James Watt

How to use this course

James Watt did not invent the steam engine. Thomas Newcomen’s atmospheric engine had pumped water from mines since 1712. What Watt did, starting in 1765, was to find out by measurement why that engine wasted most of its fuel, and to redesign it from the physics up. His separate condenser cut fuel consumption by roughly three quarters. In the next twenty years he made the engine turn wheels, push on both strokes, use steam expansively, guide its piston with a linkage and regulate its own speed. With his partner Matthew Boulton he sold it across Britain, and his name became the unit of power.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Part II follows Watt’s inventions in roughly the order he made them. The last lesson connects his engine to the theory of Sadi Carnot, who set out in 1824 to explain the machine Watt had built. For the physics of latent heat see also the course on Joseph Black.

Timeline

Greenock and London, 1736–1756

James Watt was born in Greenock, a port on the Firth of Clyde, on 19 January 1736. His father, also James Watt, was a shipwright, shipowner and contractor, and served as a magistrate of the town. His mother, Agnes Muirhead, came from a well-connected family. Several of the couple’s children died young, and James himself was often ill as a child, so much of his early teaching was done at home. He later attended Greenock grammar school, where he showed an aptitude for mathematics.

The boy spent much of his time in his father’s workshop, where ships’ instruments, cranes and fittings were made and repaired. He learned to work wood and metal and to make models. When his father’s business declined, an instrument maker’s trade seemed a sound choice. In 1754 he went to Glasgow, and in 1755, after his mother’s death, to London.

The London instrument makers were organized in guilds and expected a seven-year apprenticeship. Watt found a master willing to teach him for a fee and spent a year learning to make quadrants, compasses, scales and other mathematical instruments, working long hours and avoiding the press gangs that took young men for the navy. In 1756, his health strained, he returned to Scotland with a set of tools and the skills of a trained maker.

Instrument maker to the university, 1757–1765

Watt wanted to set up in Glasgow, but the Glasgow guild of hammermen refused to admit him because he had not served a full apprenticeship. The University of Glasgow, outside the guild’s jurisdiction, solved the problem. A consignment of astronomical instruments had arrived for the university and needed cleaning and repair, and in 1757 Watt was given a workshop within its walls and the title of mathematical instrument maker to the university. From 1759 he also ran a shop in the town in partnership with John Craig, making instruments and even musical instruments.

The workshop placed him among the professors. Joseph Black, then lecturer in chemistry, was working out his doctrine of latent heat and became Watt’s friend and adviser. John Robison, a student who later held the chair of natural philosophy at Edinburgh, introduced him to the idea of a steam carriage. Watt read widely in mechanics and chemistry and taught himself enough German and Italian to follow the technical literature.

In 1763–64 the university asked him to repair its working model of a Newcomen engine, used in the natural philosophy class. The model ran for only a few strokes before it exhausted its boiler, although the boiler was proportioned like those of full-sized engines. Watt treated this as a scientific problem. He measured how much steam the engine used, how much water a given weight of steam could heat, and how the pressure of steam rose with temperature. In July 1764 he married his cousin Margaret Miller. In May 1765, walking across Glasgow Green on a Sunday afternoon, he saw the solution (Lesson 05).

Roebuck, surveying and Boulton, 1765–1775

An idea is not an engine. To build a full-sized machine Watt needed money, skilled workmen and cylinders bored more accurately than any foundry could manage. Black introduced him to John Roebuck, a physician and industrialist who had founded the Carron ironworks. Roebuck paid Watt’s debts and the costs of a patent in return for a two-thirds share. Watt built a trial engine at Roebuck’s house at Kinneil, near Bo’ness, but its cylinder leaked badly and the work went slowly. The patent, for a method of lessening the consumption of steam and fuel in fire engines, was granted on 5 January 1769.

Meanwhile Watt had to earn a living. From 1766 to 1774 he worked as a land surveyor and civil engineer, surveying canal routes, harbours and river improvements in Scotland. Among other projects he surveyed a route between Fort William and Inverness that anticipated the Caledonian Canal, and he worked on the Monkland Canal near Glasgow. He disliked the work, the haggling with contractors and the travel, and suffered from headaches and low spirits for much of his life.

In 1773 two blows fell. Margaret died in childbirth while Watt was away surveying, leaving two young children. Roebuck went bankrupt, and his share in the patent passed to one of his creditors, Matthew Boulton, owner of the Soho Manufactory near Birmingham. Boulton had the capital, the workforce and the business instinct that Watt lacked. In 1774 Watt moved to Birmingham, and in 1775 Boulton secured an Act of Parliament extending the patent to 1800. The partnership of Boulton & Watt began. John Wilkinson’s new method of boring cannon gave them cylinders true to a fraction of an inch, and in March 1776 the first engine began pumping at Bloomfield Colliery, Tipton.

The Newcomen engine and latent heat

For the general reader. Newcomen’s engine worked by making a vacuum. Steam filled a cylinder under a piston; a jet of cold water condensed it; the air outside then pushed the piston down, and a beam pulled up a pump rod in the mine. The trouble was that the cold jet chilled the cylinder itself, so the next charge of steam had to reheat the metal before it could fill the space. Watt measured this loss and found it enormous.

The atmospheric stroke

A piston of area \(A\) moves a distance \(L\) with atmospheric pressure \(p_0\) above it and residual pressure \(p_r\) below. The work per stroke is

The pressure \(p_r\) is the vapour pressure of water at the temperature of the cylinder after injection. To get a good vacuum the cylinder must be cold: at 60 °C the vapour pressure is about 0.2 atm, at 40 °C about 0.07 atm.

The heat budget

At each stroke the injection water cools the cylinder walls, the piston and the condensate. The next charge of steam condenses on them until they return to 100 °C, and only then does steam fill the cylinder. Watt found that his model consumed several times its own cylinder volume of steam at each stroke. He also measured that steam, when condensed, could heat about six times its own weight of water from cold to boiling. Black explained this as latent heat: about 540 calories per gram are released when steam condenses, against 100 calories to heat water from 0 °C to boiling.

The separate condenser

For the general reader. Watt’s solution was to stop condensing steam in the cylinder. Connect the cylinder to a separate vessel kept permanently cold. Steam rushes into the cold vessel and condenses there, leaving a vacuum behind it, while the cylinder stays as hot as the steam. A pump removes the water and air that collect in the condenser. With a jacket of steam around the cylinder and the top closed, Watt kept the cylinder hot all the time.

Why it works

The pressure of saturated steam depends only on temperature. If two connected vessels contain water vapour and one is colder, the vapour pressure in the cold one is lower, so vapour flows from the warm vessel into the cold one and condenses there until the pressure everywhere equals the vapour pressure of the coldest surface. The cylinder is therefore exhausted to the condenser pressure without being cooled.

The new budget

With the cylinder held at \(T_s\), the reheating loss of Lesson 04 disappears. Each stroke consumes the steam that fills the cylinder, plus small losses by conduction and leakage. The condenser can be kept cold, say at 40 °C, giving a better vacuum than the Newcomen engine could afford. The cost is the injection water, about seven times the weight of the steam, and the work of the air pump.

Watt’s law of steam

Watt also measured the total heat needed to raise water from cold and turn it into steam at different pressures. He concluded that it was nearly the same at all pressures, the latent heat falling as the boiling temperature rose. This rule, known as Watt’s law, was believed until the 1840s, when Henri Victor Regnault showed that the total heat increases slowly with temperature.

Expansive working and double action

For the general reader. If steam is let into the cylinder for only part of the stroke and then shut off, it continues to push the piston as it expands, with falling pressure. The engine does a little less work per stroke but much more work per pound of steam. Watt understood this by 1769 and patented it in 1782, together with the double-acting engine, in which steam pushes the piston both down and up.

Work with cut-off

Let steam at pressure \(p_1\) enter a cylinder of volume \(V\) during the first fraction \(1/r\) of the stroke, so the admitted volume is \(V_1=V/r\). Then the valve closes and the steam expands to \(V\). Watt assumed the expanding steam obeys Boyle’s law, \(pV=\text{const}\). Against a back pressure \(p_b\),

The gain grows without limit in theory, but slowly, and the back pressure, the larger cylinder required, and the cooling of the cylinder by expanding steam set a practical optimum. Watt’s engines usually worked at only a little above atmospheric pressure, and he distrusted high-pressure steam for reasons of safety. In practice the cylinder was jacketed, and the expansion was roughly isothermal, which is why Boyle’s law served.

Double action

In the double-acting engine, steam is admitted alternately above and below the piston, each side being opened to the condenser in turn. The engine produces power on both strokes, doubling the output of a cylinder of given size and making the motion far more uniform. But the piston now pushes as well as pulls, so the chain that connected the piston rod to the arc-headed beam of the pumping engine had to be replaced by a rigid connection. That problem led to the parallel motion of Lesson 07.

Rotary motion and parallel motion

For the general reader. Mines needed pumps, but mills needed shafts that turn. In 1781 Watt converted the beam’s rocking into rotation with a pair of gears, the sun and planet. In 1784 he found a way to guide the top of the piston rod in a nearly straight line using only hinged bars, so that it could push as well as pull. He later wrote that he was prouder of the parallel motion than of any other mechanical invention he had made.

Sun and planet

A crank was the obvious way to make rotation, but a patent on the use of a crank with a steam engine was held by James Pickard. Watt’s alternative, worked out with William Murdoch, fixed a gear (the planet) rigidly to the connecting rod and meshed it with a gear (the sun) on the output shaft. The planet’s centre is held on a circular path by a link.

Derivation. Let the planet centre move through angle \(\phi\) about the shaft. The rolling contact requires the arc rolled to match on both gears: \(R_s(\theta_s-\phi)=-R_p(\theta_p-\phi)\), where \(\theta\) are absolute rotation angles. The planet barely rotates (\(\theta_p\approx0\) on average), so over a full circuit \(\theta_s=\phi(1+R_p/R_s)\), and \(R_p/R_s=N_p/N_s\).

The straight-line linkage

Take two arms of length \(r\), pivoted at fixed points \((-r,\tfrac b2)\) and \((r,-\tfrac b2)\), so that in the middle position they are horizontal and point toward each other. Join their free ends by a coupler of length \(b\), vertical in the middle position. As the arms swing, each end of the coupler deviates from the vertical by about \(y^2/2r\), in opposite directions. At the midpoint of the coupler these errors cancel.

Why fifth order. The half-turn symmetry makes \(x\) an odd function of \(y\). The quadratic deviations of the two ends cancel at the midpoint, and a careful expansion shows that the cubic terms cancel too, leaving a fifth-order error. The coefficient can be checked numerically, and the hero figure is computed from the exact geometry. With unequal arms \(r_1,r_2\), the straight-line point divides the coupler in the ratio \(r_2:r_1\), lying nearer the end of the longer arm.

Watt combined this linkage with a pantograph so that the straight-line point could be placed over the piston rod while the arms fitted within the beam. Watt chose his proportions by trial. The question of how to choose them optimally led Pafnuty Chebyshev in the 1850s to the theory of best uniform approximation, and later geometers to ask whether any linkage could draw an exact straight line, which Charles-Nicolas Peaucellier answered in 1864.

The governor and feedback

For the general reader. A mill engine must turn at a steady speed while the load changes. Millwrights already used spinning weights to regulate windmills. In 1788 Watt adapted the idea: two heavy balls on hinged arms spin with the engine; if it speeds up, the balls fly outward and rise, and a linkage partly closes the steam valve. The engine controls itself. The device became the emblem of feedback control.

The conical pendulum

A ball of mass \(m\) on a light arm of length \(l\), hinged on a vertical shaft rotating at angular speed \(\omega\), settles at angle \(\theta\) from the vertical. In the rotating frame the centrifugal force \(m\omega^2l\sin\theta\) balances the horizontal component of tension, and gravity the vertical component:

where \(h\) is the depth of the balls below the hinge. The height of the balls is a measure of speed, and a linkage converts it into a valve setting.

Engine and governor

Let the shaft have moment of inertia \(J\), and let the steam torque be \(\tau_s=k\,u\) for valve opening \(u\), against a load torque \(\tau_L\). The governor sets \(u=u_0-K(\omega-\omega_0)\). Then

This permanent offset, called droop, is a property of all proportional controllers. James Clerk Maxwell, in On governors (1868), distinguished such moderators from true governors with integral action, and showed that when the inertia of the governor itself and the valve linkage are included, the equations become third order and the engine can oscillate, or hunt, if the gain is too high.

Horsepower, duty and the indicator diagram

For the general reader. To sell engines Watt needed to say how much work they did. He defined a horsepower to compare engines with the horses they replaced, measured fuel economy by the duty, and in 1796, with his assistant John Southern, built an instrument that drew the pressure in the cylinder against the motion of the piston. The area of that drawing is the work of a stroke. The firm kept the indicator a trade secret for decades; later it became the founding diagram of thermodynamics.

Horsepower

Around 1782–83 Watt estimated the work of a mill horse walking a circle of radius 12 ft, about 144 turns an hour, against a pull of 180 lbf, and rounded the result to 33,000 ft·lbf per minute.

Boulton & Watt charged for their pumping engines a premium of one third of the value of the coal saved compared with a Newcomen engine of equal work, which required accurate duty measurement. Watt engines of the late 1770s typically gave several times the duty of ordinary atmospheric engines.

The indicator

The indicator was a small cylinder connected to the engine cylinder, with a piston held by a spring, so that its rise measured the steam pressure. A pencil on the indicator piston drew on a board moved back and forth by the engine’s beam, in step with the main piston. The closed curve showed admission, cut-off, expansion and exhaust, and revealed leaky valves or poor vacuum at a glance. Émile Clapeyron’s 1834 use of the pressure–volume diagram for Carnot’s cycle put the same picture at the centre of thermodynamics.

From Watt’s engine to thermodynamics

For the general reader. Watt improved the engine by eliminating wasteful flows of heat, keeping the hot parts hot and the cold parts cold, and by letting steam expand. In 1824 Sadi Carnot explained why these were the right moves: an engine wastes motive power whenever heat passes between bodies at different temperatures without doing work, and its best possible efficiency is set by the temperatures of its hot and cold sides. Watt’s condenser had created the cold side.

Reading Watt through Carnot

In the Newcomen engine the same metal is heated by steam at 100 °C and cooled by water at perhaps 20 °C at every stroke. Heat flows across a large temperature difference without doing work: a large irreversibility. Watt’s separate condenser places this flow in a vessel whose temperature never changes, and the jacket keeps the cylinder at the steam temperature. Expansive working lets the steam cool while doing work instead of being dumped hot into the condenser. Each of Watt’s improvements reduces the entropy produced per cycle.

Watt’s steam rarely exceeded about 100–120 °C. With a condenser near 40 °C the Carnot limit is only about 16–20%. To go further, the upper temperature had to rise, and that meant higher pressures, which Watt resisted. Richard Trevithick in Cornwall and Oliver Evans in America built high-pressure engines from about 1800, after the Watt patent expired, and Cornish engines combining high pressure, expansion and Watt’s condenser reached far higher duties in the 1830s.

Soho, patents and the Lunar Society, 1775–1800

Boulton & Watt did not at first manufacture whole engines. They supplied drawings, supervised erection and provided precision parts, notably valves; cylinders came from John Wilkinson and the rest was built by the purchaser. The first two engines worked in 1776, at Bloomfield Colliery and at Wilkinson’s blast furnace at Broseley. From 1777 the Cornish copper and tin mines, where coal was expensive, became the main market. Watt spent long periods in Cornwall, where William Murdoch was the firm’s resident engineer, and where mine owners resented paying the premium.

Around 1776 Watt married Ann MacGregor, daughter of a Glasgow dyer. The rotative engines of the 1780s opened the market of mills: the Albion Flour Mills in London, cotton mills, breweries and ironworks. Watt also patented a letter-copying process in 1780 that remained in office use for over a century, and in 1786, after visiting Claude Louis Berthollet in Paris, introduced chlorine bleaching to Britain through his father-in-law’s business.

In Birmingham Watt joined the Lunar Society, an informal club that met monthly near the full moon, so that members could ride home by moonlight. Its members included Boulton, Erasmus Darwin, Joseph Priestley, Josiah Wedgwood and William Withering. In 1783, in letters to Priestley, Watt argued that water is not an element but a compound of the gases now called hydrogen and oxygen. Henry Cavendish reached the same conclusion from his experiments, and a priority dispute was argued long after both men had died. Watt became a fellow of the Royal Society of Edinburgh in 1784 and of the Royal Society of London in 1785.

Defending the patent occupied the 1790s. The firm sued engine builders who used separate condensers without licence, among them Edward Bull and later Jabez Carter Hornblower, and in 1799 the courts upheld Watt’s patent. Meanwhile in 1795–96 the partners built the Soho Foundry and began making complete engines, and there Watt and John Southern devised the indicator. By 1800 the firm had built several hundred engines. When the patent expired in 1800, Watt retired, leaving the business to his son James and Boulton’s son Matthew Robinson Boulton.

Heathfield, death and legacy, 1800–1819

Watt’s retirement at Heathfield Hall, Handsworth, near Birmingham, was more contented than his working life. He travelled, kept up a wide correspondence, and filled a garret workshop with tools and experiments, including machines for copying sculpture. His son Gregory, a promising geologist, died in 1804. Glasgow gave him an honorary doctorate of laws in 1806, and the French Academy of Sciences made him a foreign associate in 1814. In 1816 he gave money to Greenock for a collection of scientific books, the origin of the town’s Watt library. He died at Heathfield on 25 August 1819, aged 83, and was buried at St Mary’s Church, Handsworth, near Boulton.

His garret workshop was left nearly untouched after his death and is now preserved at the Science Museum in London.

Legacy

• Engineering: the separate condenser, the double-acting rotative engine, expansive working, the parallel motion and the indicator made the steam engine a general source of power for factories, and later for ships and railways. The firm’s methods of measurement, testing and drawing helped create mechanical engineering as a profession.
• Physics: his measurements on steam, the indicator diagram and the engine itself were the raw material from which Carnot, Clapeyron and later Clausius and Kelvin built thermodynamics.
• Control and mechanism: the governor led to Maxwell’s theory of feedback; the parallel motion led to Chebyshev’s approximation theory and the study of linkages.
• Honours: the watt, proposed as a unit of power in 1882, was adopted by the British Association in 1889 and by the International System of Units in 1960. Heriot-Watt University in Edinburgh bears his name, and his portrait appeared on the Bank of England £50 note from 2011, alongside Boulton.

Connections

People linked to James Watt across this collection. A name without a link has no page here yet. See James Watt in the network of all 337 lives →

Influenced by

• Thomas Newcomen

Influenced

• James Clerk Maxwell
• Pafnuty Chebyshev
• Sadi Carnot

Colleagues and collaborators

• Joseph Priestley
• Claude Louis Berthollet 1786
• John Roebuck 1765-1773
• John Southern 1796
• John Wilkinson
• Matthew Boulton 1775-1800
• William Murdoch 1777-1800

Rivals

• Henry Cavendish
• Jabez Carter Hornblower
• John Smeaton
• Richard Trevithick

Friends

• Joseph Black 1757-1799
• Joseph Priestley
• Erasmus Darwin
• John Robison
• Josiah Wedgwood

Family

• Gregory Watt

Also mentioned in this life

• Robert Boyle
• Rudolf Clausius
• William Thomson, Lord Kelvin
• William P. Thurston

Fields

• heat 3 lives

Sources and further reading

Biography

1. James Watt, Wikipedia (with extensive references).
2. Science Museum Group, James Watt, 1736–1819.
3. J. P. Muirhead, The Life of James Watt, John Murray, 1858.
4. H. W. Dickinson and R. Jenkins, James Watt and the Steam Engine, Clarendon Press, 1927.
5. R. L. Hills, James Watt, 3 vols., Landmark, 2002–2006.
6. J. Uglow, The Lunar Men, Faber, 2002.

Physics and engineering

1. Watt steam engine, Wikipedia.
2. Horsepower, Wikipedia.
3. John Southern, Wikipedia; Science Museum Group, Watt’s steam engine indicator.
4. Institution of Civil Engineers, Smeaton vs Watt: the race to improve the steam engine.
5. D. S. L. Cardwell, From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age, Heinemann, 1971.
6. J. C. Maxwell, On governors, Proc. R. Soc. London 16 (1868).
7. O. Mayr, The Origins of Feedback Control, MIT Press, 1970.
8. E. S. Ferguson, Kinematics of mechanisms from the time of Watt, United States National Museum Bulletin 228 (1962).
9. S. Carnot, Reflections on the Motive Power of Heat, trans. R. H. Thurston, 1890.