[ 148 ] 



X. Supplementary Note to Paper ' ' On the Criterion for the 

 Oscillatory Discharge of a Condenser"*. By Dr. E. H. 

 i- Bakton and Prof. W. B. Moktonj. 



IN the discussion which followed the reading of this paper 

 before the Physical Society it was pointed out that the 

 result obtained — viz., that on taking into account the distri- 

 bution of the current in the wire a condenser having the 

 critical capacity on the simple theory gives an oscillatory 

 discharge — seems to be contradicted by the well-known fact 

 that the resistance of a wire is greater, and its inductance 

 less, for oscillatory than for steady currents. Both the 

 increase of resistance and the decrease of inductance should 

 favour a non- oscillatory discharge. The explanation of the 

 apparent paradox is to be found in the effect of the damping 

 on the inductance. It was shown in the paper by one of us j 

 which has been already quoted, that the damping of the oscil- 

 lations causes an increase in both Ii and L. When the 

 damping is great and the frequency small, as in the neigh- 

 bourhood of our critical case, what may be termed the equi- 

 valent inductance L" becomes greater than the steady-current- 

 value. The investigation of the present paper shows that this 

 increase of L outweighs the increase of R, in its effect on the 

 criterion for oscillatory discbarge. It seems worth while to 

 examine this effect of damping on the inductance a little more 

 closely. 



The formula for equivalent inductance for current of the 

 form e~ lcpnipt is (eq. 16, loc.cit.) 



which shows that when the damping kp is sufficiently large 

 compared with p, then L">/(A + ^u), i. e. greater than 

 the steady-current value. We can form an approximate 

 notion of the stage at which this takes place by noticing that 



when k= — - the small terms written above are all positive. 



If we take the numerical value for a/i in case of iron, used in 



the beginning of the paper, viz. a^= \ and put a= 1 mm., 



we have roughly -^ as the value of ap. This would make 



* See page 143 supra. 



f Communicated by the Physical Society : read May 12th, 1899. 

 J Barton, " The Equivalent Resistance and Inductance of a Wire to an 

 Oscillatory Discharge : "read January 27th, 1899. Phil. Mag. May 1899. 



