Resistance and Inductance of a Wire to a Discharge. 433 



a platinum tube, and less simple than the current in the 

 wire. 



The results of the foregoing experiments were communicated 

 to Section Gof the British Association at Toronto, and a brief 

 abstract appears in the B. A. Report for 1897, but the curves 

 were not reproduced. 



In conclusion, I should like to thank Professor Oallendar 

 for kind suggestions and other assistance. 



Macdonald Physics Laboratory, 

 December 20, 1898. 



XL. The Equivalent Resistance and Inductance of a Wire 

 to an Oscillatory Discharge. By Edwin H. Bakton, 

 D.Sc, F.R.S.E., Senior Lecturer in Physics, University 

 College, Nottingham *. 



I.N an article in the Philosophical Magazine for May 

 1886 f, Lord Rayleigh, whilst greatly extending Max- 

 well's treatment of the self-induction of cylindrical con- 

 ductors, confined the discussion of alternating currents to 

 those which followed the harmonic law with constant ampli- 

 tude. The object of the present note is to slightly modify 

 the analysis so as to include also the decaying periodic 

 currents obtained in discharging a condenser and the case of 

 the damped trains of high-frequency waves generated by a 

 Hertzian oscillator and now so often dealt with experi- 

 mentally. In fact, it was while recently working with the 

 latter that the necessity of attacking this problem occurred 

 to me. 



Resume of previous Theories. — To make this paper in- 

 telligible without repeated references to both Maxwell and 

 Rayleigh, it may be well to explain again the notation used 

 and sketch the line of argument followed. 



The conducting wire is supposed to be a straight cylinder 

 of radius a, the return wire being at a considerable distance. 

 The vector potential, H, the density of the current, w, and 

 the " electromotive force at any point " may thus be con- 

 sidered as functions of two variables only, viz., the time, t, 

 and the distance, r, from the axis of the wire. The total 

 current, C, through the section of the wire, and the total 

 electromotive force, E, acting round the circuit, are the 

 variables whose relation is to be found. It is assumed that 



H=S + T + V 2 + .... +T,r* . . . (1) 



* Communicated by the Physical Society : read January 27, 1899. 

 f " On the Self-induction and Resistance of Straight Conductors." 



