64 Electric and Magnetic Science 



where the vector (A, B, C) or I represents the magnetic moment 

 per unit- volume, or, as it is generally called, the magnetization. 

 The function Fwas afterwards named by Green the magnetic 

 potential. 



Poisson, by integrating by parts the preceding expression for 

 the magnetic potential, obtained it in the form 



F = [[(I . dS). \ - fjp div I dx dy dz* 



the first integral being taken over the surface $ of the magnetic 

 body, and the second integral being taken throughout its volume. 

 This formula shows that the magnetic intensity produced by the 

 body in external space is the same as would be produced by a 

 fictitious distribution of magnetic fluid, consisting of a layer 

 over its surface, of surface-charge (I .- dS) per element dS y 

 together with a volume-distribution of density - div I through- 

 out its substance. These fictitious magnetizations are generally 

 known as Poisson's equivalent surface- and volume-distributions 

 of magnetism. 



Poisson, moreover, perceived that at a point in a very small 

 cavity excavated within the magnetic body, the magnetic 

 potential has a limiting value which is independent of the shape 

 of the cavity as the dimensions of the cavity tend to zero ; but 

 that this is not true of the magnetic intensity, which in such a 

 small cavity depends on the shape of the cavity. Taking the 

 cavity to be spherical, he showed that the magnetic intensity 

 within it is 



grad F 4 ^-7rl,f 

 where I denotes the magnetization at the place. 



* If the components of a vector a are denoted by (a x , a y , a z ), the quantity 

 drbjc + a y b y -f- a t k z is called the scalar product of two vectors a and b, and is denoted 

 by (a . b). 



The quantity ^ ' + ^ + ^ is called the divergence of the vector a, and is 



fix dy 02 



denoted by div a. 



t The vector whose components are - , - ?, - - is denoted by grad V. 



C dy dz J 



