512 Mr. E. C. Rimington on Luminous 



The current 



c=§= T Q T fmiU= ^-e at smbt. . . . (3) 



at 6KL un 



Now the electric stress acting in the bulb is proportional to 



dc 

 the rate of change of current, or to 



and 



w 



° '- ~ dt 9 



d G V at / . 1x . , 7jX 



— = —- e (a sin bt + o cos 6n 

 dt on v 



The current itself will be a maximum or minimum when 



do 



dt 



=0 



?\ e. when 

 or when 



. tt 



a sin bt + & cos fa = 0, 



tanbt=- b = x /-^±-l. 

 a V KR 2 



Therefore bt — 0, and is in general nearly equal to* ^ 



The maximum values of the current occur when 



bt = 0, 2tt + 0, 4tt + 0, &o., 



and the minimum values when 



bt = 7r + 0, 3tt + 0, 5tt + 0, &c. 



This is shown in the curve (fig. 9), the points M 1? M 2 , M 3 , 

 &c, representing the maximum and minimum values of the 



current. The distance A represents 0, and AB= - —0 = 7]. 



It is now necessary to consider when the rate of chance of 



the current is greatest. — will be a maximum or minimum 



° dt 



d 2 c 

 when^-g =0. 



dt 2 



Now 



Hence 



Let 



d 2 c V 



d? = 0L ta *{( a2 - h ' 2 ) si » I>t+2ab cos bt\ = 0. 



tan fa = 



'lab 

 tf-b 1 



__R v/K(4L-KR 2 ) 



2L-KR 2 



fniW ftVK(4h-KR 2 ) 



2L-KR* X ' 



fy will be in general a small angle. 



