of the Compound Dynamo. 473 
Tn both these last cases ¢ has no maximum value; for in (II.) 
X is positive but >(BP—AQ) /(Q—P), while in (IIL.) it is 
negative. 
Next, taking cases in which A —B is positive, we see that 
oy ThA) BS i>? / Q, 
¢ is negative for all positive values of z. 
Pee A/S BS PL Q> 1, 
¢ is positive for values of e>(AQ—BP) /(P—Q). 
oe) EP/Q>A/B> vyP/VQ>1, 
¢ is positive for all positive values of z. 
In cases (V.) and (VI.) @ has a maximum yalue corre- 
~ sponding to a positive value of w. . 
aE) 1h./P//Q>A/B>1, 
is positive for all positive values of 2, and X is negative, so 
that there is no maximum value of ¢. 
The physical meaning of these different conditions may be 
best understood by considering the inequalities 
fee > or <1 and P/Q> or <A/B: 
If ¢ represents the external electromotive force, the first of 
these becomes, in the case of the Short-Shunt and Long-Shunt 
Machines respectively, 
MM (sap1+ Spa) > OF <PyTat+P\patTapa, » ~ (14) 
and 
ee OR Fi 10a be, acy '* Seely Sida ae) eae al 
But, by equation (1), the condition that the velocity is 
greater or less than the critical speed is 
nM> or <R/S; 
and if, in the case of the Short-Shunt Machine, we put 7.=0, 
this becomes for the values of R and 8 given above, 
nM> or < Citar Pat apa, 
SaP1t $1Pa 
which is identical with (14). 
Similarly, in the case of the Long-Shunt Machine, we get 
for the same condition, 
nM > or < moh, 
which is identical with (15). 
Hence, in these cases, 
B/S orc 
