168 



[Mar. 10, 



induced therein may be neglected. We further suppose for simplicity 

 that the line integral of magnetic force within the armature core may 

 be neglected. 



Let A 1 be the effective area of the space between the pole piece and 

 armature core when the cores are in line, l Y the distance from iron to 

 iron. 



Let A 3 be the section of magnet core, l 2 the effective length of a 

 pair of magnet limbs, so that Z 2 may be regarded as the length of the 

 lines of force as measured from one pole face to the next. 



Let m be the number of convolutions in a pair of magnet limbs, 

 and 



n, the convolutions in one armature section, 

 T, the periodic time. 



The time is measured from an epoch when the armature coil we 

 shall cousider is in a symmetrical position in a field which we shall 

 regard as positive. 



x and y are the currents in the magnet and armature coils, the 

 positive direction being that which produces the positive field at time 

 zero. 



At time t the armature coil considered has area A/, 



= cos(2tt£/T) + \ cos(47T*/T)+&c. 



in a positive field ; and area A 1 ", 



= cos(2tt£/T) + Z> 2 cos(4tt*/T)-&c. 



in a negative field, where 



and + • • • = 0. 



The coefficients b , b v &c, are deducible by Fourier's theorem from 

 a drawing of the machine under consideration. 



