A History of the Theories of Aether and Electricity

by Edmund Taylor Whittaker

DUBLIN UNIVERSITY PRESS SERIES.

---

A HISTORY

OF THE

THEORIES OF AETHER AND ELECTRICITY

FROM THE AGE OF DESCARTES TO THE CLOSE OF
THE NINETEENTH CENTURY.

 

BY
E. T. WHITTAKER,
Hon. Sc. D. (Dubl.); F. R. S.; Royal Astronomer of Ireland.

 

LONGMANS, GREEN, AND CO.,
39 PATERNOSTER ROW, LONDON,
NEW YORK, BOMBAY, AND CALCUTTA.
HODGES, FIGGIS, & CO., Ltd., DUBLIN.
1910.

DUBLIN:
PRINTED AT THE UNIVERSITY PRESS,
BY PONSONBY AND GIBBS.

The author desires to record his gratitude to Mr. W. W. Rouse Ball, Fellow of Trinity College, Cambridge, and to Professor W. McF. Orr, F. R. S., of the Royal College of Science for Ireland; these friends have read the proof-sheets, and have made many helpful suggestions and criticisms.

Thanks are also due to the Board of Trinity College, Dublin, for the financial assistance which made possible the publication of the work.

Contents.

 

Chapter I.

The Theory of the Aether in the Seventeenth Century.

Page

Matter and aether, ....................................................................................................................................................................................................................................................

1

The physical writings of Descartes, ....................................................................................................................................................................................................................................................

2

Early history of magnetism : Petrus Peregrinus, Gilbert, Descartes, ....................................................................................................................................................................................................................................................

7

Fermat attacks Descartes' theory of light: the principle of least time, ....................................................................................................................................................................................................................................................

10

Hooke's undulatory theory: the advance of wave-fronts, ....................................................................................................................................................................................................................................................

11

Newton overthrows Hooke's theory of colours, ....................................................................................................................................................................................................................................................

15

Conception of the aether in the writings of Newton, ....................................................................................................................................................................................................................................................

17

Newton's theories of the periodicity of homogeneous light, and of fits of easy transmission, ....................................................................................................................................................................................................................................................

20

The velocity of light: Galileo, Roemer, ....................................................................................................................................................................................................................................................

21

Huygens' Traité de la lumière: his theories of the propagation of waves, and of crystalline optics, ....................................................................................................................................................................................................................................................

22

Newton shows that rays obtained by double refraction have sides: his objections to the undulatory theory, ....................................................................................................................................................................................................................................................

28

 

Chapter II.

Electric and Magnetic Science, Prior to the Introduction of the Potentials.

The electrical researches of Gilbert: the theory of emanations, ....................................................................................................................................................................................................................................................

29

State of physical science in the first half of the eighteenth century, ....................................................................................................................................................................................................................................................

32

Gray discovers electric conduction: Desaguliers, ....................................................................................................................................................................................................................................................

37

The electric fluid, ....................................................................................................................................................................................................................................................

38

Du Fay distinguishes vitreous and resinous electricity, ....................................................................................................................................................................................................................................................

39

Nollet's effluent and affluent streams, ....................................................................................................................................................................................................................................................

40

The Leyden phial, ....................................................................................................................................................................................................................................................

41

The one-fluid theory: ideas of Watson and Franklin, ....................................................................................................................................................................................................................................................

42

Final overthrow by Aepinus of the doctrine of effluvia, ....................................................................................................................................................................................................................................................

48

Priestley discovers the law of electrostatic force, ....................................................................................................................................................................................................................................................

50

Cavendish, ....................................................................................................................................................................................................................................................

51

Michell discovers the law of magnetic force, ....................................................................................................................................................................................................................................................

54

The two-fluid theory: Coulomb, ....................................................................................................................................................................................................................................................

56

Limited mobility of the magnetic fluids, ....................................................................................................................................................................................................................................................

58

Poisson's mathematical theory of electrostatics, ....................................................................................................................................................................................................................................................

59

The equivalent surface- and volume-distributions of magnetism: Poisson's theory of magnetic induction, ....................................................................................................................................................................................................................................................

64

Green's Nottingham memoir, ....................................................................................................................................................................................................................................................

65

 

CHAPTER III.

Galvanism, from Galvani to Ohm.

Sulzer's discovery, ....................................................................................................................................................................................................................................................

67

Galvanic phenomena, ....................................................................................................................................................................................................................................................

68

Rival hypotheses regarding the galvanic fluid, ....................................................................................................................................................................................................................................................

70

The voltaic pile, ....................................................................................................................................................................................................................................................

72

Nicholson and Carlisle decompose water voltaically, ....................................................................................................................................................................................................................................................

75

Davy's chemical theory of the pile, ....................................................................................................................................................................................................................................................

76

Grothuss' chain, ....................................................................................................................................................................................................................................................

78

De La Rive's hypothesis, ....................................................................................................................................................................................................................................................

79

Berzelius' scheme of electro-chemistry, ....................................................................................................................................................................................................................................................

80

Early attempts to discover a connexion between electricity and magnetism, ....................................................................................................................................................................................................................................................

83

Oersted's experiment: his explanation of it, ....................................................................................................................................................................................................................................................

85

The law of Biot and Savart, ....................................................................................................................................................................................................................................................

86

The researches of Ampère on electrodynamics, ....................................................................................................................................................................................................................................................

87

Seebeck's phenomenon, ....................................................................................................................................................................................................................................................

90

Davy's researches on conducting power, ....................................................................................................................................................................................................................................................

94

Ohm's theory: electroscopic force, ....................................................................................................................................................................................................................................................

95

 

CHAPTER IV.

The Luminiferous Medium, from Bradley to Fresnel.

Bradley discovers aberration, ....................................................................................................................................................................................................................................................

99

John Bernoulli's model of the aether, ....................................................................................................................................................................................................................................................

100

Maupertuis and the principle of least action, ....................................................................................................................................................................................................................................................

102

Views of Euler, Courtivron, Melvill, ....................................................................................................................................................................................................................................................

104

Young defends the undulatory theory, and explains the colours of thin plates, ....................................................................................................................................................................................................................................................

105

Laplace supplies a corpuscular theory of double refraction, ....................................................................................................................................................................................................................................................

109

Young proposes a dynamical theory of light in crystals, ....................................................................................................................................................................................................................................................

110

Researches of Malus on polarization, ....................................................................................................................................................................................................................................................

111

Recognition of biaxal crystals, ....................................................................................................................................................................................................................................................

113

Fresnel successfully explains diffraction, ....................................................................................................................................................................................................................................................

113

His theory of the relatire motion of aether and matter, ....................................................................................................................................................................................................................................................

115

Young suggests the transversality of the vibrations of light, ....................................................................................................................................................................................................................................................

121

Fresnel discusses the dynamics of transverse vibrations ....................................................................................................................................................................................................................................................

123

Fresnel's theory of the propagation of light in crystals, ....................................................................................................................................................................................................................................................

123

Hamilton predicts conical refraction, ....................................................................................................................................................................................................................................................

131

Fresnel's theory of reflexion, ....................................................................................................................................................................................................................................................

133

 

CHAPTER V.

The Aether as an Elastic Solid.

Astronomical objection to the elastic-solid theory: Stokes' hypothesis. ....................................................................................................................................................................................................................................................

137

Navier and Cauchy discover the equation of vibration of an elastic solid, ....................................................................................................................................................................................................................................................

139

Poisson distinguishes condensational and distortional waves, ....................................................................................................................................................................................................................................................

141

Cauchy's first and second theories of light in crystals, ....................................................................................................................................................................................................................................................

143

Cauchy's first theory of reflexion, ....................................................................................................................................................................................................................................................

145

His second theory of reflexion, ....................................................................................................................................................................................................................................................

147

The theory of reflexion of MacCullagh and Neumann, ....................................................................................................................................................................................................................................................

148

Green discovers the correct conditions at the boundaries, ....................................................................................................................................................................................................................................................

151

Green's theory of reflexion : objections to it, ....................................................................................................................................................................................................................................................

152

MacCullagh introduces a new type of elastic solid, ....................................................................................................................................................................................................................................................

154

W. Thomson's model of a rotationally-elastic body, ....................................................................................................................................................................................................................................................

157

Cauchy's third theory of reflexion: the contractile aether, ....................................................................................................................................................................................................................................................

158

Later work of W. Thomson and others on the contractile aether, ....................................................................................................................................................................................................................................................

159

Green's first and second theories of light in crystals, ....................................................................................................................................................................................................................................................

161

Influence of Green, ....................................................................................................................................................................................................................................................

167

Researches of Stokes on the relation of the direction of vibration of light to its plane of polarization, ....................................................................................................................................................................................................................................................

168

The hypothesis of aeolotropic inertia, ....................................................................................................................................................................................................................................................

171

Rotation of the plane of polarization of light by active bodies, ....................................................................................................................................................................................................................................................

173

MacCullagh's theory of natural rotatory power, ....................................................................................................................................................................................................................................................

175

MacCullagh's and Cauchy's theory of metallic retlexion, ....................................................................................................................................................................................................................................................

177

Extension of the elastic-solid theory to metals, ....................................................................................................................................................................................................................................................

179

Lord Rayleigh's objection, ....................................................................................................................................................................................................................................................

181

Cauchy's theory of dispersion, ....................................................................................................................................................................................................................................................

182

Boussinesq's elastic-solid theory, ....................................................................................................................................................................................................................................................

185

CHAPTER VI.

Faraday.

Discovery of induced currents: lines of magnetic force, ....................................................................................................................................................................................................................................................

189

Self-induction, ....................................................................................................................................................................................................................................................

193

Identity of frictional and voltaic electricity: Faraday's views on the nature of electricity, ....................................................................................................................................................................................................................................................

194

Electro-chemistry, ....................................................................................................................................................................................................................................................

197

Controversy between the adherents of the chemical and contact hypotheses, ....................................................................................................................................................................................................................................................

201

The properties of dielectrics, ....................................................................................................................................................................................................................................................

206

Theory of dielectric polarization : Faraday, W. Thomson, and Mosgotti, ....................................................................................................................................................................................................................................................

211

The connexion between magnetism and light, ....................................................................................................................................................................................................................................................

213

Airy's theory of magnetic rotatory polarization, ....................................................................................................................................................................................................................................................

214

Faraday's Thoughts on Ray-Vibrations, ....................................................................................................................................................................................................................................................

217

Researches of Faraday and Plücker on diamagnetism, ....................................................................................................................................................................................................................................................

218

 

CHAPTER VII.

The Mathematical Electricians of the Middle of the Nineteenth Century.

F. Neumann's theory of induced currents: the electrodynamic potential, ....................................................................................................................................................................................................................................................

222

W. Weber's theory of electrons, ....................................................................................................................................................................................................................................................

225

Riemann's law, ....................................................................................................................................................................................................................................................

231

Proposals to modify the law of gravitation, ....................................................................................................................................................................................................................................................

232

Weber's theory of paramagnetism and diamagnetism: later theories, ....................................................................................................................................................................................................................................................

234

Joule's law: energetics of the voltaic cell, ....................................................................................................................................................................................................................................................

239

Researches of Helmholtz on electrostatic and electrodynamic energy, ....................................................................................................................................................................................................................................................

242

W. Thomson distinguishes the circuital and irrotational magnetic vectors, ....................................................................................................................................................................................................................................................

244

His theory of magnecrystallic action, ....................................................................................................................................................................................................................................................

245

His formula for the energy of a magnetic field, ....................................................................................................................................................................................................................................................

247

Extension of this formula to the case of fields produced by currents, ....................................................................................................................................................................................................................................................

249

Kirchhoff identifies Ohm's electroscopic force with electrostatic potential, ....................................................................................................................................................................................................................................................

251

The discharge of a Leyden jar: W. Thomson's theory, ....................................................................................................................................................................................................................................................

253

The velocity of electricity and the propagation of telegraphic signals, ....................................................................................................................................................................................................................................................

254

Clausius' law of force between electric charges : crucial experiments, ....................................................................................................................................................................................................................................................

261

Nature of the current, ....................................................................................................................................................................................................................................................

263

The thermo-electric researches of Peltier and W. Thomson, ....................................................................................................................................................................................................................................................

264

CHAPTER VIII.

Maxwell.

Gauss and Riemann on the propagation of electric actions, ....................................................................................................................................................................................................................................................

268

Analogies suggested by W. Thomson, ....................................................................................................................................................................................................................................................

269

Maxwell's hydrodynamical analogy, ....................................................................................................................................................................................................................................................

271

The vector potential, ....................................................................................................................................................................................................................................................

273

Linear and rotatory interpretations of magnetism, ....................................................................................................................................................................................................................................................

274

Maxwell's mechanical model of the electromagnetic field, ....................................................................................................................................................................................................................................................

276

Electric displacement, ....................................................................................................................................................................................................................................................

279

Similarity of electric vibrations to those of light, ....................................................................................................................................................................................................................................................

281

Connexion of refractive index and specific inductive capacity, ....................................................................................................................................................................................................................................................

283

Maxwell's memoir of 1864, ....................................................................................................................................................................................................................................................

284

The propagation of electric disturbances in crystals and in metals, ....................................................................................................................................................................................................................................................

288

Anomalous dispersion, ....................................................................................................................................................................................................................................................

291

The Maxwell-Sellmeier theory of dispersion, ....................................................................................................................................................................................................................................................

292

Imperfections of the electromagnetic theory of light, ....................................................................................................................................................................................................................................................

295

The theory of L. Lorenz, ....................................................................................................................................................................................................................................................

297

Maxwell's theory of stress in the electric field, ....................................................................................................................................................................................................................................................

300

The pressure of radiation, ....................................................................................................................................................................................................................................................

303

Maxwell's theory of the magnetic rotation of light, ....................................................................................................................................................................................................................................................

307

 

CHAPTER IX.

Models of the Aether.

Analogies in which a rotatory character is attributed to magnetism, ....................................................................................................................................................................................................................................................

310

Models in which magnetic force is represented as a linear velocity, ....................................................................................................................................................................................................................................................

311

Researches of W. Thomson, Bjerknes, and Leahy, on pulsating and oscillating bodies, ....................................................................................................................................................................................................................................................

316

MacCullagh's quasi-elastic solid as a model of the electric medium, ....................................................................................................................................................................................................................................................

318

The Tall effect, ....................................................................................................................................................................................................................................................

320

Models of Riemann and FitzGerald, ....................................................................................................................................................................................................................................................

324

Vortex-atoms, ....................................................................................................................................................................................................................................................

326

The vortex-sponge theory of the aether: researches of W. Thomson, FitzGerald, and Hicks, ....................................................................................................................................................................................................................................................

327

 

CHAPTER X.

The Followers of Maxwell.

Helmholtz and H. A. Lorentz supply an electromagnetic theory of reflexion, ....................................................................................................................................................................................................................................................

337

Crucial experiments of Helmholtz and Schiller, ....................................................................................................................................................................................................................................................

338

Convection-currents: Rowland's experiments, ....................................................................................................................................................................................................................................................

339

The moving charged sphere: researches of J.J. Thomson, FitzGerald, and Heaviside, ....................................................................................................................................................................................................................................................

310

Conduction of rapidly-alternating currents, ....................................................................................................................................................................................................................................................

344

FitzGerald devises the magnetic radiator, ....................................................................................................................................................................................................................................................

345

Poynting's theorem, ....................................................................................................................................................................................................................................................

347

Poynting and J.J. Thomson develop the theory of moving lines of force, ....................................................................................................................................................................................................................................................

349

Mechanical momentum in the electromagnetic field, ....................................................................................................................................................................................................................................................

352

Now derivation of Maxwell's equations by Hertz, ....................................................................................................................................................................................................................................................

333

Hertz's assumptions and Weber's theory, ....................................................................................................................................................................................................................................................

356

Experiments of Hertz on electric waves, ....................................................................................................................................................................................................................................................

357

The memoirs of Hertz and Heaviside on fields in which material bodies are in motion, ....................................................................................................................................................................................................................................................

365

The current of dielectric convection, ....................................................................................................................................................................................................................................................

367

Kerr's magneto-optic phenomenon, ....................................................................................................................................................................................................................................................

368

Rowland's theory of magneto-optics, ....................................................................................................................................................................................................................................................

369

The rotation of the plane of polarization in naturally active bodies, ....................................................................................................................................................................................................................................................

370

 

CHAPTER XI.

Conduction in Solutions and Gases, from Faraday to J. J. Thomson.

The hypothesis of Williamson and Clausius, ....................................................................................................................................................................................................................................................

372

Migration of the ions, ....................................................................................................................................................................................................................................................

373

The researches of Hittorf and Kohlrausch, ....................................................................................................................................................................................................................................................

374

Polarization of electrodes, ....................................................................................................................................................................................................................................................

375

Electrocapillarity, ....................................................................................................................................................................................................................................................

376

Single differences of potential, ....................................................................................................................................................................................................................................................

379

Helmholtz' theory of concentration-cells, ....................................................................................................................................................................................................................................................

381

Arrhonius' hypothesis, ....................................................................................................................................................................................................................................................

383

The researches of Nernst, ....................................................................................................................................................................................................................................................

386

Earlier investigations of the discharge in rarefied gases, ....................................................................................................................................................................................................................................................

390

Faraday observes the dark space, ....................................................................................................................................................................................................................................................

391

Researches of Plücker, Hittorf, Goldstein, and Varley, on the cathode rays, ....................................................................................................................................................................................................................................................

393

Crookes and the fourth state of matter, ....................................................................................................................................................................................................................................................

394

Objections and alternatives to the charged-particle theory of cathode rays, ....................................................................................................................................................................................................................................................

395

Giese's and Schuster's ionic theory of conduction in gases, ....................................................................................................................................................................................................................................................

397

J.J. Thomson measures the velocity of cathode rays, ....................................................................................................................................................................................................................................................

400

Discovery of X-rays : hypotheses regarding them, ....................................................................................................................................................................................................................................................

401

Further researches of J.J. Thomson on cathode rays: the ratio m/e, ....................................................................................................................................................................................................................................................

404

Vitreous and resinous electricity, ....................................................................................................................................................................................................................................................

406

Determination of the ionic charge by J. J. Thomson, ....................................................................................................................................................................................................................................................

407

Becquerel's radiation: discovery of radio-active substances, ....................................................................................................................................................................................................................................................

408

 

CHAPTER XII.

The Theory of Aether and Electrons in the Closing Years of the Nineteenth Century.

Stokes' theory of aethereal motion near moving bodies, ....................................................................................................................................................................................................................................................

411

Astronomical phenomena in which the velocity of light is involved, ....................................................................................................................................................................................................................................................

413

Crucial experiments relating to the optics of moving bodies, ....................................................................................................................................................................................................................................................

416

Lorentz' theory of electrons, ....................................................................................................................................................................................................................................................

419

The current of dielectric convection: Röntgon's experiment, ....................................................................................................................................................................................................................................................

426

The electronic theory of dispersion, ....................................................................................................................................................................................................................................................

428

Deduction of Fresnel's formula fron the theory of electrons, ....................................................................................................................................................................................................................................................

430

Experimental verification of Lorentz' hypothesis, ....................................................................................................................................................................................................................................................

431

FitzGerald's explanation of Michelson's experiment, ....................................................................................................................................................................................................................................................

432

Lorentz treatise of 1895, ....................................................................................................................................................................................................................................................

433

Expression of the potentials in terms of the electronic charges, ....................................................................................................................................................................................................................................................

436

Further experiments on the relative motion of earth and aether, ....................................................................................................................................................................................................................................................

437

Extension of Lorentz transformation : Larmor discovers its connexion with FitzGerald's hypothesis of contraction, ....................................................................................................................................................................................................................................................

440

Examination of the supposed primacy of the original variables: fixity relative to the aether: the principle of relativity, ....................................................................................................................................................................................................................................................

444

The phenomenon of Zeeman, ....................................................................................................................................................................................................................................................

449

Connexion of Zeeman's effect with the magnetic rotation of light ....................................................................................................................................................................................................................................................

452

The optical properties of metals, ....................................................................................................................................................................................................................................................

454

The electronic theory of metals, ....................................................................................................................................................................................................................................................

456

Thermionics, ....................................................................................................................................................................................................................................................

464

 

Index, ....................................................................................................................................................................................................................................................

470

Memorandum on Notation

Vectors are denoted by letters in clarendon type, as E.

The three components of a vector E are denoted by E_x, E_y, E_z, and the magnitude of the vector is denoted by E, so that

$E^{2}=E_{x}^{2}+E_{y}^{2}+E_{z}^{2}$

The vector product of two vectors E and H, which is denoted by [E.H], is the vector whose components are (E_yH_z - E_zH_y, E_zH_x - E_xH_z, E_xH_y - E_yH_x). Its direction is at right angles to the direction of E and H, its magnitude is represented by twice the area of the triangle formed by them.

The scalar product of two vectors E and H is E_xH_x + E_yH_y + E_zH_z. It is denoted by (E.H).

The quantity ${\frac {\partial E_{x}}{\partial x}}+{\frac {\partial E_{y}}{\partial y}}+{\frac {\partial E_{z}}{\partial z}}$ is denoted by div E.

The vector whose components are

$\left({\frac {\partial E_{z}}{\partial y}}-{\frac {\partial E_{y}}{\partial z}},{\frac {\partial E_{x}}{\partial y}}-{\frac {\partial E_{z}}{\partial x}},{\frac {\partial E_{y}}{\partial x}}-{\frac {\partial E_{x}}{\partial z}}\right)$

is denoted by curl E.

If V denote a scalar quantity, the vector whose components are $\left(-{\frac {\partial V}{\partial x}},-{\frac {\partial V}{\partial y}},-{\frac {\partial V}{\partial z}}\right)$ is denoted by grad V.

The symbol ∇ is used to denote the vector operator whose components are ${\frac {\partial }{\partial x}}$, ${\frac {\partial }{\partial x}}$, ${\frac {\partial }{\partial x}}$.

Differentiation with respect to the time is frequently indicated by a dot placed over the symbol of the variable which is differentiated.