34 Messrs. E. B. Eosa and A. W. Smith on a Resonance 



parallel, as in fig, 11. Of course there is a slight leakage 

 current in every case, if the resistance of the dielectric is not 

 infinite. Boucherot* says of his paraffin-paper condensers 



Fig. 11. 



WWWWV- 1 



that the " heating is chiefly due to the Joule 

 effect, that is, to leakage current; the action 

 of dielectric hysteresis, if it exists at all, 

 being very slight." We shall give reasons in 

 a subsequent paper for believiug that this is 

 seldom, if ever, true of good condensers, but 

 at present let us assume it to be true. Then 

 the condenser current is 90° ahead of, and the 

 leakage current in phase with, the impressed 

 electromotive force. I being the total cur- 

 rent, the condenser current is I sin <f> and the 

 leakage current is I cos <£. The energy 

 stored is 



W = iCE 1 2 , 



and the energy dissipated per second is 



JExIj cos <£, 



or per half-period 



™ = 4n ElIlC0S( ^ 

 The maximum condenser current, I x sin <£, =pCE 1 . 



w 



_ E 1 2 .joCcos<j> _ 1 

 4n . sin (f> ~ 2 



CExV cot (f>. 



w 



as before. 



V 6=1 — ™.= 1 — 7T COt (py 



Referring to fig. 13, we can derive anew the value of the 

 net efficiency. Curve 1 is the electromotive force, curve 2 

 is the current, in advance in phase by the angle (/>, nearly 

 90° ; curve 3 is the power, the positive and larger loop being 

 the work done on the condenser, and the negative and smaller 



* VEclairage Electrique, Feb. 12, 1898. 



