of the Compound Dynamo. 475 
The fact that if P/Q be sufficiently large there is no maxi- 
mum value of @ for any positive value of 2, means that if the | 
velocity is so great that the inducing magnets are saturated 
so that the total electromotive force is constant, any increase 
in the resistance of the external circuit must be accompanied 
by a decrease in the current which flows through it and an 
increase in the electromotive force at its extremities. In the 
former case #=72, and in the latter e=1/ 7, so that in both 
cases an increase in w produces a decrease in ¢. ‘This state of 
things is reached before complete saturation, viz. at the point 
when the prejudicial effect due to the weakening of the cur- 
rent produced by an increase in 7, overbalances the advantage 
gained by the fact that a larger proportion of the whole cur- 
rent passes through the shunt. This point is reached when 
VP/VQ=A/B. 
We are now in a position to discuss the amount of change 
in @ produced by a given finite change in 2, i. e. the self- 
regulating power of the dynamo. 
The treatment of this question must be slightly varied, 
according as a maximum value of ¢@ does or does not occur for 
a value of x intermediate to ~ and m, the largest and smallest 
values of that quantity between which self-regulation is 
aimed at. 
If it does not, we may write 
P rast 
eee Bema ee | 
se il gee 
At+pm Btp 14¢7’ 
where ¢, is the value of the electromotive force or current to 
be kept constant, and g is a quantity which will be smaller as 
the self-regulation is more perfect, and which will be positive 
or negative according as @ diminishes or increases as « 
increases. 
If, on the other hand, X lies between » and m, then the 
equations corresponding to (16) become. 
aia ele) 
Pee Os. ie @ 
At+m Btm 1+ p” 
P Q © Rrgeer rete ne (Aly) 
where © is the maximum value of ¢. 
If the constants are so chosen that the values of ¢ corre- 
