CH. XII ARMATURE REACTION 263 



current in the armature is nothing when s 3 = o, i.e. at the 

 centre of the pole, and increases to a maximum at the tip 

 of the pole. If we denote as before by A the number of 

 conductors counted round the surface of the armature, and 

 by <f> the angular breadth of the pole-piece subtended at 



the centre of the armature, we can put --$- for 2s 3 , so that 



360 



the intensity at either pole-tip will then be given by 



H =-- iA $ a 15^ 



" 573 T 



This is the expression for the intensity of magnetisa- 

 tion in lines per square centimetre under the pole-tips 

 produced by a current of i amperes flowing in each of the 

 A conductors round the armature ; if the machine has two 

 poles the current from the line will be 2i ; 8 is the width 

 of the air gap from iron to iron measured in centimetres. 



The curve of magnetisation due to the armature can be 

 drawn by calculating the value of H under the tip by 

 Equation 115, and then drawing a straight line as that 

 in Fig. 64, marked ' armature only,' through the centre of 

 the pole. We shall call the two curves thus found the 

 curves of magnet and armature magnetisation. 



For points along the surface of the armature outside 

 the pole the magnetisation due to the armature will 

 diminish rapidly on account of the increased reluctance of 

 the magnetic circuit. The intensity at each point may be 

 found by changing 28 in Equation 115 into 8 + x, where 

 x is the distance between any point and the tip of the 

 pole ; if 'a is the distance between the tips of two adjacent 

 poles, the intensity at a point midway between them is 

 twice that due to the action of the wires under one pole 



