106 Mr. J. Swinburne on 



a apparent " watts ; 7000 watts is only a small percentage of 

 this. 



Another unexpected effect has occurred at Deptford. There 

 is an extraordinary rise of pressure. No authoritatively accu- 

 rate accounts have been published, so it is difficult to say what 

 has happened ; but it is said that when the mains are put on 

 the pressure rises. This is generally explained by saying the 

 mains have capacity, and there is self-induction in the circuit, 

 and the capacity and self-induction have a period which cor- 

 responds with the frequency of the dynamo, so that the 

 system sympathises, or acts as a sort of electric resonator, 

 thus giving abnormally high pressure. A little consideration 

 will show that this theory is untenable. With such a capacity 

 as that of the Deptford cables the self-induction would have 

 to be enormous. 



Let the capacity of the cable be K, and the self-induction 

 of the circuit L, in farads and henries or quadrants. Call E 

 and C the electromotive force and current respectively. Then 



■ -L* 



dt 



and n _ xr ^ 



"~ dt' 



Combining these equations, 



so 



and integrating, 



dt 2 ~ KL ; 



dEcP]Z_ E_dE 

 dt dt 2 ~ KL dt ; 



where a is a constant ; 

 or 



so 



and integrating, 



dlfi 1 //-I7I9 . 



-dt=--^KL^ + ° n 



^SB=-dt, 



y/W-ha 



E 



\/KL cos -1 — =t. 

 a 



