of the Compound Dynamo. AT1 
tuting the resistance of the shunt for >, and the sum of the 
resistances of the armature and series-coil for R,,. 
If the maximum efficiency is attained when 7, has its usual 
value, we may put the last expression in a form which will be 
useful hereafter. Let Y be a quantity which has with regard 
to > the same meaning as w with regard to 7; 7. e. let it be 
=> or 1/> according as ¢ represents the external current 
or external electromotive force. Then ; 
n=(VY¥~ VA)/(S¥+VA) 5 
and if the maximum efficiency is attained for the usual value 
of x, 
PHVA. 
Conditions of Maximum Power. 
Since the power of a dynamo is expressed by either of the 
formule: e} / 2 or c3r2, it is in all cases given by ¢7z. 
This has a critical value if 
d 
24 = +6=0 . 
i.e, if 
ls Q \ le Qe 
8) — crea (aay A ee ee ee 
dr O.18 Piha) OBLn 
Gta * Gra 
Conditions of Self-Regulation. 
Ee EAS, 
Oe Boe 
e Dees 18 BY op ae e 
eis (A+xz) (B+z2) 
Hence ¢ has two critical values corresponding to the values 
of x given by the equation 
a(/ PE/Q)=—BvPLAVQ. 
If we take the lower signs, w is necessarily negative unless B 
is negative ; which can only be the case if some of the indu- 
cing spirals are wound in the negative direction, 7. e. so that 
they reduce the strength of the magnetic field. If B is nega- 
tive, it is evident that ¢ is infinite for a positive value of «. 
This unintelligible result is explained by reference to the 
Since 
