AN INTERESTING CASE OF RESONANCE 
191 
One example will show how the positions of the points on 
such a hodograph are determined. If we assume a voltage of 
forty volts to be impressed upon the parallel portion (a) of the 
circuit the coil branch receives a current which can be repre- 
sented by the vector 0 40, while the condenser branch re- 
ceives a current 40 40. The total current will be represented 
by the vector sum of the two, which is the vector O' 40. It 
is possible to compute the magnitude and phase of the cur- 
rent for each frequency, as indicated by the lower hodograph 
and to add to these the corresponding' currents in the con- 
denser branch giving the upper hodograph as the locus of the 
ends of the total currents or total current hodograph. As 
shown by the vector diagram and the curve of figure 23 (e) 
the total current in such a parallel circuit lags at low frequencies 
and with increase of frequency decreases in magnitude, passes 
through a minimum near the frequency corresponding to unity 
power-factor, and then increases as a leading current. Thus in 
the case of inductance and capitance in parallel there are two 
frequencies at which the current has the same value and two 
frequencies at which the power-factor has the same value. 
A consideration of the characteristic current curves for series 
and parallel circuits containing both inductive and condensive 
reactance led the writer to believe that it might be possible to 
combine a series and a parallel circuit in such a way as to 
obtain much more complicated phenomena than those just de- 
scribed. It was conceived as possible that identical values of 
current and power-factor might be obtained at more than two 
frequencies, A little thought at once revealed the inadequacy 
of any conclusion based on current (admittance) curves like 
those of figure 23 (c) for they take no account of phase rela- 
tions. Also it is from the standpoint of impedance that cir- 
cuits are added in series. Some romgh calculations led to 
the belief that such a circuit as is represented diagramatically 
in figure 23 would yield interesting results. 
The circuit was made up of inductance coils, non-inductive 
resistances, and telephone condensers. A variable frequency 
generator was employed and the voltage kept constant at fifty 
volts. The current curve represented by the heavy line of fig- 
ure 24 (e) was secured. This curve was something of a dis- 
appointment but the power-factor curve, figure 24 (d) was more 
encouraging. Two attempts were then made to adjust the con- 
