Index:Aether and Matter, 1900.djvu

Title	Aether and Matter
Author	Joseph Larmor
Year	1900
Publisher	Cambridge University Press
Location	Cambridge
Source	djvu
Progress	To be proofread
Transclusion	Index not transcluded or unreviewed

Pages (key to Page Status)

– – – – – – – – – – v vi vii viii ix x xi xii xiii xiv xv xvi xvii xviii xix xx xxi xxii xxiii xxiv xxv xxvi xxvii xxviii xxix xxx

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CONTENTS

	Page
Chapter I Introduction	1
SECTION I
Chapter II Historical survey	6
Astronomical aberration of light: Bradley's guiding ideas. Optical refraction uninfluenced by the Earth's motion: Fresnel's explanation. Aberration as measured by a water-telescope. Theoretical views of Cauchy. Views of Sir George Stokes as to constitution of the aether: suggested partial analogy of material substances like pitch; irrotational viscous motion unstable, also involves dissipation of energy: irrotational character of finite motions of the aether explained by its high rigidity or rotational elasticity. Maxwell's formulation of Fresnel's theory. The general absence of any optical influence of the Earth's motion suggests that the aether may move along with the Earth: the difficulties of this mode of explanation. Maxwell's discussion of electrodynamic theory relative to moving bodies. Introduction of atomic electric charges into the aether theory. Aether stagnant. Alleged difficulties of the electric theory. Maxwell's original scheme effective for systems at rest: nature of its adaptation to moving systems. A constitutive aether affords the only explanation of an atomic constitution of matter: the various atomic theories: electric aspect of an atom. MacCullagh's optical aether is the electric aether. Molecules may be systems of electrons: the duality of positive and negative dynamically necessary. Maxwell's elimination of ' electricity ' from the theory is available for ordinary electrodynamics, but cannot be extended to problems involving radiation.
Chapter III General kinematic theory of optical rays in moving media	30
Specification of a ray: ray-velocity: wave-velocity: wave-front: principle of Least Time: application to a moving medium. Theories of aberration: if the aether moves sensibly its motion must be irrot- ational: influence of its elasticity in this direction: evidence of water-telescope. Influence of convection of the material medium on velocity of propagation; Fresnel's law necessary whether there is aethereal flow or not. Ray-velocity in moving medium. Influence of convection on positions of optical foci: on period of the light: on phenomena of diffraction and interference, application to diffraction-grating. Inclusion of the second order of small quantities: theory of Michelson's interference experiment; law of reflexion by rotating mirror. General analysis of interference relative to moving media: the retardation may be calculated on the undisturbed path: applied to Michelson's arrangement.
Chapter IV The problem of optical convection: indications towards a dynamical theory	54
Examples of convection of wave-trains by simple media: sound waves in air, waves on stretched cord. Maxwell's equations for the compound medium, aether and matter: various possible constitutive hypotheses considered. Fresnel's law obtained; the electric theory of moving media which it requires; same expressed without the aid of potentials. Sketch of results to be derived from a precise molecular theory: Michelson's interference experiment gives a clue as regards the constitution of a molecule. Magnetic effect of convection of an electric charge with the Earth: Röntgen's null result explained by countervailing charges: the electric effect of the convection of a magnet must be similarly null.

SECTION II
Chapter V On method in general physical theory	68
On the scientific utility of hypothesis: illustrated from the history of the corpuscular theory of light, and of the Weberian theory of electrodynamics. Helmholtz's criticism of the latter not destructive; it is now included in modified form in the aether theory: the same applies to MacCullagh's optical theories, which were at one time rejected. On vector terminology. Hypothesis of aethereal constitution of matter; necessary in order to avoid an irreconcilable duality of matter and aether; historical. Phenomena are expressible in terms of matter alone, unless velocities or alternations comparable with those of radiation are concerned. This electric theory of aether and matter is precisely formulated; thus even if itself incomplete, it will throw light on the possibilities of correlation in that remote region: ordinary molecular theories suppose the molecules so far apart that their interactions can be expressed by 'forces.'
Chapter VI Dynamical theory of electrical actions	82
Least Action, fundamental in general dynamics. Dynamical equations for free aether, derived from its energy function: the two fundamental vectors, circuitally related: velocity of elastic propagation. Introduction of electrons, as point-charges. Modification of relation of aethereal strain to displacement in a medium containing electrons: displacement of an electron equivalent to a local aether strain: two independent variables, electric flux and aether strain: combined they form Maxwell's circuital total current. Generalization of Stokes' theorem of circuit and barrier integration, for a medium containing singularities. In ordinary electrodynamics, aether strain inconsiderable compared with electric flux: expression of the kinetic energy of the aether in terms of electric flux, viz. in terms of true flux of electrons and 'apparent' flux the equivalent of change of aether-strain, involves the introduction of the vector potential of the electric flux: the potential energy involves the aether strain alone. Application of Action principle to the energy as thus specified: introduction of the additional condition that each electron is a pole of the aether strain: variation performed as regards a moving electron: interpretation of result as giving the electric force acting on the electrons and the aethereal force straining the aether: modification required in magnetized media to obtain the 'mechanical' part of the electric force which excludes the purely local part: the mechanical force on an electric current. Electric currents of conduction, due to motions of ions, constituted half by positive and half by negative ions. Currents producing material electric polarization. Current arising from convection of charged bodies. Current arising from convection of a polarized dielectric, expressible primarily as a quasi-magnetization. Any magnetization identical mechanically with a distribution of current. Total mechanical force on the material medium, as constituted by the force on the true current, that on the magnetism, that on the electric polarization and the true electric charge: the part of it arising from the convection of the medium. The vector potential of magnetism must be defined as that of the equivalent distribution of electric flow: this equivalence extends to magnetic induction, not to magnetic force.
Chapter VII Review of the electrodynamic equations of a material medium	109
Exact dynamical relations. Exact relations inherent in the constitution of the medium. Consequences: the static electric force due to the actual distribution adds to the kinetically induced force. Approximate constitutive relations of the material medium: dielectric and magnetic coefficients: analysis of aeolotropic conduction, any rotational character must De due to extraneous vector influence. Elimination of mathematical potentials: the circuital relations. Maxwell's purely abstract scheme; determinate for media at rest and identical with the present scheme: illustration from theory of double refraction, compared with Helmholtz's wider theory. The aether sufficiently defined by its dynamical equations. The transition from molecular to mechanical theory: the latter involves only the principal values of the integrals expressing the potentials.
Chapter VIII Optical and other developments relating to energy and stress	127
Mechanical electrodynamic forces expressed in terms of a stresssystem: limited validity of Maxwell's expressions, their physical meaning: his dielectric stress invalid except in free aether. Application to repulsion of conducting masses by magnetic alternators: copper filings lie along lines of force. Contrast between relations of obstacles to electric waves and to sound waves. Mechanical pressure of radiation; on a black body is given by Maxwell's law. Absorption of radiation: character of surface of a perfectly black body; of a perfect reflector. Relation of the complete radiation to the temperature: Boltzmann's proof of Stefan's law. Dynamical and material symmetry: general deductions regarding perversion, reversibility, chirality: influence of convection through the aether on structure. Adiabatic compression of radiation: its mechanical value: legitimacy of an ideal screen impervious to radiation but pervious to aether.

SECTION III
Chapter IX Influence of steady motion on an electrostatic material system	149
Existence of an electric potential in every steady_state. Equations for case of uniform translation: characteristic equation of the potential, solved: electric distribution and force unaffected, but magnetic field altered: correlation with a stationary system. Null results of convection of magnets. Convection of a dielectric system. Uniform rotation of an electrostatic system: electric potential not constant in conductor: solution for a rotating di electric; for a spherical conductor.
Chapter X General problem of moving matter treated in relation to the individual molecules	161
Analytical specification of an electron as a moving pole in the electric field necessitating a singularity in the magnetic field. The problem, formulated so as to take cognizance of the electrons individually, is determinate in terms of the aether alone if matter is constituted of electrons: arguments in favour of its being mainly so constituted. The equations relative to the convected material system; transformed back to the standard form: resulting correlation with same system stationary, but with a time-origin varying from point to point; includes the previous special investigations: in static distributions the charges and electric forces are the same in both systems to the first order, but not the aethereal displacements and magnetic forces.
Chapter XI Moving material system: approximation carried to the second order	173
Electrodynamic equations, taking account of individual electrons: referred to moving system: restored to standard form by change of scale in space and time: resulting correlation. Second-order shrinkage in an aethereally constituted system arising from convection. Optical propagation in moving matter: Earth's motion optically inoperative.; Null effect on structure of a molecule. Null effect on conductivity of the medium. Discussion_of null effect_to second order in Michelson's interference experiments. Are the linear equations of the aether exact? Inference as to structure from the definiteness of atomic masses: gravitation not involved with the present subject.

SECTION IV
Chapter XII On optical rotations magnetic and structural	194
Magneto-optic energy term: deduction of relation between polarization and electric force: the magnetic influence purely rotational. Equations of propagation: coefficient of rotation. A hypothesis as to relation of rotation to density: not experimentally verified. Physical explanation of the rotation. Theory of magneto-optic reflexion and the Kerr effect. Structural rotation: the equations: its kinetic origin. Chiral relations of ions. flotation produced by artificial twisted structure. See Appendix F.
Chapter XIII Influence op the earth's motion on rotational optical phenomena	211
Equations for moving rotational medium: influence of convection on velocity of propagation: the convective effect simply superposed. Verification of Mascart's null result as regards structural rotation: consistent with the electron theory. Null result as regards magnetic rotation.

SECTION V
Chapter XIV On the mechanism of molecular radiation	221
The aethereal disturbance propagated from a moving electron. The field of a vibrating doublet; of an electron describing an orbit. The type of radiation emitted from a moving electron: its intensity: a uniformly moving electron does not radiate. Isolated pulse caused by sudden disturbance: its energy conserved as it moves onward: mode of establishment of a steady magnetic field as the trail of such a pulse. Conditions for absence of radiation from a molecule: concentration of its energy
Chapter XV On the nature of ordinary radiation, and its synthesis into regular wave-trains	235
Röntgen radiation, not of vibratory origin: its intensity per molecule: absorption proportional to density. The Fourier analysis, how far objective. Analysis of radiation by a series of simple damped receivers: response to a discontinuous pulse, to a damped wave-train: case of Hertzian radiation. Character of radiation from gases: periods, effective phase, interference. Periodicity created or intensified by the analyzer; case of a grating; case of a prism. Röntgen radiation would analyze into high periods.
Appendix A On the principles of the theory of magnetic and electric polarity: and on the mechanical significance of divergent integrals	252
Definition of polarity: its relation to the Maxwellian electric displacement: polarization of dielectric matter. Distribution of polarity replaced by a distribution of density. Formal laws of induced polarization. Transition from the aggregate of molecular polar elements to the polarized mechanical medium. The potential of mechanical theory defined: the actual magnetic vector potential must be modified to a mechanical form. The integrals occurring in mechanical theory are defined by their principal values. The formula for electric force always consists of an electrokinetic part added to the electrostatic force.
Appendix B On the scope of mechanical explanation: and on the idea of force	268
General mechanics based on principle of virtual work and principle of d'Alembert. Generalized law of mechanical reaction. Scope and physical reality of statics: idea of force fundamental and prior to mechanical motions. The method of molecular dynamics. Mechanics a growing science as regards its principles. General kinetics formulated with regard to relative motions alone, in special cases: in other cases the stagnant aether is the ultimate datum of reference. Kirchhoff's exposition of the Lagrangian formulation on the basis of the Action principle applied to systems of 'particles.' The Lagrangian scheme implies that the system is conservative as regards its energy, and involves that it is conservative (e.g. reversible, dynamically permanent) in other respects. Hertz's objection that rolling motions are not included. Physical concepts are abstract ideas cultivated under the gu idance of observation. If matter is aethereally constituted, all dynamics ultimately rests on that of the aether: mechanical Action principle in this way deduced. The approximate inclusion of actual conservative material systems under the ideal Action principle involves observation and experiment. Thermodynamics a branch of statics: its aim is the formulation of the available energy, on which alone mechanical effect depends. Physical explanation of law of uniformity of temperature: temperature not a dynamical concept. Mechanical analogies. Mechanics of permanent systems is independent of molecular dynamics: illustrated by theory of osmotic pressure. Energy not an ultimate concept. Vital activity not mechanical as regards its stimulus.
Appendix C On electrolysis: and the molecular character of electric conduction	289
Laws of Faraday and Kohlrausch: they require that electrolysis is accompanied by convection of the electrolyte. Independent diffusion of the ions: their equations of transfer: relation of their diffusion constants to their electric mobilities. Diffusivity connected with electric data: electromotive forces arising from concentration. Ions not free in metallic conduction. Ultimate steady gradient of concentration established by electrolysis. Special case of no current . Hall effect in electrolytes. Influence of motion through the aether. Equations for mixed electrolytes: electromotive forces: simple cases. Convective material flow due to bodily charge, compared with electric osmosis. Thermoelectric influence: the moving ions carry their heat along with them: the thermoelectric gradient along an unequally heated conductor not a true voltaic effect.
Appendix D On the historical development of atomic and radiant theory	310
Fermat on Least Time or Action in optics. The aether-theory of Huygens: on transmission by waves: on the nature of the elasticity of solids, contrasted with that of gases: ideas as to elasticity of the aether: kinetic theory of gases, and of matter in general: matter freely permeable to aether: his limited acceptance of the law of gravitation. Gravitation uninfluenced by structure. The aether-theory of Newton: an aether essential to his views: compelled by absence of explanation of shadows to introduce the extraneous aid of luminiferous corpuscles: would welcome any constitutive aether that would not disturb the motions of the planets: atoms necessary to physics. Young's plea that the electric aether may also be the medium of optical propagation. Davy's view that electric attraction is of the essence of the atom, and is the cause of chemical affinity. Gauss on the necessity of a medium for the transmission of electric force between atoms. Kelvin's view that atoms are structures. Graham's view that an atom is a vortex in the aether. Fresnel's views on the optical influence of motion of material bodies.: the Earth's motion does not disturb the aether: his law of optical convection deduced from his hypothesis that the aether is denser in material media: consequence that ordinary optical phenomena are uninfluenced by the Earth's motion.
Appendix E On kinematic and mechanical modes of representation of the activity of the Aether	323
Mechanical models and illustrations. Rotational elasticity: Kelvin's gyrostatic illustration, its limitations. Model of an electron in a rotational aether: its creation by a supernatural process: analogous constructions in elastic matter. Mechanical analysis of attractions between electrons; involves dissection of the aether by strain-tubes connecting complementary electrons: illustration from the generalized form of Stokes' analytical theorem. The ultimate foundation in physical theory is the Action principle. The electron effectively a point-charge: the details of its structure unknown. All physical representations are at bottom comparative or illustrative: the scheme of a rotational aether merely consolidates the various hypotheses into a single one. Static attraction transmitted, not propagated. A constitutive aether contrasted with an accidental one. The electron theory essential to the formulation of ordinary electrodynamics as well as for radiation. Neumaun-Helmholtz electrodynamic potential theory invalid; experimental tests by FitzGerald and Lodge. The expression for the electrokinetic potential of two electrons compared with Weber's formula: they lead to the same results in the electrodynamics of ordinary currents.
Appendix F Magnetic influences on radiation as a CLUE TO MOLECULAR CONSTITUTION	341
The Zeeman effect: determined for a molecule in which the mobile electrons are all negative: same results apply when there are mobile positive ions relatively very massive. Nature of magnetic polarization of a molecule, it does not involve orientation: the exceptional phenomena of the magnetic metals arise from cohesive aggregation of molecules. The polarizations of the Zeeman lines indicate the characters of the vibrations of the molecular system: the methods of dynamics of particles adequate to the problem: the system referred to rotational coordinates; the condition for circular principal vibrations. Any purely constitutive potential energy for the molecule leads to the Zeeman phenomena, with the requisite generality. Inference as to effective isotropy of the molecule. The Faraday effect and Becquerel's law of dispersion deduced from the Zeeman effect when the freely mobile electrons are all negative; or when the dispersion is controlled by one absorption band, or by several bands for which the Zeeman constant is the same. Optical rotations necessarily of dispersional type; and therefore not simply related to material structure. Direct kinematic analysis of optical rotations for crystalline media, b y reference to rotating frame: law of rotation in different directions: the permanent types of vibration when rotation is superposed on double refraction: problem of refraction into a chiral medium not determinate.
Index	357