Maxwell: central claims
Source note: all four documents have a readable text layer (OCR for the two Maxwell scans, noisy, with garbled equations). Equations were checked on page images for the key pages of both Maxwell papers (1856 paper: pp.13-14, 17, 22-23, 28, 36-54; 1865 paper: pp.15-20, 29, 31-34, 47, 52). The second QE deep read also checked 1865 pp.53-60 on page images (printed pp.505, 509, 511, 512: sunlight field strength, coil data and the three inductance values). Not checked on page images: the 1856 paper's Part III worked examples (pp.56-75), most of 1865 pp.25-28, 35-46 and 48-51 (digest only), the two-circuit formulas on 1865 pp.21-23 (text layer only) and the Part VII series on pp.54-56 and 58. Claim 7 rests on one secondary source (Hunt 2012). Any statement about experimental tests of the claims below is [memory] unless a reviewer retagged it.
- Maxwell (1855-56) gives Faraday's lines of force an exact mathematical form through an incompressible-fluid analogy, explicitly as notation and not as a physical hypothesis. In the model the force is the pressure gradient and the fluid velocity is force divided by the resistance k (X = k u), so velocity equals force only when k = 1.
- In 1856 Maxwell identifies Faraday's "electro-tonic state" with a vector function A at each point (B = curl A, with free gauge function, and EMF = -dA/dt, in his units -(1/4 pi) dA/dt). The mathematics has precursors (Thomson 1847 and 1851, Stokes 1849, Neumann); Maxwell claims only the identification and its use for induction, and the 1865 "electromagnetic momentum" restates it.
- Maxwell (1865) states a field theory with displacement current and with energy in the field (magnetic energy as motion in the space round circuits) as twenty equations in twenty variables. As printed, the signs of equations (F) and (G) conflict with his own prose, and the twenty are redundant and gauge-ambiguous.
- In that theory only transverse disturbances propagate (Maxwell: "entirely magnetic disturbances"), at speed V = v, the ratio of electromagnetic to electrostatic units, in non-magnetic media (mu = 1). Using Weber and Kohlrausch's v = 310,740,000 m/s against measured light speeds (Fizeau 314,858,000; Foucault 298,000,000; aberration 308,000,000) he finds agreement within about 5 % (+3.65 %, +5.03 %, -0.60 %, +2.74 % from the modern value) and concludes light is an electromagnetic wave; Hertz (1887-88) made it a confirmed fact. Maxwell credits Faraday's 1846 "Thoughts on Ray Vibrations" with the same theory in substance, lacking only the speed datum. His own comparison of a calculated coil self-inductance (British Association coil, 313 windings, mean radius 0.158194 m) with two measurements differs by about 5-6 % (calculated 430,165 m; least-squares fit 456,748, +6.18 %; rough electric balance 410,000, -4.69 %), a yardstick for 1860s accuracy; Maxwell trusts the calculation as 'probably much more accurate' with no error estimate. His sunlight estimate (peak field 60,000,000 units, about 600 Daniell cells per metre, from 83.4 ft-lb/s/ft^2) does not reproduce from his own formula P = sqrt(8 pi mu V W): the inputs give about 975 V/m, about 1.6 times his printed figure, for an unexplained reason (not a sqrt 2 or peak-versus-RMS issue; the modern peak value for the same flux is 958 V/m), and his Sun-surface value (about 13,000) is about ten times too small for inverse-square scaling. He also records that transmission of light through gold leaf conflicts with the theory unless losses are smaller at light frequency. His stated reason for leaving Weber is only the 'mechanical difficulties' of velocity-dependent forces,.
- Maxwell believed in an all-pervading ether and gave indirect evidence for it (light through vacua, Thomson's energy argument, Faraday and Verdet rotation) but states that his conclusions are independent of any mechanical hypothesis about it; a detectable-motion ether was later excluded by experiment (Michelson-Morley 1887) while the equations survived.
- Heaviside (1884-85) recast the field equations into the four vector equations in E and H used today and obtained the energy-flow vector S = E x H, shortly after Poynting; the claim that the real action in a circuit lies in the surrounding field is an interpretation, since both descriptions give the same integrated power. Hertz's 1890 restatement (per Belrose, second-hand) was equivalent but written in components.
- Heaviside, a self-taught outsider, met three separate kinds of resistance: Preece's blocking of the 1887 loading paper, an editorial cancellation of his Electrician series (cause unproven), and the Royal Society's 1893 rejection of an operator paper on rigour grounds. The loading result was vindicated in practice (Pupin's patent, 1899) and the operator calculus by later rigour (Bromwich, Wagner from 1916). Hunt's account is single-source; it documents Lodge's own wire-wave experiments but not a replication of Hertz.