560 



BELL SYSTEM TECHNICAL JOURNAL 



The envelope of the oscillations is proportional to 



vhere A{ij.) is Airey's Inlenral" and 



Hf)' 



t-B'{u>) 

 y/B"'{o,)/V. 





(O))" 



(8) 



(9) 



(10) 



At time t = B'{<ji) the envelope A' has reached 1 3 of its ultimate steady 

 value and its rate of building-up is inversely proportional to -s/5"'(a)). 



Fig. 1 



The cur\e of Fig. 2 is a plot of the envelope function ^ + ^ / A (m)^/u 



3^2^o 



to the argument y and is therefore of general applicability under the 

 circumstances where case II obtains. 



The practical value of the foregoing propositions resides in llie fact 

 that they enable us tt) calculate two important criteria of tiic trans- 

 mission properties of the line: (1) the variation with respect to fre- 

 quency of the time interval t required for the current tn build-up to 



' See Watson, Theory of Bessel Functions, p. 190. 



