Ampere · Source catalogue

A 548-page scholarly book (1.89 million characters of extracted text; 43 pages needed OCR) by two Weber-school authors. It explains Ampère's force law between current elements, traces how he found it after Ørsted's 1820 discovery, argues it is a better foundation than the field concept, and includes a full English translation of Ampère's 1826 Théorie [read]. Page numbers: PDF p.N = printed p.N-3. Structure [read]: Part I (Ch. 1-2) the terms of the force law. Part II (Ch. 3-7) how Ampère got there: first experiments, null-method equilibrium cases, the Biot-Savart experiments, Faraday's rotation, and the 1822 determination of k = -1/2. Part III (Ch. 8-10) the bridge experiment, Savary, the directrix, solenoids and the magnet/current-loop equivalence. Parts IV-V (Ch. 11-22) controversies: Ørsted, Biot-Savart, Faraday, Grassmann and the field concept against Ampère, his replies, the strong form of Newton's third law, and Weber. Part VI and the Théorie translation are listed as separate entries below. Central content [read]: the force is (ii' ds ds'/r^n)(sin a sin b cos g + k cos a cos b) with n = 2 and k = -1/2, central and obeying the strong third law. k was fixed by null experiments and the surprising prediction that collinear same-sense elements repel was checked in the 1822 mercury-bridge experiment (Ampère and de la Rive, Geneva). The authors argue that Grassmann's force (Biot-Savart plus Lorentz) violates the strong third law and gives zero force between collinear elements, and that Weber's 1846 law is the later unification. Checked results (QE and deep read): (1) the SI form of the force is d2F = -(mu0/4pi)(II'/r^2)[2(ds.ds') - 3(r.ds)(r.ds')] r-hat (eq. 2.16), with ii' <-> (mu0/2pi)II' (eq. 2.21) [read: PDF p.32]. (2) The book itself concedes that Grassmann's force explains the measured bridge force if the bridge's force on itself is included [read: PDF p.271]; the Deep read shows by calculation that this is an identity for closed source circuits, so the bridge cannot discriminate between the laws. (3) Ampère never performed the 'law of similarity' equilibrium; he said he had not had time to build the apparatus; Ettingshausen (1878), Felici (1882) and Tricker later ran variants and found n = 2 [read: PDF p.191-192, digest p.463]. (4) Ampère said n = 2 had 'no proof deduced directly from experiment' because the experiments used magnets, not two conductors [read: PDF p.141]. (5) The January 1821 Ampère-Despretz experiment (a magnet near perpendicular wires did not turn) was a refuted prediction made with k = 0; his own law gives torque proportional to [(1-k)+(1+2k)sin^2 b]/c so zero torque implies k = -1/2 [read: digest/PDF p.119-120, eq. 6.7; not deep-read]. (6) Savary (1823) combined n-1+2k = 0 with the Gay-Lussac-Welter ring-magnet null result (kn+1 = 0): two solutions (k,n) = (1,-1) or (-1/2,2); the bridge (k<0) selects the second [read: digest p.155-156]. (7) Biot and Savart's first bent-wire result (torque proportional to the bend angle) was wrong; integrating gives tan(rho/2), which their 1824 experiment confirmed [read: digest p.165-167, 240-243, 475]. (8) Ampère's energy argument: distance-only forces cannot sustain rotation against friction, so continuous rotation needs moving electricity driven by the battery [read: digest p.248-251, 425-426, 459-460]. (9) Ampère did not regard his force as ultimate; he suggested it may come from motion of electric fluids or an ether [read: digest p.424-428], but the digest of p.461 says 'ether theories unnecessary'; the two digest lines are unresolved. (10) Smaller items: a 1914 Nature note calling Kamerlingh Onnes's persistent superconducting current 'an Ampère molecular current' [digest p.111]; Fresnel and transverse light waves [digest p.106-107]; Grassmann (1845) and Clausius found the same element force [digest p.218]; the Gay-Lussac/Thenard spark-gap observation kept k = 0 until 1822 [digest p.91]; Ettingshausen's bifilar tangential-force experiment [digest p.329]. Ch. 21 deep read [read: PDF pp.266-281]: Ampère made a magnet spin about its own axis (Nov-Dec 1821, announced 7 Jan 1822); Faraday doubted it, and explained it with the magnet's pole pushing on current inside the magnet; Biot (1824) agreed in mechanism. The authors say the modern field explanation gives a self-torque, violating the strong third law, and that Ampère instead had the torque come from current in the mercury or external circuit, with an opposite reaction torque there (confirmed by Davy 1823 and modern counter-rotation demonstrations, all cited, none described with numbers). Ampère's insulating-coat control (Théorie Sec. 29.22) says the motion is unchanged when the magnet is coated so current cannot pass through it. The deep reader judged the self-torque charge to be a bookkeeping point, not a net self-torque for steady closed circuits. Ch. 21.1 also gives three objections to Biot-Savart's transverse-magnet model of wire attraction (45-degree rotation; 1/d^3 vs 1/d; closed ring magnets exert no external force). The quantitative bridge calculations are only cited (Assis and Bueno 1995-2000; Bueno and Assis 2001 book), not shown, and no force values are given. Not read in depth: Ch. 22 (Weber, PDF pp.282-289), Sec. 9.6-9.7 and Ch. 17 (Biot-Savart errors), PDF pp.420-428 and 459-465 (digest only). The authors are partisans of Ampère and Weber (Assis wrote books on Weber and Relational Mechanics) [read].

Key claims

• The force between two current elements ids and i'ds' separated by r is (ii' ds ds'/r^2)(sin(alpha) sin(beta) cos(gamma) - (1/2) cos(alpha) cos(beta)), a central force obeying Newton's third law in the strong form.
• Ampère's constant k = -1/2 follows from null results: the 1821 Ampère-Despretz non-rotation (in hindsight), the 1822 null rotation of a mobile conductor about a loop axis, and Savary's 1823 combination with the Gay-Lussac-Welter ring-magnet null result.
• The exponent n = 2 was asserted by Ampère in 1822 as not directly proved by experiment, derived by Savary in 1823 from k and the ring-magnet result, and tested directly only by Ettingshausen (1878), Felici (1882) and Tricker; Ampère never performed his own 'similarity' equilibrium.
• Two collinear, parallel current elements carrying current in the same sense repel each other (Ampère and de la Rive bridge experiment, Geneva, 1822), a surprising prediction that was confirmed.
• Grassmann's force (Biot-Savart plus Lorentz) gives zero force between collinear elements and violates the strong third law for open elements, yet gives the same force as Ampère's on every element of a closed circuit when the source circuit is closed (a general result, which the deep read confirmed numerically; at fixed prefactor the family indexed by k scales as (2/3)(2+k) and agrees with Grassmann only at k = -1/2).
• The net bridge force can be matched by the field law only if the bridge's force on itself is included; with Ampère's law that self-force is zero. Both give the same measured net force, so the bridge cannot tell the laws apart (book concedes the match, PDF p.271; identity shown by the Ch. 21 deep read).
• A magnet can be spun about its own axis by a current passing through it (Ampère, 1821-22); the authors claim the field explanation needs an impossible self-torque and that the real torque comes from the external circuit, which feels an equal and opposite reaction.
• Continuous rotation under a current shows that the force source is moving electricity driven by the battery and not static poles, because distance-only forces cannot sustain rotation against friction (Ampère's energy argument).
• All of magnetism reduces to electric currents: magnets and the Earth contain molecular currents, a magnetic dipole is equivalent to a small current loop and a solenoid is equivalent to a magnet.
• Biot and Savart's first bent-wire law (torque proportional to the bend angle) was wrong; the correct integral is tan(rho/2), and the book says their deduction contained three errors (the three errors themselves were not itemised in the digests or deep read).
• Weber's 1846 force law (depending on relative distance, radial velocity and acceleration) reproduces electrostatics, Ampère's force and Faraday induction while obeying Newton's third law and conservation laws (rests on the book's summary; Ch. 22 not deep-read).

Relevance: This is the whole project. It gives both a historical account of how Ampère's force law was found and an alternative-physics argument that Ampère/Weber action at a distance is a better foundation than the field concept. The key physics is the comparison of three element laws (Ampère, Grassmann/Biot-Savart-Lorentz, Weber) and the fact that they agree on closed-circuit forces.

Mainstream conflict: The authors dispute the textbook field view (Biot-Savart plus q v x B), saying it breaks the strong third law and cannot explain the collinear repulsion or the spinning magnet without a self-force or self-torque. Mainstream physics accepts that Ampère's and the Lorentz-force laws give identical forces on closed circuits (and the Ch. 21 deep read confirmed this numerically), accepts that momentum is shared with the electromagnetic field in general, and does not treat the third-law failure for open elements as an observable defect. Weber's law was superseded by Maxwell/Lorentz electrodynamics and special relativity [memory, medium].

English translations of Ampère's early papers announcing his first experiments after Ørsted's discovery, as listed in the book's contents and covered in the digests. Because this part was read only through digests, its details (including the experiments the main chapters comment on) were not independently verified against the primary text [read: digests].

Key claims

• Ampère's first papers describe attraction and repulsion between current-carrying wires and the equivalence of a solenoid and a magnet (as summarised in the digests).

Relevance: Primary-source support for the history in Parts I-III; secondary to the commentary.

Mainstream conflict: none (historical record).

Ampère's masterpiece in English: the four 'cases of equilibrium', the derivation of the force law, the bridge-related and Biot-Savart discussions, and Notes. The deduction of n and k (Sec. 29.3-29.11, PDF pp.359-383) and Note 31.1 (PDF pp.479-490) were not read in depth [read: digests]. The Notes 31.2-31.4 (force formula in derivative form, the directrix, force of an indefinite angular conductor on a magnet pole, PDF pp.481-490) were not digested and not read [per QE reading of page markers]. Key quotes verified [read]: 'I have not had time to build the instruments shown in figure 4 ... the experiments for which they are intended have not yet been done' (PDF p.191, digest p.463); Sec. 29.22 on the insulating-coat control (PDF p.275).

Key claims

• Ampère's law was 'uniquely deduced from experience' using four cases of equilibrium (the title's claim; the similarity case was never performed by Ampère).
• Sec. 29.22: motion of a magnet is unchanged when it is insulated so that current cannot pass through it, which Ampère takes as proof that current traversing a magnet does not act on it.

Relevance: Primary source for the law that the whole project is about; its deduction is only partly checked here.

Mainstream conflict: The force law itself is mainstream-equivalent on closed circuits; the claim of unique deduction from experiment is a rhetorical reconstruction (the book quotes Maxwell on this, digest p.54).

PDF p.494: the Conclusion quotes Maxwell ('undoubtedly the best', 'Newton of electricity'), Whittaker, Williams and Tricker; the authors write 'We subscribe to them' [read, per QE]. PDF pp.496-517 are Appendix A, redrawn figures only. PDF pp.518-519 start the bibliography. Not digested because the chunk 31 digest was never written.

Key claims

• Ampère's electrodynamics is a masterpiece (Maxwell's appraisal quoted with approval).

Relevance: Closing appraisal and bibliography; no new physics.

Mainstream conflict: none