DIRECT-CURRENT DYNAMOS AND MOTORS. 89 
The cores are only 9 inches long instead of 133, hence, 
the path in the frame is 9 inches shorter, or /,,’’ = 50 
inches, and we have: 
Atm = 51 X 50 = 2,550 ampere-turns, 
The compensating ampere-turns are also less in the case of 
a toothed armature, since the angle of field distortion is 
smaller; taking a = 12°, we obtain: 
125 X 240 x 12° 
2 180 
The number of armature ampere-turns, however, is greater 
for a toothed than for a smooth armature, because the 
flux in the teeth is higher than that in the solid portion of 
the core. Assuming a tooth density of 120,000 lines per 
square inch, which is often employed, the specific magnet- 
izing force for the teeth would be 700 ampere-turns per 
inch (see Table 26), and if the slots are 1 inch deep the 
tooth ampere-turns would be: 
at,’ = 700 X 2 = 1,400 ampere-turns. 
For the remaining 9 inches of the path, the flux density is 
80,000 lines per square inch, as before, hence the magnet- 
izing force required for the solid portion of the armature 
core 
Gf, —-1,26 X = 1,250 ampere-turns. 
at,, = 31 X 9 = 280 ampere-turns. 
The total number of armature ampere-turns for the 
toothed armature, therefore, is: 
at, = 1,400 + 280 = 1,680 ampere-turns, 
instead of 340, as in the case of the smooth armature. 
The total magnetizing force required in case of the toothed 
armature, consequently, is: 
A T=3,520+2,550-+1250+-1,680=9,000 ampere-turns, 
as against 17,650 ampere-turns for the smooth-armature 
machine. 
68. Calculation of Ampere-Turns for Four-Pole 
Smooth-Armature Dynamo.—Referring to Fig. 
26, the mean lengths of the path for the smooth-armature 
