DIRECT-CURRENT DYNAMOS AND MOTORS. 67 
probable flux in the armature being given by (21), it is 
necessary to make the cross-section of the field cores, and 
other portions of the field magnet, large enough to carry 
this useful flux plus the leakage lines which do not pass 
through the armature. 
The number of leakage lines is usually from J0 to 50 per 
cent. of the useful flux for bipolar toothed-armature 
machines. With bipolar smooth-core armatures the 
leakage is considerably greater, ordinarily amounting to 
from 25 to 100 per cent., according to the size and type of 
the machine. Hence, the total flux of a bipolar machine 
is from 1.10 to 2.00 times the useful flux, this multiplier 
being called the leakage factor (see Par. 55). For 
multipolar machines the general form that has been 
adopted almost universally is the ring type, represented 
in Figs. 21 and 22; with this form of field magnet the 
leakage factor ranges from 1.08 to 1.20 in case of a toothed 
armature, and from /.15 to 1.50 in case of a smooth arma- 
ture, according to the size (see Table 24). 
Denoting the leakage factor by A, it follows from the pre- 
ceding that the cross-section of the field magnet is: 
g —~ 1 X?_ 6X1! xXnm x EXA 
ea se N Xn, X Bn 
where all symbols have the same meaning as in (21), 
and B,, is the flux density in the field magnet. The lat- 
ter should be taken between 80,000 and 100,000 lines per 
square inch for wrought cron and cast steel, and between 
40,000 and 50,000 lines per square inch for cast tron. 
In case of bipolar machines, S, is the cross-section of one 
core; but for multipolar machines, since ® is the sum of 
the lines which enter the armature from all the north 
poles, S, is the total cross-section of all the north poles, 
and must therefore be divided by the number of pairs of 
poles, mp, in order to give the area of one core. 
The yoke, or other part connecting the cores, should have a 
sq. ins.,....(36) 
cross-section of o square inches, if it carries all the lines 
ts 
