The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 14 of 35

(3) We have, lastly, effects dependent chiefly upon the maximum ordinate I, or upon the rate of change of the cur- rent— that is, upon the steepness of the slope of the current curve. These are the physiological, telephonic, luminous, and magnetic 'effects.

The physiological effect of a discharge in giving a shock appears to depend in great part upon the suddenness with which the maximum current strength is reached. Of two dis- charges which reached equal maxima, that which arrived at it in the shortest time would be the most effective in producing shocks. The value of the maximum current strength is also important. Two induced currents of equal quantity but different durations cause a greater shock in proportion to their lesser duration. The telephone in this respect resembles the animal body. It is affected more by the rate of change of the current strength than by the absolute current strength at any instant.

The magnetic effect depends, as has been shown by Lord Rayleigh,* upon the maximum current strength during the

• See Phil. Mag., Ser. 4, Vol. XXXVIIL, 1869, p. 8 : The Hon. J. W Strutt (Lord Rayleigh), " On some Electromagnetic Phenomena." Also Phil. Mag., Ser. 4, Vol. XXXIX., 1870, p. 431.

232 MUTUAL AND SELF INDUCTION.

discharge, or upon the initial current strengMi, in those cases in which the current dies gradually away. In the two Papers referred to below it is shown by direct experiment that, since the time required for the permanent magnetisation of steel is small compared with the duration of induced currents generally, the amount of acquired magnetism depends essentially on the initial or maximum current strength during a transitory current, without regard to the time for which it lasts. It is, then, not difficult to understand that the effort to settle by experiment with a magnetising coil the direction of induced discharges may lead to very conflicting results, and, in any case, it is hardly competent to do more than indicate the direction in which the maximum current flow takes place during the discharge.

The spark effects are also included in this category. The air or other dielectric is broken down when the difference of potentials between the two discharging points reaches a certain magnitude, and in the case of a varying electric pressure the question whether a spark will pass or not is evidently determined by the maximum magnitude of that quantity.*

It is evident from the above considerations that the complete analysis of the effects and phenomena of induced currents of the higher orders, and of those of secondary currents due to discharges from condensers, requires a knowledge of the form of the current curve in each case. We proceed to consider the problem of the theory of induced currents in some of its simpler aspects.

§ 6. Elementary Theory of the Mutual Induction of Two Circuits. — Aiming rather at the elucidation of principles than very copious treatment, we shall consider in the next place the problem of the mutual induction of two circuits in its simplest form. Let there be two bobbins of wire in suitable positions for producing mutual induction and without iron cores. Let the constant inductance of the first or primary coil be denoted by L and its resistance E, and the similar quantities for the

• See Bertin, " Notes on Electrodyuamic Induction," Ann. de Chimie, 4th Sen, Vol. XXII., April, 1871, p. 486.

MUTUAL AND SELF INDUCTION. 233

second or secondary coil be N and S, and let M be the co- efficient of mutual induction.*

Let there be a source of constant electromotive force, E, •which can be applied or withdrawn from the primary circuit. We shall denote by x the strength of the current in the primary at any time t after closing the primary circuit by applying the battery to it. Also we shall denote by y the current in the secondary circuit at any time reckoned from the same zero.

If, then, at any instant the currents are x and y, the follow- ing state of things exists in the circuits.

The electromotive force E is the impressed force on the primary circuit.

That part of the impressed electromotive force producing the current x is E«. That part employed in overcoming the

counter-electromotive force of self-induction is L — , and the

dt

counter-electromotive force of mutual induction due to the

current y at that instant in the secondary circuit is - M _^.

dt

Hence the relation which at any instant holds good between these quantities is

The above equation is an expression of the fact that the external impressed electromotive force at any instant is equal to the internal electromotive forces and the effective electro- motive force driving the current.

Similarly, for the secondary circuit we have an induced electromotive force due to the induction of the primary on

the secondary equal to M — and a counter-electromotive force

— a t

of self-induction N — ^. a t

Hence N+M

d t d t

since there is no external impressed electromotive force. The complete solution of the problem of finding the currents x

• Continental writers often call L and N" the potentials of the bobbins on themselves, and M the potential of one bobbin on the other.

234 MUTUAL AND SELF INDUCTION.

and y at any instant is obtained by the solution of these simultaneous differential equations —

dt

at dt

As our object is to illustrate principles rather than mathe- matical methods, we shall simplify the problem by supposing that the two circuits are similar in every respect. This makes R = S and L = N, and the equations become

L^+M^+Bs-E, .... (83) ..... (84)

Bearing in mind that the inductance L is, in ordinary parlance, the "number of lines of force" which are linked with the primary circuit when unit current flows in its own circuit, and that M signifies the number of lines of force which are common to both, or linked in with both circuits, when unit current flows in each, we see that M can never be greater than L, but that under all circumstances we must have

M <or = L,

also M < or = N ;

hence M2<or = LN,

or LN — M2 always a positive quantity, and the maximum value which the co-efficient of mutual inductance M can have is x/L N, or the square root of the product of the self- induc- tances of the separate circuits.

In order to separate the differentials- in (83) and (84) we differentiate each equation with respect to t, and obtain —

MUTUAL AND SELF INDUCTION. 235

Multiply (85) by L, (86) by - M, and (83) by E, and then adding the three equations together we obtain — #x , 2LE dx . R2 EE

, v La-Md L'-M3* ' '

and a similar elimination gives us

We have now separated the differentials in x and ?/, and the solution of these equations depends, as is well known,* upon the solution of an auxiliary quadratic equation —

the solution of which is —

R

m= - - — — , or-

• M' L-M

Hence the general solution of (83) and (84) is—

•-Ar*-i+B/1-«+!f . . . (89)

and y = A.'e L+* +BVL-M, (90)

where A, B, A', B' are constants of integration to be determine J from the circumstances of the flow. To do this, however, a preliminary discussion is necessary. Let us suppose that the primary current is fully established, and has a steady value Ir and hence that M I lines of induction penetrate through the secondary circuit. This quantity is then the electromagnetic momentum of the secondary circuit, because when the current ill the primary is steady there is no current in the secondary circuit.

Let us now suppose that the primary circuit is broken, and that the circumstances of the " break " are such that all these MI lines of induction are removed at a uniform rate in a small time B t from the secondary circuit.

During this time 8 1 an electromotive force will operate upon

the secondary circuit equal in magnitude to — ~^T, or to the rate

of decrease of the included lines of force. We have seen in

• See Boole's " Differential Equations," p. 192, 2nd Edition.

236 MUTUAL AND SELF INDUCTION.

Chap. III. that when an electromotive force E acts on a circuit of inductance L and resistance E that the current i at any time after the commencement of the application of the electro- motive force is given by the equation

In the case' considered the inductance and resistance of the secondary circuit are L and E, and the impressed electro-

motive force applied during a time 8 t is -yr- . Hence, at the end of the interval of time St, the value of the secondary current is given by the equation

This gives us the value of the inverse induced current at the instant of breaking the primary. Expand the above expression by the exponential theorem, and it becomes

i M MBSt M E2 8 t2

_ _ ITL'l-2+L3l-2-3'

At the instant when the removal of lines of force or the ces- sation of the induction through the secondary takes place the impressed electromotive force ceases and the secondary current begins to die away. If we suppose the "break" of the primary to be very sudden, 8 1 becomes practically zero, and we have

that is to say, the secondary current starts with a value equal

to — of that of the steady primary. '

Li

The state of things in the secondary circuit immediately after the break of the primary is, then, this : The electromotive impulse due to stoppage of the primary has generated a current

of initial value — I in the secondary, but there is no impressed

L

electromotive force in the secondary circuit. If at any instant after the break the current in the secondary circuit is i, the law of decay of this current is expressed by the equation : 1

dt

MUTUAL AND SELF INDUCTION. The solution of this is

237

and the constant C is found from the condition that when

t = 0 i = — I. Hence we have L

(91)

This gives us the value of the direct or "break" induced' current in the secondary at any instant after the break of the primary. Graphically, this may be represented by a curve, such as that in Fig. 85. During the time 0 T in which the primary is being broken the induced electromotive force is

FIG. 85.

creating an induced current, the rising strength of which is represented by the rise 0 P. The time occupied by the break 8 t is 0 T. As 0 T is diminished in value, the magnitude of the maximum ordinate P T approximates to —I, and this is

the initial value of the inverse secondary current when the break is very sudden. After the break the current decays away along a path represented by P Q, and becomes zero only after an infinite time.

The whole quantity of the induced current is obtained by integrating equation (91) with respect to the time from zero to- infinity, thus :

MT -?' ,. MI

238 MUTUAL AND SELF INDUCTION.

We see, then, that both the maximum value and whole quantity of the direct secondary current are proportional to the coefficient of mutual induction and to the strength of the primary current, and, moreover, that the whole quantity of electricity set in motion in a secondary circuit of total resis- tance R by suddenly removing from it M I lines of force is equal to the quotient of number of lines removed by the total resistance of the secondary circuit.

If the induced current is sent through a galvanometer the

indications are proportional to the magnitude of - If, how-

R

ever, the induced current is employed to magnetise steel needles, the magnetisation acquired is dependent upon the

magnitude of — -, and is therefore greater in proportion as

the coefficient of self-induction of the secondary circuit is less. Lord Rayleigh has pointed this out,* and shown by experi- ment that, within certain limits, the magnetising effect of the ^break-induced current on steel needles is greater the smaller the number of turns of which the secondary consists, the •opposite being, of course, true of the galvanometer. The galvanometer takes account of the total quantity of the induced current ; whilst the magnetising power depends mainly on the magnitude of the current at the first moment of its formation, without regard to the time which it takes to subside.

Returning to the equations (89) and (90), we can now find the constants of integration, counting the time from the instant of " make " of the primary. It is obvious that when t = 0, y = 0 and x = 0, and that the whole quantity of the make-induced

/QO y d t, must be equal to the whole quantity of the D

break-induced current, which we have seen is equal to .

R In (90) put t = 0, »/ = 0 ; we get

A' + B' = 0, or B'=-A'.

/ Rt Rt \

Hence, y = A' ^~£?B-«-e=sY

and

*Phil. May., Ser. 4, Vol. XXXIX., 1870, p. 429.

MUTUAL AND SELF INDUCTION. 239

Hence the whole quantity of the "make "-induced current is

• p     ,  and  this  must  be  equal  to  Mi  which  is  the  whole 
  

ti K

quantity of the " break " current. Hence A' = - _.

2

Therefore we get for the instantaneous strength of the " make " .secondary current

i^5 • • • (92)

Again, in (89) put t = 0, x = Q, and we get A + B + I = 0,

or B=-(I+A);

and by substitution in (89)

3 = A eL+ai-(A + I) eZ=*+I. From this equation we can find the value of A by substitut-

ing the value of -^derived from equation (92), and— derived

dt dt

from the above in the original differential equation (83), and we

find A= -_. Hence we arrive at the equation for the value

of the primary current at any instant, and it is

nt\ ^ . . . (93)

This gives the law according to which the primary current grows up in its circuit. If M = 0, that is, if there is no secon- dary circuit ; then

( i-

which is the ordinary law of current growth. If M = L, which is the greatest possible value of M, then

Hence it is obvious that the presence of the secondary circuit hastens the rise of the primary current and operates on it to reduce its inductance.

On making the primary we get a " make " or inverse secondary current according to the law of growth expressed by the equation

240

MUTUAL AND SELF INDUCTION.

and we see that under the circumstances assumed the " make ' secondary starts from an initial value zero, rises up to a maxi- mum, and then decays aWay again. To find the time of reach- ing maximum, equate _ to zero, and we find

f_L2-M2

~TKM

and this function increases as M decreases. So that the more nearly M is equal to L the sootier does the secondary reach its maximum. It is not difficult to show that when M = L the

above value for £' becomes zero, and when M = 0 «' = -.

^,-M=L (nearly)

O ( nearly J

FIG. 86.

Curves representing roughly the current value of the make-induced current for different and increasing values of M.

If, then, we trace a series of curves (Fig. 86) representing the values of y, or the make-induced current at each instant

for various and increasing values of — , as the coils are moved

M

further apart, we find a series of curves with decreasing maxima, but the maxima happening later as M decreases.

Lastly, on breaking the primary current we have a break- induced current in the same direction as the primary, which at

MUTUAL AND SELF INDUCTION. 241

any instant after the " break " is decaying away according to the law

.-!.-

L

If the break was absolutely instantaneous, the induced current would start with a finite value equal to __ of that of the primary,

but as no form of break entirely eliminates sparking, the rise of the direct secondary current is a gradual one. Also we have another element of disturbance which enters into the case. The self-induction of the primary creates direct electromotive force in its own circuit at the instant when the induction through the primary due to its own current vanishes. When the primary is broken either at a mercury cup or at a platinum point the fusion and volatilisation of metal which takes place keeps open for a little time a conductive path through which flows the extra current due to the self-induction of the primary. As will be explained later, the decay of the current on breaking a circuit may often be by a series of oscillations or diminishing periodic currents.

This direct extra current in the primary will have its effect in introducing a very short inverse-induced current, which will precede the main direct-induced current due to the decay of the primary current. In any event it will introduce an electrical oscillation tending to render the growth of the direct secondary current a gradual matter. It is an interesting case to examine the relative maximum values and duration of the two induced currents under an assumption very nearly realised when the primary and secondary are wound together on the same bobbin, viz., when M = L. In this case the values of y and z become

I -R<

The maximum of the direct currents ("break") is I, and that of the inverse (or "make") is -. If we wish to know at the end of what times * and t' the strengths of the two induced currents y and z are reduced to — of that of the primary we

242 MUTUAL AND SELF INDUCTION

obtain by substitution of — for y and z in the two above equa-

tions the following : —

1 _?.'

_=<? "IT for the direct-induced current,

in

1 "| R £'

and _ = _g~2L for the inverse-induced current.

m 2

and therefore _ = 2 l -

We see that t' is always greater than t, and that, in propor- tion as m increases, t' tends towards a limit 2 t, or the inverse current has a duration about double that of the direct secondary. We shall now see how this theory is confirmed by experiment.

§ 7. Comparison of Theory and Experiment. — Masson and

Breguet carried out a series of experimental researches on induced currents which illustrate and confirm the foregoing theory. The principal part of their apparatus was a commutator keyed on a revolving shaft, which enabled them to separate the direct and inverse-induced currents. Two brass wheels were keyed on one shaft, but insulated from it, and the wheels had depressions cut in their periphery which were filled up with ivory. These wheels could be shifted relatively to each other, and were insulated from each other and from the shaft (see Fig. 87). Two springs pressed against the edge of the wheels, and two against the hub of the wheel. The whole arrangement served as a means to break and make one circuit, and at the same time to control a second circuit so that it was broken at the time when the first was made, and made at the time when the first was broken, or vice versa. One of these wheels was inserted in the circuit of a primary coil and battery, and the other in the circuit of a secondary coil and galvanometer. On rotating the wheel at a certain fixed speed the series of "break" and " make "-induced currents are separated out ; all one set are stopped out and all the other are sent through the galvanometer. In this way it was shown that the quantities of the induced currents were equal, but very different in maximum magnitude, and hence in duration, the break-induced currents being greatly superior in making sparks.

MUTUAL AND SELF INDUCTION.

243

Lenz* wound a spiral of wire on the soft iron armature of a magnet and connected the ends of the wire to a ballistic gal- vanometer. He detached the armature suddenly, and observed the throw of the galvanometer. If 0 denotes the angle of deflection and x the number of windings, he found that the

1 /9

product - sin _ was a constant quantity, which shows that x A

cceteris paribus, the quantity of electricity set in motion was in proportion to the number of lines of induction withdrawn from the circuit. He also established experimentally, in con- firmation of Faraday, that the electromotive force of induction was independent of the width, thickness or material of the

FIG. 87.

wire windings,! and by other experimentalists also the fact has been established that the electromotive force is indepen- dent of everything except the form of the conductor and the nature of the change it experiences in relation to the magnetic induction through it. FeliciJ carried out an extensive series of experiments on induction, using a form of induction balance.

• Lenz, Poggendorff's Annalen, Bd. XXXI., 1835, p. 385.

t See Faraday, " Exp. Researches," Ser. II., § 193, et seq. ; also for Electrolytic Circuits, see L. Hermann, Pogg. Ann., 1871, p. 586.

t Felici, Nvovo Cimento, Vol. IX., 1859, p. 345, also Ann. de Chimic [3], Vol. XXXIV., 1852, p. 64.

244

MUTUAL AND SELF INDUCTION.

In this apparatus a secondary circuit, consisting of two coils, is arranged in series with a galvanometer. These coils are so far apart as not to influence one another. In contiguity to each secondary coil is a primary coil, and the primaries are wound in opposite directions. The primaries are in circuit with a battery and a key. The circuits can be so arranged, by adjusting the distances of the coils, that the induction of the primaries on their respective secondaries balance each other, and the galvanometer indicates no current, however strong may be the primary current. If three pairs of coils (see Fig. 88) are thus taken and balanced, two and two, so that the induction of A on a is equal to that of B on b and C on c, then, if we con- nect the primary A in series with B and C in parallel, so that

Fio. 88.

the current divides between them in the ratio of their resis- tances, and connect the secondaries with a galvanometer, all in series, so that the current in a is opposed to that in b and in c, then no induced current is detected when the battery circuit is made and broken. This proves that the quantity of the induc- tion current is proportional to the strength of the primary current.

If a primary and secondary coil are taken in fixed positions and the " throw " of a galvanometer observed when a definite steady electromotive force E is applied to the primary, then, if the position of battery and galvanometer are reversed, the application of the same electromotive force E to the secondary

MUTUAL AND SELF INDUCTION. 245

will give the same " throw" on the galvanometer now attached to the primary circuit, provided that the galvanometer and battery either have equal internal resistance or that their resistance is negligible in comparison with that of the coils. Hence we may assert that the induction of a circuit A upon B is the same as that of B upon A. For, if the resistances are R and S, then we have seen that the total quantity Q of the secondary

current is t— -, where I is the steady value of the primary

and M is the mutual inductance; but I = — , hence Q = .

R SR *

If, then, the positions of battery and galvanometer are reversed,

M F

we get a quantity of induced current equal to , which is

R S

the same as before. For any two coils it is possible to find a number of relative positions in which the interruption of a current in one produces no induced current in the other. In such cases the coils are said to be conjugate to each other. It is manifest that when in these positions the lines of induction produced by one coil do not pass through the other. It is possible to use one coil in this way to explore the field of another.

Let P be a primary coil and S be a small flat secondary coil, both being shown in section in Fig. 89. Then, if S is placed in a position conjugate to P, it will be found possible to move the coil S along a certain line ABC, maintaining the flat face of the coil always tangent to that line and so that in all these positions P and S are conjugate. It is evident that such a line is a line of induction of the coil P.

When one coil is in a conjugate position to the another, as far as regards inductive action they may be considered to be at an infinite distance apart. It follows, therefore, that if a coil is moved suddenly from a conjugate position to one not conju- gate in the field of a primary traversed by a steady current, and then the primary current is stopped at the instant of arriv- ing at the second position, a galvanometer in the second circuit will have its needle jerked from one position of rest to another of rest, because the interruption of the current takes out of the circuit of the second coil just as many lines of induction due to the first coil as the motion from one position to the

246

MUTUAL AND SELF INDUCTION.

other put in. A series of well-devised experiments on the conjugate positions of two coils has been carried out by Mr. W. Grant.*

An elaborate investigation into the duration of induced currents was made by Blaserna.f

A commutator was constructed which consisted of two insu- lating cylinders keyed on one shaft and having on part of their surface brass coverings cut into steps (see Fig. 90). These cylinders were capable of being set in any relative position to each other on the shaft. The shaft could be revolved at a high rate of speed, and its velocity ascertained by a siren plate attached to the axis. This siren plate consisted of a disc pierced with holes against which was directed a jet of air.

From the pitch of the musical note given out, when ascertained by comparison with standard tuning forks, the speed could be determined. Two springs pressed against the hubs of these cylinders and two against the surfaces of these cylinders, and a current entering by the hub was conducted to the brass coating and escaped by the other spring, if the cylinder was in such a position that this last spring was pressing on the metal part. The apparatus, therefore, formed a device by which each

• See Proc. Physical Soc., London, Vol. III., p. 121 ; also Proc. Physical Soc. London, VoL IV., p. 361.

t Blaserna, " Sul sviluppo e la durata delle Correnti d'induzione," Gwrnale di Science Naturali, Vol. VI. (Palermo, 1870).

MUTUAL AND SELF INDUCTION. 247

pair of springs might be brought into electrical contact for a definite portion of the time of a revolution of the cylin- 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 m M 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

C dd

FIG. 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 Mt. 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

248

MUTUAL AND SELF INDUCTION.

current, and this was the duration of the " make "-induced current. Blaserna 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 -000275 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

FIG. 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 AND SELF INDUCTION. 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' = d t • then the area P P' X' X = y d t represents the quantity of elec- tricity which has passed in the time XX'. Call this dQ.

Hence dQ = ydt, or y = ^.

dt

Suppose another curveA'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 P'YX' (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.

Blaserna 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 BO 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 electrical oscillations.

250 MUTUAL AND SELF INDUCTION.

By the help of the same apparatus Blaserna 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

B

FJG. 92.

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 I', arranged as a shunt on the coil. The break in the battery circuit at p was so arranged that each time the current was fully established before being broken again. The break in the

MUTUAL 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 f ally 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.*