Mémoires sur l'action mutuelle de deux courans électriques, sur celle qui existe entre un courant électrique et un aimant ou le globe terrestre, et celle de deux aimans l'un sur l'autre.

[Paris: Feugeray, 1821?].

First edition, probable first issue, extremely rare and inscribed by Ampère, of this continually evolving collection of important memoirs on electrodynamics by Ampère and others. “Ampère had originally intended the collection to contain all the articles published on his theory of electrodynamics since 1820, but as he prepared copy new articles on the subject continued to appear, so that the fascicles, which apparently began publication in 1821, were in a constant state of revision, with at least five versions of the collection appearing between 1821 and 1823 under different titles” (Norman). The collection begins with ‘Mémoires sur l'action mutuelle de deux courans électriques’, Ampère’s “first great memoir on electrodynamics” (DSB), representing his first response to the demonstration on 21 April 1820 by the Danish physicist Hans Christian Oersted (1777-1851) that electric currents create magnetic fields; this had been reported by François Arago (1786-1853) to an astonished Académie des Sciences on 4 September. In this article he “demonstrated for the first time that two parallel conductors, carrying currents traveling in the same direction, attract each other; conversely, if the currents are traveling in opposite directions, they repel each other” (Sparrow, Milestones, p. 33). This first paper is mostly phenomenological, but it is followed here by the important and much more mathematical sequel, ‘Additions au mémoire précédent – note sur les expériences électro-magnétiques de MM. Oersted, Ampère, Arago et Biot,’ in which Ampère gave the first quantitative expression for the force between current carrying conductors. Ampère attempted to explain his observations by postulating a new theory of magnetism – according to him, magnetic forces were the result of the motion of two electric fluids; permanent magnets contained these currents running in circles concentric to the axis of the magnet and in a plane perpendicular to this axis. By implication, the earth also contained currents which gave rise to its magnetism. Ampère’s theory was attacked by the great Swedish chemist Jöns Jacob Berzelius in a letter to his French colleague Claude Louis Berthollet, to which Ampère replied in a letter to François Arago. These are the third and fourth items in this collection; the fifth and final part is the text of a lecture to the Académie on 2 April 1821 in which Ampère again stressed the identity of electricity and magnetism. The bibliographical complexity of this work is a direct result of Ampère’s modus operandi: “His work was marked by flashes of insight, and it often happened that he would publish a paper in a journal one week, only to find the next week that he had thought of several new ideas that he felt ought to be incorporated into the paper. Since he could not change the original, he would add the revisions to the separately published reprints of the paper and even modify the revised versions later if he felt it necessary” (Norman). Only three other copies of this work listed by ABPC/RBH (all later issues). OCLC lists only one copy of this issue of the collection (University College, London), and we found no record of any earlier issue.

Provenance: Société Philotechnique d’Ostende (presentation inscription from the author).

The collection opens with the ‘Premier Mémoire’ [1] (numbering as in the list of contents, below), first published in Arago’s Annales de Chimie et de Physique at the end of 1820 (Series 2, Tome 15, pp. 59-76 in the October issue & 170-218 in November, read 18 & 25 September). “There is some confusion over the precise nature of Ampère’s first discovery. In the published memoir, "Mémoire sur 1’action mutuelle de deux courants électriques,” he leaped immediately from the existence of electromagnetism to the idea that currents traveling in circles through helices would act like magnets. This may have been suggested to him by consideration of terrestrial magnetism, in which circular currents seemed obvious. Ampère immediately applied his theory to the magnetism of the earth, and the genesis of electrodynamics may, indeed, have been as Ampère stated it. On the other hand, there is an account of the meetings of the Académie des Sciences at which Ampère spoke of his discoveries and presented a somewhat different order of discovery. It would appear that Oersted's discovery suggested to Ampere that two current-carrying wires might affect one another. It was this discovery that he announced to the Académie on 25 September. Since the pattern of magnetic force around a current-carrying wire was circular, it was no great step for Ampère the geometer to visualize the resultant force if the wire were coiled into a helix. The mutual attraction and repulsion of two helices was also announced to the Académie on 25 September. What Ampère had done was to present a new theory of magnetism as electricity in motion …

Ampère’s first great memoir on electrodynamics was almost completely phenomenological, in his sense of the term. In a series of classical and simple experiments, he provided the factual evidence for his contention that magnetism was electricity in motion. He concluded his memoir with nine points that bear repetition here, since they sum up his early work.

  1. Two electric currents attract one another when they move parallel to one another in the same direction; they repel one another when they move parallel but in opposite directions.
  2. It follows that when the metallic wires through which they pass can turn only in parallel planes, each of the two currents tends to swing the other into a position parallel to it and pointing in the same direction.
  3. These attractions and repulsions are absolutely different from the attractions and repulsions of ordinary [static] electricity.
  4. All the phenomena presented by the mutual action of an electric current and a magnet discovered by M. Oersted … are covered by the law of attraction and of repulsion of two electric currents that has just been enunciated, if one admits that a magnet is only a collection of electric currents produced by the action of the particles of steel upon one another analogous to that of the elements of a voltaic pile, and which exist in planes perpendicular to the line which joins the two poles of the magnet.
  5. When a magnet is in the position that it tends to take by the action of the terrestrial globe, these currents move in a sense opposite to the apparent motion of the sun; when one places the magnet in the opposite position so that the poles directed toward the poles of the earth are the same [S to S and N to N, not south-seeking to S, etc.] the same currents are found in the same direction as the apparent motion of the sun.
  6. The known observed effects of the action of two magnets on one another obey the same law.
  7. The same is true of the force that the terrestrial globe exerts on a magnet, if one admits electric currents in planes perpendicular to the direction of the declination needle, moving from east to west, above this direction.
  8. There is nothing more in one pole of a magnet than in the other; the sole difference between them is that one is to the left and the other is to the right of the electric currents which give the magnetic properties to the steel.
  9. Although Volta has proven that the two electricities, positive and negative, of the two ends of the pile attract and repel one another according to the same laws as the two electricities produced by means known before him, he has not by that demonstrated completely the identity of the fluids made manifest by the pile and by friction; this identity was proven, as much as a physical truth can be proven, when he showed that two bodies, one electrified by the contact of [two] metals, and the other by friction, acted upon each other in all circumstances as though both had been electrified by the pile or by the common electric machine [electrostatic generator]. The same kind of proof is applicable here to the identity of attractions and repulsions of electric currents and magnets.

“Here Ampère only hinted at the noumenal background. Like most Continental physicists, he felt that electrical phenomena could be explained only by two fluids and, as he pointed out in the paper, a current therefore had to consist of the positive fluid going in one direction and the negative fluid going in the other through the wire. His experiments had proved to him that this contrary motion of the two electrical fluids led to unique forces of attraction and repulsion in current-carrying wires, and his first paper was intended to describe these forces in qualitative terms. There was one problem: how could this explanation be extended to permanent magnets? The answer appeared deceptively simple: if magnetism were only electricity in motion, then there must be currents of electricity in ordinary bar magnets.

“Once again Ampère’s extraordinary willingness to frame ad hoc hypotheses is evident. Volta had suggested that the contact of two dissimilar metals would give rise to a current if the metals were connected by a fluid conductor. Ampère simply assumed that the contact of the molecules of iron in a bar magnet would give rise to a similar current. A magnet could, therefore, be viewed as a series of voltaic piles in which electrical currents moved concentrically around the axis of the magnet. Almost immediately, Ampère’s friend Augustin Fresnel, the creator of the wave theory of light, pointed out that this hypothesis simply would not do. Iron was not a very good conductor of the electrical fluids and there should, therefore, be some heat generated if Ampère’s views were correct. Magnets are not noticeably hotter than their surroundings and Ampère, when faced with this fact, had to abandon his noumenal explanation.

“It was Fresnel who provided Ampère with a way out. Fresnel wrote in a note to Ampère that since nothing was known about the physics of molecules, why not assume currents of electricity around each molecule. Then, if these molecules could be aligned, the resultant of the molecular currents would be precisely the concentric currents required. Ampere immediately adopted his friend's suggestion, and the electrodynamic molecule was born. It is, however, a peculiar molecule. In some mysterious fashion, a molecule of iron decomposed the luminiferous ether that pervaded both space and matter into the two electrical fluids, its constituent elements. This decomposition took place within the molecule; the two electrical fluids poured out the top, flowed around the molecule, and reentered at the bottom. The net effect was that of a single fluid circling the molecule. These molecules, when aligned by the action of another magnet, formed a permanent magnet. Ampere did not say why molecules should act in this way; for him it was enough that his electrodynamic model provided a noumenal foundation for electrodynamic phenomena” (DSB).

The first quantitative expression for the force between current carrying conductors appeared in Ampère’s less well-known ‘Note sur les expériences électro-magnétiques’ [2], which originally appeared in the Annales des Mines(Series 1, Tome 5, pp. 535-553). Ampère stated, without proof, that, if two infinitely small portions of electric current A and B, with intensities g and h, separated by a distance r, set at angles α and β to AB and in directions which created with AB two planes at an angle γ with each other, the force they exert on each other is

gh (sin α sin β sin γ + k cos α cos β)/r2,

where k is an unknown constant which he stated could ‘conveniently’ be taken to be zero. This last assumption was an error which significantly retarded his progress in the next two years before he stated correctly that k = − ½.

As far as Ampère was concerned, “The physical theory of electrodynamics was now complete. Given the concepts of the ether and the electromotive force of matter as Ampère had formulated them, all the observed effects could be explained; not only explained, but subjected to mathematical analysis. The combination was a potent one and the accuracy of Ampère’s calculations and the depths of his insight led many to embrace his theory” (Williams, p. 150).

Not everyone was convinced of the identity of electricity and magnetism, however. Humphry Davy (1778-1829) expressed doubts in a letter to Ampère of 20 February 1821. Ampère’s idea of magnetism created by circulating electric currents was also in direct opposition to a theory put forward by Johann Joseph von Prechtl (1778-1854), and supported by Berzelius (1779-1848), according to which electromagnetism was ‘transverse magnetism’ – whereas Ampère eliminated magnetism and showed how all the phenomena could be accounted for by the action of two electric fluids, Prechtl and Berzelius reduced electromagnetism to magnetic action. Berzelius expressed this view in his letter [3]; Ampère responded in a letter to Arago [4]. Ampère again stressed the ‘identity’ of electricity and magnetism in a lecture to the Académie on 2 April 1821 [5].

The exceptionally complicated bibliography of this work has yet to be subjected to scholarly analysis. The text of the first article, ‘Mémoires sur l’action mutuelle de deux courans électriques’, appears to be essentially identical to that of the ‘Extrait’ from the Annales (Dibner 62; Norman 43; Sparrow 8). However, there are very significant textual differences between the Extrait and the journal article in the Annales. The journal article and Extrait begin to diverge at p. 16 of the Extrait (p. 73 of the journal): the last paragraph on p. 16, through to the end of p. 18, has been moved (with minor changes) from pp. 212-214 of the journal version. There are many other changes, too numerous to detail. The Extrait is thus not simply a separately-printed version of the journal article, and should perhaps not be regarded as an ‘offprint’ in the usual sense. The second article in the present collection, ‘Note sur les expériences électro-magnétiques …’, was first published in the Annales des Mines; the journal volume is dated 1820, but as the article was read on December 4 it seems likely to have been published early in 1821. No offprints of this article are known. Again there are many significant textual differences between the version that appears in this collection and the journal article. The first such difference occurs on p. 70 (p. 536 in the journal): the sentence ending “soit qu’ils soient enveloppés d’un papier ou introduits dans un tube de verre, afin qu’ils ne puissant communiquer avec ces filets” in the present work reads “soit qu’ils soient enveloppés d’un papier, ou introduits dans un tube de verre qui empêche leur contact direct” in the journal. The last three items in this collection are published here for the first time. It seems to us that the Extrait of the ‘Mémoires sur l’action mutuelle’ could be considered as the ‘zeroth’ version of this collection. We have found no record of any version intermediate between the Extrait and the present version of the collection, which is thus probably the first to contain any works other than the Extrait.

List of Contents (author is Ampère unless otherwise stated):

  1. Premier Mémoire. De 1’Action exercée sur un courant électrique, par un autre courant, le globe terrestre ou un aimant, pp. 3–68
  2. [AMPÈRE & Gillet de LAUMONT] Additions au mémoire précédent – note sur les expériences électro-magnétiques de MM. Oersted, Ampère, Arago et Biot, pp. 6992
  3. [BERZELIUS] Lettre à M. Berthollet sur l’État magnétique des corps qui transmettent un courant d’électricite, pp. 9399
  1. Lettre de M. Ampère à M. Arago, pp. 99–108
  1. Notice sur les Experiences électro-magnétiques de MM. Ampère et Arago, lue à la séance publique de l’Académie royale des Sciences de Paris, le 2 avril 1821, pp. 109–112

Ekelof 819; Norman 44 & 45 (later issues with 278 & 360 pages, respectively); Ronalds 10; Wheeler Gift 784. Assis & Chaib, Ampère’s Electrodynamics, 2015. Grattan-Guinness, Convolutions in French Mathematics, 1800-1840, 1990. Hofmann, André-Marie Ampère, 1995. Williams, Michael Faraday, 1965.



8vo (219 x 133mm), pp. [3], 4-112 with five folding engraved plates (a few faint scattered spots). Original pink wrappers, uncut (lacking backstrip, one cord partly broken with a few leaves just holding, slightly darkened, chip to corner of upper cover); modern cloth box. An untouched copy in its original state.

Item #4821

Price: $22,500.00

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