122 KENNELLY AND VELANDER— POTENTIOMETER 



dance or admittance is impressed, will give rise to 7i-i new circular 

 variations of current ; i.e., one in each of the other elements, assum- 

 ing all impressed e.m.f.'s simultaneously acting on the system re- 

 main constant. The circular variations in terminal p.d.'s through- 

 out the system will be of the order n-, neglecting intermediate po- 

 tentials between terminals. 



APPENDIX. 

 Circular Variation in Networks of Conductors. 



It is proposed to establish the following main proposition : 



In any network of conductors, all the elements of which obey 

 generalized Ohm's law, subjected in the steady state to any fre- 

 quency of constant e.m.f. (including zero frequency as the 

 limiting continuous-current case), circular variation of the im- 

 pedance of any element will produce a corresponding circular 

 variation in the current in every element of the network. 

 Moreover, the p.d. between any two points of the network will 

 be caused to vary circularly. The sending-end impedance or 

 admittance between any two points on the network will be like- 

 wise caused to vary circularly. By " circular variation " is 

 meant variation over a planevector circular locus, including the 

 straight-line locus as a limiting case. 



The prevalence of circular loci in relation to alternating-current 

 circuits has been recognized in the literature of the subject,^ which 

 contains various scattered theorems bearing upon special cases. A 

 few of these theorems may advantageously be collated here in pre- 

 senting the demonstration of the main proposition. 



It was shown by Clerk INIaxwell'^ that if, in any continuous- 

 current network, two terminals, say ^ and 5^ are selected as sending- 

 end terminals, and two other terminals, say C and D, are selected as 

 receiving-end terminals, a current / applied to the network at A B 

 would produce the same p.d., at CD, as would be produced at A B, 

 if the same current / were applied at CD. This theorem may be 



5 Bibliography, 5, 6, 7, ja, 10. 

 ^ Bibliography, 3 ; also 4, 8. 



