304 CONSTITUTION OF MAGNETS. 



In like manner we shall have 



c 



Of 



The potential of the entire magnet will be obtained by extending 

 these expressions to the whole volume, which gives 



The potential at the point P is thus expressed as a function of 

 the distance r of this point from the different elements of volume of 

 the magnet, and of the intensity of the magnetisation. 



Each of the terms of which the second member of the equation 

 (3) is composed contains a factor which is an exact differential, and 

 may be integrated by parts ; we then obtain 



the former integral should be extended to the whole surface, and tfce 

 second to the volume of the magnet. 



Let I be the intensity of magnetisation at a point of the surface 

 S (Fig. 73), and the angle which its direction makes with the 

 perpendicular ; a, /?, y, the cosines of the angles of the perpendicular 



Fig. 73- 



with the axes; lastly dS, an element of surface at the point in 

 question, we have 



L/S cos = L/S (a A + /?/* + yv) 



= U. cw/S + . J&/S + Iv. 



