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

Title	A Treatise on Electricity and Magnetism
Author	James Clerk Maxwell
Year	1873
Publisher	Clarendon Press
Location	Oxford
Source	djvu
Progress	To be proofread
Volumes	Vol. 1 • Vol. 2

Pages   (key to Page Status)   

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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 $\Phi$ exceeds that on the nearest point on the negative side by$4\pi \Phi$	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. $\Pi$ 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 $\kappa$ is large	58
433. When $i=1$	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 $\kappa$ 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, ($T_{p}$)	188
561. Hamilton's equations of motion	189
562. Kinetic energy in terms of the velocities and momenta, ($T_{p{\dot {q}}}$)	190
563. Kinetic energy in terms of velocities, ($T_{\dot {q}})$	191
564. Relations between $T_{p}$ and $T_{\dot {q}}$, $p$ and ${\dot {q}}$	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, ${\mathfrak {A}}$	214
591. Its relation to the magnetic induction, ${\mathfrak {B}}$. 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 ${\frac {1}{8\pi }}{\mathfrak {K}}^{2}$, where ${\mathfrak {K}}$ 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 $R$	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 velocity $R$	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 $Q_{i}^{'}$	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 $G_{1}$	353
754. Determination of $g_{1}$	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