314 
IOWA ACADEMY OF SCIENCE 
rent. The line Lm upon which end the vectors representing the 
various values of the total current is, of course, parallel to On. 
If the angle ■©- has been taken correctly all of these total cur- 
rent vectors as found by the parallelogram method will check 
exactly with the observed values. If -©-is taken too small the 
resultants will all be too short, if is too long the resultants 
will be larger than the observed values. A cut and try method 
could be employed but there is one of the total current vectors 
which has such properties as to make it possible for it to be used 
to determine the position of the line L m. This vector is the 
one shown in figure 19 as 0 H represents the minimum value 
of the total current and as the figure shows must be perpendicu- 
lar to the line L m. 0 L, 0 B^, and L B^ must then form a right 
angled triangle of which two sides are known. Thus the slope 
of A m is determined and with it the slope oi 0 n and ultimately 
the value of the angle -e- which is the phase difference of the con- 
densers. The method of procedure is as follows : 
The required data are secured for a parallel circuit such as 
that of figure 16 and plotted as in figure 17, smooth curves being 
drawn which are more accurate than the single observations. 
The vector 0 L is drawn with its length proportional to the cur- 
rent in the coil. As the impressed electromotive force is taken 
as the axis of reference, 0 L lags behind 0 Y by an angle de- 
termined by the resistance and impedance of the coil. With 0 
as a center and with a radius corresponding to the minimum 
value of the total current the are d is described. From the point 
L a line L m is drawn tangent to this arc. From 0 a line 0 n 
is drawn parallel to L m, this line giving the direction of the 
capacity current vectors. 0 y drawn ninety degrees ahead of 
the axis of reference. The angle between 0 y and 0 n is there- 
fore the phase difference of the condensers. 
The phase difference may also be determined from the fol- 
lowing formula 
—\r — 1 IL 
-e- = Cos — — Cos — 
It 
in which r is the resistance of the coil, z its impedance, I l the 
coil currents, and I t the minimum value of the total current. 
In the development of the above theory a sine wave electro- 
motive force has been assumed. If there are higher harmonies 
the effect will be to increase the apparent value of the phase 
difference. In this case there will be no value of the capacitj^ 
