of the Compound Dynamo. 469 
or 
+ Pa — 7? 
Pairs + pit pal = p,Pibhs p ) ae 
we have a (Pik pe) 
(2, s+ pi)(?a “++ Pa) oi TaPa 
=pa} +p1 op let Pa) Os a} 
™o—(p\ + pa) 
Be 1 5p, 
E50; aaa) 
Substituting this in the expression for 9, we get 
= AFP, ot pit pamr'(1-+n)/(—2). 
Hence, from (7), 
___ "at Po == eae 
Pia + pa) + Papa 1—n 73° 
and from (3) and (4), 
Ay= ot rad Ay th. 
if we suppose 7’, to cau == Pale eit - anitine is so de- 
signed that the usual value of the external resistance is that 
which gives the maximum efficiency. 
2, Long-Shunt Machine. 
In this case 
_ & a Pe Fe 
(774+ pay *R 
"o 
x< ee 
i; ae Po Va Ta +P: + Po) + Polat pi)’ 
and, as before, dy / dr,=0 if 
1 1 Tat Pit P2 
Sh el ale i es Ga Gea Be a 
2 oe ee Mee tenets) 
or 
Pal py—1'5) ='3(P1 + 2) — PiPs- 
Hence 
Ta(1_+ pa) +1'2(p1 + pa) + Pipe 
v2 
+ 
= TAT hoe @ PUP? + /9(p1 + p2) + pips 
195 
Af 
P2 Ff 2 
