
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 
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. Vectorpotential 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 lineintegrations 
38 
420. $\Pi$ expressed as a determinant 
39 
421. The solid angle is a cyclic function 
40 
422. Theory of the vectorpotential of a closed curve 
41 
423. Potential energy of a magnetic shell placed in a magnetic field 
42 
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. 
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 
