132 Dr. 0. J. Lodge on Intermittent Currents 



Equation to a continuously Intermittent Current, 



9. It would be interesting to obtain an expression for the 

 current when the resistance of the circuit varies continuously 

 from some finite value to infinity and back again in a short 



regular period -. Thus E might be supposed to be p sec 2 cot; 



and the equation would be 



di 

 L— +pisec 2 cot=ft, * (9) 



of which the solution is 



i=Ce l +je L \e l dt; . . (10) 



but the integral je tan x dx does not appear to be evaluable except 

 bj an unmanageable lot of series. 



Equation to an Alternating Current. 



10. Instead of varying the resistance, we may produce an 

 alternating current by a periodic electromotive force, as, for 

 instance, when the circuit contains an electromagnetic machine 

 of constant resistance, such as a telephone itself. The electro- 

 motive force is then representable by a simple harmonic func- 

 tion or by a sum of a number of these. Take the simplest 

 case, 



di 

 L^- + Ei=Esin27rw*, .... (11) 



where the electromotive force oscillates from E to — E and 

 back again n times a second. The solution of this is 

 "P 

 •r T-sm27rnt—27rn cos lirnt tti 



i= c^' + L _ _.£. • (12) 



The first term rapidly dies out; and so the permanent value 

 is 



._ E sin& )£— \q)Cos cot /1Q n 



l ~R- ITxw ' ••••••• Wfc 



writing co for 2irn and \ for the time-constant ^. 



On the Law of Variation of a Battery-current in a 

 Polarizable Circuit. 

 11. In the previous sections we have considered the elec- 

 tromotive force E of the battery to be constant. Now this 



