174 PARTICULAR CASES OF EQUILIBRIUM. 



The needle is in equilibrium in a direction perpendicular to the 

 line of force, but it is evident that then the electrification is a mini- 

 mum and that equilibrium is unstable. 



When the needle is oblique to the force of the field, the two 

 positive and negative electrical layers are symmetrical in reference 

 to the centre, and the action of the field evidently produces a couple, 

 which tends to move the needle in the direction of the force. 



The law of distribution is independent of the force of the field, 

 and each of the layers is proportional to this force. Hence the 

 moment of the couple which acts upon the needle, for a given 

 deviation from its position of equilibrium, is proportional to the 

 square of the force <. Lastly, the duration of the oscillation is 

 inversely as the force, and we may write 



t- A 

 ?' 



the constant A only depending on the ratio between the longitudinal 

 and transverse dimensions of the needle. 



