no BELL SVSTRM ILCHXIC.IL JOURNAL 



and i=?'- (^3") 



4 4 



Whence Kb^% = \. (138) 



J, _ij _ Lid j^ _/l /,Qg^ 



and K.,^j^-jj^,- ^^,-j^ KMi) 



where /i and j-i are the lower and upper cul-ofT frequencies, respec- 

 tively, and /.\/ is the mean frequency {'^fi ft) of the structures of 

 Fig. 50. 



From (135) and (139) 



Therefore, when the relationships between the constants of the two 

 structures of Fig. 50 satisfy equations (138), (139) and (140), the 

 structures will have the same mid-shunt image impedance character- 

 istics. Explicit relations for the values of d', Li and Li may be 

 obtained from equations (138), (139) and (140) as follows: 



G' = G, (141) 



U = L.j\ (142) 



U = ^j^I^. (143) 



V/. fJ 



<f 



Therefore, if the constants and cut-off frccjucncies of a continent 

 structure are known, the constants of a structure of the 1' — 4 form 

 having an identical mid-shunt image impedance characteristic can be 

 deri\ed from equations (141), (142) and (143). 



BIHLlOGkAl'IIY 



1. Thrvi-nin, M. L., "Sur un .N'huvimu Thi-oremed'ElectricitO Dynamlquc," Cotnptes 

 Rrndus, Vol. 97, pp. I5<>-161 (188.1l. 



2. KtnnfUy, \. K., "The Kqiiivalunce of Triangles and Three-Pointed Stars in 

 Coiiducting Networks," lUectricai World and Engineer , New York, Vol. XXXIV, 

 pp. 4I.J-JI4, Sept. U>, 1899. 



i. CamplK-ll, (;. A., "Cisoidal Oscillations," Trans. A. L li. E., Vol. X.\.\, 

 I'arl II. p[). ,S73 <XW (1911). 



4. CamplH.ll, C. A.. U. S. Patents Nos/ 1,227,113 and 1,227,114 (1917). 



5. Gherarili, U. and Jewett, V . B., "Telephone Rerwaters, ' Trans. A.L E. E., 1919. 

 0. Wagner, K. W., Ardi. fur Eleklrolechnik, \o\. 8, p. 61 (1919); E. T. Z., Aug. 7, 



1919. 



