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FIVE Simple Arithmetic

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GENERAL RUFUS PUTNAM had had a good war in every sense. His rank was a reward for the sterling service he had rendered Washington both at the siege of Boston and during the fighting in New York. When the continental army’s strategic retreat in 1776 pulled the focus of the war further south, Rufus had returned home to command the 5th Massachusetts Regiment in defence of his own state. There he had found time to father three more children, two in the dark days of defeat, and a third to celebrate the approach of victory – not for nothing were there rampant boars on the Putnam coat of arms – and to acquire the fine estate of Rutland that formerly belonged to a wealthy loyalist. But he was not content to rest on his laurels. With the return of peace, he was impatient to stretch his surveyor’s chain across the wide-open spaces beyond the Ohio river.

In April 1783, Timothy Pickering, a delegate to the Continental Congress, reported that ‘there is a plan for the forming of a new State Westward of the Ohio. Some of the principal officers of the Army are heartily engaged in it. The propositions respecting it are in the hands of General Huntington and General Putnam, the total exclusion of slavery from the State to form an essential and irrevocable part of the Constitution.’

Rufus was not a speculator – his stand against slavery, effectively ruling out land sales to Southern planters, was evidence of that – but he was proposing to acquire as much land as any of the pre-revolutionary companies, almost eighteen million acres from the Ohio to Lake Erie. Nevertheless, he wanted to divide this land up into ‘756 townships of six miles square’, because, as he told his former commander George Washington, ‘I am much opposed to the monopoly of lands and wish to guard against large patents being granted to individuals … it throws too much power in the hands of a few.’ Instead, he hoped to see the entire area settled by veterans of the continental army who could acquire land either by using the warrants issued on completion of service or by paying a fixed, small price. This would have the double benefit of settling a part of the United States vulnerable to British invasion from Canada with reliable soldiers, and of reviving the value of the military warrants, whose worth was ‘no more than 3/6 & 4/- on the pound [i.e. less than 20 per cent of the face value] [but] which in all probability might double if not more, the moment it was known that Government would receive them for lands in the Ohio Country’. Rufus petitioned Congress to grant him the land, and when it did not respond he wrote again to George Washington in April 1784 to ask, as was his habit, what should be done.

‘The Settlement of the Ohio Country, Sir, ingrosses many of my thoughts and much of my time since I left Camp,’ he wrote, and the delay was making the veterans impatient. ‘Many of them are unable to lie long on their oars waiting the decition [sic] of Congress on our petition.’

Washington, who had retired from command of his victorious troops and returned to his estates, was no less impatient for Congress to reach some decision about the land beyond the mountains. Throughout the war a stream of settlers had moved into Tennessee and Kentucky, and the increase in their numbers after the fighting was over prompted Washington to warn the Congress that without some policy, ‘the settling, or rather overspreading of the Western Country will take place by a parcel of Banditti who will bid defiance to all Authority’. The thorny pre-revolutionary conflict between settlers and squatters, proprietors and Goths, had not gone away.

Yet nothing could be done until the states agreed to give up individual claims to territory that they had all won from the British. Virginia, for example, as the original colony, had some rights to all the land from Lake Erie west to modern-day Wisconsin and south to St Louis, while Massachusetts could point to a phrase in its charter giving it ‘the mayne Landes from the Atlantick … on the East Parte, to the South Sea [the Pacific] on the West parte’. States like Maryland and New Jersey whose western boundaries had been drawn by surveyors refused even to sign the Articles of Confederation, which bound them to act together against the British, until these gigantic claims had been abandoned.

Although Rufus Putnam seems not to have been aware of it, the key to the deadlock was in the hands of the Arch Enemy. In 1781 Jefferson as Governor had ceded Virginia’s claim to the Western Territory to the Continental Congress. One by one, the other claimant states followed suit, and the Articles of Confederation were at last signed in 1781, shortly before the war ended. But true to his Enlightenment self, Jefferson had added a reservation. Only the United States government could acquire the territory from the native American nations who owned it. Consequently any claims made by pre-revolutionary land companies were cancelled. Congress, however, was filled with company sympathisers. No United States territory could exist until one or other side backed down.

Over the next twenty years Jefferson was to engage in an ideological war with land speculators whose interests were diametrically opposed to his. In the Continental Congress their ringleader was Robert Morris. He had out-manoeuvred Jefferson over Virginia’s disposal of land within her existing boundaries, and was now the Congress’s Superintendent of Finance, an influential position which helped ensure that the congressional mood remained in favour of the land companies.

The two men were polar opposites: Morris, whose fat, friendly, asthmatic appearance distracted attention from a cold, abacus mind, and the lean, controlled, complex Jefferson, concealing his emotional weakness and high-flown idealism behind a stream of words and studied informality. ‘His whole figure has a loose, [shambling] air,’ observed Senator William Maclay of Jefferson in 1790. ‘He has a rambling vacant look, and nothing of that firm, collected deportment which I expected … He spoke almost without ceasing. But even his discourse partook of personal demeanour. It was loose and rambling, and yet he scattered information, wherever he went, and some even brilliant sentiments sparkled from him.’

Unlike Jefferson’s privileged background, Morris’s past was one of unremitting effort from his arrival as a penniless immigrant from England in 1747, through long years as an accountant working for the wealthy Philadelphia merchant Charles Willing, until he was made a partner in Willing’s company, and became one of the wealthiest men in America. During the war he had used his wealth to underwrite contracts for the purchase of supplies and munitions for Washington’s army, and with the goodwill this earned he secured still more profitable contracts for himself.

The second skirmish in Jefferson and Morris’s long campaign occurred over currency.

When George Washington replied to Rufus Putnam in April 1784, his letter illustrated the basic money problem facing the new republic. Pointing out that Congress was still deadlocked on the land question, Washington offered instead to lease his thirty thousand acres in the Ohio valley to the impatient Massachusetts veterans. The rental would be high, about $36 per hundred acres, he explained, because ‘it is land of the first quality’ and the cost of improvements he had made amounted to ‘£1568 Virginia, equal to £1961/3/3d Maryland, Pennsylvania or Jersey currency’. If Rufus was still not sure how much that meant in Massachusetts, Washington added that ‘a Spanish milled dollar shall pass in payment for six shillings’.

The handicap to Washington’s real-estate deal was one that hobbled every commercial transaction in the United States at that time. Although the legal tender remained officially the British pound, divided into twenty shillings, each in turn subdivided into twelve pennies, its value in America differed from one state to the next. The commonest single coin, the Spanish dollar, was worth five shillings in Georgia, but thirty-two shillings and sixpence across the border in South Carolina, and six shillings in New Hampshire, while the official London rate was four shillings and sixpence. Still more confusingly, it was divided into eight bits in Pennsylvania, but contained ten bits in Virginia. Along with Spanish dollars and doubloons, there were also French louis d’or and écus; Portuguese moidores, pistoles and half-Joes, so called because they carried the image of King Johannes V; Dutch florins; Swedish dollars or riksdalers; as well as the sovereigns, shillings and pennies of Britain. Familiarity taught most people to juggle all these currencies, and just as the teenage George Washington casually reckoned up his pay in pistoles and doubloons, so Thomas Jefferson, scribbling a quick note of a sale of land, recorded that the price had been ‘200 [pounds] of which 20 half-Joes are paid’, or $950 and $160 respectively. Opinion in Congress, however, held that a single currency was needed to help hold the new nation together.

The first recommendation came from Congress’s Superintendent of Finance, Robert Morris. It was based on an unrealistically small unit, a fraction of a penny, and in the opening shot of their campaign, Jefferson replied with a report early in 1784 recommending instead the adoption of the Spanish dollar as the most convenient basis of the new currency. In the interests of simplicity he suggested that instead of being divided up into eight bits, it should be decimalised. ‘Every one remembers,’ he told Congress, ‘that when learning money arithmetic, he used to be puzzled with adding the pence, taking out the twelves and carrying them on; adding the shillings, taking out the twenties and carrying them on. But when he came to the pounds where he had only tens to carry forward, it was easy and free from error. The bulk of mankind are school boys thro’ life. These little perplexities are always great to them.’ Accordingly, the dollar should be subdivided into tenths or dismes, hundredths or cents, and thousandths or mills.

It was an argument that everyone could understand, and less than eighteen months later, on 6 July 1785, Congress resolved that ‘the money unit of the United States of America be one dollar’, and that ‘the several pieces shall increase in decimal ratio’. This was not just an intellectual victory for Jefferson; it effectively prevented Morris from achieving his goal of running the United States Mint, a source of potentially enormous profits.

In the course of the currency debate, Morris had declared, ‘it is happy for us to have throughout the Union the same Ideas of a Mile and an Inch, a Hogshead and a Quart, a Pound and an Ounce’. Even without their earlier hostilities, this would have set him on a collision course with Virginia’s representative, for it was clear to Jefferson that the rationale for replacing pennies and shillings with a decimal unit applied equally to American weights and measures.

Officially each state had adopted the system of Troy and avoirdupois that Elizabeth I had imposed on sixteenth-century England and that subsequent legislation in London had amended; but barely a single unit was the same from one state to the next – except for Gunter’s chain and the acre. A Virginia tobacco-grower like Thomas Jefferson measured his crop in hogsheads, well aware that a Virginia hogshead was larger than a New York hogshead but smaller than one from Maryland, and that a tobacco hogshead from any state was a different size to a brewer’s hogshead. A Boston brewer might also refer to his hogshead of beer as a pipe, butt or puncheon, knowing that each of them contained two cooms, four kilderkins, eight rundlets, or sixty-four gallons. But a Baltimore brewer who used the same measures somehow ended up with only sixty-three gallons of beer in his Maryland hogshead, while the number of gallons in a Pennsylvania brewer’s hogshead actually changed depending on where the beer was sold, because the law required innkeepers to sell beer inside the inn by the wine gallon, which was smaller than the beer gallon that was used for selling beer outside the inn. And the confusion over liquid measurements was nothing compared to the labyrinth of quarts, gallons and bushels used for measuring corn or flour. Because of flaws in English legislation, each of them could be one of eight different sizes, and might be measured either heaped above the brim of the container, or struck, meaning level with the brim, as custom or the local market dictated.

Round three of the Jefferson – Morris war was, therefore, bound to occur over weights and measures. The direction of Jefferson’s ideas can be found on a sheet of paper dating from the spring of 1784 and headed innocuously ‘Some Thoughts on a Coinage’, which shows that he conceived of the dollar and a new, decimal American set of weights and measures as being two parts of a single system. The weights would be co-ordinated with the dollar, so that a pound would equal the weight of ten dollar-coins. The lengths were to be derived from the size of the earth.

The idea that the earth might serve as a scientific basis for a system of measures had first been put forward by the French astronomer and cartographer Jean Picard in 1671. The circle of the equator is divided into 360 degrees, and each degree is subdivided into sixty minutes. The distance of one of those minutes was equal to one nautical mile, a unit that navigators had used since the sixteenth century, and which remains in use today by pilots, mariners and other navigators. Picard’s successor, Jacques Cassini, had estimated the total distance round the equator to be more than twenty-five thousand miles (today’s best figure puts it at 24,902 miles, or 40,075 kilometres), which made each degree a little less than seventy statute miles.

Notes and tables soon fill the page, to be followed on a separate line by Jefferson’s calculation for the length of a minute, or ‘geographical mile’, in his words: ‘Then a geographical mile will be of 6086.4 feet.’ Acknowledging the difficulty of physically measuring the equator, he comes up with a way of checking the length of this new mile: ‘A pendulum vibrating seconds is by S[i]r I[saac] Newton [calculated to measure] 39.2 inches’.

It was Galileo, allegedly dreaming in church and watching the slow swing of a chandelier, who first noted that the amount of time a pendulum took to move through its arc from one end to the other depended on its length. The longer the pendulum, the more time it needed – to be exact, the time was proportional to the square root of its length. In London, Isaac Newton’s calculations had shown that the swing of a pendulum 39.1682 inches long took exactly one second (nearer the pole, the stronger pull of gravity would slow the pendulum fractionally), and it was this scientifically testable unit – known as a second’s pendulum – that Jefferson proposed to use to check the length of his mile.

By the time he starts to compare his new decimal lengths with traditional units, the geographical mile has already become the American mile in his mind:

Then the American mile = 6086.4 [feet].

English = 5280 f[eet].

furlong = 608.64 f[eet]. = 660 [feet]

chain = 60.864 f[eet]. = 66 [feet]

pace = 6.0864 [feet] fathom = 6 [feet]

The widest discrepancy was with the English mile, but perhaps to comfort himself Jefferson lists all the other miles in use, from the Russian – barely fifteen hundred old yards – and ascending through the Irish, Polish and Swedish to the Hungarian, which stretched for almost seven old miles. In such company there would be nothing strange about the American mile. There the ‘Thoughts’ end, a remarkable race through what was evidently a vast fund of knowledge stored in Jefferson’s mind.

It was no academic exercise. Jefferson intended to apply his new system to the most important subject facing the new republic – the measurement of the Western Territory.

That same spring, the Continental Congress, desperate to raise money from the sale of its land, had at last accepted the Virginian condition, and on 1 March 1784 Jefferson led his state’s delegation formally ceding its claims to the immense region to the north-west of the river Ohio. For the first time the United States had a territorial reality to match the spiritual identity outlined in the Declaration of Independence.

On the same day, and as part of the deal, a committee chaired by Jefferson produced a report on how the Western Territory was to be governed. It covered each stage of the process, starting with the land’s acquisition from the Indians – it could be obtained only by the United States government – through the delineation of boundaries, choice of government, and eventual admission as states to the United States. Once the land had been acquired and surveyed, settlement could take place, and as the region filled up with people, they could apply for their territory to become one of the states of the Union on a level of equality with the original thirteen founders.

Even the names of some of the proposed states were specified, among them Michigania and Illinoia, which more or less survived, and Assenisipia and Metropotamia, which did not. What was striking was their shape. Except for river and lake boundaries, all were defined by parallels of latitude running east – west, and meridians of longitude running north – south. The Atlantic seaboard states which had given up claims to the territory also had their western borders chopped off straight on a meridian. Consequently the future shape of the United States would not be long and thin, but square and geometrical.

The next day Jefferson was appointed chairman of a committee to choose the best way of surveying and selling off the land inside those imaginary states, and when it reported on 30 April 1784, it too opted for squares.

The Virginian method of allowing purchasers to choose their property and of surveying it by metes and bounds was ruled out. Instead it was to be surveyed before occupation and marked out in squares aligned with each other, following the New England model, so that no land would be left vacant. At Jefferson’s insistence these squares were to be called ‘hundreds’, while Hugh Williamson, another committee member, was probably responsible for proposing that their sides should run due east and west, and north and south. But the square was integral to what the geographer W.D. Pattison termed ‘their ambitious attempt to realise a dream of democratic rationality for the American West’.

To those who had not read Jefferson’s ‘Thoughts on a Coinage’, the report’s second sentence detailing the dimensions of those squares must have appeared inexplicable: ‘[The Western Territory] shall be divided into Hundreds of ten geographical miles square, each mile containing 6086 feet and four tenths of a foot, by lines to be run and marked due north and south, and others crossing these at right angles.’ The hundreds could be sold entire or divided into lots measuring one geographical mile square. Whether or not his fellow legislators understood Jefferson’s thinking, they would certainly have recognised the political wisdom of tacking a potentially unpopular measure onto one that was both desirable and vitally important. The United States would have the opportunity not only to raise money by the sale of land, but as a bonus would have the first decimalised system of measurements in the world.

In a letter written a few days later to an old friend, Francis Hopkinson, Jefferson gloated over the audacity of his plan. ‘In the scheme for disposing of the soil an happy opportunity occurs for introducing into general use the geometrical mile in such a manner as that it cannot possibly fail of forcing it’s [sic] way on the people,’ he began. There would be objections, he acknowledged. Legislators would argue that the report could not be passed into law because it bore ‘some relation to astronomy and to science in general, which certainly have nothing to do with legislation’. He imagined crusty conservatives advocating the retention of both the penny and the inch in order to ‘preserve an athletic strength of calculation’. But, he predicted, all opposition was bound to fail: ‘This is surely an age of innovation, and America the focus of it!’

In those first years, the republic had substance, but was not yet formed, and the quality that marked its leaders was the certainty that all their actions helped give it shape. The second President, John Adams, thought of his role in terms of making a watch. ‘When I consider … that I may have been instrumental in stretching some Springs and turning some Wheels,’ he wrote to his wife, ‘I feel an Awe upon my Mind which is not easily described.’

Jefferson saw himself as the architect of a self-regulating, land-owning democracy. Notes on the State of Virginia contained his goal for the disposal of the western lands: ‘the proportion which the aggregate of the other classes of citizens bears in any state to that of its husbandmen [farmers],’ he stated, ‘is the proportion of its unsound to its healthy parts, and is a good-enough barometer whereby to measure its degree of corruption. While we have land to labour then, let us never wish to see our citizens occupied at a work-bench, or twirling a distaff.’ In the short term, the health of the republic might depend on raising cash, but in the long term, ‘It is the manners and spirit of a people which preserve a republic in vigour.’ The future of the United States depended on settling as many of its citizens on the land as possible. Democracy would grow from decimals, squares and surveys.

The land plan in its entirety was Jefferson’s, and only he could act as its advocate. But in the summer of 1784, before he could present his report, he was appointed the United States’ envoy to France. In his absence, a new chairman was appointed to the committee. Changes were made, and the decimal measures were the first to go. What Congress took from Jefferson’s report was the grid pattern, with the east – west lines cutting the north – south at right angles, and the land survey before sale. The dimensions of the squares, however, owed more to Edmund Gunter than to Thomas Jefferson.

In the Ordinance which Congress passed on 20 May 1785, for ‘disposing of lands in the western territory’, it was laid down that ‘the surveyors shall proceed to divide the said territory into townships of 6 miles square, by lines running due north and south, and others crossing these at right angles, as near as may be … The lines shall be measured with a chain; shall be plainly marked by chaps on the trees, and exactly described on a plat.’

The thirty-six-square-mile townships were to be divided into one-square-mile lots, four of which in each township were reserved to the government ‘for the maintenance of public schools’. Every alternate township was to be sold whole, and the intervening ones by square-mile lots. The surveyors were also to make note of prominent features like salt-licks, mines, mills, mountains and the quality of soil, and their compasses were to be adjusted to due north.

Rufus Putnam was delighted by the proposals, which were almost identical to those he advocated, but in a report to the absent Jefferson, James Monroe commented discreetly, ‘It deviates I believe essentially from your [recommendations].’ Nevertheless, the measuring of America could at last begin.

Measuring America

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