The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 28 of 36

width of the room was only 8'6 metres. All pendant gas- fittings were removed, and the room left empty, with the^ exception of wooden tables and forms, which would not exert any appreciable disturbing effect. The end wall, from which the waves were to be reflected, was of solid sandstone, with two doors in it, and the numerous gas pipes attached to it gave it, to a certain extent, the character of a conducting surface, and this was increased by fastening to it a sheet of zinc four metres high and two metres broad, connected by wires to the gas pipes and a neighbouring water pipe. Specis^ care was taken to provide an escape for the electricity at the upper and lower extremities of the zinc plate, where a certain accumulation of electricifcy was to be expected.

The primary conductor was the same that was employed in the experiments described on page 456, Fig. 161, and was placed at a distance of 18 metres from the zinc plate, and, therefore, two metres from the wall at the other end of the room. The conducting wire was placed vertically, so that the E.M.F.s to be considered increased and diminished in a vertical direction* The centre of the primary conductor was 25 metres above the floor of the room, which left a clear space for the observations above the tables and benches. The point of intersection of th& reflecting surface with the perpendicular from the centre of the primary conductor will be called ** the point of incidence," and the experiments were Hmited to the neighbourhood of this point, as the investigation of waves striking the wall at a con siderable angle would be complicated by the differences in their polarisation. The plane of vibration was therefore parallel ta the reflecting surface, and the plane of the waves was perpen* dicular to it, and passed through the point of incidence.

The secondary conductor consisted of the circle of 85 centi* metres radius, which has been already described. It was movable about an axis through its centre perpendicular to its plane, and the axis itself was movable in a horizontal plane about a vertical axis. In most of the experiments the secon** dary conductor was held in the hand by its insulating wooden support, as this was the most convenient way of bringing it into the various positions required. The results of these expeii<» ments, however, had to be checked by observations made with the observer at a greater distance from the secondary, as

DYNAMICAL THEOEY OF INDUCTION.

471

the neighbonrhood of his body exerted a slight influence npon the phenomena. The sparks were distinct enough to be observed at a distance of several metres when the room was darkened, but when the room remained light they were practically invisible even when the observer was quite close to the secondary.

When the centre of the secondary was placed in the line of incidence, and with its plane in the plane of vibration, and the air space was turned first towards the reflecting wall and then away from it, a considerable difference was generally observed in l^e strength of the sparks in the two positions. At a distance of about 0*8 metre from the wall the sparks were much stronger when the air space was directed towards the wall, and its length could be adjusted so that, while there was

fej 1@I Yi@fr

•©I • 101 « I®' 4

l^m ^m 3m. ^^in. S-m. Crx 7rn^ jin,

FlQ. 162.

a steady stream of sparks when in this position, they disap- peared entirely when the air space was directed away from the wall. These phenomena were reversed at a distance of 8 metres, and recurred, as in the first case, at a distance of 5*5 metres. At a distance of 8 metres the sparks were stronger when the air space was turned away from the wall, as at the distance of 8 metres, but the difference was not so well marked. When the distance was increased beyond 8 metres no further reversal took place, owing to the increase in the direct effect of the primary oscillation and the complicated distribution of the E.M.F. in its neighbourhood.

The positions I., II., III. and IV. (Fig. 162) of the secondary circle are those in which the sparks were strongest, the distance

472 DYNAMICAL THEORY OF INDUCTION.

from the wall being shown by the horizontal scale at the foot. When the secondary circle was in the positions V., VI., and Vn., the sparks were equally strong in both positions of the air space, and quite close to the wall the difference between the sparking in the two positions again diminished. Therefore the points A, B, G, D in the diagram may in a certain sense be regarded as nodes. The distance between two of these points must not, however, be taken as the half wave-length, for if all the electrical motions changed their directions on passing through one of these points the phenomena observed in the secondary circuit would be repeated without variation, since the direction of oscillation in the air space is indifferent.

The conclusion to be drawn from the experiments is that in passing any one of these points part of the action is reversed, while another part is not. The experimental results, however, warrant the assumption that twice the distance between two of these points is equal to the half wave-length, and when this assumption is made the phenomena can be fully explained.

For suppose a wave of E.M.F., with oscillations in a vertical direction, to impinge upon the wall, and to be reflected with only slightly diminished intensity, thus giving rise to stationary waves. If the wall were a perfect conductor, a node would necessarily be formed in its surface, for at the boundary and in the interior of a perfect conductor the E.M.F. must be infinitely small. The wall cannot, however, be considered as a perfect conductor, for it was not metallic throughout, and the portion which was metallic was not of any great extent* The E.M.F. would therefore have a finite value at its surface, and would be in the direction of the impinging waves. The node, which in the case of perfect conductivity would occur at the surface of the wall, would, therefore, actually be ^tuated a little behind it, as shown at A in the diagram. If, then, twice the distance A B — tbat is to say, the distance A G — ^is half the wave-length, the steady waves will be as represented by the continuous lines in Fig. 162. The E.M.F.S acting on each side of the circles, in the positions I., H, III., and IV., will, therefore, at a given moment be represented in magnitude and direction by the arrows on each side of them in the diagram. If, therefore, in the neighbourhood of a node, the air space is turned towards the node, the strongest E.M.F. in

DYNAMICAL THEORY OF INDUCTION. 473

4>he 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, in 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 Tibration 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 0, 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 ^. At G, on the other hand, the sparking continued throughout the notation, 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 4ill distances the sparking vanished at the highest and lowest points of the circle, and attained a maximum value at the |)oints in the horizontal plane through the point of incidence.

474 DYNAMICAL TREORT 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 abscisssB.

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 inductioni 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 abscissae, the

DYNAMICAL THEORY ORlNDVCTfON. 475

onrve shown by the dotted Imes 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 0, 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 108 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 285 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 farther increased the phenomena recurred in the same order as before.

Hertz found that the position of C could be determined

I

476 DYNAMICAL TEEOBY OF INDUCTION.

within a few centimetres, the determinations of its distance from the wall varying from 410 to 415 metres ; he gives its most probable value as 412 metres. The point B could not be observed with any exactness, the direct determinations varying from 6 to 75 metres as. its distance from the wall. It could, however, be determined indirectly, for the distance between B and C being found to be 24 metres, taking this as the true value, A must have been 068 metre behind the surface of the wall, and G52 metres in front of it. The half wave-length would be 48 metres, and by an indirect method it was found to be 45 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 155 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 tue two waves should be of approximately equal

DYNAMICAL THEOBY OF INDUCTION. 477

intensities, and therefore the distance of the primary from the wall had to he 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 favomrable 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 he due to the decrease in tho 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 FresnePs 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 DYNAMICAL THEORY OF INDUCTION.

§ 12. Farther 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 ligJu, 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 h'ght 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 sarfEkoes,

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 «lectro-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 «ar, 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 and 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-milhon oscillations per second, or are of the order of S X 10".

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 determii^ed

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 metaUic 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 {Comptea Rendus, Vol. CI., July, 1886, 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 O^C. These experiments have been greatly extended by Dewar and Fleming {Phil. Mag,^ September, 1893), who have shown that perfectly pwrtf 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 oscillationfi of about 10^ 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 Profo, Ayrton and Perry, Proceedings of the Physical Society, London, YoL IV., p. 345.

t " On the Resistance of Electrolytes to the Passage of Rapidly Alter> nating Currents," Proeeedings of the Physical Society, London, Vol. XLV., Ko. 276, 1889.

1

DYNAMICAL THEORY OF INDUCTION. 4S1

gold-leaf supported on glass at onoe stopped completely the secondary sparks. This is a very interesting confirmation of the theory of magnetic screening laid down on p. 255 of Qhap. ly. We have seen that for moderately rapid alterna- tions the condnctivity of tinfoil is not sufficient to make it opaque to electro-magnetic radiations, but for disturbances of a frequency equal to about 10^ the tinfoil affords a perfect screening, or, in other words, is opaque.

With regard to the gold-leaf, Prot Thomson remarks thai 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 10^ 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 electrio enxrent in a. wire we must divest ourselves of the idea that the

II

482 DYNAMICAL THEORY OF INDUCTION.

eo-called flow of current is analogous to the movement of & 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 tranunels 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, eoid 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 jielded 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—rhow does the energy connected with an electric current pass from point to point, by what paths does it

V * " On thiB Transfer of Energy in the Electro-Magnetic Field," bjr Prof. J. H; Poynting, Phihtophical Trantactions of the Royal Society,. 1884, Part II., VoL CLXXV., p. 343. Also " On the Connection between Electric Current and the Electric and Magnetic Inductions in the Surrounding tileld," by Prof. J. H. Poynting, Philosophical Tramaetiom of the Boj^

Society, 1885, Part II., VoL GLXXVL, p. 277.

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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, farther, 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 tlie 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 tlie two forces multiplied by the sine of the angle between tliem and divided by 4ir. If 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 jpomi in the electro-magnetic field these forces are inclined at an angle 6, then there is a flow of energy e at this point in a •direction perpendicular to the planes of £ and H, and equal per second to the value of

E H sin ^

•'■"4^;

'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 appearancci then we know that either an equal quantity

it2

484 DYNAMICAL THEORY OF INDUCTION.