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Elementary Theory of Magnetism.
Art.
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Page
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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
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magnetic force and magnetic induction.
Art.
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Page
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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
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particular forms of magnets.
Art.
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Page
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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
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Art.
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Page
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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
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Weber's Theory of Magnetic Induction.
Art.
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Page
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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
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Art.
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Page
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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
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Art.
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Page
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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
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Art.
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Page
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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.
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Page
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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
|
Induction of Electric Currents..
Art.
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Page
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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
|
Induction of a Current on Itself..
Art.
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Page
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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.
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Page
|
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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
|
Application of Dynamics to Electromagnetism.
Art.
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Page
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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.
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Page
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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.
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Page
|
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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
|
Art.
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Page
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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
|
Dimensions of Electric Units.
Art.
|
Page
|
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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 , 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
|
Art.
|
Page
|
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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
|
Art.
|
Page
|
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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
|
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
|
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
|
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  |
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
|
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 self-induction 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 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
|
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
|
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.
|
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
|
|