,-^^-' ELECTROMAGNETIC THEORY BY OLIVER HEAVISIDE VOLUME III. LONDON: THE ELECTRICIAN" PRINTING AND PUBLISHING COMPANY, LIMITED, Salisbury Court, JB'lkkt stkkkt, E C. [All Bights Fully Reserved.} ÆTHERFORCE Printed and Psblished by THK EI.ECTUICIAN" PRINTING AND PUBLISHING CO. 1,2 and 3, Salisbury Court, Fleet Street, London, E.G. ÆTHERFORCE PREFACE TO VOL. III. Long ago I had the intention, if circumstances were favour- able, of finishing the third vohinie of this work about 1904, and the fourth about 1910. But circumstances have not been favourable. That is all that need be said about it here, save to add that I have excluded parts of the third volume, and included parts of the fourth. It would be as wrong to love your enemies as to hate your friends. Nevertheless, '' the way of life is wonderful ; it is by renunciation." Especially when prodding is no longer neces- sary. If my life is spared, I hope to be able to present a bust of the eminent electrician who invented everything worth mentioning to the Institution over which he once ruled, to be placed under that of Faraday. Oliver Heaviside. August 23, 1912. ÆTHERFORCE IN MEMORY OF George Francis FitzGerald, f.r.s. " We, needs must love the highest when we " knoiv him. ÆTHERFORCE CONTENTS OF VOLUME III. [The dates within brackets are the dates of first 'publication, or of printing. All up to p. 158 was published in " The Electrician " ; the rest of the articles in the Jouriials indicated ; but if only printed at the dates given, they are now first published, 1912.] CHAPTER IX. WAVES FROM MOVING SOURCES. (Pages 1 to 130.) SECTION PAGE 450 [Feb. 23, 1900.] Adagio. Andante. Allegro moderato 1 451 [Feb. 23, 1900.] Simple Proof of Fundamental Property of a Plane Wave 3 452 [Feb. 23, 1900.] The General Plane Wave 4 453 [Feb. 23, 1900.] Generation of Waves by a Plane Source of Induction 6 454 [Feb. 23, 1900.] Generation of Waves by a Plane Source of Displacement 8 455 [Feb. 23, 1900.] Comparison of Electromagnetic with Aerial Waves 9 456 [March 23, 1900.] Waves ending perpendicularly upon a Conductor. Conduction and Convection 10 457 [March 23, 1900.] Oblique Reflection at a Conducting Surface with H tangential. Transformation to a Convection Problem 13 458 [March 23, 1900.] Generation of a Pair of Inclined Plane Waves by Motion of an Electrified Strip, n > v. The applied force required 15 459 [March 23, 1900.] Generation of a Pair of Inclined Plane Waves by a Moving Source of Induction, when u->v 18 400 [April 20, 1900.] Two ways of Dividing a Pair of Crossing Pure Plane Waves to make Convection Problems, u>v 18 461 [April 20, 1900.] Slanting Plane Waves generated by a Moving Magnet, and by an Electrified Strip moving normally to its Plane 20 462 [April 20, 1900.] Generation of a Single Plane Wave by Motion of an Electrified Electret. Also of Two separated Plane Waves 23 ÆTHERFORCE VI. CONTENTS. SECTION PAGE 463 [June 8, 1900.] Theory of the Steady Rectilinear Motion of a Point-Charge or " Electron " through the Ether when u<^v and when u>-v 25 464 [June 8, 1900.] Construction of the Slanting Plane Waves generated by an Electrified Line by means of the Potential of an Electron 28 465 [June 8, 1900.] The steady Rectilinear Motion in its own Line of a Terminated Electrified Line when n > v, and interpretation of the Impure Conical Wave following an Electron 30 466 [July 13, 1900.] The Wave from a Straight Line Source of Induction in a Non-conducting Dielectric 33 467 [July 13, 1900.] The Wave from a Straight Line Source of Induction in a Conductor 37 468 [July 13, 1900.] The Waves due to a Ci rowing Plane Sheet of Sources of Induction, and to Travelling Filaments, at any Speed 39 460 [Aug. 17, 1900.] Reversion to Divergent Plane Waves. Is the Ether Fixed ? 43 470 [Aug. 17, 1900.] Drag of Matter upon Ether. Modified Cir- cuital Equations, and the Wave -speed resulting 44 471 [Aug. 17, 1900.] C<imparison of Wave-speeds in Special Cases 46 472 [Aug. 17, 1900.] Effect of Modified Circuital Equations on Electrical Distributions 50 473 [Oct. 5, 1900.] Lorentz's Equations of a Moving Dielectric 52 474 [Oct. 5, 1900.] The Wave-speed according to Lore ntz 55 475 [Oct. 5, 1900.] Possible Equations for a Moving Magnetised Substance 57 476 [Oct. 5, 1900.] Larmor's Equations for a Moving Body 59 477 [Nov. 2, 1900.] Theory of Moving Electrified Cones ; u>v. The Moving Force upon them and upon an Electrified Line 61 478 [Nor. 2, 1900.] Theory of an Electrified Line of Finite Length moving Transversely, u> v 65 479 [Nov. 30, 1900.] Motion of Electrified Hyperboloids, u >v 69 480 [Nov. 30, 1900.] Growing Plane Source of Induction. Transition from u>v to u <v 72 481 [Nov. 30, 1900.] The Waves from a Plane Strip Source of Induction suddenly stai'ted 76 482 [Jan. IS, 1901.] Impressed Current along a Straight Axis. The Operational Solution in General 78 483 [Jan. 18, 1901.] Algebrisation of the Operational Solution in the case of Steady Motion of an Electron or of an Electrified Line, u>v 81 ÆTHERFORCE CONTENTS. Vn. SECTION PAGE 484 {Jan. 18, 1901.] Application of Simply Periodic Analysis. The Transition from w < to «> ?; 84 485 [March 29, 1901.] Train of Simply Periodic Forced Waves along an Axis. The Work done and Waste of Energy 86 486 [March 29, 1901.] Construction of the Simply Periodic Wave Train from the Two Electronic Steady Solutions 90 487 [March, 29, 1901.] Connection between Moving Electrifica- tion and Moving Electrisation. Transition from Cylindrical to Conical Wave 92 488 [May 10, 1901.] Spherical Impulsive Wave due to Sudden Displacement of an Electron 95 489 [May 10, 1901.] Splierical Impidse due to Sudden Change of Velocity of an Electron. Rontgen Rays 98 490 [May 10, 1901.] Wave Train due to Damped Vibrations 100 491 [May 10, 1901.] Investigation of the Electromagnetic Field due to an Impressed Electric Current growing in a Si raight Lin^. The Solutions in Sphere and Cone 102 492 [Aug. 9, 1901.] The Elhpsoidal and Conical Equipotential Surfaces 105 493 [Aiig. 9, 1901.] The Magnetic Force and Electric Current in the Cone and Sphere. The Spherical Current Sheet 107 494 [Aug. 9, 1901.] The Manner of Continuity of the Electric Current HO 495 [Aug. 9, 1901.] The Electric Force, and Time Integral of Magnetic Force 112 496 [Oct. 11, 1901.] The Distribution of Displacement 114 497 [Oct. 11, 1901.] Solutions for an Electron Jerked Away from a Stationary Compensating Charge. The Spherical Pulse 117 498 [Oct. 11, 1901.] Solutions for a Jerked Electron Without Compensating Charge 120 499 {Nov. 29, 1901.] Comparison of Two Cases of Motion of Electrification at the Speed of Light 122 500 {Nov. 29, 1901.] Peculiarities at the Speed of Light 125 501 [Nor. 29, 1901.] The Energy Wasted in the Spherical Pulse from a Jerked Electron, and the Energy left behind . . . 127 502 [Nov, 29, 1901.] The Potential of a Charged Spheroid mov- ing along its Axis 129 APPENDIX J. [April 4, 1902.] Note on the Size and Inertia of Electrons 131 APPENDIX K. [March 21, 1902.] Vector Analysis 136 ÆTHERFORCE Vm. (JONTENTS. CHAPTER X. WAVES IN THE ETHER. (Pages 144 to 519.) SECTION PAGE 503 [Feb. 14, 1902.] Matter, Electricity, Ether and the Pressure of Radiation 144 504 [Feb. 14, 1902.] The Moving Force Acting on a Deformable Ether 146 505 [Feb. 14, 1902.] How to have Constant Speed through Space of Phme Radiation Traversing a Moving Compressible Ether 149 506 [June 6, 1902.] Connection Between the Compressed Elec- tromagnetic Wave and Rankine's Wave of Compression 152 507 [Jutie 6, 1902.] Theory of the Rankinian Wave of Compression 154 508 [Jnne 6, 1902.] Crossing of Two Waves. Riemann's Solution 155 509 [June 6, 1902.] Modification of the Rankinian to make a C-ompressed MaxweUian Wave 156 510 [Natxre, Oct. 30, 1902.] Tlie Waste of Energy from a Moving Electron 158 511 [N'ature, Jan. 1, 1903.] S(tund Waves and Electromagnetics. The Pan-potential 164 512 [Nature, Jan. 2S, 1904.] The Radiation from an Electron describing a Circular Orbit 1 69 513 [Nature, Feb. 11, 1904.] The Radiation from an Electron moving in an Elliptic, or any other Orbit 173 514 [Nature, Jan. 29, 1903.] The Principle of I^ast Action. Li grange's Equations 175 515 [Nature, Feb. 19, 1903.] The Principle of Activity and Lagrange's Equations. Rotation of a Rigid Body 178 516 [Nature, May 21, 1903.] The Undistorted Cylindrical Wave 180 517 [Nature, May 2S, 1903.] Extension of Kelvin's Therm - electric Theory 183 518 [Nature, March 9, 1905.] The Pressure of Radiation 186 519 [Nature, April 27, 1905.] Electromagnetics in a Moving Dielectric 190 520 [Electrician, Dec. 23, 1904.] The Charging of a Cable through a Condenser and Resistance 194 521 [1905.] Other Critical Cases. Mathematical Excursion 205 522 [1905 Ji The Curbing Effect of an Inductance Shunt 209 523 [Nature, Aug. 31, 1905.] The Transverse Momentum of an Electron 211 524 [1905.] Extension to Helixal Motion 213 525 [1906.] Deep water Waves 214 526 [1906.] The Solution of Definite Integrals by Differential Transformation 234 ÆTHERFORCE CONTENTS. IX. SECTION FAGE 527 [1907.] Given the Effect, Find the Cause. The Inversion of Operations 291 528 [Ency. Brit., 10th Ed., June, 1902.] Theory of Electric Telegraphy 331 520 [1907.] Some Plane and Cylindrical Waves 34(3 530 [1907.] Piano Waves in a Dielectric Loaded in a Certain Way 383 531 [1908.] The Generation of Spherical Pulses in an Elastic Solid 388 532 [1909.] Plane Waves in Moving Mediums. The Energy and Forces 401 533 [1909.] The Electromagnetic Circuital Equations and Con- nected Matter 422 534 [1910, 1911.] Theory of an Electric Charge in Variable Motion 432 535 [1911.] Slanting Motion of Electrified Straight Line 498 536 [Nature, Apr. 19, 1906.] The Magnetic Inertia of a Charged Conductor in a Field of Force 502 537 [Electrician, Sept., 1897.] Boltzmann's Interpretation of Maxwell 503 538 [Nature, April 6, 1893.] Vectors versus Quaternions 507 539 [Nature, Jan. 11, 1894.] Quaternionic Innovations , 510 540 [Nature, Oct. 4, 1900.] The Teaching of Mathematics 513 541 [Perry's book; 1901.] The Teaching of Mathematics 515 542 [1912.] The Pan-potential as a Surface Integral 517 543 [1912.] Scientific Limitations on Human Knowledge 518 ÆTHERFORCE ÆTHERFORCE [...]... the strip, - < "1 -> -> Q P -* -> "t -^ D 1 ~ -^ J '- * Fig 6 Fig 5 Fig 4 since* the electrification cannot leave the sheet, a generated, beginning the It is cylindrical, having moment its new wave simplify matters, is the wave reaches the edge axis at the edge It, together with the plane wave, form the complete new state of D is too complicated for present discussion To -> "*'D o - -> "t" ~ 1 - But right... makes ^ = 2T' - E= |- = ±.^H between the plane of The same must be under- g and the two wave fronts Fig stood H E 2 will do for this case, only for two waves Otherwise stated, H = J/i on the and - \h on the left whilst H - A = - JA on both The work is done by h only where there is magnetic in the right side sides (3) ; current If the impressed force in the slab is sented is e, the problem repre- that of... force per unit volume What it generates is momentum ÆTHE ORCE RF 10 ELECTROMAGNETIC THEORY CH IX, then what G generates is matter in another a source, real or effective, of condensation Comparing with the corresponding equations for electromagnetic plane waves, viz., And G = pg^ if form, ; is it where / is the measure of the curl of e, and - g that of h, we may conclude that u= ±vsi3 the relation corresponding... of people, if yet other people do not like it So, if ; ; : ; electromagnetics, in spite of the abstract nature of the theory, involving quantities whose nature real is entirely unknown at and truly founded upon the observation of Newtonian forces, electric and magnetic respectively I present, VOL is m really B ÆTHE ORCE RF ELECTROMAGNETIC THEORY 2 CH IX cannot appreciate much the objection that they... ÆTHE ORCE RF ELECTROMAGNETIC THEORY 26 CH IX, to be underntood that the electric force is derived potential in the eolotropic manner specified from thfe by E =-( iVi+3V2 + ' . Ed., June, 1902.] Theory of Electric Telegraphy 33 1 520 [1907.] Some Plane and Cylindrical Waves 34 (3 530 [1907.] Piano Waves in a Dielectric Loaded in a Certain Way 38 3 531 [1908.] The Generation of Spherical Pulses in an Elastic Solid 38 8 532 [1909.] Plane. ,-^ ^-& apos; ELECTROMAGNETIC THEORY BY OLIVER HEAVISIDE VOLUME III. LONDON: THE ELECTRICIAN" PRINTING AND PUBLISHING COMPANY, LIMITED, Salisbury Court, JB'lkkt stkkkt, E. Elastic Solid 38 8 532 [1909.] Plane Waves in Moving Mediums. The Energy and Forces 401 533 [1909.] The Electromagnetic Circuital Equations and Con- nected Matter 422 534 [1910, 1911.] Theory of an Electric Charge in Variable Motion 432 535 [1911.] Slanting Motion