\t {\ty (\ty ' ^^^^^ 



ELECTRIC CIRCUIT THEORY 59 



Now identify \/p with l/x^irt in accordance with the Heaviside rule, 

 and 1/p with ) dt. We get 



Vap+^= yj ^ I 1 + 1]— 3! +5! ^^^^- • • I • (180) 



Now in the terms of the expansion (178) identify p" with d"/dl" 

 and substitute (180) ; we get 



'^-■- I '+U4+^)+U'''4-+'-4+^')+ ■■ 

 This series is hopelessly complicated to either interpret or compute. 

 It is, in fact, an excellent illustration of the grave disadvantages under 

 which many of Heaviside's series solutions labor. We shall there- 

 fore attack the solution by aid of the theorems and formulas of a 

 preceding section. The simplicity of the solutions which result is 

 remarkable. 



The operational formula for the voltage is 



V=e~^°^+^. (175) 



Now the operational formula for the voltage in the non-leaky cable 

 is (see equation (164) ) 



In order to distinguish between the two cases, let us denote the voltage 

 in the latter case by V°; thus 



^o^g-V^. (182) 



Now by theorem (\'II) and equation (182) we have 



FV-X' = ^ (>- \'o.(p+\) 



(183) 



Now write (175) as 





=0+1) 



pj p-\-\ 



(184) 



