Burg Theatre in Vienna of Eschylus, translated into German by Wilamowitz-Mollendorff, and by the suggestion of the critic Paul Schlenther that modern playwrights should render classic themes in a free fashion. 'Electra' appeared in 1903; and in 1908, in the version of Arthur Symons, it was played in English with Mrs. Patrick Campbell in the title rôle. It has also served as the libretto for an opera by Richard Strauss.

The piece is in one act and dispenses with the classic chorus, partly because this would be counter to our stage conventions, and partly because it would detract from the lyrical fervor of the individual characters. The Sophoclean story of Electra's yearning for the return of her brother Orestes to whom she may confide the task of avenging her mother's murder of her father is repeated, with the weakness of her sister Chrysothemis, the appearance of Orestes as a messenger come to announce his own death, and his slaying of his mother, Clytemnestra, and her paramour, Ægisthus. Von Hofmannsthal, however, has made no effort to achieve the noble dignity of the Greek. Instead, he has sensualized Electra, whose lust for vengeance on her guilty mother becomes hysterical and insane. Hatred, she says, has been her bridegroom; curses and despair have been her children. When Orestes finally ⚫slays his victims, Electra dances in very ecstasy of joy. As an American critic, Mr. W. P. Eaton, has remarked: "Pity and fear are not aroused by von Hofmannsthal's play, but curiosity and horror. The emotions are not purged, but scraped, irritated, made to shiver and creep." The best account of von Hofmannsthal is Dr. August Köllmann's monograph in German (1907); he is discussed in English by Elizabeth Walter in 'Poet Lore' (1915), and by Ashley Dukes in 'Modern Dramatists' (1912).

FRANK W. CHANDLER.

ELECTRIC ALTERNATING CURRENT MACHINERY. A loop of wire revolving in a magnetic field is the simplest form of an alternating current generator. The direction of induced electromotive force in the two halves of the loop, which cut the magnetic flux in opposite directions, is such that the combined electromotive force at the terminals is double that of either revolving conductor alone. This induced electromotive force is proportional to the rate of cutting the magnetic lines, and therefore to the sine of the angle by which the plane of the coil differs from the plane midway between the poles and normal to the magnetic flux. At its zero position, or when the planes coincide, the coil is cutting no lines of force and we have sine a=0. The electromotive force, however, grows as we depart from this zero position, assuming uniform speed, until, when 90 degrees is reached the rate of cutting of the lines becomes a maximum, sine 90 degrees 1. Passing on, the electromotive force dies away until 180 degrees is reached, when the value again is zero. From this to 270 degrees we have an increasing electromotive force, but of opposite polarity and at the end of the revolution, or 360 degrees, again reach zero. Thus we have in one revolution in a two-pole field two waves of pressure of the same form but of opposite sign. The one is called the positive wave and the other the negative. One such

revolution, or one positive wave and one negative wave, constitute what is called a cycle, or period, which in technical literature is designated by the symbol one sine wave. The great majority of systems have a frequency between 60 and 25. Both of these frequencies are standard practice in this country, and the values between are chosen for special cases. Owing to the high frequency of commercial systems, alternators are built with more than one pair of poles, in order to keep the revolving speed within reasonable limits.

Average and Effective Values. If we plot the values of the instantaneous pressures as ordinates, with time as abscissa, we have a correct representation of the generation of alternating currents, and the shape of the wave. When the total number of lines cut per revolution by a coil revolving at constant speed remains the same, the average induced electromotive force remains constant, regardless of the distribution of the magnetic flux. The effective value, however the value read by the metre and the value which corresponds in its heating effect to the direct current value is not independent of this distribution.

The Place of Alternating Current Systems. The direct current for the railway at 550 volts, and for the lighting and power systems of the densely populated centres of our large cities in the Edison three-wire system 110 to 220 volts, seems to have become standard practice. Nevertheless the low radius of distribution without excessive cost of copper, even in the 550volt railway system with a grounded return, makes necessary a great multiplicity of moderate-sized or small plants, operating at low efficiency. It is here that the alternating current comes to the front. While commutators (q.v.) can be built for collecting direct current for 1,000 volts, alternators can be built for 12,000 volts and step-up transformers of high economy are quite possible at 75,000 to 100,000 volts. Remembering that the copper cost is inversely as the square of the voltage, the great possibilities of the alternating current system are at once

seen.

Energy from Waterfalls.-Electrical energy from waterfalls that a few years ago were merely points of scenic interest is now supplied to hundreds of cities in North America. There are numerous power plants of from 50,000 to 200,000 horse-power capacity, sending currents with voltage from 25,000 to 150,000 to distances up to 250 miles. See HYDRO-ELECTRIC DEVELOPMENT and ELECTRIC TRANSMISSION OF ENERGY.

The Alternator.- Small alternators and those of moderate potential usually collect their current from insulated rings mounted on the shaft and connected to the ends of the armature winding. Through brushes, the current is taken to the external circuit. In some machines a rectifier is added for supplying sufficient undimensional current to produce the necessary additional field to overcome the drop due to increase of load. All commercial alternators are supplied with an exciter, or direct current dynamo, whose function is to supply current to the field windings. The field spools are usually connected in series. The amount of current thus necessary on a full non-inductive load varies from 1 to 3 per cent of the total output of the alternator. Owing to the difficulty of collecting

large currents by means of brushes and of preserving good insulation between the rings and shaft, the revolving field type of machine is now used in almost all large installations, the field current from the exciter being supplied through cast-iron rings mounted on the shaft, or in the case of the inductor type, consisting of an annular ring surrounding the inductor or revolving element, which consists of laminated iron poles suitably spaced and keyed to the shaft. The windings being stationary, there are no moving connections, either for the field current or the main current of the machine. In either type the alternating current is taken from the terminals of the windings, usually at the bottom of the frame.

Polyphase Machines.-If two armatures, of the same number of turns each, be connected to the shaft at 90 degrees from each other, and revolved in a bi-polar field, and each terminal be joined to a collector ring, we have two separate electromotive forces differing in phase by 90 degrees or a two-phase machine. With 120 degrees phase difference and three sets of armatures we have a three-phase winding. By properly interconnecting the three circuits, we may use but three wires for transmission, or four, in accordance with the system used. The construction of multiphase machines is similar to that of the single-phase type, excepting that in the former we have as many armatures, series connected, as there are phases.

In the two-phase three-wire system, the wire from the common junctions of the phases carries 1.414 times the current of the outer wires. The electromotive force between the outer wires is also V2 E, when E is the electromotive force per phase, or between either outer wire and the common return. When this system is used it is important that the load be carefully balanced on the phases and that the power factor be kept as high as possible in order to keep the voltage on the phases nearly alike at the receiving end. Single phase motors or lamps may be connected to either or both phases, but it is very important that no load be connected between the outerwires, as the effect is to badly unbalance the voltages on the different phases.

In the three-phase star connected system the line voltage is V3-1.732 times the voltage on the coils of the machine, or the machine voltage, which is the pressure between any one of the three line connections and the common neutral. The line current in this system is the current that flows through any one of the machine windings. In the delta connection, the line voltage is the same as the voltage across any phase of the machine, while the line current, being the resultant of two currents, is V3=1.732 times the current flowing through any phase of the machine.

Energy Polyphase. In a two-phase circuit, whether three or four wire, the energy flowing is the sum of the products of each phase current by the phase pressure. Two wattmeters are used. In the three-phase system when E volts between lines; I= amperes on lines; W= total watts output of machine, then, whether the connection be star or delta, the total 3E X 1 output is 1.732 EI, always supposing V3 the system be balanced. Thus the output of the

machine is not changed by changing the connections from star to delta. In the balanced three-phase system, one wattmeter will register the total output if its constant be multiplied by 1.732. Two wattmeters are usually employed.

Regulation of Alternators.-The regulation of modern alternators varies from 5 to 6 per cent, which means that in case the full, noninductive load of an alternator be taken off, the speed and excitation being kept constant, the terminal pressure will rise by an amount corresponding to from 5 per cent to 6 per cent of its full load voltage. Close regulation means a much better voltage-regulation on the system and stronger synchronizing power. A certain amount of armature reaction is necessary to avoid large cross currents on changing the field of one or more machines operating in parallel, in the attempt to preserve the same terminal voltage. The efficiency of large alternators is about 96 per cent to 97 per cent.

Frequency. In regard to the frequency best adapted to transmission work, or to local distribution, various factors enter into the problem. At 60 both arc and incandescent lamps can be operated satisfactorily. The transformers are smaller and cheaper than at 25 ~ and motors are very satisfactory both as to low first cost, range of speed, and good starting torque (q.v.). Frequencies over 60 have been abandoned. The line drop, due to reaction, increases with the frequency: a change of frequency from 25 to 125 ~ would, on the same line, more than double the line drop. While a rule 60 ~ apparatus is cheaper than that for 25 yet the increase in polar speed often becomes difficult without increasing the number of poles to an undesirable extent, which, in 60 apparatus, may be sufficient to make the parallel operation of low speed direct-connected alternators quite difficult.

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Self-induction.- When a current is introduced into a circuit a magnetic field is produced, surrounding the conductor, the rise of which causes a counter electromotive force. This electromotive force is called the electromotive force of self-induction. The effect of self-induction upon electric currents is directly comparable to the effect of inertia on a material body. It is that quality that tends to hinder the introduction, variation or extinction of the current in a circuit. As this effect is greatest at times of most rapid change of magnetism set up by the current, in alternating current circuits, it becomes a maximum when the inducing current is passing through zero, and, therefore, the counter electromotive force of self-induction lags 90 degrees behind the current in the circuit. It also follows the sine curve provided the current flowing is sinusoidal.

In a circuit containing several impedances in series, the joint impedance is not the sum of the individual impedances, but is obtained by taking the square root of the total added reactances squared plus the total added resistances, squared. That is, Impedance

pedance and its reciprocal amount will give the reciprocal of its length. For more than two, the method of the polygon of forces is applied. The effect of self-induction varies with the frequency of the current supplied, and as the square of the number of turns in a circuit. The self-induction in the armature of an alternator has two effects. The first is to produce a lagging current and thus lower the terminal voltage, and the second is a demagnetizing effect. The current is thrown into such a phase that it produces lines of force directly opposed to the field and thus lowers the voltage by reducing the total flux. The effect of armature reaction depends upon whether the current is leading or lagging in phase. A lagging current lowers the voltage of an alternator and a leading current raises it.

Capacity. All insulated conductors have the quality of being able to hold, stored on their surfaces, a certain quantity of static electricity, and are thus condensers. The charging and discharging of an alternating current circuit causes the current to flow from the generator into the line and then back into the generator again, with the frequency of the alternator, in order to keep up the static potential on the line. As this charging current is greatest when the rate of change of electromotive force is greatest, a sinusoidal wave of capacity electromotive force with 90 degrees difference in phase from the machine electromotive force is produced. This leads the active electromotive force by 90 degrees and is thus directly opposite to the electromotive force of self-induction. If we have a circuit in which the electromotive force of self-induction is just equal to the capacity electromotive force, and these two parts of the circuit are in series, the effect of both is neutralized and we have, as in direct currents, W=EXC.

The Transformer.- The one piece of apparatus that more than all else has made possible the electrical transmission of energy to long distances is the transformer. This is the apparatus that receives in one set of coils the dangerous potential of the line and transforms it into whatever potential is desired for lights or motors, which are supplied from an entirely separate winding. The transformer consists of a magnetic circuit of laminated iron or mild steel interlinked with two electric circuits, one, the primary, receiving electrical energy and the other, the secondary, delivering it to the consumer. The effect of the iron is to make as many as possible of the lines of force set up by the primary current cut the secondary winding and there give rise to an electromotive force of the same frequency, but different voltage.

Not only does the transformer make possible the transformation of voltages, but it also permits of changing from one system to another. Thus a single-phase primary may supply a three-wire Edison system, of course, with alternating current. A two-phase system can be changed to a three-phase or vice versa; a four-wire two-phase may make a three-wire two-phase, and many other useful combinations may be effected. The Scott connection for changing two-phase to three-phase, or the opposite, uses but two transformers. One has a ratio of, say 10 to 1, with a tap at the middle

of its secondary coil. The other must then have a ratio of 10 to .866-10 to V. One terminal of the secondary of this transformer is connected to the middle of the other secondary, and the remaining free ends of both secondaries form the three terminals of a three-phase circuit. The value V is the altitude of an equilateral triangle of which the base is unity, and thus we may consider the current to be taken from the corners of an equilateral triangle, which represent, in phase and potential difference, a true three-phase system. The current in the transformer of secondary, .866 being the resultant of the other two-phases, is greater than under normal two-phase conditions; and, therefore, the windings must have about 15 per cent more copper. If two similar transformers are used the secondary of each has taps giving 50 per cent and 86.7 per cent of full voltage. In many large installations, notably at Niagara Falls, we find two-phase generators feeding three-phase lines through Scott connected stepup transformers. In small systems standard transformers may be used having ratios of 10 to 1 and 9 to 1 respectively, and the results will be quite satisfactory.

The Induction Motor.- Acting upon the well-known fact that a copper disc could be made to revolve by rotating a horseshoe magnet so that the lines of force cut the disc, Ferraris, Tesla, Dobrowolsky and others have developed the present type of induction motor. The credit for the first commercial application of the rotating field caused by currents of displaced phase probably belongs to Tesla. At the present day the value of these discoveries in the transmission and distribution of power can hardly be estimated. The induction motor is somewhat similar to the direct-current shunt motor. Both motors have field and armature windings. In both cases, also, the field is connected directly across the mains. In the shunt motor the armature current is supplied through brushes and a commutator to the windings, while in the induction motor the armature current is an indirect current, the field acting as the primary of a transformer of which the armature is the secondary. In both motors the efficiency is inversely proportional to the armature resistance, as is also the speed regulation of the motors. The less the armature resistance the higher the efficiency and the closer the regulation of speed between no load and full load. In practice, either element may be the one to revolve. The rotation is produced by the reaction of the armature, or indirect current, on the revolving magnetic field, which results in dragging the moving element around in order to keep up with the field flux, as it passes around the face of the primary windings. This field, being the resultant of two or more alternating fields of different phases, rotates with the polar frequency of the supplied voltage. The secondary winding is made up of copper bars set in slots in a laminated iron core and running across the armature parallel with the axis of rotation. This separating of the old copper disc into narrow bars constrains the current to flow into the best direction for producing torque and avoids the waste of the unconstrained Foucault currents in the Arago disc, and thus makes the motor much more