James Jeans on gases, electrons and quanta (1904, 1911, 1925): a primer

Project: three books by J. H. (Sir James Hopwood) Jeans (1877-1946): The Dynamical Theory of Gases (Cambridge, 1st edition 1904), The Mathematical Theory of Electricity and Magnetism (2nd edition 1911), and Atomicity and Quanta (Rouse Ball lecture, Cambridge, 11 May 1925, printed 1926).

Inputs: arbiter.md (final verdicts, including its "QE revision" section of 2026-10-08; this primer adds none), physicist.md, mathematician.md, contrarian.md, the deep reads in deep/, facts.json, claims.md, qe.md, and the Investigator's sites.md and research/ notes. Worked example: example.py in this folder. Revised 2026-10-09 to apply the QE remediation (qe.md section 8); what changed is listed at the end under "Corrections to earlier documents".

Source tags: [read] = from Jeans's books (equations from page images where the scan's text layer was garbled, as recorded in the deep reads); [web] = found online, with URL (most found by the Investigator or the reviewers); [memory] = from model training, with confidence; [calc] = arithmetic re-run in example.py or by a reviewer.

Source note: there is no Source gap. All three books have readable text. The two long books are OCR scans with garbled equations, and every equation a verdict depends on was read from page images. Deep reads (from page images where needed) cover the gas book's Chapters III-IV (Maxwell's law), VII-X (equipartition and its failure), XVI (sound), XVII (planetary atmospheres), XVIII (molecular aggregation) and XIX (size of molecules); the 1911 book's sections 145-155 (Mossotti theory, molecular count, action at a distance), 192 (stability of atoms), 496-501 (Ampere's rule and element forces) and Chapters XIX-XX (the electron); and the whole 1925 lecture. The remaining chapters (the gas book's Chapters I-II, V-VI and XI-XV; the electrostatics, potential-theory, network and magnetism chapters of the 1911 book) were covered by digest only; they are standard material and no verdict rests on them.

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1. The idea in one paragraph

Jeans was not an outsider: he was a Cambridge mathematical physicist and later a Fellow and Secretary of the Royal Society [memory, high]. What makes him worth studying here is that, at three moments, he tried as hard as anyone to explain new, "lumpy" facts of nature with smooth, classical physics. In 1904 he faced a famous puzzle: gases whose atoms show thousands of spectral lines should, by the classical rule that every mode of motion gets an equal share of heat, soak up enormous amounts of heat, yet they behave as if those modes were switched off. Jeans proposed that the modes are real but starved: a collision is too slow and smooth a push to set a fast vibration going, so energy trickles into the vibrations exponentially slowly, and what does arrive leaks away as light. In 1911 he presented the electron as a ball of pure electric field in an ether (which he adopted as a working hypothesis), whose mass is the energy of its own field and which really shrinks when it moves. In 1925, with quantum theory accepted, he argued that the quantum lives in how matter trades energy, not in light itself, and he sketched a way for a smooth wave to deliver a whole quantum to one absorber: let the absorbing atom send out a wave that runs backwards in time (an "advanced" wave), meeting the forward wave from the emitter. Some of this is now standard physics with his name on it (the Jeans escape of planetary atmospheres; the Jeans-Landau-Teller slow-energy-transfer law); some was overtaken, mostly by Jeans himself; and the 1925 backwards-wave idea was never worked out far enough to be tested.

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2. What you need to know first

Equipartition of energy and heat capacity. In classical statistical mechanics, every independent "square term" in a molecule's energy (for example (1/2) m u^2 for motion along x, or (1/2) b phi^2 for the stretch of a spring) has, at equilibrium, an average energy of (1/2) k T, where k = 1.380649e-23 J/K is Boltzmann's constant and T the absolute temperature. Jeans calls each kinetic square term a "momentoid"; we would call it a quadratic degree of freedom. The heat capacity follows by counting square terms, and so does gamma, the ratio of the heat capacity at constant pressure to that at constant volume: with f square terms per molecule, gamma = 1 + 2/f. A monatomic gas (f = 3) gives 5/3 = 1.667; a rigid diatomic (3 translations + 2 rotations, f = 5) gives 7/5 = 1.4. Read: Daniel Schroeder, An Introduction to Thermal Physics (equipartition in Chapter 1; the Boltzmann factor in Chapter 6) [memory, high].

The Boltzmann factor and the quantum "freeze-out". In quantum physics a vibration of angular frequency omega can hold energy only in steps of hbar omega (hbar = h/2 pi = 1.0546e-34 J s, h being Planck's constant). At temperature T the chance that a mode is excited is roughly exp(-hbar omega / kT). If hbar omega is much bigger than kT the mode is "frozen" and adds nothing to the heat capacity, however long you wait. Same textbook, Chapters 6-7.

A driven harmonic oscillator. An oscillator obeying a phi'' + b phi = U(t) (a = inertia, b = stiffness, angular frequency p = sqrt(b/a), U = applied force) that starts at rest and is pushed by a brief force U(t) ends with energy |integral U(t) e^(i p t) dt|^2 / (2a). In words: only the part of the push that "rings" at the oscillator's own frequency counts. This is the key to Jeans's 1904 argument. Read: John R. Taylor, Classical Mechanics (driven oscillators and Fourier series) [memory, high]; any ODE text that covers the variation-of-parameters (Duhamel) solution.

Contour integration (only for section 5's background). For a smooth function, the Fourier integral above can be evaluated by moving into the complex t-plane; the answer is controlled by the nearest point where U(t) blows up (a "pole"). If that pole is at distance beta from the real axis, the integral is proportional to e^(-p beta). You do not need to do this yourself: example.py checks the result directly. Read: Mary Boas, Mathematical Methods in the Physical Sciences, the chapter on functions of a complex variable [memory, high].

Maxwell's equations, potentials, retarded and advanced solutions. Electric and magnetic fields can be written from a scalar potential V and a vector potential A, which satisfy wave equations with the charges and currents as sources. The usual ("retarded") solution says the potential here and now depends on the source at the earlier time t - r/c, when the signal left it (r is the distance, c the speed of light). The wave equation is just as happy with the "advanced" solution, which uses the later time t + r/c; it is normally discarded because effects are not seen before their causes. Read: David Griffiths, Introduction to Electrodynamics, Chapter 10 (potentials, retarded potentials) and Chapter 11 (radiation, the Larmor formula) [memory, high].

Special relativity basics. Length contraction by the factor sqrt(1 - v^2/c^2), the Lorentz transformation, and E = m c^2. Griffiths, Chapter 12 [memory, high]. No tensors are needed for this primer.

Kinetic theory of gases. Molecules move with a spread of speeds (the Maxwell distribution); the root-mean-square speed is C = sqrt(3kT/m), m the molecular mass. Jeans uses C for this speed, and in his electricity book he also uses C for the speed of light; this primer says which each time. Schroeder Chapter 6 covers the Maxwell distribution.

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3. The textbook view

3a. Heat capacities of gases (what Jeans faced, and what replaced his answer)

Count of square terms per molecule, f; heat capacity at constant volume per molecule C_v = (f/2) k; gamma = 1 + 2/f.

The puzzle (one of the famous "clouds" over classical physics around 1900 [memory, high]): an argon atom shows thousands of spectral lines, so if each line is a vibration it should add two square terms. Jeans's own number: 1000 lines give f = 3 + 2000 = 2003 and gamma = 1 + 2/2003 = 1.0010, against 1.667 observed [read: deep read of Gases, section 1; calc].

Textbook answer (from 1907-1913, Einstein for solids, then Nernst, Eucken and others for gases [memory, high]): modes with hbar omega much bigger than kT are frozen by the Boltzmann factor. An optical line at 1.3 eV (an electron-volt, eV, is the energy an electron gains across one volt: 1.602e-19 J; kT at room temperature is about 0.025 eV) has hbar omega / kT = 56 at 273 K, so its excitation is about e^-56 = 5e-25 [calc: example.py Part 3]. Molecular rotation is frozen at low temperature too: hydrogen gas loses its rotational heat capacity (about k per molecule) as it is cooled from room temperature toward 40 K (Eucken 1912 [web: https://en.wikipedia.org/wiki/Arnold_Eucken, checked by the contrarian]; full theory Dennison 1927, which treats ortho- and para-hydrogen [memory, high]).

The Rayleigh-Jeans law: the same puzzle seen from the radiation side. Apply equipartition not to the molecules but to the standing waves of the electromagnetic field (the "ether") in a closed box at temperature T. Each wave mode gets kT, and the number of modes per unit volume with frequency between nu and nu + d nu is (8 pi nu^2 / c^3) d nu, so the radiation energy per unit volume is

u(nu) d nu = (8 pi k T / c^3) nu^2 d nu (the Rayleigh-Jeans law; c = speed of light).

Planck's law, which is what is measured, is u(nu) d nu = (8 pi h nu^3 / c^3) d nu / (e^(h nu/kT) - 1). The two agree when h nu is much less than kT; above that, Planck's law is cut off by the Boltzmann-like factor while the Rayleigh-Jeans law keeps growing as nu^2, so its total energy, the integral over all frequencies, is infinite (later called the "ultraviolet catastrophe" [memory, high]). Numbers [calc]: the ratio Planck / Rayleigh-Jeans is x / (e^x - 1) with x = h nu / kT; for microwaves at 1e11 Hz and 300 K it is 0.992; for green light (5e14 Hz) at 300 K it is 1.5e-33; at the Sun's surface temperature (5800 K) it is 0.067.

Jeans is half of the name. In 1905 Rayleigh wrote to Nature (71, 559, 13 April 1905) that appealing to the ether only brings in "an infinitude of new modes of vibration"; Jeans replied (Nature 71, 607, 27 April 1905) that for air in a perfectly reflecting box equipartition gives, "in the final state", a ratio of 5 : infinity between the energy of the five translational and rotational terms and everything else, whereas observation suggests 5 : 0; his point was that "millions of years would hardly suffice for any perceptible change", so that "although (1) may be the true final ratio, it is quite impossible to obtain experimental evidence of it" [web: research/2026-10-08-montambaux.md, page image of the letter]. Rayleigh's formula had a factor 64 pi; Jeans "speedily pointed out a source of error" and the 8 pi is his (Phil. Mag., July 1905), as Oliver Lodge recorded (Nature 118, 81, 17 July 1926) [web: same note]. The 1904 gas book already names this end state as the one "failure case" of its theory: equipartition between matter and ether, "not likely to occur in nature" (section 257) [read: deep read, Gases section 8]. The 1925 lecture prints the classical law, (8 pi R T / c^3) nu^2 d nu with Jeans's R = k per molecule, as the h -> 0 limit of Planck's law [read: deep read, Atomicity section 2d]. So claim 1 (molecules) and the Rayleigh-Jeans law (radiation) are one argument about one equilibrium. Not yet read by any role: the rest of the 1905 exchange (Nature 72, 54, 101 and 243), Jeans's Proc. Roy. Soc. 1905 paper and his 1911 Solvay report, all saved in research/files/montambaux/.

3b. Slow energy transfer in collisions (where Jeans's mathematics survives)

For the driven oscillator of section 2, a push of duration tau gives the vibration an energy that falls off roughly as exp(-p tau) once p tau is large: a slow, smooth push lets the oscillator follow along and return to rest, with almost no energy left over (this is called adiabatic invariance [memory, high]). In 1936 Landau and Teller built the standard theory of vibrational relaxation on this [memory, high]; Italian mathematical physicists (Benettin, Galgani, Giorgilli 1989; Benettin, Carati, Gallavotti 1995) proved rigorous versions for model systems and call it the Jeans-Landau-Teller approximation, after Jeans [web: research/2026-10-08-unimi-boltzmann-jeans.md]. Measured relaxation times are short on human scales: the CO2 vibration relaxes in about 7 microseconds at 1 atmosphere and room temperature [web: https://pubs.rsc.org/en/content/articlelanding/1966/tf/tf9666202655, abstract only].

3c. Escape of planetary atmospheres (a Jeans result in every planetary-science textbook)

A molecule at the top of the atmosphere escapes if its speed exceeds the escape speed. The governing number is the escape parameter

x = G M m / (a k T),

where G is the gravitational constant, M and a the planet's mass and radius (strictly, the radius of the exobase: the height above which collisions are so rare that a molecule moving upward faster than the escape speed is lost without being knocked back; on Earth about 500 km up [memory, medium]), m the molecular mass, k Boltzmann's constant and T the temperature there. It is the ratio of the gravitational binding energy of one molecule to kT. Jeans wrote it as x = 3 g a / C^2 (g = surface gravity, C = rms speed); since g = GM/a^2 and C^2 = 3kT/m the two are identical [calc: example.py Part 5]. Jeans's 1904 rule: lost if x < 15, kept "through millions of years" if x > 30 [read: Gases p.340]. With his own rough loss rate, 10^-2 (1 + x) e^-x of the outer atmosphere per second, x = 30 gives a half-life of 0.76 million years and x = 40 gives 1.3e10 years [calc: example.py Part 5]. So "x > 30" is a million-year criterion; a planet keeps a gas for billions of years only at x of about 40 or more.

Numbers for Earth: molecular hydrogen (H2) at 500 K has x = 30.4; at 1000 K, x = 15.2; nitrogen at 1000 K has x = 212 [calc: example.py Part 5]. But hydrogen in the exosphere is mostly atomic (H, half the mass of H2), and x is proportional to the mass, so atomic H has x = 15.2 at 500 K and 7.6 at 1000 K [calc: example.py Part 5]. Atomic H is the relevant species. Earth's real outer atmosphere (the exosphere) runs at about 740-1350 K [web: https://en.wikipedia.org/wiki/Thermosphere], so by Jeans's own rule atomic hydrogen (x about 10 at 740 K down to about 6 at 1350 K) is well inside the "lost" range (x below 15), and Earth does lose about 3 kg/s of hydrogen and about 50 g/s of helium, partly by Jeans escape and partly by other (non-thermal) processes [web: https://en.wikipedia.org/wiki/Atmospheric_escape].

3d. Electromagnetic mass and relativity

A charged sphere of charge e and radius a carries field energy outside it. When it moves slowly at speed u, the magnetic field it drags along adds kinetic energy as if it had extra mass

m_em = (2/3) e^2 / (a c^2) (Gaussian units, c = speed of light).

This is correct classical electromagnetism and Jeans derives it correctly (his eq. 626, with C for c) [read: Electricity p.563; mathematician re-derived it with SymPy]. The known trouble (the "4/3 problem"): the electrostatic energy of the sphere is U = e^2/(2a), so Einstein's rule m = U/c^2 gives e^2/(2 a c^2), and the ratio of the two is exactly 4/3. Poincare showed in 1905-06 that a stable charged sphere needs extra, non-electrical forces holding it together ("Poincare stresses"), and those fix the mismatch [web: https://en.wikipedia.org/wiki/Electromagnetic_mass].

In special relativity every mass, whatever its origin, carries the same speed factors: longitudinal mass m (1 - v^2/c^2)^(-3/2) and transverse mass m (1 - v^2/c^2)^(-1/2) [memory, high]. Length contraction sqrt(1 - v^2/c^2) is a property of space and time measurements, not a squeezing force. The electron today is treated as point-like: electron-positron scattering at LEP (the Large Electron-Positron collider at CERN, Geneva, run 1989-2000 [memory, high]) limits any radius to below 2.8e-19 m at 95% confidence [web: https://arxiv.org/pdf/hep-ph/0002172, via the arbiter's search].

The radiated power of an accelerated charge (Larmor formula): P = (2/3) e^2 a_acc^2 / c^3 (a_acc = acceleration) [memory, high; Griffiths Chapter 11].

3e. Photons, retarded and advanced waves

Modern quantum theory treats light as a quantum field: energy is exchanged in quanta h nu (nu = frequency), but a single photon still interferes with itself. Coincidence experiments in 1925 (Bothe-Geiger, April; Compton-Simon, 1 September) showed that in Compton scattering energy and momentum are conserved event by event, not just on average, which killed the Bohr-Kramers-Slater statistical proposal [web: https://en.wikipedia.org/wiki/Bothe%E2%80%93Geiger_coincidence_experiment]. In 1986 Grangier, Roger and Aspect showed that one photon going to a beam splitter is never detected on both sides at once, yet the same light interferes with 98% visibility [web: https://courses.physics.illinois.edu/phys513/sp2019/reading/week1/GrangierSinglePhoton1986.pdf].

Time-symmetric electrodynamics is a respectable minority tradition: Schwarzschild 1903, Tetrode 1922, Fokker 1929, Wheeler and Feynman 1945 ("absorber theory"), Cramer 1986 ("transactional interpretation") [web: Investigator, Wikipedia absorber-theory page]. In it each charge produces half retarded plus half advanced fields, and the usual behaviour (outgoing radiation, radiation reaction) is recovered when the advanced waves of all the absorbers in the universe are added up. Dirac (1938) showed that the radiation-reaction field on a charge is half of (retarded minus advanced) [memory, high].

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4. Where Jeans departs

Jeans's starting points are real physics in every case. The departures are in what he concluded from them.

4a. The 1904 gas book

What Jeans got right: the dynamics. His replacement for Liouville's theorem for a dissipative system, D rho / Dt = rho Delta F, is correct (rho is the density of systems in phase space, F the dissipation function, Delta F a positive sum of its second derivatives); his loaded-sphere toy model really does settle onto a "normal state" with the rotation nearly empty (the deep reader integrated it numerically and every start converged onto Jeans's curve) [read: deep read, Gases sections 4-6]. His remark that the limits "dissipation to zero" and "temperature to zero" do not commute is a sharp mathematical point.

What he admitted himself: the general theory proves only that a normal state exists, not what it is (section 234: "we must be content to rest the remainder of our investigation upon hypothesis") [read: p.212]; cubic terms he neglected are as large as those kept (section 219) [read]; and with plausible hard-sphere collisions his own law fails (section 242, below). Within a year, replying to Rayleigh in Nature (27 April 1905), he narrowed the claim to a time-scale statement: equipartition "may be the true final ratio", but the approach takes "millions of years" [web: Investigator, research/2026-10-08-montambaux.md]. He moved to the quantum side during 1910 [read: Atomicity p.9, "Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed"; web: Hudson 1989, abstract], and his 1916 second edition calls the quantum account "at best only partial" but "probably ... satisfactory" [web: Investigator, archive.org]. The classical position still had defenders after Jeans left it: at the British Association meeting in Birmingham in 1913, Larmor and Love defended classical dynamics, as Jeans's own 1914 Report records (section 18) [web: research/2026-10-08-archive-org.md].

The misfit of the integer rule, and Jeans's own answer. Measured gammas do not all fit n+3 = 3, 5, 6: Jeans's tables give CO2 n+3 = 6.98, chlorine 6.08, bromine and iodine about 6.8, CCl4 15.4, ethylene about 8 [read: deep reads]. The reviewers cite this against him. Jeans answered it himself in Chapter XVIII ("Molecular Aggregation and Dissociation") [read: deep read, Gases Ch. XVIII, page images pp.350-355]: - Aggregation: loosely bound clusters of molecules (doubles, triples) would distort the measured gamma. His evidence: wet steam gives n+3 = 32 against 6.6 for dry steam; Lussana's CO2 at high pressure (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. - The rule (section 407): "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 411 adds that radiative damping of the forced vibrations leaves the two atoms of a diatomic molecule in circular orbits, which gives five degrees of freedom. - His own limits: he "cannot even determine the sign" of the clustering correction and calls evaluating it "fruitless" (section 403); he computes no cluster fraction for any gas; and at ordinary pressure the values for CO2, chlorine, bromine, iodine, CCl4 and ethylene are not covered by his evidence. - Why it fails today: the low gammas of CO2, the heavy halogens and polyatomic molecules come from vibrations that are partly excited (low-frequency modes unfreezing gradually as the Boltzmann factor allows), not from aggregation, which is negligible in a dilute gas at room temperature [memory, high; arbiter QE revision 1]. The arbiter rules the chapter a candid but unquantified hypothesis; claim 1's verdicts are unchanged.

Contemporary evidence for and against collision-excited light (sections 248-250). For his mechanism Jeans cites Schuster and Hemsalech's observation of electric arcs (Phil. Trans. A 193, p.189): the violet light comes from the faster molecules, which his hypothesis "seems capable by itself of accounting for". Against it he records Pringsheim (Wied. Ann. 45, p.428), who held that "no light is ever produced in gases by collisions alone"; Paschen (Wied. Ann. 50, p.409) and Smithells contested Pringsheim [read: deep read, Gases section 7, pp.224-226]. These are the only contemporary experiments the 1904 book cites for the claim 2 mechanism; they were a dispute among physicists that the book leaves undecided. They do not change the verdicts, but they are part of the record.

Sound: the measurable side of slow exchange (Chapter XVI). Jeans also worked out what a lag in the exchange between translational and internal (rotational) energy does to sound [read: deep read, Gases Ch. XVI, page images pp.319-325]. One lagging reservoir gives a complex dispersion relation with the right limits (gamma = 7/5 at low frequency, 5/3 if the mode is frozen), an extra damping that grows as the square of the frequency, for his diatomic model "about one-seventh as great as that caused by viscosity", and a change of sound speed of only about 4e-11 at 16 kHz. He concluded the effect was "quite imperceptible", on the stated proviso that the exchange takes about one collision. The structure is that of later molecular acoustic relaxation, the effect by which vibrational relaxation times (such as CO2's 7 microseconds) were measured from the 1920s on (Herzfeld and Rice, Phys. Rev. 31, 691, 1928 [web: confirmed by the arbiter, https://en.wikipedia.org/wiki/Karl_Herzfeld]; Landau and Teller 1936, whose paper is titled "Zur Theorie der Schalldispersion", "On the theory of sound dispersion" [memory, high]). The arbiter rules the structure Established as classical dynamics and the "imperceptible" conclusion Plausible, untested as a statement about rotation. A link Jeans did not draw (a reader's inference): feeding his own slow exp(-2 p beta) rate for vibrations into the Chapter XVI formulas moves the dispersion into the kHz-MHz range where it was later found. Whether Chapter XVI influenced the later literature is unknown.

One open side dispute (Chapters III-IV). Jeans's proof that Maxwell's speed distribution is "infinitely probable" was criticised by S. H. Burbury, who held that molecules are correlated except in an infinitely rare gas (Phil. Mag. 6, p.529; 7, p.467); Jeans replied and says he "cannot persuade myself" the criticism is well founded [read: deep read, Gases Ch. III-IV]. Neither side's papers have been read by any role; no verdict rests on it.

The planetary-atmosphere chapter departs from today's view only in its inputs: Jeans took Earth's outer atmosphere to be "certainly less than 230 C" [read: page image p.340], so he concluded there was "no perceptible escape". The real exosphere is far hotter (3c). He credits G. Johnstone Stoney for the idea and G. H. Bryan for the mathematics, and reports, without answering it, Stoney's June 1904 view that the kinetic theory "is not competent to decide on the question" and that its conclusions "are inconsistent with the facts" (Phil. Mag. vii p.690) [read: page image p.342]. Stoney's letter is not in the folder; it is the originator's own dissent and stays in the record.

4b. The 1911 electricity book

Much of the book's electron chapter is simply correct textbook physics, read fairly: the Lorentz force, retarded potentials, the Larmor formula, the Hall effect, the normal Zeeman effect, radiation pressure (4.3e-5 dyne/cm^2 for sunlight) [read; arbiter claim 4d]. His "electron theory proves the Ampere law" (section 624) is really a derivation of the slow-speed Biot-Savart field of a moving charge summed over a wire element: correct as such, but it does not decide between the different force laws proposed for isolated current elements, which agree for closed circuits only. That matters for other projects in this collection that rest on Ampere-type element forces.

How firmly did Jeans hold the ether in 1911? Less firmly than the table's left-hand summary suggests. In sections 153-155 he finds no a priori proof of a medium: the arguments from inductive capacity, induction and finite speed "prove nothing" about whether energy resides in the 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 he adopts the medium as a "tentative hypothesis", to be judged by whether its properties come out consistent and probable [read: deep read, Electricity sections 153-155, pp.150-152]. So the 1911 book is a working ether hypothesis, not an asserted fact, and action at a distance was still an open option for him.

The element forces, from his own sections 496-500 [read: deep read, Electricity pp.448-453, page images]. The force between two closed circuits is measured and fixed; the force between two short pieces of them (current elements, ds and ds') is not, because any term that integrates to zero round a closed loop can be added. Jeans writes the mutual energy of two elements, carrying currents i and i' at distance r with angle eps between them, as -i i' ds ds' (cos(eps)/r + k d^2 r / ds ds'), where k is an undetermined constant (Helmholtz's): every value of k gives the same force on closed circuits. He names k = 1 ("a system of forces originally suggested by Ampere", which includes a couple) and k = 3/2 (related to the energy of two magnetic particles). Note that his k = 1 system is not the element force usually called Ampere's law today (the 2 cos(eps) - 3 cos(theta) cos(theta') form with no couple) [memory, medium; arbiter QE revision 4], so section 499 should not be quoted as the textbook statement of Ampere's law. He then argues (section 498a) that a force out of the plane of r and ds is "almost inconceivable" for pure action at a distance, and concludes (section 500) that "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 put the energy of the currents in the medium. That is exclusion by plausibility, not by experiment. Arbiter verdicts: the non-uniqueness of the element force is Established (as mathematics); the conclusion "give up action at a distance" is Not testable as stated and Historically superseded but instructive. For other projects that use Ampere-type forces the lesson is precise: say which member of the family you use, and remember that only closed circuits can be measured.

4c. The 1925 lecture Atomicity and Quanta

The problem the 1925 idea answers was already in his 1911 book (section 192) [read: deep read, Electricity p.178]. There he uses Earnshaw's theorem (no arrangement of charges under inverse-square forces can hold an electron at rest in stable equilibrium) to argue that the 1/r^2 law cannot hold down to zero distance, or charges would pair off and "the matter in the universe would tend to shrink into nothing"; he calls Larmor's model of orbiting electron rings "a sort of 'perpetual motion' machine", with "a difficulty in understanding how its energy can be continually replenished"; and he concludes that the electron must be "something more complex than a point charge". He does not say in 1911 that an orbiting electron must radiate. The link to 1925 is the arbiter's and the deep reader's inference: the half-sum field gives zero mean radiation, which answers the replenishment worry in a classical way; motion side-steps Earnshaw; and the 1925 "infinite field energy" is the 1911 zero-distance problem again. Note also the shift, which Jeans does not comment on, from the potential as "a convenient mathematical fiction" (1911) to advanced and retarded potentials that decide physical outcomes (1925).

The reviewers checked the core mathematics of the time-symmetric field: for strictly periodic motion, the half-sum field is a standing wave whose radial energy flow averages to zero (the Poynting flux goes as -sin(2 omega t) sin(2kr), positive and negative in turn) [calc: mathematician; physicist]. Two limits Jeans does not state: the "non-radiating" atom has an incoming wave of infinite extent cancelling its outgoing one (the source-free difference between the half-sum and the retarded field is exactly Dirac's radiation-reaction field), and a solution for prescribed sources is not yet a solution of the coupled motion of charges and fields [arbiter claim 6].

Also in the lecture, and correct: a free electron cannot absorb or emit a whole quantum of non-zero frequency (energy and momentum cannot both balance). The mathematician notes that Jeans's proof quietly uses photon momentum h nu / c, a particle property he elsewhere denies free light [arbiter ruling 8]. One step there is wrong: Jeans infers that a radiation field "produces no acceleration" in a free electron. Classically m dv/dt = e E0 cos(omega t) gives an oscillation with zero net work, and that oscillation is what Thomson scattering of light by free electrons, which is observed, comes from. Jeans derives his statement from quantum dynamics ("as we have just seen"), so a classical equation does not by itself refute it; what refutes it is observation (Thomson scattering, the low-frequency limit of Compton scattering) and quantum electrodynamics, which gives the same quiver [memory, high]. The arbiter's verdict is therefore Tested, not supported (changed from "Refuted by calculation" in its QE revision) [arbiter claim 5e]. He printed the same in his 1924 Report, so it was a held belief, not a slip.

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5. Worked example: does a smooth collision starve a fast vibration? (example.py)

This is the calculation at the heart of the 1904 book. We derive Jeans's law, re-run his own numbers, put the quantum answer beside it, and then apply both to a case that decides between them: the rotation of hydrogen molecules. Run it yourself:

.venv/bin/python review/Jeans-JH/example.py

Step 1. The law (example.py Part 1)

Model the internal vibration as a phi'' + b phi = U(t), with angular frequency p = sqrt(b/a). Jeans's model collision is a Lorentzian force pulse (his eq. 493):

U(t) = I c / (pi (c^2 + t^2)),

where I is the total impulse (integral of U over all time; SymPy confirms it equals I) and c is the half-width; the full width at half height, 2c, plays the role of the collision time tau.

The vibration, at rest before the collision, ends with energy |integral U e^(ipt) dt|^2 / (2a). Because U is even in t only the cosine part survives, and

integral from -inf to inf of I c cos(pt) / (pi (c^2 + t^2)) dt = I e^(-pc).

(SymPy does this integral; by hand it is the contour argument of section 2: the pulse has a pole at t = ic, distance beta = c from the real axis.) So

energy given = (I^2 / 2a) e^(-2pc) = (I^2 / 2a) e^(-p tau).

This is exactly Jeans's eq. 495. As c goes to 0 (an instantaneous kick) the factor goes to 1: the vibration gets the full I^2/(2a) whatever its frequency, "as it should be". Numerical check: integrating the equation of motion step by step (fourth-order Runge-Kutta) for p c = 0.5, 1, 2 and 3 reproduces the formula to within 0.02%. Each unit increase of p c cuts the transfer by e^-2 = 0.135.

Step 2. Jeans's own numbers (Part 2)

Jeans takes an infrared vibration p = 2e15 rad/s, molecular radius about 1e-8 cm, and air molecules moving at C = 5e4 cm/s [read: Gases pp.221-222, sections 242-243].

(a) Hard molecules that interpenetrate by 1/100 of their radius: the path in and out is 2e-10 cm, travelled at about C/2 = 2.5e4 cm/s, so tau = 8.0e-15 s and p tau = 16. Then e^-16 = 1.1e-7. With more than 10^7 collisions per second each molecule's vibration is fed about once a second, and Jeans himself concludes that the loss "would be much too great to agree with observation" [read]. Under his own most natural assumption, the theory fails, and he says so.

(b) Soft molecules that interpenetrate by half their radius: tau is 50 times longer, 4.0e-13 s, p tau = 800, and e^-800 = 10^-347.4. With 10^10 collisions a second the energy would take 10^329.9 years to fall by a factor e. Jeans: "about 10^330 years" [read; calc]. But he adds that there is "not the slightest evidence" for such soft molecules [read: p.222].

(c) Rare fast collisions short enough to excite the vibration directly: the fraction of collisions faster than a threshold is e^-x (1 + x), with x the threshold energy over the thermal scale. Jeans's x = 1200 gives 10^-518.07 ("about 10^-518"). At ten times the speed, i.e. 100 times the absolute temperature (273 K x 100 = 27,300 K, his "28,000 C"), x = 12 and the fraction is 13 e^-12 = 8.0e-5, enough to drain the gas in a microsecond. Hence his "temperature of incandescence" somewhere between 0 C and 28,000 C, which he himself calls "almost worthless as a confirmation" except that it fixes the speed to within a factor of 10 [read: p.224].

All of Jeans's printed numbers reproduce. Note the misprint the reviewers found: his italic summary (section 241) says slow dissipation needs the product of collision time and frequency to be "small"; the mathematics requires "large" [read: page image p.221; not in the book's corrigenda].

Step 3. The quantum answer for the same mode (Part 3)

One quantum of p = 2e15 rad/s is hbar p = 1.0546e-34 x 2e15 = 2.11e-19 J = 1.32 eV. At 273 K, kT = 3.77e-21 J, so hbar p / kT = 56.0 and the Boltzmann factor is e^-56 = 5.0e-25. At 1000 K it is 2.3e-7; at 5000 K, 0.047.

Both theories say this mode is nearly empty at room temperature. The difference is in kind. The quantum factor is an equilibrium statement: it does not depend on the collision shape, the pressure, or how long you wait. Jeans's factor is a rate: it says the mode is empty because it has not yet filled, and it depends on the unknown collision shape (p tau = 16 versus 800 is the difference between failure and success). To tell them apart we need a mode where the predictions differ.

Step 4. The deciding case: hydrogen rotation (Part 4)

Hydrogen (H2) rotates. Its rotational energy levels are E_J = h c B J(J+1) with B = 60.853 cm^-1 [memory, high], J = 0, 1, 2, .... For para-hydrogen the first step is J = 0 to 2, energy 6B = 365.1 cm^-1, which is 525 K in temperature units, angular frequency omega = 2 pi c (6B) = 6.88e13 rad/s.

Two facts make this case decisive:

1. H2 has no electric dipole, so its rotation cannot radiate [memory, high]. Jeans's ether sink is absent; on his own 1905 terms such a mode must reach equipartition eventually, and the only question is how fast.
2. Experiment: the rotational heat capacity of hydrogen disappears on cooling from room temperature toward 40 K (Eucken 1912) [web: https://en.wikipedia.org/wiki/Arnold_Eucken].

What Jeans's own 1904 theory says about H2 is simple and already decisive: H2 is in his n+3 = 5 list (sections 258, 270), so its two rotations are full momentoids at the gas temperature and gamma = 7/5 at every temperature [read: deep read, Gases sections 8, 10]. Eucken's 1912 measurement of rotation switching off below about 100 K contradicts that directly.

The table below goes further, and it is an extension, not something Jeans did. His collision-time rule was for vibrations of a fixed frequency p; classical rotation has no fixed frequency. As a "what if" most favourable to him, we apply his rate law to the quantum J = 0 to 2 rotational step, using his collision-time rule with H2's own speed (rms 1.839e5 cm/s at 0 C from his table, scaling as sqrt(T)), and collision rates from the hard-sphere formula with kinetic diameter 2.89e-8 cm at 1 atm [memory, medium]):

So even on this extension, and with the softest collisions Jeans considered, hydrogen rotation would fill to equipartition within milliseconds at 40 K. A calorimeter, which takes seconds to minutes, would then measure the full rotational heat capacity. The measured heat capacity shows rotation switched off.

Being fair to Jeans: his penetration depth is a free parameter. If we choose it to freeze rotation for one minute at 40 K, we need omega tau of at least 28.6, a collision time of at least 4.2e-13 s, i.e. penetration of 0.73 of the radius. That fitted model does freeze rotation at low temperature and leave it active at room temperature. But it then predicts something the quantum picture does not: the "freezing temperature" moves with how long you measure. With that penetration it would be about 112 K for a millisecond measurement, 55 K for one second, 30 K for an hour and 18 K for a year (and it would also shift with pressure, since the collision rate does).

The quantum rule has no free parameter beyond B, which comes from spectroscopy. The equilibrium population ratio of the J = 2 and J = 0 levels of para-hydrogen is 5 e^(-525 K / T): 0.87 at 300 K, 0.026 at 100 K, 1.0e-5 at 40 K. That reproduces the measured fall of the heat capacity (quantitatively once ortho- and para-hydrogen are treated as two species, Dennison 1927 [memory, high]).

An honest footnote that cuts in Jeans's favour: hydrogen does have one genuinely slow, time-dependent effect, the conversion between ortho- and para-hydrogen, which takes days to weeks without a catalyst [memory, high], and it was exactly what Dennison needed to explain the data. So "some degrees of freedom are out of equilibrium on laboratory times" is a real phenomenon; but the reason is a quantum selection rule on nuclear spin, not Jeans's smooth-collision law.

What the example shows: the exp(-p tau) law is right (Established; it is Landau-Teller's law), and Jeans's 1904 numbers are right; the inference "therefore the internal modes of real gases are empty because they never fill" fails where it can be tested: in a mode with no radiative sink whose freezing is an equilibrium effect, fixed by the spectrum.

Correction recorded below: arbiter.md ("What would settle it", claim 1) gives Jeans's rate for H2 rotation as "p t of order 2" with omega about 7e13 rad/s and collision time about 1e-13 s. Those two numbers multiply to about 7, which is what example.py finds (7.5) for Jeans's half-radius penetration; the arbiter's conclusion ("no strong suppression, yet rotation freezes") stands.

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6. Evidence table

Verdicts are the arbiter's (arbiter.md, "Corrected claim list", summary table and "QE revision").

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7. What a learner should take away

Solid. The mathematics in all three books is largely sound, and parts of it are now standard physics under Jeans's name: the escape parameter x = GMm/(akT); the exponential law for energy transfer from a smooth collision to a fast vibration (Jeans-Landau-Teller); the generalisation of Liouville's theorem to dissipative systems; the electromagnetic-mass integral; the Larmor formula; the proof that a free electron cannot absorb a whole quantum; the classical collapse time of the hydrogen atom; the Rayleigh-Jeans law (his 8 pi); the single-relaxation structure of sound dispersion by lagging internal energy (1904, Chapter XVI); and the proof that element forces between pieces of circuits are not unique (1911). The worked example reproduces his 1904 numbers exactly.

Wrong, and why that is instructive. - 1904: A correct rate law was turned into an explanation of an equilibrium fact. The tell-tale sign is that the theory's success depended on a parameter (how far molecules interpenetrate) for which Jeans himself said there was "not the slightest evidence", and with his natural choice it failed. The radiation sink also assumed the ether stays at absolute zero, which Kirchhoff's law rules out for a gas in an enclosure at its own temperature. Lesson: when an "explanation" needs a free parameter tuned by hundreds of orders of magnitude, ask what else it predicts (here: heat capacities that drift with measurement time). His Chapter XVIII answer to the misfit of his integer rule (molecular aggregation) shows the same pattern: a new effect whose size and even sign he could not compute. His own theory already failed for H2, which it says keeps gamma = 7/5 at all temperatures. - 1911: Bucherer's data could not have shown that the electron's mass is electromagnetic, because relativity gives every kind of mass the same speed dependence. Lesson: a fit that two theories predict identically cannot choose between them. The ether-contraction reading is observationally equivalent to special relativity, which is why it is "not testable", not "refuted". - 1925: The argument against localised "bullet" photons was sound, but the conclusion that free light is a purely classical wave sampled independently by each absorber was overtaken within months by the coincidence experiments. The inference that radiation gives a free electron "no acceleration" confuses "no net energy gain" with "no motion".

Genuinely open. - The 1925 time-symmetric source-and-sink scheme was never written in calculable form, by Jeans or anyone else, and it is missing from the standard histories of absorber theory (one history, Kennefick 1997, has zero mentions of Jeans [web: Investigator]). Competing explanations recorded by the arbiter: it was never calculable as stated; quantum mechanics (Heisenberg 1925, Schrodinger 1926) made the programme moot within months; Jeans turned to cosmology; the lineage reached Wheeler through Einstein's remarks on Tetrode and Ritz, not through Jeans. Suppression: nothing found (it was reviewed by Adams, Tolman and Loring). Records that would decide: whether G. N. Lewis 1926, Fokker 1929 or the Wheeler-Feynman correspondence cite Jeans; Jeans's letters (Royal Society JHJ papers; letters to O. W. Richardson at the Harry Ransom Center). A modern single-author line of work (Shuang-ren Zhao's "mutual energy flow", arXiv:1606.08710) uses the same retarded-source plus advanced-sink structure; nobody in this review has read it [web: Investigator]. - Whether classical dynamics with exponentially slow exchange can reproduce quantum-like equilibrium statistics (the Carati-Galgani programme) has not been settled either way; the reviewers found no completed derivation of Planck's law or the H2 heat capacity. - Stoney's 1904 objection to the kinetic-theory escape argument: what it rested on, and whether Jeans ever answered it. - How Jeans defended claim 1 in 1905 beyond the two letters read so far: the rest of the Rayleigh-Jeans exchange in Nature, his Proc. Roy. Soc. 1905 paper and his 1911 Solvay report are saved in research/files/montambaux/ but not yet read by any role. - Whether Jeans's 1904 sound chapter (XVI) was known to Herzfeld, Rice, Kneser or Landau and Teller (a citation search would settle it). - The Burbury-Jeans dispute over molecular chaos in the proof of Maxwell's law (Phil. Mag., sixth series, vols 5-7, about 1903-04 [memory, low on the years]): the papers have not been read. - Wien's measurement of the H-alpha decay time (5.4e7 per second) and Taylor's 2000-hour exposure are known here only through Jeans; the original sources were not located. - What stellar ages and masses lay behind Jeans's 1925 "atom of energy" argument; the lecture gives no numbers.

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8. Check yourself

1. A gas of molecules with 3 translational and 2 rotational square terms, plus 500 spectral lines each counted as a full harmonic vibration. What gamma does classical equipartition predict? What is measured for a diatomic gas at room temperature?
2. Using energy = (I^2/2a) e^(-p tau), by what factor does the energy given to a vibration change if the collision time doubles from p tau = 10 to p tau = 20?
3. Mars has g a about 0.2 of Earth's (Jeans's table). By how much is the escape parameter x of a given gas at a given temperature reduced compared with Earth? If H2 has x = 30 at Earth's exobase (the level defined in section 3c) at 500 K, what is x on Mars at the same temperature, and what does Jeans's rule say?
4. Why can Bucherer's measurement of the transverse mass of fast electrons not tell you whether the electron's mass is purely electromagnetic?
5. In Jeans's 1925 half-retarded, half-advanced atom, why does the radiated power average to zero, and what does the absorber-theory tradition (Wheeler-Feynman) need to add to recover ordinary spontaneous emission?

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9. Further reading

Mainstream. - Daniel V. Schroeder, An Introduction to Thermal Physics (Addison-Wesley, 2000): equipartition, Boltzmann factor, heat capacities, including the hydrogen example [memory, medium]. - David J. Griffiths, Introduction to Electrodynamics (4th ed.): Chapter 10 (retarded potentials), Chapter 11 (radiation, Larmor formula, radiation reaction), Chapter 12 (relativity) [memory, high]. - John R. Taylor, Classical Mechanics: driven oscillators. - L. Landau and E. Teller, "Zur Theorie der Schalldispersion" ("On the theory of sound dispersion"), Physikalische Zeitschrift der Sowjetunion 10, 34 (1936): vibrational relaxation, introduced through its effect on sound [memory, medium on volume and page]. Jeans's 1904 Chapter XVI (sound in a gas whose internal energy lags) has the same single-relaxation structure and is a classical precursor in its mathematics; whether Landau and Teller knew it is unknown. K. F. Herzfeld and F. O. Rice, Phys. Rev. 31, 691 (1928), is an earlier paper in the same line [web: via the arbiter]. - J. A. Wheeler and R. P. Feynman, "Interaction with the Absorber as the Mechanism of Radiation", Reviews of Modern Physics 17, 157 (1945) [memory, high]. - G. Benettin, A. Carati, G. Gallavotti, "A rigorous implementation of the Jeans-Landau-Teller approximation for adiabatic invariants" (1995); Benettin, Galgani, Giorgilli (1989) [web: research/2026-10-08-unimi-boltzmann-jeans.md; copies in research/files/]. - Planetary escape: D. C. Catling and J. F. Kasting, Atmospheric Evolution on Inhabited and Lifeless Worlds (Cambridge, 2017) [memory, medium]; the Wikipedia page "Atmospheric escape" for figures. - Electromagnetic mass and the 4/3 problem: Wikipedia "Electromagnetic mass" (a good start with references); history of the Kaufmann-Bucherer-Neumann experiments on Wikipedia. - R. Hudson, "James Jeans and radiation theory", Studies in History and Philosophy of Science 20 (1989): Jeans's 1910 turn to the quantum [web: research/files/montambaux/].

Jeans's own key works. - The Dynamical Theory of Gases (1904), Chapters VII-X (equipartition and its failure), XVI (propagation of sound), XVII (planetary atmospheres), XVIII (molecular aggregation, his answer to the misfit of the integer rule), XIX (size of molecules) (in the project folder). The 2nd edition (1916) adds the quantum account (archive.org, dynamicaltheoryo00jeanuoft) [web: Investigator]. - Rayleigh, Nature 71, 559 (13 April 1905), and Jeans's reply, Nature 71, 607 (27 April 1905): the Rayleigh-Jeans exchange; "On the partition of energy between matter and aether", Phil. Mag. [6] 10, 91 (1905) (research/files/) [web: Investigator]. O. Lodge, "Supplementary Note on Radiation", Nature 118, 81 (1926), on the 8 pi factor [web: Investigator]. - The Mathematical Theory of Electricity and Magnetism, 2nd ed. (1911), Chapters XIX-XX, and sections 148-155 (molecular count, action at a distance), 192 (stability of atoms) and 496-500 (Ampere's rule and element forces) (in the project folder); 4th ed. 1919 adds relativity; 5th ed. 1927 (archive.org 5thedmathematica00jeanuoft) [web: Investigator]. - Report on Radiation and the Quantum-Theory (Physical Society, 1914; 2nd ed. 1924): most of the 1925 lecture's arguments, with references [web: Investigator, archive.org]. - Atomicity and Quanta (Cambridge, 1926) (in the project folder). Contemporary reviews: E. P. Adams, Bull. AMS 32, 720 (favourable; note that the lecture uses Adams's own 1901 experiment, so he was not a neutral reviewer); R. C. Tolman, Phys. Rev. (1926); Loring, Chemical News 134, 129 (1927) [web: Investigator]. - G. H. Bryan, "The Kinetic Theory of Planetary Atmospheres", Phil. Trans. A 196 (1901), and G. Johnstone Stoney, "Escape of Gases from Atmospheres", Phil. Mag. vii, 690 (1904) [read: cited by Jeans; not in the folder].

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Answers

1. f = 3 + 2 + 2 x 500 = 1005, so gamma = 1 + 2/1005 = 1.002. Measured for N2 or O2 near room temperature: about 1.40 = 1 + 2/5, as if only translation and rotation count.
2. The factor is e^-20 / e^-10 = e^-10 = 4.5e-5: doubling the collision time cuts the transfer by more than twenty thousand times. That extreme sensitivity is Jeans's point ("the extreme rapidity with which the rate of dissipation decreases"), and also the weakness: the answer depends on a collision time nobody could measure.
3. x = 3 g a / C^2 is proportional to g a at fixed temperature and gas, so it falls to 0.2 of Earth's: x = 0.2 x 30 = 6 for H2 at 500 K. That is below 15, so by Jeans's rule hydrogen is lost from Mars; this is his own conclusion ("hydrogen and helium would escape ... water vapour, air, and heavier gases would be retained") [read: p.341].
4. In special relativity every mass, mechanical or electromagnetic, grows with speed by the same factor (1 - v^2/c^2)^(-1/2) (transverse). So the data fit "m0 = 0, all electromagnetic" and "all mechanical" equally well; Jeans's form m0 + (EM term)(factor) assumed that only the EM part grows. Separately, Bucherer's 1908 data were disputed and only later experiments were clean.
5. Half the field is an outgoing wave and half an incoming wave of equal strength; together they make a standing wave whose energy flow alternates in and out with zero average (Poynting flux proportional to -sin(2 omega t) sin(2kr)). An isolated time-symmetric charge therefore feels no radiation reaction (Dirac: reaction = half of retarded minus advanced) and would not decay. Wheeler and Feynman recover ordinary emission by assuming a complete absorber: the advanced responses of all the distant absorbers add up to supply the missing half, giving purely outgoing radiation and the usual radiation reaction.

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Corrections to earlier documents

1. arbiter.md, "What would settle it", claim 1: "Jeans's rate with p t of order 2 for H2 rotation (omega about 7e13 rad/s for the J = 2 to 0 transition, collision time about 1e-13 s)". The product of the two quoted numbers is about 7, not 2. Recomputed with Jeans's own collision-time rule and H2's speed (example.py Part 4): omega = 6.88e13 rad/s; omega tau = 0.15 at 1/100-radius penetration and 7.5 at half-radius penetration, at 0 C. Suggested wording: "p t between about 0.15 and 7.5 (Jeans's two penetration assumptions) at 0 C; relaxation in under a microsecond, and in milliseconds at 40 K, yet rotation freezes". The arbiter's conclusion is unchanged.
2. This primer, earlier version (2026-10-08), corrected here under CORRECTIONS ARE WELCOME (qe.md sections 3, 6, 7 and 8; arbiter.md "QE revision"): - Section 5, Step 4 called the H2 rotation table "Jeans's recipe for H2". That over-attributed: Jeans's collision-time rule was for vibrations of fixed frequency, classical rotation has none, and his own 1904 theory counts H2's rotations as full momentoids (gamma = 7/5 at all temperatures). The table is now labelled as an extension of his rate law, and the direct conflict with Eucken 1912 is stated first. example.py Part 4 comments were changed to match (the code and numbers are unchanged). - Section 3c gave only the H2 escape parameter ("hydrogen is at the edge of loss"). Exospheric hydrogen is mostly atomic; atomic H at 1000 K has x = 7.6, well inside Jeans's loss range. Both values are now given (example.py Part 5 now prints atomic H). - Section 4c dated Lorentz's starlight argument 1906, repeating the lecture. Jeans's own 1924 Report cites Lorentz 1910 and the 1913 Birmingham meeting; both dates are now given. - Evidence table, claim 5e ("no acceleration"): verdict was "Refuted by calculation"; the arbiter's QE revision changed it to "Tested, not supported", and section 4c now gives the reason. - Evidence table, claim 3: "Jeans's molecule count 4e19 was 49% high" read as a slip; it was the best value of 1904, and Jeans revised it himself to 2.75e19 by 1911 (Electricity section 149, book p.132). - Omissions now filled: the Rayleigh-Jeans law and the 1905 exchange (section 3a); Jeans's Chapter XVIII answer to the misfit of his integer rule, the Schuster-Hemsalech and Pringsheim-Paschen evidence, the Chapter XVI sound analysis, the 1913 Birmingham debate and the Burbury dispute (section 4a); the ether as a "tentative hypothesis" and the element-force family (section 4b); the 1911 background to the non-radiating atom (section 4c); new evidence-table rows for the arbiter's added verdicts; definitions of eV, exobase and LEP; and the source note, which listed Chapters XVI and XVIII as digest only after they had been deep-read.