## ‘Mémoire sur la théorie mathématique des phénomènes électro-dynamiques déduite de l’expérience, dans lequel se trouvent réunis les Mémoires que M. Ampère a communiqués a l’Académie royale des Sciences, dans les séances des 4 et 26 décembre 1820, 10 juin 1822, 22 décembre 1823, 12 septembre et 21 novembre 1825.’ Pp. 175-388 in: Mémoires de l’Académie Royale des Sciences de l’Institut de France, Tome VI, Année 1823.

Paris: Firmin Didot, 1827.

First edition, journal issue in the original printed wrappers, of the “Principia of electrodynamics” (DSB). “Having established a noumenal foundation for electrodynamic phenomena, Ampere’s next steps were to discover the relationships between the phenomena and to devise a theory from which these relationships could be mathematically deduced. This double task was undertaken in the years 1821-1825, and his success was reported in his greatest work ... In this work, the Principia of electrodynamics, Ampère first described the laws of action of electric currents” (DSB). “The experimental investigation by which Ampère established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of electricity.' It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics” (James Clerk Maxwell, *Treatise on Electricity and Magnetism*, Vol. II, p. 162). Rare in the original printed wrappers.

“By that time, early 1823, Ampère’s electrodynamics had reached maturity. With the perfected Ampère law, the Ampèrean currents, and proper analytical tools, one could calculate every known magnetic or electromagnetic effect. However, a systematic account of the theory was still wanting. This Ampère gave in 1826 with his masterful ‘Mémoire sur la théorie des phénomènes électro-dynamiques, uniquement déduite de l’expérience.’

“Imitating the rhetorics of Newton’s *Principia *or Fourier’s *Théorie Analytique de la Chaleur, *Ampere presented his results as the plain expression of experimental truths: ‘I have solely consulted experiment to establish the laws of these phenomena, and I have deduced the only formula that can represent the forces to which they are due.’ Later commentators have had no difficulty detecting a few unwarranted hypotheses in Ampere's theory, for example the central character of elementary forces, the absence of elementary torque, and the Ampèrean currents. There is no reason, however, to doubt Ampere's sincerity. As was mentioned, the concept of *physical *current elements, on which the character of the action between current elements depended, seemed to be materialized in his apparatus. The currents in magnets were not a hypothesis, as far as they were the only consistent way to unify magnetism and electromagnetism: 'The proofs on which I base [my theory] mostly result from the fact that they reduce to a single principle three sorts of actions which all phenomena prove to depend on a common cause, and which cannot be reduced in a different manner.

“Most important, Ampère’s formula for the force between two current elements did not depend on any assumption regarding the nature of the electric current and connected mechanisms: ‘Whatever be the physical cause to which we may wish to relate the phenomena produced by this action, the formula obtained will always remain the expression of facts.’ As we shall see, this turned out to be largely true, since Ampère’s formula (at least its consequences for closed currents) remained an essential basis for the construction of all later theories of electrodynamics. Ampère again compared himself to Fourier, whose equations for heat propagation had survived Fresnel's wave theory of light and heat. Extending the parallel, Ampère did not exclude the search for physical causes. He himself speculated on various mechanisms for the production of electrodynamic forces, as will be seen in a moment. But he required a clean separation between laws and causes.For the determination of the force between two current elements, Ampère offered a polished version of the null method, which was ‘more direct, simpler, and susceptible of great precision.’ The first equilibrium case concerned the lack of action of two contiguous opposite currents. The second established the equivalence of rectilinear and sinuous currents, in the manner of 1821. The third replaced the no-rotation devices of 1822 and proved that the force acting from a closed circuit on a current element was perpendicular to the element. The fourth established the scale invariance of the electrodynamic action … The complete expression of the force still involved obvious factors: the lengths of the elements and the intensities of the currents. In Ampère’s mind the latter factor constituted a quantitative *definition *of the intensity of a current, including a definite current unit as soon as the unit of force was defined.The experiments and reasonings of the null method had an air of great systematism. A closer look at them, however, reveals serious flaws. Ampère did not quantify the precision of his apparatus, as if measuring a zero quantity required zero efforts at error analysis. Even worse, his third case of equilibrium was utterly unstable and hardly observable, and the apparatus for the fourth one was never built, on Ampere's own admission. Could it be that Ampère’s law rested on paper evidence? Certainly not … For the sake of a reductionist rhetoric, however, he preferred an ideal justification of his formula that would not depend on the complicated physics of magnets.

“In the bulk of his memoir, Ampère developed the consequences of his formula for closed currents, Savary’s solenoids, and magnets. The diversity of his mathematical techniques must be emphasized …

“As a special case of a closed current, Ampère considered a single infinitesimal loop of current, and showed that it was equivalent to a magnetic dipole. A finite closed current, he went on, could be replaced by a net of infinitesimal current loops, and was therefore mathematically equivalent to a double sheet of boreal and austral fluid. The ingenious equivalence played little role in Ampère’s deductions, save for a proof that the continuous rotations were impossible for closed rigid circuits. Yet it could be very helpful to anyone who, unlike Ampère, wished to derive the law of electrodynamics from those of magnetism.

“Toward the end of his memoir, Ampère relaxed his severe attitude and indulged In speculations on the cause and nature of electric motions. In his previous researches he had repeatedly tried to understand electrodynamic forces in terms of a propagated action in a medium. In his youth he condemned ‘the supposition of an action between bodies that do not touch each other.’ In the early 1820s, the success of Fresnel’s optical ether revived his desire to reduce all physics to the local motions of a medium. When he discovered the equivalence of rectilinear and sinuous current, he imagined a corresponding superposition of ether motions. Later, the equivalence between a closed circuit and a net of infinitesimal current loops suggested to him a rotary motion in the medium. In each case, the fact preceded the intuition, and Ampère remained very discreet about his ether.

“Ampère was more open about his conception of the electric current. In 1821, he gave up Volta's idea of an electric motion of which the substratum of the conductor was the only obstacle. He adopted instead Oersted’s idea of a series of compositions and decompositions of the two electricities starting in the battery and propagating along the conductor. In lengthy speculations, he combined this view with the atomistic conception of matter to explain contact tension and electrolysis. More succinctly, he imagined an ether made of the neutral fluid resulting from the combination of negative and positive electricity.

“In the memoir of 1826 Ampère expounded his view of the electric current, and mentioned the related conception of the ether. He briefly suggested a propagation of electromagnetic actions through this ether, but favored a more conservative approach in which Coulomb’s electrostatic law remained basic. The idea was to take the average of the Coulomb forces between the separated fluids in the interacting currents. Since the separation was a temporary, spatially directed process, the angular dependence of the net forces could perhaps emerge in this manner.

“In sum, Ampère’s influential memoir of 1826 was not just the reunion of the equilibrium cases, the Ampere formula, and the Ampèrean currents in magnets. It also involved a store of mathematical techniques from which successors could borrow, and it prefigured two ways of deepening our understanding of electrodynamic forces: by reducing them to motions in the ether or by summing the direct actions of the electric fluids running in conductors.The magnificent architecture of the memoir rested on a fictitious three-stage history. In the first stage, fundamental experiments established general properties of electrodynamic forces. In the second, a general force formula was inferred from these properties. In the third, all known phenomena of electrodynamics and magnetism were deduced from the force law and the assumption of Ampèrean currents. This architecture helped clarify the subject and convince Ampère's readers. At the same time, it obscured the dynamical interplay of experiment, mathematical techniques, and theoretical ideas in the actual genesis of electrodynamics.

“Oersted’s new effect, Newtonian analogy, and the principle of unity were the sources of Ampere's initial theoretical convictions. Then Ampère conceived, ordered, and used apparatus intended to support these convictions. The infinitesimal analysis of the theory conditioned the structure of the apparatus. Reciprocally, this structure suggested the notion of a physical current element as a separable entity with regard to the principles of mechanics. In general, the experiments confirmed the original intuitions. However, the few failed experiments played a crucial role. They removed previous indeterminations of the theory, they redirected Ampère toward the null method, and they prompted the development of new mathematical techniques. In turn, these techniques permitted a confirmation of the more qualitative components of Ampère’s theory, and suggested more fundamental explanations of electrodynamic forces.

“This complex history and Ampère’s simple reconstruction of electrodynamics share a common trait: the mathematics is rigorous and adaptable, while the experiments lack precision and flexibility. This asymmetry, later regarded as a basic defect of the otherwise impressive French physics, has a natural explanation: the experiments were intended to found the theory at the simplest level of analysis, for which effects are small and geometrical configurations highly constrained. There were two obvious ways of avoiding the difficulty: to deny the control of mathematical theory over experiment, as Faraday did, or to relocate the control at the level of more complex, but still computable systems, as Weber later did” (Darrigol).

“Ampère presented the work to the Académie des Sciences in 1823, and it was first printed, under the title ‘Mémoire sur la théorie mathématique des phénomènes électro-dynamiques,’ on pp. 177-387 of Vol. VI of the Mémoires de l’Académie des Sciences” (Norman). As Vol. VI was the volume for 1823 this date appears on the first page of each signature as an identifying mark for the printer; the whole volume, however, was not published until late in 1827.

Dibner 62; *En Français dans le Texte* 240; Grolier/Horblit 3a; Honeyman 85; Norman 50 (all for the book edition).

4to (275 x 220 mm), pp. clxxvi [1], 612 with 2 folding engraved plates for the Ampère paper, uncut. Original printed wrappers (some wear and slight loss at extremities of wrappers).

Item #5459

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Price:
$4,500.00
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