DISPLACEMENT OF BODIES IN A MAGNETIC FIELD. 379 



position in which the values of the same quantities are </> 2 , A 2 , A' 2 , A", 

 the change of energy is 



W, - W, = - lt-SAj + k'\'\ + k"X'\[ - $*A| + k'X'\ + k"X" J] . 



This variation is negative, and the displacement tends to take place 

 under the influence of magnetic forces alone, when the quantity in 

 brackets is positive. 



If the body is compelled to move parallel to itself, the preceding 

 expression becomes 



W 2 - W, = - - [ktf + 'A' 2 + " A" 



We thus see that the body tends in all cases to move towards 

 points in which the force is a minimum. This tendency will be the 

 more marked, the greater is the second factor; it is a maximum 

 when the principal axis of the greatest magnetisation, is parallel to 

 the field, and a minimum when it is perpendicular to it. 



397. If the body is diamagnetic, the values of , k', k" are 

 negative, and the conclusions are just the opposite of the preceding. 

 Stable equilibrium in a uniform field takes place when the axis of 

 feeblest magnetisation is parallel to the direction of the field. In a 

 variable field the body tends to move in a direction in which the 

 force decreases, and the action is a maximum when the axis of the 

 feeblest magnetisation is parallel to the lines of force. These two 

 causes may act in opposite directions, and produce opposite effects 

 according as one or the other predominates. In this way may be 

 explained many experiments which have long appeared contradictory 

 or paradoxical. 



The results would be still more complicated for bodies whose 

 three principal coefficients of magnetisation are not all of the same 

 sign. 



Such bodies would be magnetic in certain conditions and 

 diamagnetic in others. None such are known ; but the case might 

 be realised artificially by placing in a non-uniform field, a crystallized 

 magnetic sphere surrounded by an equally magnetic liquid, whose 

 coefficient of magnetisation would be intermediate between the 

 coefficients of the greatest and the smallest magnetisation of the 

 sphere. The sphere would be magnetic along the axis of the 



