470 Prof. A. W. Riicker on the Self- Regulation 
Substituting in the expression for 7, we obtain 
Po—"o / 
= OY po=r (1+ 1l—n). 
ay pots” Pe A¢l+7)/(1—n) 
Hence, from (5), (6), and (9), if, as before, 7’,=79, 
1+ : el a) eae 
ete as (10) 
7 aM 7, e e 
Ae Sree 
ey tee Lay 
The above values for A will be required hereafter ; but if 
we replace A by its value in terms of R,,, equations (8) and 
(10) may all be summed up in the formula 
(1—)/A+7)=RBn/ 1s, 
= (9"%9—Rn)/ (72+ Rn). 
In the case of the Short-Shunt Machine, 
3=(P1+pa)Rm from equation (7). 
n= (V7 pit pa Bn) /(/ pit patV Rn): 
In the case of the Long-Shunt Machine, 
3=poRm, from equation (9). 
* 1=(V/p2—V Bm) /(/p2+V Bn). 
These formulz may be put in another form, which is useful 
as it is very easy to remember. In either kind of compound 
machine, and in the ordinary shunt dynamo, if the resistance 
of the armature is infinite, it is possible for a current generated 
in the external circuit to pass from one extremity of the external 
circuit to the other, 7. e. from one terminal to the other, exclu- 
sively through wires which form parts of the magnetizing 
spirals. In the case of the Short-Shunt Machine this path 
includes both spirals ; in the ordinary Shunt or in the Long- 
Shunt Compound Machine it includes one spiral only. If 
we call the resistance of this path 2, then in all three cases 
the maximum efficiency is given by the equation 
n=(Va—V Rn) | (VS+ VW Rn); 
and the value of the external resistance for which the maxi- 
mum efficiency is attained by 
ees Pr 6 hee 
In cases where the resistance of the shunt is large, approxi- 
mate expressions may be deduced from the above by substi- 
or 
