I. General 132. The direction of rotation of a direct-current motor, whether shunt- or series-wound, is independent of the direction of the current supplied thereto; that is, when reversing the current in a direct-current motor the direction of rotation remains the same. Thus theoretically any continuous-current motor should operate also with alternating currents. Obviously in this case not only the armature but also the magnetic field of the motor must be thoroughly laminated to exclude eddy currents, and care taken that the currents in the field and armature circuits reverse simultaneously. Obviously the simplest way of fulfilling the latter condition is to connect the field and armature circuits in series as alternating-current series motor. Such motors are used to a considerable extent, but, like the shunt motor, have the dis- advantage of a commutator carrying alternating currents. • The shunt motor on an alternating-current circuit has the objection that in the armature winding the current should be power current, thus in phas£ with the e.m.f., while in the field winding the current is lagging nearly 90 deg., as magnetizing current. Thus field and armature would be out of phase with each other. To overcome this objection either there is inserted in series with the field circuit a condenser of such capacity as to bring the current back into p>hase with the voltage, or the field may be excited from a separate e.m.f. differing 90 deg. in phase from that supplied to the armature. The former arrange- ment has the disadvantage of requiring almost perfect con- stancy of frequency, and therefore is not practicable. In the latter arrangement the armature winding of the motor is fed by one, the field winding by the other phase of a quarter-phase sys- tem, and thus the current in the armature brought approximately into phase with the magnetic flux of the field. Such an arrangement obviously loads the two phases of the system unsymmetrically, the one with the armature power current, the other with the lagging field current. To balance the system two such motors may be used simultaneously and 306 INDUCTION MACHINES 307 combined in one structure, the one receiving power current from the first, magnetizing current from the second phase, the second motor receiving magnetizing current from the first and power current from the second phase. The objection that the use of the commutator is complicated and greatly limits the design to avoid serious sparking can be en- tirely overcome by utilizing the alternating feature of the current ; that is, instead of leading the current into the armature by com- mutator and brushes, producing it therein by electromagnetic induction, by closing the armature conductors upon themselves and surrounding the armature by a primary coil at right angles to the field exciting coil. Such motors have been built, consisting of two structures each containing a magnetizing circuit acted upon by one phase and a primary power circuit acting upon a closed-circuit armature as secondary and excited by the other, phase of a quarter-phase system (Stanley motor) . Going still a step further, the two structures can be com- bined into one by having each of the two coils fulfill the double function of magnetizing the field and producing currents in the secondary which are acted upon by the magnetization produced by the other phase. Obviously, instead of two phases in quadrature any number of phases can be used. This leads us by gradual steps of development from the con- tinuous-current shunt motor to the alternating-current polyphase induction motor. In its general behavior the alternating-current induction motor is therefore analogous to the continuous-current shunt motor. Like the shunt motor, it operates at approximately constant mag- netic density. It runs at fairly constant speed, slowing down gradually with increasing load. The main difference is that in the induction motor the current in the armature does not pass through a system of brushes, as in the continuous-current shunt motor, but is produced in the armature as the short-circuited secondary of a transformer; and in consequence thereof the primary circuit of the induction motor fulfills the double func- tion of an exciting circuit corresponding to the field circuit of the continuous-current machine and a primary circuit produc- ing a secondary current in the secondary by electromagnetic induction. 308 ELEMENTS OF ELECTRICAL ENGINEERING 133. Since in the secondary of the induction motor the cur- rents are producjed by induction from the primary impressed currents, the induction motor in its electromagnetic features is essentially a transformer; that is, it consists of a magnetic cir- cuit or magnetic circuits interlinked with two electric circuits or sets of circuits, the primary and the secondary circuits. The difference between transformer and induction motor is that in the former the secondary is fixed regarding the primary, and the electric energy in the secondary is made use of, while in the latter the secondary is movable regarding the primary, and the me- chanical force acting between primary and secondary is used. In consequence thereof the frequency of the currents in the sec- ondary of the induction motor differs from, and as a rule is very much lower than, that of the currents impressed upon the pri- mary, and thus the ratio of e.m.fs. generated in primary and in secondary is not the ratio of their respective turns, but is the ratio of the product of turns and frequency. Taking due consideration of this difference of frequency be- tween primary and secondary, the theoretical investigation of the induction motor corresponds to that of the stationary trans- former. The transformer feature of the induction motor pre- dominates to such an extent that in theoretical investigation the induction motor is best treated as a transformer, and the elec- trical output of the transformer corresponds to the mechanical output of the induction motor. The secondary of the motor consists of two or more circuits displaced in phase from each other so as to offer a closed sec- ondary to the primary circuits, irrespective of the relative motion. The primary consists of one or several circuits. In consequence of the relative motion of the primary and secondary, the magnetic circuit of the induction motor must be arranged so that the secondary while revolving does not leave the magnetic field of force. That means, the magnetic field of force must be of constant intensity in all directions, or, in other words, the component of magnetic flux in any direction in space be of the same or approximately the same intensity but differing in phase. Such a magnetic field can either be considered as the superposition of two magnetic fields of equal intensity in quad- rature in time and space, or it can be represented theoretically by a revolving magnetic flux of constant intensity, or rotating INDUCTION MACHINES 309 field, or simply treated as alternating magnetic flux of the same intensity in every direction. 134. The operation of the induction motor thus can also be considered as due to the action of a rotating magnetic field upon a system of short-circuited conductors. In the motor field or primary, usually the stator, by a system of polyphase impressed e.m.fs. or by the combination of a single-phase impressed e.m.f. and the reaction of the currents produced in the secondary, a rotating magnetic field is produced. This rotating field produces currents in the short-circuited armature or secondary winding, usually the rotor, and by its action on these currents drags along the secondary conductors, and thus speeds up the armature and tends to bring it up to synchronism, that is, to the same speed as the rotating field, at which speed the secondary currents would disappear by the armature conductors moving together with the rotating field, and thus cutting no lines of force. The secondary therefore slips in speed behind the speed of the rotating field by as much as is required to produce the secondary currents and give the torque necessary to carry the load. The slip of the induction motor thus increases with increase of load, and is approximately proportional thereto. Inversely, if the secondary is driven at a higher speed than that of the rotating field, the field drags the armature conductors back, that is, consumes mechanical torque, and the machine then acts as a brake or induction generator. In the polyphase induction motor this magnetic field is pro- duced by a number of electric circuits relatively displaced in space, and excited by currents having the same displacement in phase as the exciting coils have in space. In the single-phase motor one of the two superimposed mag- netic quadrature fields is excited by the primary electric circuit, the other by the . secondary currents carried into quadrature position by the rotation of the secondary. In either case, at or near synchronism the magnetic fields are practically identical. The transformer feature being predominant, in theoretical investigations of induction motors it is generally preferable to start therefrom. The characteristics of the transformer are independent of the ratio of transformation, other things being equal; that is, dou- bling the number of turns for instance, and at the same time reducing their cross section to one-half, leaves the efficiency, regulation, etc., of the transformer unchanged. In the same way, 310 ELEMENTS OF ELECTRICAL ENGINEERING in the induction motor it is unessential what the ratio of primary to secondary turns is, or, in other words, the secondary circuit can be wound for any suitable number of turns, provided the same total copper cross section is used. In consequence hereof the secondary circuit is mostly wound with one or two bars per slot, to get maximum amount of copper, that is, minimum resist- ance of secondary. The general characteristics of the induction motor being inde- pendent of the ratio of turns, it is for theoretical considera- tions simpler to assume the secondary motor circuits reduced to the same number of turns and phases as the primary, or of the ratio of transformation 1 to 1, by multiplying all secondary cur- rents and dividing all secondary e.m.fs. by the ratio of turns, multiplying all secondary impedances and dividing all secondary admittances by the square of the ratio of turns, etc. Thus in the following under secondary current, e.m.f., impe- dance, etc., shall always be understood their values reduced to the primary, or corresponding to a ratio of turns 1 to 1, and the same number of secondary as primary phases, although in prac- tice a ratio 1 to 1 will hardly ever be used, as not fulfilling the condition of uniform effective reluctance desirable in the start- ing of the induction motor.