TRANSIENTS IN GROUNDED CIRCUITS 769 



result for this case then becomes 



VM = ^Ae-'- - e-'^") 





P „-Tr\xi jt 



e 2/3 + /3/4 , 6/4 + 6/3/5 + 132/6 



+ 



irXx^ (7rXx2)2 ' (7rXx2)3 



24/5 + 36/32/6 4. 12^2^7 _|_ ^3^8 



uxx^y 



+ 



(19) 



For large values of time, introduce a new variable ^ — /3r of integration 

 in the integral in (18). Then 



^^^(^^ = ■^2iC^-^' - ''~''^'") (20) 



where 



C= 1 + r e-(^i^^+id^,\ 



*^" ^ (21) 



s = xXjc2/3. J 



The values of C are given on Fig. 3 for important ranges of r and 5. 

 For 5 equal to and less than 10~2, C is for practical purposes inde- 

 pendent of s. 



I am indebted to Dr. F. H. Murray, and Mr. R. M. Foster of the 

 American Telephone and Telegraph Company for valuable suggestions 

 during the course of this work, and to Miss R. Pedersen who carried 

 out all the numerical calculations. 



