MAGNETIC INDUCTION. 309 



For a narrow slit, the perpendicular of which makes an angle 

 with the direction of magnetisation, the internal force of the surface 

 layers is perpendicular to the slit, and has the value 



477-0- = 471-1 cos 6. 



The influence of the shape of the cavity is well marked in these 

 various examples. 



323. MAGNETIC FORCE. In the case of an elongated cylindrical 

 cavity, or of a slit parallel to the lines of magnetisation, the force 

 at a point only depends on the potential V of masses external to 

 the volume-element which has been removed. The components 

 of this force are 



5V 3V 3>V 



.A , x , Z/= . 



ox oy 02 



The expression magnetic force > or resultant force at a point of the 

 magnetised mass, is more especially assigned to the force thus denned. 



324. MAGNETIC INDUCTION. If the cavity is a very flattened 

 cylinder, or an infinitely thin slit perpendicular to the lines of mag- 

 netisation, the components of the true force F x have the values 



(7) 



The force F x plays an important part in the study of magnetisation 

 by influence ; it is called magnetic induction. 



The sum of the three partial differentials of the function F x 

 gives the equation 



r +-r- + ^ 



ox oy oz 



= 47T/0 4?T/3 = . 



Hence magnetic induction satisfies Laplace's equations both for 

 points inside and outside the magnetised media. It is, moreover, 

 identical with the magnetic force for all external points, since the 

 magnetisation I, and its components A, B, and C, are then equal to 

 zero. Magnetic induction has therefore the same properties as 

 electrostatic induction (116). 



