The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 24 of 35

The jars charge up as they stand on the same wooden table, and when the potential rises to sparking amount they discharge at A, and a violent electric rush then takes place between the two plates, and the conductors between are struck. If the same three kinds of conductors are used, and they be adjusted until they are all about equally struck, we find that the smaller and shorter-stemmed knob no longer protects the larger one, and the sharp point no longer protects either ; all three, large ball, small ball and point, are liable to be struck equally if at the same height, and if they differ in height the highest is most likely to be struck, no matter what it is. Points are, then, no protection against these impulsive rushes of electricity. The special virtue of a point in the case of the slower-timed dis- charges is that it prepares the path of the discharge to itself,

FIG. 146.

for in this case the path is pre-arranged by induction. If one of the conductors has a large resistance — say a liquid megohm inserted in it — then this one is no longer struck ; it ceases to protect the other conductors even if higher than them, and even if it be so raised in height that it touches the top plate, thus connecting the plates by a bad conductor, the two other conductors get struck with apparently the same ease as before. This indicates that a lightning conductor with a bad earth can- not protect well against discharges of the nature of a sudden rush. Mr. Wimshurst has, however, shown reason for consider- ing that in this experiment the electrical state of plates, as regards sign of electrification, may be of importance. The question how far the point protects from the impulsive rush is not altogether cleared up. It is still sub judice.

410 DYNAMICAL THEORY OF INDUCTION.

In performing the first experiment of the alternative path (Fig. 141) it was noticed that the B spark was longer than the A spark. Plainly this indicates that the discharge at A sets up electrical oscillations. The manner in which this is brought about is as follows : — On the commencement of the discharge the air-space is intensely heated, and its conductivity so far increased that the conditions as to the relation of inductance, resistance and capacity of the discharger and condenser are ful- filled, and the discharge takes the oscillatory form. If a couple of long leads are attached to the A discharger (Fig. 147), the farther ends being insulated, and a discharger B bridged across at BH B.J or B3, then it is found that at every discharge at A a spark can be obtained at B, and for a certain length of A spark the B spark will be longer at B3 than at the nearer positions. Evidently what happens is that the electrical oscillation across

FIG. 147.

the A discharge intervals sets up violent surgings to and fro in the open circuit wires, just like water in a long trough when it is tilted, and the recoil at the insulated ends, combined with the inductance of these leads, produces a cross flash at B. It is, in fact, a case of resonance ; the long open circuit leads act like resonators to the oscillating discharge across A, and the nearer the length of the leads approaches to half a wave length or to some multiple of half a wave length the more perfect will be the resonance and the greater the recoil at the open ends, and hence the greater the spark at B3.

If the experiraent is tried in the dark, the B discharger being removed, it is seen that the leads glow at the ends with a vivid brush light at the moment when the jars are dis- charged. When the proper length of open circuit lead has

DYNAMICAL THEORY OF INDUCTION. 411

been found which resonates best in accord with the jars used as dischargers, then the whole of the effects described can be made to disappear by connecting a very small Leyden jar to the ends of the wires. The increase of static capacity thus given to the leads reduces their potential below sparking point. Arranging the jar so as to leave an air-space between it and one of the wires, a spark passes into it at each A spark ; but the jar is not in the least charged afterwards, proving that the spark is a double one, first in and then out of the jar, a real recoil of the reflected pulse. Hence, also, we see that the brush visible in the dark is the same on each wire, and one is not able to say that one brush is positive and the other negative, for each is both.

A curious experiment illustrating the electrical surgings or oscillations set up in a conductor which is suddenly discharged at one end is as follows : Attach one end of a long wire to one knob of a "Wirnshurst machine, and connect the other pole to

FIG. 148.

earth. The wire is otherwise insulated, and now forms one coating of a condenser of which the other is the walls of the room. The wire is bent round so that its free end nearly touches its initial end (see Fig. 148). Under these circumstances one would naturally say that a spark at B was absurd, and yet it is found that even if the wire is a stout copper wire a spark happens at B when one is produced at A. This B spark is caused by an electrical oscillation in the wire. The wire is, as it were, pumped full of electricity by the machine, and when the spark happens at A a release is given at that end for one brief instant. Then ensues a rebound of the electricity, and the pressure rises at the free end to sparking amount. The whole effect is just analogous to the effect of suddenly opening and closing a tap on a high-pressure water service — a concussion is heard in the tap on shutting, and if one could see the water it would be found that it rebounds, and a reflected

412 DYNAMICAL THEORY OF INDUCTION.

wave is set up in the pipe, which, if the pipe is not strong enough, will burst it at some weak point. The practical moral of this is that any large conductor suddenly discharged has set up in it violent electrical surgings, which may cause it to spit off discharges at other points, and these sparks may be as long as the principal spark.

Another way of making these electrical surgings conspicuous is by their effect in causing a Leyden jar to overflow, i.e., to spark round its edge. A jar does this when its coat- ings are very suddenly raised to a great potential difference. Fig. 149 shows the arrangement. The inside of the jar is made to communicate direct to one machine pole, and the outer coating, through the intervention of a long wire, to the other pole.

When a spark happens at A, and the length of the wire L is sufficiently great, the jar sparks over its edge. The explanation

FIG. 149.

of this is as follows : — Whilst the handle of the machine is being turned the potential difference of the j ar coatings increases. At a certain limit the air in the A space breaks down, and, being lieated, becomes for a moment a very good conductor ; there is, therefore, a rush of electricity out of the inner coating and into the outer coating, but the spark at A ceasing, this outflow from the jar is suddenly stopped and rebounds, whilst at the same time the inductance of the wire L causes a rush to continue into the jar. The rebound of the flow when the rush through the air space is suddenly stopped causes the potential difference of the coatings to rise to a point at which they spark over the edge of the glass. In an example given by Dr. Lodge the jar was a one gallon jar, with glass fully three inches above the tinfoil. L was a thick No. 1 copper wire circuit round a room. The jar

DYNAMICAL THEORY OF INDUCTION. 413

ovei-flows every time a spark happens at A, even though the length of this spark is only 0-64in. If the long lead L is short- circuited, then the jar refuses to overflow until the A spark has been increased to l-Tin. The higher potential difference needed to cause overflow or rebound in the case with a short circuit is illustrative of the fact that a little self-induction in the dis- charging circuit bestows momentum on the flow and assists in making a back splash.

A hydraulic analogue to the above might be found in con- sidering the case of a liquid flowing steadily along a trough or canal. If an obstruction was suddenly created, as by closing a valve or sluice, the liquid would rebound and a wave would be created ; and, as in the case of the hydraulic ram, the rebound of the liquid against a closed valve might be made to lift some of it to a higher level than that from which it originally fell. In the electrical case, the rebound is made to raise the jar coatings to a greater potential difference than that which existed at the instant when the jar commenced to discharge.

§ 9. Theory of Experiments on the Alternative Path. — We may proceed, following Dr. Lodge,* and quoting freely from him in what follows, to examine a little more in detail the electrical oscillations set up in an open circuit by Leyden jar discharges. These stationary electrical oscillations in linear conductors resemble those which can be set up in a cord fixed at one end, or in a trough of liquid, by suitably-timed im- pulses. As we have seen, if a jar discharges at A (see Fig. 150) in the ordinary way, simultaneously an even longer spark may be obtained at B, at the far end of two long open circuit leads. Or if the B ends of the wire are too far apart to allow of a spark, the wires glow and spit off brushes every tune a discharge occurs at A. The theory of the effect seems to be that oscillations occur in the A circuit with a period T = 2?r ,/LC, where L is the inductance of the A circuit and C the capacity of the jar. These oscillations disturb the surrounding medium, and send out radiations of the precise nature of light, only too long in wave length to affect the

• See Phil. Mag., August, 1838; also The Electrician, August 10, 1888, p. 435.

414 DYNAMICAL THEORY OF INDUCTION.

retina of our eyes. The velocity of these electro-magnetic impulses is, as we have seen, equal to v, where

so the wave length of the oscillations is

Now — is the electro-magnetic measure of inductance, and — P K

is the electrostatic measure of capacity, //, being the magnetic permeability, and K the electrostatic inductivity of the medium surrounding the wire.

Each of these quantities is of the dimensions of a length, and the wave length of the radiation is 2?r times their geometric mean. We may look upon it, then, that the magnetic field due to the oscillatory current in the A circuit, which circuit

FIG. 150.

consists partly of metal wires, partly of the dielectric of the jar, and partly of the heated air in the spark space, acts inductively upon the other or B circuit which is adjacent to it, and has, in fact, the jar dielectric as a common boundary. The pulsating field induces oscillatory currents in the open B circuit. These electric pulses rush along the surface of the wires with a certain amount of dissipation, and are reflected at the distant end, producing a recoil kick or impulse tending to break down the dielectric in the air gap B with production of a spark. These currents continue to oscillate to and fro unti damped out of existence by the resistance of the wires. The best effect in the way of spark at B is observed when the length of each wire is such that the time occupied by an elec- tric pulse in travelling along the wires and back again is equal to the time of a complete oscillation in the A circuit ; that is,

DYNAMICAL THEORY OF INDUCTION. 415

when the length of the open circuit wires is equal to half a wave length or to some multiple of half a wave length. The natural period of oscillation in the long wires will then agree with the oscillation period of the discharging circuit and the oscillations in the open circuit wires, and the field due to the oscillations in the A circuit will vibrate in unison like a column of air in a pipe resonating a tuning fork, or like a string vibrating when attached to the tongue of a reed.

The elementary theory of the open circuit oscillations is as follows : —

Let li and i\ be the inductance' and resistance of the straight wires per unit of length, as affected ~by the periodicity, and let cx be the capacity per unit of length. It has been shown by Lord Eayleigh (Phil. Mag., May, 1886) that with very rapid oscillations owing to the circumferential distribution of the current the inductance and resistance have values different from the steady current values, and when the frequency of the oscil- lations is very great the resistance r: per unit of length is the geometric mean, of its ordinary value r and ^ p /*„, where /^ is the magnetic permeability of the material of the conductor, or ri= *J%P Po?', P being, as usual, 2?r n, n being the number of complete oscillations per second.

And again, when n is very great, the inductance Zx per unit

of length is equal to a constant plus ^, or

I being the induction for slowly fluctuating currents.

In the case of the two parallel wires we have for the slope

of the potential -^J- along them the usual equations,

4S'--g ..... (U4)

i being the instantaneous current in the section of the length lying at a distance #*from the origin ; and also for the accumu- lation of charge in this element dx of the length we have the equation

-11 = 1 «± ..... (145) dt (jdx

416 DYNAMICAL THEORY OF INDUCTION.

The elimination of i between these equations gives us a differential equation for V, and shows that stationary waves of current are set up in finite wires of suitable length under the action of an alternating electromotive force. The solution of the equation for a long wire when i\ is small and p is very large is

mi

V0«~ "i* cosy* (*---),

\ ?ij/

where w, = — 1- and wt = . -.

2 L v -Uj O|

The velocity of propagation of the wave is therefore 7^ and the

wave length is — nr

P

For two parallel wires, as in the Ley den jar case, we have each wire

i= •ppor>

r being the ordinary resistance. And again, as Lord Kayleigh has shown (Phil. May., May, 1886), we have

b being the distance between the parallel wires and a the radius of either, and /* the magnetic permeability of the material of the conductors.

For immensely quick oscillations the second term is zero. Also, the capacity G: of the wires per unit of length is, by a known theorem,

0,-

"

hence

and the velocity of the pulse along the wires is the same as in the dielectric round them. In other words, the electric pulses set up in the wires rush to and fro with a velocity equal to that with which the electro-magnetic impulse is propagated through the dielectric round them. Hence, we have here a means of determining experimentally the wave length of a given discharging circuit. Either vary the size of the A circuit or

DYNAMICAL THEORY OF INDUCTION. 417

adjust the length of the B wires until the recoil spark B is as long as possible. Then measure, and see whether the length of each wire is not equal to

A small condenser can be made having an electrostatic capacity of, say, two or three centimetres, and if such a coated pane be made to discharge over its edge, the discharged circuit will have an electro-magnetic inductance of a few centimetres. Under these circumstances the electrical oscillations would be at the rate of a thousand million a second, and the wave length of the electro-magnetic disturbance radiated would be about 20 to 30 centimetres.

If a conductor as small as an atom could have its electrical charge disturbed in the same way, oscillations would be set up of the frequency of light waves and electro-magnetic disturb- ances of light wave length radiated ; and it seems probable that this is just what light waves are, viz., electro-magnetic disturbances propagated through the ether and due to electric oscillatious set up in the atomic charge.

§ 10. Impulsive Impedance. — In the experiments of the "alternative path," as described by Dr. Lodge, the main result is very briefly summed up by saying that when a sudden dis- charge had to pass through a conductor it was found that iron and copper acted about equally well, and indeed iron sometimes exhibited a little superiority, and that the thickness of the conductor and its ordinary conductivity mattered very little indeed. We are led by this to see that the impedance which a conductor offers to a sudden discharge, and which may be called its impulsive impedance, is something quite different from its ordinary or ohmic resistance, or even its impedance, defined as Vft2+p'2L'2, to slowly periodic or oscillatory cur- rents. As already mentioned, the resistance of a conductor to very rapidly changing currents is expressed by Eu where

E being the resistance to steady current, /*0 the permeability of the material of the conductor and I its length, and p = 2ir

418 DYNAMIC AL THEORY OF INDUCTION.

times the frequency of the oscillation. Also the corresponding inductance Lx is

L.-L+?..

where L is a constant depending, on the size and form of the circuit, but only in a small degree upon its thickness. Hence, forming the function VR^+y-L^, and calling this Im1, 'we have

im

where

In the case of enormously rapid oscillations the value practically reduces to p L, and hence the impulsive impedance varies in simple proportion to the frequency, and depends on the form and size of the circuit, but not at all on its specific resistance, magnetic permeability, or diameter.

All this is borne out by experiment. In some of his experiments Dr. Lodge found the impedance of a No. 2 wire of two and a-half metres length bent into a circle to be 180 ohms at twelve million oscillations per second, and for a No. 40 wire the impedance was only 300 ohms, although the ohmic resistances of these wires were respectively -004 ohms and 2'6 ohms. At three million oscillations per second, or at one-fourth the frequency, the impedances of the same circuits were 43 ohms and 78 ohms. At one-quarter million oscillations per second the impedances are reduced to four and six ohms respectively for the thick rod and fine wire. Hence, for frequencies of a million per second and upwards, such as occur in jar discharges, and perhaps in lightning, the impedance of all reasonably conducting circuits is the same, and independent of conductivity and permeability, and hardly affected greatly by enormous changes in diameter.

§ 11. Hertz's Kesearches on the Propagation of Electro- magnetic Induction. — The classical researches of Hertz on electrical oscillations and the propagation of electro-magnetic induction through space form an epoch in the history of

DYNAMICAL THEORY OF INDUCTION. 419

electrical science. These investigations have been well described by Dr. Lodge in his book on " The "Work of Hertz,"* and the reader is referred to this for an account of the chief work of Hertz and his followers. There is therefore no need to enter here at very great length into an account of these discoveries ; but a very excellent abstract of Hertz's work has been given by Mr. G. W. de Tunzelmann.f

Preliminary Experiments. — It is known that if in the second- ary circuit of an induction coil there be inserted, in addition to the ordinary air space across which sparks pass, a Eiess spark micrometer, with its poles joined by a long wire, the discharge will pass across the air space of the micrometer in preference to following the path of least resistance through the wire, provided this air spaca does not exceed a certain limit ; and it is upon this principle that lightning protectors for telegraph lines are constructed. It might be expected that the sparks could be made to disappear by diminishing the length and resistance of the connecting wire ; but Hertz found that though the length of the sparks could be diminished in this way, it is almost impossible to get rid of them entirely, and they can still be observed when the balls of the micrometer are con- nectsd by a thick copper wire only a few centimetres in length.

This shows that there must be variations in the potential measurable in hundreds of volts in a portion of the circuit •only a few centimetres in length, and it also gives an indirect proof of the enormous rapidity of the discharge ; for the differ- ence of potential between the micrometer knobs can only be due to self-induction in the connecting wire. Now the time occupied by variations in the potential of one of the knobs must be of the same order as that in which these variations can be transmitted through a short length of a good conductor to the second knob. The resistance of the wire connecting the knobs is found to be without sensible effect on the results.

• Published by " The Electrician " Printing and Publishing Company, Limited.

t This section originally appeared as a series of articles in the pages of The Electrician, in Vol. XXI., pp. 587, 625, 663, 696, 725, 757, 788 (1888). The writer felt it would be difficult to make a more complete digest of Hertz's work than is contained in these excellent articles, and, by the kind permission of their author, he is allowed to reproduce them in these pages.

EE2

420

DYNAMICAL THEORY OF INDUCTION.

In Fig. 151, A is an induction coil and B a discharger. The wire connecting the knobs 1 and 2 of the spark micrometer M consists of a rectangle, half a metre in length, of copper wire two millimetres in diameter. This rectangle is connected with the secondary circuit of the coil in the manner shown in the diagram, and, when the coil is in action, sparks, sometimes several millimetres in length, are seen to pass between the knobs 1 and 2, showing that there are violent electrical oscil- lations not only in the secondary circuit itself, but in any conductor in contact with it. This experiment shows even more clearly than the previous one that the rapidity of the oscillations is comparable with the velocity of transmission of electrical disturbances through the copper wire, which, accord-

FIG. 151.

ing to all the evidence at our disposal, is nearly equal to the velocity of light.

In order to obtain micrometer sparks some millimetres in length a powerful induction coil is required, and the one used by Hertz was 52 centimetres in length and 20 centimetres in- diameter, provided with a mercury contact breaker, and excited by six large Bunsen cells. The discharger terminals consisted of brass knobs three centimetres in diameter. The experiments showed that the phenomenon depends to a very great extent on the nature of the sparks at the discharger, the micrometer sparks being found to be much weaker when the discharge in-

DNTAM1CAL THEORY OF INDUCTION. 421

the secondary circuit took place between two points or between a point and a plate than when knobs were used. The micro- meters sparks were also found to be greatly enfeebled when the secondary discharge took place in a rarefied gas, and also when the sparks in the secondary were less than half a centimetre in length ; while, on the other hand, if they exceeded 1| centi- metres the sparks could no longer be observed between the micrometer knobs. The length of secondary spark which was found to give the best results, and which was therefore em- ployed in the further observations, was about three-quarters of a centimetre.

Very slight differences in the nature of the secondary sparks were found to have great effect on those of the micrometer, : and Hertz states that after some practice he was able to deter- mine at once from the sound and appearance of the secondary spark whether it was of a kind to give the most powerful effects at the micrometer. The sparks which gave the best results were of a brilliant white colour, only slightly jagged, and accompanied by a sharp crack.

The influence of the spark is readily shown by increasing the distance between the discharger knobs beyond the striking distance, when the micrometer sparks disappear entirely, although the variations of potential are now greater than before. The length of the micrometer circuit has naturally an important influence on the length of the spark, as the greater its length the greater will be the retardation of the electrical wave in its passage through it from one knob of the micrometer to the other.

The material, the resistance, and the diameter of the wire of which the micrometer circuit is formed have very little influence on the spark. The potential variations cannot, therefore, be due to the resistance ; and this was to be expected, for the rate of propagation of an electrical disturb- ance along a conductor depends mainly on its capacity and coefficient of self-induction, and only to a very small extent on its resistance. The length of the wire connecting the micrometer circuit with the secondary circuit of the coil is also found to have very little influence, provided it does not exceed a few metres in length. The electrical disturbances must therefore traverse it without undergoing any appreciable

422

DYNAMICAL THEORY OF INDUCTION.

change. The position of the point of the micrometer circuit which is joined to the secondary circuit is, on the other hand, of the greatest importance, as would be expected, for, if the point is placed symmetrically with respect to the two micro- meter knobs, the variations of potential will reach the latter in the same phase, and there will be no effect, as is verified by observation. If the two branches of the micrometer circuit on each side of the point of contact of the connection with the secondary are not symmetrical the spark cannot be made to disappear entirely; but a minimum effect is obtained when the point of contact is about half-way between the micrometer knobs. This point may be called the null point.

Fig. 152 shows the arrangement employed, e being the null .point of the rectangular circuit, which is 125 centimetres long

M

12

FIG. 152.

by 80 centimetres broad. When the point of contact is at !a or b sparks of from three to four millimetres in length are observed ; when it is at e no sparks are seen, but they can be made to reappear by shifting the point of contact a fetor centimetres to the right or left of the null point. It should be noted that sparks only a few hundredths of a millimetre in length can be observed. If, when the point of contract is at «, another conductor is placed in contact with one of the micro- meter knobs, the sparks reappear.

Now, the addition of this conductor cannot produce any alteration in the time taken by the disturbances proceeding

• DYNAMICAL THEORY OF INDUCTION. 423

from e to reach the knobs, and therefore the phenomenon can- not be clue simply to single waves in the direction c a and d b respectively, but must be due to repeated reflection of the waves until a condition of stationary vibration is attained, and the addition of the conductor to one of the knobs must diminish or prevent the reflection of the waves from that ter- minal. It must be assumed, then, that definite oscillations are set up in the micrometer circuit just as an elastic bar is thrown into definite vibrations by blows from a hammer. If this assumption is correct, the condition for the disappearance of- the sparks at M will be that the vibration periods of the two branches e 1 and e 2 shall be equal'. These periods are deter- mined by the products of the coefficients of self-induction of these conductors into the capacities of their terminals, and are practically independent of their resistances.

In confirmation of this it is found that if, when the point of contact is at e and the sparks have been made to reappear by connecting a conductor with one of the knobs, this con- ductor is replaced by one of greater capacity, the sparking is greatly increased. If a conductor of equal capacity is con- nected with the other micrometer knob, the sparks disappear again ; the effect of the first conductor can also be counter- acted by shifting the point of contact towards it, thereby diminishing the self-induction in that branch. The conclusions were further confirmed by the results obtained when coils of copper wire were inserted into one or other and then into both of the branches of the micrometer circuit.

Hertz supposed that as the self-induction of iron wires is, for slow alternations, from eight to ten times that of copper wires, therefore a short iron wire would balance a long copper one ; but this was not found to be the case, and he concludes that, owing to the great rapidity of the alternations, the magnetism of the iron is unable to follow them, and therefore has no effect; on the self-induction.*

• In a note in Wiedemann's Annalcn, Vol. XXXI., p. 543, Dr. HertZ stated that since the publication of his Paper in the same volume he had found that Von Bezold had published a Paper, in 1870 (Poggendorff 8 Annalcn, Vol. CXL., p. 541), in which he had arrived by a different method of experimenting at similar results and conclusions as those given by him under the head of Preliminary Experiments.

424

DYNAMICAL THEORY OF INDUCTION.

Inditction Phenomena in Open Circuits. — In order to test more fully his conclusion that the sparks obtained in the last experiments described were .due to self-induction, Hertz placed a rectangle of copper wire with sides 10 and 20 centi- metres in length respectively, broken by a short air space, with one of its sides parallel and close to various portions of the secondary circuit of the coil and of the micrometer circuit, with solid dielectrics interposed to obviate the possibility of sparking across, and he found that sparking in this rectangle invariably accompanied the discharges of the induction coil, the longest sparks being obtained when a side of the rectangle was close to the discharger.

CXZZEDO

FIG. 153.

A copper wire, igh (Fig. 153), was next attached to the flischarger, and a side of the micrometer circuit, which was supported on an insulating stand, was placed parallel to a portion of this wire, as shown in the diagram. The sparks at M were then found to be extremely feeble until a conductor, C, was attached to the free end, h, of the copper wire, when they increased to one or two millimetres in length. That the action of C was not an electrostatic one was shown by its pro- ducing no effect when attached at g instead of at h. When

DYNAMICAL THEORY OF INDUCTION. 425

•the knobs of the discharger B were so far separated that no .sparking took place there, the sparks at M were also found to disappear, showing that these were due to the sudden dis- charges and not to the charging current. The sparks at the discharger which produced the most effect at the micrometer were of the same character as those described under the head •of Preliminary Experiments. Sparks were also found to occur between the micrometer circuit and insulated conductors in its vicinity. The sparks became much shorter when conductors of large capacity were attached to the micrometer knobs, or when these were touched by the hand, showing that the •quantity of electricity in motion was too small to charge these conductors to a similarly high potential. Joining the micrometer knobs by a wet thread did not perceptibly diminish the strength of the sparks. The effects in the micrometer circuit were not of sufficient strength to produce any sensation when it was touched or the circuit completed through the body. In order to obtain further confirmation of the oscillatory nature of the current in the circuit k i h g (Fig. 153), the con- ductor C was again attached to h, and the micrometer knobs drawn apart until sparks only passed singly. A second con- ductor, C', as nearly as. possible similar to C, was then attached to k, when a stream of sparks was immediately observed, and it continued when the knobs were drawn still further apart. This effect could not be ascribed to a direct action of the portion of circuit i k, for in this case the action of the portion of circuit g h would be weakened, and it must therefore have consisted in C' acting on the discharging current of C — a result which would be quite incomprehensible unless the current in g h were of an oscillatory character.

: Since an oscillatory motion between C and C' is essential for the production of powerful inductive effects, it will not be sufficient for the spark to occur in an exceedingly short time, 'but the resistance must at the same time not exceed certain .limits. The inductive effects will therefore be excessively small if the induction coil included in the circuit C C' is replaced by an electrical machine alternately charging and discharging itself, or if too small an induction coil is used, or, again, if the air space between the discharger knobs is too great, as in all these cases the motion ceases to be oscillatory.

426

DYNAMICAL THEORY OF INDUCTION.

The reason that the discharge of a powerful induction coil gives rise to oscillatory motion is that, firstly, it charges the terminals C and C' to a high potential ; secondly, it produces a sudden spark in the intervening circuit ; and thirdly, as soon as the discharge begins the resistance of the air space is so much reduced as to allow of oscillatory motion being set up. If the terminal conductors are of a very large capacity — for example, if the terminals are in connection with a battery — the current of discharge may indefinitely reduce the resistance of the air space, but when the terminal conductors are of small

. capacity this must be done by a separate discharge, and there- fore, under the conditions of Hertz's experiments, an induction

. coil was absolutely essential for the production of the oscilla- tions.

FIG. 154.