THE EVIDENCE

The Greek dioptra served several functions. When self-suspended it took heights and levels, and when mounted horizontally it took angles in a more or less horizontal plane. For these purposes the Romans, in contrast, had not one but two instruments. The groma worked purely in the horizontal plane and was applied particularly to land surveying, while the libra worked purely in the vertical plane, most notably in levelling for aqueducts. Libra is therefore not a simple synonym for dioptra, as Vitruvius makes plain in distinguishing them (Source 3). Indeed it is quite clear from what the sources say – and from what they do not say – that Greek and Roman instruments differed markedly. No source written in Greek mentions the libra, or anything that might be interpreted as the libra, although it remains perfectly possible, and indeed likely, that the libra was used for surveying aqueducts in the Greek world once Roman technical influence had made itself felt there. Similarly there is a dearth of references in Latin sources from the western half of the Mediterranean to the dioptra as a surveying instrument. This dearth is not total, since Vitruvius is aware of it; but his words in no way prove that it was ever used by the Romans.

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 1 in 8000 for twenty-five kilometres or 1 in 20,000 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 recognised, 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 sanctified 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.

EARLY CANAL SCHEMES

The canal from the Nile to the Red Sea at Suez had a long, complex and uncertain history. Its origins go back far into the pharaonic period, and it remained in intermittent use until over a century after the Arab conquest. Precisely what work was done by which ruler is largely irrelevant to us. What concerns us is the persistent tale (Sources 88–91) that until the Ptolemies the canal was not completed because it was reported that the Red Sea was higher than the Nile and, if the land were cut through, would either drown Egypt or pollute the river. This report need not detain us long because, as Strabo saw, it was total nonsense.

The canal was approximately 120 km in length and originally left the Nile near Bubastis (though the take-off was later moved upstream to near Cairo) and ran east down Wadi Tumilat to Lake Timsah, where it turned south through the Bitter Lakes to Suez (Fig. 9.1). Its purpose was no doubt primarily for irrigation and to supply fresh water to the settlements along its course, ending at the various towns that have existed in the Suez area; the sweet-water canal completed in 1863, which largely follows its route, has exactly the same function today. Navigation was probably a secondary consideration.

The hodometer, as a vehicle provided with gearing to measure the distance travelled, cannot be reckoned among the more important surveying instruments of antiquity. But while its interest lies more in its mechanical complexities than in its contribution to the surveyor's work, it does deserve brief discussion.

We have two detailed specifications, by Vitruvius and by Hero. In Vitruvius'version (Source 59), which was ‘handed down by our predecessors’, the road wheel is one 400th of a mile in circumference. Attached to its hub is a disc carrying a single tooth. At every revolution of the wheel this tooth advances a vertical pinion, which carries 400 teeth, by one tooth. Similarly at every revolution of the vertical pinion a projecting tooth advances a horizontal pinion by one tooth. In the horizontal pinion is a series of holes, one corresponding to each tooth and each containing a pebble. After a mile, therefore, the road wheel has revolved 400 times, the vertical pinion has revolved once, and the horizontal pinion advances by one tooth. The first hole containing a pebble now coincides with a hole in the casing below, which allows the pebble to drop through into a bronze bowl, giving audible notice that a mile has been completed. At the end of the journey the number of pebbles in the bowl indicates the miles travelled.

First, a few definitions. Surveying is the science based on mathematics which involves measuring any part of the earth's surface and any artificial features on it, and plotting the result on a map or plan drawn to a suitable scale. Often, though by no means always, it also involves levelling or some similar process to record relative heights. Setting out is effectively the converse process, namely locating intended boundaries, structures or engineering works on the ground, in the correct position in all three dimensions. The surveyor will often have to carry out both procedures, especially when linear features such as aqueducts or railways are to be built: first to record the existing shape of the terrain and then, in the light of this information, to decide the best route and to mark it on the ground.

Almost without exception, surveying with instruments that rose above the level of low technology began with the Greeks and Romans, and a proper understanding of their achievements entails straddling two very different disciplines. The present-day surveyor who is curious about the origins of his profession may not be deeply informed on ancient history or engineering, while the classical historian may not have a detailed command of the principles of surveying. The resulting challenge, constantly encountered by historians of technology, is to try to put across the background, the material and the arguments at such a level that no reader feels neglected or patronised. I have done my best to strike a happy mean.

The attempts by the Greeks to measure the circumference of the earth have generated much discussion. Two protagonists stand out among a cast of lesser actors: Eratosthenes, who produced a figure of 252,000 stades, and Posidonius, who is said to have produced one of 180,000 stades. Although both figures were variously accepted by later writers, it was the lower one that was adopted by Ptolemy. Backed by his immense authority, it came to rule the roost; and because it underestimated the size of the earth it was ultimately responsible for seducing Columbus into thinking that the Indies were readily accessible across the Atlantic. Eratosthenes' method is well known. What has not been clear, however, is how Posidonius, if it really was he, obtained his result. The answer can now in part be given.

The broad outline of the story, shorn of many of the much-debated details, must first be spelled out. The earliest figure for the circumference is given by Aristotle in the 340s BC in his De Caelo, quoting unnamed mathematicians, as 400,000 stades. A generation later this was refined, perhaps by his pupil Dicaearchus of Messana in Sicily, to 300,000 stades.

The foundations of instrumental surveying were laid down by Greece and Rome. With the fall of the western empire in the fifth century AD the science of engineering surveying, like so much else, seems to have been lost; certainly little was built in western Europe over the next five centuries or more which required anything like the same techniques. But what happened in the East? How much survived in the Byzantine empire and in Islam, and was that knowledge transmitted back to medieval Europe? And did the contemporary or later practices of China display any features which might suggest some interaction with the West?

To tackle this last question first, China, which in terms of technology paralleled Greece and Rome in so many ways and at the same kind of period, had just as much need of surveying. Its system of major and minor canals made up for the almost complete absence of urban aqueducts, cartography flourished, and agrimensorial and military needs were comparable. Needham, however, the great authority, can give little detail of instruments or techniques. Not surprisingly, the most basic tools – gnomon, plumb-line, cord, chain and graduated rod or staff – were much as in the West. His arguments for the existence in China by the second century BC of the sighting tube and by the second century AD of the groma are not very convincing, nor does he explain how they might have been used.

THE SIGHTING TUBE

The dioptra evolved from the humblest of beginnings to become the surveying instrument par excellence of the Greeks. The word means simply ‘something to look through’, and as such it bears a number of connotations which are quite irrelevant to our purposes – a spy, a translucent mineral such as talc or mica for use in windows, a gynaecologist's vaginal speculum or dilator for internal examination. In a catapult, the dioptra was the window in the main frame through which the arrow was discharged and through which, using it as a foresight, the operator took aim. Dioptra could even be used figuratively, meaning ‘perspicacity’.

It was long appreciated that looking at a distant object through a tube clarifies the vision by cutting out extraneous light and unwanted parts of the field of view. Aristotle remarked that

He does not call the tube a dioptra.

Surveying no doubt began at the humblest of levels, and for millennia evolved only slowly. Its functions would encompass the recording of the boundaries of plots of land, estimating their area and, if new-won land was being distributed, dividing it fairly; where irrigation or drainage was involved, ensuring that the gradient of water channels was adequate; in architecture, particularly of prestige buildings, establishing a reasonably horizontal level for foundations and sometimes, especially for religious monuments, the appropriate orientation. All these activities, as at every stage in the history of surveying, were based on geometry. At first this was doubtless entirely empirical and of the simplest kind; and at first the surveyors employed the simplest of tools. The real breakthrough to more complex requirements, to a deeper understanding of geometrical theory, and to procedures and instruments of considerably greater sophistication and precision, was due to the Greeks and Romans in the third and second centuries BC, and it is this revolution which forms the main subject of this book. But to understand its nature we need first to look at what it grew out of. A satisfactory investigation, unfortunately, is impossible simply because, before the treatises on the dioptra of Hellenistic Greece and the Corpus Agrimensorum of imperial Rome, our information is deplorably scanty.

For some topics, like measuring cords and plumb-line levels which hardly changed over centuries, the story is here continued to the end of the Roman period.