60 BELL SYSTEM TECHNICAL JOURNAL 



If we assume a solution ot tlie torni 



where A and B are arbitrary constants, substitution shows that the 

 solution satisfies the differential equation for T' provided 



7^ = (L/>+i?)(Cp+G). (199) 



From equation (19G) it then follows that 



^^+^ (200) 



y 



Now restricting attention to the infinitely long line extending along 

 the positive x axis, with voltage Vo impressed directly on the line at 

 x = 0, the reflected wave vanishes and we get 



v=Voe-y\ 



I = ^l±^Voe-y\ (201) 



7 



y'-^iLp + R)iCp^G). 



y2^\[(p+py-a^ (202) 



Now let us write 

 where 



v^l/VLC, 

 ^ 2L^2C 



2L 2C 

 Then setting I^o = l, the operational equations of the problem become 



" 2L 2C 



F=g-T^'(^+P)'-''S (203) 



j^,(c+^)/> % ^ (204) 



V p) V(^ + p)^-cr- 



Now consider the operational equation, defining a new \-ariable F: 



F = p ^ - ' (205) 



V(^+p)=^-cr^ 



