ELECTRICAL MOTORS. 537 



order that the motion may be kept up, the current in one part 

 of the circuit must be reversed by a commutator twice during each 

 period, so that the electromotive force of induction be at each 

 instant in the opposite direction to E that of the exciting current. 



When a regular state is attained, the work of the reciprocal 

 actions is entirely consumed in overcoming external resistances, 

 for the velocity resumes the same value at the end of each 

 period. 



The energy expended by the source, during each period $, is 

 equal to the external work increased by the energy which corre- 

 sponds to the heating of the conductors. If R is the resistance 

 of the circuit, we have then, 



PEL#= fpR^+ 



Jo Jo 



(59) E \dt= FR<#+ EI<#. 



The reversals of the current by the commutator produce sparks 

 which absorb part of the work, and which affect the equation if we 

 take count of the corresponding variations in the resistance R of 

 the circuit. 



In the general case the values of the integrals depend on the 

 law according to which the current varies during a period ; but 

 if the strength is sensibly uniform, equation (59) reduces to 



(60) E -E = IR. 



The efficiency p of such a motor is the quotient of the external 



work El in unit time, by the total energy expended E I, or the 



p 

 ratio of the electromotive forces. If I is the strength of the 



E o 

 current which the electromotive force E would produce in the 



circuit at rest, we have 



E IR I 



(61) p = =i =i . 



EO E I 



The expression for the external work itself is 



(62) EI 



