EXPRESSION FOR POTENTIAL. 303 



All magnetic phenomena may be expressed as a function of this 

 quantity alone. 



319. EXPRESSION FOR POTENTIAL. Let I be the intensity of 

 magnetisation at a point M of the magnet whose co-ordinates are x, 

 y, and z. If the intensity of magnetisation makes, with the axes, 

 angles whose cosines are A, ^ v, its components A, B, C, along the 

 axes will be expressed by 



A-U, 



The magnetic moment of a volume element is mds = Idv. Its 

 potential at a point P at a distance r along a right line, making an 

 angle B with the direction of the magnetic axis (that is to say, with 

 the direction of the strength of magnetisation), is equal to (151) 



This potential may be regarded as the sum of the potentials 

 dVtf dV b , dV c , due to the three components A, B, C, of the 

 magnetisation. If we denote by 8 the angle which the right line 

 MP makes with the axis of x, and by f, yu, , the co-ordinates of the 

 point P, we have, 



On the other hand, the equation 



gives 



and, therefore, _ I 



> > * ~ 



-x i^r r 



From these we deduce 



