ON FARAD AYS LINES OF FORCE. 215 



Substituting the values of the moments of the imaginary magnets 



v k k' , I da dB dy\ k^k' a 3 d , 

 A = , . 7 , a ( a + /3 + y-r-] = ^, . ,, -5- (< 



' ' .'' 



The force impelling the sphere in the direction of x is therefore dependent 

 on the variation of the square of the intensity or (a 2 + /S 2 + y 2 ), as we move along 

 the direction of x, and the same is true for y and z, so that the law is, that 

 the force acting on diamagnetic spheres is from places of greater to places of 

 less intensity of magnetic force, and that in similar distributions of magnetic 

 force it varies as the mass of the sphere and the square of the intensity. 



It is easy by means of Laplace's Coefficients to extend the approximation 

 to the value of the potential as far as we please, and to calculate the attew> 

 tion. For instance, if a north or south magnetic pole whose strength is M, be 

 placed at a distance b from a diamagnetic sphere, radius a, the repulsion will be 



a 3 / 2 . 1 3.2 a 2 4.3 a 4 



,,, ,, 7/N 

 = M> (k-k ) 





When Y is small, the first term gives a sufficient approximation. The repul- 

 sion is then as the square of the strength of the pole, and the mass of the 

 sphere directly and the fifth power of the distance inversely, considering the 

 pole as a point. 



IV. Two Spheres in uniform Jield. 



Let two spheres of radius a be connected together so that their centres are 

 kept at a distance 6, and let them be suspended in a uniform magnetic field, 

 then, although each sphere by itself would have been in equilibrium at any part 

 of the field, the disturbance of the field will produce forces tending to make the 

 balls set in a particular direction. 



Let the centre of one of the spheres be taken as origin, then the undis- 

 turbed potential is 



p = Ir cos 6, 



and the potential due to the sphere is 



T k-k' a' 



