Luigi Galvani

How to use this course

Luigi Galvani was a physician and anatomist, and his frogs are the most famous experimental animals in the history of physics. In 1791 he reported that a dissected frog’s legs contracted when nerve and muscle were joined by a metal arc, and he argued that the animal itself was a source of electricity. Alessandro Volta answered that the electricity came from the metals, and the pile he built to prove it launched the age of electric current. History long scored the dispute as a victory for Volta. Physiology later showed that Galvani had found something just as real: every nerve and muscle cell is a charged capacitor.

This course tells both stories. Parts I and III follow Galvani’s life in Bologna. Part II follows his experiments in order, and for each one explains the physics with modern tools: capacitance, electrochemical potentials, the Nernst equation, cable theory and the Hodgkin–Huxley model. The companion course on Volta covers the contact theory and the pile; Lesson 07 here takes the physiologist’s side of the same quarrel.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Galvani wrote before the electron, before Ohm’s law and before ions were understood, so each lesson also says what he actually saw and how he described it.

Timeline

Bologna, 1737–1759

Luigi Galvani was born in Bologna on 9 September 1737. The city was the second capital of the Papal States, governed jointly by a papal legate and its own senate, and proud of the oldest university in Europe. His father, Domenico Galvani, was a goldsmith; his mother was Barbara Caterina Foschi. An older half-brother, Francesco, trained in canon law and became a lawyer, and it was in the family house that Luigi would die sixty-one years later.

He was educated by the Oratorian fathers of San Filippo Neri, and religion remained central to his life. In 1780 he joined the Franciscan Third Order as a lay member.

The medical school

In 1754 Galvani entered the University of Bologna to study medicine and philosophy. His teachers included Jacopo Bartolomeo Beccari, a physician and chemist best known for discovering gluten in wheat flour, the surgeon and obstetrician Giovanni Antonio Galli, and the anatomist and physicist Domenico Gusmano Galeazzi. He also attended lectures on natural history and experimental physics. In Bologna these subjects were taught not only in the old university but also at the Istituto delle Scienze, founded in 1711 by Luigi Ferdinando Marsili, which had laboratories, collections and an observatory. On 15 July 1759 Galvani received his degree in medicine and philosophy.

Anatomist of the Institute, 1759–1780

A Bologna medical graduate who wanted to teach had to defend theses in public. In 1762 Galvani published and defended De ossibus, a set of theses on the anatomy and physiology of bones, and began to lecture. In the same decade he married Lucia Galeazzi, the daughter of his teacher. Lucia was educated in science and is remembered as an active partner in his laboratory. In later years his niece Camilla and his nephew Giovanni Aldini helped in the experiments.

In March 1766 the Bologna senate appointed him curator and demonstrator of the anatomical museum of the Istituto delle Scienze, with its famous wax models. In the same year he joined the Benedettini, the paid academicians of the Institute’s Academy of Sciences whose places had been endowed by Pope Benedict XIV, himself a Bolognese. Membership obliged him to present a memoir to the Academy each year. In December 1775 he became Galeazzi’s adjunct in anatomy at the university, and in 1782 he was elected professor of obstetrics at the Institute, a post he held for some sixteen years. He was a careful teacher of surgery and childbirth, and a busy practising physician.

Comparative anatomy

His first research was in comparative anatomy. He studied the structure of the bird’s ear, publishing his results on hearing in birds shortly before the anatomist Antonio Scarpa published on the same subject. This work trained him in fine dissection and in reading physiology from structure. It also led him to the nervous system, and to the question that would occupy the rest of his life: what is the agent that travels along a nerve and makes a muscle contract?

Earlier answers ranged from Galen’s animal spirits to Albrecht von Haller’s doctrine of irritability, which separated the irritability of muscle from the sensibility of nerve. By the 1770s several naturalists suspected that the nervous agent was electrical. The torpedo ray and the electric eel had been shown to give real electric shocks, and John Walsh had demonstrated in 1772 that the torpedo’s shock was electrical. Galvani set out to test the idea directly.

Electricity enters the laboratory, 1780–1791

Late in 1780 Galvani began a long series of experiments on frogs. The standard preparation was a frog cut across the body, keeping the lower spinal cord, the crural (sciatic) nerves and the legs. Frogs were cheap, survived dissection well, and their leg muscles stayed excitable for hours. Galvani’s laboratory had an electrostatic machine, Leyden jars and the other apparatus of eighteenth-century electricity. For the following decade he spent much of every month at the bench and kept detailed notes, many of which survive in the archives of the Bologna Academy of Sciences.

The first result, which he later placed at the opening of his book, came by chance. A prepared frog lay on a table near the electrical machine. When one person touched the nerves lightly with a scalpel while another drew a spark from the machine’s conductor, the legs contracted violently, though the spark did not touch the frog. The popular story that Lucia noticed the effect cannot be checked. Galvani’s account says only that one of those helping him saw it.

He then varied every condition. The effect needed a conductor in contact with the nerve, and it worked at a distance of several metres from the machine. It worked with Leyden jars as well as with the machine. Next he took his frogs outside to see whether lightning would do the same, and during these experiments he found that contractions could occur with no external electricity at all, when nerves and muscles were joined by metal. Lessons 04 to 06 follow these three steps.

The work took more than ten years to reach print. The result, De viribus electricitatis in motu musculari commentarius (Commentary on the forces of electricity in muscular motion), appeared in 1791 in the proceedings of the Bologna Institute and Academy, with plates showing the frogs, the machines and the metal arcs. It was divided into four parts: the effects of artificial electricity, the effects of atmospheric electricity, the effects of animal electricity, and Galvani’s conjectures and conclusions. Copies went to scientists across Europe, and within months the frog experiments were being repeated in Italy, France, Britain and the German states.

Leyden jars and the distant spark

For the general reader. Galvani’s first discovery was strange: a spark drawn from a machine across the room made a frog’s legs jump, provided a metal blade touched the nerve. Nothing visible crossed the gap. The explanation is electrostatic induction. A charged machine pulls charge onto nearby conductors, and when the spark suddenly discharges it, that induced charge rushes back, briefly passing through the nerve.

The instruments

An eighteenth-century electrical machine rubbed a glass globe or plate and collected the charge on an insulated metal conductor. A Leyden jar was a glass jar coated inside and outside with metal foil: in modern language, a capacitor whose dielectric is the glass.

The distant spark

Let the machine’s prime conductor stand at potential \(V_0\), and let the scalpel, the nerve and the frog form a conductor connected to ground through the frog’s tissue. The two conductors are coupled by a small mutual capacitance \(C_c\). While the machine is charged, the frog-side conductor carries an induced charge \(q\approx -C_cV_0\), drawn up from ground through the tissue so slowly that nothing happens. When a spark discharges the prime conductor in a fraction of a microsecond, the induced charge is released at once and returns to ground through the frog:

The current pulse is short and intense. A nerve is excited when enough charge passes through its membrane in a short time (Lesson 09), so a brief pulse of a few tens of nanocoulombs can suffice. Galvani found the effect needed a conductor touching the nerve, and that longer conductors worked better. Both follow from the model, since a larger conductor has a larger \(C_c\). Nineteenth-century physicists recognized here the first recorded detection of a rapidly changing electric field, an ancestor of Heinrich Hertz’s spark-gap experiments of 1887.

Storms, railings and metal arcs

For the general reader. If a spark in the laboratory could move a frog, could lightning? Galvani hung prepared frogs outdoors on a long wire and watched them twitch with each flash. Then he noticed that frogs hung by brass hooks on an iron railing also twitched in calm weather, whenever the hook touched the iron. That observation led him to animal electricity, and Volta to the battery.

Atmospheric electricity

Following Benjamin Franklin, Galvani raised a long conductor high on his house and attached it to the nerves of a frog, while a second wire ran from the legs down into well water. During storms the legs contracted at each lightning flash, often before the thunder arrived. In modern terms, the cloud charge produces a vertical field \(E\) near the ground; the raised conductor takes up a charge proportional to \(E\); and when a flash suddenly changes the field, the charge flows to ground through the frog.

The railing

Galvani had hung prepared frogs by brass hooks, passed through the spinal cord, on the iron railing of a terrace. Contractions occurred not only with lightning but also in fair weather when the hooks were pressed against the iron. Indoors, he laid a frog on an iron plate and pressed the hook in its spinal cord against the plate: the legs contracted again. Arcs of two different metals worked best; non-conductors such as glass or resin did nothing. He concluded that the source of the electricity was the frog, and that the metal merely closed the circuit.

Today the two-metal arc on moist tissue is understood as a short-circuited electrochemical cell. Each metal in contact with the salt solution of the tissue has its own electrode potential, and the difference drives a current through the arc and the tissue.

A single metal can also stimulate. Two pieces of the same metal differ slightly in surface condition, and the tissue at the two contacts differs in composition, so small emfs arise even in a “monometallic” arc. Galvani’s 1794 demonstration of contractions with a single metal therefore did not refute Volta, and Volta’s explanation of them did not refute Galvani (Lesson 07).

The muscle as a Leyden jar

For the general reader. Galvani’s explanation was bold. He proposed that each muscle fibre holds opposite charges on its inside and outside, like a Leyden jar, and that the nerve is the jar’s conductor. A metal arc from nerve to muscle surface discharges the jar, and the discharge makes the muscle contract. In outline this is the modern picture of the cell membrane, which is a capacitor with a charge of a few millivolts per nanometre across it.

Galvani’s hypothesis (1791)

In Part IV of the Commentarius Galvani argued that an animal electric fluid is secreted by the brain, carried by the nerves, and accumulated in the muscles. Each muscle fibre is charged with opposite electricities on its inner and outer surfaces, so that it behaves like a small Leyden jar. The nerve communicates with the inside of the fibre. When an arc connects the nerve to the outer surface, the jar discharges along the nerve and through the arc, and the passage of the fluid causes the contraction. Modern measurements show that the inside of a resting fibre is negative relative to the outside.

So Galvani’s Leyden jar exists, and its glass is a film of fat a few nanometres thick. The field inside it is several times the breakdown field of air, sustained only because the bilayer is an excellent insulator. The analogy breaks down in one important way. A Leyden jar stores charge put there by a machine, while the membrane maintains its own charge through ion pumps and selective channels (Lesson 08). Galvani’s “secretion by the brain” was wrong; the battery is in every cell.

Without metals: the injury current

For the general reader. Volta argued that the frog was only a detector and the metals were the source. To answer him, Galvani removed the metals. In 1794 he made a leg contract by letting its own nerve fall onto its muscle, and in 1797 by touching one frog’s nerve to another’s. Electricity was flowing from living tissue alone. The source is the difference in potential between injured and intact parts of the tissue, later called the injury current.

Volta’s objection

In 1792 Volta at first accepted animal electricity, then noticed that contractions were strongest with two different metals and that a bimetallic arc on his tongue produced a taste. He concluded that the electricity arose at the contact of dissimilar conductors, and that the frog’s nerve was merely an extremely sensitive electroscope. His law of contact tensions and its consequences are the subject of Lesson 07 of the Volta course.

The experiments without metals

Galvani’s anonymous treatise of 1794 on the use and activity of the conducting arc contained, in a supplement, the decisive test. He dissected a frog so that a long stretch of sciatic nerve remained attached to the leg, then lifted the nerve with a glass rod and let its cut end fall onto the thigh muscle. The leg contracted. No metal was involved anywhere. In the Memorie of 1797, addressed to the naturalist Lazzaro Spallanzani, he went further. He placed the cut surface of one sciatic nerve against the intact surface of the other, and both legs contracted. Only nervous tissue was in contact, ruling out any difference between nerve and muscle as the source. Emil du Bois-Reymond later called this the founding experiment of electrophysiology.

A simple equivalent circuit is a source of emf \(|V_m|\) with internal resistance \(r\) (the fibre interiors and the cut), driving current through an external path of resistance \(R\). The voltage that appears across the external path is

Because the surrounding fluid shunts much of the current, the measured injury potential is usually only a fraction of \(|V_m|\). Carlo Matteucci measured it with a galvanometer in the 1840s, and du Bois-Reymond made it the starting point of his electrophysiology.

Who was right?

Both. Volta was right that two metals on moist tissue form a source, and the pile proved it on a grand scale. Galvani was right that living tissue is itself a source, and his metal-free experiments proved that. Each side could explain away the other’s results with the concepts of the time. A full reconciliation required the electrode potential of metals in electrolytes and the membrane potential of cells, neither of which was understood before the late nineteenth century.

The resting potential

For the general reader. Why is the inside of a cell negative? Cells pump potassium in and sodium out, and their membranes at rest let potassium leak much more easily than sodium. Potassium ions drift outward until the charge they leave behind holds them back. The balance point is a voltage set by the ratio of concentrations, given by a formula due to Walther Nernst.

Derivation. At equilibrium the electrochemical potential \(\mu=\mu^\circ+RT\ln c+zF\phi\) is the same on both sides. Setting \(\mu_i=\mu_o\) gives \(RT\ln(c_i/c_o)=-zF(\phi_i-\phi_o)\), which is the formula. Equivalently, the Boltzmann factor \(c_i/c_o=e^{-zFV/RT}\) gives the relative population of an ion in two regions whose energies differ by \(zFV\) per mole.

The anion’s concentrations appear inverted because its charge is negative. When one permeability dominates, the equation reduces to that ion’s Nernst potential. The resting potential is not an equilibrium: sodium leaks in and potassium leaks out continuously, and the sodium–potassium pump, discovered by Jens Christian Skou in 1957, uses ATP to restore the gradients. Galvani’s Leyden jar is kept charged by a molecular machine.

Stimulation, threshold and cables

For the general reader. Galvani’s frogs responded to sparks, lightning, metal arcs and their own nerves. All these stimuli push current through a membrane. A nerve fires when its membrane is depolarized past a threshold, and how much current is needed depends on how long it flows: a brief spark needs a large current, a slow trickle a smaller one. Inside a long fibre the effect of a stimulus spreads only a short distance before leaking away.

Strength and duration

Model a patch of membrane as a capacitor \(C\) in parallel with a resistor \(R\), with time constant \(\tau=RC\). A current step \(I\) applied at \(t=0\) raises the potential as \(\Delta V(t)=IR(1-e^{-t/\tau})\). Excitation occurs if \(\Delta V\) reaches a threshold depolarization \(\Delta V_{th}\) by the end of the pulse.

This is why Galvani’s sparks and lightning worked so well: they delivered a fixed charge in a very short time, and for short pulses only the charge matters.

The cable equation

A long fibre of radius \(a\) has membrane resistance \(R_m\) times unit area (\(\Omega\,\mathrm m^2\)), membrane capacitance \(c_m\) per unit area, and axial resistivity \(\rho_i\). Let \(V(x,t)\) be the deviation of the membrane potential from rest. Conservation of current gives

In the steady state with a constant current injected at \(x=0\) into an infinite fibre, \(V(x)=V_0e^{-|x|/\lambda}\). The length constant \(\lambda\) is the distance over which a passive signal decays by a factor \(e\). William Thomson (Kelvin) derived the same equation in 1855 for the transatlantic telegraph cable.

The nerve impulse

For the general reader. Galvani imagined a fluid flowing through the nerve. What travels is a wave of discharge: the membrane briefly lets sodium rush in, the inside swings positive, and the change spreads to the next patch, which fires in turn. The wave moves at tens of metres per second, far slower than electricity in a wire, as Hermann von Helmholtz discovered in 1850 by timing frog muscles.

From Galvani to Hodgkin and Huxley

Leopoldo Nobili recorded a current in a frog with his astatic galvanometer in 1828. Matteucci measured injury currents in the late 1830s and 1840s. Du Bois-Reymond, from 1843, detected the “negative variation”, a transient drop of the injury current when a nerve was excited: the first record of the action potential. In 1902 Julius Bernstein proposed that the resting membrane is permeable mainly to potassium and loses this selectivity during excitation. In 1939 Alan Hodgkin and Andrew Huxley recorded inside a squid giant axon and found the potential overshooting zero during the impulse, which Bernstein’s theory could not explain. Their voltage-clamp experiments led to the model of 1952.

The impulse proceeds in four steps. Depolarization opens sodium channels quickly (\(m\) rises), sodium enters, and the potential rushes toward \(E_{Na}\): the overshoot. Then sodium channels inactivate (\(h\) falls) and potassium channels open (\(n\) rises), restoring the negative potential. During inactivation the membrane cannot fire again: the refractory period, which makes the impulse travel in one direction. Hodgkin and Huxley shared the 1963 Nobel Prize in Physiology or Medicine with John Eccles.

Controversy and the oath, 1791–1798

The Commentarius made Galvani famous almost overnight. A second edition appeared at Modena in 1792, with a dissertation and notes by his nephew Giovanni Aldini, who had graduated in physics at Bologna in 1782 and worked as his assistant. In Britain, Richard Fowler published a book of experiments on the new “influence” in 1793. In Germany the young Alexander von Humboldt performed hundreds of galvanic experiments, many on himself, and from 1797 published a two-volume study of stimulated muscle and nerve fibres that took a middle position.

Volta’s critique dominated the debate. Galvani, by temperament reserved and devout, disliked public polemic. He replied mainly through experiments and left much of the argument to Aldini. The anonymous treatise of 1794 and the Memorie of 1797 contained his strongest evidence, the contractions without metals (Lesson 07). They were read less widely than Volta’s letters, and the death of his wife Lucia in 1790 had already darkened these years.

The oath

In 1796 French armies under Napoleon Bonaparte occupied Bologna, ending papal rule. The city became part of the Cispadane Republic and then, in 1797, of the Cisalpine Republic. The new state required public employees, including university professors, to swear loyalty to its constitution. Galvani refused, holding that the oath conflicted with his religious convictions. He lost his university chair, his position at the Institute and his salary.

Deprived of his income, he moved into the family house where he had been born, then the home of his brother Francesco. Aldini and others petitioned for his reinstatement, and the authorities eventually agreed to restore him as an emeritus professor without requiring the oath. The decision came too late. Galvani died on 4 December 1798, aged 61. He was buried in the church of Corpus Domini in Bologna beside his wife.

Galvanism and its heirs

Eighteen months after Galvani’s death, Volta announced the pile. For most physicists it ended the argument: a stack of metals and wet cloth gave everything the frog had given, and much more. Volta himself, despite disagreeing with Galvani, called the new science of current electricity galvanism, and the name stuck.

Aldini carried his uncle’s cause across Europe. His most notorious demonstrations took place in London in January 1803, when he applied a powerful pile to the body of George Forster, just hanged at Newgate, and made the face and limbs move. He published his Essai théorique et expérimental sur le galvanisme in Paris in 1804. Such spectacles, and the debates over whether electricity might be the principle of life, formed part of the background to Mary Shelley’s Frankenstein (1818), whose 1831 introduction mentions galvanism.

The return of animal electricity

Galvani’s physiological claim was vindicated in stages. Nobili detected the frog current with a galvanometer in 1828. Matteucci, from the late 1830s, demonstrated muscle currents and the “induced twitch”, in which a contracting muscle excites a nerve laid across it. Du Bois-Reymond, who began publishing his Untersuchungen über thierische Elektricität in 1848, founded electrophysiology as a quantitative science and paid tribute to Galvani as its originator. The line runs on through Helmholtz’s measurement of conduction velocity, Bernstein’s membrane theory, Willem Einthoven’s electrocardiogram and Hans Berger’s electroencephalogram, to Hodgkin and Huxley.

Legacy

• Physiology: the discovery that nerves and muscles are electrically excitable and generate their own potentials. Every ECG, EEG and pacemaker descends from it.
• Physics: his frogs gave Volta the clue that led to the pile, and thus to electrochemistry and electromagnetism.
• Language: galvanism, the galvanometer, the galvanic cell, galvanization of iron and the verb “to galvanize”.
• Memorials: a nineteenth-century statue of Galvani contemplating a frog stands in Piazza Galvani in Bologna, and his instruments and papers are kept by the University of Bologna and its Academy of Sciences, which published his collected works in 1841.

Connections

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

Teachers and advisors

• Domenico Gusmano Galeazzi
• Jacopo Bartolomeo Beccari

Influenced by

• Benjamin Franklin

Influenced

• Alexander von Humboldt
• Carlo Matteucci
• Emil du Bois-Reymond

Colleagues and collaborators

• Lazzaro Spallanzani 1797

Rivals

• Alessandro Volta 1792-1798

Family

• Giovanni Aldini
• Lucia Galeazzi

Also mentioned in this life

• Ludwig Boltzmann
• Charles-Augustin de Coulomb
• Hermann von Helmholtz
• Heinrich Hertz
• William Thomson, Lord Kelvin
• Georg Simon Ohm

Fields

• physiology 5 lives

Sources and further reading

Biography

1. Luigi Galvani, Wikipedia; and the more detailed Italian article, Luigi Galvani, Wikipedia (Italian).
2. Galvani, Luigi, Complete Dictionary of Scientific Biography, via Encyclopedia.com.
3. University of Bologna, Scienza Giovane, Luigi Galvani.
4. Luigi Galvani, Encyclopaedia Britannica.
5. M. Piccolino and M. Bresadola, Shocking Frogs: Galvani, Volta, and the Electric Origins of Neuroscience, Oxford University Press, 2013.
6. M. Pera, The Ambiguous Frog: The Galvani–Volta Controversy on Animal Electricity, Princeton University Press, 1992.
7. M. Piccolino, Animal electricity and the birth of electrophysiology: the legacy of Luigi Galvani, Brain Research Bulletin 46 (1998).
8. Giovanni Aldini, Wikipedia.

Physics and physiology

1. L. Galvani, De viribus electricitatis in motu musculari commentarius, Bologna, 1791. Scan at the Internet Archive.
2. L. Galvani, Memorie sulla elettricità animale, Bologna, 1797. Scan at the Internet Archive.
3. L. Galvani, Opere edite ed inedite, Bologna, 1841. Scan at the Internet Archive.
4. Galvanism, Wikipedia.
5. A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952) 500–544.
6. B. Hille, Ion Channels of Excitable Membranes, 3rd ed., Sinauer, 2001.
7. J. Keener and J. Sneyd, Mathematical Physiology, 2nd ed., Springer, 2009 (Nernst and GHK equations, cable theory, Hodgkin–Huxley).
8. P. Nelson, Biological Physics, W. H. Freeman, 2004 (membrane potentials and nerve impulses for physicists).