The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 16 of 36

•the field of magnetic force inside the copper, due to the cur- rents induced in its mass, will more or less oppose the field of force at every instant which is by its fluctuations generating those currents. If the thick line 11 1 in Fig. 99 represents the sinusoidal or simple periodic change of induction or magnetic field in the interior of the copper, due to the primary helix, and if the dotted line 22 represents roughly the changing field due to the eddy currents generated in the core, which are nearly 180° behind the primary in phase, the integral or sum of both superimposed fields represented by 8 8 at any instant is less than the original one due to the primary alone at the corresponding instant. Also the mean rate of chanye of the resultant field is less, and the secondary circuit experiences at every instant a less inductive electromotive force. The same reasoning which we have employed in the case of magnetic

206 MUTUAL AND SELF INDUCTION,

shielding applies here, and the differences in the reducing- effect of cores of various metals would be found to be less at high speeds of alternation than at low. In some small induction coils used for medical purposes the strength of the secondary current is graduated by drawing in or out of the primary coil a copper tube which slips over the bundle of fine iron wires used as a core. The rationale of the action of this copper tube in so operating is in a general way to be found in the principles laid down above.

When Henry obtained possession of the ** Experimental Researches " of Faraday, as detailed in the fourteenth series of his " Experimental Researches,'* he was exercised in his mind to reconcile the results obtained by Faraday on the interposi- tion of metallic screens between inducing and induced circuits with his own. Faraday had found that when the galvanometer was used as a current finder ^' it makes not the least differ- ence '* whether the space between the primary and secondary coils was air, sulphur, shellac, or such conducting bodies as copper and other non-magnetic metals. On the other hand, Henry found that a shock from a secondary coil which would paralyse the arms was so much reduced by the inter- position of a metallic plate as hardly to be sensible on the tongue. Here was evidently something to be explained, and in a long memoir {rhil. Mafj.y Series 8, Vol. XVIII., 1841, p. 492 ; also Transactions of the American Philosophical Society, Vol. VIII., 1840) Henry examined this and other matters. He first verified Faraday's experience by attaching the ends of a secondary coil to a galvanometer and bringing up suddenly towards it a permanent magnet, or a coil traversed by a steady current. The swing of the galva- nometer was found to be quite unaffected in extent by the interposition of a plate of copper. Again, in place of the copper plate, a closed metallic conductor (an endless coil) was employed, but whether the circuit of this coil was open or closed it made not the shghtest difference on the galvano* meter deflection.

Forty feet of copper wire, covered with silk, were wound ovt a short cylinder of stiff paper, and into this was inserted a hollow cylinder of sheet copper, and into this again a rod of soft iron. When the latter was rendered magnetic, by

MUTUAL AND SELF INDUCTION. 267

suddenly bringing in contact with its two ends the different poles of two magnets, a current was generated in the wire, but the strength of this current, as measured in the galvano- meter, was the same w^hcther the copper cylinder was present or was removed. Henry then noticed that there was one element of difference between the indications of a galvano- meter and that of the magnetising spiral. If the two secondary currents at "break" and "make" of a primary were sent through a magnetising spiral and through a gal- vanometer, the arrangement might be such that the induced ooirent at "make" of the primary was unable to give any sensible magnetisation to the steel needle enclosed in the spiral, but at " break " was able to magnetise it to saturation. Nevertheless, in both cases the " throw " of the galvanometer was the same. Similarly with the degree of shock felt, the galvanometer indications being alike for the inverse and direct induced current ; yet that induced current gave the greatest shock which was able to produce the greatest magne- tisation. The explanation of these facts became clear as soon as it was seen that the deflections of the galvanometer depended upon the whole quantity of the discbarge, and must necessarily be alike for the inverse and for the direct current, but that the magnetising effect and the physiological shock depended upon the maximum value of the instantaneous discharge current, and might therefore be very different for the two induced currents. It was then evident that any actions by which this maximum value of an induced current was decreased, whilst its duration was increased and total quantity left unaltered, would result in rendering this current less easily detectable by shock or magnetisation, but make no difference in its effect on a galvanometer. Aided by this thought, he repeated Faraday's experiment with the balanced coils referred to in § 8 (" Experimental Researches," Vol. I., § 1,790 et seq,), A galvanometer was provided having two equal wires of the same length and thickness wound on the same frame, and also a double magnetising spiral was pre- pared by winding two equal wires round the same piece of hollow straw. Coil No. 1, connected with a battery, was supported perpendicularly on the table, and coils Nos. 8 and 4 were placed parallel, one on each side, and each coil connected

268 MUTUAL AND SELF INDUCTION.

in series with one coil of the differential galvanometer and with one spiral of the magnetising helix. The two outside <$oils were then adjusted so that when the battery circuit was made and broken, and the current started and stopped in the middle coil, no indication was given by the galvanometer, and no magnetisation produced in a steel needle placed in the double helix. A thick zinc plate was then introduced between the primary coil and one of the secondaries, and it was found that the needle of the galvanometer still remained stationary on making and breaking the primary current, but that the rsteel needle in the spiral became powerfully magnetic. This indicated that the two secondary currents, whilst still equal in total quantity, had been so affected that one had a less maximum value than the other, and hence a differential magnetising action was produced. A similar effect was observed when a galvanometer and magnetising spiral were together introduced into the secondary circuit of a single primary and secondary circuit. The interposition of a metal sheet considerably reduced the magnetising power or the shock, but left the galvanometer deflection unaltered. In order to increase the number of facts, this last experiment was varied by the exchange of a soft iron needle for the hard steel needle in the magnetising coil, the metal screen being interposed in each case, and it was found that whereas the metal screen cut off almost entirely the power of the secondary current to magnetise hard steel, it could yet slightly magnetise the soft iron. A screen of cast iron half an inch thick, how- over, not only neutralised the power to magnetise hard steel, but reduced the deflection of the galvanometer as well. The general explanation of the foregoing facts, as due to Henry, is as follows : — The secondary current, as we have seen, is a brief discharge, which rises very suddenly to its maximum value and then fades gradually away. The current curve of the secondary current, due to the rupture of a primary circuit, may be represented by the thick firm line in Fig. 100. If a metal screen is interposed between the primary and the secondary circuit the screen gets a similar secondary curremt generated in it, and this last again acts by induction to gene- rate a tertiary current in the secondary circuit. This tertiary current consists of two portions — first, an inverse part opposite

MUTUAL AND SELF INDUCTION.

26»

in direction to the secondary oorrent in the screen, and, secondly ». ft succeeding direct current. Let the current curve of thi& tortiary current in the secondary circuit be represented by the fine firm line in Fig. 100. The total quantities of electricity flowing in each part of the two portions of the tertiary current are equal. The resultant effect, then, of the action of the primary current when interrupted is to cause in the secondary circuit the true secondary current, which is an unidirectional flux (thick curve), and a superimposed tertiary current, which, is a bi-directional fiux, its algebraic : total of quantity being, zero.

Fig. 100.

If we add together at each instant the ordinates of the two* current curves we get a resultant curve (dotted line) which represents the actual current curve in the secondary circuits The total area (electric quantity) enclosed between the hori- zontal line and the dotted curve must be equal to the total area enclosed between the thick firm Une and the horizontal^ because we have added and substracted equal areas ; but the maxmum ordinate of the dotted curve will be less than that of

370 MUTUAL AND SELF INDUCTION.

the thick firm line curve, and the form of the curve "will be very different also. It is, then, clear that the superposition of a complete tertiary current, which is of itself but very little able to affect a galvanometer on a secondary current which gives a definite galvanometer indication, is not able to alter that galvanometer deflection, depending as it does on the total quantity of the discharge. The magnetising power and shock, however, depend upon the maximum value or suddenness with which the induced current rises to its maximum value, and this factor is very much affected by the overlaying of a secondary current by a tertiary. We see, then, that the experiences of Faraday and Henry may be completely recon- ciled, and that the detection of magnetic screening depends upon the nature of the detecting instrument in the secondary <;ircuit.

The practical outcome of much of the foregoing discussion of magnetic screening is that the use of lead-covered cable for the conveyance of periodic currents of the usual frequency (60 or 100 alternations per second) is of no a^dvantoije in respect of prevention of inductive disturbance in neighbouring tele- phone wires. Not only is the lead too poor a conductor, but the frequency of alternation is too small to render the magnetic screening effective. The only effective method of annulling the inductive disturbance is to carry the periodic •current along a conductor which lies in the axis of, and is insulated from, a concentric enclosing tube or sheath, which acts as a return. This return must be itself insulated from the earth, and the condition to be fulfilled is that at any instant, and at any section the algebraic sum of the currents in the core and sheath must be zero ; reckoning current in one direction positive, and in the other negative.

The whole question of magnetic screening has been worked out mathematically by several mathematicians, and besides the section in Clerk-Maxweirs Treatise (Vol. 11. § 654, 2nd Ed.), the advanced student may be referred to memoirs by Prof. Charles Niven " On the Induction of Electric Currents in Infinite Plates and Spherical Shells*' {Phil. Trans. Roy. Soc., 1881, p. 807), and also to Prof. H. Lamb " On Elec- trical Motions in a Spherical Conductor" {Fhil. Trans, Roy. Soc, 1888, p. 619).

MUTUAL AXD iiELF INDUCTION, 271

§ 9. Reaction of a Closed Secondary Oircnit on the Pri- mary.— If a Bell telephone is placed in series with a coil of many turns of fine wire wound on a hollow bobbin, and if both are placed in series with the secondary circuit of a small induction coil, the strength of the secondary current can be so adjusted that the telephone emits a low murmur or rattle. This being the case, let a solid bar of copper be introduced into the bobbin of fine wire, and it will be found that the noise of the telephone is increased. If a bundle of fine iron wires is substituted for the copper rod it will, on the other hand, reduce the noise or stop it altogether. The explanation of this effect is to be found in the reaction which a closed secondary circuit has upon its primary in changing the resultant impedance of the primary. We have shown in Chapter III. (p. 180), that the re-active effect of the secondary is to increase the resistance and reduce the inductance of the primary circuit, and we have deduced two formulas given by Maxwell for the value of the equivalent resistance BJ and the equivalent inductance U of a primary coil of resistance B and inductance L in the presence of a secondary coil of resistance S and inductance N, the mag- netic circuit having a constant resistance, and the mutual inductance being M. Hence, the equivalent impedance of the primary coil in presence of the secondary is A/K'^-f j&'^L', and that which we may call its isolated or intrinsic impedance is equal to v^R+^L*. For b^e^dty we may write the symbol Im for ^"Bi^+p'SJ and Im' for VW^TfTI\ also Imj for v^S*+i?N. The question then arises, which is the greater — Im' or Im ? To discover this, take for R' and L' the values given on page 180, and we have

and L «L- c

Forming from these the function R'* + //^L'*, we have

272 MUTUAL AND SELF INDUCTION.

or (Im')«=(Im)^-,^l^{;,«(2LN-M«)-2RS}.

If S » X , or the secondary circuit is open, the right-hand side of the above equation is zero, and we find that the impedance of the primary circuit is not altered by the pre- sence of the open secondary, as of course it should not be.

If S is not infinite, that is if the secondary circuit is closed^ then the above equation shews us that, if the quantity 2B& is greater than the quantity />* (2 L N - M*), then Im' is greater than Im, or the impedance of the primary circuit is increased by closing the secondary. But if 2 B 8 is less than ;>' (2 L N — M^), then Im' is less than Im, or the impedance of the primary ia decreased by closing the secondary circuit.

If ttj stands for ^, and a, for ^, and also if P stands for

M -7==, it is not difficult to show* that to make Im' greater V L N

than Im we must have

a^ a, less than

2-^

When the secondary circuit has a certain critical value it is possible to show experimentally that above this value closing the secondary circuit increases the primary impedance, but below this value closing the secondary circuit decreases the primary impedance.

The following experiment was made in the laboratory of Prof. Elihu Thomson f: — A small induction coil had its primary circuit arranged in series with nine incandescent lamps joined in parallel, thus exciting it with an alternating current of about ten amperes. When the secondary circuit was closed by means of a vacuum tube of high resistance, a- marked fall occurred in the candle-power of the lamps used as a resistance in the primary circuit. The impedance of the

• See Mr. K C. RimingtoD, *'0d the Behaviour of aD Air Core Transformer when zhe Frequency is Below a Certain Critical Value," Proo, Physical Soc, London, October 27, 1893.

t See The Electrician, Vol. XXXIL, p. 225.

MUTUAL AND SELF INDUCTION. 273

primary -was thus increased. When the secondary circuit was closed through a water resistance, the lamps brightened up, thus showing that the primary impedance was decreased.

Hence the closing of the secondary circuit does not always decrease the primary impedance. Mr. Bimington {loc. cit) quotes an experiment with an air core transformer or induction coil consisting of two circuits without iron core, in which closing the secondary circuit had the effect of decreasing the primary current by about 8 per cent., thus showing an increased primary impedance. Generally speaking, however, the closing of the secondary circuit so that the total secondary circuit resistance is small has the effect of decreasing the primary circuit impedance.

Hence also holding a conductor or conducting circuit of low resistance near a primary coil has the effect of decreasing the impedance of that coil and therefore increasing the flow of primary current through it under the influence of a constant impressed primary electromotive force.

The explanation of our experiment with the induction coil and the copper rod is now simple. The introduction of the copper rod into the fine wire helix is equivalent to approxi- mating to a primary coil a closed secondary circuit. The impedance of the fine wire circuit to the alternating current from the secondary circuit of the induction coil is hence reduced ; it gets more current, and the telephone is made to emit a louder sound. If, however, a core of divided fine iron wire is introduced into the fine wire helix, the result is simply to increase the impedance of that circuit, and therefore to reduce the current actuating the telephone. When considering in particular the theory of the induction transformer as applied to electric distribution we shall see the above principles have important practical bearings.

In a Paper recording some experimental results on the self-induction and resistance of compound conductors* Lord Bayleigh has given some comparisons of the results of theory and experiment on Maxwell's formulas above alluded to. By the use of a resistance and inductance bridge, very similar to one designed by Prof. Hughes, the measurements of tho inductance and resistance of a circuit can be made separately

• See PhU. Mag,, December, 1886, p. 469.

274 MUTUAL AND SELF INDUCTION.

with ease. A pair of wires was wound on one bobbin ; each wire had a resistance of nearly '1 ohm, and a diameter of '0d7in. Each coil consisted of nine double convolutions. In certain arbitrary units the resistance of one of these copper wires to steady currents was 176, and its inductance 11 '2". These values were obtained when the other coil was on open circuit. On closing the unused coil, the resistance of the first rose to 2-67 and its inductance fell to 47*. To compare this with the theory.

The formula are R' « E + f ^^',^,

S'^ + p'^N'

Now B=8=l-76x'0492xl0* absolute O.-G.-S. units of resistance,

and L » N » ll°-2 x 1558 centimetres,

M = 11° X 1658 centimetres,

and jp = 2fl- « = 2 X 8-1415 x 1060.

The periodic current used had a frequency of 1060 per second ;

Therefore R' -B (1 + -6) = 1-6 R,

and L'- = L (l--6)= •4L;

but 1-6 X 1-75- 2-8 = R',

and •4xll°-2 = 4°-6=L'.

These calculated values compare very favourably with the observed values, viz. :

R" = 2-67, L'-4 7% and experimentally confirm the truth of Maxwell's formulsd for the increased resistance and diminished inductance of a circuit when placed near a closed secondary circuit.

§ 10. Hughes's Induction Balance and Sonometer. — In 1879 Prof. Hughes constructed and described a very perfect induc- tion balance, with which he was able to conduct researches of an exceedingly interesting character. In order to have a perfect induction balance he found it necessary to make all the

MUTUAL AND SELF INDUCTION.

276

four coils exactly similar.* Four boxwood bobbins {see Fig. 101) are each wound over with 100 metres of No. 82 copper wire. These coils are arranged in pairs at a considerable distance apart, so that the coefficient of mutual induction between the separated pairs is negligible. Two of the coils, A and B, are joined in series with each other and with a battery and interrupter I, and the other two coils, G and D, are employed respectively as secondary coils to these two. These secondary coils are in series with each other and with a telephone receiver T, and are so joined up that the direction of the induction of A on G is oppo- site to that of B on D. One pair of coils is placed in a fixed position, and the other pair can be slightly moved to or from

FiQ. 101.

each other by means of a micrometer screw. The coils are first adjusted so that the inductions are equal and opposite, and on listening at the telephone the opposing secondary currents produce at best but a very slight sound, which can be perfectly abolished by adjusting the distance of one pair of coils. When this is the case, if we insert in the opening of the bobbin of one of the primary coils a disc or piece of metal dy the balance is destroyed, and we hear sounds more or less intense. In order to get some comparative measurements, Prof. Hughes designed

• " On an Induction Current Balance." By Prof. D. E. Hughes. Proe, Hoff. Soe., No. 196, May 5, 1879.

T 2

276 MUTUAL AXD SELF INDUCTION.

a companion instrument, called a sonometer. In this instrument a pair of primary coils are, as before {see Fig. 102), joined in series with each other and with a battery. The coils are fixed at the extremities of a bar. Between these primary coils slides a single secondary coil, and the primary coils are so wound that their inductions on this secondary coil are equal and opposite. When this secondary coil is exactly between the two primary coils, a telephone placed in series with the secondary coil gives out no sound when the primary current is rapidly interrupted. If, however, the secondary coil is slid from one primary and towards the other, the differential action creates an induced current detected by the telephone. By reading off on the bar the extent of displacement necessary to create in the telephone a sound of a certain magnitude an arbitrary reading can

be obtained corresponding to every different value of the secondary current. A switch is provided, by means of which the same telephone can be shifted rapidly from the induction balance secondary ckcuit to the sonometer secondary circuit. The experiments first performed consisted in placing within one primary coil of the induction balance certain equal-sized discs of different metals, and then so arranging the sono- meter secondary coil that the noise in the telephone produced by the current in the secondary of the sonometer was judged by the ear to be equal to the sound produced in the telephone when it was shifted to the secondary circuit of the induction balance, and in which the inductive balance had been broken

MUTUAL AND SELF IXDUGTION. 277

down by the insertion of the disc of metal. Discs of various metals the size and shape of an English shilling were made, and, when inserted in the induction coil, the sonometer bar readings, reckoned from the centre or absolute zero of sound given in certain arbitrary degrees, were as follows : —

Qerman Sihrer 50

Iron (pure) 40

Copper (alloy) 40

Sflver (chemically pure) 125

Gold 117

Silver coin 115

Aluminium 112 I Lead .'. 38

Copper 100 i Antimony 35

Zinc 80

Bronze 76

Tin 74

Iron (ordinary) 52

Mercury 30

Bismuth 10

Zinc (alloy) 6

Carbon 2

This list does not agree in order entirely with that of any of the lists of electrical conductivity. In some degree it evidently has reference to conductivity, because, roughly speaking, the best conductors come at the top and the worst at the bottom ; but whilst it is headed by silver, which has the highest conductivity per unit of volume, we find aluminium, which has the highest conductivity per unit of mass, occupying a position above that of copper. The disturbing effect of the metal on the inductive balance is not, however, simply proportional either to the conductivity per unit of mass or per unit of volume. In more recent experiments a graduated zinc wedge pushed in more or less between one pair of coils of the induction balance was employed to obtain comparative numbers representing the disturbance produced when discs of various metals are inserted in the other coil. The elementary theory of the induction balance is of course contained in all that has gone before in this and the last chapter. It is, generally leaking, dependent for its action on effects similar to those producing magnetic shielding. If the discs are slit so as to prevent circumferential electric currents in their mass, their action in disturbing the inductive balance is mitigated or annulled. If the metal disc is replaced by a copper coil with open extremities no effect is observed on the inductive balance. If the ends of the coil are joined, the coil behaves as if it were a metallic disc and causes loud sounds in the telephone. The effect due to the iron disc is a mixed one. It in part acts like any other metal disc, but it differs from them in one respect. If any non-magnetic disc is placed edgeways in the centre of

278 MUTUAL AND SELF INDUCTION.

the primary bobbin it has a diminished effect in disturbing the balance ; in the case of iron the disturbance is increased by turning the disc edgeways. In order to have before us a typically simple case, imagine an induction balance made of two very long primary helices and each embraced near the centre by a small secondary coil. Let the primary coils be traversed by a simple periodic current. We have then in the interior of the primary coil a uniform magnetic field varying synchronously with the primary current in a simple periodic manner, and the rate of change of the magnetic field at any instant will be a measure of the electromotive force acting in the secondary circuit. Suppose into one primary helix is inserted a thin copper tube ; this will form a closed secondary circuit, and secondary periodic currents will be induced in it, flowing round the cylinder in directions parallel to the turns of the primary helix. As this copper cylinder possesses a very sensible time constant^ the phase of these secondary currents in the copper cylinder will be nearly opposite to that of the primary current. The resultant magnetic field in the interior of the cylinder is therefore that due to the resultant of these two simple periodic currents which are nearly opposed in phase. Hence the absolute magnitude of the interior field and its rate of variation will be less than if the copper cylinder was removed. It results, therefore, that the induction through the secondary helix and the electromotive force impressed on it will be diminished by the presence in the primary coil of this copper cylinder. The diagram given on page 177, showing a geometrical construction for the magnitudes of the primary and secondary currents in an induction coil without iron, shows us why the primary and secondary currents are thus more or less opposite in phase. Since, in a general way, the higher the conductivity of the tube or disc introduced into the primary the greater the time constant, and the greater the lag in phase of the currents induced in this metallic circuit behind the phase of the inducing primary, it follows that the resultant interior field acting to produce inductive electromotive force in the secondary helix will be diminished by the introduction of discs of very high conductivity more than by discs of very low conductivity.

MUTUAL AND SELF INDUCTION. 279

From the principles discussed under the head of magnetic shielding it would appear that the differences between various metals inserted as discs in the induction balance would be less marked at very high speeds of interruption than at very low ones. With respect to the action of iron, two effects have to be considered which are the results of very different actions. The introduction of the iron into the primary coil reduces the magnetic resistance of the circuit of induction of that coil, and this cause, if ,it operated alone, would destroy the inductive balance by raising the inductive electromotive force in that secondary circuit corresponding to the primary into which the iron is introduced; but the iron disc, like every other disc, gets circumferential induced currents created in it, and these, U they acted alone, would destroy the inductive balance by lowering the inductive electromotive force in that secondary coil.

These two effects conflict, and it is an interesting confirmation of theory to find that Prof. Hughes says it is possible to intro- duce into one primary coil of the induction balance a disc of iron and some soft iron wires in such positions that these opposite actions nullify each other, and, though each mass of iron separately would destroy the induction balance, yet the two together being introduced complete silence in the tele- phone is the result. The sensibility of the induction balance to minute differences of electric conductivity and magnetic permeability is very remarkable. If into one coil of a carefully- adjusted balance we place a good sovereign, or shilling, and into the other a bad one, the telephone detects the base coin with unerring certainty by the loud noise given out. In the same way, if two pieces of soft iron are introduced into the two primary coils, and a balance is obtained, the mere magnetisa- tion of one of them will be at once detected, because that magnetised piece becomes thereby less permeable, and destroys the balance. We may present the rough general theory of the induction balance in another way. Let the " coin " be simply regarded as a closed circuit, between which and the primary circuit surrounding it there is a certain coefficient of mutuid induction. The two primary coils forming one primary drooit have, on the whole, no action on the two secondary coils forming one secondary circuit, and we may therefore

280

MUTUAL AND SELF INDUCTION.

consider the primary circuit as if it were in a position conjiujate to the secondary. The coin, however, is acted upon inductively by the primary circuit, and the eddy currents or secondary currents generated in it react on the secondary circuit, causing in it tertiary currents, which affect the telephone. Looking at it from this point of view, we might construct an induction balance thus. Let A {^ee Fig. 103) be a single primary coil, and B a secondary coil, having a telephone in series with it. Place the coil B in a position conjugate to A — that is, with its axis at right angles to that of A. Then let variation of current in A produce no current in B. Now hold a sheet of copper anywhere, say at C, and the telephone will be caused to sound. For A, though it

Fig. 103.

cannot affect B inductively directly, yet it can produce a secondary current in C held at a non -conjugate position, and these secondary currents in C will create other tertiary currants in B. The experiment thus appears to indicate a sort of reflection of inductive power.*

This was experimentally shown by Mr. Willoughby Smith in his Paper on " Volta-Electric Induction " (see Journal of Society of Telegraph-Engineers, Vol. XII., page 465).

• The fuU theory of the induction balance has been given by Prof. Oliver Lodge. See Proc, Pkys. Soc. London^ Vol. III., p. 187. Alao in the same volume is a Note by Prof. J. H. Poyuting " On the Graduation of the Sonometer."

MUTUAL AND SELF-INDUCTION. 281

An interesting experiment due to Mr. Willoughby Smith is to employ a simple Bell telephone receiver, nnconneoted with any circuit, as an induction finder. If a coil of wire is traversed by an electric current, either rapidly intermittent or alternating, then a Bell telephone held anywhere in the magnetic field «mits a sound. The pulsating field disturbs the magnetism of the telephone magnet, and enables us, therefore, to detect rapid electromagnetic disturbances at the place where it is held. It is obvious, then, that the induction balance, combined with a telephone, is an apparatus of extreme sensitiveness. It <3an render evident the smallest differences of weight, nature, degree of purity or temperature of two conductors of identical dimensions, such as two coins placed in identical conditions in respect of the two systems of coils.

It enables us to detect very small masses of metal in a badly conducting body, and may be employed with much advantage in verifying the insulation of the different windings of a coil, the ends of which are open. At the same time, however, it lends itself better to qualitative than to quantitative work, as it is difficult to interpret rigorously the results obtained.*

§ 11. The Transmission of Rapidly Intermittent or Alter- nating Ourrents through Conductors. — Some experiments by Prof. Hughes in 1886 on the self-induction of metalUc wires were the means of directing the general attention more closely than before to the nature of the propagation of electric currents of high frequency through metallic conductors, and although mathematical writers, particularly Maxwell and Ohver Heaviside, had previously considered the problem theoretically, the experimental results drew the attention of many to this question to whom the more recondite mathematical investigations were unknown. Prof. Hughes's

• For further information on the use and theory of the induction balance the student may consult, with advantage, Mascart and Joubert's "Elec- tricity," Vol. IL, § 986 ; al^o Hughes, P/iiZ. Mag. [5], Vol. II., p. 60, 1879. On the differential telephone, 9U Chrystal, PhiL Tran9. Roy, Soc. Edin», Vol. XXIX., p. 609, 1880. 0. Lodge, Proc, Physical Soe, London^ Vol. III., p. 187, on intermittent currents and the theory of the induction balance.

282

MUTUAL AND SELF INDUCTION.

experiments* on the self-induction of metallic wires were made with a combined resistance and induction bridge of somewhat novel form. Suppose that a quadrilateral arrange- ment be formed of four conductors P, Q, E, S, only one of which, P, has any sensible self-induction, and let the diagonals be completed by a telephone T, and battery B, with interrupter I. In the first place, let the resistance- balance be obtained for steady currents. This can be achieved by placing the telephone with the interrupter as a conjugate circuit to the battery (see Fig. 104), and altering one resistance, say, 11, until a balance is obtained. By a suitable

Fig. 104.

adjustment of the four resistances complete silence can be- obtained in the telephone.