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Fundamentally, electric motors are electric generators reversed in function: they convert into mechanical energy the continued stresses between two electro magnetic fields relatively movable, just as generators convert into electromagnetic stresses the mechanical energy applied to them. Since no transformation of energy is ever absolutely quantitative, the conversions just considered are not accomplished without loss of energy to about the same extent in both cases. The sources of this loss are ohmic loss in the conductors, hysteresis, friction of bearings and brushes, air friction and eddy currents; the sum of these losses in large modern machines does not exceed 5 or 6%. The torque of the motor is the dynamical result of the electromagnetic stresses between the magnetic field of the motor and that due to the armature currents, the latter field being proportional to the strength of the current sheet due to the numerical strength of the current and the number of its effective convolutions. This applies to all types of motors, if one remembers that whenever either of these two stress factors is a periodic variable, as in the case of alternating motors, the torque is proportional to their geometrical co-directed product and not merely to their numerical product. At this point it will be convenient to distinguish between the various types of motors. The first broad distinction is between continuous-current and alternating-current motors, a distinction rather of convenience than of necessity, for in point of fact the two depend upon the same broad principles and can be considered on precisely the same lines.

Electric motors may be conveniently divided as follows: - _ (A) Continuous Current. 1. Separately excited.

2. Series-wound constant current.

3. Series-wound constant potential.

4. Series-wound interdependent current and potential.

5. Shunt-wound constant potential.

(B) Alternating Current. I. Synchronous constant potential.

2. Induction-polyphase constant potential.

3. Induction-monophase constant potential.

4. Repulsion-commutating.

5. Series-commutating.

Of these, the series-wound constant potential, shunt-wound constant potential, and polyphase induction motors do a very large proportion of the active work of power transmission: the first mentioned furnish power for electric railways; the second chiefly power distribution from public electric supply stations; while the third are mainly relied upon in long-distance transmission systems. The fourth and fifth groups of class (B) are old in principle but have been slow in practical development. They include many modifications and transition forms not involving radical changes in the principles or properties of the machines. Their chief use has been for electrical traction, with reference to which they have, in the main, been developed, and their performance is best at low frequency, 15 to 25 cycles per second.

In class (A) in general, for a certain value of the torque current must be forced through the armature against the motor electromotive force which results from the rotation of the armature in a given field. This demands a certain greater applied electromotive force to produce the current required, which is determined by the effective electromotive force, equal to the geometrical difference between the applied and motor electromotive forces, and by the impedance of the armature. For steady currents this last is of course the same as the ohmic resistance, just as for steady electromotive force the geometrical and the numerical difference of the applied and motor electromotive forces are coincident. The torque depends, as heretofore noted, on the field strength and the strength of the current sheet due to the current thus determined. For small values of the torque the speed practically depends upon the applied electromotive force and the field, so that if the former and the latter be constant the speed is also sensibly constant. This is likewise the case if the armature resistance be very small; and in general the variations of speed at constant potential are determined by the product of this resistance and the torque, while the absolute speed depends essentially upon the field strength. Motors for low speed or high electromotive force must have both a strong field and many turns upon the armature, so that both the fundamental stresses may be large. As the field is generally strong - to secure economy of iron - low-voltage and high-voltage machines differ principally in the number of armature turns. For variable speed, this latter factor being fixed, field strength and applied electromotive force are the factors easily altered, and most of the speed variation is accomplished by changing one or both of them. Torque, neglecting field distortion, is at a maximum when the current is the greatest possible at the given applied voltage - that is, when the motor is at rest. With a small armature resistance this current is generally far too great for convenience; hence the motors are usually started with a rheostat in series with the winding if the current is not limited by the generator itself. The torque then depends on the sum of the resistances in circuit, and can be made just sufficient to start the motor under the required load. By the same device the motor can run at reduced speed, although with a considerable loss of energy in the rheostat; it is indeed, as a rule, difficult to get effective speed variation in motors of any kind without serious loss of energy. The field can be changed within wide limits only by a considerable increase of the iron in the magnetic circuit, the applied electromotive force cannot usually be varied except by increasing the resistances in circuit, and the number of armature turns cannot be varied without complication, although the effective number can be modified by shifting the brushes, probably at the expense of sparking. Altogether, if the speed variation demanded be more than 15 or 20%, it causes, in one way or another, considerable expense and trouble, particularly if each speed must be closely held irrespective of load. No large change in absolute speed can readily be made without considerable change in the percentage variation of speeds at various loads. Practically, the best results are obtained from motors of very low armature resistance, in which the field or the applied electromotive force, or both, are varied. The whole problem is nearly identical with the production of constant potential or constant current from generators driven at constant speed, and is solved by similar means. For any one absolute speed a generator can be made to give constant potential, nearly irrespective of load, by compound winding. Similarly, a motor may give a very nearly constant speed at constant potential by a differential winding in series with the armature, weakening the field as the armature current rises. This device, however, obviously increases the energy required for magnetization, and decreases the effective torque at starting. Practically, the best continuous-current motors can be made to hold their speed to within T or 2% from no load to full load. Commercial machines, however, generally vary from 5 to To% in speed. With respect to the direction or rotation of a motor, the torque changes sign with a change of sign in either field or armature current, but not with a change of sign in both. The input of the motor is numerically equal to the product of the current and the applied electromotive force, while the output is determined by the product of the current and motor electromotive force; hence the efficiency of the motor as a transformer of energy is the ratio between these two quantities. The output is a maximum when the applied electromotive force is double the motor electromotive force, and the efficiency is a maximum when the motor and applied electromotive forces are substantially equal. At the point of maximum output the speed is that sufficient to reduce the current to one-half its static value. No motor is worked at or near this point, except momentarily, on account of the low efficiency and severe heating in the armature. These theoretical values are slightly modified in practical machines by the small miscellaneous losses subject to independent variations.

The practical output of electric motors is limited in machines of normal design by the temperature they can safely endure. As a rule the working temperature, which is commonly reached only after six hours or more of continuous running, should not rise more than 40° to 50° F. above the temperature of the surrounding air. In case of traction motors and others subjected to occasional severe overloads, separated by periods of rest or of subnormal load, the temporary rise of temperature tolerated may be much higher, say 60° to 75° F., after a run of an hour or so. The temperature of the air is assumed at 70° F. in most cases, and the temperature of the motor-windings is preferably ascertained by the rise in electrical resistance due to the heating. Thermometers can seldom be so applied as to measure the full heating effect.

The actual output obtainable from a motor structure of given dimensions under these conditions with respect to heating depends chiefly upon the practicable rotative speed of the armature, since the chief losses are proportional to the torque, while the mechanical output at given torque is approximately proportional to the speed. Most makers utilize a single structure for several standard motors varying in speed and output, a 15 h.p. machine at, say, 1200 r.p.m. becoming a 10 h.p. at 800 r.p.m. or a 20 h.p. at 1600 r.p.m. There is no practically fixed relation between the rating and the speed, although it is approximately linear, for in winding the same carcass for different speeds the ratings are settled rather by commercial convenience than by exact determinations. Motors generally have approximately the same efficiencies as the corresponding sizes of generators. Small motors, say from 1 to 5 h.p., are commonly of 70-80% efficiency at full load, medium sized machines of 5 to 50 h.p. about 80 to 90%, and the larger sizes run up to 95% or thereabouts. In the effort to get low-speed motors without immoderately increasing the cost they are generally dropped a little in efficiency and allowed to run hotter than if wound for higher speeds.

The weight of motors per h.p. of output is therefore very variable. In machines of medium size and speed it is likely to be 50 to 75 lb per h.p., falling to 30 or 40 in large or specially high speed machines, and rising to 80 or Too lb in small or very low speed motors. High-voltage motors, particularly if small, lose somewhat in relative output on account of the space taken up by the necessary insulation.

In all ordinary motors the magnetization of the iron is, for economy of material, pushed high; and hence the field, even at heavy loads, is fairly stable and the conditions of commutation remain good. When, however, motors are designed to stand severe overloads, or to admit of a wide range of speed regulation by varying the field strength, the commutation is likely to be unstable, and severe sparking may result. To meet this condition the commutating-pole motor - really a recrudescence of an old idea - has been introduced on a considerable scale. In this construction auxiliary pole pieces, excited by series coils from the motor circuit, are set midway between the ordinary field poles. The office of these poles is to neutralize the magnetomotive force due to the armature winding, thus checking field distortion, and also to ensure the proper reversal of the current in the armature coil directly under the brush. Of the total magneto-motive force due to the windings of the commutating pole, the major part, perhaps three-fourths, is devoted to the former work and the remainder to the latter, the proportion varying widely according to the design of the motor. The result of this construction is excellent, sparkless commutation being ensured over a wide range of load and field strength. The commutating-pole motor is intrinsically more expensive and slightly less efficient than the ordinary type, but for the particular kind of service it is designed to perform is extremely effective. It gives promise of especial value in high-voltage traction motors.

(A) 1. Separately excited Motors are interesting principally on account of the very efficient method of speed regulation possible by their use. In this method the field of the motor is excited from the supply mains, and the armature current is furnished by a motorgenerator running at constant speed. A rheostat in the shunt field of the latter element enables the applied electromotive force to be varied to any desired extent, and hence the working motor can be given full torque at any speed up to that assigned by the maximum value of the electromotive force which can be applied to the armature. Moreover, if the armature resistance be small, the motor is fairly self-regulating at all speeds. The effect is rather startling, since the motor may be giving a very great torque when it is merely turning over at a few revolutions per minute; and although the process is complicated, it leads to excellent results, and is widely used where delicate speed regulation is required.

(A) 2. Series-wound Constant-current Motors were early worked to a considerable extent on arc-lights circuits, but have now passed out of use save in a small number of constant-current power-transmission systems on the continent of Europe. In these motors the motor electromotive force is directly proportional to the output, the torque being constant. They will not start with more than a certain definite load, but once started the speed will increase until added work (internal or external) balances the torque. The type is intrinsically bad in speed regulation, and must be treated by the same methods as are adopted to secure constant current in arc machines. The most successful device in most cases is to vary the field strength by shunting the field coils or to vary the number of effective armature conductors by shifting the brushes. Both methods are carried out mechanically rather than by purely electrical means - in the first case by an automatic rheostat, and in the second by an automatic brush shifter, but neither is wholly satisfactory. Nevertheless, such motors have proved capable of excellent commercial service in some of the European plants, especially in the larger sizes.

(A) 3. Series-wound Constant-potential Motors comprise nearly all motors used for electric traction - aggregating not less, probably, than one and a half million horse-power; hence they are of great practical importance. These traction motors are usually highly specialized machines with very powerful armatures and fields strongly saturated at all working values of the current. The brushes have an invariable position. Such motors behave much like separatelyexcited motors, having a rather large armature resistance. Speed regulation has to be obtained by varying the applied electromotive force. In early traction motors this variation depended upon inserting a rheostat; in modern practice it is customary to employ two, or even four, identical motors on each car, operated in series for low speeds and in parallel for full speed. In practice, however, resistances are inserted when necessary, to prevent too sudden changes of speed and to secure intermediate steps between those obtained by the series-parallel connexions. In rare instances a still further variation is secured by the use of a field only partially saturated at ordinary loads.

(A) 4. Series-wound Motors with Interdependent Current and Potential are used only in connexion with generators of similar design, motor and generator forming a dynamical unit. This system is occasionally used with good results in power transmission. Assuming the motor field to be saturated, if the speed is to be constant the applied electromotive force must rise with the load to an amount depending on the resistances in circuit. If the corresponding generator has a field less fully saturated, the increase in current demanded by the increment of torque in the motor can be made not only to raise the applied electromotive force enough to compensate for armature resistance, but for the total resistances in circuit, including the line. With this difference in saturation the motor will automatically maintain constant speed. The fields of the machines need not be designed for a given saturation, since shunting them with a suitable resistance will give the same result.

(A) 5. Shunt-wound Motors at Constant Potential are the mainstay of continuous-current distributions for industrial purposes. At constant potential the field remains sensibly constant and the torque is directly proportional to the current. The motor then behaves much like a separately-excited motor, and the armature resistance being generally very small, the speed is very nearly constant, varying less than 5% from no load to full load in the best commercial machines. Operating on a compound-wound generator, a single motor of this type can be made to regulate with great precision, as in the previous case. If the motor field be only moderately saturated, its strength, and hence the motor electromotive force, rises and falls with the applied electromotive force; and therefore at constant load these motors run at very nearly constant speed, in spite of small variations of voltage. If speed variation be required, it can be obtained to a moderate extent by a rheostat in the field circuit. At starting a rheostat is necessary in the armature circuit. The differentially wound modification is now seldom used.

(B) t. Synchronous Alternating-current Motors. - The simplest starting point in the consideration of this class is the continuouscurrent generator. This machine actually generates within the armature alternating currents; and if the commutator be replaced by two or more slip-rings connected symmetrically to two or more points on the armature winding, alternating currents, monophase or polyphase, according to the number of connexions and the points touched, can be withdrawn therefrom. The simplest case involves only two slip-rings, joined to the winding at diametrically opposite points. Consider two such modified machines as motor and generator. The condition of complete reversibility is that the instantaneous values of the currents, and the instantaneous values of the angular displacements between poles and armature coils, shall be equal throughout. This evidently requires that the rotation of the motor should be synchronous, pole for pole, with that of the generator. Here, as before, the torque depends on the two fundamental stresses, but the torque has no determinate sign in the absence of an initial rotation. The instantaneous value of the torque depends on the instantaneous value of the current and on its angular displacement. The speed of the motor being invariable, its motor electromotive force depends only on the effective excitation, including the armature reactions, and it may or may not, according to the conditions of load, be in phase with the impressed electromotive force. In the case of the continuous-current motor, the motor output is numerically equal to the product of current and motor electromotive force; and since, in the alternating circuit, these quantities are usually not in phase, in alternating motors the activity is determined by the co-directed part of their product. The current in the alternating motor depends, not on the ohmic resistance alone, but upon the impedance and upon the geometrical difference between the applied and motor electromotive forces. At a given applied electromotive force, and an armature impedance assumed constant, the fundamental variables in the motor are the output, motor electromotive force, and motor current. The two last factors are interdependent, so that the current may have a wide range of values, according to the excitation, while the output remains constant, or, itself remaining constant, may cover a variety of values of the power corresponding to different excitations. These changes involve changes in the phase angle between the motor electromotive force and the current, so that at given output the power-factor of the motor - that is, the ratio between the numerical and geometrical products of current and electromotive force - may be given various values at will by changing the field excitation of the motor, a most unique and valuable property. If the motor electromotive force be fixed and the output varied, the phase angle between current and motor electromotive force varies by reason of the armature taking up a new angular position with respect to the field, backward for increasing load, forward for decreasing load. The minimum value of the current for a given load is reached when the excitation is such that the applied electromotive force and current are in phase, at which point the real and the apparent energy in the circuit coincide. The input can then be accurately measured by voltmeter and ammeter readings, and the motor is working at its best efficiency for the given load. For greater values of the motor electromotive force the current leads in phase with respect to the applied electromotive force; for less values it lags. The former condition is accompanied by the rising of the electromotive force at the motor terminals, the latter by its fall. It therefore becomes possible to use a synchronous motor, if the necessary current due to the load be not too great, as a voltage and phase regulator upon an alternating circuit, a function very valuable in power-transmission work. If the excitation be set to produce leading phase at small loads, the phase angle will gradually diminish as the load rises, and then, passing through zero, increase again with the lagging current, thus holding the power-factor near to unity at all working loads. In a well-designed synchronous motor, by proper initial adjustment of the field, the power-factor can easily be kept between 0.95 and i from quarter load to full load, and very close to unity within the ordinary working range. Save for its inability to start independently, the synchronous motor is a highly desirable addition to a transmission system. Starting is generally accomplished by the help of an induction motor or other auxiliary power, and the motor is treated exactly like an alternator, to be thrown in parallel with the supply circuit. A synchronous motor will pull itself up to synchronism if brought near to its synchronous speed, but this requires a very large amount of current. Operating from a generator of its own, it can be brought to speed by giving it a small initial rotation and raising the generator speed very carefully and gradually, when the two machines will accelerate in synchronism. Polyphase synchronous motors obey these same general laws; they can, however, be started as quasi-induction motors with an open field circuit, the pole faces serving as secondary conductors, but require so large currents in thus starting themselves that it is better practice to bring them to speed by extraneous means.

Synchronous motors sometimes cause serious trouble by "pumping," a phenomenon closely allied to the surging of current between alternators in parallel, and due to similar causes. If not due to defective governing of the prime mover, it usually starts with a change of load or of phase, producing fluctuations in the electromotive force in the system great enough to interfere seriously with incandescent lighting, and continuing with nearly uniform amplitude and frequency for hours if unchecked. The amplitude varies with the conditions, but in the same machine the frequency is nearly constant. The fluctuation affects both the armature and the field circuits, the latter inductively by changes in the armature magnetomotive force, but it can as a rule be controlled by varying the excitation until a neutral point is found, usually when the phase angle is near to zero. Motors with solid pole pieces give little trouble of this sort, the oscillations being rapidly damped by the eddy currents. In motors with laminated fields the most effective remedy is chamfering away the edges of the pole pieces so as to admit heavy copper shoes running along and under the edges, and even bridging the spaces between the pole pieces. The eddy currents in these shoes completely check the "pumping." Synchronous and other Converters. - It seems here appropriate to refer to these converting devices, not in their general functions, but merely in so far as they are directly related to motor practice. The synchronous converter proper is in effect a synchronous motor, in spite of its commutating function. Owing to the fact that the direct current voltage is dependent on the alternating current voltage of supply, the converter cannot advantageously be used to control the power factor by variation of the field strength, but the field can be adjusted once for all to hold the power factor reasonably near unity, provided independent means are available for so adjusting the applied alternating voltage as to give the required result at the commutator. If close regulation of the direct-current voltage is not demanded the converter field can be used more freely. As a matter of fact the synchronous converter finds its chief use in electric traction where close regulation is not important, and motor-generators in one form or another have been found more suitable for electric-lighting work. The synchronous converters have the liability to "pumping" or "hunting," to which reference has already been made, sometimes even of sufficient amplitude to throw the machine out of step, and are often provided with the shoes or bridges found useful with ordinary synchronous motors.

Synchronous motor-generators, so far as the motor function is concerned, present no peculiarities at all. Synchronous commutators, "permutators," and the like, usually have motor-parts of very moderate capacity, and must be kept rigorously free of hunting in order to preserve the conditions of commutation.

In many instances, particularly in American practice, motor generators with induction motors have been used for ease of starting and to secure immunity from hunting. A modification of interest from the motor standpoint is found in the "cascade converter." In this machine the rotor of an induction motor is directly coupled to the armature of a commuting converter of equal output, the windings of the two being in series and approximately equivalent. In this case the normal motor-electromotive force is reached at approximately half synchronous speed, and half the energy is delivered to the output end of the machine by the rotor acting as frequency changer, the rest by torque on the shaft. Commutation takes place therefore at half the initial frequency, which is often a great advantage.

(B) 2. Polyphase Induction Motors. - Speaking broadly, an induction motor is one in which the armature current is introduced into the armature windings by electromagnetic induction instead of by brushes. It is at once an alternating current transformer and an alternating current motor, operating in the latter function by virtue of the current received from the former. In the commonest form the alternating currents are of two or more phases interacting in carrying on these duplicate functions. Induction motors consist of two concentric masses of laminated iron taking the form of short hollow cylinders, of which the outer is fixed and the inner fitted to revolve. The outer surface of the inner drum and the inner surface of the outer drum are slotted or perforated to receive the primary and secondary windings of the apparatus. The outer winding is usually the primary, and the inner (or armature) winding the secondary. The primary winding is almost universally a multipolar drum in character; the secondary is, in the most highly developed motors, of the same character, but very often consists merely of numerous insulated armature bars united at each end of the drum by a common end-plate or end-ring, forming the structure usually known as a "squirrel-cage" winding. In polyphase motors of the usual type the primary drum winding is in duplicate or triplicate, resembling very closely the armature winding in a twoor threephase generator. The actions which go on in these motors have been the subject of much debate; most of the theoretical discussions of the matter have been based upon the concept of a rotary magnetization produced by two simple sinusoidal magnetisms superimposed in quadrature upon the same core, or, in the case of a three-phase motor, three superimposed in a similar symmetrical manner. This hypothesis is often most convenient, being merely an application of the general physical thesis that two equal simple harmonic motions in quadrature produce circular motion, as in the case of the conical pendulum. All the results of this hypothesis follow, however, from the introduction of two alternating magnetizations, acting in quadrature in time but independently; and one or the other view of the matter is convenient according as, in the structure considered, the effective magnetizations do or do not produce a definite physical resultant. There is no discrepancy between the two hypotheses; they are merely two points of view of the same phenomena. In the general case, one need make no supposition as to the existence or non-existence of the physical resultant rotary magnetization; it is merely necessary to note that if one phase-winding predominately produce a magnetic field, and the other a current in the rotary member fitted to react with that field, torque will result, whether the two phase-windings act upon the same magnetic structure or upon two entirely separate magnetic structures merely connected by the leads which deliver current from one to the other.

Induction motors having both these forms of structure are in successful use. If one considers the latter case, the two-phasewindings have exchanged functions every 90° in the two-phase structure, each phase-winding serving to produce a magnetic field and to deliver, almost as if it were merely a pair of brushes, current to react with this field alternately, and the two halves of the motor structure exchange functions every 90°. Considering the motor in which the two-phase-windings are superimposed on the same core, there is a virtual magnetic resultant rotating at a speed determined by the frequency of the current and the number of poles, and setting up induced currents in the secondary member, which currents are so disposed as to react with the field to produce rotary motion. At rest, the secondary electromotive force produced by the machine as a transformer is a maximum; when the motor is running at speed, unloaded, it is a minimum, and an increment of load causes the secondary member merely to slip behind synchronous speed far enough to receive an increment of transformed energy sufficient to carry the new load. If the secondary member is of very low resistance, the slip behind synchronism is very small, even at full load - less than 2% in motors developed for this particular property. An increase of secondary resistance produces increased falling behind from synchronous speed; and if resistance be added to the secondary member by interpolating rheostats in its circuits, the motor can be made to produce uniform torque over a very wide range of speed, as is the case with continuous current motors. The percentage of slip is the percentage of energy lost in the secondary member, as likewise in continuous-current motors if one regards their synchronous speed as that at which the motor electromotive force would equal that impressed. Polyphase induction motors start, when properly designed, with a very powerful torque, even up to three or four times the full load running torque of the same motor. With a very low-resistance secondary member this torque demands an immensely large current, the structure acting almost like a shortcircuited transformer, and the lag in the secondary circuit is considerable. In motors in which this large starting current is objectionable, it may be reduced very greatly by interpolating resistances in the secondary circuits at starting, the effect of these being to diminish the lag in the secondary circuit and to decrease the demand for primary current. A certain critical value of this resistance gives a maximum torque per ampere in the primary circuit with a given motor, being approximately that total secondary resistance which equals the secondary reactance. For maximum torque obviously both resistance and reactance should be equal and as small as possible. Where a small primary current in starting is of considerable importance, this extra resistance is frequently introduced at starting and cut out afterwards, particularly in cases where large torque is necessary. If great starting torque is not necessary, the primary electromotive force is often diminished by inductive resistances, or a change in the connexions of the transformer from which the motor is fed. Both methods of starting are in commercial use on a very large scale.

In efficiency and closeness of speed regulation and good general running properties polyphase induction motors approximate very closely to the best continuous-current practice. They produce, however, a certain amount of lag between primary electromotive force and current, which causes the apparent input to be larger than the real input, as generally happens in alternating-current work. The ratio between the real and the apparent watts input is the power factor of the motor. In well-designed modern machines this is usually from 85 to 90% at rated load; it should seldom fall below the former figure, and rarely rises more than I or 2% above the latter, though in rare instances power-factors as high as 94 or 95% have been obtained. Condensers have sometimes been employed in connexion with such motors to increase the power-factor, and with considerable success, particularly in maintaining the power-factor at low and moderate loads; but their use is generally unnecessary, and condensers of sufficient capacity at any reasonable value of the voltage have proved troublesome to build and maintain. The weakest point in these polyphase induction motors is the importance of employing a very small clearance between armature and field, in order to increase the power-factor by !making the structure more efficient, considered merely as a transformer. The clearances in ordinary use are seldom greater than 1 1 6 in., even in motors as large as too h.p., and in smaller machines are frequently not more than 3 1 3 in. Induction motors, however, possess many valuable properties, and are the mainstay of long-distance power-transmission work at the present time.

(B) 3. Monophase Induction Motors closely resemble the polyphase motor in construction, but have only a single-phase winding in the primary. The theories of their action are very similar to those of polyphase motors. The essential point of difference is that the stable angular displacement between the field magnetization and the armature currents which co-act with it is obtained in the polyphase motor by the time-displacements in the several phase windings, while in the single-phase motor it is obtained by the angular space-displacement of the armature, which has to be set up by an initial rotation. Single-phase motors therefore are not inherently self-starting, and run in either direction equally well when once started. The torque is always in the direction of the initial rotation. This rotation is sometimes given by hand and sometimes by auxiliary phase-windings supplied by derived current from the main circuit, or merely short-circuited on themselves and receiving induced currents from the main winding. Both these devices give a small initial torque in a definite direction, setting up a so-called elliptical rotary field, i.e. one produced by the composition of two unequal magnetizations, in this case at some indeterminate angle, seldom large. Once up to speed, the single-phase motors act much like the polyphase. They are conspicuously weak in the matter of power-factor, however, as well as in that of startingtorque, and have as yet not come into very extensive commercial use, although under special conditions they have been and are successfully employed. A theoretically interesting form of induction motor is a modification which runs at absolutely synchronous speed, receiving the necessary energy in the secondary not in virtue of slip behind synchronous speed, but from great difference in wave form between the primary and secondary circuits, so that energy due to harmonics of the fundamental frequency is periodically received by the armature in spite of synchronism in speed. Such motors are not employed commercially, but sometimes find a field for usefulness in the laboratory.

(B) 4. Repulsion-commutating Motors constitute a class of singlephase alternating-current motors which has risen to considerable commercial importance. They are fundamentally induction motors in the sense that the armature currents are supplied by the inductive action of the field. The armature winding is, however, provided with a commutator and (for a two-pole motor) two diametrically opposite brushes, which are short-circuited on each other and placed at an angle with the line of field magnetization. By this device the magnetic axis of the armature is held at a fixed angle with the field flux, so that the condition for steady torque is always fulfilled, its amount depending on the position of the brushes. Were these either in line with, or exactly at right angles to, the field poles, the torque would be zero - in the first case from lack of angular displacement, in the second from lack of secondary current. The brushes being skewed, however, the secondary current is maintained at a suitable value, and the motor runs in a definite direction. The general principle is merely that of a transformer with a movable secondary under magnetic thrust. During reversal of the current the torque relation remains fixed, since the primary and secondary currents both change sign, preserving the magnetic relations as in a series-wound continuous-current machine.

If such a motor is of moderate reactance, the currents are large and the torque very considerable. The repulsion-commutating connexion is considerably used as a starting device for single-phase induction motors, the commutator being short-circuited as a whole when the armature reaches synchronous speed. Thereafter the machine operates as a pure induction motor of the sort just described. The advantage of this change is that the commutator is eliminated, save at starting, and the motor becomes practically a constant speed machine like any other properly-designed simple induction motor. Such motors can be made to start if necessary with several times the normal running torque and a nearly proportionate increase of current. The short-circuiting of the commutator is generally performed automatically by a centrifugal governor. When at speed, efficiency and power factor are those of the typical motor of class(B)3.

The pure repulsion-commutating motor, worked as such, on the other hand, resembles a series-wound motor in its characteristics, having no fixed speed and being capable of running far above nominal synchronism. This results from the fixed angular relation maintained by the brushes between the armature and field magnetizations, whereby the torque conditions are preserved. Above the nominal synchronous speed, however, difficulties of commutation set in, so that some modifications of this simple type are desirable for wide ranges of speed. The power factors of these motors compare well, both in starting and in running, with those of the best pure induction motors, and their efficiencies are similar. These machines are reversible, serving as alternating generators when driven mechanically at "negative" speed.

Instead of simply skewing the brush line in the repulsion motor, an entirely analogous effect may be produced by dividing the field coils into pairs placed in quadrature, the brush line being parallel to one pair and at right angles to the other. This merely amounts to dividing the function of the original field physically into its components, a change which sometimes tends to improve the stability of the running conditions.

A more radical departure is found in the group of so-called "compensated-repulsion" motors, of which there are several members, due to various inventors, all material improvements on the pure repulsion type just described. Their common characteristic is that while possessing like simple commutator-repulsion motors, a transformer field acting upon the armature as secondary, and a pair of short-circuiting brushes holding the resulting armature magnetization in definite alignment, they also send the primary current in series through the armature via a second pair of brushes in quadrature with the first. The substantial effect of this series connexion is to cut down the virtual reactance of the armature as the speed rises, practically annulling it at synchronous speed. In alternating motors the motor-electromotive force is not merely that due to the motion of the armature conductors but the geometrical resultant of this and the reactance E.M.F.'s. In the motor here considered and analogous machines an auxiliary E.M.F. is applied either as here, conductively or inductively, in such direction as to compensate more or less perfectly the armature reactance E.M.F. The result is to secure, at least for a certain speed, a power factor near unity, as in the motor under discussion, although the starting conditions are not particularly good and the performance deteriorates above synchronism. In some motors of this type the compensating E.M.F. is introduced by an auxiliary winding in series and in quadrature with the main field, instead of by supplementary brushes. The modifications of the general scheme are rather numerous, and out of them have come some excellent single-phase motors now widely used for traction purposes.

(B) 5. Series Commutating Motors. - This important and interesting type is derived directly from the ordinary series motor for continuous current. The torque in these does not change sign with reversal of the current in both field and armature, and consequently alternating current can still produce in them unidirectional torque. Practically the first step toward an alternating current series motor is lamination of the field to reduce parasitic currents; the second is to keep down the reactance. A laminated field motor performs fairly well at a frequency of io periods or thereabouts, but to render it useful at ordinary frequencies requires modification in design. The motor E.M.F. being as before the geometrical sum of the reactance E.M.F. and that due to motion of the armature conductors, the first improvement can be made by making the latter dominant, i.e. by making the armature relatively very powerful. The plain series commutating motor has then a relatively weak laminated field'and a powerful armature. To check trouble with commutation due to short-circuiting coils under a brush, it usually has high resistance commutator leads, and thus equipped is capable of very fair performance, having the same general characteristics as the continuous-current series motor. Even so the armature reactance is somewhat excessive, so that with this simple construction the power factor is apt to be bad. Practically the plain series commutating motor is hardly used at all, but rather modifications of it corresponding very closely to those mentioned in connexion with the repulsion motor. In other words, an auxiliary electromotive force tending to annul the reactance E.M.F. of the armature is imposed upon the armature circuit. This is accomplished generally by a "compensating coil" in series and in space-quadrature with the main field. In another modification the compensating coil is closed upon itself, forming a short-circuited secondary, to which the armature itself acts as primary. The end to be attained is the addition of an E.M.F. such that the vector sum of the E.M.F.'s in the armature shall reduce as nearly as may be to the E.M.F. due to the motion of the armature conductors, as in a continuous-current motor. Obviously it is difficult to secure full compensation for all loads and speeds, but it can be made nearly complete for some particular load and speed.

These "series-compensated" motors behave much like continuouscurrent series motors, and, when properly designed, run well on continuous current. They have been developed particularly for heavy traction purposes, to which they are well adapted, owing to their ability to work well at all speeds. They give a very high maximum power factor and a reasonably good one over a considerable range of speed and load. Obviously both the field proper and the compensating field can be made subject to regulation to increase the range of successful action. Motors of this type have already come into successful use for fast and heavy railway service. Commutation appears to be reasonably good, although it is a far more difficult problem than with continuous-current machines.

The efficiency and output for unit weight in all alternatingcurrent motors is a little less favourable than with continuouscurrent motors. In the last resort the supply of energy to a singlephase motor is essentially discontinuous, and there is inevitable extra loss from hysteresis and parasitic currents, whether the motor is single phase or polyphase. The result is that an alternatingcurrent motor requires, other things being similar, more or better material, and loses a little more energy than a continuous-current motor of equal output. Motor design is a compromise, and while any one property can be exaggerated, it will be at the expense of others. One could probably build, for instance, a series-compensated motor of as high efficiency or as large output per unit weight as any commercial motor, but there would be sacrifice somewhere, in cost if not conspicuously elsewhere. As a matter of fact, the difference in efficiency usually amounts only to a very few per cents., and the difference in output per unit weight to a few more. The gain in the use of alternating-current motors is in facility and economy of distribution, which in many cases is far more than enough to overweigh any inherent disabilities in the machines themselves. Hence they are coming steadily into extended use. (L. BL.)