/! ' USSO 'Ti'’ FRANKLIN INSTITUTE LIBRARY PHILADELPHIA Class Book»2i6.vf:j..4-^ Accessioa S^^.c:^.!:^ C Given by.. . ■f* r‘ '■ • 'A' ' I f, i !' (: \ ■ '{ V4 umn m stonecutting. A KUDIMENTAKT TREATISE CN PLATES ONtY. 3 1 ^ 7 ^^ referred to in the separate TEXT: CONTAINING FIFTY-ONE DIAGRAMS IN EIGHT PLATES ILLUSTRATING THE TEXT. AND four plates of specimens of gothic MASONRY. BEING PLATE IX., ELEVATION OP THE PULPIT, ST. MARIE’S ABBEY, BEAULIEU. PLATE X. FOLIAGE ON ST. MARIE’S ABBEY, BEAULIEU. PLATE XL, ALMONRY OF THE CHURCH OF ST. JOHN THE BAPTIST, WILTSHIRE. PLATE XII CHANCEL-WINDOW AND PARAPET OP SACRISTY, OP THB CHURCH OF ST. JOHN THE BAPTIST, WILTSHIRE. EY EDWAKD DORSON Asscc. I.C.E. and LONDON: JOHN WE ALE, 59, HIGH HOLBOEN. 1857. CCA/S TH S4ol fssy « « c < c * t e c « , C C < < . - t « C C C C ' ' ' C C C < * * 't t c C < 1 c I ‘ ‘ « c ‘ < C « C c C , C C C c *c « C c e < « c C < ^ EIGHT PLATES EEEEEEED TO BY THE TEXT. No. of Plate. Fio. 1 2 3 8 18 79 19 82 20 83. 21 84 22 86 23 86 24 87 25 88-' 26 91 27 93 28 94 29 99 2 11 39 12 41 3 13 42 4 37 102 38 109 5 43 120 6 44 45 46 47 7 71 72 73 Description. 7 Method of ohtainlng the profile of a groin hy means of ordinates. Roman groined vault, ■with waving groins. Diagram showing the best way of setting off a right angle. Solution of right-angled triangles. h Diagrams illustrating problems on circular curves. Mocle of drawing an ellipse. Another method. A third method. Diagram illustrating the manner of obtaining the lengths of lines inclined to the horizon from their plan and elevation. Diagram illustrating the common method of budding an oblique arch. Diagram illustrating Mr, Hart’s system. Diagram illustrating Mr. Adie’s system. Development of a sphere. Diagram illustrating the projections of the cone. Diagram illustrating the projection of spirals on a cylinder. 126 Method of drawing an oblique arch with a curved face, 128 Intersection of semi-cylindrical vaults of equal span. 131 Welsh Groins. 133 Intersection of a hemispherical dome with four semi- cylindrical vaults. Diagrams illustrating the construction of battering wing- , I walls, on a curved plan, with conical beds, loo J PLATES REFERRED TO BY THE TEXT. Art. Description. 169 Mode of working the voussoirs of a dome with the least waste of stone. j- Different methods of working the soffit of an arch. Oblique Akches. 77 171 Diagram explaining the construction of an oblique arch. 8 78 174 Diagram showing the adjustment of the angle of intrados; to be unnecessary in a brick arch with stone quoins. 79 176 Method of cutting the backs of the springers to bond with the masonry of the abutments. 80 180 Diagram illustrating the calculation of the principal dimensions of a skew arch. 811 jgg f Method of finding the templets for working the skew-i 821 L backs. ' 83 191 Twisting rules. 192 ■[ relative to the method of finding the templet L for the curve of the soffit. 87 193 Templet for marking the heading joints on the beds. 881 jgg J Diagrams illustrating the mode of applying the templets 89 / L in working the voussoirs. 90 199 Instrument for measuring the angles of the coursing and face joints. No. of Plate. Fig. 7 74 75 76 Groined Vaulting. Roman Vaulting. 91 2031 Diagrams illustrating the manner of working the groin 92 204 J stones. Gothic Vaulting, 93 209 Plan of a quarter of one compartment of a rihbed vault with the elevations of the ribs. 94 '210 { Different methods of adjusting the curvature of th diagonal ribs. And an addition of Four Plates as described in Title. INTRODUCTION. I. This little work has been written in continuation the articles on Masonry, contained in a previous dume* of the Rudimentary Treatises. The reader ill there find an outline of the principles of equi- orium of retaining walls and arches, and a sketch of le operations of the mason, with descriptions ^ the ,ols and implements used m stone-cutting. Ihese ibiects, therefore, have not been touched upon in the .llowing pages, which are devoted inore particularly to le scientific operations of stone-cutting, and to the ex- lanation of the methods by which the mason obtains, om the designs of the architect, the exact shape ot ich stone in a building, so that when set in its place shall exactly fit the adjacent stones, without previous jference to them. . . i II. The necessity for geometrical projection, in order 3 construct the moulds and templates by which the lason is guided in his work, must com a very early period; indeed, it would be irnpossi 0 erect a stone building of any architectural preten- ions, without first arranging the joints of the masonry .n a large drawing, and making full-sized projections ot ome portions, such as the profiles of the mgs. III. It would be interesting to trace the history ot lescriptive geometry in its application to masonic pro- ection; to examine how far the geometrical rules in * Rudiments of the Art of Building. B 2 INTRODUCTION. current use amongst masons at different periods, anj out of the necessities, so to speak, of the architectr! of the time when they were practised, and to ascertf^ what influence they, in their turn, exercised on the ch racter of succeeding styles. Thus, the exquisite profil of the Greek mouldings are true conic sections, t properties of which were well understood by the Greel whilst the corresponding members in Roman buildin^ are tame and spiritless, and composed of circular curv only. Again, whilst the later works of the Roman ar betray a total want of rule and system, the architects of the middle ages exhibits a very perfect and comph geometrical system of construction, arising natural out of, and yet quite distinct from, that of the classic architecture of earlier times, and equally removed fro that of the Italian revival of classic architecture, whi( sprang up at the commencement of the fifteenth cei tury, and which, in the course of the sixteenth, spref so extensively over Europe, as completely to obliterat so to speak, all traces of the rules of the medieevl architects. n IV. The history of the geometrical methods prafl tised at different periods is not, however, merely! matter of antiquarian interest, but is also an essentif branch of knowledge, in connection with the art | stone-cutting. The character of all genuine architel ture, no matter of what age or country, is so depended on its mechanical structure, that we cannot successful! imitate the style of any period, without thoroughly uif derstanding the principles of construction which prl vailed at that time. This is especially the case will Gothic masonry, which cannot be properly executcl without a thorough appreciation of the peculiar ch| racteristics of mediaeval architecture, and of the e.l sential differences which exist between the methods » the Gothic masons and those of our own day, whic are almost exclusively derived from the practice of til Italian school of architecture. | V. In former times the mason had probably littj INTRODUCTION. C\ o leral acquaintance with the principles of projection, iving no occasion for any rules, besides those re- ired by the architecture of his own time, he worked them without departing from the beaten track, ex- pt when some startling architectural novelty rendered modification of them absolutely necessary. But in e present day the case is quite different. We copy e architecture of all nations and all times; we intro- ce in our designs every variety of curves ;* and we ecute our works in every conceivable material, from anite to gutta-percha. . . i ^ i VI. In this absence of any settled principles ot de- \rn or construction, the mason can no longer work Dm traditional rules, or confine himself to one parti- ‘dar style of architecture, and it becomes necessary 'r him* to master the principles of his art, that he ’ ay be able to invent for each problem that may come ” jfore him the solution best adapted to the character ■ the w'ork in hand. . VII. In selecting and arranging the materials lor his little volume, the object aimed at throughout has een, therefore, to lay down general principles rather San to multiply examples, and vvill be found to ditiei /om most works on stone-cutting, in the omission o ' lany problems usually inserted, which are simp y so ^ lany exercises on the cone, the cylinder, and t e Shere, and have reference only to the round forms o Jie Italian school, whilst we have written at some ^ mgth on the subject of ribbed vaulting, the principles ®f which have not been explained, except in compara- re ^ * The nature of the curves made use of in architectural design has a iry marked influence on the character of the work. The curves ^ le Greeks were principallv conic sections, which appear o rav nknown to the Romans. In the genuine specimens of the pomtea styie, rcular curves only, or curves made up of circular arcs of di eren , re employed, although the profiles of the diagonal ribs, in some exarnp f vaulting, present curves very similar to the ellipse, being s ruc^ r iree centres. In Italian architecture, elliptical curves, forme y itersection of cylindrical surfaces, are of constant occurrence. e f spiral curves as lines of construction, and not merely of ’ uite modem, and dates from the introduction of the oblique aic ■n Q. 4 INTRODUCTION. tively expensive works of a class not usually to be four on the book-shelves of the mason. VIII. The work is divided into three sections^ ! follows:— ,v Section I .—On the Construction of Vaults and Arches, '! ^ The problems vdiich present the greatest difficultiel j m masonry are those relating to vaulting, the perfecj execution of which, from the knowledge it requires Cj; projection and of the nature of the lines produced b; the intersections of curved surfaces, has always bee the severest test to which the skill of the mason ca be exposed. We have, therefore, in the first sectio| briefly sketched the history of stone-cutting in con nection with this class of problems, for the purpose c explaining the essential characteristics of the two grea classes of vaults, viz. the rib and pannel vault of medi aeval architecture, and the solid vault of jointed ma sonry, v^hich belong to the Roman and Italian styles Several pages also have been devoted to the explana tion of the principles of skew masonry, and of th diflFerent methods of constructing oblique arches, tha have been advocated by different writers. ^ I Section II .—On Projection. \ IX. The drawings of the architect are usually mad on a rectangular drawing-board, the horizontal an vertical lines being drawn with a T square. In th working drawings of the mason the largeness of th scale renders it impossible to make use of such aids and a considerable amount of care and system is re quired to produce a large drawing which shall be trul correct. Again, in the designs of the architect minute accr racy is comparatively of minor importance if the draw ings are properly figured, as the mason should be guide by the written dimensions, and not by the actual siz( of the different parts of the drawing. But the workin introduction. wines of the mason exhibit the actual sizes of the aesfany inaccuracy in the drawings materially affect- the soundness of the work. , Ne have therefore, in the second section given a ^hints on the management of large drawings, which V he useful to those who have not learnt, by pamfu lerience the necessity of minute accuracy. rhTsubjects treated of in this section are arranged ZVmcirijrs.— Materialsinstruments; scales; aring; “PM"? ’'unes; protraction of Linear Drawing. — nne^ , i Ties; measurement of right-angled P[ ’ms relating to circular curves; modes of drawi „ Sfcs of ProjecHon.-f.rf.ces; solids; problems ating to the proiecdon and development of the cone, Sr, and Vere; spiral lines; intersections of rved surfaces. Section III. —On Practical Stone-Cutting. X The! is a class of problems connected with rail- .ymason^y^thatW^^^ arking The construction of curved :,™fir“Se of the twist of the cop ng ■ds have been explained at greater length than the nits of this little work would at first seem to warrant, u our reaLn for this has been, that the same rules iply, with trifling modifications, to all oonstructions uilt in horizontal courses with conical l^oda (“ for e mple, to take two instances apparently most dissiml , Ten^ispherical dome and the ault); Ld therefore the system of lines here aid own may be considered, to use the 7many Villis, “ as a general formula which me f •articular instances, * . WiUis “Oa the Conti,uclion of the VauUt of Jt' Jaetiont of.he Royal InatUnteof Britith Architeets, Vol. I. Pt. 2. 6 INTRODUCTION. The subjects treated of in the third section are ^ follows:— Part I.— General Principles of Stone-Cuttini Formation of Surfaces. —Plane, curved, and windir surfaces. Solid Angles. —Nature of solid angles; problems d lative to the trihedral. Surfaces of Operation. Part II.— Application of Principles to parti cuLAR Constructions. Battering Walls on Curved Plans. Domes. Arches. —Arches on rectangular plans, circular ar elliptical; oblique arches. Groined Vaulting. —Roman vaulting; ribbed vaul ing. XI. In concluding these introductory remarks, may be necessary to add that the reader is presumed 1 have a knowledge of plane and solid geometr}’-, as we as of the elements of plane trigonometry. I As not only acquaintance, but familiarity with the: subjects is indispensable to the proper understanding i the more difficult problems in stone-cutting, especial' those connected with skew masonry, no purpose wou’ have been answered by inserting in this volume a pn paratory treatise on geometry, which must have m cessarily been too brief to be of any real value; ar the introduction of which wmuld have excluded muc matter bearing more immediately on the subject of tl 'work. E. Dobson. rudiments OF THE art of masonry. SECTION I. ON THE CONSTRUCTION OF VAULTS and arches. VAULTING. 1 The construction of plain cylindrical Tanlts in hich the faces, beds, and joints of all the stones are plane Hfaces, either perpendicular to, or radiating from the ris of the cylinder, presents no particular difficulties, ,e only lines that have to be made use of being straight nes and circular curves; and accordingly we find that, rom the earliest times, the construction of common ylindrical vaults, both in brick and stone, appears to ,ave been well understood, arched vaults being found .mongst the ruins of Nineveh,* whilst arches of brick ,nd stone are stiU remaining atThebesf and Saqquara, n evidence of the knowledge of the arch possesse y Jie ancient Egyptians. Whether the Greeks were ac¬ quainted with the principle of the arch, is still a disputed * X^idp Lavard’s “ Nineveh.’ . , .n ” t ni Wilkinson’s » Manners and Customs of the Ancient Egyptians. 8 RUDIMENTS OF THE point. Further than this the ancients do not appe to have advanced, and we have no evidence to she that the now familiar problem of finding the profile a groin from the square sections of a vault by means ordinates, was at all known before the eleventh, or th it was generally practised before the fifteenth centu of the Christian era. 2. The very curious dome-shaped building at M cenae, in Greece, known by the name of the “ Treasui of Atreus,^’ afi’ords valuable evidence as to the amount knowledge possessed by its builders of the principh of dome vaulting. The inside of the building forms pointed dome of 48 ft. diameter, and of about the san height, the section presenting two intersecting arcs < about 70 ft* radius. The difficulties which attend tf working of such a vault wit radiating beds have bee here evaded by making th beds horizontal throughou' the top being formed of a fit stone. Nothing more, there fore, was necessary than to ci; the soffit of each course to th required angle with its bed which could readily be don by means of a templet cut t the radius of the vault, a shown in fig. 1. Fig. 1. 3. Although the principle of the arch was known e a very early period, the arch was never employed t any great extent before the Roman age. Its form dii not harmonize with the severe horizontal features c the columnar architecture of Egypt and Greece, whils its employment was not a principle of construction a ART OF MASONRY. 9 10 longst the Romans, who built in a great measure th brick, and who probably had not the means of h ill 1 or t( ) 1 ( IS ,10 ecuting the flat massive stone roofs with which the ryptians covered their halls and porticoes. 4 . We must, however, guard against assuming, from e o-eneral absence of the arch in Grecian architecture, at the Greek architects were unacquainted with geo- strical methods of describing elliptical or any other rves. The singular facts respecting the curved lines of the reek temples, which have been recently placed beyond e possibility of dispute by the careful measurements Mr. F. C. Penrose,* who devoted five months to e investigation of the curves of the Parthenon alone, ow that they must have possessed very perfect ethods of setting out and executing their work, the irfection of which it would be impossible to excel, id which it wmuld be difficult at the present day to [ual. The leading facts to which we refer are briefly ese; that the lines of the pavements, architraves, and irnices are not horizontal, but curved; and that the itasis or vertical curvature of the columns, and the rofiles of the mouldings are true conic sections; being ther hyperbolic or parabolic curves. No traces of a uowledge of conic sections are to be found in the ’chitecture of the Romans, whose works are often cecuted in a coarse and slovenly manner, and whose louldings are formed of circular curves only, instead presenting the delicate curves we find in the works : the Greeks. 5. With the introduction of the arch by the Romans i a leading principle of composition, commences a new * “ Two Letters from Athens, by F. C. Penrose, Esq." r the Society of Dilettanti. B 3 Published 10 RUDIMENTS OF THE era in the history of construction. The arches of Theb^' and Nineveh were of small dimensions and of little inf this contrivance, which w'as also made use of in our )wn country before the twelfth century, when plain TOSS vaulting began to be superseded by rib and pannel vaulting, which, in its turn, fell into disuse on the le- /ival of the classic style of architecture in the fifteenth ind sixteenth centuries. In Germany another contri¬ vance appears to have been adopted, wffiich we shall pre¬ sently describe. 9. So earlv as the time of Constantine, the art of constructing vaults seems to have been on the decline, and the roofs of the early Christian churches in Italy were of wood, with the exception of the eastern semi¬ circular apse, which was always covered with a plain semi-dome. 10. In the sixth century was erected the celebrated dome of St. Sophia, at Constantinople. This is a flat dome, 115 ft. in diameter. Soon afterwards was built the church of St. Vitalis, at Ravenna, which has a 12 rudiments of the hemispherical dome, 54 ft. in diameter. This latte dome is the first example of the re-introduction ^ dome-vaulting into Italy, after the decline of the Rd man art. These two celebrated domes were constructe of earthenware and pumice-stone, and presented, cor sequently, no difficulties in stone-cutting. After the erection of St. Vitalis, plain groined vault of small span became very common, although the nav roofs of the Italian churches continued to be constructee of wood, with flat ceilings, until the 13th century, whei the pointed style was first introduced into Italy. Thes- vaults are usually divided into compartments, by fla bands, an arrangement which continued to be practise! long after the introduction of ribbed vaulting. 11 . The crowns of the Roman vaults were mad( level throughout, and we find this arrangement to hav( prevailed in our own country until the introduction o- the more complex forms which we shall presently de¬ scribe. But on the Continent a different system seems to have prevailed, the nature of which we shall endea¬ vour to explain. 12 . In the construction of a plain waggon vault with cross vaults, the easiest way of forming the centering IS to make a complete centering for the main vault, and on it to place the centres for the cross vaults! This dispenses with the necessity for finding the curves of the groins, and the cross vaults may be made of any shape, without regard to their intersection with the mam vault, as the groins, to use a familiar phrase, will ^^find themselves” The irregularities of the groin lines of the Roman vaults would seem to indicate that they were built in this way. A centering of this kind IS, however, very defective, being weak at the most important parts, namely under the groins. ART OF MASONRY. 13 The obvioufe remedy is to construct the centering :h diagonal ribs. But here comes the important estion—how is the profile of these ribs to be ob- ned ? 13. It is very evident that, for the vaulting surfaces be cylindrical, the rib must be of a -flatter curve an the square section of the vault. If the latter be semicircle, the former will be a semi-ellipse, and if e form of the vault be pointed, that of the rib will be pointed arch formed of two elliptical curves. We ive already said, that the method of obtaining the •ofile of a groin by ordinates does not appear to have ;en formerly known, and in the early German vaults le difficulty is got over in a very simple and satisfac- ■ry manner, by abandoning the principle of keeping the surfaces cylindrical and making the groins portions of circular curves.* The structure of these early vaults is highly domical, the curvature of the groins being such as to throw their intersection much higher than the summit of the trans- Fig. 4. erse and longitudinal ribs, by which each compartment f the vault was bounded. (See fig. 4.) 14. This expedient does away also with all difficulty rising from the unequal span of two intersecting aults, and introduced the important principle of de¬ igning the profiles of the groins, and leaving the form if the vaulting surface to adapt itself to them, whilst, n the Roman and Italian styles, the form of the vault- * Probably in many cases a semicircle, to judge from the domed ap- learauce of the vaulting in most of the early German churches ; hut, in he absence of careful measurements, it is impossible to say what rule was ollowed in this respect. 14 rudiments of the ing surface is first settled, and the profile of the crroio follows from it as a matter of necessity. The domiq form of vault was extensively used abroad, especiallyT Italy; but in England it is not common, and our ear vaults were constructed on the principle of keeping tl crowns level. ° 15. The early Norman vaults of our own count! are plain rubble vaults, similar to those of the Romam and exhibiting the same expedients of stilted springins and waving groins. But at an early period the syster of solid vaults, with continuous vaulting surfaces, bega to be superseded by a less massive mode of constrac tion, appropriately called, by Professor Willis “Rf and pannel work.- This style of vault consists of framework of light stone ribs, filled in with panneh either built in courses of small stones, or formed of thi slabs, cut to fit the spaces betv^een the ribs 16. The introduction of diagonal ribs 'rendered i necessary to make use of some method of obtaining face-mould for the groins but this was not done by thi methods described above The common system appear to have been, either to mak< the diagonal ribs semicircu lar, and to stilt the springing of the transverse and longi tudinal ribs; or, to make th diagonal ribs segmental. Ii either case, the intersection of the vaulting surfaces rosi considerably above the dia gonal ribs at the haunches .1,.. K 1 r this difficulty the backs of these ribs were packed up to meet tb Fiff. 5. ART OF MASONRY. 15 ilting, which thus rests on thin walls of rubble, in- ad of on the walls themselves. This is shown in fig. 5. I example of the first-named expedient is to be seen a vaulted apartment in the castle at Newcastle-upon- ne. The aisles of the nave of Peterborough cathe- il are examples of the second. Sometimes we find 3 diagonal ribs semicircular, and the transverse ribs \nted, arches. This construction may be seen in me vaults on the west side of the south transept of iterborough cathedral. 17 . But although the above described arrangements jre those in common use, there are instances of plain ults without diagonal ribs, which present the modern rangement of making the profile of the groin de- mdent on the form of the principal vault. The ruins of some old buildings in Southwark, for- erly belonging to the Prior of Lewes, in Sussex, mtained vaults of this description. One of them is escribed in the ‘‘^Archseologia,^^ Vol. XXIIL, and also I Brayley’s “ Graphic Illustrator,” from which the ac- ampanying illustration, fig. 6, is copied. The length * Fiff. 6. 16 RUDIMENTS OF THE of the vault here shown was 40 ft. 3 in., the wid( 16 ft. 6 in., and the height 14 ft. 3 in. The mai vault was semicylindrical, and was intersected by foi} cross vaults of elliptical section. The ribs were < stone 5 the vaultings of chalk. The arch over .th entranee doorway of the apartment was also of aj elliptical form. The building is supposed to have bed erected in the twelfth century, but we have no precis information on the subject. 18. It might naturally be expected that the nex step m ribbed vaulting, beyond the rude expedient o baeking up the diagonal ribs, would have been to ac commodate the curvature of the diagonal ribs to that o the vaulting surfaces; but, instead of this, we find } new principle of design introdueed, which was to ad. just the vaulting surfaces to the curvature of the ribs to whieh they were made perfectly subordinate, eacl rib being struck from one or more centres, and designee without any immediate reference to the curvature of the adjoining ones. 19. In the Roman system of vaulting, the vaulting surface is everywhere level in a^ direction parallel to the axis of the vault; and any horizontal section of the spandril of a groined vault taken between the spring¬ ing and the crown would be a rectangle. But in the Gothic ribbed vault this is not the case, for the planl thus formed would present as many angles as ribs, andj admits of great variety according to the curvature of| the latter. Thus in fig. 7*, the plan of the spandril atil A, by a trifling alteration in the curves of the ribs,| might be made at pleasure to form any of the figures shown at a, b, c, and d. 20. The varieties of ribbed vaulting practised during the Middle Ages may be divided into three classes. ART OF MASONRY. 17 1st. The Plain Ribbed Vault. 2nd. The Lierne Vault; in which numerous liernes short ribs are introduced, disposed in connection with 3 principal ones, so as to form star-shaped figures and the imposts, as well as a regular pattern at the ntre of each compartment. 3rd. The Fan Vault; in which all the main ribs ,ve the same curvature, and form equal angles with ch other at their springing. We do not propose to enter upon any description of e architectural design of these vaults or of their deco- tive features, but it is necessary to say a few words 1 their mechanical construction. 21. Plain Ribbed Vaulting .—A simple example of is is shown in fig. 7- These vaults are sometimes Fig. 7 . PERSPECTIVE VIEW. )und without ridge ribs, and sometimes with them, le latter case being of the most frequent occurrence, ometimes there are only diagonal, transverse, and 18 RUDIMENTS OF THE longitudinal ribs in other example} we find intermeJ diate ribs intro-< duced between the diagonal andtrans-J verse, and longiJ tudinal ones. Th^ ridges are gene¬ rally horizontal, but not universally so. Plain ribbed vaults were much used in France, and in the Italian churches, and were often decorated with painting. j 22. Lierne Vaulting .—In this class of vaults the ribs are very numerous, and the liernes divide the spaces into compartments, which are filled with tracery. In the previous class of vaults, each rib marked a groin j that is, a change in the direction of the vaulting sur¬ face ; but in these many of the ribs are merely surface ribs; that is, they lie in a vaulting surface, whose forni is determined independently of them, and regulates their curvature. Many vaults of this class, although apparently of very intricate design, are in reality vaults of simple forms decorated with a profusion of surfacf ribs. A good example of this kind of vaulting, from the cloisters of St. Stephen’s, Westminster, is given in fig. 8. The construction of vaults of this class requires a very thorough knowledge of projection, as the pattern of the vault must be first laid down upon the plan ART OF MASONRY. 19 k Fig. 8. in which the curved lines of the ribs will of course become so foreshorten¬ ed, that it gives very little idea of the perspec¬ tive effect of the work in execu¬ tion. The de¬ signers of these .vaults must erefore have possessed the power of conceiving in eir minds the effect they washed to produce, and have iderstood how to distort the plans accordingly. It is not probable that this was done by any regular •ometrical methods; it was more probably the result experience and observation on the effect of existing lults. This is confirmed by the very unequal charac- r of remaining examples; in some, the meaning of the isign is hardly to be made out from the plans, whilst . others the plans exhibit symmetrical arrangements, hich are lost in execution from the distortion of the nes. 23. Fan Vaulting.—In the fan vault, the main ribs have .1 the same curvature, and form equal angles with each ther: the liernes also are horizontal, each set forming quadrant, where the vault is divided into rectangular ompartments, as at King’s College Chapel, Cambridge, nd where this is not the case, a semicircle, as m the xample given in fig. 9, which is from the cloisters of •t. Stephen’s, Westminster. Lierne and fan vaults were ften used in the same building, as in the examples 20 RUDIMENTS OF THE Fig. 9. here given frorf* the cloisters d® St. Stephen’s, d' which the walk are covered witi* fan vaulting, whilst the compartmenti at the angles ar< vaulted as showr in fig. 8. But witl the invention oj the fan vault camt also a change in the system of construction, which was also applied tc the latter lierne vaults when executed in connection with fan vaults. 24. The early lierne vaults display the same systenj of construction as the plain ribbed vaults, viz. a skele¬ ton of ribs filled in with thin pannels. In proportion to the complex character of the designs the ribs became more numerous and the pannels smaller, until it was found more convenient to execute the whole vault oi jointed masonry, the pannels being sunk in the soffits of the stones instead of being separate stones resting on the ribs. This new system was first introduced on the! crowns of the fan vaults, where, from the ramificationsi of the tracery, the ribs were most crowded, and was! soon extended to the construction of the entire vault,! although in many instances we find the lower portions,! which consist of plain ribs only, to be of ordinary rib! and pannel work, whilst the more decorated portions! are of jointed masonry. The vaulted roof of King’s College Chapel, Cambridge, is an example of the latter! mode of construction; that of King Henry the Seventh’s | ART OF MASONRY 21 apel at Westminster, on the other hand, is built en- ily of jointed masonry. 25. The art of stone-cutting appears to have reached highest development at the commencement of the teenth century; the works of this date exhibiting a I 22 RUDIMENTS OF THE perfect mastery of the subject. Some idea of the con^i plex character of the masonry of a fan vault may bj | obtained from an inspection of fig. 10, which is reduce^:] by permission of Professor Willis, from one of thje plates accompanying his valuable paper on the Coii t struction of the Vaults of the Middle Ages/^ in thin first volume of the Transactions of the Royal Institufiti of British Architects. , j 26. Ribbed vaulting was introduced into Italy in th^j thirteenth century, the church of St. Andrea di Vercelli. ■ in Piedmont, of which the first stone was laid a.d i 1219, being the first example of its use. , Although the pointed style attained to considerabh perfection in Italy, the round forms of the Roman | style of vaulting were never entirely superseded. In. deed, the greater part of the Italian ribbed vaults are merely plain vaults with ribs oh the groins, and are, in many examples, divided into compartments, by the flat band of the earlier round vaultings, which in the ge-j| nuine Gothic became a moulded rib. There are many|, peculiarities in the Italian ribbed vaults, which mark ^ their distinct character, and show that the pointed style , never became perfectly naturalized in Italy. We dof; not find in them either ridge ribs or liernes, and evenft the vaulted roof of the cathedral of Milan is a plain*! ribbed vault, ornamented with painted tracery. 27 . In Germany and the Netherlands w^e find liernes, vaults of very complex character, some of them exhi-g biting designs which would seem to have been invented|| solely for the purpose of showing the skill of the mason J in overcoming the difliculty of their execution. The'^ use of fan vaulting appears to have been confined ex- |, clusively to our own country. 28. The principal authorities referred to in writing-i ' & I , ART OF MASONRY. 23 brief sketch of the history of ribbed vaulting are— paper by Professor Willis before referred to; the k by the same author, “ Remarks on the Architecr j of the Middle Ages, especially of Italy; Archi- ural Notes on German Churches,^’ by the Rev. Dr. ewelland Gaily Knight’s “ Ecclesiastical Archi- ure of Italy.” These valuable works cannot be too I studied by those who wish to obtain a clear insight I the principles of ribbed vaulting, as practised in own and other countries. 9. The abandonment of the principles of the ribbed It, and the revival of solid vaulting with elliptical ins, may be dated from the commencement of the h century. In 1417 Brunelleschi brought forward plan for the erection of the celebrated cupola over crossing * of the Duomo, at Florence, which was rly completed at his death, which took place a.d. ••4. This magnificent cupola, which was the first at work of the revival, is built of brick,t like most er Italian domes; it is octagonal in plan, 138 ft. in meter, and 133 ft. in height, from the springing of vault to the base of the lantern. Vbout the same time an Italian architect built the 1 existing Church of the Assumption, at Moscow, of ich the vaults are of hewn stone. 10. The Italian architects who flourished during the nainder of the 15th century, followed classic models lost exclusively; and the revival of the columnar les, and of the round forms of vaulting, gradually ’ead northwards, although it w’as not until the middle The crossing is that part of a cross church at the iatersection of the e and transepts. ■ Lined with marbles of different colours. 24 rudiments of the of the sixteenth century that the principles of the revi^t produced any decided effect on the architecture of ot own country.* 31. The great masterpiece of the modern Italu style of vaulting is the dome of St. Peter’s at Rom 139 ft. in diameter, built at the close of the sixteen century, from the designs and instructions left for th purpose by Michel Angelo. I This was only a few years after the completion, i England, of the exquisite vaulted roofs of King’s Co lege and Henry the Seventh’s Chapel, before alluded t The dome of St. Peter’s exhibits an advanced kno^ ledge of the application of stone-cutting to dome being executed of regular masonry; whilst the earlh domes and cupolas were built of bricks, hollow earthei ware pots, pumice stone, and similar materials. It i however, defective in design, from its form not beir suited to support the weight of the lantern, and partit failure has taken place. 32. In the year 1568, a century after the erection ( the cupola of the Duomo, at Florence, and during th building of St. Peter’s, at Rome, Philibert De Lorme, celebrated French architect, published a work on arch tecture, which contains a complete system of lines fc stone-cutting. This is the first published book whic treats of masonic projection, all earlier writers bein silent on the subject. In De Lorme’s time, ribbed vaulting had fallen int disuse, and he speaks of Gothic vaults, and of tK The eastern windows of the choir at Lichfield cathedral are fiUe With stained glass, brought from Germany, the execution of which dah about 1530. The architecture introduced i character, with columns, entablatures, and which had not then reached England. n tnese paintings is of Itali other features of the reviv ART OF MASONRY. *' ;'hods practised for the adjustment of the’curvatures 8 ,he ribs, as belonging to a bygone age, considering works of the Italian school to be the only ones •thy of the name of true architecture. At the same e he acknowledges the extraordinary mechanical 1 displayed hi their construction, which appears, in eyes, to have been their chief merit. 13. From De Lorme’s time to our own there is little rth noticing in the history of the art. His work was owed by those of other French writers, who copied constructions, and on the Continent the study of (metrical projection has always formed a prominent nch of the education of the architect. 54. The admirable construction of the vaulted roof* St. Paul’s cathedral attests the knowledge of the hitect, and the mechanical skill of the workmen ployed in its construction. But, with the excep- n of a treatise by Halfpenny, published a.d. 1725, have no works of that date on stone-cutting, and leed possess scarcely any English publications on ! subject, except those published within the last few irs, amongst which the works of Mr. Peter Nichol- 1 stand conspicuous for their completeness. Mean- ile the principles of the construction of the medieeval bed vaults seem to have been completely forgotten, i so totally misunderstood, that both Halfpenny and cholson give methods, in their works, for construct- ; Gothic vaults, with diagonal ribs projected from ; transverse rib by ordinates; a system which we ^re shown to be quite at variance with the genuine aracter of ribbed vaulting. The dome of St. Paul’s is only a wooden covering placed round the ;k cone supporting the lantern, and is merely a picturesque addition to structure, not an essential part of the construction. C 26 rudiments of the OBLIQUE ARCHES. I’' 35. We now come to a new era in the history of t*^ arch. About twenty years ago was introduced a n(, system of building arches, totally unpractised before ! this country; we allude to the erection of oblique * skew bridges built in spiral courses. ' Oblique bridges seem to have been known on t ^ Continent long before their introduction into this cou ’ ^ try, and Vasari mentions one built over the river M gnone, near Florence, as early as 1530*; but the a does not appear to have been generally understoo( for, very recently, the Chevalier Mosca, whilst desig: ing the stone bridge built by him over the Dora E paria, near Turin, considered the erection of an ol lique arch too hazardous an undertaking, and went' a heavy expense in forming new approaches, in ord that the bridge should cross the river at right angles 1 the stream. 36. In England the art of building oblique bridg< arose simultaneously with the development of the rai way system. Before the introduction of railways, fe bridges were built except for carrying common roac' over rivers and canals, and such bridges were uniforml erected on a rectangular plan; and, in cases where th direction of the road was not at right angles to th stream to be crossed, the approaches were turned a might be necessary to effect this. The speed of th * locomotive engine rendered this arrangement quite inad * Vasari, “Vite dei Piu Eccellenti Pittori.” Firenze, 1568. The editio: of 1550 contains no notice of this work. The bridge in question was buil by Nicolo, surnamed II Tribolo, on the main road to Bologna, outside th gate of San Gallo, at Florence, and seems to have excited much interes at the time of its erection. No details are given of the principles on whicl it was constructed. ART OF MASONRY. 27 ible to bridges erected for carrying railways across >ing communications; and accordingly, with the introduction of locomotives, arose the necessity for tructing arches on oblique plans. . Amoqgst the first stone skew bridges built in this try of any size was one erected by Mr. John ey, A.D. 1830, over the River Gaunless, near Dur- > on the Haggar Leases Branch Railway, a mineral joining the Stockton and Darlington Railway. The 3 of this bridge is 26° 54', the direct span 12 ft., the oblique span 42 ft., and it was at that time idered a very bold undertaking, ther skew bridges were built about the same time he Stockton and Darlington, the Liverpool and Chester, and other railways; they soon became uon, and their construction is now well understood. . If an arch could be built in such a manner that nortar joints should be as strong as the voussoirs iselves, it would signify but little in what direction ourses are built; and the construction of an oblique built either of brick or rubble, offers no difficulty ; cementing material can be depended upon in this ict. But in building with common mortar, or in ;ructing arches of regular masonry, in which no ndence is placed on the adhesion of the cement, it nes necessary to place the courses at right angles e faces of the bridge, in order to bring the thrust of rch in the right direction, and to keep the obtuse IS from sliding outwards. is this which constitutes the peculiarity of the ue arch; for the courses not being horizontal, their lation will be constantly varying, from the springing e it is least, to the crown, where it is greatest; and ccurate working of this twist, as it is called, of the c 2 28 RUDIMENTS OF THE beds, is the great practical problem to be solved in J j execution of skew masonry. 39. The ordinary method of building a skew arch, ] 11, plate 2, is to make it a portion of a hollow cylinC ; the arch-stones being laid in parallel spiral courses, a i their beds worked in such a manner that in any sectJn of the cylinder perpendicular to its axis, the lines forruji by their intersection with the plane of section sh radiate from the axis of the cylinder. In this mode ( construction the soffit of each stone will be a portionl a cylindrical surface, and the twist of the beds will | uniform throughout the whole of the arch ; so that have only to settle the amount of the twist, and t stones can then be worked with almost as great facil as the voussoirs of an ordinary arch. The headii joints, or those which divide the stones of each coulL are portions of spirals intersecting at right angles coursing joints, or those which separate the courses,! that the voussoirs are rectangular on the soffit. 1| quoins, or voussoirs in the faces of the arch, are, ho ever, exceptions to this rule, for the following reas( If a heading spiral be drawn on the centering of arch, touching the extreme points of the imposts, it v lie partly within, and partly beyond, the plane of l| face. The heading joints, therefore, will not be parali to the face-line, and all the quoins will differ more| less from a rectangular form. Another peculiarityHi this mode of construction is, that the joints in the fi# of the arch are not straight, but curved lines, wkli chords will all radiate from a point below the axisji the cylinder, the distance increasing with the obliqUijj? of the bridge. 40. The merit of first explaining the construction/i the oblique arch is due to Mr. Peter Nicholson; ivl | ART OF MASONRY. 29 528, published his “Practical Treatise on Masonry Stone-cutting,” in which directions are given for dng the voussoirs of a skew arch in spiral courses. ; remained the only work on the subject until 1836, n Mr. Charles Fox published a pamphlet “ On the struction of Skew Arches,” which enters into the ect very fully, and explains the mode of working beds with twisting rules. This was followed in 1 by Mr. Buck’s Treatise, in which the subject is died with great clearness and simplicity, and tri- Dmetrical formiilee are given for obtaining the di- sions of every part of a skew arch by calculation, 3 ad of by geometrical constructions. In 1845, Barlow brought out a pamphlet, as a kind of lel to Mr. Buck’s work, containing a diagram for lining, by measurement with the scale, most of the I required in the erection of oblique arches. The of this diagram greatly facilitates the practical ap- ation of Mr. Buck’s formulee. In 1839, Mr. Peter holson published his “Treatise on the Oblique h,” which explains the subject very fully, though with the conciseness and precision which charac- ses Mr. Buck’s work. It is, however, a very valu- 5 treatise; and, from the number of problems intro- ed, is well suited to be put into the hands of the lent. 1. All the treatises above mentioned are written 1 one common object, viz. the construction of cylin- ;al skew arches in spiral courses, with beds of uni- n twist radiating from the axis of the cylinder. It carcely necessary to remark that skew arches may constructed in a variety of ways. Thus an ordinary w arch, built as above described, is a semicircle, or le portion of a circle, on the square section, and 30 RUDIMENTS OF THE elliptical on the face, which is an oblique section on portion of a cylinder. But it is quite possible to ma| the square section elliptical j in which case the faceis the arch will present an elliptical curve, flatter than tl i of the square section. Again, instead of radiating 1 1 bed-joints from the centre of the cylinder, they may - made perpendicular to the curve of the soffit on tl,( oblique section, as in fig. 12, plate 2, which certainly a better appearance in the elevation of the face of tl i arch. Both the last-named methods, however, introdu > more complexity in the working of the stone; as 4 twist of the beds will be constantly varying from til springing to the crown, and a great number'^of twisth r rules will be required. So, again, the irregularity in tl ;| soffit plans of the face quoins may be done away wil 1 by making the heading joints lie in planes parallel t ji the face of the arch (see fig. 12, plate 2), which givi the soffit a very regular appearance, but weakens tlj voussoirs by throwing them out of square; the acuj angles being liable to be fractured by a very trifling se tlement. ° In 1837, Mr. John Hart published a “Practici Treatise on the Construction of Oblique Arches,^^ i which these methods are described, with many othei which we need not here particularize. The peculia features of Mr. Hart’s system are shown in fig. IJi plate 2, which is taken from the work just mentioned, j 42. About the year 1838, Mr. A. I. Adie, the.! resident engineer on the Bolton and Preston Railwayl executed several oblique bridges on that line, the coni struction of which differs in many respects from Mi methods above described. The construction ofone(ir these bridges, viz. that over the Lancaster canal, iki shown in fig. 13, plate 3, which is copied from the draWji ART OF MASONRY. 31 3 presented by Mr. Adie to the Institution of Civil gineers, to accompany a paper on these bridges read session 1839, and is here published by permission of Institution. The peculiarity in the design of this ige consists in twisting the coursing joints, so that y shall be perpendicular to all sections of the soffit, de by planes parallel to the face of the arch. The ult of this arrangement is, that the courses are not uniform width, but diverge from the springing, where y are narrowest, to the crown, where they are widest, e square section of the arch is elliptical, not circular, 1 the bed-joints are worked so as to be everywhere ■pendicular to the curve of the soffit on the oblique tion. 13. The object proposed by Mr. Adie in the arrange- nt here described w'as to bring the thrust of the arch npletely parallel to the face, which can only be lomplished approximately with spiral courses of uni- m width. But the curved plans of the stones at the 'inging, and the difficulties wffiich arise in the ma- Tement of the face joints, from the stones not being one width, form great obstacles to its general in¬ duction. 44. In the Bath viaduct on the Great Western ilway are two skew arches of peculiar construction. ,ese arches cross the public roads to the west of the ,th Station; they are four centered gothic arches, d are built with courses diverging from the springing the crown. 45. We have gone to some length in our remarks on 3 different methods of constructing skew arches in der to induce* a careful study of the subject on the rt of the reader. In ordinary cases the cylindrical •m is the best that can be' adopted; but cases may 32 RUDIMENTS OF THE sometimes occur to which this is inapplicable, and t architect will then find it necessary to adapt the mo of construction to the necessities of the case. I specific rules can be laid down for the treatment i such cases j but the student who has thoroughly mai tered the principles of the subject will find no difficult in applying them in any instance that may occui however complicated. i SECTION II. ON PROJECTION. WORKING DRAWINGS. 46. As some of our readers may not be practicalli acquainted with the routine usually adopted in th, erection of large buildings, it may be desirable to saV a few words on the subject, that the nature of thi working drawings required by the mason may be fulh explained. "j 47 . On receiving the designs and instructions of th(| architect, the mason's first proceeding is to select a cou venient spot of ground for a stone-yard as near to th(' site of the works as practicable, and to erect his work ' shops and the necessary machinery for lifting the blocks if the scale of the works be such that they cannot hi conveniently moved without mechanical aid. 48. These preliminaries being arranged, the next thing is to order the stone from the quarries that have been chosen; and m order to determine the shapes and sizes of the blocks that will be required, the mason prepares from the designs of the architect a series of drawings ART OF MASONRY. 33 a large scale, on which he marks the heights of the eral courses and the arrangement of the stones in h course, numbering all the stones that require to worked to definite dimensions. He then makes a edule of the numbers and sizes of the blocks required, ich is sent to the quarry. Each stone being dis- ^uished by its proper number from the time it leaves quarry to its finally resting in its appointed place the building, no confusion will arise during the pre¬ ss of the work, care being taken to number the cks as nearly as possible in the order in which they to be set, as attention to this point saves much time 1 trouble in the execution of the work. 49. Whilst the blocks are being hewn at the quarry, ; mason is busily engaged in preparing the rules and nplets which will be required in dressing them to 3ir exact shape. For this purpose he lays down on arge wooden floor, or platform, full-size plans and itions of the work, course by course, carefully mark- ; the joints according to the working drawings pre- )usly made; and from the full-size drawings the nplets and bevels are made. Each templet is num- red, to correspond with the number of the block to lich it is to be applied, so that no mistake shall occur )m working a wrong block, and so wasting the stone, here the forms of the stones are irregular, a duplicate t of templets is sent to the quarries in order that they ay be roughly scrappled into shape by the quarry- an, which saves expense of carriage, and also much of e subsequent labour of the mason. 50. It will be seen from the above brief outline how uch depends upon the accuracy of the working draw- gs, and how important it is that a mason should be thorough practical draughtsman. The large size of c 3 34 RUDIMENTS OF THE I many working drawings (as for instance an elevation d: a church spire to an inch scale) renders it oftentimdl necessary to work on them piecemeal, as it were; anf great care and method are required in order to produd a correct drawing. We propose, therefore, to give j few practical hints on the management of large draw, ings, under the following heads, viz. Materials, Instrif ments. Scales, Figuring, Copying, and Platform-work.| The best material for working drawl ing is stout drawing-paper mounted on linen, and wel seasoned before use. This is somewhat expensive, and for common purposes strong cartridge paper will suffice, but on no account should unmounted paper be used foi any but the most temporary purposes, as it is easilj torn, and is spoilt by a few hours’ exposure in damp weather, whilst drawings on mounted paper will sustain no material injury during many months’ rough usage in the workshop and on the scaffold. 52. Indian ink* should be used for the prineipalj lines, red and blue colour being employed for centrejj lines, and for such lines of construction as it may be!^ desirable to mark in a permanent manner. ji Common writing-ink should never be used,nor shouldl any marks be made with it on a drawing, as the firsti* shower of rain to which it may be accidentally exposed!? causes the ink to run into an unintelligible blot. ^ 53. It is desirable to avoid the use of colour and.^ shading as much as possible, as the use of the brush?* causes the paper to shrink in those parts where colour'* has been applied. Indeed, pictorial effect and delicacy!) *The ink should be rubbed up fresh every time it is used. Beginnen I, sometimes, to save trouble, content themselves with adding water to ink ^yhlch has been allowed to dry on the slab. Lines drawn with stale ink are not/asit, hut will smear with the slightest moisture. ART OF MASONRY. 35 finish are out of place in large working drawings, lich should rather be executed with strong lines that 11 not be effaced by dirt or by the rough handling to ich they are exposed; accuracy and neatness are all it is required. ),|54. Instruments. —The principal drawing instruments fl^uired by the mason are—the needle-pointer, silk il'ead, the straight edge and set-square, lead-weights, ^^mmon and beam compasses, the ruling pen, and a set scales. 55. The Needle-Pointei' is simply a needle fixed in a art handle, the stump of a pencil for instance. It is 3d for marking points, which it does in a permanent inner and with greater accuracy than can be obtained the use of the point of a lead pencil. The pointer is o very useful as a rest to keep the straight-edge in % place when drawing long lines; and for copying swings by pricking through the principal points so as ; form corresponding punctures on a sheet of paper ^iced under the original drawing. 56. Lead-Wnghts are useful for a variety of purposes; t their principal use is to keep the straight-edge ;ady whilst drawing long lines, or when working a t square against it. Some draughtsmen keep an Instant at their side when setting out the leading lines 4 large drawings; but it is much more convenient i| be quite independent of the assistance of others in 1iose matters, and half-a-dozen heavy weights and «i'ew pointers will often supply the place of an extra ] ir of hands. 57 . The Silk Thread a reel of strong sewing silk, 4 d is constantly in use for setting out and testing the j^curacy of lines which are too long to be drawn with te straight edge at one operation. 36 RUDIMENTS OF THE 58. The Straight Edge is one of the mostimportad implements used in drawing, as everything depencw upon its accuracy. It should be made either of metJ or of some tolerably hard wood of uniform texturJ Wainscot and mahogany are objectionable materialsJ but pear-tree and sycamore answer very well. The! best way of testing the accuracy of the straight-edge is' to compare three together by holding them up against the light, two by two with their working edge in eon- tact. If the light can be seen through them, or if any one of the three do not perfectly coincide Avith the other two, the edges must be eorreeted again and again, until this degree of accuracy is obtained. 59. The Set-Square requires the same degree of accuracy as the straight-edge 5 and the straightness of its edges may be tested in the same way. To examine whether the angle contained by the working edges is exactly 90 , draw a straight line on a board, and set up| a perpendicular to it by means of the set-square j then reverse the square, and if the edge, when reversed, exactly coincides with the perpendicular just drawn, the square may be considered correct. The lines for a test of this kind should be cut on the board with a drawing-knife, as a pencil line is too coarse to be a satisfactory check. 60. Both straight-edges and set-squares should be kept flat in a dry place. If hung up against a wall they will warp and soon become untrue. 61. The Compasses are used for drawdng circular curves. Two pairs are required, one for curves not ex¬ ceeding 8 in. radius, and another for larger curves up to 15 in. radius. There are many different constructions of com- [ passes, each of which has some peculiar advan -1 37 ^ ART OF MASONRY. !. The reader may consult on this subject the reatise on Mathematical Instruments” of this Series, ;re he will find engravings and descriptions of all se in common use. These instruments are expen- , but no economy will result from buying inferior s, which are worse than useless. 2. The curved rulers manufactured in Paris of thin eer, and sold under the name of French curves, are f useful for drawing in between points previously srmined small portions of elliptical or other curves, ch cannot conveniently be struck from centres. 3. The Beam-Compass is used for drawing circular ires from 15 in. to 4 ft. or 5 ft. radius. It is an ex- sive instrument, but it is indispensable in making wings on a small scale, in which the curved lines are y close together. See ‘^Treatise on Mathematical truments” before referred to. For the purposes of •king drawings, however, a very simple and excellent m-compass may be made, as shown in fig. 14. This Fig. 14. g '' 4,1111111111 le^i 111111111 m»i ii 1111111111111 ii I ly 1 :rument consists of a clean pine lath 14 - in. wide, jk, and about 5 ft. long. At one end is attached a 1 piece of veneer with a nick in it, in which to rest pen or pencil. A slip of drawing paper glued on upper side of this rule keeps it from splitting, and, ng carefully graduated, serves as a scale. [*0 use this beam-compass a pointer is passed through lath into the drawing table at the proper distance n the rest, and the pen or pencil is placed in the k. The only thing to be attended to in the con- action of the instrument is to take care that the un- 38 RUDIMENTS OF THE derside of the rest is raised sufficiently above the unde side of the rule, so as not to smear the lines drawn wi the pen. The divisions on the scale should be drawn with curved lines, having the nick for their comm centre, by which means the pointer can be set pleasure in any part of the width of the wood. For setting out work on a platform, a lath with ^ brad-awl at each end, one as a centre, and the other ^ mark the curves with, forms a very good beam-compass 64. Sweeps .—When the radius of a curve exceeds 5 ftJ> it generally becomes necessary to describe it withoil making use of the centre; and for this purpose sweeps or curved rulers, are used, by means of which the curvet n are drawn in between points previously ascertained by calculation. These sweeps are made of thin wood, oi which the curve is first struck with the trammel as fol* lows:—Find by calculation or otherwise three points ic the curve, the middle point being in the centre betweei the extreme ones or nearly so. Fix a pointer at eachl of the extreme points, and lay against them two straight¬ edges, so that their intersection shall coincide with thf central point. Secure the straight-edges in this position with a cross-piece, as shown in fig. 15, and the curve Fig. 15. a I i ■ may then be drawn with a fine-pointed pencil placed atl the interseetion of the rules, the trammel being pressed^* steadily against the pointers whilst the curve is drawn. Take off the superfluous wood with a plane, and the sweep is ready for use. An instrument called a cyclograph, constructed on I ART OF MASONRY. 39 1 principle, is sometimes used for drawing arcs of les, but it is expensive; and the use of sweeps is ferable, if the length of the curve is such that the •k cannot be done without shifting the instrument, it is very difficult to make a neat junction between different portions of the curve. k. method of calculating the position of a number of- ats in a curve of which the radius is known, will be ad in art. 84. 5. Scales. — Drawing scales are made of brass, *y, box-wood, and card-board. They are divided a variety of ways, some being covered with divi- is, whilst others are divided at the edge only. )se of the latter kind are called plotting scales, and preferable to the former, as the dimensions can be iked off at once on the paper along the edge of the le, whilst the others require them to be transferred n the scale to the paper with compasses, an opera- i which tends to deface the scale, and introduces a nee of error, which it is well to avoid. ■ffie engine-divided card-board scales, manufactured 'Holtzapffel and Co., possess many advantages, of ch the principal ones are, their extreme accuracy their low price. They are sold at 95. the dozen; , although made of perishable material, will last ly years. Box-wood plotting-scales 12 in. long are ally sold at about 45., and ivory scales of the same ^th at about 105. 6. Before commencing a large drawing, it is advisable :ut a strip from the edge of the paper, and to make n it a scale of the whole length of the intended ving. The use of a scale of this kind saves much 3 that would otherwise be spent in setting off, and sking long dimensions by numerous applications of 40 RUDIMENTS OF THE a comparatively short scale; and, the scale being kep rolled up with the drawing, will generally contract an! expand with it, and thus obviate the perplexing difS culties which arise from the expansion and contractia of the paper from atmospheric changes. Independently, however, of the constant variatioi which is daily taking place with every change in thi weather, all paper is subject, when worked upon, to : certain amount of permanent contraction, which musi be allowed for in making the paper scale. The amount of this correction in the scale must depend upon th seasoning the paper has received, and the texture d the paper itself, so that no precise rule can be given for it. During many years’ observation of parish andj railway plans, we have found it vary from ^ to and a mean between the two may be safely taken;! that is, the length of each foot on the scale should bfl T303 ft. After a very few days’ work, the warmth o‘ the hand will cause the paper to shrink to the corre0i|| length, or nearly so. ? 67" Both box-wood and ivory scales are subject toj expansion and contraction, but the amount of this too trifling to be taken into account. . * 68. Standard Scale .—In order to ensure uniformity* in the dimensions of a large building, every master* mason should keep a standard metal scale very accu-* rately divided, by which all the scales used in making* the working drawings, and the rods employed in set-* ting out the work, should be carefully tested. Unless* this is done, it is very difficult to keep the work exact,* particularly in erecting bridges of large span. * 69. Centre Lines ,—On commencing a drawing, two* centre lines at right angles to each other should drawn through the middle of the work, of the whole J! ART OF MASONRY. 41 ;th and breadth of the paper. Lines parallel to :e should be drawn in pencil at regular distances, ■esponding to some even division of the scale, divid- the paper into squares or rectangles of convenient . The intersections of the lines should be punc- id with a needle, and marked in faint colour thus +, r which the pencil lines may be rubbed out. 'his precaution is of great use in keeping the work fectly true and square, as the divisions are a com¬ ic check on the parallelism of the lines of the draw- and afford a ready means of drawing lines in a ;n direction, on any part of the paper, without the essity of reference to the principal centre lines. ^hey also are of great use in ascertaining the exact )unt of contraction which the paper may undergo n time to time, and in checking the distances from centre lines. 0. Figuring .—The manner in which working draw- 3 are figured is of considerable importance. The izontal dimensions should be referred to centre lines tked on the ivhole of the plans, and the positions of the principal points should be obtained in the exe- ion of the work by direct reference to the centre ',s, and not by measurement from intermediate points. IS precaution confines any trifling error to the spot ere it occurs, instead of its being carried forward ough the work, as would otherwise be the case. To ble this to be readily done, two sets of dimensions I be required: 1st, the dimensions from point to nt; and 2nd, those from the principal points to the tre lines. If any clerical error be made in figuring ' of the dimensions, it can by this means also be ected and corrected, as every leading dimension is en once in gross, and can be also obtained by addi- 42 KUDIMENTS OF THE tion in two other ways. In spite of the utmost caf errors will creep into the working drawings, and tho| who have lost valuable time through some apparent! trivial mistake in a figure, can appreciate the advanta| of being able to correct mistakes as well as to detcf them. 71 . Elevations and sections should be figured on th same principle as the plans, vertical lines correspondii^ to the centre lines of the latter being marked upS them whenever practicable.* The vertical heights should all be referred to a com mon datum line, which should coincide, if possible, will some leading line in the design. In the execution « the work, the height of the datum line should be per¬ manently marked by a stout stake driven firmly ink the ground at the proper level. 72 . It generally happens in the execution of largj works that their levels require to be determined witlj great precision. Before making the working drawingsj therefore, it is always advisable to put down a perma l nent mark at the intended site, and to ascertain ifc height with reference to the levels of the proposed works. In figuring the elevations and sections, the position of the datum line with reference to this mail must be accurately noted, and there will then be no difficulty when commencing operations in ascertaining the proper level at which to start the work. 73 . Copying Drawings .—To make a correct dupli¬ cate-of a large drawing is a work of some difficulty. The most correct method is to draw the whole afresh^ to scale, but this is very tedious. Two methods are ini use for abridging the labour of the draughtsman. One is6 * This is done on the assumption that the work is intersected by vertical i planes passing through the centre lines of the plans. I ART OF MASONRY. 43 ay the drawing over the blank paper, and to prick Dugh the leading points with a needle. The copy is n easily lined in between the points thus formed, i other method is to place a sheet of transparent >er over the drawing, and having secured the two ether, so as to prevent all possibility of their shifting, copy is drawn on the transparent paper. 3oth these methods possess the common defect of ducing a copy of the original, not of exactly the le size, but, from the shrinking of the paper, a little aller, and in Consequence the real scale will be less n the nominal one. And this is not the only evil, in a large drawing the contraction of the paper is 3n so irregular, that the straight lines become twisted re or less; and these irregularities becoming still re distorted in the copy, the latter is of little value, ere is also great difficulty in pricking off a large iwing with accuracy, as it is difficult to get the paper lie sufficiently flat for that purpose. f4. The method the author would recommend is, first, divide the blank paper into squares or rectangles filar to those of the original; next, to make a care¬ tracing of the latter, marking the divisions of the lares; and, lastly, to lay this tracing on the blank oer, and to prick it through, adjusting the work in ;h square to the new lines. By this means the ors of shrinkage and distortion will be corrected, i the copy, when quite finished, will be of exactly ! same size as the original. The tracings, being efully laid aside, will serve for any number of copies it may be required. 75 . Platform Work .—The laying down of the work its full size on a platform is done by methods pre- ely similar to those in use for making large drawings 44 RUDIMENTS OF THE on paper, except that all the instruments are on a large scale, and that the brad-awl and chalk line take tl® place of the needle and silk thread. To ensure accuracil and uniformity in the work, the rods used for setting off the’ dimensions should all be divided from th| standard scale referred to in a previous article. Great care should be taken to render the platforrn perfectly level and quite firm, so that there shall be ^ no chance of any of the lines shifting their position. LINEAR DRAWING. 1 STRAIGHT LINES. 76. To draw a straight Line between two given Points .—Insert a needle at each of the given points; j press the straight-edge gently but firmly against them, and draw the line with the pen or the pencil held against the straight-edge, so as exactly to range with i the centres of the needles. | If the line to be drawn be of considerable length, say 15 ft. or 20 ft., so that it cannot be drawn with the straight-edge at one operation, the silk thread must he used as follows :— Insert the needles at the extremities as before, and strain the silk tightly between them; puncture the | paper in the line of the thread at short intervals,! and draw the line in between the points thus founded | as before. L This method should be always resorted to where ex-1 treme accuracy is required. A common but vicious | mode of drawing long lines is to produce them with I the straight-edge until they are of the required length; i but this method is not susceptible of minute accuracy. ^ 77* To draw straight Lines parallel to a given straight 45 ART OF MASONRY. Q ,—If the lines to be drawn do not exceed 2 ft. in ^th, they may be drawn by placing the working edge a large set-square to coincide with the given line, 1 fixing a straight-edge against the bottom of it, ping it steady with two needles and a weight or two lecessary. All the lines drawn with the set-square L of course he parallel to each other. If the lines to drawn are parallel to either of the centre lines, nothing re will be required than to set the straight-edge to nearest divisions of the paper. if the lines are very short, a small set-square and aight-edge may be used, the latter being steadied h the left hand, whilst the set-square is moved, and ! lines drawn with the right hand. For short lines also, the parallel ruler is much used professional draughtsmen, but it requires a practised ad to ensure perfect accuracy in its use, and we have t, therefore, mentioned it previously. Long lines must be drawn with the straight-edge ■ough points previously marked off. Let it be re¬ quired, for in- Fig. 16. LEVEL OfI SPRlNfclNC ORDIWARY SUMMER V/ATF.R stance, in making an elevation of a bridge, to draw a series of lines pa¬ rallel to the line a by fig. 16, which we will suppose to be 20 ft. long. rect perpendiculars to a h at such distances apart that e straight-edge will extend over three divisions or more, d on these perpendiculars set off by scale the exact stances from a 6 at which the parallel lines are to be awn. This is best done by setting off the distances i a strip of paper, and pricking them off on each per- 46 rudiments of the pendicular. The lines can then be drawn through the points thus found with great accuracy, as the slightest error in any part of a line is at once detected by re¬ ference to the more distant points. 78. To divide a straight Line into a given Number oj unequal Parts, which shall diminish in regular Pro^ gression, and so that a given Division shall pass through a given Point .—Let a b, fig. 17 , be the height of the pier of a bridge, which it is proposed to divide Fig. 17. into eleven quoins, the top of the second quoins being required to coincide with c, the level of the springing of the arch. Assume any convenient point' d, and join a d, c d, b d; take a slip of paper, divide its edge into eleven equal parts of convenient size, and slide it over the triangle until the zero, and the 2nd division, are respectively on the lines b d,c 6?, whilst the last division is on the line a d. Prick off the points d:, 5, 6, 7j 8, 9, 10, and draw lines through them, intersecting the line a b, which will then be divided as required. The method of arranging the sizes of the courses of a building, so that the first and last shall be of given heights, is precisely similar. ART OF MASONRY. 47 iie above is a very convenient practical rule, but only be applied within certain limits. ANGLES. ). To set off a right Angle .—There are three ways oing this in common use. It may be done on a small ; mechanically with a straight-edge and set-square, a large scale it may be performed by describing with Q-compasses a triangle, of which the sides are re- tively as 3, 4, and 5 ; or by describing two isosceles igles on a common base, of which the centre is the t through which the perpendicular is to pass, see fig. date 1. This last method is the most perfect of the e, as the accuracy of the work is at once checked rying with a silk thread whether the vertices of the Igles range with the centre of their common base. ). To set off an acute Angle .—This may be done . small scale by pricking off the angle from the edge protractor; but this method is inapplicable to large /ings, as the sides of the angles would have to rocluced from a line probably not exceeding a few es in length. he best method of setting off an angle, of which the 5 are of considerable length, is to describe with beam passes an isosceles triangle of which the base and 5 are respectively as the chord and radius of the angle, length of the chord is obtained as follows: since the d of any arc is double the sine of half the angle sub- ed by that arc, we can find the chord for any angle, aking from a table of natural sines the sine of half angle and doubling it.* Tables of natural sines are dated for radius = 1, the length of the sines being 1 in decimals; in plotting an angle by this means it istead of doubling the sine, we may use half the radius, which is a simpler plan, although the principle is not so immediately apparent. 48 RUDIMENTS OF THE is therefore necessary that the scale should be dividec decimally, and that the radius chosen should be ten, oi some multiple of that number. Example .—To set off an angle of ^0°, the sides t( be not less than 8 ft. long. Look in the table for th natural sine of 35°, which is *5735764. The length e the chord will be twice this, or T1471528. Taking tk radius in inches, the nearest convenient number will be 100, and accordingly the decimal point must bi shifted two places, making the length of the chon 114*71528 inches. It is always desirable in plotting angles, that tbi points found should be beyond the work, and noi within it, so that there may be no necessity for pn ducing their sides. 81. An Obtuse Angle is plotted by producing oneo: the sides and setting off the supplement of the requiiet angle. ' 82. Measurement of right-angled Triangles .—In aw right-angled triangle, if one side and one of the acul; angles be given, the remaining sides can be readib found by calculation, with the help of a table of sines, cosines, secants, and tangents. AVe presume the reade; to be familiar wdth the method of doing this, but it raayj be useful here to insert the formulae. In the right-angled triangle ab c, fig. 19, plate 1. Let z a b che, the given angle—the L b a c wdll of course be its complement. 1 st, Let the hypothenuse « 6 be the given side, then side a c = a b x sine Labe and side b c = a b x cos Labe. 2 nd, Let the given side be one of those containing the right angle, as 6 c. then side a b = b e x sec Labe and side a e — b e x tang Labe. ART OF MASONRY. 49 • any two sides are given, the third side may be id arithmetically in the absence of a table of sines. [ the hypothenuse be one of the given sides, then the a c = y/ a b^ — b c^, and side bc=s/ a b^ — c‘. f the two sides containing the right angle be given, then side a b = a + b c^. ’he solution of right-angled triangles is very fully lained in Mr. Heather’s “Treatise on Mathematical truments,”* to which we w'ould refer the reader who ot familiar with the subject: the foregoing cases are :ely inserted here to assist the memory. CURVED LINES. 53 . Circular Curves. —The following problems will found useful. "divert the Span and Rise of a Circular Arc, to find Radius. ^et r = radius. s = half-span. V — rise, or versed sine. rhen r = 2v Demonstration (fig. 20, plate 1).—Let a d e he the of which the radius is required: a b the half-span, \b d the rise, and let c be the centre of the circle. Join ac, dc, and ad; bisect ad in f and join f c. e right-angled triangles, bad,fc d, are similar, having common anglec; therefore, b d : d a :: f d : d c = “ A Treatise on Mathematical Instruments,” in the Rudimentary atises. 50 RUDIMENTS OF THE da^ alP‘-\-hd’^ s^-\-v^ dc — Ij^ 2bd ' 2bd ' 2v Q.E.D 84. The Radius being given, to find the Length of at Offset at any given Point on a tangent Line. Let r — radius. t = distance on tangent line from the point oi contact, 0 = offset. Then o — r— sj — P. Demonstration (fig. 21, plate 1).—Let c e be the given tangent, c the centre of the circle, and e h the offset, of which the length is required. Join ac,ht and draw bd parallel, and, by construction, equal to at Then eh — ad—ac — dc. Now, dc — ch"^ — dJf .'. eb = a c- ^ c b'^ -d b^ = r - V - P. Q.E.D, 85. In designing large works it is often requisite to connect two straight lines by a circular curve. Before j the offsets can be calculated for this purpose the fol¬ lowing data must be known, viz. the angle formed by the lines to be connected, the radius of the curve, and the distance from the point of intersection to the points of contact. The first of these conditions is generally determined by the circumstances of the case; with re¬ gard to the second and third conditions, one of the two must be assumed and the other calculated from it. 86 . First Case.—7%e Distance of the Points of Con¬ tact from the Point of Intersection being given, to find the Radius. ART OF MASONRY. 51 !n the lines to be connected, let h and d (fig. 22, plate be the points of contact, which will necessarily be lidistant from the point of intersection, foin h d; bisect it at e, and join a e; then be X ah radius = -. a e Demonstration.—Let c be the centre of the circle; \ be and ec. The right-angled triangles abe and b are similar, having the angle b ac common to ,h; ae : be :: ab : be = be X ab a e Q.E.D. The construction made use of in the above problem aseful for determining the radius of curvature of a ig-wall of a bridge. Thus (fig. 23, plate 1), let df he the front of the idge, d the point at which the curve is to com- ^ nce, and b the point at which the wing-wall is to il. Join bd; bisect it at e, and erect the perpen- lular ea cutting c?/*produced in a; join ab, and cal- ?ate the radius as above. 37* Second Case .—The Radius being given, to find Distanee of the Points of Contact from the Point of f ersection. To do this, assume any approximate points, as b^ d^ 24, plate 1), and find the corresponding radius bi Ci- Let r = given radius = be, 7*1 = assumed radius = bi c,, t = required length on tangent line = ab, ti = assumed length on tangent line = a^ b^. n, 7*1 : :: 7’ : / = — 38. To find the length of a Circular Arc .—If the radius D 2 52 RUDIMENTS OF THE is not known, it may be found as described in art. 83. Let abe (fig. 25, plate 1) be a portion of the circumfe¬ rence of a circle, of which the radius = r. Assume any convenient angle, as ac h, and calculate its chord as in art. 80. Set it off on the curve with beam-compasses, and measure the remainder, be, as n straight line, which may be done without sensible error, by assuming such an angle as will leave a very small remainder. The semi-circumference of a circle is equal to radius X3T416; the -rhrth part, or that corresponding to a single degree, is therefore equal to radius x *017453. If we call n the number of degrees in any angle, acb, we have for finding the length of any arc, a b, the simple formula: length of arc = wr x *017453. Example .—Let r = 134 ft. On examination let it be found, that the number of degrees which will give the smallest remainder is 70. The length of the arc, a h, will therefore be 70 x 134 ft. x *017453 = 163*70914 ft.; to which must be added the remainder, b e, the sum of | the two making up the whole length of the arc abe. t 89. This problem is of great service in ascertaining the length on soffit of an arch of known span and rise, either for the purpose of dividing the arch-stones, oij for laying down a development of the soffit. I Its converse is equally useful in setting off on a cir- ji cular arc, a distance equal to a given straight line, i Let it be required on the curve abe (fig. 25, plate 1) toi set off a portion, ae, that shall be equal to a given j straight line, say 164 ft. long. . jl Let the radius of the curve be 134 ft. as before, then ^ _-= 70’14. Reiecting the decimak,!^ 134 X *017^53 » find the chord of 79°, which for radius = 134 ft. is;» 153*718 ft.; and the length of the arc a 6 = 163*709 ftH ART OF MASONRY. 5.3 iucting this last quantity from 164 ft., we find the lainder he = *291 ft. .^o set off the required distance on the curve, set off chord ah = 153'7l8 ft., with beam-compasses, and n b set oiF be = *291 ft.; the length of the arc abe be 164 ft., as required. 0 . It is often necessary to transfer the divisions of arch-stones from the development to the elevation .n arch. The best way of doing this is to set them from the development on a long lath, and to bend latter round the curve in the elevation, to which the sions can then be readily transferred. This method fines any little inaccuracy to the joint where it occurs; if it be attempted to set oif the joints stone by stone 1 compasses, great difficulty will be experienced in dng the minute allowance which is necessary for the erence between the length of the curve included veen two joints and the corresponding chor5, which be distance to which the compasses must be set. 1 . Method of describing an Ellipse .—On a small e, and w'here it is desirable to avoid defacing the er with the points of the compasses,—as, for example, rawing the coping of a curved wing-wall,—the sim- it mode of proceeding is to find a number of points be curve, and to connect them by means of a curved r, the edges of which are cut into a continuous series urves of different radii. my number of points in an ellipse may be found as )ws :—Let af ef (fig. 26, plate 1) be the respective i-diameters of the ellipse*. With /"as a centre and ind ef as radii, describe two quadrants. Divide the er quadrant into any convenient number of divisions? , 2, 3, and draw the lines 1 Ij/, 2 2i/, 3 3i/, cutting lesser quadrant at Ij, 2^, S^. From the points 1 and Iraw lines parallel to the diameters cutting each 54 RUDIMENTS OF THE other at b, then h will be a point in the ellipse. In a similar manner will be found the points c and d. 92. When an ellipse has to be drawn on a large scale, the best way is to strike it from centres; and, although this is only an approximation, no portion of an ellipse being a circular curve, no appreciable error will result if a sufficient number of centres be taken. The following method is very simple. Having found a number of points in the curve, as Z>, c, d, draw the chords ab, b c, c d, de. Bisect d e with a perpendicular cutting/’e produced in g; then g will be the centre for the portion of the curve between e and d. Join dg and bisect cd wdth a perpendicular cutting dg in h; then h will be the centre, for the portion of the curve between c and d. The centres i and k are found in a similar manner. 93. To set out an ellipse on a platform; when the scale is such that the operation must be performed without making use of centres, we must proceed ratherdifferently. Divide the right angle contained between the two semi-diameters into any convenient number of angles, as j af\, af 2, af^ (fig. 27 , plate 1), and multiply their re¬ spective sines and cosines, the former by radius e f, and the latter by radius af. This will enable us to lay down i the points b, c, d, by means of offsets from the diame- j ters, as shown in the figure. The curves e d,d c,-.&c., must be drawn in with curved ■ rules, made as directed in article 64. « To find the radii, draw the chords e d, dc, &c.; bisect t the angles formed by their intersections with short lines 1 as shown in the figure. On these bisection lines, let | fall perpendiculars, as d d^^, c Cj, &c., and the several radii t can then be calculated as in article 83. j 94. An ellipse of moderate size can also be struck on a platform, from the foci, as follows:— ART OF MASONRY. 55 'rom e as a centre (fig. 28, plate 1), with radius af, jribe arcs cutting a a in w, I, which will be the foci he ellipse. Put in a brad-awl at each of the foci, round them pass an endless cord of such length when strained tight, it will just reach the point e. ! curve may then be drawn in with a brad-awl or a ving knife pressed firmly against the cord. 'his is a very expeditious method; but it requires siderable management to produce an even line, and lot susceptible of minute accuracy. The practical culty arises from the elasticity of the cord. 5 . To draw a Line perpendicular to the Circurnfe- :e of an Ellipse at any Point, as n (fig. 28, plate 1). oin mn, nl: a line bisecting the angle mnl will be pendicular to the curve at n. ''his problem is required in drawing the joints in the 'ation of an elliptical arch. 6 . Spiral Curves .—In making drawings of oblique Iges, numerous projections of spiral lines have to be wn; and it is of importance that this should be done 1 great exactness. The best method of accomplish- this, is to make a very accurate template for each of curves in cardboard or veneer, which will ensure feet uniformity in the work, and also save much of draughtsman’s time. '7. Principles of Projection .—The working drawings he mason may be classed under two heads:—First, metrical projections; and, secondly, developments of faces. The geometrical projections are always made either horizontal or vertical planes; the drawing ig called in the first case a plan, and in the second 3 an elevation. When the plane of projection cuts object represented in a vertical direction, the draw- is called a sectional elevation, or, in brief, a section. RUDIMENTS OF THE 5G It will be observed that most plans of buildings. are, in fact, horizontal sections, but the term is technicallv applied to vertical projections only. Developments are representations of the surfaces of solids, as they would appear if unwrapj^ed and laid flat, and are made use of to obtain the dimensions of surfaces which, from their inclined position, become foreshortened both in plan and section; and for the delineation of curved surfaces, wdiicli cannot be accurately represented in any other manner. The nature of plans and elevations ma)’^ be clearly understood by considering them as perspective projec¬ tions on a sphere of infinite radius of which the centre is the point of sight. 98. The following properties of geometrical projec¬ tions should be kept in mind, Lhies .—All horizontal lines will be represented of their true length and curvature on plan. All vertical straight lines will be represented of their true length in elevation. All lines inclined to the horizon will be more or less foreshortened in plan. 99. The length of any inclined straight line may be obtained from the plan and elevation by a simple construction. Thus to find the length of the arrises of a square pyramid: let c c (fig. 29, plate 1) be the vertical height of the pyramid, and c b the half-diagonal of the base; then the required length ab is the hypothenuse of the right-angled triangle acb, and can be formed by constructing the triangle and measuring the hypothenuse, or by calculation, since ab = yj a (f -j* b 100 . Surfaces .—Horizontal planes will be represented by identical figures on plan, and by straight lines in ele¬ vation. Thus the plan of a circle parallel to the horizon will be a circle, and its elevation will be a straight line; [ ART OF MASONRY. 57 if a s a; e' it a ci P iclined to the horizon^ its plan will be an ellipse in positions except the vertical, when its plan will be a ight line, and its elevation a circle, a straight line or ellipse, according to the position of the plane of ■ation. 01 . Solids .—The plan of a right cone standing on jase will be a circle, and its elevation a triangle. 'he plan of a right cylinder, similarly placed, will be rcle, and its elevation a rectangle. , 'he plan and elevation of a sphere will always be les. 'igs. 30, 31, 32, 33, and 34, explain the manner of jecting the plan and elevation of the prism, pyra- , cone, cylinder, and sphere. Fig. 30. Fig. 31. Fig. 32. Fig. 33. D 3 58 RUDIMENTS OF THE Fig. 34. 102. Sections .—^The follow¬ ing properties of the cone, cy¬ linder, and sphere, should be borne in mind:— Every plane section of a cone perpendicular to its axis will be a circle. Every plane section of a cone passing through the vertex and the base will be an isosceles triangle. Every plane section of a cone cutting its axis at an acute angle, greater than that made by the slant side, will be an ellipse, or a segment of one. Every plane section of a cylinder parallel to its axis will be a rectangle. Every plane section of a cylinder perpendicular to its axis will be a circle. Every plane section of a cylinder cutting the axis obliquely wall be an ellipse, or a segment of one. Every plane section of a sphere will be a circle. 103. The sections above enumerated can be pro¬ jected in any position with very few lines; the projec¬ tion of an ellipse being always either a straight line, a circle, or an ellipse, and the only data required for drawing the latter figure are the lengths of the major and minor axes. There are however many other curves, such as those formed by the intersection of two curved surfaces, which are not so easily described, and which require a considerable amount of projection, and transference of lines, in order to represent them accurately. i 104. Developments .—The curved surfaces of solids j may be classed under two heads; 1st, those with which . ART OF MASONRY. 59 i traight-edge will coincide in one direction, as the ■viifaces of the cone and cylinder; and 2nd, those with .viich a straight-edge will not coincide in any direc- = i 1 , as the surface of a sphere. The former are some- = i es called curved planes, and their development, in ll case of the cone and the cylinder,* is very simple. I s latter can only be developed approximately, be- vse it is impossible to bend a plane, so as to coincide vih a spherical, surface. 05. The development of the curved surface of a lilt cone will be a sector of a circle, whose radius is ; 1 slant height of the cone; the length of the arc ung equal to the circumference of the base of the iiiie; see fig. 35. ' Fig. 35. Fig. 36. ri i 06. The development of the curved surface of a it cylinder will be a rectangle, whose length is the al length of the cylinder, and-whose width equals circumference of its base; see fig. 36. Winding surfaces cannot be developed even approximately, being Jt -ex in one direction, and concave in the opposite. 60 RUDIMENTS OF THE 107 . The surface of a sphere may be developed approximately in three different ways ; 1st, it may be considered as a polyhedron, of which each side will be a plane surface ; 2nd, it may be divided into gores like the gores of a balloon, in which case each gore will be a portion of a cylindrical surface; lastly, it may be divided into zones, each of which may be treated as a portion of a conical surface. This last method is the one most practically useful, and will be understood by inspection of fig. 37, plate 4. PROJECTIONS OF THE CONE. 108. The several projections of the cone which we are about to describe*' are principally required by the mason in the execution of battering w’alls, on a curved plan, which form portions of hollow cones. The pro¬ jections and development of a right cone have been explained above, in arts. 101 and 105. 109. To draw the Projections of an inverted Com from which an oblique Frustum has been removed .— j In fig. 38, plate 4, side elevation, \&tbde be the inverted cone, and b d m the frustum removed. Bisect b m in and through the point n draw e^n o b^ parallel to the base, and cutting the axis of the cone at e^. Draw b bi parallel to the axis of the cone, cutting e^n 0 b^ in and making e^ b^ equal to c b, the radius of the base. It may be easily shown that e^n^ ■= 0 b^. In the plan draw the diameters det^and a e c perpendicular to each other, so that all straight lines drawn on the plane of intersection, parallel to a e c, shall be horizontal. Set off e n,b 0 respectively equal to e^ n, 0 bi in side elevation. With radius e 0 , and centre e, describe the quadrant 0 qr, and through n draw p n q parallel to a c, cutting the arc 0 q r in g, and make n p — q n. ART OF MASONRY. 61 t off m = w 6; then h m and g p will be respec- ely the major and minor axes of the ellipse, which is } horizontal projection of the oblique section of the le. Since by construction n b = e q, the length of the ni-axis minor qn — sj n Jr — en\ In ordinary cases, 3 difference of the lengths of the major and minor es is so small, that the quarter ellipse may be drawn thout sensible error, as a circular curve, with radius j and centre on g g?, removed from n by the differ- ce between the semi-axes. 110 . It will be seen ' , by inspection of fig. 39 that in building a curved wing-wall, ter¬ minating in a pier as there shown, the hori¬ zontal distance b n (fig. 39) should not exceed bn \n fig. 38, plate 4 : or the coping would have a very unpleasing appearance, as shown in fig. 40. 111 . When the plan of the coping is less than a quarter ellipse, the side of the pier must be made square with a tangent to the ellipse at the point of intersection with the w'ing-wall. 112 . To draw the front Elevation ,—Set off = 6^' 62 RUDIMENTS OF THE in side elevation, and nm = bn. Through n draw q np parallel to a c, and set otF nq = nq in plan; and np = n q. Then q p, bm are respectively the major and minor axes of the ellipse b qmp, which is the ver¬ tical projection of the oblique section of the cone. 113. In drawing curved wing-walls to support an embanked approach to a bridge, the data given or as¬ sumed are the height b b ^; the inclination of the slope of the bank, which should coincide with that of the top of the wall ;* and the batter or slope of the face of the wall. As we have often found beginners to be very much at a loss how to draw the plan and elevation of such a wall without covering the paper with unneces¬ sary lines, we subjoin an example. Fig. 41. * The coping of a wing-wall is sometimes made to stand up above the slope of the bank, but this has an awkward appearance. To make the top of the wall form a spiral plane, as recommended in “ IN'icholson's Railway Masonry,” is perhaps the worst plan that can be adopted as the coping is not parallel to the slope of the bank. ART OF MASONRY. 63 ■"'o avoid confusing the diagram the coping of the w{l is omitted. I jet 6 = 12 ft. I jet the slope of the top of the wall be 1| horizontal vertical. ,jet the batter of the face of the wall be 1 horizontal "d) vertical. i?hen w 0 = 12 ft. x 1^ = 18 ft. i and e n = 0 = '■/ ft. = 2 ft. transfer these dimensions to the plan. n b = e 0 = e q = IS it, q n = \/ n fr — e 'if = 324—4 = 17'88 ft. IPhe plan of the front line of the top of the wall will tlirefore be a quarter ellipse, whose semi-diameters are ■'♦pectively 18 ft. and 17‘88 ft. 'The Front Elevation of the front line of the top of J wall will be a quarter ellipse, of which the semi- dmeters are respectively 12 ft. and 17'88 ft. j|114. Development of the Cone. —Divide the circum- I ence of the base into any convenient number of equal •ts as shown in the plan (fig. 38, plate 4) by the points , h, &c., and transfer these divisions to the side eleva- n. From the new points thus found draw lines radi- ig to the apex of the cone, cutting6 min&c. rough /i, ^ 1 , Ai, &c., draw lines parallel to the base, cutting the sides of the cone. Having drawn the ^^■elopment of the slant surface of the cone, divide the a( b d bio correspond with the divisions of the base in |l.n, and draw the radiating lines/e, g e, h e, &c., cor- 1 ^ ponding to the radiating lines in the side elevation. |From the points found on the slant side of the cone, v^.h e as a centre, draw circular arcs cutting the radia- jttg lines/e, g e, h e, &c., in /, g^, /q, &c. A curve :Ciwn through these last points will be the develop- 64 RUDIMENTS OF THE merit of the line bounding the oblique section of the cone. The oblique section of the cone will form an ellipse, whose major axis = bni in the side elevation, and whose minor axis = qp in the plan. 115. To project the Lines of the Coping of a curved Wing-Wall. —The coping of a curved wdng-wall is worked in such a way that its bed shall be every¬ where level in a direction perpendicular to the curve of the wall. Thus, fig. 42, any number of lines, as 1, 2, 3, drawn perpendicular to the curv^ of the wall, will be horizontal lines. If the coping bed were made level in the direction of the centre : of the cone, as shown by I the line e q, it is evident i that the intersection of the i coping with the pier will not be a level line, the front ) of the coping being higher than the back, which would j have a most unsightly appearance. 1 116. If the top of the wall be worked as above de- 1 scribed, the front and back edges will lie in planes^ of \ different inclinations, intersecting each other on the line i q n. It is usual to make the hack of the wall coincide f wfill the slope of the bank. The front line will there- < fore be found in side elevation, without any transference li of lines, by setting off the width of the top of the wall ji i * If the front and back edges of the top of the wall are made to lie in j planes, so as to be represented in side elevations by straight lines, all level | lines in the coping bed will be curved, and not straight; but the curvature i is too small to be measured in so short a distance, and cannot be distin¬ guished from a straight line. Fig. 42. ART OF MASONRY. 65 f M the top of the slope as shown in fig. 41, and draw- a straight line from the point thus found to n. In ffrit elevation all the lines of the coping will be ellip- t|d curves. 3l 17- It may be necessary to remark that the top and |[|;tom lines of the coping in side elevation will not be j| allel to each other. This arises from the thickness l[|ng set off at the top in a vertical, and at the bottom ijan inclined direction, so that the lines will diverge fjm the top downwards. (See fig. 41.) i L18. Intersection of a Cone and a Cylinder (fig. 38, te 4).—This is a problem of not unfrequent occur- ice, as in the case of a cylindrical culvert passing ough the curved wing-wall of a bridge. In a dia- ,m here given the axes of the cone and cylinder are ,de to intersect each other at right angles. In front elevation the projection of the intersection the cylinder with the slant surface of the cone, will a circle. Draw two diameters, the one parallel to ; base, the other to the axis of the cone. Divide the cumference of the circle into any convenient num- ' of equal parts, as 16. Divide one of the diameters o 8 parts by perpendiculars drawn through the divi- ns on the circumference, and transfer these divisions the axis of the cone in side elavation, as shown at a., &c. Through these points draw lines parallel to ; base, and cutting the slant side of the cone in 1,2,3, . Transfer the divisions on the diameter of the inder to the diameter a c in plan, and through the ints thus found draw the perpendiculars a a^, h h., &c. aw the diameter he d oX, right angles to a ec, and set c on e d the divisions el, e2, &c., respectively equal t the corresponding lengths 1 a«, 2h^, &c., in the side € vation. Through the points thus found, with centre e, 66 RUDIMENTS OF THE draw circular arcs cutting the perpendiculars just drawn in a, c, d, &c. A curve traced through these points will be the plan of the curve forme'd by the intersection of the cone and cylinder. In side elevation make a a«, b &c., respectively equal to a b b^c Co, &c., in plan ; and a line drawn through the points a, b, c, d, &c., will be the side ele¬ vation of the curve of intersection. The development of the curve of intersection on the surface of the cone is found by transferring the distances € m, e\,e 2, &c., on the slant side of the cone, in the side elevation, to the corresponding line in the development, and through the points thus formed drawing with the ^ centre e, circular arcs, a q, bp, c o, &c., respectively equal to the corresponding arcs, a q, b p, &c., in plan. To find the development of the surface of the cylinder draw the straight line w,, equal to the circumfer¬ ence of the right section of the cylinder, and divide it into the same number of equal divisions. At the points i fli, bi, Cl, &c., thus found, erect perpendiculars, a^, a, b^ b, Cl c, &c., respectively equal to the corresponding lines, «! a, by b, &c., in the side elevation. The curved line mab c, &c., drawn through the points thus found, will be the development of the curve of intersection in the surface of the cylinder. I PROJECTIONS OF THE CYLINDER. I, 119. The projections ahd development of the cylinder f have been already described in arts. 101 and 106 ; but , as it is of great importance that the subject should be thoroughly understood, we return to it again, for the purpose of explaining the nature of spiral lines, and the manner of projecting them. i. I ART OF MASONRY. 67 20. In the diagram (fig. 43, plate 5) the right cylin- is supposed to be in a horizontal position, in order t t the application of the projections here described t :he construction of vaults and arches may be more c irly understood. i''he elevations of the ends of the right cylinder, js c D, fig. 43, plate 5, will be circles exactly coin- c ;ng with the square sections. The plan will be a r tangle, and the development, b a b c d c, will also b a rectangle, whose wddth, b a b, = circumference 0 he circle formed by the square section. 21. If the cylinder be cut obliquely by a plane s face, as shown by the line e b on plan, the resulting s lion w’ill be an ellipse, whose major axis = e b, and V Dse minor axis = diameter of the cylinder. ?he development of the curve of the oblique section i: ound as follows:—Divide the circumference of the are section into any convenient number of parts, as ,een. Divide the width of the development in the s le manner as shown at 1, 2, 3, &c. Transfer the isions on one-half of the square section to the plan, as wn at c 1 2 3 4 5 6 7 D- Through the points thus nd, draw lines parallel to the axis of the cylinder ting the line a ^ at a b c d e f g. Through the points 3 4 5, &c., in the development, draw lines 1 a, 2 b, &c., parallel to the side of the cylinder, and re- ctively equal to the lines 1 a, 2 3 c, &c., m plan, jurve drawn through the points abed, &c., wall be development of the curve of the oblique section. 22. If we draw on the development any straight 1 in an oblique direction, as c e b, this line, when pped round the surface of the cylinder, will form a •al line whose inclination to the base of the latter . be uniform*throughout its whole extent. 68 RUDIMENTS OF THE 123. In building cylindrical arches on an oblique plan in spiral courses, the lines of the coursing joints are called coursing spirals; and those drawn perpen¬ dicular to them, for the purpose of determining the position of the heading joints, are called heading spirals. 124. Let it be required to project a spiral, as c e b, which makes one revolution in the length c n. Having divided the plan and development, to correspond with the divisions on the circumference of the square section as before described, join c b, and this line will be the development of the spiral c e b. Make the lengths 1 a., 2 b„, 3 c^, See., on plan, re- ’ spectively equal to the lengths 1 a^, 2 b^, 3 C 2 , &c. on the development. A curved line drawn through the points a., b., &c., will be the horizontal projection of the spiral CEB. 125. In the Elevation of the Face of an oblique cylindrical Arch, to draw the spiral Lines in the Soffit, as, for example, the heading Spiral b a^ b^ c^ d e^f g^ e in the Plan. —The plan and development of the spiral are found as above described. Draw e b = e b in plan. Bisect it in d^, and on e d^ b, with d^ as a centre, draw the square section of the arch, divide it into eight equal parts, as before done to obtain the development of the cylinder, and through the opposite divisions, 1 7? 2 6 , 3 5, draw lines parallel to e b. From the points a^, b^, c,, &c., in plan, let fall perpendiculars on e b, and transfer the points thus formed to e b in elevation. Erect perpen¬ diculars at these points, cutting the lines 1 7, 2 6 , 3 5, in fli, 61 , Cl, &c., and a line drawn through these points will be the elevation of the spiral projected on a plane parallel to that of the face of the arch. The elevation | of a coursing spiral is obtained in the same way. 126. To draw an oblique semi-cylinSrical Arch with ? ART OF MASONRY. 69 irved Face (fig. 44, plate 6).—Draw the square section I divide the soffit into any convenient number of equal ts, as eight. Transfer these divisions to the plan, as )wn in the diagram; and through the points 1,2, 3,4, }, 7, draw lines parallel to the springing lines of the h a «i, i h, cutting the face of the arch sX b c d efg h. To develop the soffit, draw — the length of the fit on the square section; and, having divided it into ; same number of equal parts, set up the perpen- ulars, i, 7 f, &c., respectively equal to i, , 6 g, &c., on plan. A curve drawn through ihgfe, ., will be the development of the front line of the fit. To develop the face, draw ai = ai\n plan, and set off , 1 2, 2 3, &c., respectively equal to a b, b c, c d, &c. ect the perpendiculars \ b, 2 c, ^ d, &c., respectively lal to the heights 1 b^, 2 Ci, 3 d^ in the square section, i a curve drawn through abode, &c., will be the v'elopment of the face of the arch. Cases similar to that here given are not of frequent mrrence, but they are sometimes unavoidable, as in ilding a skew culvert in the face of a curved wing- 11 . 127 . IntersecViom of the cylindrical Surfaces ,—The ider who has carefully studied the preceding pages jll find little difficulty in applying the principles of |Djection to the delineation of the intersections of cy- 1 drical surfaces. We shall therefore, in the follow- examples of the intersections of vaulting surfaces, 4 lit the detailed description of the manner of con- ! ‘ucting the several projections and developments, lasting that the diagrams themselves will be found ijfficiently explanatory. 128. Fig. 45, plate G, represents the intersection of 70 RUDIMENTS OF THE two semi-cylindrical vaults of equal span. Each groin will form a straight line on plan, and its profile will be a semi-ellipse, whose semi-axis major = c e, and whose semi-axis minor d b. 129. Fig. 2, plate 1, represents the intersection of a semi-cylindrical vault, a b c, with a cross vault, Aj Bj c of smaller span, but of the same height, the groins being in vertical planes, and forming straight lines in the plan. In this case the square section of the smaller vault will be a semi-ellipse whose minor axis = Aj c, and whose semi-axis major = d b. The profile of the groins will' be elliptical, as in the last instance. 130. Fig. 3, plate 1, shows a method commonly adopted in the infancy of vaulting for constructing intersecting vaults of the same height, but of different spans. The smaller vault, as well as the larger one, was usually a semi-cylinder, and its springing was raised above that of the larger vault just so much as was required to make the crowns of the two vaults coincide. By this awkward expedient, the necessity for which appears to have arisen from the builder’s ignorance of the principles of projection, the groins are made to lie in twisted planes, and form waving lines on the plan. \ The groins themselves, when viewed from below, appear}; crippled, and have an unsightly appearance. 131. In fig. 46, plate 6, is shown the intersection of' two vaults of different spans, springing from the same; level. The groin thus produced is called a Welsh groin. I PROJECTIONS OF THE SPHERE. |] 132. We have already stated that the plan and ele-ii vation of a sphere will always be a circle; and thatjl every plane section of a sphere will be a circle, thei; ART OP MASONRY. 71 jection of which will be a circle, an ellipse, or a light line, according to its position. It is therefore lecessary to say anything further here, either as to projections or development of the sphere, beyond f jrring the reader to articles 101, 102, and 107 , and t' igures 34 and 37^ plate 4, the latter of which illus- t: :es the approximate development of a sphere, by con- i 3ring it as a series of conical zones. 33. Fig. 47 , plate 6, represents the intersection of a h flispherical dome, with four semi-cylindrical vaults, 1 [ will be understood without any verbal description. 34. If the reader has made himself master of the blems given in this section, he will have no difficulty projecting the intersections of any curved surfaces itever, of which the profiles and directions are given. : think it therefore unnecessary to swell the bulk of 5 little volume by any further examples, and proceed mce to the subject of the Third Section, namely, the dication of masonic projection to the scientific opera- is of Stonecutting. SECTION III. PRACTICAL, STONECUTTING. PART I.—GENERAL PRINCIPLES OF STONECUTTING. FORMATION OF SURFACES. s) ti k 35 . In working a block of stone the workman Ins by bringing to a plane surface one of its largest 3s, which will generally form one of the beds. Its uired shape having been marked on the surface thus med, either with the square or with a templet, chisel- 72 RUDIMENTS OF THE drafts are sunk across the ends of one of the adjacent faces, by means of a Fig 48. square or a bevel, as; shown in fig. 48, andr this second face is work-! ed between these drafts. The position of a third side is then determined, and its face worked in the same manner, and this process is repeated until the block is brought to its required shape. 136. To form a Plane Surface. —1st, when the sur¬ face is of consider- Fig. 49. able size. Two dia¬ gonal drafts, as a h. c d (fig. 49), are run across the surfjwje and connected bj cross drafts, as a ’ c h. The superflu¬ ous stone is then knocked-off between the drafts, unti the surface coincides in every part with a straight-edg^ _2nd, when the surface is small. In this case | chisel-draft is sunk along one edge of the stone, and i rule with parallel edges placed upon it. The workmaij then takes a second similar rule, and sinks it in a dralj on the opposite edge, until the upper edges of the rule! are out of winding, when the two drafts will be in tbi same plane, and the face may be dressed between tbO drafts. ' !* 137 . To form a winding Surface .—For this purposi the w'orkman prepares two rules, one with parallel, tb ^ other with divergent, edges; the amount of divergent depending on the distance at which they are to be place ART OP MASONRY. 73 art. Thus rules are sunk into drafts across the ends the stone, until their upper edges are out of winding, le extremities of the drafts are connected by addi- nal drafts along the sides of the block, the surface of lich is then knocked off until it coincides throughout ;fch a straight-edge applied in a direction parallel to it of the drafts. The diverging rule is called the winding-strip, and ; rules are called twisting-rules. The parallel rule .1 of course form a rectangle, whilst the form of the erging rule will be that of a triangle with a rectangle added to it. See fig. 50. As the width of the rectansrular o portion of the rules has nothins; to do with the twist, we shall, throughout the following pages, consider the parallel rule as a straight line, and the winding- |p as a triangle, which will much simplify the dia- Ims. Fig. 50. I m building oblique bridges with spiral courses, the |< er aie worked so that their winding-beds form por- i IS of spiral planes; and the accurate determination Jilthe twist is a problem of great importance. < 38. We have already (articles 122 and 124, and a, 43, plate 5) described the manner of tracing a spiral i'! on the surface of a cylinder. f a cylinder be cut along a spiral line traced upon ^jsurface in such a manner that the resulting section w everywhere coincide with a straight-edge applied Ijpendicularly to the axis of the cylinder, the surfaces Jll? produced are called spiral planes. A familiar ajoaple of a spiral plane whose width is equal to the ■a us of the circumscribing cylinder, is afforded by E ^"4 RUDIMENTS OF THE the soffit of a cork-screw staircase, such as may be seen in many church towers. 139. To find the Dimensions of the Winding-Strip for ivorking a Spiral Plane. —In order that the principle on which the dimensions of the winding-strip are formed may be more clearly understood, we shall first assume the width of the spiral surface to be equal to the radius of the cylinder. Fig. 51 is the perspective view of a quarter of a cy¬ linder, of which fig. 52 is the development, and fig. 53 the right section. Fig. 51. Fig. 52. Fig. 53. Let b c, fig. 52, be the development of the spiral be fig. 51. In fig. 53, make the arc e c = ec in fig. 52 join dc, and the sector dec will represent the winding strip. i In applying the twisting-rules to the stone, they musi be kept in parallel planes at a distance — ad, an. perpendicular to the axis of the cylinder. It will be olj served that tfie working edges of the rules will diver2| from each other, the distance b c being greater tha a d. To keep these edges, therefore, at the proper di: gree of divergence, it is convenient to connect the rulj with light iron rods, of which the lengths can be readi ART OF MASONRY. tained from the development. If any difficulty is perienced in keeping the side of the winding-strip in lirection perpendicular to the axis of the cylinder, a lall bevel may be used as shown in fig. 51, set to the gle e ch \n fig. 52. The twisting-rules should be made as thin as possible, d the working edges should be rounded, so that they ly rest on the stone in the middle of their thickness ly, as it would otherwise be necessary to form them a winding surface. The drafts ah, dc, fig. 51, having been sunk to the oper twist, the surface abed will be dressed off so to coincide everywhere with a straight-edge applied the two drafts with its ends equidistant from the ints a and d. 140. If a straight line be drawn between any two ints in the circumference of a spiral plane, it will not incide with the spiral surface, and will only meet the '.ter in the extreme points lying in the circumference d at a point midway between them. It should be 3 arly understood, therefore, that the process just de- ribed does not produce a spiral surface, although the proximation is so near in ordinary cases that the fference is scarcely appreciable, the distance between e twisting-rules being made so small, that for practical irposes the spiral b c may be considered as a straight le. 141. Let us now take the case of a spiral surface, lose width is less than the radius of the circumscribing Under. Let figs. 54, 55, and 56, be respectively the perspec- v’e view, the development, and the right section of the larter cylinder, the axial length 6y being the distance which the twisting-rules are to be^ applied. E 2 76 RUDIMENTS OF THE Fig. 55. Fig. 56. Let b c, fig. 55, be the development of the spiral b c, fig. 54: in fig. 56, make the arc fc = /c in fig. 55 .—Join ch, and from d, the point in which ch cuts the arch g d, draw d e parallel to lif. Then dec repre¬ sents the winding-strip. The mode of applying the i twisting-rules is precisely the same as described in art. 139; in fact these rules are merely portions of the] larger rules shown in fig. 51. ! 142. Instead of applying the twisting-rules across the i ends of the stone as above described, some masons prefer placing them in the length of the bed. In this| case the dimensions of the winding-strip are obtained! on the assumption that it is a continuation of thejt extradosal cylindrical surface. |] The working edges of the rules will be same dis-r Fig. 57. Fig. 58. tance apart at eachr end, whilst theirj \ ',1 outer edges will bei \ divergent. ■ Let figs. 56, 57, and 58 be respect- tive view, and the' ART OF MASONRY. 77 velopment, as before. Find c e fig. 56, as before, the development, make f e = f e, fig. 56; join b e, 3 n ^ e c is the winding-strip. We have already said that when the twisting-rules ; to be applied to the length of the stone, the winding- tip is assumed to be a continuation of the extradosal 4 iindrical surface. But as the wide end of the winding- ^ ip in reality is the chord of the arc c e, and as the •^irking edges of the rules do not coincide with the ex- dosal and intradosal spirals, but are chords to them; 3 dimensions given by the process above described, uld be subject to a slight correction, were they required be mathematically correct. Practically, however, both 3 spirals and the arc c e may be considered as straight es, and the correction is therefore unnecessary. The length of the working edge of the parallel rule d be found by setting off on the development ' =z g d, fig. 56, and joining d b, which will be the igth required. 143. There is yet a third way of obtaining thewind- i-strip, which is to consider it as portion of a spiral iding plane. In the development, fig. 59, draw c i per- idicular to c b, and meeting b e produced in i; set oW cd = c d, fig. 56, and join i dj then die represents the winding-strip. This, again, is only an approximation, as the top of the winding-strip should not be a straight line, but a spiral, of which c i is the development. This cor¬ rection, however, is too tri¬ fling to be worth notice. The working edges of IJQ rudiments of the these twisting-rules will be applied with the same de¬ gree of divergence as those described in art. 141, but their outer edges will also be divergent, not parallel. The top of the winding-strip will form a right angle with the extradosal spiral. 144. Of the three methods above described, the first is the most accurate, as the dimensions of the wind¬ ing-strip are obtained correctly, whilst in the other ( two the dimensions obtained are merely approxima- | tions, to which corrections must be applied if very great accuracy be required. The last method is, how- j ever, most convenient for the workman, who will always, unless otherwise directed, apply the winding-strip so that its wide end shall be square to the surface of the ; stone. SOLID ANGLES. 145. Solid angles are those formed by the meeting of; three or more faces in one point, and require for their e execution two kinds of bevels, viz.:— | 1 . The face bevel, containing the angle formed by the^f meeting of two arrises bounding one of the faces. i 2 . The dihedral bevel, containing the angle formedji, bv the intersection of two adjacent faces. 146. The angles of the faces, or, as w^e shall tern) them, the plane angles, are best worked from a thinj templet applied on the face of the stone, as shown atji u B V (fig. 60). _ , In making a bevel to work a dihedval, the sides o the bevel are set to the angle that would be formeti by the intersection of a plane perpendicular to th(j comnmn arris; and in applying the bevel to the stonej it must on each face be kept square to this line, af| ART OF MASONRY. 79 own at r b / (fig. 60), making a b r, a b/, each right gles. 147 . The solid angle occurring most frequently in ictice, is that formed by the junction of three plane :es, to which the name of trihedral has been given, trihedral has three plane angles and three dihedrals, which six, any three being given the remaining three ; also given, and may be obtained, all of them, by culation, some of them by construction. We shall re, however, consider only how in those cases which ; of most common occurrence they may be obtained construction, viz.:— 1st. When the three plane angles are given. 2nd. When two plane angles and the included dihe- d are given. 3rd. When one plane angle and the two adjacent « iedrals are given. 1148. In each of these cases the remaining angles can found by a simple geometrical construction; and as 3 lines to be drawn are the same in each case, it will ,^e repetition to describe the whole of the figure in 3 first instance. Fig. 60. Fig. 60 is a per¬ spective view of a tri¬ hedral of which the faces A B T, c B T, are supposed to be bounded by a plane, r T 5, parallel to the face A B c, at a dis¬ tance, B 0 , measured at right angles to the face, ABC. The di- 80 RUDIMENTS OF THE hedral angles, r bj, s b adjacent to the face, a b c, are shown as formed by the intersections of the cutting planes, x r Ti j, iv s n n, perpendicular respectively to the arrises a b, b c. Figs. 61 and 62 are developments of the trihedral (the plane an- Fig, 61. gles being in the one case all obtuse, in the other all acute), the plane an- A B A, c B e, corresponding to the angles c B T, ABC, in fig. 60, and the lines b Ji, b e, being of eqhal length and corresponding to the arris b t (fig. 60), hi, e f being Fig. 62. parallel respectively to a b, B c. Erect the perpendicu¬ lars B i, B f I draw e d, h D, respectively, parallel to / B, i B, and meeting each ij other at D ; join b d, and ^ draw D A:, D ^ respectively^ parallel to a b, b c. Then || A B D c will be a plan on a j plane of projection parallel to the face a b c, b ^ being = 0 s (fig. 60), and b A: = o r (fig. 60). Now, in order 1 to project the sections x r and w n (fig. 60)j; set oflf on the lines b a, b c (figs. 61 and 62), equal) ART OF MASONRY. 81 stances b I, ^ q, corresponding to the perpendicular stance b o (fig. 60) of the two parallel planes; erect e perpendiculars I m, q j); and join / k, q g. If i b, . B be produced to any points, y, beyond k g, re- ectively, then z k I m, g g q p will be the respective ejections of the sections xrnj, w s b n, so that I h p q g are equal to j b r, n b s; and I k, q g to r, B s, that is, to b i and b f respectively. 149. In applying this diagram to practice, a b c is : rays made one of the given angles, and the per- ndiculars, b i, Bf. having been drawn of convenient igths, the remainder of the figure is completed either I m the plane or the dihedral angles, as the case may [uire. 150. Case 1. Given three Plane Angles of a Trihe- lU to find the Dihedrals. —Draw the development i find the point g, as in art. 148. With ^ as a itre, and raaius g q = b f, describe an are eutting ■ ^■t q- Join g q, and draw q p perpendicular to b c; IB g q p will be one of the dihedrals, and the other 3 may be found in a similar manner. 151. Case 2. Given two Plane Angles and their ^luded Dihedral, to find the remaining Angles. —Let ii|j c, e B c, be the given plane angles, and g q p their ^luded dihedral angle. Having found the point d, ^w D h parallel to b i, and with b as a centre and ius B e, describe an arc cutting b h h : join b h, ^1 A b ^ will be the remaining plane angle. The re¬ fining dihedrals will be found as in art. 150. Jl52. Case 3. Given one Plane Angle and two ad- ^snt Dihedrals, to find the remaining Angles .—Let |AEj c be the given plane angle, and k I m and g q p adjacent dihedrals. Make b i, b f respectively E 3 82 RUDIMENTS OF THE equal to Ik, q g. Draw nh, T) e, i h, f e as described in art. 148, and join b b e; then a b A, c b e are the remaining plane angles, and the remaining dihe¬ dral can be found as in art. 150. SURFACES OF OPERATION. 153. No difficulty occurs in working'a block of!; stone, of which the faces, beds, and joints are to be either vertical or horizontal planes, as the several di-' mensions required can be obtained directly from the ■ plan and elevation. Nor is any difficulty introduced if some of the surfaces are cylindrical, as a cylindrical i surface can be worked with almost as much facility as a plane; the only difference being that a curved rule is used in one direction and a straight one in the opposite, whilst in the latter case the strajght-edge alone is used. 154. If however any of the sides of the block are to be formed into conical, spherical, or spiral surfaces, : the matter becomes somewhat complicated, and it is necessary first to bring the stone to a series of plane or cylindrical surfaces on which to apply the bevels and templets required for finishing the work. These pre-f paratory surfaces are called surfaces of operation. In! cases where the blocks are of large size, they are broughtj to their approximate shape at the quarry, and it is oi importance that the quarryraan should be enabled to dcj this in such a manner as to reduce the subsequent laboni of the mason as much as possible. 155. The simplest plan is to make the surfaces o: ' operation either horizontal or vertical, by which mean; , the lines required for making the bevels and templet!! ART OF MASONRY. 83 Fig. 63. can be taken directly from the plan and section, which are horizontal and vertical projections. Thus, let it be required to work a voussoir of a dome—we may first work the block roughly, so as to form a portion of an upright hollow cy¬ linder, as shown by the dotted lines in fig. 63, and transferring the lines of the plan and section to the surfaces of operation thus formed, the subsequent opera¬ tions become very simple. When the stones are small, and stone abundant, this will generally be the best mode of proceeding; but, with large blocks, the waste of material and labour would be very se¬ rious, and it is necessary to use such methods as will en¬ able us to economize the ma¬ terial as much as possible. PART II.—APPLICATION OF PRINCIPLES TO PARTICULAR CONSTRUCTIONS. 156. Having now explained the general principles stonecutting, we proceed to show their application some few particular constructions, each of which may regarded as the type of a class to which the same t 84 RUDIMENTS OF THE rules are applicable, with such trifling modifications as the circumstances of each individual case may render desirable. 157. Curved Wing-Walls .—To execute a wall with a straight batter on a curved plan requires much care and attention, and a considerable number of templets for the proper working of the conical beds of the courses, and for obtaining the twist of the coping. We have already described in detail the manner of constructing the several projections required in design¬ ing a conical wall, and therefore need not say anything further on the subject in this place, but will proceed at once to describe the manner of obtaining the necessary templets, and of working the stone. 158. Arrangement of the Courses .—On a platform draw a straight Fw- 64. line equal to n the vertical ) height of the wall at its highest point; calculate how much the wall will batter in this height, and set off the dis¬ tance at right angles to the first line, as shown in fig. 64, where a b is the vertical height of the wall, and b c the amount of batter. Draw ART OF MASONRY. 85 ['e face line a c, and divide it into the intended num- [ r of eourses. When the stone provided for the work runs of various icknesses, measure the thickest and the thinnest blocks d gauge the bottom and top courses accordingly; set ' these dimensions on the face line a c, and arrange e intermediate eourses as deseribed in art. 78, Section . Number the bed-joints as shown in the figure, ginning from the bottom of the wall. Provide a rod, and mark on it the radius of each bed- nt, numbering each joint in succession to correspond th the numbers on the line a c. 159. To work the top Bed .^—The beds of the courses a battering wall are made to dip at right angles to 3 face, whilst their front arrises lie in horizontal mes. The first operation therefore will be to form a rizontal surface of operation on which to apply a rved templet, cut to the radius of the front arris. Fig. 65. Make a bevel, as shown in fig. 65, so that the angle ab c shall be the dip of the bed. The length of ^ c will be regu- lated by the width of the stones to be worked; that of abhy <' their length—the width, d e, of / the rectangular portion, a d e f. ■ We are not aware that this method has been previously published. 1! method most commonly in use is the first of the two methods described t Mr. Peter Nicholson in his ‘ Practical Masonry,’ etc. Mr. Nichol- I’s rule is a very excellent one, but the construction of the hyperbolic ^iplet for obtaining the wind of the bed is too complicated to be under- ■|)d by an ordinary workman. In the rule here given, the lines of t templets are those of the work itself, and can be taken directly from t plan and section. 86 RUDIMENTS OF THE is of little consequence; 3 inches is a convenient dimen¬ sion. Call this bevel No. 1. It will apply to the whole of the courses. Make a curved templet to the radius of the front arris, as set out on the rod described in art. 157. The length of this templet must be a little more than that of the longest stone in the course. Call this templet No. 2. Each bed-joint requires a separate templet, but the same templet will work the top bed of one course and [| the bottom bed of that next above it ; With No. 1 sink a shaft ab c (fig. 66) across the ; centre of the length of the block, so that a is equal to the versed sine of the curve ; of the front arris. Through b draw h b g, perpendicular to b c, and knock off the front edge of the block, so as to form the horizontal surface of operation e a f g b h. On this surface apply No. 2, and draw the curve of the front arris ebf, keep¬ ing the curve perpendicular to b c. Make a duplicate of No. 1, and with these two rules bring the top bed to its proper wind. To do this, one rule must be placed at b c, and the other on successive portions of the sur¬ face, the rule being kept square to the curved line, e bf, and placed so that the point b coincides with it. The second rule must then be sunk till the upper edges of both rules are out of winding. (See fig. 66.) On the bed thus worked draw a line square to the front arris as shown in fig. 67, and make a flexible tem¬ plet to the angle eb c. This templet when laid flat will be a portion of the development of the conical surface of the bed, and when bent round the stone will give Fig. 66. ART OF MASONRY. 87 rig. G7. Fig, 68. k he direction of the joint. Call this templet No. 3. Cach course requires two templets, but the same emplet will work the tojJ bed of one course and the ottom bed of that next above it. Gauge the top bed 0 a regular width, and mark off the radiating ends with 'To. 3. The stone is now brought to the state shown :i fig. 68. 160. To work the Face .—With a common square ap- »lied at the ends of the top bed, sink a draft at each xtremity of the face as shown in fig. 68. On these rafts mark the thickness of the course as shown at i k. ’ake No. 2, corresponding to the front arris of the ottom bed, and sink the draft in k —keeping the tern- let so that b n=.ei^ the thickness of the course. Work he face between the top and bottom drafts with a traight-edge. Gauge the arris line ink parallel to eh f. )raw a line h n (fig. 69) square to the top arris, and lake a flexible templet to the angle e b n. This tem- 'let when laid flat will be a portion of the development f the conical face of the wall, and, when bent into the urved face, will give the direction of the upright joint 1 the face. Call this templet No. 4. A separate tern- let will be required for each course. Complete the mrking of the face by marking oflf the face-joints e i, k, with No. 4, as shown in fig. 69. 161. To work the Ends .—The ends of the stones will 88 RUDIMENTS OF THE bevertical planes^andaretbereforeworked with a straight¬ edge applied to the arris lines, lf,fk and me,ei, fig. 69. Fig. 70. Fig. 69. 162. To work the bottom Bed .—This is done with No. 1 and its duplicate, simply reversing the rules, end for end, as shown in fig. 70 ^ keeping the point c on the arris i n k. The top bed is round, and is worked from the centre to the ends. The bottom bed is hollow and is worked from the ends to the centre. 163. To build the Wall .—Set up an iron rod at the centre of the cone, and steady it as may be most convenient (see fig. 71 ^ plate 7; in which however the stays are omitted, to avoid confusing the drawing). Provide two battering rules, on which mark the bed- joints and fix them very accurately at the extremities of the wall. Then, as each course is laid, try its correct¬ ness with the rod described in art. 158, or with a stout measuring tape, of which the ring is passed round the iron rod at the centre of the cone. These precautions are especially necessary in building curved walls either in brick or in rubble, as without being able to refer to a centre it is very difficult to keep the courses to the proper curve. In building an ashlar wall, the stones being previously brought to the curva¬ ture of the face, this difficulty is much lessened; but ART OF MASONRY. 89 i appearance of the coping depends so completely i the accuracy with which the work is carried on, that ; use of the centre rod cannot well be dispensed with ;hout a risk of the coping being slightly crippled, 164. To form the Top of the Wall to receive the ( 0 %.—Shift the rod to n, fig. 72. String two lines i the plane of the front edge of the top of the wall, as s »wn at n b, n b, figs. 7 l and 72, plate 7. On a plat- f m strike out a quarter ellipse, with serai-axis major : i b, and semi-axis minor = 5 - n. Make a templet to 5 curve, in any convenient number of pieces, and call } templet No. 5. Beginning at q, fig. 72 , place No. 5 gainst the face of the wall, piece by piece, keeping it 3 of winding with nb,nb, and draw the line of the it arris on the top stones, which will have been car- 1 a little above this line. The top of the wall must n be dressed off to this line, keeping the surface level he direction of the centre rod, and it will then be rJiy to receive the coping. 165. To work the Coping .—Divide the front edge of wall into the number of stones which the coping is ■Contain, and square the joints across from the face. it be required to work the stone No. 3 , fig. 72— ^n a point b in the front of the wall, corresponding to ^ centre of the stone, draw two lines perpendicular to 4 arris, viz. « 6 on No. 5, and 6 c on the top of the i'll* Make a bevel to this angle, and call it No. 6 . A irate bevel will be required for each coping-stone, n working the stone it is convenient to begin with ii top surface. The block being roughly scappled to it shape; ivith No. 6 sink a draft, a b c, across the :^tre of the top surface, as shown in fig. 73 , plate 7 j Bi form a surface of operation, e a f g bh,2i5 described iSiTt. 159; the only difference being that, in the present 90 RUDIMENTS OF THE case, the surface of operation is not horizontal, but lies in the plane qnh, fig. 72. On this surface apply No. 5, by which draw the front edge, eh f. The dimen¬ sions of the twisting-rules required for working the top surface are found by actual measurement from the wall itself. The number of twisting-rules required for each stone will vary according to the degree of twist, which increases from the foot of the wall upwards.* These twisting-rules must be applied in a direction radiating from the face-line, and the workman must commence at the centre of the stone, on the draft h c, and work each way to the ends. The top surface having been worked to the proper twist, the radiating joint lines are marked with a bevel; the angles being taken from the lines previously marked ^ on the top of the wall. The width of the top of the stone is then gauged parallel with the front line, and the fronts and backs worked. The ends should be left rough until the whole of the coping is worked, in order to ensure an accurate fit. In applying the square to work the front face, it should be placed so that a plumb-line suspended from any part of the front edge shall coincide with the face. If the square be applied perpendicular to the arris, fiie bottom edge of the coping will appear underset, whickf has a wretched effect.t . I The front and back having been worked, the stone nl ji * It must be remembered, that the top and bottom arrises of the co^ ping do not lie in parallel planes, as explained in art. 117. The dififerencj in the twist at the top and bottom beds arising from this cause is searcel^ appreciable ; but it may be allowed for in taking the twist from the top o the wall, when the curve is sufficiently sharp to make this necessary. t Some persons prefer to make the front of the coping battering: t • is simply a matter of taste. i ART OF MASONRY. 91 i ged to its proper thickness on each side, and the tom bed can be worked with a straight-edge applied ilween these lines. I 66. We have described the front of the coping to y worked with No. 5, and this would be perfectly ; rect were the coping set flush with the face of the \ 1. But, as it is always overset to a slight extent, ii two inches, it is evident that the front of the coping 1 st be made to curve a little quicker than the front ) ;he wall. In ordinary cases, the difference between |se two curves is not perceptible in the length of a ! ne, but when the radius of curvature is very small, t templets will be required, one to work the top of wall, and the other to work the front of the coping, j 67. There are very many ways in which the twisted i ing of a wing-wall may be worked; but the fore- ng method appears to us the simplest, and that uiring fewest templets. As each stone requires a se¬ nte bevel, face-mould, and twisting-rules, the trouble making the templets adds greatly to the cost of ^king the stone, and the last-named consideration sberefore one of great importance. 68. Walls are sometimes built on elliptical plans, r this should always be avoided if possible, as the iTi'king of the stone is a very complicated process. DOMES. • 69. The foregoing rules apply with trifling modifica- ™is to the execution of domes, spherical niches, and Fi, vaults, and generally to all constructions in which tl beds of the courses form conical surfaces, and of ■ ch the joints lie in vertical planes. A single example w. suffice to show the nature of these modifications. 92 RUDIMENTS OF THE Let it be required to work the voussoir ah c d efg, fig. 74 , plate 7j of a hemispherical dome. The top bed in this case is hollow, and the bottom bed rounded, therefore begin with the latter. Obtain the front arris, and work the bed as in art. 159. Work the face, adej\ so as to form a conical surface of operation, as in art. 160 j except that the chisel drafts at the ends of the face will be sunk with a bevel set to the angle a d c, instead of a common square being used. Work the ends as de¬ scribed in art. 161. Obtain the arris af, and work the top bed as described in art. 162; except that, as the in¬ clinations of the top and bottom beds are not the same, there must be as many sets of winding rules as there are courses. Lastly, work the conical surface of opera- ^ tion to the proper curve, with a curved rule, as shown in the figure. ARCHES. 170 . The construction of either circular or elliptical arches, of which the abutments are square with the face, offers but little difficulty. As the depth of the arch-stones is generally greater than their thickness, the workman commences by work¬ ing one of the beds. This being done, the ends are squared, and their exact shape marked from a templet. ' r I iL. ... 1 1 . ^ 1. .i. ..n «... ^ ^ ^ 1 ^ .i.1.«««. V The opposite bed is now worked to the lines thus found.; Lastly, drafts are sunk at each end of the soffit tof the curves previously marked, and the soffit is dressed off to coincide with a straight-edge applied between^ the drafts in the length of the stone. This will be un¬ derstood by inspection of fig. 75, plate 7* I Another method is to work the soffit from the bed! first formed, by means of an arch-square or curved! bevel, as shown in fig. 76, plate 7* One bed and the| ART OF MASONRY. 93 St being worked, the other bed is worked from the it in the same way. This method dispenses with the :essity of squaring the ends before working the soffit, ich is sometimes an advantage, n both these methods the straight-edge is used for ing the surface between the chisel-drafts at the is of the curved soffit; but in the first method these fts are got by applying a templet on the squared s, and in the second by means of the arch-square. 71 . Oblique Arches .—We have in the first section his volume described the different methods in which ique arches may be constructed. In the following ) es, therefore, we propose to speak only of cylindrical i: les built in spiral courses, of which the beds radiate n the axis of the cylinder. The reader who will take trouble thoroughly to master the rules here laid m, will find no difficulty in executing any other de- ption of arch. ffie construction of a skew arch of which the span, , width of siffit, and angle of skew are given, re- res but very few lines to be drawn for finding the plets and bevels. But it is always desirable, before l^imencing operations, to make a large drawing to an Bh scale, for the purpose of ascertaining the sizes of y stones that will be required, the best manner of iT nging the heading joints in the soffit, and such other Upiculars as cannot well be obtained from a small I. :ch; and we shall therefore briefly describe the Elections and developments that are required for this 71 pose. (See fig. 77 ? plate 7 *) : [72. Plan .—Draw two lines, c b,d y, parallel to each ii ir, at a distance, d e, corresponding to the square ^ th of the soffit of the arch. Set off the angle of the Tfllge, and draw one impost line, c d. Draw the 94 RUDIMENTS OF THE second impost line parallel to the firstj at a distance, a b, corresponding to the span of the arch on the square section. 173 . /Siec^iow.--With the given span a b, and rise h i,| draw the square section of the arch. I 174 . Development.—Draw a development, b g k y, of, the soffit of the arch from the data thus obtained. Draw, on it the development of a heading spiral, passing through the extremities of the impost lines in one of tb^ fronts. Divide this line into any convenient numbei, of equal parts, as 13, corresponding with the intended number of stones in each face of the arch; an uneveE; number being always taken, to allow for a key-stone. From k, the opposite end of the impost line making, an acute angle with the face, let fall a perpendicular k /, on the heading spiral just drawn, which will reprej; sent the development of a coursing joint. If this lira, pass through one of the divisions on the heading spiral^ the design may be proceeded with without any altera tion of the dimensions; but this will nffost probably n«g be the case. It will then be necessary to adjust th j dimensions, so as to make the coursing spiral pa^jj through one of the divisions ; which may be done— 5 1 st. By altering the width of the bridge. 1 , 2 nd. By altering its span. 3rd. By altering the angle of skew; or, lastly, by slight adjustment applied to all these data. d If the dimensions of the arch are unalterably fixer ^ this first coursing joint must be drawn through th ^ nearest face-joint; but, in this case, as the coursingan| heading spirals are not perpendicular to each other, tli| soffits of the stones will be out of square*, which is ver| objectionable. In building arches of brick, with stori That is, if the stones are worked to form regular bond. || ART OF MASONRY. 95 c s j 0 c c tl d d 1 :r )ins, as shown in fig. 78, plate 8, this difficulty is rcely felt, because it is not necessary that the face- its of the opposite fronts should range with each er; all that is required being that they should coin- 3 with some joint of the brickwork, so that, in this 3 , the necessary adjustment can never exceed half thickness of a brick. 'he angle made in the development, by the intersec- i of the coursing joints with the impost, is called angle of intrados. The corresponding angle, in a elopment of the extrados, is called the angle of ex- los. 75. Arrangement of Heading-Joints.—DWide each D ost into as many parts as there are divisions cut off >ij;he heading spiral by the coursing joint first drawn, ch, in this example, are five in number; and through 1 ; divisions on the impost^ and on the heading spiral, h V the developments of the coursing spirals, which V be parallel to and equidistant from each other. ough the divisions on the imposts draw heading [ ils parallel to that first drawn, and arrange the ling joints on these lines and on others parallel to 3, so as to form regular bond throughout the whole le soffit. (See fig. 11, plate% art. 39.) will be seen that, from the heading spirals not g parallel to the face line, the quoin-stones will be iry irregular lengths; and this is particularly con- lous in brick arches with stone quoins, whose ends portions of continuous heading spirals. The best of avoiding this is to draw on the development parallel to the face-lines at distances corresponding iC intended lengths of the long and short quoins, to make the end of each quoin a portion of a se- -e heading spiral, passing through the intersections 96 RUDIMENTS OF THE of these lines with the coursing joints, as shown in fig 78, plate 8. Some persons, in building brick archei with stone quoins, make the ends of the latter paralk with the face-line, which is very objectionable, as i throws them out of square with the brickwork, which i ofiFensive to the eye, and makes unsound work. 176. Skewbacks—The next thing to be considerei is the arrangement of the joints in the imposts. Th top of each impost must be cut into checks or skew backs to receive the ends of the courses; and, as th beds of the courses are worked to radiate from th centre of the cylinder, the checks will be square to it axis, and to the faces of the abutments, as shown in fi^ 77. In settling the sizes of the stones forming th imposts, it must be borne in mind that the stone at th obtuse quoin will be wider at the back than at the fron whilst the reverse takes place at the acute quoin; an it is of importance that the latter stones shall be ( sufficient size to bond into the rest of the work. Th thrust of a properly built skew arch being in a directio parallel to its fronts and not at right angles to tl abutment, it will always be desirable to make the join of the masonry square to the fronts, and, therefore, tl backs of the impost stbnes should be cut so as to bor with the rest of the masonry, as shown in fig. 79, plate The last thing to be attended to in the design is ti elevation of the arch, and the arrangement of the cours of the spandrils. j 177« To draw the Elevation .—The curves of tj intrados and of the extrados are both portions of ellips| of which the spans are to be taken from the plan and tjl heights from the section. The positions of the joints | the intrados are taken from the divisions on ih^face-M of the development of the intrados. Their position ART OF MASONRY. 97 extrados maybe formed by developing the extrados, manner of doing which may require some little ex¬ nation. hnce the joints are made to radiate in a direction pendicular to the axis of the cylinder, it follows that axial lengths* of the intradosal and extradosal O •als willbe the same (see fig. 77? plate but, as the umference of the extrados is longer than that of intrados, the angles made with the abutments by extradosal spirals will be greater than those made the coursing joints in the soffit; or, in other words, angle of extrados wull be greater than the angle atrados, and, as a consequence, the extradosal plans he stones will be out of square, as shown in the elopment of extrados, fig. 77* In drawing the ding spirals in the development of the extrados, they not be perpendicular to the coursing spirals, nor they pass through the intersections of the face and ost lines, but they will fall within the face at the ise, and beyond it at the acute, quoins. This will ully understood by reference to the figure. Divide extreme heading spirals into as many equal parts as heading spirals of the intrados, and through these sions draw the developments of ther extradosal cours- joints. Transfer the divisions on the /ace-line of extrados to the curve of the extrados in elevation, draw in the face-joints, between the points thus rmined in the extrados and intrados. In strictness, face-joints are not straight lines, but curves; as y intersection of a plane with a spiral surface will curved line, except when the plane of intersection jrpendicular to the axis of the cylinder; but, unless 3y axial length is here meant the distance measured on the axis of a ler, corresponding to an entire revolution of a spiral. F 98 RUDIMENTS OF THE the bridge is very much on the skew, the curvature is not worth noticing in the drawings, as its omission does; not in any way atfect the work. 178 . Focal Eccentricity .—It was first pointed out by Mr. Buck,* that the face joints of an oblique arch of equal thickness from the springing to the crown have a remarkable Dcoperty, viz. that their chords all radiate from a point below the axis of the cylinder, the dis¬ tance increasing with the angle of obliquity; and he gives in his work the following simple rule for ascertain¬ ing this distance, which he calls the focal eccentricity (see the lower part of fig. 77 ? plate 7 ) • Draw ab — radius of extrados, and b c perpendicular to it, making the angle acb — angle of skew; draw c d perpendicular to b c, making the angle cb d = angle of intrados; then c d is the focal eccentricity. For the demonstration of this rule we refer the reader to Mr. Buck’s work. By taking ad¬ vantage of this property of the face-joints, we can draw the elevation without the trouble of making a develop¬ ment of the extrados, which saves much time. 179 . Spandrils .—The face-joints having been drawn, the last thing to be done is to arrange the lengths of the quoin stones, and the heights of the spandril courses. This is sometimes troublesome to manage, as it is neces¬ sary for the appearance of the work that the heights of the spandril courses should diminish regularly from the springing to the crown, and the lengths of the quoins must be adjusted so as to effect this. If the elevation is carefully drawn to an inch scale, the lengths of the quoins can be obtained from it with sufficient accuracy without drawing a full-sized elevation; which is an expensive^ operation, as it requires a large extent of platform. * ‘ A Practical and Theoretical Essay on Oblique Bridges,’ bv the latej George Watson Buck. (See Chap. II.) ART OF MASONRY. 99 We now proceed to describe the manner of finding e bevels and templets for the execution of the work. 180. In fig. 80, plate 8, let z.d cb = angle of skew. ah = span on square. hi — versed sine of arch. d e = width of soffit on the square. ax =■ radius of intrados. ch — oblique span. c d = length of impost. bf = development of square section. b g = development of heading spiral. Lgk'l = angle of intrados. Of these data, the four first are known, and the others ust be found from them, either by geometrical con- ruction on a platform, or by calculation; the latter plan iing the most correct, the quickest, and the cheapest. 181. Radius. ax= ^ ^ see art. 83, 2ih 182. Oblique Span, cb = ab x cosec l deb. 183. Length of Impost, cd = de x cosec A deb. 184. Development of Square Section. —The natural ne of the angle axh =■ Look in a table of na- ax' Lral sines for this number, and call the corresponding amber of degrees n; then b f ■= aib = 2n x ax x 17453 (as in art. 88). 185. Development of Heading Spiral. —First fg — ac ■ ab X cotang A deb. Then b g = f bf^i- f — development of heading )iral. 186. Angle of Intrados. — sine of A fbg — ne of Agkl. F 2 100 RUDIMENTS OF THE 187. The above calculations are best performed by the aid of a table of natural sines, secants, and tangents, without using logarithms, and may be made, with a table of natural sines only; but the operation is some¬ what tedious in the latter case, as it involves dividing by the sine of the angle of skew, which is very trouble¬ some, as the sine should not be taken to less than six » places of decimals :— Thus, the oblique span, h — ———j ’ ^ ^ ’ sin Z a c 0 and the impost length dc = —— ^ \ j- Sin ct c 188. These dimensions having been calculated, the lengths of the imposts and of the development of the heading spiral must be set out very exactly on long rods, and divided into the number of equal divisions previously determined on. The divisions of the impost rod will give the exact length of the checks to be cut on the springers, and the divisions on ,the other rod will show the exact width of the courses. 189. Templets for the Skew-backs. —On a sheet of zinc, draw two lines at right angles to each other, as ah, be, fig. 81, plate 8; set off 6c = width of a course on the soffit, and b a = b c x cot Z of intrados. Join a c. Then the triangle a b c will be the form of the templet for the impost checks in the soffit, and a c should exactly agree with the length of check previously ascertained. From b let fall on a c the perpendicular b d. On a platform draw a straight line a b c, fig. 82, plate 8 , making ab = radius of intrados, and h c = thickness of arch at springing. With centre a, and radius a b, draw the arc b e = b d, fig. 81. Through e draw a e d, making ed — be. With centre a, and radius a c, draw c d. ART OF MASONRY. 101 putting a e dind. In fig. 81, produce b d to e, making |- 6 e = c?c in fig. 82; join a e,e c; then a e c\s the form j|f the temjfiet for the impost checks on the extrados. 190. In working the springers, they are first brought ito a cjdindrical form, and divided into the proper umber of checks by the impost rod. The templets are len ajDplied on the intrados and extrados, and their rofiles marked on the stone, which is then cut away to lese lines. 191. Twisting-Rules. —On tne platform set out the igle of intrados, as g k I, fig. 80, plate 8, and let k m j! the axial distance at whieh the parallel ends of the usting-rules are to be applied. Draw m n perpendicular k g; n k will be in the distance between the rules on e intrados. On the platform with radius of intrados, oe, fig. 83, plate 8, draw nm — nmvo fig. 80. Draw n p and xno, and the concentric arc o p, making on = p = thickness of arch. On n m produced, fig. 8, set mo — po^^ig. 83. Join ^ 0 ; then ^ o is the distance a which the twistmg-rules are to be applied on the ex- Idos. In fig. 83, draw n q parallel to m p; then n o q V1 be the divergent portion of the winding-strip. ■ When a bridge skews to the left, as shown in fig. 80, I te 8, the winding-strip must be applied on the right- mid side of the parallel rule, and vice versd. The rules here described are to be applied as di¬ eted in art. 141. 92. Templet for the Curve of the Soffit.^—Tho por- The Reader must not be discouraged if he do not, on the first perusal, ui -.rstand the object of the operations here described. Some assistance ■ be derived from an inspection of fig. 77, in which figs. 84,85, 86, and 5 xe repeated on a small scale in connection with each other ; but the best V would be to lay down the several lines on the surface of a cylinder, 1 the princijile on which the rule is founded becomes immediatelv i| xent. 102 RUDIMENTS OF THE tion of a coursing spiral included in the length of any voussoir may be treated as an arc of a circle, and may he obtained approximately as follows: Draw on the i platform the lines a b, b c,fig. 84, plate 8, of any conve¬ nient length, making Labe — angle of intrados. On a b let fall the perpendicular c a. In fig. 85, plate 8, draw ax = radius of intrados, and with a? as a centre draw the arc a c = a c, fig. 84. From c let fall on a x- the perpendicular c d. Draw two lines parallel to each other, fig. 86, at a distance apart = a d, fig. 85. From any point, b, in one line as a centre, with radius = b c, fig. 84, describe two arcs cutting the other line, as shown at a and c. This will give three points in the curve, which may then be drawn in with a trammel, as described in art. 64. Make a templet to the curve thus t found, and call it templet No. 1. ^ _ J 193. Templet for marking the Heading-Joints on the Beds.—TdlkQ a sheet of zinc, and mark on it the a curve of the soffit with templet No. 1. With intersecting : arcs, set up a perpendicular to the curve as a 6, fig. 87, plate 8, making a b — thickness of arch, or a little more. Cut the zinc to the angle a c, as shown by the t shaded part of the figure, and this will be the templet f required; which call No. 2. ■ 194. Templet for marking the Heading-Joints on the > ^oj^^_This is simply a rectangular piece of zinc ofjl any convenient length, and of which the width is thaffi of a course : it is best however to make it the length) i of the longest voussoir. Call this templet No. 3; seel' fig. 89, plate 8. ’ 195. Arch-Square.— arch-square, required foil working the soffit from the bed, is precisely similar to thaij shown in fig. 76, art. 170 , and needs no further description 196. Method of working the Voussoirs.—\st Bed ART OF MASONRY. 103 Jring one side of the stone to a plane surface. With 'I’o. 1, draw on it the curve of the intradosal coursing Dint, a b c, fig. 88, plate 8. With No. 2, draw one f the heading-joints, as a e. Take the twisting-rules, nd, applying the parallel rule to the line just drawn, work he bed a b c d e to the proper twist. With No. 2, draw he second heading-joint c d. This completes one bed. -Soffit. With the arch-square applied so that it shall e always in a plane perpendicular to the axis of the ylinder, work the soffit to a cylindrical surface. If any ifficulty is found in applying the arch-square in the roper direction, a small bevel may be applied to the Dffit, set to the complement of the angle of intrados, as Down in fig. 89, plate 8. With No. 3 gauge the soffit to :s proper width, and mark the heading-joints. This ompletes the soffit.— 2nd Bed. This is worked from le soffit with the arch-square, and the heading-joints rawn with No. 2.— Ends. These are worked with a traight-edge applied between the joint-lines drawn on le beds with No. 2. 197 . Centerinf/. —As soon as the abutments have een carried up to the spring, and the impost stones 3t, the centering must be erected. The ribs should be laced parallel to the face, and not square to the abut- lents; as the former plan ensures greater accuracy in le curvature of the fronts. The laggings must be icurely fastened, and their upper surface planed per- ctly true, so as to coincide everywhere with a templet it to, the curve of the soffit. Too much importance innot be attached to this, as upon it mainly depends le accuracy of the work. The surface of the laggings having been made per- ctly true, the lines of the coursing and heading joints ust be marked upon it, to assist the workmen in setting le arch-stones. 104 RUDIMENTS OF THE This is done in the following manner; which will be understood by reference to fig. H, plate 2. Draw the face lines, and, having bisected them, draw a level line along the crown of the centering from centre to centre of each face. Take the impost rod, and transfer the divisions on it to this centre line. Prepare a thin flexible board as a straight-edge, and, having planed its edges very true, transfer to it with great care the divisions of the heading spiral, which must be set oif from the rod previously prepared, as described in art. 188. This straight-edge need not be longer than is necessary to extend from the impost to the crown of the arch. Then, beginning at the extremities of one of the imposts, bend the straight-edge round the centering, and draw a series of heading spirals, from impost to impost, through the divisions on the centre line, and the corresponding lines of the checks on the springing stones. It may be necessary to observe that the laggings must project a little way beyond the fronts of the arch, or there will not be room for drawing the extreme heading spirals. Transfer the divisions on the straight-edge to these heading spirals, taking care that the centre line at the crown passes through the centre of a division in each case. Through the points thus found, draw the coursing ji spirals, which will again coincide with the coursing > joints in the soffit of the arch. The heading-joints must . then be marked, and the numbers of the arch-stones painted on, so that no delay shall occur in setting the j stones, from their being brought in the wrong order. | 198. Face Quoins.—Templets for Soffits .—The soffits j of the ordinary voussoirs are rectangular; but this is j not the case with the quoins, the soffits of which are all, out of square more or less. The templets for marking j off the face-line on the soffits of these stones are best j ART OF MASONRY. 105 obtained from the lines on the laggings, which is done jy bending round templet No. 3, and cutting off the md to coincide with the face-line. 199. Templets for Angles of Coursing and Face- joints .—In the ordinary voussoirs the heading-joints re all perpendicular to the curve of the soffit. This 5 not the case with the face-joints, which make varv- ag angles with the coursing joints, according to their istance from the springing; the joints lying between ae crown and the acute quoins, making acute angles nth the soffit joints, whilst the angles on the opposite alves of the fronts are obtuse angles. There are many ays of obtaining these angles by geometrical con- - ructions ; but these methods are very intricate, and ■quire a great many lines. We prefer, therefore, to ke these angles at once from the lines on the center- g, which may be done with great facility and accuracy follows:— Apply templet No. 1 to a thin strip of deal; and, having arked on the latter the curve of the soffit, cut away the perfluous wood, so as to make a corresponding con- ve rule. Take this rule and frame it to three arch- i uares, set in planes perpendicular to the axis of the Under, as shown in fig. 90, plate 8; so that when e curved ed^e, ab c,\s placed on a coursing joint on 1;3 centering, the curved edges of the arch-squares shall < incide with the surface of the laggings. Mark the ihtre of a c as shown at b. Then, beginning at the j*nt nearest to the acute quoin, place the edge ab c to f.ncide with the coursing joint; and so that the face 1 e shall pass through the point b. Take a plumb-line ^ ffi a pointed bob, and pass it carefully along the arris j / until the point of the bob is exactly over the face 1 e. Mark this point as shown at e. Then ab e will F 3 106 RUDIMENTS OF THE be the angle required, and eb c will be the angle for the corresponding obtuse quoin. Find the angles for the other joints in the same manner. Take templet No. 2, place it so that its curved side corresponds with a b, and cut the templet to the angle abe, and this will be the templet for marking off the face-joint on the adjacent beds of the two first courses from, the springing. The remain¬ ing templets will be constructed in the same manner. 200 . Angle of Twist .—As in all books on skew ma¬ sonry a great deal is said about the angle of twist, it i may be desirable that we should say a few words on the subject. The term angle of twist is an expression used to denote the difference between the angle of intrados and extrados, and is often spoken erroneously of as syno¬ nymous with the angle of the twisting rule.^ Thus in figure 57 and 58 (art. 142) the angle c 6 e is the angle of the twisting-rule, and cb cT\^ the angle of twist, being a somewhat smaller angle, which must necessarily be the case, as may be seen by inspection of fig. 56, as e/ will always be less than d g. In practice however the difference between these angles is not appreciable, and no sensible error will result from considering them as identical. 201. The whole of the projections, bevels, and tem¬ plets, above described, are shown in a connected form in : fig- 77j plate 7 ; a careful study of which will materially assist the reader in obtaining a clear understanding of the principles which we have endeavoured to explain. There is, however, so much difficulty in understanding the nature of spiral planes wnthout models, that we would recommend the reader to procure a wooden cylinder, | say three feet diameter, and to work out upon it all I the problems connected with skew masonry. The de- I * That is, when the rules are appUed to the length of the stone. ART OF MASONRY. 107 relopments may be made on drawing-paper, and their iccuracy tested by bending them round the model. The templets and bevels may be cut out of cardboard; ind the accuracy of the face bevels may be proved by etting up in cardboard an elevation of the face, and rying them against it. The construction of a model of his kind is the best method of obtaining a knowledge •f the subject, and more will be learnt by this means in . few days than could ever be done by the study of Irawings alone. GROINED VAULTING. 202 . Roman Vaulting .—The principles of Roman aulting have been explained at considerable length in lection I.^ and in Section II., articles 119 to 131, the lethods of obtaining the profiles of the groins, and the evelopments of the soffits of cylindrical vaults, have een fully shown. We have, therefore, in this place nly to apply the application of these principles to le working of the groins, no other portion of a common roined vault offering any particular difficulty. 203. The simplest way of working a groin-stone is to ring the stone into a cubical form, as shown in fi^. 92, late 8; and on the vertical and horizontal surfaces of Deration thus obtained, to npply templets taken from full-sized plan and elevation j see fig. 91, plate 8. This the easiest way of proceeding; but the waste of stone very considerable. 204. If the stone to be worked is only sufficiently rge to contain its intended form without any waste, we ust begin by working two plane faces at right angles ■ each other, to contain the heading joints abed, bighy j. 92, plate 8. These having been worked, and the rm of the stone marked with a templet taken from a rudiments of the 108 full-sized section of the vault, the top and bottom bed can be worked with a common square, and the arris lines drawn upon them. The curved soffits can then be finished with a curved rule, cut to the proper curve and applied between the top and bottom arrises. This method makes the most of the stone, and saves the labour of making surfaces of operation; but it requires considerable care to keep the angles perfectly true. 205. The above methods suppose that the main and the cross vault are built in horizontal courses, which would always be done in the Italian style; but it is quite possible to keep the courses of the main vault horizontal, and to make those of the cross vault radiate from the centre of the main vault. This arrangement may be seen in fig. 6 (art. 17 )» It is only suited to rough rubble-work, as the execution of such a vault in regular masonry would be a most complicated process. 206. Gothic Vaulting—In Gothic vaulting, as ex¬ plained in Section I., the profiles of the groins are always formed of circular curves, and the forms of the vaulting surfaces are made to depend on the curvature of the groins, instead of the groins following the form of the vaulting surface, as in Roman vaulting. It is true that, in the decline of the pointed style, elliptical groins were used to a certain extent; but this |j was after the introduction of vaults of solid masonry, as j| the fan vault, and the later lierne vaults, which assimilate j, very closely in their construction, although not in their i decoration, to the vaults of the modern Italian school. | For this reason we do not propose here to take into j consideration the construction either of fan vaults or of j; the late pointed vaults, which are chiefly built of jointed j masonry. I The construction of a pointed waggon vault of solid j ART OF MASONRY. 109 lasonry is precisely similar in principle to that of a com- lon cylindrical arch, however complicated the tracery hich may be sunk upon its soffit; and the construction F a fan vault may be accomplished either by the rules wen in art. 158 and following articles, or by forming orizontal surfaces of operation, as shown in fig. 10, art. 5; which seems to have been the plan adopted by the lasons of the middle ages; although in many existing lults the extrados is parallel to the soffit, the surfaces • operation having been chipped off, so as to bring the pper surface of the vault to a curved form. 207 . Rib and Pannel vaulting is quite different in its mstruction, both from Roman vaulting and from the te pointed vaults of which we have just spqken. It consists, as has been before explained, of a frame- ork of light ribs, each of which is -worked in the same anner as a cylindrical arch; and of light pannels hich rest on this framework, and are either built in mrses or formed of thin slabs of stone scribed to the bs; the general principle on which the vaulting sur- ces are formed being, that the soffits of the pannels tpuld everywhere coincide with a straight-edge applied a horizontal direction from rib to rib; although when e pannels are built in courses they are made slightly mcave as the stones would otherwise have little to keep em from falling. No difficulty occurs in working the )s themselves, since each stone forms a portion of a lindrical arch; but a considerable amount of projec- )n and transference of lines is required in arranging the rves of the ribs, and to obtain the bevels for working e stumps of the ribs on the boss-stones, at their inter- ctions. We propose, therefore, to conclude this little ilume by a brief description of the projections required r the execution of a plain ribbed vault, with an expla- 110 RUDIMENTS OF THE nation of the manner of finding the curvature of the liernes and the bevels for the boss-stones in the simplest class of lierne vaults. 208. The various ribs introduced in Gothic vaulting may be classed under six heads, viz.:— 1st. Transverse ribs, which are placed at right angles to the length of the vault. 2nd. Longitudinal ribs, which are parallel to the length of the vault. If the apartment be vaulted in one span, the longitudinal ribs are called, from their position, wall ribs. ,1 3 rd. Diagonal ribs, or cross springers. Upon these the main strength of a Gothic vault depends ; whilst, in the Roman groined vault, without ribs, the groins are the weakest parts. 4 th. Intermediate ribs. These are ribs introduced between the transverse and diagonal ribs, and may be either surface ribs, that is, ribs coinciding with a pre- la viously determined vaulting surface; or they may be independent ribs, each of which marks a groin; that is, a change in the direction of the vaulting surface. 5 th. Ridge ribs. Ridge ribs, as essential portions of !,; the construction of a vault, are unnecessary where no j; intermediate ribs are introduced; and, in this case, the j]; ridge ribs of the Gothic vaults were frequently built in I with the pannels instead of being previously built as a portion of the framework of the vault. An example of this may be seen in a vault in the ruins of Wingfield Manor House, Derbyshire. In this vault, the central bosses have been prepared for the reception of the ridge ribs; but the latter, instead of being moulded to corre¬ spond with the mouldings of the bosses, are plain canted strips, built in as keystones to the rubble arches forming the pannels. Where intermediate ribs are introduced, r ART OF MASONRY. Ill he ridge ribs become essential as struts to keep the ormer in their place previous to the insertion of the >annels. In making the ridge ribs form part of the framework ■f the vault to be built with a light skeleton centre, a •ifficulty occurs, unless the vault be highly domical in :s structure; as there is otherwise nothing but the entering to keep them in their places until they an be supported by the pannels. A common remedy Dr this was to make each portion of the ridge from 'Oss to boss slightly concave. A very striking example if this may be seen at Tiincoln Cathedral ; where the osses appear to be placed in a level line, or nearly so, whilst the ridge ribs of the several compartments form a cries of flat arches between them. 6 th. Liernes. These are short ribs introduced be- ween the principal ribs, so as to form ornamental atterns. Their forms are generally governed by the aulting surface, although they are built as separate rches, not as portions of the pannel. When many ernes are introduced, the construction of the vault ecomes complicated; and, instead of the skeleton entre, which is all that is requisite for constructing a lain ribbed vault, a regular boarded centering must be rovided. In the complex lierne vaults, the principle of le plain ribbed vault, viz., the making the vaulting arface to depend upon the curvature of the ribs, is, in a reat measure, lost sight of; as it becomes necessary rst to design the general form of the vault, with which le curves of the ribs must be made to correspond. 209. Curvature of the Ribs .—^In designing a plain ibbed vault, it is simplest to begin with the transverse lbs, as their form, in a great measure, governs the ppearance of the work. 112 RUDIMENTS OF THE Each rib may be struck as a single arc of a circle, or from two centres; so that each pair of ribs forms a four-centered arch. Whichever plan is adopted, the centre of the curve at the springing should be on the springing line ; neither above nor below it, as either of these positions produces an unpleasant effect; the curve in the former case becoming horse-shoed, and, in the latter, forming an acute angle with the springing line. Fig. 93, plate 8, shows the plan of a quarter of one compartment of a ribbed vault, with the elevation of ' each rib placed on its plan —a 1 6 is the plan, and a a ^ b, the elevation, of the transverse rib. 210. The transverse ribs having been decided on, the next thing to be settled is the form of the cross- springers, and here some little arrangement is neces¬ sary. Two objects should be kept in view ; the first, to make the radius of curvature as nearly as possible the same as that of the transverse ribs ; and the second, to make the curve at the springing start at right angles to the springing line. The simplest way of accomplishing these objects is to strike the transverse and the diagonal ribs with the same radius ; the centre of the curve being placed in both cases on the springing line. This is shown in fig. 94, plate 8, where « b is the elevation of the I transverse, and a c that of the diagonal, rib. This was P a common arrangement in Continental vaulting; but it j’ has the peculiarity of producing a highly-domed vault, I the intersections of the cross-springers ate being much above that of the transverse ribs at b. If we wdsh to keep the ridges horizontal, we have a new condition | introduced, and the complete solution of the problem cannot be effected with single arc ribs only. If we confine ourselves to ribs formed of a single arc, we may f make the diagonal rib of the same radius as the trans- ART OF MASONRY. 113 rse 5 placing the centre below the springing line, as fig. 95, plate 8; or we may keep the centre of the agonal rib on the springing level, and diminish the iius, as shown in fig. 96, plate 8. By the employment of two-centred ribs, however, the justment of the curvature can be accomplished with jat facility ,• this is shown in fig. 97, plate 8, where 3 first portions of the diagonal and transverse ribs are uck with a common radius ad; the remainder of the nsverse rib beingstruck from/, and that of the diagonal from e, so that each pair of diagonal ribs forms a ee-centred arch, of which the flatness at the crown concealed by the boss. These examples will suffice to )w the variety of ways in which the curvature of the gonal ribs may be determined. 511. The curvature of the cross-springers determines general plan of the spandril, and this governs, to a tain extent, the curvature of the intermediate ribs. 3 longitudinal rib may be determined either as shown igures 96 and 97, or the proportion of the rise to the n may be kept the same as in the transverse ribs and springings stilted, as shown in the elevation of the I rib e f, fig. 93. This last arrangement was a Y common one in church roofs; the stilting of the I ribs being necessary in order to leave proper space the clerestory windows. o ascertain the general plan of the spandril solid, ; any point, as halfway up the transverse rib, and fall the perpendicular a* 1. Set off this height on elevations of the diagonal and wall ribs, and from h points d, eb where a horizontal line at this level cuts h ribs, let fall the perpendiculars c* 2 and 3. Join > 2,3; then a, 1 2 3 e, is the general plan of the pidril at the height aK RUDIMENTS OF THE 114 We have already spoken (Section I., art. 19) of the variety of form that may be produced in the middle plan of the spandril by a slight alteration in the curvature of the ribs; and the reader will, therefore, understand, without further explanation, the method about to be described of obtaining the curves of the intermediate ribs from this middle plan. Thus let it be determined to make the intermediate ribs project before the lines 1,2; 2,3. Design the plan a 1 4 2 5 3 e, so as to give to the spandril the form that may be wished; and from the points 4, 5, erect the perpendiculars 4 g\ 5 1', each respectively equal to 1 o}» Then the form of the ridge le having been previously decided on, (in the example shown in fig. 93, both the longitudinal and transverse ridges are made horizontal,) we have three points in each intermediate rib through which to draw the required curve, which may be struck either from one or two centres, according to circumstances. In fig. 93, the whole of the ribs are made single arcs of circles; the centre of the intermediate rib i k being placed above, and that of the rib g h being placed below, the spring-l ing level. If the ridge-ribs are not horizontal, their ele-| vations must be drawn before those of the intermediate| ribs, and the points h, k, ascertained accordingly. j 212. For the purpose of showing the manner of find'|,, ing the curvature of a lierne lying in a given vaulting surface, we have introduced in fig. 93 two liernes i h anci I k. From any convenient point m on the diagonal ribf about halfway between i and d, set up the perpen dicular m m, and from i set up the perpendicular 1 1 Draw m' m, l i', parallel to the springing. On th^ elevation of the intermediate rib^r h set off h ?^' = d m} draw n parallel to the springing, and from n let fa the perpendicular n n. Join nm, cutting i hat p; m ART OF MASONRY. 115 'ill be the plan of a level line on the soffit. On i h 'ect the perpendiculars h h' and p p, making li = ' and ^ p = V-. Then i, p and are three points i the soffit of the lierne, through which the required irve may be readily drawn with a trammel. The curvature of the lierne i A: is obtained in the i.me manner. 213. The voussoirs forming the ribs are worked in a .;ry simple manner, as each stone forms a portion of a dindrical arch. Two parallel faces of operation are •st formed, at a distance apart equal to the maximum ickness of the rib, and on one of these faces the curve the soffit is marked with a templet. The soffit is ; en worked with a common square, and the ends of i e stone cut to radiate from the curve of the soffit, [€her with an arch-square or with a templet applied on I' -.e of the faces. The profile of the mouldings is then {"Marked on the ends with a templet, and the soffit * Fig. 98 , gaugedto its proper width; lastly, the lines bounding the parallel faces of the rib are scribed on the latter with agauge applied to the soffit, and the mouldings are sunk by means of a mould applied to these lines and to the arris lines \ 1 of the soffit as shown in ' • fig. 98, which however is only intended to show the ] nciple of operation, as practically each member is 1 rked in succession, with a separate templet, surfaces < operation being formed, containing the arrises of the Ijiuldings between which the templets are applied. 116 RUDIMENTS OF THE A rebate must be sunk in the upper part of each face, to receive the pannels. 214. In arranging the positions of the feet of the ribs upon the impost, care must be taken to make each rib as much as possible distinct and independent; which is done by making the ribs start at different distances from the intersections of their centre lines. This will be understood by reference to fig. 93 ; in which the inter¬ mediate ribs are made to spring from behind the inter¬ sections of the diagonal and transverse and longitudinal ribs. The ribs cease to be worked as separate arches, from the level at which the mouldings begin to inter¬ sect each other. Below this point, the springing must be worked in horizontal courses ; the upper bed of the top course being cut into a series of inclined planes, so as to form a proper abutment for the foot of each rib. To work these springers the top and bottom beds are first worked, and the centre lines of the ribs marked upon them. The position of the soffit of each rib is then transferred to these lines from a full-sized eleva¬ tion, and the soffits worked with convex templets applied to the top and bottom arrises. Lastly, the soffits are gauged to the proper widths, and the mouldings worked out with moulds applied in a direction radiating from i the curve of each rib. ! 215. In working the keystones at the intersections j of the ribs some little difficulty occurs, inasmuch as , from each rib being a separate arch, its middle section i must be a vertical plane, and the mouldings of the ribs j will therefore not mitre, but intersect each other in a | very awkward manner: see fig. 99. i To hide this, the keystones are worked with a round > lump or boss, ornamented with foliage and sculpture; so I! 1 1 ART OF MASONRY. 117 Fig. 99. that the mould¬ ings die into the ornament with¬ out intersectino- each other. • X !o i'30 :N !o \x ‘SECTION, OF RIBS thod adopted by the Gothic ma¬ sons to obtain the form of the boss-stones, and the position of the stumps of the ribs, was to take 216. The me- X n I irge block, and to work upon it an upper horizontal i itface of operation, to which the centre lines of the i were transferred from a full-sized plan of the vault; the form of the soffit was then obtained by squaring m from this upper surface. 17- This method occasions much extra labour, and ■eat waste of stone. The following is preferable:_ ipose it is required to work the boss-stone at i, fio-. 93 , e 8 . lake a short templet to the curve of the soffit of Fig. 100. the rib c d, so that its bottom edge shall be horizontal; and mark on it a vertical line, corresponding to the axis of intersection of the ribs (see fig. 100 ). Make similar templets for the two liernes, i h, I k. Mark on each THE ART OF MASONRY. 118 templet the form of the boss, and cut away the upper edo-es; so that when the three templets are applied to the soffit of the finished stone, the ends of each shall exactly coincide with the soffit of each rib; the carving of the boss lying in the hollows thus formed. To work the stone, begin by sinking a draft to the templet for the diagonal rib ; and then, placing one of the lierne templets at the proper angle with the first templet, sink it into the stone until the horizontal edges of the two are out of winding. Apply the third templet in a simi- lar manner. Knock off the superfluous stone square to the drafts, and we have then three curved surfaces of operation containing the soffits of the three ribs. The rest of the operation presents no difficulty. The above method applies to all the boss-stones in a vault, whatever their shape or position, and will be un¬ derstood by inspection of figs. 99 and 100.^ 218. The stumps on the boss-stones should always' be squared to form proper abutments for the ends of the ribs. This was not always done by the mediaeval architects, who often worked the stumps of the liernes on the bosses, so as to form acute angles with their .soffits. APPENDIX. j - ^ - 1E following interesting Investigation has been kindly for- ided by T. A. Walter, Esq., the Government Architect at Ishington, United States, which will, it is presumed, be ijt instructive, on this valuable building material:— I ort of Fi^fessov TF^altev R. Johnson on the Ruilding Stone ied in constructing the foundations of the extension of the 'nited States Capitol. 1 conformity with directions and instructions to test the e used in the foundation w'alls of the extension of the itol, with respect to their strength and durability, I pro- ed to inspect the walls of the two wings, and to note, as »as practicable, the general character, and the apparent irences in the stones which have actually been laid in the jhere was no difficulty in ascertaining that some diversity, ■ in appearance and texture, existed among the materials, tt it consequently became evident that no one sample which y 1 be selected would adequately represent the entire mass. therefore became necessary to select a moderate number f imples, from different parts of the two wings, and, as far ■(dcable, with reference to the proportions in which they If ed to prevail in the walls. IS evident that this proportionality could only be approxi- 6 ly obtained. is confidently believed that the extremes of character fe been reached, but it is to be remarked that the sample h b was taken to show the least probable strength was one s very few which appear mostly in the foundation of the Hi wing. 120 APPENDIX. Three samples were taken from the walls of each wing, besides which a block lying within the north wall was taken to furnish a series, of cubes of different sizes to test the question of increase of resistance according to enlargement of area, and one sample of the sandstone used in two or three of the interior projections only of the walls of the south wing. This sandstone is of the same character as that of which the Capitol is built. The samples were prepared for trial by sawing out from each six cubes of one and a half inch on a side, which were all carefully dressed by rubbing down in the ordinaiy manner; and the faces which were to receive the compressing force were made parcillel, and all the specimens of very nearly the same height, by finishing within a steel frame, which enclosed and held all the six specimens at the same time, and which, bein" turned over after dressing one set of faces, allowed the opp(Tsite set to be rubbed in like manner, and made parallel to the first. This frame is understood to be the same which was em¬ ployed by Messrs. Totten, Henry, Ewbank, and Walter in their recent trials of the marbles. Of the six cubes from each sample, one was selected and reserved for trials of at¬ mospheric effects, and the others carefully gauged to the thousandth part of an inch, preparatory to the operation ^ crushing. In general the specific gravity of every specimen was taken in the ordinary way before crushing. For the sandstone it was found necessary to take account of the water absorbed when immersed for the purpose of taking its specific gravity. The machine used for crushing is that employed for the ordnance service of the Navy, in testing the various materials required for that service. It consists essentially of a lever of the first kind, having fulcrum distances of 20 to 1, acting by its shorter arm on s lever of the second ordei, having fulcrum distances of 10 tc 1 , and consequently the relation of the weight applied to thf first lever to the force exerted by the second is one to 200. | The fulcra of the machine are all steel knife-edges, and n(i allowance is made for friction. ij The compression of the specimens, when under trial, waa ascertained from time to time by suitable callipers applied bi steel plates above and below the stone, and the modulus o| resistance to compression was thus ascertained with consider able exactness. This modulus varies considerably in differen APPENDIX. 121 mples, and even in different cubes from the same sample. order to obtain a standard of comparison of the different ecimens of the stone operated on, a sample of a rock was ited largely used in this country, and to some extent bv )vernment, for building and other purposes. This was the Quincy sienite, which, as will be observed by erence to the Table, sustained a very high pressure before ishiug. In testing the action of the atmosphere on the Ferent samples, I may remark that, for the particular pur¬ se of the foundations of the Capitol, it was considered that i trials of the effect of frost are very important, as it is un- rstood that these foundations will, when the building is com- ■ted, be embanked in such a manner that frost will never ,ch them. For other uses to which this stone may be applied these ils may be of much importance. To some extent an ex- ption from water percolating the soil will also apply to the ndations, since the water falling upon the building will be stly carried away by pipes and drains, and the shielding of ■ surface by pavements or flaggings will tend to keep dry i foundation walls. Chemical trials were selected of such of the samples as ap- ired to represent the exactness of strength to resist crush- , and to subject them to such reagents as are likely to most efficient in nature in causing disintegration or disso- on. The tvro amples taken for chemical analysis were those nbered one and seven of the accompanying Table ; and for a :hanical separation of certain mineral constituents No. 5, the same Table, was chosen, being one of those which ap- red to have been freed from the action of atmospheric in- nces prior to its removal from the quarries. ^or some of the other samples, likewise, the effect of heat- was noted by way of comparison. The quarries from w'hich stone is stated to have been derived for the south wing is wn as the Smith quarry, and those from which that of the th wing is taken are the O’Neill quarries. One of the ^eill quarries is immediately adjoining that of Smith, and se two appear to furnish stone of essentially the same cha- er. 'he other quarries of O’Neill are a few hundred feet lower n the canal. At all these quarries it is judged that stone '■ be found, representing every variety embraced in the es of specimens selected for trial from the foundations of 122 APPENDIX. the Capitol. At all of them there is a covering of greater or less depth, from one or two to ten or twelve feet of soil, sand, gravely and clayey matter, with some rolled pebbles, all of which repose in beds, more or less regular, upon the upper edges of the micaceous rock, worked in the quarries. This rock lies inclined southwestwardly, in an angle of about 50 de¬ grees ; and the natural beds and fissures of the stone afford passage to the surface water to penetrate to a considerable distance below the upper edges. This penetration has caused, in some parts, a discoloration, accompanied by a greater or less alteration of the consistency of the rock, the natural bluish or greenish colour being changed to a yellowish-brown or drab colour ; and for about twenty or twenty-five feet from the top, the rock has been so affected by these surface influences as to be unfit for use in building. Below that level, varying however in the different strata, the workable stone is found. In some of the softer portions it appears that the decomposition has extended Turther down than in adjoining firmer beds. In breaking the blocks the depth to which atmospheric in¬ fluences have penetrated is in general sufficiently indicated by the colour. A careful inspection enables the quarryman to re¬ ject those parts which have been materially affected by the in¬ fluences above referred to ; and the large heaps of rejected matter near the quarries, evince the necessity and the exercise of a discrimination in the selection of such parts as are fit for building purposes. The discoloration of the stone is some¬ times only superficial, or extends to the depth of but a few lines. The upper edges of the rock next to the covering of sand, gravel, etc., afford little more than a mass of micaceous sand, with barely cohesion enough to bear handling. The rock in its normal, or solid state, appears to occupy an intermediate place between true mica slate, of which flag-stones are made, and gneiss, which has the mineral composition of granite. This rock has quartz and mica in large proportions I as compared with feldspar. It exhibits many nodules of quartz, | nearly pure, and small garnets, together with iron pyrites, and I magnetic oxide of iron. I A Table is given exhibiting, first, the number of samples' tested ; second, the part of the foundation walls from which j they were severally taken; third, the numbers of the several j specimens taken from each sample ; fourth, the external cha-. racters of each specimen ; fifth, the specific gravity; sixth, the ^ weight of each sample per cubic foot, derived from the average APPENDIX, 123 )ecific gravity; seventh, the height of each specimen crushed; ghth, the observed compression; ninth, the force producing le observed compression; tenth, the area of the base of each •ecimen operated on; eleventh, the modules of resistance to mpression of each specimen; twelfth, the average modulus r each sample ; thirteenth, the average crushing force per uare inch, in pounds; fourteenth, the absorption of water * each sample; and, fifteenth, the loss of each sample by the ect of heat. No. of the Sample. 124 appendix. 2 1 3 4 Parts of the Foundation Walls from which the Samples were taken. Mark of the Specimen, | External Characters of each Specimen. From the inner wall, 1 Nodule of flint on one side; a few 2 south-east corner of minute crystals of pyrites. the north wing, and 2 Nodule of flint near one corner ... 2 about halfway up the 3 Colour nearly uniform grey; no pyrites 2 wall, from a block observed. partly uncovered, ow- 4 Whitish band, with pyrites on one side; 2 ing to the wall being light spot on opposite side. unfinished. 5 White spot on one corner; the rest dark grey ; pyrites on two sides. From an unfinished but- 1 Colour dark grey; few speeks of pyrites; 2 tress on the inside of nodule of quartz on one side. the wall, near the 2 Colour dark grey; few specks of pyrites ; 2 north-west corner of thin seams of mieaceous matter. the south wing, and 3 Numerous dark red specks of garnets; 2 about halfway up quartz nodule; few specks of pyrites; from the bottom. colour dark grey. 4 Colour dark grey ; two thin beds of grey- 2 ish white; dark brown specks of garnets, and one or two minute crys¬ tals of pyrites. 5 Colour dark grey; garnets and pyrites very sparse. From the inside of the 1 Colour dark grey; five or six specks wall, near the north- of pyrites; brown siliceous matter. east corner of the in fine particles. north wing, about the 2 Five specks of pyrites visible; several middle height of the garnets in light coloured spaces; small wall, still unfinished. cavity on one side. 3 Colour dark grey; two specks of pyrites visible; garnets in light spaces. 4 A nodule of flint; three or four fine specks of pyrites; garnets in light coloured spaces. 5 Two or three light grey spaces; four specks of pyrites. Stiecific Oravity of the APPENDIX 125 No. of the Sample. 126 APPENDIX. •5 Parts of the Foundation' Walls from which the Samples were taken. From the bottom of the ■wall (at the opening left for carts), in the north-west corner of the north wing. The block from w'hich this sample was detached rests directly on the earth. From the loose stones lying near the north wall, inside the north wing. From a part near the top of the wall still unfinished, on the south side of the south wing. External Characters of each Specimen. Colour dark grey; a few blocks of whitish matter. Three small nodules of quartz on ditfer- ent sides, thin irregular bands of whitish matter resembling talc, but probably is mica. One white band containing pyrites; white matter very easily cut; dark- coloured siliceous matter in spots. Flint at one corner, white quartz at an¬ other ; one or two specks of pyrites. Small nodule of whitish matter resem¬ bling “ feldspar.” A block one inch on a side; dark bluish- grey. Block two inches on a side . . . . a5) GQ 2-721 2-76; 2-78’ 2-75' 2-79 Quartz nodule,colour light grey; pyrites; long nodule of flint on one side; whitish specks of partly decomposed feldspar penetrated by atmosphere. Two crystals of pyrites; whitish bed mica, greenish in certain parts; de¬ composing feldspar; no brown streak. Light grey specks; no pyrites; brownish streak crosses the beds; a few garnets. Brownish streak vertical to beds ; no py¬ rites observed; numerous specks of yellowish-white feldspar. No nodule of pyrites, l-5th of an inch in diameter; light grey spot; rhombic white spaces. 2-78 2-71 2-7! 2-8 2-7 2-7 2-7 APPENDIX 127 7 8 9 10 11 •12 Height of the Specimens in Inches. Observed Compression in 1-10,000 of an Inch. Force producing the ob¬ served Compression in pounds Avoirdupois. Area of Base of Speci¬ mens in Square Inches. j Module of Resistance to I Compression in Pounds for a 1-lnch Base. Average Modules of Re¬ sistance to Compression for each Sample. 1-416 65 30 000 2-3639 2,764,500 1-420 35 30-000 2-2852 5,326,000 '-415 60 31-000 2-3424 3,120,700 3,263,400 .-415 45 20-000 2-3441 2,674,200 -410 100 40-000 2-3195 2,431,600 -032 • • • • 1-0660 1-00 • • • • 3-0791 • • • • • • -405 80 20-000 2-2862 1,536,200 •405 70 15-000 2-2320 1,348,600 405 70 20-000 2-2846 1,757,000 1,486,600 400 100 25-000 2-3119 1.513,900 404 140 50-000 2-3604 1,277,300 13 .ts rt o S > cz? ^ u en « ‘TS c- fl « 3 O O&H &ci->^ n •§-gl 15-978 15-865 12-944 14 cS S3 oj a O S g'SH (O ■£.«.= tr j: 01 O 3 t »oO 15 0-90 0-40 4-20 19 11 Loss by a Ij-Inch Cube in freezing 30 times in 1-100 of a Grain. No. of the Sample. 128 APPENDIX, Part of the Foundation Walls from which the Samples were taken. External Characters of each Specimen. From a block in the second tier from the ground, inside of the wall, near the south¬ east corner of south wing. The part from which it was taken is a projection beyond the face of the wall. From a block of sand¬ stone lying near one of the three interior projections on the south side of the south wing, which are constructed of the same material. The Aquia Creek sand¬ stone. A sample of sienite from the “Wigwam Quarry,” Quincy, Mass., tried for com¬ parison, being a ma¬ terial much employed in public buildings, etc. etc. Colour lighter than any of the preceding; no pyrites observed. Colour as the preceding ; garnets on one side; no pyrites. Colour as above; two nodules of quartz; one speck of pyrites ; garnets. Grey, with short strips of greenish mat¬ ter ; one nodule of quartz; no pyrites. Nodule of quartz; no pyrites ; light grey mottled colour. Reddish-yellow colour; quantities of quartz cemented by feldspar; small cavity. ditto ditto ditto ditto ditto ditto ditto ditto ditto ditto ditto ditto Colour grey or mottled; hornblende, quartz, and feldspar visible and vari¬ ously intermixed. 2-71 2-71 1-9 2-6 2-6 2-6 Snecific Gravitv of the APPENDIX. 129 7 8 9 10 11 12 13 14 15 Height of the Specimens in Inches. Observed Compression in 1-10,000 of an Inch. Force producing the ob¬ served Compression in pounds Avoirdupois. Area of Base of Speci. •mens in Square Inches. I Module of Resistance to Compression in Pounds for a 1-Inch Base. Average Modules of Re¬ sistance to Compression for each Sample. Crushing Force per Square Inch in Pounds Avoir¬ dupois. ----- 1 Absorption of Water by a Cube of 1^ Inch in Grains Troy. Loss by a IJ-Inch Cube in freezing 30 times in 1-100 of a Grain. 1-405 • • • • 2-3400 1-408 80 10-000 2-3149 760,300 o o 50 10-000 2-2970 1,020,600 1,400,600 8-156 5-88 12 1-404 40 5-000 2-1975 798,600 1-410 30 15-000 i 2-3320 3,023,200 1-413 30 10-000 2-3087 2,040,100 .-406 • * 2-3028 -417 45 10-000 2-2950 1,374,900 1,584,400 5-245 199-00 72 -410 45 10000 2-2719 1,379,000 -414 40 10-000 2-?897 l,,543i,9pp in .> 3 .* , ' # ■» ■> ’ J s ^ ■» ->.i 1 , ^ n , -410 115 60-000 2-2801 3,266,200 ^ <* 3 '1 -410 80 65-000 *' J 9 O 2-307-3 ■> j 0 > 4-^954’,i’OO J>,090v'150? 29-330 -7 V o -255 • • • • 1-6320 i ) 1^ -> , , i ) A , 130 APPENDIX. In conducting the experiments on crushing, the opportunity was embraced of ascertaining the amount of compression which the stone received under certain loads to which it was sub¬ jected. The observations have a practical bearing when ap¬ plied to materials of variable character entering into the same strncture. If the weakest varieties were at the same time those which could bear the least compression, it might happen that the blocks of stone having little strength to resist crushing, as well as little capacity to undergo compression, might be crushed and destroyed, while the stronger kinds would be yielding to the compressing force and would be eventually brought to bear the whole load. If, on the contrary, the weaker varieties were capable of yielding to eompression, with¬ out finally giving way until considerably condensed by pres¬ sure, they would still preserve their integrity, though so much compressed as to allow the stronger stones in close proximity to them to bear more of the superincumbent weight than be¬ longed to the area of their bearing surfaces. As the compres¬ sibility of stones may be considered to arise, in part at least, from their porosity, and as the latter property measures, to some extent, the power of the stones to absorb fluids, it ought to follow, that when a stone has become porous by a partial decomposition, it should be both more compressible by a given force, and more absorbent of fluids than it was in its natural or unaltered condition. The experiments furnish a remark¬ able confirmation of this view. The table proves that the samples which had been altered by partial decomposition (Nos. 6 and 7) were much more compressible ; that is, they gave a lower modulus of resistance com^freskion than any of the .sample? which w?re in the o.vdioa'ry unchanged state of the '.blyeydck;,', ;The, -samfe ultetbd samples were likewise more ab- “soibenf of water than those which .were unaltered. The fol¬ lowing^ short table .S'hovi’‘£ the jmoilillhs of resistance and ab- so.vptto^nbf'water,'‘ahran^d .with reference to increasing resist- aiibe'.foT compfessioh, and to the admission of water. f I I \ Number of sample. Modulus of resistance to compression. Absorption of water in grains. 7 weathered stone . 1,400,600 5-88 6 „ 1,480,600 4-20 1 not weathered 2,205,800 1-20 4 3,263,400 0-90 2 ,, 4,318,800 0-81 3 . 5,570,500 0-65 APPENDIX. 131 The differences of compressibility are obviously not solely ' to atmospheric action. ^ t will be remarked that, instead of the usual term “ mo- us of elasticity,” the expression “modulus of resistance to ipression is used, which seems to be more appropriate to less that character or property of building materials, which Tactically applied in architecture. r •minations to illustrate the Effects of Atmospheric Influences on the Stone. 1 testing the action of frost, the process was applied of dng the specimens after moistening them with distilled T. his mode of experimenting (not now allowed for the first u ) has the advantage over other processes sometimes re- 0 id to for imitating the effect of freezing, in producing both b' chemical and the mechanical actions on the stone which a rally result from atmospheric humidity and a freezino- 'ft)erature. ° ich cube subjected to freezing was enclosed in a thin llic box, furnished with a suitable covering, and the whole 3 of boxes containing the specimens was placed within a r vessel of thin metal, which was surrounded by a freez- nixture. Care was of course taken that all the particles ^ hed from each cube by the freezing should remain in its i^box. The gain in the weight of the box, after thirty re- Jons of the freezing process, as ascertained by a balance nble to the two-hundredth part of a grain, gave the loss I the stone had suffered under this treatment. Both in ct to the absorption of water and to the influence of frost, I I be observed that the strong rocks, such as sample No. 1 i blue quartzose mica slate, and the Quincy sienite (sam- o. 9 ), manifest great power to resist the disintegrating I of these powerful causes. While sample No. 1 lost only j.f a grain by frost. No. 6 lost No. 7 yVo. and the 'f! I Creek sandstone. No. 8 , lost or exactly 12 times as» ^ as No. 1 . While the sample No. 5 , a very sound and ^ict variety of the blue rock, absorbed but of a grain of No. 6 took 4" 20 , No. 7 5' 88 , and the Aquia Creek 'f one 199 grains. J i latter acted in fact like a sponge, and became com¬ ity wet throughout. T| s was proved by crushing some cubes of that stone im- 132 APPENDIX. mediately after they had been immersed in water. It is pro¬ per to state that the absorption of water is represented by the difference in weight, ascertained by first weighing the speci¬ mens after being thoroughly dried, and again after being per¬ mitted to absorb water by the aid of the exhaustion of an air pump, and the subsequent pressure of the atmosphere while immersed in a vessel of water within the receiver. THE END. I BRADBURY AND EVANS, PHINTEHS, WHITEFKIAKS. |spr]incim!c line i'LATE 1. A Plate 1. (2) i I LATE 2. 0) FIG. 11. Plate 2. (2) FIG. 12. Plate 3. FIG. 13. 213 Plate 4. Plate 5 Ri n. i’LATE G. SQUARE SECpON OF ARCH i Mil PLAN OF ARCH FIG 44 I ;H X DEVELOPMENT OF FACE OF ARCH PLAN FIG. 45. Elevation of Cross Vault. Plate G. (2) m r n < > H O z FIG. 47. HALF DEVELOPMENT .TE 7 fOCAL tCCENTRJClTY WINDING STRIP I'','.Ililll. 8 ( 1 ) FIG 90 FRONT ELEVATION M ii III' 41 liiiiijjj F 1 M f w B C B C B C ■d.‘ PLAN OF BOTTOM QED PLAN OF TOP BED X Scale- ST MARIE’S ABBEY, BEAULIEU. TolhCU/e on tn, 71 e^eef-ryyu . i of Feet. Plate XI rsns .^lELTCTiS^Ei ®F S’? *77 5 '* «- .'i. !i)F . ; Ki ^i[3LTSjaiy.mE,