216 ON FARADAY'S LINES OF FORCE. 



The whole potential is therefore equal to 



k-k' 



' .. 



This is the value of the square of the intensity at any point. The moment 

 of the couple tending to turn the combination of balls in the direction of the 

 original force 



, d ^/k-k' A , 



L= *de l (zkTk'") when r=b > 



k-k' 



k-k' 



This expression, which must be positive, since 6 is greater than a, gives the 

 moment of a force tending to turn the line joining the centres of the spheres 

 towards the original lines of force. 



Whether the spheres are magnetic or diamagnetic they tend to set in the 

 axial direction, and that without distinction of north and south. If, however, 

 one sphere be magnetic and the other diamagnetic, the line of centres will set 

 equatoreally. The magnitude of the force depends on the square of (k k'), and 

 is therefore quite insensible except in iron*. 



V. Two Spheres between the poles of a Magnet. 



Let us next take the case of the same balls placed not in a uniform field 

 but between a north and a south pole, M, distant 2c from each other in the 

 direction of x. 



* See Prof. Thomson in Phil Mag. March, 1851. 



