DIRECT-CURRENT DYNAMOS AND MOTORS. 11 
two end surfaces A, B, Fig. 5, is taken into account, 
which is done for the reason that the surface B, which is 
near the commutator C’, receives heat from the latter by 
radiation and convection as well as by conduction through 
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Fic. 5.—CooLiInG SURFACE OF DRUM ARMATURE. 
the armature conductors. It is, therefore, wise to con- 
sider this surface, B, as part of the cooling surface of the 
commutator, which is usually the hottest part of the ma- 
chine. 
Expressing in the above formula (7) the length Z, as a mul- 
tiple, or ratio, of the diameter, or L, = mD,, where m is 
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Elect. Engineer Institute 
Fia. 6.—CooLina SURFACE OF RING ARMATURE. 
this shape-ratio of the armature, the approximate cooling 
surface of a drum armature can be expressed as: 
S. = D.xzmD, + De = D,'x(m + 4), .cceceeeee (8) 
which contains only the diameter and the shape-ratio. 
In the case of a modern ring armature, usually the total core 
surface is open to the access of air; hence, the entire core 
