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 megajoules. The efficiency is 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?
Answer
Using absolute temperatures, , so about 21 per cent. The Newcomen engine achieved 0.47 per cent, which is around one fortieth of what its temperature range permitted, so the waste is overwhelmingly a matter of construction rather than of physics: the reheating of the cylinder, the leakage, the friction and the boiler's own losses up the chimney. The comparison also explains why every later improvement worth having pushes the top temperature up. High pressure steam is hotter steam, and hotter steam raises the ceiling itself rather than merely getting closer to it, which is why the story ends with Trevithick and not with better versions of Newcomen.
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?
Answer
Because the fee was defined by a comparison with something the customer did not have. Calculating a third of the coal saved against a hypothetical Newcomen engine of equivalent power meant estimating what that engine would have burned, which is an argument rather than a measurement, and it grew steadily less credible as Watt engines were installed in cotton mills and breweries that had previously used horses or water. Boulton and Watt increasingly resorted to a fixed premium per nominal horsepower instead, and horsepower itself was Watt's coinage for exactly this purpose: a unit that let an engine be sold to a customer who had never bought power before by comparing it with the animals he was already feeding. Defining the unit that makes your product comparable to its alternative is a commercial act as much as a technical one.
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 over seventy years, so the rate is 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 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?
Answer
Because the counterfactual asks what would have been used instead, not what would have been lost outright. A mill without a Watt engine builds a water wheel, hires horses, or installs the unimproved Newcomen engine that was still perfectly capable of pumping a mine; the cost of doing without is the extra expense of the second-best option, and in 1800 the second-best option was not much worse. This is the general shape of every social saving calculation and the same logic reappears in the next lesson applied to railways. What the figure is not saying is that steam did not matter. It is a measurement taken at one date, and it holds only while the alternatives remain close substitutes. Nothing except steam could have driven a locomotive, a steamship, or a mill in a city with no river, so as soon as the engine's uses moved beyond the ones water and horses could also serve, the second-best option got much worse and the saving got much larger. The lesson to take is that a counterfactual is always relative to an alternative, and quoting one without naming that alternative is close to meaningless.
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.