Experiments with Open Circuits. 59 



If the roots of this equation are p x and p 2 , then 

 #=Ai sinp 1 t + A 2 sin p 2 t, 



y Ma mplt+ \l sinM 



or, as it will be more convenient to write them, 

 #= A' cos pit + A! r cos p 2 t, 



W= ^1 1 COS »!« + ^ i COS 2 *. 



Now, if i and ^ are the initial currents in the coils (1) and 

 (2) respectively, and if they are produced by breaking a pri- 

 mary circuit through which a current j flowed, % andj will be 

 determined by the equations 



Li+N/=Fy, 

 N*+M;'=Gy, 

 where F and G are the coefficients of mutual induction between 

 the primary and the coils (1) and (2) respectively. Thus i 

 and j are independent of the capacities of the condensers in 

 the circuit. 



A / and B / are given by the equations 



*=A' + A", 



A! A" L 



i= W? + 03W~N (A ' + A " ); 



or 



(H?+Li)C 1 =^ + %. 

 Pi \p% p\) 



Now, if p 2 be >Pi, then A" is > A'; so that in ,v the term 

 of shortest period has the largest coefficient. 

 If the circuit (2) be closed, then 



&=i cos pt, 



