708 INDUSTRIAL APPLICATIONS. 



two symmetrical parts BjB and BB', which give flows of force of 

 opposite signs, and neutralise each other. There remains then 

 for the useful effect only the angle A'OB 1 = ?r-2^; the corre- 

 sponding flow of force, which is equal to p\_f(ir)- 2/(#)], tends 

 to make the brush B' positive, for instance, and A' negative. 



When the coil has passed the brush B', it undergoes the same 

 influence in the opposite direction in the second half of the ring, 

 so that it tends to give the same signs respectively to the two 

 brushes. 



The flow of useful force cut by a coil during an entire rotation is 



For the 4m coils, with the velocity indicated, the total flow of 

 force cut in a second is 



Q = 4 2/ [/(,) - 2/(0)] = 2P [/() - 



The current is not absolutely uniform, even if we suppose the 

 external resistance constant, for the electromotive force in each 

 half of the ring is given by the sum /o>2/'(a) of the terms rela- 

 tive to each coil, and the resistance of the induced wire varies 

 periodically. The period T of the variations of the current is the 

 time necessary for one coil to replace the preceding one that is 



to say -- , and the external current may be represented by an 

 4#M 



expression of the form 1 + A sin 2ir(^mnt + ^) in which A and fi 

 are constants. The introduction of a telephone into the circuit, or 

 into a shunt, will render evident these oscillations. 



If, however, the coils are numerous, the undulations of the 

 current are very small in comparison with its mean value I, and 

 it may be regarded as sensibly uniform. 



1264. As the current is - in each half of the induced wire, the 

 2 



electromagnetic work per second is 



W = ?[/<)-*/(*)] I -,!. 



