TO THE THEORY OF MAGNETISM. 87 



Which agrees with the equation (b), seeing that 



/ r 



x ~ y z 



cos a = , cos p = ^7 , cos 7 = . 

 r r r 



(15.) Conceive now a body A, of any form, to have a mag- 

 netic state induced in its particles by the influence of exterior 

 forces, it is clear that if dv be an element of its volume, the 

 value of the potential function arising from this element, at any 

 point p whose co-ordinates are x, y ', z, must, since the total 

 quantity of magnetic fluid in dv is equal to zero, be of the form 



x, y, z, being the co-ordinates of dv, r the distance p, dv and 

 -XT, Y, Z, three quantities dependant on the magnetic state in- 

 duced in dv, and serving to define this state. If therefore dv 

 be an infinitely small volume within the body A and inclosing 

 the point p', the potential function arising from the whole A 

 exterior to dv, will be expressed by 



^ 



the integral extending over the whole volume of A exterior 

 to dv'. 



It is easy to show from this expression that, in general, 

 although dv' be infinitely small, the forces acting in its interior 

 vary in magnitude and direction by passing from one part of it 

 to another ; but, when dv' is spherical, these forces are sensibly 

 constant in magnitude and direction, and consequently, in this 

 case, the value of the potential function induced in dv' by their 

 action, may be immediately deduced from the preceding article. 



Let ty' represent the value of the integral just given, when 

 dv' is an infinitely small sphere. The force acting on p' arising 

 from the mass exterior to dv, tending to increase x', will be 



dx'J> 



