= l+ToP 2a V-f«nAV...., . . (17) 



436 Dr. E. H. Barton on the Equivalent Resistance and 

 and 



or J- (16) 



L«=z[A+Mi+ l^-^^^V-^j^^V..-)] J 



Putting £ = in these equations and denoting by single- 

 dashed letters the corresponding values of the resistance and 

 inductance, we have 



-t*' 1 i ■*■ 2 2 2 



s =i+_^v- lTo 



and 



L'=Z[A + Ki-^*V...-)], • • (18) 



which are Lord Rayleigh's well-known formulae * for periodic 

 currents of constant amplitude. 



By taking the differences of the resistances and inductances 

 with damping and without, we have at once 



*L^K =k yaY+ ^^-V«V+ (19) 



and 



L''-L=^(j-.^+|V"V ••••)• • • (20) 



These show that if the frequency is such that a few terms 

 sufficiently represent the value of the series, then both resist- 

 ance and inductance are increased by the damping. 



High- Frequency Discharges. — Passing now to cases where 

 p is very great, as in the wave-trains in or induced by a 

 Hertzian primary oscillator, we have from equation (10), 



where s= y/l + k 2 and cot6 = k. 



On substituting this value of <p/4>' in equation (12) and 

 collecting as before, we obtain the solution sought, viz.: 



^q = (*H*ps d )* cos 2+(i—k)pya A + *s/a/j,s/p cos A; (22) 



whence R" , ,. x 6 nON 



-g- = (a/ips z ^cos-^, ^23) 



Equations (19) and (20), p. 387, loc. cit. 



