126 KENNELLY AND VELANDER— POTENTIOMETER 



In the equivalent T's of Figs. 15 and 16, all of the series im- 

 pedance appears in the upper arms, and none in the lower arms. 

 All of the impedance might, however, be transferred to the lower 

 arms, without altering the equivalence of the circuit. ^Moreover, 

 any desired share of impedance might be transferred from the 

 upper to the lower arms, according to the rules of T and / equiva- 

 lent circuits.^- Similarly, the architrave impedance of the n's of 

 Figs. 15 and 16 may be either wholly or partly transferred to the 

 lower line. 



In any dissymmetrical T and its conjugate 11, we have the re- 

 lation 



Pi R\ gl • / / ON 



— = — = — numeric Z (18) 



P2 -^2 gi 



In the case of Fig. 15, this ratio is 1.2857. In the case of Fig. 16, 

 it is 0.53348 Z 99°. 46'.47". This also means that in any a.-c. case, 

 the difference in the slopes of p-^ and p., will be the same as the dif- 

 ference in the slopes of R^ and J?o, or 



Pi - po = ;^i - ^2 = i2 - gi degrees (19) 



this difference being 99°.46'.47". 



Again in any dissymmetrical T and its conjugate or equivalent 

 n, the geometrical mean of the two T-arm impedances, times the 

 architrave admittance equals the geometric mean of the two IT-leak 

 admittance times the T-staff impedance, or 



V Vpipo = Rr'^gi-g2 numeric Z (20) 



In the case of Fig. 15, this product is o. 11 587. In that of Fig. 16, 

 it is 0.094224 Z 62°. 6'.4o". From this relation it also follows that 



^T + fi = ^ + P2 degrees (21) 



In the case of Fig. 16, this qviantity is 12°. 13'. 16". 



Returning now to the main proposition, if an alternating-current 

 network is connected, at the receiving-end terminals D C, to a. circu- 

 larly varied impedance load, the impedance of the circuit ODCO', 



^2 Bibliography 11 and iia. 



