The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 15 of 36

pair of springs might be brought into electrical contact for a definite portion of the time of a revolution of the oyUn- ders and be insulated also for a given time, each pair of springs being in connection relatively to the other in a deter- mined manner for a determined time. In the circuit of the one cylinder and pair of springs viM. was placed a battery primary coil and tangent galvanometer, and in the circuit of the other pair a secondary coil and sensitive galvano- meter. This being prepared, the primary coil P and the secondary S were placed a given distance apart. On revolving the commutator it periodically interrupts the primary current, the time during which the primary current is kept on depend- ing upon the position of the spring M on its cylinder. The other cylinder can be so set as to collect either the direct or

Fio. 90.

inverse secondary currents, and send them in series through the sensitive galvanometer, the time during which this secondary circuit is closed being capable of regulation by the adjustment of the spring M^. In his experiments Blaserna first investi- gated the duration of each of the induced currents. The interrupters were so arranged relatively to one another that, whilst the primary circuit was made and broken, the secondary circuit was not closed until a small time after ** making" the primary, and then broken again before the primary was broken. By adjusting the secondary interrupter a position could be found in which the galvanometer just showed no current. The interval between the closing of the primary and the opening of the secondary was then the interval occupied by the secondary

S48 MUftfAl AlfD SELF IltDVCtlOlf,

current, and this was the duration of the << make "-induced current. Blasema found that the <* make " secondary (inverse) lasts a longer time than the "break" current (direct). For the coils used the times were —

Inverse secondary lasts -000485 second.

Direct secondary lasts -000276 second. He next proceeded to obtain the curve of each current, and to determine the time of arrival at a maximum.

The secondary interrupter was so set that the secondary circuit was closed just before the primary, and opened after at a certain definite interval of time. The galvanometer thus

Fio. 91.

received a current which was made up of repeated doses of the whole quantity of the induced current up to a certain fraction. Knowing the speed of the commutator and the coefficient of the galvanometer, the value of the whole quantity of the induced current, extending over a certain fraction of its whole duration, was known ; and from those observations, repeated at regular progressive intervals during the whole period of the current, the value of the ordinates of the current curve can be obtained. For, if the curve (Fig. 91) A P P' B (upper figure) represents the variation of current during a time A B, so that P X = y repre-

Mutual Ant> self iifDVCTJON. 249

sents the current strength at a time X, and P' X' represents the current strength after a very small interval of time, X X' = rf t ; then the area P P' X' X = y rf f represents the quantity of elec- tricity which has passed in the time XX'. Call this c^Q.

Hence dQ^ydt, or V^-^-

a t

Suppose another curve A'P'R (lower curve) is drawn on an equal abscissa A'B', such that its ordinate at every point represents the whole area of the upper curve up to the corresponding point — that is to say, the lower curve is a curve such that its ordinate P' X' is proportional to the area A P X of the upper curve, AX (upper curve) being equal to A'X' (lower curve), when the time interval d t becomes very small. It is easily seen that if the area A P X (upper curve) is called Q, and the ordinate P X is called y^ that the tangent of the angle FYX' (lower curve) which the geometrical tangent drawn at P' makes with the axis A'B', and which is repre- sented by ~ , is proportional to the ordinate PX. Hence the dt

upper curve is a derived curve of the lower, and, if we are given a curve like the lower curve, the ordinates of which represent the whole quantity of electricity which has from a given epoch flowed past a point, we can, by drawing a curve whose ordinates represent the slope of the first curve, obtain a second curve, which is a curve of current. In this way it is possible to describe the current curve, and to determine its form and position of maximum.

Blasema found that the greater the distance apart of the primary and secondary — ^in other words, the less the mutual inductance — ^the less was the maximum value of the secondary current, and the greater the delay in the appearance of that maximum. This is in accordance with the above elementary theory. In the case of the ''break," or direct secondary current, he found the delay in establishing the maximum not 80 great, and the maximum ordinate was greater though the total duration of the current was less. He established by direct experiment the equality of the quantity of the two induced currents. When the coils were very near together the induced current at starting established itself by a series of dectncal 09cillaUons»

250

MUTUAL AND SELF INDUGTIOK.

By the help of the same apparatus Blasema investigated the rise of a current in a coil when the same is placed suddenly in connection with a constant source of electromotive force. For the "make" extra current only one of the revolving interrupters was used, and the circuit was completed by the means of a battery, galvanometer, and coil. When the com- mutator was revolved it first started the current and then after an interval cut it off again, and the effect on the galvanometer is due to the sum of all these small quantities of electricity so cut off and integrated whilst the current is in process of increasing. As the duration of the time of contact was increased the galvanometer deflection increased (speed of revolution remaining constant), but when the time of contact was long enough to fully establish the current, then increase

Fjo. 9a

of speed of rotation did not increase the galvanometer deflec- tion. By this apparatus the fact was established that the primary current established itself in its coil by a series of oscillations, or short alternating currents.

Similarly, on breaking the circuit the course of the current was investigated. For this purpose one revolving interrupter, I, was inserted in the circuit of a battery, B, and coil, C, and from the ends of the coil (see Fig. 92) other wires were brought and led through the galvanometer G, and other interrupter T, arranged as a shunt on the coil. The break in the battery eircuit at p was so arranged that each time the current was fully estabhshed before being broken again. The break in the

MUTVAL AND SELF INDUCTION. 251

galvanometer or shunt circuit was so arranged relatively to the other that the shunt circuit was closed a little before the battery circuit was broken, and then opened at a definite interval afterwards. In this way there was a little flow of current through the galvanometer due to the steady current, but this could be estimated and allowed for. On plotting out a current curve from the quantity curve it was found that the current decayed away on interrupting the circuit by a series of oscillations which followed each other much quicker than those on the establishment of it, and the whole duration of the extra current at '* break," or the time of falling from steady current to practical zero, was less than the time required to fully estab- lish the current. It was found that the first oscillation, on beginning to interrupt the steady current, had a much greater amplitude than any of those on starting the current.

The duration of an oscillation was perhaps three or four ten* thousandths of a second, and about 50 to 100 oscillations pro- bably happened before the current became steady ; hence the whole duration of the variable period, or of the extra current, was about two to three-hundredths of a second. Very roughly, the nature of the oscillatory character of the current at the make and break may graphically be represented by the curve in diagram Fig. 93.*

Blasema drew from his observations the deduction that there is an interval of delay in the starting of the secondary currents, and that a small but measurable time elapses between the instant of making or breaking the primary circuit and the beginning of the secondary current. From this he made a calculation as to the velocity of electromagnetic induction, and he also stated that the interposition of dielectric substances such as glass or shellac between the coils reduced the so* calculated velocity.

Bemsfcem (Pogg. Ann., Bd. CXLII., 1871, p. 72) repeated these observations of Blaserna, but did not confirm these last results. He found that the first oscillation always began at the instant of breaking or making the primary circuit, and he

• Tn The Electrieian for June 1, 1888, a curve is given by Mr. F. Higgins, showing the rise of current in the magnets of type- printing telegraphs,' and the osciUatoiy character of the current at starting is weU marked. Mr. Higgins's curve gives the results of actual observations.

252 MUtVtAL AlfD SELP INBTTCTIO^.

found no effect produced by the interposition of dielectric media.

Helmholtz has carefally examined these results of Blaserna and criticised them.* He remarks that Blaserna used for his coils flat spirals of wire with many turns, and also he used the current from several Bunsen cells to create the primary current. Not only do the spirals act like a condenser, giving the whole apparatus a sensible electrostatic capacity, but the use of a • battery of high electromotive force causes a considerable spark at the break, which spark has a very sensible and rather irregular duration. Also in Blaserna's experiments, the two circuits were placed at various distances apart. If a current

Fio. 93.

is started in a primary coil the effect of the induced current created in the secondary by its re-action on the primary is to hasten the rise of the primary current, and at the break to accelerate its decay. As the secondary circuit is moved further off this effect is less marked. Hence, the rise and fall of the primary is more gradual and the arrival of the secondary current at its maximum value is more delayed. From this results, then, an apparent retardation of the time of the arrival of the maximum of the induced current.

• Helmholtz, " On the Velocity of the Propagation of Electrodynamic EflfecU," PhiL Mag., Ser. 4, VoL XLIL, 1871, p. 232.

MUTUAL AND SELF INDUCTION. 253

Helmholtz conducted a series of experiments by means of liis pendulum chronoscope. A heavy iron pendulum P {see Fig. 94), the lower end of which carried two plates of agate, could be made to execute one swing and then be caught by a detent. These plates of agate in the course of the swing were caused to strike against and tip over two little levers l, l\ One of these levers was fixed, and the other could be moved forward so as to separate the blows. One was made to break the circuit of a primary coil Pr, when tipped over, and the

-=r-wj

other by its movement separated a connection between a con- denser and the ends of a secondary coil, Sec^ attached to it.

These being arranged, the fall of the pendulum executed these two ** breaks" successively, separated by an interval of time capable of being calculated from the known motion of the pendulum. The two circuits were placed 170 centimetres apart. The primary consisted of 12 turns of thick wire, and the secondary of 560 turns of fine wire. The current was sent

254 MUTUAL AND SELF INDUCTION.

from one Daniell oelL The two ends of the secondary were connected to the two plates of the condenser, and when the pendulum fell it broke the primary current and started in the secondary circuit an oscillatory current reverberating to and fro in the secondary wire, the condenser acting as a resonator. At a definite interval after rupture of the primary, the condenser was separated and examined by a quadrant dectro- meter. The charge in the condenser showed the phase of the electrical oscillation existing at the instant of such separation. In one case Helmholtz observed 85 oscillations in ^th of a second. In order to discover if any retardation took place with increased distance of the coU, it was necessary to fix attention upon some phase in the oscillations. The successive zero points of the current were very sharply defined, and suitable for this purpose. Helmholtz found that alteration of the distance between the primary and secondary coils made no perceptible difference in the position of the zero points, and that, as far as the apparatus he was using could detect, the velocity of the electro-magnetic impulse must be greater than 195 miles per second. He pointed out in this Paper that the commencement of the secondary current is not a sharply marked thing. The spark which takes place at break of the primary lasts an appreciable time, and all this time the primary is dying gradually, and the induced current therefore is increasing. The period of duration of the break spark may be something like tt^^^ ^^ ir^v^^ ^^ ^ second, and is, therefore, a large frSiCtion of the duration of a single electrical oscillation, which amounted to about ^gVr^^ ^^ ^ second. The duration of the break spark can be found by observation of the time which elapses from beginning of break up to the first zero point of the secondary current oscillations, as com- pared with the mean value of the duration of an oscillation. The interval up to the first zero point is the duration of the break spark plm the time of half a complete oscillation. The duration of the spark is never constant, and depends a good deal on the amount of platinum thrown off from the contacts each time. The average duration of the spark in Helmholtz's experiments was found to be about one-tenth of the whole period of an oscillation. Helmholtz also noticed in some ^arUer observations evidence of eleQtrical oscillations set up in

MUTUAL AND SELF INDUCTION. 256

a flat spiral, one end of whieh was insulated. In this case some 45 oscillations were detected in the space of ^th of a second. Henry also noticed that the time of subsidence of the current, when the circuit is broken by means of a 8ur£a>ce of mercury, is very small, and probably does not much exceed the ten-tbousandth part of a second. It has, however, a quite appreciable duration, for Henry found that the spark at ending presents the appearance of a band of light of considerable length when viewed in a mirror revolving at the rate of six hundred revolutions per second*

Bernstein, with the aid of a contact break somewhat different from that used by Blasema, also examined the dumtion of the oscillations set up in a secondary coil. He found that the duration of the first oscillation at breaking primary was longer than that of the subsequent ones. The mean duration when using a single Grove cell in the primary circuit was *0005 second, and when using a Daniell cell only '0001 second. We shall return later to consider more recent researches on these electrical oscillations in inductive circuits and point out that they can only occur when some part of the circuit possesses sensible electrical capacity. In the case of a coil or bobbin of wire we have not only resistance and inductance, but measurable capacity present in the conductor.

§8. Magnetic Screening and the Action of Metallic Masses in Induction Ooils. — At one stage^ of his investi- gations Henry made the important discovery that, if a primary and secondary coil are separated by a metallic sheet, a notable decrease takes place in the intensity of the shock taken from the secondary circuit when a sudden discharge is passed through the primary, or continuous current started or stopped in the primary circuits. A thick copper plate was found more effective than a thin one in thus preventing the inductive effect of the primary upon the secondaiy coil. If a radial slit was cut in a circular metallic plate the annulling effect was altogether stopped. If the two edges of the gap {see Fig. 95) were furnished with wires leading to a magnetising spiral, Henry found he could in this way make evident the existence in the plate of a current induced by the action of the primary. ' • J^huTMag,, Vol, XVI., 1940, p. 267. "" '

266

MUTUAL AND SELF INDUCTION.

A flat ooU of insulated wire was Bubstitated for the metal plate, and it was found that the screening action of this coil was only sensible when the two ends were joined so as to com- plete the circuit. This action, by which the induction of a primary coil on a secondary is prevented by the interposition of a metallic plate, cylinder, or closed circuit of insulated wire, is called magnetic screening. The elementary explanation of this effect is not difficult to arrive at. Suppose a small con- ducting circuit of resistance B to be placed in a magnetic field so that it is traversed normally by N lines of magnetic iDduction. Let the constant coefficient of self-induction of this circuit be L. If, then, in any small time dt 9, variation of the lines of induction traversing this circuit takes place, the impressed

Fio. 96.

d N electromotive force on that circuit will be represented by ^

and if at that instant the current in the circuit is i, by the principles laid down in the last chapter the current equation will be

L _ + R t = - -— -,

(It dt

or

4(^'-^'')

• Ri-0.

Suppose the conductivity of this circuit to be perfect, and R therefore zero, we have, by integratiou of the above equation,

the result

L i + N = const. ;

MUTUAL AND SELF INDUCTION. 257

in other words, the lines of induction L i, linked to the circuit at any instant due to the induced current generated in it, are appotite in direction to those whose variation is producing the current, and together with them make up a constant number. Hence, if the variation of N is such as to take lines of induction out of the circuit, the action of the current thereby induced is to add or increase them in the circuit at an equal rate. If we suppose our circuit to be a perfectly conducting metal plate, and just behind this metal plate there is another small closed circuit, then any variation of lines of induction passing through this plate will not take effect in producing any induced current in the small circuit, because the inductive action of the current induced in the plate nullifies, as &r as the small circuit is concerned, any vari- ation of the external field. It is clear that these conclusions would apply to any surface of finite extent which possessed perfect conductivity; the induced currents which any vari- ation of the external field would produce in this surface would always be such that the induction through each portion would be kept constant — in other words, that the perpendicular component of the magnetic induction at each point on the surfEkce would retain a fixed value. It follows that a closed surfjEMse of zero resistance is a complete screen for all points in the interior against the effects of variation of the field on conductors on the outside of the surface ; these effects reduce to the production of surfeu^ currents in the shielding conductor, which keep the resultant field in the interior constant or at zero.

Faraday describes (" Exp. Researches," Vol. I., §1720 et seq.) an experiment which at first sight seems to disprove the fact of magnetic screening, fie placed a flat copper wire spiral, which was in connection with a battery and key, between two other flat spirals which were respectively connected with the two coils of a differential galvanometer. The coils were so joined up that the inductive effect of a break and make of the battery circuit produced no movement of the galvanometer needle because it was subjected to two equal and opposite impulses from the two coils. When an exact balance was obtained a flat plate of copper, nearly three-quarters of an inch thick, was interposed between the primary spiral and one of

8

258 MUTUAL AND SELF INDUCTION.

the secondaries. The galvanometer needle was not, however, any more affected than if the copper was absent. To under- stand this we must bear in mind that the break or make of the primary current produces in the copper a secondary current, but as the effect of the primary coil on the secondary coil on that side is balanced by the other one we may regard the secondary coil next the copper plate as free to receive any inductive effect it can from the eddy current induced in the copper block. This secondary current induced in the copper generates a tertiary current in the secondary spiral, and this tertiary current consists, as we have seen, of a double short flux of electricity equal in quantity and opposite in sign. The galvanometer is then traversed by two small equal quantities of electricity in opposite directions, and as this does not sensibly affect a not very sensitive galvanometer no movement of the needle is seen. If, however, instead of the differential galvanometer, Faraday had used a differential telephone, he would have found distinct evidence of a screening action. Again, suppose that, instead of a simple make or break, Faraday had employed a steadily periodic or alternate cur- rent in the primary, this would have set up a steady periodic secondary current of equal frequency in the copper plate, and this again would have set up in the secondary coil on that side a steadily periodic tertiary current of equal period, and this might have been detected by the use of a sensitive differential electro-dynamometer or a soft iron needle galvanometer.

Henry found that a sheet of tinfoil afforded a very small amount of screening for shock, but a thick sheet of copper a very considerable one in the case of induction by battery cur- rents, and in the case of induction by Leyden jar discharges the same phenomenon was apparent. In the case of an iron screen there is an additional effect, due to the fact that the iron, by its small magnetic resistance, conducts away the lines of induction somewhat through its mass, and prevents them from extending to the space on the other side. In this case also a considerable thickness of metal is necessary to bring about the effect of annulment. When we are limited to the use, as we are in practice, of materials whose conductivity is far from being perfect, it is found that a thin screen of metal hardly affords any sensible protection from inductive effect.

MUTUAL AND SELF INDUCTION. 259

In other words, the field on the other side of the screen is very far from constant. This has been well demonstrated in certain investigations by Prof. D. E. Hughes in carrying •on some highly valaable experimental researches into the means of preventing induction upon lateral telegraph wires.* It has many times been proposed to annul mutual induction between telegraph and telephone wires by covering them over with thin metal covering, which covering is kept " to earth." It is now known, and well exemplified in Prof. Hughes's experiments, that this shielding a£fords no protec- tion when the covering is not very thick and when the rate oi •change of the currents is not very rapid. A gutta-percha wire was enclosed in ten coverings of tinfoil, and such arrangement was not found to afford protection to induction, as detected by a telephonic wire stretched alongside. Even when twenty coatings of thin charcoal iron were put round the wire, not only was there found to be a very sensible per- manent field outside the iron, but changes of field were made manifest also. It is not to be taken that these experiments disprove the fact of magnetic screening, but only that the low conductivity of the envelopes used is ineffective at the speed of current change employed to render visible the effect of magnetic screening. It is different, however, if the induc- tive effects are being produced by a very rapid rate of change of field. For suppose that a small circuit, as before, is placed in a uniform field, and is traversed by q lines of induction due to this external field. Suppose q varies according to a simple periodic law, so that g = Q cos^ t, where ^ = 27rn, w being the frequency of the alternations. Then we have

-^-? ^'Qp sin pt; at

but - i-i IB the value of the impressed electromotive force in dt

the circuit, and if we call the current at any instant i, then, by the principles in Chap. III., we have

1- — ^^' em(pt-0),

VK^?I? ^ ^

• See % Paper by Prof. Hughes " On Lateral Induction in Telegraph Wires," read before the Society of Telegraph Engineers, March 12, 1879. Published in The EUctrician, March 22, 1879.

82

260 MUTUAL AND SELF INDUCTION.

in which B is the resistance and L the inductance of th» circuit, and

^ = tan-^^.

Suppose that R is very small compared with Jjp, which is the case when n or the frequency of alternation is made very great, then R vanishes compared with hp, and if we call t' the value towards which i approximates in this case, we- have

t'= -^cosp«,

Li

and

'L^^^pBinpt, at h

or

dt dt

Hence

dt dt'

or

Li' + 2 -constant.

Hence the field due to the current in the circuit, together with the external field, is a constant quantity, and we get the condition of perfect shielding. We may sum up the fore- going by saying that, if a screen of absolutely no electrical resistance is interposed between a primary and secondary coil, it. effects a perfect magnetic screening, whatever may be its thick- ness. If, on the other hand, the screen has a finite conductivity,, then the screening will be very imperfect, unless a very great, thickness of material is used, and the above will be true wheni the change of field or the change of primary current is a simple^ ** make '* and ** break " or a slowly periodic change. "When, however, the change of current in the primary is very rapidly periodic, then the screening effects of even imperfect conductors will make themselves felt, and a comparatively thin screen of metal will effect a nearly perfect shielding for induction. This, theory is strikingly confirmed by some very beautiful experi- ments of Mr. Willoughby Smith, which are described in the- Journal of the Society of Telegraph Engineers (November 8,. 1883, Vol. XII., p. 458),* and entitled " Experiments on Volta-

♦ See also The Electrician, November 17, 1883, p. 10.

MUTUAL AND SELF INDUCTION.

261

Electric Induction." Mr. Willoughby Smith's apparatus con- sisted of two flat coils A and B {see Fig. 96), placed a certain distance apart. One of these was a primary coil connected with a battery, and the other was connected with a sensitive galvano- meter. In the circuit of both were current reversers, which reversed the galvanometer and battery alternately, and hence made the opposite induced currents both affect the galvano- meter in the same direction. This being arranged, the commu- tator was started so as to reverse the currents very slowly, and a sheet of copper interposed between the spirals. Under these circumstances the interposition of the copper produced but little effect. If, however, the commutator was driven at a very rapid rate the copper plate caused a marked diminution in the galvanometric deflection, and this diminution was greater in proportion as the speed was greater. In the original Paper

Fig. 96.

a curve is given (Fig. 97) which shows the decrease in the galvanometer deflection, expressed as a percentage of the original undiminished deflection, corresponding to various speeds of reversal. It will be seen that the less the conduc- tivity of the metal the greater must be the speed in order that the magnetic screening may approach perfection. Iron, of course, occupies an exceptional position. It cuts off, even at very low speed reversals, a large portion of the field, not by a true screening action, but by conducting away the lines of magnetic force and preventing their access to the secondary C3il. It will be seen that at any given speed the order in which the metals reduce the deflection is the order of their electric conductivity, and that as far as the diagram goes the lines all (except iron) slope upward, indicating that at very

202

MUTUAL AND SELF INDUCTION.

high speeds the screening of even the worst conductors wilt approach perfection. It would no doubt be found that, if the telephone were used as a detector, the magnetic screening of a copper plate or thin tinfoil sheet would become very manifest for high notes when not in any way marked or distinguishable for notes or sounds of low frequency of ^dbration.*

As far back as 1840 Dove had made experimentsf on the effect of the introduction of cores of various materials into the primary circuit of an induction coil. His apparatus consisted of two similar primary bobbins wound on tubes of non-metaUic substance and connected in series (Fig. 98) . Over each primary bobbin was wound a secondary circuit, and these secondary circuits were connected in series, but so that the induction of

50O icco

R^ver3a!5 Per Minute

Fig. 97.

aoco

the two primary bobbins operated in opposite directions and nullified on the whole secondary circuit each other's effect. Exact neutralisation was obtained by adjusting one of the secondaries. When this was the case, various cores of iron rods of different kinds were inserted in one primary bobbin^ and it was found that the induction balance was destroyed*

• The above explanation of the cause of the difference between the screening of the different metala is not that given by the distinguished investigator, but it is the explanation which to the author seems most in accordance with known principles.

t Dove, Poggendorff'a Annaleny Vol. XLIX., 1840.

MUTUAL AND SELF INDUCTION.

263

By inserting iron wires of a certain size in the other core, balance could be again obtained, but not simultaneously, as estimated by the galvanometer and by the shock. Thus, with a bar of forged iron, 110 wires had to be inserted in the other coil to obtain an equilibrium, as estimated by the galvano- meter ; but, as far as could be judged by the shock, 15 wires

Fig. 93.

were sufficient. With regard to different kinds of iron, experi- ment shows that if we class them according to galvanometrio effect we obtain a different series to that at which we arrive when classifying them in the order in which they create

sensation by shock. Thus grey rough

kind

-^^'^ulPON

264 MUTUAL AND SELF INDUCTION.

which approached nearest io bundles of soft iron wire in respect of increasing the shock. Enclosing iron wires in a brass tube reduced the action of the wires in disturbing the inductive balance and rendered them very little better than- a bar of solid iron. When the primary current was a discharge from a Leyden jar, Dove found that the physiological effect (shock) of the secondary current, as estimated, was reduced by the introduction into the primary bobbin of non-magnetic conducting cores ; in other words, the introduction of a core of non-magnetic but highly conducting material into the primary bobbin reduced the power of a primary discharge to create a secondary discharge. These last results may be obtained in a more modern form by the substitution of a Bell telephone to detect the tertiary currents generated by the metal core.

Let a Bell telephone be connected in series with the secondary coil of a small induction coil, of which the primary is wound on a hollow bobbin and the frames are wholly of wood or non-metallic substance. A convenient form is that known as Du Bois-Beymond's sliding coils. Let an interrupter in the primary circuit make and break the circuit rapidly. This being so, the telephone emits a steady rattle or hum. If a massive copper rod is introduced into the primary bobbin as a core, the telephonic rattle is more or less suppressed ; if a core of soft iron wire is introduced the noise is increased; if a core of solid iron or steel is used the noise may be increased, but not so much as when the divided iron is used. The explanation of the exalting effect of the soft iron wire is simple. The presence of the iron reduces the reluctance of the magnetic circuit. More lines of induction therefore flow through the secondary circuit, and hence the strength of the secondary current is increased, and the mean rate of change of induction through it is also increased. The diminishing effect of the copper core is explicable in the light of the knowledge that in such a conducting core the primary current generates induced currents, and these in their turn re-act upon the secondary circuit, inducing in it a tertiary current. The directions of the currents induced by the primary in the solid core and in the secondary circuit are the same. The direction, however, of the first half of the tertiary current developed in the secondary by the current in the copper core is

MUTUAL AND SELF INDUCTION.

266

opposite to the direction of the current developed in the secon- dary by the action of the primary. Hence it results that the current in the secondary circuit is more or less wiped out by the opposing inductions due to the primary circuit and the currents induced in the copper core. Otherwise the operation might be regarded thus : — Suppose the primaiy circuit to be traversed by a periodic current creating a simple periodic flux of induction through the copper core. As we have seen, under the head of magnetic screening, this variation of induction would induce currents in the copper core, which would them- selves generate a flux of induction which would, if the con- ductivity of the core were perfect, or the rapidity of change of induction infinite, be exactly equal and opposite at each instant to the flux of induction producing those currents.

If the conductivity is not quite perfect, or the rate of variation not very great, yet nevertheless the direction of

Fia. 99.