely necessary. But in the present day the case is quite different. We copy the architecture of all nations and all times ; we introduce in our designs every variety of curves ^ ; and we execute our works in every conceivable material, from granite to gutta-percha.

VI. In this absence of any settled principles of design or construction, the mason can no longer work from traditional rules, or confine himself to one particular style of architecture, and it becomes necessary for him to master the principles of his art, that he may be able to invent for each problem that may come before him the solution best adapted to the character of the work in hand.

VII. In selecting and arranging the materials for this little volume, the object aimed at throughout has been, therefore, to lay down general principles rather than to multiply examples, and will be found to differ from most works on stone-cutting in the omission of many problems usually inserted, which are simply so many exercises on the cone, the cylinder, and the sphere, and have reference only to the round forms of the Italian school, whilst we have written at some length on the subject of ribbed vaulting, the principles of which have not been explained, except in compara-

* The nature of the curves made use of in architectural design has a very marked influence on the character of the work. The curves used by the Greeks were principally conic sections, which appear to have been unknown to the Romans. In the genuine specimens of the pointed style, circular curves only, or curves made up of circular arcs of different radii, are employed, although the profiles of the diagonal ribs, in some examples of vaulting, present curves very similar to the ellipse, being struck from three centres. In Italian architecture, elliptical curves, formed by the intersection of cylindrical surfaces, are of constant occurrence. The use of spiral curves as lines of construction, and not merely of decoration, is quite modern, and dates from the introduction of the oblique arch.

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INTr.ODlJCTIOX.

lively expensive works of a class not usually to be found on the book-shelves of the mason.

VIII. The w^ork is divided into three sections, as follows : —

Section I. — On the Construciion of Vaults and Arches

The problems which present the greatest difficulties in masonry are those relating to vaulting, the perfect execution of which, from the knowledge it requires of projection and of the nature of the lines produced by the intersections of curved surfaces, has always been the severest test to which the skill of the mason can be exposed. We have, therefore, in the first section briefly sketched the history of stone-cutting in connection with this class of problems, for the purpose of explaining the essential characteristics of the two great classes of vaults, viz., the rib and pannel vault of mediaeval architecture, and the solid vault of jointed masonry, which belong to the Roman and Italian styles. Several pages also have been devoted to the explanation of the principles of skew masonry, and of the different methods of constructing obhque arches, that have been advocated by different writers.

Section II. — On Projection

IX. The drawings of the architect are usually made on a rectangular drawing-board, the horizontal and vertical lines being drawn with a T square. In the workingdrawings of the mason the largeness of the scale renders it impossible to make use of such aids, and a considerable amount of care and system is required to produce a large drawing which shall be truly correct.

Again, in the designs of the architect minute accuracy is comparatively of minor importance if the drawngs are properly figured, as the mason should be guided by the written dimensions, and not by the actual size, of the different parts of the drawing. But the working

INTRODUCTION.

drawings of the mason exhibit the actual sizes of the stones, any inaccuracy in the drawings materially affecting the soundness of the w^ork.

We have, therefore, in the second section given a few hints on the management of large drawings, which may be useful to those who have not learnt, by painful experience, the necessity of minute accuracy.

The subjects treated of in this section are arranged as follows : —

Working Draioings. — Materials; instruments; scales; figuring; copying; platform-work.

Linear Drawing, — Straight lines; protraction of angles; measurement of right-angled triangles; problems relating to circular curves ; modes of drawing the elhpse.

Principles of Projection. — Surfaces; solids; problems relating to the projection and development of the cone, cylinder, and sphere; spiral Knes; intersections of curved surfaces.

Section III. — On Practical Stone'Cutting

X. There is a class of problems connected with railway masonry that has as yet been very little studied by w^orking masons ; w^e refer to those required in working the wing- walls of bridges. The construction of curved wing-walls, and the nature of the twist of the coping beds, have been explained at greater length than the limits of this little work would at first seem to warrant. But our reason for this has been, that the same rules apply, with trifling modifications, to all constructions built in horizontal courses with conical beds (as for example, to take two instances apparently most dissimilar, a hemispherical dome and the spandril solid of a fan vault); and, therefore, the system of lines here laid down may be considered, to use the words of Professor Willis, " as a general formula which includes many particular instances."'^