Jeans-JH · Source catalogue

A 64-page lecture by Jeans (the title page lists him as D.Sc., LL.D., F.R.S., formerly Stokes Lecturer in Applied Mathematics at Cambridge and sometime Professor of Applied Mathematics at Princeton) on the 'atomicity' of nature. Part 1 (book pp.5-35) argues that space and time are continuous (relativity mixes them, and a granular continuum would need a universal constant of dimension length x time, which no one has found), that matter is atomic, and by the relativity 'rate of exchange' E = mC^2 that energy should be atomic too, in units mC^2. His only evidence offered for an 'atom of energy' is astronomical: the sun is said to radiate about 250 million tons of its mass per minute (my check from luminosity/c^2 gives about 257 million; [memory] medium on the luminosity), and young stars are said to be more massive than old ones; the lecture gives no star masses or ages and says the methods 'need not be detailed here'. He then gives the quantum story of 1900-1925 as he saw it: Planck's cavity-radiation law (the lecture prints its classical limit for h -> 0, (8 pi R T / c^3) nu^2 d nu, in Jeans's notation where R is the gas constant per molecule, i.e. k; this is the Rayleigh-Jeans law, see the 1905 exchange recorded in research/2026-10-08-montambaux.md), Einstein's law that emission and absorption occur in single quanta h nu (photochemical and photoelectric examples), the Boltzmann-factor reason the violet end is dim, and the claim that if h were zero the hydrogen atom would collapse in about 10^-10 s (the printed exponent) and the universe's material energy would vanish in 'thousand-millionth parts of a second' (stated in words; no exponent is printed, and the QE/arbiter check computes about 1.6 x 10^-11 s), whereas with h non-zero the duration is of order 10^20 s. Bohr orbits are described with an 'atom of angular momentum' h/2 pi. He says 'Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed' [read: Atomicity text line 378], which dates Jeans's own move to the quantum side to 1910. He then sets out the 'waves versus bullets' dilemma for radiation after emission and reports the evidence against indivisible bullet-like quanta: Lorentz (starlight diffraction patterns; dated 1906 in the lecture, while Jeans's 1924 Report cites Lorentz, Phys. Zeitschr. 11, p.349, 1910, and the 1913 British Association meeting at Birmingham [web: research/2026-10-08-archive-org.md]), G. I. Taylor's very feeble light (2000 hours' exposure, diffraction pattern still formed), Wien's decay time for H-alpha (1/e in 1/(5.4 x 10^7) s, so a quantum would be several metres long), and interference over about a million wavelengths. Part 2 (book pp.36-64) is mathematical. He shows that a free electron cannot absorb or emit a quantum (energy conservation plus a Galilean/relativistic change of frame forces nu = 0), then (the frame change does the work of momentum conservation with photon momentum h nu/C, so the theorem imports radiation momentum) that the momentum balance in photo-ejection (electron momentum 2h nu / v, photon momentum only h nu / C) means absorption must be by 'the atom as a corporate whole'. He floats tubes of force as a picture and notes h C / 2 pi = K (4 pi e)^2 with K 'not greatly different from unity' (my arithmetic: K = 1/(16 pi^2 alpha) = 0.868, i.e. the fine-structure constant rewritten). He argues, from Adams's 1901 rotating charged spheres (Adams worked at the Jefferson Laboratory, Harvard, with copper spheres on brass rods, measuring magnetic convection effects; Phil. Mag. [6] 2, 285, 1901 [web: Investigator, archive.org]), that radiation by charges is an irreversible process and that a hydrogen atom in equilibrium with radiation needs reversible processes, so the solutions of the wave equation must give equal weight to retarded and advanced waves: potentials Psi = integral ([rho] + {rho}) / 2r dV. He states (without showing the calculation) that the time-averaged radiation from such a system is zero, so 'even under the laws of classical electromagnetism it is possible for an atom to be a permanent non-radiating electrical system', but immediately lists two objections (infinite field energy; no selection of Bohr orbits). He proposes an alternative to Compton's bullet derivation of d lambda = (h/mC)(1 - cos theta), without writing out the equations, and a two-atom solution in which atom 1 is purely retarded and atom 2 purely advanced (a 'source and sink' of equal strength). Jeans writes down the potentials for prescribed sources; he does not compute the energy flow, and the hydrodynamic source-and-sink analogy is not exact for waves. He offers it as the way a whole quantum might flow from emitter to absorber. He closes by admitting that the atom's behaviour at frequencies it does not 'beat time' to is not understood: 'we are still very far from understanding the working of the atom or the true meaning of atomicity and quanta.'

Key claims

• Space and time are continuous because relativity mixes them and no universal constant with dimensions length x time is known.
• Energy should be atomic in units m C^2, and this 'atom of energy' is revealed by astronomy (the sun converting about 250 million tons of mass per minute to radiation) rather than by laboratory physics.
• If Planck's constant h were zero, the hydrogen atom would collapse in about 10^-10 s (printed), and the material energy of the universe would turn into radiation in 'thousand-millionth parts of a second' (words only; no exponent printed); with h non-zero the duration is of order 10^20 s.
• Radiation emission and absorption occur in single quanta h nu (Einstein's law), but radiation travelling freely in space obeys the undulatory theory, because indivisible bullet-like quanta cannot account for interference over about a million wavelengths, Wien's decay times (quantum length several metres), the diffraction patterns of feeble starlight or Lorentz's starlight argument (dated 1906 in the lecture; Jeans's 1924 Report cites Lorentz 1910).
• A free electron can neither absorb nor emit radiation of non-zero frequency (shown by combining h nu energy exchange with a change of inertial frame).
• Absorption of a quantum by a hydrogen atom must involve the atom as a whole, since the photo-ejected electron's momentum is about 2 h nu / v while the photon carries only h nu / C (the argument imports photon momentum h nu/C through the frame change).
• The relation h C / 2 pi = K (4 pi e)^2 with K near 1 suggests the quantum may be another aspect of the atomicity of electric charge (K = 0.868, i.e. 1/(16 pi^2 alpha), by the deep reader's arithmetic).
• Potentials made of equal parts retarded and advanced solutions of the wave equation describe a system in equilibrium with radiation whose time-averaged radiation is zero, so classical electrodynamics can in principle give a non-radiating atom.
• A solution with atom 1 purely retarded and atom 2 purely advanced gives the potentials of a source-and-sink pair for prescribed sources; Jeans offers it as the way radiation might flow from emitter to absorber and so account for the photoelectric effect without bullet-like quanta, but he does not compute the energy flow, and the source-and-sink analogy is not exact for waves.
• The Compton shift can be accounted for without a bullet photon: the atom absorbs a quantum, is checked, and re-emits one before the process completes, giving a spread emitted quantum and a slightly different coefficient than h/mC (equations not given).
• Jeans concedes there is no known phenomenon that explains how an atom acts as a source and sink for frequencies it does not 'beat time' to.
• The classical limit (h -> 0) of Planck's law is (8 pi R T / c^3) nu^2 d nu, with R the gas constant per molecule (Jeans's notation); this is the Rayleigh-Jeans law, printed in the lecture as a limit of Planck's law (Lodge, Nature 118, 81, 1926, credits Jeans with the 8 pi R factor [web: research/2026-10-08-montambaux.md]).

Relevance: The single most 'unusual' document in the project and the one on which any claim about Jeans as an alternative-physics figure rests. It records a mid-1925 position (before Heisenberg, Schroedinger, Born and the photon/wave-particle synthesis) in which a leading mathematical physicist, who had himself given the Rayleigh-Jeans law (1905) and had accepted the quantum hypothesis in 1910 (the lecture, p.9: 'Poincare (1912) and myself (1910)'; Hudson 1989 dates the move to 1910), argued for a purely undulatory account of free radiation with quantisation confined to matter-radiation exchange, built on time-symmetric (advanced + retarded) potentials. Time-symmetric potentials had been used by Tetrode (1922) before the lecture, and the emitter-absorber picture precedes Wheeler-Feynman absorber theory (1945) and Cramer's transactional interpretation (1986) by decades [memory] high on the order, medium on exact dates; Jeans cites none of these. The h-versus-charge-atomicity remark prefigures the fine-structure-constant problem.

Mainstream conflict: Yes on several points. The astronomical 'atom of energy mC^2' and the idea that the sun's radiation is annihilation of matter were superseded by hydrogen fusion (Eddington's 1920 suggestion) [memory] high; the stellar-mass argument is not detailed in the lecture, and the claim that it fails holds under modern stellar ages, not within the 1920s annihilation chronology. Free radiation is today described by photons as quanta of the quantised field; Jeans's refusal of indivisible quanta and his undulatory-only picture is not the accepted view, and the 1925 coincidence experiments bear on his Compton alternative: Bothe-Geiger was April 1925, about a month before the lecture of 11 May 1925, and Compton-Simon was 1 September 1925, after it; Tolman (1926) called the timing 'almost simultaneous'. Whether Jeans knew of Bothe-Geiger is unknown [web: Investigator and arbiter; arbiter correction 10]. The time-symmetric non-radiating atom is mathematically legitimate for periodic motion but, as Jeans himself notes, gives no quantisation of orbits. The claim that a radiation field does not accelerate a free electron goes beyond his own argument and conflicts with observed Thomson scattering [memory] high (observation, and quantum electrodynamics, which also gives the electron's quiver; a classical equation of motion alone does not refute it, since Jeans states it as a consequence of quantum dynamics).

Jeans's Cambridge University Press textbook on classical electromagnetism, 2nd edition, about 580 numbered book pages. Chapters I-X: electrostatics (Coulomb's law and its Cavendish/Maxwell test, lines and tubes of force, Gauss's theorem, Poisson and Laplace equations, equipotentials and equilibrium points, conductors and condensers, systems of conductors, dielectrics and Mossotti's conducting-sphere picture, Maxwell stresses in the field, Green's theorem and Earnshaw's theorem, solution methods: images, inversion, spherical harmonics, ellipsoidal coordinates, conjugate functions and Riemann surfaces), steady currents in networks and continuous media. Chapters XI-XII: permanent and induced magnetism, terrestrial magnetism, molecular theories. Chapters XIII-XVI: magnetic fields of currents, Ampere's rule (with the remark that innumerable force systems fit closed-circuit data), induction of currents, and the Lagrangian dynamical theory of currents. Chapter XVII: displacement currents, Poynting's theorem, wave equation, ratio of units C about 3 x 10^10 cm/s and Maxwell's electromagnetic theory of light. Chapter XVIII: reflection, metals, dispersion by bound electrons, light pressure (Lebedew, Nichols and Hull). The 1911 edition says Chapters XIX-XX are new: 'The Motion of Electrons' and 'The General Equations of the Electromagnetic Field'. The deep read covered these. Chapter VI opens with the two possibilities (section 153): action at a distance as an ultimate explanation, or a connecting medium. Jeans says no a priori argument rules out action at a distance, treats the finite-speed potential as 'a convenient mathematical fiction', and adopts the medium only as a 'tentative hypothesis' (section 155) to be kept while the properties it needs are consistent and plausible; section 156 then says that, since action crosses a vacuum, the medium must be the ether [read: deep read, PDF pp.150-152]. Chapter V (sections 145-151) uses Mossotti's picture of molecules as small conducting spheres: with n = 2.75 x 10^19 molecules per cm^3 (the 1904 gas book used about 4 x 10^19; no source is given for the new figure, and it is within about 2 percent of the modern 2.69 x 10^19 [memory high]) the table gives electrical radii a of 0.596 x 10^-8 cm (He) to 1.60 x 10^-8 cm (ethylene) against recalculated kinetic-theory radii of 1.09 to 2.30 x 10^-8 cm; the two sets disagree by about 30 percent and Jeans says the agreement is 'very significant evidence' of molecular polarisation but only of order of magnitude [read: PDF p.142, page image]. Section 192 uses Earnshaw's theorem: an electron cannot rest in stable equilibrium under inverse-square forces alone, so the force law must differ at small distances; he rejects Larmor's orbiting electron rings as 'a sort of perpetual motion machine' whose energy cannot be replenished, and concludes the electron must be more complex than a point charge e/r^2 [read: PDF p.178]. Sections 496-500 give the vector potential of currents, 'Ampere's rule' for the force from a circuit (the Biot-Savart form), the most general element force (differing from it by a term d2 psi / dx ds), and, for two circuits, the family of element energies -i i' ds ds'(cos eps / r + k d2r / ds ds') with Helmholtz's constant k: k = 1 is 'a system of forces originally suggested by Ampere' and k = 3/2 mimics two small magnets; all give the same closed-circuit forces. He judges a force out of the plane of r and ds 'almost inconceivable' as pure action at a distance and that 'none of these seem at all plausible', so we are 'almost compelled' to give up action at a distance and attribute the forces to stresses in the medium [read: PDF pp.448-453, page images]. Chapter XIX derives the field of a slowly moving charge (low-speed Biot-Savart), the electromagnetic mass m = m0 + (2/3) e^2/(a C^2) for a surface-charged sphere (with m = 8 x 10^-28 g wholly electromagnetic the radius is about 2 x 10^-13 cm), the magnetic Lorentz force (e/C) v x H, the Hall effect (Jeans notes it is a point where Maxwell's original theory and electron theory diverge) and Lorentz's theory of the Zeeman effect. Chapter XX gives the potentials with the Lorenz condition, the retarded solution (Jeans calls t - r/a 'local time' after Lorentz), the radiation formula (2/3) e^2 (acceleration)^2 / C^3 and the statement that radiation arises solely from acceleration, the 'pulse' theory of Rontgen rays (Stokes), the Lorentz force derived from least action, electromagnetic momentum and Maxwell stresses (and a statement that when the Poynting flux is not steady the mechanical action 'is not such as can be transmitted by ether at rest'), uniform motion at any speed with 'contracted coordinates', Abraham's rigid electron, the Lorentz-FitzGerald contraction presented as 'more than a conjecture' if all forces are electrical, the Michelson-Morley experiment presented as 'almost positive proof' of that contraction, and Lorentz's deformable electron tested by Bucherer, who is said to find exact agreement with the transverse mass formula if m0 = 0. The only mention of Einstein in these chapters credits Lorentz and Einstein with extending a corresponding-states equilibrium theorem; the word 'relativity' does not appear. The index lists 'Einstein, 577' only.

Key claims

• Electron theory gives the Biot-Savart field of a moving charge and, summed over a circuit element, the force Jeans calls Ampere's law for every element of a circuit, not only for closed circuits (section 624); in sections 496-499 he shows that element-element forces are not unique (Helmholtz's family with constant k), so the 'Ampere' of section 497 is the Biot-Savart form, not Ampere's own element-element law.
• The mass of the electron is wholly electromagnetic: a charged sphere has m = m0 + (2/3) e^2/(a C^2), and recent experiments indicate m0 = 0, fixing the electron radius at about 2 x 10^-13 cm.
• Radiation by an electron arises solely from its acceleration, at the rate (2/3) e^2 (acceleration)^2 / C^3; its velocity contributes nothing.
• A molecule radiates nothing if the sum of e times acceleration over its charges is zero in each direction (dipole approximation).
• The Hall effect shows that a magnetic field acts on the current itself, not only on the conductor, contradicting Maxwell's original theory.
• Rontgen rays are thin pulses of electric and magnetic force produced when electrons are suddenly stopped (Stokes's view, said to be 'universally believed' in 1911).
• When the Poynting flux is not steady, mechanical action in the field cannot be transmitted by ether at rest, and whether electromagnetic momentum resides in the ether like ordinary momentum 'has to remain an open question'.
• If all forces in the ether are electrical, a body moving through the ether at speed u is physically contracted by (1 - u^2/C^2)^(1/2) along its motion (Lorentz-FitzGerald hypothesis).
• The Michelson-Morley null result affords 'what amounts almost to positive proof' of this contraction.
• Lorentz's deformable electron, with transverse mass m0 + (2e^2/3aC^2)(1 - beta^2)^(-1/2), agrees with Bucherer's experiments 'exactly' on Jeans's reading if m0 = 0, so Abraham's rigid electron must be discarded and the electron's mass is purely electromagnetic (Bucherer 1908 was disputed, e.g. by Bestelmeyer, and confirmations came later; later work judged the early Kaufmann-Bucherer-Neumann data qualitative).
• The Zeeman effect (splitting proportional to H, delta p = eH/(2mC)) is explained by Lorentz's bound-electron model and indicates atoms of spherically symmetrical structure.
• No a priori argument rules out action at a distance; the potential is 'a convenient mathematical fiction' and an ether is a 'tentative hypothesis' tested by the consistency and plausibility of the properties it needs (sections 153-155).
• Earnshaw's theorem shows an electron cannot rest in stable equilibrium under inverse-square forces; the force law must differ at small distances, and Larmor's orbiting electron rings are 'a sort of perpetual motion machine' whose energy cannot be replenished (section 192).
• The force on a circuit leaves the element forces undetermined (Helmholtz's family with constant k; k = 1 Ampere's system, k = 3/2 magnetic-particle-like), a force out of the plane of r and ds is 'almost inconceivable' as action at a distance, and so 'we are almost compelled to give up' action-at-a-distance theories for stresses in the medium (sections 498a-500).
• With the molecular number n = 2.75 x 10^19 per cm^3 (revised from about 4 x 10^19 in 1904), Mossotti's conducting-sphere picture gives molecular radii of 0.6 to 1.6 x 10^-8 cm, about 30 percent below the kinetic-theory radii, which Jeans takes as significant evidence for molecular polarisation (sections 148-151).

Relevance: Documents the 1911 Jeans: a working classical field theorist and ether theorist who treats the electron as a purely electromagnetic object and the Lorentz-FitzGerald contraction as a real dynamical effect, with Einstein mentioned only in passing. It is the baseline against which the 1925 lecture (a relativist with a dissipative, time-symmetric field model) should be read, and it gives the equations (retarded potentials, Larmor radiation formula, electromagnetic mass) that the 1925 lecture and the 1904 gas theory rely on. The Ampere-law (note section 497's Biot-Savart reading and the Helmholtz family of element forces), ether (a hypothesis in sections 153-155) and electromagnetic-mass passages bear directly on other projects in the collection that rest on those ideas.

Mainstream conflict: For most of the book none: it is a textbook of Maxwellian theory consistent with the field equations as understood in 1911. The deep-read chapters conflict with later physics in the following ways, which are Jeans's 1911 positions, not errors of arithmetic. (1) A real ether and a real contraction of bodies, replaced by special relativity (1905 onward), under which the contraction is kinematic. (2) A purely electromagnetic electron mass, abandoned because of the 4/3 problem (the field-momentum and kinetic-energy mass, (2/3) e^2/(a C^2), is 4/3 of the rest-energy mass U/C^2 with U = e^2/(2a) the electrostatic energy), Poincare stresses (1905-06), and the fact that in special relativity all mass carries the same velocity factor; the same Bucherer data fit total mass times (1 - beta^2)^(-1/2) whatever its origin, and later work judged the early Kaufmann-Bucherer-Neumann data qualitative [memory] high. (3) The stability of the Lorentz electron is not discussed in the chapters read, although section 192 raises the stability of point-charge atoms. (4) The 'real ether' is a tentative hypothesis in sections 153-155, not an asserted entity; the contraction is 'inevitable' only on the stated condition that all ether forces are electrical. Jeans himself records several apparent misprints (see deep read): Y0 given as .33 where .033 is meant, 'even' for 'odd' in the Zeeman line count, 'contracted' and 'uncontracted' swapped in section 657, and 'In 1908, Kauffmann' against a footnote to the 1906 volume.

Jeans's first book (Cambridge University Press, 1904, when he was a Fellow of Trinity), an attempt 'to build the kinetic theory of gases on an exact mathematical basis'. It is a Google Books scan of a library copy with a reader's pencil marks; the text is entirely OCR and most equations are garbled, so the deep reads used page images. Chapters I-VI (digest only): the kinetic picture, hard-sphere molecules, Maxwell's velocity law by two routes (an H-theorem argument and Jeans's 'generalised space' method, in which a gas is a point in a 6N-dimensional space; in Ch. III the fluid of such points has uniform density that stays uniform, its invariance proved directly for hard spheres in section 37, and Liouville's theorem is named only at section 72; the law is 'infinitely probable', a statement about a fraction of the volume of the energy surface as N grows, and the passage to behaviour in time rests on an unstated ergodic-type assumption that energy is the only constant of motion). Ch. IV tests molecular chaos against the generalised-space measure: exactly true for point molecules, corrected by a position-only factor for molecules of finite size. On irreversibility (sections 31, 68-70) Jeans says the motion is strictly reversible and the H-theorem a statement about averages. Of Burbury's criticism of his proof (Phil. Mag. vi p.529, vii p.467; Jeans's replies vi p.720, vii p.468) the book says only that Jeans cannot persuade himself the criticisms are well founded, without stating them. Further topics: an extension to molecules of the most general conservative type with 'momentoids' (independent squared terms in the energy) each carrying mean energy (1/2)RT in equipartition, loaded spheres, then pressure, temperature, Avogadro's number (he quotes about 4 x 10^19 per cm^3; modern 2.69 x 10^19), van der Waals' equation and the virial. Chapter VII ends with the specific-heat problem and the book's central argument. For a conservative gas with n momentoids, gamma = C_p/C_v = 1 + 2/n (with n counting the three translational ones), and a gas whose molecules emit a spectrum of thousands of lines should have n of order thousands and gamma indistinguishable from 1, whereas monatomic gases show gamma about 5/3. Jeans's resolution (Chapter VII end and Chapter VIII, deep read): the molecules radiate into the ether, so the system is not conservative and equipartition does not apply to the line-producing modes. He replaces Liouville's theorem by D rho/Dt = rho Delta F (rho the density of the fluid of systems and F a dissipation function built from the Poynting flux), shows the fluid concentrates onto a single 'normal state' that depends only on the present energy, and defines a 'principal temperature' for translation and 'subsidiary temperatures' for the internal modes. The loaded-sphere example with a damping term epsilon shows the internal energy tends to zero relative to translation at low temperature and that the conservative gas is a singular special case (its equipartition result cannot be got by putting epsilon = 0). Chapters IX-X (deep read) give the mechanism for why internal modes are slowly fed: the energy a collision of duration comparable to c gives to an oscillator of angular frequency p falls as e^(-2 p beta) (eq. 492, a correct standard 'adiabatic suppression' result), so with collision times of order 10^-15 s and optical frequencies the transfer can be as small as e^-800. Jeans notes that his own first estimate (p x collision time = 16, e^-16 about 10^-7) is 'much too great to agree with observation'; p x collision time = 800 (e^-800) arises only if molecules penetrate to half their radius, for which he says there is 'not the slightest evidence', and the answer turns on the unknown interpenetration of molecules. Section 241's italic conclusion says the transfer is small when the product is 'small', where the mathematics needs 'large'. Sections 248-250 give the contemporary evidence he cites: Schuster and Hemsalech's arc observation (violet light from faster molecules) as support that needs no 'special state'; Pringsheim's view that no light is produced in gases by collisions alone, contested by Paschen and Smithells; and his own vacuum-tube estimate that electrical action 'almost' predicts emission. He predicts a 'temperature of incandescence' between 0 and 28,000 C, extends the theory to subsidiary temperatures proportional to gas density (tau = nu f(T)), and compares his formula gamma = 1 + 2/(n+3) with tables of C_v, C_p and gamma for about 15 gases (Wuellner, Wiedemann, Regnault, Masson, Lummer and Pringsheim, Leduc, Capstick, Strecker). The values are n+3 = 3 for Hg, Kr, He, Ar (argon 3.20), about 5 for H2, N2, O2, CO, NO, HCl and air, 6 to 7 for CO2, N2O and chlorine, and about 8 for ethylene; he admits the polyatomics do not fit a simple integer rule (section 271) and hands the problem to chemists (section 272; his Ch. XVIII answer is given below). He says plainly that the general theory only establishes existence of a normal state and that the internal modes being nearly empty is shown only for toy models, with the rest 'hypothesis instead of comparative certainty' (section 234). Chapters XI-XV (digest only) give mean free path, viscosity, heat conduction, diffusion and Maxwell's inverse-fifth-power theory. Chapter XVI (deep read, page images) treats sound in a gas of loaded spheres whose rotational energy lags behind translation: a single-relaxation dispersion relation with the correct limits gamma = 7/5 (fast exchange) and 5/3 (frozen), absorption proportional to the square of the frequency that acts as an extra viscosity, 'about one-seventh as great as that caused by viscosity' for an ideal diatomic molecule of two touching spheres (1.146 printed, 1.148 computed), and a speed correction V(1 + (48/1225)(3k^2/4r^2)^2 (pl/c-bar)^2) of order 10^-13 to 10^-10 across the audible range, 'quite imperceptible' because his rule makes rotation relax in about one collision. It has the structure of later molecular acoustic relaxation (Herzfeld-Rice, Kneser, Landau-Teller [memory medium-high]) but its conclusion was that no effect would be seen; whether later authors cite it is unknown. Chapter XVII (deep read): atmospheres in conductive and convective equilibrium, hydrogen predicted to dominate above roughly 80 km, and the escape criterion (derived with credit to Johnstone Stoney and G. H. Bryan, whose later objection Jeans reports but does not answer): an atmosphere is certainly lost if x = 3 g a / C^2 is below 15 and retained for millions of years if above 30, which for Earth gives critical rms speeds 3.5 x 10^5 and 2.5 x 10^5 cm/s (hydrogen at 740 C and 230 C). Jeans's text says that if the Moon ever had an atmosphere 'at a temperature much above zero' all but CO2 and denser gases would escape (a conditional statement, not an assertion of fact), that Mercury is 'exactly similar to Mars' and 'entirely devoid of atmosphere' on astronomical evidence (he does not assert that Mercury lost particular gases), and that Venus probably retains hers. His Earth premise, an outer atmosphere 'certainly less than 230 C' (the text layer's '280' is an OCR error), is superseded by the measured hot exosphere [memory high], and 'retained' means a million-year criterion. For the reader's check: hydrogen in the exosphere is mostly atomic, and atomic H at 1000 K gives x of about 7.6, well inside Jeans's 'certainly lost' range, against about 15.2 for H2 [calc]. Chapter XVIII (deep read, page images) is Jeans's own answer to the non-integer n+3 values: clusters of molecules held by weak attraction would change the measured gamma and C_p; Lussana's CO2 (C_p = 2.1096 at 85.4 atm and 13.2 C) gives n+3 = 92 (the deep read's check gives 91.4; the QE note's '9.2' is a misreading), falling to 7.66 at 1 atm, with 37, 30, 22 and 12 at the other Lussana points, wet steam 32 and dry steam 6.6, and chlorine's density drifts from 2.4807 at 20 C to 2.4502 at 200 C against Stas's 2.4501. He proposes n+3 = 3, 5, 6 for monatomic, diatomic and more complex gases as 'at any rate worth serious consideration' (section 407), which 'disposes of the tremendous difficulty' of molecules keeping large internal motions without loss of energy. He says the clustering correction to C_v 'would be fruitless to try to evaluate' and he 'cannot even determine its sign'; no cluster fraction is computed for any gas. Section 410 finds that a conservative treatment of a diatomic molecule as two bound atoms gives six degrees of freedom and gamma <= 1 1/3 against the observed 1 2/5, which suggests 'we are on the wrong track'; section 411 repairs this by dissipation: radiative damping of forced vibrations makes the atoms of a diatomic molecule settle into circular orbits (five degrees of freedom) and polyatomic molecules rotate as rigid bodies (six), at the cost of giving up the calculation of dissociation from kinetic theory. The ordinary-pressure misfit (CO2 6.6-7.7, chlorine 6.08, Br2 and I2 6.8, CCl4 15.4, ethylene about 8) is not covered by the aggregation estimate. The modern reading is that low gamma in heavy and polyatomic molecules comes from partly excited vibrations (the low-frequency modes of the halogens and the CO2 bending mode), not aggregation [memory high; not in Jeans]. Chapter XIX (deep read): molecular radii from Boyle's-law deviation, viscosity, heat conduction and diffusion (hydrogen 1.0, helium 0.9, argon 1.39, nitrogen 1.46, oxygen 1.35 x 10^-8 cm, from a molecular count of about 4 x 10^19 per cm^3; Jeans's 1911 electricity book recalculates these radii with n = 2.75 x 10^19, giving 1.09 to 2.30 x 10^-8 cm), upper limits from solid and liquid densities, a temperature correction, a cohesion correction, an aggregation correction and a Mossotti refractive-index estimate (1.054 x 10^-8 cm for air against 1.41 from kinetic theory).

Key claims

• Maxwell's velocity distribution holds for all but an infinitesimal fraction of the volume of the energy surface of a hard-sphere gas as the number of molecules grows large ('infinitely probable' in Jeans's words, not 'probability 1'), by a generalised-space counting argument in which the density of a fluid of systems is proved invariant under collisions (a special case of Liouville's theorem, named at section 72); the passage to behaviour over time assumes energy is the only constant of motion (deep read, PDF pp.48-75).
• For a conservative gas, equipartition makes gamma = 1 + 2/n with n the number of momentoids (all of them, including the three translational ones: Ch. VII, eq. 415), and for a gas whose spectrum has thousands of lines this would give gamma indistinguishable from 1, in 'flagrant opposition to experiment'. In Ch. IX-X n means the number of internal terms and gamma = 1 + 2/(n+3) (eq. 522).
• The resolution is that molecules radiate into the ether, so the system is non-conservative and equipartition does not apply to the spectral-line degrees of freedom (section 204).
• For a dissipative gas, Liouville's theorem is replaced by D rho/Dt = rho Delta F, the points representing gas states concentrate on a single normal state fixed by present energy, and the internal modes sit at subsidiary temperatures tau far below the principal translational temperature T.
• The energy transferred from translation to an internal vibration of angular frequency p falls as exp(-2 p beta), with beta of the order of the collision duration. Jeans's first estimate (p x collision time = 16, e^-16 about 10^-7) is 'much too great to agree with observation'; e^-800 arises only if molecules penetrate to half their radius, for which there is 'not the slightest evidence'. His section 234 recapitulation says the general theory proves only that a normal state exists, and the emptiness of internal modes is demonstrated for toy models.
• If the translational energy is raised (C = 5 x 10^5 cm/s, about 28,000 C) the transfer becomes appreciable, so the theory predicts a temperature of incandescence between 0 C and 28,000 C and fixes the associated molecular speed to within a factor less than 10.
• The observed gamma gives n+3 = 3 for Hg, Kr, He, Ar, 5 for H2, N2, O2, CO, NO, HCl, air and 6 to 8 for CO2, N2O, chlorine and ethylene (CCl4 15.4, Br2 and I2 6.8), and gamma should fall with temperature (Leduc: CO2 1.3190 at 0 C and 1.2827 at 100 C). Jeans admits (section 271) that polyatomics do not fit an integer rule; in Ch. XVIII he attributes the excess to molecular aggregation and proposes n+3 = 3, 5, 6 (section 407), without computing any cluster correction and saying he cannot determine its sign.
• The observation that n+3 = 4 (gamma = 3/2) is never found is taken as confirming the theory, because a molecule with only one non-small rotational energy is impossible.
• A planet or satellite loses an atmospheric constituent if x = 3 g a / C^2 is below 15 and retains it for millions of years if above 30; the Moon (if it ever had an atmosphere at a temperature much above zero) would lose all but CO2 and denser gases, Mercury is 'exactly similar to Mars' and 'entirely devoid of atmosphere', Earth keeps its atmosphere unless its outer atmosphere was ever above about 740 C (Jeans: 'certainly less than 230 C', superseded), and hydrogen would dominate above roughly 80 km.
• The radius of the molecule is of order 1 to 2 x 10^-8 cm, as shown by Boyle's-law deviation, viscosity, conduction, diffusion, solid and liquid densities and refractive index, with agreement of order 10 to 20 percent for gases.
• Chapter XVIII: molecular aggregation is the cause of non-integer n+3 (steam, CO2 at high pressure, chlorine density drift); the rule n+3 = 3, 5, 6 removes the need for large persistent internal motions; dissipation (section 411) makes diatomic atoms move in circular orbits and polyatomic molecules rotate rigidly.
• Chapter XVI: a lag in the exchange between translational and rotational energy damps sound and raises its speed; for an ideal diatomic molecule the extra damping is about one-seventh of the viscous damping, and the speed change is imperceptible for audible frequencies if exchange takes about one collision.
• Contemporary evidence cited for collision-excited light (sections 248-250): Schuster and Hemsalech (arc spectra, violet light from faster molecules) in support; Pringsheim against ('no light is ever produced in gases by collisions alone'), contested by Paschen and Smithells.

Relevance: The earliest of the three works and the one that reveals the logic behind Jeans's later positions. The 1904 dissipative-gas theory is a classical attempt to explain why spectral-line degrees of freedom do not show in specific heats, the same specific-heat anomaly that quantum theory (Einstein 1907, Nernst and Eucken 1910-12) resolved by freezing-out. Jeans's 1905 exchange with Rayleigh (Nature 71, 559 and 607; 72, 54, 101 and 243; research/files/montambaux) restates the claim as a time-scale claim and concedes the ultraviolet-catastrophe end state. Its Section 257 endpoint (equipartition between matter and ether) is the classical equilibrium that, applied to the ether's own modes, is the Rayleigh-Jeans law, and it supplies the 'conservative versus radiating system' and 'thousands of spectral lines' ideas that Jeans carries into the 1925 lecture. The e^(-2 p beta) result survives in Landau-Teller vibrational relaxation theory [memory] high.

Mainstream conflict: Jeans's dissipative explanation of why internal degrees of freedom are not seen in the specific heats was superseded by quantum freeze-out; equilibrium heat capacities are now explained quantum mechanically, not as a radiative steady state [memory] high. Jeans himself did not defend the classical explanation long: he accepted the quantum hypothesis in 1910 ('Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed', Atomicity lecture; Hudson 1989 dates the move to 1910), and his 1914 Report on Radiation and the Quantum-Theory spread it. In 1905 he had narrowed the equilibrium claim to a time-scale claim. The British Association discussion at Birmingham in 1913 (Larmor and Love defending classical dynamics) shows the classical position still had defenders [web: research/2026-10-08-archive-org.md]. The treatment of the ether as a zero-temperature sink with no return radiation conflicts with Kirchhoff's law in an enclosure at the gas's own temperature [memory] high (the deep read flags this as the assumption to watch). Numerical conventions are dated: N = 4 x 10^19 per cm^3 (about 49 percent above the modern 2.69 x 10^19; Jeans himself revised it to 2.75 x 10^19 by his 1911 electricity book, section 150, and recalculated the radii), hydrogen molecule mass 2.25 x 10^-24 g (true 3.35 x 10^-24 g), corpuscle mass 1/700 of hydrogen (modern 1/1836). The deep readers record several slips in the book itself: section 241's italic conclusion says dissipation is slow if collision-time times frequency is 'small' where the mathematics requires 'large'; the Mossotti equation printed as mu - 1 = (1/2) pi N sigma^3 lacks a factor 2 that his numerical 1.054 x 10^-8 uses; the 'two million years' half-life for x = 30 is nearer 0.7 million; the Ch. XVI figure 1.146 computes to 1.148 and 'pl/c-bar about 10^-7' to about 10^-6 (neither affects the conclusions). Ch. XVIII is open about its own difficulty: section 410 finds that the conservative theory gives gamma <= 1 1/3 for a diatomic molecule, 'on the wrong track'.