Thompson-JJ (J. J. Thomson): Physicist review (STEP 2)

Reviewer: PhD physicist, 2026-10-09. Inputs read: claims.md, facts.json (via claims.md summaries), all eight deep/ files, sites.md and the research notes' leads, and the key page image of Corpuscular Theory p.33 (PDF p.48). Source tags: [read] from the project's documents (deep reads, which I checked against the page image noted), [web] with URL, [memory] with confidence, [calc] my arithmetic. No source gap: all eleven documents are primary and readable; Chapter I of the Corpuscular Theory rests on the digest only (its deep read was overwritten, see claims.md).

Units note for the reader. Thomson writes in CGS electromagnetic units (emu): charge e_emu = e_esu / c, so 1 emu of charge = 10 coulombs. His electron charge is about 10^-20 emu (modern 1.602 x 10^-20 emu = 1.602 x 10^-19 C). Every formula below was checked in these units [read: deep/Corpuscular, section 0].

How to read the verdicts

Thomson was an experimenter first and a model-builder second. Where he reports a measurement (e/m of cathode rays, Zeeman e/m, positive-ray masses) he is largely right and often decisively so. Where he builds a mechanical model of the atom, the model is a stage in the history of physics and was replaced. The verdict scale is applied claim by claim, with split verdicts where the strong and weak forms differ.

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Claim 1. Corpuscles (electrons): universal, negative, e/m about 10^7 emu/g, constituents of all atoms, source of Zeeman light

a. Mathematics. Internally consistent. The Lorentz-Zeeman algebra (circular orbit with a central restoring force plus H e v) reduces to omega = omega_0 +/- (1/2) He/m, and the exact splitting omega_+ - omega_- = He/m holds without approximation [read: deep/Corpuscular s.8; my check agrees]. Worked number: at H = 10^4 gauss and e/m = 1.76 x 10^7 emu/g the shift is 0.012 nm at 500 nm, which is why "very delicate apparatus" was needed [read, calc]. One slip of language: he calls omega "the frequency" though it is the angular frequency.

b. Experiments. Consistent with every later measurement. e/m = 1.759 x 10^7 emu/g (modern) against his 1.7 x 10^7; the ratio to the hydrogen ion's e/m (about 10^4 emu/g in his book) is 1700, modern 1836 [memory, high]. The Zeeman triplet gives the sign (negative) and magnitude of e/m for singlet lines exactly (Delta E = mu_B B) [memory, high]. His own value of the charge is low: 3.1-3.4 x 10^-10 esu against 4.80 x 10^-10 [read: deep/Corpuscular s.5 and Electricity and Matter; memory, high], and the book is inconsistent with itself (Chapter I e = 1.03 x 10^-20 emu, Chapter VII e = 1.2 x 10^-20 emu) [read]. The anomalous Zeeman patterns he treats with multi-corpuscle normal modes are really spin effects (Lande 1921; Uhlenbeck and Goudsmit 1925) [memory, high].

c. Tested? Yes, many times, by many groups: Zeeman and Lorentz (1896-97), Wiechert and Kaufmann (1897, cathode-ray e/m), Thomson (1897, deflection), Millikan (charge, 1909) [memory, high]. Replicated: yes. Priority is shared: Thomson's is the clearest early statement that the particle is a universal constituent of matter and that it is far lighter than any atom, not the first measurement of e/m [memory, high].

d. If true. Nothing; it is now textbook. The old picture it displaced was the indivisible atom.

Verdict: Established. Qualifier: "emitters of Zeeman light" and "constituent of all atoms" are established; the claim that the number of corpuscles per atom equals the atomic weight is a different claim (see Claim 4).

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Claim 2. All of the corpuscle's inertia is electromagnetic: m = (2/3) e^2/a, rises with speed, a about 10^-13 cm; mass is the "bound ether" of Faraday tubes

a. Mathematics. Split. - Low speed: the field-energy integral gives magnetic energy e^2 V^2/(3a), hence apparent mass m + (2/3) e^2/a. I redid the integral (integral of sin^2 theta over the sphere = 8 pi/3) and it is correct [read: deep/Corpuscular s.1; calc]. In Gaussian units this is 2e^2/(3ac^2). - The radius: a = (2/3) e (e/m) = 1.1 x 10^-13 cm with his numbers, 1.9 x 10^-13 cm with modern ones, two-thirds of the classical electron radius [calc]. The reasoning is circular as a measurement: a is defined as whatever makes the field mass equal the measured mass. - The "4/3 problem" is hidden in his own numbers. His electrostatic self-energy is U = (1/2) e^2 c^2/a, so m = (2/3) e^2/a means U = (3/4) m c^2; equivalently the field-momentum mass is 4/3 of U/c^2 [read: deep/Corpuscular s.5 and Conduction s.6]. Thomson does not remark on it. It is resolved only by non-electromagnetic stresses (Poincare, 1905-06) [memory, high]. - Velocity dependence: the Heaviside field of a uniformly moving charge he quotes is exact [read: deep/Corpuscular s.6]. What a magnetic-deflection experiment measures is momentum/velocity (the "transverse mass") and his Art. 353 is right for that [read: deep/Conduction s.3]. - The Conduction (1906) general formula (1) for the field momentum fails its own slow-speed limit [read: deep/Conduction]. - Internal tension: in the same book (Conduction Art. 355) and in the Corpuscular Theory preface he states that corpuscles cannot carry all of an atom's mass, because there are only about as many as the atomic weight [read]. So "all mass is electrical" is limited by Thomson himself to the corpuscle.

b. Experiments. Velocity dependence of m/e: confirmed in its qualitative form by Kaufmann (1901-06), Bucherer (1908), Neumann (1914) and everything since; at high energy to far better than 1% today [memory, high; web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments and the arXiv summary https://arxiv.org/pdf/1205.5951 say Bucherer 1908 favoured Lorentz-Einstein over Abraham, and that the early experiments were later judged qualitative only; the web search summary says doubts lasted until a 1940 test]. But velocity dependence does not prove the mass is electrical. Relativity (1905) makes m = gamma m_0 for all mass, electromagnetic or not. Thomson's 1906-07 books do not mention Abraham's rigid electron, Lorentz 1904, Einstein 1905 or Kaufmann's 1906 results [read: deep/Corpuscular s.3, item 4].

The table. My recalculation of his stated model (a point charge outside radius a) gives 2.87, 2.15, 1.82, 1.64, 1.51 at his five speeds; gamma gives 3.20, 2.37, 1.98, 1.78, 1.62; Abraham's rigid sphere gives 2.22, 1.85, 1.65, 1.53, 1.44 [calc, deep/Corpuscular s.3]. Neither Kaufmann's five points (beta 0.79-0.95, scatter about 10%) nor Thomson's table separate these models.

Correction to the deep reads (new, from my own check; see "Corrections to Step 1"). The two deep reads assign Thomson's two columns oppositely. The Corpuscular Theory prints the columns "values found by Kaufmann" = 3.09, 2.43, 2.04, 1.83, 1.65 and "alpha calculated" = 3.1, 2.42, 2.0, 1.66, 1.5 [read: page image p.33, which I viewed]. The Conduction chapter prints p' (observed, Kaufmann) = 3.1, 2.42, 2.0, 1.66, 1.5 and p (calculated) = 3.09, 2.43, 2.04, 1.83, 1.65 [read: deep/Conduction s.4]. The Conduction Table 1 of Kaufmann's measured e/m (0.63, 0.77, 0.975, 1.17, 1.31 x 10^7) supports the Conduction labelling: dividing a single slow-speed e/m by the observed ratio should give those numbers, and (e/m) x (3.1, 2.42, 2.0, 1.66, 1.5) = 1.95, 1.86, 1.95, 1.94, 1.97 is nearly constant, whereas multiplying by (3.09, 2.43, 2.04, 1.83, 1.65) gives 1.95, 1.87, 1.99, 2.14, 2.16, which drifts [calc]. So the better reading is that Thomson's calculated column is 3.09, 2.43, 2.04, 1.83, 1.65 (close to the later gamma factor, within 3%, but 8-14% above his own stated point-charge model at the top speeds), and Kaufmann's observed ratios are 3.1, 2.42, 2.0, 1.66, 1.5 (which agree with the exact point-charge model at the two lowest speeds, 1.64 and 1.51). One of the two printings has the column headings swapped. This remains unresolved from the text alone; the 1906 Conduction book and the 1907 Corpuscular book contradict each other, and the verdict below does not depend on which is right.

c. Tested? Velocity dependence: tested and confirmed (qualitatively in 1901-06, quantitatively later) but as a relativistic kinematic effect. "All mass is electromagnetic": the electron radius is now bounded far below 10^-13 cm; the electron behaves as a point at the 10^-18 m (10^-16 cm) level or below [memory, medium; not web-checked]. A purely classical field mass of a point charge diverges, and in quantum electrodynamics the divergence is absorbed into a renormalised mass, so the "radius from the mass" argument has no counterpart. The strong form was not so much refuted by one experiment as made unnecessary and then ruled out by the point-like electron.

d. If true. The electron would need a finite size of order 10^-13 cm (ruled out by scattering and g-2 data [memory, medium]) and an ether to carry the "bound mass"; relativity would need its mass-energy relation to be a special feature of electromagnetism rather than universal. A modern echo worth noting for the reader: most of a proton's mass is field (gluon and quark-motion) energy [memory, high], so "mass as field energy" lives on, but in quantum chromodynamics, not in the electron.

Investigator's findings. Faraday tubes and bound ether: the 1893 Notes on Recent Researches (not read) and, much later, The Structure of Light (Fison Lecture 1925) and Beyond the Electron (1928), in which the quantum is an "anchor ring of closed lines of electric force" moving at c and the electron has "a dual structure" of tubes plus a guiding wave train [web: https://hdl.handle.net/2027/mdp.39015064384293, https://archive.org/details/beyondelectron0000unse; read only as quoted in sites.md, the books themselves not read by me]. These keep the tube-and-ether picture alive after photons and relativity. Mainstream view: closed-line "anchor rings" at c do not follow from Maxwell's equations (free fields spread out), and the photon is not a tube loop; the pages are interesting as the last statement of the Faraday-Thomson tradition. Rayleigh's 1942 life records Thomson's Faraday-tube argument that X-ray wave fronts have "specks of great intensity", which is a localised-radiation idea made before photons were accepted [web per sites.md]. I keep it in the record as a historically interesting anticipation of localisation, not as support for the ether picture.

Verdict (split). - Weak form (a charged body carries field momentum, giving m_em = (2/3)e^2/(a c^2), rising with speed): Established as classical electrodynamics (with the 4/3 caveat). - Strong form (the whole inertia of the corpuscle is electromagnetic, a about 10^-13 cm, carried by bound ether): Historically superseded but instructive. It was a reasonable position in 1903-07 (the data could not separate it from the alternatives) and it is not what electrons are. - "Bound ether" as a physical substance: Not testable as stated (it gives the same numbers as the field momentum D x B and has no separate measurable consequence in these texts [read: deep/Conduction s.6]).

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Claim 3. Roentgen rays are thin pulses from a suddenly stopped charge; the rays make matter conduct by splitting molecules

a. Mathematics. Consistent. The kink construction (tangential field E = c e v sin(theta)/(r delta), pulse energy (2/3) e^2 v^2/delta) checks against Gaussian-unit results; the Larmor power (2/3) e^2 f^2/c in emu is right [read: deep/Corpuscular s.7; calc]. One missing factor e in the printed pulse magnetic force (a misprint) [read: deep/Corpuscular s.7]. Stokes's diffraction estimate (beta^2 = 2 r r' lambda/(r+r'), 1/250 inch) checks [read: deep/Rontgen]; the 1/250 inch is 2 beta, the full width of the zone. Note that Stokes's pulse thickness of about a millionth of an inch (25 nm) is an assumption, not derived [read: deep/Rontgen s.1.7].

Worked number [calc]: a 30 keV corpuscle (v about 10^10 cm/s) stopped within delta = 10^-8 cm radiates (2/3) e^2 v^2/delta = 1.7 x 10^-12 erg, about 1 eV, a fraction 3.5 x 10^-5 of its 30 keV. This is the right order for the very small X-ray efficiency of a tube [memory, medium]. For the pulse to carry the whole field energy, delta would have to be the corpuscle diameter, 10^-13 cm.

b. Experiments. Three pieces. 1. The 1896 note: X-rayed insulators and gas conduct; both signs of charge leak; no leakage threshold down to 3-4 V; no charge on an uncharged plate; leakage independent of direction along or across the rays [read: deep/On the Discharge]. These are correct and are the basis of ionisation-chamber physics. The "splitting of molecules like electrolysis" is the right idea in outline (ionisation, the word "ion" in the electrolytic sense). All qualitative: no numbers, pressures or rates are given. 2. The pulse picture of the continuous radiation. This is classical bremsstrahlung, correct as far as it goes, and the radiated power from a decelerating charge is Larmor's. But the theory as stated, "Roentgen rays are not waves but impulses; no periodicity needed" [read: deep/Rontgen s.1.4, 2.2], was settled the other way. Laue's crystal diffraction (1912) showed X-rays are electromagnetic waves of wavelength about 0.01-1 nm, i.e. periodic and diffractable, with the sharp spectral lines (Barkla characteristic radiation, then Moseley 1913) and the short-wavelength cutoff (Duane-Hunt, 1915) that a pure-pulse theory cannot give [memory, high]. Absence of refraction and diffraction was explained by the wavelength (comparable to atomic spacing, refractive index differing from 1 by about 10^-6), not by pulse thinness. X-ray polarisation (Barkla, 1904-06) had already suggested transverse waves; Stokes himself concluded transversality [read: deep/Rontgen s.1.2]. Thomson in 1906-07 treats the wave versus particle question as open, mentioning Bragg's neutral-pair hypothesis [read: deep/Corpuscular s.7 status; memory, high]. 3. Barkla scattering as a corpuscle counter (Chapter VII, Method I). It uses Thomson scattering (sigma_T = 6.65 x 10^-25 cm^2 per electron, (8 pi/3) N e^4/m^2 in his emu form) [read; memory, high]. This is correct physics. See Claim 4 for the numbers.

c. Tested? The 1896 observations were confirmed within weeks by Lodge's correspondents and by Rutherford, in the Royal Society record on the same page of the meeting minutes (a St Petersburg telegram reports the discharge effect independently) [read: deep/On the Discharge p.3]. The pulse theory was tested by the diffraction experiments of 1899-1912 (Haga and Wind, Walter and Pohl, Sommerfeld; Laue, Friedrich and Knipping 1912) and lost [memory, high]. Replications of the ionisation result: universal.

d. If true. For the strong "impulse, not waves" form: X-rays would show no Bragg diffraction and no sharp lines. Neither is true.

Investigator's findings. C. N. Wall (Phil. Mag. 1924) extended the pulse theory to a "selection principle" [web per sites.md; not read, so no judgement]. The pulse picture's quantum counterpart (photons from stopped electrons) is the standard account.

Verdict (split). - Ionisation (X-rays make gases and dielectrics conduct by splitting molecules into charged parts): Established. - Continuous X-rays are radiation from decelerated charge (Larmor): Established (bremsstrahlung). - "Roentgen rays are thin non-periodic pulses and not waves": Historically superseded but instructive; superseded by Laue 1912 diffraction; Stokes and Thomson are reasonable for 1897-98, when only the absence of refraction and diffraction was known.

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Claim 4. The atom is a uniform sphere of positive charge holding N = atomic-weight corpuscles in rings; rings explain the periodic law, valency and spectral series

a. Mathematics. Internally consistent as a model, with errata. - Static equilibria in a uniform sphere: for N = 1-4, Q = 0.9, 2.1, 3.6, 5.4 e^2/a with nearest-neighbour distance exactly a; my minimisation reproduced all four [read: deep/Corpuscular Ch.VI s.2]. The octahedron of 6 is stable and the cube of 8 is unstable, as he says. Aggregation versus dissociation depends on whether the positive sphere keeps its radius or its volume [read]. - Rings: a hollow regular ring is stable only up to 5 (confirmed, in-plane [read]); the inner-number table i = f(n) is reproduced to about n = 20, with n = 30, 40 values about 30% below a crude model (not reconstructible without the 1904 paper) [read]. The scaling i proportional to n^3 holds. - The ring table (N up to 100): built by a greedy graphical rule. It lists 13, 8, 3 twice and omits N = 23. Against full numerical energy minimisation of the same planar model, the table's rings differ for N = 9, 13, 16, 17, 19, 21 (his are metastable, 0.02-0.15% above the lowest found, and for 13 his arrangement is not stable), and the outer-ring boundaries at 58/59 and 67/68 on which the valency argument rests do not survive [read: deep/Corpuscular Ch.VI s.5]. The text swaps the valencies of the 62-group compared with Thomson's own table [read]. Web check: the 2D Coulomb cluster ground states of this planar problem are tabulated by Bedanov and Peeters (Phys. Rev. B 49, 2667 (1994)); a "Mendeleev table" of shell structures to N = 52 and magic rings at N = 6, 19, 37 are reported by a citing paper [web: https://arxiv.org/pdf/cond-mat/9802034; https://repository.uantwerpen.be/link/irua/9366]. I did not read their N = 9, 13, 16 entries, so the deep reader's [memory, medium] comparison with that paper is not confirmed beyond this. - Valency from barriers: the rule "an atom N can lose N - 59 and gain 67 - N" reproduces the table; the sum of valencies 8 is, by his own statement, "quite accidental" ("If we take the number in the outer ring to be 20 the sum ... is 8; this happens to agree with the number usually assigned ... however, quite accidental") [read: deep/Corpuscular s.9]. The model has a 10-member period for the next series (outer ring 21), not the 9 of Ne to Ar [read: deep/Corpuscular]. Thomson also notes the model is two-dimensional "chosen solely on the ground of simplicity". - Electricity and Matter: premise n = 1000 corpuscles for hydrogen yields 1.02 x 10^19 erg per gram; arithmetic correct, premise wrong (he revised it in 1906) [read: deep/Electricity and Matter s.6]. The radiation-loss table has a power-of-ten slip in the n = 5 row and it is labelled "each corpuscle" though the values are group totals [read; calc]. - The corpuscle counting. This is the weakest part. Barkla's datum (secondary radiation from air about 0.00025 of primary per cc) gives with Thomson's e = 1.2 x 10^-20 emu N = 21.5 n, which he rounds to 25 (molecular weight of N2 = 28); with the modern e and e/m it gives 14 corpuscles per air molecule, about A/2 (the atomic number), not A [read: deep/Corpuscular Ch.VII s.1.2; calc; memory, high that Barkla about 1911 and Rutherford, van den Broek and Moseley (1913) moved to A/2]. My own check agrees: sigma_T x 2.69 x 10^19 molecules/cc x 14.4 electrons = 2.6 x 10^-4 per cm, matching Barkla's 0.00025 [read: deep]. So Barkla's own measurement, worked with the right e, contradicts "N = atomic weight". Method II (cathode-ray opacity) gives 2.2-3.6 corpuscles per unit atomic weight with Thomson's formula, not "the same order" in a way that agrees with Method I; Crowther's value 150 would give 0.27 and the beta-ray values 5-10 would give 0.01-0.02, which he dismisses as measuring a different quantity [read: deep]. Method III (dispersion) gives n of about 1 for hydrogen (0.8 to 1.6 on my numbers). So the "three methods agree" statement in claims.md is too strong: they give about 1 (Method I with modern e, Methods III), 2-4 per unit A (II) and 21-25 per N2 (Thomson's value of e) [calc].

b. Experiments. The uniform-positive-sphere model: Geiger and Marsden (1909) saw alpha particles scattered through large angles (about 1 in 8000 reflected from platinum foil); a uniform sphere of 10^-8 cm radius cannot give this, so Rutherford (1911) put the positive charge into a tiny nucleus [memory, high]. Bohr 1913 and the quantum shells followed. Periodic structure from rings: the modern periods 2, 8, 8, 18, 18, 32 come from quantum numbers and the exclusion principle, not from planar ring stability; the magnet ring breaks (6, 15, 27) do not match [memory, high; read: deep/Electricity and Matter s.8]. Spectral splitting: alkali doublets widen with atomic weight for real (Na D 0.6 nm; K 3.4 nm), but due to spin-orbit coupling [memory, high]. His "Darwin periodic orbit" argument is a qualitative analogy; no orbit is computed [read: deep/Corpuscular Ch.VII s.4]. The Mayer floating-magnet experiment (1878) does reproduce rings of 3, 4, 5, 6 = (5,1), 7 = (6,1), which test the planar model at small N; no data are given for N = 9 or 13 where Thomson's table and the true minimum differ [read: deep/Corpuscular Ch.VI s.6].

c. Tested? Yes: by Geiger-Marsden-Rutherford and by Moseley (atomic number counting). Not supported. Thomson's own caveat on the number of corpuscles per atom: that they cannot carry all the mass [read].

d. If true. Rutherford scattering would be absent; the electron count would be A (about 238 for uranium), contradicting Moseley's Z = 92 and the X-ray scattering of 1911.

Investigator's findings. LaFave (J. Electrostatics 71:1029 (2013); arXiv:1403.2591) reports that energies of N electrons on a sphere (the "Thomson problem") show patterns resembling shell filling and ionisation energies and conjectures a link to the periodic law [web per sites.md; I read only the abstract record in the sites log, not the paper]. This is one published paper by one author (I found no second source); I record it fairly: it concerns point charges on the surface of a sphere with 1/r repulsion, a different problem from Thomson's 1904 ring-in-uniform-sphere model, and the matches to ionisation patterns are numerical similarities. They do not rescue the plum-pudding model, because that model fails on alpha scattering, but they do show the Thomson problem is a live mathematical object (Smale's 7th problem; Levin and Arenzon 2003 per sites.md [web, Wikipedia]) and that his ring idea had real structure to it. I leave the weighing to the reader.

Verdict (split). - Uniform positive sphere with corpuscles (the plum-pudding model): Tested, not supported (alpha scattering, 1909-11). - Number of corpuscles = atomic weight, "supported by three counting methods": Refuted by calculation, using Barkla's own datum with the modern e (about A/2), plus Moseley. His e was 25% low and his rounding pushed the answer to A. - Ring stability mathematics and the ring table: Internally consistent as mathematics; table has errata (23/24, 62 valencies) and some entries are not ground states. The idea that valency and periodicity come from the stability of recurring shell structures: Historically superseded but instructive: the principle survived in quantum shells, the mechanism did not. Thomson himself calls the 8-valency match accidental.

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Claim 5. Positive rays: mass-22 line beside neon; mass-3 line as H3; helium and neon liberated by cathode-ray bombardment, linked (not proved) to disintegration

a. Mathematics. Consistent. The parabola formula e/m = y^2 A/(x B^2) and the comparison m_2/m_1 = y_1^2/y_2^2 at equal x are right [read: deep/Positive Rays s.1]; the 22 line sits only sqrt(22/20) - 1 = 4.9% from neon in deflection [calc]. The chemistry arithmetic (Na - He = 19, K - He = 35, Be - He = 5, C - He = 8) is right.

b. Experiments. Part by part. - Mass-22 line. Thomson excluded doubly charged CO2 (removing CO2 did not change the line), considered NeH2, and wrote that it "must, I think, be a new element", yet closed with the suspicion that the gas might be inseparable from neon, and he cites radioactive analogies; Aston's failed separations (charcoal, then partial diffusion success with a clay pipe) are recorded [read: deep/Positive Rays s.2]. Modern view: neon-22 is a stable isotope (about 9.25% abundance), found by Aston's mass spectrograph (1919) after Soddy's coining of "isotope" (1913) [memory, high; the 1921 second edition of Rays of Positive Electricity cautious on Aston's chlorine-37 per sites.md [web]]. The "much fainter than neon" statement agrees with that abundance. So: his observation is Established; "a new element or inseparable form of neon" is the isotope result, and he did not use the word in 1913. - Mass-3 line. He rules out C^4+ (the C^2+ and C^3+ lines would have to be stronger and are not), shows the product depends on hydrogen-containing salts (KOH, LiCl, CaCl2 vs KI, Li2CO3, KCl), and concludes H3. The modern identification: the ion is H3+, formed in the discharge by H2+ + H2 -> H3+ + H, stable and abundant in space; neutral H3 is not a stable ground-state molecule [memory, high; web: Kragh 2011 Centaurus 53:257 and 2012 Phil. Trans. A 370:5225, per sites.md: H3+ "firmly established", neutral H3 abandoned by the mid-1930s]. Thomson was right that the particle is made of three hydrogens and that the line is not carbon; he was wrong that the observed stable stored gas was neutral H3 (HD+ at mass 3 would also contribute but deuterium was unknown until 1931 [memory, high]). What the weeks-stable stored gas, destroyed by light plus oxygen or by hot copper oxide, actually was cannot be settled from the book and remains unexplained here; he reports a negative spectroscopic search (no lines attributable to X3) [read]. This is an honest anomaly in his own record, not a reason to omit it. - Helium and neon from bombarded solids. What he did, with real controls: helium from 1 cc of air (about 4 x 10^-6 cc) would give a stronger line than most of his signals, so entry of air must be excluded; yield rose with bombardment time; salts were dissolved and evaporated up to 10-12 times with undiminished helium; a split-aluminium blank (one half exposed to helium for two days) differed by about the scatter; yield depended on the salt and on whether the rays hit it; cathodes used for months showed no diminution [read: deep/Positive Rays s.4]. Things he himself notes against: large specimen-to-specimen variation; helium (unlike X3) decays with prolonged bombardment; he calls the transmutation view one that "few will be prepared to accept ... until every other explanation has been shown to be untenable" [read]. He says the deciding test is detecting residues, especially from carbon or beryllium, which he could not complete [read]. In 1921 (second edition) he is still giving two explanations, adsorbed air or "loosened" helium [web per sites.md: https://archive.org/details/in.ernet.dli.2015.160862].

c. Tested? By whom? Replicated? Priority: Ramsay (Nature, 18 July 1912, helium from heated old X-ray bulbs) [read]. Collie and Patterson (J. Chem. Soc. 103:419, 1913) reported neon and helium in discharge tubes and, with Masson, in Proc. Roy. Soc. A 91 (1914), and their paper's referee (Baker, Royal Society) recorded that the results were "currently unexplained" [web: https://makingscience.royalsociety.org/items/rr_21_53/ per my search]. Negative or contrary tests: Strutt (Proc. A 89:499, 1914), Merton (Proc. A 90:549, 1914), Egerton (Proc. A 91:180, 1915), Harkins and Wilson (1915), Allison and Harkins (1924) [web per sites.md, bibliography at https://www.alchemywebsite.com/nelson2_6.html; I confirmed through my own search that Egerton's 1914 paper "The analysis of gases after passage of electric discharge" was refereed by Rayleigh at the Royal Society]. Redgrove (1922) says the Collie-Patterson and Ramsay results "failed to be satisfactorily confirmed" [web per sites.md: https://www.gutenberg.org/files/43240/43240-h/43240-h.htm]; Nelson (an alternative-science author) says "The matter never has been resolved" [web per sites.md]. My search also turned up a later partial support: Baly and Riding (1925) report small quantities of the rare gases from a discharge in oxygen when a nitride-coated anticathode was used and attribute them to disintegration of nitrogen, and say they confirm earlier observations of Collie, Patterson and Masson [web search summary only; I could not open the primary paper, so I treat this as a lead]. The 1922 exploding-tungsten helium claim of Wendt and Irion and Thomson's own Proc. A 101:290 (1922) analysis of "deflagrated metals" are in the Investigator's leads; the result of Thomson's 1922 paper was not read and is unknown to me. I do not claim it supports or refutes anything [web per sites.md]. My memory (medium) is that the Wendt-Irion claim was not reproduced by others and was attributed to helium from the glass; this is not web-checked here. In short: positive and negative results were both published in the period; no neutral, decisive test of the Thomson apparatus itself is on record in what I have read.

Energy budget (the key calculation). Thomson's cathode rays are tens of keV (about 10^10 cm/s). Removing an alpha particle from Na-23 or K-39 needs a binding-energy separation of order 10 MeV for a light nucleus like Na and a few MeV for K [memory, medium; not web-checked]. A 30 keV electron has about 3 x 10^-3 of the lowest of these. Electron-induced nuclear reactions require electron energies in the MeV range and have cross sections of 10^-30 cm^2 or smaller, so the rate is vanishingly small compared with the 10^-3 cc of helium per run he detects. His "loosened alpha" hypothesis (a process analogous to alpha decay that nearly but not completely ejects the helium) has no counterpart: alpha decay needs a positive Q-value, and for these nuclei the alpha-separation energy is positive (the nucleus is stable against alpha emission), so there is nothing to loosen [memory, medium]. This is accepted nuclear physics applied as stated, but the thresholds are [memory, medium] and not web-checked here.

Mainstream explanation of the helium. Atmospheric helium adsorbed or occluded in glass, metal and salt surfaces (Ramsay's own first report is of helium in the glass of old X-ray bulbs), diffusion from the walls under heating, and implanted ions; the sensitivity he proudly cites (1 cc of air = a strong line) is exactly the sensitivity that makes contamination hard to exclude [memory, medium for the consensus; read for the sensitivity]. His time-dependence control (helium grows with bombardment time) does not exclude slow release of occluded gas from heated surfaces, and the solution-and-evaporation control removes surface gas but not gas trapped in the crystal lattice or in the reagent [inference]. I note the one internal inconsistency in the book: 3 x 10^-6 cc (p.130) versus 4 x 10^-6 cc (p.148) of helium per cc of air; the modern figure is about 5.2 ppm [read; memory, high]. It does not affect his argument.

d. If true. Cold (10^5 eV) electrons would transmute sodium and potassium into helium plus fluorine and chlorine, contradicting nuclear energetics and the whole of nuclear physics from Rutherford's 1919 nitrogen transmutation (which needed MeV alpha particles) to modern accelerator thresholds. This is also why the claim is now cited in low-energy nuclear reaction (LENR) lists and reviews, which describe Wendt-Irion as an early precedent [web per sites.md: New Energy Times list, which has no Thomson 1913 entries]. As interested-party material, those lists are characterisations by LENR advocates; the physics community's reading is the one above. Both are reported.

Verdict (split). - Mass-22 line beside neon: Established (neon-22). - Mass-3 line as a hydrogen-containing species, and as H3: the ion H3+ is Established; Thomson's neutral stable H3 is Tested, not supported by later work (neutral H3 is unstable) while the nature of his stored gas is Never properly tested (no controlled repeat of his chemical tests on a stored mass-3 gas is known to me). - Helium and neon from bombardment as evidence of atomic disintegration: Refuted by calculation for transmutation by tens-of-keV electrons (energy budget above), and the experimental reports were Tested, not supported by the later negative experiments, with contamination and occlusion the standard explanation. Thomson's own text does not claim proof, and a fair statement is that he presented it as a possibility to be settled by detecting residues, which he did not do. - Positive-ray analysis as a method: Established (it is the origin of mass spectrometry; Aston's Nobel Prize in Chemistry 1922 [memory, high]).

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Claim 6. (1883) Vortex rings in a perfect fluid interact by computable laws; vortex atoms as a gas reproduce kinetic pressure and might explain chemical combination

a. Mathematics. Sound method, with errata that matter. Treating each ring by its dipole far field and integrating along undisturbed paths reproduces the in-plane deflection (eq. 69) exactly and the inverse-cube law; the radius-change eq. 74* needs k^4 for k^3; out-of-plane eq. 71 is 3 times too small (by his own integrand and by an independent dipole calculation), which reverses the p.75 comparison between crossing and non-crossing paths; the sphere total angle lacks 1/u [read: deep/Vortex Rings s.1, s.11]. Part III (linked vortices): quick and slow vibration frequencies check; the stability of n vortices on a circle: his linearised equations and circulant factorisation are exactly right, but the verdict that seven are unstable rests on a rounding error: seven are neutral at linear order, eight or more unstable, so "six is the greatest number" should read "seven is marginal, eight is unstable" [read: deep/Vortex Rings III.0; calc]. Web: I did not check; my memory (medium) is that Havelock (1931) reached the same stability result for a ring of point vortices [memory, medium].

b. Experiments. Vortex rings are real fluid objects (smoke rings; ideal-fluid dynamics is exact for them at high Reynolds number) and the attraction, leapfrogging and linking calculations belong to the real mathematics of vortex dynamics [memory, high]. As a model of atoms it was Kelvin's vortex atom (1867) and Thomson's Adams-prize essay develops it. It failed because: an ideal fluid ether is needed with no friction; the model gives no spectral lines or e/m; and after 1897 the electron was an independent constituent. Quantised vortex rings in superfluid helium exist but are not atoms [memory, high].

c. Tested? The mathematics was checked by later fluid dynamicists; the physical claim (atoms are vortex rings) was never testable in the form that gave line spectra and was dropped. Gas of vortex atoms reproducing kinetic pressure is a calculation in the essay, not a test [read: claims.md; deep not read for Part I, IV].

d. If true. The ether would have to be a perfect fluid carrying permanent knotted vortices, in conflict with relativity and with the discreteness of atomic spectra.

Investigator's findings. Thomson's 1881 "On the Vibrations of a Vortex Ring" (Proc. Roy. Soc.) is the precursor; the 1925-28 "anchor ring" light quantum and the tubes-of-force electron model can be read as the late relatives of the vortex ring (the ring as a closed line structure) [web per sites.md; not read]. This is a thematic link, not evidence for any of them.

Verdict (split). The ring-interaction mathematics: Internally consistent, with the printed errata above (one conclusion reversed, "seven unstable" a rounding artefact). The vortex-atom as physics of atoms: Historically superseded but instructive.

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Summary of verdicts

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Corrections to Step 1 (for the orchestrator)

1. Kaufmann table, columns swapped between two books. claims.md and the Corpuscular Theory deep read treat 3.09, 2.43, 2.04, 1.83, 1.65 as Kaufmann's observed ratios and 3.1, 2.42, 2.0, 1.66, 1.5 as Thomson's alpha. The Conduction chapter (deep/Conduction s.4) prints them the other way round. I viewed the Corpuscular Theory page 33 image and it does print 3.09 ... 1.65 under "values found by Kaufmann" [read: page image]. The Conduction table of Kaufmann's e/m values (e/m x observed ratio constant to 5% only for 3.1, 2.42, 2.0, 1.66, 1.5) favours the Conduction labelling [calc]. Later documents should say that the two printings by Thomson disagree on which column is observed, and not repeat "Thomson's alpha is 8-12% above my calculation" as if the Corpuscular labelling were certain. The deep read of the Corpuscular Theory (deep/Corpuscular s.3 findings, point 82-83) should be amended.
2. claims.md, claim 4, "supported by three counting methods". Too strong: the methods give different numbers (Method I 21.5 per air molecule from his own inputs, 14 with modern e; Method II 2.2-3.6 per unit atomic weight; Method III about 1 for hydrogen), and Barkla's datum, with the modern e, gives about A/2. Say "three counting methods, which he reports as agreeing with N proportional to atomic weight; recalculation does not support the agreement".
3. claims.md, claim 6, "stability of up to 6 vortices on a circle". Add that seven is marginal (neutral at linear order) and eight is unstable; the printed "seven unstable" is a rounding artefact. Already in the Corrections section of claims.md; I confirm it.
4. Investigator log (sites.md), no error found. One caution: the sites log lists Merton 1914 and Strutt 1914 as "negative or contrary tests" from [web] bibliography; my own search could not open those papers, and a Royal Society referee page flags the Strutt and Merton identifications with a question mark. They should be kept as leads. Also, Baly and Riding (1925) came up in my search as a later partial confirmation, which is not in sites.md and should be added as a lead [web search summary only].
5. Deep read of Positive Rays, context paragraph on the 1913 controversy. It says the episode "is generally regarded as having ended with the effects attributed to atmospheric contamination and gas occlusion [memory, medium]". My web check found sources (Redgrove 1922, Nelson, a Royal Society referee note) that say "failed to be satisfactorily confirmed", "never has been resolved" and "currently unexplained", and later partial positive reports (Baly and Riding 1925); I found no source explicitly demonstrating contamination as the explanation. Hold this as the standard explanation in the field, not as a documented demonstration in the record. My own verdict for transmutation rests on the energy budget, not on the contamination story.
6. Sources I could not verify. The statements about Geiger-Marsden, Laue 1912, Duane-Hunt, Moseley, Barkla A/2, H3+ and Aston's isotope result are [memory, high] and are not additional web-cited; the electron-radius bound and the alpha-separation energies are [memory, medium] and are marked as such where used.