of the Coefficients of Induction. 475 



In these equations T x and T 3 are the two quantities whose 

 sum is KR and whose product is KL ; T x is the larger of the 

 two, hut is less than KR. 



The values of /3 and 7 are given by the equations 



a , 1 R 2 2L/3 



The time taken to discharge is proportional to T 2 or to 

 -tp-, according as L is less or greater than £KR 2 . Both these 



XL 



values are less than KR, provided L<|KR 2 ; so that the 

 insertion of self-induction up to this value only hastens the 

 discharge. The time will be a minimum when L = ^KR 2 ; 

 and in this case T X = ^KR. It is therefore possible to halve 

 the time of discharge of a condenser by using a suitable 

 amount of self-induction in the discharge-circuit. 



A lightning discharge is essentially the same as that of a 

 condenser, and it therefore seems likely that a small amount 

 of self-induction in a lightning-conductor will only improve it. 

 The value of K may be small, but that of R is large, since it 

 quite possibly includes the resistance of the air-gap between 

 the lightning-conductor and the charged cloud ; so that the 

 product KR 2 , which determines the allowable value of L, 

 may be quite comparable with the self-induction of iron 

 lightning-rods, and may indeed far exceed it. 



Quite recently Dr. Oliver Lodge has shown experimentally 

 that an iron conductor is better than a copper one for high- 

 tension electric discharges, and has suggested that, owing to 

 magnetic lag, iron may have less self-induction for such dis- 

 charges, than in cases where time is an unimportant factor. 

 The foregoing considerations offer quite a different explana- 

 tion. Further experiments will no doubt be necessary to 

 settle the question ; but in the meanwhile there seems to be 

 no real basis for the idea that self-induction in a lightning- 

 conductor is necessarily a disadvantage. 



The writer, in conclusion, desires to thank Professor Ayrton 

 for many valuable suggestions received while the experiments 

 were being carried out. 



