# Index:A Treatise on Electricity and Magnetism - Volume 2.djvu

Part III. Magnetism. Chapter I. Elementary Theory of Magnetism.
|- |391. Expansion of the potential of a magnet in spherical harmonics|| align="right"|16 |- |392. The centre of a magnet and the primary and secondary axes through the centre|| align="right"|17 |- |393. The north end of a magnet in this treatise is that which points north, and the south end that which points south. Boreal magnetism is that which is supposed to exist near the north pole of the earth and the south end of a magnet. Austral magnetism is that which belongs to the south pole of the earth and the north end of a magnet. Austral magnetism is considered positive|| align="right"|19 |- |394. The direction of magnetic force is that in which austral magnetism tends to move, that is, from south to north, and this is the positive direction of magnetic lines of force. A magnet is said to be magnetized from its south end towards its north end|| align="right"|19 |} Chapter II. magnetic force and magnetic induction.
Chapter III. particular forms of magnets. Part III. Magnetism. Chapter I. Elementary Theory of Magnetism.
xiv CONTENTS. Art. Page 580. Electromagnetic force 208 581. Case of two circuits 208 582. Theory of induced currents 209 583. Mechanical action between the circuits 210 584. All the phenomena of the mutual action of two circuits depend on a single quantity, the potential of the two circuits .. .. 210 ��CHAPTER VIII. EXPLOEATION OF THE FIELD BY MEANS OF THE SECONDARY CIRCUIT. 585. The electrokinetic momentum of the secondary circuit .. .. 211 586. Expressed as a line-integral 211 587. Any system of contiguous circuits is equivalent to the circuit formed by their exterior boundary 212 588. Electrokinetic momentum expressed as a surface-integral .. .212 589. A crooked portion of a circuit equivalent to a straight portion 213 590. Electrokinetic momentum at a point expressed as a vector, $1 .. 214 591. Its relation to the magnetic induction, 33. Equations (A) .. 214 592. Justification of these names 215 593. Conventions with respect to the signs of translations and rota tions 216 594. Theory of a sliding piece 217 595. Electromotive force due to the motion of a conductor .. .. 218 596. Electromagnetic force on the sliding piece ..218 597. Four definitions of a line of magnetic induction 219 598. General equations of electromotive force, (B) 219 599. Analysis of the electromotive force 222 600. The general equations referred to moving axes 223 601. The motion of the axes changes nothing but the apparent value of the electric potential 224 602. Electromagnetic force on a conductor 224 603. Electromagnetic force on an element of a conducting body. Equations (C) 226 CHAPTER IX. GENERAL EQUATIONS. 604. Recapitulation 227 605. Equations of magnetization, (D) 228 606. Relation between magnetic force and electric currents .. .. 229 607. Equations of electric currents, (E) 230 608. Equations of electric displacement, (F) 232 �� � CONTENTS. xv Art - Page 609. Equations of electric conductivity, (G) 232 610. Equations of total currents, (H) 232 611. Currents in terms of electromotive force, (I) .. .. .. .. 233 612. Volume-density of free electricity, (J) 233 613. Surface-density of free electricity, (K) 233 614. Equations of magnetic permeability, (L) 233 615. Ampere s theory of magnets 234 616. Electric currents in terms of electrokinetic momentum .. .. 234 617. Vector-potential of electric currents 236 618. Quaternion expressions for electromagnetic quantities .. .. 236 619. Quaternion equations of the electromagnetic field 237 CHAPTER X. DIMENSIONS OF ELECTRIC UNITS. 620. Two systems of units .. .. 239 621. The twelve primary quantities 239 622. Fifteen relations among these quantities 240 623. Dimensions in terms of [e] and [m] 241 624. Reciprocal properties of the two systems 241 625. The electrostatic and the electromagnetic systems 241 626. Dimensions of the 12 quantities in the two systems .. .. 242 627. The six derived units 243 628. The ratio of the corresponding units in the two systems .. 243 629. Practical system of electric units. Table of practical units .. 244 CHAPTER XL ENERGY AND STRESS. 630. The electrostatic energy expressed in terms of the free electri city and the potential 246 631. The electrostatic energy expressed in terms of the electromotive force and the electric displacement 246 632. Magnetic energy in terms of magnetization and magnetic force 247 633. Magnetic energy in terms of the square of the magnetic force .. 247 634. Electrokinetic energy in terms of electric momentum and electric current 248 635. Electrokinetic energy in terms of magnetic induction and mag netic force 248 636. Method of this treatise 249 637. Magnetic energy and electrokinetic energy compared .. .. 249 638. Magnetic energy reduced to electrokinetic energy 250 �� � xvi CONTENTS. Art. Page 639. The force acting on a particle of a substance due to its magnet ization 251 640. Electromagnetic force due to an electric current passing through it 252 641. Explanation of these forces by the hypothesis of stress in a medium 253 642. General character of the stress required to produce the pheno mena 255 643. "When there is no magnetization the stress is a tension in the direction of the lines of magnetic force, combined with a pressure in all directions at right angles to these lines, the magnitude of the tension and pressure being ^ 2 , where <> oTf is the magnetic force 256 644. Force acting on a conductor carrying a current 257 645. Theory of stress in a medium as stated by Faraday .. .. 257 646. Numerical value of magnetic tension 258 CHAPTER XII. CURKENT-SHEETS. 647. Definition of a current-sheet 259 648. Current-function 259 649. Electric potential ,. .. 260 650. Theory of steady currents , 260 651. Case of uniform conductivity 260 652. Magnetic action of a current-sheet with closed currents .. .. 261 653. Magnetic potential due to a current-sheet 262 654. Induction of currents in a sheet of infinite conductivity .. .. 262 655. Such a sheet is impervious to magnetic action 263 656. Theory of a plane current-sheet 263 657. The magnetic functions expressed as derivatives of a single function 264 658. Action of a variable magnetic system on the sheet 266 659. When there is no external action the currents decay, and their magnetic action diminishes as if the sheet had moved off with constant velocity R 267 660. The currents, excited by the instantaneous introduction of a magnetic system, produce an effect equivalent to an image of that system 267 661. This image moves away from its original position with velo city R 268 662. Trail of images formed by a magnetic system in continuous motion . 268 �� � CONTENTS. xvii Art. Page 663. Mathematical expression for the effect of the induced currents 269 664. Case of the uniform motion of a magnetic pole .. ., .. 269 665. Value of the force acting on the magnetic pole r . .. ,. 270 666. Case of curvilinear motion 271 667. Case of motion near the edge of the sheet 271 668. Theory of Arago s rotating disk 271 669. Trail of images in the form of a helix 274 670. Spherical current-sheets 275 671. The vector- potential 276 672. To produce a field of constant magnetic force within a spherical shell 277 673. To produce a constant force on a suspended coil 278 674. Currents parallel to a plane 278 675. A plane electric circuit. A spherical shell. An ellipsoidal shell .. 279 676. A solenoid 280 677. A long solenoid 281 678. Force near the ends 282 679. A pair of induction coils 282 680. Proper thickness of wire 283 G81. An endless solenoid .. .. .. .. 284 CHAPTER XIII. PARALLEL CURRENTS. 682. Cylindrical conductors .".."<. .. 286 683. The external magnetic action of a cylindric wire depends only on the whole current through it .. 287 684. The vector-potential ^ .. .. .1 288 685. Kinetic energy of the current .. .. .. ... ... ... .. 288 686. Repulsion between the direct and the return current .. 289 687. Tension of the wires. Ampere s experiment 289 688. Self-induction of a wire doubled on itself 290 689. Currents of varying intensity in a cylindric wire 291 690. Relation between the electromotive force and the total current 292 691. Geometrical mean distance of two figures in a plane .. .. 294 692. Particular cases 294 693. Application of the method to a coil of insulated wires .. .. 296 CHAPTER XIV. CIRCULAR CURRENTS. 694. Potential due to a spherical bowl *. 299 695. Solid angle subtended by a circle at any point 301 VOL. II. b �� � xviii CONTENTS. Art. Page 696. Potential energy of two circular currents .. 302 697. Moment of the couple acting between two coils 303 698. Values of Q? 303 699. Attraction between two parallel circular currents 304 700. Calculation of the coefficients for a coil of finite section .. .. 304 701. Potential of two parallel circles expressed by elliptic integrals 305 702. Lines of force round a circular current. Fig. XVIII .. .. 307 703. Differential equation of the potential of two circles 307 704. Approximation when the circles are very near one another .. 309 705. Further approximation 310 706. Coil of maximum self-induction . 311 ��CHAPTER XV. ELECTROMAGNETIC INSTRUMENTS. 707. Standard galvanometers and sensitive galvanometers .. .. 313 708. Construction of a standard coil 314 709. Mathematical theory of the galvanometer 315 710. Principle of the tangent galvanometer and the sine galvano meter 316 711. Galvanometer with a single coil 316 712. Gaugain s eccentric suspension 317 713. Helmholtz s double coil. Fig. XIX 318 714. Galvanometer with four coils 319 715. Galvanometer with three coils 319 716. Proper thickness of the wire of a galvanometer 321 717. Sensitive galvanometers 322 718. Theory of the galvanometer of greatest sensibility 322 719. Law of thickness of the wire .. .. 323 720. Galvanometer with wire of uniform thickness 325 721. Suspended coils. Mode of suspension 326 722. Thomson s sensitive coil 326 723. Determination of magnetic force by means of suspended coil and tangent galvanometer ..327 724. Thomson s suspended coil and galvanometer combined .. .. 328 725. Weber s electrodynamometer 328 726. Joule s current-weigher 332 727. Suction of solenoids 333 728. Uniform force normal to suspended coil 333 729. Electrodynamometer with torsion-arm 334 �� � CONTEXTS. xix CHAPTER XVI. ELECTROMAGNETIC OBSERVATIONS. Art. Page 730. Observation of vibrations 335 731. Motion in a logarithmic spiral 336 732. Rectilinear oscillations in a resisting medium 337 733. Values of successive elongations .. ... 338 734. Data and qusesita 338 735. Position of equilibrium determined from three successive elon gations 338 736. Determination of the logarithmic decrement 339 737. When to stop the experiment - .* .. .. 339 738. Determination of the time of vibration from three transits .. 339 739. Two series of observations .. .. 340 740. Correction for amplitude and for damping .. .. .. ..341 741. Dead beat galvanometer .. .. .. .. .* ... .. .. 341 742. To measure a constant current with the galvanometer .. .. 342 743. Best angle of deflexion of a tangent galvanometer 343 744. Best method of introducing the current .. .. 343 745. Measurement of a current by the first elongation 344 746. To make a series of observations on a constant current .. .. 345 747. Method of multiplication for feeble currents 345 748. Measurement of a transient current by first elongation .. .. 346 749. Correction for damping .. * .. .. 347 750. Series of observations. Zurilckwerfungs methode 348 751. Method of multiplication ? . .. .. 350 CHAPTER XVII. ELECTRICAL MEASUREMENT OF COEFFICIENTS OF INDUCTION. 752. Electrical measurement sometimes more accurate than direct measurement 352 753. Determination of G l .. ..- 353 754. Determination of g l 354 755. Determination of the mutual induction of two coils .. .. 354 756. Determination of the self-induction of a coil 356 757. Comparison of the self-induction of two coils 357 CHAPTER XVIII. DETERMINATION OF RESISTANCE IN ELECTROMAGNETIC MEASURE. 758. Definition of resistance ~ 358 759. Kirchhoff s method 358 �� � xx CONTENTS. Art. Pa * e 760. Weber s method by transient currents .......... 360 761. His method of observation .............. 361 762. Weber s method by damping .............. 361 763. Thomson s method by a revolving coil .......... 364 764. Mathematical theory of the revolving coil ..- ...... 364 765. Calculation of the resistance .......... 365 766. Corrections .................... 366 767. Joule s calorimetric method .............. 367 ��CHAPTER XIX. COMPARISON OF ELECTROSTATIC WITH ELECTROMAGNETIC UNITS. 768. Nature and importance of the investigation ........ 368 769. The ratio of the units is a velocity ............ 369 770. Current by convection ................ 370 771. Weber and Kohlrausch s method ............ 370 772. Thomson s method by separate electrometer and electrodyna- mometer ...................... 372 773. Maxwell s method by combined electrometer and electrodyna- mometer ...................... 372 774. Electromagnetic measurement of the capacity of a condenser. Jenkin s method .................. 373 775. Method by an intermittent current ............ 374 776. Condenser and "Wippe as an arm of Wheatstone s bridge .. 375 777. Correction when the action is too rapid .......... 376 778. Capacity of a condenser compared with the self-induction of a coil ........................ 377 779. Coil and condenser combined .............. 379 780. Electrostatic measure of resistance compared with its electro magnetic measure .................. 382 CHAPTER XX. ELECTROMAGNETIC THEORY OF LIGHT. 781. Comparison of the properties of the electromagnetic medium with those of the medium in the undulatory theory of light 383 782. Energy of light during its propagation .......... 384 783. Equation of propagation of an electromagnetic disturbance .. 384 784. Solution when the medium is a non-conductor ...... 386 785. Characteristics of wave-propagation ............ 386 786. Velocity of propagation of electromagnetic disturbances .. .. 387 787. Comparison of this velocity with that of light ........ 387 �� � CONTENTS. xxi Art. Page 788. The specific inductive capacity of a dielectric is the square of its index of refraction ..... .. 388 789. Comparison of these quantities in the case of paraffin .. .. 388 790. Theory of plane waves 389 791. The electric displacement and the magnetic disturbance are in the plane* of the wave-front, and perpendicular to each other 390 792. Energy and stress during radiation 391 793. Pressure exerted by light .. .... ..391 794. Equations of motion in a crystallized medium .. .. .. 392 795. Propagation of plane waves 393 796. Only two waves are propagated 393 797. The theory agrees with that of Fresnel .. .. 394 798. Relation between electric conductivity and opacity .. .. 394 799. Comparison with facts 395 800. Transparent metals 395 801. Solution of the equations when the medium is a conductor .. 395 802. Case of an infinite medium, the initial state being given .. 396 803. Characteristics of diffusion 397 804. Disturbance of the electromagnetic field when a current begins to flow .. .. .. ,. .. 397 805. Rapid approximation to an ultimate state 398 ��CHAPTER XXI. MAGNETIC ACTION ON LIGHT. 806. Possible forms of the relation between magnetism and light .. 399 807. The rotation of the plane of polarization by magnetic action .. 400 808. The laws of the phenomena 400 809. Yerdet s discovery of negative rotation in ferromagnetic media 400 810. Rotation produced by quartz, turpentine, &c., independently of magnetism 401 811. Kinematical analysis of the phenomena 402 812. The velocity of a circularly-polarized ray is different according to its direction of rotation 402 813. Right and left-handed rays 403 814. In media which of themselves have the rotatory property the velocity is different for right and left-handed configurations 403 815. In media acted on by magnetism the velocity is different for opposite directions of rotation 404 816. The luminiferous disturbance, mathematically considered, is a vector 404 817. Kinematic equations of circularly-polarized light .. .. .. 405 �� � xxii CONTENTS. Art. Page 818. Kinetic and potential energy of the medium 406 819. Condition of wave-propagation 406 820. The action of magnetism must depend on a real rotation about the direction of the magnetic force as an axis 407 821. Statement of the results of the analysis of the phenomenon .. 407 822. Hypothesis of molecular vortices 408 823. Variation of the vortices according to Helmholtz s law .. .. 409 824. Variation of the kinetic energy in the disturbed medium .. 409 825. Expression in terms of the current and the velocity .. .. 410 826. The kinetic energy in the case of plane waves 410 827. The equations of motion 411 828. Velocity of a circularly -polarized ray 411 829. The magnetic rotation 412 830. Researches of Verdet 413 831. Note on a mechanical theory of molecular vortices 415 CHAPTER XXII. ELECTRIC THEOKY OF MAGNETISM. 832. Magnetism is a phenomenon of molecules 418 833. The phenomena of magnetic molecules may be imitated by electric currents 419 834. Difference between the elementary theory of continuous magnets and the theory of molecular currents 419 835. Simplicity of the electric theory 420 836. Theory of a current in a perfectly conducting circuit .. .. 420 837. Case in which the current is entirely due to induction .. .. 421 838. Weber s theory of diamagnetism 421 839. Magnecrystallic induction 422 840. Theory of a perfect conductor 422 841. A medium containing perfectly conducting spherical molecules 423 842. Mechanical action of magnetic force on the current which it excites 423 843. Theory of a molecule with a primitive current 424 844. Modifications of Weber s theory 425 845. Consequences of the theory 425 CHAPTER XXIII. THEORIES OF ACTION AT A DISTANCE. 846. Quantities which enter into Ampere s formula 426 847. Relative motion of two electric particles 426 �� � CONTENTS. xxiii ��Art. 848. Relative motion of four electric particles. Fechner s theory .. 427 849. Two new forms of Ampere s formula 428 850. Two different expressions for the force between two electric particles in motion 428 851. These are due to Gauss and to Weber respectively 429 852. All forces must be consistent with the principle of the con servation of energy 429 853. Weber s formula is consistent with this principle but that of Gauss is not 429 854. Helmholtz s deductions from Weber s formula 430 855. Potential of two currents 431 856. Weber s theory of the induction of electric currents .. ..431 857. Segregating force in a conductor 432 858. Case of moving conductors 433 859. The formula of Gauss leads to an erroneous result 434 860. That of Weber agrees with the phenomena 434 861. Letter of Gauss to Weber 435 862. Theory of Riemann 435 863. Theory of C. Neumann 435 864. Theory of Betti 436 865. Repugnance to the idea of a medium 437 866. The idea of a medium cannot be got rid of 437 �� � |