(iyi Prof. J. J. Tlioin<on on. Ihc Mwinetk Pi-oik liic.i of 



and picking out the non-periodic terms, we find, neglecting 

 terms in p', 



, . . .( ^ ^ d'\\ ^ ep iii^^ + i^^ 



-(^o--^)}(4^-£)^' 



or 



The first term represents the force due to the particle in 

 its undisturbed orbit, and may for our present purpose be 

 neglected. At the time ^ = the particle was describing a 

 circular orbit with angular velocity w, so that 



2/o^+^o^+.v=«^«^ 



^^oHyoH^o'=«^ 



where a is the radius o£ the orbit : hence^ as far as the term 

 involving H is concerned, 



Thus the particle produces the same effect as a little magnet 

 whose moment is parallel to the axis of x and equal to 



8m U^ V* 



10. Suppose that the plane of the orbit makes an angle <^ 

 with the plane xz^ the line of intersection of the orbit with xz 

 making an angle i^ with the axis of x^ then if Q^ is the angle 



Fio-. 2. 



the radius to the particle makes with the line of intersection at 

 the time ^ = 0, we have 



,■^0 = a (cos ^1 cos -v/r + sin 6^ sin -v/r cos </>) , 



io = aw ( -- sin ^1 cos -^ + cos Qi sin ^ cos (/>) ; 



