DIRECTION OF A DIELECTRIC NEEDLE IN A FIELD. 171 



X 



whose co-ordinates are x and y, the component < of the force, parallel 

 to the plane, will have an expression of the form 



The components X and Y of the force will be 



The component tangential to the circle which the volume-element du 

 describes is 



T = X sin 9 - Y cos = (A sin - B cos 0). 



The position of equilibrium corresponds to the condition 



A sin - B cos = 0, or tan 6 = , 



A 



that is to say, to the direction along which the variation of the force 

 is a maximum. 



When the element is turned through an angle dO from its position 

 of equilibrium, the tangential component is 



dT = (A cos B + B sin 0)d0, 



the angle being determined by the condition of equilibrium ; from 

 this is deduced 



Acos0 + Bsin<9 



We have then 



</T = 



2 



