S^if-'^teins of Corjxi.^clcs iJcsc/'ihifn/ ("iiciilar Orhils. G77 



Ijet us hc^'in with the single })iirticle and take first the 

 terms indej^eiideiit of the time. These terms are given by 

 the equation 



' \ad- d>/-/ r at- r 



^ d d 1 

 d.c dz r 



^ . d d I 



dy dz r 



i. e., the part of the magnetic force which is independent of 

 the time is that due to a small magnet magnetized in the 

 direction of the axis of -e and whose moment is ea^cu. 



For the periodic terms we have, retaining only the lowest 

 ])owers of a, 



« = ,,,eo -^ - -;. COS \^t- -y j + ^sm(^a;^- y-j| ; 



/5 = ^«a) j^ - ^-^^-sm^o,^- -^j - y-,cos (^o)^- -y- j|. 



When r the distance from the centre of the orbit con- 

 siderably exceeds Y/cw, the terms involving the lowest powers 

 of \\r are the most important; confining our attention to 

 these we have 



l=Y^\y ^'os \^t - Y j - X sm ^0)^ - -^ ) j ; 



Thus if is the centre of the orbit, 0,; the normal to its 

 ])lane, then the magnetic force at the point P is equivalent to 



a magnetic force 





