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

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A Treatise on Electricity and Magnetism - Volume 2.djvu

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Part III.

Magnetism.

Chapter I.

Elementary Theory of Magnetism.

Art. Page
371. Properties of a magnet when acted on by the earth 1
372. Definition of the axis of the magnet and of the direction of magnetic force 1
373. Action of magnets on one another. Law of magnetic force 2
374. Definition of magnetic units and their dimensions 3
375. Nature of the evidence for the law of magnetic force 4
376. Magnetism as a mathematical quantity 4
377. The quantities of the opposite kinds of magnetism in a magnet are always exactly equal 4
378. Effects of breaking a magnet 5
379. A magnet is built up of particles each of which is a magnet 5
380. Theory of magnetic 'matter' 5
381. Magnetization is of the nature of a vector 7
382. Meaning of the term 'Magnetic Polarization' 8
383. Properties of a magnetic particle 8
384. Definitions of Magnetic Moment, Intensity of Magnetization, and Components of Magnetization 8
385. Potential of a magnetized element of volume 9
386. Potential of a magnet of finite size. Two expressions for this potential, corresponding respectively to the theory of polarization, and to that of magnetic 'matter' 9
387. Investigation of the action of one magnetic particle on another 10
388. Particular cases 12
389. Potential energy of a magnet in any field of force 14
390. On the magnetic moment and axis of a magnet 15
391. Expansion of the potential of a magnet in spherical harmonics 16
392. The centre of a magnet and the primary and secondary axes through the centre 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 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 19

Chapter II.

magnetic force and magnetic induction.

Art. Page
395. Magnetic force defined with reference to the magnetic potential 21
396. Magnetic force in a cylindric cavity in a magnet uniformly magnetized parallel to the axis of the cylinder 22
397. Application to any magnet 22
398. An elongated cylinder. Magnetic force 23
399. A thin disk. Magnetic induction 23
400. Relation between magnetic force, magnetic induction, and magnetization 24
401. Line-integral of magnetic force, or magnetic potential 24
402. Surface-integral of magnetic induction 25
403. Solenoidal distribution of magnetic induction 25
404. Surfaces and tubes of magnetic induction 27
405. Vector-potential of magnetic induction 27
406. Relations between the scalar and the vector-potential 28

Chapter III.

particular forms of magnets.

Art. Page
407. Definition of a magnetic solenoid 31
408. Definition of a complex solenoid and expression for its potential at any point 32
409. The potential of a magnetic shell at any point is the product of its strength multiplied by the solid angle its boundary subtends at the point 32
410. Another method of proof 33
411. The potential at a point on the positive side of a shell of strength exceeds that on the nearest point on the negative side by 34
412. Lamellar distribution of magnetism 34
413. Complex lamellar distribution 34
414. Potential of a solenoidal magnet 35
415. Potential of a lamellar magnet 35
416. Vector-potential of a lamellar magnet 36
417. On the solid angle subtended at a given point by a closed curve 36
418. The solid angle expressed by the length of a curve on the sphere 37
419. Solid angle found by two line-integrations 38
420. expressed as a determinant 39
421. The solid angle is a cyclic function 40
422. Theory of the vector-potential of a closed curve 41
423. Potential energy of a magnetic shell placed in a magnetic field 42

Chapter IV.

Induced Magnetization.

Art. Page
424. When a body under the action of magnetic force becomes itself magnetized the phenomenon is called magnetic induction 44
425. Magnetic induction in different substances 45
426. Definition of the coefficient of induced magnetization 47
427. Mathematical theory of magnetic induction. Poisson s method 47
428. Faraday's method 49
429. Case of a body surrounded by a magnetic medium 51
430. Poisson's physical theory of the cause of induced magnetism 53

Chapter V.

Magnetic Problems.

Art. Page
431. Theory of a hollow spherical shell 56
432. Case when is large 58
433. When 58
434. Corresponding case in two dimensions. Fig. XV 59
435. Case of a solid sphere, the coefficients of magnetization being different in different directions 60
436. The nine coefficients reduced to six. Fig. XVI 61
437. Theory of an ellipsoid acted on by a uniform magnetic force 62
438. Cases of very flat and of very long ellipsoids 65
439. Statement of problems solved by Neumann, Kirchhoff and Green 67
440. Method of approximation to a solution of the general problem when is very small. Magnetic bodies tend towards places of most intense magnetic force, and diamagnetic bodies tend to places of weakest force 69
441. On ship's magnetism 70

Chapter VI.

Weber's Theory of Magnetic Induction.

Art. Page
442. Experiments indicating a maximum of magnetization 74
443. Weber s mathematical theory of temporary magnetization 75
444. Modification of the theory to account for residual magnetization 79
445. Explanation of phenomena by the modified theory 81
446. Magnetization, demagnetization, and remagnetization 83
447. Effects of magnetization on the dimensions of the magnet 85
448. Experiments of Joule 86

Chapter VII.

Magnetic Measurements.

Art. Page
449. Suspension of the magnet 88
450. Methods of observation by mirror and scale. Photographic method 89
451. Principle of collimation employed in the Kew magnetometer 93
452. Determination of the axis of a magnet and of the direction of the horizontal component of the magnetic force 94
453. Measurement of the moment of a magnet and of the intensity of the horizontal component of magnetic force 97
454. Observations of deflexion 99
455. Method of tangents and method of sines 101
456. Observation of vibrations 102
457. Elimination of the effects of magnetic induction 105
458. Statical method of measuring the horizontal force 106
459. Bifilar suspension 107
460. System of observations in an observatory 111
461. Observation of the dip-circle 111
462. J. A. Broun's method of correction 115
463. Joule's suspension 115
464. Balance vertical force magnetometer 117


Chapter VIII.

Terrestial Magnetism.

Art. Page
465. Elements of the magnetic force 120
466. Combination of the results of the magnetic survey of a country 121
467. Deduction of the expansion of the magnetic potential of the earth in spherical harmonics 123
468. Definition of the earth's magnetic poles. They are not at the extremities of the magnetic axis. False poles. They do not exist on the earth s surface 123
469. Gauss' calculation of the 24 coefficients of the first four harmonics 124
470. Separation of external from internal causes of magnetic force 124
471. The solar and lunar variations 125
472. The periodic variations 125
473. The disturbances and their period of 11 years 126
474. Reflexions on magnetic investigations 126

Part IV.

Electromagnetism.

Chapter I.

Electromagnetic Force.

Art. Page
475. Örsted's discovery of the action of an electric current on a magnet 128
476. The space near an electric current is a magnetic field 128
477. Action of a vertical current on a magnet 129
478. Proof that the force due to a straight current of indefinitely great length varies inversely as the distance 129
479. Electromagnetic measure of the current 130
480. Potential function due to a straight current. It is a function of many values 130
481. The action of this current compared with that of a magnetic shell having an infinite straight edge and extending on one side of this edge to infinity 131
482. A small circuit acts at a great distance like a magnet 131
483. Deduction from this of the action of a closed circuit of any form and size on any point not in the current itself 131
484. Comparison between the circuit and a magnetic shell 132
485. Magnetic potential of a closed circuit 133
486. Conditions of continuous rotation of a magnet about a current 133
487. Form of the magnetic equipotential surfaces due to a closed circuit. Fig. XVIII 134
488. Mutual action between any system of magnets and a closed current 135
489. Reaction on the circuit 135
490. Force acting on a wire carrying a current and placed in the magnetic field 136
491. Theory of electromagnetic rotations 138
492. Action of one electric circuit on the whole or any portion of another 139
493. Our method of investigation is that of Faraday 140
494. Illustration of the method applied to parallel currents 140
495. Dimensions of the unit of current 141
496. The wire is urged from the side on which its magnetic action strengthens the magnetic force and towards the side on which it opposes it 141
497. Action of an infinite straight current on any current in its plane 142
498. Statement of the laws of electromagnetic force. Magnetic force due to a current 142
499. Generality of these laws 143
500. Force acting on a circuit placed in the magnetic field 144
501. Electromagnetic force is a mechanical force acting on the conductor, not on the electric current itself 144


Chapter II.

Mutual Action of Electric Currents.

Art. Page
502. Ampère's investigation of the law of force between the elements of electric currents 146
503. His method of experimenting 146
504. Ampère's balance 147
505. Ampère's first experiment. Equal and opposite currents neutralize each other 147
506. Second experiment. A crooked conductor is equivalent to a straight one carrying the same current 148
507. Third experiment. The action of a closed current as an element of another current is perpendicular to that element 148
508. Fourth experiment. Equal currents in systems geometrically similar produce equal forces 149
509. In all of these experiments the acting current is a closed one 151
510. Both circuits may, however, for mathematical purposes be conceived as consisting of elementary portions, and the action of the circuits as the resultant of the action of these elements 151
511. Necessary form of the relations between two elementary portions of lines 151
512. The geometrical quantities which determine their relative position 152
513. Form of the components of their mutual action 153
514. Resolution of these in three directions, parallel, respectively, to the line joining them and to the elements themselves 154
515. General expression for the action of a finite current on the element of another 154
516. Condition furnished by Ampère's third case of equilibrium 155
517. Theory of the directrix and the determinants of electrodynamic action 156
518. Expression of the determinants in terms of the components of the vector-potential of the current 157
519. The part of the force which is indeterminate can be expressed as the space-variation of a potential 157
520. Complete expression for the action between two finite currents 158
521. Mutual potential of two closed currents 158
522. Appropriateness of quaternions in this investigation 158
523. Determination of the form of the functions by Ampère's fourth case of equilibrium 159
524. The electrodynamic and electromagnetic units of currents 159
525. Final expressions for electromagnetic force between two elements 160
526. Four different admissible forms of the theory 160
527. Of these Ampère's is to be preferred 161

Chapter III.

Induction of Electric Currents..

Art. Page
528. Faraday's discovery. Nature of his methods 162
529. The method of this treatise founded on that of Faraday 163
530. Phenomena of magneto-electric induction 164
531. General law of induction of currents 166
532. Illustrations of the direction of induced currents 166
533. Induction by the motion of the earth 167
534. The electromotive force due to induction does not depend on the material of the conductor 168
535. It has no tendency to move the conductor 168
536. Felici's experiments on the laws of induction 168
537. Use of the galvanometer to determine the time-integral of the electromotive force 170
538. Conjugate positions of two coils 171
539. Mathematical expression for the total current of induction 172
540. Faraday's conception of an electrotonic state 173
541. His method of stating the laws of induction with reference to the lines of magnetic force 174
542. The law of Lenz, and Neumann's theory of induction 176
543. Helmholtz's deduction of induction from the mechanical action of currents by the principle of conservation of energy 176
544. Thomson's application of the same principle 178
545. Weber's contributions to electrical science 178

Chapter IV.

Induction of a Current on Itself..

Art. Page
546. Shock given by an electromagnet 180
547. Apparent momentum of electricity 180
548. Difference between this case and that of a tube containing a current of water 181
549. If there is momentum it is not that of the moving electricity 181
550. Nevertheless the phenomena are exactly analogous to those of momentum 181
551. An electric current has energy, which may be called electrokinetic energy 182
552. This leads us to form a dynamical theory of electric currents 182

Chapter V.

General Equations of Dynamics.

Art. Page
553. Lagrange's method furnishes appropriate ideas for the study of the higher dynamical sciences 184
554. These ideas must be translated from mathematical into dynamical language 184
555. Degrees of freedom of a connected system 185
556. Generalized meaning of velocity 186
557. Generalized meaning of force 186
558. Generalized meaning of momentum and impulse 186
559. Work done by a small impulse 187
560. Kinetic energy in terms of momenta, () 188
561. Hamilton's equations of motion 189
562. Kinetic energy in terms of the velocities and momenta, () 190
563. Kinetic energy in terms of velocities, ( 191
564. Relations between and , and 191
565. Moments and products of inertia and mobility 192
566. Necessary conditions which these coefficients must satisfy 193
567. Relation between mathematical, dynamical, and electrical ideas 193

Chapter VI.

Application of Dynamics to Electromagnetism.

Art. Page
568. The electric current possesses energy 195
569. The current is a kinetic phenomenon 195
570. Work done by electromotive force 196
571. The most general expression for the kinetic energy of a system including electric currents 197
572. The electrical variables do not appear in this expression 198
573. Mechanical force acting on a conductor 198
574. The part depending on products of ordinary velocities and strengths of currents does not exist 200
575. Another experimental test 202
576. Discussion of the electromotive force 204
577. If terms involving products of velocities and currents existed they would introduce electromotive forces, which are not observed 204

Chapter VII.

Electrokinetics.

Art. Page
578. The electrokinetic energy of a system of linear circuits 206
579. Electromotive force in each circuit 207
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.

Exploration of the Field by Means of the Secondary Circuit.

Art. Page
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, 214
591. Its relation to the magnetic induction, . Equations (A) 214
592. Justification of these names 215
593. Conventions with respect to the signs of translations and rotations 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..

Art. Page
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
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. Ampère'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.

Art. Page
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 XI.

Energy and Stress.

Art. Page
630. The electrostatic energy expressed in terms of the free electricity 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 magnetic force 248
636. Method of this treatise 249
637. Magnetic energy and electrokinetic energy compared 249
638. Magnetic energy reduced to electrokinetic energy 250
639. The force acting on a particle of a substance due to its magnetization 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 phenomena 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 , where 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.

Current-Sheets.

Art. Page
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 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 velocity 268
662. Trail of images formed by a magnetic system in continuous motion 268
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 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
681. An endless solenoid 284

Chapter XIII.

Parallel Currents.

Art. Page
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 288
685. Kinetic energy of the current 288
686. Repulsion between the direct and the return current 289
687. Tension of the wires. Ampère'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.

Art. Page
694. Potential due to a spherical bowl 299
695. Solid angle subtended by a circle at any point 301
696. Potential energy of two circular currents 302
697. Moment of the couple acting between two coils 303
698. Values of 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.

Art. Page
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 galvanometer 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

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 quæsita 338
735. Position of equilibrium determined from three successive elongations 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. Zurückwerfungs methode 348
751. Method of multiplication 350

Chapter XVII.

Electrical Measurement of Coefficients of Induction.

Art. Page
752. Electrical measurement sometimes more accurate than direct measurement 352
753. Determination of 353
754. Determination of 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.

Art. Page
758. Definition of resistance 358
759. Kirchhoff's method 358
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.

Art. Page
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 electrodynamometer 372
773. Maxwell's method by combined electrometer and electrodynamometer 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 electromagnetic measure 382

Chapter XX.

Electromagnetic Theory of Light.

Art. Page
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
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.

Art. Page
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. Verdet'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
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 Theory of Magnetism

Art. Page
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.

Art. Page
846. Quantities which enter into Ampère's formula 426
847. Relative motion of two electric particles 426
848. Relative motion of four electric particles. Fechner's theory 427
849. Two new forms of Ampère'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 conservation 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