744 BELL SYSTEM TECHNICAL JOURNAL 



frequencies. Experience has indicated that the CS and CIF insulators 

 reduce the daily leakage (and attenuation) variations due to change 

 in weather conditions to about one-third and one-half, respectively, of 

 their value for DP insulators. This degree of stabilization is not indi- 

 cated by the differences between the dry and wet weather leakage 

 values shown in the figure, but it must be recalled that these values 

 represent extreme conditions, while the stabilization referred to above 

 is for average conditions. 



Attenuation 



The attenuation constant is the real part a of the propagation con- 

 stant 7 as given in the familiar formula 



7 = a +i^ = V(i? +7Xco)(G + jCco). (5) 



The attenuation constant is also given by the following expression 



a^ = 1/2 [V(i?' + L2co2)(G2 + CV) - (LCco^ - RG)]. (6) 



Where L-co^ is large compared to I^ and CW is large compared to 6^, it 

 can be shown ^ that Equation (6) reduces to 



"^iVz + lVc- ^^^ 



This formula is very useful for computing the attenuation of open-wire 

 circuits at carrier frequencies, in which case its accuracy is adequate 

 for all practical purposes. It is frequently of value also for quick 

 computations of the approximate attenuation of open-wire circuits in 

 the voice range. 



The first term of Equation (7) represents the series losses, and is 

 commonly referred to as the "resistance component of attenuation," 

 while the second term represents the shunt losses, and is called the 

 "leakage component of attenuation." It will be observed that the 

 resistance component of attenuation varies inversely with the quantity 



'-^ , while the leakage component varies directly with the same quan- 

 tity. This quantity -i /-^ , as will be seen later, represents the nominal 



characteristic impedance of the circuit. 



It is shown in Appendix II that a circuit of fixed resistance and leak- 

 age conductance will have minimum attenuation when the ratio of L to 



^ See "Transmission Circuits for Telephonic Communication," by K. S. Johnson, 

 N. Y., Van Nostrand, 1927. 



