The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 18 of 36

Consider a long level tank or canal full of liquid. There are, amongst others, two ways in which we might suppose this Hquid to be set in motion. A paddle or the hand might be placed in the liquid, and by giving the liquid bodily a push it might be made to move forward ; or we might suppose some body floating on the surface, such as a. plank of wood to be dragged along the surface. The friction between the plank and the layer of water beneath it would then cause the subjacent layer of liquid to move with the plank, and the motion of this layer would be gradually com- municated to the other and deeper-lying layers by reason of the viscosity of the fluid. Or take the case of a basin containing water. The liquid might be set in rotation by stirring it with a paddle or the hand, but it might also be set in rotation by twisting the basin rapidly. In this las: case the rotation of the basin would be communicated by friction to the water in contact with its sides, and then handed

• DiflcuMioQ on a Paper by Mr. >V. H. Preece on " Eleofcrical ConductorB,*" Proceedings In&t Civil EDgineers, Vol. LXXV., 1883.

t ''Electromagnetic Theory." by Oliver Heaviaide in The SUetrieian. taiee, And ** Eleotrioal Papers," published by Messrs. Macmillan.

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on from layer to layer of the water by internal fluid friction. Thus the twist or spin of the basin would be gradually propa- gated inwards from the circumference to the centre. Imagine the whole mass of the liquid divided up into very thin con- centric shells, like the coats of an onion. If the liquid were & perfect fluid there would be no friction between these layers, but since every liquid possesses some degree of viscosity or internal fluid friction, the sliding of one layer of fluid over Another gradually causes the second layer to partake of the motion of the first. Hence, when the rotation of the basin commences the friction between its sides and the first layer of fluid starts that gradually in motion ; this motion is then transmitted to the second layer, and so on, until the whole mass of the liquid possesses an equal angular velocity round the Axis of rotation. The greater the fluid friction or viscosity the more rapid will be this equalisation of the angular velocity of All parts of the fluid, and so a rotating vessel full of tar would Arrive at a stationary condition as regards angular velocity sooner than one filled with a limpid liquid as alcohol or ether. Just as the angular velocity diffuses inwards from the circum- ference to the centre in the case of such a revolving basin of liquid, so, according to modem views, does the current diffuse inwards from the circumference to the axis of the electric con- ductor, The student who has been accustomed to think of a ourrent as produced in a conductor by a sort of push given to it in the conductor — such conception being based on a rough working hypothesis of a hydrodynamic nature — will perhaps have some difficulty in discarding this notion and realising that the current in a wire may perhaps be generated in it by an action taking place at all parts of the surface of the wire which gradually soaks or diffuses into the conductor out of the sur- rounding dielectric, but he will find that this new hypothesis serves to establish a mode of viewing the induction phenomena which makes various experimental results much more easily cor- related. It was well demonstrated by the experiments of Prof. Hughes and others that a flat sheet or strip of metal has a less self-induction than a round wire of equal cross-sectional area. On the present hypothesis, this is explained by saying that the flat strip offers a greater absorption surface to the dielectric ; the xsurrent therefore soaks in more quickly to the centre and arrives

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At a uniform distribution over the cross section very soon — in other words, the variable state is sooner over, and we express this flEkct by saying that the self-induction is small. Again, if the electromotive force is oscillatory or rapidly periodic, we see at once that the current has not time to penetrate right into the core of the conductor before its sign or direction is reversed. It has hardly started on its journey inwards, soaking from sur- face to centre, before it is recalled ; hence the flow of a current when very rapidly periodic is confined to the surface of the conductor, the real or ohmio resistance is increased^ and the self-induction is diminished.

Lord Kelvin has shown (Bath British Association Meeting, 1888) that for alternating currents of a frequency equal to about 150 complete alternations per second, the depth to which the •currents penetrate into the substance of the copper is about three millimetres, so that portions of the conductor beyond this distance from the surface are almost useless for conduction. The practical moral of this is that the proper form for a con- <luctor for alternate currents is either a flat sheet of copper or a copper tube, in which, for the above frequency, the thickness of material is not more than one-quarter of an inch. It is useful in this connection to note a few facts with regard to cables as used for alternating currents. A seven strand cable has an overall diameter of three times one strand. A nine- teen strand cable has an over-all diameter of five times one strand. A No. 12 wire (S.W.G.) has a diameter of 0109 inch. Hence a 19/12 cable has a diameter of 05 inch, and a cross- sectional area of 0*1615 square inch. At a current density of 600 amperes per square inch this cable will carry 100 amperes, and it has a resistance of one-sixth of an ohm per 1,000 yards. For alternating currents, therefore, of about 100 frequency, a 19/12 stranded cable is about the largest size that should be employed. For alternating currents of 100 frequency, beyond about 100 amperes, a form of cable must be employed in which the thickness of the conductor is not at any part greater than about one quarter of an inch ; and this is only to be achieved by the employment of concentric tubes or concentric stranded cables in which the core or central strand is not of greater thickness than half an inch, and which con- dition necessitates, therefore, that when above a certain cross-

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seotioiial area the central conductors should also be of tubular form. One of the advantages to be gained by the employment of altematmg currents of low frequency is that the limiting diameter of the conductors is much larger for low than for high frequency. To return to our illustration of the twisting basin of fluid. Suppose the action on the vessel consists in rapidly twisting it through a small angle, first one way and then the other, the liquid in the interior would be subjected ta a strain which would consist in the various concentric layers of the liquid sliding backwards and forwards over each other. The interior of the liquid would be thrown into stationary waves, in which the nature of the wave motion consisted in each particle of water being displaced first one way and then another along an arc of a circle described on a horizontal plane, with its centre in the axis of rotation. The more rapid the motion the greater would be the rate of decrease in the amplitude of each wave in passing from the circumference ta the centre of the vessel ; in other words, for very rapid oscilla- tions the bulk of the water in the centre of the basin would remain nearly at rest.

Every experiment as yet made on the self-induction or change of self- induction in conductors is consistent with the above hypothesis. It shows, for instance, why a conductor composed of thin insulated wires or thin insulated strips has a less self- induction than a solid conductor of equal cross-section. Prof. Hughes says*: — 'We can reduce the self-induction of & current upon itself to a mere fraction of its previous value by simply separating the contiguous portions of a current from eaoh other, the results proving that a comparatively small separation, such as is obtained by employing ribbon conductors in place of a wire of the same weight, reduces the self-induction 80 per cent, in iron and 85 per cent, in copper, and if we still divide the current by cutting the ribbon into several strips (separating the strips at least 1 centimetre from each other), then the combined but separated strips show a still greater reduction, being 94 per cent, in iron and 75 per cent, in copper.'

These, and many other experiments of a similar sort, indicate that we may regard the inductance of a conductor as an effect which is due to the fact that the current takes Hme to pene*

• luauguml Addreds, Journal Soo. TtL £ng,, 1886.

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trate into the conductor, and that a reduction of the time required to arrive at an equal current density in all parts of the conductor can be effected by any change of form which brings the inner parts of the conductor nearer the surfiEU3e, or makes them more get-at-able from the dielectriCi The better the conductor the slower is the rate of equalisation of current density over its cross-section — ^in other words, the less rapid is the rate of diffusion of the current inwards from circumference to centre; and the "time constant" of the circuit, or the time in which, under the operation of a constant electromotive force, the current will rise to a definite fraction of its maximum value, is a quantity proportional to the con- ductivity of the circuit, and to another factor (the formal inductance), which may be considered as expressing the accessibility of the conductor as regards geometrical form to the entrance of the current into it ; and finally, in the case of magnetic condactors, to a quantity (the permeability) deter- mined by the capacity of the conductor to utilise part of this mcoming energy in producing magnetisation of its substance.

We are indebted to a Paper read before the Austrian Academy by Prof. Stefan for a simple and intelligible analogy helping to comprehension of the electrical distribution of current in a conductor. Imagine a cylinder or cylindrical wire heated throughout to a uniform temperature ; let it be suddenly brought into a chamber where the temperature is higher. The outer layers of the cylinder will rise first in temperature, and gradually convey the heat to the successive interior layers. Precisely the same order of phenomena occurs if an E.M.F. is suddenly set up between tiie ends of the wire or cylinder. The current during the variable state passes first through the outer layers alone, and gradually penetrates the inner layers. When the external E.M.F. is suddenly removed, the action, of ceasing in the current resembles the cooling of the cyUnder. The current ceases first, or, rather, most quickly, in the outer layers.

Now, let us imagine the cylinder transferred to and fro from a very hot place to a cool one. It is easy to see that waves of heat will pass in and out radially, and also that the condition at any instant will depend largely upon the rate of transference.

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' When the rate of motion is sufficiently slow, the waves of heat passing any given point in the radius of the wire follow exactly with the periodic changes of position. The amplitudes of these variations have values which decrease from the sur- &ce inwards. When the rate of change is increased, the amplitude of the waves gets shorter and shorter, and at an infinite velocity of transference the wire would acquire an equable temperature throughout. In the electrical analogue the rate of transference corresponds to the inverse of the periodic time of an alternating current. The heat conducting power of the material corresponds to electrical resistance.

Prof. Stefan gives some numerical illustrations which are useful. If an alternating current have a frequency of 250 per second and is passed through an iron wire of 4mm. diameter, the amplitude of the waves of current density is about twenty- five times greater upon the surface than at the axis of the wire. For double the number of vibrations per second the external amplitude becomes only six times as great. The difference of phase is one-third the duration of the vibration in the first case and one-half in the second. The latter statement implies that the external current is at a given moment actually in the reverse direction to the internal current.

For non-magnetic wires the difference is not nearly so marked, and it decreases as the specific resistance increases. For a copper wire of 4mm. diameter, with a periodic time of one 500th second, the difference between the current density at the surface and at the centre is only 14 per cent. If, how- ever, the copper wire be increased to 20mm. diameter, then we should get the same difference as in the particular iron wire quoted.

It is obvious that this non-homogeneous distribution of current must increase dissipation of energy, which is, of course, proportionate in each transverse section to the square of the current strength at that spot. In the case of the iron wire quote4i the increase of resistance is 48 per cent, at the 250 per second frequency, and 100 per cent, at the higher speed. As the frequency of alternation is increased, the resultant self-induction of the circuit is lessened, but although the true resistance is increased, the impedance may be diminished on the whole.

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§ 12. Electromagnetic Beptdsions. — The effects of self and mutual induction in conducting circuits are well illustrated in studying the dynamical actions taking place between con- ductors conveying currents and other circuits. On the 2nd day of October, 1820, Ampere presented to the Boyal Academy of Sciences in Paris an important memoir, in which he summed up the results of his own and Arago's investigations in the ^hen new science of electro-magnetism, and crowned that labour ty the announcement of his great discovery of forces of attraction or repulsion existing between conductors conveying electric currents.* Respecting that achievement, when deve- loped in its experimental and mathematical completeness, "Clerk Maxwell speaks of it as ** one of the most brilliant in the history of physical science." Our wonder at what was then accomplished is increased when we remember that hardly more than two months before that date John Christian Oersted had startled the scientific world by the announcement of the discovery of the magnetic qualities of the space near a current- traversed conductor. Oersted named the actions around the conductor, which we now refer to as the magnetic field, the electric conflict, and in his first Paper, t in describing the newly-observed facts, he says : '< It is sufficiently evident that the electric conflict is not confined to the conductor, but is dispersed pretty widely in the circumjacent space.** "We may likewise collect," he adds, " that this conflict performs circles round the wire, for without this condition it seems impossible that one part of the wire when placed below the magnetic needle should drive its pole to the east and when placed above it to the west.*' These words are taken from the •original paper, which stimulated the philosophic thought of

• Mdmoire pi^sent^ ^ I'Acad^mie Boyale dee Sciences le 2 Octobre, 1820, oh 86 trouve compris le r^umd de ce qui avait ^t^ lu & la mSme AcadSmie les 18°>* et 25"* Septembre, 1820, sur lea e£fet8 dee courants Electrique, par M. Ampere. See YoL XY. Annalet de Chimie, 1820.

t In the AwMle of PhUotophy for October, 1820, YoL XYL, p. 274, u to be found an EngliBh tranalation of Oersted's original Latin essay, dated July 21, 1820, describing his immortal discovery. This Paper is entitled "Experiments on the Effects of a Current of Electricity on the Magnetic Keedle," by John Christian Oersted, Ejoight of the Order of Danneborg, IVofessor of Natural Philosophy in Copenhagen.

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Ampere, and finally led him to the valuable discovery of the electro-dynamio actions between conductors conveying currents.

Beferring the student to text-books on Physics for the complete statement of Ampere's work, we may describe briefly some illustrations of the interactions of two circuits traversed by currents in the same or opposite directions. Holding a circular coil traversed by a continuous electric current near ta a similar circuit free to move, we find that when the circuits are parallel to each other there is an attractive force between them if the currents in adjacent parts of the circuits flow in the same direction, and a repulsive efifect if they flow in the opposite. This is the electro-dynamic action discovered by Ampire and utiUsed in the construction of instruments for the measurement of electric currents in practical work. If one conducting coil, such as that of an electro-magnet, is traversed by an alternating current, and the other is simply a closed circuit or coil placed a little distance off, but in its field, it has been previously explained that the closed circuit becomes the seat of an alternating induced current, which, if the inducing current is sufficiently powerful, can be made to render itself evident by illuminating a small incandescent lamp placed uk the secondary circuit.'*^ We notice, however, that in perform- ing the experiment the secondary circuit must be so placed that the magnetic induction of the primary coil perforates through the secondary circuit. If the secondary circuit is held in such a position that the reversal of direction of the primary current causes no reversal of direction of the magnetic field traversing the secondary circuit, because it is not linked with any of the lines of induction of the primary, the secondary circuit is no longer the seat of any induced current.

• The experiments described in the following paragraphs can be shown with an alternating current magnet, having a core formed of a handle of fine iron wire about 3in. in diameter and 12in. long, excited bj an alternat- ing-current dynamo, giving a current at an electromotive force of about 100 volts. A small shelf around the core a little above the middle serves as a support for rings, &c., to be projected. The performance of these experiments on a scale suitable for large audiences requires from 10 to- 15 horse-power at least, and can hardlj be shown well unless the alternator can provide a current of 100 amperes at 100 volts available at the moment of maximum demand.

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This electromagnetio induction thus taking place across space is not stopped by the interposition of a non-conducting screen. The magnetic induction passes freely through a deal board or a plate of glass, but if we interpose a thick sheet of copper (Fig. 112) we thereby screen the secondary circuit from tiie inductive action of the primary. The rapid heating of this copper screen makes us aware that the secondary currents are induced in the copper sheet in the form of eddy currents, and it therefore screens the secondary circuit, as already explained, because the inductive action of these eddy

Fig. 112. — Copper Plate interposed between a Primary and a Secondary Coil and shielding the Secondary from Induction.

currents on the side remote from the magnet is exactly equal and opposite in inductive effect to that of the primary circuit on the secondary coiL

If a continuous current is sent through the coils of an electro-magnet, and magnetises its iron core very powerfully, it is found to be impossible to strike the pole of the magnet a sharp blow by means of a sheet of copper. Holding a sheet of copper over such a magnetic pole, and exciting the magnet, the hiemd holding the copper sheet feels a repulsive action at

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tHe moment when the current is put on and an attractive action when it is cut off. If we try to slap the magnet pole sharply with the copper sheet, it is found that this repulsive force prevents anything like such a sharp blow being given to the pole when the current is on as can be given when the current is off. Moreover, when a very powerful electro- magnet is employed, it is found that a disc of copper let fall over the pole does not fall down sharply and quickly on to it when the current is flowing through the coils of the magnet, but settles down softly and slowly as if falling through some viscous fluid. The correct explanation of these facts is to be found in the statement that the motion of the conductor towards the magnetic pole causes eddy electric currents to be generated in it by electro-magnetic induction, and that these, being in the opposite direction to the exciting current of the magnet, cause a repulsive force to exist between the inducing and secondary circuits, which creates the apparent resistance we feel.

In order to exhibit the stress brought into existence between an electro-magnet and a metal sheet held near it when induced currents are set up in the disc, we may arrange the following experiment: — Over the pole of a powerful electro-magnet we balance a small disc of copper, the size of a penny, carried on one end of a delicately-balanced bax. A mirror attached to that bar serves to reflect on to a screen a ray of light indicating the smallest motion of the copper disc. On magnetising the magnet the copper is suddenly repelled, but comes to rest again immediately in its initial position* When the magnet is demagnetised the copper experiences a momentary attraction. Or we may illustrate the same action in another way. Consider, for instance, a ring of copper hanging in front of the pole of an electro-magnet {see Fig. 118), having the plane of the ring perpendicular to the lines of magnetic force proceeding out from the pole. Let the magnet be an electro-magnet, and let the pole be suddenly made a north or marked pole. Lines of magnetic force are thrust into the aperture of the ring. This magnetic flux, in Accordance with a well-known law, generates an inductive electromotive force, which causes a transient current to flow round the ring in a counter-clockwise direction, as looked at

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311

ftom the north magnetic pole. The ring hecomes virtually a. niagnetic shell, having a north pole facing the north pole of the exciting magnet. By the fundamental laws of action between currents and magnets established by Ampere, the ring experiences a slight repulsive force, due to the electro- dynamic action between the current in the ring and the magnetic pole. The generation of the momentary induced current in the ring is accompanied by an electro-dynamic impulse tending to thrust it away from the pole.

Suppose, next, that the electro-magnet is demagnetised. The ring has generated in it a reverse induced current flowing in the direction the hands of a clock move when looked at from the magnetic pole. This is also accompanied by an electro-dynamic attraction of the ring towards the pole, but

Fio. 113. — Copper Riog hung in the Field of an Electro-magnet, and Repelled or Attracted when the Current is put on or cut off.

which is much more feeble than the previous repulsion. These attractions and repulsions are obviously due to the Ampdrian stress set up between the magnet and the metal by reason of the induced currents set up in the latter. It has been pointed out by Prof. S. P. Thompson that Ampere himself probably observed an effect of this kind {Proc. Phys. Soc. of London, Vol. XIII., p. 493, " Note on a Neglected Experiment of Ampere.*'). Impulsive effects of this nature have been also studied by Prof. Vernon Boys (see Proc. Phys. Soc. of London, Vol. VI., p. 218, " A Magneto-electric Phenomenon ").

Let us in the next place consider a circuit, say a closed conducting ring, suspended in front of the pole of an electro- magnet, and let the coils of the electro-magnet be trans-

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versed by an alternating current of electricity (Fig. 118)« The magnetic field of the magnet is then an alternating field. We shall suppose it to vary in strength according to ft simple periodic law. The closed circuit is therefore subjected to an inductive action, and we know that the induced electro- motive force in that circuit is at any instant proportional to the rate of change of the magnetic field in which it is immersed. If, therefore, the variation in strength of that field is represented geometrically by the ordinates of a periodic curve, the varying electromotive force acting in the ring circuit is represented by the ordinates of another such curve of equal

I

Fia. 114. — Diagram showing the Equality of the Attractive and Repulsive Impulses in a Non-inductive Circuit when held in an Alternating Magnetic Field.

wave length, shifted a quarter of a wave length behind the first. In the diagram (see Fig. 114) the variation of the in- duced magnetic field, and the induced electromotive force in the circuit, are represented as usual by two harmonic curves. This induced electromotive force creates an induced current flowing backwards and forwards in the ring, and we shall, in the first instance, suppose that this current flows in exact synchronism with its electromotive force. The induced current and the inducing magnetic field may there- fore be represented as to relative phase and strength by the curves in the diagram (Fig. 114). The dynamical action,

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or the force which the ring experiences, is at any instant proportional to the product of the strength of the mafgnetio field in which the ring is immersed and to the strength of the indaced current created in it. If we multiply together the numerical values of the ordinates of these two curves at any :and every point on the horizontal line, and set up a new ordinate at that point representing this product, the extremi- ties of these last ordinates define a curve, which is a curve representing the force acting on the secondary circuit ; and it is seen from the diagram (Fig. 114) to be a wavy curve having a wave length equal to half that of the first two curves. More- over, the whole area enclosed between the outline of this force onrve and the horizontal line represents to a certain scale the time integral of that force, or the impulse acting on the secon- •dary circuit, and the theory shows us that, under the assump- tions made, the secondary circuit so acted upon experiences in each period of the current four impulses, two positive or repul- sive, and two negative or attractive. Hence, it follows that such an ideal conducting circuit held in front of an alter- nating electro-magnet should experience a rapid alternate series of equal pushes and puUs, or of little impulses to and from the magnet. These equal and opposite impulses in quick succession would neutralise one another, and our supposed circuit would not, on the whole, be subject to any resultant force.

When we present a real conducting circuit to the pole of an •electro-magnet traversed by a powerful alternating current, we find that under the actual circumstances there is a powerful repulsive action between the pole and the circuit. With a powerful alternating current electro-magnet striking effects of repulsion may be thus shown.

If we hold a copper ring over the pole of a powerful vertical alternating electro-magnet, we find at once that there is a perceptible and strong repulsion. Letting the ring go, it jumps up into the air, impelled so to do by the electro-magnetic repulsion acting upon it (Fig. 116). All good conducting rings will execute this gymnastic feat, and rings of copper and aluminium are found to be most nimble of all. Bings of zinc and brass are sluggish, and a ring of lead will not jump at all. Prof. Elihu Thomson was the first to call attention to this strong repulsive action between conducting rings and an

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idternating electromagnet. He has thus described his first notice of these eflTects : — " In 1884, while preparing for the International Electrical Exhibition at Piuladelphia, we had occasion to construct a large electro-magnet, the cores of which were about Gin. in diameter and about 20in. long. They were made of bundles of iron rod about ^^in. in diameter. When complete the magnet was energised by a current from a continuous-current dynamo, and it exhibited the usual powerful magnetic effects. It was found also that a disc of sheet copper of about yir^n. in thickness and lOin. in diameter, if dropped flat against a pole of the magnet, would settle down softly upon it, being retarded by the development of currents

Fig. 115.

in the disc, due to its movement in a strong magnetic field, and which currents were of opposite direction to those in the coils of the magnet. In fact, it was impossible to strike the magnet pole a sharp blow with the disc, even when the attempt was made by holding one edge of the disc in the hand and bringing it down forcibly towards the magnet. In attempting to raise the disc quickly off the pole a similar but opposite action of resistance to movement took place, showing the development of currents in the same direction as those in the coils of the magnet, and which current, of course, would cause attraction as a result. The experiment could be tried in another way. Holding the sheet of copper by one

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edge, just over the magnet pole {see Fig* 115), the eurrent in the magnet coils was cut off by shunting them. At that moment ^was felt an attraction of the disc, or a dip towards the pole* On starting the current the plate experienced a powerful re- pulsion." The question may then be asked : Why is it the rdetal rings are always repelled by the alternating magnet? The explanation is not difficult to find. The real ring possesses a quality, called its inductance, of which we took no account in our examination of the case a moment ago. As a oon-

Fio. 116. — Aluminium Kiog projected from the pole of an Alternating Electro-magnet, and floating over the pole when restrained by three strings.

sequence of this inductance we have seen that the current induced lags in phase behind the inducing electromotive force. We have then to correct the diagram considered just now, to make it fit in with the facts of nature, and we must repre- sent the periodic curve which stands for the fluctuations of iihe induced current in the ring as shifted backwards or lagging behind the curve which represents the electromotive forci) in the circuit brought into existence by the fluctuating

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magnetic field* Making this change (Fig. 117), and formingi as before, a force curve to represent the impulses on the ring, we then find that, owing to the <* lag " of the secondary currenti one set of the impulses, namely, the positive or repulsive impulses, has been enlarged at the expense of the negative or attractive impulses. Theory, therefore, points out that, as a consequence of the self-induction of the ring, the balance between the attractive impulses and the repulsive impulses is upset, and that the latter predominate. The real ring behaves therefore, very differently to the ideal non-inductive ring. The real ring is strongly repelled, because the resultant action

Fio. 117.— Diagram showing the Inequality of the Attractive and Repnl- eive Impulses in the case of an Inductive Circuit when held in an Alter- nating Magnetic Field.

of all the impulses is to produce, on the whole, an electro- magnetic repulsion. This repulsion is evidence of the self- induction or inductance of the circuit exposed to the magnetic field, and it forms a new way of detecting it. But although this is part of the truth, it is not the whole truth. The lag of the induced current in the ring, and hence the predominance of the repulsive impulses, depends on the conductivity of the material of which the ring or circuit is made ; and the better

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{his oondnctivity the greater is that repulsion, because both the induced current and the lag are thereby increased. Hence it comes to pass that there are two factors involved in making this repulsive effect, the conductance of the ring or disc and its inductance. For equal conductivities, the greater the self- induction the greater the repulsion. For equal self-inductions, the greater the conductivity of the circuit so much the more repulsive effect will be produced.

We can show the effect of the relative conductivity of discs of equal size, and therefore of equal self-induction, by weighing similar discs of various metals over an alternating pole. If we take discs of copper, zinc, and brass of equal form and size, and weigh these discs on the scale pan of a balance placed over the pole of an alternating current magnet, the scale pan being made of a good non-conductor, we can measure the electro-magnetic repulsion on the disc by the loss in weight it experiences.*

The same result can be illustrated by placing over the pole of our alternating magnet a paper tube. Taking one of the copper rings, and first exciting the magnet, we let the ring drop down the tube. It falls as if on an invisible cushion that buoys it up, and it remains floating in the air. If rings of different metals and equal size are placed 'on the tube, they float at different levels like various specific-gravity beads in a liquid. The greater the conductivity of the ring the greater is the repulsion on it in any given part of the alternating field, and hence the highly conducting rings will be sustained in a weaker field than the feebler conducting ring, assuming the rings to have about equal weights. Moreover, we are able to show by another experiment the fact that these rings are traversed, when so held, by powerful electric currents. If we press down the copper ring upon the zinc or brass ring floating •l)eneath it, the rings are attracted together and the copper ring holds up the zinc. This is obviously because the rings are all traversed by induced currents circulating in the same direction.