AN INTERESTING CASE OF RESONANCE 197 
the shape of the hodographs lies in the fact that diagram (f) 
is plotted with the total voltage as reference and diagram (g) 
with the voltage over the parallel circuit as reference. Plate 
X (h) shows this same total current plotted with the voltage 
over the series circuit as the axis of reference. 
Just why the current hodcgraphs have these particular shapes 
is best understood by a consideration of the voltages over the 
two parts of the circuit. Plate X (j) is a polar diagram of the 
voltage over the parallel portion and Plate X (k) is a similar 
diagram for the series circuit. If these two voltages are added, 
frequency by frequency, the total voltage diagram, Plate X (1) 
is obtained. 
Returning to diagram (g) which represents the currents in 
the parallel circuit, we find three broken curves. These hodo- 
graphs represent the currents that would exist in the parallel 
circuit with a constant voltage of twenty volts. With increase 
of frequency the condenser current would become greater, while 
at the same time the coil current would become smaller. At 
sixty cycles the two would be equal. The resultant total cur- 
rent vectors would all end along the broken , line symmetrical 
with the voltage axis. The current would be a minimum at 
sixty cycles and in phase with the voltage. It would increase 
in magnitude and lag by a larger angle with decreasing fre- 
quencies and with increase of frequency would increase in value 
and lead by an increasing amount. In order for the hodo- 
graph to bend back violently, as it actually does, the voltage 
must be greatly reduced at the more extreme values of fre- 
quency. If we examine diagram (j) we find that such is the 
case and if we examine diagram (k) we see the reason, for the 
series circuit with its high impedance at extreme frequencies 
requires by far the greater voltage. 
If we now look to the broken curve of diagram (h) which 
is the current hodograph for the series circuit on the basis of 
a constant voltage of twenty volts, we see that the current has 
been reduced far below normal for the frequencies close to sixty 
cycles. It must be that at these frequencies the voltage is very 
much reduced for the series circuit and correspondingly large 
for the parallel circuit. A glance at diagrams (k) and (j) shows 
this to be the case, 
