MEASUREMENTS AT TELEPHONIC FREQUENCIES. 129 



The current h- passing through the constant load a at C Z) is 



3'2 E.-y2 

 Ic = Ia ' — , — = 7 , 77 , ^— , — amperes Z (28) 



The denominator in this expression is a vector which undergoes cir- 

 cular variation, when s^ is varied circularly, and since Ey^. is con- 

 stant, Ic must also vary circularly. This means that the receiving- 

 end impedance of the network at CD, with respect to constant e.m.f. 

 at AB, undergoes circular variation as 2^ is varied circularly. 



If constant current and not constant e.m.f. is impressed at AB, 

 through a circularly varied impedance s^, a similar expression for 

 receiving-end current and voltage at CD is obtained. 



Finally, if with s-^ and a constant, the impressed e.m.f. and cur- 

 rent are varied circularly at AB, it is manifest that the p.d. and the 

 current in each and every element of the network, including the 

 load at CD, will be varied circularly and in the same simple propor- 

 tion. In this case, the circular variations reproduced are all of the 

 same type throughout the network, whereas in the preceding cases 

 discussed, the circular variations produced are, in general, different 

 in the dift'erent elements. 



We have hitherto considered only the pairs of terminals A B 

 and CD. Since, however, these are chosen arbitrarily in the net- 

 work, the above propositions must apply between any pairs of termi- 

 nals ; so that if the impedance load at any pair of receiving termi- 

 nals is varied circularly, the impedance of the system, including the 

 load, will be caused to vary circularly at any other pair of terminals. 

 Moreover, if either the current or the voltage impressed at any pair 

 of terminals is varied circularly, the potential and current at any 

 other pair of terminals will be caused to vary circularly. The case 

 of constancy, or zero variation, must be included as belonging to a 

 circular locus of zero radius. Zero variations will occur if the termi- 

 nals AB are "conjugate" to the terminals CD}^ 



Finally, the current in any element of the network must vary 

 circularly when a constant e.m.f. is impressed at any pair of termi- 

 nals and any other element has its admittance, or impedance, circu- 

 larly varied. This is seen from an examination of Kirchhoff's or 



1* Bibliography i and 3. 



PROC. AMER. PHIL. SOC, VOL. LVIII, I, JULY I I, I9I9. 



