198 IOWA ACADEMY OF SCIENCE Vol. XXIV, 1917 
The hovering of the power-factor around unity must of ne- 
cessity appear in diagram (i) in which the total voltage is 
plotted vectorially with the total current as the axis of refer- 
ence. As the frequency increases the voltage vector swings 
from a lagging position up beyond the axis. It then swings 
below the axis and finally swinging across the axis for the third 
time continues to lead the current at an increasing angle. 
The lower part of Plate X (i) shows the power-factors of the 
parallel and series circuits for comparison with the power-factor 
of the whole circuit. In Plate X (m) are plotted the values 
of the three voltages. 
The control which can be exercised over the results is very 
well illustrated in figure 25. It was decided, if possible, to 
cause the power-factor to have two minimum values equal to 
each other and equal to the values at the extreme frequencies. 
A glance at Plate X (c), (f), or (1) will show that this neces- 
sitated a nice adjustment of the constants. Figure 25 gives the 
circuit and the results. The current curve and the power curve 
are also interesting. 
In the two circuits that have just been described an attempt 
was made to secure certain definite results, one of them being 
that the curves should be of symmetrical form. It is perfectly 
evident that current and power-factor curves of various forms 
