AN INTERESTING CASE OF RESONANCE 
199 
might be secured by the proper choice of constants. For in- 
stance, if the frequencies at which the two portions of the circuit 
passed through resonance were not the same, the “wind up” 
parts of the total impedance and current hodographs could be 
made to occur either above or below the axis or be brought tangent 
to the axis. In this way the current curves could be made to as- 
sume a large variety of forms and the power-factor to hover 
around any chosen value. Many other results could be obtained 
by the variation of the fundamental constants together with 
the frequency or with the frequency constant. The present 
discussion is intended to be suggestive of the possibilities of an 
alternating current circuit. By variation of the frequency it was 
possible to make every reactance change and secure particularly 
complicated and unusual results. Equally interesting results 
could be obtained by keeping the frequency constant and varying 
one or more of the constants of the circuit, there being an in- 
finite number of ways in which this could be done. 
In working out this problem the writer was not concerned 
with any particular application. But since every alternating 
current circuit and machine can be reduced to an equivalent cir- 
cuit of this kind a study of an artificial circuit cannot but be 
suggestive. In fact variation of frequency is nothing but change 
of speed and the starting of a synchronous motor may be com- 
pared to what goes on in this circuit. In actual practice the 
constants of a circuit often depends upon the other constants or 
upon the current, or still other factors. If these relationships 
are known the equivalent artificial circuit may be altered ac- 
cordingly. 
Again, the different frequencies may be regarded as repre- 
senting the various harmonics usually present in the voltage of 
a generator. The response of a circuit to the various harmonics 
will, as is well known, always cause conditions in the circuit quite 
different from what would be expected from sine wave theory. 
Usually the assumption is made that inductance tends to choke 
out the higher harmonics and capacitance to emphasize them. 
However, the circuits which have been considered make it per- 
fectly evident that a complex circuit may exercise a surprising 
selective action. 
