38 DIRECT-CURRENT DYNAMOS AND MOTORS. 
generated is 7, times as great as that produced by J foot 
of inductor. If the armature revolves with a velocity of 
v feet per minute, the voltage generated is uv times as 
great as when moving at the rate of 1 foot per minute. If 
the magnetic density in the air gaps is B, lines per square 
inch, the voltage is B, times that for a field density of J 
line per square inch. On account of the fact that the 
polepieces do not completely surround the armature, not 
all of the inductors are cutting lines at the same time. 
The number of zdle inductors usually varies from 14 to 
25 per cent., and averages about 17 per cent.; hence, the 
effective length of the inductors is 100 — 17 = 83 per 
cent., or .83 of the total length of inductors. If the 
armature winding consists of n, pairs of parallel branches, 
the voltage generated by the .83/, feet of useful inductors 
must be divided by 2n,, since the total voltage is gener- 
ated in-each of the 2n, branch circuits. Thetotal E M. F. 
generated in an armature is therefore given by the | 
formula: 
.83X 1, P O° 
H=2.4X10" x oh ee xuxBe_/ Xox Be X1 ,.. (18) 
2Ny Ny 
from which the length of the armature inductor required 
to generate the voltage H,is found, in feet: 
1 = EX XI 
OSE te 3 ne 
The E. M. F., EH. and the number of bifurcations, or 
pairs of armature circuits, n), being given, the fitness of 
the result depends upon the correct assumption of the 
velocity, v, and of the field density, B,. The former has 
already been discussed in Par. 14, the latter is treated 
in Par. 32. 
32. Field Density.—The density of the magnetic field, or the 
gap induction, as it is sometimes called, must be properly 
chosen according to the size of the machine, the number 
of poles, the form of the armature, and the material 
of the polepieces. In general, the density is taken the 
