474. Prof. A. W. Riicker on the Self-Requlation 
according as the speed is greater or less than the critical speed 
for the resistance of the circuit when the external resistance 
is Zero. 
In like manner, it can be shown that if @ represents the 
external current, the expression P/Q > or < 1 according as 
the speed is greater or less than the critical speed when the 
external resistance is infinite. 
Inasmuch, however, as =1/7, when @¢ is the external 
electromotive force, and 2=72 when @ is the external current, 
these results may be briefly expressed by saying that P/Q is 
> or <1, according as the speed is greater or less than the 
critical speed when w is infinite. 
Similarly it may be proved that 
~ P/Q> or <A/B according as the speed is greater or less 
than the critical speed when & vanishes. 
On referring to the conditions laid down in the seven cases 
distinguished above in the light of these explanations, we see 
that they may be readily interpreted. The constant P is 
proportional to the speed, and we may conceive the ratio P/Q 
to be gradually increased by augmenting the velocity of 
revolution. 
Thus when A—B is positive, Case IV. is that in which the 
velocity is less than the critical velocities when e=0 or w. 
In Case V. the velocity is greater than the critical velocity 
when w=, and less than that when «=0. 
In Cases VI. and VII. it is greater than either of these 
critical velocities. 
The condition that there shall be a maximum value of ¢ is 
fey epee Vales | 0) salle 
As an example of how such general formule can be applied 
to a particular case, we deduce from this relation and from 
equations (3) that, in the case of the Short-Shunt Dynamo, the 
external electromotive force can only have a maximum value if 
a+ Pa Sapi + 8194 ny ( 2M (spi + S1pa) ) 
+ . “~~ —_ > 1; 
pi(Ta+ Pa) + Papa Sa Pi ("a+ Pa) + apa 
or if $4 Ta 
ee aM!” rte eee 
Ta Tat Pa 8] i 
Ps epee Pit, Pa 
whence it follows that we must have 
om ey 
Sa) Vat Pa 
Similar deductions can be made in the other cases. 
