130 KENNELLY AND VELANDER— POTENTIOAIETER 



Maxwell's demonstration/' when the reasoning is extended to com- 

 plex quantities. It may be seen that in the symbols here employed, 



A-\-By 

 irs = Epq • r -i. J) amperes Z (29) 



where irs is the current in the element rs, when the e.m.f. Epq is 

 inserted in the element pq, and y is the admittance of any third ele- 

 ment ttv, which is subject to circular variation ; while A, B, C, and D 

 are system constants, independent of y. It is well known, from the 

 theory of functions of a complex variable, that the linear transfor- 

 mation represented by (29) gives rise to a circular locus, if y varies 

 along a circle. 



It may be noted that by reason of the known principle of vector 

 superposition of currents in a network, the multiplication of circular 

 loci extends to cases where a plurahty of e.m.f. 's coexist. The 

 proposition may also be extended to include mutual inductances. 

 Strictly speaking, iron-cored inductances are excluded, however, 

 owing to the imperfect application of Ohm's law to them, under 

 varying permeability and magnetic skin effect. 



If the impressed alternating e.m.f. or e.m.f. 's are impure, so that 

 harmonics are present, any rectilinear variation in the impedance or 

 admittance of any element in the network will also be rectilinear for 

 any harmonic frequency, and so will give rise to circular variations 

 in the harmonic voltages and currents throughout the network as 

 well as in the fundamental. In other words, the multiplication of 

 circular variations in a network, due to rectilinear variation in the 

 impedance or admittance of one element, applies not only to the 

 fundamental frequency, but also to any superposed frequencies. 



Summary. 



1. Experimental results obtained with a new type of a.-c. poten- 

 tiometer are discussed. 



2. The circular graphs of current and admittance are analyzed, 

 for the case of a simple RLC circuit, at the successive constant fre- 

 quencies of 500, 1,000 and 2,010 cycles per second, when either R 

 or C is varied alone. 



15 Bibliography i, p. 25 and 3, Vol. i, Section 282a. 



