SINGLE-PHASE COMMUTATOR MOTORS 351 fundamental importance in the study of the alternating-current commutator motor, and the control of this short-circuit current the main problem of alternating-current commutator motor design. Various means have been proposed and tried to mitigate or eliminate the harmful effect of this short-circuit current, as high resistance or high reactance introduced into the armature coil during commutation, or an opposing e.m.f. either from the out- side, or by a commutating field. High-resistance brush contact, produced by the use of very narrow carbon brushes of high resistivity, while greatly improv- ing the commutation and limiting the short-circuit current so that it does not seriously demagnetize the field and thus cause the motor to lose its torque, is not sufficient, for the reason that the resistance of the brush contact is not high enough and also is not constant. The brush contact resistance is not of the nature of an ohmic resistance, but more of the nature of a counter e.rn.f.; that is, for large currents the potential drop at the brushes becomes approximately constant, as seen from the volt-ampere characteristics of different brushes given in Figs. 167 and 168. Fig. 167 gives the voltage consumed by the brush contact of a copper brush, with the current density as abscissae, while Fig. 168 gives the voltage consumed by a high-resistance carbon brush, with the current density in the brush as abscissae. It is seen that such a resistance, which decreases approximately in- versely proportional to the increase of current, fails in limiting the current just at the moment where it is most required, that s, at high currents. Commutator Leads 198. Good results have been reached by the use of metallic resistances in the leads between the armature and the commuta- tor. As shown diagrammatically in Fig. 169, each commutator segment connects to the armature, A, by a high non-inductive resistance, CB} and thus two such resistances are always in the circuit of the armature coil short-circuited under the brush, but also one or two in series with the armature main circuit, from brush to brush. While considerable power may therefore be consumed in these high-resistance leads, nevertheless the effi- ciency of the motor is greatly increased by their use; that is, the reduction in the loss of power at the commutator by the reduction ,1)