# André-Marie Ampère

**André-Marie Ampère** (Lyons 20 January, 1775 – Marseilles 10 June, 1836) was a French physicist and mathematician. His most important contributions are Ampere's law, which describes the relation between electric current and magnetic field and Ampere's equation, which gives the force between two current carrying wires. The unit of electric current ampere is named after him.

## Biography

André-Marie did not receive a formal education—he was tutored by his farther—and was a child prodigy. At the age of thirteen he submitted his first mathematical paper. This work attempted to solve the problem of constructing a line of the same length as an arc of a circle.^{[1]} However, the work was refused and André-Marie realized that he had to become better skilled in mathematics. So, he read d'Alembert's article on the differential calculus in the Encyclopédie and undertook a study of works by Leonhard Euler and the Bernoullis (almost all these writings are in Latin). He started to read the 1788 edition of Lagrange's *Mécanique analytique* and later claimed that he was able to repeat all the calculations in it.

Four years after the French Revolution of 1789 Ampère's father was beheaded by the Jacobins.
The effect on André-Marie of his father's death was devastating. François Arago relates in his 1839 eulogy of Ampère^{[2]}, that during these days André-Marie found consolation in the memory of three peaks in his young life: His first communion, the reading of Antoine-Léonard Thomas' eulogy of René Descartes, and the taking of the Bastille. After the execution of his father André-Marie gave up his studies of mathematics and only regained his taste for the sciences after he fell in love with his future wife, Cathérine-Antoinette (Julie) Carron. They married on August 2, 1799 and their son Jean-Jacques was born in 1800. In 1802 Ampère was appointed teacher of physics and chemistry in Bourg-en-Bresse at l'École Centrale du Département de l'Ain (now the Lycée Lalande). This was a difficult time for Ampère since Julie became ill and he had to leave her behind in Lyons. Nowadays Lyons and Bourg are seen as close (Bourg is about 60 km North-East of Lyons), but in the beginning of the nineteenth century travel was difficult. While Ampère was in Bourg he found time to perform research in mathematics. He wrote *Considérations sur la théorie mathématique du jeu* [Considerations on the Mathematical Theory of Games] in 1802. After his wife died in July 1803, Ampère decided to go to Paris.

He found a job as répétiteur d'analyse (tutor in analysis) at the École Polytechnique on 20 October 1804, where Augustin-Louis Cauchy was one of his students. Soon he embarked on a disastrous marriage (1806) with a girl called Jenny (Jeanne-Françoise Potot). Before the birth of their daughter Josephine-Albine on 6 July 1807, the couple had separated. They were legally divorced in 1808 and Ampère was given custody of their daughter. Notwithstanding these private problems, Ampère was productive in mathematics. Among other things he wrote about variational calculus and about the rest term of the Taylor series (1806).

In 1809 Ampère was promoted to professor of mathematical analysis at the École Polytechnique, a post he held until 1828. In 1824 he became also professor at the Collège de France where he was allowed to teach electrodynamics. In the first half of the 1820s Ampère and Cauchy shared the teaching of analysis at the École Polytechnique and both were criticized heavily at times, because it was judged that both mathematicans overloaded the future engineers by too much abstruse mathematics.

In November 1814 Ampère was elected to the Academy (not yet royal) of the Sciences of the Institut de France, when he defeated his former student Cauchy, who also applied for membership. For his denomination he had summarized the functions he had fulfilled thus far together with his mathematical contributions^{[3]}. This was apparently a convincing résumé since it gained him the membership he applied for.

Also in 1814 he made independently the same discovery in chemistry^{[4]} that Amedeo Avogadro made three years earlier, namely that the same volumes of different gases contain the same number of molecules. His work had the same fate as Avogadro's, their discovery went largely unnoticed by the chemists of the time.

In Parisian scientific circles of the 1810s there was some controversy about the theory of light. Augustin-Jean Fresnel had rejected Newton's corpuscular theory and had replaced it by a wave theory. Biot and Laplace still followed Newton, while François Arago and Ampère were on Fresnel's side. Doubtedlessly inspired by this discussion, Ampère published on the refraction of light in 1816.

From 1814 until 1820 Ampère did not perform the kind of research that would have made it into the annals of the history of science, but on September 11, 1820 when he heard François Arago speak about Oersted's work, he got fresh inspiration and started the work that made him famous. Arago related how Oersted had found that a steady electric current influences the orientation of a compass needle. After a week Ampère had determined experimentally that that two straight, parallel, and current-carrying, wires execute a force on each other. The magnitude of the force is inversely proportional to the distance between the wires and proportional to the strengths of the currents. This is what Ampère reported at a meeting of the Académie royale des Sciences on September 18, 1820 (see Ampere's equation). He was so excited about the phenomenon that he gave talks about it again on September 25 and October 2.^{[5]}

During the following years he continued his researches, both experimentally and theoretically.
He built an instrument for measuring electricity that later was developed into the galvanometer.
Finally, in 1825 he presented his collected results to the Academy in one of the most celebrated memoirs in the history of natural philosophy.^{[6]} In 1827 he published a long memoir summarizing his work on electricity and magnetism over the last seven years.^{[7]} He formulated an equation, commonly known as Ampère's equation that describes the magnetic force between two electric currents and a law—now known as Ampere's law, an incomplete version of one of Maxwell's laws—that relates an integral over a closed path in a magnetic field to the electric current through the surface bounded by the path.

Ampère’s theories were fundamental for nineteenth century developments in electricity and magnetism. James Clerk Maxwell writes of Ampère:

We can scarcely believe that Ampère really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration he removed all traces of the scaffolding by which he had raised it.

In the last ten years of his life Ampère gradually lost interest in physics, for example, he did not follow the work of Michael Faraday. André-Marie Ampère died from pneumonia on June 10, 1836, when wintering in Marseilles, in his fifty-second year. In 1869 he was reburied in the cimetière Montmartre in Paris.

## References

- ↑ A.-M. Ampère,
*Sur la rectification d'un arc quelconque de cercle plus petit que la demi-circonférence*[On the rectification of an arbitrary arc smaller than half the circumference of a circle], July 8, 1788 - ↑ F. Arago,
*Ampère, biographie*, Lue par extraits en séance publique de l'académie des sciences, August 21 (1839) - ↑
*Notice des fonctions remplies et des principaux mémoires publiés ou lus à l'Institut et encore inédits, composés par A.M. Ampère*. [Note on the functions fulfilled and the main memorandums published or presented at the Institut and not yet published, composed by A.M. Ampère] - ↑
*Lettre de M. Ampère à M. le comte Berthollet sur la détermination des proportions dans lesquelles les corps se combinent d'après le nombre et la disposition respective des molécules dont les parties intégrantes sont composées,*[Letter of mr. Ampère to mr. the count Berthollet on the determination of the proportions in which bodies combine according to the number and the suitability of the molecules of which the integral parts are composed] Annales de chimie, vol.**90**pp. 43-86 (1814). - ↑ A. M. Ampère,
*Mémoire présenté à l'Académie royale des Sciences, le 2 octobre 1820, où se trouve compris le résumé de ce qui avait été lu à la même Académie les 18 et 25 septembre 1820, sur les effets des courans électriques.*[Memoir presented at the Royal Academy of Sciences, of October 2, 1820 where one finds a summary of the ones read before the same Academy on September 18 and 25, on the effects of electric currents]. Annales de chimie et de physique, vol.**15**, pp. 59-74, and pp.170-218 (1820) - ↑ A. M. Ampère,
*Mémoire sur une nouvelle expérience électro-dynamique, sur son application à la formule qui représente l'action mutuelle de deux éléments de conducteurs voltaïques, et sur de nouvelles conséquences déduites de cette formule: lu à l'Académie royale des sciences le 12 septembre 1825*. [Memoir on a new electrodynamic experience, about its application to a formula that gives the mutual action between two Voltaic conductors and about the new consequences deduced from this formula: read at the Royal Academy of Sciences September 12, 1825] Annales de chimie et de physique, 1825, vol.**29**and**30**, pp. 381-404 and p. 29-41. - ↑ A.-M. Ampère
*Théorie mathématique des phénomènes électro-dynamiques uniquement déduite de L'expérience*[Mathematical theory of electrodynamic phenomena, uniquely deduced from experience.] Mémoires de l'académie royale des sciences de l'institut de France. (1827)