1 70 PARTICULAR CASES OF EQUILIBRIUM. 



The electrical moment T3 is therefore the moment of the couple 

 which this sphere would experience in a field equal to unity, the force 

 of which is perpendicular to the axis of electrification. 



If we adopt the conception of Poisson and of Faraday regarding 

 the constitution of dielectrics, and consider them as formed of con- 

 ducting spheres disseminated in an insulating medium ; if we admit, 

 further, that the electrification of each of them is not modified by the 

 adjacent ones, the electrical moment of a body of any given form in 

 a uniform field is 



U 



where U is the volume of the dielectric, n the number of spheres 

 which it contains, and u the volume of each one of them. 



The expression of this moment is therefore the same as for a 

 homogeneous sphere. 



On this hypothesis, a body of any given form in a uniform field 

 would also be in equilibrium in reference to its centre of gravity, 

 whatever was its direction. For all the volume-elements become 

 electrified parallel to the force of the field, and the couple of rotation, 

 being null on each of them, is null upon the whole. 



In a variable field, on the contrary, a very small body, fixed by its 

 centre of gravity, tends to take a certain direction. As each volume- 

 element du is only acted on by the force of the field, it tends to 

 move towards points where the force increases, and the components 

 of the force which it undergoes are 



z = -- . 



2 02 



183. Consider a short and infinitely thin needle, and let </> be 

 the force of the field at the centre of gravity O of the needle. Let 

 us take the direction of the force for the #-axis ; suppose that the 

 needle can turn about the .s-axis, and that it makes the angle 6 

 with < . 



For the volume element du at a distance a from the centre, and 



