Theory of Induced Magnetism. 

 Fig. 7. 



217 



and as «§ and 6 are increased the equilibrium becomes neutral, 

 that is to say, the condition of instability is reached, when 



rfe 1 ^ v }i d6 pp'2 



These two equations serve to determine the value of $ and 

 of 6 at which instability occurs. If we have to deal with a 

 long line of magnets instead of a single pair, we have to 

 write 2m 2 instead of m l in the restoring moment. 



A considerable amount of stable deflexion is possible when 

 the distance between the poles is not small compared with r. 

 When the direction of <£j is not much inclined to CC X (that is, 

 when a has a value approaching 0) there is no instability. In 

 rows with various inclinations to »£), the first to become 

 unstable as *£) is increased will be that for which a — is equal 

 to \7r. 



If a, the half distance between the poles in the undeflected 

 position, be small compared with r, there is but little deflexion 

 before instability occurs, and in that case, provided a be not 

 small, nor nearly equal to 7r, the occurrence of instability is 

 defined by the condition 



d ON 



d6 RP 72 ~ ? 



