114 KENNELLY AND VELANDER— POTENTIOMETER 



current of circular locus in the main circuit. The p.d. at the termi- 

 nals qq' must also have a circular locus, as it consists of the vector 

 difference between the constant impressed e.m.f. E, and a vector 

 drop of circular locus due to a circular-locus current in the constant 

 impedance of L and C. Consequently, the fixed branch / must re- 

 ceive a current of circular locus. The current in the variable con- 

 denser branch must also have a circular locus, as will be seen from 

 the following relations. The main current / is 



E , , 



I = amperes Z (13) 



= 7 — , 7 N I -7 amperes Z (14) 



where g is the fixed admittance of the coil / or i/{r -\- jIm) in mhos 

 Z , and Z is the fixed impedance, in ohms Z , of the main EC circuit, 

 outside of the Ic combination. 



This main current / has already been shown to have a circular 

 locus, in reference to Fig. 9, and the conclusion is confirmed alge- 

 braically from (14), by Mobius' theorem, as will be further dis- 

 cussed in the appendix. 



The branch current in the condenser Ic is 



jcoi Ejcoj E 



Ie = I — 7-^ =7 — , ^ X 1 -y = n^ amperesZ (15) 



g+JCo: (l+Zg)+jZcco .I+Zg 



Z-J-- 



Ceo 



In its last form, the expression for h indicates the inversion of a 

 straight line, which shows that h has a circular locus, passing 

 through the origin. The branch current in the fixed inductance I is 



1 1 = I — — ^ = 7 — , „ X , -y amperes Z (16) 



g-\-JCoo (l +Zg) -fjZcco 



also evidently a circular locus when c varies. 



Consequently, by analysis based on purely electrical relations, 

 the vector circular locus Im is resolved into a pair of component 

 vector circular loci h and Ic, such that at any assigned value of the 



