OSCILLATING DISCHARGES. 513 



The general integral of this equation is 

 (20) Q = A^ + Ay ;/ , 



p and p' being the roots of the quadratic equation, 



which gives 



= - + / R2 _L 



"~~ 



According as L^ -- , these roots are real or imaginary. 

 4 



The constants A and A' are determined by the condition that 

 for /=0, we have Q = Q , and 1 = 0, which gives Q = Ap + A'p. 



If the roots of the equation (21) are real, then representing 



the radical 



Q = Q ^ 2L 

 (22) 



/"R* ~ 

 ical^/- , 



I R\ a, /x R\ -a,"] 



-+ r ) e + ( --- r ) e h 

 2 4 aLy \2 4 aLy 



at -at\ 



'-' ) 



When the roots are imaginary, we may still take the integral 

 in the same form, and replace the constants by their imaginary 



V~i R2~ 

 --- , we get then 



r R i 



cosaV + sinaV 



(2$ 



O - 



^fLC e ' 



L L 



