430 



dv 4V h* - h 4^° 



dt\ 7T ck 1 





Mr. O. Heaviside on Telegraphic 

 1 1 



1 + 



4W 



(2i-l) 



2„-2 



(2t— l)wa? 



8=3 ' Mn — 2Z— 



(2t-l)2tr2< 

 . g 4ckfl 



1 + 



J / 2f -_i\ > (2i-1)to 



(2i-l)V 



2^.2 



, € 4cAr/2 > 



This becomes, when A=0, 



— as • y, (2z — ll.SlU- ' .6 4ckP 



dt ckP Zl[ } 2/ 



A unit of time of a very convenient magnitude for practical 

 calculations is 



ckP 



>{7) 



(8) 



« = 



IOtt 2 



log, 10. 



dv 

 Employing this unit, we have the following series for v and — 



when x—l and h = 0: — 



1 9* ". 1 25* 



(9) 



V =V-— (10"^-i.l0~«« + ^.10 ioS-&c). 



7T O O 



//75 Vtt f 9* _25« 



^ = -^(10""4o5-3.10"ioi+5.10 ioi-&c). 



(10) 



The " arrival- curve " for v, calculated from equation (9), is 

 shown in fig. (2). 



Fig. 2. 



uo 

 90 



80 



70 

 60 



50 

 40 





























































































































































10 









































(in 



