286 Mr. 0. Heaviside on the 



f-!J(i+AH^V...}]V (85) 



10 



105.99.91 



where 



tf'=(L'S)-^ and h=(R f /L'n) 2 . 



The factor outside the [ ] is the electromagnetic impedance ; 

 and, if we take only the first term within the [ ], we shall 

 obtain the former infinite conductivity formula (84). The 

 effect of resistance is shown by the terms containing h. 

 With this v l and h notation (83) becomes 



V /O o =iLV(H-70 i {6 2PZ + 6- 2P? -2cos2QZ}" ; (86) 

 where 



Ql=(nl/v% VT+A + l)"- sj\ 



Pl=(nl/v')( s/T+h-l)^ \/2. 



Choose Q so that 2Q£=2tt, and let h=l. This requires 

 nl/v' = 2' 85. Then 



V /C =iLV. 2* [e 8284 - + €-•• — 2]*, 

 = 60*61/ ohms, 



if we take v = 30 10 cm. = 30 ohms. This implies L'=L , and 

 the dielectric air. Without making use of current-density 

 differences, we may suppose that the conductors are thin 

 tubes. Therefore, 



Impedance 60 , 6L , .10 9 , . ono 

 Resistance = ~ -^-^bout fgf, 



by making use of the above values of h and nl/v'. 



But take 2Ql = \ir y or one fourth of the above value. Then 



V /C =28L'ohms, 

 and 



Impedance , ' * 



^ . ; = about #. 



Kesistance a 



Thus the amplitude of the current, from being less than 

 the steady-flow strength in the last case, becomes 42 per cent, 

 greater than the steady-flow current by quadrupling nl/v', 

 and keeping h=l. We have evidently ranged from some- 

 where near the first maximum to the first minimum value of 

 the impedance. These figures suit lines of any length, if we 



