Jeans-JH: Arbiter (Step 3)

Project: three books by J. H. (Sir James Hopwood) Jeans: The Dynamical Theory of Gases (1904), The Mathematical Theory of Electricity and Magnetism (2nd ed. 1911), Atomicity and Quanta (Rouse Ball lecture 11 May 1925, printed 1926). Inputs weighed: claims.md, facts.json, deep/ reads, physicist.md, mathematician.md, contrarian.md, and the Investigator's sites.md and research/ notes.

Tags: [read] project documents (through the reviewers' page-image checks); [web] URL; [memory] with confidence; [calc] arithmetic I re-ran (project venv, CODATA-level constants).

Source gap

No Source gap: all three books have readable text. The two long books are OCR scans with garbled equations; every equation a verdict turns on was read from page images by a deep reader, and again by at least one reviewer (mathematician: Atomicity pp.25, 28, 32, Gases p.221, Electricity p.587; contrarian: Gases p.221, Atomicity p.21, Electricity p.588; physicist: Atomicity p.28). Digest-only coverage remains for peripheral chapters; no verdict rests on a digest alone. Where a conclusion rests on [memory] alone, I say so below. Jeans is the author of every experiment he reports, so those are his descriptions, not the original papers (Wien's decay time, Taylor's 2000-hour exposure, Adams 1901 are not in the folder; Adams 1901 was read by the Investigator).

How to read this project

Jeans was a Fellow of the Royal Society and a first-rate mathematical physicist, not an outsider. The three reviewers agree there is no suppression story: his positions were mostly replaced by Jeans himself (quantum hypothesis during 1910; relativity chapter in the 1919 edition of the electricity book; quantum account of specific heat in the 1916 edition of the gas book). The useful question for the reader is therefore: which parts were correct mathematics later absorbed into the mainstream, which were reasonable for their date and then overtaken, and which (the 1925 time-symmetric idea) were never worked out far enough to test.

Disagreements between the reviewers, and my rulings

I recomputed or web-checked every point where they differ.

1. Strong form of claim 1 (physicist: Refuted by calculation + Tested, not supported; mathematician: Historically superseded; contrarian: Tested, not supported). The three agree on the facts: Jeans needed the ether as a zero-temperature sink (his section 206, "kept at a zero temperature" [read]); a gas in an enclosure at its own temperature absorbs what it emits (Kirchhoff) [memory high]; Jeans conceded in print that equipartition "may be the true final ratio" and that approach takes "millions of years" (Nature 71, 607, 27 Apr 1905 [web: Investigator, research/2026-10-08-montambaux.md]). Ruling: "Refuted by calculation" suits a result where accepted laws, correctly applied, rule a claim out with no experiment. Kirchhoff's law does that only for the version "the equilibrium state has internal modes cold because of radiation loss", and Jeans himself had retreated from that version within a year. The data that discriminate are experiments (H2 rotational freezing, Eucken 1912 [web: https://en.wikipedia.org/wiki/Arnold_Eucken, checked by the contrarian]; low-temperature solids). So I use Tested, not supported for the equilibrium form, and note the Kirchhoff argument as the theoretical reason.
2. Claim 4a, radius and "m0 = 0" (physicist: Historically superseded; mathematician: Internally inconsistent + superseded; contrarian: Tested, not supported). Ruling: not "Internally inconsistent". Within the 1911 book Jeans derives the mass from the field energy only (section 625), and the integral is right (SymPy by the deep reader, again by the mathematician). The 4/3 mismatch (energy-route mass (2/3)e^2/(aC^2) against Einstein's U/C^2 = e^2/(2aC^2); ratio exactly 4/3 [calc]) appears when that mass is compared with the field energy taken as rest energy (E = mC^2); the momentum and kinetic-energy routes agree with each other [QE revision, item 4]. Jeans does not make that comparison in 1911. It is a gap Jeans does not address, and the reason Poincare introduced non-electromagnetic stresses in 1905-06 [web: https://en.wikipedia.org/wiki/Electromagnetic_mass, which gives the 4/3 factor and the Poincare stresses]. Radius: the contrarian's collider bound is the better evidence. The physicist's figure (below 10^-16 cm, [memory medium]) was loose. Web check: LEP Bhabha-scattering limit on the electron radius, r < 2.8e-19 m at 95% CL (form-factor analysis) [web: https://arxiv.org/pdf/hep-ph/0002172 and https://arxiv.org/pdf/2506.02450; confirmed through a search summary, the abstract page itself gave no number]. Jeans's 2e-13 cm = 2e-15 m is about 7000 times larger [calc]. That test was unavailable to Jeans. Verdict: Tested, not supported (radius, by scattering limits); Historically superseded but instructive (purely electromagnetic mass).
3. Claim 4b, the real Lorentz contraction (physicist: Historically superseded; contrarian: Not testable as stated). Both are partly right. The contraction formula is a correct result of special relativity (kinematic there). The claim that it is a real dynamical contraction of bodies in a real ether is observationally equivalent to special relativity (Lorentz ether theory) [memory high, all three], so Not testable as stated. The inference "Michelson-Morley is almost positive proof" is unsound as worded, because a null result with equal arms does not by itself fix the contraction; Kennedy-Thorndike (1932) shows contraction alone cannot account for the nulls and a time effect is also needed [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment, physicist]. Verdicts: formula Established (as special relativity); real-ether contraction Not testable as stated and Historically superseded but instructive; "almost positive proof" overstated.
4. Claim 5b, the "atom of energy mC^2" from stellar mass loss (physicist: Historically superseded; contrarian: Refuted by calculation for the astronomical premise). My recomputation: Sun L/c^2 = 4.26e9 kg/s = 256 million tonnes per minute [calc], so Jeans's "250 million tons a minute" is right. Over 4.6 Gyr the Sun radiates 3.1e-4 of its mass; over 10 Gyr 6.8e-4; a 40-solar-mass star at 3e5 L_sun for 4 Myr, 2e-3 [calc; luminosity and mass illustrative]. On modern ages, radiated mass cannot explain mass differences of tens of percent between young and old stars: the contrarian is right under modern ages. But the lecture gives no numbers ("methods which need not be detailed here" [read: p.7]), and in 1924-28 Jeans lengthened stellar lifetimes by annihilation of matter "by a factor of the order of a million" over the 2e7-year estimate [web: search summary of Jeans's Nature 1924 and 1926 articles, https://www.nature.com/articles/117018a0 and https://mathshistory.st-andrews.ac.uk/DNB/Jeans.html; the 10^13 figure itself did not appear]. Over 1e13 years the Sun-like loss is 0.68 of a solar mass [calc], so within Jeans's own chronology the calculation does not refute it. What fails is the timescale and energy source (hydrogen fusion; Eddington's 1920 suggestion [memory high]); and the inference from a continuous loss rate to atomicity is a non sequitur either way. The 10^13-year link to this lecture is my inference, not stated in the text. Verdict: Historically superseded but instructive; the step from a continuous rate to "atoms of energy" is Not testable as stated.
5. Claim 5d / 6, do the 1925 coincidence experiments count against Jeans's scheme? (physicist: Tested, not supported for the wave-only form; contrarian: Never properly tested for the scheme, Tested, not supported only for quanta having no individuality.) Facts: Bothe-Geiger reported April 1925 (before the lecture), Compton-Simon published 1 September 1925 [web: https://en.wikipedia.org/wiki/Bothe%E2%80%93Geiger_coincidence_experiment, via the Investigator]; they refuted the Bohr-Kramers-Slater statistical conservation of energy, whereas Jeans's scheme keeps whole-quantum, event-by-event conservation. Tolman (1926): they "greatly increased the difficulties of the wave theory" [web: Investigator]. Ruling: the contrarian is right on scope. The experiments (and Grangier-Roger-Aspect 1986 anticorrelation, 98% interference visibility [web: https://courses.physics.illinois.edu/phys513/sp2019/reading/week1/GrangierSinglePhoton1986.pdf]) exclude a free classical wave that independent absorbers each sample. A source-and-sink handshake correlates the absorber with the emitter by construction (as in Wheeler-Feynman and Cramer), so those results do not directly test Jeans's version, which he never wrote down in calculable form. So claim 5d gets Tested, not supported and claim 6's mechanism gets Never properly tested.
6. Claim 3, Moon and Mercury. The contrarian's reading of the text is right: for Mercury Jeans says the critical speeds are "exactly similar to that of Mars", i.e. hydrogen and helium lost, heavier gases retained at moderate temperatures, and that astronomy "leaves little doubt Mercury is entirely devoid of atmosphere" [read: deep read 1.5-1.6]; the Moon statement is conditional. claims.md wording ("lose hydrogen, helium and most other gases") overstates. Current record: both bodies have tenuous exospheres (Moon: helium, neon, argon-40 dominant per LADEE; Mercury: hydrogen, helium, oxygen, sodium) [web: https://www.earthmagazine.org/article/lunar-atmosphere-more-active-we-thought/ and https://www.lpl.arizona.edu/~shane/PTYS_395_MERCURY/reading/domingue_etal_ssr_2007.pdf, via search summaries], consistent with Jeans's pattern: light gases mostly gone.
7. Retention at x = 30. Both calculators agree. Jeans's flux fraction 1e-2 (1+x) e^-x per second gives half-life 0.45 yr at x = 15, 0.76 Myr at x = 30 (mean life 1.1 Myr), and 1.3e10 yr (half-life) at x = 40 [calc]. So "retained through millions of years" is a million-year criterion, not retention over 4.5 Gyr. The book's "two million years" is a small slip.
8. Free-electron theorem (claim 5e). Physicist and contrarian: Established. The mathematician adds a real refinement: demanding the energy equation in every inertial frame is equivalent to momentum conservation with photon momentum hv/C (boost algebra: difference = (h nu_w - h nu) + m w (v' - v)), so the proof quietly imports a particle-like property of radiation that Jeans denies free radiation elsewhere. Accepted; it does not change the verdict.
9. Zero mean flux (claim 6a). Physicist and mathematician both obtain a time-averaged radial flux of zero for the half-sum field: Poynting flux proportional to cos^2(wt - kr) - cos^2(wt + kr) = -sin(2wt) sin(2kr) [calc, mathematician; analytic, physicist], with local ebb and flow. Agreed. Two additions I accept: (i) the half-sum field has no radiation-reaction (Dirac 1938: reaction field is half of retarded minus advanced) [memory high], so an isolated symmetric atom would not decay spontaneously, and observed spontaneous emission needs the absorber side supplied (Wheeler-Feynman completeness); (ii) the source-and-sink picture is not exact for waves: retarded and advanced energy are present everywhere and cancel only on average [mathematician's scalar analogue, not a numerical field plot].
10. Wien's H-alpha time. 1/(5.4e7) s = 18.5 ns; c tau = 5.55 m [calc]. The physicist compared it with hydrogen n = 3 lifetimes of about 16 ns [memory]; my web check failed (the Wikipedia spectral-series page has no lifetimes). From memory (medium confidence) 3p is about 5 ns, 3d about 16 ns, 3s about 160 ns, so Jeans's number is of the right order and the "several metres" length follows. The original Wien measurement is still unlocated (Investigator search negative).

Corrected claim list (final verdicts)

Scale: Established; Plausible, untested; Never properly tested; Tested, not supported; Refuted by calculation; Internally inconsistent; Not testable as stated; Historically superseded but instructive.

Claim 1. Real gases do not follow equipartition because molecules radiate (1904)

Corrected statement. Jeans argued that a molecule with thousands of spectral lines, treated as thousands of independent oscillators, would give gamma near 1.001 under equipartition against 5/3 observed. He proposed that radiation to the ether makes the system non-conservative, so the internal modes settle into a "normal state" at far lower "subsidiary temperatures", giving gamma = 1 + 2/(n+3) (n+3 = 3, 5, 6, ... by structure). By 1905 he restated it as a time-scale claim (equipartition may be the final state; approach takes millions of years). He gave up the explanation for the quantum one during 1910.

a. Mathematics: the bookkeeping (gamma = 1.0010 for 2000 extra terms [calc]), the replacement of Liouville's theorem by D rho/Dt = rho Delta F, and the non-commuting limits (section 233) are sound. Weak points, all Jeans's own admissions: the general theory proves only that a normal state exists (section 234); cubic terms are of the same order as retained terms (section 219); the emptiness of internal modes is shown only for toy models (two vessels; damped loaded spheres, eps H = (1/3) beta nu K^(3/2)). Hidden assumptions: zero-temperature ether; every spectral line an independent harmonic oscillator (the Ritz combination principle and Bohr's model later removed that picture [memory high; contrarian]). b. Experiments: his gamma tables (5/3, 7/5) agree equally with quantum freeze-out; the discriminating data are against him: H2 rotation (no radiating dipole) freezes below about 100 K (Eucken 1912), CO2 vibrational relaxation is about 7 microseconds at 1 atm [web: https://pubs.rsc.org/en/content/articlelanding/1966/tf/tf9666202655, abstract only], not millions of years; polyatomics and halogens do not fit his integers (He 3.07, Ar 3.20, CO2 6.98, Br2/I2 about 6.8; CCl4 15.4). Boltzmann factor for a 1.89 eV mode at 300 K: e^-73 = 1.8e-32 [calc]. c. Tested: not by a test designed to separate the accounts; overtaken by 1910-13 measurements and abandoned by Jeans (1916 2nd edition: quantum account "at best only partial" but "probably... satisfactory"; classical difficulties "left unsolved" [web: Investigator, archive.org dynamicaltheoryo00jeanuoft]). No suppression: Rayleigh objected (13 Apr 1905), Jeans replied, and the record is open. d. If true: low-temperature heat capacities and Planck's law would be quasi-steady, non-equilibrium effects; Kirchhoff's law makes that fail in an enclosure.

Final verdict (split): - Equilibrium form (radiation loss explains observed gamma): Tested, not supported (H2, solids, polyatomics); the theoretical reason is Kirchhoff's law and Jeans's own 1905 concession. - Time-scale form as classical dynamics for model systems: Established (proved later: see claim 2). - Time-scale form as the explanation of real gases' heat capacities: Tested, not supported. - As a historical position: Historically superseded but instructive.

Claim 2. Slow feeding of internal modes: exp(-2 p beta) and the "temperature of incandescence" (1904)

Corrected statement. A collision acting as a smooth force pulse transfers to an oscillator of angular frequency p an energy proportional to exp(-2 p beta), beta being the distance of the nearest pole of the force from the real time axis (of the order of the collision time). Jeans's own worked cases: hard-sphere penetration of 1/100 radius gives p t = 16, e^-16 = 1.1e-7, "much too great to agree with observation"; only an assumed half-radius penetration gives p t = 800, e^-800 = 10^-347.4 [calc], and he says there is "not the slightest evidence" for either. (facts.json states only the e^-800 case; correct it.) The italic conclusion of section 241 says "small" where the mathematics requires "large" (page image confirmed by two reviewers; not in the corrigenda).

a. Mathematics: correct and standard (mathematician re-derived; Lorentzian pulse gives exp(-p c) exactly; sech^2 pulse pole at pi tau/2). Gaps: resonance (q = p) set aside; analyticity assumed; the nearest pole is taken to dominate. b. Experiment: exponential growth of relaxation time with frequency is real (Landau-Teller 1936 [memory high]); microsecond relaxation for CO2 means heat capacity is seen on laboratory times. The incandescence prediction (0 to 28,000 C; 28,000 C is 100 x 273 K = 27,300 K [calc]) is too wide to test; Jeans calls it "almost worthless as a confirmation". c. Tested: the law as dynamics, yes: the Milan-Padua school proved it rigorously for classical models (Benettin-Galgani-Giorgilli 1989; Benettin-Carati-Gallavotti 1995; the approximation is called Jeans-Landau-Teller) [web: Investigator, research/2026-10-08-unimi-boltzmann-jeans.md]. Carati and Galgani pursue a classical-metastability programme that claims to reproduce quantum-like statistics for models [web: https://sites.unimi.it/carati/papers.html, search-level]; neither reviewer found a completed derivation of Planck's law or H2 heat capacities, and I have not examined their papers. This is the one place where mainstream silence on a live minority programme should be called open. d. If true (strong form): equilibrium heat capacities and Planck's law would be metastability effects; the need for h would weaken.

Final verdict (split): - The exp(-2 p beta) law as classical dynamics: Established. - Its use to explain observed gamma and heat capacities: Tested, not supported; Historically superseded but instructive. - The strong classical-metastability form (equilibrium quantum statistics from classical dynamics): Never properly tested (not dismissed; a minority programme continues). - "Temperature of incandescence" 0 to 28,000 C: Not testable as stated.

Claim 3. Kinetic theory fixes planetary atmospheres and molecular sizes (1904)

Corrected statement. The criterion x = 3 g a/C^2 (C the rms speed) equals G M m/(a k T), today's Jeans parameter at radius a [calc]. Below about 15 an atmosphere is lost; above about 30 it is retained "through millions of years" (a roughly million-year criterion, not retention over the age of the planet). Moon (conditional on "a temperature much above zero"): all but CO2 and denser gases escape; Mercury "exactly similar to Mars" and "entirely devoid of atmosphere" by astronomy; Earth and Venus keep their atmospheres. Molecular radii of order 1-2e-8 cm from several methods. Credits: Stoney (idea), Bryan (mathematics). Stoney's June 1904 dissent (the kinetic theory "is not competent to decide" and its conclusions are "inconsistent with the facts") is reported by Jeans and unanswered in the pages read; Stoney's letter is not in the folder. It is the view of the originator of the escape idea, so it stays in the record as a lead.

a. Mathematics: every table and threshold reproduces (deep reader, mathematician, physicist). Slips: N = 4e19 cm^-3 against 2.69e19 modern (49% high; viscosity radii rise by (4/2.69)^(1/2) = 1.22 with the modern N [calc, contrarian]), H2 mass 2.25e-24 g against 3.35e-24 g, the Mossotti equation printed without a factor 2, "two million years" (0.76 Myr half-life, 1.1 Myr mean life). b. Experiment: Earth: Jeans said the outer atmosphere is "certainly less than 230 C", so no perceptible escape. Exospheric temperatures are about 740-1350 K [web: https://en.wikipedia.org/wiki/Thermosphere via the mathematician]; at 1000 K his own rule gives x(H2) = 15.2, the edge of loss, and x = 7.6 for atomic H, the main exospheric form, well inside the loss range [QE revision, item 3]; Earth now loses about 3 kg/s of hydrogen (Jeans escape 10-40%, the rest charge exchange and polar wind) and about 50 g/s of helium [web: https://en.wikipedia.org/wiki/Atmospheric_escape]. Moon and Mercury: tenuous exospheres only (see ruling 6). c. Tested: planetary and in-situ data; transport-coefficient radii scaled for modern N agree with modern kinetic radii to about 10% (modern values [memory medium]). d. If true: nothing changes; this is mainstream.

Final verdict (split): - Jeans escape and the planetary pattern (light gases lost from Moon, Mercury, Mars; Venus keeps its atmosphere): Established. - Earth "no perceptible escape" of hydrogen and helium (input temperature wrong; atomic H at 1000 K lies inside his own loss range; non-thermal channels unknown): Historically superseded but instructive. - Molecular radii 1-2e-8 cm: Established as an order of magnitude (some vapour values "almost worthless except as regards order of magnitude", Jeans section 419).

Claim 4. The electron is a purely electromagnetic object in a real ether; bodies physically contract (1911)

Corrected statement. m = m0 + (2/3) e^2/(a C^2); recent experiments (Bucherer) are read as m0 = 0, radius a = 2e-13 cm (2.00e-13 cm from m = 8e-28 g [calc]); the Lorentz-FitzGerald contraction is "more than a conjecture" if all ether forces are electrical; Michelson-Morley is "almost positive proof"; Bucherer is read as "agree exactly" with Lorentz's deformable electron and Abraham's must be "discarded"; radiation from acceleration is (2/3) e^2 (acceleration)^2/C^3; electron theory "proves the Ampere element law". Qualifications from the record: Jeans hedged ("seem to shew"); the 1911 text keeps a real ether and never says "relativity" (4th edition 1919 adds a relativity chapter; the 5th, 1927, still prints Bucherer as showing the mass wholly electromagnetic, a = 1.874e-13 cm [web: Investigator, archive.org 5thedmathematica00jeanuoft]). Bucherer's 1908 result was disputed by Bestelmeyer and "seriously questioned"; decisive agreement came about a decade later (Neumann 1914; Rogers 1940 to about 1%); Zahn-Spees (1938) and Farago-Janossy (1954/57) judged the early data qualitative [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments]. So "exactly" and "must be discarded" outran the data. Printed slips: Y0 = .33 for .033 (section 615), "even" for "odd" in the Zeeman line count, "contracted/uncontracted" swapped (section 657), "In 1908, Kauffmann" against a 1906 footnote.

Final verdict (five parts): - 4a. Electromagnetic mass integral (correct) and radius 2e-13 cm: radius Tested, not supported (electron radius limit 2.8e-19 m, LEP; modern theory treats the electron as pointlike); "m0 = 0, purely electromagnetic mass": Historically superseded but instructive (4/3 mismatch, Poincare stresses, not addressed by Jeans). - 4b. Contraction: formula Established (special relativity); contraction as a real dynamical effect in an ether: Not testable as stated (empirically equivalent to special relativity) and Historically superseded but instructive; "Michelson-Morley almost positive proof": overstated (Kennedy-Thorndike 1932 shows contraction alone is not enough). - 4c. Transverse and longitudinal mass formulas: Established (identical in form to special relativity, which is why Bucherer's fit cannot show the mass is electromagnetic); Abraham's rigid electron: Tested, not supported. - 4d. Larmor radiation, Lorentz force, retarded potentials, Hall effect, Zeeman splitting (normal effect), radiation pressure 4.3e-5 dyne/cm^2: Established. - 4e. "Electron theory proves the Ampere element law": what Jeans derives (section 624) is the low-speed Biot-Savart field of a moving charge, summed over carriers: Established. As a statement about the Ampere force between isolated, non-closed current elements: Not testable as stated (such elements are not physical; Ampere, Grassmann and Lorentz forces agree for closed circuits only). Relevant to other projects in this collection that rest on Ampere-type element forces.

Claim 5. Energy is atomic; quantisation is in matter-radiation exchange; free radiation is wave-like (1925)

Corrected statement. Space and time are continuous (relativity mixes them; a granular continuum would need a universal constant of dimension length x time) but energy may be atomic. Emission and absorption occur by single quanta; with h = 0 the hydrogen atom would collapse in about 10^-10 s. Free radiation must stay undulatory because indivisible quanta conflict with interference over about 10^6 wavelengths, Wien's decay time, Lorentz's starlight argument (dated 1906 in the lecture; Jeans's 1924 Report cites Lorentz 1910 and the 1913 Birmingham meeting [web: Investigator, research/2026-10-08-archive-org.md]), and Taylor's feeble-light pattern (1909; the 2000-hour figure rests on Jeans's own 1924 Report). A free electron cannot absorb or emit a quantum of non-zero frequency. Most of this was already in print in the 1924 Report, with references (and the h-(4 pi e)^2 relation); only the advanced-potential step is new in 1925 [web: Investigator]. A numerical note: the printed "rate of exchange is taken to be C" should read C^2. R is Boltzmann's k per molecule in Jeans's notation, so (8 pi R T/c^3) nu^2 d nu is the Rayleigh-Jeans law and exp(-h nu/RT) is the Boltzmann factor (Lodge 1926 credits Jeans with the 8 pi R factor [web: Investigator]).

Final verdict (split by sub-claim): - 5a. Space-time continuity: Not testable as stated (the Planck length now supplies a scale but cannot be probed). - 5b. "Atom of energy mC^2" from stellar mass loss: Historically superseded but instructive (rate 256 Mt/min is correct; continuous loss does not show atomicity; stellar-mass premise tied to annihilation and 10^12-10^13-year stellar lifetimes; see ruling 4). - 5c. Exchange by single quanta E1 - E2 = h nu; collapse of hydrogen for h = 0: Established (classical collapse time a0^3/(4 r_e^2 c) = 1.56e-11 s [calc]; Jeans's 1e-10 is the right order but about 6 times high; the initial shrink rate 1.13 m/s is "over a metre a second" as he says). - 5d. Free radiation purely wave-like, quanta cannot be bullets: the argument against a localised bullet photon is sound and modern single-photon states agree; the conclusion of purely classical free radiation with independent absorbers: Tested, not supported (Bothe-Geiger, Compton-Simon, Grangier-Roger-Aspect 1986). A weak semiclassical form (quantised matter in a classical field) gives the photoelectric threshold and onset without photons: Plausible, untested as a whole (Lamb and Scully 1969 note that photons are still needed for blackbody radiation, Compton scattering and spontaneous emission [web: https://ntrs.nasa.gov/citations/19690054849, search summary]). - 5e. Free electron cannot absorb or emit a quantum: Established (with the mathematician's refinement that it imports photon momentum). His inference that a radiation field "produces no acceleration" in a free electron: Tested, not supported (revised from "Refuted by calculation" in the QE revision: Jeans derives it from quantum dynamics, "as we have just seen", so a classical equation of motion does not refute it; what refutes it is observed Thomson scattering, the low-frequency limit of Compton scattering, and quantum electrodynamics, which gives the same quiver [memory high]. The classical estimate m dv/dt = e E0 cos(wt) remains the way to see the size of the effect). He printed the same in the 1924 Report, so it is a settled belief, not a slip. - 5f. Bound-electron momentum 2h nu/v against photon momentum h nu/C (ratio v/(2C), 1e-3 at 1 eV, 3e-2 at 1 keV), so absorption is by the atom as a whole: Established.

Claim 6. A time-symmetric (advanced plus retarded) field can make a non-radiating atom and carry a whole quantum from emitter to absorber (1925)

Corrected statement. The potentials are the half-sum Psi = integral ([rho] + {rho})/2r dV, with [ ] retarded and { } advanced (page image Atomicity PDF p.28, read by physicist and mathematician); "averaged over a sufficient time" the radiation is zero, so classical electrodynamics can in principle allow a permanent non-radiating atom. A two-atom solution (atom 1 purely retarded, atom 2 purely advanced) is offered as the way a whole quantum is gathered onto one absorber and as an alternative to Compton's bullet derivation. Jeans gives formulas for prescribed sources, not the energy flow, and no equations for the Compton alternative. His own list of gaps: infinite field energy, no selection of Bohr orbits, no phenomenon explaining sources and sinks at frequencies atoms do not "beat time" to ("I know of no phenomenon in the whole of physics which helps"). He offers it as something that "has nothing to fear".

a. Mathematics: consistent as mathematics (any F and Phi solve the wave equation; zero mean flux for strictly periodic motion). Limits not stated by Jeans: a solution for prescribed sources is not a solution of the coupled charge-and-field dynamics (the retarded emitter would lose energy to radiation damping); the zero average hides local in-and-out flows; the pair needs coincident periods; the half-sum differs from the retarded solution by a source-free field (the Dirac radiation-reaction field), so the "non-radiating atom" has an incoming wave cancelling its outgoing one, of infinite extent. b. Experiment: no experiment tests this scheme as Jeans wrote it. Time-symmetric electrodynamics is a legitimate classical lineage (Schwarzschild 1903, Tetrode 1922, G. N. Lewis 1926, Fokker 1929, Wheeler-Feynman 1945; Cramer 1986) built to match ordinary electrodynamics [web: Investigator, Wikipedia absorber-theory page]. It does not by itself explain a quantised atom. c. Reception: E. P. Adams (Bull. AMS 1926, favourable and brief; Adams's 1901 experiment is used in the lecture, so he is not a neutral reviewer); R. C. Tolman (Phys. Rev. 1926, fair; flags the new coincidence results); Loring (Chemical News 1927, found convergent waves "promising" while noting Jeans did not offer them as a solution); Nature 117, 46 (12 Jun 1926) not read (paywalled). Related modern work: Shuang-ren Zhao's "mutual energy flow" papers (arXiv:1606.08710) use the same retarded-source plus advanced-sink structure; outside mainstream journals; not opened by the Investigator or any reviewer; recorded as related work, not as support.

Final verdict (split): - Mathematics of the half-sum field and its zero mean flux: Established (as mathematics, for periodic motion). - Time-symmetric atom as a classical non-radiating model: Plausible, untested. - Source-and-sink flow as the mechanism that gathers a whole quantum onto one absorber, and the Compton alternative: Never properly tested (no calculable version was written; not dismissed by test). The coincidence experiments of 1925 and later do not directly test it (ruling 5). - Historical priority (Jeans 1925 before Wheeler-Feynman 1945 for advanced-plus-retarded absorber ideas applied to the quantum): a matter of record; Tetrode 1922 and Ritz-Einstein 1909 are earlier in the lineage.

Claim 7. The quantum may be another face of charge atomicity (1925, conjecture)

Corrected statement. h C/2 pi = K (4 pi e)^2 with K "not greatly different from unity". In Gaussian units hbar c = e^2/alpha, so K = 1/(16 pi^2 alpha) = 0.8678 [calc], the fine-structure constant rewritten; 16 pi^2 = 157.9 against 137.04, a 13% miss. The mathematician's test (1 of 88 products 2^a pi^b falls within 20% of 137) shows the near-coincidence is not trivially cheap in that family, but the family is arbitrary and no derivation supplies the 16 pi^2. The same relation is in the 1924 Report (section 85), with Jeans adding that atomicity of e would not by itself give the quantum theory "for if it did the quantum-theory would have been fully developed long ago" [web: Investigator, archive.org bwb_W9-CSF-029]. His tube-of-force picture is rejected on his own evidence (beta-particle scattering shows the full nuclear force acts on an entering electron).

Final verdict: arithmetic Established; as physics Not testable as stated. Why alpha is near 1/137 has no accepted derivation [memory high].

Summary table

What would settle it

• Claim 1 (equilibrium form): already settled by data. The discriminating measurement is heat capacity versus temperature of a homonuclear gas whose rotation cannot radiate (H2, Eucken 1912; ortho/para theory Dennison 1927). A computation to settle any remaining doubt: Jeans's rate with p t of order 2 for H2 rotation (omega about 7e13 rad/s for the J = 2 to 0 transition [calc], collision time about 1e-13 s) gives no strong suppression, yet rotation freezes.
• Claim 2 (strong classical-metastability form): a worked classical simulation of coupled oscillators with Jeans-Landau-Teller collisions, reproducing the measured H2 or Einstein-solid heat capacity and the Planck spectrum on laboratory time scales and without a free parameter. The Carati-Galgani papers need reading against this standard. Also: the penetration depth beta from an actual intermolecular potential, which Jeans lacked.
• Claim 3: nothing needed; exobase-level modelling of Earth hydrogen and helium loss refines the superseded part. Stoney's June 1904 Phil. Mag. letter would show what exactly he disputed.
• Claim 4: settled by Kennedy-Thorndike (1932), Ives-Stilwell (1938) [memory high], Rogers (1940), and electron-scattering limits. The remaining interpretive question (real ether versus kinematic relativity) is not settled by experiment.
• Claim 5: Bothe-Geiger, Compton-Simon, Grangier-Roger-Aspect already bear on the independent-absorber form. To test the weak semiclassical form: a full calculation of Compton scattering and spontaneous emission in a semiclassical model (Lamb and Scully say it fails there). To check the stellar argument: the age and mass data Jeans used in 1925 (not stated in the lecture).
• Claim 6: a single calculation: write the full retarded-plus-advanced field energy flow for two coupled atoms with matched periods (not just the potentials), show whether the energy of one quantum moves from atom 1 to atom 2 and whether the angular correlation of Compton-Simon follows. Wheeler-Feynman and Cramer have taken some of this ground; whether Jeans's version differs measurably has never been computed. The decisive records are in the open questions below.
• Claim 7: a derivation of alpha from any principle; none exists.

Open questions

1. Did Jeans know of Tetrode (1922), Ritz-Einstein (1909) or G. N. Lewis (1926) when he wrote the advanced-wave passage? Records: Jeans's letters (Royal Society JHJ/2, JHJ/4; 23 letters to O. W. Richardson at the Harry Ransom Center); whether Lewis's 1926 PNAS paper cites Jeans (scan located, not read).
2. What did Stoney's 1904 objection to the kinetic-theory escape argument rest on, and did Jeans answer it later?
3. Is the classical-metastability programme (Benettin, Galgani, Carati) able to deliver quantum-like equilibrium heat capacities, or only exponentially long times?
4. What were Jeans's stellar-age figures behind "the star's total radiation ... represents the observed difference in mass" in 1925?
5. Where is Wien's H-alpha decay measurement (the 5.4e7 per second figure)? The Taylor 2000-hour exposure is known only through Jeans's 1924 Report.
6. How did Jeans himself weigh the 1925 scheme afterwards (1927 5th edition, Physics and Philosophy, correspondence)?
7. Not read by any role: Montambaux's Rayleigh-Jeans PDFs beyond the 1905 exchange, Solvay 1911, Hudson 1989 in full (abstract only), Milne's 1947 obituary memoir (located, no text layer), Nature 117, 46, Kragh-Carazza 1994, the Ritz-Einstein 1909 note, Zhao's papers.

Absence of evidence: where the record goes dark

A. The 1925 advanced-wave idea drops out of the time-symmetric literature. Wikipedia's absorber-theory history cites Schwarzschild, Tetrode, Fokker, Wheeler-Feynman, and Kennefick 1997 has zero mentions of Jeans [web: Investigator]. Competing explanations: - (i) It was never calculable: Jeans wrote no equations for the flow or the Compton alternative. For: his own list of gaps; the mathematician's finding that the flow is not displayed. Against: nothing found. A later calculation would decide it. - (ii) Quantum mechanics (Heisenberg 1925, Schrodinger 1926) made the physical-picture programme moot within months. For: timing; Tolman's reception. Against: Wheeler-Feynman revived the picture in 1945 anyway. - (iii) Jeans moved to cosmology (1928 Astronomy and Cosmogony manuscripts in JHJ/5 [web: Royal Society catalogue, Investigator]). For: his later output. Against: it does not explain why historians of absorber theory omit him. - (iv) The lineage was transmitted through Einstein's remarks to Wheeler (Tetrode, Ritz), not through Jeans, so Jeans was simply not in that chain [web: Wikipedia history, Investigator]. - (v) Jeans used or dropped the idea in a later text: not checked. - (vi) Suppression: nothing found. Reviewers engaged (Adams, Tolman, Loring); Jeans was senior and widely read. Not supported on this record. Records that would decide: citations of Jeans 1925 in Lewis 1926, Fokker 1929, and the Wheeler-Feynman correspondence; Jeans's letters (JHJ, Richardson); the 1927 edition and later books.

B. Jeans's own gas-theory retreat (1905-1916). The 1904 explanation was not killed by a decisive test; Jeans narrowed it in 1905, moved to the quantum side during 1910, and wrote it up in 1916. The Royal Society's 1901-07 sanatorium letters (written while he finished the gas theory) are unread and could show how he weighed the objections. No sign of suppression.

C. Nature 117, 46 (the only contemporary journal review not read) and Milne 1947. Gaps because of paywall and scan, not because the records are missing. Competing explanations: none needed; obtaining them is the remedy.

D. Wien's decay-time source and the Taylor figure. Evidence cited by Jeans but not located (Investigator: negative on Wien). It is single-source evidence (Jeans's lecture and his 1924 Report), still evidence; the order of magnitude agrees with modern hydrogen lifetimes. A second source would settle the exact figures.

Single-source and interested-party notes

• Stoney's dissent is in one published source (Jeans's own report of it, p.342). Stoney originated the escape idea, so he is an informed party, not a rival.
• E. P. Adams reviewed the lecture favourably, and Jeans's lecture uses Adams's 1901 experiment, so Adams has a stake in its presentation; his 1901 paper measured magnetic convection effects, not radiation, so "the spheres radiate" is Jeans's calculation, not an Adams measurement.
• Jeans is the sole source of the stellar-mass observations in the lecture (no numbers given).
• Zhao's mutual energy flow papers are by a single author outside mainstream journals.

Corrections to earlier documents (for the orchestrator)

1. claims.md (Thread), facts.json (Gases, mainstream_conflict) and the Gases deep read section 9: "accepted quantum theory by 1913-14 [memory medium]" is wrong. Evidence: the lecture says "Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed" [read: Atomicity p.9]; Hudson 1989 dates the move to 1910 (abstract). Use: accepted the quantum hypothesis during 1910; the 1914 Report spread it. Confirmed by all three reviewers.
2. claims.md (Thread) "giving up each in turn as experiment advanced" is too strong; replace with "seeks classical wave or field explanations as long as he can; he kept the 1904 theory as a time-scale claim in 1905, moved to quantum theory in 1910, added relativity in 1919, and in 1925 defended a classical-wave position against the bullet photon".
3. claims.md claim 1 and facts.json (Gases): restate claim 1 as above (Jeans himself narrowed the equilibrium claim to a time-scale claim in 1905; the zero-temperature ether sink; non-integer observed n+3). Note that n changes meaning between Ch. VII (gamma = 1 + 2/n, all momentoids, eq. 415) and Ch. IX-X (gamma = 1 + 2/(n+3), n internal terms, eq. 522).
4. claims.md claim 2 and facts.json (Gases, e^-800): state both Jeans estimates (p t = 16, e^-16 "much too great"; p t = 800 only with half-radius penetration, with "not the slightest evidence"), the section 234 admission, and the section 241 misprint "small" for "large".
5. claims.md claim 3 and facts.json: "the Moon and Mercury lose hydrogen, helium and most other gases" overstates; Mercury is "exactly similar to Mars" and "entirely devoid of atmosphere"; the Moon statement is conditional. Also add: the Earth premise ("certainly less than 230 C") is superseded; "retained through millions of years" is a million-year criterion; N = 4e19 is 49% high.
6. Atomicity deep read section 2c and any facts.json repeat: the "RT per mole units used loosely" remark is wrong; R is the gas constant per molecule (= k) in Jeans's notation (Gases deep read symbol list; Lodge 1926 "8 pi R"). Evidence: mathematician.
7. Atomicity deep read section 10b: Adams was at the Jefferson Laboratory, Harvard (not Princeton), copper spheres on brass rods, measuring magnetic convection effects (Phil. Mag. [6] 2, 285, 1901 [web: Investigator, archive.org londonedinburgh621901lond]).
8. Atomicity deep read section 2e and facts.json: the printed collapse time is about 10^-10 s; facts.json's "10^-9 s" for the material energy of the universe has no printed exponent (words only: "thousand-millionth parts of a second"); computed 1.56e-11 s.
9. Atomicity deep read section 8b: the frame choice does the work of momentum conservation with photon momentum hv/C (boost algebra); the theorem imports radiation momentum.
10. Atomicity deep read and facts.json (mainstream_conflict): Bothe-Geiger was April 1925 (before 11 May), Compton-Simon 1 September 1925 (after); Tolman 1926 called the timing "almost simultaneous". The lecture did not ignore Compton-Simon, but post-dates Bothe-Geiger by about a month; whether Jeans knew is unknown.
11. facts.json (Electricity, mainstream_conflict item 2): "abandoned because Poincare stresses and quantum effects" is loose. Precise: the 4/3 problem (energy and momentum routes differ) (superseded by correction 19: the two routes give the same mass; 4/3 is the ratio to U/C^2), Poincare stresses 1905-06, and in special relativity all mass carries the same velocity factor; later work judged the early Kaufmann-Bucherer-Neumann data qualitative.
12. claims.md claim 4: "Bucherer's experiments as confirming Lorentz's deformable electron" needs the qualification that Bucherer 1908 was disputed (Bestelmeyer) and confirmations came later; "proves the Ampere element law" should read "derives the Biot-Savart field of a moving charge and its sum over a circuit element".
13. Physicist, memory item on the electron size bound ("below 10^-16 cm, [memory medium]"): replace with [web] the LEP Bhabha-scattering limit r < 2.8e-19 m (95% CL).
14. Contrarian claim 5, "Refuted by calculation" for the stellar-mass premise: true under modern stellar ages, not within the 1920s annihilation chronology; see ruling 4.
15. claims.md claim 6: "can carry a whole quantum" should read: Jeans gives the potentials of a two-atom solution for prescribed sources, not the energy flow; the source-and-sink analogy is not exact for waves.
16. claims.md claim 5: the lecture gives no star masses or ages; it does not detail the stellar-mass argument ("methods which need not be detailed here").
17. Physicist's Moon and Mercury statement (tagged [memory medium-high; not web-checked]) is now [web] checked, see ruling 6. Physicist: Hudson's 1910, Adams, and the Bothe-Geiger dates were accepted from the Investigator.

Web checks done (budget 8; 6 used)

1. Electromagnetic mass, 4/3 problem and Poincare stresses: https://en.wikipedia.org/wiki/Electromagnetic_mass (Jeans not mentioned there).
2. Electron radius limit: https://arxiv.org/abs/2506.02450 (abstract only, no number) and a search confirming r < 2.8e-19 m at 95% CL from LEP Bhabha scattering, https://arxiv.org/pdf/hep-ph/0002172 (not opened by me).
3. Jeans, annihilation of matter and stellar lifetimes: search summary citing https://www.nature.com/articles/117018a0 and https://mathshistory.st-andrews.ac.uk/DNB/Jeans.html; the "factor of a million" is stated; the 10^13-year figure did not appear.
4. Moon and Mercury exospheres: search summary (LADEE; Domingue et al. 2007), not opened.
5. Hydrogen n = 3 lifetimes: https://en.wikipedia.org/wiki/Hydrogen_spectral_series had no lifetimes; check failed, so 3p, 3d and 3s lifetimes stay [memory medium].
6. Not re-checked on the web: Kennedy-Thorndike and Ives-Stilwell (the first checked by the physicist; the second [memory high]), Dirac 1938 radiation reaction [memory high], Ritz combination principle [memory high], Landau-Teller [memory high], modern viscosity radii [memory medium], N2 vibrational relaxation (no figure given).

Bottom line for the reader

The durable parts of the three books are the mathematics and several standard results: the pulse-energy law exp(-2 p beta) (Jeans-Landau-Teller), the Jeans escape parameter, Larmor radiation, the free-electron theorem, and the classical collapse time of hydrogen. The explanations built on them were overtaken, mostly by Jeans himself: radiation loss as the reason for cold internal modes (1904), a purely electromagnetic electron and a real contraction (1911), purely classical free radiation (1925). The single idea left genuinely uncalculated is the 1925 advanced-plus-retarded absorber scheme; the record shows nobody tested or refuted it, and it is missing from the standard histories for reasons not yet established.

QE revision (2026-10-08)

Trigger: qe.md (verdict MINOR) and the new deep reads of Gases Ch. XVIII (PDF pp.343-355), Gases Ch. XVI and section 277 (PDF pp.319-325, 245), Electricity sections 153-155 and 192, 496-501 and 145-151, and Gases Ch. III-IV (PDF pp.48-75). The seven central claims stand. Two sub-verdicts change (5e "no acceleration"; the 4/3 wording in claim 4a is corrected without a verdict change), and two sub-verdicts are added (sound damping, element-force family). The table above and the "Corrected claim list" were edited in place; this section gives the reasons. Tags: [read] deep reads (page images); [calc] my arithmetic; [web] URL; [memory] with confidence. One web search was made in this revision (see the end).

1. Claim 1: Jeans's own answer to the polyatomic and halogen misfit (qe S1/R1)

My earlier text and the three reviews cited the misfit (CO2 6.98, Cl2 6.08, Br2/I2 6.8, CCl4 15.4, ethylene about 8) against Jeans without his reply. His reply, from the deep read of Ch. XVIII [read: page images pp.350-355]:

• Aggregation. Clusters of molecules (doubles, triples) bound by weak attraction would change measured gamma. Evidence he gives: wet steam n+3 = 32 against dry steam 6.6; Lussana's CO2 at 54-85 atm (n+3 about 92 at 85 atm and 13 C, falling to about 7.6 at 1 atm); chlorine's density drifting from 2.4807 at 20 C to 2.4502 at 200 C against Stas's 2.4501. Chlorine arithmetic: 0.0108/0.0001 = 108, so his "about 100" is correct but rests on the fourth decimal of a density [read, deep read section 3].
• The rule. Section 407: "the supposition that we have n+3 = 3 for all monatomic gases, n+3 = 5 for all diatomic gases, n+3 = 6 for all more complex gases, seems at any rate to be worth serious consideration. It disposes of the tremendous difficulty of explaining how it is possible for the molecules of a gas to keep up large internal motions without loss of energy." Section 410 reports that the plain conservative theory gives six degrees of freedom for a diatomic molecule, gamma at most 1 1/3, "which suggests that we are on the wrong track". Section 411 repairs this with dissipation: radiative damping of the forced vibrations leaves circular orbits (diatomic, five degrees) or rigid rotation (polyatomic, six).
• Limits, in his own words and in the deep reader's reading. He "cannot even determine the sign" of the clustering correction to C_v and calls an evaluation "fruitless" (section 403). No cluster fraction is computed for any gas. The ordinary-pressure values (CO2 6.6-7.7, chlorine 6.08, Br2/I2 6.8, CCl4 15.4, ethylene 8) are not covered by the chapter's evidence. The rule reverses Chapter IX section 271, where low gamma meant real internal motion, and the two escapes are not reconciled. Section 411's step 4 concludes "large" forced vibrations from a short oscillation time, which sits uneasily with the Chapter IX law that fast driving transfers little energy; the deep reader left that tension unresolved, and so do I.
• Modern reading: low gamma in CO2, halogens and heavy polyatomics comes from partly excited vibrations (quantum freeze-out, gradual unfreezing of low-frequency modes) [memory high]. It is the same direction and size as the data, with no aggregation fit.

Ruling: Chapter XVIII is a stated, unquantified hypothesis. It is candid (he states the sign problem and the "wrong track" result himself) and it does not answer the ordinary-pressure misfit. I record both sides. Verdicts for claim 1 are unchanged. The earlier phrase "Jeans hands the problem to chemists" is true of section 272 only. The deep reader also lists, as a weak point of section 411, that its "rough numerical calculation" is not shown and that classical rotation of a charged pair would itself radiate (deep read, section 8, point c; I have not weighed that further). I add the 1913 Birmingham meeting (Larmor and Love defending classical dynamics, Jeans's 1914 Report section 18 [web: Investigator, research/2026-10-08-archive-org.md]) as evidence that the classical position of 1904 still had defenders nine years on.

Rayleigh-Jeans link (qe missed item 1): Gases section 257 names equipartition between matter and ether as the one failure case, and the lecture prints (8 pi R T/c^3) nu^2 d nu as the h = 0 limit of Planck's law. The 1905 Nature exchange (Nature 71, 559 and 607) and Lodge 1926 credit the 8 pi factor to Jeans [web: Investigator]. Applied to the ether's own modes the same equilibrium gives the ultraviolet catastrophe, the "final ratio" Jeans conceded in Nature 71, 607. This is the same claim 1 seen from the radiation side, and it should be in the primer.

2. Claim 2: contemporary evidence, dissent, and the sound-damping chapter (qe S2, R2)

Contemporary evidence and dissent on collision-excited light [read: deep read Gases section 7, pp.224-226]. For: Schuster and Hemsalech's arc observation (Phil. Trans. A 193, p.189): violet light comes from faster molecules, which Jeans says his hypothesis "seems capable by itself of accounting for". He also predicts that lower frequencies appear first on heating; he says this "cannot be verified by direct observation" in gases but is everyday experience in solids (red heat before white heat). Against: Pringsheim (Wied. Ann. 45, p.428) held that "no light is ever produced in gases by collisions alone"; Paschen (Wied. Ann. 50, p.409) and Smithells contested him. These are the only contemporary experimental statements the 1904 book cites for the claim 2 mechanism, and they are one dispute among physicists, undecided in the text. They stay in the record next to the verdicts; they do not change them.

Sound damping, Chapter XVI [read: page images pp.319-325, SymPy by the deep reader]. Jeans works out how a lag in the exchange between translational and rotational energy damps and disperses sound. For one lagging mode he gets a complex dispersion relation with the correct limits (gamma = 7/5 at low frequency, 5/3 when the mode is frozen); amplitude decay proportional to frequency squared, equivalent to an extra viscosity 1 + (27 pi/800)(k^2/r^2); for his two-sphere diatomic, "about one-seventh as great as that caused by viscosity" (1.148 by [calc], printed 1.146); and a speed correction of second order, V[1 + (48/1225)(3k^2/4r^2)^2 (p l/c)^2], about 4e-14 at 480 Hz and 4e-11 at 16 kHz [calc, deep read]. He concluded it was "quite imperceptible", on the stated proviso that the exchange takes about one collision. Section 277 had guessed this from 10^7 collisions per sound wave.

Weighing: the structure is that of later molecular acoustic relaxation (one reservoir relaxing to equipartition, normal dispersion, f^2 absorption at low frequency, an effective bulk viscosity). I rule the classical dynamics Established. The numerical conclusion depends on the one-collision assumption. The later literature on ultrasonic relaxation (Herzfeld and Rice, Phys. Rev. 31, 691, 1928 [web: confirmed through a search listing; https://en.wikipedia.org/wiki/Karl_Herzfeld]; Kneser; Landau and Teller 1936 [memory high]) deals with slow vibrational exchange, and a NASA report states that translational-rotational exchange is "unusually difficult for hydrogen" [web: search summary, https://ntrs.nasa.gov/api/citations/19640005928/downloads/19640005928.pdf, not opened]. I could not find a source for specific collision numbers, and I could not verify Pierce's 1925 CO2 dispersion work. So I treat the figures "about 5 collisions for N2, hundreds for H2" in the deep read as [memory medium]. Whether Jeans's Chapter XVI influenced that literature is unknown; the stronger tie to Landau-Teller is the adiabatic exponential of Chapter IX, as the deep reader says. The link that Jeans did not draw (feeding the slow exp(-2 p beta) rate into the Chapter XVI machinery moves the dispersion region down to kHz-MHz) is a reader's inference, not a statement by Jeans, and it is a calculation the reader can do (the exp law gives the rate; the chapter gives the response). The exp(-2 p beta) law was the one place where Jeans's 1904 mathematics met later measurement, and Chapter XVI is how that contact can be tested. Verdict additions (in the table): sound-damping structure, Established as classical dynamics; the "imperceptible" conclusion, Plausible, untested as a statement about rotation (not compared with data in this revision). No other claim 2 verdict changes.

3. Claim 3: the molecular count and the hydrogen species (qe items 6 and 7.5)

• Jeans revised his own molecular count. In 1911 he uses n = 2.75e19 per cm^3 and recalculates the gas-book radii "using the value n = 2.75 x 10^19", with no source given [read: Electricity section 149 and 150, page image p.142]. The 1904 value was 4e19, which he supported with J. J. Thomson 3.6e19, H. A. Wilson 4.0e19 and Townsend 4.1e19 as quoted in the deep read. The modern Loschmidt value is 2.687e19 [memory high], so the 1911 figure is 2.3% high [calc] and the 1904 figure 49% high. Earlier I called 4e19 "a slip"; it was the best electrical-method value of 1904, revised by Jeans within the decade. The radius change is as expected: kinetic radii scale as n^(-1/2), a factor 1.206 [calc]; table ratios 1.18-1.23 (hydrogen 1.33, row possibly misassigned in OCR).
• 1911 comparison table [read: p.142]. Mossotti electrical radii 0.596e-8 (He) to 1.60e-8 cm (C2H4); kinetic-theory radii 1.09e-8 to 2.30e-8 cm; the electrical radius is 0.55 to 0.76 of the kinetic one. Jeans calls the agreement "very significant evidence" for molecular polarisation but "order of magnitude only", and explains the difference by the electrical radius measuring the outermost electron shell while the collision radius includes the field. He had suggested the field extension in 1904 [read: deep read]. Verdict on radii: Established as an order of magnitude, unchanged.
• Hydrogen escape: hydrogen in the exosphere is mostly atomic, with mass half of H2, so x = 15.2/2 = 7.6 at 1000 K [calc], inside the "certainly lost" range of Jeans's rule (below 15). The H2 figure was the wrong species for the point I made. Edited in claim 3b. Consequence: Jeans's "no perceptible escape" is wrong by his own rule once the exospheric temperature and the species are corrected; the verdict "Historically superseded but instructive" stands and is better supported.

4. Claim 4: wording corrections, the ether as hypothesis, and the Ampere element forces (qe S3, section 7.1)

4/3 wording. Ruling 2 and correction 11 said the mismatch "appears only when the momentum route or E = mC^2 is added". That is wrong, and the physicist's version ("the field momentum gives 4/3 instead of 2/3") is also wrong. Correct statement: for a charged shell of radius a, the kinetic-energy route and the field-momentum route both give m = (2/3) e^2/(a C^2); the rest energy of the field is U = e^2/(2a), so U/C^2 = e^2/(2 a C^2); the ratio is (2/3)/(1/2) = 4/3 [calc; the standard 4/3 problem, memory high]. The mismatch is between the dynamical mass and the energy-equivalent mass. Jeans only does the first. The verdict (purely electromagnetic mass: Historically superseded but instructive) is unchanged, and the primer's section 3d is already correct.

The ether is a hypothesis in 1911 [read: Electricity sections 153-155, pages 150-152]. Jeans finds no a priori proof of a medium: the arguments from inductive capacity, induction and finite speed "prove nothing" about whether energy resides in charges or in the ether; electrical action "stands on just the same level as gravitational action"; the potential "can only be regarded as a convenient mathematical fiction"; and section 155 adopts the medium as a "tentative hypothesis" tested by whether its properties are consistent and probable. So my "real ether" wording in the corrected statement for claim 4 should read: a working ether hypothesis that Jeans expected to win on plausibility for currents, not an asserted fact. The deep reader also says that calling the 1911 text "the Lorentz ether theory" must not be read as Jeans asserting an established ether. The verdicts on the contraction (Not testable as stated; Historically superseded) are unaffected, and "Michelson-Morley almost positive proof" is still overstated, but it is conditional on his stated premise.

Ampere element forces (claim 4e) [read: page images pp.448-453]. Findings that qualify my earlier text: - Section 497's "Ampere's law" is the field of a current element in Biot-Savart form, not Ampere's element-element force. - Section 498a: the force on a circuit element from a pole is fixed by the circuit force only up to a term d2(psi)/dx ds; the freedom gives a force with a component in the plane of r and ds. Jeans: "It is almost inconceivable that such a force could be the result of pure action at a distance". This is a plausibility argument and he hedges it. - Section 499: the mutual energy -i i' cos(eps)/r ds ds' can be replaced by -i i' ds ds' (cos(eps)/r + k d2r/ds ds'), where k is an undetermined constant (Helmholtz); every k gives the same force on closed circuits. Written out, w = -(i i' ds ds'/r){cos(theta) cos(theta') + (1 - k) sin(theta) sin(theta') cos(phi - phi')}. Jeans names two values: k = 1 ("a system of forces originally suggested by Ampere", which includes a couple and a force along the joining line proportional to cos(theta) cos(theta')), and k = 3/2 (the energy of two magnetic particles times r^2/2, the radial force one sixth of r^2 times the magnetic-particle force, 1/6 verified by the deep reader at 300 dpi). The k = 1 system is not the central element force usually credited to Ampere (2 cos(eps) - 3 cos(theta) cos(theta') form, no couple) [memory medium]. So nobody should cite section 499 as the textbook statement of Ampere's law. Possible misprint: the sign of the "repulsion" for k = 1 (w = -A/r gives -dw/dr = -A/r^2 at fixed angles, an attraction for A > 0); unresolved. Section 501's "(424)" is a slip for (426). - Section 500: "none of these seem at all plausible, so that we are almost compelled to give up all attempts at explaining the action between the circuits by theories of action at a distance ... [and] to assume that the energy of the system of currents resides in the medium." Exclusion by implausibility, not by experiment.

Weighing for 4e. The non-uniqueness of the element force is mathematics Jeans himself proves; I add it as Established. His conclusion in favour of the medium is a judgement about plausibility in 1911; it is Not testable as stated (all members of the family give the same measurable closed-circuit force) and is Historically superseded but instructive as an argument. The remark that other projects in this collection rest on Ampere-type element forces stands, and gains a precise point: those projects must say which k (or other member of the family) they use, and that only closed circuits are measurable.

5. Claim 5: dating and the "no acceleration" verdict

• "Lorentz's starlight argument (1906)" repeated the lecture's date. Jeans's 1924 Report cites Lorentz, Phys. Zeitschr. 11, p.349 (1910) and the 1913 Birmingham meeting [web: Investigator]. Edited above.
• 5e "no acceleration" changed from Refuted by calculation to Tested, not supported (see the edit above). Reason: Jeans derives it from quantum dynamics ("as we have just seen"), and the deep read's analyst note says it goes further than the argument. A classical equation of motion cannot refute a statement about quantum dynamics. Observation does: Thomson scattering, the low-frequency limit of Compton scattering, and an electron quivering in a laser field [memory high; not web-checked]. The mathematician and contrarian already leaned this way. The substance is unchanged: the sentence is wrong.

6. Claim 6: the 1911 background to the non-radiating atom (qe item 7)

Electricity section 192 [read: page 178]: Earnshaw's theorem shows an electron cannot rest in stable equilibrium under inverse-square forces; the 1/r^2 law cannot hold down to zero distance (charges would pair into permanent doublets and "the matter in the universe would tend to shrink into nothing"); Larmor's orbiting rings are "a sort of 'perpetual motion' machine", with "a difficulty in understanding how its energy can be continually replenished"; and the electron must be "something more complex than a point charge". Jeans does not say that an orbiting electron must radiate. The link to 1925 is the deep reader's inference and mine: the half-sum field gives zero mean radiation, which answers the replenishment worry in the classical way; Earnshaw is bypassed by motion; "infinite field energy" in 1925 is the form of the 1911 problem at zero distance; and the shift from the potential as "convenient mathematical fiction" (1911) to advanced and retarded potentials that decide physical outcomes (1925) is a change Jeans does not comment on. Section 155 is also the basis for noting that action at a distance was an open option for him in 1911, which is closer to Wheeler-Feynman style action than the "real ether" reading suggests [memory medium for the Wheeler-Feynman comparison]. The claim 6 verdicts are unchanged.

7. Maxwell's law and Burbury (qe S5, optional deep read)

The reviews rest nothing on this. For the record, the deep read finds that facts.json key claim 1 for the gas book is substantially right but should say "infinitely probable", not "probability 1", that Liouville's theorem is not named in Chapter III (invariance is proved collision by collision for hard spheres), and that the "almost always in time" step (sections 58-59) rests on an unstated ergodic-type assumption. Burbury maintained that correlation exists except in an infinitely rare gas and criticised Jeans's proof (Phil. Mag. 6, p.529; 7, p.467); Jeans replied (Phil. Mag. 6, p.720; 7, p.468) and says he "cannot persuade myself" the criticism is well founded. The book does not set out Burbury's objections, and Jeans's own result of a position-only correction factor for finite molecules is a form of the correlation Burbury maintained [deep read analysis]. The papers themselves have not been read by any role, so the dispute is an open lead, not a verdict. No verdict changes.

8. Corrections to earlier documents (additions to the 17 above, for the orchestrator)

18. arbiter.md claim 3 text, "N = 4e19" described as a slip: it was the 1904 best value, revised by Jeans to 2.75e19 by 1911 (section 149). claims.md claim 3 and facts.json (Gases) to say so.
19. physicist.md claim 4a and arbiter correction 11: the field-momentum route gives (2/3) e^2/(a C^2), the same as the kinetic-energy route; 4/3 is the ratio to U/C^2. Edited here in ruling 2.
20. contrarian.md claim 5a "uses RT for kT ... a unit slip": wrong, as the mathematician showed (correction 6).
21. arbiter claim 5e verdict: "Refuted by calculation" changed to Tested, not supported. Also primer (check yourself and evidence table) and facts.json, if they repeat it.
22. Digest-only claims in claims.md and the primer source note: Gases Ch. XVI and XVIII and Electricity sections 496-500 are now deep-read; remove them from the digest-only list.
23. Gases digest .11 (Ch. XVI): the deep reader lists seven misreadings (the "13" for 1 2/3, H and K swapped, gamma = 1 for 1 2/3, viscosity mu for kappa, k and r values, p = 10^4 for 10^5). Use the deep read, not the digest.
24. Gases Ch. XVIII text layer: Lussana temperature 13.2 not 132; chlorine boiling point as printed 33.4 not 334; n+3 = 32 not 3.2 for wet steam; Thomsen's masses are transposed in the printed section 410 (2 g hydrogen with 16 g oxygen).
25. Primer section 3c and arbiter claim 3b should give x for atomic H (7.6) beside H2 (15.2) and define "exobase", "LEP" and "eV". Primer section 5, Step 4 and example.py Part 4: relabel the H2 table as an extension of Jeans's rate law, not "Jeans's recipe"; his 1904 theory predicts gamma = 7/5 for H2 at all temperatures, against Eucken 1912 [qe 7.4; I agree: Jeans's collision-time rule was for vibrations of fixed frequency, and classical rotation has none].
26. claims.md source note and the primer: the Electricity section 148-151 table gives both radius columns; cite page 132.

9. Net effect on verdicts

10. What stays open, and what was not done

• Not read by any role: Montambaux files 05-11 and 13 (rest of the 1905 exchange, Jeans's Proc. Roy. Soc. 1905 paper, Solvay 1911), Jeans's 1903 Phil. Mag. papers, Hudson 1989 in full, Milne 1947, Nature 117, 46, and Burbury's Phil. Mag. papers. QE asked for these as an Investigator task.
• Web check in this revision: one search. Confirmed the Herzfeld and Rice 1928 reference; found no collision-number source and no source for Pierce 1925. Those figures remain [memory medium]. The 6 checks recorded above plus this one are within the budget of 8.
• The primer is not edited here; the orchestrator's list above and qe.md section 8 give its changes.