The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 29 of 36

must have passed into that space from out&ide, or that aiif equivalent quantity of some other form already in the enclosure must have been transformed. If energy ^appears at one point and reappears at an adjacent point in equal amount, we can with perfect propriety speak of it as having been transferred from one point to the other, although we are unable to identify the respective portions of it as we can in the case of the movement of matter. Applying this view to the simple phenomena of a battery producing heat in a> conducting wire, the notion to be grasped is that the potential energy of the chemical combinations in the battery causes energy to be radiated out along certain lines, the means of conveyance being the electro-magnetic medium ; this energy flows into the wire at all points, and is there- re-transformed into heat or light. A simple illustration- of Poynting's law is to consider the case of a section of a straight conductor traversed, as we usually say, by a current. Let the conductor be a right cylinder, or round wire, of length I, radius r, and let E be the electric force at any point in the wire, and H the magnetic force at the surface ;. also let V be the potential difference between the ends, G the steady current, and B the total ohmic resistance. Consider the energy flowing in on this section of the wire through its- sur&ce. It is equal per second to the area of the surfeuse,

,,. ,. ;! u EH . 2irriEH

multiphed by -- — , or to .

4;r 4;r

Now 23r r H is the line integral of the magnetic force takei» round the wire following the circular surface, and this, as pre« viously shown (p. 25) is equal to 4;rO. Also we have the potential difference at the ends of the cylinder equal to the line- integral of the electric force, or to Z E. Since, then, 2r r H •B4irC and E {»¥, we get, by substitution in the value of the energy sent per second into the section of the wire, viz.^

?L!lL5^, the equivalent 0 V. But by Ohm's law 0 R « V ^

4a'

hence the energy absorbed per second by the conductor is CB, and we know by Joule's law that this is the measure of the- energy dissipated per second in the wire as heat. We see» then, that the energy dissipated in each section of the con- ductor is absorbed into it from the dielectric, and the rate o£

DYNAMICAL THEORY OF INDUCTION. 485

-this supply can be calculated by Poyntiog^s law for each element of the surface. None of the energy of a current travels along the wire, but enters mto it from the surrounding non- •conductor, and as soon as it enters it begins to be transformed into heat, the amount crossing successive layers of the wire decreasing tiU, by the time the centre, where there is no magnetic force, is reached, it has all been transformed into heat.

In the Paper another simple case treated is that of a con- •denser discharged by a wire. In this case, before the discharge, we know that the energy resides in the dielectric between the plates. If the plates are connected by an external wire, accord- ing to these views the energy is transferred outwards, along the •electrostatic equipotential surfaces, and moves on to the wire, and is there converted into heat. According to this hypothesis, "we must suppose the lines or tubes of electrostatic induction Tunning from plate to plate to move outwards as the dielectric strain lessens and, whilst still keeping their ends on the plates, finally to converge in on the wire and be there broken up and their energy dissipated as heat. At the same time the wire iu^uires transient magnetic qualities. This means that some part of the energy of the expanding lines of electrostatic induc- tion is converted into magnetic energy. The magnetic energy is contained in ring-shaped tubes of magnetic force, which •expand out from between the plates and then contract in upon some other part of the circuit.

The whole history of the discharge niay be divided into three parts. First, a time when the energy associated with the system is nearly all electrostatic and is represented by the energy of the lines or tubes of electrostatic induction running . from plate to plate; second, a period when the discharge is at . its maximum, when the energy exists partly as energy asso- ciated with lines of electrostatic induction expanding outwards, and partly in the form of closed rings or tubes of magnetic force expanding from and then contracting back on the wire ; 4i.nd lastly, a period when nearly all the energy has been absorbed or buried in the wire, and has there been dissipated in the form of heat, which is radiated out again as energy of 4ark or luminous radiation. The function of the discharging wire is to localise the place of dissipation, and also to localise lihe place where the magnetic field shall be most intense ; and

486 DYNAMICAL THEORY OF INDUCTION.

all that observation is able to tell us abont a condactor wUdK is conveying that which we call an electric current is that it is a place where heat is being generated, and near whicb there is a magnetic field. These conceptions lead us to fresh views of very familiar phenomena. Suppose we are sending a current of electricity through a submarine cable by a battery, say, with zinc to earth, and suppose the sheath is^ everywhere at zero potential, then the wire will be everywhere at a higher potential than the sheath, and the level surfaces will pass through the insulating material to the points where- they cut the wire. The energy which maintains the current and which works the receiver at the distant end travels through the insulating material, the core serving as a means to allow the energy to get into motion or to be continually propagated^ The energy absorbed by the core is, however, transformed into heat and radiated again as dark heat.

In the case of an arc or glow-lamp worked by an alter- nating current, we have to consider that the energy which moves in on the carbon is returned again, with no other change than that of a shortened wave-length, and the carboiv 'filament performs the same kind of change on the electro- magnetic radiation as is performed when we heat a bit of platinum foil to vivid incandescence in a focus of dark heat. If we adopt the electro-magnetic theory of light, it moves out again still as electro-magnetic energy, but in & different form, with a definite velocity and intermittent in type. We have, then, in the case of the electric light this curious result — that energy moves in upon the arc or filament from the surrounding medium, there to be con- verted into a form in which it is sent out again, and which, though the same in kind, is now able to affect our senses. A current passing through a seat of electromotive force is therefore a place of divergence of energy from the conducting circuit into the medium, and this energy travels away and is converged and transformed by the rest of the circuit. Front this aspect the function of the copper conducting wire fades into insignificance in interest in comparison with the function of the dielectric. When we see an electric tramcar, or motor, or lamp, worked from a distant dynamo, these notions invite us to consider the whole of that energy, even if it be thousands

DYNAMICAL THEORY OF INDUCTION, 487

of horse-power per hour, as conveyed through the electro- magnetic medium, and the conductor as a kind of exhaust valve, which permits energy to he continually supplied to the dielectric.

Consider, for instance, the simple case of an alternating- current dynamo connected to an incandescent lamp by con- ducting leads. We have in this case a closed conducting loop, consisting partly of the armature wire, partly of the leads, and lastly of the lamp filament. The action of the dynamo when at work consists in alternately inserting into and withdrawing tubes of magnetic induction from a portion of this enclosed area or loop The insertion of this induction causes an electro-magnetic disturbance which travels away through the enclosed dielectric in the form of an ether displacement in its most generalised sense. In reaching the surface of the enclosing conductor this wave begins to soak into it, the electro-magnetic energy at the same time dissipating itself in it in the form of heat. By a suitable arrangement of the resistances and surfaces of various portions of the circuit, we are able to localise the principal place of transformation, and to control its rate so as to compel this transformation of energy to take place at a certain rate in a limited portion of the cond actor. Energy is then sent out again in a radiant form — partly in the form of ether waves capable of exciting the retina of the eye, but very largely in the form of dark heat. The ether, or electro-magnetic medium, is, therefore, the vehicle by which the energy is carried to the lamp and conveyed away from it in an altered form; and, whatever be the translating device employed, the ether is the seat of the hidden operations, which are really the fundamental ones, and the visible apparatus is only the con- trivance by which the nature of the energy transformation is determined and its place defined.

These views are the outcome of that half-century of scientific thought which dates from the period of Faraday's conception of an electro-magnetic medium. We can with- out hesitation predict that the ideas which have thus guided to so much discovery are destined to conduct to further revelations of the nature of the unseen mechanism which lies behind the apparent actions taking place in the

488 DYNAMICAL THEOBT OF INDUCTION.

eleciro-magnetio field, and of which these actions are the result.

§14. Propagation of Ourrents along Oonducton. — We have in a previous section enunciated the modem ideas on this subject, according to which the propagation of a current in a conductor depends upon actions taking place in the dielectric, and various illustrations were given in explanation of this process. We owe to Hertz, however, an absolute experimental demonstration of the correctness of the opinions on this matter, which had previously, from a mathematical standpoint, been put forward by Oliver Heaviside, Poynting, and Lodge. Hertz placed on record his experimental demonstrations in a remarkably interesting Paper which we shall quote here almost verbatim,*

Dealing with the deductions made by the above writers from Maxwell's equations Hertz described {loc. cit.) his experiments in confirmation of their views, and makes the following remarks : —

'* Mathematical investigation points to the conclusion that the electric force which determines the current is in no wise propagated in the wire itself, but under all circumstances enters the wire from without and spreads itself in the metal com- paratively slowly, and according to laws similar to those governing the changes of temperature in a conductor of heat. If the forces in the neighbourhood of the wire are continually altering in direction, the efi'ect of these forces will only enter to a small depth into the metal ; the more slowly the changes take place, so much deeper will the effect penetrate ; and if, finally, the changes follow one another infinitely slowly, the force has time to fill the whole interior of the wire with uni- form intensity."

The first and most important question with regard to this theory is, whether it agrees with fact. Since, in the experiments which Hertz carried out on the propagation of electric force, he made use of electric waves in wires which were of extraordinarily short period, it was con-

• This Paper was translated from Wiedemaon's Annalen, XXXVIL, p. 395, July, 1889, by Dr. J. L. Howard for the PhiL Mag, of AugUBt^ 1889, and by kind permission of the tranalator is given here.

DYNAMICAL THEORY OF INDUCTION. 489

lenient to prove, by means of these, the accuracy of the inferences drawn. In fact, the theory was proved by the -experiments which will now be described; and it will be found that these few experiments suffice to confirm in the highest degree the view of Messrs. Heaviside and Poynting. Analogous experiments, with similar results, but with quite .different apparatus, had already been made by Dr. 0. J. Lodge,* chiefly in the interest of the theory of lightning, conductors. Up to what point the conclusions which were drawn by Dr. Lodge in this direction from his experiments are just must depend in the first place on the velocity with which the alterations of the electrical conditions really follow each other in the case of lightning. The apparatus and methods which are here mentioned are. those which Hertz described in full in previous memoirs, f The waves used were such as had in wires a distance of nearly three metres between the nodes.

'< If a primary conductor acts through space upon a secondary •conductor, it cannot be doubted that the effect penetrates the latter from without. For it can be regarded as established that the effect is propagated in space from point to point ; there- fore it will be forced to meet first of all the outer boundary of the body before it can act upon the interior of it. But a closed metallic envelope is shown to be quite opaque to this effect. If we place the secondary conductor having a spark ^ap in such a favourable position near the primary one that we obtain sparks 5mm. to 6mm. long, and surround it with a closed box made of zinc plate, the smallest trace of sparking •can no longer be perceived. The sparks similarly vanish if we enUrely surround the primary conductor with a metallic box. It is well known that, with relatively slow variations of current, the integral force of induction is in no way altered by a metallic screen. This is, at the first glance, contradio. tory to the present experiments. However, the contradiction is only an apparent one, and is explained by considering the •duration of the effects. In a similar manner, a screen which conducts heat badly protects its interior completely from

• Lodge, /oum. Soe. of Arts, May, 1888 ; Phil. Mag, [5], XXVI., p. 217 '(1888).

t Hertz, Wied. Ann,, XXXIV., p. 551 (1888).

490 DYNAMICAL THEORY OF INDUCTION.

rapid changes of the outside temperature, less from sknr changes, and not at all from a continuous raising or lowering of the temperature. The thinner the screen is the more rapid are the variations of the outside temperature which can be- felt in its interior. In this case the electrical action must plainly penetrate into the interior, if we only diminish suffi- ciently the thickness of the metal — ^a box covered with tinfoil, protected completely, and even a box of gilt paper, if care were taken that the edges of the separate pieces of paper were in metallic contact. In this instance the thickness of the con- ducting metal was estimated to be barely ^V^^* Hertz then fitted the protecting envelope as closely as possible round the secondary conductor. For this purpose its spark-gap was widened to about 20mm., and, in order to detect electrical disturbances in it, an auxiliary spark-gap was added exactly opposite to the one ordinarily used. The sparks in this latter were not so long as in the ordinary spark-gap, since the effect of resonance was now wanting, but they were still very bril- liant. After this preparation the conductor was completely enclosed in a tubular conducting envelope as thin as possible, which did not touch it, but was as near it as possible ; and in the neighbourhood of the auxiliary spark-gap (in order to be able to use it) the envelope contained a wire-gauze window. Between the poles of this envelope brilliant sparks were pro- duced, just as previously in the secondary conductor itself ; bat in the enclosed conductor not the slightest electrical move- ment could be recognised. The result of the experiment is not affected if the envelope touches the conductor at a few points ; the insulation of the two from each other is not necessary in order to make the experiment succeed, but only to give it the force of a proof. Clearly we can imagine the envelope to be drawn more closely round Ihe conductor than is possible in the experiment ; indeed, we can make it coincide with the outer- most layer of the conductor. Although, then, the electrical disturbances on the surface of our conductor are so powerful that they give sparks 5mm. to 6mm. long, yet at ^^mm. beneath the surface there exists such perfect freedom from dis- turbance that it is not possible to obtain the smallest sparks. We are brought, therefore, to the conclusion that what we call an induced current in the secondary conductor is a phenomenon*

DYNAMICAL THEORY OF INDUCTION. 491

which is the result of actions taking place in the surrounding dielectric.

^* One might grant that this is the state of affairs when the* electric disturbance is conveyed through a dielectric, but main- tain that it is another thing if the disturbance, as one usually says, has been propagated in a conductor. If we place near one of the end plates of our primary conductor a conducting- plate, and fasten to it a long straight wire, we have already seen in the previous experiments how the effect of the primary oscUlation can be conveyed to great distances by the help of this wire. The usual theory is that a wave travels along the wire in this case. But we can show in the following manner that all the alterations are confined to the space outside and on the surface of the wire, and that its interior knows nothing of the wave passing over it. A piece about 4 metres long was removed from the wire conductor and replaced by two strips^ of zinc plate 4 metres long and 10cm. broad, which were laid flat one above the other, with their ends permanently connected together. Between the strips along their middle line, and therefore almost entirely surrounded by their metal, was laid along the whole 4 metres length a copper wire covered with gutta-percha. It was immaterial for the experiments whether the outer ends of this wire were in metallic connection with or insulated from the strips ; however, the ends were mostly soldered to the zinc strips. The copper wire was cut through in the middle, and its ends were carried, twisted round each other, outside the space between the strips to a fine spark-gap, which permitted the detection of any electrical disturbance taking place in the wire. When waves of the greatest possible intensity were sent through the whole arrangement, there wa& nevertheless not the sUghtest effect observable in the spark- gap. But if the copper wire was then displaced anywhere a few decimetres from its position, so that it projected just a. little beyond the space between the strips, sparks immediately began to pass. The sparks were the more intense according to the length of copper wire extending beyond the edge of the zinc strips and the distance it projected. The unfavourable relation of the resistances was, therefore, not the cause of the previous absence of sparking, for this relation had not been changed ; but the wire being in the interior of the conducting

492 DYNAMICAL THEORY OF INDUCTION.

mass, was at first deprived of the influence coming from without. Moreover, it is only necessary for us to surround the projecting part of the wire with a little tinfoil in metallic -communication with the zinc strips in order to immediately stop the sparking again. By this means we have brought the hopper wire back again into the interior of the conductor. If we bend another wire into a fairly large arc round the pro- jecting portion of the gutta-percha wire, the sparks will be likewise weakened ; the second wire takes off from the first a 'certain amount of the effect due to the outer medium. Indeed, it may be said that the edge of the zinc strip itself cakes away in a similar manner the induction from the middle of the strip. For if we now remove one of the strips, and leave the insulate wire simply resting on the other one, we certainly obtain sparks continuously in the wire ; but they are extremely weak if the wire lies along the middle of the strip, and much stronger when near its edge. Just as in the case of dis- tribution under electrostatic influence the electricity would prefer to collect on the sharp edge of the strip, so also here the current tends to move along the edge. Here, as there, it may be said that the outermost parts screen the interior from outside influence."

The following experiments are somewhat neater and equally <^onvincing. Hertz inserted into the conductor transmitting the waves a very thick copper wire, 1'5 metre long, whose ends carried two circular metallic discs of 15cm. diameter. '* The wire passed through the centres of the discs ; the planes of the discs were at right angles to the wire ; each of them had on its rim 24 holes, at equal distances apart. A spark- gap was inserted in the wire. When the waves traversed the wire they gave rise to sparks as much as 6mm. long. A thin •copper wire was then stretched across between two corre- sponding holes of the discs. When this was done the length of the sparks sank to d*2mm. There was no further alteration if a thick copper wire was put in the place of the thin one, or if, instead of the single thin wire, twenty-four of them were taken, provided they were placed near each other through the same two holes. But it was otherwise if the wires were distributed over the rim of the discs. If a second wire was inserted opposite the first one, the spark-length fell to l-2nmi«

DYNAMICAL THEORY OF INDUCTION. 493^

When two more wires were added midway between the first two, the length of the spark sank to 0-5mm. ; the insertion of foor more wires still in the mean positions left sparks of scarcely O'lmm. long ; and after inserting all the twenty-four wires at equal distances apart, not a trace of sparking was perceptible in the interior. The resistance of the inner wire was nevertheless much smaller than that of all the outside- wires taken together. We have also a still further proof that the effect does not depend upon this resistance. If we place by the side of the partial tube of wires, and in parallel circuit with them, a conductor in all respects similar to that in the- interior of the tube, we have in the former brilliant sparks, but none whatever in the latter. The former is unprotected, the latter is screened by the tube of wires. We have in this an electro-dynamic analogue of the electrostatic experiment known as the electric birdcage."

Fio. 163.

Hertz again altered the experiment, in the manner depicted* in Fig. 168.

<<The two discs were placed so near together that they formed, with the wires inserted between them, a cage (A) just large enough for the reception of the spark-micrometer. One of the discs, a, remained metallically connected with the central wire; the other, /?, was insulated from the wire by means of a circular hole through its centre, at which it was connected to- a conducting-tube, y, which, insulated from the central wire, surrounded it completely for a length of 1*5 metre. The free end of the tube, 8, was then oonnected with the central wire. The wire, together with its spark-gap, is once more situated in a metaUically protected space; and it was only to be expected, firom the previous experiments, that not the slightest electrical disturbance would be detected in the wire in which- ever direction waves were sent through the apparatus. So Car, then, this arrangement showed nothing new, but it had the advantage over the previous one that we could replace the-

494 DYNAMICAL THEORY OF INDUCTION.

protecting metallio tube, y, by tubes of smaller and smaller thickness of wall, in order to investigate what thickness is still sufficient to screen off the outside influence. Very ihin brass tubes — tubes of tinfoil and Dutch metal — ^proved to be perfect screens* Glass tubes were taken which had been silvered by a chemical method, and it was then perfectly easy Tto insert tubes of such thinness that, in spite of their pro- tecting power, brilliant sparks occurred in the central wire. But sparks were only observed when the silver film was no longer quite opaque to light, and was certainly thinner than y^i^mm. In imagination, although not in reality, we can conceive the film drawn closer and closer round the wire, and finally coinciding with its surface ; we should be quite certain that nothing would be radically altered thereby. However actively, then, the real waves play round the wire, its interior remains completely at rest ; and the effect of the waves hardly penetrates any more deeply into the interior of tb^ wire than ^oes the light which is reflected from its surface. For the real seat of these waves, therefore, we ought not to look in the ^re, but rather to assume that they take place in its neigh- bourhood; and, instead of asserting that our waves are propagated in the wire, we should be more accurate in saying that they glide along on the wire.

'< Instead of placing the apparatus just described in the cir* <;uit in which we produced waves indirectly, we can insert it in one branch of the primary conductor itself. In such experiments results similar to the previous ones are obtained. Our primary oscillation, therefore, takes place without any participation of the conductor in which it is excited, except at its bounding surface ; and we ought not to look for its existence in the interior of the conductor.

" To what has been said above about waves in wires we wish to add just one remark concerning the method of carrying out the experiments. If our waves have their seat in the neighbourhood of the wire, the wave progressing along a single isolated wire will not be propagated through the air alone ; but, since its effect extends to a great distance, it will partly be transmitted by the walls, the ground, &c., and will thus give rise to a complicated phenomenon. But if we place opposite each pole of our primary conductor, in exactly the

DYNAMICAL THEORY OF INDUCTION. 495

«im6 way, two auxiliary plates, and attach a wire to each of them, carrying the wires straight and parallel to each other to equal distances, the effect of the waves makes itself felt only in the region of space hetween the two wires. The wave progresses solely in the space hetween the wires. We can thus take precautions to propagate the effect through the air alone or through another insulator, and the experiments will be more convenient and firee from error by this arrangement. For the rest, the lengths of the waves are nearly the same in this case as in isolated wires, so that with the latter the effect of the disturbing causes is apparently not considerable.

** We can conclude firom the above results that rapid electric oscillations are quite unable to penetrate metallic sheets oi any thickness, and that it is, therefore, impossible by any means to excite sparks by the aid of such oscillations in the interior of closed metallic screens. If, then, we see sparks produced by such oscillations in the interior of metallic con- -ductors which are nearly, but not quite, closed, we shall be obliged to conclude that the electric disturbance has forced itself in through the existing openings. This view is also correct, but it contradicts the usual theory in some cases so completely that one is only induced by special experiments to give up the old theory in favour of the new one. We shall choose a prominent case of this kind, and, by assuring ourselves of the truth of our theory in this case, we Shall demonstrate its probability in all other cases. We again take the arrangement which we have described in the previous flection and drawn in Fig. 168 ; only we now leave the protect- ing tube insulated from the central wire at 6. Let us now send a series of waves through the apparatus in the direction from A towards 8. We thus obtain brilliant sparks at A; they are of similar intensity to those obtained when the wire was inserted without any screen. The sparks do not becotne materially smaller, if, without making any other alteration, we lengthen the tube y considerably, even to 4 metres. According to the usual theory it would be said that the wave ikrriving at A penetrates easily the thin, good-conducting metal disc a, then it leaps across the spark-gap at A, and travels on in the central wire. According to our view, on ihe^ contrary, we must explain the phenomenon in- the follow^

496 DYNAMICAL THEORY OF INDUCTION.

mg manner. The wave arriving at A is quite nnable ixy penetrate the metallio disc ; it therefore glides along the disc over the outside of the apparatus and travels as &r as the- point 6, 4 metres away. Here it divides: one part, which does not concern us at present, travels on immediately along the straight wire, another bends into the interior of the tube^ and then runs back in the space between the tube and the central wire to the spark-gap at A, where it now gives rise to the sparking. That this view, although more complicated,, is still the correct one, is proved by the following experiments. Firstly, every trace of sparking at A disappears as soon as- we close the opening at B, even if it be only by a stopper of tinfoil. Our waves have only a wave-length of 8 metres;, before their effect has reached the point 8 the effect at A has passed through zero and changed sign. What influence, then, could the closing of the distant end S have upon the spark at A, if the latter really happened immediately after the passage of the wave through the metallic wall ? Secondly, the sparks disappear if we make the central wire terminate inside the- tube y, or at the opening B itself; but they reappear when we allow the end of the wire to project even 20cm. to 80cm. only beyond the opening. What influence could this insignificant lengthening of the wire have upon the sparks in A, unless the^ projecting end were just the means by which a part of the wave breaks off and penetrates through the opening 8 back into the interior? Thirdly, we insert in the .central wire between A and B a second spark-gap £, which we also com- pletely cover with a gauze cage like that at A. If we make^ the distance of the terminals at B so great that sparks can^ no longer pass across, it is also no longer possible to obtain visible sparks at A. But if we hinder in like manner th&^ passage of the spark at A, this has scarcely any influence on the sparks in B. Therefore, the passage of the spark at B* determines that at A, but the passage of a spark at A doe» not determine that at B. The direction of propagation in the interior is therefore from B towards A, not from A to B.

'*We can moreover give further proofis, which are more^ convincing. We may prevent the wave returning from B to A from dissipating its energy in sparks, by making the spark- gap either vanishingly small or very great. In this case thor

JDYNAMtCAL THUOHY Of tNDUGtlOlf. 497

wave "will be reflected at A, and will now return again from A towards 8. In doing so it must meet the direct waves from S to A, and combine with them to form stationary waves, thus giving rise to nodes and ventral segments. If we succeed in proving their existence, there will be no longer any doubt as to the truth of our theory. For this proof we must give somewhat different dimensions to our apparatus in order to be able to introduce electric resonators into its interior. Hertz therefore led the central wire through the axis of a cylindrical tube 6 metres long and 80 centimetres diameter. It was not constructed of solid metal, but of 24 wires arranged parallel to each other along the generating surface, and resting on seven equidistant and circular rings of strong wire, as shown in Fig. 164. He made the requisite resonator in the following, manner: — A closely-wound spiral of 1cm. diameter was formed from copper wire of 1mm. thickness ; about 125 turns of this spiral wore taken, drawn out a little, and bent into a circle of 12cm. diameter; between the free ends an

Fio. 164.

adjustable spark-gap was inserted. Previous experiments had shown that this circle responded to waves 8 metres long in the wire, and yet it was small enough in size to admit of its insertion between the central wire and the surface of the tube. If now both ends of the tube were open, and the resonator was then held in the interior in such a way that its plane included the central wire, and its spark-gap was not directed exactly inwards or outwards, but was turned towards one end or the other of the tube, brilliant sparks of ^mm. to 1mm. length were observed. On now closing both ends of the tube by four wires arranged crosswise and connected with the central conductor, not the slightest sparking remained in the interior, a proof that the network of the tube is a suffi- ciently good screen for our experiments. The end of the tube on the side ^, that, namely, which was furthest away from the origin of the waves, was now removed. In the immediate

KK

498 DYNAMICAL THEORY OF INDUCTIOIT.