The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 19 of 35

One more experiment in this part of the subject may be referred to. Eeturning to the use of the electro-magnet, in which the iron circuit is all but complete, we find that, when a highly-conducting disc is put between the closely approximated half -shielded jaws of this electro-magnet, and an alternating current employed to excite it, the conducting disc is held up in the air gap by reason of the attraction set up between the currents induced in the disc and the shielding polar plates. If, however, the disc has a relatively poor con-

324 MUTUAL AND SELF INDUCTION.

ductivity the attraction is not nearly so marked. A good or bad silver coin can thus be discriminated, because the good silver coin has sufficient conductivity to be the seat of power- ful induced currents, but the bad coin has not.

Closely akin to the foregoing, but more difficult to explain, are the rotations in copper and iron discs which can be caused by the approximation to them of a laminated iron bar alternately magnetised. These actions have been carefully studied by Prof. Elihu Thomson, and applied by him and others in many practical devices. Across the top of an electro-magnet is placed a long bar of laminated iron with the plane of the lamination vertical (Fig. 125). This bar is

FIG. 124. — Electromagnetic Gyroscope Revolving over the Pole of an Alternating Current Electro-magnet.

surrounded at intervals by copper bands, which form small closed secondary circuits upon it. If we excite the magnet and hold near the bar an iron disc capable of free rotation, it begins to rotate rapidly. Not only can this be done with a laminated bar throttled by conducting circuits, but even a solid bar of hard steel will serve the same purpose, and a couple of steel files placed across the poles can cause rapid rotation in pivoted discs of copper or of iron held with their edges close to the bars so alternately magnetised.

To understand the operations which produce this rotation, we have to return to some elementary principles. Consider

MUTUAL AND SELF INDUCTION.

325

a conducting ring held in front of the electro-magnet as in Fig. 113. Let a sudden flux of magnetic induction be made through the ring aperture, that is, in common parlance, let " lines of force " be thrust through the opening of the ring. If these lines proceed out from a north pole, they will create an electromotive force in the ring in such a direction as to make a current flow counter-clockwise round the ring as seen from the pole. This current in the ring itself creates a magnetic field round the ring, and a consideration of the direction of the current -will show that in the central aperture of the ring the dire :tion of the inducing field and the field due to the induced current are in opposite directions. The effect of

C

'FiG. 125. — Alternating Current Magnet with Laminated Iron Bar across its pole causing Revolution of two Iron Discs held near its extremities.

this opposition is to retard the formation of the field due to the magnet in the aperture of the ring. In other words, the current induced by the internal field causes the lines of induction due to the external pole to be, as it were, momen- tarily thrust out laterally, and resisted in their endeavour to pass through the aperture of the ring.

If we consider a bar of iron surrounded with a copper band, and imagine that this bar is suddenly acted upon by a magnetising force at one end, the result of the current induced in the ring will be that for a brief time the

326 MUTUAL AND SELF INDUCTION.

magnetic induction in the bar will be caused to leak out laterally, and go round the copper ring on the out- side, its passage through the ring being resisted. If, then, we throttle a magnetic circuit, such as a laminated iron bar, with copper coils closed upon themselves, and place a mag- netising coil at one end, the closed conducting circuits hinder the rise of magnetic induction in the bar ; or, in other words, give it what may be called magnetic self-induction. If the source of magnetism is a rapidly-reversed pole, the consequences of this delay or " lag " in the induction is that a series of alter- nating magnetic poles are always travelling with retarded speed up the bar, and these may be considered to be represented by tufts of lines of magnetic induction which spring out from and move laterally up the bar. If the bar is not laminated and not throttled, the eddy currents set up in the mass of the bar itself act in the same way, and operate to resist the rise of induction in the bar and to delay the propagation of mag- netism along it. Hence we must think of such a throttled bar, when embraced by a magnetising coil at one end, as sur- rounded by laterally moving bunches of lines of magnetic induction, which move up the bar. Each reversal of current in the magnetising coil calls into existence a fresh mag- netic pole at the one end of the bar, which is, as it were, pushed along the bar to make room for the pole of opposite name, which appears the next instant behind it. When an iron disc is held near such a laminated and throttled bar, these laterally moving lines of force induce poles in the disc which travel after the inducing poles, and hence the disc is continually pulled round. If the disc is a copper disc, the laterally moving lines of magnetic force induce eddy currents in the disc, and these, by the principle already explained, create a repulsion between the pole and that part of the disc in which the eddy currents are set up, causing revolution of the disc.

An interesting application of the above principle has been made in the meter of Messrs. Borel, Wright and Ferranti for measuring alternating currents. It consists of a pair of vertical electro-magnets (see Fig. 126), with laminated iron cores, and each magnet bears at the top a curved horn of laminated iron which is throttled by copper rings. These curved horns, springing from the magnets, embrace and

328 MUTUAL AND SELF INDUCTION.

nearly touch a light iron-rimmed -wheel, free to turn in the centre. The actions just explained drive the wheel round, when the magnet coils are traversed by an alternating current. The iron wheel can* es on its shaft a set of mica vanes, which retard the wheel by air friction. Under the opposing influ- ences of this retardation and the electro-magnetic rotation forces, the wheel takes a certain speed corresponding to different current strengths in the magnetic coils, and hence the total number of revolutions of the wheel in a given time, as recorded by a counter, serves to determine the total quantity of alternating current which has passed through the meter.

The rotation of iron discs can be shown also by means of a badly-designed transformer. If a closed laminated iron ring

FIG. 127. — Magnetic Leakage across a Throttled Iron Ring, causing rotation of an Iron Disc placed near the Secondary Coil.

(Fig. 127) is wound with a couple of conducting circuits, such an arrangement constitutes a transformer. If these two circuits are wound on opposite sides of the iron ring, the previous explanations show that the arrangement will be productive of great magnetic leakage across the iron circuit. In designing transformers for practical work,' one condition amongst others which must be held in view is to so arrange the conductive and magnetic circuits that a great magnetic leakage of lines of force across the air does not take place. If, however, this leakage exists, it indicates that the secondary circuit is not getting the full benefit of the induction created by the primary. To detect it we have merely to hold near the

MUTUAL AND SELF INDUCTION. 329

iron circuit a little balanced or pivoted iron disc, and if it is set in rapid rotation it indicates that there are laterally- moving lines of magnetic force outside the iron, which have escaped from the iron in consequence of the back-magneto- force of the secondary circuit.

The above described phenomena have been utilized in the construction of measuring instruments of various kinds, and the effects due to the magnetic leakage of magnetic fields will be found to have applications which will be considered more carefully in discussing the action of transformers.

of the effects described in the present chapter will have dis- closed to the careful reader that there is a complete symmetry between the two fundamental quantities, electric current and magnetic induction. Let the diagrams in Fig. 128 represent a circuit of iron (magnetic circuit) linked with a circuit of copper (conductive circuit) and let the iron circuit have wound on it a magnetising coil capable of imposing a magneto-motive force (M.M.F.) on it, whilst the conductive •circuit has a source of electromotive force (E.M.F.), say a battery, introduced into it. Suppose, then, that this E.M.F. is suddenly introduced in the conductive circuit, the linking of this circuit with the iron circuit bestows considerable self- induction on the conductive circuit, and this operates to delay the rise of the current strength in the conductive circuit when the E.M.F. is suddenly applied. If the two circuits were plunged into a good conducting liquid medium, the action of the iron circuit would be to cause a leakage of current across the conductive circuit. Quite similarly, we find that if a magnetomotive force is suddenly applied to the iron circuit, the induced current set up in the conductive circuit opposes the growth of the induction in the magnetic circuit, and, as air is not an insulator for magnetic induction, it causes a leakage of magnetic induction across the circuit. Hence the growth of electric current in the conductive circuit is hindered by linking it with an iron circuit, and the growth of magnetic induction in an iron circuit is hindered by linking it with a copper circuit. This is only one instance of the fact that the laws of current establishment in conductive circuits are similar

a^U MUTUAL AND SELF INDUCTION.

to the laws of establishment of magnetic induction in magnetic circuits.

The growth of current from surface to centre of con- ductors has been described in sections of this chapter. The gradual soaking in, or growth of the magnetic induction, from the surface to the centre of the iron cores of electro-magnets, when a sudden external magnetising force is applied, has been experimentally examined with great skill by Dr. J. Hopkinson and Mr. E. Wilson, and the reader is referred for a full account

Electric Ci

Magnetic Circuit.

Copper

Iron.

FIG. 128. — Diagrams illustrating the Symmetry in relation between Electromotive Force and Electric Current, and Magnetomotive Force and Magnetic Induction.

of their work to The Electrician, Vol. XXXIV., 1895, p. 510. Very briefly it may be said that these experiments consisted in showing experimentally that in the case of an electro-magnet with a very large solid iron core the magnetic induction in the iron is not established instantaneously at its full value at all points in the iron when the magnetising force is

MUTUAL AND SELF INDUCTION. 331

applied, but it begins at the surface of the core and slowly works inwards to the centre. In an entirely similar manner we know that in a conductor of large cross-section the actions involved in the production of a current in the conductor establish the current first at the surface of the conductor, and the central portions of the conductor are only reached by it after a certain finite time. We shall return in the next chapter to the discussion of some of these theoretical Questions.

CHAPTEE Y.

DYNAMICAL THEORY OF INDUCTION.

§ 1. Electromagnetic Theory. — In the matter so far before the reader attention has been directed to the chief facts ot electromagnetic induction without any inquiry into the possible mechanism by which this may be effected. Attention may at this stage be directed to modern views of the subject, •which have been the outcome of the work of Faraday and Maxwell and all their illustrious followers in this field of study. The cardinal principle of these methods of viewing the phenomena is the denial of action at a distance. That is to say, if at any point in a field we find a force due to a current flowing in some conductor, this force cannot be regarded as appearing there without anything happening in the interspace, but must be the consequence of successive changes in closely contiguous places, and not the result of operations at a distance without intermediate machinery. Whenever we find an electromagnetic effect taking place at any locality we are directed therefore by these notions to look for its antecedents or consequences at the adjacent places, and the apparent phenomenon is not to be regarded as the whole of it, but to be taken as a portion of the whole of the effects which are produced in every part of the region or medium. The finite velocity of light, and the impossibility of accounting for its propagation on any other hypothesis than that of actual transmission of something across space, or the propagation of a state of stress and strain or periodic change of some kind through a medium, led to attempts to settle between the rival hypotheses by crucial experiment, with the result that the vast bulk of the accumulated evidence decides

DYNAMICAL THEORY OF INDUCTION, 333

in favour of the existence in space of a medium which has properties not possessed by the ordinary atomic matter, hut which may certainly be called a material substance in the sense that it can be the recipient or vehicle of energy. The study of the phenomena of liyht indicates that along the path of a ray there are certain changes which are periodically repeated, such that at portions of the medium separated by a distance called a wave-length, changes of a similar kind are being coincidently effected. The application of mathematical analysis to optical phenomena has led to the conclusion that we can offer a tolerably satisfactory account of them by making the supposition that there exists such a universally diffused ether or medium in which these changes go on. At this point, however, the profound difficulties of the subject begin. To offer a complete account of the phenomena of light, and to deduce all the observed effects from a fundamental principle, we have to construct a hypothesis as to the structure of this ether and the nature of the periodic changes which constitute the wave motion in it. The periodic changes which in the case of sound and fluid waves are known to exist suggested that in the case of the ether the periodic changes are motions of the parts of the ether relatively to one another, and that these motions are the result of displacements taking place under certain stresses. We cannot even attempt here a sketch, however brief, of the various hypotheses which have formed as to the sort of motions which may occur. On one assumption the ether has been regarded as capable of having displacements or deformations made in it against internal forces, resisting these changes similar to the shearing strains and stresses in solids. From this point of view, now some- times called the elastic solid theory of light, we may picture this ether to ourselves as a distortable but incompressible jelly-like solid, which exists everywhere and penetrates into the interior of all material bodies. As long as the hypothesis of a universal ether was demanded merely to correlate the observed phenomena of light a limited order of facts had alone to be considered ; but the conception that electric and magnetic effects also required a similar assumption, increased the difficulties to be dealt with. The mind of Faraday con- tinually turned to the thought that the medium assumed

334 DYNAMICAL THEORY OF INDUCTION.

in both these regions of phenomena might be the same ; and his great disciple, Maxwell, was led more definitely to formu- late a similar conception. If an ether or medium is demanded as a fundamental cause of two or more classes of facts, then it is certainly unscientific to fill space several times over with ethers of different kinds until the attempt has been made to ascertain if one alone cannot be found to fulfil all the required functions. Maxwell was led therefore to the con- clusion that both luminous, electric, and electromagnetic phenomena might be explained by the supposition of one single medium capable of certain internal changes, and possessing certain mechanical properties, and he thus avoided the unscientific process of thought of postulating two different ethers by boldly adopting the hypothesis that the medium on which electric effects and optical phenomena depend for their existence is one and the same. We shall see later how this supposition has been supported.

One important element in Maxwell s electric theory is his conception of electric displacement. When an electromotive force acts upon any part of a dielectric which is uniform and non-crystalline it is assumed that at all points along the line of electrostatic induction there is an electric displacement, as Maxwell calls it. The theory does not tell us what is the physical nature of this displacement. We may, in the first place, merely for the purpose of illustration, suppose that the unknown something which we call electricity is moved along a line of induction, and that on the removal of the electric force it returns to its original position, and that a dielectric or insulator is a material in which the electricity, when dis- placed by the application of an electrostatic stress or force, resists this displacement in virtue of an electric elasticity. The apparent charge on conductors, according to this view, is the electricity displaced out of, or into, the dielectric, and positive charge or electrification may be regarded as the possession of an excess which is extruded from the dielectric on to the con- ductor, and negative as a deficit when the conductor gives up some to the dielectric.

Maxwell's next principle is that change in electric displace- ment is an electric current whilst the change lasts. He calls this a displacement cutrent, to distinguish it from a current in

DYNAMICAL THEORY OF INDUCTION. 335

conductors called the conduction current. The displacement current is supposed to have, however, all the properties of an electric current. Conducting bodies must he regarded as those in wh'ch there is no elastic force resisting displacement, or, in other words, have no electric elasticity, and in which, therefore, electric displacement can go on continuously. The existence of a current of conduction is recognised by two co-existing effects — first, the dissipation of energy into heat ; and second, the existence of magnetic force the direction of which is along closed lines described around the line of the current. The displacement current in dielectrics, which takes place at the instant of applying or changing the electric force, is also considered to be accompanied by magnetic force. In other words, we must consider the displacement current which takes place in a dielectric when electrostatic force acts on it as a very brief conduction current, and as originating a system of lines of magnetic induction — surrounding it, just as a con- ducting wire is so surrounded, by its loops or closed lines of magnetic induction. Conversely, when lines of magnetic force penetrate through an insulator or dielectric, any change in the density of these lines creates eddy displacement cur- rents in the mass. If the lines penetrate through a conductor they produce, under similar circumstances, eddy currents of conduction, whose energy is ultimately frittered down into heat. Also, if a conductor is moved across a magnetic field so that it " cuts " lines of induction we have seen that if the conductor is a portion of a closed circuit it has a current of conduction produced in it. Similarly, if a dielectric body is moved in a magnetic field in a like manner it has during the continuance of the motion a displacement current produced in it. Since a dielectric circuit is always a closed circuit, a dis- placement current, or the production of electric displacement in it is always the result of any change in the magnetic field in its interior. For the purpose of obtaining a rough illustrative working model of the actions going on in a dielectric submitted to the action of electric force, it is necessary to fall back on some material, hypothesis of elec- tricity— that is, we must conceive of electricity as a something which can be displaced relatively to the molecules of the dielectric, and that it resists this displacement, and that

336 DYNAMICAL THEOfiY OF INDUCTION.

when this displacement is made under the action of electric stress the removal of this stress causes a disappearance of the displacement. Dr. Lodge has suggested a form of apparatus serving as a rough working model of this dielectric action, iA which buttons sliding along a rod, and held in certain positions by elastic strings, represent the electric particles capable of elastic displacement.*

We may quant tatively define electric displacement by saying that in a homogeneous non-crystalline dielectric, if a plane be drawn perpendicular to the line of action of the resultant electric force, then under th.3 operation of this electric force the quantity of electricity displaced normally across a unit of area of this plane is called the electric displacement. This displace-

FIG. 129.

ment is of the nature of an elastic strain, and is removed when the electric force is removed. Let us fix our ideas by imagin- ing a sphere immersed in a dielectric medium to receive an electric charge of quantity Q. Suppose this sphere to be sur- rounded by a concentric spherical shell (Fig. 129) also immersed in the dielectric. On giving the central sphere a charge + Q we know that on the inside surface of the insulated concentric shell will appear an inductive charge - Q of equal quantity and opposite sign, and a charge -f Q on the outside surface.

• See Dr. 0. J. Lodge "On a Model Illustrating Mechanically the Passage of Electricity through Metab and Dielectrics," Phil. Mag.t November, 1876.

DYNAMICAL THEORY OF INDUCTION. 337

Let this spherical shell be very thin and be placed at a distance

• from the central sphere, supposed to be very small. The electric force due to the central charge Q at the surface of the

concentric shell is represented by . , and this force exerts a

displacing action on the electricity of the shell, causing posi- tive electricity to be displaced outwards or in the direction of the force and negative electricity to be displaced inwards or against the force.

The quantity K which appears in the above expression for the magnitude of the electric force is called the dielectric con- stant, or the specific inductive capacity, according to Faraday, of the medium. If the dielectric is air or other gas, K is very nearly unity, and the law of the force becomes the ordinary Newtonian law, viz., force varies as quantity divided by square of distance — that is, the electric force at any point due to a small quantity, Q, collected on a sphere is numerically equal

to - , where r is the distance of the point from the centre of

the sphere. The quantity K is assumed to have a value of unity in the case of a vacuum, and varies for known dielectrics from a little above unity for dry air up to a value of 6 to 10 for glass. In the case of metals and conducting bodies we may consider K to be infinitely great, and generally K is a number which expresses the ratio of the displacement in the given dielectric to the displacement which would take place under the same electric force if the dielectric was removed and a vacuum left in its place. The whole quantity of electricity displaced out- wards through the conducting shell is + Q, and since the radius of this spherical shell is r, its surface is 4?r r2 and the quantity displaced through unit of area of this shell in the direction of

the force is JSL. This quantity, then, Maxwell calls the 47T r*

electric displacement, and denotes by the symbol D.

The electric force or resultant electric intensity at all points

over the spherical shell is , and this quantity Maxwell calls Kr2

the electromotive intensity at that point, and denotes it by E We may also speak of D as the electric strain and E as the electric stress by an extension of usual mechanical language.

338 DYNAMICAL THEORY OF INDUCTION.

The quotient of a stress by its corresponding strain is, in mechanics, called the coefficient of elasticity corresponding to that stress. For instance, the quotient of stretching force by longitudinal extension in the case of solid rods subjected to extending forces is called Young's Modulus of Elasticity, or the longitudinal elasticity. By a similar use of language the quotient electric stress by electric strain may be called the electric elasticity, and we have Q

— -- = — - = tJie electric elasticity.

Q

47T7-2

Hence the series of numbers obtained by dividing the number 4 x 3'1416 by the specific inductive capacities give a series of numbers which are the electric elasticities of these substances.*

§ 2. Displacement Currents and Displacement Waves. — Maxwell's second fundamental conception, as we have men- tioned, is that a displacement of electricity whilst it is taking place is an electric current. That is to say, the variation of displace- ment, whether of increase or decrease, is a movement of elec- tricity which is in effect an electric current. A dielectric must, however, be considered as a body which does not permit any but a very transient electric current passing through it. If •continuous electric force is applied to it the dielectric is soon .strained to its utmost extent, and no more current or flow or •displacement takes place through it until the sign or direction of the electric force is reversed. A dielectric may be considered to be pervious to very rapidly reversed periodic currents, but very opaque or impervious to continuous currents. This is familiarly illustrated by the fact that a condenser inserted in a telephonic circuit does not stop telephonic communication, but .does stop continuous currents. If D be at any instant the displacement at any point in a dielectric, and if D varies with

• The occurence of this 4^r in electric and magnetic equations is an objection from some points of view. Mr. Oliver Heaviside has discussed the subject fully in his writings in The Electrician, and proposed a system of rational units in which it is suppressed.

DYNAMICAL THEORY OF INDUCTION. 339

the time so that - — is its time rate of variation, then ( — , or

d t dt

as it may be best written in Newtonian fashion D, is the dis- placement current, or rate of change of displacement. If at any point in a dielectric rapid changes of displacement are taking place, these variations of electric displacement are in effect electric currents producing magnetic induction in the surrounding portions of the dielectric. When we come to discuss the investigations of Hertz we shall see that this view receives support from experimental research. An electric displacement taking place all along a certain plane is equi- valent to a current sheet, and an electric displacement taking place along a certain line is a linear current. Electrostatically speaking, lines of electric displacement are lines of electro- static induction, and these lines, when the displacement is changing, become lines along which electric current flow is taking place. The denial of action at a distance involves the assumption that the only portions of a dielectric which can act directly upon each other are those which are in immediate contact or are contiguous.

§ 3- Maxwell's Theory of Molecular Vortices. — Given a medium possessing certain mechanical qualities, such as elas- ticity, a definite density, a capability of relative displacement of its parts, we may ask, is it possible to imagine a structure which will mechanically account for the effects we have to consider in electrical phenomena ? A full discussion of ether theories is not possible here, but it may be of assistance to the student to place before him a general account of one such attempt to construct a mental imagery of its mechanism. We should always remember, however, that even if we are able to imagine a mechanism capable of producing even all the effects we find in Nature in any region of fact, it does not in the least follow that the real state of affairs agrees with •our conception of it. Maxwell put forward his theory of Molecular Vortices in the Philosophical Magazine for 1861 and 1862. A general account of this theory has been given in the " Life of James Clerk Maxwell," and as the limits of such an elementary treatise as the present one preclude any detailed account of the mathematical portion of this theory, we shall

z2

340 DYNAMICAL THEORY OF INDUCTION.

borrow the language of the authors of the above-mentioned work* hi describing it. Maxwell supposes that any medium which can serve as the vehicle of electro-magnetic energy consists of a vast number of very small bodies called cells, capable of rotation, which we may consider to be spherical,. or nearly so, when in their normal position. When magnetic force is transmitted by the medium or acts through it, these cells are supposed to be set in rotation with a velocity propor- tional to the intensity of the magnetic force, and the direction of rotation is related to the direction of the force in the same manner as the twist and thrust of a right-handed screw- We have thus all the magnetic field filled with molecular vortices, as Maxwell calls them, all rotating round the lines offerees as axes. These cells as they revolve tend to flatten out like revolving spheres of fluid, and to become oblate spheroids ; they thus con- tract along the lines of force and expand at right angles, creating a tension along the lines of force, and a pressure at right angles to them. These cells are supposed to be elastic spheres closely packed together and incapable of separating from each other. If any line of cells is set rotating the contraction of each cell along its axis of revolution must set up a tension or pull along that line, it behaves like a filament of muscular tissue, and contracts in length and swells out or increases in thickness. If several adjacent lines of cells or vortices are all set revolving; in the same direction, the swelling out of each line causes them to press on each other ; hence there is a lateral pressure and a longitudinal tension. In any space filled with these cells so- revolving the lines of tension or axes of revolution of the cells will take up certain positions, depending on the necessity exist- ing for the stresses to adjust themselves to equilibrium, and Maxwell has shown mathematically that such a system of cells in tension and pressure is a system which will behave- in a manner similar to that in which we find actual lines of magnetic force do, and that the behaviour of magnetic poles to each other can be explained fully by the assumption of a_

• "Life of James Clerk Maxwell." By Lewis Campbell and William. Garnett. 1st Edition. 1882. The general description of Maxwell's views in the above-mentioned work is due to Prof. Garnett, and in the annexed paragraphs the expository account of this theory is taken in part almost- verbatim from the pages of this book.

DYNAMICAL THEORY OF INDUCTION. 341

tendency on the part of the lines of force between them to contract like elastic threads along their length, and to push one another apart when laid parallel and proceeding in the same direction. To account for the transmission of rotation from one cell to another in the same direction, and from one line of cells or vortex to the next, Maxwell supposed that there exists bet-ween the cells a number of extremely minute spherical bodies which can roll without sliding in contact with the vortex cells. These bodies serve the same purpose as "idle wheels" in machinery, which coming between a driving wheel and a following wheel serve to cause both to turn in the same direction. These minute spheres Maxwell supposed to constitute electricity. We shall speak of them collectively as the electric matter. These electric particles are furthermore supposed to be free to move in conductors ; but in dielectrics they are tethered to one spot, or rather into one molecule of the substance, and can only be displaced a little way against an elastic resilience, which brings them back to their original position when the displacing force is withdrawn. Furthermore, we must assume that both cells and particles are very small, compared with the molecules of matter. The passage of electric particles from molecule to molecule in conductors, however, sets up molecular vibration, or generates heat. Something of the nature of friction must, therefore, be also postulated to account for the fact that the electric particles, when set moving in a conductor, give up energy to the molecules, and the energy is in them dissipated in the form of heat. That there is some kind of rotation going on along the lines of magnetic force has been held by Maxwell to be indicated by the behaviour of a ray of polarised light when passing through a dielectric along a line of magnetic force, and he states* that Faraday's discovery of the magnetic rotation of the plane of polarised light furnishes complete dynamical evidence that wherever magnetic force exists there is matter small portions of which are rotating ! about axes parallel to the direction of that force. The further , assumption is made that the cells are composed of an elastic ; material, and that they can be distorted or squeezed slightly, I returning again in virtue of their resistance to their original

• Article "Faraday," Encyclopaedia £ritannica, 9th Edition.

342 DYNAMICAL THEORY OF INDUCTION.