The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 28 of 35

the circle will act under more favourable conditions against a weaker one under less favourable conditions. If, however, the air space is turned away from the node, the stronger E.M.F. acts under less favourable conditions against a weaker one under more favourable conditions. In the latter case the resultant action must be less than in the former, whichever of the two E.M.F.s has the greater effect, which explains the •change of sign of the phenomenon at each quarter wave- length.

This explanation is further confirmed by the consideration that, if it is the true one, the change of sign at the points B and D must take place in quite a different manner from that of the point C. The E.M.F.s acting on the secondary circle, an the positions V., VI., and VII., are shown by the corre- sponding arrows, and it is clear that in the positions B and D, if the air space is turned from one side to the other, the vibration will change its direction round the circle, and there- fore the sparking must, during the rotation, vanish either once or an uneven number of times. In the position C, however, the direction of vibration remains unaltered, and therefore the sparks must disappear an even number of times, or not at all.

The experiments showed that at B and D the sparking dimi- nished as the air space receded from a, vanished at the highest point, and again attained its original value at the point ft. At •C, on the other hand, the sparking continued throughout the rotation, being a little stronger at the highest and lowest points. If, then, there is any change of sign in the position •C, it must occur with very much smaller displacements than in the other positions, so that in any case there is a distinction such as is required between this and the other two cases.

Another very direct proof of the truth of Hertz's repre- sentation of the nature of the waves was obtained. If the secondary circle lies in the plane of the waves instead of in the plane of vibration, the E.M.F. must be equal at all points of the circle, and for a given position of the air space the sparking must be directly proportional to its intensity. When the experiment was made, it was found, as expected, that at all distances the sparking vanished at the highest and lowest points of the circle, and attained a maximum value at the points in the horizontal plane through the point of incidence.

474 DYNAMICAL THEORY OF INDUCTION.

The air space was then placed at such a point and close to the wall, and was then moved slowly away from the wall, when it was found that, while there was no sparking quite close to the metal plate, it began at a very small distance from it, rapidly increased, reached a maximum at the point B, and then diminished again. At C the sparking again became excessively feeble and increased as the circle was moved still further away. The sparking continued steadily to increase after this, as the motion of the circle was con- tinued in the same direction, owing, as before, to the direct action of the primary oscillation.

The curves shown by the continuous lines in Fig. 162 were obtained from the results of these experiments, the ordinates representing the intensity of the sparks at the distances repre- sented by the corresponding abscissa?.

The existence in the electrical waves of nodes at A and C, and of loops at B and D, is fully established by the experi- ments which have been described; but in another sense the points B and D may be regarded as nodes, for they are the nodal points of a stationary wave of magnetic induction which, according to theory, accompanies the electrical wave and lags a quarter wave-length behind it.

This can easily be shown to follow from the experiments, for when the secondary circle is placed in the plane of vibration with the air space at its highest point, there will be no spark- ing if the E.M.F. is uniform throughout the space occupied by the secondary. This can only take place if the E.M.F. varies from point to point of the circle, and if its integral round the circle differs from zero. This integral is proportional to the number of magnetic lines of force passing backwards and for- wards across the circle, and the intensity of the sparks may be considered as giving a measure of the magnetic induction, which is perpendicular to the plane of the circle. Now, in this position vigorous sparking was observed close to the wall, diminishing rapidly to zero as the point B was approached, then increasing to a maximum at C, falling to a well-marked minimum at D, and finally increasing continuously as the secondary approached still nearer to the primary. If the intensities of these sparks are taken as ordinates, positive and negative, and the distances from the wall as abscissa?, the

DYNAMICAL THEORY OF INDUCTION. 475

curve shown by the dotted lines in Fig. 162 is obtained, which therefore represents the magnetic waves.

The phenomena observed in the first series of experiments described above may therefore be regarded as due to the resultant electric and magnetic actions. The former changes sign at A and C, the latter at B and D, so that at each of these points one part of the action changes sign, while the other does not, and therefore the resultant action which is their product must change sign at each of these points, as was found to be the case.

When the secondary circle was in the plane of vibration the sparking in the vicinity of the wall was observed to be a maxi- mum on the side towards the wall and a minimum at the opposite side, and as the circle was turned from one position to the other there was found to be no point at which the sparks disappeared. As the distance from the wall was increased, the sparks on the remote side gradually became weaker, and vanished at a distance of 1-08 metre from the wall. When the circle was carried further in the same direction the sparks appeared again on the side remote from the wall, but were always weaker than on the side next to it ; the sparking, how- ever, no longer passed from a maximum to a minimum merely, but vanished during the rotation once in the upper and once in the lower half of the circle. The two null points gradually receded from their original coincident positions until at the point B they occurred at the highest and lowest points of the circle. As the circle was moved further in the same direction the null points passed over to the side next to the wall, and approached each other again, until, when the centre was at a distance of 2-35 metres from the wall, the two null points were again coincident. B must be exactly half-way between this point and the similar point previously observed, which gives 1 -72 metre as the distance of B from the wall — a result which agrees, within a few centimetres, with that obtained by direct observation. Moving further in the direction of C, the spark- ing at different points of the circle became more nearly equal, until at C it was exactly so. In this position there was no null point, and as the distance was further increased the phenomena recurred in the same order as before.

Hertz found that the position of C could be determined

476 DYNAMICAL THEORY OF INDUCTION.

•within a few centimetres, the determinations of its distance from the wall varying from 4-10 to 4-15 metres; he gives its most probable value as 4-12 metres. The point B could not be observed with any exactness, the direct determinations varying from 6 to 7-5 metres as its distance from the wall. It could, however, be determined indirectly, for the distance between B and C being found to be 2*4 metres, taking this as the true value, A must have been 0-68 metre behind the surface of the wall, and G-52 metres in front of it. The half wave-length would be 4-8 metres, and by an indirect method it was found to be 4-5 metres, so that the two results agree fairly well. Taking the mean of these as the true value, and the velocity of light as the velocity of propagation, gives as the vibration period of the apparatus 1-55 hundred-millionth of a second, instead of 1-4 hundred-millionth, which was the theoretically •calculated value.

A second series of experiments was made with smaller apparatus, and though the measurements could not be made with as much exactness as those already described, the results showed clearly that the position of the nodes depends only on the dimensions of the conductors, and not on the material of the wall.

Hertz states that after some practice he succeeded in obtain- ing indications of reflections from each of the walls. He was also able to obtain distinct evidence of reflection from one of the iron columns in the room, and of the existence of electro- dynamic shadows on the side of the column remote from the primary.

In the preceding experiment the secondary conductor was always placed between the wall and the primary conductor — that is to say, in a space in which the direct and reflected rays were travelling in opposite directions, and gave rise to stationary waves by their interference.

He next placed the primary conductor between the wall and the secondary, so that the latter was in a space in which the direct and reflected waves were travelling in the same direction. This would necessarily give rise to a resultant wave, the inten- sity of which would depend on the difference in phase of the two interfering waves. In order to obtain distinct results it was necessary that tne two waves should be of approximately equal

DYNAMICAL THEORY OF INDUCTION. 477

intensities, and therefore the distance of the primary from the wall had to be small in comparison with the extent of the latter, and also in comparison with its distance from the secondary.

To fulfil these conditions the secondary was placed at a dis- tance of 14 metres from the reflecting wall, and, therefore, ahout 1 metre from the opposite one, with its plane in the plane of vibration, and its air space directed towards the nearest wall, in order to make the conditions as favourable as possible for the production of sparks. The primary was placed parallel to its former position, and at a perpendicular distance of about 80 centimetres from the centre of the reflecting metallic plate. The sparks observed in the secondary were then very feeble, and the air space was increased until they disappeared. The primary conductor was then gradually moved away from the wall, when isolated sparks were soon observed in the secondary, passing into a continuous stream when the primary was between 1-5 and 2 metres from the wall — that is, at the point B. This might have been supposed to be due to the decrease in the distance between the two conductors, except that as the primary conductor was moved still further from the wall the sparking again diminished, and disappeared when the primary was at the point C. After passing this point the sparking continually increased as the primary approached nearer to the secondary. These experiments were found to be easy to repeat with smaller apparatus, and the results obtained confirmed the former conclusion — that the position of the nodes depends only on the dimensions of the conductor, and not on the material of the reflecting wall.

Hertz points out that these phenomena are exactly analogous to the acoustical experiment of approaching a vibrating tuning- fork to a wall when the sound is weakened in certain positions and strengthened in others, and also to the optical phenomena illustrated in Lloyd's form of Fresnel's mirror experiments ; and as these are accepted as arguments tending to prove that sound and light are due to vibration, his investigations give a strong support to the theory that the propagation of electro- magnetic induction also takes place by means of waves excited in a medium. They therefore afford a confirmation of the Faraday-Maxwell theory of electrical action.

478 D YNA M1CAL THEOR Y OF IND UCTION,

§ 12- Further Researches on Electro-Magnetic Radiation. — When once the experimental proof had been given that the result of electrical oscillations in a conductor is to propagate out into surrounding space radiations which are in all respects of the same nature as light, except in that they cannot affect the eye, it became evident that a new and vast field of investigation had been opened, and one in which it would be possible to produce the electro-magnetic analogues of all the more familiar optical phenomena.

The reflection, refraction, dispersion, and polarisation of light waves are well-known optical phenomena. We can perform analogous experiments with rays of dark heat which differ only from light rays in having a greater wave-length, and in being thereby unable to affect the optic nerve. In performing these experiments with dark heat or non-luminous radiation we have to make use of the thermopile as a perceiver of the ray. The electro-magnetic radiation scattered from a conductor in which electric oscillations are set up differs again from light and dark heat in having a still longer wave-length. In performing experiments with electro-magnetic radiation we have seen that Hertz's invention of the electro-magnetic resonator put us in possession of an apparatus which is the exact equivalent of a thermopile, or the human eye, as a ray localiser ; and more recent researches have shown us how to construct a large number of forms of receiver of even more sensitive character, by means of which we can detect this electro-magnetic radiation.

In these electro-magneto-optic experiments of Hertz, the source of radiation is a divided metallic cylinder about one inch in diameter and twelve inches long. This is divided in halves, and the two parts separated by a small distance. They are respectively attached to the ends of the secondary coil of a small induction coil. When the coil is put in action, electrical oscillations are set up in these cylinders which result in the outward propagation of ethereal undulations of about two feet in wave-length and having a frequency of about five hundred millions a second.

In order to see these waves, Hertz employed a resonator consisting of a metallic circuit having a small spark interval. With these simple appliances he has been able to show the reflection of the electro -magnetic waves from plane surfaces,

DYNAMICAL THEORY OF INDUCTION. 479

and the concentration of radiation by parabolic mirrors of sheet zinc, repeating in fact. the old experiment of the con- jugate mirrors. The radiation from this source could, he found, be gathered up by one parabolic mirror, reflected to a second and concentrated again to a focus. Another achieve- ment was the refraction of the rays by a great prism of pitch. Placed in the path of an electro-magnetic ray, he found that this pitch prism refracted it through an angle of 22deg., and that the material had a refractive index of 1-7 for these long waves. Again, it was found that metallic sheets were opaque to this radiation, but that it passed through such non- conductors as dry wood, and that a laboratory door, although opaque to light, is transparent to this ultra-ultra red or electro-magnetic radiation.

The reader may be referred to Dr. Lodge's book on the "Work of Hertz, and some of his Successors" for a full account of the experimental proofs that electro-magnetic radiation and that radiation we commonly call light are one in essential nature, although differing in wave-length. These experiments are akin to the acoustic ones in which air waves, too short to be audible, are generated ; and in place of the ear, now useless, a sensitive flame is employed to find or indicate the waves, and inform us of the presence or absence of aerial wave motion. In the same way all well-known optical effects can be reproduced with ether radiation too long in wave-length to affect the eye, but capable of acting on a proper receiver.

It is a necessary corollary of Maxwell's electro-magnetic theory of light that good conducting bodies should be opaque a,nd good insulators transparent. As a matter of fact, for dis- turbances of the period of light many good insulators, such as ebonite, are opaque, even in very thin sheets, and conversely gold, silver, and platinum are semi-transparent when in very thin sheets. It must be borne in mind, however, that the frequency of light oscillations falls between 400 and 700 million-million oscillations per second, or are of the order of 5 x 1014.

We cannot .by any of Hertz's methods produce electrical oscillations so rapid as this. Hence, since conductivity and insulating power of materials have generally been determined

480 DYNAMICAL THEORY OF INDUCTION.

with reference either to steady currents or to moderately great oscillations, we cannot institute a comparison between these qualities as possessed by any given substance and opacity or transparency for the much greater frequency of luminous electro-magnetic waves. It has been shown that ebonite is very transparent to long waves of dark heat,* and hence there is no difficulty in understanding that it is trans- parent to the longer waves produced by electrical oscillations set up in moderately small conductors, whilst it is opaque to the very short ones of light. Also the transparency of thin metallic sheets to light is an indication of imperfect conducti- bility. We have seen that an infinitely perfect conductor is a perfect magnetic screen, and accordingly we should expect that the more perfect the conductivity of a metal the greater would be its opacity even in very thin films. It is well known that cooling copper increases its conductivity. Wroblewski showed (Comptes Rendus, Vol. 01., July, 1885, p. 160) that by cooling copper to -200°C., or to the temperature of the solidification of nitrogen, its conductivity is increased to about nine times its value at 0°C. These experiments have been greatly extended by Dewar and Fleming (Phil. Mar/., September, 1893), who have shown that perfectly pure metals have most probably no electrical resistance at the absolute zero of temperature. It would be interesting to know if the opacity of a very thin film of copper is increased by cooling to

• 200° to any perceptible extent. With respect to electrolytes some interesting experiments have been made by Prof. J. J. Thomson.! In these experiments electrical oscillations of about 108 per second in frequency were established in a primary circuit by means of an induction coil. These alter- nating currents were caused to induce secondary oscillations in a neighbouring parallel circuit of appropriate size. The secondary circuit oscillations were rendered visible by minute sparks at a break in that circuit. The interposition of a thin sheet of tinfoil or of the thinnest sheet of Dutch metal or

• See note on " The Index of Refraction of Ebonite," by Profs. Ayrton and Perry, Proceedings of the Physical Society, London, Vol. IV., p. 345.

t " On the Resistance of Electrolytes to the Passage of Rapidly Alter- nating Currents," Proceedings of the Physical Society, London, Vol. XLV., No. 276, 1889.

DYNAMICAL THEORY OF INDUCTION. 481

gold-leaf supported on glass at once stopped completely the secondary sparks. This is a very interesting confirmation of the theory of magnetic screening laid down on p. 255 of Chap. IV. We have seen that for moderately rapid alterna- tions the conductivity of tinfoil is not sufficient to make it opaque to electro-magnetic radiations, hut for disturbances of a frequency equal to about 108 the tinfoil affords a perfect screening, or, in other words, is opaque.

With regard to the gold-leaf, Prof. Thomson remarks that he has not been able to get any leaf thin enough to be trans- parent to oscillations of this rate. On inserting a sheet of ebonite between the primary and secondary circuit, it was found to produce no effect on the sparking, indicating that ebonite, although opaque to ordinary light, is transparent to ether disturbances of the rate here employed. A thin layer of transparent electrolyte was then used as a screen, and it was found that whilst a very thin layer produced little or no effect, a depth of three to four millimetres of dilute sulphuric acid was sufficient to stop the sparking. Experiment showed that the conductivity of various electrolytic solutions was about the same for currents reversed 120 times a second as for currents reversed 100 million times a second. As, however, these electrolytes are transparent, they must, according to the electro-magnetic theory, be insulators for currents reversed about 1015 times per second, and the molecular processes on which electrolytic conduction depends must occupy a time between one-hundred millionth and one-thousand billionth of a second. Space will not permit further reference to this exceedingly promising department of future research more than to say that if the electro-magnetic theory of light is true it will be able to furnish an electrical explanation, not only of the simpler optical phenomena, but of such complex phenomena as those embraced in the sciences of spectroscopy and photo- graphy.

§ 13. Propagation of Electro -Magnetic Energy.— In our exposition of the various electro-magnetic phenomena we have directed attention to the facts which make it evident that even in the simple phenomenon of the propagation of an electric current in a wire we must divest ourselves of the idea that the

ii

482 DYNAMICAL THEOEY OF INDUCTION.

so-called flow of current is analogous to the movement of a material fluid in a pipe. It is true that there are effects in the case of the electric current which correspond to the inertia and resistance effects in the case of water flow ; but the progress of knowledge has indicated that what we are in the habit of calling the electric current is as much outside the wire as in it, and that we must release ourselves from the trammels of any ideas which cause us to concentrate attention exclusively or mainly on the actions in the conductor. In fact, at the absolute zero of temperature there would be no dissipation of energy in the conductor at all, if it were a pure metal, and all the processes would be confined to the medium. "We are indebted to, amongst others, Prof. Poynting for an enlargement of our views on the nature of electric current propagation, and in two valuable memoirs these matters have been discussed by him.* He says : — A space containing electric currents may be regarded as a field where energy is transformed at certain points into the electric and magnetic form by means of batteries, dynamos, thermopiles, &c., and in other parts of the field this energy is being again transformed into heat, work done by electro-magnetic forces, or any other form yielded by currents. Formerly a current was regarded as something travelling in the conductor, and the energy which appeared at any part of the circuit was supposed to be conveyed thither through the conductor by the current. But the existence of induced currents and electro-magnetic actions has led us to look on the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, we are forced to conclude that the surrounding medium is capable of containing energy, and that it is capable of being transferred from point to point. We are thus led to consider the problem — how does the energy connected with an electric current pass from point to point, by what paths does it

• " On the Transfer of Energy in the Electro-Magnetic Field," by Prof. J. H. Poynting, Philosophical Transactions of the Royal Society, 1884, Part II., VoL CLXXY., p. 343. Also " On the Connection between Electric Current and the Electric and Magnetic Inductions in the Surrounding Field," by Prof. J. H. Poynting, Philosophical Transactions of the Royal : Society, 1835, Part II., Vol. CLXXVL, p. 277.

DYNAMICAL THEORY OF INDUCTION. 483

travel, and according to what laws? Let us put a specific case. Suppose a dynamo at one spot generates an electric current, which is made to operate an electric motor at a dis- tant place. We have here in the first place an absorption of energy from the prime motor into the dynamo. We find the whole space between and around the conducting wires mag- netised and the seat of electro-magnetic energy. We have, further, a re-transformation of energy in the motor. The •question which presents itself for solution is to decide how the -energy taken up by the dynamo is transmitted to the motor.

Briefly stated, the general tendency of recent views is that this energy is conveyed through the electro-magnetic medium, or ether, and that the function of the wire is to localise the direction or concentrate the flow in a particular path, and is at the same time also a sink or place in which energy is dissipated. A consideration of the whole phe- nomenon has enabled Prof. Poynting to formulate an im- portant law, as follows: — At any point in the magnetic field of conductors conveying currents the energy moves perpendicularly to the plane containing the lines of electric force and the lines of magnetic force, and the amount crossing a unit of area of this plane, per second is equal to the product of the intensities of the two forces multiiilied by the sine of the angle between them and dicided by 4ir. Tf E denote the electric force, or force on a very small body •charged with a unit of positive electricity, and H denote the magnetic' force, or force on a unit magnetic pole, and if at any point in the electro-magnetic field these forces are inclined at an angle 0, then there is a flow of energy e at this point in a direction perpendicular to the planes of E and H, and equal per second to the value of

j. E H sin 0

"1^

The full proof of this law is given in the first of the Papers mentioned on the preceding page.

Prof. Poynting has here introduced the important notion of a flow of energy. We may remark in passing that this notion does no violence to previous notions of energy. Energy, like matter, is conserved — that is, it is unalterable in total amount ; and if in any circumscribed space some form of energy makes its appearance, then we know that either an equal quantity

n2

484 DYNAMICAL THEORY OF INDUCTION.

must Lave passed into that space from outside, or that an equivalent quantity of some other form already in the enclosure must have been transformed. If energy disappears 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 Poyn ting'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, C the steady current, and B the total ohmic resistance. Consider the energy flowing in on this section of the wire through its- surface. It is equal per second to the area of the surface,

multiplied by ^5, or to 2^EH.

Now £JT r H is the line integral of the magnetic force taken- round the wire following the circular surface, and this, as pre- viously shown (p. 25) is equal to 4?r C. Also we have the potential difference at the ends of the cylinder equal to the line- integral of the electric force, or to ZE. Since, then, 2;rrH = 4jr C and E I = V, we get, by substitution in the value of the energy sent per second into the section of the wire, viz.,.

27r '' * H E , the equivalent C V. But by Ohm's law C E = V ;

hence the energy absorbed per second by the conductor is C2R, 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 of

DYNAMICAL THEORY OF INDUCTION. 485

ihis supply can be calculated by Poynting's law for each element of the surface. None of the energy of a current travels along the wire, but enters into 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 till, 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 running 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 .acquires 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 may 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 ; .and 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 -dark or luminous radiation. The function of the discharging •wire is to localise the place of dissipation, and also to localise .the place where the magnetic field shall be most intense ; and

486 DYNAMICAL THEORY OF INDUCTION.

all that observation is able to tell us about a conductor which is conveying that which we call an electric current is that ifc is a place where heat is being generated, and near which 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 carbon 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 a 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. From 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 be continually supplied to the dielectric.