Maxwell · Source catalogue

75-page scan (226,745 characters per the manifest; one page OCR'd; the text layer is noisy and equations are garbled, so equations were read from page images in the deep reads). Printed page = PDF page + 154. Part I (pp.4-34): Maxwell's stated aim is to give Faraday's lines of force a precise mathematical form without a physical hypothesis. He uses the steady motion of an imaginary incompressible, inertialess fluid through a medium with a resisting force k per unit velocity. Unit tubes are Faraday's lines counted. Point source: v = 1/(4 pi r^2), pressure p = k/(4 pi r). Refraction at a boundary: tan(theta1)/tan(theta2) = k'/k (angles from the normal), which I re-derived in the deep read. Uniqueness, superposition and reciprocity are proved (arts. 14-17, 32); art. 33 gives the flux-plot (square cell) construction. Correction to the usual summary: the fluid velocity is not the force. The dictionary is X = -dp/dx = k u, so force is the pressure gradient, velocity is force divided by k (the flux density), and k plays the role of 1/permittivity or 1/permeability. Velocity equals force only when k = 1. The electrostatic, magnetic and steady-current cases are each mapped onto the model, but Maxwell never states one common equation set; he says the magnetic laws are 'mathematically identical' with the electric ones (p.24) and electrical tension is 'physically identical' with electrostatic potential (p.27). The text contains no modern field equations, no epsilon, mu or sigma, no time dependence, no displacement current and no light. Part II (pp.35-55): Maxwell works in a left-handed axis system (x west, z south, y up), which explains his curl sign. Ampere's law is written as a2 = d(beta1)/dz - d(gamma1)/dy (no 4 pi, no displacement current), and he notes that it forces div J = 0, so he restricts himself to closed currents (p.41). Theorems I-VII are Poisson uniqueness, Green's identity, a Thomson-type minimum principle, 'a divergence-free field is a curl' (Theorem V, with an explicit arbitrary function psi, i.e. gauge freedom, and an implicit div A = 0 choice) and a Helmholtz-type decomposition (Theorem VI; the name is anachronistic because Helmholtz's paper came later [memory: medium-high]). Defining equations: magnetic induction = curl of the electro-tonic functions (alpha0, beta0, gamma0) plus a gradient term only where 'real magnetic matter' exists. Law I: circulation of the electro-tonic intensity round a surface element = the magnetic induction through it (B = curl A in Stokes form). Law VI: EMF on a conductor element = rate of change of the electro-tonic intensity, with equation alpha2 = -(1/4 pi) d(alpha0)/dt; the 1/4 pi is a units effect, and in modern form this is E = -dA/dt. For a moving conductor Maxwell's convective derivative differs from the modern -dA/dt + v x B by a gradient, which integrates to zero round a closed circuit. The derivation is an energy balance after Helmholtz (1847). Maxwell presents all of it as 'a kind of artificial notation' with not 'even the shadow of a true physical theory' (pp.51, 53). He credits Thomson (1847, 1851) for the possibility of the mathematics, notes Stokes's similar expressions, and cites Neumann's earlier induction laws. No new experiments or measured numbers appear in pp.4-55; every experimental reference is Faraday's. He prints Weber's force law and calls it 'a really physical theory', but objects that conservation of force requires central forces depending on distance only, and says 'it is a good thing to have two ways of looking at a subject' (p.54). Part III (pp.56-75, digest only): worked examples including Thomson's electrical images, spheres and a rotating conducting shell, whose heating the digest says Foucault confirmed (p.75).

Key claims

• Faraday's lines of force can be given exact mathematical form as the unit tubes of an imaginary incompressible fluid flowing through a resisting medium, with force = k times velocity and pressure = minus potential.
• The same fluid model reproduces electrostatic, magnetic and steady-current results (inverse-square sources, refraction tan(theta1)/tan(theta2) = k'/k, Ohm's law), but Maxwell offers it as notation and not as a physical hypothesis.
• Faraday's electro-tonic state is a vector function A at each point of space with B = curl A (plus a gradient term only where real magnetic matter exists) and with a free gauge function.
• The electromotive force on a conductor element is minus the rate of change of the electro-tonic intensity (alpha2 = -(1/4 pi) d(alpha0)/dt in Maxwell's units), derived from energy conservation.
• Ampere's law in the form curl H = J implies div J = 0, so the 1856 theory is limited to closed currents.

Relevance: Maxwell's first step toward field theory. It contains the vector-potential relations B = curl A and E = -dA/dt in all but name, so 'origin of the vector potential idea' is too strong: he claims only the identification with Faraday's electro-tonic state, and credits Thomson, Stokes and Neumann for the mathematics. It is also where the gap that displacement current later fills first appears (p.41).

Mainstream conflict: none. The fluid model was explicitly offered as an analogy and dropped; the mathematics is standard.

66-page scan (181,112 characters per the manifest; 11 pages OCR'd; equations garbled in the text layer). Introduction (pp.7-14): Maxwell rejects Weber and Neumann's velocity-dependent action at a distance only on grounds of 'mechanical difficulties', calls Weber's theory 'exceedingly ingenious' and possibly still useful, and prefers actions 'in the surrounding medium'. His evidence for an ether is indirect: light and heat cross so-called vacua and transparent bodies; Thomson's 1854 energy argument for a medium of real density; Faraday's magneto-optic rotation, Verdet's opposite rotation in paramagnetic solutions, and Thomson's inference that magnetisation involves a motion in the medium, from which Maxwell says there is 'some reason to suppose' a rotation about the magnetic force; plus dielectric polarisation and electric absorption. He outlines twenty equations in twenty variables (A to H), says transverse disturbances only propagate, and states that the speed 'is so nearly that of light' that light is an electromagnetic disturbance. He credits Faraday's 1846 'Thoughts on Ray Vibrations' with 'the conception of the propagation of transverse magnetic disturbances to the exclusion of normal ones' and with the same electromagnetic theory of light 'in substance', except that in 1846 there were no data to calculate the speed (p.14). His one stated reason for not treating Weber's theory as ultimate is 'the mechanical difficulties' of velocity-dependent forces at a distance (p.8), and he says Weber's theory may yet be useful; he gives no energy-conservation or finite-propagation-time argument in the text. The medium is a 'datum' inferred from optics, not detected directly. Thomson's 1854 argument gives it a density 'capable of comparison with that of gross matter' (no number is given), and Maxwell calls the rotation of the medium about the magnetic force something there is only 'some reason to suppose' (p.9). The paper's own outline promises the first treatment of non-uniform current across a wire section and the British Association coil check (p.14). Parts I-II (pp.14-24; he says the 'force' is not ordinary mechanical force and the moving body is 'something outside the conductor', so the flywheel sits in the field, not the wire; energy 'probably as actual motion' in the space surrounding the circuits, p.18; the make-and-break current equals half the final current for time 2L/R, eqs 13-15 verified; para 31 cites equations (1),(2) where (4),(5) are meant, a numbering slip; the two-circuit formulas on pp.21-23 were checked in the text layer only): the flywheel 'reduced momentum' analogy (bodies C geared to two driving points, L = sum of C p^2, M = sum of C p q, N = sum of C q^2, so M^2 <= L N [memory high, Cauchy-Schwarz]) gives X = d/dt(Lu + Mv) and, for circuits, xi = Rx + d/dt(Lx + My); L, N are self- and M mutual induction, geometric quantities 'of one dimension in space'; magnetic energy is 1/2 L x^2 + M x y + 1/2 N y^2, 'probably as actual motion' in the space round the circuits; electromagnetic momentum is Faraday's electro-tonic state; the make-and-break transient has time constant L/R. He states the analogy illustrates mechanics only and the facts rest on Faraday's and Felici's experiments. Later parts (digest, with page images pp.29, 31-34, 47, 52): general equations including displacement current and total current; electromotive force from motion, field change and potential. The reviewers found that equations (F) and (G) are printed with signs inconsistent with Maxwell's own prose (P = -rho p; e + df/dx + dg/dy + dh/dz = 0) [read: page image p.33]; combined with (E) this gives equation (95) a negative-damping term, and the page image p.52 shows Maxwell still states that the undulation is 'weakened' (the arbiter's web source says the (G) sign was fixed in the Treatise; (F) is the reviewers' own finding). The wave derivation: only transverse disturbances propagate, V = sqrt(1/(4 pi k mu)), stated in the text as 'entirely magnetic disturbances', and V = v only for mu = 1 (non-magnetic media). Speeds quoted: Weber-Kohlrausch v = 310,740,000 m/s; Fizeau 314,858,000; Foucault 298,000,000; aberration 308,000,000 [read: text layer pp.42-43, 52, QE checked]; against the modern c these are +3.65 %, +5.03 %, -0.60 % and +2.74 % (example.py), and Maxwell concludes the agreement is close enough to identify light. Gold leaf: expected transmission about 10^-50, observed 1/500 to 1/1000 [read: page image p.52]; the digest says 1/400 to 1/900 because of an OCR error. Sunlight estimate (section 108, printed p.505; deep read, page image of PDF p.53): the printed formulas are F = A cos (2 pi/lambda)(z - Vt), energy per unit volume P^2/(8 pi mu V^2) (half magnetic, half electric), energy through unit area W = P^2/(8 pi mu V), so P = sqrt(8 pi mu V W), where P is the greatest value of the electromotive force and mu is the magnetic coefficient (the text layer drops mu; mu = 1 in air or ether). From Pouillet's data as calculated by Thomson (1854), 83.4 foot-pounds per second per square foot, Maxwell prints P = 60,000,000 (his units), 'about 600 Daniell's cells per metre' at the Earth, about 13,000 at the Sun's surface, magnetic force .193 at the Earth and 4.13 at the Sun (Kew horizontal force 1.76 in metrical units), reversed 'more than a thousand million million times in a second'. [calc] 83.4 ft-lb/s/ft^2 = 1217 W/m^2; his own formula with his V = 3.1074e8 m/s gives P = 9.75e7 units, about 975 V/m (1 volt = 1e5 of his units [memory medium, not web-checked]); the modern peak field is 958 V/m (RMS 677), and the 2 percent gap to 975 is only V versus c. The earlier QE suggestion of a factor sqrt 2 is therefore WRONG: both numbers are peak values (his W is a time average for peak P) and sqrt 2 does not reconcile them. Maxwell's printed 6.0e7 is lower than his own inputs give by a factor of about 1.6 in P (about 2.6 in energy; 600 vs 958 V/m, .193 vs .314 magnetic); this I could not explain and the deep reader did not find the cause (arithmetic or conversion slip, different W or V; unresolved). His Sun-surface values are also inconsistent with inverse-square scaling: about 215 Sun radii gives P about 215 times larger (about 129,000 cells per metre), but he prints about 13,000 (ratio 21.7), a factor-of-ten slip or misprint in the printed text [memory high for the 215 radii]. The page also states a conceded anomaly: transmission of green light through gold leaf 'cannot be reconciled with the electromagnetic theory of light, unless' there is less energy loss when the forces reverse at light frequency than when they act for sensible times. British Association coil (Part VII, pp.54-60; deep read, page images of PDF pp.57, 59, 60): L and M are obtained three equivalent ways (electromagnetic momentum of one circuit per unit current in the other, lines of force through it, or the mutual part of the magnetic energy); the coil dimensions are mean radius a = 0.158194 m, depth of each coil 0.01608, breadth 0.01841, spacing of the coils 0.02010, 313 windings in total, wire diameter 0.00126 m. Calculated L: first term 437,440 m, minus 7,345 for finite radius, plus 70 for wire spacing and non-uniform current (per unit length +0.44997 + 0.0236 + 0.0008 - 0.2500 = 0.22437, times 311.236 m of wire) = 430,165 'metres' [calc: sums reproduce; wire-diameter term 0.450 rechecked independently]. Observations from sixteen spinning-coil runs (100 revolutions in 17 s to 100 in 77 s) were fitted by least squares to the British Association 1863 method, which says the calculated L should be multiplied by 1.0618, giving 456,748 (+6.18 %); a rough electric-balance measurement gave 410,000 (-4.69 %). Maxwell writes only that the calculation 'is probably much more accurate than either of the other determinations'; no uncertainty is given and the 6 % is the size of the fitted correction, so the calculated value is not confirmed to better than about 6 %. In SI 430,165 m of EMU inductance is about 43 mH [memory high]. This about 5 % scatter is the paper's only theory-versus-measurement comparison apart from the speed of light.

Key claims

• The electromagnetic field is described by twenty equations in twenty variables (A to H), including a displacement current term; as printed, the signs of (F) and (G) conflict with his own prose.
• Magnetic energy resides in the space around circuits, as the motion of a medium: E = 1/2 L x^2 + M x y + 1/2 N y^2.
• Only transverse magnetic disturbances propagate, at speed V = sqrt(1/(4 pi k mu)), which equals v, the ratio of electromagnetic to electrostatic units, for non-magnetic media.
• Weber and Kohlrausch's v = 310,740,000 m/s agrees with the measured speeds of light (314,858,000 Fizeau; 298,000,000 Foucault; 308,000,000 aberration) to within about 5 %, so light is an electromagnetic disturbance.
• An ethereal medium filling space and permeating bodies is needed (evidence: light through vacua, Thomson's energy argument, Faraday and Verdet rotation), but Maxwell says his conclusions are independent of any mechanical hypothesis about it.
• Peak electromotive force in sunlight at the Earth is about 600 Daniell cells per metre (60,000,000 in his units), but his own formula P = sqrt(8 pi mu V W) with his V and his 83.4 ft-lb/s/ft^2 gives about 975 (about 1.6 times larger, unexplained); his Sun-surface value (about 13,000) is about ten times too small for inverse-square scaling; the calculated self-inductance of the British Association coil (430,165 m) is within about 5-6 % of two measurements (456,748 fitted; 410,000 rough balance).
• Maxwell's only stated objection to Weber's velocity-dependent action at a distance is 'mechanical difficulties'; he credits Faraday's 1846 'Thoughts on Ray Vibrations' with the electromagnetic theory of light in substance, lacking only the speed datum.
• The transmission of green light through gold leaf cannot be reconciled with the electromagnetic theory unless energy loss is smaller for forces reversing at light frequency (Maxwell's own stated anomaly, p.505).

Relevance: The central document of the project: unifies electricity, magnetism and light. It is the source of the 'Maxwell's equations' that Heaviside later compacted, and it carries the two checks a learner can redo (the speed-of-light percentages, and the sunlight field strength, which does not reproduce from his own inputs: about 975 V/m against his printed 600).

Mainstream conflict: The wave speed and the identification of light with electromagnetic waves are accepted physics (Hertz 1887-88 made it a confirmed fact). The luminiferous ether as a detectable medium was abandoned after the Michelson-Morley experiment and special relativity; the 20-equation potential-based formulation was replaced by Heaviside's four.

8-page magazine article with a clean text layer (56,445 characters per the manifest). Hunt, a historian of physics, describes Heaviside as a self-taught, reclusive telegraph engineer who recast Maxwell's 20 component equations (potentials) into four vector equations in E and H (div(eE) = rho, curl E = -mu dH/dt, div(mu H) = 0, curl H = kE + eps dE/dt; 1884-85). He found the energy-flow theorem S = E x H independently, slightly after Poynting (Poynting's abstract January 1884). Three separate episodes of resistance, which the earlier summary lumped together: (1) April 1887: the joint Arthur-and-Oliver Heaviside paper on adding inductance to telephone lines was blocked when Arthur, a Post Office employee, had to get clearance from William Preece, who declared it worthless. (2) Summer-autumn 1887: the Electrician's editor Biggs, sympathetic, feared a libel suit over Heaviside's attacks on Preece and declined them; Biggs was removed in October (he later only 'hinted' that this was because of his support), and the new editor cancelled the series saying he had found no one who read it. In November 1887 Thomson helped place a series in the Philosophical Magazine. (3) 1893: the Royal Society rejected a third instalment of 'On operators in physical mathematics' on mathematical grounds (divergent series), not because of the Preece feud; Heaviside was already an FRS (1891). Operator methods later came into wide use among engineers and 'probably influenced' Dirac. The Heaviside layer (an ionospheric conducting layer) is mentioned. Pupin patented inductive loading in 1899 and sold it to AT&T for $500,000; Heaviside never patented. Pension: he refused a Royal Society Relief Fund grant in 1894, and in 1896 accepted a government pension of 120 pounds a year, later 220. On Lodge: Hunt says Lodge's March 1888 lectures showed oscillating surges when a Leyden jar discharged into a long wire, and that Lodge hoped his experiments on waves on wires would be the hit of the September 1888 Bath meeting but were 'overshadowed' by Hertz's experiments in air, which FitzGerald hailed as the confirmation of Maxwell's field theory. Hunt does NOT say Lodge replicated Hertz (the word does not occur); Lodge's wire-wave work was parallel and independent. The 'murder of Psi' debate (a gauge-condition discussion) is mentioned. Hunt's account is a single secondary source, and the primary letters were not seen.

Key claims

• The four vector equations known as Maxwell's equations were written by Heaviside in 1884-85, not by Maxwell, who wrote about 20 component equations with potentials.
• The energy-flow vector S = E x H was published by Poynting (1884) slightly before Heaviside found it independently.
• Heaviside's loading proposal was blocked at the Post Office in 1887 by Preece; a separate editorial change at the Electrician cancelled his series; a third, separate event was the 1893 Royal Society rejection of his operator paper on grounds of rigour.
• Inductive loading improves telephone-line transmission, contrary to the Post Office view of the 1880s; Pupin's 1899 patent was sold to AT&T for $500,000.
• Lodge's 1888 wire-wave experiments were overshadowed by Hertz's experiments in air, which FitzGerald hailed as the confirmation of Maxwell's theory (Hunt does not say Lodge replicated Hertz).

Relevance: Documents how Maxwell's theory reached its modern form and gives the main alternative-science angle in this folder: a self-taught outsider's work resisted and later vindicated, with the causes of each episode kept apart.

Mainstream conflict: none. It is a mainstream history article; the conflict it describes is between Heaviside and the establishment of his day, which later accepted his results.

9-page article with a clean text layer (24,753 characters per the manifest). Belrose, a radio engineer, largely quotes and paraphrases Hunt's Physics Today article, then adds a case study of umbrella top-loaded AM broadcast antennas after C.E. Smith (IEEE Trans. Broadcasting 1989, station KVOK), modelled with the Numerical Electromagnetics Code (NEC-4D; EZNEC4 on p.3). The comparison with Smith's measured data is one unquantified sentence ('NEC-4D did in indeed model this antenna system quite effectively'); the numbers are in Belrose's earlier ACES 1999 and IEE 2001 papers, which were not seen. His model of a lattice tower shows currents on the inside surface (transmission-line currents) and the outside (radiating currents); this is a model result, not a measurement. He infers 'as Heaviside concluded 130 years ago, the real action ... is due to fields that surround it', which is a rhetorical link: NEC solves for wire currents and supports Maxwell's equations generally. The Addendum has a single unsourced sentence that Heaviside 'critized Helmholtz' because Helmholtz's theory allowed longitudinal as well as transverse waves; no date, work or reference is given. He also quotes Arthur and Forfar (Maxwell Foundation newsletter, 2012) that Hertz, after his 1887 experiments, published a 'clarification' of Maxwell's equations in 1890 that was mathematically equivalent to Heaviside's version but written in components, not vector notation. Other items: Poynting's priority, Bromwich and Wagner's 1916 rigour for operational calculus, an unsourced Einstein quote, and a claim that Maxwell's equations are compatible with special relativity as they stand.

Key claims

• Maxwell's equations in their standard four-equation vector form were written by Heaviside, not Maxwell.
• Integrating the Poynting vector E x H over a closed surface around a transmitting antenna gives the radiated power.
• NEC-4D modelling of an umbrella top-loaded tower antenna agrees with Smith's measurements (stated in one sentence, no numbers), which Belrose takes to support Heaviside's view that the real action lies in the fields around conductors.
• Heaviside criticised Helmholtz because Helmholtz's theory allowed longitudinal waves (single unsourced sentence).
• Hertz's 1890 formulation of the equations was mathematically equivalent to Heaviside's vector version but written in components (second-hand, via Arthur and Forfar).

Relevance: A secondary, engineer's reading of Heaviside's field-centred view and of the credit question around Maxwell's equations. The longitudinal-wave remark is a pointer to the scalar/longitudinal-wave theme in other projects, not evidence.

Mainstream conflict: none. The 'real action is in the field' reading is a standard way of interpreting Poynting flow, though Belrose himself notes engineers find it hard to accept.