
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

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. Lineintegral of magnetic force, or magnetic potential 
24
 402. Surfaceintegral of magnetic induction 
25
 403. Solenoidal distribution of magnetic induction 
25
 404. Surfaces and tubes of magnetic induction 
27
 405. Vectorpotential of magnetic induction 
27
 406. Relations between the scalar and the vectorpotential 
28

particular forms of magnets.
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

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

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

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 dipcircle 
111
 462. J. A. Broun's method of correction 
115
 463. Joule's suspension 
115
 464. Balance vertical force magnetometer 
117

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

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

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 vectorpotential of the current 
157
 519. The part of the force which is indeterminate can be expressed as the spacevariation 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

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 magnetoelectric 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 timeintegral 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

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

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

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

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

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 lineintegral 
211
 587. Any system of contiguous circuits is equivalent to the circuit formed by their exterior boundary 
212
 588. Electrokinetic momentum expressed as a surfaceintegral 
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

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. Volumedensity of free electricity, (J) 
233
 613. Surfacedensity 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. Vectorpotential of electric currents 
236
 618. Quaternion expressions for electromagnetic quantities 
236
 619. Quaternion equations of the electromagnetic field 
237

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

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

Art.

Page


647. Definition of a currentsheet 
259
 648. Currentfunction 
259
 649. Electric potential 
260
 650. Theory of steady currents 
260
 651. Case of uniform conductivity 
260
 652. Magnetic action of a currentsheet with closed currents 
261
 653. Magnetic potential due to a currentsheet 
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 currentsheet 
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 currentsheets 
275
 671. The vectorpotential 
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

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 vectorpotential 
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. Selfinduction 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

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 selfinduction 
311

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 currentweigher 
332
 727. Suction of solenoids 
333
 728. Uniform force normal to suspended coil 
333
 729. Electrodynamometer with torsionarm 
334

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

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 selfinduction of a coil 
356
 757. Comparison of the selfinduction of two coils 
357

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

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 selfinduction of a coil 
377
 779. Coil and condenser combined 
379
 780. Electrostatic measure of resistance compared with its electromagnetic measure 
382

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 nonconductor 
386
 785. Characteristics of wavepropagation 
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 wavefront, 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

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 circularlypolarized ray is different according to its direction of rotation 
402
 813. Right and lefthanded rays 
403
 814. In media which of themselves have the rotatory property the velocity is different for right and lefthanded 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 circularlypolarized light 
405
 818. Kinetic and potential energy of the medium 
406
 819. Condition of wavepropagation 
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 circularlypolarized ray 
411
 829. The magnetic rotation 
412
 830. Researches of Verdet 
413
 831. Note on a mechanical theory of molecular vortices 
415

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

Theories of Action at a Distance.
Art.

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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

