Measuring America

Fortunately Gunter was supported by the Earl of Bridgewater, who did like brilliance, having grown up in a house where poets like Edmund Spenser and Ben Jonson were guests and where Othello was first performed. Since his father had inherited huge estates on the Welsh border and acquired valuable land north of London, the Earl was also even richer than Savile, and it seems probable that the surveyor’s chain that Gunter designed in about 1607 was first used to measure the immense Bridgewater property.

Aided by aristocratic influence, Gunter was then appointed rector of the wealthy parish of St George’s, Southwark, in London, and, in 1619, Professor of Astronomy at Gresham’s College, London. However, both his congregation and his students were utterly neglected in favour of his scientific instruments. Like electronic devices today, these were sold with a book of incomprehensible instructions. Gunter at least had the excuse that few could understand his instructions because they were written in Latin. In 1623 the chorus of complaints persuaded him to produce a translation. ‘I am at the last contented that it should come forth in English,’ he wrote. ‘Not that I think it worthy either of my labour or the publique view, but to satisfy their importunity who not understanding the Latin yet were at the charge to buy the instrument.’

The complete collection of Gunter’s instructional books issued in 1623 was called The description and use of the sector, the cross-staffe and other instruments for such as are studious of mathematical practise. By then Gunter must have known that the last bit of the title was nonsense. The reason the book had to be in English was because his instruments were being used not by maths students but by surveyors for measuring and by sailors for navigating – and, unlike mathematicians, neither group could read Latin. Nevertheless, it contained so much new information on logarithms, trigonometry and geometry that one of his contemporaries paid him this tribute: ‘He did open men’s understandings and made young men in love with that studie [mathematics]. Before, the mathematical sciences were lock’t up in the Greeke and Latin tongues and so lay untoucht. After Mr Gunter, these sciences sprang up amain, more and more.’

It was in this book that Gunter first described the chain that was to bear his name: ‘for plotting of ground, I hold it fit to use a chaine of foure perches in length, divided into an hundred links’. Four perches measured twenty-two yards, and the fact that this strange distance eventually became integral not only to the game of cricket in his own country (it is the length of the pitch), but to the town planning of almost every major city in the United States (the lengths of most city blocks are multiples of it), was a tribute to the chain’s versatility. Its practical advantage was simply that, unlike a rod, its links made it flexible enough to be looped over a person’s shoulder, and that being made of metal it neither stretched nor shrank as cords always did. Yet there was more to it than mere practicality. As a passionate believer in the usefulness of maths, Gunter built into his chain the most advanced intellectual learning of the time, until it could almost be compared to a primitive calculating machine.

His cleverness lay in dividing the chain into one hundred links, marked off into groups of ten by brass rings. On the face of it, the chain’s dimensions make no sense – each link is a fraction under eight inches long, ten links make slightly less than six feet eight inches, and the full length is sixty-six feet. In fact this is a brilliant synthesis of two otherwise incompatible systems: the traditional English land measurements, which were based on the number four, and the then newly introduced system of decimals, based on the number ten.

It was the Dutch engineer Simon Stevin who first published an account of decimals in 1585, and Gunter was quick to grasp the concept, using them in his logarithmic tables. Where the chain was concerned, he realised that units of ten made for simple calculation, hence the hundred links with the brass rings grouped in tens; but the overall length was no less important. His twenty-two-yard chain measured four rods long, which integrated it into traditional English measurements.

The rod’s inconvenient length of 16½ feet was derived from the area of land that could be worked by one person in a day. This was reckoned to be two rods by two rods (thirty-three feet by thirty-three). Thus, there were four square rods in a daywork. Conveniently there were forty dayworks in an acre, the area that could be worked by a team of oxen in a day, and 640 acres in a square mile. All these once variable units became fixed in the sixteenth century, and it was significant that all of them were multiples of four, a number that simplified the calculation of areas.

Gunter’s chain produced the happy result that ten square chains measured precisely one acre. Thus, if need be, the entire process of land measurement could be computed in decimals, then converted to acres by dividing the result by ten. With an understandable hint of satisfaction Gunter concluded his description of its use: ‘then will the work be more easie in Arithmetick’. It was that ease in calculating acreages, as much as its accuracy and straightforward practicality, that earned Gunter’s chain its popularity among surveyors using the old four-based system of measurements. Even the least competent could come close to the standards of exactness that were now expected of them.

It would be difficult to exaggerate the need that the growing army of surveyors had for this kind of assistance. Even an oblong field, where the length was longer than the breadth, made the maths go shaky, and repeatedly the manuals are forced to remind their readers that the area of any square or rectangular field can be calculated by multiplying the length by the breadth. Yet the same mistakes kept recurring: as late as 1688 John Love, who spent many years in Carolina, claimed that he was forced to write his classic work, Geodaesia, because ‘I have seen so many young men in America so often at a loss … when a certain number of acres has been given to be laid out five or six times as broad as long.’

The problems multiplied astronomically when the area to be measured was irregular. The surveyors’ commonest trick when faced with an irregular shape was to add the lengths of all the sides, divide the total by four, then square the result. The answer thus obtained was quick, easily worked out, and always wrong – but usually not by enough to alarm the landowner. As one more scrupulous measurer, Edward Worsop, observed of such shortcuts in 1582, ‘it is the way all Syrveyors do; – whether it originates in Idleness, inability or want of sufficient pay, it is not for me to determine’. The title of Worsop’s volume is self-descriptive: A discoverie of sundrie errours and faults daily committed by [surveyors] ignorant of arithmeticke and geometrie to the damage and prejudice of many of her Majestie’s subjects.

Yet the newly landed gentry of England knew that even an imperfect survey was better than none. While they were measuring and mapping their possessions, then squeezing the highest possible rents from their tenants, the Crown ignored its lands for seventy years after Richard Benese’s book came out. In 1603, the Lord Treasurer of England, Robert Cecil, at last commissioned a report on the extent of the Crown’s lands, and ‘found the King’s Mannors and fairest possessions most unsurveyed and uncertain, [their area estimated] rather by report than by measure, not more known than by ancient rents; the estate granted rather by chance than upon knowledge’.

Inefficiently run and casually disposed of, the royal estate which had once produced enough to pay for much of royal government now generated such a small income that the monarch was forced to rely on Parliament to raise taxes in order to run the kingdom. Imperceptibly, power was passing from the land-poor Crown to the land-rich gentry. And a few years later, when it was proposed to plant colonies in the new-found land of America, those who had the money to invest were the same gentry and the merchants, people who could measure their property and count its worth, and not the king.

This was the power contained in the untidy chain that lay round the feet of Rufus Putnam’s effigy in the museum at Marietta, Ohio. What Edmund Gunter had devised was a means of making private property. So long as it was the acre that expanded or shrank, while the price remained the same, no true market in land could be established. Once the earth could be measured by a unit that did not vary, supply and demand would determine the price, and it could be treated as a commodity. That was not Gunter’s intention, but it was a consequence of the accuracy that was built into his measuring device.

TWO Precise Confusion

WHAT MAKES MEASUREMENT fundamentally important is that it allows the exchange of goods and services to take place. Measuring a length of cloth or a herd of animals or a day’s labour gives it a value in terms of size, or number, or achievement, which enables others in the community to offer something else – food, protection, even love or loyalty – of equivalent value. Consequently measurement is almost as necessary to human society as language, and it occurs in the earliest civilisations, long before the development of writing.

Incised bone and clay counters used for counting or exchange have been found at Neolithic village sites in Turkey dating from the ninth millennium BC – more than ten thousand years ago – while the Sumerian cuneiform script, which is usually accepted as the earliest form of writing, does not appear until five thousand years later. It is significant that many of the clay tablets bearing the cuneiform script refer to measurements of quantity, weight and length. Without the ability to measure, co-operative activity could hardly take place. With it, marketplaces and increasingly sophisticated economies can develop, matching barter, cash or credit to whatever is owned by one person and desired by another.

What made Edmund Gunter’s chain unique among commonly used measurements was that it did not vary. There were other chains in use, and as late as 1796 an American surveying manual suggested that in woodland a chain might measure twenty-four yards and in dense forest as much as thirty-two. But wherever a ‘Gunter’s chain’ was specified, it meant precisely one hundred links or twenty-two yards, and an area measuring ten of his chains in length by ten of his chains in breadth would always contain ten acres. In 1607, it was hard to find another measure that was so consistent.

Where modern economics would alter the price of a commodity, the usual practice before the sixteenth century was to change the size of the measure. Confectionery manufacturers do the same today, because children associate a particular price with a particular sweet, and less resentment is caused by shrinking the bar than by increasing the price. For similar reasons, the Vatican city authorities in the fifteenth century required bakers to sell loaves of bread at a fixed price, increasing the size when flour was cheap and reducing it when flour was dear.

Even in the financially sophisticated Netherlands, where banks, corporations and a stock exchange existed from the sixteenth century, it remained the custom in the textiles market to charge the same price per stone (fourteen pounds) for good flax from Zeeland as for the inferior kind from Brabant, but to make up the difference by using a lighter weight for the stone. The Dutch milling trade followed the same pattern – selling flour in larger measures to wholesalers than to retailers, but charging the same to both. At the other end of Europe in the port of Riga, the centre of trade in the Baltic and a major partner in the trading association known as the Hanseatic League, the Latvians quoted a single price on the salt fish they sold to Russian merchants, Ukrainian nobility and their Hanseatic partners, but measured them out in different scales and containers according to the importance of the customer. Accusations about false weights abound in the cahiers de doléance, the great lists of complaints that French citizens compiled in 1789, but even they were prepared to accept that using different weights was often fair. As the Sens assembly in Burgundy argued, by using smaller containers to measure out flour in remote villages, traders could charge those far from the market the same price as those nearer to it, and ‘the differences in measures are such as to defray the costs of transport’.

Just as an acre of rough pasture was larger than an acre of meadow which could produce hay, so a bushel of oats, which would only make porridge, held more than a bushel of wheat, which could be made into bread, and weak beer suitable only for quenching the thirst was gauged by a large gallon while wine which intoxicated the mind was sparingly measured in a small gallon. The principle applied equally to textiles, wood and other commodities. An ell of coarse cloth was longer than an ell of fine material, a cord of green firewood bulkier than one of dry. Each unit varied not only according to place but according to the benefit it yielded to the buyer. In short, what was being measured was not a quantity but its local, subjective, human value.

The measures themselves were derived from human activity and the shape of the human body itself. Almost universal was the width of the thumb or finger, which was equivalent to an inch, and in the first century AD, Vitruvius gave the classic definition of its relationship to other measures: ‘four fingers make one palm, and four palms make one foot; six palms make one cubit; four cubits make once a man’s height’. A bushel originated with the amount of seed required to sow an acre of ground – the actual amount varied even more than the size of the acre – while the ell, used for cloth, was either the width of the loom, or the distance from head to wrist (the easiest way to measure woven material is to hold it with an outstretched arm from the chin). Equally organic, and still less exact, were units like the bowshot (the distance an arrow would fly), the houpée (how far a shout would carry) and, among the Plains Indians of the United States, the horse-belly view (the furthest a person could see over the prairies when squatting beneath a mustang – approximately two miles).

The weakness of these variable measures was the scope they offered for cheating. From the beginning of writing, and probably earlier, there have been denunciations of those who used false measures. The commonest deceit was simply to use two sets of weights and containers, a large one for buying, a small for selling, and from the earliest times there is evidence of sacred and secular authorities thundering against the practice. ‘Thou shalt not have in thy bag diverse weights, a great and a small,’ runs the Jewish law in the Book of Deuteronomy, ‘but thou shalt have a perfect and just weight, a perfect and just measure shalt thou have, that thy days may be lengthened in the land which the Lord thy God giveth thee.’ The Koran inveighs in similar fashion, ‘Woe to those who stint the measure. Who when they take by measure from others, exact the full, but diminish when they measure to others, or weigh to them.’

The existence of variable measures, with all their opportunities for fraud, stifled any wider trade because only those actually watching the wheat bushel being filled or the linen being stretched out knew the quantities involved. The success of the great medieval trade fairs at Troyes in Champagne was largely due to the town’s capacity to impose its own measures on traders; but it was the Dutch, the first great exporting nation in Europe, who understood the advantage of accuracy better than anyone. According to the English economist Josiah Child, writing in 1668, the booming trade that produced their astonishing prosperity in the seventeenth century was largely based on ‘their exact marking of all their Native Commodities’. The Netherlands’ major export was fish – herring and cod packed into huge barrels called hogsheads which were supposed to contain sixty-four gallons. Child noted that the Dutch measures were so reliable ‘that the repute of their said Commodities abroad continues always good, and the Buyers will accept of them by the marks, without opening; whereas the Fish which our English make in Newfound-Land and New-England, and Herrings at Yarmouth … often prove false and deceitfully made, seldom containing the quantity for which the Hogsheads are marked’.

By comparison traders in India, where until the twentieth century every locality had its own, variable measures, found it almost impossible to extend their business beyond the nearest towns. ‘I never can tell what I am buying nor how I am selling,’ a Madras grain trader complained in 1864. ‘My agents inform me that rice is at so much the seer [approximately two pounds] [in one village], while in another it is double that price. I take advantage of the opportunity, invest largely, and expect great profits. When the transaction is closed I find I have lost greatly. The seer in the first place was perhaps less than half the size of that in the other.’ The result was that grain markets in India remained local, and when famine struck in one area, people there died even though food was available elsewhere.

The obvious advantages of exact measuring, and the tragic consequences of local variations, should have made it easy to impose reliable, uniform measures. Yet India has legislation on standard weights and measures dating from four thousand years ago, among the first in the world, while Europe received its inches and pounds from the Romans at the time of Christ. The reason that these systems collapsed is fundamental to the history of weights and measures. However much emperors and rulers might legislate for uniformity, the actual scales and grain containers were held by market traders, landlords and local magnates. They were a source of such profit that no one willingly gave them up, and in every locality throughout history, the clearest guide to where day-to-day power lay has always been the control of weighing and measuring.

It was in 813 that Charlemagne, newly crowned as emperor of most of western Europe by the Pope, issued a famous edict which began ‘Volumus ut pondera vel mensurae ubique aequalia sint et insta’ (We desire that weights and measures should be equal and just everywhere). For nearly a thousand years thereafter, the goal of almost every French king could be expressed euphoniously as ‘ Un Roi, une foi, un poids’ (One king, one faith, one weight). In 1543, François I asserted bluntly that ‘the supreme authority of the King incorporates the right to standardise all measures throughout his kingdom’. But in 1790, according to an authoritative estimate, France possessed thirteen separate lengths for a pied or foot, eighteen for the aune or ell, and twenty-four for the boisseau or bushel. Since the seventy-four parishes of Angoulême near Bordeaux boasted over a hundred different sizes of boisseau between them, with one parish alone offering four separate varieties, this was something of an underestimate.

Just as the power of the Dutch trading guilds was demonstrated by their ability to establish uniform measures for exports, so the bewildering variety in France was testimony to the feudal power of the seigneurs who retained the right to regulate local weights and measures. The emergence of Gunter’s chain as the one measure to determine the dimensions of landed property was due not just to its practicality but to the power of a particular class of people.

On the face of it, England was in much the same position as France. In 960 King Edgar declared that ‘the measure of Winchester [England’s capital] shall be the standard’ for the whole kingdom; but the number of later monarchs who also demanded uniformity – the call for ‘one weight and one measure’ appears identically in Richard the Lionheart’s decree of 1189 and twenty-six years later in Magna Carta – suggests that they were no more effective than their French counterparts.

The most important of these medieval laws, enacted by Henry III in 1266, introduced the sterling system linking weights to coinage, so that there were 240 pennyweights to the pound, a ratio that persisted in the currency for over seven hundred years until 1972 in Britain, and in North America until superseded by the dollar. It failed to prevent most of Henry’s successors finding it necessary to pass laws against ‘false and deceitful measures’, and in 1496 one of them, Henry VII, took the curiously modern step of dumping the sterling pound in favour of a European unit, the Troy pound. Yet in 1588, less than a century later, his granddaughter Elizabeth I had to introduce still more legislation, which she explained was ‘called forth by the uncertainty of the weights then in use, to the great slander of the realm and decency of many, both buyers and sellers’.

It is against this background of incessant variation, deceit and falsehood in weights and measures that the precision of Gunter’s chain needs to be set. More than any of her predecessors, Elizabeth was responsive to the power of the House of Commons and the people represented there. The contrast between the way she legislated for weight and for length and area was significant.

Where weight was concerned, she found it necessary to add to the Troy system the heavier avoirdupois (meaning literally ‘having weight’) range, which went from ounces through pounds and stones to hundredweights and tons. Troy was ideal for measuring small items like gold and silver, but the main English export was wool, which was traded in elephantine quantities and in the Flemish markets was always weighed in avoirdupois. It was a concession to variability to use a goldsmith’s weights for light objects and a wool merchant’s for heavy ones, and a similar surrender appeared in Elizabeth’s decision to legislate for a large gallon for measuring beer and a small gallon for wine. Adding to the confusion, sloppy wording of the specifications for containers resulted in four different sizes of bushel being legalised for measuring grains and flour.

By contrast the specifications for length were both simple and accurate. ‘Foure graines of barley make a finger,’ ran Elizabeth’s law, ‘foure fingers a hande; foure handes a foote.’ Three of these feet made a yard, and 1760 yards made a mile. This was the first time the length of a mile had been specified, and although the other dimensions were not altogether new, the need to state them legally for the flourishing market in land certainly was. In 1601, a brass yardstick of thirty-six inches was constructed as a standard for the country as a whole. Exactness was what the market required, and when Elizabeth’s yard was measured in 1797 against the inches, feet and yards used by eighteenth-century scientists, it was found to be precisely 36.015 inches long.

Elizabeth had the energy and administrative skill of a great ruler. She not only ordered new standards to be made for these weights and measures but sent copies to fifty-eight market towns with instructions that a description of them was to be pinned up in every church and read during the service twice a year for the next four years. For good and ill, it is to her that the credit must go for creating a system of weights and measures that was to persist for almost four hundred years, eventually covering all of Britain, and almost a quarter of the globe.

All in all, it was a measuring age. Accurate measurement was becoming vital to the navigation of England’s mariners, who used Gunter’s cross-staffe and quadrant to find latitude in the trackless ocean, and most notably to Francis Drake in circumnavigating the globe. It was critical to the founding father of the scientific method, Francis Bacon, who advocated measurement and experimentation as the basis of science. When Elizabethans met, they took one another’s measure, they danced tightly paced measures like the galliard and volta, and measured their poetry to the short – long rhythm of iambic pentameters. ‘Marry, if you would put me to verses or to dance for your sake, Kate, why you undid me,’ exclaims rough King Harry wooing his French princess with puns in Henry V. ‘For the one I have neither words nor measure, and for the other I have no strength in measure, yet a reasonable measure in strength.’