FORCES ON MAGNETISED BODIES 



position is Q. Let it be disturbed through a small angle 6 from 

 CQ. The force along the arc ,?, the restoring force, is 



putting ds = ad9, where a is the length CQ of the fibre. But in the 

 disturbed position x = a cos and y = a sin 0, so that 



H 2 = H c 2 - Aa 2 cos 2 + B 2 sin 2 

 and - = 2a 2 (A + B) sin cos 



= a\A. + B) sin W 

 = 2a 2 (A + B)0 

 since is small. 



The acceleration on the particle is therefore 



_ 

 pva dO 



and as we suppose K negative, this is towards Q. The vibration is 

 therefore harmonic of period 



T 



" + B) 



This is independent of a. 



If, then, a thin bar or needle is pivoted at C so that its weight 

 need not be considered, every particle of it tends to vibrate in the 

 same time, and it vibrates as a whole with the above period. 



If the bar is paramagnetic, it is easily seen that the sign of the 

 denominator must be changed, and that the time is 



2l V K (A + B) 



The experiments made by Rowland and Jacques, using this formula, 

 are referred to in Chapter XXII. 



Stresses in the medium which will account for the 

 forces on magnetic bodies. It is not so easy to work out a 

 system of stresses in the surrounding medium to account for 

 the observed forces on magnetised bodies as it is to find a system 

 which will account for the forces on electrified bodies or for 



