of the Compound Dynamo. A67 
whence we get 
p=- fra alta t prt Pa) + Pa(at Pr) VL, 
79( sy + Sp) i SPQ 
Also, since 
Go esl 
ar 
1+ Pz 
i My, rs, 
OL (rat pit pr) +polreatp:)  %o(8, +52) +512 9” 
which may be written 
ae Le Qs : 
Asta, Bz,+a3 
if i 
pee J _ Tat pit po 
P3= Gay ea) Para ey (05) 
‘ie 1 81 + So 1 
Q=—-, Batt, » 
3" bere 
Sip. 7 "9 
And, as before, 
ae aa aie 
2 Ayta, Bata 
if 
pe eee elon’ Wes Palit pr) >: (6) 
o(7,+pitpe)’ Tat Pi + Po 
Q.= P2 Be 81 P29 as 
a (8, +55)’ Smyospee eae <a 
We thus see that if the current or difference of potential 
which it is required to maintain as constant as possible be 
represented by the general symbol ¢, then, in the case of 
either machine, 
g=P/(A+z2)—Q/(B+2); 
where A, B, P, and Q do not depend upon the variable resist- 
ance, and where « is either the resistance or the conductivity 
of the variable conductor. 
All problems on self-regulation in the case of either machine 
may therefore be solved by means of this formula, and the 
application of the results is made by giving to the constants 
the values proper to the machine, and to the meaning of the 
symbol ¢ in the particular case under consideration. 
It will be observed that the constant A is always either the 
resistance, or the reciprocal of the resistance offered by the 
machine to a current produced by a battery placed in the 
