MEASUREMENTS AT TELEPHONIC FREQUENCIES. 127 



Fig. i6b will also have circular variation, and the admittance of this 

 branch, including this load, must also vary circularly by the geome- 

 try of inversion. ^^ If, then, we add the constant admittance of the 

 staff leak g^, Fig. i6b, it follows that the total admittance on the 

 right-hand side of 00' will have circular variation, under circular 

 variation of the load at B C. Taking the reciprocal of this circular 

 admittance, the impedance of the system on the right-hand side of 

 00' will also have circular variation. Adding to this the constant 

 impedance A O , the total sending-end impedance at terminals A B 

 must have circular variation, as likewise the sending-end admittance. 



Consequently, a circular variation of load a.t D C must produce 

 a circular variation of current a.t A B under constant impressed 

 e.m.f., or a circular variation of voltage at A B under constant im- 

 pressed current. 



Again, referring to Fig. i6c, if the constant e.m.f. impressed at 

 ab is E, and an admittance load 3', which varies circularly, is applied 

 at terminals dc, then the admittance at ab, excluding the constant 

 leak ab is the circularly varying admittance : 



Y = mhos Z (22) 



P + —J— 



Hence the entering current in the architrave ad will be 



^ = ^3'=,+pfe + y) amperes/ (23) 



Of this current, the fraction y/igo-^y) will pass through the load 

 and the current i in this load will therefore be 



^■ = i-+pJ+3,) amperes/ (24) 



The ratio E/i is the receiving-end impedance of the loaded system 

 and is 



I -\- pgo 



Z = p -\- ohms Z (2=5) 



y ^ >^/ 



^3 Bibliography 2. 



