FIELD OF A MAGNET. 579 



components Z and H, one perpendicular and the other tangential 

 to the sphere of radius R, are thus expressed (153) 



M M 



P3 3 ^ = : P2 3 COS W Sm 



M 



Z = 2 COS 0> , 



M 

 H = sin o> . 



The expressions of these different forces are much more com- 

 plicated when the distance R is not very great compared with the 

 length 2L of the magnet. If they are expanded in increasing powers 



of the ratio , they will be formed of a principal factor given by the 



value which agrees for great distances, multiplied by a series the first 

 term of which is unity, and which will only contain even powers of 

 the ratio in question. 



For all these forces retain the same values, to within the sign, 

 when the magnet is reversed that is to say, when the sign of L 

 is changed ; as the moment M, which exists in the principal factor, 

 changes its sign, the terms of the series should not change. 



1152. In order to get an idea of the form of these expressions, 

 the magnet may be compared to two masses +m situate at the 

 poles, and defined by the condition 2Lm = M. The distances from 

 the point P to the masses + m and - m being r and r', the magnetic 

 potential is 



V = i 



the components Z and H are respectively equal to 



- and . 



Putting 



2 LR 



P P2 



