248 PROCEEDINGS OF THE AMERICAN ACADEMY. 



where, according to Figure 1, i?i and R^ are the resistances ; L^ and 

 L^ the constant coefficients of self-induction, in the two branches ; 



/f. Ir 



Fig. 1. 



p ^= 2 IT n\ I, I\, and I^ are the maximum values of ^, ?'i , and ^2, or 

 the square root of their mean square values multiplied by the square 

 root of 2.* Formula? (1) and (2) may be written 



z\ — /i sin {j) t + ^i), 



i2 = I2 sin {p t -\- 6^; 

 where 



(3) A= iVR^ + fW 



V(Ri + R,r+p'{L, + L,y 



(4) i,= iVB^+rL^ 



Dividing (3) by (4), we obtain 



so that by measuring p, Ri, Ro, and -y? , we can calculate the value 

 of L,. " ^' 



Now, considering the practical case, we see that, though the current 

 curve is distorted by the varying permeability of the iron core and 



* See Fleming, Alternate Current Transformer, I. 133. 



