Lorentz-HA · Source catalogue

Google Books scan of a University of California library copy. Title page: Teubner series Band XXXIX; 'a course of lectures delivered at Columbia University, New York, in March and April 1906'; second edition, Leipzig 1916. The preface (Leiden, January 1909) says publication was delayed so the subject could be developed further and that numerous additions were made; Voigt's magneto-optics is only mentioned in a note, and Planck's radiation views and Einstein's principle of relativity are not adequately treated [read: digest p.8]. The 2nd edition keeps the 1909 text and adds footnotes and Notes marked [1915] [read: deep p.1-2]. Contents: Ch. I general principles and free electrons; II emission and absorption of heat; III Zeeman effect; IV propagation of light in a body of molecules, inverse Zeeman effect; V optical phenomena in moving bodies; then Notes and index. The preface (p.8) names Larmor only in the list of authors whose work 'is not mentioned' [read: QE grep of text layer, p.8].

Key claims

• The text is a 1906 lecture course whose Chapter V content was fixed in 1909 and annotated in 1915.

Relevance: Dates the material: Chapter V was written before 1909 and the 1915 notes are Lorentz's later self-assessment.

Mainstream conflict: none

Lorentz builds the theory on a few assumptions without needing a mechanical picture of the ether. Notation (vector products, div, rot) is introduced. The ether equations (Heaviside-Lorentz units, no 4 pi) give waves at speed c. Matter contains charged particles (electrons); charge density is continuous; convection current rho*v acts like conduction current (Rowland). Force on a charge is d + (1/c)[v.h]. Retarded potentials (d'Alembert equation) are derived (Note 4). Poynting flow of energy (sec.17-18); Maxwell stresses and the ether being immovable (sec.19-23), radiation pressure (Lebedew 1901; Nichols and Hull), electromagnetic momentum G. An electron in uniform motion gets field, energy and momentum; longitudinal and transverse electromagnetic masses m' and m'' are defined (sec.26-28), with Abraham's rigid spherical electron giving m' > m'' at speed. Kaufmann's beta-ray deflection data are discussed (sec.31-32); Lorentz takes the negative electron's mass to be wholly electromagnetic (see the QE deep read below). Radiation from accelerated electrons (energy flow proportional to the square of acceleration), radiation damping force (sec.37-41), a polarised particle (sec.42-43). Sec.44-46 introduce the moving system, first-order coordinates x' = x - wt and the 'local time' t' = t - w.r/c^2, and a moving mirror (frequency n(1-2w/c)). Sec.47-50: Drude electron theory of metals (ratio of thermal to electrical conductivity proportional to T) [read: digest pp.10-76]. QE DEEP READ (sections 31-35, page images). Kaufmann (Ann. Phys. 19, 1906, p.487): as w runs from about 0.5 to over 0.9 c, e/m 'diminishes considerably'; Kaufmann's effective-mass ratio k agrees within experimental error with Abraham's electromagnetic ratio kappa from (69), so 'Kaufmann's numbers show no trace of an influence of the material mass m0'. Lorentz's hedge: 'we are free to believe ... some small material mass ... say equal to one hundredth part of the electromagnetic one, but with a view to simplicity, it will be best to admit Kaufmann's conclusion, or hypothesis, if we prefer so to call it, that the negative electrons have no material mass at all. This is certainly one of the most important results of modern physics' [read: p.51-52]. So 'wholly electromagnetic' is, in Lorentz's own words, a conclusion or hypothesis adopted for simplicity, with about 1 percent material mass not excluded. He also says the electron 'has lost much of its substantiality' and must keep an inherent property by which its parts cannot be torn asunder [read: p.52]. Numbers (page images): e/m = 1.77e7 c sqrt(4 pi) for negative electrons, 9650 c sqrt(4 pi) for the hydrogen ion (about 1800 times smaller); hydrogen atom 1.5e-24 g; ion charge 1.5e-20 c sqrt(4 pi); m = 7e-28 g; R = 1.5e-13 cm from (72) [read: page image p.53, p.55]. Lorentz's e/m list: Simon 1.878, Kaufmann 1.823, Bestelmeyer 1.72, Bucherer 1.763 (Ann. Phys. 28, 1909, p.513), Wolz 1.767 (Ann. Phys. 30, 1909, p.273), in units of 1e7 c sqrt(4 pi). QE arithmetic [calc]: his three printed numbers (e, m, R) are not mutually exact under (72); they agree within a factor of about 1.4 (e/(e/m) gives 8.5e-28 g; R = 1.5e-13 cm would match m = 1.0e-27 g), consistent with his 'not far from the truth' remark. The 'wholly electromagnetic' statement in Chapter I carries no 1915 note, although the Abraham formula it was tied to is superseded for Lorentz's model by (313) and Note 86; the 1915 reversal appears only in the footnote to section 179 ('This can no longer be said now. [1915]') and in Note 86. Section 179 (same data): Kaufmann 'has repeated his experiments with the utmost care and for the express purpose of testing my assumption. His new numbers agree ... with the formulae given by Abraham, but not so with the second of the equations (313), so that they are decidedly unfavourable to the idea of a contraction' [read: p.221-222]. Section 34: he is 'quite willing to adopt an electromagnetic theory of matter' but whether a positive electron's mass is electromagnetic is 'an open question' [read: p.54-55]. Section 50 (digest): his more rigorous electron theory makes the Drude ratio of thermal to electrical conductivity agree worse than the cruder one; he calls the earlier agreement possibly 'a fortuitous coincidence', and a [1915] footnote names Kamerlingh Onnes's low-temperature results as unexplained [read: digest pp.75-76].

Key claims

• A moving electron's field energy and momentum give it longitudinal and transverse electromagnetic masses that grow with speed (Abraham rigid-sphere formulae).
• Kaufmann's 1906 beta-ray data fit Abraham's electromagnetic mass ratio within error, and Lorentz adopts, for simplicity and as 'Kaufmann's conclusion, or hypothesis', that the negative electron has no material mass (about 1 percent material mass not excluded).
• An electron in uniform motion radiates nothing; an accelerated one radiates energy proportional to the square of its acceleration.
• To first order in w/c, moving-system fields can be expressed by the same equations if one uses local time t' = t - w.r/c^2.
• Radiation exerts a pressure equal to its energy density per unit volume for a normally incident absorbed beam (observed by Lebedew, Nichols and Hull).
• Lorentz's numbers: e/m = 1.77e7 c sqrt(4 pi) for negative electrons; m = 7e-28 g; R = 1.5e-13 cm; hydrogen-ion e/m 9650 c sqrt(4 pi).
• Lorentz's own application of the Drude conductivity theory to the ratio of thermal to electrical conductivity agrees worse when done more rigorously; he calls the earlier agreement possibly fortuitous.

Relevance: Sets out the electron-theory machinery (fields, momentum, masses, local time) that Chapter V extends to all orders in w/c.

Mainstream conflict: Rigid-electron mass formulae and the immovable ether are superseded by relativity; the equations themselves match standard electrodynamics.

Radiation by a black body. Kirchhoff's law, radiation pressure, thermodynamic argument K = C T^4 (Stefan-Boltzmann), Wien displacement law, Planck's formula with h and k, Hagen-Rubens absorption of metals. Lorentz derives the long-wave radiation law from free electrons in a metal plate (Drude model, Maxwell velocity distribution) and obtains the form of Planck's formula in the long-wave limit; then a derivation by equipartition over ether normal modes (Rayleigh-Jeans), and discusses Jeans's conclusion that the ether would absorb all energy into very short ripples. Note 42* [1915] adds the Planck quantum case [read: digest pp.77-106, 297-299]. QE DEEP READ. Lorentz's route: Kirchhoff's law makes F(lambda,T) = E/A universal; for a thin metal plate with Drude free electrons, A comes from the conductivity and the emission E from electron impacts (like X-ray production, after Wiechert and J. J. Thomson); N, l and the thickness drop out of E/A, giving the long-wave law (148), which equals the equipartition (Rayleigh-Jeans) result 16 pi alpha T dlambda/(3 lambda^4) and matches Planck's formula only for long waves (alpha = (3/2)k); he cites Hagen and Rubens (1903) for 8-25 micron absorption of metals [read: pp.89-99]. Section 75 gives Jeans's difficulty (infinite degrees of freedom of the ether; energy 'wasted ... for the production of extremely short electromagnetic ripples') and section 76 three ways out: (1) infinite degrees of freedom for matter (rejected: contradicts specific heats), (2) a structured ether with finitely many degrees of freedom (no objection stated), (3) abandon equipartition as a general law (must then explain why it holds for long waves) [read: p.105-106]. Note 42 (silver in the dark): silver reflects about 90 percent of yellow light, so A = 1/10; by Kirchhoff E1 = (1/10) E3; by Jeans E3 = (288/1473) E2 = (1/5) E2 for a black body at 15 C against 1200 C; so E1 = E2/50, and 'it ought certainly to be visible in the dark'. Lorentz concludes bodies emit much less light than Jeans requires except for very long waves, that only Planck's equation fits, and that for short waves the link between matter and ether must be particles like Planck's resonators to which equipartition does not apply [read: page image p.296-297; numbers checked by deep reader, 288/1473 = 0.196, product 1/51]. He lists residual difficulties (free electrons in metals seem nearly inactive for short waves; intermediate waves unexplained; J. J. Thomson's long-wave difficulties). Note 42* [1915]: 'Later researches have shown that in all probability the theorem of equipartition holds for systems subject to the ordinary laws of dynamics and electromagnetism. A satisfactory theory of radiation will therefore require a profound modification of fundamental principles. Provisionally we must content ourselves with Planck's hypothesis of quanta'; mean resonator energy E = h v/(e^(hv/kT) - 1), reducing to kT for kT >> hv, and Planck's law via the ether-mode count 8 pi q1q2q3 dlambda/lambda^4 (Debye 1910) [read: page image p.298-299]. Deep-reader remark [calc, modern constants]: at 580 nm Planck's law gives a silver-to-hot-body ratio of order 1e-31, i.e. undetectable.

Key claims

• For long wavelengths the electron theory of metals reproduces the Planck/Rayleigh-Jeans form of black-body radiation.
• Equipartition applied to ether modes leads to Jeans's difficulty (energy flowing to ever shorter wavelengths).
• Jeans's equipartition law would make a polished silver plate at 15 C glow visibly in the dark (emissivity one-fiftieth of a 1200 C black body at yellow); it does not, so equipartition cannot hold for short waves (Note 42).
• Lorentz in 1915 (Note 42*) says equipartition probably holds for ordinary dynamics and electromagnetism, so radiation theory needs a profound modification of fundamental principles; provisionally, Planck's quanta.

Relevance: Peripheral to the moving-body claims, but shows Lorentz's electron theory predicting radiation laws and meeting the quantum problem.

Mainstream conflict: Classical equipartition result fails at short wavelengths (ultraviolet catastrophe), as Lorentz himself notes via Jeans.

Faraday rotation, Zeeman's discovery, elementary triplet theory with circular motions of an electron in a magnetic field; Zeeman's e/m compared with cathode-ray values. Rydberg series formulae, doublet and triplet series, Runge and Paschen's observations, complicated splittings (Cornu quartet, sextets). Lorentz's electron-shell and tetrahedral four-electron models (Thomson-like atom), and the proposal of a rotation of the whole particle during field build-up. Mirror-image argument on polarisation of light along the lines of force [read: digest pp.107-140].

Key claims

• In a magnetic field a spectral line of a single electron oscillator splits into a symmetric triplet with circularly polarised outer components.
• Zeeman's splitting gives e/m of the same order as cathode-ray and beta-ray electrons.
• Complex Zeeman patterns are not explained by the simple models, which Lorentz admits are illustrations.

Relevance: Background on why the electron hypothesis was credible in 1906; not on the moving-body claims.

Mainstream conflict: Anomalous Zeeman patterns are explained by quantum mechanics and spin, not by these classical models.

Mean-value fields for matter; polarisation P, D = E + P; Lorentz-Lorenz field E + (4 pi/3)P in cubic or isotropic media; one electron per particle with elastic, resistive and magnetic forces. Refractive index (mu^2 - 1)/(mu^2 + 2) proportional to density (Lorentz-Lorenz law; Clausius-Mossotti for static case); dispersion, absorption bands, additivity of refractivity. Inverse Zeeman effect, Faraday rotation and magnetic double refraction in a sodium flame (Voigt; Macaluso-Corbino; Zeeman; Hallo; Geest); estimate tau about 1e-8 s. The electron mass enters the dispersion formula only through the term m*n^2 in (201), which is used later in Brace's test [read: digest pp.141-176, deep p.226].

Key claims

• Refractive index obeys the Lorentz-Lorenz relation with density.
• The refractive-index dispersion and absorption bands follow from a damped electron oscillator.
• The electron mass appears in the optics only via the combination m*n^2 (so changing m equals changing n by m^(1/2)).

Relevance: Supplies the optics formulae (esp. eq. 201) used in the Rayleigh-Brace double-refraction argument of Chapter V.

Mainstream conflict: Classical dispersion is accepted at the macroscopic level; quantum theory replaces the oscillator picture.

Huygens construction and 'relative rays'. Stokes's aberration theory assumes the ether around the earth moves with it, irrotationally and with no sliding at the surface; Lorentz shows these are incompatible for an incompressible ether: for a sphere the sliding at the surface is 3/2 w (Note 66, p.325). Planck's rescue lets the ether be condensed by the earth's gravity: Note 67 (pp.325-326) gives remaining sliding 0.011 w0 for mu omega/R = 10 (density ratio epsilon^10, about 22,026) and 0.0056 w0 for mu omega/R = 11 (epsilon^11, about 59,874); the deep reader recomputed both with SymPy and they match (the main text p.182 says 'no more than one half percent' for the second) [read: page image p.325-326]. Lorentz's verdict on the idea: 'in making his suggestion Planck has certainly done a good thing. Yet I dare say that this assumption of an enormously condensed ether, combined ... with the hypothesis that the velocity of light is not in the least altered by it, is not very satisfactory'; he says Planck too prefers Fresnel's immovable ether 'if it can be shown that this conception can lead us to an understanding of the phenomena that have been observed' [read: p.182-183]. The text on these pages does not itself argue Stokes against Fizeau's result. Fresnel's drag coefficient (1 - 1/mu^2) (letter to Arago, 1818) is derived from the electron model twice: a continuous-charge model (sections 156-159) giving c^2/v'^2 = c^2/v^2 + 2w/v', so v' = v - w/mu^2, and a molecular derivation by corresponding states and local time (sections 160-163) giving 1/v' = 1/v + w_n/c^2; both are first order in w/c and need elastic and resistive constants unchanged by the motion [read: p.191-199; deep reader's algebra agrees]. To first order the course of relative rays is independent of the earth's motion (section 154, p.187-189). Fizeau and Michelson-Morley (1886) flowing-water tests: Michelson-Morley omitted the dispersion term, and Lorentz says including it makes agreement 'somewhat worse; it remains however fairly satisfactory' [read: p.199-200]. Note 69/69*: see the Notes 62-86 entry.

Key claims

• To first order in w/c the path of relative light rays, and interference fringes, in terrestrial apparatus are unaffected by the earth's motion through an immovable ether.
• Fresnel's drag coefficient (1 - 1/mu^2) follows from the electron theory (two derivations, first order in w/c).
• Stokes's theory of a fully dragged, irrotational ether with no sliding is internally inconsistent for an incompressible ether (sliding 3/2 w at the surface of a sphere); Planck's condensed ether reduces the sliding to 0.011 w0 or 0.0056 w0 but needs a density ratio of about 2e4 to 6e4 and unchanged light speed, which Lorentz calls 'not very satisfactory'.

Relevance: First-order foundations of the moving-body theory; sets up the Michelson problem.

Mainstream conflict: Fresnel drag is correct in special relativity; the ether is not.

Deep read. Lorentz generalises the first-order theorem to any w < c. With l, k = 1/sqrt(1-w^2/c^2), he writes the transformation (285-288): x' = kl(x - wt), y' = ly, z' = lz, t' = kl(t - wx/c^2); l = 1 gives the modern Lorentz transformation. A Voigt footnote concedes that Voigt (1887) used an equivalent transformation. He derives the force relation F(S) = (l^2, l^2/k, l^2/k)F(S0) (300) and argues that if molecular forces obey (300), bodies contract by k in the direction of motion: this reproduces the Fitz Gerald-Lorentz contraction required to explain Michelson-Morley. Masses must differ in the systems: m' = k^3 l m0, m'' = k l m0 (305). Setting l = 1 for the deformable electron gives m' = k^3 m0, m'' = k m0 (313), the relativistic masses; he needs Poincare's non-electromagnetic stress S = e^2/(32 pi^2 R^4) to account for Abraham's extra-energy objection, concedes stability is not shown and that perhaps 'we are wholly on the wrong track when we apply to the parts of an electron our ordinary notion of force'. In 1906 Kaufmann's data (Ann. Phys. 19, 1906) were 'decidedly unfavourable' to the deformable electron and agreed with Abraham's rigid sphere; Brace's optical null result (Lorentz: a difference of principal indices of 10^-12 'could not have escaped him', about one twentieth of the 2e-11 predicted for a rigid spherical electron; the constant-volume electron gives an effect 'even a little stronger') went against the rigid and Bucherer-Langevin constant-volume electrons [read: page image p.228, rendered by physicist, contrarian, arbiter and QE]. Note 86 [1915] says Bucherer (1908), Hupka, Schaefer and Neumann and Guye and Lavanchy confirmed (313). Lorentz shows clocks of a moving observer run k times slow, the round-trip light speed is measured c, optical-signal synchronisation yields exactly his local time, and the reciprocity (328-334) between observers A0 and A (Einstein) holds. He concedes Einstein 'simply postulates what we have deduced, with some difficulty and not altogether satisfactorily', and that Einstein's variables give exactly the same form of equations for moving axes while his do not. Lorentz still regards the ether as having 'a certain degree of substantiality' and prefers ether-fixed rods and clocks. Note 72* [1915]: 'If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity... The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity.' [read: deep read, whole]. CORRECTIONS AND ADDITIONS AFTER QE (2026-10-08). (a) Brace's reach in Lorentz's text is 10^-12, not 10^-13; the earlier '1e-13' came from the deep read's section 7 and the garbled text layer. Brace's own paper gives 7.8e-13 and 'about 1600 times greater than the smallest effect', and a 30-metre water path [web: https://en.wikisource.org/wiki/On_Double_Refraction_in_Matter_moving_through_the_Aether, QE check]; that is a different statement from Lorentz's figure. (b) Michelson-Morley 1887 (Lorentz p.204): 2L about 22 m, expected shift 0.4 of a period; Morley-Miller 'less than one hundredth part'. The 1887 result is best stated as certainly below one twentieth of the expected shift (at most 0.02 of 0.4 fringe) and probably below one fortieth (the 1887 paper's wording [memory, high]; Wikipedia says 'as small as one-fortieth' [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]). (c) Reversal date: Lorentz's change of view on the deformable electron dates from the 1909 first edition (Note 87, citing Bucherer 1908); the [1915] Note 86 widened it. (d) 'Wholly electromagnetic' holds for the momentum only; with the Poincare stress a quarter of the rest energy is stress energy. (e) Section 177 (p.218): if the sun is at rest in the ether, sunlight D-lines and a terrestrial sodium flame would differ in relative frequency by a factor of order w^2/c^2, which Lorentz calls 'of a purely theoretical interest'; the one second-order effect his theory leaves for celestial sources [read: deep read p.218]. (f) Who the book credits [read: QE grep of the text layer; index p.351]: Poincare appears only on pp.222-224 for the electron's stress and stability (sections 181-182, Palermo 1906); the book does not credit him with the transformation, its group property or the principle of relativity. The transformation is credited to Voigt (footnote p.207, 'escaped my notice all these years') and the interpretation to Einstein (sections 189-194); Larmor is named only in the 1909 preface among authors whose work 'is not mentioned' (p.8). The book states no reasons; any priority question is separate. (g) Digest .08, line p.206, wrongly gives u_x' = u_x; the page image has u'_x = k^2 u_x (eq. 289) [read: page image p.206]. (h) Claim 1 caveat: l = 1 is fixed only through the electron-mass assumptions; with sources the 1909 equations are not exactly form-invariant (Lorentz says so, p.239 and Note 72*), and reciprocity needs l = 1.

Key claims

• The transformation x' = kl(x - wt), t' = kl(t - wx/c^2) with l = 1 leaves the free-ether Maxwell equations of form and equals the modern Lorentz transformation.
• If molecular forces transform like electrostatic forces, a body moving through the ether contracts by factor k along its motion, so Michelson-Morley sees no fringe shift.
• The electron mass depends on speed as m' = (1 - beta^2)^(-3/2) m0 (longitudinal), m'' = (1 - beta^2)^(-1/2) m0 (transverse) for a deformable electron contracted by k.
• A deformable electron needs a non-electromagnetic Poincare stress S = e^2/(32 pi^2 R^4) to be in equilibrium; stability is not demonstrated.
• Rayleigh-Brace double refraction (reach 10^-12 as Lorentz states it) would have shown about 2e-11 for rigid spherical electrons, a factor of about 20 above the reach; none was seen.
• A moving observer's clocks run k times slower, the measured round-trip light speed is c, and light-signal synchronisation reproduces local time.
• Observers A0 (at rest in the ether) and A (moving) have reciprocal descriptions, so no experiment can show which moves through the ether.
• Lorentz derives the same results as Einstein's postulate from the field equations plus added hypotheses, but his equations for moving axes are not exactly form invariant.
• In 1906 Kaufmann's beta-ray data disfavoured the deformable electron; Lorentz's reversal dates from 1909 (Note 87, Bucherer 1908) and his 1915 Note 86 cites further experiments as confirming it.
• Poincare is credited in the book only for the electron's stress and stability; the transformation is credited to Voigt and its interpretation to Einstein; Larmor is named only in the preface.
• If the sun is at rest in the ether, sunlight and a terrestrial sodium flame would differ in relative frequency by a factor of order w^2/c^2 (section 177), which Lorentz calls of purely theoretical interest.

Relevance: The central text: Lorentz's own derivation of the Lorentz transformation, contraction, relativistic mass and time dilation within an ether theory, and his own comparison with Einstein.

Mainstream conflict: Retains a substantial ether with a privileged frame (undetectable by his own results) and treats t' as mere local time in 1909; relativity postulates the principle instead. Mass and contraction are derived with extra force hypotheses rather than invariance.

Derivations omitted from the text: elimination of field components, Kirchhoff retarded-potential solution (Note 4), vector potential gauge, Poynting and Maxwell stress, momentum and mass of the electron (Notes 14-15 with closed forms in beta and log((1+beta)/(1-beta))), falling charged bodies (Note 16*), Note 21* [1915] on X-ray diffraction by crystals (Laue, Bragg), radiation damping, local-time derivations (Notes 24-26), kinetic theory of electron conduction (Note 29), moving-mirror radiation (Note 30), Jeans and Planck (Notes 42-44), the tetrahedral four-electron Zeeman model (Note 48), Lorentz-Lorenz field (Notes 53-59). Many equations garbled by OCR [read: digest pp.240-321]. QE DEEP READS. Note 16* [1915] (PDF pp.259-260): after describing the falling-body (Stokes drag) method, Lorentz writes: 'Millikan has found values for e which can be considered as multiples of a definite elementary charge. Ehrenhaft, however, has been led to the conclusion that in some cases the charges are no multiples of the elementary one and may even be smaller than it. The question cannot be said to be wholly elucidated.' References: Ehrenhaft, Wiener Sitzungsber. IIa 128 (1914) p.58; Millikan, Phys. Zeitschr. 11 (1910) p.1097. The note gives no values, names no oil or metal, and does not cite Millikan's 1913 paper [read: p.259-260, grep-checked]. Lorentz's numbers for mass and radius rest on one common e, so sub-electron charges would change m and R in proportion [calc]. Note 17 begins a self-induction test of the 'wholly electromagnetic' assumption and concludes experiments 'have never shown an effect' beyond the ordinary formulae (continues on p.261, unread) [read: p.260]. Notes 42 and 42*: see the Chapter II entry (silver in the dark; Planck mean energy).

Key claims

• The electromagnetic momentum and mass of a uniformly charged moving sphere are derived in the Notes and yield the Abraham formulae.
• Note 16* [1915]: Millikan's charges are multiples of one elementary charge; Ehrenhaft concluded that some charges are not multiples and may be smaller; Lorentz: 'The question cannot be said to be wholly elucidated.'

Relevance: Supporting derivations; the moving-body Notes are covered in the next entry.

Mainstream conflict: none

Note 67: condensed-ether model of Stokes's sliding. Note 69 (original): Lorentz's dispersion-corrected drag coefficient for water at the sodium D line is 1 - 1/mu^2 - (1/mu) lambda dmu/dlambda = 0.451, against Fresnel's 0.438; Michelson and Morley deduced epsilon = 0.434 +/- 0.02, which does not separate the two [read: page image p.328]. Note 69* [1915] (Zeeman, Proc. Amsterdam Acad. 17 (1914) p.445, 18 (1915) p.398), transcribed from page image p.329 (shifts in fringe spacings; observed / Fresnel-only / with dispersion term): 4500 A, 6 obs.: 0.826 +/- 0.007 / 0.786 / 0.825; 4580 A, 6 obs.: 0.808 +/- 0.005 / 0.771 / 0.808; 5461 A, 9 obs.: 0.656 +/- 0.005 / 0.637 / 0.660; 6440 A, 1 obs., no error: 0.542 / 0.534 / 0.551; 6870 A, 10 obs.: 0.511 +/- 0.007 / 0.500 / 0.513. Ratio of shifts at 4500 and 6870 A: observed 1.616, formula without dispersion term 1.572, with it 1.608 (Zeeman's ratio test removes errors in flow speed and tube length). Deep-reader arithmetic: observed minus dispersion-corrected formula is within about 1 sigma in every row but the single-observation row (-0.009); observed minus Fresnel-only is +0.040 (about 5.7 sigma at 4500 A), +0.037, +0.019, +0.008, +0.011; the quoted error type (probable or standard) is not stated. Caveats: a secondary report of Zeeman by Lorentz, who is an interested party (the formula tested is his own, section 164); the number 0.826 is a fringe shift, not the drag coefficient [read: page image p.329]. Note 67: sliding 0.011 w0 and 0.0056 w0 (see Chapter V first part entry). Notes 70-72 (pp.329-330): proofs for mirrors and crystals, with Bockwinkel (1908) cited for absorbing bodies; second-order deviations of relative rays introduce no error. Note 72* [1915]: Lorentz's admission quoted above; l = 1 is Einstein's substitution; the invariance of x^2+y^2+z^2-c^2t^2 up to l^2; relativistic velocity and density transformations. Note 75* [1915]: from F = dG/dt, G = m0 v/sqrt(1-v^2/c^2) and l = 1 follow; relativity requires all forces to obey the general law (141); electromagnetic forces do; forces depending only on distance do not; gravitation must propagate at c. Note 76: electric-moment transformation; Lorentz admits trouble with the moment (p.206) came from not treating t' as real time. Notes 77-81: sphere energy and momentum, Poincare stress, instability of the sphere under shape change. Notes 83-85: signals and clocks, mass assigned by the moving observer. Note 86 [1915]: later experiments (Bucherer, Hupka, Schaefer and Neumann, Guye and Lavanchy) confirm (313) and 'the only objection ... against the hypothesis of the deformable electron and the principle of relativity has now been removed' [read: deep; digest pp.322-348]. Note 86's list was added in 1915; the reversal on the deformable electron first appears in the 1909 edition (Note 87, Bucherer 1908) [read: QE].

Key claims

• After 1915 Lorentz states that the transverse electromagnetic mass formula (313) is confirmed by Bucherer, Hupka, Schaefer and Neumann, and Guye and Lavanchy.
• Relativity requires all natural forces, gravitation included, to obey the same transformation law and to propagate at the speed of light.
• Lorentz attributes his 1909 shortfall to treating local time t' as only an auxiliary quantity.
• Zeeman's 1914-15 repetition of Fizeau's experiment (Note 69*) gave fringe shifts matching Lorentz's dispersion-corrected formula (e.g. 0.826 +/- 0.007 observed against 0.825 calculated at 4500 A) and not the Fresnel-only values (0.786).

Relevance: Contains Lorentz's own later reassessment, including the attributions to Einstein and the Kaufmann reversal.

Mainstream conflict: none; this is the mainstream relativistic position.

Alphabetical index (Aberration to Zeeman, with entries such as Kaufmann, Michelson, Morley, Einstein), colophon, advertisements for Teubner's physics and mathematics books (including entries for Abraham, Einstein and Minkowski's Das Relativitatsprinzip, and Lorentz's own works), the 'Sammlung mathematisch-physikalischer Lehrbucher' list, a Google digitisation page, a University of California loan slip and a spine label [read: digest pp.349-361].

Relevance: None to the claims; the index is a navigation aid and the catalogue shows 1916 contemporaries (Einstein and Minkowski's relativity reprint).

Mainstream conflict: none