DIRECT-CURRENT DYNAMOS AND MOTORS. 
it is best toemploy. This is a question partly of select- 
ing a size and number of field cores, coils, etc., convenient 
for making and handling, but it is chiefly a matter of the 
number of magnetic cycles per second occurring in the 
armature core. If we consider any particular cubic inch 
of the iron forming this core, it is evident that its mag- 
netism is reversed once for each pole that it passes. A 
complete cycle of magnetic changes takes place tn passing 
a north and a south pole, hence the number of cycles per 
second is the number of pazrs of poles passed in one sec- 
ond, that is, 
In this expression, / is the number of cycles per second, 
corresponding to the frequency of an alternating cur- 
rent; n, is the speed of the armature, in revolutions per 
minute; and mp is the number of pazrs of field magnet 
poles. , 
Direct-current machinery is designed, generally, so that f 
is between JO and 35 cycles per second. This limits the 
nuinber of poles, the object being to reduce the core 
losses, that is, the losses due to hysteresis and eddy cur- 
rents in the armature, the former, as we have seen in 
Par. 44, being proportional to f, whereas the latter in- 
crease with the square of f, Par. 45. The lower fre- 
quency of about 10 or 15 cycles applies to low-speed 
machines for direct connection to engines, etc., and the 
higher frequency of 30 or 35 is adopted in high speed, 
belt-connected generators and motors. 
By transformation of (35), it follows that the maximum 
speed of a fouwr-pole machine (? pairs of poles) should 
be 
na OXF _ OX 8 
. is 9 = 1050 revs. per min. 
In some instances, four-pole machines are run at higher 
speeds than this; for example, 1200 revs. per min., which 
