Heaviside: Science Contrarian review

Source gap (repeated from Step 1). Only contents pages (Electrical Papers Vol. 1; Electromagnetic Theory Vol. 1, secs. 20-85) and three body pages (Electromagnetic Waves pp. 139, 142, 143) were available as page images. I read the six Waves/Theory images myself [read: page image]. No full chapter was read. Everything about Heaviside's wider results rests on [web] (Wikipedia pages cited below) or [memory]; where a verdict rests on those alone I say so.

Framing. Heaviside is the contrarian's favourite case study in how mainstream institutions treat an outsider (self-taught, no degree, no institutional post), and the case is unusual: nearly all of his central claims were vindicated. The honest contrarian job here is therefore (1) to separate "dismissed without testing, later vindicated" from "tested and confirmed", (2) to examine how he was resisted, and (3) to apply the same rigour to Heaviside himself, whose papers leave proofs to the reader and whose late positions (relativity) were wrong.

Source tags: [read] = from the page images; [web] = URL given; [memory] = recall with confidence.

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Claim 1. Maxwell's theory can be written as four compact vector equations

• a. Mathematics consistent? Yes. The contents show the two circuital laws (secs. 34-36, 62-65) and curl/divergence defined (secs. 36, 51) [read: p.xiv-xv]. The four-equation form (curl and divergence of E and H) is the textbook form (Griffiths ch. 7-8 level). [memory, high]
• b. Consistent with experiment? Yes: every classical EM result, including Hertz's 1887-88 waves, is reproduced.
• c. Tested? Used for over a century in engineering; the test is continuous practical success. Replicated (independently re-derived/used by Hertz, Gibbs, others). [memory, high]
• d. If true, what changes? Nothing; it is mainstream.
• Rejection/priority note. The reduction is reported as "twelve of the original twenty equations in twenty unknowns down to the four" in 1884 [web: https://en.wikipedia.org/wiki/Oliver_Heaviside]. Credit is shared in the vector-form story with Gibbs [memory, medium; not verified, not needed for the verdict].
• Verdict: Established. (A reformulation, not new physics: same predictions as Maxwell, much easier to use.)

Claim 2. Energy is localised in the field and flows at E x H (Poynting flux)

• a. Consistent. Sec. 70 "Electromagnetic Application. Medium at Rest. The Poynting Flux" and sec. 67-69 on continuity of energy are listed [read: Theory contents p.xv]. The standard conservation law (rate of change of field energy + divergence of S = -J.E, with S = E x H) is internally consistent. [memory, high]
• b. Consistent with all circuit and radiation experiments (radiated power from antennas, energy delivered to a load flows in the fields around wires, not inside the wire). [memory, high]
• c. Not tested as a single experiment but underlies every power-transmission and antenna calculation; independently derived by Poynting (1884) and Heaviside (1885) [web: Wikipedia Heaviside page says he "independently discovered the Poynting vector"].
• d. Nothing.
• Contrarian notes. Heaviside himself flags an unresolved weakness: sec. 73 is titled "Uncertainty regarding the General Application of the Electromagnetic Stress" and sec. 79 admits the internal stress is "statically indeterminate" [read: p.xv]. The Poynting flux is only determined up to adding a curl-free-divergence term (any vector with zero divergence can be added without changing energy conservation) [memory, high]. This is a genuine, still-discussed ambiguity, not a refutation. The "gravitational difficulty" of sec. 68 [read] shows he knew the energy-flux picture raised puzzles.
• Verdict: Established (with the known non-uniqueness of the flux as an open footnote).

Claim 3. Added inductance reduces attenuation and distortion on telegraph/telephone lines (Heaviside condition); Preece was wrong

• a. Consistent. The condition is R/L = G/C (R series resistance, L inductance, G leakage conductance, C capacitance, all per unit length) [web: https://en.wikipedia.org/wiki/Heaviside_condition]. Check by calculation: for a line meeting it, attenuation is alpha = sqrt(R*G), independent of frequency, which is why the wave shape survives; and alpha = R/(2 Z0) + G Z0/2 with Z0 = sqrt(L/C) is minimised when Z0 = sqrt(R/G), i.e. exactly the Heaviside condition. [memory, high; derivation checked by me]. For a leaky-free (G small) cable, raising L lowers attenuation. This is the key point Preece got backwards.
• b. Yes, consistent with measured cable behaviour: cable attenuation and distortion fall with added inductance.
• c. Tested? Yes, by others, in the field. George Campbell at AT&T demonstrated loading coils on a 46-mile cable on 6 Sept 1899; Pupin filed a competing patent in Dec 1899; AT&T bought Pupin's patent (reported $200,000 initially, later $455,000) partly because Heaviside's prior publication was a legal risk; Krarup built continuously loaded cable in 1902; permalloy/mu-metal loaded cables followed (1923-24); AT&T savings estimated at about $100 million [web: https://en.wikipedia.org/wiki/Loading_coil]. Heaviside proposed discrete inductors in 1893 per the same page [web]. Replicated across companies and countries. I did not read Heaviside's own derivation (Electrical Papers Art. 20 heading only [read]).
• d. Nothing in physics; it corrected engineering practice.
• How it was rejected (the contrarian core). William Preece of the Post Office, a powerful official, had declared self-inductance harmful; he blocked the 1887 Heaviside-and-Arthur paper "Bridge System of Telephony" that proposed loading coils [web: https://en.wikipedia.org/wiki/Oliver_Heaviside]. So: dismissed without testing by a gatekeeper with a stake in his own earlier position, later confirmed experimentally by an industrial lab, with the financial reward going to others (Pupin), not Heaviside. Wikipedia's wording that Preece's motive was protecting his reputation is an interpretation; I cannot verify motive. The blocking itself is sourced.
• Verdict: Established. Dismissed without testing (1887), later tested and confirmed (1899 onward).

Claim 4. Signals in conductors/dielectrics obey wave-plus-diffusion equations; magnetic diffusion is repeated internal reflection; a perfect conductor is a perfect reflector

I read pp. 139, 142, 143 myself [read: page image].

• a. Mathematics.
• p.139, eqs. (47)-(48): Bessel-function solutions of the form exp(-qt) times J0{(s/v) sqrt(z^2 - v^2 t^2)}. J0 of an imaginary argument is the modified Bessel function I0, the known Green's-function form for the telegraph equation inside |z| < vt [memory, medium]. This is consistent in form; I did not independently verify the exact operator prefactors (-s + d/dt). Heaviside admits he gives no proof: "I forbear from giving a detailed demonstration, leaving the satisfaction of the proper conditions to be the proof... although they were very laboriously worked out by myself" [read: p.139]. That is a rigour weakness by the standards of the day and of ours (an unproved result asserted), though it is checkable.
• The "tail" behind an attenuated pulse and "persistence of momentum" (integral of H dz stays constant when k is introduced) [read: p.139] is a correct qualitative statement of the telegraph-equation wake, a known property. [memory, medium]
• p.142, eqs. (58)-(59): a plane sheet where impressed force e jumps gives H = -e/(2 mu v) and E = -/+ e/2 either side. The two halves radiate left and right at speed v with E = mu v H each, so |E| = e/2 and |H| = e/(2 mu v). Self-consistent. [read]
• p.143, eqs. (60)-(62): boundary conditions E1 + E3 = E2 and H1 + H3 = H2 + 4 pi k1 z E2 with E3 = -mu v H3 and E2 = mu v H2 give E2/E1 = H2/H1 = 1/(1 + 2 pi mu k1 z v). I rederived it: substituting H = E/(mu v) gives (E1 - E3)/(mu v) = E2/(mu v) + 4 pi k1 z E2, and E1 + E3 = E2 then gives 2E1 - E2 = E2 + 4 pi k1 z mu v E2, so E2/E1 = 1/(1 + 2 pi k1 z mu v). Correct. Reflected wave carries H positively, E negatively. A perfect conductor (k1 -> infinity) gives E2 -> 0, H on the incident side doubled to 2H1, E destroyed. Consistent. [read + my derivation]
• Numerical check of eq. (63). With k1 = 1/1600 (copper, EM CGS units, abmho/cm) and mu v = 3 x 10^10, z = 1/(2 pi x 3e10 / 1600) = 8.5 x 10^-9 cm, matching his (8/3 pi) x 10^-8 = 0.85 x 10^-8 cm. Independent SI cross-check: the standard thin-film transmission is 1/(1 + sigma z Z0 / 2), Z0 = 377 ohm; half transmission needs z = 2/(sigma Z0); with copper sigma = 5.8e7 S/m, z = 9.1 x 10^-11 m = 9.1 x 10^-9 cm. The 7 percent difference comes from his 1/1600 versus modern 1/1724 for conductivity. In EM CGS, Z0 = 4 pi mu v, which is why his "2 pi" appears. So the units are correct. [memory, high for sigma and Z0; arithmetic by me]
• Minor internal sloppiness (page glyph partly hard to read): after eq. (63) the text states the H disturbance "is made 3/2 H1" and E "reduced to 1/2 E1 on the transmission side". From the boundary conditions, total H on the incident side is H1 + H3 = 3/2 H1 and total E there is 1/2 E1 (continuity makes E the same on both sides of the sheet), so the "transmission side" wording is loose. I read the fraction as 3/2 [read: page image p.143, small print; medium confidence in the glyph].
• Physical caveat on eq. (63). The result is for a sheet of ideal bulk conductivity at a thickness of about 0.85 nm, roughly three atomic layers, where bulk conductivity is not applicable; real nanometre metal films have higher resistivity. Heaviside's remark that this is a small fraction of a visible-light wavelength is true; the formula is a thought experiment, not a prediction for a real foil. [memory, medium: thin-film resistivity increase]
• b. Experiment. Skin effect, eddy-current shielding and reflection from metals are standard measured phenomena; semi-transparent metal films a few nanometres thick are routine optics. [memory, high]
• c. Tested? The concepts are continuously tested in electromagnetic engineering. I have no source for a specific named experiment of eq. (63) itself; I do not claim one.
• d. Nothing.
• Verdict: Established (diffusion/wave behaviour, reflection from conductors; the quantitative thin-sheet formula as an idealisation). Eqs. (47)-(48) are plausible, not verified by me because Heaviside gave no proof and I did not independently check them.

Claim 5. Operational calculus (treat d/dt as an algebraic operator) solves differential equations

• a. Heaviside's procedure was not rigorous in his time. Later, Bromwich "devised a rigorous mathematical justification" using contour integration, connecting it to the Laplace transform [web: https://en.wikipedia.org/wiki/Oliver_Heaviside]. Heaviside's expansion theorem is a legitimate special case of the inverse Laplace transform for rational functions. [memory, high]
• b/c. The results agree with solutions obtained by other (rigorous) methods; the Laplace transform is standard in circuit and control theory. Tested by comparison with known solutions and by electrical engineers; replicated. [memory, high]
• d. Nothing; mathematics was extended to catch up.
• Rejection/resistance. Mathematicians of the era were hostile to unproven manipulations. Heaviside's Vol. 1 contents carry the section "On the nature of Anti-Mathematicians and of Mathematical Methods of Enquiry" [read: Theory contents], showing his combative stance. The resistance was partly on legitimate grounds (no proof) and partly a clash of cultures. Heaviside's phrase that he would not refuse dinner because he did not understand digestion is a well-known paraphrase [memory, medium, not read here]; do not rely on exact wording.
• Verdict: Historically superseded but instructive as a method (replaced by Laplace transform and distribution theory with rigorous proofs), and Established as to correctness of its outputs.

Claim 6. A reflecting ionised layer in the upper atmosphere explains long-distance radio

• a. Consistent: a plasma reflects radio waves below the plasma frequency. [memory, high]
• b. Yes: ionospheric reflection is measured (HF skip, ionosondes).
• c. Tested? Predicted independently in 1902 by Kennelly and Heaviside; experimentally shown by Edward Appleton in 1924 (Nobel Prize 1947); Breit and Tuve mapped altitude in 1925 [web: https://en.wikipedia.org/wiki/Kennelly%E2%80%93Heaviside_layer]. Replicated and routine since. Note: Step 1 had "confirmed 1923" from the Heaviside Wikipedia page; the layer page says 1924 (see corrections).
• d. Nothing; it filled a gap.
• Verdict: Established. Heaviside's role was an inference, not a measurement; priority is shared with Kennelly.

Claim 7. Minor and unusual positions (three separate claims)

7a. Maxwell's treatment of force on intrinsically magnetised matter is "probably wrong" (sec. 83, p.103). [read: contents only] - a/b/c/d: I only saw the heading (and neighbouring headings, secs. 82, 82A, 83, 84, 85, e.g. "Special Estimation of Energy of a Magnet and the Moving Force it leads to" [read: p.xv]). I did not read the argument, so I cannot assess the mathematics, and I have no source about whether anyone tested it. [unknown] - Verdict: Not assessable from the available pages. If forced: Never properly tested as stated; in modern terms the force on magnets depends on how magnetisation is modelled (a known textbook subtlety, [memory, low]; not verified).

7b. Gravity-electromagnetism analogy (1893). - a. Heaviside's formulation is an analogy extending Newton's law of gravitation with magnetic-like terms; the equations "differ only by small factors" from the later linearised GR form [web: https://en.wikipedia.org/wiki/Gravitoelectromagnetism]. - b/c. Gravity Probe B measured frame dragging in line with general relativity's gravitomagnetic prediction (the effect Heaviside's analogy resembles) [web: same page]. The page says this supports GR's prediction, not Heaviside's historical formulation specifically. The Heaviside Wikipedia page's wording that Heaviside's extension was "confirmed by Gravity Probe B" overstates the case; I treat it as not supported. - d. Nothing new: GR (linearised weak-field limit) covers it. - Verdict: Historically superseded but instructive (a good analogy that GR later made precise; credit to Heaviside for the idea only).

7c. Opposition to Einstein's relativity. - Heaviside was "an opponent of Albert Einstein's theory of relativity" with invective that "often bordered on the absurd" [web: https://en.wikipedia.org/wiki/Oliver_Heaviside]. I have no read text of his arguments, so I cannot say what they were. - Relativity has been tested extensively (time dilation, GPS, light bending), [memory, high; no URL checked]. Opposition by Heaviside is not an experimental result. - Verdict: Not testable as stated for what I can see (no argument read); his position is, as far as the record shows, Tested, not supported by later relativity experiments, but this is the claim I know least about.

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Strongest honest case for Heaviside as the contrarian's exhibit

1. Dismissed without testing, then vindicated. A senior establishment engineer (Preece) blocked the loading-coil paper (1887); industrial testing in 1899 showed loading coils worked; an AT&T-paid patent went to another inventor [web: Heaviside and Loading coil Wikipedia pages]. This is a documented case where authority, not experiment, decided the early outcome.
2. Outsider mathematics later became the standard. The four-equation form, vector analysis and the operational method all became textbook-standard or were made rigorous by others [web].
3. Prediction ahead of confirmation. The ionospheric layer predicted in 1902, confirmed in 1924 [web].
4. Cautions the contrarian must apply. None of this supports the idea that outsiders are generally right. Heaviside's physics claims that were confirmed were conventional-physics extensions with clear tests; his anti-relativity stand lost. The "anti-Mathematicians" polemic (sec. 63, "Advice to anti-Maxwellians" [read]) shows an abrasive style that did not help his reception; the key claims were nevertheless right on the evidence, not on rhetoric.
5. Evidence quality limits. I could not read the original arguments for most claims; "vindicated" for claims 1-3 and 6 rests on [web] and [memory] summaries, not on the primary works.

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Corrections to Step 1

1. Claim 1 wording. claims.md says the four equations replaced "Maxwell's twenty component equations". Wikipedia says Heaviside reduced "twelve of the original twenty equations in twenty unknowns" to four [web: https://en.wikipedia.org/wiki/Oliver_Heaviside]. Corrected.
2. Claim 6 date. claims.md says "confirmed 1923" (from the Heaviside page). The Kennelly-Heaviside layer page says shown by Appleton in 1924 and mapped by Breit and Tuve in 1925 [web: https://en.wikipedia.org/wiki/Kennelly%E2%80%93Heaviside_layer]. Sources conflict by a year; I use 1924 and flag it as unresolved.
3. Claim 3. The Preece dispute was tagged [memory, high]; now verified [web]: Preece blocked the 1887 paper proposing loading coils. Added tests: Campbell 1899, Pupin patent, Krarup 1902 [web: Loading coil page]. Step 1 omitted any testing record.
4. Claim 7 (gravitoelectromagnetism). Step 1 relied on Wikipedia's Heaviside article, which says confirmed by Gravity Probe B; the GEM page says the experiment supports GR's gravitomagnetism, not Heaviside's original analogy. Flagged as overstated.
5. facts.json, Electromagnetic Waves entry. The statement that p.143 gives z = (8/3 pi) x 10^-8 cm is correct (checked numerically). The "H disturbance made ?H1" detail was not recorded; I read it as 3/2 H1 on the incident side (consistent with the boundary conditions). Facts also describe a "thin sheet attenuates an incident plane wave" (key claim 2): the formula gives the transmitted amplitude and is valid for a sheet much thinner than a skin depth. Minor clarification.
6. No error found in: Theory contents (sections 33-85, sec. 70 Poynting flux, sec. 83 magnetised matter, dates Mar-Sept 1891), eqs. (58)-(62) content, the unit statement (EM CGS; mu v = 3e10 cm/s).

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Investigator findings (2026-10-05)

Weighed: every "Leads for review" entry in sites.md and the six research notes dated 2026-10-05 (archive.org, Google, Grace's Guide, IET Archives, Physics Today/Hunt 2012, Royal Society Publishing/Bruton 2018). None had been weighed in the review above (dated 2026-10-02). No files were saved to research/files/ (the Investigator could not get download approval), so everything below rests on the Investigator's reading of the pages in a browser, tagged [web] with the URL it gave. I have not re-opened these sources myself. Where a quotation comes from OCR the Investigator marked equations as garbled; I treat formulas as unread. Hunt (historian, no stake) and Bruton (Science Museum historian) are secondary sources with archival references; the 1925 IEE and Nature obituaries are written by admirers; Preece, Biggs and Heaviside are parties with a stake in the 1887 dispute, and their statements are reported as theirs.

Effect on the Source gap

The review's main weakness was that the primary texts were unread. The Investigator read, on archive.org, parts of Electrical Papers vol. 2, Electromagnetic Theory (EMT) vols. 1-3 and the 1902 Britannica article. That closes the gap for claims 3, 6, 7a and 7b in part, and for 7c in a negative sense (see below). Claims 1, 2 (beyond sec. 68) and 4 gain nothing new. Formulas in EMT1 secs. 83 and App. B remain unread (page images needed).

Claim 3 (inductance, distortionless line, Preece)

Finding 3.1, Heaviside's own 1887 statement. Electrical Papers vol. 2, Sec. XL (The Electrician, 1887, pp. ~119-124): "Increasing the inductance is another way of improving things... There is a critical value of the inductance for minimum attenuation-ratio"; leakage increases attenuation "but the distortion is reduced. This has led me to a theoretically perfect arrangement. Make R/L = K/S, and the distortion is annihilated"; solution V = f(x - vt) e^(-Rt/L), "half electric, half magnetic" [web: https://archive.org/details/electricalpapers02heavrich]. K is leakage conductance, S permittance per unit length, so this is the modern R/L = G/C. The OCR reads "E L K S"; the Investigator reconstructed R/L = K/S. I checked it against my earlier derivation (condition for frequency-independent attenuation sqrt(RG)): it agrees. - (a) Consistent with what I derived above. He also states a self-flagged "unbelievable result" (sinusoidal current at the far end of an Atlantic cable exceeding the steady current) and attributes it to reflections to be avoided; this is a candid caveat, not an error I can find. - (c) This is a public, dated statement of the condition in 1887, twelve years before Campbell's 1899 test. It shows the idea was in print and available before the test; so "dismissed without testing" applies to the Post Office/STE gatekeeping of the joint paper, not to a complete absence of publication. The section does not show discrete coils at intervals; it shows raising inductance by spacing wires and by iron, and cites (cautiously, "I do not wish to magnify its importance") reports of good long-distance telephony with copper-covered steel wire. The coil proposal rests on the secondary sources I used earlier (Wikipedia: 1893; Grace's Guide: 1893; Hunt: coils at regular intervals in the 1886-87 work). Those disagree on date. I correct my earlier text: the loading-coil date is 1887 per Hunt's account of the blocked paper, 1893 per Wikipedia and Grace's, not fixed by a primary text I have seen. - Bearing on the verdict: strengthens "Established"; no change.

Finding 3.2, the block: two mechanisms, four sources. - Hunt (2012) and Bruton (2018): joint Oliver/Arthur paper completed April 1887 for the Journal of the Society of Telegraph Engineers; Arthur, a Post Office employee, needed clearance from his superior Preece, who "promptly declared the paper worthless and blocked it" [web: https://physicstoday.aip.org/features/oliver-heaviside-a-first-rate-oddity ; https://royalsocietypublishing.org/rsta/article/376/2134/20170454/115714/From-theory-to-engineering-practice-shared]. Blocked before submission. - 1925 IEE obituary (Grace's Guide, author unnamed): Preece's circle "caused his papers and those of his brother... to be rejected by the Society of Telegraph Engineers" [web: https://www.gracesguide.co.uk/Oliver_Heaviside]. Rejection by the society. - Grace's chronology: Heaviside "suspected" Preece blocked publication and caused the cancellation of his Electrician articles. This is Heaviside's belief as reported. - Bruton, footnote 18 (IET SC MSS 005/I/1/12, 1886-89 notebook): notes on Phil. Mag. Parts VIII and IX of "On the Self Induction of Wires", "declined by the Philosophical Magazine and blocked by Preece, and partly published in The Electrician" (Bruton's description of the notebook; I have not seen it). So a second blocked item exists, not only the STE paper. - The two accounts differ on mechanism; both agree Preece obstructed. The deciding records are the STE council minutes for 1887 and the IET notebook; neither has been obtained. I leave the discrepancy open rather than choose. - Effect: the review's phrasing "Preece blocked the 1887 paper" stands but should read "blocked before submission (Hunt, Bruton) or caused rejection (IEE 1925 obituary)". The contrarian reading "a gatekeeper's block decided the early outcome" is supported by four sources; their mechanisms differ.

Finding 3.3, Preece's own position (party with a stake). Preece's pencil draft reply to Kelvin (IET SC MSS 022/VII/526, n.d.) per the catalogue description: "Heaviside and his dreadful twaddle", calculates "Kelvin's formula to show that he is correct and Heaviside is wrong", criticises "'drawing room philosophers' like Oliver Heaviside and Sylvanus Thompson" [web: https://iet.adlibhosting.com/Details/archive/110008739]. Only the catalogue description was seen, not the letter. It gives a first primary glimpse of Preece's reasoning: he relied on the Kelvin (KR) cable formula, which Heaviside's 1887 text says "wholly ignores inertia" (inductance) and "gives results which have no resemblance whatever to the real" for telephony. This fits Hunt: Preece had publicly justified the costly shift from iron to copper wire by the need to reduce inductance, so he had a public position and expenditure to defend. Contrarian assessment: this is better evidence of conviction plus stake than of bad faith; the review's earlier caution about attributing motive stands. A model-based objection (the KR law is correct for slow cable signalling, wrong for telephony frequencies) would explain the dispute without suppression, and nothing found refutes that reading.

Finding 3.4, evidence that complicates the outsider-victim story (applying the same rigour to Heaviside). - Kelvin to Preece, 12 July 1887: a footnote in a Heaviside Phil. Mag. article "should not have appeared as it was so ill natured" (cataloguer's wording) [web: https://iet.adlibhosting.com/Details/archive/110008793]. Kelvin sided with Preece on tone in that month, then praised Heaviside's propagation theory in his Jan 1889 IEE address (Hunt) and helped him into Phil. Mag. in Nov 1887. So the resistance was not uniform; Heaviside's abrasiveness is documented by a sympathetic senior figure. - 1873: Heaviside's duplex paper disparaged Culley's and Preece's work and did not cite Preece's 1855 duplex patent. Preece to Culley: "most pretentious and impudent... He must be met somehow"; Culley: "We will try to pot Oliver somehow" (Bruton, archival ref. [22]; I have not seen the letters). Both facts matter: it documents a pre-existing hostility with a stake on Preece's side, and it shows Heaviside also gave provocation. Bruton's source is archival; this is single-source (Bruton) so far, and I weigh it as reported. - Arthur Heaviside "supported Preece against his own brother when it came to loading" (Bruton); Oliver's 1922 characterisation: "AWH was very afraid of P... The greatest mistake AWH ever made was to throw me overboard" (IET SC MSS 068; Heaviside's own words, 35 years after). Heaviside's characterisation, not independently confirmed.

Finding 3.5, loss of the Electrician outlet (absence-of-evidence analysis). Heaviside's series "Electromagnetic Induction and its Propagation" ran from 3 Jan 1885 to the 46th section in Sept 1887, "when the great pressure on space and the want of readers appeared to necessitate its abrupt discontinuance... Perhaps there were other reasons than those mentioned... We do not dwell in the Palace of Truth" (EMT1 sec. 1) [web: https://archive.org/details/electromagnetict01heavuoft]. A straggler 47th section appeared 31 Dec 1887. His article "Mr. W. H. Preece on the Self-Induction of Wires" is dated 24 Sept 1887 yet "now first published" in 1892 (EP2 Art. 38): "Mr. Preece is wrong... radically wrong". Hunt (citing Mahon 2009 p. 79): editor Biggs, Heaviside's supporter, declined his anti-Preece letters for fear of libel, was "abruptly removed" in Oct 1887 ("a move he later hinted was prompted by his support for Heaviside"); the new editor cancelled the series after asking around and finding no one read them. Competing explanations for the dated silence in print: 1. Commercial/editorial: space pressure and low readership, as stated in print by both the editor (per Hunt) and Heaviside. Evidence for: given contemporaneously; the series was long and mathematical. Evidence against: the timing coincides with the Preece dispute and Biggs's removal. 2. Pressure from Preece or his circle on the journal. Evidence for: Biggs's own hint (one source, Mahon via Hunt, from the interested editor); Heaviside's insinuation; the timing. Evidence against: no document yet found shows contact between Preece and the proprietors; the hint is a hint. 3. Libel caution (Biggs's stated fear): consistent with either of the above. Decisive records: Electrician proprietors' and editorial papers, the 1887 volumes (HathiTrust, not reached), STE minutes. I do not rate 2 as proven. I note that an explanation resting on "an editor said he feared a libel suit" is at least as documented as one resting on suppression.

Finding 3.6, Pupin's payment: three figures. $455,000 (Wikipedia, used earlier), "over $400 000" (IET blog), $500,000 (Hunt, who calls the circumstances "somewhat shady"; his characterisation). The primary AT&T/Pupin contracts have not been found. Does not change the verdict; the earlier review's figures ($200,000 initial, $455,000 later) are one of three versions.

Finding 3.7, support by others. 1925 IEE obituary: Silvanus Thompson "among the first to take the theory up", then Pupin "with considerable success"; Russell (Nature 1925): Pupin worked "on these lines some ten years later" [web: Grace's Guide]. Both admirers' accounts. Wiener "denounced AT&T and Pupin as thieves" (Hunt; Wiener's The Tempter, 1959). These are pro-Heaviside characterisations of Pupin's priority; the legal fact reported earlier (AT&T paid for the patent partly because of Heaviside's prior publication) remains from Wikipedia only. No court or patent-office record of the priority question has been found. Note: I do not know whether Pupin's loading design was independent of Heaviside; the Investigator's records do not settle it.

Verdict, claim 3: Established, unchanged. Refinement: the 1887 condition was published by Heaviside himself; the gatekeeping concerned the joint paper (and Phil. Mag. Parts VIII-IX) and the Electrician series; the mechanism of the block is reported two ways.

Claim 5 (operators)

Finding 5.1. Hunt (2012) verbatim: in 1893 Heaviside sent two instalments of "On operators in physical mathematics" to the Royal Society; "pure mathematicians objected to the cavalier way he handled divergent series, and when he submitted a third installment, it was sent to a referee and rejected" [web: Physics Today]. A Google snippet of Hunt's 1991 chapter names the referee: William Burnside, Royal Naval College Greenwich (snippet only; the chapter was not opened). The referee's report has not been found (Royal Society archive series RR, not reached). Finding 5.2. EMT2 sec. 425 (p. ~434): "if investigations of this matter are not good enough for Another Place, how can they be good enough for Electromagnetic Theory?... the wet blankets of rigorists." "Another Place" is the Royal Society (the Investigator's reading). EMT2 p. ~9: "Shall I refuse my dinner because I do not fully understand the process of digestion? No, not if I am satisfied with the result." (verified in OCR; Hunt cites p. 9) [web: https://archive.org/details/electromagnetict02heavrich]. This replaces my earlier "[memory, medium]" tag on the dinner remark. A secondary source (deadreckonings.com, via Google snippet) says vol. 2 contains a modified version of the rejected Part III. Weighing (rejection of the third part): the referee's grounds were rigour, and the review above already says part of the resistance was legitimate. A Royal Society refusal of a paper (not a lasting ban) with the content reappearing in print is a weaker case of suppression than 3.5. The referee report is the missing record. Bromwich's later justification remains the vindication. Verdict, claim 5: unchanged (Historically superseded as method, Established as to outputs).

Claim 6 (ionised layer)

Finding 6.1, the 1902 text itself. Britannica 10th ed., new vol. XXXIII, "Telegraphy", I. Theory (pp. ~213-215): "There may possibly be a sufficiently conducting layer in the upper air. If so, the waves will, so to speak, catch on to it more or less. Then the guidance will be by the sea on one side and the upper layer on the other." [web: https://archive.org/details/in.ernet.dli.2015.209824]. The passage frames wave guidance between two conductors (sea and layer), tentatively ("may possibly"); it does not state reflection or the radio-skip mechanism. Reading-list entries cite Electrical Papers and EMT. The author initials on the page are OCR-garbled (likely O. H., not confirmed). The 1925 IEE obituary says he put "sarcasms, in a veiled form" in the concluding part of this article, a claim the Investigator did not check. Finding 6.2, priority. Kennelly, "On the Elevation of the Electrically-Conducting Strata of the Earth's Atmosphere", Electrical World and Engineer 39(11): 473, 15 March 1902 (several search-result citations; text not read); Bruton: Kennelly March 1902, Heaviside December 1902 [web]. So Kennelly's publication precedes by about nine months. My earlier text called the 1902 predictions "independent" and credited Heaviside with a shared prediction; the primary text read supports "shared in date of year, second in publication, tentative in content". Finding 6.3, dates. Appleton's experiments began late 1924 (Bruton); the IET blog says Appleton demonstrated the layer in 1924. This supports the 1924 date I adopted over "1923" and removes part of the unresolved flag; the 1923/1924 disagreement in Wikipedia still stands but the Bruton date favours 1924. Verdict, claim 6: split. (i) Existence of a reflecting ionised layer: Established, unchanged. (ii) Heaviside's role: previously "an inference, shared with Kennelly"; now, on the primary text, a tentative 1902 suggestion of waveguide-type guidance, published after Kennelly, which I weigh as a lesser contribution than the review's earlier wording implied. Verdict for (ii): Plausible, untested in the form stated (guidance between sea and layer); the reflection form is Kennelly's and later Appleton's. This is a change from my earlier "Established" for the attribution.

Claim 7a (force on magnetised matter, Maxwell "probably wrong")

Finding 7a.1, his argument. EMT1 sec. 83 (pp. 103-104), heading "Difficulty. Maxwell's Solution probably wrong...": the resultant force on a magnet can be had from the surface stress outside, but "it is impossible that the real forcive can be represented merely by the surface traction"; surface-equivalent magnetisation or fictitious surface currents are "purely artificial"; to get the real forcive "we must go inside the magnet. This can only be done hypothetically, and with precarious validity." Maxwell's way he "believe[s] to be quite erroneous for many reasons, the principal being that it does not harmonise with his scheme generally, and that it lumps together intrinsic and induced magnetisation, which have essential differences and are physically distinct" [web: https://archive.org/details/electromagnetict01heavuoft]. Formulas not read (OCR garbled). - (a) Cannot check mathematics. (b) Consistent with the modern textbook point I flagged ([memory, low]) that the internal force distribution depends on how magnetisation is modelled; his own text admits the internal distribution is hypothetical. The total force is fixed by the outside stress, which he accepts. - (c) No test found. The distinction needs a measurement of internal stress, and he himself says that route is "hypothetical... precarious". So the claim is not "tested and failed" nor "dismissed without testing"; it is a distinction the available measurements (total force) cannot separate. - (d) Nothing changes in mainstream results for total forces. Verdict, claim 7a: changed from "Not assessable" to Never properly tested (an interpretive distinction in the internal force distribution; the total force is not in dispute; the formulas are still unread).

Claim 7b (gravity-electromagnetism analogy, and the sec. 68 "gravitational difficulty")

Finding 7b.1. EMT1 sec. 68 (p. ~75-76): gravitational energy is obscure; "the energy must have been in the ether... we are entirely ignorant of its distribution in the ether, and of its mode of transference" [web]. So the difficulty is that gravitational energy has no known flux comparable to E x H. This also answers my claim 2 note: the "gravitational difficulty" is a statement about gravitational energy, not a flaw in the Poynting flux of electromagnetism. Finding 7b.2. EMT1 App. B (EMT1 pp. 455-466; The Electrician, 1893): gravity assumed to propagate at speed v via the ether; "no aberrational effect, but only a slight alteration in the intensity of force in different directions round a moving body... a slight weakening of the force in the line of motion, and a slight strengthening equatorially. The direction is still radial." - Arithmetic flag. The Investigator reports u = 3 x 10^6 cm/s ("the speed of fast stars"), v = speed of light, and (u/v)^2 = 10^-6. With v = 3 x 10^10 cm/s, u/v = 10^-4 and (u/v)^2 = 10^-8, not 10^-6. A value of u = 3 x 10^7 cm/s (300 km/s) gives 10^-6. Either the Investigator's note has an exponent error, the OCR dropped one, or the source figure is different. The text says forces are "one-millionth of the full force" and Sun-Earth attraction rises "one two-millionth part", which matches 10^-6. I cannot resolve this without the page image; I record it as unresolved and do not rely on the number. [my arithmetic; source unread] - (b/c) No frame-dragging (gyroscope) prediction was seen in the passages read. His result is a velocity-dependent, radial, order-(u/c)^2 correction. Gravity Probe B measured frame dragging and geodetic precession and supports the GR gravitomagnetic prediction [web: Gravitoelectromagnetism, per earlier]; it does not test this correction. My earlier treatment of the Wikipedia "confirmed by Gravity Probe B" wording as overstated is supported by the primary text read: what Heaviside wrote is not the GR frame-dragging effect. - Whether the (u/c)^2 correction exists in linearised GR is not something I have checked. I do not claim it does or does not. Verdict, claim 7b: unchanged (Historically superseded but instructive); now rests partly on primary text. The numerical comparison with linearised GR remains undone.

Claim 7c (opposition to relativity)

Finding 7c.1. EMT vol. 3 (1912) OCR: "Einstein" 0 hits, "Minkowski" 0, "relativ" 21 (e.g. "the principle of relativity of motion" for a moving ether), "Lorentz" 30, "FitzGerald" 15; sec. 473 is "Lorentz's Equations of a Moving Dielectric" (dated 5 Oct 1900) [web: https://archive.org/details/electromagnetict03heavuoft]. The Investigator's lead: any anti-Einstein remarks are in the unpublished fourth-volume notes (2003 AMS Chelsea edition, lending-only on archive.org, not opened) or in letters. Silence in vol. 3 is not evidence that he did not oppose relativity: the volume predates the 1915-16 general theory and was written when special relativity was new. The Wikipedia claim of invective remains single-sourced (Wikipedia); I could not weigh its wording, and now cannot place it in a published text. Other items: Russell (Nature 1925) says Heaviside "was one of the first to predict the increase of mass of a moving charge" (Grace's Guide). Heaviside's 1902 paper "The Waste of Energy from a Moving Electron" and 1905 "Electromagnetics in a Moving Dielectric" are listed by the Investigator as unread Nature items. Verdict, claim 7c: unchanged (the least-known claim); the new evidence shows I should not describe his anti-relativity position as documented in his published volumes.

Claims 1, 2, 4

• Claim 1. Hunt: Föppl's 1894 textbook carried Heaviside's form of the equations, "from which Albert Einstein, among others, would learn electromagnetic theory" [web: Physics Today]. Supports the transmission of his four-equation form; no change. Established.
• Claim 2. EMT1 sec. 68 as above clarifies sec. 68. FitzGerald's notebook, 9 Sept 1888: "Very important... Must be all in O. Heaviside" (Trinity College Dublin, per Hunt) records contemporary regard. No change. Established.
• Claim 4. No new evidence. Unchanged.

New own-work items (kept in the record)

• British patent 1880 no. 1407, "Improvements in Electrical Conductors...", granted to Oliver Heaviside alone (Arthur, a Post Office servant, could not hold it); Bruton calls it "essentially the patent for what later came to be known as a 'coaxial cable'", recognised by C. S. Bright, Submarine Telegraphs (1898) [web: Bruton]. The patent text has not been read. Bearing: an inventor-claim not in the folder; testable by patent office record; no verdict from me beyond "not reviewed".
• IET SC MSS 005/I/1/12 notebook (1886-1889), MS copy of "Self Induction of Wires" with notes on blocked Parts VIII-IX.
• IET SC MSS 005/I/2/057, Preece, "America Revisited - 1907", proof with Heaviside's MS notes (1908) [web: https://iet.adlibhosting.com/Details/archive/110005818]; contents not seen.
• IET SC MSS 005/I/6/43, C. A. Stevenson correspondence 1897-1921, partly on "Heaviside's brother's career and being blocked by Preece" [web: https://iet.adlibhosting.com/Details/archive/110007369]; contents not seen.
• Other IET records the Investigator saw only in search results (notebook: "occasional comments referring to his disputes with Sir William Preece and Lord Kelvin", record 110000639; a typed copy of A. W. Heaviside's report, probably 1936, in correspondence with The Times, 110008809). Not opened.
• Further own writings listed but unread: Electromagnetic Waves (1889), and Nature letters 1892-1905 (including "The Undistorted Cylindrical Wave", 1903).

Records that go quiet (anomalies to analyse, not neutral gaps)

1. The 1887 joint paper (Oliver and Arthur). Blocked (per Hunt, Bruton) before submission; content partly absorbed into EMT1 (1893) and the Electrician sections (Bruton); Arthur published his part only in his 1900 IEE Newcastle address (Bruton). Competing explanations of why the full paper itself is not on record: it was never submitted so no council record exists (consistent with the block-before-submission account); it was rejected and lost (IEE 1925 obituary version); it was reworked into later publications and the original discarded. Deciding record: IET notebook 005/I/1/12 and STE minutes, plus any BT Archives file (TCB 274/1, not reached). I do not choose.
2. EMT vol. 4 and later papers. Russell (1925): Heaviside planned vol. 3 for 1904 and a concluding volume for 1910, "but this he found impossible" and issued vol. 3 in 1912 as "concluding". Bruton: papers "discovered under the floorboards of OH's former home in Paignton around 1957" (used by H. J. Josephs, GPO), and a 1932 GPO report, "The Application of the Heaviside Analysis to Electrical Engineering Problems", "no copies of which survive". The 2003 AMS Chelsea edition, with the vol. 4 notes, is a lending item. Competing explanations for the loss and non-appearance: the author's health and poverty (consistent with Russell's "impossible"); loss of papers in moves (the floorboard find is evidence that some papers were hidden rather than lost); institutional neglect (the GPO engaged formally only after Appleton, 1924-25, per Bruton). I see no evidence of suppression in these records; I also see no evidence of an effort to preserve until 1957. Decisive record: the Chelsea edition and the Josephs papers.
3. The 1932 GPO report. "No copies survive" (Bruton); whether it was lost or withdrawn is unknown.

Unexamined records still named by the Investigator

Royal Society referee report on Part III (RR series); BT Archives (TCB 274/1, TCK 89/23, POST 30/2668B); HathiTrust The Electrician 1887 (Biggs's removal; Preece's British Association paper 16 Sept 1887 p. 400); Journal of the STE 1887 and council minutes; Kennelly's 1902 article (ETHW); AIM25 description of SC MSS 005 (blocked: browser had no read permission); De Gruyter Hunt 1991 chapter (did not load); IET catalogue records not opened. Yavetz (2011) and ODNB were seen only as snippets.

Summary of verdict changes (this update)