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 times as productive as hand spinning, and the self-actor is 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?
Answer
The factor is 205 over eighty years, so the rate is , about 6.9 per cent a year sustained for eighty years. It is a fair proxy because Britain grew no cotton at all, so every pound spun had to enter through a customs house and be recorded, which makes this one of the cleanest output series in the whole of economic history. The qualifications are small: some raw cotton was re-exported unspun, and waste in processing changed as machinery improved, so the series slightly overstates the growth of finished cloth. Neither matters at this scale. Note also what the rate implies for the previous lesson's arithmetic on weights: a sector growing at 6.9 per cent while the economy grows at 1.5 per cent doubles its share of that economy roughly every thirteen years.
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 . Taking both as proportional changes, the implied elasticity is : 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 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?
Answer
It requires that the supply of raw cotton expanded roughly forty-fold in fifty years without the price being bid up at all, which is a remarkable fact in its own right and is usually left out of the story told about the machines. Had the fibre price risen with demand instead, it would have put a floor under the price of yarn that no further mechanisation could break through: by the 1830s the fibre was already about a third of the price of the finished yarn, and the spinning margin, the part machinery could attack, had been squeezed down to the remainder. Every further improvement would have bought less. It did not happen because the American South could expand output almost without limit, on new land in Alabama, Mississippi and Louisiana, with the gin solving the cleaning bottleneck and enslaved labour supplying the picking. The British price collapse therefore rests on a second expansion happening on another continent, and that dependence is taken up directly in the final lesson.
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?
Answer
To the bargaining power of labour rather than to its scarcity, and the distinction matters. Mule spinners were skilled adult men, hard to replace, organised into some of the earliest effective trade unions, and repeatedly on strike in the Manchester district in the early 1820s. Richard Roberts was commissioned by a committee of masters during one such dispute and produced a machine that removed the skilled judgement from the job. The general point is that the price of labour that drives mechanisation is not only the wage in a scarcity sense but the whole cost of employing a worker, including the risk of being stopped. This does not contradict the argument that high wages drove British invention. It sharpens it, and it is a caution against reading technology as something that happens to industrial relations rather than inside them.
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.