The Industrial Revolution

Almost everything you would call normal about modern life depends on output per person rising year after year, and for most of recorded history it did not do that at all.

This course is about the sharpest change in how humans live, so it has to start with the condition that changed. That condition is not poverty as such. It is the absence of a trend: across the four hundred years between a peasant in Oxfordshire in 1300 and a labourer in the same county in 1700 there is no direction in the data, only oscillation. The first thing to establish is that this is a fact about the evidence rather than a slogan, and the second is why it should have been so.

What the numbers do, and do not, do

Angus Maddison's reconstruction of world income, the most widely used long series there is, puts output per head at roughly 450 international dollars around the year 1000 and roughly 666 in 1820, both in the same 1990 prices. That is a rise of 48 per cent spread over eight hundred and twenty years, which works out at 0.048 per cent a year. Between 1820 and 2003 the same series rises by a factor of 9.8, at 1.25 per cent a year. The second number is about twenty-six times the first.

These are estimates built from fragmentary evidence and argued about vigorously, so treat the precise values as indicative and the contrast as robust. The contrast does not depend on the level of the early figures at all, only on the fact that pre-modern series have no slope and modern ones do.

England has the best long series in the world, because English institutions happened to write things down and keep them: manorial accounts, cathedral building records, Oxford and Cambridge college accounts, wage assessments by justices of the peace. Stephen Broadberry, Bruce Campbell and colleagues used them in 2015 to rebuild English national income annually from 1270, and Gregory Clark has assembled day wages for building craftsmen and labourers over much the same span. Both series wander. Neither climbs.

The most quoted single fact from this literature is the one that startles people: on the Phelps Brown and Hopkins index of builders' real wages, begun in the 1950s and still the reference point, the highest real wage before the nineteenth century is in the 1450s, and English building workers did not reliably exceed that level again until the 1870s. Four centuries of Renaissance, empire, banking, navigation and printing left the man who carried bricks no better off.

Malthus states the mechanism

The reason was written down before anyone had the data, by a clergyman who was arguing about something else. Thomas Robert Malthus published An Essay on the Principle of Population anonymously in 1798, aimed at the optimism of Condorcet and Godwin, who expected human society to improve without limit. Malthus said the limit was arithmetic.

He starts from two postulates he takes as obvious: food is necessary, and the passion between the sexes is necessary and will continue. From these he claims that population, when unchecked, grows geometrically while subsistence grows at best arithmetically. His own worked illustration is worth doing exactly as he does it. Take population doubling every twenty-five years, which is 2.81 per cent a year, and take food supply increasing by one unit per twenty-five year period. After nine periods, which is two hundred and twenty-five years, population stands at $2^9=512$ and food at $1+9=10$. Malthus prints that ratio, 512 to 10, and rests his case on it.

The doubling figure was not invented. Malthus took it from the American colonies, where land was abundant and the check was weak. The United States census, which he could see the first two rounds of, gives 3.93 million in 1790 and 5.31 million in 1800, a growth rate of 3.06 per cent a year, which doubles a population in twenty-three years. By 1820 the count was 9.64 million, two and a half times the 1790 figure in thirty years. Malthus's premise was, for the case he chose, correct.

Example. Malthus's argument is often dismissed on the grounds that food supply obviously did not grow by a fixed increment. Does the argument survive if food grows geometrically too, at 1 per cent a year?

It survives completely, and this is the point most often missed. Suppose population grows unchecked at 2.81 per cent and food at 1 per cent. The ratio of people to food then grows at about 1.79 per cent a year compounding, which doubles the number of mouths per loaf in thirty-nine years and multiplies it by 5.9 in a century. Nothing in the argument requires food growth to be arithmetic. It requires only that unchecked population growth be faster than food growth, for any reason, and since population growth is a percentage of a stock while food growth depends on land, that is a safe bet in an agrarian economy. Malthus chose the weakest version of his premise and it made him easier to refute than he should have been.

Now you. If food supply could be made to grow at 2.81 per cent a year, matching unchecked population, would the trap be broken?

The trap as a feedback loop

Stated as a mechanism rather than as arithmetic, the model is a loop with a stable resting point, and the loop is what matters.

Suppose the wage rises above the level at which a family reproduces itself exactly. Two things then happen, and Malthus names both. The positive check weakens: better fed people die less, especially infants, so more children survive. The preventive check relaxes too: couples with land or a wage marry earlier, so more of a woman's fertile years fall inside marriage and more children are born. Population therefore grows. But land does not, so each worker now farms a smaller share of a fixed quantity of the scarce input, and output per worker falls. The wage falls with it, until it returns to the level where births exactly balance deaths.

Run the loop from the other side and it works the same way. A wage below replacement raises mortality and postpones marriage, population shrinks, land per worker rises, the wage recovers. The resting point is stable in both directions, which is what makes it a trap rather than a tendency.

The consequence that shocks a modern reader follows immediately. In this world, a permanent improvement in technology does not raise living standards in the long run. It raises the population. A better plough, a new crop, a drained fen: each raises output per acre, raises the wage briefly, and is then absorbed entirely by extra people, leaving the wage exactly where it was and the country more crowded. Technical progress in a Malthusian economy is converted into population, not into income. The model also inverts the sign of things we think of as good and bad: a plague raises wages, and peace and hygiene lower them. Malthus, who was a decent man and knew how this read, said so anyway.

The Black Death, which is the experiment

The awkward thing about a model like this is that you cannot run it. Except that in 1348 something ran it.

Plague reached England in the summer of 1348 and killed, on the best current estimates, something close to half the population within three years, with further outbreaks in 1361, 1369 and 1375 preventing recovery. England had roughly 4.8 million people on the eve of the plague and something near 2 million by the middle of the fifteenth century, which is a fall of about 58 per cent. Land, buildings, mills and livestock were mostly untouched. This is as close to a controlled shock to the labour-to-land ratio as history offers.

The model predicts that wages should rise sharply and stay high while the population is small, then decline as it recovers. That is what happened. Real wages roughly doubled over the century after the plague, reaching the fifteenth century peak already mentioned. Landlords tried to legislate them back down: the Ordinance of Labourers in 1349 and the Statute of Labourers in 1351 fixed wages at their pre-plague levels and made refusing work at those rates a criminal offence. The statutes were enforced, extensively, and they failed, which is a useful reminder of what a price control is up against when the underlying scarcity is real.

Then the recovery. English population climbed back through the sixteenth century, and real wages fell as it did, roughly halving between the 1450s and the 1610s on the Phelps Brown and Hopkins index. Nothing about English agriculture got worse. There were simply more people on the same land, exactly as the loop requires.

Example. A landlord in 1360 complains that his labourers demand double the customary wage and will leave if refused. His neighbour argues that a stronger statute, properly enforced, will fix it. On the model, who is right?

Neither, in the sense each intends. The wage has risen because the ratio of workers to land has changed, and no statute can change that ratio. What enforcement can do is redistribute: a landlord with the local justices on his side holds his own wages down and pushes the shortage onto someone else, which is why the statutes were both vigorously used and nationally ineffective. The real test is what a landlord does once the law has failed, and the record answers it, which is to convert arable land to sheep, since sheep need far less labour per acre than grain. That is a genuine adjustment to the new price of labour, and exactly the kind of substitution that will matter enormously later, when English labour becomes expensive again for a different reason.

Now you. Explain why the same model predicts that improved sanitation, on its own, would make a pre-modern population poorer.

Subsistence is not the same as starvation

One correction is needed before leaving the model, because "subsistence wage" invites a false picture of a continent permanently at the point of death.

The resting point of the loop is wherever births equal deaths, and that level depends on what a society does about marriage and childbearing, not on physiology. Northwestern Europe had an unusual arrangement that historians call the European Marriage Pattern: couples formed independent households at marriage rather than joining the husband's family, which meant they had to accumulate the means to run one first. Women married in their mid-twenties, late by world standards, and a substantial minority never married at all, which held the birth rate well below its biological maximum.

A society with a strong preventive check settles at a higher wage than one without, because it takes a better living standard to trigger the population growth that pushes the wage back down. That is why England could be Malthusian and comparatively well off at the same time, and why English labourers ate wheat bread and drank beer while their equivalents further east ate rye and worse. The trap fixes the absence of a trend. It does not fix the level.

Where the model starts to fail

The last section is the hinge of the course, and it is a piece of evidence rather than an argument.

Reconstructed from parish registers by Edward Wrigley and Roger Schofield, the English population stands at about 5.77 million in 1751, 8.66 million in 1801 and 16.74 million in 1851. That is a population nearly tripling in a century on an island whose acreage did not change, and the second half of it runs at a rate no English century had come near.

Example. Turn that English population growth into a doubling time and compare it with the American rate Malthus called unchecked.

From 8.66 million in 1801 to 16.74 million in 1851 is a factor of 1.93 in fifty years. The annual rate is $(16.74/8.66{)}^{1/50}-1=0.0133$, so 1.33 per cent a year, and a population growing at that rate doubles in $\ln 2/\ln (1.0133)=52$ years. Malthus's unchecked American benchmark was a doubling every twenty-five years, so England was running at roughly half the frontier rate. That is the useful comparison, because it shows England was not at the biological maximum: the checks were still operating, just far more weakly than in any previous century. A country at half the unchecked rate for a hundred years still ends with four times the people, and England very nearly did.

Now you. Do the same for the previous half century, 5.77 million in 1751 to 8.66 million in 1801, and say what the two figures together suggest about when the change began.

The loop says that wages should have collapsed. They did not. They were flat for a long and contested stretch, which a later lesson takes apart carefully, and then they rose, and by the 1870s they had passed the fifteenth century peak and kept going. Population and living standards went up together, which is the one thing the model forbids.

Malthus published in 1798, at the precise moment the mechanism he described was ceasing to apply to his own country. He was not wrong about the past. Nothing in the previous five hundred years of English data contradicts him. He was writing the definitive account of a world that was, just then, ending.

That is the fact to be explained, and it is worth being clear about how strange it is: not that people got richer, but that they got richer while multiplying. Before explaining it, the next lesson does something less exciting and more necessary, which is to find out exactly how fast the escape actually happened, because the answer turns out to be much slower than the word revolution suggests, and that slowness is itself a clue.

If the escape from the Malthusian trap was the sharpest change in human history, the first thing to ask is how fast it actually went, and the honest answer disappoints almost everyone who asks it.

The previous lesson left English population growing at rates no earlier century had reached while wages failed to collapse. That is the thing to be explained. Explaining it requires knowing its shape: when growth began, how quickly it accelerated, and where in the economy it was happening. Those questions have been answered twice, with different numbers, and the second answer is the one now used.

Two sets of national accounts

Britain has no official national accounts before 1948. Everything said about growth in 1780 is a reconstruction, assembled from tax records, port books, output series for individual trades and guesses about everything else, and the quality of the answer depends entirely on how those pieces are weighted.

The first serious attempt was Phyllis Deane and William Cole's British Economic Growth 1688 to 1959, published in 1962 and the standard for a generation. Their picture matched the textbook story: industrial output accelerating hard from about 1780, growing above 3 per cent a year, with national income following it upward. A reader of Deane and Cole would conclude that Britain took off somewhere around 1780 and that the takeoff was visible in the aggregate figures.

Nicholas Crafts and Knick Harley rebuilt the estimates in the 1980s and published the joint revision in 1992, and the picture changed. Industrial output growth in the late eighteenth century came down to roughly 2 per cent a year. Growth of output per head came down further. The revised series has British output per head rising at about 0.2 per cent a year between 1760 and 1801, about 0.5 per cent between 1801 and 1831, and about 1.3 per cent between 1831 and 1873.

Look at what those rates do over the periods they cover. Compounded across the forty-one years to 1801 the first gives a total rise of 8.5 per cent, which is less than the fluctuation between a good harvest and a bad one. The second gives 16 per cent over thirty years. Only the third, running from the 1830s, produces the 72 per cent rise that a lifetime would notice. On these numbers the classic period of the Industrial Revolution, 1760 to 1830, is not a period of rapid growth in living standards at all.

Why the first estimate was too high

The revision was not a matter of finding new documents. It was a matter of weights, and the mechanism is worth understanding because it recurs whenever anyone builds an index of a changing economy.

Deane and Cole had good output series for exactly the industries that were transforming: cotton, iron, coal. They had almost nothing for building, food processing, leather, clothing, retailing, domestic service and the hundreds of small urban trades that together employed far more people. Where a series was missing they filled the gap by assuming the missing sector moved with something they could measure, and the things they could measure were the fast ones. The result was an index that gave the exciting industries more weight than their share of the economy justified.

Crafts and Harley's correction was to weight each sector by its actual contribution to value added, using the 1841 census of occupations and contemporary estimates of output per worker to pin the shares down. The fast sectors did not slow down under the new treatment. They simply stopped standing for the whole.

Example. Suppose an economy is 10 per cent modern industry growing at 6 per cent a year and 90 per cent everything else growing at 0.5 per cent. What is aggregate growth in the first year, and what is it on average over thirty years?

In the first year the aggregate rate is the share-weighted average, $0.1\times 6+0.9\times 0.5=1.05$ per cent. The modern sector is growing twelve times as fast as the rest and moves the total by half a percentage point, because nine tenths of the economy is not doing what it is doing. Over thirty years the arithmetic changes, though, and in the direction that matters. Starting from 10 and 90 units, the modern sector reaches $10\times {1.06}^{30}=57.4$ and the rest reaches $90\times {1.005}^{30}=104.5$. Total output has gone from 100 to 161.9, an average of 1.62 per cent a year, and the modern sector is now 35 per cent of the economy rather than 10. Slow aggregate growth and violent sectoral change are perfectly consistent, and the aggregate accelerates on its own as the fast sector's weight rises, with no change in any underlying growth rate.

Now you. Run the same economy on for another thirty years at the same two sectoral rates. What is the modern sector's share then, and what is aggregate growth over that second period?

The economy underneath

What the revised accounts describe, then, is a dual economy, and the duality is the finding rather than an inconvenience.

On one side sit three or four industries growing at rates no economy had sustained before. Raw cotton consumption in Britain rose from about 6.8 million pounds in 1780 to about 56 million in 1800, which is 11.1 per cent a year for twenty years. Pig iron output went from about 68,000 tons in 1788 to about 244,000 in 1806, 7.4 per cent a year. Coal output roughly tripled across the eighteenth century.

On the other side sits the great majority of British work, doing more or less what it had always done. In the 1851 census, the largest single occupation for women in Britain was domestic service, with over a million of them; agriculture was still the largest employer of men; and the numbers in the celebrated cotton factories were around half a million across the whole United Kingdom. A visitor to Manchester in 1835 was looking at the future, but a visitor to almost anywhere else in Britain was not.

This is why the period will not resolve into a single adjective. The rate of aggregate growth was modest by any modern standard. The rate of change inside particular industries was without precedent. And the structural shift, the movement of workers out of one kind of activity into another, was enormous and permanent.

What the occupations say

The best evidence for that structural shift is not output at all. It is what people did for a living, which the Cambridge Group's reconstruction of English occupational structure has now traced back well before the census.

The startling number is the starting one. By around 1710, only about 35 per cent of the English male labour force worked in agriculture. That is already an extraordinarily low figure for a pre-industrial society, far below France or anywhere in eastern Europe, and it means England had begun shedding farm labour long before any machine was involved. By 1817 the share was near 29 per cent, and by 1851 it was under a quarter.

The other landmark is urban. In the 1851 census, slightly more than half the population of England and Wales lived in towns, which made Britain the first society in history where the majority of people did not live in the countryside. Nothing in the growth rates prepares you for that. It is a change of kind rather than of degree, and it happened while output per head was growing at rates a modern economy would consider a recession.

Example. Deane and Cole put late eighteenth century industrial growth above 3 per cent a year; Crafts and Harley put it near 2 per cent. Neither found new records for the missing trades. What kind of evidence decided between them?

Evidence about shares rather than about rates. The disagreement was never over how fast cotton grew, which both sides took from the same import figures, but over how much of the economy behaved like cotton. Crafts and Harley pinned the shares down with the occupational census, since the number of people working in a trade is a usable proxy for its contribution when direct output data are missing, and that is a source Deane and Cole had underused. The general lesson applies well beyond this argument: when a composite index is disputed, look first at the weights, because a weighting assumption is usually doing more work than any individual series and is far less visible. It is also the reason the revision has itself been revised repeatedly since 1992, always by a percentage point or two, never back to Deane and Cole.

Now you. Someone objects that if aggregate growth was really only 0.2 per cent a year to 1801, the Industrial Revolution is a myth. What is wrong with the inference?

Where the growth came from

One more piece of accounting sharpens the question the rest of the course has to answer. Growth can come from more workers, more capital per worker, or better use of both, which economists call total factor productivity, and Crafts's decomposition assigns it.

For 1760 to 1830 the striking result is how little total factor productivity contributed: something like 0.1 to 0.2 per cent a year, most of it traceable to a handful of industries. Capital accumulation did not carry the period either, because Britain's investment rate rose only modestly, from perhaps 6 per cent of national income in the mid eighteenth century to around 12 per cent by the 1830s. Britain did not industrialise by saving furiously. It industrialised by changing how a few things were made, and by having many more people to make them.

That last clause matters. Much of the raw output growth in this period came simply from a population rising at 1 per cent a year and more, which is why output per head grew so much more slowly than output. Britain got bigger before it got richer.

Example. England's population was about 6.15 million in 1761 and about 8.66 million in 1801, on Wrigley and Schofield's reconstruction. With output per head growing at 0.2 per cent a year, how fast did total output grow, and how much of that growth was simply more people?

Population growth is $(8.66/6.15{)}^{1/40}-1=0.86$ per cent a year. Total output is population multiplied by output per head, so its growth rate is the sum of the two, $0.86+0.2=1.06$ per cent a year. Of that, 0.86 points out of 1.06, or 81 per cent, is extra people rather than extra product per person. This is the arithmetic behind almost every disagreement about how impressive the period was. Someone quoting aggregate output is quoting a figure that is four fifths demography; someone quoting output per head is quoting the fifth that is left. Both are correct and they describe different things, which is why the honest practice is to say which one you mean every time.

Now you. Across those same forty years population rose 41 per cent and output per head rose 8.5 per cent. In the model of the previous lesson, what should have happened instead, and what does its failure to happen tell you?

So what needs explaining

The question has now been narrowed twice. It is not, why did Britain grow fast, because it did not grow fast for the first seventy years. It is: why did a handful of British industries change their methods so radically, and why did the resulting growth, unlike every earlier episode, never stop?

Both halves have to be answered in the right order. Before any account of machines can start, though, a prior condition has to be met, and the occupational figures have already flagged it. An economy where two thirds of men are not farming is an economy where somebody else is producing their food. England was that economy by 1710, before the first cotton mill existed, and how it managed that is the next lesson.

Every worker who moves into a factory is a worker who has stopped growing food, and somebody has to make up the difference before the move can happen at all.

The previous lesson ended with a number that makes this concrete: by around 1710, on the Cambridge Group's reconstruction of English occupations, only about 35 per cent of the male labour force worked in agriculture. That is a pre-industrial society in which two men in three are already doing something else. This lesson asks how the food got produced and where the extra people came from, because both had to be settled before a single spinning machine mattered.

The problem as a ratio

Put the occupational figure to work. If 35 per cent of workers farm, then each farm worker is producing food for himself and for the 65 per cent who are not, so on average he supports $1/0.35=2.86$ people's worth of food, counting himself. By 1851 the agricultural share was under a quarter, call it 22 per cent, and the same calculation gives 4.55. Output per agricultural worker therefore had to rise by a factor of about 1.6 over that century and a half simply to hold the country's food supply level per person.

Except that it did not have to hold food level per person. The population was more than doubling at the same time, and living standards, in the end, rose. So the true requirement on English agriculture was larger than 1.6, and the gap could be closed in only three ways: grow more per acre, farm more acres, or import.

All three happened, in that order of importance for most of the period, and the third eventually overtook the others in a way that decided British politics for a generation.

What actually changed in the fields

The central technical change is easy to state and easy to underrate: the fallow disappeared.

Under the medieval three-field system, a third of the arable lay idle each year to recover its fertility. That is not superstition. Cereals draw nitrogen out of the soil, there was no way to put nitrogen back, and resting the ground let weeds and grazing animals restore a little of it. The cost is severe, since a third of the best land grows nothing.

The Norfolk four-course rotation removed the fallow entirely by giving each field a useful crop every year: turnips, then barley, then clover, then wheat. Turnips are a root crop that can be hoed clean of weeds and fed to livestock through the winter, which had previously been the season when animals were slaughtered for lack of fodder. Clover is a legume, and legumes host bacteria that fix nitrogen from the air into the soil. Nobody in eighteenth century Norfolk knew that, since the nitrogen cycle was not understood until the 1880s, but they could see that wheat after clover did well.

The livestock half of the loop matters as much as the crops. More winter fodder means more animals kept alive, which means more manure, which means more nitrogen returned to the arable. The rotation is a machine for accumulating fertility, and it works whether or not the farmer can explain it.

Example. Take a hundred acres of arable under a three-field rotation with one field fallow, and convert it to a four-course rotation with no fallow. How much does the cropped area rise, and why is that not the whole gain?

Under three fields with one resting, two thirds of the land carries a crop, so 66.7 acres. Under the four-course all 100 acres do. The cropped area rises by $1/(2/3)-1=50$ per cent, and that is before any change in yield per cropped acre. It is not the whole gain because two of the four courses feed animals rather than people, so the extra 33 acres are not 33 acres of extra grain, and because the fodder crops raise the number of livestock, which raises manure, which raises the yield on the grain courses in later years. The honest summary is that the direct arithmetic gives a large one-off gain in land use, and the indirect nitrogen effect gives a slower compounding gain in yield, and separating the two in the historical record has proved very hard.

Now you. English wheat yields are usually put at roughly 10 bushels an acre around 1300 and roughly 20 by 1700, before the four-course spread widely. What does that timing imply about the standard story?

Enclosure

The change everyone remembers is not a technique but a change in property. Enclosure converted land held in scattered strips in open fields, with common rights of grazing and gleaning attached, into consolidated fields in single ownership with those rights extinguished.

Much enclosure happened privately by agreement over centuries. What is distinctive about the eighteenth and early nineteenth centuries is that it went through Parliament: roughly four thousand private acts, covering something like 6.8 million acres of England, which is about 21 per cent of the country, concentrated between 1750 and 1830. Each act appointed commissioners who surveyed a parish, extinguished the common rights, and reallocated the land in consolidated blocks.

The economic case made at the time was that consolidated holdings could be improved, drained and rotated by an owner who captured the whole benefit, while open fields required collective agreement to change anything. That is a real argument. What is much less clear is whether enclosure delivered the productivity gain claimed for it. Robert Allen's work on the south Midlands found the yield advantage of enclosed over open fields to be modest, and argued that the substantial gains had come earlier from yeoman farmers on open fields, while parliamentary enclosure mainly transferred income from small occupiers to landlords by removing common rights that had real cash value to a cottager.

The cost side is not in doubt. A family with a cow on the common and a right to gather fuel lost both, and the compensation, where any was allotted, was often a plot too small to be worth fencing. Enclosure did not empty the villages by itself, since the enclosed farms still needed labour, but it converted people with a stake in the land into people with only a wage, and that is the population the mills would later hire.

Example. Four thousand acts covering 6.8 million acres, concentrated in the eighty years from 1750 to 1830. What was a typical act doing, and why did the procedure itself hurt the smallest holders?

The averages are $6\{,\}800\{,\}000/4\{,\}000=1\{,\}700$ acres an act and $4\{,\}000/80=50$ acts a year. Seventeen hundred acres is about one parish, so the unit of enclosure is the village, decided as a whole and at once, which is why a minority of occupiers in a parish could not opt out. The procedure hurt the smallest holders because it was expensive and the cost was charged to the people who received land. A private bill, a survey, the commissioners' fees and then fencing and ditching the new allotment commonly ran to a pound or two an acre. Set that against a southern agricultural labourer on about ten shillings a week, £26 a year: a cottager allotted two acres faced perhaps £3 of unavoidable fencing, six weeks of wages, for a plot too small to farm. Selling to a neighbour was the rational response, and the concentration of land after enclosure is partly this, a cost threshold rather than a conspiracy.

Now you. Allen found the yield advantage of enclosed over open fields to be modest. Enclosed rents, though, commonly rose steeply, often by half or more. How can both be true, and what does it mean?

The people

The other half of the problem is where the extra bodies came from, and here the answer overturned a century of assumption.

The obvious guess is that death rates fell: better food, better medicine, fewer plagues. When Edward Wrigley and Roger Schofield reconstructed English population from 404 parish registers, published in 1981, they found the opposite emphasis. Most of the acceleration in English population growth between the late seventeenth century and the early nineteenth came from rising fertility, not falling mortality.

The mechanism is marriage. In an economy with the European Marriage Pattern described in the first lesson, almost all births happen inside marriage and couples marry only when they can support a household. If wages and opportunities improve, people marry younger and fewer stay single, and both effects raise the birth rate without anyone deciding to have more children per marriage. The mean age at first marriage for English women fell from around 26 in the late seventeenth century to around 23 by the early nineteenth, and the proportion of women never marrying fell sharply.

Example. Show roughly how much a three year fall in the age at first marriage adds to completed family size, and what that does to the growth rate.

Marital fertility in this population runs at something like 0.3 births per year of marriage in a woman's twenties. Three extra years of marriage therefore adds about $3\times 0.3=0.9$ births per woman, close to one extra child per family, on a completed family size of four or five. Feed that through the vital rates: an English crude birth rate rising from about 30 per thousand to about 40 per thousand, against a crude death rate near 28, turns natural increase from 0.2 per cent a year into 1.2 per cent. A change in the average wedding date, spread across a whole population, is enough to take a stagnant population to one that doubles in sixty years, with no change in medicine or in anyone's intentions.

Now you. Why does this finding make population growth a consequence of the economic change rather than an independent cause of it?

What English farming could not do

Agriculture bought the time, and it ran out of room. England had been a net exporter of grain in the first half of the eighteenth century, encouraged by an export bounty, and became a net importer from the 1760s as the population climbed. Imports were small at first, a few per cent of consumption, and rose steadily.

That turned food into the central political question of the period. The Corn Laws of 1815 blocked imported wheat until the domestic price reached a high threshold, protecting landlords' rents at the cost of the price of bread, and the fight over them ran until repeal in 1846. The economics were plain on both sides: an industrial workforce eats imported food, and the people who own the land do not want it imported. Which side won tells you which interest had become the more powerful, and the answer arrived in 1846.

By the 1870s Britain was importing roughly half its wheat, which settles the question of whether British agriculture fed British industrialisation. It fed the first century of it and then handed the job to the world market, which the country could reach because it had ships, an empire and, by then, the manufactured goods to trade for grain.

What this leaves

England entered the eighteenth century with a farming sector productive enough to release two thirds of its men to other work, a property system that concentrated land and cut cottagers loose from it, and a marriage pattern that turned improving conditions directly into more people.

None of that explains a single machine. A country can have all of it and remain a prosperous agrarian economy, which is roughly what the Dutch Republic was. The preconditions are necessary and they are not sufficient, and the next lesson takes the four serious explanations of why the machines appeared in this country rather than another and tries to break them against each other.

The hardest question in the subject is not what happened but why it happened in one medium-sized kingdom off the northwest coast of Europe rather than in China, India, France or the Netherlands.

The previous lessons have narrowed it. Britain did not grow quickly at first, so the answer is not that something made everything better at once. It had already released most of its men from farming, so the answer is not simply agricultural. What has to be explained is why a small number of industries changed their production methods radically, here, between roughly 1760 and 1830. Four explanations are seriously defended, and this lesson sets them against a test they can actually fail.

The test

An explanation of invention should predict what gets invented. That is a stronger demand than it sounds, because most accounts of the Industrial Revolution predict only that something will happen, which any of them can do after the fact.

The machines that appeared in Britain have a common signature, and it is very specific. They replaced human labour with machinery, and they consumed prodigious quantities of fuel to do it. Spinning machinery replaced hand spinners. Steam engines replaced muscle and horses while burning coal at rates that would have been absurd anywhere fuel was dear. Coke smelting replaced charcoal with mineral fuel. Nothing in the British inventive record is aimed at economising on fuel for its own sake, and a great deal of it is aimed at economising on hands.

So the question to put to each explanation is whether it predicts labour-saving, fuel-hungry technology in particular. Keep that in mind through what follows.

Relative prices

Robert Allen's account, set out in The British Industrial Revolution in Global Perspective in 2009, is the one that meets the test most directly. His claim is that Britain had a unique price structure: labour was expensive and energy was cheap, so machines that swapped coal for hands paid there and nowhere else.

The wage evidence comes from building workers, chosen because a bricklayer's mate does much the same job in every city and every century, which makes the comparison meaningful. Paid in grams of silver per day around 1750, a London labourer earned something like 11 grams, an Amsterdam labourer nearly as much, a Parisian roughly 4, and a labourer in Delhi or Beijing between 1 and 2. A London wage was several times an Asian one in silver, and remained well above it even after correcting for what the silver would buy locally.

The energy evidence runs the other way. Coal at the Newcastle pithead was the cheapest heat in the world, because the seams outcropped near navigable water and the coal could go to London by sea. Energy in Paris, dependent on wood hauled overland, cost several times as much relative to a day's wage; in Beijing the coal was in Shanxi, hundreds of miles from the cities that would have used it.

Put the two together and Britain, and northern England especially, had the highest ratio of the price of labour to the price of energy anywhere on earth. An invention that turns coal into work is worth having only where that ratio is high. Allen's conclusion is that the British were not more inventive; they were solving a problem that only they had.

Example. Take a machine that costs £70 and does the work of two spinners. In Britain a spinner's annual earnings are £10; in a low-wage economy they are £2. Work out whether the machine is worth buying in each place.

In Britain the machine saves £20 of wages a year on an outlay of £70, a return of $20/70=28.6$ per cent a year and a payback in three and a half years. That is an obviously good investment, and a manufacturer who declines it will be undersold by one who does not. In the low-wage economy the same machine saves £4 a year, a return of 5.7 per cent and a payback of seventeen and a half years, which is worse than lending the money and considerably worse once the risk of breakdown, obsolescence and a fall in yarn prices is counted. The machine is identical, the knowledge is identical, and the rational decision is opposite. Allen's calculations for the actual spinning jenny of the 1780s give the same shape: a return of tens of per cent in England, single figures in France, and nothing worth having in India.

Now you. A critic says this cannot be the explanation, because if British labour was expensive then British goods should have been uncompetitive, not dominant. Answer the objection.

Useful knowledge

Joel Mokyr's account, developed across The Gifts of Athena and The Enlightened Economy, accepts that incentives matter and denies that they are enough. Incentives cannot call into being knowledge that nobody has.

His claim is that eighteenth century Britain had an unusual relationship between people who understood nature and people who made things. The Royal Society, founded in 1660, took as its motto that nothing should be taken on authority. Provincial groups like the Lunar Society of Birmingham, which met at full moon so members could ride home by its light, put Matthew Boulton, James Watt, Josiah Wedgwood and Joseph Priestley around the same table: two manufacturers, an engineer and a chemist. Encyclopedias, published lecture courses, itinerant demonstrators with air pumps and an unusually thick layer of skilled instrument makers, millwrights and clockmakers spread technique rather than hoarding it.

Mokyr's evidence for the mechanism rather than the atmosphere is that British invention typically ran ahead of the science that explained it, then fed back. Nobody understood why clover fertilised a field, why a blast furnace worked, or, for a long time, why a steam engine had a maximum efficiency. What Britain had was not correct theory but a large population of people willing to measure things, publish the result, and act on someone else's measurement.

The test above treats this less kindly than Allen's account does. A culture of useful knowledge predicts more invention. It does not, by itself, predict labour-saving invention in particular, and it has to explain why France, which had at least as good a scientific establishment and rather better formal engineering education, produced fewer usable machines.

Institutions

The third account starts in 1688. Douglass North and Barry Weingast argued in 1989 that the Glorious Revolution, by making the Crown answerable to Parliament for taxation and spending, converted England into a state that could credibly promise not to expropriate its creditors.

The evidence they lead with is a price. Before 1688 the English Crown borrowed at punitive rates and defaulted when convenient; within a few decades of the settlement, with the Bank of England founded in 1694 and the debt funded by parliamentary taxation, the government could borrow at something close to 3 per cent. That is not a small thing: on a million pounds of debt the difference between 14 per cent and 3 per cent is £110,000 a year. A state that can borrow cheaply can fight wars without confiscating, and a country where the government does not confiscate is one where private investment is worth making.

Around that sit secure property in land, a functioning patent system dating from the Statute of Monopolies of 1624, courts that enforced contracts, and a Parliament that could be petitioned by manufacturers and canal companies and generally listened.

The difficulty is timing and geography. The institutional changes are late seventeenth century; the machines are late eighteenth. The Dutch Republic had comparable protections earlier and did not industrialise. And patents in Britain cost around £100 to obtain, several years of a labourer's earnings, which meant most invention happened outside the system rather than because of it. Institutions look better as a permissive condition than as a cause.

Example. English patents sealed run at roughly 90 in the 1750s and roughly 650 in the 1790s. How much does that support the claim that Britain became more inventive, and what would you need to know before believing it?

The ratio is $650/90=7.2$, from about nine patents a year to about sixty-five, and the timing sits neatly on top of the machinery. It is still weak evidence, for three reasons that apply to any count of a legal act rather than of the thing the act refers to. First, it measures patenting, not invention, and patenting is a decision about cost and enforceability: at £100 a patent, nearly four years of a labourer's earnings, the count is filtered by who could afford one and by whether a court would uphold it. Second, the economy itself grew across those forty years, so some of the rise is simply more people making more things. Third, the count is unweighted, and it puts a better mousetrap and the separate condenser on the same footing. To believe the series measured inventiveness you would want it deflated by the size of the economy, some independent weighting by importance, and evidence that the propensity to patent a given invention did not change, and the third of those is exactly what did change across the period.

Now you. Samuel Crompton never patented the mule and was eventually voted £5,000 by Parliament in 1812 instead. Richard Arkwright's patents were thrown out by the courts in 1785. What do those two facts do to the institutional account?

Empire and coal

The fourth account, associated above all with Kenneth Pomeranz's The Great Divergence of 2000, argues that the interesting comparison is not Britain against France but Britain against the most advanced parts of Asia, and that on that comparison Britain's advantages were two: coal, and colonies.

Pomeranz's case is that the Yangzi delta around 1750 was about as commercialised, as market-integrated and as prosperous per head as England, and was hitting the same ecological ceiling: land was finite, and land had to supply food, fuel, fibre and building material at once. What Britain got that the Yangzi did not was a coal field under its industrial districts and a set of colonies supplying land-intensive goods it would otherwise have had to grow. Sugar, cotton, timber and fish arriving from across the Atlantic amount to what he calls ghost acreage, land Britain used without owning.

The comparison has been fought over hard, and Broadberry, Allen and others have produced income and wage estimates putting England well ahead of the Yangzi by 1750 rather than level. But the coal half of the argument is unanswerable and is not really in dispute: Britain was producing something like ten million tons of coal a year by 1790 against perhaps seven hundred thousand in France, a factor of fourteen, and that gap is the fuel side of Allen's price ratio arriving from a different direction.

Example. The Netherlands in 1700 had the highest wages in Europe, the best commercial institutions, a strong scientific culture and an overseas empire. It did not industrialise. Which explanation does that fact test hardest?

It tests the institutional and knowledge accounts hardest, and it supports the price account. The Dutch had almost everything the institutionalists point to and much of what Mokyr points to, several decades earlier than Britain, and produced no cotton mills. What they did not have was cheap energy: their peat bogs were being worked out, peat was costly to move once the easy diggings were gone, and they had no coal of their own. So the Dutch faced high wages with expensive energy, which pushes an economy towards trade, finance and skill rather than towards machines that eat fuel. The Netherlands is the closest thing this subject has to a controlled comparison, since it holds institutions and knowledge roughly fixed and varies the energy price, and the outcome falls on Allen's side.

Now you. What would have to be true for the Dutch case to be evidence against Allen instead of for him?

What the answer probably is

The four accounts are not really rivals across their whole length, and pretending otherwise is the commonest mistake made with this material.

Institutions and useful knowledge are best read as necessary conditions with long lead times. They explain why Britain could respond, why an idea could be published, financed, patented and built, and why the response was not confiscated. Neither explains the timing or the direction, because both were in place decades before the machinery and were shared with countries that did not industrialise.

Relative prices explain the direction and much of the timing. They say why the invention that got made was labour-saving and fuel-burning, why it got made in the north of England, and why the same machines were ignored in France and India by people who knew perfectly well what they were.

Coal and colonies explain why the response did not run into a wall. Every previous burst of growth in an organic economy had been strangled by the land needed to feed it, fuel it and clothe it, and Britain evaded all three constraints at once.

The next lesson takes the prediction and checks it against the industry where it first came true. If dear labour and cheap fuel is the right account, the earliest and most spectacular gains should appear in the most labour-intensive process in the largest manufacturing trade, and that is the spinning of cotton yarn.

If dear labour and cheap fuel is the right explanation for British invention, the first place to look is the most labour-hungry process in the biggest manufacturing trade, and in Britain that was the spinning of yarn.

The previous lesson set up a prediction: British machines should save hands and spend fuel. Cotton spinning is where the prediction first came true, at a scale that is hard to believe until the numbers are laid out. It is also where the ugly half of the change first appeared, because the same machines that made spinning cheap destroyed the livelihood of the people who wove the results.

Why cotton, of all things

Britain grows no cotton and never has. That turns out to be one of the reasons the industry could grow without limit, because unlike wool it competed for no British acre, and unlike linen or silk it had no ancient guild, no protective regulation and no established workforce with customary rights to defend.

Cotton arrived as an import of finished Indian cloth, calico and muslin, which was fashionable enough by 1700 that the woollen interest got it banned. The Calico Acts of 1700 and 1721 prohibited the wearing of imported printed cotton, and the effect was the opposite of what was intended: they created a protected home market for anyone who could make cotton cloth in Britain. Legislation designed to protect wool incubated its replacement.

The technical problem was that cotton is harder to spin than wool. Its fibres are short and slippery, and the yarn produced on a hand wheel was not strong enough to serve as warp, the threads held under tension on a loom. British cotton cloth before the 1770s was therefore a mixture, linen warp with cotton weft, called fustian. Making an all-cotton fabric required a spinning method that could produce strong yarn, which is precisely what one of the four machines below delivered.

The bottleneck

Cloth making has two stages and they were badly out of balance. Spinning turns fibre into thread and weaving turns thread into cloth, and spinning was much the slower: on the usual estimates it took somewhere between four and eight spinners at wheels to keep one handloom weaver supplied. Spinning was consequently the largest employment of women's labour in the country, done in cottages, paid by the piece, and fitted around everything else.

John Kay's flying shuttle, patented in 1733, made the imbalance intolerable. It let a weaver throw the shuttle across the loom by pulling a cord rather than passing it from hand to hand, roughly doubling weaving speed and allowing wider cloth. It did nothing whatever to spinning. A trade in which spinning was already the constraint now needed something like twice as many spinners per weaver, and by the 1760s manufacturers could not find them.

This is the mechanism Mokyr calls a technological imbalance, and it is one of the more reliable engines of invention: improving one stage of a linked process turns the next stage into a visible, profitable, well-defined problem. The prize for solving it is obvious to everyone, which is why three people solved it within fifteen years.

Four machines

The spinning jenny, built by James Hargreaves around 1764 and patented in 1770, was the crude and brilliant first answer. It held a row of spindles driven by a single wheel, with a movable carriage that drew out the fibres, so one worker could spin eight threads at once and later many more. It was cheap, hand-powered, small enough for a cottage, and produced soft yarn fit for weft but not for warp.

The water frame, patented by Richard Arkwright in 1769, drew the fibres between pairs of rollers turning at different speeds and twisted the result on a flyer, producing yarn strong enough for warp. All-cotton cloth became possible. But the frame needed continuous power, so Arkwright put it in a building on a stream, and the mill he opened at Cromford in Derbyshire in 1771 is where the factory as an institution begins.

The mule, built by Samuel Crompton in 1779, combined the two: Arkwright's rollers to draw the fibres and the jenny's moving carriage to complete the draw and twist. The result span yarn that was both strong and fine, fine enough to undercut Indian muslin, which nothing European had ever done. Crompton had no money to patent it and sold the design to a subscription of manufacturers.

The self-acting mule, patented by Richard Roberts in 1825, made the mule's carriage return automatic. Until then the mule needed a skilled adult male spinner to control the carriage on its return stroke, and those men were organised, well paid and inclined to strike. Roberts built his machine on commission from Manchester masters during a strike, which is worth remembering when machinery is described as a neutral response to scarcity.

Example. Robert Allen's comparison of spinning methods gives the hours needed to spin 100 pounds of cotton: about 50,000 for an Indian hand spinner, about 2,000 on Crompton's 100-spindle mule, and about 135 on Roberts's self-acting mule. What do those numbers say?

Taken as ratios, the mule is $50\{,\}000/2\{,\}000=25$ times as productive as hand spinning, and the self-actor is $50\{,\}000/135=370$ times. A change of that size is not an improvement in the ordinary sense, because no adjustment of effort, wages or organisation on the hand spinner's side can close a gap of 370 to one. It also explains the geography of what followed: a British mill could sell yarn in Bengal, having shipped the raw cotton thousands of miles and the yarn back, and still undercut a spinner sitting next to the cotton field. Two cautions belong with the figures. They compare machine hours with hand hours and ignore the capital, the buildings and the power, all of which the machine needs and the wheel does not. And 50,000 hours is a benchmark for one worker with a simple wheel, so the ratio measures the gap between the extremes rather than the average gain in any actual year.

Now you. Britain's raw cotton imports rose from about 6.8 million pounds in 1780 to about 1,391 million in 1860. What annual growth rate is that, and why is the figure a fair proxy for output?

What happened to the price

Productivity figures are convincing to economists and prices are convincing to everyone, so take the price of yarn.

The finest commonly quoted grade, number 100 twist, sold for about 38 shillings a pound in 1786. By 1800 it was about 9 shillings 6 pence, and by the early 1830s under 3 shillings. In pence, 38 shillings is 456 and 2 shillings 11 pence is 35, so the price fell to under 8 per cent of what it had been in less than fifty years.

Now decompose it, because the decomposition is the interesting part. Raw cotton in that period cost on the order of 1 to 2 shillings a pound. So in 1786 the buyer was paying roughly 2 shillings for the fibre and roughly 36 for the work of turning it into fine yarn. By the 1830s the fibre still cost around a shilling and the spinning added under 2 shillings. Essentially the whole of the price collapse is the collapse of the spinning margin, which is exactly what a labour-saving machine does and is not what a cheaper raw material would look like.

The consequence reached ordinary people quickly, which very few results in this course do. Cotton cloth is washable, and washable clothing changed how people lived, particularly for anyone who could not previously afford to change their clothes at all. By 1830 cotton goods were around half of Britain's exports by value.

Example. Between the mid 1780s and the early 1830s the price of fine yarn fell to about 7.7 per cent of its former level while Britain's raw cotton imports rose from 6.8 million pounds to about 264 million. Treat that as a price and a quantity and see what it gives.

The quantity ratio is $264/6.8=38.8$. Taking both as proportional changes, the implied elasticity is $\ln (38.8)/\ln (0.077)=3.66/(-2.57)=-1.43$: quantity rose about one and a half per cent for every one per cent the price fell. Now the caution, which matters more than the number. This is not a demand curve. A demand curve is what happens when price alone moves, and across those fifty years British population grew by half, incomes rose, tastes shifted, and the machines opened export markets that had not previously bought British cloth at any price. What the calculation actually shows is where the two curves crossed at the start and where they crossed at the end, with both of them moving in between. Quoting $-1.43$ as the elasticity of demand for cotton would be wrong; quoting it as evidence that demand was far from saturated, so that each fall in price found buyers rather than filling a fixed need, is fair and is the point.

Now you. Raw cotton stayed between one and two shillings a pound across the whole period, with no upward trend. What does that require, and what would have happened had it risen instead?

Water, and its limit

Arkwright's frames needed power, and until the 1780s that meant falling water. The mills went where the water was: Cromford, Belper, Styal, the Derwent and the Pennine streams, which is why the earliest factory districts sit in valleys rather than in cities.

The constraint that follows is severe. A given stream yields a fixed power, the best sites fill up first, water fails in a dry summer and freezes in a hard winter, and no amount of demand for yarn will make a river bigger. By the 1790s the good sites in Derbyshire and Lancashire were taken.

That is the sentence that connects this lesson to the two after it. An industry growing at 7 per cent a year against a power source that cannot grow at all has one option, which is a power source with no site constraint and no season. Steam had exactly that property, provided somebody could make an engine efficient enough to be worth running away from a coal pit, and provided somebody could make iron cheap enough to build it out of.

Example. Between 1813 and 1850 the number of power looms in Britain rose from about 2,400 to about 250,000, while the number of handloom weavers fell from a peak near 240,000 in the 1820s to a few tens of thousands. Handloom weavers' weekly earnings fell from around 20 shillings to around 6. Why did handloom weaving expand before it collapsed?

Because the machines came to the two stages in the wrong order for the weavers. Spinning was mechanised from the 1770s and weaving was not, since Edmund Cartwright's power loom of 1785 did not work well enough to be worth having for another thirty years. Cheap machine yarn therefore poured out of the mills and had to be woven by hand, so handloom weaving boomed, wages rose, and tens of thousands of people entered a trade that appeared to have a future. When the power loom finally became reliable in the 1820s, all of those people were caught in a trade whose product was being made for a fraction of the price. Their earnings fell to 30 per cent of what they had been, and the fall was slow enough that leaving looked worse each year than staying had the year before.

Now you. Was the self-acting mule of 1825 a response to a shortage of labour or to something else?

What cotton proved

Cotton established three things that the rest of the course depends on. Machinery could raise output per worker not by a fifth but by a factor of hundreds. That gain showed up in prices fast enough to change what ordinary households owned. And the gains and the losses landed on different people, with the spinner's family better off and the weaver's ruined, which is why the political history in the later lessons is not an appendix to the economics.

It also left the industry pressed against a physical ceiling. The next lesson is about the material and the fuel that lifted it, and after that the engine that turned the fuel into motion.

Every organic economy runs on the annual output of its land, and the way to see how tight that constraint was is to work out how many acres of woodland a ton of iron used to cost.

The previous lesson left cotton spinning growing at 7 per cent a year against water power that could not grow at all. The way out ran through two materials. Iron had to become cheap enough to build machines from, and a fuel had to be found that did not compete with food for land. Both problems were solved in the same coalfields by the same people, and the second solution is the more fundamental of the two.

The acreage of an iron industry

Iron is made by reducing its ore with carbon at high temperature. Before the eighteenth century the carbon was charcoal, and charcoal is made by burning wood slowly under cover, which converts about four tons of wood into one ton of charcoal.

Take the numbers through. Smelting a ton of pig iron in an eighteenth century blast furnace consumed roughly two tons of charcoal, so roughly eight tons of wood. A managed coppice woodland, cut on rotation as English woods were, yields something like two tons of dry wood per acre per year. Therefore each ton of pig iron produced annually required about $8/2=4$ acres of woodland kept permanently in production.

That ratio is the whole story of pre-industrial metallurgy. British pig iron output in 1806 was about 244,000 tons, which on the same arithmetic would have needed nearly a million acres of dedicated coppice. Output in 1850 was about 2.25 million tons, needing 9 million acres, which is 28 per cent of the surface of England including its cities, mountains and arable. A charcoal iron industry of the size Britain actually had by 1850 is not merely expensive. It is geometrically impossible.

Britain had been feeling the constraint for two centuries. Iron making had migrated to wherever wood remained, the Weald and then the Forest of Dean and then Scotland and Wales, and by 1700 Britain was importing much of its bar iron from Sweden and Russia, where the forests were.

Coke

Abraham Darby, a Quaker brassfounder who had learned about coke in the malting trade, smelted iron with coke at Coalbrookdale in Shropshire in 1709. Coke is coal baked in the absence of air, which drives off the volatile matter and leaves a hard porous carbon, and it does what charcoal does without the woodland.

The story is usually told as though 1709 changed everything, and it did not, which is instructive. Coke smelting spread slowly for forty years, and the reason is chemical. Coal contains sulphur, sulphur passes into the iron, and sulphurous iron is brittle when worked hot, so early coke iron was fit for casting into pots, cylinders and rails but hard to forge into the bar iron that smiths and toolmakers needed. Darby's local coal happened to be unusually low in sulphur, which is one reason it worked for him first.

What made coke win in the end was a property charcoal lacks. Charcoal is soft and crushes under its own weight, which limits how tall a blast furnace can be; coke is hard, so the furnace can be built taller and blown harder, and a taller furnace with a stronger blast is more efficient and produces far more per day. Coke did not merely replace charcoal, it removed the ceiling on furnace size, and by the 1790s almost all British pig iron was coke-smelted.

Example. Compare the coke and charcoal routes on land use alone, for Britain's 1850 output of 2.25 million tons of pig iron.

The charcoal route needs about 4 acres of permanent coppice per annual ton, so 9 million acres. The coke route needs coal: roughly 3 tons of coal per ton of pig iron by the 1840s, so about 6.75 million tons of coal a year, which came out of pits occupying a few thousand acres of surface between them. Expressed as land, the ratio is on the order of a thousand to one. That comparison is the reason it is a mistake to treat coal as simply a cheaper fuel. Charcoal is a flow, limited by the rate at which trees grow on a fixed area; coal is a stock, limited by how fast it can be dug. An economy running on a flow has a ceiling set by its acreage, and an economy running on a stock does not, at least not on any timescale the people involved can see.

Now you. Britain's coal output was about 15 million tons in 1800 and about 62 million in 1850. Express each as the acreage of coppice woodland that would have been needed to supply the same energy, and compare with the land area of Great Britain, 51.7 million acres.

From pig to bar

Smelting is only the first half. Pig iron straight from the furnace holds three or four per cent carbon, which makes it hard and brittle, good for casting and useless for anything that must bend, be hammered or take a thread. Turning it into malleable wrought iron means burning most of that carbon out, and until the 1780s that too was done with charcoal in a finery forge.

Henry Cort patented the two processes that fixed it, rolling in 1783 and puddling in 1784. Puddling melted pig iron in a reverberatory furnace, where the flame passes over the metal and the coal never touches it, so the sulphur problem disappears and coal can be used directly. A workman stirred the melt with a long bar until the carbon burned off and the purified iron gathered into a pasty ball, which was then hauled out and worked. Rolling replaced the hammer: passing the hot ball through grooved rollers squeezed out slag and drew it to shape maybe fifteen times faster than hammering.

With Cort's processes the whole iron industry could run on mineral fuel from ore to finished bar. British pig iron output rose from about 25,000 tons in 1720 to about 6 million in 1870, a factor of 240, at an average of 3.7 per cent a year for a century and a half.

The human cost of puddling deserves a sentence, since it is easy to lose in the output series. It was done by hand in front of an open furnace, stirring several hundredweight of molten metal for twelve hours, and puddlers were famously strong, famously well paid and famously short-lived.

The hot blast

One further improvement is worth stating because it shows how much slack remained in a process everyone assumed was mature. James Beaumont Neilson, manager of the Glasgow gas works, patented in 1828 the idea of heating the air blown into a blast furnace instead of blowing it cold.

The intuition of every ironmaster was the opposite, since cold air is denser and it seemed obvious that the furnace wanted cold. Neilson's furnaces cut coal consumption in Scotland from roughly 8 tons per ton of iron to roughly 2.5, a saving of about 69 per cent, and they could use raw coal rather than coke and work the previously useless blackband ironstone of Lanarkshire. Scottish pig iron production, negligible before, became a major share of British output within twenty years.

The point to take is not the number but the pattern. Neilson's change required no new material, no new machine and no new science; it required someone to test an assumption that had never been tested. That describes a large fraction of the improvements in this course.

Example. Put the hot blast in money. Coal at a Scottish pithead cost on the order of 5 shillings a ton and pig iron sold for around £5. What does the saving do to the cost of a ton of iron?

The saving is $8-2.5=5.5$ tons of coal per ton of iron, worth $5.5\times 5=27.5$ shillings, which is £1 7s 6d. Against a selling price near £5 that is about 28 per cent of the revenue of a ton of iron, turning up as pure margin for whoever adopted it first and as a price cut once everyone had. So adoption was not really a choice: an ironmaster who declined the hot blast was going to be undersold within a few years, which is the mechanism by which a good process becomes universal without anybody planning it. Neilson then spent much of the 1830s and 1840s in court enforcing his patent against Scottish ironmasters who had adopted it without paying, and won.

Now you. Why did the hot blast transform Scotland in particular rather than Shropshire or south Wales?

Getting the coal out

None of this works unless the coal keeps coming, and British coal output rose from about 2.6 million tons in 1700 to about 110 million in 1870, a factor of 42 at an average of 2.2 per cent a year. Britain was producing the great majority of the world's coal for most of that century.

The binding constraint on a coal pit is water. Shallow seams near an outcrop drain themselves; every metre deeper adds water that has to be lifted continuously, and by the late seventeenth century the profitable shallow coal in the northeast and the Midlands was worked out. Drainage was the reason the first steam engines were built, and the first place they were economic was at the pithead, where the small coal they burned had almost no market value. Coal paid for the engine that made deeper coal possible, which is the tightest feedback loop in the whole of industrialisation.

The other constraints were human. Deep pits are hot, dark and full of explosive gas, and the Felling colliery explosion of 1812 near Gateshead, which killed 92 men and boys, was the disaster that prompted Humphry Davy's safety lamp of 1815. The lamp made deeper and gassier seams workable, which meant more men underground in more dangerous places, and the total death toll went up rather than down. That is a recurring shape in this subject and worth naming: a safety improvement that removes a constraint on production usually raises exposure faster than it lowers risk.

Example. Britain produced about 15 million tons of coal in 1800 for a population of about 10.5 million, and about 62 million tons in 1850 for about 20.8 million. Work out coal per head, and turn the 1850 figure into something a person can picture.

Per head, 1800 gives $15/10.5=1.43$ tons and 1850 gives $62/20.8=2.98$ tons, so output per person roughly doubled while the population itself doubled. Taking a ton of coal at about 29 gigajoules, the 1850 figure is about 86 gigajoules a year for every man, woman and child in Britain. A human labourer sustains something like 100 watts of useful mechanical output for perhaps 2,000 hours a year, which is 0.72 gigajoules. The comparison is therefore about 120 to one in raw energy terms. That ratio is deliberately unfair, because heat engines of the 1850s converted only a few per cent of the heat into work, so the honest figure for equivalent workers is more like a handful per person rather than 120. Even the honest figure is unprecedented: no previous society had ever had more mechanical energy at its disposal than its own muscles could supply.

Now you. Why is coal at a pithead a fundamentally different economic good from coal delivered to London?

What cheap iron let people build

The consequences run in two directions. The first is structural: iron cheap enough to use in quantity made possible the Iron Bridge over the Severn at Coalbrookdale, cast by Abraham Darby's grandson and opened in 1781, spanning just over 30 metres with some 378 tons of cast iron in it. It was assembled with carpenter's joints, dovetails and wedges, because nobody yet knew how to design in iron, and it is standing.

The second is precision, and it is the one that unlocks the next lesson. John Wilkinson patented a boring machine in 1774 that held the cutting bar rigidly at both ends, so it bored a true cylinder rather than following the wanderings of the hole it started from. James Watt said of a cylinder Wilkinson bored for him that it erred by no more than the thickness of an old shilling across a diameter of several feet. That is roughly a millimetre and a half, and it is the difference between a steam engine and a leaky curiosity. Henry Maudslay's screw-cutting lathe around 1800 and Joseph Whitworth's standard screw threads of 1841 continued the same line, which is the substitution of measured, repeatable machine work for a craftsman's judgement.

Cheap iron and accurate holes are the preconditions for everything mechanical that follows. What the coalfields still lacked was a way of turning their fuel into motion at a price worth paying, and the engine that did it is the next lesson.

An engine that turns heat into motion is only worth building where the heat is nearly free, which is why the first ones stood at the mouths of coal pits and stayed there for sixty years.

The previous lesson left Britain with cheap coal, cheap iron and cylinders bored true. This lesson is about the machine that connected them, and it is the one place in the course where a piece of eighteenth century engineering can be graded on a scale that is still meaningful, because the people building these engines measured their fuel consumption obsessively and published the results.

The atmospheric engine

Thomas Savery patented a pumping device in 1698 and called it the Miner's Friend. It had no piston: steam filled a vessel, was condensed to make a vacuum which sucked water up a pipe, and then fresh steam at pressure pushed that water higher. A vacuum can lift water about ten metres and no further, and Savery's boilers, made of riveted plate, burst when pushed beyond that, so the device drained cellars rather than mines.

Thomas Newcomen, an ironmonger from Dartmouth, built something different around 1712, with the first well attested engine near Dudley Castle in Staffordshire. Steam at barely more than atmospheric pressure filled a large vertical cylinder under a piston. A jet of cold water was then sprayed into the cylinder, condensing the steam and leaving a partial vacuum, and the weight of the atmosphere pushed the piston down. The piston was chained to one end of a great rocking beam whose other end carried the pump rods, so the working stroke lifted water and the rods' own weight pulled the piston back up.

Two features explain why this design lasted a century. It is safe, because the steam does no pushing and the boiler never holds real pressure, which matters when boiler plate is unreliable. And it does not need a precise cylinder, because the leaks around the piston can be sealed with rope and a layer of water lying on top of it.

What it is, is grotesquely wasteful. Every stroke sprays cold water into the cylinder, so every stroke cools the cylinder walls, and the next charge of steam has to reheat several hundred kilograms of iron before it can do any work. The heat spent reheating the cylinder is spent again on every stroke, forever.

Duty, and what it hides

Engineers of the period compared engines by duty: the work done, in foot-pounds, per bushel of coal burned, where a Cornish bushel is 94 pounds. Duty figures for Cornish pumping engines were reported monthly in Lean's Engine Reporter from 1811 onwards and were a matter of professional pride, which is why the series exists at all.

The headline numbers are these. An early Newcomen engine returned about 4.3 million foot-pounds per bushel. John Smeaton, who in the 1770s improved the Newcomen design by careful proportioning rather than by any new principle, roughly doubled it to about 9.5 million. A Watt engine of the 1790s reached about 20 million. The best Cornish engines of the 1830s and 1840s ran at 60 million and above.

Example. Convert an early Newcomen duty of 4.3 million foot-pounds per bushel into a thermal efficiency, and do the same for a Cornish engine at 60 million.

A foot-pound is 1.3558 joules, so 4.3 million of them is 5.8 megajoules of work. A bushel of 94 pounds is 42.6 kilograms of coal, and coal holds about 29 megajoules per kilogram, so the input is $42.6\times 29=1236$ megajoules. The efficiency is $5.8/1236=0.47$ per cent. The Cornish engine at 60 million foot-pounds delivers 81.3 megajoules from the same bushel, an efficiency of 6.6 per cent. So the whole heroic century from Newcomen to the Cornish engine is a rise from under one half of one per cent to under seven, a factor of fourteen, and the better machine still throws away 93 per cent of the heat it is given. It is worth noticing that nobody involved could have said why the ceiling existed. Sadi Carnot's analysis, which shows that the limit is set by the temperature range and not by the design, was published in 1824 and ignored, and the men building these engines were improving them by measurement without a theory of what they were approaching.

Now you. A Newcomen engine works between steam at about 100 degrees Celsius and cooling water at about 20. What is the theoretical maximum efficiency of any engine between those two temperatures, and what does that say about the 0.47 per cent figure?

Watt's insight

James Watt was an instrument maker at the University of Glasgow, and in 1763 he was asked to repair a model Newcomen engine that would not run properly. The model failed because a small cylinder has a large surface area relative to its volume, so the reheating loss that is merely bad at full size is fatal at model scale. Watt measured the steam consumption, found it enormous, and located the reason.

His solution, which came to him in 1765 and was patented in 1769, is one line long: condense the steam somewhere else. A separate vessel, kept permanently cold and connected to the cylinder through a valve, receives the steam and condenses it there, while the cylinder itself is kept permanently hot, lagged, and later jacketed with steam. The cylinder never has to be reheated because it is never cooled.

Watt's engines roughly doubled the duty again, from Smeaton's 9.5 million to around 20 million foot-pounds per bushel, and the commercial arrangement he and Matthew Boulton built on that is worth stating precisely because it shows how confident they were of the measurement. Rather than sell an engine, they charged an annual royalty of one third of the value of the coal it saved compared with a Newcomen engine of the same power doing the same work. The customer kept two thirds of a saving he could verify himself, and Boulton and Watt were paid in proportion to how good their machine actually was.

Example. A Cornish mine runs a Newcomen engine burning 500 bushels of coal a week, and replaces it with a Watt engine of the same power. Coal costs 1 shilling a bushel. What is the annual royalty?

If duty rises from 10 million to 20 million foot-pounds per bushel, the same work now needs half the coal, so consumption falls from 500 to 250 bushels a week and the saving is 250 bushels, worth 250 shillings. Over 52 weeks that is 13,000 shillings, or £650 a year. Boulton and Watt take a third, £217 a year, and the mine keeps £433 a year for having installed a machine it did not have to buy outright. The arrangement made both parties rich and it also made both parties enemies, because as coal got dearer in Cornwall, which had no coalfield of its own and shipped its fuel from south Wales, the royalty grew with it, and Cornish mine adventurers spent the 1790s in litigation trying to escape a contract that had looked generous when they signed it.

Now you. Why was Watt's royalty scheme unworkable for a customer who had never owned an engine at all?

Turning a pump into a source of power

Watt's other patents did something the separate condenser did not, which was to make the engine useful to anyone who was not draining a mine. A pump needs a stroke in one direction only; a mill needs continuous rotation at a steady speed.

The double-acting engine of 1782 admitted steam alternately to each side of the piston, so both strokes did work rather than one. The sun-and-planet gear of 1781 converted the beam's rocking into rotation without infringing James Pickard's patent on the obvious solution, the crank. Parallel motion in 1784 let a rigid piston rod drive the end of a swinging beam in a straight line, which Watt thought his most elegant piece of work. The centrifugal governor of 1788 held the engine's speed steady against a varying load by letting the speed itself throttle the steam, and it is the first automatic feedback controller in wide industrial use.

Take those together and the machine has changed category. It is no longer a pump that happens to burn coal; it is power on demand, at a chosen speed, anywhere a boiler can be fed. That is what let the mills leave the valleys.

The patent, and what it blocked

Against all that stands the patent. Watt's 1769 monopoly was extended by a private Act of Parliament in 1775 to run until 1800, twenty-five further years, and Boulton and Watt enforced it aggressively, including against Jonathan Hornblower's compound engine.

The most consequential thing they blocked was high pressure. Watt regarded steam above atmospheric pressure as unacceptably dangerous, which given contemporary boilers was not unreasonable, and used his patent to prevent others developing it. Richard Trevithick built his first high pressure engines within a year or two of the patent expiring, ran a locomotive at Penydarren in south Wales in 1804, and produced an engine small and light enough to be portable. Everything that made steam mobile depended on pressure, and the standard judgement is that the extension of the Watt patent delayed the high pressure engine by something close to two decades. The patent system, which the institutional account in an earlier lesson credits with encouraging invention, here spent a quarter of a century preventing it.

How much did the engine actually matter

The honest answer, for the classic period, is less than its fame suggests, and this is where the second lesson's arithmetic has to be applied to the subject's own emblem.

Total installed steam capacity in Britain in 1800 was on the order of 35,000 horsepower on the standard reconstructions, against something like 120,000 from water. Steam did not overtake water in British industry until well into the nineteenth century, and in some textile districts water wheels were still competitive in the 1830s. Nicholas von Tunzelmann's counterfactual calculation, which asks what British national income in 1800 would have been if Watt's engine had never existed and everyone had used the next best alternative, produces a shortfall of about one tenth of one per cent.

That figure is not an argument that the steam engine was unimportant. It is an argument about dates. In 1800 the engine was a good machine with a small installed base; by 1870 installed steam capacity in Britain was around two million horsepower, and by then nothing about the economy worked without it. A technology's contribution is close to zero for as long as almost nobody has it, which is true of every general purpose technology and is the reason contemporaries and historians so often disagree about when a revolution happened.

Example. Put 35,000 horsepower of steam in 1800 against two million in 1870. What is the growth rate, and what share of mechanical power did steam hold at the start?

The factor is $2\{,\}000\{,\}000/35\{,\}000=57$ over seventy years, so the rate is ${57}^{1/70}-1=5.9$ per cent a year, a doubling every twelve years, held for seven decades. The share in 1800, against roughly 120,000 horsepower of water, is $35/(35+120)=23$ per cent. Both halves of the answer are needed together, and each is misleading alone. Steam in 1800 is a minority power source in an economy still turned mostly by falling water, which is the fact that supports the modest verdict. Steam compounding at 5.9 per cent inside an economy growing at 1.5 is the fact that makes the modest verdict temporary, since a share doubling relative to the whole every sixteen years goes from a quarter to nearly everything within two working lifetimes. The engine looks unimpressive in 1800 for the same reason the second lesson's fast sector looked unimpressive: it is being weighed before it has grown.

Now you. Von Tunzelmann's counterfactual removes Watt's engine from 1800 and finds British national income lower by about a tenth of one per cent. Why is that number so much smaller than the engine's reputation, and what is it not saying?

The engine had one further consequence that the next lesson is built on. Once Trevithick had made steam portable, the machine could be put on wheels or in a hull, and the cost of moving a ton of anything was about to collapse.

A mill can only sell as far as its goods can be carried at a price someone will pay, so the size of the market is set by the cost of moving a ton of it.

The previous lessons have built an industry that produces enormously more than it used to, out of materials dug from particular places and burned in particular places. None of that is worth much if a ton of coal doubles in price forty miles from the pit, which is roughly what happened in Britain before 1760. This lesson is about the two transport revolutions that removed the constraint, and about how to measure what the second of them was actually worth, which turns out to be a genuinely hard question with a surprising answer.

What it cost to move a ton

Start with a horse, because before 1830 every land carriage cost is a horse cost.

A packhorse carries about an eighth of a ton on its back. Harnessed to a wagon on a decent turnpike road, the same horse moves perhaps 2 tons. Harnessed to a barge on still water, it moves 30 tons, because water supports the load and the only resistance is drag. On iron rails, before any locomotive exists, it moves around 8 tons, since a smooth hard wheel on a smooth hard rail has very little rolling resistance.

Those four numbers, one eighth, two, eight and thirty, are most of the transport history of the period. Water beats road by a factor of 15 for the same animal and the same wage to its driver, and that ratio shows up directly in freight rates: land carriage cost on the order of a shilling per ton-mile in the eighteenth century, canal carriage on the order of one to two pence, and coastal shipping less again.

The consequence is that before the canals, heavy low-value goods simply did not travel overland. Coal, iron ore, limestone, bricks, timber and grain moved by sea and river or did not move. An industry that consumed tons of raw material per ton of product had to sit on top of its raw material or on a navigable waterway, and Britain's early industrial geography is that constraint made visible.

Canals

The Duke of Bridgewater owned coal mines at Worsley and a market seven miles away in Manchester that he could not reach cheaply. In 1759 he obtained an act of Parliament and put James Brindley, a millwright who was close to illiterate and one of the finest engineers of the century, in charge of building a canal from the mine to the town, including an aqueduct carrying the canal over the River Irwell that people came from all over England to disbelieve.

The canal opened in 1761 and the price of coal in Manchester fell by about half, from around 7 pence per hundredweight to around 3½. That was the demonstration, and it was followed by seventy years of building: the Trent and Mersey, the Leeds and Liverpool, the Grand Junction, and by the 1830s a network of several thousand miles of canal and improved river joining all four of England's major estuaries.

Example. Compare a horse hauling a canal barge with the same horse hauling a wagon, in ton-miles per day, and say what fraction of the freight rate that ratio explains.

Take a ten hour day. On the canal the horse moves 30 tons at about 2½ miles an hour, so $30\times 25=750$ ton-miles. On the road it moves 2 tons at about 3 miles an hour, so $2\times 30=60$ ton-miles. The ratio is 12.5 to 1, and the horse, its feed and its driver cost about the same either way. That accounts for most, though not all, of the eight to twelve-fold gap between road and canal rates: the canal also has costs the road does not, since somebody had to pay for the cutting, the locks and the tolls, and a canal is a fixed asset that must earn a return whether or not traffic uses it. The general shape is worth holding on to, because it recurs with the railway: the productivity gain in the vehicle is larger than the fall in the price charged, and the difference is the capital.

Now you. Coal at a Lancashire pithead cost about 4 shillings a ton. Using a land rate of 12 pence per ton-mile, how far could it travel before carriage doubled its price, and how far at a canal rate of 1.5 pence?

What canals could not do

Canals are slow, at two or three miles an hour. They freeze in a hard winter and run short of water in a dry summer, since every lock cycle empties a lockful downhill. They cannot climb without locks, and locks cost money and time. Each company built to its own dimensions, so a boat that fitted the Bridgewater might not fit the Birmingham canals, and cargo had to be transhipped. And where a route had one canal it had a monopoly.

None of that mattered much for coal. It mattered enormously for anything perishable, anything urgent, and for people. A canal was a good answer to the question of how to move a ton of stone and a poor answer to almost every other transport question, and the gap it left is precisely the one the railway filled.

The railway

Rails and steam existed separately for decades before they were joined. Wooden and then iron wagonways had served collieries since the seventeenth century, hauled by horses, and Trevithick had put a high pressure engine on wheels at Penydarren in 1804. What was missing was a demonstration that a locomotive could do useful work reliably enough to be worth the capital.

The Stockton and Darlington, opened in 1825, was the first public railway to use steam locomotives, and it was essentially a colliery line. The decisive event was the Liverpool and Manchester, which set out to connect two large cities and held a competition at Rainhill in October 1829 to decide what should pull the trains. Rocket, built by George and Robert Stephenson, was the only entrant to complete the trials, averaging around 14 miles an hour over the distance and touching about 30. It combined a multi-tube boiler, which puts far more heating surface in contact with the water, with an exhaust blast directed up the chimney to draw the fire, and those two features are in every steam locomotive built afterwards.

The line opened in September 1830, and the opening day killed William Huskisson, a member of Parliament, who stepped onto the adjacent track in front of Rocket. It was a fair warning of what a machine moving at 30 miles an hour meant among people whose intuitions had been formed by horses.

Growth was then extraordinarily fast. British railway mileage went from about 100 in 1830 to about 1,500 in 1840, about 6,000 in 1850 and about 13,500 in 1870, an average of 13 per cent a year for forty years. The middle of that was the railway mania of 1844 to 1847, in which Parliament authorised thousands of miles at once, share prices doubled and collapsed, and railway investment reached something like 5 to 7 per cent of national income in a single year, a rate of construction Britain has never matched since.

Example. Set peak railway investment of about 7 per cent of national income against Britain's total investment rate, which by the 1840s was running at roughly 12 per cent. What follows, and what should make you cautious about the comparison?

The ratio is $7/12=0.58$: at the peak, close to three fifths of everything Britain built that year was railway. Nothing else in the period comes near that concentration, and it explains why the mania shows up in the general economy rather than only in the share price, drawing in navvies, iron, timber and bricks from every other use and then releasing them all at once when the money stopped. Two cautions. The peak year is not the decade, and averaged over 1840 to 1870 railways take a much smaller share, so quoting the peak as though it described the period is exactly the weighting error the second lesson warned about. And both figures are reconstructions with wide error bars, the investment rate especially, so 58 per cent should be read as "over half" rather than as a measurement.

Now you. The mania wiped out a great deal of shareholder wealth. Why is that not the same as wiping out a comparable amount of national wealth?

What the railway was actually worth

Here the subject gets interesting, because the obvious way to measure the railway's contribution is wrong, and knowing why is worth more than the answer.

The obvious method is to add up what railways earned, or what they carried, and call that their contribution. That double counts, because the goods would have moved anyway, more expensively, by canal and road. Robert Fogel's answer in 1964, applied to American railways, was the social saving: take the traffic the railways actually carried in a given year, cost it out at what the next best alternative would have charged, and subtract what the railways did charge. The difference is what the country saved by having railways rather than not.

Example. Work the method with round figures. Suppose the railways carry 5 billion ton-miles of freight in a year at 1 penny a ton-mile, the alternative would have cost 1.6 pence, and national income is £270 million. What is the social saving?

The extra cost of the alternative is 0.6 pence per ton-mile, so $5\times {10}^9\times 0.6=3\times {10}^9$ pence. At 240 pence to the pound that is £12.5 million, which against £270 million of national income is 4.6 per cent. So on these figures a country that woke up one morning with no railways at all, and had to move exactly the same freight by canal and road, would be about 4.6 per cent poorer. Gary Hawke's actual calculation for England and Wales in 1865, published in 1970, produced a freight social saving of about 4 per cent, and adding passengers takes the total to somewhere around 10 per cent depending on how comfort is valued. Those are large numbers for a single industry and much smaller than the railway's reputation, which is the finding.

Now you. Give one reason the social saving overstates the railway's contribution and one reason it understates it.

What no calculation captures

Two effects deserve naming because they change the country rather than its accounts.

The first is time. Before railways every town kept its own solar time, so Bristol clocks ran about ten minutes behind London. A timetable makes that intolerable, and the railways simply imposed London time on their own stations from the 1840s; by the mid 1850s nearly every public clock in Britain was set to it, a generation before Parliament made it law in 1880. A private company standardised the hour of an entire country because its trains would otherwise collide.

The second is the market itself. When freight rates fall by an order of magnitude and delivery becomes reliable, a producer in Manchester and a producer in Glasgow are in the same market for the first time, competing on price rather than being protected by distance. Local prices converged, local monopolies died, provincial breweries and brickworks and mills either got large or got out, and perishable food began arriving in cities from far away, which is a public health matter as much as an economic one.

By the middle of the century Britain therefore had cheap power, cheap iron, cheap transport and machines that outproduced hands by factors of hundreds. What it had not yet been asked is where and how the people using them actually worked, and why that turned out to be a large building full of strangers under supervision. That is the next lesson.

A factory is a strange thing to invent, because for most trades in most centuries it was cheaper to leave the worker at home and collect the product.

The previous lessons have built the machines, the fuel and the transport. What they have not explained is the building. It is tempting to treat the factory as an automatic consequence of machinery, since big machines need big sheds, but some of the earliest factories held no powered machinery at all and one of the earliest powered ones produced no imitators for fifty years. This lesson asks why work moved out of the cottage, tests three answers against each other, and ends with the awkward fact that in 1851 most British workers had still never been inside one.

Work before the factory

The system the factory displaced is called putting out, and it was the ordinary way of organising manufacturing across Europe.

A merchant bought raw wool, cotton or yarn and distributed it to households over a wide district. The household worked it on its own equipment, in its own time, and returned the product to be paid for by the piece. The merchant owned the material and not the tools; the worker owned the tools and the hours and not the material. Nobody supervised anybody. In the West Riding, the Lancashire cotton districts and the Nottinghamshire hosiery villages this supported hundreds of thousands of people and had done so for generations.

Its virtues are worth stating before its faults. It needed almost no fixed capital, so a merchant met a slump by putting out less work rather than by idling a mill he had paid for. It drew on labour that could not have gone anywhere else, since a woman with small children could spin between other tasks and could not have left the house to do it. And it fitted the agricultural year, letting the same family harvest in August and weave in January.

What was wrong with putting out

The complaints of the merchants are documented in detail, because they took them to Parliament repeatedly, and they are not mainly about speed.

The first is embezzlement. When material worth more than a week's wage is in the hands of a worker the merchant cannot see, some of it stays there. Weft was retained, wool was substituted, yarn came back short weight and cloth came back wetted to make up the weight. Parliament legislated against it repeatedly, and in 1777 the Worsted Act created something genuinely unusual: a salaried inspectorate, funded by a levy on the manufacturers themselves, with power to search premises across the worsted districts.

The second is quality. A merchant collecting cloth from four hundred households receives four hundred slightly different cloths, and a piece that fails at finishing has already had everyone's labour spent on it. The third is time. Work went at the household's pace, so it stopped for harvests, fairs, funerals and Saint Monday, the widely observed custom of not working on the first day of the week after a Sunday spent drinking. A merchant with an export order could not promise a date he did not control.

Example. A worsted manufacturer puts out £10,000 of wool a year and earns a gross margin of 10 per cent on the trade. Contemporaries claimed that something like 5 per cent of material issued was retained by the workers. What does that do to his business, and why did competing firms agree to pay for a shared inspectorate rather than hire their own?

His margin is £1,000 and his losses are $0.05\times 10\{,\}000=\pounds 500$, so embezzlement takes half his profit, which is enough to explain the vehemence of the petitions. The reason he will not simply hire his own inspector is that the deterrent is a public good among the firms. An outworker frightened out of retaining wool stops retaining everybody's wool, and since workers in a district spun for several merchants in turn, a firm paying for enforcement is buying protection for its rivals. Left to themselves each firm underspends on monitoring and all of them lose, which is exactly the situation a compulsory levy fixes. Hold on to the logic, because it points somewhere else too: if monitoring at a distance is expensive and hard to share, then bringing the work to a place where monitoring is nearly free solves the same problem by a different route.

Now you. Why could the merchant not solve embezzlement by simply paying a higher piece rate?

Cromford

Richard Arkwright's mill at Cromford in Derbyshire, opened in 1771, is where the institution begins, and it begins for a reason the previous section does not supply.

Arkwright's water frame, described in an earlier lesson, could not be worked by hand. It needed continuous rotary power at a steady speed, and in 1771 that meant a water wheel. A wheel is one indivisible lump of capital, arriving with a weir, a leat, a pond and a train of gearing, and none of it can be cut into pieces and delivered to cottages. The machines had to come to the power.

What Arkwright built around that necessity is the genuinely new part. The mill ran day and night in two twelve hour shifts, and employed around 800 people by the end of the 1780s, perhaps two thirds of them children. Because Cromford is a hamlet with no labour force in it, he built the workforce too: cottages, a market, a chapel, an inn, and a preference for hiring large families in which the children worked the frames and the father was found other work. He enforced attendance by rules, fines and dismissal in a way no merchant putting out work had ever been able to.

Example. A mill wheel develops about 10 horsepower and a water frame absorbs about a quarter of a horsepower. How many frames does one wheel serve, and what does that argument prove?

It serves $10/0.25=40$ frames, and that is the whole case for gathering: the wheel, the weir and the gearing are one purchase that cannot be divided forty ways, so the forty frames must stand within a few hundred feet of it. What the argument proves is narrower than it looks. It proves that powered spinning had to be centralised. It says nothing about the trades that gathered into large workshops with no prime mover at all, and it does not even show that power is sufficient, because John Lombe's silk throwing mill at Derby, five storeys high, water powered and employing hundreds, opened in 1721 and produced no imitators for half a century. Power made the factory necessary in one industry. Something else has to explain why the form spread to industries that did not need it.

Now you. Josiah Wedgwood's Etruria works, opened in 1769, gathered several hundred potters into one site to throw, mould, fire and paint by hand. What does that case do to the power explanation?

Three explanations, and how to tell them apart

The disagreement is old and unusually sharp, and it sets out as three claims that predict different things.

The technological account, argued most forcefully by David Landes, says the factory follows the machine: where production needs a central source of power, or machines too large for a household, work must be centralised and everything else follows. It predicts that factories appear in an industry at the same date as its prime mover and not before.

The disciplinary account, put by Stephen Marglin in 1974 in an article titled "What Do Bosses Do?", says the factory won not because it produced more per hour but because it let the employer control the pace, the hours and the division of the product. What was being sold was supervision, and its purpose was to capture for the owner a surplus the outworker had kept as leisure. It predicts factories with no new machinery in them, and rules about attendance rather than technique.

The transaction cost account says the factory solves the information problems of the previous section: embezzlement, adulteration, unverifiable quality and undeliverable dates. It predicts that centralisation comes earliest in trades where the material is valuable, concealable and easy to spoil, whichever way the technology is running.

The evidence does not award the argument to one of them. Cotton spinning fits the technological account almost perfectly. Pottery, silk throwing before power, tailoring and the Birmingham metal trades fit the other two, and Wedgwood's rule book fits the disciplinary account so well that Marglin quotes it. The workable position is that the three answer different industries, and that once the factory existed for any one reason it collected the advantages of the other two for nothing. That is how institutions usually spread: invented for one purpose, kept for another.

The clock

Whatever brought people into the building, what happened once they were there was the imposition of time, described first and best in E. P. Thompson's 1967 essay "Time, Work-Discipline and Industrial Capitalism".

His argument is that pre-industrial work is task-oriented. A task takes as long as it takes, the day has no edges, and the line between work and life is weak. Factory work is clock-oriented: the employer buys hours rather than output, so the hour must be measured, and both parties begin to argue about it. Workers who had never owned a watch acquired them, employers who owned the only clock were accused of tampering with it, and the rule books fined lateness in minutes.

There is a hard economic reason underneath, and it explains why the owner cared so much.

Example. A mill holds £5,000 of machinery, on which interest and depreciation come to 15 per cent a year. It works the standard cotton week of the 1830s, twelve hours on five days and nine on Saturday, for fifty weeks. What does an hour of that machinery cost, and what happens if the mill works a forty hour week instead?

The annual capital charge is $0.15\times 5\{,\}000=\pounds 750$. The standard week is $12\times 5+9=69$ hours, so the machinery runs $69\times 50=3\{,\}450$ hours a year and each hour carries $750/3450=\pounds 0.217$, which is 4 shillings 4 pence. At forty hours it runs 2,000 hours a year and each hour carries 7 shillings 6 pence, a rise of 73 per cent in the capital cost of every hour of production, with nothing about the workers, the cotton or the machines changed. A putting-out merchant whose capital sat in bales of wool lost nothing when a weaver took Monday off, because wool keeps; a mill owner whose capital sits in a building loses the charge on it every hour the building is dark. Time became expensive to the owner before it became expensive to anybody else, and the fines, bells and locked gates follow from that arithmetic.

Now you. The same mill installs gas lighting and runs two shifts, taking its weekly hours from 69 to 138. What happens to the capital charge per hour, and why did the length of the working day then become a matter for Parliament rather than for each employer?

Who was inside

Who was in the building follows from the machines and from the wage structure, and it is not what a modern reader expects.

Arkwright's frames required attentiveness, small hands and almost no strength, so they were worked by children and young women, who were also far cheaper than adult men. At Cromford and Styal much of the workforce was parish apprentices, children handed over by poor law authorities in London and elsewhere and bound until adulthood. Where the machine did need an adult, as the mule did before the self-actor, the spinner was a man who hired his own assistants, often his own children, out of his own wage. That family hiring system is why so much testimony about child labour describes a father driving his own son at the machine, and why the first attempts to limit children's hours were opposed by some of the parents.

The other half of the picture is that factory work paid. A young woman in a mill earned more, in cash of her own, than she could earn in service or at a wheel, which is why mills that were free to recruit generally could. Pretending the mill was simply worse than what came before makes the history unintelligible, because people walked to these places.

How much of Britain was a factory

The last correction is one of scale, and it repeats the lesson of the revised national accounts earlier in the course.

Around half a million people worked in cotton factories across the United Kingdom at the middle of the century, against an occupied population in Great Britain of about nine and a half million at the 1851 census, so roughly 5 per cent. Agriculture still employed more men than anything else, over a million women were domestic servants, and most manufacturing was still done by hand in small workshops. Raphael Samuel made the point at length in 1977 by counting the trades Victorian Britain actually ran on: building, tailoring, shoemaking, furniture, food processing, the Sheffield cutlery shops and the Birmingham metal trades, almost none of them mechanised, several of them growing because cheap factory-made inputs gave them more to work with.

The factory in this period is therefore a form that had conquered two or three industries completely and the rest of the economy hardly at all, while setting the terms on which everyone would eventually work. It is also where the effects of industrialisation on ordinary bodies first became measurable, and whether those effects were good or bad is the most argued question in the subject. That argument, and the four kinds of evidence that refuse to agree with each other, is the next lesson.

Whether the Industrial Revolution made ordinary people better or worse off is the oldest argument in the subject, and it has stayed alive because the four best kinds of evidence point in different directions.

The previous lesson put people inside the factory and noted that they walked there, which suggests it paid. This lesson asks what happened to the people who lived through the change, and it is the one place in the course where the honest answer is a set of numbers that will not reconcile. Real wages say one thing, the bodies of the people who earned them say another, and death rates say a third. Learning to hold all three at once is the point.

Why the question is hard

Start with what a standard of living measurement has to do, because most of the disagreement is buried in the method rather than in the archives.

To say a wage rose you need the money wage, which survives in wage books and contracts, and a price index to deflate it by, which has to be built from the prices of things people actually bought. The index is where the trouble is. Weight it towards bread and it says one thing; weight it towards tea, sugar and cotton cloth, which were falling in price, and it says another. The basket also changed: a family in 1850 bought goods a family in 1780 could not have bought at any price.

Three further problems have no clean solution. The money wage is a rate, not an income, so a series of daily wages tells you nothing about how many days were worked, and unemployment in this period was heavy, seasonal and unrecorded. Second, much of what a rural family consumed never passed through a market at all, so a labourer who lost common rights at enclosure and gained a cash wage may show up in the series as better off while eating worse. Third, a wage is paid to a person and a standard of living is enjoyed by a household, so anything that changed how many members of a household earned changes the answer without changing any wage.

Two traditions

The argument has a shape worth knowing, because it is one of the few historical debates where both sides were largely right about different things.

The pessimist tradition runs from Engels, whose Condition of the Working Class in England of 1845 described Manchester from the inside, through the Hammonds and to Eric Hobsbawm, who reopened the question in the Economic History Review in 1957. Its evidence is mortality, housing, food riots, and the testimony collected by parliamentary commissions. The optimist tradition, argued by Max Hartwell against Hobsbawm in the same journal in 1961 and later by Peter Lindert and Jeffrey Williamson, is built on wage series and consumption, and its strongest version, published in 1983, had blue-collar real wages roughly doubling between 1820 and 1850.

Charles Feinstein settled the wage half of it in 1998, in an article whose title, "Pessimism Perpetuated", says what he found. Rebuilding both the money wages and the cost of living index with more care, and allowing for unemployment, he got average real earnings rising by about 30 per cent across the seventy years from 1780 to 1850, with almost nothing before 1820. That is a real improvement and a slow one: compounded, ${1.30}^{1/70}-1$ is 0.38 per cent a year, a rate at which forty years of work leave a household about a sixth better off than it started.

Example. Money wages in a district rise by 50 per cent over a period while the cost of living rises by 40 per cent. What happens to the real wage, and how much can the answer be moved by the choice of price index?

The real wage index is $150/140=1.071$, so real wages rose about 7 per cent. Now consider how firm that is. Suppose bread is 60 per cent of the basket and rose 55 per cent, while everything else is 40 per cent and rose 17.5 per cent, giving the 40 per cent average used above. A statistician who thought bread was only 40 per cent of spending would compute $0.4\times 55+0.6\times 17.5=32.5$ per cent inflation and report a real wage rise of $150/132.5=13$ per cent, nearly double. A statistician who thought bread was 75 per cent of spending would get 45.6 per cent and report 3 per cent. The same wages, the same prices, and three different answers, none of them wrong. This is why the standard of living debate outlived every attempt to settle it with a single series, and why Feinstein's contribution was as much about the deflator as about the wages.

Now you. During the French wars, from about 1790 to 1810, British money wages rose roughly 40 per cent while the cost of living rose roughly 70 per cent. What happened to real wages, and what does that do to the dating of any improvement?

Engels' pause

The most useful modern framing of the whole argument is Robert Allen's, and it turns the disagreement into a measurable gap rather than a difference of opinion.

Allen set the growth of output per worker beside the growth of real wages over the same years. Between 1780 and 1840, output per British worker rose by about 46 per cent while real wages rose by about 12 per cent. Both series go up, so both the optimists and the pessimists can quote one of them, but the interesting quantity is the distance between them. If workers produce 46 per cent more and are paid 12 per cent more, the share of output going to labour must fall, and the rest accrues to profits, which were reinvested. Allen named the period Engels' pause, after the man who described it while it was happening.

Example. Output per worker rises 46 per cent and the real wage rises 12 per cent over the same sixty years. What happens to labour's share of output, and what is the annual growth rate of each?

Labour's share is the wage divided by output per worker, so it changes by $1.12/1.46=0.767$: a fall of 23 per cent in the fraction of what is produced that reaches the people producing it. Annualised over sixty years, output per worker grows at ${1.46}^{1/60}-1=0.63$ per cent a year and the real wage at 0.19 per cent. Neither rate would be visible to anyone living through it, which is exactly the difficulty: over a single working life of forty years the wage improves by about 8 per cent, less than the difference between a good and a bad year, while the country visibly fills with mills, ships and railways. That gap between what people could see being built and what they could see in their own household is a better description of the politics of the 1830s than any wage index on its own.

Now you. If real wages had instead kept pace with output per worker, what would they have done, and why might the eventual outcome have been worse?

What the bodies say

Wages are a price. A height is an outcome, and it is one of the few measurements of this period that was taken on hundreds of thousands of ordinary people for reasons that had nothing to do with the argument.

Final adult height depends on nutrition and disease during growth, net of the work the body had to do at the same time. Armies, navies, prisons and charities all measured recruits, and those records let historians build a series by year of birth. Roderick Floud, Kenneth Wachter and Annabel Gregory published the major British reconstruction in 1990, and the finding that startles is the level rather than the trend: fourteen year old boys taken in by the Marine Society from the London poor in the 1770s averaged around 130 centimetres, more than 30 centimetres below a British fourteen year old today.

The trend is the part that bears on the argument, and it goes the wrong way for the optimists. Heights rose for cohorts born through the eighteenth century, then stalled and fell for those born roughly between 1820 and 1850, the very decades in which Feinstein's real wages were finally rising. The decline is of the order of an inch, it is contested in size, and the samples are awkward because armies impose minimum heights and recruit selectively from the poor. But the direction has survived a great deal of re-examination, and men born in towns were consistently shorter than men born in the countryside.

Reading the mortality evidence

The third body of evidence is death, and it comes with a trap that is worth walking into deliberately, because the same trap is set in a great deal of nineteenth century social statistics.

Edwin Chadwick's Report on the Sanitary Condition of the Labouring Population of Great Britain of 1842 tabulated the average age at death by class and place. In Manchester he gave 38 years for professional persons and gentry, 20 for tradesmen and their families, and 17 for mechanics and labourers. In rural Rutland the same three groups gave 52, 41 and 38. Liverpool was worse than Manchester, at 35, 22 and 15.

Those figures are real and the conclusion usually drawn from them is wrong. Average age at death is not life expectancy, and it is not a measure of how long an adult could expect to live.

Example. Take two populations. In the first, half of all deaths are of infants aged 1 and half are of adults aged 60. In the second, one fifth are infants and four fifths are adults at the same two ages. What is the average age at death in each, and what has changed about adult life?

The first gives $0.5\times 1+0.5\times 60=30.5$ years and the second $0.2\times 1+0.8\times 60=48.2$ years. The average age at death differs by nearly eighteen years between the two populations, and nothing whatever has changed about how long an adult lives, which is sixty in both. The entire difference is infant mortality. So when Chadwick reports 17 years for Manchester labourers, he is not saying that a Manchester labourer died at 17; he is reporting a figure dominated by the fact that a very large share of labourers' children died before their fifth birthday. The number is evidence about infant death, and it is powerful evidence, but it will mislead anyone who reads it as a lifespan.

Now you. Give a second reason why Chadwick's figure is lower for Manchester than for Rutland even if adults in the two places were equally healthy.

Putting the three together

The three bodies of evidence look contradictory and are not, once each is asked the question it can answer.

Real wages measure the purchasing power of an hour of work. Heights and death rates measure what happened to a body in the place where that wage was spent. There is no contradiction in a worker being paid more, in a currency that buys more, while living in a town with no sewer, drinking water drawn downstream of a privy, working sixty-nine hours a week and losing two children in five before they were five years old. Wages rose. The environment in which they were spent deteriorated faster, for about two generations, and then improved.

That resolution has a consequence that shapes the rest of the course. If the losses were environmental rather than contractual, then no bargain between an employer and a worker could have fixed them, and neither could a higher wage. What was needed was drains, water, housing regulation and hours legislation, which is to say collective action of a kind that did not yet exist. The next lesson goes to the place where the environmental damage was worst and most measurable, which is the city, and the lesson after it to the political response.

One honest closing caution. Everything in this lesson is a national average built from unrepresentative samples, and averages hide the thing that mattered most to the people living through it, which is that the gains and the losses landed on different households. The mule spinner's family and the handloom weaver's family lived in the same town under the same wage index and had opposite experiences of the same fifty years, and E. P. Thompson's objection to the whole quantitative debate was that no index can capture what the weaver lost, which included a trade, a status and a way of ordering his own day.

A town that trebles in fifty years has to put its new people somewhere, and what it did with them killed a great many of them.

The previous lesson found real wages rising slowly while heights fell and infant deaths stayed appalling, and suggested the resolution lay in the place the wage was spent rather than in the wage. This lesson goes to that place. It is about what happens when population arrives faster than drains, why the resulting death rate was measurable long before it was understood, and how one of the cleanest natural experiments in the history of science was conducted on the water supply of south London.

The first urban society

At the 1851 census slightly more than half the population of England and Wales lived in towns, which had never been true of any country before. The change was concentrated in a few places and it was very fast.

Manchester township held about 75,000 people in 1801 and about 303,000 in 1851. Liverpool went from about 82,000 to about 376,000 over the same fifty years. Glasgow, Birmingham, Leeds and Bradford all did something similar, and Bradford, the fastest, multiplied its population by about eight. These are rates of growth that no earlier city had sustained, because no earlier city had a food supply, a water supply or a labour market that could support them.

Example. Take Manchester from 75,000 in 1801 to 303,000 in 1851. What is the annual growth rate, and how many dwellings a year did the town have to build to house the increase at five people to a house?

The factor is $303/75=4.04$, so the rate is $(4.04{)}^{1/50}-1=0.0283$, about 2.8 per cent a year, which doubles a population in 25 years. The increase is 228,000 people, so at five to a house the town needed $228\{,\}000/5=45\{,\}600$ new dwellings across fifty years, which is 912 a year, every year, for half a century, in a place with no building regulations, no municipal corporation until 1838, and no public authority responsible for streets, water or sewers. The arithmetic is the explanation for what the housing was like. Cheap, fast and unregulated is the only kind of building that meets a requirement of nearly a thousand houses a year, and back-to-back terraces with shared privies and no through ventilation are what that produces.

Now you. Suppose Manchester's crude birth rate was 35 per thousand and its death rate 33 per thousand, giving natural increase of 0.2 per cent a year. How much of the 1851 population could natural increase account for, and what does the remainder mean?

What the growth produced

The physical result is documented in obsessive detail, because the men who investigated it were trying to shock Parliament and succeeded.

The characteristic Manchester and Leeds housing was the back-to-back: terraces built in pairs sharing a rear wall, so each house had windows on one side only and no through draught. They were built around courts reached through a tunnel, and a court of a dozen houses shared one or two privies over a cesspool or midden that was emptied when somebody paid a nightsoil man to empty it. Water came from a standpipe or a well, ran for an hour or two on some days of the week, and had to be carried and stored.

Liverpool added a form of its own. Its cellars, dug under the houses, were let as separate dwellings, and in the early 1840s something like 39,000 people, about one Liverpudlian in eight, lived below ground in rooms that flooded when it rained. Liverpool appointed the first Medical Officer of Health in the country, William Duncan, in 1847, and it is not a coincidence that the worst-housed large town produced the first public health officer.

The urban penalty, measured

Here the evidence becomes precise, because from 1837 England and Wales had compulsory civil registration of births, marriages and deaths, and because the man put in charge of the statistics, William Farr, was one of the founders of modern epidemiology.

Farr's life tables from the 1841 data give life expectancy at birth of about 41 years for England and Wales as a whole, and about 26 for Liverpool. That gap of fifteen years is not a matter of the poor dying young everywhere; it is a matter of where they lived. The mechanism is overwhelmingly infant and child mortality: urban infant death rates ran at 150 to 200 per thousand live births and higher in the worst districts, against something closer to 100 in healthy rural counties.

The consequence is the fact that dominates the demography of industrial Britain. The great towns did not reproduce themselves. Deaths in Liverpool and Manchester ran close to or above births, so the cities grew by consuming the surplus population of the countryside, and had they been sealed off they would have shrunk. Urbanisation raised national mortality simply by moving people from places where they survived to places where they did not, which is why national life expectancy barely improved between the 1820s and the 1860s while the country was getting richer.

Example. A city of 300,000 has a crude death rate of 33 per thousand while the national rate is 22. How many excess deaths a year is that, and how should the figure be qualified?

The excess rate is 11 per thousand, so the city loses $300\{,\}000\times 11/1000=3\{,\}300$ extra people a year, and 33,000 across a decade, which is more than the British dead of most contemporary wars. The qualification matters. A crude death rate is affected by age structure, and this city is full of young migrants, whose death rates are low, so the crude comparison understates the true penalty rather than exaggerating it: correcting for the young age structure would make the excess larger. Working the other way, migrants arrived from poor rural districts already carrying the effects of a poor childhood, so not all of the excess was caused by the city. Farr's own way through this was to standardise, comparing each town with a healthy district at each age separately, and on that basis he put the avoidable excess at a scale he was willing to call a national emergency.

Now you. Why did the urban penalty make cheap food and cheap cotton clothing less useful to a worker than the wage series suggests?

Cholera

Cholera did not cause most of the deaths, and it caused most of the legislation, which is worth being clear about.

The disease reached Britain from the Continent in 1831 and returned in 1848, 1853 and 1866. It killed something over 30,000 people in the first epidemic and about 60,000 in the second, which set against the steady annual toll from tuberculosis, typhus and infant diarrhoea is not the largest killer of the period. What made it decisive is that it was new, terrifying, sudden, and indifferent to class in a way the endemic diseases were not. A healthy adult could be dead within a day, and cholera walked into the houses of people with political power.

The explanation everyone accepted was miasma: disease arising from the foul air of decomposing filth. Chadwick believed it, Florence Nightingale believed it, and it is not a stupid theory, because it correctly predicts that filthy places are dangerous places and it motivated a great deal of useful cleaning. Its practical failure was specific and severe. Acting on it, Chadwick's sanitary reforms flushed the contents of London's cesspools into the sewers and thence into the Thames, which was where London's water companies had their intakes, and so improved the smell while distributing the disease.

Snow's experiment

John Snow, a London physician, argued from 1849 that cholera was spread by something swallowed rather than something breathed, on the evidence that the disease attacks the gut first and that it followed the movement of people and water rather than of air.

His famous investigation is the Broad Street pump in Soho in 1854, where he mapped 600 deaths in a few days around a single well and had the handle removed. The map is a fine piece of work and it is not decisive, because a cluster of deaths around a pump in a filthy district is equally consistent with a local miasma.

What is decisive is the other study, and it is one of the best natural experiments ever conducted.

Example. In south London two companies supplied water to houses along the same streets, often to adjacent houses. In 1852 the Lambeth company moved its intake upstream to Thames Ditton, above the sewage outfalls; the Southwark and Vauxhall company kept drawing from the tidal Thames at Battersea. In the first seven weeks of the 1854 epidemic Snow counted 1,263 cholera deaths in 40,046 houses supplied by Southwark and Vauxhall, and 98 deaths in 26,107 houses supplied by Lambeth. What is the death rate in each, and why is this stronger evidence than the Broad Street map?

Southwark and Vauxhall gives $1263/40046\times 10\{,\}000=315$ deaths per 10,000 houses, and Lambeth $98/26107\times 10\{,\}000=38$, a ratio of 8.4 to one. The strength of the design is that everything except the water is held constant. The two companies' pipes ran down the same streets to houses of the same kind, occupied by the same sort of people breathing the same air, with the supplier determined years earlier by which company's salesman had called; as Snow put it, the two groups were mingled in every way and differed in nothing except the water. A miasma cannot distinguish between neighbouring houses on one street. A water supply can, and did, by a factor of eight. Snow also had to do the legwork that made the numbers possible, calling at the house of each recorded death and, where the occupants did not know their supplier, testing the water for the chloride that distinguished tidal river water from clean.

Now you. Snow published this in 1855 and the medical establishment was not convinced for another decade. Give the strongest objection available to a competent contemporary.

The sanitary state

The response to all this is the most important institutional change in the whole period, and it happened because the counting made the problem impossible to ignore.

Chadwick's 1842 report sold tens of thousands of copies and argued, in terms a Treasury could follow, that disease cost more in poor relief for widows and orphans than sanitation would cost to build. The Public Health Act of 1848 followed, creating a General Board of Health and letting localities set up boards of health, with compulsion where the death rate exceeded 23 per thousand. It was permissive, underfunded and widely resisted by ratepayers who objected to being taxed for a benefit they could not see, and Chadwick, who was personally impossible, was forced out in 1854.

What broke the resistance was the Great Stink of the summer of 1858, when the Thames beside the Palace of Westminster became unbearable and Parliament voted the money for Joseph Bazalgette's intercepting sewers within eighteen days. Bazalgette built about 82 miles of main intercepting sewer and some 1,100 miles of street sewers, carrying London's waste far downstream, and he sized the pipes at roughly twice his own estimate of requirement on the grounds that it would only be done once, which is why they still work. The Sanitary Act of 1866 made action compulsory rather than permissive, and the Public Health Act of 1875 consolidated the whole into the framework that governed British sanitation for a century.

The results arrive after the period this course covers, which is the honest and uncomfortable conclusion. Urban mortality does not begin to fall decisively until the 1870s, and the biggest gains are later still. Thomas McKeown argued in the 1970s that the mortality decline was driven by better nutrition rather than by medicine or public health, and Simon Szreter's reply in 1988 used the local records to show that the timing follows the arrival of municipal water and sewerage town by town, which is now the better-supported view. Either way, the people who lived through the growth of Manchester and Liverpool got the counting, the reports and the arguments, and their grandchildren got the drains.

They did not accept any of it quietly, and the next lesson is about what they did instead.

Everything described so far was done to a population that could not vote, could not lawfully combine, and had no representative in the Parliament that made the rules.

The previous lessons have established the costs: a wage that barely moved for two generations, a workplace organised around the owner's clock, and a city that killed a fifth of its children. This lesson is about what the people carrying those costs did, and about the long, grudging, and in the end substantial legislative answer. It is easy to write this as a story of good intentions triumphing. The more useful reading is that reform arrived when it became cheaper than the alternative, and the alternative was supplied by the people in the streets.

The legal position

Begin with what was and was not allowed, because the constraints explain the tactics.

The Combination Acts of 1799 and 1800 made it a summary offence for workmen to combine to raise wages or shorten hours, triable by two magistrates who were frequently themselves employers. They were repealed in 1824 largely through the manoeuvring of Francis Place, and a wave of strikes immediately followed, so Parliament passed an amending act in 1825 that permitted combination for wages and hours alone while leaving almost any effective action prosecutable as intimidation or as conspiracy at common law.

Representation was narrower still. Before 1832 the franchise in England and Wales rested on a patchwork of ancient qualifications; Manchester, Birmingham and Leeds returned no members at all, while Old Sarum, an uninhabited mound in Wiltshire, returned two. The Reform Act of 1832 redistributed seats to the industrial towns and standardised the borough franchise at a £10 householder, raising the electorate in England and Wales from roughly 400,000 to roughly 650,000, which is about one adult man in five. The Act enfranchised the middle class and confirmed the exclusion of everyone below it, and that specific disappointment is where the largest working-class movement of the century begins.

Luddism

The Luddites are the most misremembered episode in the subject. They were not opposed to machinery in general, and they were not a mob.

The attacks ran from March 1811 to about 1816, in three distinct districts with three distinct grievances. Nottinghamshire framework knitters attacked wide stocking frames used to make cut-ups, cheap stockings cut from a knitted sheet rather than fashioned to shape, which undercut the trade and, they argued, defrauded the customer. Yorkshire croppers, who finished woollen cloth by hand with 40 pound shears and were among the best-paid workmen in England, attacked gig mills and shearing frames that did their work. Lancashire attacks were aimed at power looms and were mixed up with the collapse of handloom weaving described in an earlier lesson.

What united them is that each group was appealing to a body of regulation that had recently been swept away. Apprenticeship rules, quality standards and the old statutory machinery for fixing wages had been repealed or left unenforced, and petitions to Parliament to restore them had failed. Machine breaking was what happened after the legal route closed. It was disciplined, it was aimed at specific frames belonging to specific masters who had broken custom, and frames belonging to masters who paid the customary rate in the same workshop were often left untouched.

The state's response was severe out of all proportion. Frame breaking was made a capital offence in 1812, against which Byron made his maiden speech in the Lords, and something like 12,000 troops were deployed in the disturbed districts, a force comparable to the army Wellington then had in the Peninsula. The York special commission of January 1813 hanged seventeen men.

Example. A master can install a machine costing £200 that saves £60 a year in wages. Money can otherwise be lent at 5 per cent. If there is a one in four chance each year that the machine is destroyed, is it still worth installing?

Without any risk the machine returns $60/200=30$ per cent a year, which is obviously worth having. With a 25 per cent annual chance of losing the whole £200, the expected loss is $0.25\times 200=\pounds 50$ a year, so the expected net gain falls to $60-50=\pounds 10$, a return of 5 per cent, exactly what lending the money would earn without the trouble. At that point the master is indifferent, and any higher risk makes him decline. This is the real logic of machine breaking, and it explains why it was targeted rather than general: the threat does not have to destroy every machine, only to make the expected return on installing one no better than the alternative. Historians have called this collective bargaining by riot, and in a country with no lawful unions, no factory inspectors and no vote, it was the only bargaining instrument available.

Now you. The government floods the district with troops and hangs seventeen men, cutting the annual risk of destruction to 2 per cent. What happens to the calculation, and what does that say about what the state was actually doing?

Peterloo

The other route was mass peaceful assembly, and the state's answer to that is the event that gave British radicalism its founding memory.

On 16 August 1819 a crowd generally estimated at 60,000, drawn from the mill towns around Manchester, walked in disciplined contingents to St Peter's Field to hear Henry Hunt speak for parliamentary reform. The magistrates ordered Hunt's arrest, and the Manchester and Salford Yeomanry, local men on horseback, rode into the crowd with sabres drawn. Eighteen people were killed and something like 650 to 700 were injured.

The name Peterloo, coined by a radical journalist against Waterloo four years earlier, stuck because it named the thing exactly: cavalry used against British civilians. The government thanked the magistrates and passed the Six Acts within four months, restricting public meetings, seizing seditious publications and taxing the cheap press out of existence. It also produced, indirectly, the Manchester Guardian, founded in 1821 by a merchant who had watched the field.

The Factory Acts

Regulation of the workplace took forty years and moved in a pattern worth extracting, because the same pattern recurs whenever a state first regulates an industry.

The Health and Morals of Apprentices Act of 1802 limited parish apprentices in cotton mills to twelve hours and required some schooling, and did nothing, because enforcement was left to local magistrates and there was no inspector. The Act of 1819 barred children under nine from cotton mills and limited those aged nine to sixteen to twelve hours, and did almost nothing, for the same reason.

The Factory Act of 1833 is the hinge, and the reason is administrative rather than moral. It excluded children under nine, limited those aged nine to thirteen to nine hours a day and 48 a week, limited those aged fourteen to eighteen to twelve hours and 69 a week, required two hours of schooling a day, and, decisively, created four salaried factory inspectors with the power to enter any mill, question anyone, and prosecute. Four men for the whole country is a derisory number and it was still transformative, because for the first time the law had someone whose job was to notice.

What followed built on that machinery. The Mines Act of 1842, prompted by a royal commission whose illustrations of women and children hauling coal underground were circulated to horrified members of Parliament, banned women and boys under ten from working below ground. The Factory Act of 1844 limited women to twelve hours, cut children to six and a half, and required dangerous machinery to be fenced. The Ten Hours Act of 1847 limited women and young persons to ten hours, which owners evaded with relay systems until the Act of 1850 fixed the hours between which anyone could work, producing a normal day of ten and a half hours.

Example. Nassau Senior argued in 1837 that a ten hours bill would destroy manufacturing profit entirely, because in an eleven and a half hour day the profit is made in the last hour. Test the argument on a mill with revenue of £10,000, materials and wages of £8,500, and a fixed capital charge of £1,000.

Profit is $10\{,\}000-8\{,\}500-1\{,\}000=\pounds 500$. Cutting the day from 11.5 hours to 10 is a reduction of $1.5/11.5=13.0$ per cent, so revenue falls to £8,696 and materials and wages, which vary with output, fall to £7,391. The fixed charge stays at £1,000, since the building and machinery cost the same whether they run or not. Profit is therefore $8\{,\}696-7\{,\}391-1\{,\}000=\pounds 305$, a fall of 39 per cent. That is a serious loss and it is not the annihilation Senior predicted. His error was to assign the fixed capital charge to particular hours of the day, as though the first ten hours paid the wages and the eleventh paid for the machinery, when a fixed cost is by definition spread across all the hours worked. The prediction also assumed output would fall in exact proportion to hours, which it did not: after 1847 output per hour rose as workers worked less exhausted and owners raised machine speeds, and by the 1850s the industry was producing more than ever on a shorter day.

Now you. Why was it politically easier to regulate the hours of children than the hours of adult men, and how did the reformers turn that to their advantage?

Chartism

The largest movement of all came directly out of the exclusion of 1832 and the New Poor Law of 1834, which abolished outdoor relief in principle and sent the destitute to a workhouse deliberately made worse than the worst available job.

The People's Charter of 1838 set out six demands: universal male suffrage, the secret ballot, no property qualification for members of Parliament, payment of members, equal electoral districts, and annual parliaments. Every one of them is a mechanism rather than a policy, and taken together they amount to the claim that the working population could not fix any of its other problems until it could vote.

The movement's instrument was the mass petition, and the scale is easy to underrate.

Example. The 1842 Chartist petition carried about 3.3 million signatures. Great Britain's population in the 1841 census was about 18.5 million, of whom roughly 26 per cent were men aged over twenty. What share of adult men signed, and how does that compare with the electorate?

Adult men numbered about $18.5\times 0.26=4.8$ million, so 3.3 million signatures is about 69 per cent of them, and roughly five times the 650,000 men entitled to vote in England and Wales after 1832. Parliament declined even to hear it, by 287 votes to 49. Treat the share with care: petitions were signed by women and by boys, and were not verified in 1842, so the true figure for adult men is lower. The 1848 petition, which claimed 5.7 million, was checked by the House and found to hold about 1.9 million genuine names, one third of the claim. Even discounted heavily this is a level of organised participation without precedent in British history, achieved by a population with no vote, no money and a twelve hour working day.

Now you. Five of the six points eventually became law. Why is Chartism usually described as a failure?

The Corn Laws, and who had won

The last of these fights is the one that settles which interest now ran the country.

The Corn Laws of 1815 blocked imported wheat until the domestic price reached a high threshold, protecting landlords' rents at the cost of the price of bread. The Anti-Corn Law League, founded in Manchester in 1838 and led by Richard Cobden and John Bright, ran what is recognisably the first modern political campaign: paid lecturers, a national newspaper, mass mailing made possible by the penny post of 1840, and the systematic buying of 40 shilling freeholds to create voters in county constituencies.

Robert Peel repealed the laws in June 1846, using the Irish famine as the occasion and splitting his own party permanently in the process. Two readings of the outcome are worth holding together. It was a victory for cheap food, and the working population benefited from it. It was also a victory of the manufacturing interest over the landed interest, since a manufacturer who wants low wages wants cheap bread, and the League was funded by employers, several of whom were resisting the Ten Hours Bill at the same moment. Cobden and Bright both opposed factory regulation.

That is the shape of the whole period's politics in one line. The industrial classes won their argument against the landowners in 1846, the working population won its argument about hours in 1847, and the two victories were won by opposed coalitions in consecutive years. By the middle of the century Britain had an industrial economy, an inspected workplace, a beginning of a sanitary state, and a political system that had absorbed enough pressure to survive the year Europe spent in revolution.

What it also had, by then, was imitators, customers, and colonies whose own manufacturing it had destroyed. The final lesson takes the argument outward, to what the technology did when it left.

A technology that raises output per worker by a factor of hundreds does not stay in one country, and what it did on its way out is the balance sheet of the whole subject.

The previous lessons have taken Britain from a flat wage series to an inspected, drained, partly reformed industrial economy. This last one asks what the change meant for everybody else: who copied it and why they could, whose manufacturing it destroyed, what it ran on, and what it left in the atmosphere. It is also the place to state plainly what the course as a whole has argued, since a reader who has followed the chain should now be able to account for the break.

How the technology left

Britain tried to keep it. Exporting textile machinery was illegal until 1843, and the emigration of skilled artisans was prohibited until 1825, with penalties on anyone who recruited them.

Neither ban worked, because the knowledge was in people and people walk. Samuel Slater, who had served an apprenticeship under a partner of Arkwright's, sailed for New York in 1789 having memorised the machinery, since he could carry no drawing past the customs officers, and built the first successful water-powered spinning mill in the United States at Pawtucket in 1793. Francis Cabot Lowell toured British mills as a gentleman visitor in 1810 to 1812, memorised the power loom, and built an integrated spinning and weaving mill at Waltham in 1814. William Cockerill, an English carpenter, built spinning machinery at Verviers from 1799 and his son founded the ironworks at Seraing in 1817 that made Belgium the first industrial power on the Continent.

The pattern is consistent. The bans slowed diffusion by a decade or two and did not prevent it, because tacit knowledge held in a skilled head is not something a customs house can search for. Every subsequent attempt at technological containment has run into the same problem.

Why some countries could copy it and others could not

The interesting question is not who wanted the machines, since everybody did, but who could use them.

Belgium had coal, iron ore, a dense population and proximity to Britain, and industrialised first. Germany had coal in the Ruhr and Silesia and, after the Zollverein customs union of 1834, a market large enough to be worth building for; its industrialisation ran through railways, banks and chemicals rather than through cotton, and in the first years of the twentieth century German pig iron output passed Britain's. The United States had land, coal, iron and, above all, a chronic scarcity of labour that made labour-saving machinery pay even more obviously than it had in Lancashire. Japan is the case that breaks any argument from geography or culture: after 1868 the Meiji state bought the technology deliberately, built model factories like the Tomioka silk mill of 1872, sent students abroad, hired foreign engineers on enormous salaries and dismissed them once their knowledge had been absorbed.

Alexander Gerschenkron's account of this, published in 1962, is the one that generalises. His argument is that late industrialisers do not repeat the leader's path: the later a country starts, the more the missing pieces have to be supplied by institutions rather than by private accumulation, so Britain industrialised on reinvested profits, Germany on investment banks, and Russia on the state itself. He also observed that late starters skip stages, importing the newest technique rather than working through the sequence, which is why Japan built its first mills around ring spinning while Lancashire was still running mules.

The other side of the ledger

For a smaller group of countries, British industrialisation was not an opportunity but a demolition, and India is the case everyone argues about.

Paul Bairoch's estimates of world manufacturing output shares are the standard frame. In 1750 India produced roughly a quarter of the world's manufactures and Britain about 2 per cent. By 1880 Britain was at nearly 23 per cent, its peak, and India at under 3. India, which had clothed much of the world, was importing British cloth by the 1820s and had lost its export trade entirely by mid century.

Example. Take India's share of world manufacturing as 24.5 per cent in 1750 and 2.8 per cent in 1880. If world manufacturing output rose sixfold over that period, what happened to India's output in absolute terms, and what would world output have had to do for India's absolute output to be unchanged?

Set world output at 1 in 1750, so India produces 0.245. In 1880 world output is 6 and India produces $0.028\times 6=0.168$. So India's absolute output fell by $1-0.168/0.245=31$ per cent, not by the 89 per cent that the fall in share suggests. For the absolute level to be unchanged, world output would have had to multiply by $0.245/0.028=8.75$. The distinction between a share and a level is the single most abused piece of arithmetic in this whole literature, in both directions: a share can collapse while the level rises, if the world grows fast enough, and a stable share can hide a collapse. It is worth adding that the sixfold figure is itself an estimate with wide error bars, and that Bairoch's shares are reconstructions rather than measurements, so this exercise establishes the shape of the correction rather than a number to quote.

Now you. How much of India's deindustrialisation should be attributed to British tariff policy rather than to the productivity gap?

What the mills ran on

There is one input the British cotton industry could not have replaced, and by the 1850s most of it was grown by enslaved people in the American South.

The chronology fits together uncomfortably well. Eli Whitney's gin of 1793 made short-staple upland cotton, which grows across the whole southern interior, cheap to clean, and the crop moved west into Alabama, Mississippi and Louisiana with the people forced to grow it. The enslaved population of the United States rose from 697,681 at the 1790 census to 3,953,760 in 1860, a factor of 5.7, much of that increase moved south and west by an internal slave trade that broke up families as a matter of routine.

Example. United States cotton output was about 1.5 million pounds in 1790 and about 4.5 million bales of roughly 450 pounds in 1860. What growth rate is that, and what does output per enslaved person do?

The 1860 crop is $4.5\times {10}^6\times 450=2.03\times {10}^9$ pounds, which is 1,350 times the 1790 figure, a growth rate of ${1350}^{1/70}-1=10.8$ per cent a year sustained for seventy years. Per enslaved person, output goes from $1.5\times {10}^6/697\{,\}681=2.2$ pounds to $2.03\times {10}^9/3\{,\}953\{,\}760=512$ pounds, a factor of about 240. Two cautions are essential. The denominators include children, the elderly, and the majority of enslaved people who did not pick cotton at all, so this is a crude ratio for the whole enslaved population rather than a measure of anyone's work. And the rise has several causes competing for credit: the gin, the far better land of the southwest, improved cottonseed varieties documented by Alan Olmstead and Paul Rhode, and, in Edward Baptist's account, systematic escalation of violence to raise picking rates, a claim Olmstead and Rhode have disputed on the evidence of the plantation records.

Now you. Eric Williams argued in 1944 that profits from slavery and the slave trade financed British industrialisation. What is the strongest evidence against the strong version of that claim, and what survives it?

The carbon

The last item on the balance sheet was invisible to everyone at the time and is the one that has outlasted the rest.

Burning coal turns its carbon into carbon dioxide. Take British coal as roughly 70 per cent carbon by mass; then a ton of coal yields 0.7 tons of carbon, and since carbon dioxide has a molecular mass of 44 against carbon's 12, that is $0.7\times 44/12=2.57$ tons of carbon dioxide per ton of coal.

Example. Britain produced about 62 million tons of coal in 1850 for a population of about 20.8 million. What was that in carbon dioxide per head, and how does it compare with Britain today, which emits roughly 250 million tons for about 68 million people?

The 1850 output gives $62\times 2.57=159$ million tons of carbon dioxide, which is $159/20.8=7.6$ tons per person. Present-day Britain gives $250/68=3.7$ tons per person. So Britain in 1850, with no cars, no aircraft, no electricity and no central heating, emitted about twice as much carbon dioxide per head as Britain does today. The result is not a trick, though it needs two honest qualifications. Some of that coal was exported or converted to coke and gas rather than burned domestically, so the figure overstates British consumption somewhat. And modern Britain imports a great deal of embodied carbon in manufactured goods, so its consumption-based figure is considerably higher than its territorial one. The core finding survives both: an economy running on nothing but coal is an extraordinarily carbon-intensive economy, and Britain's per-head emissions peaked long before living memory.

Now you. Estimate the total carbon dioxide from British coal between 1750 and 1900, taking output as roughly 5, 15, 30, 62, 110 and 225 million tons in 1750, 1800, 1830, 1850, 1870 and 1900. World emissions today run about 37 billion tons a year. What does the comparison suggest?

The balance sheet

Set the whole thing out, since a reader who has come this far is entitled to the summary.

What was gained is the end of the trap the course opened with. For four centuries English real wages oscillated without trending, and the model that explained why had no exit. After about 1820 output per head rose and kept rising, at rates that compound into transformation, and the population rose with it, which is the one thing the Malthusian model forbids. Everything now taken for granted about modern life, including the expectation that a child born today will outlive their parents' generation, rests on that break.

What was paid is a list this course has tried not to soften. Two generations of workers produced 46 per cent more and were paid 12 per cent more. The people who moved into the towns lost fifteen years of life expectancy on Farr's tables. Children worked in mills until Parliament stopped them, and the stopping took forty years and a factory inspectorate. Indian spinning was destroyed by a productivity gap of several hundred to one and Indian industrialisation was postponed by policy. The largest British industry ran on cotton grown by enslaved people. And the fuel that made all of it possible has left a bill nobody knew was being run up.

Both halves are true, and holding them together without discounting either is what the subject actually requires. The change was worth having and it was not free, and it was not paid for by the same people who first received it. That is not a paradox: it is the ordinary shape of large historical changes, and it is the reason arguing about the Industrial Revolution has never stopped.

One question is left open, and it is the one a reader should take away. The escape happened once, in one place, under a specific set of conditions: dear labour, cheap coal, a state that would enforce a contract, and a culture of measurement. Every country that has escaped since has done it by imitation, with a working example in front of it. Whether the same escape can be made a third time, out of the carbon economy and into something else, with the same speed and without the same costs, is the practical form of the question this course has been asking about the past.