222 Prof. 0. J. Lodge on the Theory 



R the discharge is thoroughly oscillatory, and the strength 

 of the current at any instant is 



C=^e~ mt sin nt, (3) 



where m= 9 y , and n 2 = ^ — m 2 . The impedance is, there- 

 fore, nL. 



When the discharge is thoroughly oscillatory n is greatly 

 bigger than m, so that the above is practically 



c =^k^ sin v(k) « 



^ 2L 



The time-constant of the dying-away amplitude is -j^; the 

 period of the alternation is 27rV(LS). 

 The frequency constant, 



is very great, being usually something like a million a second, 

 more or less. 



Now Lord Rayleigh has shown (Phil. Mag. May 1886) 

 that with excessive frequencies of alternation the resistance of 

 a conductor acquires the following greatly modified value, R 

 being its ordinary amount, 



B'=vU«V R!, (5) 



V(*-4 



Or, taking the permeability of the conductor the same as that 

 of the space outside, 



R^I^RB.) (6) 



The actual resistance is, therefore, some fraction, something 

 like say an eighth, of the geometric mean of the ordinary 

 resistance of the conductor and the critical resistance (2). 



Under the same circumstances the value given by Rayleigh 

 for the inductance is 



L'=(L for space outside conductor) + a / (— — Y 



or, as we shall now write it, 



L'=M« 2 +? (7) 



