The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 20 of 36

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 witii

• The occurence of this 4t in electric and magnetic equations is^an

objection from eome points of view. Mr. Oliyer Heaviside has disoained

the subject fully in hiB writings in The EUotrioian, and proposed a i

. of sational units in which it is suppressed.

DYNAMICAL THEORY OF INDUCTION. *9

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

dt [ dt

as it may be best written in Newtonian fashion D, is the dis- pl^cemsnt 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 •discusu 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. liaxwall's Theory of Molecnlar 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 <ion8ider in electrical phenomena ? A full discussion of ether theories is not possible here, but it may be of assistance to the indent 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 And 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* m 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 cella, 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, a& Maxwell calls them; all rotating round the lines of forces as axes. These cells as they revolve tend to flatten out like revolving spheres of fluid, and to become oblate spheroids ; they thuB 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 hke a filament of muscular tissue, and contracts in length and swells out or increases in thickness. If several adjacent hnes 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. Qamett, and in the annexed paragraphs the expository account of this theoiy is taken in part almost, verbatim from the pages of this book.

DYNAMICAL THEORY OF INDUCTION. 341

-tendency on the part of tlie lines of force between them to contract Uke 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 between 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, returning again in virtue of their resistance to their original

• Article " Faraday," Encydopadia BriUinnica, 9th Edition.

342 DYNAMICAL THEORY OF INDUCTION.

form. In order to obtain a clear conception of the inter* relation of the idle wheels or the electric particles and the* revolving cells or lines of induction, we may construct a mechanical illustration of one element of the mechanism as it is supposed to exist in the dielectric.

Consider A and B {mb Fig. 180) to be two wheels of india- rubber, and that C is another small wheel lying between A and B and transmitting motion from one Xo the other. Let 0 be tethered to a fixed point, D, by an elastic spring, and let 0 be at the same time capable of rotation round its centre*. Suppose A is set in rotation, clock-hand wise, whilst B is held* fast, and that the wheel G cannot slip on A, the result will be to drag down 0 to the position of C^, stretching the spring and displacing G. Let B be then set free ; the wheel G continues to roll on A, and transmits its rotation to B. Owing to the

Fio. 130.

assumed elasticity of the discs A and B, the wheel C can be drawn down between them, and jet within the limits of its displacement equally transmit the rotation of A to B without slip. The same action of a preliminary displacement of G and subsequent rotation of B will take place if the wheel B possesses inertia — that is, if we assume it to be a heavy wheel which cannot in virtue of its mass be set rolling with finite speed in an infinitely short time.

If, then, we suppose a long row of such wheels with inteN mediate displaceable idle wheels, the main wheels being heavy bodies, the result of causing the first wheel to rotate would be to propagate along the line a successive displacement of the idle wheels, and to set the main wheels successively in rota-

DYNAMICAL THEOBY OF INDUCTION. 843

tion. Translating these meohanical concepts into their elec- trical equivalents, Maxwell considers that the heavy wheels are the analogues of the molecular vortices or lines of force, and that their density is determined by what we call the magnetic permeability of the medium; the elastically dis- placeable idle wheels are the electricity in the dielectric ; and that when a line of force is brought into existence in a diekotriCy or, in other words, when a line of cells is set rotating, this action propagates itself outwards, producing successive displacements of the electric particles, or generates a displacement wave, and is accompanied by the successive appearance of rotation in the cells, or by the propagation of a wave of electromagnetic force.

The velocity of propagation of this wave will depend on the dastic forces restraining displacement, and on the inertia of the revolving vortices. We have seen that the elasticity of

the dielectric is expressed by the quantity —^ where E is the

specific inductive capacity. We shall see later on that the electromagnetic density of the medium is expressed by 4*- /a, where /i is the magnetic permeability.

The velocity of propagation of a disturbance through an elastic medium is numerically equal to the quotient of the square root of its effective elasticity e, by the square root of

its density d, or by r- a/1.

If, then, for the electromagnetic medium «-^ and

1 dmrniir fjk, we have v « ■, or the velocity of lateral propaga.

tion of a wave of electric displacement or of magnetic force in a medium is numerically equal to the square root of the reciprocal of the product of its specific inductive capacity and its magnetic permeability. Such a mechanical hypothesis shows us how the spin of one line of vortices results in pro- ducing displacement of the idle wheels or electricity along lines which are circles described round the initial vortex as axis, and in propagating outwards the vortex spin or mag- netic force with a finite velocity from one line of molecular vortices to another.

344 DYNAMICAL THEORY OF INDUCTION.

By the aid of the idea» which were discussed in the last section we are enabled to arrive at a mechanical conception which helps us to connect together observed facts, and which, ev^n if not a real representation of what is taking place, is at least a working model, which may assist us to correlate the actions taking place when an electric current is started in a wire.

An electric current on this hypothesis is a flow or pro- gression of the electric particles which are free to move forward in a conductor, and which only can move steadily forward, owing to their incompressibility, when the circuit in which, they flow is a complete circuit. Suppose a thin con- ductor bent into the form of a very large circle, and that an electromotive force urges a procession of electric particles round it. As these particles go forward they cause the electric cells next them to rotate, and the motion of this line of cells embracing the line of current will be just like that which would take place if a bracelet of spherical beads strung on an elastic thread were rolled along a round rod which it closely embraces. Each bead would turn over and over, rolling on the rod, and the motion of the whole bracelet would be like that of a tightly-fitting india-rubber umbrella ring pushed along a round ruler. The progression of the electric particles would start circular vortex rings revolving round the line of motion. This corresponds to the fact that a linear current creates a magnetic field composed of circular embracing lines of forces. The first or adjacent line of vortices would, by the intervention of the idle wheels, set in rotation another set pf cells lying on a concentric line, and cause them to rotate in the same manner as the first ones. Also, it would cause a back- ward displacement of the intermediate idle wheels, if we con- sider that only the central line of electric particles are conduct- ing matter, and that the next and all succeeding rows are in a dielectric. The starting of ihe progressive movement of the line of electric particles in the conductor will result in an elastic displacement in the opposite direction of all surrounding electric particles in the dielectric along lines parallel to the line of current; and also in setting up a system of molecular vortices composed of revolving cells, the axes of these vortices being co-axial circles described round

DYNAMICAL THEORY OF INDUCTION.

345

the line of flow, the rotations and displacements being propa- gated out laterally from the line of current. In consequence, of the fact that the revolving cells are supposed to possess inertia or mass, and that all the mechanism is supposed to bei rigidly connected together, a steady force applied to set the central line of electric particles in motion will not be able to produce in them the full velocity until time has elapsed suffi- •cient to allow the inertia of the connected mechanism to be overcome. We are thus able mechanically to imitate the phenomena of self-induction of the circuit and the gradual rise of current strength in an inductive curcuit under the operation of a steady impressed electromotive force, and to deduce it aa a consequence of the fundamental hypothesis.

Otir theory, then, points out that a current should rise ^adually in strength, and also that the embracing lines o{

magnetic force must be considered to come into existence successively as the rotation is taken up in ever-widening circles by the molecular vortices successively receiving motion of rotation. Also, on withdrawing the impressed electromotive force the inertia of the mechanism tends to make it run on for a little and the electric particles, which by their motion started the vortices, are now themselves urged forward for a little in the same direction, and this constitues the extra current at ** break."

Let us next endeavour to see what ought to happen on the flupposition that there are two conducting circuits in the fieldi both forming closed circuits, and to one of which an impressed ^electromotive force can be appUed. Let V^, Vg, Vg, &c. (Fig. 181),

I

346 DYNAMICAL THEORY OF INDUCTION.

represent the sectional view of a series of vortex lines of eleotrio cells, and let I^ I^, Ig, &o.» be the idle wheels or electric particles. Let the row of electric particles I^ be supposed to be lying inside a conducting circuit, A, represented by the dotted lines, and by our fundamental supposition, the particles \ are quite free to move along the conductor, and to rotate on their axes. Let there be another conductor, B, placed parallel to A, and let I5 be the electric particles in it. The space G between is supposed to be occupied by a dielectric, and in it the electric particles can only be displaced elastically from a fixed position. We may regard these idle wheels I3 13 14 as tethered by springs to one spot. Such being the mechanism, imagine that the row of particles I^ is urged forward in a downward direction* As the row of particles pass between the cells V^ Vg they will set them in rotation in opposite directions. Owing to the inertia of the vortices tha first effect of the rotation of V^ will be to cause I, to roll over V3 and be displaced in an upward direction ; its displacement is resisted by the elastic force of the spring. The rotation of I^, however, sets Yg in rotation, and after a short interval V3 is rotating at the same f^peed and in the same direction as V,. 1^ then ceases to be displaced, because the action of V, on I^, and the reaction of V3 on I,, simply amount to a couple or twi»t on Ij. The same sort of action results in a gradual handing on of the rotation from vortex to vortex, and a propagation of displacement from one idle wheel to the other. When the motion reaches the conductor B, the first result is to cause a displacement of the electric particles upwards, the rotation of V5 not being instantly acquired by Vq. This amounts to a current in the upward or opposite direction. As soon, however, as the vortex V^ has accepted the full speed of rotation, then the forces on the electric particles I5 amount only to twists^ and not to forces of displacement; hence the particles I^ cease to experience any force impelling them forward, and come to rest in virtue of the fact that the conductor offers a resistance to their motion. They fritter down their energy of motion into heat, and come to rest. Hence the induction current in the conductor after a short flow ceases, and the vortex spin becomes equal in the vortices on either side of it. Suppose now that the impressed force in the circuit A is withdrawn, the electrio

DYNAMICAL THEORY OF INDUCTION. 347

particles in the A circuit are driven forward for a short time by the energy etored up in the adjacent vortices ; these last, however, give up one by one their energy to the circuit A, where it is dissipated as heat. This surrender of velocity is propagated outwards until at the surface of the circuit B the state of things finally is, that when the vortex V5 has come nearly to rest, the motion of Vg still continues. The energy of Ye and of vortices beyond expends itself in moving forward the electric particles in circuit B in the same direction as that in which the current in A was travelling originally — ^in other words, part of the energy of the field is spent in making a transitory current in B as well as in A in the same direction. It follows, therefore, that there is a less induction current in A at breaking circuit when a closed circuit B is present than if B were not there — that is to say the presence of a closed secondary circuit B diminishes the self-induction of the primary circuit, as is known to be the case. We see, therefore, that the theory is so far in accordance with observed

The theory must, however, be taJcen for no- more than it is worth, viz.: an attempt to construct a mechanical system which shall act in the manner in which we find electro-magnetic fields and circuits do act. The true mechanism may be very different; the one described has at least the utility that it shows a way in which the observed effects might be produced. The various dynamical elements in the supposed mechanism have their equivalents in the recognised electrical and electro-magnetic qualities. The angular velocity of the cells or vortices around their axis represents the intensity of the mag- netic force, or the strength of the magnetic field. The angular momentum of the vortices represents the magnetic induction^ hence the mass of each cell, or the density of the medium, is the analogue of the magnetic permeability. This is greater in paramagnetic substances than in air or vacuum, and greatest of all in iron ; in fact, so exceptional is it in iron that Maxwell supposed the particles of the iron themselves to take part in the vortex action. Hence, the energy of a magnetic field is greater if that field contain iron, and accordingly the presence of iron in a core immensely increases the vortex energy for a given vortex velocity, that is, it increases the inductance of

348 J)YNAMICAL THEOIiY OF INDUCTION.

the circuit. The energy associated with any reYolving cell or vortex is proportional to the product of its velocity and momentum, or the product of the magnetic force, and the magnetic induction estimated in the same direction is a measure of the energy per unit of volume existing in that portion of the field. The *' number of lines of force " passing through any circuit is on this theory to be identified with the whole momentum of the molecular vortices linked with that circuit. If any circuit is traversed by lines of force or linked with lines of molecular vortices, and the cause creating this field is removed, say, by withdrawing the magnet or repressing the electric current creating it, the vortices give up their energy gradually to this secondary circuit, and it appears there as energy of motion of the electric particles or as an electric cur- rent. When one system of bodie;^ in motion sets another set in motion by mutual action and reaction, and there is no loss of energy by anything like friction or imperfect elasticity, then the momentum gained by one must be equal to thac lost by the other, and the rate of gain of momentum of the one system is at any instant equal to the rate of loss of momentum by the other. Hence, if the vortices lose momentum their rate of loss of momentum — that is, the rate of withdrawal of lines of induction from the circuit, must be equal to the rate of gain of momentum of, or to the force acting on, the electric particles which are absorbing the momentum. Hence we see that the impressed electromotive force in the circuit must be equal to the rate of withdrawal of lines of induction, and the theory conducts us to Faraday's law of induction, as a necessary dynamical consequence of our fundamental assump- tion. Maxwell has extended the theory of molecular vortices to the explanation of electrostatic phenomena, with which we are not, however, here directly concerned. We have seen that the theory is capable of atrording an explanation on mechanical principles, of self-induction, mutual induction, and the law of electro-magnecic induction. In order to complete the theory as far as regards the phenomena of magnetism, it is necessary to suppose that the particles of magnetisable metals, such as iron, are set in rotation by the molecular vortices which traverse them, and that an increase of speed of these vortices does not increase proportionally the rotation of

DYNAMICAL THEORY OF INDUCTION. 349

the iron molecules. These last behave like wheels dtmg loosely on a shaft, between which shaft and the wheel there is friction decreasing as the speed of rotation of the shaft increases. If, then, the wheel experiences a constant frio- tional resistance from external causes, indefinite increase of speed of the shaft would accelerate the wheel's rotational velocity up to a certain point, and the wheel would then cease to ro&ace. This supposition would enable us to make our theory agree with the fact that increase of magnetic force does not iucrease indefinitely the magnetic induction through iron, but brings it up to a point at which, approximately speaking, the iuducbion remains stationary. To sum up, we may say that the hypothesis of molecular vortices is an endeavour to imagine a mechanism capable of accounting for electro-magnetic induction on dynamical principles, and on the assumption that the energy of a magnetic field is energy stored up in a medium in virtue of a particular kind of rotation of its parts.

This medium consists of portions capable of elastic displace- ment when we consider parts of it lying in dielectrics or capable of progressive movement when in conductors, and these portions constitute what we call electricity. Other por- tions are capable of rotation round closed axes of rotation, and these constitute what we call *' lines of force." The medium possesses, therefore, an elastic resilience, and the reciprocal of this quality, or its freedom of yielding to electromotive force, is recognised as the specific inductive capacity. The medium possesses also density, and we call this its magnetic permeability, or magnetic inductance. The mass of unit of length of the vortices is equal for all vortices, whether in vacuum, air, or non-magnetic bodies, but in iron the vortices are loaded by the adhesion to them of the molecules of the metal, and the density is increased, and hence the permea- bility ; but for very great angular velocities — that is, for great magnetic forces — the adhesion of the molecules and vortices must be supposed to cease, and the permeability approximates to unity. The magnetic force at any point in a field is the angular velocity of the vortex motion at that point, and the magnetic induction is the angular momentum. Magnetic attraction and repulsion is due to the tension set up along a

360 DYNAMICAL THEORY OF INDUCTION.

^vortex line by the polar contraction and equatorial expansioii •of the vortex cells. At places where there is magnetic polarity or free magnetism there is a discontinuity in the angular velocity of the vortices within and without the iron. Self-induction is the result of the inertia of the molecular vortices, whereby motion set up in them cannot be generated or checked instantaneously. Mutual induction, or the pro* •duction of induction currents, is due to the fact that differences in the angular velocity of adjacent vortex filaments or cells •cause a displacement of the electric particles or idle wheels. FinaUy, electromotive force is the force causing displacement •of the electric particles, and electric currents consist in con- tinuous or periodic movements of these electric particles* Electric currents always produce magnetic fields because there is nothing of the nature of slip between the particles ■and cells, and, therefore, any progressive movement of the first sets up rotation in the second, and conversely differential rotations or spins of the cells or vortices sets up displacement of the electric particles, causing either electric strain in a dielectric or electric current in a conductor.

§ 4. Oomparison of Theory and Experiment. — The test of any physical theory is its power to predict new phenomena ■as well as to interpret ascertained experimental results. The theory of molecular vortices leads to the conclusion that electro-magnetic induction must be propagated through the medium with a finite velocity, and that in dielectrics of unit permeability the velocity of propagation is inversely as the square root of the specific inductive capacity. In the dynamical theory of Ught it is shown that the ratio of •the velocity of light in vacuo to its velocity in any given transparent medium is a constant quantity for each definite wave length, and is called the index of refraction of that body for that wave length, and is denoted in physical optics by the symbol fi. Hence, the velocity of light of definite wave-lengih is inversely as the refractive index for that wave-length. The refractive index for very long wave-lengths can be calculated £rom observed values of /a for definite rays, and hence numbers obtained representing the relative velocity of these undulations in various transparent bodies. The values of the dielectric

DYNAMICAL THEORY OF INDUCTION.

351

contiMUit or reciprooal of the electrio elasticities, of various transparent and semi-transparent bodies have also been deter- nuned, and it has been found that for a large group of bodies ihere is a tolerably close agreement between the values of the square root of the dielectric constant and the index of refraction fix for very long waves, as shown by the selection from the results of some experimental determinations given in Table A.

Table A.

(Dielectric Constant).

VK

(Refrac- tive Index).

Authority.

Reference.

43ulphur 3-84

Colophonium.. .. 2'55 Paraffin 2-32

Pure rubber 2-12

Oil of turpentine 221

PetroUum 2057

Benzine 2*198

Petroleum spirit 1*92 Petroleum oil ...2-07

Ozokerite 2*13

Turpentine 2*23

1*96 1-69 1-62

1-46

149 143 148 138 1^ 146 149

1*60

Boltzmann

Schiller

Silow

J. HopkinsoD

rPo3Fi.i4nn.,CLI., [ lb74,p.482.

I Potty, ilnn., \ CLU.,p.536. ' Fogg, Awn,, CLVL, 1876, p. 395.

f Trani, Roy. Soc. { 1877, 1878 and \ 188L

For some otber dieleotricSi such as glass and the vegetable And animal oils, the agreement is not by any means so close but for gases, as determined by Boltzmann {Pogg, Ann., GLL» 1875| p. 408), there is a fair coincidence. (See Table B.)

Table B.

Gas.

Air

Carbonic acid

Hjdrogen

Carbonic oxide ... ,

Kitrous oxide

01e6ant(eas

liarsh gas

-v/K

1*00059

1*000946

1*000264

1*000690

1*000994

1*001312

1*000944

1-000296 1-000473 1000132 1000346 1000097 1000666 1000472

1000294 1000449 1000138 1-OQ0340 1000503 1-000678 1-000443

The gases are taken at O'^C. and 760 millimetres pressure. Aecordingly, we can say that, for a large group of dielectrics, of which the magnetic permeability is unity, and hence the ▼elooity of propagation of an electro-magnetio impulse propor-

352 DYNAMICAL THEORY OF INDUCTION.

tional to the square root of the electric elasticity or to Qie reciprocal of the square root of the dielectric constant, we- do find a fair agreement between these numbers and the numbers representing the refractive indices or the relative- velocities of propagation of very long waves or disturbances in the ethereal medium postulated to account for the phenomena of light. The imperfect agreement between the values of the- refractive index for long wave-Jengths and the square root of the dielectric constant for some other bodies shows that the theory is only approximately in agreement with fact, and that the results obtained by the methods adopted for deter- mining the dielectric constant are perhaps impure, and da not give the true value of the electric elasticity. When we consider that the displacements which constitute the light wave motion of the luminiferous ether are changed some- billions of times per second, it is seen to be highly prob- able that measurements of the specific inductive capa- city in which the electric stresses are only reversed tens or hundreds of times in a second may be rendered impure or mixed owing to the presence of effects due to an imperfect electric elasticity introduced by the superposition of electric conduction or of electrolytic transport upon thiB true or elastic displacement effect. In fact those bodies, such as glass and the vegetable oils, which exhibit the greatest discrepancy, are- those in which the chemical composition indicates a possibility of electrolysis. There may be an electro displacement in such, electrolisable bodies over and above the true eleotrostatie displacement which is engendered by a molecular change in the body, which change results in actual decomposition when the electric force reaches a certain limit. Put broadly, ii may amount to this, that the true electric displacemeni is a displacement of electricity within the molecule, but that in electrolisable bodies electric stress sets up a strain of the molecule itself which, within certain limits, is an elastio strain, and disappears with the removal of the stress, but that beyond these limits molecular disruption takes place. In these cases the displacement measured in taking the specific: inductive capacity is the true or dielectric displacement plf» ft displacement due to strain of the molecule, and the result, would be to make E appear too great, and, in faot, for glasa

i -

DYNAMICAL TBEOltY OF INDVCTIOK.

353

and certain oils the values in Table G have been obtained, which in all cases are such that JK exceeds the value of fi^ , or the refractive index, for very long waves of light.*

Table 0.

Substance.

Glass, extra dense flint

„ light flint

„ crown

« plate

Castor oil

Sperm oil

Olive oil

Neatafoot oil

K

n/K

9-896

31

6-72

2-59

6-96

2-63

8-45

2-90

4-78

2-18

302

1-73

316

1-77

307

1-75

M» (approx.)

1-5 to 1-6

1-46 1-46 1-46 1-45

J. Elemencio (abstract in the Jownal of the Society of Tele^ graph Engineers, 1886, p. 108) has experimented also on the specific inductive capacity of gases and vapours, and given a table {see Table D) in which he compares VK with fi (refrac- tive index) of these same bodies. It is seen that the agree- ment of n/K and /x is very close for the simple gases, but that a marked difference exists in the case of more complicated molecules.

Table D.

Gas.

Air...

Hydrogen

Carbonic acid ,