by Unknown
Another valuable, if problematic, source of information is the set of drawings by Francesco Piranesi, mentioned earlier, that was based on the surveys made with his father, Giovan Battista. In the lower third of Piranesi’s plate reproduced here as Fig. 4.7, on the left, the perspectival drawing is entitled “Dimostrazione dell’ottava parte della cupola, come si vede quando fu spogliata dell’antica intonacatura” (an eighth part of the dome viewed without the ancient plasterwork). The arches depicted at the bottom are the same as those drawn by Antonio da Sangallo the Younger. Above them Piranesi drew a system of ribs and compartments, which would have numbered eight in all. This engraving by Piranesi conditioned subsequent studies and publications on the Pantheon for over a century, but the web of arches above the first row is mere conjecture. As a matter of fact, subsequent inspections confirmed only the existence of the arches drawn by Sangallo. Piranesi’s web reflected the building techniques of the 1700s but not the dome of the Pantheon.
In 1892–1893, the Italian government commissioned repair work to “some coffers near the springing of the dome, on the right of the main altar.”75 Scaffolding was installed up to eight meters above the level of the springing of the dome. In charge of operations were Giuseppe Sacconi and Luca Beltrami. The French architect Chedanne was given permission to make sketches of the dome from the scaffolding.76 Beltrami discovered that the arches at the springing of the dome do not follow its spherical curvature but rise vertically. In fact, he made an opening for inspection in the concrete at the level of the second row of coffers. He found the brick key of the arch one and a half meters from the surface of the recessed central field of the coffer (Fig. 4.9).77 In addition, he discovered 1) that the arches are built with two rings of bipedales; 2) that under each arch there are three minor arches, corresponding to the spacing between the Corinthian columns far below; and 3) that there are no other arches in the dome or ribs of the kind that Piranesi envisaged.78
4.9. Detail of dome intrados at the springing with plaster knocked off, 1892. (American Academy in Rome, Fototeca Unione, no. 3595)
Photographs show the ribs of the coffers without the plasterwork. Some are faced in brick, others appear to be concrete, but this aspect does not seem to have been adequately investigated (the brick may be modern). To return to the drawing on the bottom right of Piranesi’s plate (Fig. 4.7), this shows a detail of the ring of bricks around the oculus. The bipedales are not arranged vertically but into flat arches. The veracity of this document has been confirmed by modern inspections and photographs, and a schematic drawing by Guglielmo De Angelis d’Ossat shows eight flat arches in all.79 The oculus of the Tempio della Tosse in Tivoli has a similar arrangement; here, the flat arches push against each other with the springer bricks embedded like ribs in the concrete shell.80
The oculus was a structural device, too. Its rigid perimeter ring of bipedales acts like a boss in a vault or the keystone in an arch, except that in being a void, it simplifies the difficult problem of building the crown. Indeed, it replaces a stretch of vault 9.1 meters wide. Thus, the critical part of the dome is reduced to the portion from the top of the third story to the edges of the oculus (see Plate XI and Fig. 1.12).81
To conclude, investigation carried out under the plasterwork of the Pantheon dome has revealed a series of eight relieving arches resting on the exedrae; they rise vertically rather than following the curvature of the dome and are embedded in the concrete vault. These arches are actually the faces of the barrel vaults that cover the ring of chambers of the third story of the drum (Figs. 4.5 and 4.6). The tops of the arches rise to 8.4 meters above the springing of the dome. So the dome is embedded in the drum for almost 40 percent of its height, taken from the springing to the oculus. A further 25 percent of the height is masked on the exterior by the step-rings, and only from above that level does the dome correspond to a simple calotte. The dome embedded in the diaphragmatic drum was the architect’s trick.
Materials
As in most construction in Rome, the mortar used is a mixture of lime82 and pozzolana. This is a volcanic powder named after the town of Pozzuoli, between Naples and Baiae, while a similar material can also be found in Rome itself.83 Vitruvius describes its exceptional qualities:
There is also a type of powder that brings about marvellous things naturally. It occurs in the region of Baiae and in the countryside that belongs to the towns around Mount Vesuvius. Mixed with lime and rubble, it lends strength to all the other sorts of construction, but in addition, when moles [employing this powder] are built into the sea, they solidify underwater.84
Concrete made with pozzolana can cure without drying, even in water and in the absence of air. It is perfect, therefore, for walls of great thickness. To the mortar are added types of aggregate, such as brick fragments, tufa, and volcanic slag. On the basis of detailed inspections by Gioacchino De Angelis d’Ossat and other scholars, we know this material to be graded carefully for the sake of performance,85 as illustrated in Figure 1.12 and summarized in words by Kjeld De Fine Licht:
Up to 11.75 metres above the level of the springing the cupola is composed of layers of brick fragments set in mortar. Six through–courses of bipedales, which slope 1 in 10 inwards are set in this zone at irregular intervals. The unit weight of the mass of concrete is calculated to be about 1600 Kg/m3. Above this there is a belt 225 cm high which at the top and bottom is delineated by courses of bipedales, and in this belt the layers of brick alternate with layers of tufa. In that section about 9 m high which makes up the top part of the cupola, there are alternating layers of light tufa and volcanic slag in blocks about 20 cm in size, the unit weight being 1350 Kg/m3. ... The thickness of the cupola is reduced from about 590 cm at the foot to nearly 150 cm at the top.86
The distribution of the materials is an expression of a conscious and rational arrangement. The heavier brick and tufa with a greater resistance to stress is placed at the foot of the dome. Above this follow layers of filling of increasing lightness: Cappellaccio, tufo giallo, pumice, and volcanic slag.87 Volcanic slag (or scoria), such as is used in the vaults of the Baths of Caracalla, is a light material that at first floats if immersed in water since it contains air pockets. The judicious use of volcanic slag reflects the building traditions of Baiae and its great domes. The benefits of this approach are threefold: 1) the weight of the material lessens as the structure rises; 2) this reduces compression on the underlying layers, and 3) this produces less thrust.88
Masons’ Criteria
In traditional Italian terminology, “volta romana,” that is, Roman vault, means a vault filled with masonry from the intrados to the crown. This construction technique is completely different from that of medieval or Renaissance vaults, where the abutment is not made of concrete masonry but simple earth or rubble and the structure formed by voussoirs, or wedge-shaped stones. In medieval and Renaissance vaults, the stones are, as a rule, arranged radially on a centering, so that each row of stones forms an arch or rib. The mass of earth filling on the extrados helps stability. On the other hand, in Roman concrete vaults, a radial alignment of aggregate in sympathy with the curvature is rare. It is found in the dome of the Temple of Mercury in Baiae,89 the barrel vaults of the Sanctuary of Fortuna Primigenia in Praeneste, and the Temple of Hercules in Tivoli.90 The stones, or caementa, of Roman vaults are generally arranged in horizontal layers, even where they run up against the centering. This is the case in the original vaults on the radial cunei of the Colosseum, in the Domus Aurea, and in many other ruins.91 For us today, this arrangement seems illogical because the caementa do not follow the curvature or the stress flow. The method is, in fact, more reminiscent of corbeling techniques, as noted by Gustavo Giovannoni:
As a construction concept, a vault of horizontal concrete layers ... is far removed from a voussoir vault of cut stone. Indeed, it seems to bear greater resemblance to the Mycenaean false dome, made with horizontal stones, that is, by corbelling layers inwards like cantilevers on rings below.92
&nb
sp; Studies by Rowland Mainstone come to similar conclusions.93 The principle of corbeling can be seen in certain types of vault indigenous to the Mediterranean. In Apulia, in southeast Italy, the casella,94 or casiddu (Fig. 4.10), is a kind of beehive house “built of rough stones set in projecting courses to form a dome.”95 Similar shelters are also found in Liguria, the island of Minorca, and the Basque region.96 The casiddi and the trulli in Apulia go back to the sixteenth century and are built without any mortar. But the tradition goes back to former times. Another very ancient building type similar to the casiddu is the cyclopean nuraghe, built in Sardinia from circa 1800 BC until ancient Roman times.97 Aristotle mentions such constructions in a minor work entitled On Marvellous Things Heard: “In the island of Sardinia they say that there are many fine buildings arranged in the ancient Greek style, and among others domed buildings (Greek tholos), carved with many shapes.”98
4.10. Section through a casiddu near Santa Cesarea Terme, Puglia. (Gerhard Rohlfs, Primitive costruzioni a cupola in Europa, Florence 1963, Fig. 4)
The largest nuraghe corbel vault, Is Paras (fifteenth century BC) located in Isili near Barúmini, has a span of 6.4 meters and a height of 11.8 meters, and inside the corbel vault is made by 37 rows of rough stones (Fig. 4.11). It is reminiscent of the “Treasury of Atreus” in Mycenae, a tholos of the Greek Bronze Age (thirteenth century BC), except that this has a far greater extension: a 14.5 meter span and a height of 13.2 meters, while inside the false dome is constructed by 33 rows of much larger hewn blocks. In terms of size, this bears comparison with the domical vault of the Octagonal Hall, which spans 14.40 meters at the diagonal and rises 10.25 meters on the extrados. Tholos-type structures can also be seen in other Mediterranean lands and civilizations. The stonework of the Etruscan “Tomba dei Carri” in Populonia (seventh century BC) is quite remarkable.99
4.11. Nuraghe “Is Paras,” near Ìsili, Sardinia, detail of corbeled dome. (Photo author)
Just as props and centering were not needed to construct any of these structures mentioned, the same could be the case for the lower portions of the dome of the Pantheon. Here, the horizontal layers of mortar with tufa and brick fragments were built up as a series of corbels in structural terms, while the profile would probably have been defined by a system of wooden boards tied back to the intrados. There was no need for solid props beneath for this, the lower part of the dome.
To be more specific, the method of progressive corbeling, without props, would have encompassed an angle of approximately 40 degrees to the center of the sphere (see Fig. 7.4), that is to say, up to a height of 14 meters from the springing of the cupola, with an overhanging span of more than 5 meters or so.100 Since the oculus did away with any structure for the central portion of the dome, only the “doughnut-shaped” portion that lies inside the step-rings would have been built on solid scaffolding centering. In this area, the slope of the dome becomes impracticable for corbeling, while the mixture of volcanic slag, yellow tufa, and pumice cannot exercise thrust before the mortar has completely dried and set. The calotte requiring centering thus measures a rise of 7.4 meters and a span of 12.2 meters. Leaving aside proposals for flying centering favored by Eugène-Emmanuel Viollet-le-Duc,101 Jean Pierre Adam, and others (see Fig. 7.3),102 Licht concludes that “only the topmost part of the cupola presumably required a more extensive scaffolding”.103 This view was held by De Angelis d’Ossat and more recently by Lamprecht and Lancaster;104 Gene Waddell, Mark Wilson Jones, and I are all in agreement on this point. In his recent book on the Pantheon worksite, Gerd Heene comes to similar conclusions.105
What relationship is there, then, between the false dome of a casiddu, or ancient beehive house, and the dome of the Pantheon? Is one the forerunner of the other, preserving traces of its genetic heritage? This relationship can better be illuminated by applying Claude Lévi-Strauss’s famous comparison of “the engineer and the bricoleur” in La pensée sauvage.106 Enrico Comba outlines Lévi-Strauss’s concept:
A bricoleur is a person who can use whatever is at hand to produce something that serves a purpose. Unlike an engineer, he does not have to use specific raw materials or expressly conceived instruments to carry out a task. ... ‘La pensée sauvage’ (The savage mind) is not primitive or archaic nor does it correspond to a rudimentary state of scientific thought, but is parallel to it. These two forms of thought often coexist and differ only in the way they apply data deriving from experience to build an ordered coherent system of things.107
Modern studies on the statics of vaults have distanced us from “the science of the concrete,” to use another expression of Lévi-Strauss.108 As far as vaults are concerned, this came about during the Enlightenment when a distinction started to develop between intellectual science and “concrete science.” In Roman architecture, this “concrete science” was a combination of refined design, of which we have some knowledge of principles,109 and the empiricism of bricklayers, the cognition of which we have lost through lack of experience. Roman construction is a wonderful example of this marriage between the engineers and the bricoleurs.
This study is dedicated to the memory of Professor William Melczer, of Syracuse University, New York, who taught me the importance of objectivity in research work, during the many visits we made between 1983 and 1995 to the monuments of ancient Rome in the company of students.
I would like to thank Giovanni Belardi, director of the Pantheon, of the Soprintendenza per i beni architettonici ed il paesaggio di Roma. Many thanks are also due to Mr. Fred Moffa of the British Institute of Rome, for his care and attention in the translation of this work, and to Cinzia Conti of the Soprintendenza Archeologica di Roma for her help with discussing many questions raised in this study. A special thank you to Mark Wilson Jones for taking my first manuscript to pieces and reassembling it in an improved sequence.
1 Mark Wilson Jones, Principles of Roman Architecture, New Haven 2000.
2 A. Palladio, I quattro libri dell’architettura, Venice 1570, vol. 4, p. 73.
3 Giangiacomo Martines, “Argomenti di geometria antica a proposito della cupola del Pantheon,” Quaderni dell’Istituto di Storia dell’Architettura 13, 1989, pp. 3–10; M. Pelletti, “Note al rilievo del Pantheon,” Quaderni dell’Istituto di Storia dell’Architettura 13, 1989, pp. 10–18. In 2005, the Karman Center for Advanced Studies in the Humanities at the University of Bern conducted a new digital survey.
4 Vitruvius, 5.10.5 (Vitruvius: Ten Books on Architecture, trans. Ingrid D. Rowland, commentary and illustrations by Thomas Noble Howe with additional commentary by Ingrid D. Rowland and Michael J. Dewar, New York 1999, p. 72).
5 L. Crema, L’architettura romana, Turin 1959, p. 376.
6 Mark Wilson Jones, “Principles of Design in Roman Architecture: The Setting Out of Centralised Buildings,” Papers of the British School at Rome 57, 1989, pp. 106–151.
7 T. L. Heath, The Works of Archimedes: On the Sphere and Cylinder I, Proposition 34, Cambridge 1897; M. Clagett, Archimedes in the Middle Ages, 5 vols.,Madison-Philadelphia, 1964–1984; Carl Boyer, Uta Merzbach, and Isaac Asimov, A History of Mathematics, New York 1989; A. Frajese, Opere di Archimedes, Turin 1974; Archimedes, The Works: 1. The Two Books on the Sphere and the Cylinder, with Eutocius’ Commentaries, third century BC, ed. and Eng. trans. R. Netz, Cambridge 2004. The notation π is recent and dates back only to the seventeenth century. This is the initial letter of the Greek word periphéreia, i.e., “circumference.”
8 Frajese 1974, pp. 51–60. See also Heath 1921; T. L. Heath, The Thirteen Books of Euclid’s Elements, New York 1956; A. Frajese and L. Maccioni, Gli Elementi di Euclide, Turin 1970.
9 Martines 1989.
10 Wilson Jones 2000, pp. 40–43; P. Gros, “Les fondements philosophiques de l’harmonie architecturale selon Vitruve,” Aesthetics: Journal of the Faculty of Letters, Tokyo University 14, 1989, pp. 13–22.
11 Heath 1897; E. J. Dijksterhuis, Archimedes, Copenhagen 1956, p. 142.
12 Frajese 1974, p. 23.
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bsp; 13 Cicero, Tusculanae Disputationes, 5. 23 (trans. J. E. King, Cambridge 1960).
14 Dijksterhuis 1956, pp. 313–314.
15 J. L. Heiberg, “Eine neue Schrift des Archimedes,” Bibliotheca Mathematica 7, 1906–1907. In 1906, Heiberg discovered in the monastery of the Holy Sepulchre in Jerusalem a tenth-century manuscript copy of Archimedes’ Method, overwritten with prayers in the thirteenth century.
16 Hermann Schöne, Herons von Alexandria Vermessungslehre und Dioptra Griechisch und Deutsch, Leipzig 1903, p. 80 line 17, p. 84 line 11, p. 130 lines 15 and 25. Method translates the Greek word ephodikón, i.e. “system.”
17 C. M. B. Carra de Vaux, “Les Mécaniques: ou l’élévateur de Héron d’Alexandrie,” Journal Asiatique 1893, vol. 1, pp. 386–472; 1893, vol. 2, pp. 152–192, 227–269, 461–514; Hero Alexandrinus, Mechanica, ca. AD 50, ed. L. Nix and W. Schmidt, Leipzig 1900; Drachmann, The Mechanical Technology of Greek and Roman Antiquity, Copenhagen 1963; G. Di Pasquale, Tecnologia e meccanica. Trasmissione dei saperi tecnici dall’età ellenistica al mondo romano, Florence 2004. For the date, see Otto Neugebauer, “Über eine Methode zur Distanzbestimmung Alexandria-Rom bei Heron,” Det. Kongelige Danske Videnskabernes Selskab. Historik-filologiske Meddelelser 26.2, 1938, pp. 21–24.
18 Wilson Jones 1989b, p. 129; Gert Sperling, Das Pantheon in Rom, Neuried 1999; Wilson Jones 2000, pp. 184–187. Cf. H. Geertman, “Aedificium Celeberrimum: studio sulla geometria del Pantheon,” Bulletin Antieke Beschaving 55, 1980, pp. 203–229.