TO THE THEORY OF ELECTRICITY. 73 



thus see that their effect is to polarise the body in the direction 

 of y positive, making the angle - TT 4- 7 with the direction of 



the constant force J; and the degree of polarity will be the 

 same as would be produced by a force equal to /3, acting in 

 this direction on a perfectly conducting body of the same 

 dimensions. 



We have hitherto supposed the constant force to act in a 

 direction parallel to the equatorial plane of the body, but what- 

 ever may be its direction, we may conceive it decomposed into 

 two ; one equal to b as before, and parallel to this plane, the 

 other perpendicular to it, which last will evidently produce no 

 effect on the value of F, as this is due to the coercive force, and 

 would still be equal to zero under the influence of the new force, 

 if the body conducted electricity perfectly. 



Knowing the value of the potential function at the surface 

 of the body, due to the rotation, its value for all the exterior 

 space may be considered as determined (Art. 5), and if the body 

 be a solid sphere, may easily be expressed analytically ; for it is 

 evident (Art. 7), from the value of F just given, that even in 

 the present case all the electricity will be confined to the surface 

 of the solid; and it has been shown (Art. 10), that when the 

 value of the potential function for the point p within a spherical 

 surface, whose radius is a, is represented by 



the value of the same function for a point p, situate without 

 this sphere, on the prolongation of r, and at the distance r from 

 its centre, will be 



But we have seen that the value of F due to the rotation, for 



the point ;/, is 



F=/3/=/3rcos<9'; 



& being the angle formed by the ray r and the axis of y '; 

 the corresponding value for the pointy/ will therefore be 



, _ /3a 3 cos(9' 



V To 



