DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
343 
reckoned positive in the direction of the resultant E.M.F. of the machine, i.e., positive 
when the machine is used as a generator of electricity. Taking any closed line 
through magnets and armature, symmetrically drawn as ABCDEEA (fig. 4), it is obvious 
that the line integral of magnetic force is diminished by the current in the armature 
included between angle X in front and angle \ behind the plane of symmetry. If m 
be the number of convolutions of the armature, the value of this magnetising force is 
771 2 \ • • 
47tC— ~- = 4\vnC opposed to the magnetising force of the fixed coils on the magnets. 
Thus, if we know the lead of the brushes and the current in the armature we are at 
once in a position to calculate the effect on the electromotive force of the machine. 
A further effect of the current in the armature is a material disturbance in the 
distribution of the induction over the bored face of the pole-piece ; the force along 
BC (fig. 4) is by no means equal to that along DE. Draw the closed curve 
BCGHB, the line integral along CG and HB is negligible. Hence the difference 
IYl k, 
between force HG and BC is equal to 47rC~— = 2/cmC where k is the angle COG. 
Pig. 4. 
This disturbance has no material effect upon the performance of the machine. But 
the current in the armature also distorts the arrangement of the comparatively weak 
field in the gap between the pole-pieces, displacing the point of zero field in the 
direction of rotation in a generator and opposite to the direction of rotation in a 
motor ; and it is due to this that the non-sparking point for the brushes is displaced. 
A satisfactory mathematical analysis of the displacement of the field in the gap 
between the pole-pieces by the current in the armature would be more troublesome 
than an d priori analysis of the distribution of field in this space when the magnet 
current is the only magnetising force. Owing to the fact that the armature is divided 
into a finite number of sections there is a rapid diminution of the displacement of the 
field during the time that a section is being commutated, the diminution being 
