Otto von Guericke

How to use this course

Otto von Guericke spent most of his working life as a city official. He was an engineer, a mayor and a diplomat of Magdeburg, a city that had been almost wiped out in 1631. In the time left over he built the first air pump, settled by experiment an argument about empty space that was two thousand years old, and staged the most famous demonstration of the seventeenth century: teams of horses failing to pull apart two hemispheres held together by nothing but the air.

Part I covers his education and the war that shaped his career. Part II turns his experiments into modern physics: hydrostatics, the mathematics of pumping, pressure forces on curved surfaces, the barometric formula, electrostatics and the question of what fills space. Part III follows how his work reached Robert Boyle and the rest of Europe, and how his long life ended.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Dates before 1700 are given in the Gregorian calendar unless marked; Protestant Magdeburg used the Julian calendar, ten days behind.

Timeline

A Magdeburg patrician, 1602–1625

Otto Gericke was born in Magdeburg on 30 November 1602 (20 November in the Julian calendar the city then used). His family belonged to the city’s patrician class; for generations its men had sat on the council and several had served as burgomaster. He was taught privately until he was fifteen.

In 1617 he went to the University of Leipzig to study arts. His father’s death in 1620 interrupted his studies; after a few weeks at Helmstedt he moved to Jena, where he studied law from 1621 to 1623. He then spent a year at Leiden. Besides law he took courses there in mathematics, physics and the art of fortification, the subjects that would later make him useful to armies and to his city. A tour of England and France completed his education, and he was back in Magdeburg in November 1625.

In 1626 he married Margaretha Alemann, from another council family. Their daughter died at birth and a younger son in childhood; their son Otto, born in 1628, outlived his father. By 1630 Gericke sat on the city council. A conventional civic career lay ahead, and the Thirty Years’ War, under way since 1618, destroyed it.

The destruction of Magdeburg, 1631

Magdeburg was a leading Protestant city, and in 1630 it allied itself with the invading king of Sweden, Gustavus Adolphus. Imperial and Catholic League forces under Count Tilly besieged it. On 20 May 1631 they stormed the walls. The sack that followed was the worst atrocity of the war. Of more than 25,000 inhabitants, perhaps four in five died, and fire destroyed about 1,700 of some 1,900 buildings. The name of the city became a byword across Europe.

Gericke and his family escaped, but he lost everything he owned. He worked as a fortress engineer in Erfurt, then in 1632 returned to Magdeburg in Swedish service. One of his first tasks was to survey the ruins; his scale plan of the city survives. From 1636 to 1646 he served Saxony in the same capacity, rebuilding fortifications and bridges. To restore his family’s fortunes he also became a brewer.

These years explain much about his later science. He was a practical man who trusted machines, measurements and public demonstration, and he worked in German, in a city whose recovery depended on his reputation and connections.

Engineer, mayor, diplomat

In 1646 Gericke was elected one of Magdeburg’s four burgomasters, who rotated in office. His main political task was to defend the city’s independence. Magdeburg wanted the status of a free imperial city, answerable only to the emperor; its neighbours, Saxony and Brandenburg, wanted it as a subject town. Between 1642 and 1663 he travelled repeatedly as its envoy: to Dresden in 1642, to the negotiations of the Peace of Westphalia that ended the war in 1648, to the congress at Nuremberg in 1649–50 and to the Imperial Diet at Regensburg in 1653–54.

Diplomacy meant long weeks of waiting among princes and their scholars, and conversation turned to natural philosophy. The question of the day was whether empty space could exist. In 1643 Evangelista Torricelli’s mercury tube had produced an apparent vacuum, and Blaise Pascal’s experiments of 1647–48 had tied the height of the column to the weight of the air. Guericke approached the question as an engineer. If a vacuum was possible, he would make one, large enough to see and to work with.

Around 1647–50, back from Westphalia, he began. In 1652 he married his second wife, Dorothea Lentke. In 1654 he took his apparatus to the Diet at Regensburg (Lesson 11).

Nature’s horror of the void

For the general reader. For centuries scholars taught, following Aristotle, that nature abhors a vacuum, and that this is why water rises in a pump. Yet pump makers knew that no suction pump could lift water more than about ten metres. The limit has a simple cause. The pump does not pull the water. The weight of the atmosphere pushes it, and the atmosphere can only balance a column of water about ten metres high.

Hydrostatics

Derivation. Consider a horizontal slab of fluid of area \(A\) and thickness \(dz\). Its weight \(\rho g A\,dz\) is balanced by the difference of pressure forces on its faces, \(-A\,dp\). Hence \(dp/dz=-\rho g\), which integrates to the law. In the tube, the pressure at the open surface level is \(p_0\) outside and \(\rho g h\) inside (zero pressure above the column), so equilibrium requires \(\rho g h=p_0\).

With standard pressure \(p_0=101\,325\) Pa, mercury (\(\rho=13\,595\) kg/m\(^3\)) stands at 760 mm, and water at 10.33 m. A suction pump works by lowering the pressure above a water column; at best it lowers it to zero, and the column then rises to 10.33 m and no further.

From Torricelli to Pascal

Torricelli’s experiment of 1643 filled a glass tube with mercury and inverted it into a dish. The mercury fell to about 76 cm and left a space at the top. Was it empty? Plenists said it held subtle matter or vapour. Torricelli argued that the column was held up by the weight of the air, the “sea of air” at whose bottom we live. In 1648, at Pascal’s request, his brother-in-law Florin Périer carried a barometer up the Puy de Dôme and found the mercury lower at the summit. Guericke knew of this work only in outline when he began. His contribution was to make the vacuum large, to make it with a machine, and to show its effects with objects people could handle.

The air pump

For the general reader. Guericke first tried to pump water out of a sealed wooden cask, expecting empty space to remain. Air whistled in through the wood. He then pumped air out of a copper sphere, which suddenly crumpled with a bang. His third attempt, with a stronger, more nearly spherical vessel and a better pump, worked. Each stroke of the pump removed a fixed fraction of the air left inside.

The machine

Guericke’s pump, built around 1649–50, was a brass cylinder with a tight piston, worked by a long lever, with leather flap valves. On the down stroke a valve opened to the vessel and air from the vessel expanded into the cylinder; on the up stroke that valve closed and a second one let the air out. The joints were sealed under water, so that any leak drew in water instead of air.

Derivation. At the start of a stroke the gas at pressure \(p_{n-1}\) occupies \(V\). When the piston is withdrawn it occupies \(V+v\) at the same temperature, so by Boyle’s law (Lesson 07) its pressure is \(p_{n-1}V/(V+v)\). The valve to the vessel then closes, the cylinder’s contents are expelled, and the next stroke begins.

Reason. On the intake stroke the trapped gas expands from \(d\) to \(v+d\), reaching pressure \(p_0d/(v+d)\). The intake valve opens only if the vessel pressure exceeds this. When the two are equal, no gas leaves the vessel. Leaks, outgassing from wet leather and the vapour pressure of the sealing water set further limits. Guericke’s vessels probably reached a few percent of an atmosphere.

Why the first sphere collapsed

A small dent or flat spot greatly reduces the strength, which is consistent with Guericke’s experience. His later vessels were thicker and more carefully shaped.

The Magdeburg hemispheres

For the general reader. Two copper bowls, fitted rim to rim with a greased leather ring, fall apart at a touch. Pump the air out and they cling together so hard that teams of horses cannot separate them. Open a tap, let the air in, and they fall apart again. Nothing holds them. The air outside pushes them together, with a force equal to the weight of a small car.

The demonstrations

The experiment is described in a letter of 1657 and in Gaspar Schott’s book of the same year. It was performed in Magdeburg between July 1656 and August 1657, with eight horses on each side, and was repeated in Berlin in 1663 before the Elector Frederick William, with 24 horses. Popular accounts often place the horse experiment at Regensburg in 1654, where Guericke did show his vacuum experiments; the documentary record for the horses at Regensburg is weaker. Guericke described the hemispheres as three-quarters of a Magdeburg ell across, roughly 40–50 cm. The originals are in the Deutsches Museum in Munich.

Proof. Use spherical coordinates with the axis along \(z\). The surface element is \(dA=r^2\sin\theta\,d\theta\,d\phi\), and the pressure force on it is normal to the surface. By symmetry the horizontal components cancel. The axial component of the force on \(dA\) is \(\Delta p\cos\theta\,dA\), so

The result is the pressure times the projected area. It also follows without integration: a closed surface in a uniform pressure feels zero net force, so the force on the hemisphere must balance the force on the flat disc that would close it.

For \(r=0.25\) m and a perfect vacuum, \(F=\pi(0.25)^2\times101325=19.9\) kN, the weight of about two tonnes. A strong draft horse can exert a few kilonewtons in a short pull, so eight horses on a good footing come close to the force needed. The real experiment was a near thing, which made it all the more convincing.

The weight and spring of the air

For the general reader. Guericke weighed a glass globe full of air, pumped it out and weighed it again. It was lighter. Air has weight. He also saw that the little air left in a pumped vessel did not sit in a corner but filled the whole space. Air is springy: it expands to fill whatever room it is given. Together these two facts explain why the atmosphere thins out as one climbs.

Weighing air

Guericke’s “air balance” of about 1650 compared a vessel with and without its air. The mass difference is \(\Delta m=\rho_aV\), where \(\rho_a\approx1.2\) kg/m\(^3\) at room conditions. He also hung an evacuated globe in a balance against a counterweight and watched the balance shift as the weather changed, a use of buoyancy to detect changes in air density.

The spring of the air

Guericke observed that air expands to fill an evacuated space and that its pressure falls as it does so. The quantitative law was found by Robert Boyle and Richard Towneley and published by Boyle in 1662, using the improved pump of Robert Hooke.

An atmosphere of finite height

Guericke argued that the air, being heavy and springy, is compressed most at the bottom and grows thinner upwards until it fades into empty space. Combining the hydrostatic law with the ideal gas law makes this precise.

Derivation. \(dp/dz=-\rho g=-\dfrac{Mg}{RT}\,p\). Separating variables and integrating from \(0\) to \(z\) gives the formula. For air, \(M=0.029\) kg/mol, and at \(T=288\) K the scale height is \(H=8.4\) km. The total mass above unit area is \(p_0/g\approx10\) t/m\(^2\), the same as a homogeneous layer of sea-level density \(H\) thick.

The water barometer and the weather

For the general reader. Guericke built a barometer filled with water, about ten metres tall, against the wall of his house. Watching it day by day, he saw that the air’s pressure rises and falls with the weather. In 1660 a sudden drop warned him of a violent storm, which arrived a few hours later. Weather forecasting from pressure had begun.

A tall, sensitive instrument

A water column moves 13.6 times as far as a mercury column for the same change in pressure. A change of 1 hPa, imperceptible in a mercury tube (0.75 mm), moves water by about 1 cm. Guericke later described a barometer and its use in forecasting in Book III of Experimenta nova, and he urged a network of observers to collect pressure readings across the country.

The space above a water column is not empty: it fills with water vapour at the saturation pressure \(e_s(T)\), which varies strongly with temperature. A water barometer is therefore also a crude thermometer, an effect that complicated Guericke’s readings.

Why pressure predicts weather

Air flows from high to low pressure, but on a rotating Earth it is deflected until, away from the ground, the pressure-gradient force is balanced by the Coriolis force. Falling pressure signals an approaching low, with converging, rising air, clouds and strong winds.

The balance follows from setting the Coriolis acceleration \(-f\,\hat k\times\mathbf v\) equal and opposite to the pressure-gradient acceleration \(-\nabla_h p/\rho\). It was formulated in the nineteenth century; Guericke worked purely empirically.

The sulphur globe

For the general reader. Around 1663 Guericke cast a ball of sulphur in a glass flask, broke away the glass, mounted the ball on an axle, and rubbed it with his dry hand as it turned. The ball attracted feathers, chaff and paper, and a feather that had touched it was then pushed away. Guericke thought he was showing the hidden forces by which the Earth holds things. Today the globe is counted among the first machines for producing static electricity.

What Guericke saw

The experiments are described in Book IV of Experimenta nova (1672). The rubbed globe attracted light bodies; light bodies that touched it were then repelled; a feather could be kept floating above it. Guericke read these effects as instances of the virtutes mundanae, cosmic powers by which a celestial body attracts, repels and keeps its parts. Robert Boyle repeated the experiments for the Royal Society in late 1672 and early 1673. Guericke did not separate electricity from his cosmic forces, so historians debate how far he can be credited with the first electrical machine. The physics of what he saw is clear.

A feather that touches the globe picks up some of its charge. Now it carries the same sign, and the Coulomb repulsion pushes it away. If it touches a neutral or grounded object it loses the charge and is attracted again. This sequence, attraction, contact, repulsion, is what Guericke recorded.

A limit on the charge

Air breaks down when the field exceeds about \(E_b\approx3\) MV/m. A sphere of radius \(R\) with charge \(Q\) has surface field \(E=Q/(4\pi\varepsilon_0R^2)\), so the charge is limited to \(Q_{\max}=4\pi\varepsilon_0R^2E_b\). Discharge before that limit shows up as faint crackling and sparks.

Empty space and the cosmos

For the general reader. Guericke’s vacuum was not only a laboratory curiosity. He believed it was the same thing as the space between the planets and stars: an empty, boundless container, distinct from the matter in it. The Earth and the planets move through it, held together by their own forces, and the air is a thin envelope that the Earth carries with it.

The plan of the book

Experimenta nova has seven books: on the world and its systems; on empty space; on his own experiments, including the pump and the barometer; on the cosmic powers; on the Earth and the Moon; on the planetary system; and on the fixed stars and their bounds. Experiments occupy the middle; the frame is cosmological.

Guericke’s cosmos

Guericke was a convinced Copernican. Following William Gilbert and Johannes Kepler, he held that celestial bodies act on one another across empty space through powers of a magnetic kind, and that the Sun’s rotating power drives the planets. The fixed stars, he argued, are suns, possibly with their own planets. Space itself, as distinct from created matter, has no bounds. He also suggested that the return of comets should be calculable. Much of the detail, such as circular concentric orbits, did not survive Isaac Newton’s Principia of 1687, published the year after his death. The separation of matter from empty space, with forces acting across it, did.

Regensburg, Schott and Boyle, 1654–1663

At the Imperial Diet in Regensburg in 1654, Guericke showed his vacuum experiments to Emperor Ferdinand III and the assembled princes, in public demonstrations on the city’s Haidplatz. Johann Philipp von Schönborn, Archbishop-Elector of Mainz and Prince-Bishop of Würzburg, bought one set of apparatus and gave it to the Jesuit college at Würzburg.

There it came into the hands of Gaspar Schott, a Jesuit professor of mathematics and a student of Athanasius Kircher. Schott began corresponding with Guericke in 1656 and in 1657 printed an account of the “Magdeburg experiment” as an appendix to his Mechanica hydraulico-pneumatica. It was Guericke’s first appearance in print, and it was in Latin, so it travelled. Schott’s Technica curiosa of 1664 carried more of the experiments, including the horse teams.

In England, Robert Boyle read Schott’s book. With Robert Hooke he built a more convenient pump, with a glass receiver through which experiments could be watched, and in 1660 published New Experiments Physico-Mechanical, Touching the Spring of the Air. A Latin edition reached Guericke. Boyle’s pump, more versatile than Guericke’s, became the standard instrument of the new experimental science. In November 1663 Guericke demonstrated his own apparatus to the Elector Frederick William in the Elector’s library in Berlin, using 24 horses, and was granted a pension.

Experimenta Nova and the last years, 1663–1686

Guericke finished the manuscript of his own book in 1663, but it appeared only in 1672, printed in Amsterdam: Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio, dedicated to the Elector of Brandenburg. Its plates of horse teams and men straining at ropes became some of the most reproduced images in the history of physics.

Politics continued alongside. In 1666 he was first signatory for Magdeburg of the Treaty of Klosterberg, under which the city accepted a Brandenburg garrison and paid dues to the Elector, ending its hopes of independence. On 4 January of the same year Emperor Leopold I raised him to the nobility, and he changed the spelling of his name from Gericke to Guericke. He also corresponded with Gottfried Wilhelm Leibniz. He withdrew from the burgomaster’s office in 1676 and was formally released in 1678.

In 1681, during an outbreak of plague in Magdeburg and in a dispute over his tax exemption, he moved with Dorothea to Hamburg, where his son lived. He died there on 21 May 1686 (11 May, Julian), aged 83. His body was taken back to Magdeburg for burial.

Legacy

• Physics: the first air pump, and the experimental demonstration that the effects ascribed to nature’s horror of the void are effects of atmospheric pressure. Boyle, Hooke and Christiaan Huygens built on his machine.
• Meteorology: one of the first to use pressure changes to forecast weather, and an early advocate of coordinated observation.
• Electricity: the rubbed sulphur globe, ancestor of the frictional electrical machines of the eighteenth century.
• Honours: the Otto von Guericke University of Magdeburg bears his name; his bust stands in the Walhalla near Regensburg; a lunar crater and the asteroid (11537) Guericke are named after him; his statue stands before Magdeburg’s town hall.

Sources and further reading

Biography

1. Otto von Guericke, Wikipedia.
2. Otto von Guericke, German Wikipedia (detailed chronology).
3. Linda Hall Library, Scientist of the Day: Otto von Guericke.
4. Science Story Telling, Background: Otto von Guericke (PDF).
5. D. Schneider, Otto von Guericke: Ein Leben für die Alte Stadt Magdeburg, Teubner, 1997.
6. P. Rubini, Leibniz und Guericke, 2019.

Physics

1. O. von Guericke, Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio, Amsterdam, 1672. English translation by M. G. Foley Ames, The New (So-Called) Magdeburg Experiments, Kluwer, 1994.
2. G. Schott, Mechanica hydraulico-pneumatica, Würzburg, 1657.
3. Magdeburg hemispheres, Wikipedia.
4. R. Boyle, New Experiments Physico-Mechanical, Touching the Spring of the Air, Oxford, 1660.
5. S. Shapin and S. Schaffer, Leviathan and the Air-Pump, Princeton University Press, 1985.
6. W. E. K. Middleton, The History of the Barometer, Johns Hopkins Press, 1964.
7. J. L. Heilbron, Electricity in the 17th and 18th Centuries, University of California Press, 1979.