568 Prof. Morton on the Propagation of Polyphase 



7. Effective Resistance, Capacity, and Inductance of the 

 Leads. — For slow oscillations along a line of resistance R, 

 inductance L, capacity C, and leakage conductance S, all per 

 unit length, we have 



m*=-(K + ipL) (S + *j?0); 



With no leakage, as in the present case, 



m 2 =—ipC(R-{-ipL) 



•2tt 



(?-)■ 



If the attenuation is small we get from this 



R 



2LV 



If we throw into the above form the m 2 found for a poly- 

 phase system, we can find the R, L, and C of a lead which 

 Avould produce on slow oscillations the same diminution of 

 speed and the same attenuation. In separating out the 

 constants we are guided by the fact that, when p vanishes, R 

 must become the ordinary steady-current resistance. 



We have 



log 



J hjxd x {k 2 a) ' 



fxk 2 [~ k 2 2 a' 2 1 k 2 a^ 1 k 2 6 a 



~k 2 2 a 2 L W V ' « 



7 2 2_ 47T/J,a 2 ip _ 4cifMp 



/to (Z - 



2 " ~ - - R ' 



'writing R n for-^-s, the steady-current resistance of unit 



length of wire. 



.-. m 2 = — z/>C (R -f iph) 



- v* L 1 ]ocr ^ ^ r + Bo + e R 2 "" u r; • • JJ. 



