Famous Engineers and Mathematicians

Friday, September 30, 2011

Félix Savart

Felix Savart

Born: 30 June 1791 in Mézières, France
Died: 16 March 1841 in Paris, France

Félix Savart's father was Gérard Savart who was an engineer. The family had a long association with Mézières, Gérard's father (Félix's paternal grandfather), also a native of that city, had been involved with the founding of the engineering school there in 1748. Gérard Savart moved to Metz where he was in charge of draftsmen at the engineering school. Félix and his older brother Nicolas (born 1790) had their early schooling in Metz. With a strong family tradition of involvement with military engineering schools, one might have expected Félix Savart to also go down that path. In fact his early training did take him in that direction but in 1808, at the age of seventeen, he decided to train for a career in medicine.

Savart spent around two years from 1808 to 1810 studying at a hospital in Metz. Of course he had grown up in a period when France was enjoying military victories under Napoleon who had led French armies to victories over the armies of Austria, Prussia, Great Britain, Spain and the Netherlands between 1792 and 1797. Victories over three further coalitions set up to try to curb French power saw Napoleon at the height of his power in 1810. It was at this time, after training in the Metz hospital, that Savart became a regimental surgeon in Napoleon's army. He did follow certain family traditions by serving in the first battalion of engineers. However, during the years in which he served from 1810 to 1814, Napoleon suffered defeats in the Spanish and Russian campaigns. In 1814 Savart was discharged from the army and resumed his medical training.

It was to Strasbourg that Savart went in 1814 and, two years later, he graduated from the university with a medical degree. The topic for his thesis was varicose veins. During his medical studies Savart became interested in Aulus Cornelius Celsus (first century AD), one of the greatest Roman medical writers, author of De medicina. After completing his degree Savart remained in Strasbourg where he both gained further medical experience and also worked on a translation of Celsus' De medicina. After returning to Metz in 1817 where he set up a medical practice, Savart spent more time studying physics than treating patients. He set up an excellent physics laboratory to carry out experiments and became fascinated with a study of sound, in particular the acoustics of musical instruments such as the violin. He began to build violins trying to base the form of the instrument on mathematical principles.

With Savart showing little interest in his medical practice, and patients showing little interest in joining, he decided to go to Paris in 1819 and seek a publisher for his translation of Celsus' De medicina. He had another reason to go to Paris, and that was to see Biot so that he could discuss with him the acoustics of musical instruments that was by now fascinating Savart. As it happened, at the time that Savart reached Paris Biot was lecturing on acoustics at the Faculty of Science. He found Savart's work on the acoustics of bowed string instruments very interesting and he presented a memoir that Savart had written Mémoire des instruments à chordes et à archet to the Academy of Sciences; it was published in 1819. This memoir contained a design of a trapezoid violin which Savart claimed to have superior acoustic performance to the traditional violin. He used experimental results achieved using techniques similar to those of Chladni. It is reasonable to ask how successful he was with his trapezoid violin. Dostrovsky writes [1]:-

When the instrument was played before a committee that included Biot, the composer Cherubini, and other members of the Academy of Sciences and the Académie des Beaux-Arts, its tone was judged as extremely clear and even, but somewhat subdued.

When Savart arrived in Paris, Biot was undertaking research on electricity in addition to lecturing on acoustics. The two began a collaboration and when, early in 1820, Hans Christian Oersted reported that a compass needle placed near a wire carrying current pointed at right angles to the wire, they began to research more deeply into the field produced by the wire. Using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what today is called the Biot-Savart law. Magnetic fields produced by electric currents can be calculated using the Biot-Savart law which they presented to the Academy of Sciences on 30 October 1820. They took magnetism as the fundamental property rather than using the approach due to Ampère which treated it as derived from electric circuits. A joint Biot-Savart paper Note sur le magnétisme de la pile de Volta was published in the Annales de chemie et de physique in 1820.

Biot helped Savart find a teaching position in Paris and from 1820 he taught science in a private school there. On 5 November 1827, Savart was elected to the physics section of the Academy of Sciences to replace Fresnel who had died in July of that year. He taught at the Collège de France from 1828, becoming a professor of experimental physics there to succeed Ampère. He continued to hold this position until his death in 1841, a few months short of his fiftieth birthday.

In addition to the 1819 paper we mentioned above, Savart also carried out experiments on sound which became important for later students of acoustics. Among other papers he published on this topic we mention Mémoire sur la communication des mouvements vibratoires entre les corps solides (1820), Recherches sur les vibtarions de l'air (1823), and Mémoire sur les vibrations des corps solides, considérées en général (1824). His contributions to music are summed up in Grove's Dictionary of Music and Musicians [2]:-

In general he threw light on the nature of the complicated relation between a vibrating body which is the source of sound and other bodies brought into connection with it, by virtue of which the original sound is magnified in intensity and modified in quality, well-known examples of such an arrangement being furnished by the sounding board of the violin tribe and the pianoforte.

He also developed the Savart disk, a device which produced a sound wave of known frequency, using a rotating cog wheel as a measuring device. McKusick and Wiskind write [5]:-

About 1830 Savart invented a toothed wheel for determining the number of vibrations in a given musical tone. He attached tongues of pasteboard to a hoop of the wheel and arranged for these to strike a projecting object as the wheel was turned. Alternately, he had cogs of a wheel strike a tongue of pasteboard. Presumably he employed this instrument to determine the vibrations per second of the tones he elicited from his experimental models. he would speed up the rotation of the wheel until a tone which matched the experimental one was produced. Since the frequency of the tone produced by the wheel could be easily determined, the frequency of the unknown tone produced by the model was ascertained. by an extension of this method, Savart compounded musical notes. For example, he would use, in combination, wheels with numbers of teeth which bore a simple relationship to each other. he used this method to explore the physical basis of harmonious and discordant sounds.

There were other topics that interested Savart and on which he undertook research. For example he studied turbulence and the medical implications of his research is studied in detail in [5]. The authors write in summary:-

In the latter half of the nineteenth century, in medical and physiological writings on the genesis of heart murmurs, Savart's "fluid veins" were repeatedly referred to. When it was realised that, in the case of partial obstruction to the flow of blood, the murmur is produced not at, or proximal to, the site of obstruction but in the fluid beyond, it was presumed that a mechanism like that revealed by Savart was involved.

The paper [4] discusses a detailed experimental study of the existence of water bells when a cylindrical jet impacts with the velocity normal to a circular disc, which was first studied by Savart in 1833.

Let us end this biography with giving two postscripts. First let us note that although one of Savart's main aims in going to Paris was to publish his translation of Celsus' De medicina the work never appeared. It seems that Savart became diverted into more interesting directions. As a second postscript we note some facts about Savart's older brother Nicolas Savart. Unlike Félix, Nicolas studied at the École Polytechnique and then followed the family tradition of becoming an officer in the engineering corps. The reason for mentioning him in this postscript is that Nicolas, like his brother, also published papers on acoustics. For example he published Quelques faits résultant de la réflexion des ondes sonores (1839), and at least three further papers after the death of Félix.

Félix Savart was honoured by having a street in Mézières named after him.

Article by: J J O'Connor and E F Robertson

Jean Baptiste Biot

Born: 21 April 1774 in Paris, France
Died: 3 Feb 1862 in Paris, France

Jean-Baptiste Biot's father was Joseph Biot, whose ancestors were farmers in Lorraine, had achieved an important role working in the Treasury. Jean-Baptiste was educated at the college of Louis-le-Grand in Paris, where he specialised in classics. He completed his studies at Louis-le-Grand in 1791 following which, since his father wanted him to make a career in commerce, he took private lessons in mathematics from Antoine-Rene Mauduit who was professor of mathematics at the Collège de France. Joseph Biot then sent his son to Le Havre to become a clerical assistant to a merchant. His job there consisted of copying vast numbers of letters (we have to be thankful for photocopiers!) which bored Biot so much that he volunteered for the army. He joined the French army in September 1792, and served in the artillery at the Battle of Hondschoote in September 1793. In this battle the French defeated the British and Hanoverian soldiers besieging Dunkirk. After the battle Biot, suffering from an illness, decided to leave the army and return to his parents. As he was walking towards Paris, he was befriended by an important person who passed in his carriage. He took Biot in his carriage to Paris where he (Biot) was arrested as a deserter (he was still in uniform) and brought before a revolutionary committee. This would have had serious consequences for Biot had not the stranger intervened and he was set free. Despite Biot's efforts, he was not able to identify the important stranger and thank him.

It took Biot some months to recover from the illness during which time he continued with his studies of mathematics. He took the entrance examinations for the École des Ponts et Chausées and was accepted in January 1794. The École Polytechnique was founded later in 1794 (actually named 'École centrale des travaux publics' for its first year) and Biot transferred there in November of that year. Gaspard Monge, one of the founders of l'École Polytechnique who taught the first intake of students, quickly realised Biot's potential. Biot, however, quickly became involved in student politics and was made a section leader. There was an attempted insurrection by the royalists against the Convention and Biot took part. He was captured by government forces and taken prisoner. Had it not been for Monge, who could not see someone with such talents remain in jail, or even die, pleading successfully for his release his promising career might have ended. It is not surprising that for a second time he had come close to a death sentence, giving the dangerous times in Revolutionary France through which he lived. He returned to his studies at the École Polytechnique, befriending a fellow student, Siméon-Denis Poisson, and graduated in 1797. He had found a patron in Sylvestre-François Lacroix who was highly influential in helping Biot develop his career.

He became Professor of Mathematics at the École Centrale de l'Oise at Beauvais in 1797. It might seems remarkable that even someone as able as Biot could move from being an undergraduate straight into a professorship. However, things had worked in his favour [7]:-

The Convention, in a law of 25 February 1795 had called for a system of écoles centrales, one in each large town, to replace the collèges of the ancien régime as seats of secondary education. The curricula of the new schools was practical and modern and included two years devoted to mathematics, experimental physics and chemistry. These subjects had never been taught before on a high school level, so, inevitably, there was a shortage of qualified teachers.

Biot got to know of the vacant mathematics professorship through his friendship with Barnabé Brisson, the son of Antoine François Brisson de Beauvais, while studying at l'École Polytechnique. Through Barnabé Brisson, Biot had got to know his sister Gabrielle. Although Gabrielle was only sixteen years old, they married in 1797 soon after Biot took up his position at Beauvais. Biot taught Gabrielle mathematics and physics so that she might translate into French a German text by Ernst Gottfried Fischer. It was Claude Louis Berthollet who had asked Biot to make the translation which was published as Physique mécanique in 1806. Biot's wife was well educated and fluent in German, so her translation was excellent. However, in line with the practice of the time, the book records Biot himself as the translator rather than his wife. Biot and his wife had a son Edouard Constant Biot who was born in 1803.

It was largely through Lacroix that Biot had been appointed at Beauvais and Lacroix advised him frequently through the first years that he worked there. However, he also managed to get support in his career from Laplace. In fact in late 1799 Biot approached Laplace, who had taught him at l'École Polytechnique, and offered to proof-read the Mécanique céleste which at that time was with the publisher. He didn't give up when Laplace said "No thanks" but persisted in a polite way and eventually Laplace agreed. Biot was, by this time, an entrance examiner at the École Polytechnique so was frequently in Paris. He wrote [7]:-

From that time on, each time I went to Paris I brought my proof-reading work and personally presented it to M Laplace. He always received it with kindness, examined it and discussed it, and that gave me the opportunity to submit to him the difficulties that had stopped me. His willingness to explain them was boundless. But even he could not always do it without stopping to think for a long while. This usually occurred in places where he had used the expedient phrase 'it can easily be seen'.

Certainly the effort required by Biot was enormous. He wrote near the end of 1799 [7]:-

I spent all of my days at this work [proof-reading the 'Mécanique céleste'] which I felt to be important in several respects, and I hope I have succeeded. I worked like a devil to finish it on time, and 1 remained at the task eighteen hours in a row the last day, without eating or drinking. Finally, thank heaven, it is finished, and I can flatter myself that I understand the 'Mecanique celeste'. If this were to be the only benefit I would get from it, it would still be a lot.

Laplace was also interested in the research on mathematics which Biot was undertaking and gave him advice both on the material and on getting it published. In 1800 he was appointed Professor of Mathematical Physics at the Collège de France, an appointment which was due mainly to the influence of Laplace. In 1800 Biot was elected an associate to the First Class of the Institute, replacing Jean Montucla who died in December 1799. Again Laplace's support was important to Biot in this election. In January 1803 the Institut was reorganised and Delambre became perpetual secretary, creating a vacancy in the Mathematics Section. Although Biot had produced excellent mathematics memoirs in the years up to 1800, he had concentrated on experimental physics from that time on. However, presumably to improve his chances of gaining a place in the Mathematics Section, he submitted a memoir on the axes of tautochronous curves just before the election was to take place. It was sufficient to keep his mathematical reputation high and he was elected on 11 April 1803.

The first balloon ascent made for scientific purposes was by Biot and Joseph-Louis Gay-Lussac from the garden of the Conservatoire des Arts on 24 August 1804. They achieved a height of 4000 metres and measured magnetic, electrical, and chemical properties of the atmosphere at various heights. In 1806, again with the support of Laplace, Biot was appointed as an assistant astronomer at the Bureau de Longitudes in addition to his other roles. On 3 September of that year he set out with François Arago to Formentera, in the Balearic Islands, to complete earlier work begun there on calculating the measure of the arc of the meridian. They were still undertaking measurements when, in May 1808, Napoleon declared his brother Joseph Bonaparte as Spanish ruler and the War of Independence began. Biot and Arago must have looked extremely suspicious; two Frenchmen with sophisticated measuring instruments working on Spanish territory. Biot fled back to France immediately. Later in 1808, together with Claude-Louis Mathieu, he embarked on a series of measurements of the length of the seconds pendulum at different points on the meridian, in particular at Bordeaux and at Dunkirk. Both Mathieu and Biot received a prize from the Académie des Sciences in 1809 for this highly accurate work, and in 1812 they received a second prize from the Academy for their achievements. In 1809 Biot was appointed Professor of Physical Astronomy at the Faculty of Sciences. He held this position for over fifty years.

Biot studied a wide range of mathematical topics, mostly on the applied mathematics side. He made advances in astronomy, elasticity, electricity and magnetism, heat and optics on the applied side while, in pure mathematics, he also did important work in geometry. He collaborated with Arago on refractive properties of gases. Biot, together with Felix Savart, discovered that the intensity of the magnetic field set up by a current flowing through a wire varies inversely with the distance from the wire. This is now known as Biot-Savart's Law and is fundamental to modern electromagnetic theory. Morris Kline, reviewing [8], writes:-

Biot depended entirely upon experiments to determine the interaction of a magnet and a straight line of electrical current and then inferred a mathematical law concerning the force between current and magnet.

Light was the topic on which Biot devoted most time, making the major discovery of the laws of rotary polarization by crystalline bodies. Having discovered these laws he used them in analysis of saccharine solutions using an instrument called a polarimeter which he invented. For this work on the polarisation of light passing through chemical solutions he was awarded the Rumford Medal of the Royal Society of London in 1840. He had been elected as a foreign member of the Royal Society in 1815.

One of his important works was Mémoire sur la figure de la terre (1827) which describes the shape of the Earth. Among his other major works we mention: Analyse de la mécanique céleste de M Laplace (1801); Traité analytique des courbes et des surfaces du second degré (1802); Recherches sur l'intégration des équations différentielles partielles et sur les vibrations des surfaces (1803); Essai de géométrie analytique appliqué aux courbes et aux surfaces de second ordre (1806); Recherches expérimentales et mathématiques sur les mouvements des molécules de la lumière autour de leur centre de gravité (1814); Traité de physique experimentale et mathématique (1816); Precis de physique (1817); (with Arago) Recueil d'observations géodésiques, astronomiques et physiques exécutées en Espagne et Écosse (1821); Mémoire sur la vraie constitution de l'atmosphère terrestre (1841); Traité élémentaire d'astronomie physique (1805); Recherches sur plusieurs points de l'astronomie égyptienne (1823); Recherches sur l'ancienne astronomie chinoise (1840); Études sur l'astronomie indienne et sur l'astronomie chinoise (1862); Essai sur l'histoire générale des sciences pendant la Révolution (1803); Discours sur Montaigne (1812); Lettres sur l'approvisionnement de Paris et sur le commerce des grains (1835); Traite d'astronomie physique (1850); and Mélanges scientifiques et littéraires (1858).

He tried twice for the post of Secretary to the Académie des Sciences and to improve his chances for election to this post he wrote Essai sur l'Histoire Générale des Sciences pendant la Révolution. However he lost out in 1822 to Fourier for this post, then again when Fourier died in May 1830 he applied again for the post of Secretary, only to lose to Arago on this occasion. The rivalry between Arago and Biot was again evident in 1839 when different photographic processes were competing [10]:-

Arago and Biot, France's leading authorities in the field of optics, had spent the past thirty years disagreeing about the ability of optical instruments to represent the world. Photography became one more opportunity for them to disagree, and they did not shrink from the task. The debate extended beyond questions of assigning priority and apportioning credit. At its heart was the question of what the photographic surfaces showed, what relation the visible inscription bore to the real world.

Arago supported the Daguerre photographic process with silver plates while Biot championed an approach with paper soaked in a silver solution as developed by Henry Fox Talbot. This was not because he thought this process produced clearer photographs, rather it was because he believed that the images captured 'chemical radiation' invisible to the eye. We should note that the idea of 'chemical radiation' was widely believed at this time. Biot also believed that the photographic process should be one reserved for scientific use and not made available for public use. There was a period of collaboration between Biot and Talbot, the two exchanging letters frequently. Basically the photographic process became another tool for Biot to use in his investigations of light which had always been a major interest to him.

As well as interests in almost every branch of science, Biot was interested in the history of the subject. He published works on this topic such as: Essai sur l'histoire générale des sciences pendant la Révolution française (1803); Notice historique sur la vie et les ouvrages de Newton (1822); Recherches sur plusieurs points de l'astronomie égyptienne appliquées aux monuments astronomiques trouvés en Égypte (1823); Sur la manière de calculer les positions des étoiles relativement à l'équateur et à l'écliptique pour les époques anciennes (1823); Opuscule sur l'Astronomie ancienne des Chinois, des Indous et des Arabes (1840); Mémoire sur le Zodiaque de Denderah (1844); Précis de l'histoire de l'Astronomie planétaire (1847); and Études sur l'astronomie indienne et l'astronomie chinoise (1862).

In [4] St Beuve says that Biot was endowed to the highest degree with all the qualities of curiosity, finesse, penetration, precision, ingenious analysis, method, clarity, in short with all the essential and secondary qualities, bar one, genius, in the sense of originality and invention.

A contrasting comment by Olinthus Gregory in 1821 is:-

With regard to M Biot, I had an opportunity of pretty fully appreciating his character when we were together in the Zetland [= Shetland] Isles; and I do not hesitate to say that I never met so strange a compound of vanity, impetuosity, fickleness, and natural partiality, as is exhibited in his character.

In addition to the honours we mentioned above, Biot was also honoured by being made chevalier of the Legion of Honour in 1814 and commander in 1849. He was elected to the to the Academy of Inscriptions and Belles-Lettre in 1841 and to the French Academy in 1856.