INTODUCTION Engineering Is One of the Skills for Which The

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INTODUCTION

Engineering is one of the skills for which the Romans are most renowned. Some of their works, such as bridges carrying roads or water, are visually spectacular because of their sheer scale and daring. Others are equally impressive for the less obvious reason that they required very precise surveying. Examples which leap to mind are roads which cut across country as straight as an arrow, kilometre-long tunnels whose headings met deep underground without significant error, and aqueducts on gradients that can average  in  for twenty-five kilometres or  in , for eight. Such feats of engineering would have been impossible without good surveying techniques and good instruments. That these existed has of course long been rec- ognised, and many historians of technology have commented on them, although there has been no fundamental discussion of the evidence for many years. The regular conclusion has been that the standard instrument for laying out straight lines and right angles was the groma, that the standard instrument for levelling was the chorobates, and that Hero’s dioptra was a non-starter. Constant repetition has almost sanc- tified this opinion into a dogma. But while it is partly true, it is also partly wrong, and it is very incomplete in that it is biased towards the Romans and ignores much of the evidence available in Greek. One of my aims is to remedy the deficiency, and in the process to restore to the Greeks their rightful share of the credit. ‘The Greeks had the brains, the Romans had good drains’, runs the jingle, in tune with the perception, common to the ancient Romans and to more recent generations alike, that it was Rome which borrowed the bright but unrealised ideas of Greece and brought them to fruition. Yet the Greeks were engineers too, even if their achievements in this field were often more modest and less immediately obvious. In contrast to the wealth, peace and unity of the Roman Empire at its height, the geography of Greece was divisive and its political units were smaller and incessantly at loggerheads. There was therefore less opportunity for major undertakings. But this did not inhibit creativity; and in the realm 

INTODUCTION of instrumental surveying, as in so much else, it was the Greeks who developed not only the theory but much of the practice too, and their pioneering contribution deserves our wholehearted respect. This book embraces a thousand years, from the archaic Greek tunnels of the sixth century  to the Roman aqueducts which were still being built in the fifth century . During that time span, two major revolutions which altered the political map of the Mediterranean also increased the demand for surveyors and indirectly affected their instruments. First, the death in   of Alexander the Great ushered in the Hellenistic Age, when his huge empire was carved up by his generals into what, compared with the previous norm of small units, were super-states. Of these, Egypt, ruled by the Ptolemies, at first dominated the scientific and mechanical scene, with a profound input from the royal research institute, the Museum of Alexandria, founded about  . At the same time Archimedes was engaged in largely independent but equally mould-breaking work in Syracuse. After a hundred years or so the influence of Alexandria waned. Its scientific lead seems to have been assumed by the emergent kingdom of Pergamon in Asia Minor in the realm of surveying and by the city state of Rhodes in the related pursuit of instrumental astronomy. The Hellenistic Age was ended by the coming of Rome. But it had seen the foundations of geometry laid, most notably by Euclid, and it had also seen the rise, rooted in that geometry, of the theory of surveying and of precision instruments. Surveyors could now answer questions asked by natural philosophers, such as the size of the earth and the heights of mountains, and more practically they could serve the state both in its military and its civil role. The second revolution was the rise of Rome and its acquisition between  and  , both by force of arms and by diplomacy, of most Greek territories. Its surveying instruments and even some of the uses (notably road building) to which it put them differed from those of the Greeks, but they evidently went back just as far in time. With the Roman take-over of the eastern Mediterranean these two largely independent traditions met and to some extent melded. Roman engineering expanded eastwards, Greek theory (but not perhaps Greek surveying instruments) was exported west: Vitruvius, for example, the major Latin source of the first century , derived his material on surveying almost entirely from Greek sources. Nor was Greek enterprise 

INTODUCTION stifled. Alexandrian science experienced a revival, exemplified by Hero in the first century , by Ptolemy the astronomer in the second and by Theon in the fourth. With its empire established and for two centuries in relative harmony, Rome was at leisure to undertake its mightiest engineering works. The profession of the ancient surveyor, whether Greek or Roman, may be divided into four distinct categories. . The land surveyor (geometres or geodaistes in Greek, finitor, mensor, agrimensor or gromaticus in Latin) carried out relatively localised work on the ground surface. He might record the exact shape of an existing expanse of ground such as a field or an estate and calculate the areas enclosed. He might divide land into plots, normally rectangular, whether in the country for distribution to settlers, or in a town for setting out a grid of streets, or in a military context for laying out a fort. His work is the subject of the Roman compilation known as the Corpus Agrimensorum. Land surveying was concerned essentially only with horizontal measurement, not with vertical. . The cartographical surveyor (chorographos, geographos) made maps, usually of larger areas than the land surveyor, for example of regions or provinces or even of the whole known world. At least in theory, this might involve establishing latitudes and, indirectly, longitudes by a combination of astronomical and terrestrial methods, and the spheric- ity of the earth had to be taken into account. A related pursuit was the enquiry, originally philosophical, into the size of the earth and the heights of mountains. . The military surveyor (mensor) supplied practical information to the commander and his engineers, who might call in particular for two precise dimensions that were highly dangerous to measure directly in the presence of the enemy: the height of a city wall in order to prepare ladders or a siege tower of the right height, and the width of a river in order to prepare a pontoon bridge of the right length. . The engineering surveyor (mensor or librator) investigated terrain with a view to imposing man-made features on it. Roads and aqueducts are the most obvious instances, but hand in hand with aqueducts went drainage and irrigation channels and navigable canals; and with them, on occasion, went tunnels and mine adits with their particular 

INTODUCTION problems of maintaining direction and gradient underground. Harbour works could also require the services of a surveyor. These categories were by no means mutually exclusive. Surveyors in the different branches could employ the same instruments and similar techniques, and could even be the same men. Some of their instruments and techniques were also shared by astronomers who, especially with the rise of mathematical astronomy, wished to find the angular distances between stars and planets and the apparent diameters of the sun and moon, and to establish the celestial coordinates of stars and planets relative to the equator or the ecliptic. The various branches of surveying will not receive equal treatment in this book. The work of the agrimensor has already been much dis- cussed, and little can be added to our still imperfect understanding of its principal instrument, the groma. Nor can much new be said of map making, considerable though it evidently was. 1 Ptolemy, its greatest exponent, claimed (Source ) that places could be accurately located by coordinates determined either by astronomical observation or by terrestrial measurement. In practice, however, the vast majority of the latitudes and longitudes which he gives are the result of nothing more than dead reckoning.2 None the less, new light can be shed on the use of instruments in calculating the size of the earth and the heights of mountains. Astronomers and terrestrial surveyors shared the dioptra, which was one of the parents of that important and long-lived device the plane astrolabe; but otherwise astronomical instruments have little direct relevance to terrestrial surveying and will receive short shrift here. Part I of this book therefore concentrates on instruments for military and especially for engineering surveying. Since it would be non- sensical to discuss the instruments and not their application, Part II includes a number of examples of how different surveying tasks might have been undertaken. The subject, too, is one that cries out for experimental archaeology, and the results are presented here of trials with versions of the dioptra and libra which have never, as far as I am aware, been reconstructed before.

11 Dilke , Sherk . 12 Toomer , . As Ptolemy himself admitted (Geography  .), the apparent exactitude of his coordinates was merely to allow places to be plotted on a map: see Aujac , . 

INTODUCTION As already remarked, most historians of engineering have hitherto focused their attention on three instruments. One is the groma, which was primarily the tool of the agrimensor, although it had a role to play in laying out roads. The second is the chorobates which, taking Vitruvius at face value, historians wrongly assume to have been the standard device for levelling. The third is Hero’s sophisticated version of the dioptra, described in his treatise of that name, which they rightly regard as having been too complex and expensive to find widespread use. In concentrating on Hero’s instrument, however, they have over- looked the evidence in the rest of his manual for a pre-existing literature on surveying procedures. They have moreover been almost totally unaware that a considerable part of this literature survives in the form of other Greek treatises (or parts of treatises) on surveying. Compiled in their surviving form by Julius Africanus and the Anonymus Byzantinus, these contain much information about the ‘standard’ Hellenistic dioptra and its uses. The original of another such manual, part of which is embedded in an Arabic treatise by al-Karaji, is shown by new techniques of dating to be Hellenistic too. In Part III, therefore, Hero’s Dioptra, Africanus, the Anonymus and al-Karaji are collected together, along with a host of lesser ancient references to surveying and surveying instruments, for the first time. In most cases, too, this is the first time they have been translated into English. The evidence, however, is very uneven. While the literature is sur- prisingly extensive, and a great variety of engineering work survives as the end product of surveying, in between we are missing a great deal, most notably (with the exception of the groma) the instruments themselves. If the Greek dioptra can now be reconstructed from the new sources with some confidence, we have no description or example of its Roman counterpart for levelling, the libra. In this case there is only its name and its achievements (in the form of the aqueducts themselves) to work on, and discussion of it must necessarily be much more specu- lative. Even the groma, despite the fact that it is the only ancient surveying instrument to be attested archaeologically, has clouds of uncertainty hanging over it. And the possibility always remains that instruments and techniques existed which are not on record at all. Modern surveying is so highly developed a science that we need to exercise caution in our expectations of ancient surveying. Recent developments in satellite surveying and laser technology, needless to 

INTODUCTION say, would be far beyond the comprehension of the ancient world, and when I speak of modern practice I use the phrase as a convenient short- hand for the equipment and techniques available to, say, the Victorian railway engineer, who confronted problems not dissimilar to those of the Roman aqueduct engineer, and who made use of instruments which in a sense were not dissimilar either. There were of course some fundamental differences. We are dealing with a period before optics and before the spirit level, both of which were developments of the seventeenth century.3 Optics markedly increase the distance at which accurate instrumental readings can be taken. The spirit level markedly improves the precision with which an instrument is set in the horizontal plane. Without it there are only two methods of finding a horizontal, namely the open water level and (by means of a line at right angles to the vertical) the plumb-line; a useful variation on this last theme is to suspend the instrument itself so that it acts as its own plumb bob. Another difference between the ancient and the modern is that trigonometry was then in its earliest infancy – in essence it began in the second century  with Hipparchus and his chord tables4 – and Greek and Roman surveyors worked entirely with simple Euclidean geometry, notably in the form of similar triangles. All that, however, having been said, the principles of ancient surveying were basically and recognisably similar to the modern, and there is consequently a family resemblance between Greek surveying manuals and those of the nineteenth and twentieth centuries.5 It seems entirely legitimate to make direct comparisons between the old and the new, and to reconstruct ancient instruments as faithfully as the sources allow and to test their accuracy in the field. But, to revert to the caution expressed earlier, we should not be disappointed if they do not all measure up to the performance of their modern counterparts. Without optics and the spirit level – and indeed without long experience on the part of the surveyor – they could not hope to do so. But an impressive advance in accuracy is readily discernible from classical Greece through the Hellenistic world to Rome, and the sophistication

13 Kiely . Although his section on the instruments of antiquity is brief and out- dated, Kiely’s magisterial survey, which extends up to the end of the seventeenth century, remains invaluable. 14 Toomer . 15 They are numerous. Three entirely typical examples are Merrett , Williamson  and Clancy . 

INTODUCTION of the engineering of each period was dictated by the capabilities of its surveying instruments. A Greek aqueduct of the second century  would typically be a pipeline with an overall gradient of  in , and only the most massive of surveying errors with the dioptra would prevent the water from flowing. In contrast, a Roman aqueduct of the first century  would be a channel with an overall gradient, sometimes, of  in , and the smallest of errors with the libra might spell disaster. It is therefore reassuring that a reconstructed libra, even in pre- liminary tests, proved itself capable of working to this degree of precision. It is widely accepted that practical engineering in the ancient world, whether (in modern terms) civil or mechanical, generally owed little to theoretical science. It was more a case of the theory, if any, being based on practical results. This may be seen as early as the third century  in the pseudo-Aristotelian Mechanical Problems; and it may be seen later in such hydraulic theory as came to arise from observation of the working of water clocks, aqueducts and the like.6 At first there would doubtless be little if any quantified data available for engineers to draw on; but, as time passed, experience and comprehension accumulated to assist later generations. Norman Smith has rightly remarked that ‘design is achieved by one of three techniques: [] theoretical analysis, [] objec- tive testing, [] empiricism based on experience and intuition and more or less codified into sets of rules and procedures’. But while he can cite plenty of examples from the ancient world of the third category, he apparently finds none of the first, and of the second only a few such as the calibration of catapults by a procedure which is more controlled than mere trial-and-error. The relevant parameters are identified and assembled into a quantitative relationship whose solution is intricate to the point of requiring the determination of cube roots. We can reasonably postulate the calibration of other pieces of equipment such as Vitruvius’ hodometer, water-clocks and surveying instruments.7 While Smith’s attribution of catapults and water clocks to this second category is undoubtedly correct, it is hardly fair to bracket surveying instruments and the hodometer with them, for these were devices whose design and application were founded wholly on theory.

16 Lewis . 17 Smith , . 

INTODUCTION They belong to a family of instruments generated directly by the sciences – mathematics, geometry and astronomy – in which the Greeks most excelled. Thus, thanks to the geometrical invention of the plani- sphere, the anaphoric clock could display the position of the sun in the heavens at any given time (see Chapter .). Observation of the beha- viour of the heavenly bodies, translated first into mathematical rela- tionships and hence via the mathematical ratios of cog wheels into an enormously complex gear train, allowed the calendrical computer known as the Antikythera mechanism to display an even wider variety of astronomical information for any date and time set on it.8 Similarly but more simply the mathematical gearing of the hodometer recorded the distance travelled as accurately as its construction allowed. This is the category, ruled by theoretical analysis, to which other surveying instruments also belong. Both the instruments and the procedures for using them were designed strictly according to the rules of geometry. Their fallibility arose not from defective theory but from defective technology. This is most clearly seen in levelling, where the evidence is fullest. Four different procedures are recorded, all of them theoretically impeccable; but in practical terms some are better than others, and in the end the best one triumphed (Chapter .). Surveying was therefore one of the relatively few areas where engineering and science rubbed shoulders. The relationship was fully appreciated at the time. According to Strabo, when discussing a survey of the intended Corinth canal, ‘mathematicians define engineering (architektonike) as a branch of mathematics’.9 So too did Hero define geodesy (geodaisia, surveying).10 Surveying instruments, moreover, ultimately achieved an accuracy which can only have come from a combination of intelligent design, of meticulous procedure in the field and of good workmanship. Technical limitations, of course, prevented them from approaching the precision of modern equipment. But, like the  per cent efficiency of a few ancient pumps,11 their ability to level an aqueduct to  in , let alone to  in ,, is a sign of something well above ordinary crafts-

18 Price . 19 Strabo, Geography . (Source ). Architektonike embraced not only (in modern terms) architecture but civil and sometimes mechanical engineering as well. 10 Hero, Deﬁnitions .; and see Source . 11 Those from the Dramont D wreck: Rouanet , . 

INTODUCTION manship. Needless to say, it took time to reach this standard, and earlier and cruder surveying instruments and methods survived alongside later and more sophisticated ones. At some point along this path of development – it is hard to say exactly when – they moved out of the realm of low technology into that of high technology. The first of these useful descriptions embraces, in Price’s definition, the sort of crafts that all men in all cultures have used in all ages for building houses and roads and water supply, making clothes and pots, growing and cooking food, waging war, etc. [High technology, in contrast, means] those specially sophisticated crafts and manufactures that are in some ways inti- mately connected with the sciences, drawing on them for theories, giving to them the instruments and the techniques that enable men to observe and experiment and increase both knowledge and technical competence.12 Price is talking in particular of the Antikythera mechanism, which was emphatically a product of high technology. So, equally emphatically, were the more advanced surveying instruments and techniques, which thus formed another rare example of spin-off from science and of feed- back to it in return. This, then, is the theme of this book. It is divided into three parts. The first discusses the instruments and the methods of using them, progress- ing from the simpler and then the transitional devices to those pinnacles of ancient surveying, the Greek dioptra and the Roman libra, with the groma and hodometer calling for quite brief treatment. Second, a number of different practical circumstances are investigated, in an attempt to understand how surveyors applied their instruments in the field and what their results imply. This is of profound importance because these instruments, and consequently these results, comprise one of the most successful technical achievements of the ancient world. Finally, the literary sources which, alongside the archaeological evidence, supply the raw materials for this study are assembled in translation. I hope that, by virtue of a certain novelty of approach and by drawing on largely untapped sources, my analysis will revive a debate that has largely ground to a halt. But I am fully aware that it is not exhaustive, and it is emphatically not the last word. There is much still to be discovered, and much to be argued.

12 Price , . 

 

INSTUMENTS AND METHODS