30 Prof. E. Taylor Jones on Electrical 



27rT and 2ttT' are the longer and shorter periods of oscillation 

 of the circuits, i = v / — I, and j3 is given by 



2/3(T 2 -T /2 )=-(6' 1 -6> 2 )(T 1 2 -T 2 2 ). ... (2) 



When the oscillations are started by breaking a current i Q 

 in the primary circuit, the initial conditions are 



- QdVt/dt^ito Yi = Ri« , dY 2 /dt=0, V 2 = 0, when t=Q. 



Hence 2A = Ity'o? 









2 A 

 y 



— — 



s'o/Ci, 









SB 



-o, 





, • 







2* 

 y 



= 0. 





It can 



; aiso be 



sho 



vvn * that 





2By=^ 21 (T 2 2 + 2 2 )^ 



= -G„ say; 

 and that 



2B/=p 21 (T 2 2 + 2 2 )2A - 2<9 2 2By 



=p 2 i(T 2 2 M 1 ) • H^io + p 2 i(T 2 2 + VMc/Ci 

 = 2p 2l [T/ + 2 2 ) (^ + <9 2 ) iVd = G 2 , say. 



Hence, in order to determine the coefficients B we have the 

 four equations : 



Bi + B. + B. + B^O, 



Bi+B^ ^ + B 4=()5 



Ui 1/2 :i/3 y± 

 . B^ -f B 2 ?/ 2 -4-B 3 z/ 3 +B 4 ;^ = — Gi, 

 Bi^/r + B 2 */ 2 2 + B 3 y 3 2 + B 4 y 4 2 = Go. 

 Solving these for B^, we find 



B i - G^yg + ,y 3 + ,y 4 ) -' r G 2 



-* cy.iDi'ude, £<& p. 587. 



