TERRESTRIAL MAGNETISM 309 



ment, we find the ratio of these two quantities. The two results 

 combined give us H, and incidentally M. 



The vibration experiment. If a magnet of moment M 

 suspended so as to be horizontal and is displaced through from 

 the magnetic meridian, it is easily seen that the magnetic couple 

 tending to restore it to the meridian is MH sin 0, or, if is very 

 small, it is MHO, and we shall have a simple harmonic vibration. 

 If K is the moment of inertia of the magnet and if the magnetic 

 couple alone acts, the time of vibration is 



T = 27TA/ 

 V MH 



47T 2 K 



or 



To find K, a non-magnetic bar of calculated moment of inertia B 

 is attached to the magnet and the new time of vibration T' is 

 observed and 



T' = 



K+B 



MH 

 or MH = 4 ^ T/ + B) . 



Equating the two values of MH we obtain 

 K+B_T /2 

 K T 2 



and K = 



The value of K need not be redetermined for each vibration 

 experiment. 



The vibration experiment is carried out by suspending a needle 

 like that used in the declination experiment in the same torsion box, 

 Fig. 224. The vibration needle, however, is provided with a holder 

 for the bar B. Corrections, into which we shall not enter, are made for 

 the additional torsion couple dueto the thread, for the arc of swing 

 not being negligibly small, and for the change in the magnetic 

 moment M due to the temperature and for its increase due to the 

 magnetisation induced by the earth's field. 



The deflection experiment. In this experiment the 

 vibration needle used in the previous experiment is set to deflect 

 another needle from the meridian. The general principle of the 

 method is as follows : 



If the vibration needle ScN, Fig. 230, is set end on, E or W 

 of another needle it will deflect it through 0, given by (p. 215) 



