58 



Mr. J. J. Thomson on some Electromagnetic 



Scheme of coils. 



BA— DC 



BA— DC 

 BA— DC 



BA— DC 



BA— DC 

 BA— DC 



AB— DC 



AB— DC 

 AB— DC 



First Experiment. 



Number of vibrations of 



needle per minute. State of coil EF. 



Ends E and F to plates 

 of condenser. 



36 



21 



34 



Second Experiment. 



Ends free. 

 Circuit closed. 



35 



17 

 33 



{ 



Ends E-andF to plates 



of condenser. 

 Ends free. 

 Circuit closed. 



Third Experiment. 

 40 | 



12 

 35 



Ends to plates of con- 

 denser. 

 Ends free. 

 Circuit closed. 



r orking may perhaps throw some light on 



The following w 

 these results. 



If we have two coils, (1) and (2), with ends connected with 

 the plates of two condensers whose capacities are Cx and C 2 

 respectively, and if L and M be the coefficients of self-induc- 

 tion of the coils (1) and (2), and N the coefficient of mutual 

 induction between them, then, if x and y are the quantities of 

 electricity that are in the condensers at any time, the equations 

 satisfied by x and y are 



cPy 



L S +N 5# 



0, 



=0, 



N 





+ M§ + 



or if 



then 



0, ' 



x=A sin pt, 

 ,?/ = B sin pt, 



A(A -Lp 2 )-BNj5 2 = 0, 



-ANp 2 + B(A _Mp 2 )=0. 

 Eliminating A and B, we get 



p LM-MCj Cj (LM-N 2 )C,C 2 



