The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 31 of 35

Hence we have the following classification of transformers, understanding by this term any electrical arrangement con-

THE INDUCTION COIL AND TRANSFORMER. 517

sisting of two conducting circuits, both linked with a magnetic circuit, and in which the variation of current in one circuit gives rise to a production of electromotive force in the other : —

1. Transformers may be —

(a) Iron core transformers, with core wholly or partly of

iron;

(b) Air core transformers, with core wholly of non-

magnetic substance. Iron core transformers may be —

(c) Closed iron circuit transformers, with core wholly of

iron;

(d) Open iron circuit transformers, with core partly of

iron.

Transformers may be used —

(e) To transform a potential difference in a constant ratio,

called constant-pressure transformers ; (/) To transform a current strength in a constant ratio,

called constant-current transformers. Transformers may be employed —

(g) To raise pressure or current, called then step-up

transformers ; (li) To lower pressure or current, called then step-down

transformers.

The above is not a complete or exhaustive classification, but is sufficient to mark out broadly the various forms of the apparatus.

In whatever form it is used, the primary current must give rise to a variation of the magnetic induction in the core, and this in turn gives rise to an electromotive force in the secondary circuit.

The transformer or induction coil can evidently be operated either by intermittent, continuous, or by alternating currents. Whichever mode is adopted, the instrument is, of course, essentially and merely an energy-translating device. The current passing through the primary circuit magnetises the core. The intermittance or reversal of the primary current causes a variation or reversal of the magnetisation of the core. The variation or reversal of the magnetic induction in the core creates an electromotive force in the secondary

sis fna INDUCTION COIL A~$D

circuit which is linked with it, and this sets up a secondary current in the secondary circuit if it is closed. The energy supplied to the primary circuit partly reappears in the secondary circuit, and the difference is represented by energy losses, called the copper losses, caused by the resistance of the conducting circuits, and partly by energy losses in the core, called the iron losses, and due to the hysteresis and eddy-currents set up in it.

The complete examination of the transformer involves, therefore, a knowledge of the manner in which the variation of the primary current, the magnetic induction in the core, the secondary current, and the secondary terminal potential difference is taking place when a certain assigned and varying primary terminal potential difference is created. It involves, also, a knowledge of the magnitude of the energy losses above described, and of the efficiency of transformation or the ratio between the power given to the external secondary circuit and the power given to the primary circuit. In addition to this, the relation of the values of the primary and secondary currents, and the primary and secondary terminal potential differences, for various states of the transformer from no load to full load, has to be ascertained. The following is, then, a summary of the operations going on in the transformer or induction coil which must be known before we can consider the action as fully understood ; and the problem of transformer construction is to predetermine these variables from certain data, so as to foretell the result of construction. Given a potential difference created between the primary terminals of the transformer following any assigned law of variation, we shah1 have the following effects taking place as a conse- quence, and the practical problem is to determine or predeter- mine their mode and magnitude.

(1.) We have a primary current in the primary circuit following a certain mode of variation in strength, and causing a definite copper loss in the primary circuit ;

(2.) A magnetic induction in the core following a definite mode of variation, and having a certain magnitude at every instant, this magnetic induction causing, by its variation, iron core losses due to hysteresis and eddy currents in the iron core :

THE INDUCTION COIL AND TRANSFORMER. 519

(3.) A secondary current and secondary terminal potential difference following some definite law of variation and accom- panied by a copper loss in the internal secondary circuit due to its resistance and a contribution of power to the external secondary circuit.

The transformer problem in all its completeness would be solved if we could in all case predetermine the above effects from the known primary potential difference. This, however, is not capable of being effected in a perfect manner, for reasons presently to be stated.

In early discussions of the transformer problem it was customary to make arbitrary assumptions as to the mode of the variation of the currents, the induction and potential differences. These artificial assumptions did not, however, assist real knowledge. The only useful method is to endeavour, in the first place, to ascertain what does go on inside the transformer, and then, on the basis of this analysis, to construct as far as possible a true working theory of the transformer. We have accordingly abandoned all discussion of imaginary transformers with air cores and currents and inductions, which are simple sine functions of the time and base, for such theory as we are able to build up on an actual knowledge of what does take place in the transformer. The only scientific method of treating the problems involved is, we repeat, first to endeavour to ascertain what are the actions really taking place, and to make them the basis for further reasoning.

§ 2. The Delineation of Periodic Curves of Current and Elec- tromotive Force. — The method which has proved most fertile in enabling us to understand the operations taking place in the transformer is that which consists in graphically repre- senting the form and relative position of the curves of periodic current and electromotive force in the two circuits and deducing that of the magnetisation of the core. When the primary electromotive force is an alternating one, derived from a single alternating-current dynamo which is accessible, the method of obtaining a graph of the various periodic quantities required is some modification of the arrangement

520 THE INDUCTION COIL AND TllANSFOBMER.

first suggested by Joubert,* in which a circuit is closed for a very short but assigned period during the phase, and puts some electrical instrument intermittently into connection with the circuit, so that it reads, not the mean-square value of the current or potential difference, but the instantaneous value at the assigned instant. The modern method of delineating transformer curves is as follows :

Let the ordinates of the periodic curve in the Fig. 168 represent the varying potential difference between two con- ductors connected to an alternator, and let a condenser be connected across the circuit in series with a switch. If the switch is permanently closed, the condenser has a flow of current into and out of it, and the potential difference of its

FIG. 168.

terminals varies periodically. If, however, the switch is closed intermittently at intervals which are equal to the periodic time of the alternator, then the condenser has a series of short con- tacts made with it, and its terminal potential difference is equal to the instantaneous value of the periodic potential difference of the circuit corresponding to the instant when the contact is broken. The difference of the potentials of terminals of the condenser has then to be determined. Several methods may be adopted. The condenser plates may be connected to the terminals of an electrostatic voltmeter, and the potential difference of the condenser plates thus determined. The con- denser may be discharged through a galvanometer, and the

• Comptcs Rendus of the Academy of Science, France, Vol. XCL, July, 1380, p. 161.

THE INDUCTION COIL AND TRANSFORMER. 521

condenser plate discharge determined by the quantity of the charge found in the condenser. We can thus charge the condenser by a series of contacts made with the circuit, for a very short time, always at the same position during the com- plete cycle or period of the varying potential difference. The condenser acquires, after a short time, a potential difference between its terminals which is exactly equal to that of the instantaneous value of the potential difference of the circuit at the instant, when the contact is made. If, instead of connect- ing the condenser across the circuit, it is connected to the extremities of a suitable non-inductive resistance inserted in any alternating - current circuit, we can obtain from its terminal potential difference the instantaneous values of the periodic current.

We have next to consider the various practical details of the process. If the alternator is accessible, or if a single alternator is providing the current, then the intermittent contact may be made by an apparatus fixed on the shaft of the alternator. If the alternator is not accessible, and if the primary potential difference is derived from a battery of alternators running in parallel, then it is necessary to operate an intermittent contact by means of a synchronous alterna- ting-current motor, driven from that part of the circuit which is accessible. As this last method is capable of so much more general application than that of the contact-maker driven off the shaft of the alternator, we shall describe in some detail the arrangement of a suitable motor and associated apparatus. In addition to tbe early experiments by Joubert above mentioned, the delineation of periodic curves of current and electromotive force by means of an intermittent contact on the shaft of the alternator was suggested and carried out by Dr. Louis Duncan, and experiments by this method were effec- tively conducted by Messrs. Duncan, Hutchinson and Wilkes, and also by Prof. Eyan hi the United States.* It has also been largely employed by Dr. J. Hopkinson, M. Blondel, by

• See a Paper by Messrs. Duncan, Hutchinson and Wilkes in the Electrical World of New York for March, 1888, referred to in The Electrician, Vol. XXL, p. Ill, June 1, 1888. Also see Prof. Harris J. Kyan on Transformers in the Transactions of the American Institute of Elec- trical Engineers, Vol. VIL, January, 1890.

522 THE INDUCTION COIL AND TKANSFORMER.

the author, and by many others for alternating current researches. The general arrangement of the apparatus required for the complete study of the periodic quantities in a transformer, under any circumstances, is as follows : — The principal instrument required is a small alternating-current synchronous motor. A suitable form has been devised and used by the author in investigations of this character,* and a view of it is shown in Fig. 169 on next page.

The general details of the machine are as follows: — The motor, as constructed by the author, consists of two sets of field magnets, MM, which are secured to two cast-iron discs. Between these field magnets revolves a small armature, A, the iron core of which is formed of a strip of very thin transformer iron, wound up into a ring, the armature coils being wound upon this ring. The armature coils are joined up in series with one another, so as to give a series of contrary polarities round the iron ring. The diameter of this armature is about Gin. The field magnets have eight poles, and the armature eight coils. The field-magnet cores are bobbins about 2in. long and l|in. in diameter, and when joined up in series in the proper manner the field magnets take a current of about 4 amperes to give them the proper amount of saturation. The armature is carried upon a hard wood boss fixed to a steel shaft. This steel shaft is carried through small ball bearings like bicycle bearings, the shaft being borne upon seven or eight balls carried in gun-metal cells. In order to prevent any side shake of the armature, there are at the opposite ends of the base cast iron pillars with a gun-metal screw at each end, against which the rounded end of the shaft bears. The shaft can thus be adjusted with great nicety, and runs with great freedom from friction. The ends of the armature coils are brought to two small insulated collars, fixed on the shaft, against which press two light brass brushes, marked B B, kept gently against the collars by means of an expanding steel wire, W. On the armature shaft is an ebonite disc, which carries a transverse steel slip let into it. Two insulated springs, S S, are carried upon a rocking arm, H ; the rocking arm can be traversed over through half a

• See The Electrician, Vol. XXXIV., p. 460, February 15, 1895, " On the Delineation of Alternating Current Curves."

THE INDUCTION COIL AND TRANSFORMER. 523

circumference, and is centred upon the gun-metal end screw, which prevents side shake in the shaft. A pointer and

graduated scale, G, enables the exact angular position of the contact springs, S S, to be determined.

524 THE INDUCTION COIL AND TRANSFORMER.

One of the springs, S, is carried on a small adjusting screw, so that one spring can be given a little lead over the other, and in this manner the duration of the contact made when the steel transverse piece passes underneath and electrically con- nects the springs S S is determined. By means of a set screw the springs can be lifted off from the ebonite disc, and their pressure also adjusted. This little synchronising motor with its attached contact-breaker forms the apparatus for determin- ing the form of the current and electromotive-force curves. The motor is started in step with the alternating current flowing through the armature coils by passing round the end of the steel shaft which projects at the end opposite to the contact-breaker a tape or thin leather strap sprinkled with rosin. To start the motor the following arrangements are made : — The field magnets are excited by current obtained from a small secondary battery, or from any other constant source of continuous current. The armature circuit requires about 2 amperes to make it run properly. Let us assume that the potential difference curve is to be taken from two 100 volt alternating-current mains which come into a building. The armature of the motor is joined across these mains in series with two or three incandescent lamps placed in parallel. The field magnets being excited in the proper direction by a con- tinuous current from a few secondary cells, the operator passes the strap or tape half round the shaft, and by pulling on one side of the tape the motor can gradually be set in rotation with an increasing speed. If the frequency of the alternating current is, say, 100 c\j , then the 8-pole motor has to be brought up to run at something approaching to 1,500 revolutions per minute before it will drop into step ; but at a certain speed the incandescent lamps in series with the armature begin to blink, and by a little skill in adjusting the speed by suitable pulls on the tape the motor will drop into step and continue to run in synchronism with the circuits. If the springs are then put down gently upon the revolving contact piece, a contact is made from one spring to the other at an assigned position during the phase of electromotive force, depending on the position of the rocking arm. If the maximum electromotive force to be read does not exceed 160 volts, then by far the most convenient instrument to employ

THE INDUCTION COIL AND TRANSFORMER. 525

for reading the electromotive force, and the one which has been constantly employed in these tests, is Lord Kelvin's vertical or horizontal pattern multicellular voltmeter. As these volt- meters only begin to read at about 60 or 80 volts, it is necessary to add a constant electromotive force in series with them, and this is done by employing a set of small secondary cells. About fifty cells in one tray form a convenient arrange- ment, provided they have contacts at every cell, so as to take off any required electromotive force. The battery is joined up in series with the electrostatic voltmeter, and the terminals of the voltmeter are short-circuited by a condenser having a capacity of about half a microfarad. This arrangement of volt- meter and battery is then connected across the two points between which the potential is to be determined through the two springs S S. The motor being started, the needle of the voltmeter takes a certain deflection, which is due to the electro- motive force of the cells, plus the value of the difference of potential between the mains at an instant depending upon the position of the rocking handle. By blocking up the voltmeter in this way, and using more or less cells as required, so as to add a known amount to the electromotive force to be measured, the electrostatic voltmeter can be employed to measure potential differences over the whole range varying from zero to 160 volts in either direction. These observations are taken at equal short intervals as the rocking arm H is swept over through a quarter of a circle. It is possible to thus measure the instantaneous values of the alternating potential difference between the two points at equi- distant instants throughout the phase. It has been found by experiment that this small alternating-current motor, when working on the circuits of any alternator of a size such as would be used in a generating station, does not sensibly affect the form of the curve of electro- motive force. The motor is only used as a means of making the contact with a voltmeter at an assigned instant during the phase. The current which passes through its armature is not in any way measured or taken account of ; the motor simply acts as a synchronising arrangement, which connects the contact-breaker electrically to the distant alternator.

The synchronising motor can, therefore, be set to run in step with any alternating-current circuit, and to make a

526 THE INDUCTION COIL AND TRANSFORMER.

contact or close a circuit for a short instant during every period at an assigned instant in the phase, which depends on the position of the rocking arm carrying the contact- making springs.

This apparatus may be employed to determine any of the curves of current or potential of a transformer, as follows : — Let us suppose the transformer is one intended to be operated with a primary terminal potential difference of 2,000 volts, and that the secondary terminal potential difference is 100 volts. Across the primary terminals of the transformer a non- inductive resistance is connected, which is divided into two sections in the ratio of 1 to 19, and in series with the primary circuit of the transformer is placed another non-inductive resistance having such a magnitude that, when traversed by the primary current of the transformer, it will create a fall of potential of about 100 volts. The synchronising motor is then suitably arranged to be operated from the same circuit which supplies the primary current for the transformer, and the armature circuit of the motor may be fed through a step- down transformer, which reduces this circuit pressure to a convenient magnitude.

The motor contacts are then arranged to close the circuit of a voltmeter, which is placed across one or other of the resistances. It is found necessary to connect a condenser across the termi- nals of the voltmeter to increase its capacity, or else the leakage of the voltmeter in the intervals between the moments when the contact is made causes irregularity and uncertain deflections of the instrument. The process of getting the complete set of curves of current and electromotive force of a transformer is then as follows : The curve of primary potential difference is obtained by connecting the voltmeter through the motor contacts across the smaller section of the divided resis- tance which bridges over the primary terminals. The motor being started, the voltmeter will read a potential difference, which is one-twentieth of the whole primary potential diffe- rence, and if the rocking arm of the motor is moved over step- by-step the indications of the voltmeter will successively give the values of this fraction of the primary potential differ- ence corresponding to the different intervals of the whole period.

THE INDUCTION COIL AND TRANSFORMER. 527

In the same way the curve of primary current can be obtained by connecting the voltmeter circuit across the termi- nals of the resistance inserted in series with the primary circuit of the transformer. The curves of secondary potential difference and secondary current, if necessary, can be obtained by connecting the contact-maker and voltmeter across the secondary terminals of the transformer when closed by a known non-inductive resistance.

The curves of current and potential thus obtained can be set down in a chart, the horizontal abscissae in which repre-

4000

1

..

/~

••

^0

)0

\

,

• • *

//

20(

\

)Q

\

1

*9

100

0

A

."

."

.1

^

(

V-

\

^

•

7

S

%

.

3

\ \

•

.

1

100

°:

\

\

•

•

/

0

w

20(

)0

%

^

' /

/

4.QOO

30

DO

•••.^

••

\

^

/

"f

0 30 60 90 120 150 18

0 210 2^

0 970 300 33

o se

FIG. 170. — Primary Current, Primary Terminal, Potential Difference, ind Induction Curves of Ganz 10 H.P. Transformer taken off a Kapp Alternator by the Alternating-current Curve Tracer.

sent fractions of the complete periodic time, and the vertical ordinates represent the instantaneous values of the potential differences or currents.

In Fig. 170 is shown a set of curves taken from a Ganz transformer connected to a Kapp alternator. The dotted curve marked volt curve is the curve of primary electromotive force,

628 THE INDUCTION COIL AND TRANSFORMER.

or difference of potential at the primary terminals of the transformer. The dotted curve marked current curve is the curve of primary current, and the dots show the actual posi- tion of the observations. The figures on the horizontal line indicate degrees of phase. The scale on the left-hand side is the scale of volts, and that on the right-hand side the scale of current. From the curves of current and potential differ- ence we can obtain the curve of magnetic induction in the core as follows : — Let b be the induction density in the iron core — that is, the number of lines or unit tubes of induc- tion per square centimetre of cross-section of the core. This induction density will not in general be the same in all parts of the core or the same at full load as at no load. If, in the first place, we consiJer the case of the transformer when the secondary circuit is open, we have a definite relation between the current and the primary circuit, the magnetic induction in the core, and the primary terminal potential difference or electromotive force at any instant. Let i be the instantaneous value of the current in the primary circuit, e the instantaneous value of the primary potential difference, and b the induction density in the core. If Nx is the number of turns of the primary circuit, B the resistance of the primary circuit, and S the area of cross-section of the core, then from the ordinary current equation for inductive circuits we have the relation

1 dJ or b =

In most cases of closed iron circuit transformers, the second term or integral on the right-hand side of the last equation is a very small quantity compared with the first term, and may be neglected. Hence when/id* is small we can obtain the value of b by integrating the primary E.M.F. curve, or by finding the value offedt between proper limits. Take, for

THE INDUCTION COIL AND TEANSFOEMEE. 529

instance, the case of the Ganz transformer, the curves of which are given in Fig. 170. The resistance of the primary circuit E is 2-5 ohms and the maximum value of the primary current i is nearly 0-34 amperes. Hence the value of Rz never exceeds 0-85 of a volt. The value of e, the primary electromotive force, varies from 0 to nearly 3,000 volts, and hence at any instant, except very near the moment when e is zero, the value of R i is quite negligible compared with that of e.

In order to obtain the induction curve we have to integrate the curve of primary electromotive force, and to do this properly the following procedure must be followed. The whole area included by the primary E.M.F. curve must be obtained, and the integration of the curve must be started from that point on the horizontal axis which corresponds with the bisection of the area of the E.M.F. curve. Starting from this point the area of the E.M.F. curve is obtained by successive increments, and corresponding to the limit of each increment an ordinate is set up whose length on some scale is proportional to the whole area of the E.M.F. curve measured from the abcissa corresponding to the semi-area of the curve to the limit considered. This ordinate will then be an ordinate of the curve of induction. In making this integra- tion the area of the E.M.F. curve below the time axis must be reckoned as negative. To obtain the absolute value of the induction at any point, the area of the E.M.F. curve must be reckoned out in volt-seconds and then divided by the value of Nj S, S being measured in square centimetres. The result must be multiplied by 108 to reduce to G.G.S. measure and give the induction density in C.G.S. units.

In this manner the firm line curve which is marked induc- tion curve in Fig. 170 was obtained. If the curve of secondary terminal potential difference has been obtained, we can, by a similar integration of this curve, obtain another induction curve which is generally practically identical with that obtained from the primary E.M.F. curve if the transformer secondary circuit is unloaded, but which does not agree with it if the secondary circuit is closed and a secondary current is being produced therein. Into the causes of this we shall enter later. The full set of transformer curves for the currents,

MM

530 THE INDUCTION COIL AND TRANSFORMER.

potential differences and induction constitutes what may be called the indicator diagram of the transformer, and shows us all that is going on inside. The quick description of these curves becomes, therefore, an important matter. Many investi- gators have devised methods for expediting this process. One effective method was described by M. A. Blondel* in 1891. M. Blondel employs a rotating contact-maker with two brushes, and the contacts are so arranged that a condenser is periodically charged at a certain moment during the complete phase of the potential and then immediately afterwards is discharged through a galvanometer. The two brushes are fixed to an arm movable about an axis co-axial with that of the revolving motor or alternator, and this brush holder is revolved by clockwork at a regular rate. Hence the galvanometer indicates a current which is varied as the brush holder rotates. If the brush holder is held at rest, the galvanometer has a series of rapid charges from the condenser sent through it, and takes a steady deflection. If the brush holder rotates, this deflection varies from moment to moment, but at any instant is pro- portional to the instantaneous potential at which the condenser is being charged. If a mirror d'Arsonval galvanometer is employed, and the image of an illuminated opening thrown on a photographic scale which is moved transversely to the motion of the spot of light, a photographic trace of the alter- nating-current curve can be obtained. By using a pair of contact-makers and two galvanometers the current and E.M.F. curves can be delineated at the same time. Such a photo- graphic record of the current and E.M.F. curve for an alternating-current arc lamp worked off a Meritens alternator is shown in Fig. 171.

A very similar arrangement has been described by Messrs. Barr, Burnie and Eodgers.f These investigators employ a revolving contact -maker of a particular kind. It is thus described by them : The shaft of the alternator or motor is fitted with a contact-making disc, and the contact brush is moved slowly and continuously through its successive angular positions. Contact is thus made each time at a slightly

• See La Lumiere Electrique, September 12, 1891, and September 16, 1893 ; also see The Electrician, Vol. XXVII., p. 603. t See The Electrician, September 27, 1895.

THE INDUCTION COIL AND TRANSFORMER. 531

different position of the armature. Thus the potential difference at each contact differs slightly from that at the preceding contact. This potential difference is used to charge a condenser across the terminals of which is connected either a reflecting electrometer or a high-resistance galvanometer.

The deflection of the instrument so used follows the value of the potential difference of the wave form to be determined, and accurately follows it, for the mean rate of variation of the potential differences between the terminals of the condenser is exceedingly small in comparison with the rate of change of the electromotive force to be investigated.

FIG. 171. — Photographic Trace of Current Curve I and Electromagnetic Force Curve E of an Alternating Current Arc Lamp.

Fig. 172 shows the arrangement of the contact disc and accessories, a galvanometer being used, but for which an electrometer might be substituted. In this diagram, for the sake of clearness, the vulcanite foundation work is omitted and the brass only shown. ~Dl is the contact disc, with knife edge a'ad contact brush, which is rigidly fixed to the shaft of the dynamo or motor. The rings D.2 and D3, and the rods and brushes Bj and B4, are mounted on a vulcanite sleeve loose

M M 2

632 THE INDUCTION COIL AND TRANSFORMER.

upon the shaft, and are revolved slowly. The brush Bj is joined to the ring D2, with which the brush B2 is in permanent connection, so that when the brush B! makes contact with the knife edges the condenser G is charged to the potential difference between the terminals T^ T2. The condenser is throughout the whole revolution of the disc Dx discharging through the galvanometer G by way of ~Blt B4, B5, and the resistance K.

As the brushes Bj and B4 are moved slowly round, a suc- cession of charges passes through the galvanometer, the value of each of which is proportional to the potential of the con- denser— that is, to the potential difference of the points Tlt T2. This contact apparatus, in fact, performs the operation of

FIG. 172.

charging a condenser at a definite instant during the period at the terminals Tx and Ta, which are the terminals of the alternating-current circuit under investigation, and then immediately afterwards discharges this condenser through a galvanometer. The galvanometer, therefore, gives a steady deflection which is proportional to the instantaneous potential difference between the points T! and Ta at the instant corresponding to the moment when the contact with the condenser is broken.

The rapidity with which the curves of instantaneous potential can be determined depends to a large extent upon the perfection of the insulation of the condenser and voltmeter.

TEE INDUCTION COIL AND TKANSFORMEB. 533

If these leak to any sensible degree they lose charge in the intervals between the contacts, and the resulting permanent deflection is too small, and the time required for the volt- meter to take its full steady deflection when the place of contact is changed is greatly increased. Hence it is necessary to examine this question of leakage carefully before placing implicit reliance on the voltmeter and condenser actually used.

The value of the instantaneous potential may also be determined by balancing it against some point on a slide wire down which a known fall of potential is created by a battery. The arrangement known as a potentiometer consists of a uni- form fine wire stretched over a scale down which a uniform fall of potential is created by a cell or two of a secondary battery attached to its extremities. If a sliding contact moves over this wire, we can insert between one end of the potentio- meter wire and this slider any source of electromotive force, and, by moving the slider, balance the fall of potential down any length of the slide wire against this other potential difference. If the revolving contact-maker, connected in series with a condenser, is placed across a proper section of a divided resistance, which resistance is across the terminals of the transformer, the contact-maker will close the circuit of the condenser at equal periodic intervals and give it a potential which depends upon the position of the contact of the contact- maker. The potential of this condenser can then be measured •on the slide wire, and, knowing the value of the two sections of the divided resistance, we are able to determine the value of the instantaneous potential difference between the terminals of the transformer.

A revolving contact-maker for determining alternating- current and potential curves has also been devised by Prof. Hicks.* In this instrument the same principle is adopted as in the one just described. A revolving contact-maker connects a condenser intermittently, but at definite instants in the period, to a source of alternating potential, and then in between these contacts discharges the condenser through a galvanometer. The shifting of the brush contacts varies the galvanometer deflection, but so that it is always proportional to the instan-

• See The Electrician, Vol. XXXIV., 1895, p. 698.

534 THE INDUCTION COIL AND TRANSFORMER.