The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 27 of 35

zontal, its centre still lying in the base-line. This may be called "the third principal position." When the centre of the circular secondary conductor was kept fixed at the null point, and the air space was made to travel round the circle, vigorous sparking was observed in all positions. The sparking distance attained its maximum length of about six millimetres when its air space was nearest to that of the primary, and its minimum length of about three millimetres when the distance between the two air spaces was greatest. If the secondary had been influenced by the electrostatic force, sparking would only be expected when the air space was close to the base-line, and a cassation of sparks in the intermediate positions. The direction of the oscillation would, moreover, be determined by the direc- tion of the E.M.F. in the portion of the secondary furthest from the air space. There is, however, superposed upon the electrostatically excited oscillation a second oscillation, due to the E.M.F. of induction, which produces a considerable effect, since its integral round the circle (considered as a closed circuit) does not vanish; and the direction of this integral E.M.F. is independent of the position of the air space, opposing the electrostatic E.M.F. in the portion of the secondary next to A A', and assisting it in the portion furthest from A A', as explained previously.

The electrostatic and electro-dynamic E.M.F.s, therefore, act in the same direction when the air space is turned towards the primary conductors, and hi opposite directions when the air space is turned away from the primary. In the latter position it is the E.M.F. of induction which is the more powerful, as is shown by the fact that there is no disap- pearance of sparking in any position of the air space, for when this is 90deg. to the right or left of the base-line it coincides with a node with respect to the electrostatic E.M.F. In these positions the inductive action in the neighbourhood of the primary can be observed independently of the electrostatic action.

Waves in Rectilinear Wires. — In order to produce in a wire- by means of the primary oscillations a series of advancing waves of the character required for these experiments, the following arrangements were made : — Behind the plate A was placed a plate, P, of equal size. A copper wire one millimetre

DYNAMICAL THEORY OF INDUCTION. 45£

in diameter connected P to the point M of the base-line. From M the wire was continued in a curve about a metre in length to the point N, situated about 30 centimetres above the air space, and was then further continued in a straight line parallel to the base-line for such a distance as to obviate all danger of disturbance from reflected waves. In the present series of experiments the wire passed through a window, and after being carried to a distance of about 60 metres, was put to earth, and a special series of experiments showed that this length was sufficient. When a wire, bent so as to form a nearly closed circuit with a small air space, was brought near to this straight wire, a series of fine sparks was seen to- accompany the discharges of the induction coil. Their intensity could be varied by varying the distance between the plates P and A. The waves in the rectilinear wire were of the same period as that of the primary oscillations, as was proved by their being shown to be in unison with each of the two secondary conductors previously described. The existence of stationary waves showed that the waves in the rectilinear wire were of a steady character in space as well as in time. The nodal points were determined in the following manner : — The further end of the wire was left free, and the secondary con- ductor was brought near to it in such a position that the wire lay in its plane, and had the air space turned towards it. As the secondary was moved along the wire, points of no sparking were observed to recur periodically. The distance from the point n to the first of these was measured, and the length of the wire made equal to a multiple of this distance. The experiments were then repeated, and it was found that the nodal points occurred at approximately equal intervals along the ware.

The nodes could also be distinguished from the loops in other ways. The secondary conductor was brought near to the wire, with its plane perpendicular to it, and with its air space neither directed completely towards the wire nor com- pletely away from it, but in an intermediate position, so as to produce E.M.F.s perpendicular to the wire. Sparks were then observed at the nodes, while they disappeared at the loops. When sparks were taken from the rectilinear wire by means of an insulated conductor, they were found

460 DYNAMICAL THEORY OF INDUCTION.

to be stronger at the nodes than at the loops ; the difference, however, was small, and was, indeed, scarcely distinguishable unless the position of the nodes and loops was previously known. The reason that this and other similar methods do not give a well-defined result lies in the fact that irregular oscillations are superposed upon the waves considered ; the regular waves, however, can be picked out by means of the secondary, just as definite notes are picked out by means of a Helmholtz resonator. If the wire is severed at a node, no effect is produced upon the waves in the portion of wire next to the origin ; but if the severed portion of wire is left in its place the waves continue to be propagated through it, though with somewhat diminished strength.

The possibility of measuring the wave-lengths leads to various applications. If the copper wire hitherto used is replaced by one of different diameter, or by a wire of some •other metal, the nodal points retain their position unchanged. It follows from this that the velocity of propagation in a wire has a definite value independent of its dimensions and material. Hertz states that even iron wires offer no exception to this, showing that the magnetic susceptibility of iron does not play any part in the case of such rapid motions. This conclusion is not, however, confirmed by the researches of Prof. J. Trowbridge, and investigations, referred to on page 431, show that the magnetisability of the iron does exert an influence sensible though small. It would be interesting to investi- gate the behaviour of electrolytes in this respect. In their •case we should expect a smaller velocity of propagation, because the electrical motions are accompanied by motions of the molecules carrying the electric charges. It was found that no propagation of the waves took place through a tube 10 millimetres in diameter, filled with a solution of sulphate of copper ; but this may have been due to the resistance being too high. By the measurement of wave-lengths the relative vibration periods of different primary conductors can be deter- mined, and it therefore becomes possible to compare in this manner the vibration periods of plates, spheres, ellipsoids, &c.

In the experiments made by Hertz, nodes were very dis- tinctly produced when the wire was severed at a distance of .either 8 metres or 5-5 metres from the null point of the base-

DYNAMICAL THEORY OF INDUCTION. 461

line. In the first case the nodes occurred at distances from the null point of - 0-2 metre, 2-3 metres, 51 metres, and 8 metres, and in the latter case at distances of -0-1 metre, 2-8 metres, and 5-5 metres. It appears, therefore, that the (half) wave- length in a free wire cannot differ much from 28 metres. The fact that the wave-lengths nearest to P were somewhat smaller was to be expected from the influence of the plates and of the curvature of the wire. This wave-length, with a period of one hundred-millionth of a second, gives 280,000 kilometres per second for the velocity of propagation of electrical waves in wires. Fizeau and Gounelle (Poggendorffs Annalen, Vol. LXXX., p. 158, 1850) obtained for the velocity in iron wires 100,000 kilometres per second, and 180,000 in copper wires. W. Siemens (Poggendorff's Annalen, Vol. CLVIL, p. 309, 1876), by the aid of Leyden jar discharges, obtained a velocity of from 200,000 to 260,000 kilometres per second in iron wires. Hertz's result is very nearly the same as the velocity of light. Space will not allow us to fully discuss the causes which led to certain discrepancies in Hertz's earlier results. Suffice it to say that he subsequently found that the velocity of propagation of an electromagnetic disturbance along a wire was the same as in free space, viz., the velocity of light. The apparent difference between the velocity of long and short waves was afterwards explained by Hertz himself, and the causes of this were made clear by the experiments conducted in the large hall of the Rhone waterworks by MM. Sarasin and de la Rive. From these experiments it became clear that the interference due to surrounding objects was the cause of the apparent difference between the velocities of long and short waves, but that in a sufficiently large space this difference disappeared, and the velocity of both long and short electromagnetic waves was the same. The reader may consult with advantage on this point the notes and text of the full translation of Hertz's electrical Papers made by Mr. D. E. Jones.*

Interference of tlie Direct Actions with those transmitted through the Wire. — If the square circuit B is placed at the null point in the second principal position, with the air space

• " Electric Waves." Authorised English translation of Hertz's Papers, by D. E. Jones.

462 DYNAMICAL THEORY OF INDUCTION.

at its highest point, it will be unaffected by the waves in tha wire, but the direct action when in this position was found to produce sparks 2 millimetres in length. B was then turned about a vertical axis into the first principal position, in which there would be no direct action of the primary oscillation, but the waves in the wire gave rise to sparks, and by bringing P •near enough to A a sparking distance of 2 millimetres could be obtained. In the intermediate positions sparks were pro- duced in both these ways, and it would therefore be possible to get a difference of phase, such that one should either increase or diminish the effect of the other. Phenomena of this nature were, indeed, observed. When the plane of B was in such a position that the normal drawn towards A A' was directed away from that side of the primary conductor on which P was placed, there was more sparking than even in ths principal position ; but if the normal were directed towards P the sparks disappeared, and only reappeared when the air space was made smaller. When the air space was at the lowest point of B, the other conditions remaining the same, the sparks disappeared when the normal was turned away from P. Further variations of the experiment gave results in accordance with these.

It is easily seen that these phenomena were exactly what were to be expected. To fix the ideas, suppose the air space to be at the highest point, and the normal directed towards P, as in Fig. 161. Consider what happens at the moment that the plate A has its greatest positive charge. The electrostatic, and therefore the total, E.M.F. is directed from A towards A'. The oscillation to which this gives rise in B is determined by the direction of the E.M.F. in the lower portion of B. There- fore positive electricity will flow towards A' in the lower portion, and away from A' in the upper portion.

Consider next the action of the waves. As long as A is positively charged, positive electricity will flow from the plate P. This current is at the moment considered at its maximum value at the middle point of the first half wave-length. A quarter of a wave-length further from the origin — that is to say, in the neighbourhood of the null point — it first changes its direction. The E.M.F. of induction will here, therefore, impel positive electricity towards the origin. A current will

DYNAMICAL THEORY OF INDUCTION. 463

therefore flow round B towards A' in the upper portion and away from A' in the lower portion. The electrostatic and electro -dynamic E.M.F.s are therefore in opposite phases and oppose each other's action. If the secondary circuit is rotated through OOdeg., through the first principal position, the direct action changes its sign, but not so the action of the waves, so that they now tend to strengthen each other. The same reasoning holds when the air space is at the lowest point of B.

Greater lengths of wire were then included between m and n, and it was found that the interference became gradually less marked, until within a length of 2-5 metres it disappeared entirely, the sparks being of equal length whether the normal were directed towards or away from P. When the length of wire between m and n was further increased, the distinction between the different quadrants reappeared, and with a length of 4 metres the disappearance of the sparks was fairly sharp. The disappearance, however, then took place (with the air space at the highest point) when the normal was directed away from P, the opposite direction to that in which the disappearance pre- viously took place. With a still further increase in the length of the wire the interference reappeared, and returned to its original direction with a length of 6 metres. These phenomena are clearly to be explained by the retardation of the waves in the wire, and show that here again the direction of motion in the advancing waves changes its signs at intervals of about 2-8 metres.

To obtain interference phenomena with the secondary circuit C in the third principal position, the rectilinear wire must be removed from its original position and placed in the horizontal plane through C either on the side of the plate A or of the plate A'. Practically it is sufficient to stretch the wire loosely, and to fix it by means of an insulated clamp on each side of C alternately. It was found that when the wire was on the same side as the plate P the waves in it diminished the previous sparking, and when on the opposite side the sparking was increased, both results being unaffected by the position of the air space in the secondary circuit. Now it has been already pointed out that at the moment when the plate A has its maximum positive charge, and at which, therefore, the primary current begins to flow from A, the current at the first

464 DYNAMICAL THEORY OF INDUCTION.

node of the rectilinear wire begins to flow away from the origin. The two currents, therefore, flow round C in the same direction when C lies between the rectilinear wire and A, and in opposite directions when the wire and A are on the same side of C. The fact that the position of the air space is indifferent confirms the conclusion formerly arrived at that the direction of oscillation is that due to the electro-dynamic E.M.F. These interferences are also changed in direction when the wire m n, I metre in length, is replaced by a wire 4 metres in length.

Hertz also succeeded in obtaining interference phenomena when the centre of the secondary circuit was not in the base- line, but these results were of no special importance, except that they confirmed the previous conclusions.

Interference Phenomena at Various Distances. — Interference may be produced with the secondary at greater distances than that of the null point ; but care must then be taken that the action of the waves in the wire is of about the same magnitude as the direct action of the primary circuit through the air. This can be effected by increasing the distance between P and A.

Now, if the velocity of propagation of the electro-dynamic disturbances through the air is infinite, the interference will change its sign at every half- wave length in the wire — that is to say, at intervals of about 2-8 metres. If the velocities of propagation through the air and through the wire are equal, the interference will be in the same direction at all distances. Finally, if the velocity of propagation through the air is finite, but different from the velocity in the wire, the interference will change in sign at intervals greater than 2-8 metres.

The interferences first investigated were those which occurred when the secondary circuit was rotated from the first into the second principal position, the air space being at the highest point. The distance of the secondary from the null point was increased by half-metre stages from 0 up to 8 metres, and at each of these positions an observation was made of the effects of directing the normal towards and away from P respectively. The points at which no difference in the sparking was observed in the two positions of the normal are marked 0 in Table I. Those in which the sparking

DYNAMICAL THEORY OF INDUCTION. 465

was least, showing the existence of interference, when the normal was directed towards P, are marked + , and those in which the sparking was least when the normal was directed away from P are marked — . The experiments were repeated with different lengths of wire m n, varying by steps of half a metre from 1 metre up to 6 metres. The first horizontal line in the table gives the distance, in metres, of the centre of the secondary circuit from the null point, while the first vertical line gives the lengths of the wire m n, also in metres.

Table I.

—

0

1

1

2

3

4

5

6

7

8

100 150 200 250

300 ?50

nr\n

1 1 00+ +

0

0

i

0

0

• • • O O O 1

0

•f

n

0 0

0 0

0

00 + +OOC

0

0 0 0

0+000 1

0 0 0

•f

0

0

1 | 00+ +

1 I 000 +

450 500 550 600

0

0 0

i- + + + +

0

0

o

h +00 1

0

0

0

0

1 000 1

I +001

• 001

0 0

0

An inspection of the table shows, in the first place, that the changes of sign take place at longer intervals than 2-8 metres ; and, in the second place, that the change of phase is more rapid in the neighbourhood of the origin than at a distance from it. As a variation in the velocity of propagation is very unlikely, this is probably due to the fact indicated by theory that the electrostatic E.M.F., which is more powerful than the electro-dynamic E.M.F. in the neighbourhood of the primary oscillation, has a greater velocity of propagation than the latter.

In order to obtain a definite proof of the existence of similar phenomena at greater distances, Hertz continued the observa- tions, in the case of three of the lengths m n, up to a distance of 12 metres, and the result is given in Table II.

If we make the assumption that at the greater distance it is only the E.M.F. of induction which produces any effect, the experiments would show that the interference of the waves

466

DYNAMICAL THEORY OF INDUCTION.

exsited by the E.M.F. of induction with the original wares in the wire changes its sign only at intervals of about 7 metres.

Table II.

—

0

1

2

3

4

5

6

7

8

9

10

11 | 12

100

0

_

_

0

0

0

•   0 
  

260

0

_

0

0

0

0

0

400

0

0

0

0

0 I 0

Table TIL

.—

0

1 2

3

4

ICO

_

_

_

_

0

150

0

0

0

200

0

0

0

4-

250

0

-t-

300

350

0

400

-I-

0

450

0

0

500

0

0

0

550

0

0

0

_

600

0

—

—

—

—

In order to investigate the E.M.F. of induction close to the primary oscillation, where the results are of special importance, Hertz made use of the interferences which were obtained when the secondary circuit was in the third principal position, and the air space was rotated through 90deg. from the base-line. The direction of the interference at the null point, which has already been considered, was taken as negative, the interference being considered positive when it was produced by the passage of waves on the side of C remote from P, which make the signs correspond with those of the previous experiments. It must be borne in mind that the direction of the resultant E.M.F. at the null point is opposed to that of the E.M.F. of induction, and therefore the first table would have begun with a negative sign if the electrostatic E.M.F. could have been eliminated. The present experiments showed that up to a distance of 8 metres interference continued to occur, and always of the same sign as at the null point. It was unfortunately impossible to extend these observations to a greater distance than 4 metres on

DYNAMICAL THEORY OF INDUCTION. 467

Account of the feebleness of the sparks, but the results obtained were sufficient to give distinct evidence of a finite velocity of propagation of the E.M.F. of induction. These observations, like the former ones, were repeated with various lengths of the wire mn in order to exhibit the variation in phase, and the results obtained are given in Table III., which shows that, as the distance increases, the phase of the interference changes in such a manner that a reversal of sign takes place at intervals of from 7 to 8 metres. This result is further con- firmed by comparing the results of Table III. with the results for greater distances given in Table II., for in the former series the effect of the electrostatic E.M.F. is eliminated, owing to the special position of the secondary circuit, while in the latter it becomes insensible at the greater distances owing to its rapid decrease with increasing distance. We should therefore expect the results given in the first table for distances beyond 4 metres to follow without a break the results given in Table III. for distances up to 4 metres. This was found to be the case, as is evident from inspection of Tables II. and III.

To show this more clearly, the signs of the interference of the waves, due to the electro-dynamic E.M.F., with the waves in the wire are collected together in Table IV., the first four columns of which are taken from Table III., and the remain- ing columns from Table II.

Table IV.

_

0

^

2

3

4

5

6

7

8

9

10

11

12

ICO

_

_

_

_

0

0

0

0

250

0

0

0

0

0

_

400

0

0

—

—

—

—

0

0

0

From the results given in this table Hertz drew the following conclusions : —

1. The interference does not change its sign at intervals of •2-8 metres. The electro-dynamic actions are therefore not propagated with an infinite velocity.

2. The interference is not in the same phase at all points. Therefore the electro-dynamic actions are not propagated through air with the same velocity as electric waves in wires.

HH2

468 DYNAMICAL THEORY OF INDUCTION.

3. A gradual retardation of the waves in the wire has the effect of displacing a given phase of the interference towards the origin of the waves. The velocity of propagation through the air is therefore greater than through a wire.

4. The sign of the interference is reversed at intervals of 7-5 metres, and therefore in traversing this distance an electro- dynamic wave gains one length of the waves in the wire.

Thus, while the former travels 75 metres, the latter travels 75 - 2-8 = 4-7 metres, and therefore the ratio of the velocities is 75 I 47, which gives for the half wave-length of the electro- dynamic action 2-8 x 75/47 = 4-5 metres. Since this distance is traversed in 1-4 hundred-millionth of a second, the absolute velocity of propagation through the air must be 320,000 kilo- metres per second. This result can only be considered reliable as far as its order is concerned ; but its true value can hardly exceed half as much again, or be less than two-thirds of this amount. In order to obtain a more accurate determination of the true value it will be necessary to determine the velocity of electric waves in wires with greater exactness.

It does not necessarily follow from the fact that in the imme- diate neighbourhood of the primary oscillation the interference changes its sign after an interval of 2-8 metres, that the velocity of propagation of the electrostatic action is infinite, for such a conclusion would rest upon a single change of sign, which might, moreover, be explained independently of any change of phase, by a change in the sign of the amplitude of the resultant force at a certain distance from the primary oscillation. Quite independently, however, of any knowledge of the velocity of propagation of electrostatic actions, there exist definite proofs that the rates of propagation of electrostatic and electro dynamic E.M.F.s are unequal

In the first place, the total force does not vanish at any point on the base line. Now, near the primary the electro- static E.M.F. is the greater, while the electro-dynamic E.M.F. is the greater at greater distances. There must, therefore, be some point at which they are equal, and since they do not balance they must take different times to reach this point.

In the second place, the existence of points at which the direction of the resultant E.M.F. becomes indeterminate does not seem capable of explanation, except on the supposition.

DYNAMICAL THEORY OF INDUCTION. 469

that the electrostatic and electro-dynamic components perpen- dicular to each other are in appreciably different phases, and, therefore, do not compound into a rectilinear oscillation in a fixed direction. The fact that the two components of the resultant are propagated with different velocities is of con- siderable importance, in that it gives an independent proof that one of them at any rate must have a finite velocity of propagation.

Further researches of Hertz on electrical oscillations, of which accounts have been published, are to be found described in a Paper, "On Electro-Dynamic Waves in Air, and their Reflection," in Wiedemann's Annalen, Vol. XXXIV., p. 609. The author had been endeavouring to find a more striking and direct proof of the finite velocity of propagation of electro- dynamic waves than those which he had hitherto given ; for, though these are quite sufficient to establish the fact, they can only be properly appreciated by one who has obtained a grasp of the results of the entire series of researches.

In many of the experiments which have been described, Hertz had noticed the appearance of sparks at points in the secondary conductor where it was clear from geometrical con- siderations that they could not be due to direct action, and it was observed that this occurred chiefly in the neighbourhood of solid obstacles. It was found, moreover, that in most positions of a secondary conductor the feeble sparks produced at a great distance from the primary became considerably stronger in the vicinity of a solid wall, but disappeared with considerable suddenness quite close to the wall. The most obvious explanation of these experiments was that the waves of inductive action were reflected from the wall and interfered with the direct waves, especially as it was found that the phenomena became more distinct when the circumstances were such as to favour reflection to the greatest possible extent. Hertz therefore determined upon a thorough investi- gation of the phenomena.

The experiments were made in the Physical Lecture Theatre, which is 15 metres in length, 14 metres in width, and 6 metres in height. Two rows of iron columns, running parallel to the sides of the room, would collectively act almost like a solid wall towards electro-dynamic action, so that the available

470 DYNAMICAL THEORY OF INDUCTION.

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. Special 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 electricity 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 13 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 2-5 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 the reflecting surface with the perpendicular from the centre of the primary conductor will be called " the point of incidence," and the experiments were limited 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 to 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 35 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 experi- 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 neighbourhood of his body exerted a slight influence upon 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 its a considerable difference was generally observed in the 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

tear

,_t I--'!* -^ j

W\ * 0 c @

FIG. 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 3 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 3 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 L, 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 VII., 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, C, 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 situated a little behind it, as shown at A in the diagram. If, then, twice the distance A B — that is to say, the distance A C — 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 L, II., 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