Simple Resonance Experiment. 625 



We may proceed in another way. Taking a suitable value 

 for the current I which we maintain constant, we slowly 

 remove the iron bar D from the electromagnet, and we 

 observe, as above, the same variable periodic movement of 

 the magnetic needle, which illustrates in a striking manner 

 the phenomena known under the general name of resonance. 



3. If we do not insist on accuracy, it is possible to estimate 

 the amplitude of the vibration of the needle for different 

 values given to the current I, and plot resonance curves for 

 different values of the frequency of the current flowing 

 through the field-coil B. For different experiments we can 

 alter also the relative positions of the needle N and the 

 electromagnet A as is shown in fig. 2 and fig. 3. Fig. 2, 

 for instance, gives the resonance curves for the relative 

 positions sketched alongside, and frequencies 8 and 24 for 

 the current flowing through the coil B. Fig. 3 gives, 

 similarly, curves for the positions sketched alongside, and 

 for/=8, 16, and 24. 



4. In order to be able to justify the shapes of these curves 

 it would be necessary to go into the mathematical theory of 

 the phenomena, which is a very elaborate one. We shall 

 only consider a particular case, for the mathematical treatment 

 of which we suppose the relative positions of the different 

 fields given in fig. 3. We suppose that the magnet is 

 reduced to its two poles, and is of magnetic moment AJ, that 

 its oscillations have only a small amplitude, that the resultant 

 field Hi produced by the electromagnet and the earth is 

 constant and at right angles to the field A= H cos kt produced 

 by the coil. 



If we suppose h = 0, the needle is able to oscillate when 

 disturbed out of its normal position. If there is no damping, 

 the deviation angles correspond to the equations 



a = A sin kyt, hi = 27r/i, 



the frequency /i being given by the relation 



i /mth; 



K being the moment of inertia of the needle. In increasing 

 Hx or the current I we increase/]. 



If we consider damping exists, the equation of the movement 

 becomes 



^ + u . a + 2p -=0, 



and can be studied graphically by means of the kinematic 

 Phil Mag. S. 6. Vol. 30. No. 178. Oct. 1915. 2 S 



