DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
345 
eliminating 1' 
'21 
l>An 
A 2 
T I i \ pt Ao 1 \\ I 7 /• I rl+4\»lC , frp (v —1) 
vI+4XmC — v-1) ) + l 3 f< _2 lj_ 
' L a, 
= 477WC+4XwC - -—4X?ftC 
V 
— Anne —4XtoC 
1 
The characteristic curve when 0— 0 being I=F(4 ttwc) we may write the above as 
the equation of the characteristic surface thus 
• 1+ — 4 \mC ~ 2 =f( TirriC”———V 
In applying this equation it must not be forgotten that the E.M.F. of the machine 
cannot be determined' from I unless the commutation occurs at such a time that the 
coil being commutated embraces all, or nearly all, the lines of induction in the 
armature. 
This equation enables the characteristic surface to be constructed from the 
characteristic curve. Let OL = 47mc, LM=4m\C, draw MK so that through K 
draw ordinate KR meeting characteristic curve in R, draw RQ parallel to OL meeting 
ordinate QL in Q, draw QS parallel to LM ; draw QP so that “=■—Then P is 
O (qj V 4-1 irt 
a point on the characteristic surface. 
Fig. 5. 
A very important problem is to deduce the characteristic curve of a series wound 
machine from the normal characteristic; in this case c=C, and we have 
I+ 1 y- 1 4XmC| = F{( 4 ™- 4 ^)0} 
2 Y 
MDCCCLXXXVI. 
