152 Prof. E. Taylor Jones on the Potential 



If we neglect the square of E in comparison with that o£ 

 io^TrnjCx and of i /27m 2 C 2 , these become approximately 



A 1 = 



h 



27Tn 1 (Y 



h 



27TW 9 C« 



(26) 



Also, by (25), 



ton^-i ^q + W 



, , 2t™ 2 E(1 + X 2 )C 1 . 



tan o 2 = ^ — L ' 



(27) 



and by (20), 



X^ — X 2 



! 2 2 -V 



47r 2 (L 1 + L 21 )Cr nxV ' 



Equations (22) and (23) therefore give the following 

 solutions for V 2 and Vi : — 



V, 



27r(L 1 + L 21 )i w 1 w 2 s 



n x < 



sin (2irn 1 t 4- o\) 



— ^—^-2 — y - sin(27rn 2 £+6 2 ), . (28) 



n 2 2 —n 1 2 



Vi=- 



27ri 



where 



^S?(4i/~ LiCi ) sin (*"**+*) 



+ ¥-n7^(4i?- LlCl ) Sin(W + 82) ' (29) 

 2-tt^E L 2l C, + 1/4ttV 



tan 6\ = — 

 tan So = — 



h Lj + L 21 



27re 2 E Lnd + l^TrW 

 z'o L t -4- L 2 i 



(30) 



After break, therefore, there are set up in each circuit 

 two oscillations differing in frequency, amplitude, and 

 initial phase, and the potential at any moment in either 

 circuit is the sum of the potentials in the two oscillations, 

 as represented by equations (28) and (29), to wbich must be 

 added the potential due to the rotation. 



If the resistance terms had been retained in the equations, 

 the expressions for the oscillations in each circuit would have 

 contained factors e~ kli and e~ k2 * representing the decay of the 



