274 BELL SYSTEM TECHNICAL JOURNAL 



Now in the double summation if the epoch T\s made sufficiently great, 



the factor -^^ ^ ^ vanishes everywhere except in the neighbor- 



hood of 0) = 0. Consequently, the double summation can be written as 



■G(o)G(o) 



2 r°° 1 -cos 0)7- , ^. \^ \^ G(o)G(o) l\p^rA( 



I 2(0) I 



Finally if we write A7 7' = » = average number of disturbances per 

 unit lime, and make use of formula (2j, we get 



N ^—1 Jo I Z(itxi) Y 



which can also be written as 



when ir = ir (t) is the current due to the r"' disturbance <(>, (/). 



Now the double summation vanishes when, due to the presence of a 

 condense or transformer, the circuit does not transmit direct current 

 to the receiving branch. Furthermore, if the disturbances are oscilla- 

 tory or alternate in sign at random, it will be negligibly small com- 

 pared with the single summation. Consequently, it is of negligible 

 significance in the practical applications contemplated, and will 

 be omitted except in special cases. Therefore, disregarding the double 

 summation, the foregoing analysis may be summarized as follows: 



RM = ^^\frM\' = n-r{.>), (21) 



J. «V,.rM^,„ (22) 



A ^^ Jn I Z{tw) p 



=;;^v^,,=„.^. (25) 



In these formulas n denotes the average number of elementary dis- 

 turbances per unit time, Wm the energy absorbed from the r'* disturb- 



