The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 24 of 36

similar conductor. Dr. Lodge's further researches seem to show that there is a real advantage in using iron for lightning conductors over copper, and that its greater specific resistance and higher fusing point enable an iron rod or tape to get rid safely of an amount of electric energy stored up in a dielectric which would not be the case if it were copper. This point is further elucidated by some other experiments of Dr. Lodge. Two tinfoil conductors were prepared of approximately equal resistance and length. One of these was formed into a spiral, each layer being insulated with paraffin paper, and wound on a glass tube. The other was made into a zig-zag or non- inductive resistance. These conductors were then employed as alternative paths, as in the former experiment with the copper wire. In the case when the tin-foil zig-zag was employed to short-circuit the jars it was not possible to get a B spark {see Fig. 141) until the distance of the A balls was shortened to 06 (tenths of inch). When the tinfoil spiral was used the critical spark distance at B rose to 64. When the iron wire bundle was inserted in the tube it did not in any perceptible degree increase this distance. The length of the sparking distance at A was 78, and when no alternative path was used at all to connect the jars the critical distance of the B balls, at which sparks sometimes passed and sometimes failed, was 111. Here, then, we have the non-magnetisability of iron by sudden dis- charges illustrated. Dr. Lodge has called attention to the fact that a " choking " coil having a core of divided iron and wound over with many turns of wire does not add to the apparent self-induction of a circuit discharging a Leyden jar. lb may even diminish it when the discharge is oscillatory and of sufficient frequency, although the oscillations may be as few as 500 per second. This experiment shows, as we know from other facts, that eddy currents are set up even in a core of finely-divided iron, and that these eddy currents, under suffi- ciently rapid alternations, are confined to the surface of the core, and moreover, since they are as regards phase nearly in opposition to that of the current in the coil, they actually tend to diminish the total fiux of induction through the coil, and hence diminish the self-induction of the circuit.

The inductive opposition to electric discharge presented by even a short length of conductor, when the difference of poteu*

DYNAMICAL THEORY OF INDUCTION. 407

tial between the ends is made very suddenly, is seen in the tendency under such circumstances to side flash. If a conduc- tor, say, a straight rod of copper, has one end to earth, and somewhere very near its side is the end of another conductor also " to earth," then if the free end of the first conductor is suddenly exalted in potential the impulsive rush of electricity, meeting with such an obstacle in the inductance of the conduc- tor, spits or flashes out laterally and sparks to the other con- ductor. No conductor is able to prevent side flash altogether unless it has practically no inductance. As long as a conduc- tor must be straight (like a lightning conductor) so long will there be a tendency to side flash. This is illustrated by the following experiment. A massive conductor has (Fig. 144) a very fine wire stretched alongside and air gaps in this bye- path left by bringing the ends of the fine wire very near to the sides of the large conductor. On sending an impulsive rush of electricity through the large conductor little sparks are seen at a and b, showing that some of the discharge has left the thick

^b

Fig. 144.

conductor and travelled along the fine wire, even although it had to leap across an air gap. If the bare hands are applied to the ends of an open spiral of very stout copper wire, one end of which is connected to a ''good earth," shocks will be felt when a Leyden jar is discharged through the copper. In this case the human body forms the bye-path, and the experiment indi- cates that the law of division of steady currents or slow dis- cbarges between conductors in parallel, viz. , a division in the ratio of their conductivities, does not hold good for impulsive discharge, and that the relative inductance of the circuits has more influence in the latter case in determining what happens.

The distinction between the resulting discharges due to a steady electromotive force or strain and that due to an elec- tromotive impulse or impulsive rush of electricity has been illustrated by some further experiments by Dr. Lodge on the

408 DYNAMICAL THEOBT OF INDUCTION.

behaviour of model lightning oondactors when Bubjeoted to the action of these two modes of discharge. Two tin plates are placed horizontally and insulated, and these are supposed to represent the earth and a thunder-cloud. These plates are connected, as in Fig. 145, to an electrical machine, and by work- ing the handle are brought up to a steady potential difference. On the lower plate are placed little rods of various heights, sharp, or having knobs, and these represent lightning con- ductors. At a certain potential difference the electric strain set up in the air exceeds the limit which the dielectric can sustain, and it breaks down, giving rise to a spark. A discharge then takes place towards one or other of the mimic lightning conductors. In one experiment three conductors were used — one with a large knob, 0'9in. less in height than the distance between the plates, the second with a small knob, 2in. less in height, and a sharp short point. The point even when very

Fia. 106.

low prevents discharge altogether. It may be too low to be effective, or it may be insufficient to cope with the supply of electricity if that is supplied very fast, but it acts to prevent discharge. If the point is removed or covered up we then find that the discharge takes place, when the potential difference of the plates is made great enough, to the small knob by preference, and it does so even when the stem of the short knob is lower than that of the large knob. In other words, when the stems are the same height the small knob protects the large one, and it does this until lowered in height to about two inches less than the other; when this is the case both knobs are struck indifferently. And it does this even when a resistance of one megohm is interposed in the stem of the smaller knob. The state of things is, however, very much altered if in place of bringing up the two plates gradually to a sparking potential difference they are very suddenly thrown

DYNAMICAL THEORY OF INDUCTION. 409

into opposite electrical conditions by connecting them to the electrical machine as shown in Fig. 146.

The jars C'large up as they stand on the same wooden table, and when th 3 potential rises to sparking amount they discharge at A, and & violent electric rush then takes place between the 4wo platcK, and the conductors between are struck. If the same three kinds of conductors are used, and they be adjusted until they are aU 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,

Fia. 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 weU 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 subjitdice.

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 Bi, B^ or Bs, 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 Bg 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 recoU 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 Bg.

If the experiment 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 whioh 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 foUows : Attach one end of a long wire to one knob of a Wimshurst machine, and connect the other pole to

Fio. 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 fuU 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

Fia. 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 heated, 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

overflows 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- circnited, then the jar refuses to overflow until the A spark has been increased to l'7in. 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 time a discharge occurs at A. The theory of the effect seems to be that oscillations occur in the A circuit with a period T « 2Tr JhG, where L is the inductance of the A circuit and G 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, 1888; also Tht Electrician, Auguitt 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

1

so the wave length of the oscillations is

A. = t;T = 27r

/u C V 7; • K •

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

is the electrostatic measure of capacity, /x being the magnetic permeability, and E 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 2ir 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

B

I

Fig. 160.

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 r^ be the inductance and resistance of the straight wires per unit of length, as affected by the periodicity, and let Cj be the capacity per unit of length. It has been shown by Lord Rayleigh (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 /J^i, where /xq is the magnetic permeability of the material of the conductor, or

*"i'' ^iiP H-o^y P ^^^^S> 8.S usual, ^rrn, n being the number of complete oscillations per second.

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

of length is equal to a constant plus -!j, or

P

P I being the induction for slowly fluctuating currents. In the case of the two parallel wires we have for the slope

of the potential - -— - along them the usual equations,

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

^dN_^l di ^i^^x

dt Q^dx ^ ^

416 DYNAMICAL TEEOBT OF INDUCTION.

Tho eliViiination of i between these eqaations gives ns a difforential equation for V, and shows that stationary waves of current are set up in finite wires of suitable length under iil:.^ action of nn alternating electromotive force. The solution of tii9 equation /or a long wire when r^ is small and p is very large is

Y^Yo^' ''~'' COS p ft -^y

r 1

where Wj = - L and n^ = .--—^

The velocity of propagation of the wave is therefore n^^ and tho

wave length is — n^. P For two parallel wires, as in the Leyden jar case, we have each wire

^1= Jipf^r. r being the ordinary resistance. And again, as Lord Bayleigh has shown (Phil. J/a^., May, 1886), we have

Z, = 4alog.U!:i, a p

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

For immensely quick oscillations the second term i^ zero. Also, the capacity Ci of the wires per unit of length is, bj a known theorem,

0,. ^ •

hence

and the velocity of the pulse along the wires is the same as in the dielectric round them. In rther words, the electric pulsc<i 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 rou:id them. Hence, we Imve here a means of determining experimentally the wave length of a given discharging circuit. Eitiier vary the size of the A circuit or

DYNAMICAL THEORY OF INDUCTION. 41?

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

V u K

A small condenser can be made haying an electrostatlo capacity of, saj, 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 wavelength of the electro-magnetic disturbance radiated would be about 20 to 80 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-magnetie disturbances propagated through the ether and due to electric oscillations set up in the atomic charge.

§ 10. Impulsive Impedance. — In the experiments of the iJtemative 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 V^K +/?'- L*, to slowly periodic or oscillatory cur- rents. As already mentioned, the resistance of a conductor to very rapidly changing currents is expressed by B^ where

B being the resistance to steady current, fi^ the permeability of the material of the conductor and I its length, s^ip=^2ir

EE

118 J)YKAMIGAL THEORY OF INDUCTION.

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

L, = L + ^i, V 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 n/Rj^+jp-'Lj'*, and calling this Im^/we have

^ Jp P where ^^T. ^h^f^o^'

In the case of enormously rapid oscillations the value of Imj 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 800 ohms, although the ohmic resistances of these wires were respectively -004 ohmB and 2*6 ohms. At three million oscillations per second, or at one-fourth the frequency, the impedances of the same circuits were 48 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 ^i^e 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 Researches 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. 41^

electrical science. These inyestigations 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 giv6n by Mr. G. W. de Tunzelmann.f

Preliminary Experiments. — It is known that if in the secpnd- 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 spac3 does not exceed a certain limit ; and il 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- nected 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, 767, 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 {lermifidon of their author, he is allowed to reproduce them in these pag^.

eb2

420

DYNAMICAL THEORY OF INDOCTION.

In Fig. 151, A is an induction coil and B a discharger. Th» 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, sometimeB 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-

Fia. 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 ii> 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

DNYAMICAL THEORY OF INDUCTION. 421

Die secbndary circuit took place between two points or between s point and a platiB tban 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 \ 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 dififerences in the nature of the secondary sparkd were found to have great effect on those of the micrometer, and Hertz states that after some practice he was able to detet* mine at once from the sound and appearance of the secondary spark whether it was of a kind to give the most powerfd effects at the micrometer. The sparks which gave the best results were of a brilliant white colour, only sUghtly jaggedi 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, r 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 lengtL The electrical disturbances smdsX therefore traverse it without undergoing any appreciable

422

DYNAMICAL THEORY OF INDUCTION.

ehange.' 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 aecondary 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 micrometejr knobs. This point may be called the null point.

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

^ . . . Fig. 162.

by 80 centimetres broad. When the point of contact is at h or h sparks of from three to four millimetres in length ar^ observed ; when it is at « no sparks are seen, but they can be made ' to reappear by shifting the point of contact a feW centimetres to the right or left of the null point. It ishould be noted that sparks only a few hundredths of a millimetre &i length can be observed. If, when the point of contract is at i» another conductor is placed in contact with one of the micn^ meter knobs, the sparks reappear. ^

Now, the addition of this conductor cannot produce dJUj alteration in the time taken by the disturbances proeeed&%

'DTNAUICAL THEORY OF INDUCTION, 423