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draw the line nt, which is the slope. Then draw the curve mprt, and from the point » draw the joint lines pv and rX. The centre of this gate is represented (in the upper part of the diagram) with voussoirs, and the keystone placed behind to show the mitre of the centre. The sofite moulds serve for curving the ends of the stone where the intrados meets the surface of the two walls. It must, however, be observed, that, previous to the application of the sofite mould, the concave surface of the intrados must be formed by a mould with a convex edge, and then the sofite mould or moulds of developement must be bent into the hollow, so that the two parallel edges may coincide with the corresponding edges of the stone. The angles which the intrados makes with the joints are taken from the elevation. of the face of the arch. This elevation is no more than a section of the arch perpendicular to the axis of the cylinder which forms the intrados.

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1985. To construct a semicircular-headed arch in a round tower or circular wall. Let ABDC (fig. 657.) be the plan of the tower. Bisect the are AB, and through the point of bisection draw EF parallel to the jamb line AC or BD. Through any point a in EF draw GH perpendicular to EF. Produce the lines CA and DB to meet GH in the points G, HI, and GH will be bisected in a. From a, as a centre, and with the radius a G or a H, describe the semicircular are GFH. Also describe the are of the extrados and divide the arcs each into five equal parts, and let fall the perpendiculars of the joint lines, and those of the middles of the sofite curves to the inside circu

lar line CED of the tower. Having extended the arcs of the intrados curve on the line IK, and having drawn the lines of the sofites and those in the middle of each sheet as before directed, lay off the distances between the right line GH and the circular outside line AbB, viz GA on IX and on KZ, cd on ef, Vg on hi, Sk on Im, Mn on op, ab on qr; then trace the front curve on the sofite XrZ. To find the rear curve, lay GC on IY, cC on eS, &c., by which the rear curve will be obtained.

1989. We do not consider it necessary to pursue the construction of the moulds, the operations being very similar to those already given in the previous examples.

y

K

2

B

y w

Fig. 657.

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1990. To find the moulds for an oblique semicircular arch in a circular tower. construction of this differs from the preceding only in the bevel or obliquity of the tower;

hence it requires no particular description; only observing, that the bevel causes the mould to be longer on one side than on the other (see fig. 658.), as is evident from the plan; therefore the distances taken between the right line AB and the circular line of the tower CDE, being unequal, must be transposed each on its particular line of the mould and joint to which it corresponds in the sofite, that is, the distance AC must be laid on FG, BE on HI, and so of the rest. To work the stones, dress the beds, then apply the proper moulds and cut the head and tail circular as before. Trace the breadth of the sofite on the upper bed, then hollow the sofite, and cut the joints by the bevel.

1991. To construct an oblique arch in a round sloping tower intersecting a semicircular arch within 1 it.

H

F

This is nearly the same as the two preceding cases. On one side draw the line of slope (fig. 659.) AB, and on the other the arc CD. Draw parallels from the divisions of the sofites and their middles, as in the figure, in order to cut the line of slope and arc. To work for the slope, set off all the retreats comprised between the perpendiculars AH and the line of slope AB on the perpendiculars of the sofite, square to the front line of the tower F 19 G, as follows: Transfer the retreat 9-10 on 19-20 by placing the comthat the line 19-20 would pass passes SO through the centre of the tower, and the point 20 fall on the centre of the gate 0-75, and 7-8 on 17-18, and on 21-22 in the same manner (only terminated by the lines

Fig. 658.

from the sofite instead of the centre line of B
the arch), set also 5-6 on 15-16, and on
23-24, 3-4 on 13-14 and on 25-26, and
lastly 1-2 on 11-12 and on 27-28, and
through these points trace the sofite 28-20
-11. The extrados is found in like manner,
and the middles of the joints 47, 49, 53; which
done, draw the plan of the joints 14-47-35,
18-19-37, 22-51-39, and 26-53-41.

1992. To find the curve of the plan which terminates the tails of the moulds. Set the projections of the buttress of the semicircular arc at right angles to the inside line of the tower; viz. 64-65 on 74-75; 62-63 on 72-73 and on 76-77; 60-61 on 70-71, and on 78-79, 58-59 on 68-69. and on 80-81; 56-57 on 66-67 and on 82-83; then trace by hand the curve 83-75-66. The curves of the extrados and joints are found in the same manner.

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1993. To find the moulds of the sofite. Draw the line of direction 94-84 (fig. 660.) as before, below which set off the distances I-11 or 84-85, K-12 on 86-87, L-14 on 88-89, M-16 on 90-91, N-18 on 92-93, O-20 on 94-95, and then trace the front of the sofite moulds 85-95-99. To find the rear, set I-66 on 84-33, K-67 on 86-36, L-69 on 88-100, M-71 on 90-98, N73 on 92-97, 0-75 on 94-96, and trace the rear curve of the mould 101-96-33.

Fig. 660.

1994. To find the moulds of the joints. Transfer P-19 on 31-54, Q-37 on 32-48, I-47 on 42-52, R-35 on 43-40, and through these points trace the front joint or bed moulds 93-54-48, 89-92-40. To find the rear, make 31-50 equal to PV, 32-38 equal to QX, 42-46 equal to IT, and 43-34 equal to RS; which done, trace the curve lines 97-50-38 and 100-46-34. The two other joints are found by the same method. We do not consider it necessary further to multiply examples of the kind here given the latter sort, especially, rarely occur in practice; and if they should, all that will be necessary to master the operations will be the application of a little thought and study.

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1995. III. Or DOME VAULTING. In whatever direction a hemispherical dome is cut, the section A is always the same. B represents one half (see fig. 661.) of the same in the plane of projection. The construction is sometimes such that the plan is only a semicircle, as B, as in the termination of the choir of a church: in which case the French call it a cul-de-four; with us it is called a semi-dome.

1996. Through the extremities of the joints, and through the middle of each sofite of the section A, let fall on the line ab, perpendiculars, whereof all the distances de from the centre c will be the radii of the ares, which will serve for the developement of the sofites, of the joints, and for the construction of the arch stones. The method which follows, though it will not perhaps give the sofites and joints strictly accurate, will do so sufficiently for all practical purposes. Upon the developement C make SC equal to the arc MDGC, then set out to the right of the points of division the parts ST equal to st on the plan B; then raise through the points T upon the line SC perpendiculars equal

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Fig. 661.

to the correspondents e, t, d of the plan B, and draw the curve ESD through the points so found.

1997. The sofites are terminated by four curves, whereas the joints have two right sides, as DI, EI, and DO, EO, and two curved sides, as II, DE, and OO, DE; the widths DI, DO of the joints are equal to DI, GE of the section; in one direction they are curved only one way, but as respects their so tes they are so in every way. The heights of the voussoirs are given by the section A, their bases on the plan B Thus G, I, in the voussoir next the keystone, being the most opposite points, the base of it on the plan will be comprised between the two arcs dte, which answer to the perpendiculars let all from G and I. The base of the first voussoir, according to the first method, will be equal to the surface comprised between the arc dof and the arc dse, which answers to the perpendicular let fall from the point D.

A

Section

The piers D and E are If we suppose the face or

C

1998. EF and GH are the diameters of the upper and lower bases of a truncated cone, whose lower surface is hollowed out spherically. After working the voussoirs, so as to make their bases such as we have just indicated, they must be worked to solite moulds for giving them the hemispherical form of the section; after which the angles of the moulds are joined by arcs parallel to the arrisses of each stone, or by applying a general mould of the form of the section, that is, circular, of the radius of the dome. 1999. For the pendentives formed in an hemispherical dome. supposed those of half the dome pierced by the pendentives. elevation B (fig. 662.) to make one quarter of a revolution about the point A, we obtain the elevations B and C. Through the points of division on the elevation C draw to the arc AD right lines perpendicular to CA. On the extremities of these lines upon CA, and from C, as centre, describe ares in the plan F, by which the plan of the projection on F is obtained, whose intersections with the right lines drawn from B will give the joints and faces for the level beds. The lines HF, FE, ED are right lines. The spaces GAEF, FHIK are pieces of cylindrical vaulting, so that the only difficulty is in joining to each of their voussoirs their correspondent parts in ELMHFE.

2000. The elevation B gives the height of the voussoirs;

Plan

C

M

Elevation

B

G

E

NK

Fig. 662.

their bases, as seen in the preceding example, will be OPQRNO, GSTUVKFG. length of the keystone will be XY, and a-A will be half its width.

The

2001. The part FQR is the plan of the springing stones of the pendentive in the elevation A. The remaining parts of the construction are sufficiently shown by the lines of the diagram, which will be understood by the student if he has previously made himself acquainted with the previous portions of this section.

2002. We should willingly have prolonged this part of our labours, if space had permitted us to do so without sacrificing other and important objects. If the subject be one in which more than the ordinary practice of the architect is called upon to put into execution, we refer him to Simonin, Coupe des Pierres, Paris, 1792, and Rondelet's Art de Bâtir, which we have used with much freedom, and in which many more interesting details will be found than we have thought it absolutely necessary here to introduce, though we believe we have left no important point in masonry untouched. We cannot close this section without paying our tribute of respect to the masons of this country, who are among the most intelligent of the operative builders employed in it. A very great portion of them are from the north of the island, and possess an astuteness and intelligence which far exceeds that of the other classes of artisans. We must not, however, altogether do this at the expense of those employed in carpentry, which will form the subject of our next section, among whom there will be found much skill and intelligence, when the architect takes the proper means of drawing it out; and we here advise him never to be ashamed of such

means.

2002a. IV. OF CAISSONS IN CYLINDRICAL AND HEMISPHERICAL VAULTING. — The method of setting out the caissons or sunken panels in cylindrical vaults and domes, is a process required almost in every building of importance, and imparts great beauty to the effect of the interior when properly introduced: it is. indeed, one of the elements in composing them, and must therefore be well understood before the student can succeed in developing his ideas.

20026. In setting out the ribs of cylindrical vaulting, the vertical ones are supposed as falling on supports below the springing; but if such supports fall too wide apart, the caissons themselves will be too wide, and the space must be divided into a greater number; in which case, if practicable, an odd number is to be preferred, taking care that the caissons are not too much reduced in width. This, however, is only for the purpose of ascertaining roughly how many caissons may be used in the circuit of the vault; and it is to be remembered that they must be of an odd number, because a tier of caissons should always extend along the crown of the vault. Fig. 662a, is an example of a cylindrical vault wherein the

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number of caissons is five. A is one half of its transverse section, and B a small portion of the longitudinal section. The width of the ribs between the caissons is one third of them; hence, if the number of caissons, as in the example, be five, the arch must be divided into twenty-one parts, one of which parts will be the width of a rib, and three will be given to the width of a caisson. As we have just observed, a caisson is always placed in the centre; we shall therefore have the half-arch = 1 + 1 + 3 + 1 + 3 + 1 = 10 and 10 × 2=21. The vertical lengths of the sides of the caissons thus found will regulate the horizontal lengths of their sides, inasmuch as they should be made square. If the caissons in the vault be seven in number, as in fig. 6626., the sofite or periphery must be then divided into twentynine parts; if their number be nine, into thirty-seven parts; and so on, increasing by eight each step in the progression. The caissons may be single or double sunk, or more, according to the richness required; their centres may be moreover decorated with fleurons, and their margins moulded with open enrichments. Where the apartment is very highly ornamented, the ribs themselves are sunk on their face, and decorated with frets, guilloches, and the like, as mentioned for ceilings in Book iii., c. i., s. xxiv. Durand, in his Cours d Architecture, regulates the width of the caissons entirely by the interaxes of the columns of the building; but this practice is inconvenient, because the space may in reality be so great as to make the caissons extremely heavy, which is, in fact, the case in the examples he gives.

2002c. In the case of dome or hemispherical vaulting, the first point for consideration is the number of caissons in each horizontal tier of them; and the student must recollect that allowing, as before, one third of the width of a caisson as the width of a rib, the number of parts into which the horizontal periphery (whereof e'e' on the plan A is one quarter, and its projected representation at ee on the section B) is to be divided (fig. 662c.) must be multiples of 4, otherwise caissons will not fall centrally on the two axes of the plan. Thus,

A dome having 16 caissons in one horizontal tier must be divided into 64 parts.

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and so on increasing by 16 for each term in the progression. In the figure, the number of caissons is sixteen. The semi-plan is divided into thirty two parts, three whereof are given to each caisson, and one and a half to each half-caisson on the horizontal axis of the plan. From the divisions thus obtained lines are carried up to the section ab, ab, ed, cd, As the projected representations of the great circles of a sphere are ellipses, if from b, b, d, d, we construct a series of semi-ellipses whose transverse diameters are equal

1

to the semi-diameter of the sphere, and their conjugate axes determined from the points of intersection b, b, d, d, we shall have the vertical sides of the caissons. The next part of the process is to ascertain the ratio of di minution in the heights of the tiers of caissons as they rise towards the vertex, so that they may continue square in ascending. Upon a vertical line CC', whose length is equal to the developed length of the line of dome ef, or in other words. whose length is equal to one quarter of the length of a great circle of the sphere, to the right and left of C set out at g and g the half width of the caisson obtained from the plan, and make hg, hg equal to one third of the caisson for the width of the ribs on each side. Draw lines to the vertex of the development from hh and gg. A diagonal hi being then drawn, the horizontal line ik will determine the lower edge of the next caisson upwards. Proceed in this way for the next from and so on. The heights of the caissons thus obtained, being transferred to the section on the quadrant ef, will give the proportionate diminution thereon of the caissons as they rise. They are discontinued, and the dome is left plain, when they become so small as to lose their effect from below, and indeed they could not beyond a certain limit be executed.

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2002d. V. OF GOTHIC VAULTING.-Professor Willis, in his valuable essay On the Vaults of the Middle Ages, printed in the Transactions of the Institute of British Architects, 1842, states that every rib should spring as a separate and independent arch, and that the elliptic curves produced by the method of obtaining the form by ordinates from those of the transverse ribs, are totally at variance with the characteristic forms of the Gothic style. De Lorme first taught this method, and others followed him, but it was never intended by them to be applied to Gothic rib-vaulting. This author shows (ch. viii.) that every rib is perfectly independent of the other in its curvature; each rib consists of a single arc of a circle whose centre is upon the impost level, and they cannot be therefore connected by projections. They all form pointed arches of different proportions, with the exception of the diagonal arch, which is very nearly a semicircle. "This," says Willis," may have been the genuine French method, but in our English examples the centres are commonly placed without respect to the impost level, and the general forms of the vault are different from those which are produced in this manner." Dérand, writing later than De Lorme, says, "that in this style the ribs are always made arcs of circles, elliptical or other curves being inadmissible” (p. 177). Willis, later, however, allows certain ribs in a vault to be semi four-centred arches," the others being arcs of circles. (See 1943a.) 2002e. "In the early stage of rib-vaulting,” remarks Professor Willis, "the ribs consist of independent and separate voussoirs down to the level course from which they spring. The separate stones were roughly jointed at the back, instead of being each got out of a single stone, as in later structures. The back of these ribs is concentric with the soffite. The transverse rib of the north-east transept of Canterbury Cathedral consists of about one hundred richly-moulded stones, but the workmanship is exceedingly rude "

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2002f. The rough construction of the spandril, in the early instances, was followed at once by a more artificial structure, bespeaking a great advance in the art of masonry; and it remained with very slight change to the very latest period of rib-vaulting. This system is shown in fig. 662d. The junction of the solid mass L to N with the clearstory wall, is bounded by parallel vertical lines D, and this mass is always built of solid masonry bonded into the wall and forming part of it; the French name for this block of masonry is tas de charge. It is from the level of N that the real rib and panel work of the vault begins, for separate ribs are erected upon the surface of this solid, and

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