Whittaker-ET · Source catalogue

Mathematische Annalen 57 (1903), pp. 333-355. The scan has no text layer, so the OCR loses nearly every equation; the equations were read from page images. Section 2 proves that the general solution of Laplace's equation (del^2 V = 0) is V = integral over u from 0 to 2pi of f(z + i x cos u + i y sin u, u) du, with f an arbitrary function. The proof expands V in a power series about a regular point, counts (2n+1) independent coefficients of degree n, and shows the same number of independent harmonic polynomials from the Fourier coefficients of (Z + iX cos u + iY sin u)^n. Section 3 uses it to rederive Legendre and Bessel harmonics and an example (potential of a prolate spheroid; a column of imaginary-spaced masses). Section 4 does the same for the wave equation del^2 V = k^2 d^2V/dt^2: counting (n+1)^2 independent coefficients gives V = double integral over u (0 to pi) and v (0 to 2pi) of f(x sin u cos v + y sin u sin v + z cos u + t/k, u, v) du dv. Section 5, part 1: each term is a plane wave of arbitrary profile travelling in one direction, so every finite solution of the wave equation is a sum of plane waves over all directions (Fourier-integral step needs F finite and continuous on a range). Parts 2-4 (deep read from page images): the general solution of the Helmholtz equation (del^2 V + V = 0) as a double integral of exp(i(x sin u cos v + y sin u sin v + z cos u)) f(u,v); recovery of the known solutions r^(-1/2) J(n+1/2)(r) P_n^m(cos theta) cos/sin(m phi); and generalized Bessel functions J_mn(x,y,z) defined as double Laurent coefficients, with an integral representation and an addition theorem (proved, given Laurent's theorem). These parts are pure mathematics: no medium, experiment or physical claim, and the Helmholtz equation is not named. The assertion that every solution has the integral form is true only locally and formally (bounded integrals cannot give growing solutions such as cos(sqrt2 x)e^z). The 'explained' heading of part 5 claims more than the text does. Part 5 (journal pp. 353-355): an inverse-square potential (gravity or electrostatics) satisfies del^2 V = 0 and therefore also the wave equation for any k, so it can be analysed into plane waves whose interference leaves a field that does not vary with time. Example: outgoing spherical waves (2 dmu / pi mu) sin(mu V t - mu r)/r sum to (2/pi r) integral of sin y / y dy, which equals +1/r where Vt - r > 0 ('after the waves have reached the point r'); the full sum is sgn(Vt - r)/r, i.e. -1/r outside the front, a source that changes sign from -1 to +1 at t = 0 (a static -1/r plus a switched-on 2/r) and a delta-function shell in the force at r = Vt [calc, three reviewers and the arbiter agree; the paper prints only the Vt > r case]. The field is therefore steady only inside r < Vt. The constituent waves are called longitudinal (the force is normal to the wave front, unlike light). The 1903 closing sentence (journal p.355, page image) reads that 'we have only to suppose that the medium is capable of transmitting, with a definite though large velocity, simple periodic undulatory disturbances, similar to those whose propagation by the medium constitutes, according to the electromagnetic theory, the transmission of light'; he also writes that the waves are 'in other respects exactly similar' to light, that the speed 'need not be the same as that of light, and may be enormously greater', that 'it seems probable that an identical property of the medium ensures their transmission', and that 'this investigation does not explain the cause of gravity'. The 1902 MNRAS note (62, 617-620) has the same idea one year earlier but a different closing: it says the propagation of inverse-square forces does not require 'any other property of the medium than one which has long been known and accepted' and uses 'of the same type'; the 'identical property' and 'enormously greater' sentences do match [web, research/2026-10-07-oup-mnras.md]. The 1903 closing ties the property to the electromagnetic transmission of light, not to the elastic-solid longitudinal mode of the older aether theories (see 1951 entry). The deep read separates what is proved (per-degree representation, wave-equation solutions) from what is asserted (summing over degrees without a convergence argument, so the result is local near a regular point; f periodic without loss of generality) and lists misprints: the 1/r identity on p.3 holds only for z > c (for z < c the integral is -1/r); the m = 0 Fourier factor should be 1/(2 pi); the printed Legendre series on journal p.342 has a sign error (-B1/2! should be +) and P2 for P3; a missing x on journal p.346; the spheroid equation printed '= 0' for '= 1'. Whittaker never identifies 1/k with the speed of light; he says k is any constant. His gravity field is a superposition of outgoing travelling waves, steady only inside r < Vt, not a textbook standing wave with fixed nodes. Whittaker never uses the word 'standing'; that wording is Barrett's (1993), Bearden's and Titleman's.

Key claims

• The general solution of Laplace's equation is the integral over u from 0 to 2 pi of f(z + i x cos u + i y sin u, u) du with f arbitrary (proved per degree, extended to V itself by assertion).
• The general solution of the wave equation del^2 V = k^2 d^2V/dt^2 is the double integral of f(x sin u cos v + y sin u sin v + z cos u + t/k, u, v) du dv with f arbitrary. (proved per degree; extended to V by assertion, valid locally near a regular point)
• Every finite solution of the wave equation (finite and continuous on a range, locally near a regular point) can be analysed into simple plane waves, one family for every direction in space.
• The potential of a Newtonian attracting mass, being a solution of Laplace's equation, is also a solution of the wave equation for any k and can be analysed into plane waves whose interference leaves a field that does not vary with time (shown for the example sum, which equals +1/r where Vt > r and -1/r outside the front).
• The constituent waves of such a gravitational field are longitudinal (force normal to the wave front), and their propagation speed need not equal the speed of light and may be enormously greater.
• It is probable that an identical property of the medium ensures the transmission of these gravitational waves and of light, though the investigation does not explain the cause of gravity.

Relevance: Foundational source for the project: the plane-wave / scalar-function decomposition later used in the 'scalar wave' literature (Bearden and others) and the one place where Whittaker himself suggests that gravity might be undulatory and longitudinal in the medium of light. It is the main primary evidence for a speculative hypothesis put to the review (Q07) about gravity as a longitudinal standing wave (follow-up Q07/A07). Whittaker never uses the phrase 'standing wave'; it is later writers' wording. The 1902 MNRAS note (62, 617-620) is the first statement of the idea and G. Johnstone Stoney's 1903 MNRAS critique (63, 424-428) is the first physical objection; neither is in the project folder (both read from page images on the web by the Investigator).

Mainstream conflict: The mathematics is standard and survives: the result is known as Whittaker's integral and appears in later textbooks [memory, high]. The physical suggestion (gravity as longitudinal waves in the luminiferous medium, with a speed possibly far above c) conflicts with general relativity, whose gravitational waves are tensor (transverse), travel at c (GW170817) and show no longitudinal polarization so far. Whittaker's own later work (1927) treats gravity within general relativity. The review stage, not this step, weighs these. Mathematical caveats from the deep read: the printed 1/r identity needs z > c; the 'every solution' claim is local; H. A. Munera (2018) calls the generality claim unacceptable because of the assumption of periodicity [web, research/2026-10-07-qeios.md].

Shows that the six components of the electric (dielectric displacement d) and magnetic (h) fields of any number of moving electrons, in Lorentz's form of the equations, can be written with two scalar functions F and G in place of the four of the usual potentials (scalar phi plus vector a). F and G are built from the retarded positions of the charges (F from the arcsinh of height over horizontal distance, G from the azimuth angle), so they depend only on position, not on velocity or acceleration. A third function psi drops out automatically (pure gauge). The field is then d_x = F_xz + (1/c) G_yt etc., h_z = G_xx + G_yy; in vector form d = curl curl f + curl (1/c) g-dot, h = curl (1/c) f-dot - curl curl g, with f and g directed along a fixed axis (z). Whittaker states that no symmetrical choice of f, g exists (they are tied to a chosen axis). In free aether F and G each obey the wave equation with speed c, so by the 1903 theorem F = double integral of f(x sin u cos v + y sin u sin v + z cos u + ct, u, v) du dv, similarly G with g: 'the most general type of electrodynamic disturbance' at a source-free place. For neutral systems of electrons in stationary motion he states the field is of the type F = f(t - r/c)/r, G = 0 (the field of an oscillating dipole), remarking that this may interest those who think atoms are sets of electrons with zero total charge. The deep reader checked numerically (30-digit mpmath) that the formulas reproduce the Lienard-Wiechert field of a moving, accelerating electron, including radiation terms, to 12 digits; and that each scalar plane-wave term of F or G produces an ordinary transverse electromagnetic wave. Gravity, longitudinal waves and any structure of the aether are not mentioned anywhere in the six pages. Correction to the digest: the vector formulas contain time derivatives (dots over f and g), and the coordinates in F and G are retarded positions.

Key claims

• The electromagnetic field of any number of moving electrons can be derived from two scalar potential functions F and G instead of four (phi and the three components of a).
• F and G depend only on the retarded positions of the electrons and satisfy the source-free wave equation with speed c.
• The most general source-free electrodynamic disturbance is given by d, h formed from second derivatives of F and G, each a double integral of arbitrary functions of x sin u cos v + y sin u sin v + z cos u + ct.
• The vectors f and g can always be taken parallel to one fixed direction, but no symmetric (axis-free) choice exists.
• A neutral system of electrons in stationary motion produces a field of the type F = f(t - r/c)/r, G = 0.

Relevance: Companion to the 1903 paper and the second pillar of the 'Whittaker potentials' used by later scalar-wave writers. Its own text is silent on gravity and longitudinal waves, which matters for deciding what Whittaker did and did not claim.

Mainstream conflict: None found by the deep reader: the construction is a Hertz-vector / Debye-potential type reformulation of Maxwell-Lorentz theory and was verified numerically. Readings of the paper as showing hidden longitudinal 'scalar waves' are later writers' interpretations that the text neither states nor rules out beyond: each plane-wave component yields a transverse d, h wave. Trovon de Carvalho and Rodrigues (2001), 'The Non Sequitur Mathematics and Physics of the New Electrodynamics Proposed by the AIAS Group', criticise the AIAS (Evans/Bearden) use of Whittaker's potentials; that label is those authors' characterization [web, research/2026-10-07-qeios.md]. Whittaker's own 1951 History (p.211, bk 409) calls F and G 'two plane-polarised components' [read: 1951 bk 409; PDF p.211 in the Chapter XIII deep read, PDF p.212 in the QE and mathematician citations; page image], not longitudinal waves.

The 224 PDF pages are two-page spreads. In the 1951 preface Whittaker explains that the revised first volume covers the classical theories and a second volume (now in the folder: see the 1953 entry) will cover relativity and quantum theory. He argues that the word 'vacuum' is absurd for an entity 'so rich in physical properties' (zero-point oscillations, vacuum fluctuations of charge and current, polarisation corresponding to a dielectric constant different from unity), so the historical word 'aether' may fitly be retained. Chapters: I aether theory to Newton (Descartes, Hooke, Huygens, Newton, Le Sage); II electric and magnetic science before potentials; III galvanism; IV luminiferous medium from Bradley to Fresnel; V aether as elastic solid (Cauchy, Green, MacCullagh, the contractile aether, longitudinal waves problem); VI Faraday; VII the mathematical electricians (Neumann, Weber, Helmholtz, Kirchhoff, Clausius, Riemann); VIII Maxwell; IX models of the aether (Kelvin vortex atoms); X followers of Maxwell; XI conduction in solutions and gases to J. J. Thomson; XII classical radiation theory; XIII classical theory in the age of Lorentz (electron theory, Michelson-Morley, Lorentz). The deep read of Chapter VIII found: Riemann's 1853 aether whose resistance to compression gives gravity and electrostatics and whose resistance to rotation gives light and magnetism; Maxwell's 1861-2 vortex/idle-wheel model; displacement current; light identified with electromagnetic waves, transverse; Kelvin's long resistance to displacement currents and his 1896 speculation (Nature) that electrostatic changes are propagated by condensational (longitudinal) aether waves, which FitzGerald contested in a private letter to Heaviside (one party's account); L. Lorenz's retarded potentials (1867); Maxwell's 1864 attempt to trace gravitation to the medium, abandoned because the medium would need enormous intrinsic energy ('I cannot go any further in this direction'); Maxwell stress formulas and the history of light pressure (Bartoli, Lebedev, Nichols and Hull, Poynting and Barlow). Whittaker gives no derivation of any longitudinal electromagnetic wave. Digest-only items bearing on gravity: Euler's aether-pressure explanation, Le Sage's ultramundane corpuscles, Weber/Riemann-law attempts at gravitation (Laplace's gravific fluid, Tisserand's 14 arcsec Mercury perihelion against 38 observed). Unverified by the deep reader: exact algebra of Maxwell's 1869 dispersion formula, signs in the 1864 potential equations, the Poynting-Barlow coefficient printed as '3P'. QE-remediation deep reads (2026-10-07) add the following, all as Whittaker's reports of other people's hypotheses with no test described [read: page images]. (1) Pulsation models of gravity, Ch. IX, PDF p.149-152 (bk 284-291). C. A. Bjerknes: two spheres in an incompressible fluid that pulsate in volume 'exert on each other (by the mediation of the fluid) an attraction, determined by the inverse square law, if the pulsations are concordant', repel if half a period apart, and exert no action at a quarter period; 'It is necessary to suppose that the medium is incompressible, so that all pulsations are propagated instantaneously; otherwise attractions would change to repulsions and vice versa at distances greater than a quarter wave-length' (Hicks, Proc. Camb. Phil. Soc. 1879-80, is cited for the mathematics; a Witte versus V. Bjerknes exchange of 1909-10 is cited without content). A. H. Leahy (Trans. Camb. Phil. Soc. xiv, 1884): in an elastic medium, with the wavelength large compared with the separation, Bjerknes' results are reversed (like phases repel, unlike attract), intensity still inverse square; Leahy's 'elastic medium' is not defined (it is probably an elastic solid, an inference). Korn (Berlin 1898, footnote): gravitating particles as slightly compressible spheres in an incompressible perfect fluid whose pulsation intensity corresponds to mass, giving forces of the Newtonian kind. Larmor (Phil. Trans. 1895, bk 286): gravitation between electrons might be explained if electrons are vacuous and have free periods of vibration in the fluid aether, following Bjerknes. Calculation by the deep reader: with a light-speed medium the quarter-wave condition d < lambda/4 needs a common pulsation period above 4d/c, about 33 minutes at 1 AU, about 17 hours at Neptune, about 17 years at Proxima Centauri [calc]; keeping the inverse-square law to 1 part in 10^8 at 1 AU needs lambda of order a light year. (2) Riemann's 1861 lectures (Hattendorff 1875 'Schwere, Elektricitaet und Magnetismus', p.330; bk 291): his potentials satisfy dphi/dt + c div a = 0, the same condition as L. Lorenz's, 'This appeared to Riemann to indicate that phi might represent the density of an aether, of which ca represents the velocity'; Whittaker adds that the forces then correspond to second derivatives of the displacement, which makes the field energy hard to match to the model's energy. This is the 19th-century root of the density-wave reading of Whittaker's own potentials. (3) The longitudinal wave in the light medium, Ch. V, PDF pp. 71-81: Fresnel's longitudinal speed 'indefinitely great' against the transverse (p.71, Stokes harmonised); Navier sqrt(3n/rho) (derived from k = 5n/3); Poisson transverse sqrt(n/rho), longitudinal sqrt((k + 4n/3)/rho); Cauchy's crystal-optics 'third wave' that he hoped would be found; Neumann/MacCullagh energy bookkeeping assumed transverse-to-transverse; Green's near-incompressible 'jelly' aether, speed very large, the longitudinal wave evanescent and energy-free; Cauchy/Kelvin contractile aether, longitudinal speed zero; MacCullagh's rotational aether with no longitudinal wave. Whittaker's text on these pages does not contain the phrases 'identical property of the medium' or 'enormously greater' (those are from the 1903 paper); the nearest are Fresnel's 'indefinitely great' and Green's 'very large'. (4) The gravity record, PDF pp. 16-154: Newton's aether and action at a distance as an absurdity; Cotes (1713) instantaneous; Le Sage's ultramundane corpuscles (bk 31-32); Aepinus' gravity as a residual of electric forces (bk 51-52); Euler's aether pressure 'Constant - 1/r' (bk 98-99); Laplace's gravific fluid 'at least a hundred million times greater than that of light' (10^8 c, bk 206-207; not 'millions' and not 7 x 10^6 c); Tisserand 1872 with Weber's law, h the speed of gravitation, 14 arcsec per century at h = c (3/8 of the 38 arcsec excess over 527 arcsec), Levy 1890 with Riemann's law 3/4 and a mixture of both all of it (bk 207-208); Kelvin's vortex atoms with simultaneous (instantaneous) effects (bk 294). (5) Chapter XIII (PDF pp. 200-212): the volume mentions Whittaker's own work once, the 1904 sentence 'it was however shown in 1904 by E. T. Whittaker that only two functions are actually necessary (in place of the four), namely, functions F and G' with footnote Proc. Lond. Math. Soc. (2) i (1904) p.367 (PDF p.211, bk 409), and the F and G are 'two plane-polarised components'; the name 'Whittaker' occurs elsewhere only on the title page, in the preface and in a citation of his Analytical Dynamics, and the index lists 'Whittaker, Sir E. T. 409' only. The 1902-03 undulatory gravity is not mentioned in this chapter, and a text search of the volume (47 hits for 'gravit', not all read in context) found nothing attributing it to him; this is a silence in Vol. 1; Vol. 2 (1953) is also silent on it (see the 1953 entry). Chapter XIII also contains Planck's 1899 compressible aether 'subject to gravity' to rescue Stokes' aberration theory and Michelson's 1897 null result for any dependence of light speed on height above the earth. (6) The text-layer search confirms no occurrence of 'longitudinal' in PDF pp. 200-212. QE-2 addition (2026-10-07), digest plus text-layer check only, not a deep read: Faraday's 1851 sentence (Vol. 1 PDF p.104): 'it is not at all unlikely that if there be an aether, it should have other uses than simply the conveyance of radiations'; Whittaker: 'This sentence may be regarded as the origin of the electromagnetic theory of light.' On the same page Faraday's 1846 'Thoughts on Ray-Vibrations' treats light as vibrations of lines of force. This is the earliest statement in the folder of one medium serving several jobs, the idea behind Whittaker's 1903 'an identical property of the medium'. The QE-requested deep read of PDF pp.103-104 (what Faraday proposed about gravitational lines) was not run, so whether Faraday names gravitational lines is not established here.

Key claims

• The relation between the aether filling space and the matter scattered in it is the central problem of nineteenth-century physics, and the aether was the seat of propagation of light, electric and magnetic action.
• The vacuum of quantum electrodynamics, with zero-point oscillations, fluctuations and polarisation, is an entity so rich in physical properties that the name 'aether' may fitly be retained.
• Maxwell's electromagnetic waves are transverse; the only longitudinal or condensational electromagnetic waves discussed in the chapter are Kelvin's 1896 speculation.
• Riemann (1853) attributed gravitation and electrostatics to the aether's resistance to compression and light and magnetism to its resistance to orientation change.
• Maxwell tried in 1864 to trace gravitation to a surrounding medium and abandoned the attempt because the medium would need an enormous intrinsic energy.
• Light pressure follows from Maxwell's stress formulas and was confirmed experimentally between 1899 and 1901.
• C. A. Bjerknes showed that two bodies pulsating in volume in an incompressible fluid attract with an inverse-square force when in phase, repel when half a period apart and exert no force at a quarter period; in a compressible medium the attraction changes to repulsion beyond a quarter wavelength (Whittaker's report, 1951 Ch. IX, bk 284-285).
• Leahy found that in an elastic medium, with wavelength long compared with the separation, Bjerknes' results are reversed: like phases repel (Whittaker's report, bk 285).
• Korn (1898) and Larmor (1895) based theories of gravitation on pulsating bodies in a fluid medium following Bjerknes (Whittaker's report, bk 285-286).
• Riemann (1861 lectures) read the Lorenz-type condition dphi/dt + c div a = 0 as a continuity equation, phi being the density and c a the velocity of an aether; Whittaker notes the field energy then does not match the model's energy (bk 291).
• In the nineteenth-century elastic-solid aether the longitudinal mode was kept out of optics by making its speed indefinitely great (Fresnel, Stokes, Green), zero (Cauchy, Kelvin) or absent by construction (MacCullagh) (Ch. V, PDF pp. 71-81).
• Laplace found that the velocity of his gravific fluid must be at least a hundred million times that of light (10^8 c); Tisserand's Weber-law calculation with h = c gave 14 arcsec per century of Mercury's perihelion against an excess of 38 arcsec (bk 206-208).
• The 1951 Vol. 1 mentions Whittaker's own work only for the 1904 F and G potentials (bk 409); it is silent on his 1902-03 undulatory explanation of gravity.
• Faraday (1851): if there be an aether it may have 'other uses than simply the conveyance of radiations'; Whittaker calls this sentence the origin of the electromagnetic theory of light (Vol. 1 PDF p.104; digest plus text check).

Relevance: Standard historical account (Vol. 2, 1953, is now also in the folder) of the aether theories by the author of the two scalar-function papers; it records his late view that the aether name should be kept for the physical vacuum, and supplies the historical background (Riemann, Kelvin, Maxwell, Le Sage, Weber) for gravity-in-the-medium ideas. The 1951 volume holds the closest historical relatives of the 'gravity as a longitudinal standing wave' hypothesis put to the review (Q07): Bjerknes/Leahy/Korn/Larmor pulsation models (in-phase longitudinal oscillations of a medium giving inverse-square attraction, with the constraints that all bodies pulsate in phase and, in a compressible medium, d < lambda/4) and Riemann's 1853 and 1861 compressional readings of the aether and of the scalar potential. They are context for the question, not Whittaker's own endorsement.

Mainstream conflict: None as history. The preface's proposal to retain 'aether' for the quantum vacuum is a terminology and interpretation choice that mainstream physics does not adopt, not a testable disagreement. The pulsation-gravity models are historical; none is part of current physics, and Whittaker reports no test of any of them (the status of each is for the reviewers, not this step).

Whittaker's own history of 1900-1926, written in 1953 (the volume's contents: the age of Rutherford and radioactivity; the relativity theory of Poincare and Lorentz; the beginnings of quantum theory; spectroscopy in the older quantum theory; gravitation; radiation and atoms; magnetism and electromagnetism 1900-1926; matrix mechanics; wave mechanics). 330 PDF pages, 4 of them OCR'd; the text layer is otherwise good. It is the inventor's own late, published account of exactly the questions his 1902-03 gravity note raised, and it never mentions that note. Deep read, Chapter V (Whittaker's words, with bk pages). Speed of gravity: Laplace's reasons for a speed 'vastly greater than that of light' 'do not to twentieth-century minds seem very plausible' (bk 149; footnote cross-refers to Vol. 1 pp.207-8); from 1904 Poincare showed that if relativity is true gravity 'must be propagated with the speed of light', and that observation does not contradict this (bk 151); 'gravitational waves are generated, which are propagated outwards with the speed of light' (bk 183, source: a change in the distribution of matter, e.g. a plate moving in a circle); the velocity of a signal is the group velocity, never greater than c (bk 159-160). Lorentz 1900 (bk 149-151): Le Sage's corpuscles replaced by trains of very-high-frequency electric waves; the net force on an ion 'could exist only if in some way or other electromagnetic energy were continually disappearing'; second hypothesis the Mossotti-Weber-Zoellner unequal electric forces with (gamma - alpha)/alpha of order 10^-35; Whittaker says only that no strong physical reason for it could be given in 1900 (he does not say Lorentz rejected it); Eddington (1946) later offered a Mach-principle reason. Scalar theories (bk 151-157): Planck 1907, Einstein 1907 and 1911, Abraham 1911-12 (gravity along the negative gradient of the light speed c), Einstein 1912, Nordstroem 1912-14 (named with references only, no equations given), Mie, Bateman 1909-10 credited with the variable quadratic form; Einstein-Grossmann's ten g_pq 'a tremendous innovation, because it implied the abandonment of the time-honoured belief that a gravitational field can be specified by a single scalar potential-function'; Einstein's reason is a box-versus-piston-pit radiation comparison in which a single scalar potential gives an inacceptable result (the one-third-work argument; Whittaker gives no numbers beyond 'one-third'). FitzGerald and the medium (bk 157-158): FitzGerald's 1894 'Gravity is probably due to a change of structure of the aether'; 'The aether of FitzGerald was called by Einstein simply space or space-time: and FitzGerald's somewhat vague term structure became with Einstein the more precise curvature'; in a static gravitational field feeble electromagnetic phenomena happen exactly as in a Maxwellian medium with aelotropic, position-dependent permittivity and permeability; for a point charge near a point mass the law printed is epsilon = mu = (r+1)^3/[r^2(r-1)] (E. T. Copson, Proc. R.S. A 118, 1928, p.184; the deep reader reconstructed it as the isotropic-coordinate Schwarzschild index, r = 2 rho c^2/GM, weak field 1 + 2GM/(c^2 rho)); Wiechert (Ann. d. Phys. 63, 1920, p.301) developed FitzGerald's possible dielectric-constant reading. Flat-space and alternative theories (bk 174-182): Whitehead 1920/1922 with Synge's 1952 study (action at a distance propagated at c; Whittaker: no practicable observational test yet suggested), Rosen 1940 (offered, in Whittaker's word 'claimed', as a possible account of D. C. Miller's 1925 ether-drift residuals), and A. G. Walker 1951 (Euclidean space with a Newtonian potential, kinetic energy T = (1/2) e^(-2phi/c^2) v^2, reproducing perihelion advance and light deflection; Whittaker: 'It is unwise to accept a theory hastily'). Whittaker's 1952 caution about General Relativity's tests (bk 179-181): light deflection 'there is a discordance' (table of 1919-1947 eclipse values 1.61 to 2.24 arcsec against 1.75), Mercury 'alternative explanations', red shift 'does not, properly speaking, constitute a test'; on Mach's principle he writes that it would need undetected matter and is 'no better than regarding some part of inertia as intrinsic'. Self-citations in the chapter: bk 146 (1917), 165 (1928, null geodesics from characteristics), 170 (1927 Proc. R.S. A 113 p.496, among Hilbert-variational developments), 184 and 186 (1931), 194 (1935, Gauss's theorem), and his son J. M. Whittaker 1928 (bk 153). The chapter contains no mention of his 1902 MNRAS note, the 1903 Math. Ann. paper, Stoney, Endeavour or From Euclid to Eddington, and no undulatory, longitudinal or standing-wave gravity. Other passages (text-layer check, not deep-read). The aether after relativity: of Cunningham's 1914 scheme, in which the aether has velocity c at every point so that momentum, energy and stress are kept, Whittaker writes 'The scheme is relativistically invariant: so that an objective aether is not necessarily foreign to the point of view of the principle of relativity' (bk 248); the contents also list Page's deduction of the Maxwellian theory (bk 247) and Leathem's phenomenon. Zero-point energy: Planck's second theory (1911-12) is 'the first appearance' of the doctrine 'which later assumed great importance', and 'in 1916 W. Nernst suggested that the aether everywhere might be occupied by zero-point energy' (bk 103-104; the full sentence is split across the page break, the first part of the passage was read in the text layer). Relativity framing: Einstein 'published a paper which set forth the relativity theory of Poincare and Lorentz with some amplifications', asserting the constancy of the velocity of light, 'an assertion which at the time was widely accepted, but has been severely criticised by later writers' (bk 40; chapter title 'The Relativity Theory of Poincare and Lorentz'); this is Whittaker's own framing, to be set beside the historian Navarro's characterization (web, not read in full) of the chapter as shaped by Whittaker's commitments. Potentials: Hargreaves 1908 integral form of the Maxwell-Lorentz equations and his 1922 expressions for the scalar and vector potentials of a moving electron (bk 250-252); the digest and text show no link to Whittaker's F and G of 1904. Index: 'Whittaker, Sir E. T.' appears (bk 146, 165, 170, 184 per the Vol. 2 index, which omits bk 186 and 194). Corrections of earlier QE statements by the deep reader: Chapter V runs to PDF p.207 (bk 196), not PDF p.200; Whittaker names Nordstroem without calling his theory scalar; he does not say Lorentz rejected the Mossotti model; and Vol. 2 does not contain the phrase 'not quite perfect' (that is from the 1928 lecture report [web]).

Key claims

• Whittaker (1953) writes that Laplace's assumptions leading to a gravity speed vastly greater than light 'do not to twentieth-century minds seem very plausible' (Vol. 2 bk 149, PDF p.160).
• Whittaker (1953) reports that Poincare showed relativity requires gravity to be propagated with the speed of light and that this is not contradicted by observation (bk 151, PDF p.162), and that gravitational waves, generated by changes in the distribution of matter, propagate at the speed of light (bk 183, PDF p.194).
• Lorentz (1900) tried to replace Le Sage's corpuscles by very-high-frequency electric waves; the resulting force on an ion could exist only if electromagnetic energy were continually disappearing (bk 149-150, Whittaker's report).
• Einstein's single-scalar-potential objection: for radiation in a box versus in a piston pit, a single scalar potential gives an inacceptable result (the one-third-work argument), so the gravitational field is specified by ten potentials g_pq (bk 156-157, Whittaker's report; Whittaker gives no numbers beyond 'one-third').
• FitzGerald's 1894 'change of structure of the aether' became, in Whittaker's account, Einstein's 'curvature'; in a static gravitational field feeble electromagnetic phenomena follow Maxwell's theory in a medium of position-dependent permittivity and permeability, epsilon = mu = (r+1)^3/[r^2(r-1)] for a point mass (Copson 1928; bk 157-158, PDF pp.168-169).
• Whittaker (1953): 'an objective aether is not necessarily foreign to the point of view of the principle of relativity' (of Cunningham's 1914 scheme; bk 248, PDF p.259).
• Planck's second theory (1911-12) introduced zero-point energy, and in 1916 Nernst suggested the aether everywhere might be occupied by zero-point energy (bk 103-104, PDF pp.114-115).
• Whittaker (1953) records Whitehead's, Rosen's and A. G. Walker's flat-space or scalar alternatives that reproduce classical tests, and in 1952 judges the measured light deflection discordant with Einstein's 1.75 arcsec and Mercury's perihelion open to 'alternative explanations' (bk 174-182).
• Chapter V of Vol. 2 does not mention Whittaker's 1902 MNRAS note, his 1903 Math. Ann. section 5 (undulatory gravity) or Stoney's critique; his own works cited there concern celestial mechanics, null geodesics, Hilbert's variational derivation, the de Sitter world and Gauss's theorem (bk 146, 165, 170, 184, 186, 194).

Relevance: Primary evidence of what the inventor himself published about gravity, the speed of gravity, scalar gravity, the aether and relativity fifty years after the 1903 note; it bears directly on claim 4 (undulatory gravity: his 1953 text states light-speed gravity and the abandonment of a single scalar potential, and is silent on his own note), claim 5 (the aether retained: he equates FitzGerald's aether with Einstein's space-time and gives gravity a medium reading) and the question of where the record goes dark. It also supplies a [read] primary text for Navarro's characterization of his relativity chapter. The deep reader's net reading is that the 1953 text moves weight toward 'he gave up the superluminal speed and the single scalar as relativity arrived' for the speed and scalar parts, and leaves a continuing medium-versus-geometry commitment open; neither reading is a verdict here.

Mainstream conflict: None as history. As a source it is a conventional history that states the mainstream relativistic view (gravity and gravitational waves at c). Its mild departures are Whittaker's cautions of 1952 about the evidence for General Relativity (light deflection 'a discordance', red shift not a discriminating test), which later measurements resolved in General Relativity's favour [memory, high], and his retention of the word 'aether'. For the project, the 1953 statements conflict with the 1903 'may be enormously greater' speed, not with mainstream physics.

Google Books scan of the 1910 first edition, OCR text of variable quality. Twelve chapters: I aether theory in the seventeenth century; II electric and magnetic science before potentials; III galvanism; IV the undulatory theory Bradley to Fresnel; V the aether as elastic solid; VI Faraday; VII mathematical electricians of the mid-nineteenth century; VIII Maxwell; IX models of the aether; X followers of Maxwell; XI conduction in solutions and gases from Faraday to J. J. Thomson; XII theory of aether and electrons in the closing years of the nineteenth century (index at p.470). The preface thanks W. W. Rouse Ball and W. McF. Orr and the Board of Trinity College, Dublin. Whittaker is styled Royal Astronomer of Ireland. The digest records the same material as the 1951 edition for gravity-related passages: Newton's aether and discomfort with action at a distance, Euler, Weber-law gravitation (Laplace's gravific fluid, Tisserand 1872), Faraday's idea of atoms as force fields, Riemann 1853. It ends with the electron theory at the close of the nineteenth century and does not cover relativity or quantum theory. Deep-read comparison with 1951 (2026-10-07): the Laplace/Tisserand text (at least a hundred million times the speed of light; Tisserand 14 arcsec per century, 3/8 of the 38 arcsec excess; Levy 3/4), the Bjerknes and Leahy results, the Korn footnote and Riemann's density suggestion are essentially verbatim the same in 1910 and 1951. Added in 1951: the Preface justification of the name 'aether' for the quantum vacuum; Larmor's 1895 vacuous-electron gravitation sentence; Bjerknes's quarter-period 'no action' statement and the Witte/V. Bjerknes 1909-10 exchange; a Lagrangian footnote for Riemann's law. Dropped in 1951: the 1910 closing paragraphs. These said that 'it is possible that the future may bring important changes in the conception of the aether', that the hope of an absolute-motion aether 'has been destroyed by the researches which have sprung from Fitz Gerald's hypothesis of contraction', and that some recent writings show 'a tendency to replace the classical aether by other conceptions, which, however, have been as yet but indistinctly outlined'; they also contained the six-hundred-mile-circle passage on where researchers lived and 'Let this record close with the anticipation that fellowship in the pursuit of knowledge will increase...'. Vol. 1 of 1951 ends at the 1902 thermionic-emission work and defers to Vol. 2 (1953, now in the folder). Neither edition gives Whittaker's own opinion on gravity as a wave or standing-wave phenomenon in these passages. OCR cautions: the 1910 OCR prints 'Berlin, 1908' where the page image has 1906, and loses the time-derivative dot and the fractions 3/8 and 3/4.

Key claims

• The fundamental problem of physics since Descartes is the relation between the aether filling interstellar space and the condensations of matter scattered through it.
• Newton regarded action at a distance through a vacuum without a mediating mechanism as an absurdity and proposed an elastic aether, densest in free interplanetary space.
• Many nineteenth-century writers (Weber, Laplace, Tisserand) treated gravitation as propagated through a medium in finite time.
• Laplace found that his gravific fluid must move at least a hundred million times faster than light; Tisserand's Weber-law gravity gave 14 arcsec per century of Mercury's perihelion (3/8 of the 38 arcsec excess), Levy's Riemann-law version 3/4 (1910 PDF pp. 253-255).
• In 1910 Whittaker wrote that the future may bring important changes in the conception of the aether, with other conceptions as yet indistinctly outlined (1910 PDF pp. 489-490); the 1951 edition drops this passage.

Relevance: Earlier version of the history; useful for comparing what Whittaker wrote in 1910 with the 1951 revision (including the 1951 preface remark about the vacuum), and dating his views, since the 1903 gravity suggestion predates it by seven years.

Mainstream conflict: none