Experiments with Open Circuits. 53 



Number of vibrations' per minute 





with condenser in primary. 



Number without. 



44 



47 



48 



52 



43 



53 



So that in this case the effect of putting a condenser in the 

 primary circuit was not nearly so great as when the magneti- 

 zation of the needle was due to the electrostatic capacity of 

 the coil itself. When the condenser in the secondary circuit 

 was taken away and the secondary circuit closed, a needle 

 placed in the magnetizing-spiral vibrated 23 times per minute, 

 and it was magnetized in the opposite way to what it was 

 when the secondary circuit was open : this, indeed, was found 

 to be a general rule; the magnetization of the needle pro- 

 duced by any arrangement of the secondary coils when open 

 was always of the opposite character to that produced when 

 the same circuit was closed. In the experiment just described 

 it will be seen that the needle vibrated about twice as fast 

 when the secondary was open as it did when the secondary 

 was closed, which shows that in this case the intensity of 

 magnetization was about four times greater w T ith an open cir- 

 cuit than with a closed one. 



For the explanation of these results we must go, I think, 

 to the equations giving the motion of the electricity in the 

 coil. 



If L be the coefficient of self-induction of a coil, C the capa- 

 city of a condenser to which its ends are attached, then the 

 kinetic energy of the coil when a current x is going through 



x 2 

 it is |Li 2 , the potential energy is | p ; so if we neglect the 



resistance of the coil, as we may do if the time-constant of the 

 coil be large compared with the time of electrical vibrations 

 in the coil (for then the effects of resistance will be inappre- 

 ciable during the first few electrical oscillations in the coil), 

 the equation of motion is 



or the period of electrical oscillation =2tt\/LC. Now if an 



27T 



electromotive force whose period is — , which we may repre- 



P . 



sent by F sin pt, acts on the wire of the coil, the equation satis- 

 fied by the current is 



La/'+ i =Fsin^, 



