286 THE DIRECT-CURRENT MOTOR CH. XII 



Equating this to the tension due to self-induction, we 

 have 



.................. (119). 



vdl 



This equation gives us a meastire of the tendency to 

 spark, and will serve as a guide when, as with carbon 

 brushes, there are other influences affecting sparkless 

 commutation besides that of the magnetic field in which 

 the brush is placed. 



We see that the tendency to spark increases directly as 

 the square of the number of turns per coil, as the current 

 per wire, and as the permeance of the magnetic circuit 

 surrounding the coil ; it also varies inversely as the 

 angular width of the brush, as the diameter, and as the 

 length of the armature. It is evident that in a slotted 

 a,rmature the tendency to spark will be much greater than 

 in a surface- wound armature. 



