280 THE DIRECT-CURRENT MOTOR (II. XII 



tion has to be accomplished in spite of the fact that 'the 

 brush is always in a magnetic field of the wrong sign. 



The fact that sparkless commutation can be obtained 

 under these conditions must be attributed to the little 

 understood action of the carbon brush, which is now almost 

 universally used in motors. There are, however, limits to 

 the practical use of this form of brush, but those limits 

 must be determined by what is going on under the brush 

 itself, and not by the magnetic condition under the pole- 

 tip, where in practice the brushes are never placed. 



Equation 115 gives us the value of the intensity of 

 magnetisation under the pole-tip, and it is a common rule 

 of design to allow such an armature load as will make this 

 intensify half of that due to the magnets; the effect of 

 this would be to reduce the intensity under the tip behind 

 the brush in a motor to one half of what it would be if 

 there were no current in the armature. (See a paper by 

 Mr. W. B. Esson in the ' Journal of the Institution of 

 Electrical Engineers,' Vol. XX.) 



Equation 116, however, tells us that the intensity of 

 magnetisation under the brush does not depend simply 

 upon the width of the gap, but upon the distance between 

 adjacent pole-tips, and that we can diminish it by increasing 

 a without altering B. 



By combining Equations 115 and 116, we find that 

 HM the magnetisation under the brush, can be expressed 

 in terms of H fl , that under the pole-tip due to the reaction 

 of the armature, in the form : 



where p is the ratio of a, the space between the tips, to 

 the width of gap. 



