370 ELECTRICAL APPARATUS 205. The action of the commutator in an alternating-current motor, in permitting compensation for phase displacement and thus allowing a control of the power-factor, is very interesting and important, and can also be used in other types of machines, as induction motors and alternators, by supplying these machines with a commutator for phase control. A lag of the current is the same as a lead of the e.m.f., and in- versely a leading current inserted into a circuit has the same ef- fect as a lagging e.m.f. inserted. The commutator, however, produces an e.m.f. in phase with the current. Exciting the field by a lagging current in the field, a lagging e.m.f. of rotation is produced which is equivalent to a leading current. As it is easy to produce a lagging current by self-inductance, the commutator thus affords an easy means of producing the equivalent of a leading current. Therefore, the alternating-current commutator is one of the important methods of compensating for lagging currents. Other methods are the use of electrostatic or electro- lytic condensers and of overexcited synchronous machines. Based on this principle, a number of designs of induction motors and other apparatus have been developed, using the commutator for neutralizing the lagging ^magnetizing current and the lag caused by self-inductance, and thereby producing unity power-factor or even leading currents. So far, however, none of them has come into extended use. This feature, however, explains the very high power-factors feasible in single-phase commutator motors even with consider- able air gaps, far larger than feasible in induction motors. VII.- Efficiency and Losses 206. The losses in single-phase commutator motors arc essen- tially the same as in other types of machines: (a) Friction losses—air friction or windage, bearing friction and commutator brush friction, and also gear losses or other mechanical transmission losses. (6) Core losses, as hysteresis and eddy currents. These are of two classes—the alternating core loss, due to the alternation of the magnetic flux in the main field, quadrature field, and arma- ture and the rotating core loss, clue to the rotation of the arma- ture; through the magnetic field. The former depends upon the frequency, the latter upon the speed. (c) Commutation losses, as the power consumed by the short-