DIRECTION OF A DIELECTRIC NEEDLE IN A FIELD. 169 



181. The same reasoning applies to the motion of a very small 

 body of any given form, if we neglect the effects of rotation that is 

 to say, if we assume that the body always retains the same direction 

 in reference to the lines of force. This body, in fact, becomes 

 electrified proportionally to the force of that point of the field in 

 which it is situated, and the variation of energy is proportional to the 

 variation of the square of the force. 



Independently of this progressive motion, a body which is not 

 spherical will turn on itself in every point, in such a manner that for 

 stable equilibrium about its centre of gravity the electrical energy is 

 a minimum, and the electrification is a maximum. 



Such, according to Sir W. Thomson, is the true meaning of the 

 attraction of light bodies of small dimensions in an electrical field, 

 so long at any rate as they have not been electrified by direct contact. 

 These bodies, whether conductors or not, move towards points where 

 the force is a maximum in absolute value, and they finish by coming 

 in contact with the electrified surfaces. If they were movable in a 

 medium in which an extraneous resistance would keep the velocity 

 very small, they would move towards the electrified body, not along a 

 line of force, but along a line of maximum variation of the force ; in 

 certain cases, in which the body is impeded, this motion may even 

 be perpendicular to the force. 



The body is in equilibrium for points in which we have 



d<P = 0. or <p#<z) = 0, 

 This condition may be realised in two ways 

 </> = 0, or d$ = 0. 



Hence there is equilibrium when the force is null, maximum, 

 minimum, or stationary. There is equilibrium particularly in a 

 uniform field, which was d priori evident The equilibrium is thus 

 neutral ; it is stable at the maxima of force, unstable at the minima, 

 and at the points at which the force is null. 



182. DIRECTION OF A DIELECTRIC NEEDLE IN A VARIABLE 

 FIELD. Let us suppose that on a sphere charged, as we have always 

 supposed, by layers of displacement, we cause a force F to act which 

 is constant in magnitude and direction, and which makes the 

 angle 6 with the axis of electrification ; the moment of the couple 

 produced by this force will be 



F;//.S cos = FCJ cos 0. 



