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Jeans-JH: central claims

Project: three books by J. H. (Sir James Hopwood) Jeans, spanning 1904, 1911 and 1925-26. Source: source folder: Jeans-JH. Sources are the inventor's own printed works, so every claim below is [read] from the books unless tagged otherwise.

Source note (not a Source gap): all three documents have readable text. The two long books are OCR scans with garbled equations. The equations and numbers behind the claims below were read from page images in the deep reads. After the QE round, deep reads cover the Jeans 1904 gas book at Ch. III-IV, VII end-X, XVI-XIX, and the 1911 electricity book at sections 145-156, 192, 496-501 and Ch. XVIII end-XX. Digest-only coverage remains for gas-book Ch. I-II, V-VI and XI-XV (standard kinetic theory) and for electrostatics, circuits and magnetism in the electricity book (standard textbook material). None of the central claims rests on a digest alone.

Real gases do not follow equipartition because their molecules radiate (1904). Jeans argues that a gas whose molecules emit thousands of spectral lines would, under classical equipartition, have a specific-heat ratio gamma near 1, whereas monatomic gases show 5/3. He resolves this by saying the molecules lose energy to the ether, so the system is not conservative, and the line-producing internal modes settle into a "normal state" at "subsidiary temperatures" far below the translational temperature, giving gamma = 1 + 2/(n+3) with n+3 = 3, 5, 6 and so on according to molecular structure. Observed n+3 is not always an integer (CO2 6.6-7.7, chlorine 6.08, Br2 and I2 6.8, CCl4 15.4), and n changes meaning between Ch. VII (gamma = 1 + 2/n, all momentoids) and Ch. IX-X (gamma = 1 + 2/(n+3), n internal terms). Jeans himself narrowed the equilibrium claim to a time-scale claim in his 1905 exchange with Rayleigh (the ether is a zero-temperature sink; he conceded the ultraviolet-catastrophe end state of the classical equilibrium, the Rayleigh-Jeans law). His own answer to the non-integer values (Ch. XVIII) is molecular aggregation plus the rule n+3 = 3, 5, 6 (section 407) and, in section 411, dissipation that makes diatomic atoms orbit in circles; he says the aggregation correction cannot be signed or computed, and the ordinary-pressure misfit is not covered. [read: Dynamical Theory of Gases, deep reads PDF pp.186-245 and 343-355; Montambaux files via research/2026-10-08-montambaux.md for the 1905 exchange]
Slow feeding of the internal modes comes from a collision-time effect (1904). The energy a collision passes to a vibration of angular frequency p falls like exp(-2 p beta), where beta is of the order of the collision duration, so for optical frequencies the transfer can be exponentially small, and the same effect predicts a "temperature of incandescence" below which internal modes stay empty. Jeans gives two estimates: p x collision time = 16 (e^-16, about 10^-7), which he calls "much too great to agree with observation", and 800 (e^-800), which needs molecules to penetrate to half their radius and for which he finds "not the slightest evidence". He states that the general theory proves only that a normal state exists, and that the emptiness of the internal modes is demonstrated only for toy models (section 234). His italic conclusion in section 241 says "small" where the mathematics needs "large". Contemporary evidence he cites: Schuster and Hemsalech (arc spectra, faster molecules emit violet light) in support; Pringsheim against ("no light is ever produced in gases by collisions alone"), contested by Paschen and Smithells. A testable consequence in the same book (Ch. XVI): a lag in energy exchange damps sound, about one-seventh of the viscous damping for a two-sphere diatomic molecule if exchange takes one collision, with an imperceptible speed change; the same structure later appears in molecular acoustic relaxation. [read: same deep reads, sections 4-7 and 9; section 234; Ch. XVI deep read]
Kinetic theory fixes planetary atmospheres and molecular sizes (1904). An atmospheric gas is lost by a planet if x = 3 g a / C^2 is below about 15 and retained if above about 30, so the Moon, if it ever had an atmosphere "at a temperature much above zero", would lose all but CO2 and denser gases (a conditional statement), Mercury is "exactly similar to Mars" and "entirely devoid of atmosphere" on astronomical evidence, and Earth and Venus keep theirs. Retained means over millions of years, and the Earth premise (outer atmosphere "certainly less than 230 C") is superseded. Hydrogen in the exosphere is mostly atomic; atomic H at 1000 K gives x of about 7.6 (H2 about 15.2), well inside "certainly lost". Independently, viscosity, conduction, diffusion, Boyle's-law deviation, solid and liquid densities and refractive index all give molecular radii of order 1 to 2 x 10^-8 cm, computed with a molecular count of about 4 x 10^19 per cm^3 in 1904 (49 percent above the modern 2.69 x 10^19); by 1911 Jeans had revised it to 2.75 x 10^19 and recalculated the radii (1.09 to 2.30 x 10^-8 cm), a within-2-percent value. Jeans credits Johnstone Stoney and G. H. Bryan for the escape idea and reports that Stoney now disputes the kinetic-theory conclusion. [read: deep read PDF pp.326-362]
The electron is a purely electromagnetic object in a real ether, and bodies physically contract (1911). Jeans writes the electron's mass as m = m0 + (2/3) e^2/(a C^2), concludes from recent experiments that m0 = 0 and the radius is about 2 x 10^-13 cm, and presents the Lorentz-FitzGerald contraction as "more than a conjecture" if all ether forces are electrical, the Michelson-Morley null result as "almost positive proof" of it, and Bucherer's experiments as confirming Lorentz's deformable electron over Abraham's rigid one (Bucherer 1908 was disputed, e.g. by Bestelmeyer; confirmations came later). He derives radiation from acceleration alone, (2/3) e^2 (acceleration)^2 / C^3, and states that electron theory derives the Biot-Savart field of a moving charge and, summed over a circuit element, the force he calls Ampere's law. The ether is a "tentative hypothesis" in sections 153-155 (action at a distance is not ruled out a priori; the potential is "a convenient mathematical fiction"), and in sections 498a-500 he finds action at a distance "almost inconceivable" for the forces on circuits, so "almost compelled" to attribute them to stresses in the medium; the element-element forces are not unique (Helmholtz's family with constant k; k = 1 is Ampere's system). Section 192 uses Earnshaw's theorem to say a point-charge atom under inverse-square forces cannot be stable and rejects Larmor's orbiting electron rings as "a sort of perpetual motion machine". The electron mass in this paragraph is (2/3) e^2/(a C^2), which is 4/3 of the rest-energy mass U/C^2 with U = e^2/(2a): the 4/3 problem. Einstein is credited only with extending a Lorentz corresponding-states theorem; the word "relativity" does not appear in the chapters read. [read: Mathematical Theory of Electricity and Magnetism, deep read PDF pp.557-593]
Energy is atomic, quantisation lives in matter-radiation exchange, and free radiation is wave-like (1925). Jeans argues from relativity that space and time are continuous but matter and energy can be atomic, with an "atom of energy" mC^2 shown by the sun's mass loss (the lecture gives no star masses or ages and says the methods "need not be detailed here"); that emission and absorption occur by single quanta h nu; that if h were zero the hydrogen atom would collapse in about 10^-10 s (printed; the material energy of the universe would vanish in "thousand-millionth parts of a second", in words only); and that radiation travelling freely in space must remain undulatory, because indivisible quanta contradict interference over about a million wavelengths, Wien's decay times, Taylor's feeble-light diffraction pattern and Lorentz's starlight argument (dated 1906 in the lecture; Jeans's 1924 Report cites Lorentz 1910). The lecture also prints the classical limit of Planck's law, (8 pi R T / c^3) nu^2 d nu, with R the gas constant per molecule (the Rayleigh-Jeans law). A free electron, he shows, can neither absorb nor emit a non-zero-frequency quantum. [read: Atomicity and Quanta, deep read PDF pp.4-23]
A time-symmetric (advanced plus retarded) field can make a non-radiating atom and carry a whole quantum from emitter to absorber (1925). Equal retarded and advanced potentials give zero mean radiation, so classical electromagnetism can in principle allow a permanent non-radiating atom. A two-atom solution with one purely retarded and one purely advanced source: Jeans gives the potentials for prescribed sources, not the energy flow, and offers the source-and-sink picture (not exact for waves) as a way a whole quantum might be gathered onto one absorber, and as an alternative to Compton's bullet derivation. His 1911 book (section 192) had rejected Larmor's orbiting rings as a perpetual-motion machine; the 1925 non-radiating atom is a classical answer to that worry, which is a link of ours, not stated by Jeans. Jeans lists his own gaps: infinite field energy, no selection of Bohr orbits, no equations for his Compton alternative, and no phenomenon that explains atoms acting as sources and sinks at frequencies they do not "beat time" to. [read: Atomicity and Quanta, deep read PDF pp.24-35]
The quantum may be another face of charge atomicity (1925, conjecture). Jeans notes h C / 2 pi = K (4 pi e)^2 with K "not greatly different from unity" and suggests quantum atomicity may arise from the atomicity of electric charge, perhaps via an atomicity in the metric properties of space-time. The deep reader's arithmetic shows K = 1/(16 pi^2 alpha) = 0.868, the fine-structure constant rewritten, so the claim is a dimensional near-coincidence that Jeans states only as a suggestion. [read: Atomicity and Quanta, deep read PDF p.25-26, 29-30]

Thread across the three: Jeans repeatedly seeks classical (continuous, wave, ether or field) explanations of discrete or quantum phenomena for 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. Jeans moved to the quantum side in 1910 (the lecture: "Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed"; Hudson 1989 dates it to 1910), and the 1925 lecture is written from relativity rather than the 1911 ether.