124 KENNELLY AND VELANDER— POTENTIOMETER 



order to simplify the computation. With respect to the pairs of 

 terminals A B and CD, this network reduces to the A' B' C D' con- 

 nection of six elements. By any of the known processes, this may 

 be reduced to the equivalent T of Fig. i^h, in which the staff resist- 

 ance is 40.00025 ohms. It is evident that i ampere applied to this 

 T at the A B terminals, will produce 40.00025 volts at C D, and that 

 reciprocally i ampere applied to this T at the CD terminals will 

 also produce 40.00025 volts at B A. The "mutual impedance"® of 

 the network between the pairs of terminals B A and CD is thus 

 40.00025 ohms. 



Maxwell also showed^ that if continuous e.m.f. w^ere applied at 

 A B, and a current thereby produced through the terminals C D when 

 short-circuited, the same e.m.f. applied at CD would produce the 

 same current through the terminals A B short-circuited. A similar 

 theorem had been enunciated already by Kirchhoff.^° 



This proposition may, in a similar way, be given an interpreta- 

 tion in terms of the equivalent n of the network. In Fig. i^c,b c ad 

 is the equivalent n with respect to the terminals A B, CD. It is 

 evident that an e.m.f. of i volt applied at &o would produce a cur- 

 rent of 0.4379562 milliampere at c d, and that reciprocally, i volt 

 at c rf would produce the same current at a & shorted. In other 

 words, the mutual admittance of the network with respect to the 

 two selected pairs of terminals is the architrave admittance of the 

 equivalent IT. Moreover, the equivalent IT of mutual admittance 

 is the conjugate system of the equivalent T of " mutual impedance," 

 and may be directly computed therefrom. Consequently, if the 

 " mutual impedance " T of a network, with respect to two pairs of 

 terminals, has been ascertained, the mutual admittance 11 of the 

 same network and terminals can be deduced by Ti-T substitution 

 and without further experimental investigation." 



In Fig. 16, a relatively simple alternating-current plane network 

 example is worked out. The impedance of each element of the 

 nine-element network is marked thereon. The selected terminals 

 are AB and CD. The equivalent T is shown in Fig. i6h, and the 



8 Bibliography 12. 

 » Bibliography 3, 4, 8. 



10 Bibliography I, p. 32. 



11 Bibliography 6a. 



